LMFDB - Embedded newform 552.2.bb.a.469.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.34
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.867835 - 1.11663i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.493724 - 1.93810i) q^{4} +(-4.05863 + 0.583543i) q^{5} +(-0.0753708 - 1.41220i) q^{6} +(-1.78354 + 3.90540i) q^{7} +(-2.59261 - 1.13065i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.87062 + 5.03841i) q^{10} +(-1.14978 + 3.91580i) q^{11} +(-1.64232 - 1.14140i) q^{12} +(1.92706 - 0.880060i) q^{13} +(2.81307 + 5.38080i) q^{14} +(-2.68517 + 3.09885i) q^{15} +(-3.51247 + 1.91377i) q^{16} +(-5.02005 - 3.22619i) q^{17} +(-0.981758 - 1.01791i) q^{18} +(-1.02677 - 1.59769i) q^{19} +(3.13481 + 7.57793i) q^{20} +(1.20959 + 4.11947i) q^{21} +(3.37468 + 4.68215i) q^{22} +(-0.488059 - 4.77093i) q^{23} +(-2.69978 + 0.843315i) q^{24} +(11.3345 - 3.32811i) q^{25} +(0.689672 - 2.91556i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(8.44964 + 1.52849i) q^{28} +(-2.79446 + 4.34826i) q^{29} +(1.12998 + 5.68763i) q^{30} +(-4.76520 + 5.49933i) q^{31} +(-0.911272 + 5.58297i) q^{32} +(1.69536 + 3.71231i) q^{33} +(-7.95903 + 2.80573i) q^{34} +(4.95975 - 16.8914i) q^{35} +(-1.98864 + 0.212878i) q^{36} +(-5.40131 - 0.776591i) q^{37} +(-2.67510 - 0.240007i) q^{38} +(0.880060 - 1.92706i) q^{39} +(11.1822 + 3.07597i) q^{40} +(-0.231664 - 1.61126i) q^{41} +(5.64965 + 2.22436i) q^{42} +(6.36528 - 5.51555i) q^{43} +(8.15689 + 0.295072i) q^{44} +4.10037i q^{45} +(-5.75092 - 3.59540i) q^{46} +1.49751 q^{47} +(-1.40130 + 3.74651i) q^{48} +(-7.48713 - 8.64061i) q^{49} +(6.12021 - 15.5447i) q^{50} +(-5.90660 + 0.849241i) q^{51} +(-2.65708 - 3.30034i) q^{52} +(0.541617 + 0.247348i) q^{53} +(-1.40856 - 0.126374i) q^{54} +(2.38151 - 16.5637i) q^{55} +(9.03965 - 8.10864i) q^{56} +(-1.82225 - 0.535061i) q^{57} +(2.43027 + 6.89395i) q^{58} +(-8.89448 + 4.06197i) q^{59} +(7.33162 + 3.67415i) q^{60} +(-0.615311 - 0.533170i) q^{61} +(2.00531 + 10.0935i) q^{62} +(3.61183 + 2.32118i) q^{63} +(5.44328 + 5.86265i) q^{64} +(-7.30768 + 4.69636i) q^{65} +(5.61657 + 1.32859i) q^{66} +(3.24059 + 11.0364i) q^{67} +(-3.77416 + 11.3222i) q^{68} +(-3.49315 - 3.28602i) q^{69} +(-14.5571 - 20.1971i) q^{70} +(1.90309 - 0.558799i) q^{71} +(-1.48810 + 2.40532i) q^{72} +(-1.88366 + 1.21055i) q^{73} +(-5.55461 + 5.35731i) q^{74} +(6.38659 - 9.93773i) q^{75} +(-2.58954 + 2.77881i) q^{76} +(-13.2421 - 11.4743i) q^{77} +(-1.38807 - 2.65507i) q^{78} +(-2.87414 - 6.29348i) q^{79} +(13.1391 - 9.81698i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-2.00022 - 1.13962i) q^{82} +(1.11770 + 0.160701i) q^{83} +(7.38676 - 4.37818i) q^{84} +(22.2571 + 10.1645i) q^{85} +(-0.634809 - 11.8943i) q^{86} +(0.735596 + 5.11618i) q^{87} +(7.40833 - 8.85216i) q^{88} +(-3.54339 - 4.08929i) q^{89} +(4.57859 + 3.55844i) q^{90} +9.09557i q^{91} +(-9.00558 + 3.30143i) q^{92} +7.27666i q^{93} +(1.29959 - 1.67216i) q^{94} +(5.09962 + 5.88527i) q^{95} +(2.96738 + 4.81609i) q^{96} +(0.310739 + 2.16124i) q^{97} +(-16.1460 + 0.861726i) q^{98} +(3.71231 + 1.69536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	0.867835	−	1.11663i	0.613652	−	0.789576i
$2$	0.867835	−	1.11663i	0.613652	−	0.789576i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$4$	−0.493724	−	1.93810i	−0.246862	−	0.969051i
$5$	−4.05863	+	0.583543i	−1.81507	+	0.260968i	−0.964348	−	0.264639i	$-0.914747\pi$
$5$	−4.05863	+	0.583543i	−1.81507	+	0.260968i	−0.850727	+	0.525607i	$0.823838\pi$
$6$	−0.0753708	−	1.41220i	−0.0307700	−	0.576530i
$7$	−1.78354	+	3.90540i	−0.674114	+	1.47610i	0.194648	+	0.980873i	$0.437643\pi$
$7$	−1.78354	+	3.90540i	−0.674114	+	1.47610i	−0.868762	+	0.495230i	$0.835084\pi$
$8$	−2.59261	−	1.13065i	−0.916627	−	0.399744i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−2.87062	+	5.03841i	−0.907770	+	1.59328i
$11$	−1.14978	+	3.91580i	−0.346673	+	1.18066i	0.583062	+	0.812428i	$0.301855\pi$
$11$	−1.14978	+	3.91580i	−0.346673	+	1.18066i	−0.929734	+	0.368231i	$0.879964\pi$
$12$	−1.64232	−	1.14140i	−0.474096	−	0.329493i
$13$	1.92706	−	0.880060i	0.534471	−	0.244085i	−0.129848	−	0.991534i	$-0.541449\pi$
$13$	1.92706	−	0.880060i	0.534471	−	0.244085i	0.664319	+	0.747449i	$0.268722\pi$
$14$	2.81307	+	5.38080i	0.751825	+	1.43808i
$15$	−2.68517	+	3.09885i	−0.693308	+	0.800120i
$16$	−3.51247	+	1.91377i	−0.878118	+	0.478443i
$17$	−5.02005	−	3.22619i	−1.21754	−	0.782466i	−0.235636	−	0.971841i	$-0.575717\pi$
$17$	−5.02005	−	3.22619i	−1.21754	−	0.782466i	−0.981905	+	0.189376i	$0.939354\pi$
$18$	−0.981758	−	1.01791i	−0.231403	−	0.239925i
$19$	−1.02677	−	1.59769i	−0.235558	−	0.366535i	0.703269	−	0.710923i	$-0.251723\pi$
$19$	−1.02677	−	1.59769i	−0.235558	−	0.366535i	−0.938827	+	0.344388i	$0.888086\pi$
$20$	3.13481	+	7.57793i	0.700964	+	1.69448i
$21$	1.20959	+	4.11947i	0.263953	+	0.898943i
$22$	3.37468	+	4.68215i	0.719484	+	0.998238i
$23$	−0.488059	−	4.77093i	−0.101767	−	0.994808i
$23$	−0.488059	−	4.77093i	−0.101767	−	0.994808i
$24$	−2.69978	+	0.843315i	−0.551091	+	0.172141i
$25$	11.3345	−	3.32811i	2.26690	−	0.665622i
$26$	0.689672	−	2.91556i	0.135256	−	0.571789i
$27$	−0.540641	−	0.841254i	−0.104046	−	0.161899i
$28$	8.44964	+	1.52849i	1.59683	+	0.288857i
$29$	−2.79446	+	4.34826i	−0.518918	+	0.807453i	−0.997506	−	0.0705874i	$-0.977513\pi$
$29$	−2.79446	+	4.34826i	−0.518918	+	0.807453i	0.478587	+	0.878040i	$0.341149\pi$
$30$	1.12998	+	5.68763i	0.206306	+	1.03841i
$31$	−4.76520	+	5.49933i	−0.855855	+	0.987709i	−0.999998	−	0.00184791i	$-0.999412\pi$
$31$	−4.76520	+	5.49933i	−0.855855	+	0.987709i	0.144144	+	0.989557i	$0.453957\pi$
$32$	−0.911272	+	5.58297i	−0.161092	+	0.986939i
$33$	1.69536	+	3.71231i	0.295124	+	0.646231i
$34$	−7.95903	+	2.80573i	−1.36496	+	0.481179i
$35$	4.95975	−	16.8914i	0.838350	−	2.85516i
$36$	−1.98864	+	0.212878i	−0.331440	+	0.0354796i
$37$	−5.40131	−	0.776591i	−0.887970	−	0.127671i	−0.316790	−	0.948496i	$-0.602605\pi$
$37$	−5.40131	−	0.776591i	−0.887970	−	0.127671i	−0.571180	+	0.820825i	$0.693514\pi$
$38$	−2.67510	−	0.240007i	−0.433959	−	0.0389342i
$39$	0.880060	−	1.92706i	0.140922	−	0.308577i
$40$	11.1822	+	3.07597i	1.76807	+	0.486354i
$41$	−0.231664	−	1.61126i	−0.0361798	−	0.251636i	0.963703	−	0.266978i	$-0.0860252\pi$
$41$	−0.231664	−	1.61126i	−0.0361798	−	0.251636i	−0.999882	+	0.0153425i	$0.995116\pi$
$42$	5.64965	+	2.22436i	0.871760	+	0.343227i
$43$	6.36528	−	5.51555i	0.970697	−	0.841114i	−0.0166223	−	0.999862i	$-0.505291\pi$
$43$	6.36528	−	5.51555i	0.970697	−	0.841114i	0.987319	+	0.158748i	$0.0507458\pi$
$44$	8.15689	+	0.295072i	1.22970	+	0.0444837i
$45$			4.10037i			0.611247i
$46$	−5.75092	−	3.59540i	−0.847927	−	0.530113i
$47$	1.49751			0.218434			0.109217	−	0.994018i	$-0.465166\pi$
$47$	1.49751			0.218434			0.109217	+	0.994018i	$0.465166\pi$
$48$	−1.40130	+	3.74651i	−0.202260	+	0.540763i
$49$	−7.48713	−	8.64061i	−1.06959	−	1.23437i
$50$	6.12021	−	15.5447i	0.865529	−	2.19835i
$51$	−5.90660	+	0.849241i	−0.827090	+	0.118918i
$52$	−2.65708	−	3.30034i	−0.368471	−	0.457674i
$53$	0.541617	+	0.247348i	0.0743968	+	0.0339759i	0.452266	−	0.891883i	$-0.350616\pi$
$53$	0.541617	+	0.247348i	0.0743968	+	0.0339759i	−0.377869	+	0.925859i	$0.623343\pi$
$54$	−1.40856	−	0.126374i	−0.191680	−	0.0171973i
$55$	2.38151	−	16.5637i	0.321122	−	2.23345i
$56$	9.03965	−	8.10864i	1.20797	−	1.08356i
$57$	−1.82225	−	0.535061i	−0.241363	−	0.0708705i
$58$	2.43027	+	6.89395i	0.319110	+	0.905221i
$59$	−8.89448	+	4.06197i	−1.15796	+	0.528824i	−0.899381	−	0.437166i	$-0.855982\pi$
$59$	−8.89448	+	4.06197i	−1.15796	+	0.528824i	−0.258581	+	0.965989i	$0.583255\pi$
$60$	7.33162	+	3.67415i	0.946508	+	0.474331i
$61$	−0.615311	−	0.533170i	−0.0787824	−	0.0682654i	0.614579	−	0.788855i	$-0.289326\pi$
$61$	−0.615311	−	0.533170i	−0.0787824	−	0.0682654i	−0.693362	+	0.720590i	$0.743871\pi$
$62$	2.00531	+	10.0935i	0.254675	+	1.28187i
$63$	3.61183	+	2.32118i	0.455047	+	0.292441i
$64$	5.44328	+	5.86265i	0.680410	+	0.732832i
$65$	−7.30768	+	4.69636i	−0.906406	+	0.582512i
$66$	5.61657	+	1.32859i	0.691352	+	0.163538i
$67$	3.24059	+	11.0364i	0.395901	+	1.34831i	0.880694	+	0.473685i	$0.157076\pi$
$67$	3.24059	+	11.0364i	0.395901	+	1.34831i	−0.484794	+	0.874628i	$0.661105\pi$
$68$	−3.77416	+	11.3222i	−0.457685	+	1.37302i
$69$	−3.49315	−	3.28602i	−0.420525	−	0.395590i
$70$	−14.5571	−	20.1971i	−1.73991	−	2.41402i
$71$	1.90309	−	0.558799i	0.225856	−	0.0663172i	−0.166847	−	0.985983i	$-0.553358\pi$
$71$	1.90309	−	0.558799i	0.225856	−	0.0663172i	0.392702	+	0.919666i	$0.371540\pi$
$72$	−1.48810	+	2.40532i	−0.175375	+	0.283469i
$73$	−1.88366	+	1.21055i	−0.220465	+	0.141684i	−0.646212	−	0.763158i	$-0.723648\pi$
$73$	−1.88366	+	1.21055i	−0.220465	+	0.141684i	0.425747	+	0.904842i	$0.360011\pi$
$74$	−5.55461	+	5.35731i	−0.645711	+	0.622775i
$75$	6.38659	−	9.93773i	0.737460	−	1.14751i
$76$	−2.58954	+	2.77881i	−0.297041	+	0.318751i
$77$	−13.2421	−	11.4743i	−1.50908	−	1.30762i
$78$	−1.38807	−	2.65507i	−0.157168	−	0.300628i
$79$	−2.87414	−	6.29348i	−0.323366	−	0.708072i	0.676224	−	0.736696i	$-0.263615\pi$
$79$	−2.87414	−	6.29348i	−0.323366	−	0.708072i	−0.999590	+	0.0286233i	$0.990888\pi$
$80$	13.1391	−	9.81698i	1.46899	−	1.09757i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−2.00022	−	1.13962i	−0.220888	−	0.125850i
$83$	1.11770	+	0.160701i	0.122684	+	0.0176393i	0.203383	−	0.979099i	$-0.434806\pi$
$83$	1.11770	+	0.160701i	0.122684	+	0.0176393i	−0.0806994	+	0.996738i	$0.525715\pi$
$84$	7.38676	−	4.37818i	0.805961	−	0.477699i
$85$	22.2571	+	10.1645i	2.41413	+	1.10249i
$86$	−0.634809	−	11.8943i	−0.0684532	−	1.28259i
$87$	0.735596	+	5.11618i	0.0788642	+	0.548512i
$88$	7.40833	−	8.85216i	0.789730	−	0.943643i
$89$	−3.54339	−	4.08929i	−0.375598	−	0.433464i	0.536207	−	0.844087i	$-0.319857\pi$
$89$	−3.54339	−	4.08929i	−0.375598	−	0.433464i	−0.911805	+	0.410623i	$0.865311\pi$
$90$	4.57859	+	3.55844i	0.482626	+	0.375093i
$91$			9.09557i			0.953475i
$92$	−9.00558	+	3.30143i	−0.938897	+	0.344198i
$93$			7.27666i			0.754554i
$94$	1.29959	−	1.67216i	0.134043	−	0.172471i
$95$	5.09962	+	5.88527i	0.523210	+	0.603816i
$96$	2.96738	+	4.81609i	0.302857	+	0.491540i
$97$	0.310739	+	2.16124i	0.0315508	+	0.219440i	0.999497	−	0.0317176i	$-0.0100977\pi$
$97$	0.310739	+	2.16124i	0.0315508	+	0.219440i	−0.967946	+	0.251158i	$0.919189\pi$
$98$	−16.1460	+	0.861726i	−1.63099	+	0.0870475i
$99$	3.71231	+	1.69536i	0.373101	+	0.170390i
$100$	−12.0463	−	20.3242i	−1.20463	−	2.03242i
$101$	−4.50140	−	0.647204i	−0.447906	−	0.0643992i	−0.0853288	−	0.996353i	$-0.527194\pi$
$101$	−4.50140	−	0.647204i	−0.447906	−	0.0643992i	−0.362577	+	0.931954i	$0.618103\pi$
$102$	−4.17767	+	7.33249i	−0.413651	+	0.726025i
$103$	9.78518	+	2.87319i	0.964162	+	0.283104i	0.725672	−	0.688041i	$-0.241529\pi$
$103$	9.78518	+	2.87319i	0.964162	+	0.283104i	0.238491	+	0.971145i	$0.423347\pi$
$104$	−5.99116	+	0.102829i	−0.587482	+	0.0100832i
$105$	−7.31316	−	16.0136i	−0.713691	−	1.56277i
$106$	0.746231	−	0.390128i	0.0724803	−	0.0378926i
$107$	5.58925	+	4.84311i	0.540333	+	0.468201i	0.881754	−	0.471709i	$-0.156363\pi$
$107$	5.58925	+	4.84311i	0.540333	+	0.468201i	−0.341421	+	0.939910i	$0.610908\pi$
$108$	−1.36351	+	1.46316i	−0.131204	+	0.140793i
$109$	−6.21752	+	9.67465i	−0.595530	+	0.926663i	0.404397	+	0.914584i	$0.367481\pi$
$109$	−6.21752	+	9.67465i	−0.595530	+	0.926663i	−0.999927	+	0.0120795i	$0.996155\pi$
$110$	−16.4288	−	17.0339i	−1.56643	−	1.62411i
$111$	−4.59060	+	2.95020i	−0.435720	+	0.280020i
$112$	−1.20943	−	17.1309i	−0.114280	−	1.61872i
$113$	−16.7095	+	4.90635i	−1.57190	+	0.461550i	−0.947553	−	0.319600i	$-0.896452\pi$
$113$	−16.7095	+	4.90635i	−1.57190	+	0.461550i	−0.624343	+	0.781150i	$0.714633\pi$
$114$	−2.17888	+	1.57043i	−0.204070	+	0.147085i
$115$	4.76489	+	19.0787i	0.444329	+	1.77909i
$116$	9.80707	+	3.26910i	0.910564	+	0.303529i
$117$	−0.596853	−	2.03269i	−0.0551790	−	0.187923i
$118$	−3.18322	+	13.4570i	−0.293039	+	1.23881i
$119$	21.5530	−	13.8513i	1.97576	−	1.26974i
$120$	10.4653	−	4.99814i	0.955347	−	0.456266i
$121$	−4.75771	−	3.05759i	−0.432519	−	0.277963i
$122$	−1.12934	+	0.224371i	−0.102246	+	0.0203136i
$123$	−1.23023	−	1.06600i	−0.110926	−	0.0961178i
$124$	13.0110	+	6.52028i	1.16842	+	0.585539i
$125$	−25.4113	+	11.6050i	−2.27286	+	1.03798i
$126$	5.72637	−	2.01867i	0.510145	−	0.179837i
$127$	4.51942	+	1.32702i	0.401033	+	0.117754i	0.476028	−	0.879430i	$-0.342076\pi$
$127$	4.51942	+	1.32702i	0.401033	+	0.117754i	−0.0749951	+	0.997184i	$0.523894\pi$
$128$	11.2703	−	0.990309i	0.996162	−	0.0875318i
$129$	1.19864	−	8.33675i	0.105535	−	0.734010i
$130$	−1.09777	+	12.2356i	−0.0962805	+	1.07314i
$131$	12.1999	+	5.57151i	1.06591	+	0.486785i	0.869600	−	0.493757i	$-0.164377\pi$
$131$	12.1999	+	5.57151i	1.06591	+	0.486785i	0.196310	+	0.980542i	$0.437104\pi$
$132$	6.35780	−	5.11863i	0.553376	−	0.445520i
$133$	8.07091	−	1.16042i	0.699837	−	0.100621i
$134$	15.1359	+	5.95926i	1.30754	+	0.514802i
$135$	2.68517	+	3.09885i	0.231103	+	0.266707i
$136$	9.36736	+	14.0402i	0.803245	+	1.20393i
$137$	2.67095			0.228194			0.114097	−	0.993470i	$-0.463602\pi$
$137$	2.67095			0.228194			0.114097	+	0.993470i	$0.463602\pi$
$138$	−6.70074	+	1.04883i	−0.570405	+	0.0892821i
$139$		−	8.25598i		−	0.700263i	−0.936701	−	0.350131i	$-0.886137\pi$
$139$		−	8.25598i		−	0.700263i	0.936701	−	0.350131i	$-0.113863\pi$
$140$	−35.1859	−	1.27283i	−2.97375	−	0.107574i
$141$	1.13174	−	0.980660i	0.0953099	−	0.0825865i
$142$	1.02760	−	2.61000i	0.0862343	−	0.219026i
$143$	1.23044	+	8.55787i	0.102894	+	0.715645i
$144$	1.39442	+	3.74908i	0.116201	+	0.312423i
$145$	8.80428	−	19.2787i	0.731156	−	1.60101i
$146$	−0.282965	+	3.15391i	−0.0234183	+	0.261019i
$147$	−11.3168	−	1.62711i	−0.933393	−	0.134202i
$148$	1.16164	+	10.8517i	0.0954865	+	0.892005i
$149$	3.24541	−	11.0528i	0.265874	−	0.905484i	−0.713025	−	0.701139i	$-0.752675\pi$
$149$	3.24541	−	11.0528i	0.265874	−	0.905484i	0.978899	−	0.204345i	$-0.0655065\pi$
$150$	−5.55426	−	15.7558i	−0.453503	−	1.28645i
$151$	−3.98019	−	8.71540i	−0.323903	−	0.709249i	0.675707	−	0.737170i	$-0.263839\pi$
$151$	−3.98019	−	8.71540i	−0.323903	−	0.709249i	−0.999610	+	0.0279212i	$0.991111\pi$
$152$	0.855603	+	5.30311i	0.0693986	+	0.430139i
$153$	−3.90778	+	4.50982i	−0.315925	+	0.364597i
$154$	−24.3045	+	4.82868i	−1.95852	+	0.389106i
$155$	16.1311	−	25.1004i	1.29568	−	2.01612i
$156$	−4.16935	−	0.754209i	−0.333815	−	0.0603850i
$157$	−0.916790	−	1.42655i	−0.0731678	−	0.113851i	0.802741	−	0.596327i	$-0.203374\pi$
$157$	−0.916790	−	1.42655i	−0.0731678	−	0.113851i	−0.875909	+	0.482476i	$0.839738\pi$
$158$	−9.52177	−	2.25236i	−0.757511	−	0.179188i
$159$	0.571306	−	0.167750i	0.0453075	−	0.0133035i
$160$	0.440612	−	23.1910i	0.0348335	−	1.83341i
$161$	19.5029	+	6.60307i	1.53704	+	0.520395i
$162$	−1.14727	+	0.826901i	−0.0901383	+	0.0649675i
$163$	−1.97390	−	6.72249i	−0.154608	−	0.526546i	0.845363	−	0.534192i	$-0.179384\pi$
$163$	−1.97390	−	6.72249i	−0.154608	−	0.526546i	−0.999971	+	0.00764655i	$0.997566\pi$
$164$	−3.00840	+	1.24450i	−0.234917	+	0.0971793i
$165$	−9.04712	−	14.0776i	−0.704317	−	1.09594i
$166$	1.14943	−	1.10860i	0.0892127	−	0.0860439i
$167$	−16.0524	−	10.3163i	−1.24217	−	0.798297i	−0.256433	−	0.966562i	$-0.582547\pi$
$167$	−16.0524	−	10.3163i	−1.24217	−	0.798297i	−0.985742	+	0.168265i	$0.946183\pi$
$168$	1.52168	−	12.0478i	0.117400	−	0.929509i
$169$	−5.57413	+	6.43288i	−0.428779	+	0.494837i
$170$	30.6655	−	16.0319i	2.35194	−	1.22959i
$171$	−1.72755	+	0.788948i	−0.132109	+	0.0603323i
$172$	−13.8324	−	9.61341i	−1.05471	−	0.733016i
$173$	4.13510	−	14.0829i	0.314386	−	1.07070i	−0.639065	−	0.769152i	$-0.720679\pi$
$173$	4.13510	−	14.0829i	0.314386	−	1.07070i	0.953451	−	0.301547i	$-0.0975031\pi$
$174$	6.35126	+	3.61861i	0.481487	+	0.274326i
$175$	−7.21789	+	50.2016i	−0.545622	+	3.79488i
$176$	−3.45537	−	15.9546i	−0.260459	−	1.20262i
$177$	−4.06197	+	8.89448i	−0.305317	+	0.668550i
$178$	−7.64130	+	0.407824i	−0.572739	+	0.0305677i
$179$	−7.99911	+	1.15010i	−0.597882	+	0.0859624i	−0.434610	−	0.900619i	$-0.643114\pi$
$179$	−7.99911	+	1.15010i	−0.597882	+	0.0859624i	−0.163272	+	0.986581i	$0.552205\pi$
$180$	7.94693	−	2.02445i	0.592329	−	0.150893i
$181$	−6.42976	+	5.57142i	−0.477920	+	0.414120i	−0.860224	−	0.509917i	$-0.829676\pi$
$181$	−6.42976	+	5.57142i	−0.477920	+	0.414120i	0.382304	+	0.924037i	$0.375131\pi$
$182$	10.1564	+	7.89346i	0.752841	+	0.585102i
$183$	−0.814173			−0.0601854
$184$	−4.12889	+	12.9210i	−0.304386	+	0.952549i
$185$	22.3751			1.64505
$186$	8.12533	+	6.31494i	0.595778	+	0.463034i
$187$	18.4051	−	15.9481i	1.34591	−	1.16624i
$188$	−0.739356	−	2.90233i	−0.0539231	−	0.211674i
$189$	4.24969	−	0.611012i	0.309119	−	0.0444446i
$190$	10.9973	−	0.586937i	0.797828	−	0.0425809i
$191$	8.64634	−	18.9328i	0.625627	−	1.36993i	−0.285728	−	0.958311i	$-0.592235\pi$
$191$	8.64634	−	18.9328i	0.625627	−	1.36993i	0.911355	−	0.411621i	$-0.135037\pi$
$192$	7.95298	+	0.866109i	0.573957	+	0.0625060i
$193$	−3.38006	+	23.5088i	−0.243302	+	1.69220i	0.392020	+	0.919957i	$0.371776\pi$
$193$	−3.38006	+	23.5088i	−0.243302	+	1.69220i	−0.635323	+	0.772247i	$0.719133\pi$
$194$	2.68297	+	1.52862i	0.192626	+	0.109748i
$195$	−2.44731	+	8.33479i	−0.175256	+	0.596867i
$196$	−13.0498	+	18.7769i	−0.932128	+	1.34121i
$197$	3.97409	−	1.81491i	0.283142	−	0.129307i	−0.268782	−	0.963201i	$-0.586621\pi$
$197$	3.97409	−	1.81491i	0.283142	−	0.129307i	0.551924	+	0.833894i	$0.313894\pi$
$198$	5.11476	−	2.67399i	0.363490	−	0.190032i
$199$	7.77730	−	8.97548i	0.551318	−	0.636255i	−0.409872	−	0.912143i	$-0.634426\pi$
$199$	7.77730	−	8.97548i	0.551318	−	0.636255i	0.961190	+	0.275888i	$0.0889719\pi$
$200$	−33.1489	−	4.18681i	−2.34398	−	0.296052i
$201$	9.67639	+	6.21864i	0.682520	+	0.438629i
$202$	−4.62916	+	4.46473i	−0.325707	+	0.314137i
$203$	−11.9977	−	18.6688i	−0.842073	−	1.31029i
$204$	4.56215	+	11.0283i	0.319414	+	0.772136i
$205$	1.88047	+	6.40431i	0.131338	+	0.447296i
$206$	11.7002	−	8.43297i	0.815192	−	0.587553i
$207$	−4.79183	−	0.195884i	−0.333055	−	0.0136149i
$208$	−5.08452	+	6.77915i	−0.352548	+	0.470049i
$209$	7.43681	−	2.18364i	0.514415	−	0.151046i
$210$	−24.2278	−	5.73106i	−1.67188	−	0.395481i
$211$	7.79792	+	12.1338i	0.536831	+	0.835325i	0.998666	−	0.0516409i	$-0.0164451\pi$
$211$	7.79792	+	12.1338i	0.536831	+	0.835325i	−0.461835	+	0.886966i	$0.652809\pi$
$212$	0.211977	−	1.17183i	0.0145586	−	0.0804816i
$213$	1.07233	−	1.66857i	0.0734746	−	0.114329i
$214$	10.2585	−	2.03810i	0.701257	−	0.139321i
$215$	−22.6158	+	26.1000i	−1.54238	+	1.78001i
$216$	0.450512	+	2.79232i	0.0306535	+	0.189993i
$217$	−12.9782	−	28.4183i	−0.881017	−	1.92916i
$218$	5.40722	+	15.3387i	0.366223	+	1.03887i
$219$	−0.630829	+	2.14841i	−0.0426275	+	0.145176i
$220$	−33.2780	+	3.56231i	−2.24360	+	0.240171i
$221$	−12.5132	−	1.79912i	−0.841728	−	0.121022i
$222$	−0.689604	+	7.68629i	−0.0462832	+	0.515870i
$223$	−6.05232	+	13.2527i	−0.405293	+	0.887469i	0.591413	+	0.806369i	$0.298570\pi$
$223$	−6.05232	+	13.2527i	−0.405293	+	0.887469i	−0.996706	+	0.0810996i	$0.974157\pi$
$224$	−20.1785	−	13.5163i	−1.34823	−	0.903097i
$225$	−1.68117	−	11.6928i	−0.112078	−	0.779518i
$226$	−9.02251	+	22.9162i	−0.600168	+	1.52436i
$227$	7.90981	−	6.85389i	0.524992	−	0.454908i	−0.351594	−	0.936152i	$-0.614360\pi$
$227$	7.90981	−	6.85389i	0.524992	−	0.454908i	0.876587	+	0.481244i	$0.159815\pi$
$228$	−0.137314	+	3.79588i	−0.00909384	+	0.251388i
$229$		−	23.9691i		−	1.58392i	−0.610572	−	0.791960i	$-0.709061\pi$
$229$		−	23.9691i		−	1.58392i	0.610572	−	0.791960i	$-0.290939\pi$
$230$	25.4389	+	11.2365i	1.67739	+	0.740913i
$231$	−17.5218			−1.15285
$232$	12.1613	−	8.11382i	0.798428	−	0.532698i
$233$	16.1604	+	18.6501i	1.05870	+	1.22181i	0.974271	+	0.225380i	$0.0723624\pi$
$233$	16.1604	+	18.6501i	1.05870	+	1.22181i	0.0844329	+	0.996429i	$0.473092\pi$
$234$	−2.78774	−	1.09758i	−0.182240	−	0.0717510i
$235$	−6.07784	+	0.873861i	−0.396474	+	0.0570044i
$236$	12.2639	+	15.2329i	0.798314	+	0.991578i
$237$	−6.29348	−	2.87414i	−0.408806	−	0.186695i
$238$	3.23771	−	36.0873i	0.209870	−	2.33920i
$239$	−1.99576	+	13.8808i	−0.129095	+	0.897877i	0.817609	+	0.575773i	$0.195299\pi$
$239$	−1.99576	+	13.8808i	−0.129095	+	0.897877i	−0.946704	+	0.322103i	$0.895610\pi$
$240$	3.50109	−	16.0234i	0.225994	−	1.03431i
$241$	−15.4360	−	4.53243i	−0.994322	−	0.291959i	−0.256198	−	0.966624i	$-0.582470\pi$
$241$	−15.4360	−	4.53243i	−0.994322	−	0.291959i	−0.738124	+	0.674665i	$0.764288\pi$
$242$	−7.54311	+	2.65911i	−0.484889	+	0.170934i
$243$	−0.909632	+	0.415415i	−0.0583529	+	0.0266489i
$244$	−0.729543	+	1.45577i	−0.0467042	+	0.0931963i
$245$	35.4297	+	30.7000i	2.26352	+	1.96135i
$246$	−2.25796	+	0.448598i	−0.143962	+	0.0286016i
$247$	−3.38472	−	2.17523i	−0.215365	−	0.138406i
$248$	18.5721	−	8.86988i	1.17933	−	0.563238i
$249$	0.949940	−	0.610490i	0.0602000	−	0.0386882i
$250$	−9.09440	+	38.4462i	−0.575180	+	2.43155i
$251$	0.225706	+	0.768686i	0.0142465	+	0.0485190i	0.966309	−	0.257383i	$-0.0828602\pi$
$251$	0.225706	+	0.768686i	0.0142465	+	0.0485190i	−0.952063	+	0.305902i	$0.901042\pi$
$252$	2.71544	−	8.14611i	0.171056	−	0.513156i
$253$	19.2432	+	3.57440i	1.20981	+	0.224720i
$254$	5.40390	−	3.89488i	0.339071	−	0.244386i
$255$	23.4772	−	6.89352i	1.47020	−	0.431689i
$256$	8.67494	−	13.4442i	0.542184	−	0.840260i
$257$	−21.0034	+	13.4981i	−1.31015	+	0.841985i	−0.994279	−	0.106815i	$-0.965935\pi$
$257$	−21.0034	+	13.4981i	−1.31015	+	0.841985i	−0.315876	+	0.948801i	$0.602298\pi$
$258$	−8.26884	−	8.57337i	−0.514795	−	0.533755i
$259$	12.6663	−	19.7092i	0.787048	−	1.22467i
$260$	12.7100	+	11.8443i	0.788241	+	0.734554i
$261$	3.90631	+	3.38484i	0.241795	+	0.209516i
$262$	16.8088	−	8.78762i	1.03845	−	0.542901i
$263$	3.12639	+	6.84584i	0.192782	+	0.422133i	0.981197	−	0.193011i	$-0.0618253\pi$
$263$	3.12639	+	6.84584i	0.192782	+	0.422133i	−0.788415	+	0.615144i	$0.789098\pi$
$264$	−0.198090	−	11.5414i	−0.0121916	−	0.710326i
$265$	−2.34256	−	0.687838i	−0.143902	−	0.0422536i
$266$	5.70846	−	10.0193i	0.350008	−	0.614321i
$267$	−5.35583	−	0.770052i	−0.327771	−	0.0471264i
$268$	19.7897	−	11.7295i	1.20885	−	0.716495i
$269$	−10.7340	−	4.90204i	−0.654461	−	0.298882i	0.0603735	−	0.998176i	$-0.480771\pi$
$269$	−10.7340	−	4.90204i	−0.654461	−	0.298882i	−0.714835	+	0.699293i	$0.753498\pi$
$270$	5.79055	−	0.309048i	0.352402	−	0.0188081i
$271$	3.49467	+	24.3060i	0.212286	+	1.47648i	0.765496	+	0.643441i	$0.222494\pi$
$271$	3.49467	+	24.3060i	0.212286	+	1.47648i	−0.553209	+	0.833042i	$0.686597\pi$
$272$	23.8070	+	1.72467i	1.44351	+	0.104573i
$273$	5.95633	+	6.87397i	0.360494	+	0.416032i
$274$	2.31794	−	2.98246i	0.140032	−	0.180177i
$275$			48.2102i			2.90719i
$276$	−4.64399	+	8.39246i	−0.279535	+	0.505167i
$277$			16.7004i			1.00343i	0.865033	+	0.501716i	$0.167298\pi$
$277$			16.7004i			1.00343i	−0.865033	+	0.501716i	$0.832702\pi$
$278$	−9.21887	−	7.16483i	−0.552911	−	0.429718i
$279$	4.76520	+	5.49933i	0.285285	+	0.329236i
$280$	−31.9568	+	38.1850i	−1.90979	+	2.28199i
$281$	2.65267	+	18.4497i	0.158245	+	1.10062i	0.901866	+	0.432016i	$0.142198\pi$
$281$	2.65267	+	18.4497i	0.158245	+	1.10062i	−0.743621	+	0.668601i	$0.766893\pi$
$282$	−0.112868	−	2.11479i	−0.00672122	−	0.125934i
$283$	−28.9092	−	13.2024i	−1.71847	−	0.784800i	−0.995588	−	0.0938302i	$-0.970089\pi$
$283$	−28.9092	−	13.2024i	−1.71847	−	0.784800i	−0.722884	−	0.690970i	$-0.757184\pi$
$284$	−2.02261	−	3.41250i	−0.120020	−	0.202494i
$285$	7.70807	+	1.10825i	0.456586	+	0.0656472i
$286$	10.6238	+	6.05288i	0.628198	+	0.357914i
$287$	6.70578	+	1.96899i	0.395830	+	0.116226i
$288$	5.39646	+	1.69654i	0.317989	+	0.0999694i
$289$	7.73053	+	16.9275i	0.454737	+	0.995736i
$290$	−13.8865	−	26.5619i	−0.815443	−	1.55977i
$291$	1.65015	+	1.42986i	0.0967335	+	0.0838201i
$292$	3.27618	+	3.05304i	0.191724	+	0.178665i
$293$	−17.6018	+	27.3889i	−1.02831	+	1.60008i	−0.254069	+	0.967186i	$0.581769\pi$
$293$	−17.6018	+	27.3889i	−1.02831	+	1.60008i	−0.774239	+	0.632893i	$0.781867\pi$
$294$	−11.6380	+	11.2246i	−0.678741	+	0.654632i
$295$	33.7291	−	21.6764i	1.96378	−	1.26205i
$296$	13.1255	+	8.12037i	0.762902	+	0.471987i
$297$	3.91580	−	1.14978i	0.227218	−	0.0667172i
$298$	−9.52545	−	13.2160i	−0.551795	−	0.765580i
$299$	−5.13923	−	8.76436i	−0.297209	−	0.506856i
$300$	−22.4135	−	7.47137i	−1.29405	−	0.431360i
$301$	10.1877	+	34.6962i	0.587210	+	1.99985i
$302$	−13.1860	−	3.11913i	−0.758770	−	0.179486i
$303$	−3.82576	+	2.45867i	−0.219784	+	0.141247i
$304$	6.66413	+	3.64684i	0.382214	+	0.209160i
$305$	2.80845	+	1.80488i	0.160811	+	0.103347i
$306$	1.64449	+	8.27732i	0.0940091	+	0.473183i
$307$	−12.7793	−	11.0734i	−0.729355	−	0.631990i	0.208899	−	0.977937i	$-0.433012\pi$
$307$	−12.7793	−	11.0734i	−0.729355	−	0.631990i	−0.938254	+	0.345947i	$0.887558\pi$
$308$	−15.7005	+	31.3297i	−0.894619	+	1.78517i
$309$	9.27668	−	4.23652i	0.527732	−	0.241007i
$310$	−14.0288	−	39.7955i	−0.796782	−	2.26023i
$311$	−7.98972	−	2.34599i	−0.453055	−	0.133029i	0.0472406	−	0.998884i	$-0.484957\pi$
$311$	−7.98972	−	2.34599i	−0.453055	−	0.133029i	−0.500296	+	0.865854i	$0.666775\pi$
$312$	−4.46048	+	4.00109i	−0.252525	+	0.226517i
$313$	−1.11307	+	7.74156i	−0.0629144	+	0.437579i	0.933881	+	0.357584i	$0.116399\pi$
$313$	−1.11307	+	7.74156i	−0.0629144	+	0.437579i	−0.996795	+	0.0799948i	$0.974510\pi$
$314$	−2.38855	−	0.214298i	−0.134794	−	0.0120935i
$315$	−16.0136	−	7.31316i	−0.902263	−	0.412050i
$316$	−10.7784	+	8.67761i	−0.606331	+	0.488154i
$317$	25.0902	−	3.60742i	1.40921	−	0.202613i	0.604650	−	0.796491i	$-0.293313\pi$
$317$	25.0902	−	3.60742i	1.40921	−	0.202613i	0.804555	+	0.593878i	$0.202404\pi$
$318$	0.308484	−	0.783516i	0.0172989	−	0.0439374i
$319$	−13.8139	−	15.9421i	−0.773431	−	0.892587i
$320$	−25.5134	−	20.6180i	−1.42624	−	1.15258i
$321$	7.39563			0.412784
$322$	24.2985	−	16.0471i	1.35410	−	0.894271i
$323$			11.3331i			0.630588i
$324$	−0.0723017	+	1.99869i	−0.00401676	+	0.111038i
$325$	18.9133	−	16.3885i	1.04912	−	0.909071i
$326$	−9.21955	−	3.62990i	−0.510624	−	0.201041i
$327$	1.63666	+	11.3832i	0.0905075	+	0.629493i
$328$	−1.22115	+	4.43929i	−0.0674265	+	0.245119i
$329$	−2.67086	+	5.84838i	−0.147249	+	0.322431i
$330$	−23.5709	−	2.11475i	−1.29753	−	0.116413i
$331$	16.2483	+	2.33615i	0.893087	+	0.128406i	0.573553	−	0.819168i	$-0.305565\pi$
$331$	16.2483	+	2.33615i	0.893087	+	0.128406i	0.319534	+	0.947575i	$0.396474\pi$
$332$	−0.240381	−	2.24556i	−0.0131926	−	0.123241i
$333$	−1.53737	+	5.23581i	−0.0842476	+	0.286921i
$334$	−25.4503	+	8.97180i	−1.39258	+	0.490915i
$335$	−19.5926	−	42.9017i	−1.07046	−	2.34397i
$336$	−12.1324	−	12.1547i	−0.661876	−	0.663091i
$337$	12.4174	−	14.3305i	0.676421	−	0.780632i	−0.308945	−	0.951080i	$-0.599976\pi$
$337$	12.4174	−	14.3305i	0.676421	−	0.780632i	0.985367	+	0.170448i	$0.0545215\pi$
$338$	2.34573	+	11.8069i	0.127591	+	0.642212i
$339$	−9.41521	+	14.6504i	−0.511364	+	0.795698i
$340$	8.71094	−	48.1551i	0.472417	−	2.61157i
$341$	−16.0553	−	24.9826i	−0.869445	−	1.35288i
$342$	−0.618270	+	2.61371i	−0.0334322	+	0.141334i
$343$	18.2623	−	5.36229i	0.986071	−	0.289537i
$344$	−22.7389	+	7.10280i	−1.22600	+	0.382957i
$345$	16.0949	+	11.2983i	0.866522	+	0.608282i
$346$	−12.1368	−	16.8390i	−0.652476	−	0.905269i
$347$	6.13184	+	20.8831i	0.329175	+	1.12107i	0.943323	+	0.331875i	$0.107681\pi$
$347$	6.13184	+	20.8831i	0.329175	+	1.12107i	−0.614149	+	0.789190i	$0.710500\pi$
$348$	9.55250	−	3.95164i	0.512068	−	0.211830i
$349$	−13.0248	−	20.2670i	−0.697202	−	1.08487i	−0.991620	−	0.129191i	$-0.958762\pi$
$349$	−13.0248	−	20.2670i	−0.697202	−	1.08487i	0.294417	−	0.955677i	$-0.404874\pi$
$350$	49.7926	+	51.6264i	2.66153	+	2.75955i
$351$	−1.78220	−	1.14535i	−0.0951269	−	0.0611344i
$352$	−20.8140	−	9.98757i	−1.10939	−	0.532339i
$353$	−16.0390	+	18.5100i	−0.853671	+	0.985188i	−0.999992	−	0.00404872i	$-0.998711\pi$
$353$	−16.0390	+	18.5100i	−0.853671	+	0.985188i	0.146321	+	0.989237i	$0.453257\pi$
$354$	6.40672	+	12.2547i	0.340513	+	0.651328i
$355$	−7.39787	+	3.37849i	−0.392638	+	0.179312i
$356$	−6.17600	+	8.88642i	−0.327327	+	0.470979i
$357$	7.21802	−	24.5823i	0.382018	−	1.30103i
$358$	−5.65768	+	9.93014i	−0.299018	+	0.524824i
$359$	0.535900	−	3.72726i	0.0282837	−	0.196717i	−0.970781	−	0.239969i	$-0.922863\pi$
$359$	0.535900	−	3.72726i	0.0282837	−	0.196717i	0.999064	+	0.0432517i	$0.0137718\pi$
$360$	4.63606	−	10.6307i	0.244342	−	0.560285i
$361$	6.39453	−	14.0021i	0.336554	−	0.736951i
$362$	0.641239	+	12.0147i	0.0337028	+	0.631480i
$363$	−5.59794	+	0.804862i	−0.293815	+	0.0422443i
$364$	17.6281	−	4.49070i	0.923965	−	0.235377i
$365$	6.93865	−	6.01238i	0.363186	−	0.314702i
$366$	−0.706568	+	0.909129i	−0.0369329	+	0.0475209i
$367$	18.7753			0.980061			0.490030	−	0.871705i	$-0.336986\pi$
$367$	18.7753			0.980061			0.490030	+	0.871705i	$0.336986\pi$
$368$	10.8448	+	15.8237i	0.565323	+	0.824870i
$369$	−1.62782			−0.0847412
$370$	19.4179	−	24.9847i	1.00949	−	1.29889i
$371$	−1.93199	+	1.67408i	−0.100304	+	0.0869138i
$372$	14.1029	−	3.59266i	0.731201	−	0.186271i
$373$	−24.6557	+	3.54495i	−1.27662	+	0.183550i	−0.747080	−	0.664734i	$-0.768545\pi$
$373$	−24.6557	+	3.54495i	−1.27662	+	0.183550i	−0.529541	+	0.848284i	$0.677636\pi$
$374$	−1.83554	−	34.3920i	−0.0949133	−	1.77837i
$375$	−11.6050	+	25.4113i	−0.599278	+	1.31223i
$376$	−3.88246	−	1.69315i	−0.200223	−	0.0873177i
$377$	−1.55837	+	10.8387i	−0.0802599	+	0.558220i
$378$	3.00575	−	5.27558i	0.154599	−	0.271347i
$379$	0.742356	−	2.52823i	0.0381323	−	0.129867i	−0.938227	−	0.346020i	$-0.887533\pi$
$379$	0.742356	−	2.52823i	0.0381323	−	0.129867i	0.976359	+	0.216153i	$0.0693511\pi$
$380$	8.88845	−	12.7893i	0.455968	−	0.656076i
$381$	4.28456	−	1.95669i	0.219505	−	0.100244i
$382$	−13.6374	−	26.0853i	−0.697749	−	1.33464i
$383$	5.46575	−	6.30781i	0.279287	−	0.322314i	−0.598724	−	0.800956i	$-0.704325\pi$
$383$	5.46575	−	6.30781i	0.279287	−	0.322314i	0.878010	+	0.478642i	$0.158871\pi$
$384$	7.86900	−	8.12889i	0.401563	−	0.414826i
$385$	60.4405	+	38.8428i	3.08034	+	1.97961i
$386$	23.3173	+	24.1761i	1.18682	+	1.23053i
$387$	−4.55354	−	7.08544i	−0.231469	−	0.360173i
$388$	4.03528	−	1.66930i	0.204860	−	0.0847458i
$389$	9.20803	+	31.3597i	0.466866	+	1.59000i	0.770651	+	0.637258i	$0.219931\pi$
$389$	9.20803	+	31.3597i	0.466866	+	1.59000i	−0.303785	+	0.952741i	$0.598251\pi$
$390$	7.18301	+	9.96597i	0.363726	+	0.504646i
$391$	−12.9419	+	25.5249i	−0.654498	+	1.29085i
$392$	9.64175	+	30.8670i	0.486982	+	1.55902i
$393$	12.8686	−	3.77857i	0.649136	−	0.190604i
$394$	1.42228	−	6.01263i	0.0716533	−	0.302912i
$395$	15.3376	+	23.8657i	0.771718	+	1.20082i
$396$	1.45292	−	8.03188i	0.0730117	−	0.403617i
$397$	−3.19776	+	4.97581i	−0.160491	+	0.249729i	−0.912181	−	0.409788i	$-0.865603\pi$
$397$	−3.19776	+	4.97581i	−0.160491	+	0.249729i	0.751690	+	0.659517i	$0.229239\pi$
$398$	−3.27287	−	16.4736i	−0.164054	−	0.825747i
$399$	5.33967	−	6.16231i	0.267318	−	0.308502i
$400$	−33.4429	+	33.3816i	−1.67214	+	1.66908i
$401$	−4.94507	−	10.8282i	−0.246945	−	0.540734i	0.745050	−	0.667008i	$-0.232425\pi$
$401$	−4.94507	−	10.8282i	−0.246945	−	0.540734i	−0.991995	+	0.126274i	$0.959698\pi$
$402$	15.3414	−	5.40819i	0.765161	−	0.269736i
$403$	−4.34309	+	14.7912i	−0.216345	+	0.736803i
$404$	0.968103	+	9.04371i	0.0481649	+	0.449942i
$405$	4.05863	+	0.583543i	0.201675	+	0.0289965i
$406$	−31.2581	−	2.80444i	−1.55132	−	0.139182i
$407$	9.25131	−	20.2576i	0.458571	−	1.00413i
$408$	16.2737	+	4.47652i	0.805670	+	0.221621i
$409$	−2.22202	−	15.4545i	−0.109872	−	0.764175i	−0.968038	−	0.250803i	$-0.919305\pi$
$409$	−2.22202	−	15.4545i	−0.109872	−	0.764175i	0.858166	−	0.513372i	$-0.171604\pi$
$410$	8.78318	+	3.45809i	0.433770	+	0.170783i
$411$	2.01857	−	1.74910i	0.0995685	−	0.0862766i
$412$	0.737353	−	20.3832i	0.0363268	−	1.00421i
$413$		−	41.9812i		−	2.06576i
$414$	−4.37725	+	5.18070i	−0.215130	+	0.254618i
$415$	−4.63012			−0.227284
$416$	3.15727	+	11.5607i	0.154798	+	0.566810i
$417$	−5.40652	−	6.23945i	−0.264758	−	0.305547i
$418$	4.01560	−	10.1992i	0.196410	−	0.498859i
$419$	−8.54644	+	1.22879i	−0.417521	+	0.0600304i	−0.347874	−	0.937541i	$-0.613096\pi$
$419$	−8.54644	+	1.22879i	−0.417521	+	0.0600304i	−0.0696467	+	0.997572i	$0.522187\pi$
$420$	−27.4253	+	22.0799i	−1.33822	+	1.07739i
$421$	−28.5516	−	13.0391i	−1.39152	−	0.635487i	−0.428163	−	0.903702i	$-0.640839\pi$
$421$	−28.5516	−	13.0391i	−1.39152	−	0.635487i	−0.963359	+	0.268215i	$0.913566\pi$
$422$	20.3163	+	1.82275i	0.988980	+	0.0887301i
$423$	0.213118	−	1.48227i	0.0103621	−	0.0720703i
$424$	−1.12454	−	1.25366i	−0.0546125	−	0.0608829i
$425$	−67.6368	−	19.8600i	−3.28087	−	0.963350i
$426$	−0.932575	−	2.64544i	−0.0451834	−	0.128172i
$427$	3.17967	−	1.45211i	0.153875	−	0.0702724i
$428$	6.62689	−	13.2237i	0.320323	−	0.639191i
$429$	6.53412	+	5.66184i	0.315470	+	0.273356i
$430$	9.51726	+	47.9040i	0.458963	+	2.31013i
$431$	−14.4303	−	9.27376i	−0.695081	−	0.446701i	0.144808	−	0.989460i	$-0.453744\pi$
$431$	−14.4303	−	9.27376i	−0.695081	−	0.446701i	−0.839889	+	0.542758i	$0.817380\pi$
$432$	3.50896	+	1.92022i	0.168825	+	0.0923865i
$433$	−6.89298	+	4.42985i	−0.331256	+	0.212885i	−0.695687	−	0.718345i	$-0.744900\pi$
$433$	−6.89298	+	4.42985i	−0.331256	+	0.212885i	0.364431	+	0.931230i	$0.381263\pi$
$434$	−42.9956	−	10.1705i	−2.06386	−	0.488202i
$435$	−5.97102	−	20.3354i	−0.286289	−	0.975010i
$436$	21.8202	+	7.27358i	1.04500	+	0.348341i
$437$	−7.12135	+	5.67844i	−0.340660	+	0.271636i
$438$	1.85152	+	2.56887i	0.0884690	+	0.122745i
$439$	−36.9111	+	10.8381i	−1.76167	+	0.517273i	−0.992551	−	0.121831i	$-0.961123\pi$
$439$	−36.9111	+	10.8381i	−1.76167	+	0.517273i	−0.769120	+	0.639104i	$0.779305\pi$
$440$	−24.9020	+	40.2507i	−1.18716	+	1.91888i
$441$	−9.61819	+	6.18123i	−0.458009	+	0.294344i
$442$	−12.8683	+	12.4113i	−0.612085	+	0.590343i
$443$	−4.53722	+	7.06005i	−0.215570	+	0.335433i	−0.932150	−	0.362071i	$-0.882070\pi$
$443$	−4.53722	+	7.06005i	−0.215570	+	0.335433i	0.716581	+	0.697504i	$0.245706\pi$
$444$	7.98427	+	7.44046i	0.378917	+	0.353109i
$445$	16.7676	+	14.5292i	0.794859	+	0.688749i
$446$	9.54598	+	18.2594i	0.452015	+	0.864607i
$447$	−4.78536	−	10.4785i	−0.226340	−	0.495615i
$448$	−32.6043	+	10.8019i	−1.54041	+	0.510343i
$449$	13.8010	+	4.05233i	0.651308	+	0.191241i	0.590663	−	0.806918i	$-0.298866\pi$
$449$	13.8010	+	4.05233i	0.651308	+	0.191241i	0.0606447	+	0.998159i	$0.480684\pi$
$450$	−14.5155	−	8.27016i	−0.684266	−	0.389859i
$451$	6.57572	+	0.945446i	0.309639	+	0.0445193i
$452$	17.7589	+	29.9623i	0.835307	+	1.40931i
$453$	−8.71540	−	3.98019i	−0.409485	−	0.187006i
$454$	−0.788844	−	14.7804i	−0.0370223	−	0.693677i
$455$	−5.30766	−	36.9156i	−0.248827	−	1.73063i
$456$	4.11942	+	3.44752i	0.192910	+	0.161445i
$457$	−16.8590	−	19.4563i	−0.788630	−	0.910128i	0.209070	−	0.977901i	$-0.432956\pi$
$457$	−16.8590	−	19.4563i	−0.788630	−	0.910128i	−0.997701	+	0.0677727i	$0.978411\pi$
$458$	−26.7646	−	20.8012i	−1.25063	−	0.971977i
$459$			5.96734i			0.278532i
$460$	34.6238	−	18.6544i	1.61434	−	0.869767i
$461$		−	34.1444i		−	1.59026i	−0.606437	−	0.795132i	$-0.707402\pi$
$461$		−	34.1444i		−	1.59026i	0.606437	−	0.795132i	$-0.292598\pi$
$462$	−15.2060	+	19.5654i	−0.707449	+	0.910263i
$463$	−6.72449	−	7.76048i	−0.312514	−	0.360660i	0.577663	−	0.816275i	$-0.303965\pi$
$463$	−6.72449	−	7.76048i	−0.312514	−	0.360660i	−0.890177	+	0.455615i	$0.849419\pi$
$464$	1.49387	−	20.6211i	0.0693513	−	0.957312i
$465$	−4.24624	−	29.5333i	−0.196915	−	1.36957i
$466$	34.8498	−	1.85997i	1.61439	−	0.0861616i
$467$	35.3266	+	16.1331i	1.63472	+	0.746551i	0.999664	−	0.0259159i	$-0.00825021\pi$
$467$	35.3266	+	16.1331i	1.63472	+	0.746551i	0.635055	+	0.772467i	$0.280977\pi$
$468$	−3.64489	+	2.16035i	−0.168485	+	0.0998622i
$469$	−48.8814	−	7.02808i	−2.25713	−	0.324526i
$470$	−4.29878	+	7.54506i	−0.198288	+	0.348028i
$471$	−1.62706	−	0.477747i	−0.0749709	−	0.0220134i
$472$	27.6526	−	0.474613i	1.27281	−	0.0218458i
$473$	14.2791	+	31.2669i	0.656554	+	1.43765i
$474$	−8.67106	+	4.53321i	−0.398275	+	0.208217i
$475$	−16.9553	−	14.6918i	−0.777960	−	0.674107i
$476$	−37.4864	−	34.9332i	−1.71819	−	1.60116i
$477$	0.321911	−	0.500903i	0.0147393	−	0.0229348i
$478$	13.7678	+	14.2748i	0.629723	+	0.652915i
$479$	−26.2363	+	16.8611i	−1.19877	+	0.770402i	−0.978743	−	0.205092i	$-0.934251\pi$
$479$	−26.2363	+	16.8611i	−1.19877	+	0.770402i	−0.220026	+	0.975494i	$0.570614\pi$
$480$	−14.8539	−	17.8151i	−0.677984	−	0.813145i
$481$	−11.0921	+	3.25694i	−0.505757	+	0.148504i
$482$	−18.4570	+	13.3029i	−0.840692	+	0.605932i
$483$	19.0634	−	7.78140i	0.867414	−	0.354066i
$484$	−3.57693	+	10.7305i	−0.162588	+	0.487751i
$485$	−2.52235	−	8.59033i	−0.114534	−	0.390067i
$486$	−0.325546	+	1.37623i	−0.0147671	+	0.0624272i
$487$	17.9507	−	11.5362i	0.813426	−	0.522757i	−0.0665456	−	0.997783i	$-0.521198\pi$
$487$	17.9507	−	11.5362i	0.813426	−	0.522757i	0.879972	+	0.475026i	$0.157561\pi$
$488$	0.992436	+	2.07800i	0.0449255	+	0.0940667i
$489$	−5.89407	−	3.78789i	−0.266539	−	0.171294i
$490$	65.0276	−	12.9193i	2.93765	−	0.583634i
$491$	2.00148	+	1.73430i	0.0903257	+	0.0782676i	0.698853	−	0.715265i	$-0.253694\pi$
$491$	2.00148	+	1.73430i	0.0903257	+	0.0782676i	−0.608528	+	0.793533i	$0.708240\pi$
$492$	−1.45862	+	2.91061i	−0.0657597	+	0.131221i
$493$	28.0567	−	12.8130i	1.26361	−	0.577070i
$494$	−5.36630	+	1.89174i	−0.241441	+	0.0851134i
$495$	−16.0562	−	4.71453i	−0.721673	−	0.211902i
$496$	6.21315	−	28.4358i	0.278979	−	1.27680i
$497$	−1.21190	+	8.42898i	−0.0543613	+	0.378091i
$498$	0.142701	−	1.59054i	0.00639458	−	0.0712736i
$499$	−26.0006	−	11.8741i	−1.16394	−	0.531556i	−0.262705	−	0.964876i	$-0.584614\pi$
$499$	−26.0006	−	11.8741i	−1.16394	−	0.531556i	−0.901240	+	0.433321i	$0.857342\pi$
$500$	35.0378	+	43.5201i	1.56694	+	1.94628i
$501$	−18.8873	+	2.71559i	−0.843824	+	0.121324i
$502$	1.05421	+	0.415062i	0.0470518	+	0.0185251i
$503$	17.2362	+	19.8917i	0.768526	+	0.886927i	0.996225	−	0.0868050i	$-0.0276657\pi$
$503$	17.2362	+	19.8917i	0.768526	+	0.886927i	−0.227699	+	0.973732i	$0.573120\pi$
$504$	−6.73963	−	10.1016i	−0.300207	−	0.449962i
$505$	18.6472			0.829789
$506$	20.6912	−	18.3855i	0.919836	−	0.817336i
$507$			8.51193i			0.378028i
$508$	0.340556	−	9.41427i	0.0151097	−	0.417691i
$509$	−1.47007	+	1.27382i	−0.0651595	+	0.0564611i	−0.686832	−	0.726816i	$-0.740999\pi$
$509$	−1.47007	+	1.27382i	−0.0651595	+	0.0564611i	0.621672	+	0.783278i	$0.286454\pi$
$510$	12.6768	−	32.1977i	0.561338	−	1.42574i
$511$	−1.36812	−	9.51550i	−0.0605221	−	0.420941i
$512$	−7.48373	−	21.3540i	−0.330737	−	0.943723i
$513$	−0.788948	+	1.72755i	−0.0348329	+	0.0762734i
$514$	−3.15515	+	35.1671i	−0.139168	+	1.55115i
$515$	−41.3911	−	5.95114i	−1.82391	−	0.262238i
$516$	−16.7493	+	1.79296i	−0.737345	+	0.0789306i
$517$	−1.72181	+	5.86395i	−0.0757252	+	0.257896i
$518$	−11.0156	−	31.2480i	−0.483997	−	1.37296i
$519$	−6.09721	−	13.3510i	−0.267638	−	0.586045i
$520$	24.2559	−	3.91344i	1.06369	−	0.171616i
$521$	−5.22381	+	6.02859i	−0.228859	+	0.264117i	−0.858552	−	0.512727i	$-0.828635\pi$
$521$	−5.22381	+	6.02859i	−0.228859	+	0.264117i	0.629693	+	0.776844i	$0.283181\pi$
$522$	7.16965	−	1.42442i	0.313807	−	0.0623453i
$523$	−7.80976	+	12.1522i	−0.341497	+	0.531380i	−0.968944	−	0.247279i	$-0.920463\pi$
$523$	−7.80976	+	12.1522i	−0.341497	+	0.531380i	0.627447	+	0.778659i	$0.284100\pi$
$524$	4.77476	−	26.3954i	0.208587	−	1.15309i
$525$	27.4201	+	42.6665i	1.19671	+	1.86212i
$526$	10.3575	+	2.45004i	0.451607	+	0.106827i
$527$	41.6634	−	12.2335i	1.81489	−	0.532899i
$528$	−13.0594	−	9.79487i	−0.568338	−	0.426267i
$529$	−22.5236	+	4.65699i	−0.979287	+	0.202478i
$530$	−2.80102	+	2.01884i	−0.121668	+	0.0876930i
$531$	2.75481	+	9.38202i	0.119549	+	0.407145i
$532$	−6.23382	−	15.0693i	−0.270270	−	0.653338i
$533$	−1.86443	−	2.90111i	−0.0807575	−	0.125661i
$534$	−5.50784	+	5.31220i	−0.238347	+	0.229881i
$535$	−25.5109	−	16.3948i	−1.10293	−	0.708810i
$536$	4.07670	−	32.2771i	0.176087	−	1.39416i
$537$	−5.29217	+	6.10749i	−0.228374	+	0.263558i
$538$	−14.7891	+	7.73170i	−0.637602	+	0.333337i
$539$	42.4435	−	19.3833i	1.82817	−	0.834897i
$540$	4.68015	−	6.73411i	0.201402	−	0.289790i
$541$	7.64403	−	26.0332i	0.328642	−	1.11925i	−0.615066	−	0.788475i	$-0.710871\pi$
$541$	7.64403	−	26.0332i	0.328642	−	1.11925i	0.943709	−	0.330778i	$-0.107311\pi$
$542$	30.1736	+	17.1913i	1.29607	+	0.738431i
$543$	−1.21078	+	8.42119i	−0.0519597	+	0.361388i
$544$	22.5864	−	25.0869i	0.968382	−	1.07559i
$545$	19.5890	−	42.8940i	0.839102	−	1.83738i
$546$	12.8448	−	0.685540i	0.549707	−	0.0293384i
$547$	−11.0170	+	1.58400i	−0.471052	+	0.0677271i	−0.373753	−	0.927528i	$-0.621929\pi$
$547$	−11.0170	+	1.58400i	−0.471052	+	0.0677271i	−0.0972989	+	0.995255i	$0.531020\pi$
$548$	−1.31871	−	5.17656i	−0.0563325	−	0.221132i
$549$	−0.615311	+	0.533170i	−0.0262608	+	0.0227551i
$550$	53.8330	+	41.8385i	2.29545	+	1.78400i
$551$	9.81646			0.418195
$552$	5.34105	+	12.4689i	0.227330	+	0.530711i
$553$	29.7047			1.26317
$554$	18.6482	+	14.4932i	0.792286	+	0.615758i
$555$	16.9100	−	14.6526i	0.717789	−	0.621967i
$556$	−16.0009	+	4.07617i	−0.678590	+	0.172868i
$557$	15.9136	−	2.28803i	0.674282	−	0.0969471i	0.203336	−	0.979109i	$-0.434822\pi$
$557$	15.9136	−	2.28803i	0.674282	−	0.0969471i	0.470946	+	0.882162i	$0.343913\pi$
$558$	10.2761	−	0.548447i	0.435023	−	0.0232176i
$559$	7.41229	−	16.2306i	0.313506	−	0.686483i
$560$	14.9052	+	68.8223i	0.629861	+	2.90827i
$561$	3.46585	−	24.1055i	0.146328	−	1.01774i
$562$	22.9036	+	13.0493i	0.966129	+	0.550450i
$563$	−2.72232	+	9.27137i	−0.114732	+	0.390742i	−0.996758	−	0.0804595i	$-0.974361\pi$
$563$	−2.72232	+	9.27137i	−0.114732	+	0.390742i	0.882026	+	0.471201i	$0.156179\pi$
$564$	−2.45939	−	1.70926i	−0.103559	−	0.0719727i
$565$	64.9546	−	29.6638i	2.73266	−	1.24796i
$566$	−39.8306	+	20.8234i	−1.67420	+	0.875271i
$567$	2.81157	−	3.24472i	0.118075	−	0.136266i
$568$	−5.56579	−	0.702977i	−0.233535	−	0.0294962i
$569$	−1.22679	−	0.788408i	−0.0514295	−	0.0330518i	0.514673	−	0.857386i	$-0.327913\pi$
$569$	−1.22679	−	0.788408i	−0.0514295	−	0.0330518i	−0.566103	+	0.824335i	$0.691550\pi$
$570$	7.92684	−	7.64528i	0.332019	−	0.320225i
$571$	−8.33740	−	12.9732i	−0.348909	−	0.542913i	0.621798	−	0.783177i	$-0.286402\pi$
$571$	−8.33740	−	12.9732i	−0.348909	−	0.542913i	−0.970708	+	0.240264i	$0.922766\pi$
$572$	15.9785	−	6.60993i	0.668096	−	0.276375i
$573$	−5.86391	−	19.9706i	−0.244968	−	0.834285i
$574$	8.01815	−	5.77911i	0.334671	−	0.241215i
$575$	−21.4101	−	52.4518i	−0.892862	−	2.18739i
$576$	6.57764	−	4.55353i	0.274068	−	0.189730i
$577$	−27.9718	+	8.21327i	−1.16448	+	0.341923i	−0.806173	−	0.591680i	$-0.798465\pi$
$577$	−27.9718	+	8.21327i	−1.16448	+	0.341923i	−0.358310	+	0.933603i	$0.616647\pi$
$578$	25.6106	+	6.05815i	1.06526	+	0.251986i
$579$	12.8405	+	19.9803i	0.533635	+	0.830352i
$580$	−41.7109	−	7.54524i	−1.73195	−	0.313299i
$581$	−2.62107	+	4.07846i	−0.108740	+	0.169203i
$582$	3.02869	−	0.601721i	0.125543	−	0.0249421i
$583$	−1.59131	+	1.83647i	−0.0659053	+	0.0760587i
$584$	6.25230	−	1.00874i	0.258722	−	0.0417421i
$585$	3.60857	+	7.90166i	0.149196	+	0.326694i
$586$	15.3078	+	43.4238i	0.632361	+	1.79382i
$587$	6.65025	−	22.6487i	0.274485	−	0.934811i	−0.700707	−	0.713450i	$-0.747132\pi$
$587$	6.65025	−	22.6487i	0.274485	−	0.934811i	0.975192	−	0.221361i	$-0.0710501\pi$
$588$	2.43387	+	22.7364i	0.100371	+	0.937634i
$589$	13.6790	+	1.96674i	0.563634	+	0.0810383i
$590$	5.06681	−	56.4744i	0.208597	−	2.32501i
$591$	1.81491	−	3.97409i	0.0746552	−	0.163472i
$592$	20.4582	−	7.60913i	0.840826	−	0.312733i
$593$	−4.93579	−	34.3292i	−0.202689	−	1.40973i	−0.796263	−	0.604951i	$-0.793193\pi$
$593$	−4.93579	−	34.3292i	−0.202689	−	1.40973i	0.593575	−	0.804779i	$-0.297716\pi$
$594$	2.11439	−	5.37032i	0.0867544	−	0.220347i
$595$	−79.3929	+	68.7943i	−3.25479	+	2.82029i
$596$	−23.0239	−	0.832877i	−0.943094	−	0.0341160i
$597$		−	11.8763i		−	0.486063i
$598$	−14.2466	−	1.86741i	−0.582585	−	0.0763642i
$599$	−9.86855			−0.403218			−0.201609	−	0.979466i	$-0.564617\pi$
$599$	−9.86855			−0.403218			−0.201609	+	0.979466i	$0.564617\pi$
$600$	−27.7940	+	18.5437i	−1.13469	+	0.757044i
$601$	−11.3147	−	13.0579i	−0.461537	−	0.532642i	0.476501	−	0.879174i	$-0.341905\pi$
$601$	−11.3147	−	13.0579i	−0.461537	−	0.532642i	−0.938038	+	0.346532i	$0.887359\pi$
$602$	47.5840	+	18.7347i	1.93938	+	0.763568i
$603$	11.3853	−	1.63695i	0.463644	−	0.0666619i
$604$	−14.9262	+	12.0170i	−0.607339	+	0.488965i
$605$	21.0940	+	9.63332i	0.857594	+	0.391650i
$606$	−0.574709	+	6.40568i	−0.0233460	+	0.260213i
$607$	2.38459	−	16.5852i	0.0967877	−	0.673173i	−0.882442	−	0.470421i	$-0.844102\pi$
$607$	2.38459	−	16.5852i	0.0967877	−	0.673173i	0.979230	−	0.202753i	$-0.0649887\pi$
$608$	9.85554	−	4.27652i	0.399695	−	0.173436i
$609$	−21.2927	−	6.25210i	−0.862824	−	0.253348i
$610$	4.45265	−	1.56966i	0.180282	−	0.0635535i
$611$	2.88579	−	1.31790i	0.116747	−	0.0533164i
$612$	10.6698	+	5.34707i	0.431303	+	0.216142i
$613$	10.6635	+	9.24000i	0.430696	+	0.373200i	0.843060	−	0.537819i	$-0.180752\pi$
$613$	10.6635	+	9.24000i	0.430696	+	0.373200i	−0.412365	+	0.911019i	$0.635297\pi$
$614$	−23.4552	+	4.65994i	−0.946575	+	0.188060i
$615$	5.61510	+	3.60860i	0.226423	+	0.145513i
$616$	21.3582	+	44.7206i	0.860546	+	1.80185i
$617$	38.4279	−	24.6961i	1.54705	−	0.994229i	0.560994	−	0.827820i	$-0.310419\pi$
$617$	38.4279	−	24.6961i	1.54705	−	0.994229i	0.986057	−	0.166409i	$-0.0532172\pi$
$618$	3.32001	−	14.0352i	0.133550	−	0.564579i
$619$	−2.74758	−	9.35740i	−0.110435	−	0.376106i	0.885667	−	0.464321i	$-0.153702\pi$
$619$	−2.74758	−	9.35740i	−0.110435	−	0.376106i	−0.996101	+	0.0882156i	$0.971884\pi$
$620$	−56.6115	−	18.8710i	−2.27357	−	0.757877i
$621$	−3.74970	+	2.98994i	−0.150470	+	0.119982i
$622$	−9.55337	+	6.88562i	−0.383055	+	0.276088i
$623$	22.2901	−	6.54495i	0.893033	−	0.262218i
$624$	0.596774	+	8.45299i	0.0238901	+	0.338390i
$625$	46.6745	−	29.9959i	1.86698	−	1.19984i
$626$	7.67850	+	7.96129i	0.306895	+	0.318197i
$627$	4.19038	−	6.52036i	0.167348	−	0.260398i
$628$	−2.31216	+	2.48116i	−0.0922654	+	0.0990089i
$629$	24.6094	+	21.3242i	0.981242	+	0.850251i
$630$	−22.0632	+	11.5346i	−0.879020	+	0.459550i
$631$	−12.5276	−	27.4316i	−0.498716	−	1.09204i	−0.976884	−	0.213768i	$-0.931426\pi$
$631$	−12.5276	−	27.4316i	−0.498716	−	1.09204i	0.478168	−	0.878268i	$-0.341301\pi$
$632$	0.335823	+	19.5662i	0.0133583	+	0.778302i
$633$	13.8392	+	4.06356i	0.550060	+	0.161512i
$634$	17.7460	−	31.1471i	0.704783	−	1.23701i
$635$	−19.1170	−	2.74861i	−0.758636	−	0.109075i
$636$	−0.607184	−	1.02443i	−0.0240764	−	0.0406211i
$637$	−22.0324	−	10.0619i	−0.872956	−	0.398666i
$638$	−29.7896	+	1.58990i	−1.17938	+	0.0629449i
$639$	−0.282272	−	1.96325i	−0.0111665	−	0.0776649i
$640$	−45.1640	+	10.5960i	−1.78527	+	0.418843i
$641$	25.5079	+	29.4377i	1.00750	+	1.16272i	0.986636	+	0.162938i	$0.0520972\pi$
$641$	25.5079	+	29.4377i	1.00750	+	1.16272i	0.0208670	+	0.999782i	$0.493357\pi$
$642$	6.41819	−	8.25818i	0.253306	−	0.325925i
$643$			21.8080i			0.860025i	0.902823	+	0.430013i	$0.141491\pi$
$643$			21.8080i			0.860025i	−0.902823	+	0.430013i	$0.858509\pi$
$644$	3.16838	−	41.0586i	0.124852	−	1.61794i
$645$			34.5353i			1.35982i
$646$	12.6548	+	9.83522i	0.497897	+	0.386962i
$647$	31.4584	+	36.3050i	1.23676	+	1.42730i	0.867105	+	0.498125i	$0.165978\pi$
$647$	31.4584	+	36.3050i	1.23676	+	1.42730i	0.369653	+	0.929170i	$0.379476\pi$
$648$	2.16905	+	1.81527i	0.0852085	+	0.0713106i
$649$	−5.67916	−	39.4994i	−0.222926	−	1.55049i
$650$	−1.88623	−	35.3417i	−0.0739838	−	1.38622i
$651$	−28.4183	−	12.9782i	−1.11380	−	0.508655i
$652$	−12.0543	+	7.14467i	−0.472083	+	0.279807i
$653$	−7.44886	−	1.07098i	−0.291496	−	0.0419109i	−0.00498464	−	0.999988i	$-0.501587\pi$
$653$	−7.44886	−	1.07098i	−0.291496	−	0.0419109i	−0.286512	+	0.958077i	$0.592496\pi$
$654$	14.1312	+	8.05122i	0.552573	+	0.314827i
$655$	−52.7661	−	15.4935i	−2.06174	−	0.605382i
$656$	3.89729	+	5.21614i	0.152164	+	0.203656i
$657$	0.930158	+	2.03676i	0.0362889	+	0.0794617i
$658$	4.21260	+	8.05779i	0.164224	+	0.314125i
$659$	2.08487	+	1.80655i	0.0812151	+	0.0703732i	0.694522	−	0.719471i	$-0.255616\pi$
$659$	2.08487	+	1.80655i	0.0812151	+	0.0703732i	−0.613307	+	0.789844i	$0.710161\pi$
$660$	−22.8170	+	24.4847i	−0.888151	+	0.953065i
$661$	−1.39218	+	2.16627i	−0.0541495	+	0.0842582i	−0.867273	−	0.497833i	$-0.834129\pi$
$661$	−1.39218	+	2.16627i	−0.0541495	+	0.0842582i	0.813123	+	0.582092i	$0.197765\pi$
$662$	16.7095	−	16.1159i	0.649431	−	0.626363i
$663$	−10.6350	+	6.83471i	−0.413030	+	0.265438i
$664$	−2.71607	−	1.68036i	−0.105404	−	0.0652107i
$665$	−32.0797	+	9.41945i	−1.24400	+	0.365271i
$666$	4.51228	+	6.26050i	0.174847	+	0.242590i
$667$	22.1091	+	11.2100i	0.856069	+	0.434052i
$668$	−12.0685	+	36.2046i	−0.466945	+	1.40080i
$669$	4.10466	+	13.9792i	0.158695	+	0.540466i
$670$	−64.9085	−	15.3540i	−2.50763	−	0.593177i
$671$	2.79526	−	1.79640i	0.107910	−	0.0693494i
$672$	−24.1012	+	2.99913i	−0.929723	+	0.115694i
$673$	4.49403	+	2.88814i	0.173232	+	0.111330i	0.624384	−	0.781118i	$-0.285350\pi$
$673$	4.49403	+	2.88814i	0.173232	+	0.111330i	−0.451151	+	0.892447i	$0.648987\pi$
$674$	−5.22556	−	26.3022i	−0.201281	−	1.01312i
$675$	−8.92767	−	7.73587i	−0.343626	−	0.297754i
$676$	15.2197	+	7.62715i	0.585372	+	0.293352i
$677$	8.12669	−	3.71134i	0.312334	−	0.142638i	−0.253080	−	0.967445i	$-0.581444\pi$
$677$	8.12669	−	3.71134i	0.312334	−	0.142638i	0.565414	+	0.824807i	$0.308716\pi$
$678$	8.18817	+	23.2274i	0.314465	+	0.892043i
$679$	−8.99471	−	2.64109i	−0.345185	−	0.101356i
$680$	−46.2117	−	51.5176i	−1.77214	−	1.97561i
$681$	1.48949	−	10.3596i	0.0570775	−	0.396982i
$682$	−41.8297	−	3.75291i	−1.60174	−	0.143706i
$683$	−1.85560	−	0.847426i	−0.0710027	−	0.0324259i	0.379597	−	0.925152i	$-0.376063\pi$
$683$	−1.85560	−	0.847426i	−0.0710027	−	0.0324259i	−0.450600	+	0.892726i	$0.648790\pi$
$684$	2.38199	+	2.95865i	0.0910778	+	0.113127i
$685$	−10.8404	+	1.55861i	−0.414190	+	0.0595515i
$686$	9.86096	−	25.0458i	0.376493	−	0.956253i
$687$	−15.6964	−	18.1146i	−0.598855	−	0.691116i
$688$	−11.8024	+	31.5549i	−0.449962	+	1.20302i
$689$	1.26141			0.0480559
$690$	26.5838	−	8.16697i	1.01203	−	0.310911i
$691$			9.33086i			0.354963i	0.984124	+	0.177481i	$0.0567950\pi$
$691$			9.33086i			0.354963i	−0.984124	+	0.177481i	$0.943205\pi$
$692$	−29.3356	−	1.06120i	−1.11517	−	0.0403408i
$693$	−13.2421	+	11.4743i	−0.503026	+	0.435874i
$694$	28.6402	+	11.2761i	1.08717	+	0.428036i
$695$	4.81772	+	33.5080i	0.182746	+	1.27103i
$696$	3.87748	−	14.0960i	0.146975	−	0.534307i
$697$	−4.03525	+	8.83597i	−0.152846	+	0.334686i
$698$	−33.9341	−	3.04453i	−1.28443	−	0.115237i
$699$	24.4264	+	3.51199i	0.923893	+	0.132836i
$700$	100.859	−	10.7967i	3.81213	−	0.408077i
$701$	−2.55690	+	8.70802i	−0.0965729	+	0.328897i	−0.993582	−	0.113115i	$-0.963917\pi$
$701$	−2.55690	+	8.70802i	−0.0965729	+	0.328897i	0.897009	+	0.442012i	$0.145735\pi$
$702$	−2.82559	+	0.996083i	−0.106645	+	0.0375947i
$703$	4.30517	+	9.42701i	0.162373	+	0.355547i
$704$	−29.2156	+	14.5740i	−1.10110	+	0.549279i
$705$	−4.02107	+	4.64056i	−0.151442	+	0.174774i
$706$	6.74960	+	33.9733i	0.254025	+	1.27860i
$707$	10.5560	−	16.4255i	0.396999	−	0.617743i
$708$	19.2439	+	3.48110i	0.723230	+	0.130828i
$709$	5.56131	+	8.65357i	0.208859	+	0.324992i	0.929840	−	0.367963i	$-0.119945\pi$
$709$	5.56131	+	8.65357i	0.208859	+	0.324992i	−0.720981	+	0.692955i	$0.756308\pi$
$710$	−2.64761	+	11.1927i	−0.0993629	+	0.420053i
$711$	−6.63846	+	1.94923i	−0.248962	+	0.0731017i
$712$	4.56309	+	14.6083i	0.171009	+	0.547467i
$713$	28.5626	+	20.0504i	1.06968	+	0.750895i
$714$	−21.1853	−	29.3933i	−0.792839	−	1.10001i
$715$	−9.98777	−	34.0152i	−0.373521	−	1.27210i
$716$	6.17836	+	14.9353i	0.230896	+	0.558157i
$717$	7.58172	+	11.7974i	0.283144	+	0.440581i
$718$	−3.69690	−	3.83305i	−0.137967	−	0.143048i
$719$	17.2158	+	11.0639i	0.642040	+	0.412614i	0.820750	−	0.571288i	$-0.193556\pi$
$719$	17.2158	+	11.0639i	0.642040	+	0.412614i	−0.178710	+	0.983902i	$0.557192\pi$
$720$	−7.84717	−	14.4024i	−0.292447	−	0.536747i
$721$	−28.6732	+	33.0906i	−1.06785	+	1.23236i
$722$	−10.0857	−	19.2918i	−0.375352	−	0.717967i
$723$	−14.6339	+	6.68307i	−0.544240	+	0.248546i
$724$	13.9725	+	9.71078i	0.519284	+	0.360898i
$725$	−17.2023	+	58.5857i	−0.638877	+	2.17582i
$726$	−3.95935	+	6.94931i	−0.146945	+	0.257913i
$727$	−1.30362	+	9.06690i	−0.0483487	+	0.336273i	0.951262	+	0.308383i	$0.0997878\pi$
$727$	−1.30362	+	9.06690i	−0.0483487	+	0.336273i	−0.999611	+	0.0278898i	$0.991121\pi$
$728$	10.2839	−	23.5813i	0.381146	−	0.873981i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−0.691991	−	12.9657i	−0.0256117	−	0.479881i
$731$	−49.7482	+	7.15272i	−1.84001	+	0.264553i
$732$	0.401976	+	1.57795i	0.0148575	+	0.0583227i
$733$	31.8458	−	27.5946i	1.17625	−	1.01923i	0.176864	−	0.984235i	$-0.443405\pi$
$733$	31.8458	−	27.5946i	1.17625	−	1.01923i	0.999388	−	0.0349927i	$-0.0111408\pi$
$734$	16.2938	−	20.9650i	0.601416	−	0.773833i
$735$	46.8802			1.72920
$736$	27.0807	+	1.62280i	0.998209	+	0.0598172i
$737$	−46.9424			−1.72915
$738$	−1.41268	+	1.81768i	−0.0520016	+	0.0669096i
$739$	2.56988	−	2.22681i	0.0945345	−	0.0819146i	−0.606311	−	0.795227i	$-0.707351\pi$
$739$	2.56988	−	2.22681i	0.0945345	−	0.0819146i	0.700846	+	0.713313i	$0.252806\pi$
$740$	−11.0471	−	43.3652i	−0.406100	−	1.59414i
$741$	−3.98247	+	0.572593i	−0.146300	+	0.0210347i
$742$	0.192677	+	3.61014i	0.00707339	+	0.132532i
$743$	−9.14424	+	20.0231i	−0.335470	+	0.734576i	−0.999919	−	0.0127576i	$-0.995939\pi$
$743$	−9.14424	+	20.0231i	−0.335470	+	0.734576i	0.664449	+	0.747334i	$0.268666\pi$
$744$	8.22732	−	18.8656i	0.301628	−	0.691645i
$745$	−6.72210	+	46.7532i	−0.246279	+	1.71291i
$746$	−17.4387	+	30.6077i	−0.638475	+	1.12063i
$747$	0.318131	−	1.08346i	0.0116398	−	0.0396416i
$748$	−39.9961	−	27.7970i	−1.46240	−	1.01636i
$749$	−28.8829	+	13.1904i	−1.05536	+	0.481966i
$750$	18.3038	+	35.0113i	0.668362	+	1.27843i
$751$	−14.4889	+	16.7211i	−0.528707	+	0.610161i	−0.955789	−	0.294052i	$-0.904996\pi$
$751$	−14.4889	+	16.7211i	−0.528707	+	0.610161i	0.427082	+	0.904213i	$0.359542\pi$
$752$	−5.25996	+	2.86589i	−0.191811	+	0.104508i
$753$	0.673960	+	0.433127i	0.0245605	+	0.0157840i
$754$	10.7504	+	11.1463i	0.391506	+	0.405924i
$755$	21.2399	+	33.0500i	0.773000	+	1.20281i
$756$	−3.28237	−	7.93465i	−0.119379	−	0.288580i
$757$	−7.60122	−	25.8874i	−0.276271	−	0.940893i	−0.974381	−	0.224903i	$-0.927794\pi$
$757$	−7.60122	−	25.8874i	−0.276271	−	0.940893i	0.698110	−	0.715991i	$-0.254025\pi$
$758$	−2.17886	−	3.02302i	−0.0791396	−	0.109801i
$759$	16.8838	−	9.90026i	0.612842	−	0.359357i
$760$	−6.56717	−	21.0241i	−0.238216	−	0.762624i
$761$	25.5203	−	7.49345i	0.925112	−	0.271637i	0.215723	−	0.976455i	$-0.430789\pi$
$761$	25.5203	−	7.49345i	0.925112	−	0.271637i	0.709389	+	0.704817i	$0.248971\pi$
$762$	1.53339	−	6.48235i	0.0555489	−	0.234831i
$763$	−26.6942	−	41.5370i	−0.966395	−	1.50374i
$764$	−40.9627	−	7.40989i	−1.48198	−	0.268080i
$765$	13.2286	−	20.5840i	0.478280	−	0.744218i
$766$	−2.30012	−	11.5774i	−0.0831066	−	0.418307i
$767$	−13.5654	+	15.6553i	−0.489819	+	0.565282i
$768$	−2.24797	−	15.8413i	−0.0811166	−	0.571624i
$769$	1.75755	+	3.84850i	0.0633790	+	0.138781i	0.938671	−	0.344814i	$-0.112058\pi$
$769$	1.75755	+	3.84850i	0.0633790	+	0.138781i	−0.875292	+	0.483595i	$0.839331\pi$
$770$	95.8254	−	33.7806i	3.45331	−	1.21737i
$771$	−7.03395	+	23.9554i	−0.253322	+	0.862734i
$772$	47.2313	−	5.05597i	1.69989	−	0.181968i
$773$	−3.40536	−	0.489616i	−0.122482	−	0.0176103i	0.0808011	−	0.996730i	$-0.474252\pi$
$773$	−3.40536	−	0.489616i	−0.122482	−	0.0176103i	−0.203283	+	0.979120i	$0.565161\pi$
$774$	−11.8635	−	1.06438i	−0.426426	−	0.0382584i
$775$	−35.7087	+	78.1912i	−1.28270	+	2.80871i
$776$	1.63797	−	5.95459i	0.0587996	−	0.213757i
$777$	−3.33421	−	23.1899i	−0.119614	−	0.831934i
$778$	43.0082	+	16.9331i	1.54192	+	0.607080i
$779$	−2.33642	+	2.02452i	−0.0837110	+	0.0725360i
$780$	17.3620	+	0.628060i	0.621658	+	0.0224882i
$781$			8.09463i			0.289649i
$782$	17.2704	+	36.6027i	0.617590	+	1.30891i
$783$	5.16879			0.184718
$784$	42.8345	+	16.0212i	1.52980	+	0.572187i
$785$	4.55337	+	5.25487i	0.162517	+	0.187554i
$786$	6.94859	−	17.6487i	0.247848	−	0.629507i
$787$	−3.73334	+	0.536773i	−0.133079	+	0.0191339i	−0.208532	−	0.978015i	$-0.566869\pi$
$787$	−3.73334	+	0.536773i	−0.133079	+	0.0191339i	0.0754534	+	0.997149i	$0.475960\pi$
$788$	−5.47957	−	6.80613i	−0.195202	−	0.242458i
$789$	6.84584	+	3.12639i	0.243718	+	0.111303i
$790$	39.9597	+	3.58514i	1.42170	+	0.127553i
$791$	10.6407	−	74.0079i	0.378341	−	2.63142i
$792$	−7.70774	−	8.59271i	−0.273883	−	0.305329i
$793$	−1.65496	−	0.485941i	−0.0587695	−	0.0172563i
$794$	2.78101	+	7.88889i	0.0986942	+	0.279966i
$795$	−2.22083	+	1.01422i	−0.0787647	+	0.0359706i
$796$	−21.2352	−	10.6418i	−0.752663	−	0.377188i
$797$	−26.6313	−	23.0762i	−0.943330	−	0.817401i	0.0400052	−	0.999199i	$-0.487263\pi$
$797$	−26.6313	−	23.0762i	−0.943330	−	0.817401i	−0.983336	+	0.181799i	$0.941808\pi$
$798$	−2.24706	−	11.3103i	−0.0795452	−	0.400381i
$799$	−7.51757	−	4.83125i	−0.265953	−	0.170917i
$800$	8.25193	+	66.3130i	0.291750	+	2.34452i
$801$	−4.55194	+	2.92535i	−0.160835	+	0.103362i
$802$	−16.3826	−	3.87528i	−0.578489	−	0.136841i
$803$	−2.57449	−	8.76789i	−0.0908516	−	0.309412i
$804$	7.27489	−	21.8241i	0.256565	−	0.769677i
$805$	−83.0081	−	15.4187i	−2.92565	−	0.543436i
$806$	12.7472	+	17.6860i	0.449002	+	0.622961i
$807$	−11.3223	+	3.32454i	−0.398565	+	0.117029i
$808$	10.9386	+	6.76744i	0.384820	+	0.238078i
$809$	14.4940	−	9.31472i	0.509582	−	0.327488i	−0.260457	−	0.965485i	$-0.583873\pi$
$809$	14.4940	−	9.31472i	0.509582	−	0.327488i	0.770039	+	0.637997i	$0.220237\pi$
$810$	4.17382	−	4.02557i	0.146653	−	0.141444i
$811$	12.8128	−	19.9371i	0.449918	−	0.700085i	−0.540010	−	0.841658i	$-0.681580\pi$
$811$	12.8128	−	19.9371i	0.449918	−	0.700085i	0.989928	+	0.141573i	$0.0452160\pi$
$812$	−30.2584	+	32.4700i	−1.06186	+	1.13947i
$813$	18.5581	+	16.0807i	0.650862	+	0.563975i
$814$	−14.5916	−	27.9105i	−0.511434	−	0.978263i
$815$	11.9342	+	26.1322i	0.418037	+	0.915372i
$816$	19.1215	−	14.2868i	0.669388	−	0.500139i
$817$	−15.3479	−	4.50654i	−0.536953	−	0.157664i
$818$	−19.1853	−	10.9308i	−0.670797	−	0.382185i
$819$	9.00299	+	1.29443i	0.314590	+	0.0452312i
$820$	11.4838	−	6.80651i	0.401030	−	0.237694i
$821$	6.29395	+	2.87435i	0.219660	+	0.100316i	0.522206	−	0.852819i	$-0.325109\pi$
$821$	6.29395	+	2.87435i	0.219660	+	0.100316i	−0.302546	+	0.953135i	$0.597836\pi$
$822$	−0.201311	−	3.77192i	−0.00702154	−	0.131561i
$823$	−0.189308	−	1.31667i	−0.00659887	−	0.0458962i	0.986256	−	0.165225i	$-0.0528349\pi$
$823$	−0.189308	−	1.31667i	−0.00659887	−	0.0458962i	−0.992855	+	0.119329i	$0.961926\pi$
$824$	−22.1206	−	18.5126i	−0.770608	−	0.644918i
$825$	31.5710	+	36.4349i	1.09916	+	1.26850i
$826$	−46.8774	−	36.4328i	−1.63107	−	1.26766i
$827$		−	12.2272i		−	0.425183i	−0.977141	−	0.212592i	$-0.931810\pi$
$827$		−	12.2272i		−	0.425183i	0.977141	−	0.212592i	$-0.0681904\pi$
$828$	1.98620	+	9.38376i	0.0690252	+	0.326108i
$829$		−	8.97402i		−	0.311681i	−0.987782	−	0.155840i	$-0.950191\pi$
$829$		−	8.97402i		−	0.311681i	0.987782	−	0.155840i	$-0.0498085\pi$
$830$	−4.01818	+	5.17013i	−0.139473	+	0.179458i
$831$	10.9365	+	12.6213i	0.379381	+	0.437830i
$832$	15.6490	+	6.50729i	0.542532	+	0.225600i
$833$	9.70951	+	67.5312i	0.336415	+	2.33982i
$834$	−11.6591	+	0.622260i	−0.403722	+	0.0215471i
$835$	71.1709	+	32.5026i	2.46297	+	1.12480i
$836$	−7.90385	−	13.3352i	−0.273360	−	0.461207i
$837$	7.20259	+	1.03558i	0.248958	+	0.0357948i
$838$	−6.04479	+	10.6096i	−0.208814	+	0.366502i
$839$	−50.3765	−	14.7919i	−1.73919	−	0.510672i	−0.750529	−	0.660837i	$-0.770201\pi$
$839$	−50.3765	−	14.7919i	−1.73919	−	0.510672i	−0.988661	+	0.150165i	$0.952020\pi$
$840$	0.854491	+	49.7856i	0.0294827	+	1.71777i
$841$	0.948636	+	2.07722i	0.0327116	+	0.0716284i
$842$	−39.3380	+	20.5658i	−1.35568	+	0.708745i
$843$	14.0867	+	12.2062i	0.485173	+	0.420405i
$844$	19.6665	−	21.1039i	0.676949	−	0.726426i
$845$	18.8695	−	29.3614i	0.649129	−	1.01006i
$846$	−1.47019	−	1.52434i	−0.0505463	−	0.0524078i
$847$	20.4267	−	13.1274i	0.701869	−	0.451064i
$848$	−2.37578	+	0.167728i	−0.0815848	+	0.00575981i
$849$	−30.4938	+	8.95379i	−1.04654	+	0.307293i
$850$	−80.8739	+	58.2901i	−2.77395	+	1.99933i
$851$	−1.06891	+	26.1483i	−0.0366417	+	0.896353i
$852$	−3.76330	−	1.25446i	−0.128928	−	0.0429772i
$853$	−4.75579	−	16.1967i	−0.162835	−	0.554565i	−0.999971	−	0.00757096i	$-0.997590\pi$
$853$	−4.75579	−	16.1967i	−0.162835	−	0.554565i	0.837136	−	0.546994i	$-0.184228\pi$
$854$	1.13796	−	4.81070i	0.0389403	−	0.164619i
$855$	6.55112	−	4.21015i	0.224044	−	0.143984i
$856$	−9.01491	−	18.8758i	−0.308123	−	0.645160i
$857$	−33.8546	−	21.7570i	−1.15645	−	0.743207i	−0.185538	−	0.982637i	$-0.559403\pi$
$857$	−33.8546	−	21.7570i	−1.15645	−	0.743207i	−0.970914	+	0.239431i	$0.923039\pi$
$858$	11.9927	−	2.38264i	0.409425	−	0.0813420i
$859$	3.19463	+	2.76816i	0.108999	+	0.0944484i	0.707655	−	0.706558i	$-0.249753\pi$
$859$	3.19463	+	2.76816i	0.108999	+	0.0944484i	−0.598656	+	0.801006i	$0.704298\pi$
$860$	61.7504	+	30.9455i	2.10567	+	1.05523i
$861$	6.35731	−	2.90329i	0.216656	−	0.0989437i
$862$	−22.8784	+	8.06516i	−0.779243	+	0.274700i
$863$	23.4997	+	6.90015i	0.799940	+	0.234884i	0.656057	−	0.754711i	$-0.272223\pi$
$863$	23.4997	+	6.90015i	0.799940	+	0.234884i	0.143883	+	0.989595i	$0.454041\pi$
$864$	5.18937	−	2.25177i	0.176546	−	0.0766068i
$865$	−8.56489	+	59.5701i	−0.291215	+	2.02544i
$866$	−1.03547	+	11.5413i	−0.0351867	+	0.392189i
$867$	16.9275	+	7.73053i	0.574888	+	0.262543i
$868$	−48.6698	+	39.1838i	−1.65196	+	1.32999i
$869$	27.9487	−	4.01841i	0.948094	−	0.136315i
$870$	−27.8890	−	10.9804i	−0.945526	−	0.372270i
$871$	15.9575	+	18.4160i	0.540700	+	0.624001i
$872$	27.0582	−	18.0528i	0.916307	−	0.611345i
$873$	2.18346			0.0738990
$874$	0.160550	+	12.8799i	0.00543068	+	0.435668i
$875$		−	119.939i		−	4.05469i
$876$	4.47528	+	0.161891i	0.151206	+	0.00546980i
$877$	−29.5031	+	25.5646i	−0.996250	+	0.863256i	−0.990609	−	0.136728i	$-0.956341\pi$
$877$	−29.5031	+	25.5646i	−0.996250	+	0.863256i	−0.00564161	+	0.999984i	$0.501796\pi$
$878$	−19.9306	+	50.6217i	−0.672627	+	1.70840i
$879$	4.63339	+	32.2259i	0.156280	+	1.08695i
$880$	23.3343	+	62.7374i	0.786598	+	2.11488i
$881$	19.4988	−	42.6965i	0.656932	−	1.43848i	−0.228421	−	0.973562i	$-0.573356\pi$
$881$	19.4988	−	42.6965i	0.656932	−	1.43848i	0.885353	−	0.464919i	$-0.153917\pi$
$882$	−1.44485	+	16.1042i	−0.0486507	+	0.542258i
$883$	14.9879	+	2.15494i	0.504385	+	0.0725196i	0.389810	−	0.920895i	$-0.372541\pi$
$883$	14.9879	+	2.15494i	0.504385	+	0.0725196i	0.114574	+	0.993415i	$0.463450\pi$
$884$	2.69117	+	25.1401i	0.0905139	+	0.845553i
$885$	11.2957	−	38.4697i	0.379702	−	1.29315i
$886$	3.94590	+	11.1933i	0.132565	+	0.376048i
$887$	3.09179	+	6.77006i	0.103812	+	0.227317i	0.954409	−	0.298501i	$-0.0964867\pi$
$887$	3.09179	+	6.77006i	0.103812	+	0.227317i	−0.850597	+	0.525818i	$0.823759\pi$
$888$	15.2373	−	2.45838i	0.511329	−	0.0824978i
$889$	−13.2431	+	15.2833i	−0.444159	+	0.512587i
$890$	30.7752	−	6.11423i	1.03159	−	0.204949i
$891$	2.20642	−	3.43325i	0.0739178	−	0.115018i
$892$	28.6733	+	5.18682i	0.960054	+	0.173668i
$893$	−1.53760	−	2.39256i	−0.0514539	−	0.0800639i
$894$	−15.8535	−	3.75011i	−0.530219	−	0.125423i
$895$	31.7943	−	9.33565i	1.06277	−	0.312056i
$896$	−16.2334	+	45.7812i	−0.542320	+	1.52944i
$897$	−9.62341	−	3.25819i	−0.321316	−	0.108788i
$898$	16.5019	−	11.8938i	0.550676	−	0.396902i
$899$	−10.5964	−	36.0880i	−0.353409	−	1.20360i
$900$	−21.8317	+	9.03127i	−0.727725	+	0.301042i
$901$	−1.92095	−	2.98906i	−0.0639962	−	0.0995800i
$902$	6.76235	−	6.52215i	0.225162	−	0.217164i
$903$	30.4205	+	19.5501i	1.01233	+	0.650586i
$904$	48.8686	+	6.17226i	1.62534	+	0.205286i
$905$	22.8448	−	26.3644i	0.759389	−	0.876381i
$906$	−12.0079	+	6.27773i	−0.398937	+	0.208563i
$907$	−6.75744	+	3.08602i	−0.224377	+	0.102470i	−0.524432	−	0.851452i	$-0.675722\pi$
$907$	−6.75744	+	3.08602i	−0.224377	+	0.102470i	0.300055	+	0.953922i	$0.402995\pi$
$908$	−17.1888	−	11.9461i	−0.570430	−	0.396445i
$909$	−1.28123	+	4.36348i	−0.0424958	+	0.144727i
$910$	−45.8272	−	26.1099i	−1.51916	−	0.865536i
$911$	1.85060	−	12.8712i	0.0613130	−	0.426441i	−0.935927	−	0.352194i	$-0.885436\pi$
$911$	1.85060	−	12.8712i	0.0613130	−	0.426441i	0.997240	−	0.0742470i	$-0.0236553\pi$
$912$	7.42459	−	1.60799i	0.245853	−	0.0532457i
$913$	−1.91439	+	4.19193i	−0.0633571	+	0.138733i
$914$	−36.3563	+	1.94038i	−1.20256	+	0.0641819i
$915$	3.30443	−	0.475105i	0.109241	−	0.0157065i
$916$	−46.4545	+	11.8341i	−1.53490	+	0.391010i
$917$	−43.5179	+	37.7085i	−1.43709	+	1.24524i
$918$	6.66331	+	5.17867i	0.219922	+	0.170922i
$919$	32.6514			1.07707			0.538535	−	0.842603i	$-0.318978\pi$
$919$	32.6514			1.07707			0.538535	+	0.842603i	$0.318978\pi$
$920$	9.21768	−	54.8510i	0.303898	−	1.80838i
$921$	−16.9095			−0.557186
$922$	−38.1266	−	29.6317i	−1.25563	−	0.975869i
$923$	3.17560	−	2.75168i	0.104526	−	0.0905725i
$924$	8.65093	+	33.9590i	0.284595	+	1.11717i
$925$	−63.8057	+	9.17388i	−2.09792	+	0.301635i
$926$	−14.5013	+	0.773952i	−0.476543	+	0.0254336i
$927$	4.23652	−	9.27668i	0.139146	−	0.304686i
$928$	−21.7297	−	19.5638i	−0.713313	−	0.642215i
$929$	3.26445	−	22.7047i	0.107103	−	0.744918i	−0.863520	−	0.504314i	$-0.831745\pi$
$929$	3.26445	−	22.7047i	0.107103	−	0.744918i	0.970623	−	0.240604i	$-0.0773455\pi$
$930$	−36.6628	−	20.8885i	−1.20222	−	0.684962i
$931$	−6.11743	+	20.8341i	−0.200491	+	0.682809i
$932$	28.1670	−	40.5285i	0.922641	−	1.32756i
$933$	−7.57452	+	3.45917i	−0.247979	+	0.113248i
$934$	48.6724	−	25.4458i	1.59261	−	0.832613i
$935$	−65.3930	+	75.4676i	−2.13858	+	2.46805i
$936$	−0.750849	+	5.94481i	−0.0245423	+	0.194312i
$937$	16.9981	+	10.9240i	0.555303	+	0.356871i	0.787998	−	0.615678i	$-0.211118\pi$
$937$	16.9981	+	10.9240i	0.555303	+	0.356871i	−0.232695	+	0.972550i	$0.574754\pi$
$938$	−50.2687	+	48.4832i	−1.64133	+	1.58303i
$939$	4.22844	+	6.57959i	0.137990	+	0.214717i
$940$	4.69441	+	11.3480i	0.153115	+	0.370132i
$941$	0.157131	+	0.535138i	0.00512231	+	0.0174450i	0.962014	−	0.272998i	$-0.0880154\pi$
$941$	0.157131	+	0.535138i	0.00512231	+	0.0174450i	−0.956892	+	0.290443i	$0.906197\pi$
$942$	−1.94548	+	1.40222i	−0.0633873	+	0.0456866i
$943$	−7.57413	+	1.89164i	−0.246648	+	0.0616002i
$944$	23.4679	−	31.2896i	0.763816	−	1.01839i
$945$	−16.8914	+	4.95975i	−0.549476	+	0.161341i
$946$	47.3054	+	11.1900i	1.53803	+	0.363819i
$947$	2.70348	+	4.20670i	0.0878513	+	0.136699i	0.882398	−	0.470504i	$-0.155928\pi$
$947$	2.70348	+	4.20670i	0.0878513	+	0.136699i	−0.794547	+	0.607203i	$0.792291\pi$
$948$	−2.46313	+	13.6164i	−0.0799987	+	0.442241i
$949$	−2.56456	+	3.99054i	−0.0832493	+	0.129538i
$950$	−31.1197	+	6.18267i	−1.00966	+	0.200592i
$951$	16.5995	−	19.1569i	0.538277	−	0.621205i
$952$	−71.5395	+	11.5422i	−2.31861	+	0.374084i
$953$	−5.96118	−	13.0532i	−0.193102	−	0.422834i	0.788171	−	0.615456i	$-0.211028\pi$
$953$	−5.96118	−	13.0532i	−0.193102	−	0.422834i	−0.981273	+	0.192622i	$0.938301\pi$
$954$	−0.279958	−	0.794156i	−0.00906396	−	0.0257118i
$955$	−24.0442	+	81.8869i	−0.778051	+	2.64980i
$956$	27.8878	−	2.98531i	0.901957	−	0.0965518i
$957$	−20.8797	−	3.00205i	−0.674946	−	0.0970425i
$958$	−3.94125	+	43.9289i	−0.127336	+	1.41928i
$959$	−4.76373	+	10.4311i	−0.153829	+	0.336838i
$960$	−32.7836	+	1.12569i	−1.05809	+	0.0363315i
$961$	−3.12377	−	21.7263i	−0.100767	−	0.700849i
$962$	−5.98933	+	15.2123i	−0.193104	+	0.490463i
$963$	5.58925	−	4.84311i	0.180111	−	0.156067i
$964$	−1.16317	+	32.1543i	−0.0374631	+	1.03562i
$965$		−	97.3861i		−	3.13497i
$966$	7.85493	−	28.0397i	0.252728	−	0.902163i
$967$	−7.86825			−0.253026			−0.126513	−	0.991965i	$-0.540379\pi$
$967$	−7.86825			−0.253026			−0.126513	+	0.991965i	$0.540379\pi$
$968$	8.87784	+	13.3064i	0.285345	+	0.427685i
$969$	7.42157	+	8.56495i	0.238415	+	0.275146i
$970$	−11.7812	−	4.63846i	−0.378272	−	0.148932i
$971$	−19.9507	+	2.86848i	−0.640249	+	0.0920539i	−0.454791	−	0.890598i	$-0.650286\pi$
$971$	−19.9507	+	2.86848i	−0.640249	+	0.0920539i	−0.185458	+	0.982652i	$0.559377\pi$
$972$	1.25422	+	1.55786i	0.0402292	+	0.0499683i
$973$	32.2429	+	14.7248i	1.03366	+	0.472057i
$974$	2.69658	−	30.0559i	0.0864040	−	0.963053i
$975$	3.56156	−	24.7712i	0.114061	−	0.793314i
$976$	3.18163	+	0.695179i	0.101841	+	0.0222521i
$977$	−44.1194	−	12.9546i	−1.41150	−	0.414455i	−0.514885	−	0.857259i	$-0.672166\pi$
$977$	−44.1194	−	12.9546i	−1.41150	−	0.414455i	−0.896618	+	0.442804i	$0.853984\pi$
$978$	−9.34475	+	3.29423i	−0.298812	+	0.105338i
$979$	20.0870	−	9.17341i	0.641982	−	0.293183i
$980$	42.0072	−	83.8236i	1.34187	−	2.67765i
$981$	8.69133	+	7.53108i	0.277493	+	0.240449i
$982$	3.67352	−	0.729833i	0.117227	−	0.0232899i
$983$	38.9056	+	25.0031i	1.24090	+	0.797475i	0.985552	−	0.169375i	$-0.0541748\pi$
$983$	38.9056	+	25.0031i	1.24090	+	0.797475i	0.255344	+	0.966850i	$0.417811\pi$
$984$	1.98424	+	4.15467i	0.0632552	+	0.132446i
$985$	−15.0703	+	9.68508i	−0.480179	+	0.308592i
$986$	10.0411	−	42.4485i	0.319775	−	1.35184i
$987$	1.81137	+	6.16895i	0.0576565	+	0.196360i
$988$	−2.54470	+	7.63389i	−0.0809575	+	0.242867i
$989$	−29.4210	−	27.6764i	−0.935532	−	0.880059i
$990$	−19.1985	+	13.8374i	−0.610170	+	0.439782i
$991$	30.3080	−	8.89923i	0.962765	−	0.282693i	0.237673	−	0.971345i	$-0.423615\pi$
$991$	30.3080	−	8.89923i	0.962765	−	0.282693i	0.725092	+	0.688652i	$0.241797\pi$
$992$	−26.3602	−	31.6153i	−0.836938	−	1.00379i
$993$	13.8095	−	8.87482i	0.438231	−	0.281634i
$994$	8.36032	+	8.66821i	0.265173	+	0.274939i
$995$	−26.3276	+	40.9666i	−0.834641	+	1.29873i
$996$	−1.65220	−	1.53967i	−0.0523519	−	0.0487862i
$997$	15.9712	+	13.8391i	0.505811	+	0.438288i	0.870011	−	0.493033i	$-0.164112\pi$
$997$	15.9712	+	13.8391i	0.505811	+	0.438288i	−0.364199	+	0.931321i	$0.618657\pi$
$998$	−35.8231	+	18.7283i	−1.13396	+	0.592833i
$999$	2.26686	+	4.96373i	0.0717203	+	0.157045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.34	yes	480
8.5	even	2	inner	552.2.bb.a.469.44	yes	480
23.18	even	11	inner	552.2.bb.a.133.44	yes	480
184.133	even	22	inner	552.2.bb.a.133.34	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.34	✓	480	184.133	even	22	inner
552.2.bb.a.133.44	yes	480	23.18	even	11	inner
552.2.bb.a.469.34	yes	480	1.1	even	1	trivial
552.2.bb.a.469.44	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.867835 - 1.11663i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.493724 - 1.93810i) q^{4} +(-4.05863 + 0.583543i) q^{5} +(-0.0753708 - 1.41220i) q^{6} +(-1.78354 + 3.90540i) q^{7} +(-2.59261 - 1.13065i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.87062 + 5.03841i) q^{10} +(-1.14978 + 3.91580i) q^{11} +(-1.64232 - 1.14140i) q^{12} +(1.92706 - 0.880060i) q^{13} +(2.81307 + 5.38080i) q^{14} +(-2.68517 + 3.09885i) q^{15} +(-3.51247 + 1.91377i) q^{16} +(-5.02005 - 3.22619i) q^{17} +(-0.981758 - 1.01791i) q^{18} +(-1.02677 - 1.59769i) q^{19} +(3.13481 + 7.57793i) q^{20} +(1.20959 + 4.11947i) q^{21} +(3.37468 + 4.68215i) q^{22} +(-0.488059 - 4.77093i) q^{23} +(-2.69978 + 0.843315i) q^{24} +(11.3345 - 3.32811i) q^{25} +(0.689672 - 2.91556i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(8.44964 + 1.52849i) q^{28} +(-2.79446 + 4.34826i) q^{29} +(1.12998 + 5.68763i) q^{30} +(-4.76520 + 5.49933i) q^{31} +(-0.911272 + 5.58297i) q^{32} +(1.69536 + 3.71231i) q^{33} +(-7.95903 + 2.80573i) q^{34} +(4.95975 - 16.8914i) q^{35} +(-1.98864 + 0.212878i) q^{36} +(-5.40131 - 0.776591i) q^{37} +(-2.67510 - 0.240007i) q^{38} +(0.880060 - 1.92706i) q^{39} +(11.1822 + 3.07597i) q^{40} +(-0.231664 - 1.61126i) q^{41} +(5.64965 + 2.22436i) q^{42} +(6.36528 - 5.51555i) q^{43} +(8.15689 + 0.295072i) q^{44} +4.10037i q^{45} +(-5.75092 - 3.59540i) q^{46} +1.49751 q^{47} +(-1.40130 + 3.74651i) q^{48} +(-7.48713 - 8.64061i) q^{49} +(6.12021 - 15.5447i) q^{50} +(-5.90660 + 0.849241i) q^{51} +(-2.65708 - 3.30034i) q^{52} +(0.541617 + 0.247348i) q^{53} +(-1.40856 - 0.126374i) q^{54} +(2.38151 - 16.5637i) q^{55} +(9.03965 - 8.10864i) q^{56} +(-1.82225 - 0.535061i) q^{57} +(2.43027 + 6.89395i) q^{58} +(-8.89448 + 4.06197i) q^{59} +(7.33162 + 3.67415i) q^{60} +(-0.615311 - 0.533170i) q^{61} +(2.00531 + 10.0935i) q^{62} +(3.61183 + 2.32118i) q^{63} +(5.44328 + 5.86265i) q^{64} +(-7.30768 + 4.69636i) q^{65} +(5.61657 + 1.32859i) q^{66} +(3.24059 + 11.0364i) q^{67} +(-3.77416 + 11.3222i) q^{68} +(-3.49315 - 3.28602i) q^{69} +(-14.5571 - 20.1971i) q^{70} +(1.90309 - 0.558799i) q^{71} +(-1.48810 + 2.40532i) q^{72} +(-1.88366 + 1.21055i) q^{73} +(-5.55461 + 5.35731i) q^{74} +(6.38659 - 9.93773i) q^{75} +(-2.58954 + 2.77881i) q^{76} +(-13.2421 - 11.4743i) q^{77} +(-1.38807 - 2.65507i) q^{78} +(-2.87414 - 6.29348i) q^{79} +(13.1391 - 9.81698i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-2.00022 - 1.13962i) q^{82} +(1.11770 + 0.160701i) q^{83} +(7.38676 - 4.37818i) q^{84} +(22.2571 + 10.1645i) q^{85} +(-0.634809 - 11.8943i) q^{86} +(0.735596 + 5.11618i) q^{87} +(7.40833 - 8.85216i) q^{88} +(-3.54339 - 4.08929i) q^{89} +(4.57859 + 3.55844i) q^{90} +9.09557i q^{91} +(-9.00558 + 3.30143i) q^{92} +7.27666i q^{93} +(1.29959 - 1.67216i) q^{94} +(5.09962 + 5.88527i) q^{95} +(2.96738 + 4.81609i) q^{96} +(0.310739 + 2.16124i) q^{97} +(-16.1460 + 0.861726i) q^{98} +(3.71231 + 1.69536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more