LMFDB - Embedded newform 60.3.l.a.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770813 + 1.84549i) q^{2} +(-1.12501 - 2.78107i) q^{3} +(-2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 - 4.75159i) q^{7} +(7.41783 - 2.99596i) q^{8} +(-6.46869 + 6.25748i) q^{9} +O(q^{10})$	\(q+(-0.770813 + 1.84549i) q^{2} +(-1.12501 - 2.78107i) q^{3} +(-2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 - 4.75159i) q^{7} +(7.41783 - 2.99596i) q^{8} +(-6.46869 + 6.25748i) q^{9} +(8.83710 - 4.68034i) q^{10} +11.9496 q^{11} +(-4.74911 + 11.0203i) q^{12} +(-4.22368 - 4.22368i) q^{13} +(12.4316 - 5.10644i) q^{14} +(-4.48553 + 14.3136i) q^{15} +(-0.188739 + 15.9989i) q^{16} +(-9.35253 - 9.35253i) q^{17} +(-6.56200 - 16.7613i) q^{18} -1.48848 q^{19} +(1.82579 + 19.9165i) q^{20} +(-7.86889 + 18.5601i) q^{21} +(-9.21092 + 22.0529i) q^{22} +(-11.6030 - 11.6030i) q^{23} +(-16.6771 - 17.2590i) q^{24} +(4.83510 + 24.5280i) q^{25} +(11.0504 - 4.53911i) q^{26} +(24.6799 + 10.9501i) q^{27} +(-0.158538 + 26.8786i) q^{28} +39.3671 q^{29} +(-22.9582 - 19.3111i) q^{30} -43.6522i q^{31} +(-29.3804 - 12.6805i) q^{32} +(-13.4435 - 33.2327i) q^{33} +(24.4691 - 10.0510i) q^{34} +(3.26452 + 33.4399i) q^{35} +(35.9909 + 0.809673i) q^{36} +(49.1693 - 49.1693i) q^{37} +(1.14734 - 2.74698i) q^{38} +(-6.99465 + 16.4981i) q^{39} +(-38.1631 - 11.9824i) q^{40} +27.0663i q^{41} +(-28.1871 - 28.8284i) q^{42} +(-8.84693 + 8.84693i) q^{43} +(-33.5987 - 33.9974i) q^{44} +(44.8535 - 3.62848i) q^{45} +(30.3570 - 12.4695i) q^{46} +(-15.0010 + 15.0010i) q^{47} +(44.7063 - 17.4741i) q^{48} -3.84477i q^{49} +(-48.9932 - 9.98334i) q^{50} +(-15.4883 + 36.5318i) q^{51} +(-0.140924 + 23.8923i) q^{52} +(-14.6333 + 14.6333i) q^{53} +(-39.2319 + 37.1060i) q^{54} +(-46.1533 - 37.9435i) q^{55} +(-49.4821 - 21.0109i) q^{56} +(1.67456 + 4.13957i) q^{57} +(-30.3447 + 72.6517i) q^{58} -61.7260i q^{59} +(53.3351 - 27.4840i) q^{60} -84.6009 q^{61} +(80.5598 + 33.6477i) q^{62} +(60.4695 + 1.00356i) q^{63} +(46.0485 - 44.4470i) q^{64} +(2.90182 + 29.7246i) q^{65} +(71.6932 + 0.806325i) q^{66} +(65.7467 + 65.7467i) q^{67} +(-0.312049 + 52.9050i) q^{68} +(-19.2152 + 45.3223i) q^{69} +(-64.2294 - 19.7512i) q^{70} -14.2794 q^{71} +(-29.2365 + 65.7969i) q^{72} +(16.0903 + 16.0903i) q^{73} +(52.8413 + 128.642i) q^{74} +(62.7745 - 41.0411i) q^{75} +(4.18516 + 4.23482i) q^{76} +(-56.7797 - 56.7797i) q^{77} +(-25.0555 - 25.6255i) q^{78} -9.32721 q^{79} +(51.5300 - 61.1936i) q^{80} +(2.68783 - 80.9554i) q^{81} +(-49.9507 - 20.8630i) q^{82} +(-12.7500 - 12.7500i) q^{83} +(74.9296 - 29.7979i) q^{84} +(6.42553 + 65.8195i) q^{85} +(-9.50762 - 23.1463i) q^{86} +(-44.2885 - 109.483i) q^{87} +(88.6403 - 35.8005i) q^{88} -52.4342 q^{89} +(-27.8773 + 85.5737i) q^{90} +40.1384i q^{91} +(-0.387136 + 65.6353i) q^{92} +(-121.400 + 49.1093i) q^{93} +(-16.1213 - 39.2471i) q^{94} +(5.74900 + 4.72636i) q^{95} +(-2.21192 + 95.9745i) q^{96} +(6.90848 - 6.90848i) q^{97} +(7.09551 + 2.96360i) q^{98} +(-77.2983 + 74.7745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.770813	+	1.84549i	−0.385406	+	0.922747i
$2$	−0.770813	+	1.84549i	−0.385406	+	0.922747i
$3$	−1.12501	−	2.78107i	−0.375005	−	0.927023i
$3$	−1.12501	−	2.78107i	−0.375005	−	0.927023i
$4$	−2.81170	−	2.84506i	−0.702924	−	0.711265i
$5$	−3.86232	−	3.17529i	−0.772465	−	0.635058i
$5$	−3.86232	−	3.17529i	−0.772465	−	0.635058i
$6$	5.99962	+	0.0674770i	0.999937	+	0.0112462i
$7$	−4.75159	−	4.75159i	−0.678799	−	0.678799i	0.280930	−	0.959728i	$-0.409357\pi$
$7$	−4.75159	−	4.75159i	−0.678799	−	0.678799i	−0.959728	+	0.280930i	$0.909357\pi$
$8$	7.41783	−	2.99596i	0.927229	−	0.374495i
$9$	−6.46869	+	6.25748i	−0.718743	+	0.695276i
$10$	8.83710	−	4.68034i	0.883710	−	0.468034i
$11$	11.9496			1.08633			0.543164	−	0.839626i	$-0.317226\pi$
$11$	11.9496			1.08633			0.543164	+	0.839626i	$0.317226\pi$
$12$	−4.74911	+	11.0203i	−0.395759	+	0.918354i
$13$	−4.22368	−	4.22368i	−0.324899	−	0.324899i	0.525744	−	0.850643i	$-0.323787\pi$
$13$	−4.22368	−	4.22368i	−0.324899	−	0.324899i	−0.850643	+	0.525744i	$0.823787\pi$
$14$	12.4316	−	5.10644i	0.887973	−	0.364746i
$15$	−4.48553	+	14.3136i	−0.299035	+	0.954242i
$16$	−0.188739	+	15.9989i	−0.0117962	+	0.999930i
$17$	−9.35253	−	9.35253i	−0.550149	−	0.550149i	0.376335	−	0.926484i	$-0.377184\pi$
$17$	−9.35253	−	9.35253i	−0.550149	−	0.550149i	−0.926484	+	0.376335i	$0.877184\pi$
$18$	−6.56200	−	16.7613i	−0.364555	−	0.931182i
$19$	−1.48848			−0.0783411			−0.0391706	−	0.999233i	$-0.512472\pi$
$19$	−1.48848			−0.0783411			−0.0391706	+	0.999233i	$0.512472\pi$
$20$	1.82579	+	19.9165i	0.0912896	+	0.995824i
$21$	−7.86889	+	18.5601i	−0.374709	+	0.883815i
$22$	−9.21092	+	22.0529i	−0.418678	+	1.00241i
$23$	−11.6030	−	11.6030i	−0.504478	−	0.504478i	0.408348	−	0.912826i	$-0.366105\pi$
$23$	−11.6030	−	11.6030i	−0.504478	−	0.504478i	−0.912826	+	0.408348i	$0.866105\pi$
$24$	−16.6771	−	17.2590i	−0.694880	−	0.719125i
$25$	4.83510	+	24.5280i	0.193404	+	0.981119i
$26$	11.0504	−	4.53911i	0.425017	−	0.174581i
$27$	24.6799	+	10.9501i	0.914069	+	0.405560i
$28$	−0.158538	+	26.8786i	−0.00566206	+	0.959950i
$29$	39.3671			1.35749			0.678743	−	0.734376i	$-0.262525\pi$
$29$	39.3671			1.35749			0.678743	+	0.734376i	$0.262525\pi$
$30$	−22.9582	−	19.3111i	−0.765274	−	0.643705i
$31$		−	43.6522i		−	1.40813i	−0.710133	−	0.704067i	$-0.751365\pi$
$31$		−	43.6522i		−	1.40813i	0.710133	−	0.704067i	$-0.248635\pi$
$32$	−29.3804	−	12.6805i	−0.918136	−	0.396264i
$33$	−13.4435	−	33.2327i	−0.407378	−	1.00705i
$34$	24.4691	−	10.0510i	0.719679	−	0.295617i
$35$	3.26452	+	33.4399i	0.0932719	+	0.955424i
$36$	35.9909	+	0.809673i	0.999747	+	0.0224909i
$37$	49.1693	−	49.1693i	1.32890	−	1.32890i	0.422571	−	0.906330i	$-0.361128\pi$
$37$	49.1693	−	49.1693i	1.32890	−	1.32890i	0.906330	−	0.422571i	$-0.138872\pi$
$38$	1.14734	−	2.74698i	0.0301932	−	0.0722890i
$39$	−6.99465	+	16.4981i	−0.179350	+	0.423027i
$40$	−38.1631	−	11.9824i	−0.954078	−	0.299560i
$41$			27.0663i			0.660153i	0.943954	+	0.330077i	$0.107075\pi$
$41$			27.0663i			0.660153i	−0.943954	+	0.330077i	$0.892925\pi$
$42$	−28.1871	−	28.8284i	−0.671122	−	0.686390i
$43$	−8.84693	+	8.84693i	−0.205742	+	0.205742i	−0.802455	−	0.596713i	$-0.796473\pi$
$43$	−8.84693	+	8.84693i	−0.205742	+	0.205742i	0.596713	+	0.802455i	$0.296473\pi$
$44$	−33.5987	−	33.9974i	−0.763606	−	0.772668i
$45$	44.8535	−	3.62848i	0.996744	−	0.0806329i
$46$	30.3570	−	12.4695i	0.659935	−	0.271077i
$47$	−15.0010	+	15.0010i	−0.319170	+	0.319170i	−0.848448	−	0.529278i	$-0.822463\pi$
$47$	−15.0010	+	15.0010i	−0.319170	+	0.319170i	0.529278	+	0.848448i	$0.322463\pi$
$48$	44.7063	−	17.4741i	0.931382	−	0.364043i
$49$		−	3.84477i		−	0.0784648i
$50$	−48.9932	−	9.98334i	−0.979864	−	0.199667i
$51$	−15.4883	+	36.5318i	−0.303692	+	0.716309i
$52$	−0.140924	+	23.8923i	−0.00271008	+	0.459468i
$53$	−14.6333	+	14.6333i	−0.276100	+	0.276100i	−0.831550	−	0.555450i	$-0.812546\pi$
$53$	−14.6333	+	14.6333i	−0.276100	+	0.276100i	0.555450	+	0.831550i	$0.312546\pi$
$54$	−39.2319	+	37.1060i	−0.726517	+	0.687149i
$55$	−46.1533	−	37.9435i	−0.839151	−	0.689881i
$56$	−49.4821	−	21.0109i	−0.883608	−	0.375195i
$57$	1.67456	+	4.13957i	0.0293783	+	0.0726240i
$58$	−30.3447	+	72.6517i	−0.523184	+	1.25262i
$59$		−	61.7260i		−	1.04620i	−0.852270	−	0.523102i	$-0.824775\pi$
$59$		−	61.7260i		−	1.04620i	0.852270	−	0.523102i	$-0.175225\pi$
$60$	53.3351	−	27.4840i	0.888918	−	0.458066i
$61$	−84.6009			−1.38690			−0.693450	−	0.720505i	$-0.743910\pi$
$61$	−84.6009			−1.38690			−0.693450	+	0.720505i	$0.743910\pi$
$62$	80.5598	+	33.6477i	1.29935	+	0.542704i
$63$	60.4695	+	1.00356i	0.959834	+	0.0159295i
$64$	46.0485	−	44.4470i	0.719507	−	0.694485i
$65$	2.90182	+	29.7246i	0.0446434	+	0.457302i
$66$	71.6932	+	0.806325i	1.08626	+	0.0122170i
$67$	65.7467	+	65.7467i	0.981293	+	0.981293i	0.999828	−	0.0185347i	$-0.00590012\pi$
$67$	65.7467	+	65.7467i	0.981293	+	0.981293i	−0.0185347	+	0.999828i	$0.505900\pi$
$68$	−0.312049	+	52.9050i	−0.00458896	+	0.778014i
$69$	−19.2152	+	45.3223i	−0.278481	+	0.656844i
$70$	−64.2294	−	19.7512i	−0.917562	−	0.282160i
$71$	−14.2794			−0.201118			−0.100559	−	0.994931i	$-0.532063\pi$
$71$	−14.2794			−0.201118			−0.100559	+	0.994931i	$0.532063\pi$
$72$	−29.2365	+	65.7969i	−0.406062	+	0.913845i
$73$	16.0903	+	16.0903i	0.220415	+	0.220415i	0.808673	−	0.588258i	$-0.200186\pi$
$73$	16.0903	+	16.0903i	0.220415	+	0.220415i	−0.588258	+	0.808673i	$0.700186\pi$
$74$	52.8413	+	128.642i	0.714072	+	1.73841i
$75$	62.7745	−	41.0411i	0.836993	−	0.547214i
$76$	4.18516	+	4.23482i	0.0550678	+	0.0557213i
$77$	−56.7797	−	56.7797i	−0.737399	−	0.737399i
$78$	−25.0555	−	25.6255i	−0.321224	−	0.328532i
$79$	−9.32721			−0.118066			−0.0590330	−	0.998256i	$-0.518802\pi$
$79$	−9.32721			−0.118066			−0.0590330	+	0.998256i	$0.518802\pi$
$80$	51.5300	−	61.1936i	0.644125	−	0.764920i
$81$	2.68783	−	80.9554i	0.0331831	−	0.999449i
$82$	−49.9507	−	20.8630i	−0.609154	−	0.254427i
$83$	−12.7500	−	12.7500i	−0.153615	−	0.153615i	0.626116	−	0.779730i	$-0.284644\pi$
$83$	−12.7500	−	12.7500i	−0.153615	−	0.153615i	−0.779730	+	0.626116i	$0.784644\pi$
$84$	74.9296	−	29.7979i	0.892019	−	0.354737i
$85$	6.42553	+	65.8195i	0.0755945	+	0.774347i
$86$	−9.50762	−	23.1463i	−0.110554	−	0.269143i
$87$	−44.2885	−	109.483i	−0.509063	−	1.25842i
$88$	88.6403	−	35.8005i	1.00728	−	0.406824i
$89$	−52.4342			−0.589148			−0.294574	−	0.955629i	$-0.595178\pi$
$89$	−52.4342			−0.589148			−0.294574	+	0.955629i	$0.595178\pi$
$90$	−27.8773	+	85.5737i	−0.309748	+	0.950819i
$91$			40.1384i			0.441082i
$92$	−0.387136	+	65.6353i	−0.00420800	+	0.713427i
$93$	−121.400	+	49.1093i	−1.30537	+	0.528057i
$94$	−16.1213	−	39.2471i	−0.171503	−	0.417523i
$95$	5.74900	+	4.72636i	0.0605158	+	0.0497511i
$96$	−2.21192	+	95.9745i	−0.0230408	+	0.999735i
$97$	6.90848	−	6.90848i	0.0712214	−	0.0712214i	−0.670599	−	0.741820i	$-0.733963\pi$
$97$	6.90848	−	6.90848i	0.0712214	−	0.0712214i	0.741820	+	0.670599i	$0.233963\pi$
$98$	7.09551	+	2.96360i	0.0724031	+	0.0302408i
$99$	−77.2983	+	74.7745i	−0.780791	+	0.755298i
$100$	56.1888	−	82.7213i	0.561888	−	0.827213i
$101$		−	15.0065i		−	0.148579i	−0.997237	−	0.0742894i	$-0.976331\pi$
$101$		−	15.0065i		−	0.148579i	0.997237	−	0.0742894i	$-0.0236689\pi$
$102$	−55.4806	−	56.7427i	−0.543927	−	0.556301i
$103$	10.0417	−	10.0417i	0.0974926	−	0.0974926i	−0.656678	−	0.754171i	$-0.728039\pi$
$103$	10.0417	−	10.0417i	0.0974926	−	0.0974926i	0.754171	+	0.656678i	$0.228039\pi$
$104$	−43.9845	−	18.6766i	−0.422928	−	0.179583i
$105$	89.3259	−	46.6991i	0.850723	−	0.444754i
$106$	−15.7261	−	38.2852i	−0.148360	−	0.361181i
$107$	15.4027	−	15.4027i	0.143950	−	0.143950i	−0.631459	−	0.775409i	$-0.717544\pi$
$107$	15.4027	−	15.4027i	0.143950	−	0.143950i	0.775409	+	0.631459i	$0.217544\pi$
$108$	−38.2385	−	101.004i	−0.354060	−	0.935223i
$109$			15.6958i			0.143998i	0.997405	+	0.0719992i	$0.0229379\pi$
$109$			15.6958i			0.143998i	−0.997405	+	0.0719992i	$0.977062\pi$
$110$	105.600	−	55.9283i	0.960000	−	0.508439i
$111$	−192.059	−	81.4271i	−1.73027	−	0.733577i
$112$	76.9170	−	75.1234i	0.686759	−	0.670744i
$113$	33.3231	−	33.3231i	0.294895	−	0.294895i	−0.544116	−	0.839010i	$-0.683135\pi$
$113$	33.3231	−	33.3231i	0.294895	−	0.294895i	0.839010	+	0.544116i	$0.183135\pi$
$114$	−8.93032	−	0.100438i	−0.0783362	−	0.000881038i
$115$	7.97168	+	81.6574i	0.0693190	+	0.710064i
$116$	−110.688	−	112.002i	−0.954209	−	0.965532i
$117$	53.7513	+	0.892063i	0.459413	+	0.00762447i
$118$	113.915	+	47.5792i	0.965382	+	0.403214i
$119$			88.8788i			0.746881i
$120$	9.61016	+	119.615i	0.0800847	+	0.996788i
$121$	21.7934			0.180110
$122$	65.2114	−	156.130i	0.534520	−	1.27976i
$123$	75.2732	−	30.4500i	0.611977	−	0.247561i
$124$	−124.193	+	122.737i	−1.00156	+	0.989812i
$125$	59.2087	−	110.088i	0.473670	−	0.880703i
$126$	−48.4628	+	110.823i	−0.384625	+	0.879545i
$127$	−11.9832	−	11.9832i	−0.0943557	−	0.0943557i	0.658353	−	0.752709i	$-0.271253\pi$
$127$	−11.9832	−	11.9832i	−0.0943557	−	0.0943557i	−0.752709	+	0.658353i	$0.771253\pi$
$128$	46.5320	+	119.243i	0.363531	+	0.931582i
$129$	34.5568	+	14.6510i	0.267882	+	0.113574i
$130$	−57.0934	−	17.5568i	−0.439180	−	0.135053i
$131$	228.815			1.74668			0.873341	−	0.487109i	$-0.161949\pi$
$131$	228.815			1.74668			0.873341	+	0.487109i	$0.161949\pi$
$132$	−56.7501	+	131.688i	−0.429925	+	0.997635i
$133$	7.07265	+	7.07265i	0.0531778	+	0.0531778i
$134$	−172.013	+	70.6567i	−1.28368	+	0.527289i
$135$	−60.5518	−	120.659i	−0.448532	−	0.893767i
$136$	−97.3953	−	41.3557i	−0.716142	−	0.304086i
$137$	155.485	+	155.485i	1.13492	+	1.13492i	0.989347	+	0.145578i	$0.0465042\pi$
$137$	155.485	+	155.485i	1.13492	+	1.13492i	0.145578	+	0.989347i	$0.453496\pi$
$138$	−68.8306	−	70.3965i	−0.498773	−	0.510120i
$139$	220.188			1.58409			0.792043	−	0.610465i	$-0.209018\pi$
$139$	220.188			1.58409			0.792043	+	0.610465i	$0.209018\pi$
$140$	85.9596	−	103.310i	0.613997	−	0.737932i
$141$	58.5950	+	24.8424i	0.415568	+	0.176187i
$142$	11.0067	−	26.3525i	0.0775123	−	0.185581i
$143$	−50.4714	−	50.4714i	−0.352947	−	0.352947i
$144$	−98.8919	−	104.673i	−0.686749	−	0.726895i
$145$	−152.048	−	125.002i	−1.04861	−	0.862082i
$146$	−42.0971	+	17.2919i	−0.288337	+	0.118438i
$147$	−10.6926	+	4.32542i	−0.0727386	+	0.0294247i
$148$	−278.139	−	1.64054i	−1.87932	−	0.0110848i
$149$	24.2943			0.163049			0.0815247	−	0.996671i	$-0.474021\pi$
$149$	24.2943			0.163049			0.0815247	+	0.996671i	$0.474021\pi$
$150$	27.3537	+	147.485i	0.182358	+	0.983232i
$151$			120.766i			0.799772i	0.916565	+	0.399886i	$0.130950\pi$
$151$			120.766i			0.799772i	−0.916565	+	0.399886i	$0.869050\pi$
$152$	−11.0413	+	4.45943i	−0.0726402	+	0.0293383i
$153$	119.022	+	1.97530i	0.777921	+	0.0129105i
$154$	148.553	−	61.0201i	0.964630	−	0.396234i
$155$	−138.608	+	168.599i	−0.894247	+	1.08773i
$156$	66.6048	−	26.4873i	0.426954	−	0.169790i
$157$	−77.1260	+	77.1260i	−0.491249	+	0.491249i	−0.908700	−	0.417451i	$-0.862924\pi$
$157$	−77.1260	+	77.1260i	−0.491249	+	0.491249i	0.417451	+	0.908700i	$0.362924\pi$
$158$	7.18953	−	17.2133i	0.0455034	−	0.108945i
$159$	57.1589	+	24.2336i	0.359490	+	0.152412i
$160$	73.2124	+	142.267i	0.457577	+	0.889170i
$161$			110.265i			0.684878i
$162$	147.331	+	67.3618i	0.909450	+	0.415814i
$163$	−179.764	+	179.764i	−1.10285	+	1.10285i	−0.108783	+	0.994065i	$0.534695\pi$
$163$	−179.764	+	179.764i	−1.10285	+	1.10285i	−0.994065	+	0.108783i	$0.965305\pi$
$164$	77.0052	−	76.1022i	0.469544	−	0.464038i
$165$	−53.6003	+	171.042i	−0.324850	+	1.03662i
$166$	33.3580	−	13.7022i	0.200952	−	0.0825434i
$167$	−56.8272	+	56.8272i	−0.340283	+	0.340283i	−0.856474	−	0.516191i	$-0.827349\pi$
$167$	−56.8272	+	56.8272i	−0.340283	+	0.340283i	0.516191	+	0.856474i	$0.327349\pi$
$168$	−2.76485	+	161.251i	−0.0164575	+	0.959825i
$169$		−	133.321i		−	0.788882i
$170$	−126.422	−	38.8762i	−0.743661	−	0.228684i
$171$	9.62852	−	9.31414i	0.0563071	−	0.0544687i
$172$	50.0449	+	0.295179i	0.290959	+	0.00171616i
$173$	130.746	−	130.746i	0.755756	−	0.755756i	−0.219791	−	0.975547i	$-0.570538\pi$
$173$	130.746	−	130.746i	0.755756	−	0.755756i	0.975547	+	0.219791i	$0.0705377\pi$
$174$	236.188	+	2.65637i	1.35740	+	0.0152665i
$175$	93.5725	−	139.521i	0.534700	−	0.797265i
$176$	−2.25536	+	191.181i	−0.0128145	+	1.08625i
$177$	−171.664	+	69.4427i	−0.969855	+	0.392331i
$178$	40.4170	−	96.7670i	0.227062	−	0.543635i
$179$		−	213.930i		−	1.19514i	−0.801816	−	0.597571i	$-0.796133\pi$
$179$		−	213.930i		−	1.19514i	0.801816	−	0.597571i	$-0.203867\pi$
$180$	−136.438	−	117.409i	−0.757986	−	0.652270i
$181$	155.404			0.858588			0.429294	−	0.903165i	$-0.358762\pi$
$181$	155.404			0.858588			0.429294	+	0.903165i	$0.358762\pi$
$182$	−74.0752	−	30.9392i	−0.407007	−	0.169996i
$183$	95.1771	+	235.281i	0.520094	+	1.28569i
$184$	−120.831	−	51.3070i	−0.656691	−	0.278842i
$185$	−346.035	+	33.7811i	−1.87046	+	0.182601i
$186$	2.94552	−	261.897i	0.0158361	−	1.40805i
$187$	−111.759	−	111.759i	−0.597643	−	0.597643i
$188$	84.8569	+	0.500511i	0.451366	+	0.00266229i
$189$	−65.2381	−	169.299i	−0.345175	−	0.895762i
$190$	−13.1539	+	6.96660i	−0.0692308	+	0.0366663i
$191$	102.576			0.537047			0.268524	−	0.963273i	$-0.413464\pi$
$191$	102.576			0.537047			0.268524	+	0.963273i	$0.413464\pi$
$192$	−175.415	−	78.0605i	−0.913622	−	0.406565i
$193$	138.213	+	138.213i	0.716129	+	0.716129i	0.967810	−	0.251681i	$-0.0809835\pi$
$193$	138.213	+	138.213i	0.716129	+	0.716129i	−0.251681	+	0.967810i	$0.580983\pi$
$194$	7.42441	+	18.0747i	0.0382701	+	0.0931685i
$195$	79.4017	−	41.5108i	0.407188	−	0.212876i
$196$	−10.9386	+	10.8103i	−0.0558093	+	0.0551548i
$197$	−94.4283	−	94.4283i	−0.479331	−	0.479331i	0.425586	−	0.904918i	$-0.360068\pi$
$197$	−94.4283	−	94.4283i	−0.479331	−	0.479331i	−0.904918	+	0.425586i	$0.860068\pi$
$198$	−78.4134	−	200.291i	−0.396027	−	1.01157i
$199$	−185.280			−0.931058			−0.465529	−	0.885033i	$-0.654136\pi$
$199$	−185.280			−0.931058			−0.465529	+	0.885033i	$0.654136\pi$
$200$	109.351	+	167.459i	0.546754	+	0.837294i
$201$	108.880	−	256.812i	0.541692	−	1.27767i
$202$	27.6943	+	11.5672i	0.137101	+	0.0572632i
$203$	−187.056	−	187.056i	−0.921459	−	0.921459i
$204$	147.483	−	58.6510i	0.722958	−	0.287505i
$205$	85.9433	−	104.539i	0.419235	−	0.509945i
$206$	10.7917	+	26.2723i	0.0523868	+	0.127535i
$207$	147.662	+	2.45061i	0.713342	+	0.0118387i
$208$	68.3714	−	66.7771i	0.328709	−	0.321044i
$209$	−17.7868			−0.0851042
$210$	17.3294	+	200.847i	0.0825211	+	0.956413i
$211$		−	270.850i		−	1.28365i	−0.766850	−	0.641826i	$-0.778177\pi$
$211$		−	270.850i		−	1.28365i	0.766850	−	0.641826i	$-0.221823\pi$
$212$	82.7770	+	0.488243i	0.390458	+	0.00230303i
$213$	16.0645	+	39.7120i	0.0754203	+	0.186441i
$214$	16.5530	+	40.2982i	0.0773504	+	0.188309i
$215$	62.2612	−	6.07816i	0.289587	−	0.0282705i
$216$	215.877	+	7.28629i	0.999431	+	0.0337328i
$217$	−207.417	+	207.417i	−0.955840	+	0.955840i
$218$	−28.9666	−	12.0985i	−0.132874	−	0.0554979i
$219$	26.6464	−	62.8500i	0.121673	−	0.286986i
$220$	21.8175	+	237.994i	0.0991706	+	1.08179i
$221$			79.0043i			0.357485i
$222$	298.315	−	291.679i	1.34376	−	1.31387i
$223$	173.313	−	173.313i	0.777190	−	0.777190i	−0.202162	−	0.979352i	$-0.564797\pi$
$223$	173.313	−	173.313i	0.777190	−	0.777190i	0.979352	+	0.202162i	$0.0647968\pi$
$224$	79.3511	+	199.856i	0.354246	+	0.892214i
$225$	−184.760	−	128.408i	−0.821156	−	0.570704i
$226$	35.8117	+	87.1835i	0.158459	+	0.385768i
$227$	−192.265	+	192.265i	−0.846983	+	0.846983i	−0.989755	−	0.142773i	$-0.954398\pi$
$227$	−192.265	+	192.265i	−0.846983	+	0.846983i	0.142773	+	0.989755i	$0.454398\pi$
$228$	7.06896	−	16.4034i	0.0310042	−	0.0719449i
$229$			74.6665i			0.326054i	0.986622	+	0.163027i	$0.0521258\pi$
$229$			74.6665i			0.326054i	−0.986622	+	0.163027i	$0.947874\pi$
$230$	−156.843	−	48.2309i	−0.681926	−	0.209699i
$231$	−94.0303	+	221.786i	−0.407058	+	0.960113i
$232$	292.018	−	117.942i	1.25870	−	0.508371i
$233$	−148.778	+	148.778i	−0.638532	+	0.638532i	−0.950193	−	0.311661i	$-0.899115\pi$
$233$	−148.778	+	148.778i	−0.638532	+	0.638532i	0.311661	+	0.950193i	$0.399115\pi$
$234$	−43.0785	+	98.5101i	−0.184096	+	0.420983i
$235$	105.571	−	10.3062i	0.449238	−	0.0438562i
$236$	−175.614	+	173.555i	−0.744128	+	0.735402i
$237$	10.4932	+	25.9396i	0.0442753	+	0.109450i
$238$	−164.025	−	68.5089i	−0.689182	−	0.287853i
$239$		−	214.211i		−	0.896278i	−0.893964	−	0.448139i	$-0.852087\pi$
$239$		−	214.211i		−	0.896278i	0.893964	−	0.448139i	$-0.147913\pi$
$240$	−228.156	−	74.4649i	−0.950648	−	0.310271i
$241$	167.934			0.696821			0.348411	−	0.937342i	$-0.386722\pi$
$241$	167.934			0.696821			0.348411	+	0.937342i	$0.386722\pi$
$242$	−16.7986	+	40.2195i	−0.0694157	+	0.166196i
$243$	−228.166	+	83.6009i	−0.938956	+	0.344037i
$244$	237.872	+	240.695i	0.974885	+	0.986453i
$245$	−12.2083	+	14.8498i	−0.0498296	+	0.0606113i
$246$	−1.82635	+	162.387i	−0.00742420	+	0.660112i
$247$	6.28687	+	6.28687i	0.0254529	+	0.0254529i
$248$	−130.780	−	323.805i	−0.527339	−	1.30566i
$249$	−21.1147	+	49.8027i	−0.0847982	+	0.200011i
$250$	157.528	+	194.126i	0.630110	+	0.776506i
$251$	166.809			0.664578			0.332289	−	0.943178i	$-0.392179\pi$
$251$	166.809			0.664578			0.332289	+	0.943178i	$0.392179\pi$
$252$	−167.167	−	174.861i	−0.663360	−	0.693894i
$253$	−138.651	−	138.651i	−0.548029	−	0.548029i
$254$	31.3516	−	12.8781i	0.123432	−	0.0507011i
$255$	175.820	−	91.9177i	0.689489	−	0.360461i
$256$	−255.929	−	6.03922i	−0.999722	−	0.0235907i
$257$	−16.3199	−	16.3199i	−0.0635014	−	0.0635014i	0.674643	−	0.738144i	$-0.264298\pi$
$257$	−16.3199	−	16.3199i	−0.0635014	−	0.0635014i	−0.738144	+	0.674643i	$0.764298\pi$
$258$	−53.6752	+	52.4812i	−0.208043	+	0.203416i
$259$	−467.265			−1.80411
$260$	76.4094	−	91.8325i	0.293882	−	0.353202i
$261$	−254.653	+	246.339i	−0.975683	+	0.943827i
$262$	−176.374	+	422.277i	−0.673183	+	1.61175i
$263$	121.290	+	121.290i	0.461180	+	0.461180i	0.899042	−	0.437862i	$-0.144264\pi$
$263$	121.290	+	121.290i	0.461180	+	0.461180i	−0.437862	+	0.899042i	$0.644264\pi$
$264$	−199.285	−	206.239i	−0.754869	−	0.781207i
$265$	102.984	−	10.0536i	0.388617	−	0.0379382i
$266$	−18.5042	+	7.60085i	−0.0695648	+	0.0285746i
$267$	58.9892	+	145.823i	0.220933	+	0.546154i
$268$	2.19365	−	371.913i	0.00818526	−	1.38773i
$269$	174.671			0.649336			0.324668	−	0.945828i	$-0.394747\pi$
$269$	174.671			0.649336			0.324668	+	0.945828i	$0.394747\pi$
$270$	269.349	−	18.7429i	0.997588	−	0.0694183i
$271$			306.881i			1.13240i	0.824268	+	0.566200i	$0.191587\pi$
$271$			306.881i			1.13240i	−0.824268	+	0.566200i	$0.808413\pi$
$272$	151.395	−	147.865i	0.556600	−	0.543621i
$273$	111.628	−	45.1563i	0.408893	−	0.165408i
$274$	−406.796	+	167.096i	−1.48466	+	0.609841i
$275$	57.7775	+	293.100i	0.210100	+	1.06582i
$276$	182.972	−	72.7640i	0.662942	−	0.263638i
$277$	28.5949	−	28.5949i	0.103231	−	0.103231i	−0.653605	−	0.756836i	$-0.726744\pi$
$277$	28.5949	−	28.5949i	0.103231	−	0.103231i	0.756836	+	0.653605i	$0.226744\pi$
$278$	−169.724	+	406.356i	−0.610517	+	1.46171i
$279$	273.153	+	282.372i	0.979042	+	1.01209i
$280$	124.400	+	238.271i	0.444286	+	0.850967i
$281$		−	42.3210i		−	0.150609i	−0.997161	−	0.0753043i	$-0.976007\pi$
$281$		−	42.3210i		−	0.150609i	0.997161	−	0.0753043i	$-0.0239928\pi$
$282$	−91.0124	+	88.9879i	−0.322739	+	0.315560i
$283$	341.834	−	341.834i	1.20789	−	1.20789i	0.236185	−	0.971708i	$-0.424103\pi$
$283$	341.834	−	341.834i	1.20789	−	1.20789i	0.971708	−	0.236185i	$-0.0758971\pi$
$284$	40.1493	+	40.6257i	0.141371	+	0.143048i
$285$	6.67662	−	21.3056i	0.0234267	−	0.0747564i
$286$	132.049	−	54.2407i	0.461709	−	0.189653i
$287$	128.608	−	128.608i	0.448111	−	0.448111i
$288$	269.400	−	101.821i	0.935417	−	0.353546i
$289$		−	114.060i		−	0.394672i
$290$	347.891	−	184.251i	1.19962	−	0.635350i
$291$	−26.9851	−	11.4408i	−0.0927322	−	0.0393155i
$292$	0.536856	−	91.0189i	0.00183855	−	0.311708i
$293$	252.918	−	252.918i	0.863203	−	0.863203i	−0.128506	−	0.991709i	$-0.541018\pi$
$293$	252.918	−	252.918i	0.863203	−	0.863203i	0.991709	+	0.128506i	$0.0410181\pi$
$294$	0.259434	−	23.0672i	0.000882428	−	0.0784598i
$295$	−195.998	+	238.406i	−0.664400	+	0.808156i
$296$	217.421	−	512.039i	0.734529	−	1.72986i
$297$	294.915	+	130.850i	0.992979	+	0.440571i
$298$	−18.7264	+	44.8351i	−0.0628403	+	0.150453i
$299$			98.0148i			0.327809i
$300$	−293.267	−	63.2022i	−0.977556	−	0.210674i
$301$	84.0739			0.279315
$302$	−222.872	−	93.0877i	−0.737987	−	0.308237i
$303$	−41.7340	+	16.8825i	−0.137736	+	0.0557177i
$304$	0.280934	−	23.8140i	0.000924125	−	0.0783357i
$305$	326.756	+	268.632i	1.07133	+	0.880761i
$306$	−95.3890	+	218.132i	−0.311729	+	0.712848i
$307$	−281.593	−	281.593i	−0.917240	−	0.917240i	0.0795878	−	0.996828i	$-0.474640\pi$
$307$	−281.593	−	281.593i	−0.917240	−	0.917240i	−0.996828	+	0.0795878i	$0.974640\pi$
$308$	−1.89447	+	321.189i	−0.00615086	+	1.04282i
$309$	−39.2239	−	16.6297i	−0.126938	−	0.0538177i
$310$	−204.307	−	385.759i	−0.659055	−	1.24438i
$311$	−318.688			−1.02472			−0.512360	−	0.858771i	$-0.671229\pi$
$311$	−318.688			−1.02472			−0.512360	+	0.858771i	$0.671229\pi$
$312$	−2.45768	+	143.335i	−0.00787716	+	0.459409i
$313$	−165.571	−	165.571i	−0.528979	−	0.528979i	0.391289	−	0.920268i	$-0.372029\pi$
$313$	−165.571	−	165.571i	−0.528979	−	0.528979i	−0.920268	+	0.391289i	$0.872029\pi$
$314$	−82.8859	−	201.785i	−0.263968	−	0.642629i
$315$	−230.366	−	195.884i	−0.731322	−	0.621855i
$316$	26.2253	+	26.5365i	0.0829914	+	0.0839762i
$317$	−6.74356	−	6.74356i	−0.0212731	−	0.0212731i	0.696390	−	0.717663i	$-0.254788\pi$
$317$	−6.74356	−	6.74356i	−0.0212731	−	0.0212731i	−0.717663	+	0.696390i	$0.754788\pi$
$318$	−88.7817	+	86.8069i	−0.279188	+	0.272978i
$319$	470.422			1.47468
$320$	−318.986	+	25.4516i	−0.996832	+	0.0795364i
$321$	−60.1642	−	25.5077i	−0.187427	−	0.0794633i
$322$	−203.494	−	84.9940i	−0.631969	−	0.263956i
$323$	13.9211	+	13.9211i	0.0430993	+	0.0430993i
$324$	−237.880	+	219.975i	−0.734199	+	0.678935i
$325$	83.1765	−	124.020i	0.255928	−	0.381601i
$326$	−193.189	−	470.319i	−0.592605	−	1.44270i
$327$	43.6512	−	17.6580i	0.133490	−	0.0540001i
$328$	81.0894	+	200.773i	0.247224	+	0.612113i
$329$	142.557			0.433304
$330$	−274.342	−	230.761i	−0.831339	−	0.699275i
$331$		−	278.406i		−	0.841105i	−0.907268	−	0.420553i	$-0.861836\pi$
$331$		−	278.406i		−	0.841105i	0.907268	−	0.420553i	$-0.138164\pi$
$332$	−0.425407	+	72.1238i	−0.00128135	+	0.217240i
$333$	−10.3848	+	625.737i	−0.0311856	+	1.87909i
$334$	−61.0711	−	148.677i	−0.182848	−	0.445142i
$335$	−45.1704	−	462.700i	−0.134837	−	1.38119i
$336$	−295.456	−	129.397i	−0.879333	−	0.385109i
$337$	282.964	−	282.964i	0.839656	−	0.839656i	−0.149157	−	0.988813i	$-0.547656\pi$
$337$	282.964	−	282.964i	0.839656	−	0.839656i	0.988813	+	0.149157i	$0.0476560\pi$
$338$	246.043	+	102.766i	0.727938	+	0.304040i
$339$	−130.163	−	55.1849i	−0.383961	−	0.162787i
$340$	169.194	−	203.345i	0.497629	−	0.598075i
$341$		−	521.627i		−	1.52970i
$342$	9.76741	+	24.9488i	0.0285597	+	0.0729498i
$343$	−251.097	+	251.097i	−0.732060	+	0.732060i
$344$	−39.1200	+	92.1300i	−0.113721	+	0.267820i
$345$	218.127	−	114.035i	0.632251	−	0.330538i
$346$	140.510	+	342.071i	0.406098	+	0.988644i
$347$	−36.0256	+	36.0256i	−0.103820	+	0.103820i	−0.757109	−	0.653289i	$-0.773389\pi$
$347$	−36.0256	+	36.0256i	−0.103820	+	0.103820i	0.653289	+	0.757109i	$0.273389\pi$
$348$	−186.959	+	433.835i	−0.537238	+	1.24665i
$349$			382.830i			1.09693i	0.836173	+	0.548467i	$0.184788\pi$
$349$			382.830i			1.09693i	−0.836173	+	0.548467i	$0.815212\pi$
$350$	185.359	+	280.232i	0.529597	+	0.800664i
$351$	−57.9901	−	150.490i	−0.165214	−	0.428745i
$352$	−351.084	−	151.527i	−0.997398	−	0.430474i
$353$	−215.726	+	215.726i	−0.611121	+	0.611121i	−0.943238	−	0.332117i	$-0.892237\pi$
$353$	−215.726	+	215.726i	−0.611121	+	0.611121i	0.332117	+	0.943238i	$0.392237\pi$
$354$	4.16509	−	370.333i	0.0117658	−	1.04614i
$355$	55.1517	+	45.3412i	0.155357	+	0.127722i
$356$	147.429	+	149.178i	0.414126	+	0.419041i
$357$	247.178	−	99.9899i	0.692375	−	0.280084i
$358$	394.807	+	164.900i	1.10281	+	0.460615i
$359$			473.986i			1.32030i	0.751136	+	0.660148i	$0.229506\pi$
$359$			473.986i			1.32030i	−0.751136	+	0.660148i	$0.770494\pi$
$360$	321.845	−	161.295i	0.894013	−	0.448040i
$361$	−358.784			−0.993863
$362$	−119.788	+	286.798i	−0.330905	+	0.792260i
$363$	−24.5178	−	60.6088i	−0.0675422	−	0.166966i
$364$	114.196	−	112.857i	0.313726	−	0.310047i
$365$	−11.0546	−	113.237i	−0.0302866	−	0.310239i
$366$	−507.573	−	5.70862i	−1.38681	−	0.0155973i
$367$	249.323	+	249.323i	0.679354	+	0.679354i	0.959854	−	0.280500i	$-0.0905004\pi$
$367$	249.323	+	249.323i	0.679354	+	0.679354i	−0.280500	+	0.959854i	$0.590500\pi$
$368$	187.825	−	183.445i	0.510394	−	0.498492i
$369$	−169.367	−	175.083i	−0.458989	−	0.474481i
$370$	204.385	−	664.644i	0.552392	−	1.79633i
$371$	139.063			0.374833
$372$	481.058	+	207.309i	1.29317	+	0.557283i
$373$	−108.084	−	108.084i	−0.289769	−	0.289769i	0.547220	−	0.836989i	$-0.315686\pi$
$373$	−108.084	−	108.084i	−0.289769	−	0.289769i	−0.836989	+	0.547220i	$0.815686\pi$
$374$	292.396	−	120.105i	0.781808	−	0.321138i
$375$	−372.772	−	40.8131i	−0.994060	−	0.108835i
$376$	−66.3324	+	156.217i	−0.176416	+	0.415471i
$377$	−166.274	−	166.274i	−0.441045	−	0.441045i
$378$	362.727	+	10.1013i	0.959594	+	0.0267230i
$379$	60.0656			0.158484			0.0792422	−	0.996855i	$-0.474750\pi$
$379$	60.0656			0.158484			0.0792422	+	0.996855i	$0.474750\pi$
$380$	−2.71766	−	29.6453i	−0.00715173	−	0.0780140i
$381$	−19.8448	+	46.8073i	−0.0520861	+	0.122854i
$382$	−79.0669	+	189.303i	−0.206981	+	0.495559i
$383$	375.372	+	375.372i	0.980084	+	0.980084i	0.999806	−	0.0197220i	$-0.00627811\pi$
$383$	375.372	+	375.372i	0.980084	+	0.980084i	−0.0197220	+	0.999806i	$0.506278\pi$
$384$	279.273	−	263.558i	0.727272	−	0.686349i
$385$	39.0097	+	399.593i	0.101324	+	1.03790i
$386$	−361.607	+	148.535i	−0.936806	+	0.384805i
$387$	1.86852	−	112.587i	0.00482821	−	0.290924i
$388$	−39.0796	−	0.230503i	−0.100721	−	0.000594079i
$389$	−464.374			−1.19376			−0.596882	−	0.802329i	$-0.703594\pi$
$389$	−464.374			−1.19376			−0.596882	+	0.802329i	$0.703594\pi$
$390$	15.4041	+	178.532i	0.0394977	+	0.457775i
$391$			217.035i			0.555076i
$392$	−11.5188	−	28.5199i	−0.0293846	−	0.0727548i
$393$	−257.421	−	636.351i	−0.655014	−	1.61921i
$394$	247.053	−	101.480i	0.627039	−	0.257564i
$395$	36.0247	+	29.6166i	0.0912018	+	0.0749787i
$396$	430.077	+	9.67529i	1.08605	+	0.0244325i
$397$	−125.935	+	125.935i	−0.317215	+	0.317215i	−0.847697	−	0.530481i	$-0.822011\pi$
$397$	−125.935	+	125.935i	−0.317215	+	0.317215i	0.530481	+	0.847697i	$0.322011\pi$
$398$	142.817	−	341.934i	0.358836	−	0.859131i
$399$	11.7127	−	27.6264i	0.0293551	−	0.0692390i
$400$	−393.333	+	72.7268i	−0.983332	+	0.181817i
$401$			508.065i			1.26699i	0.773745	+	0.633497i	$0.218381\pi$
$401$			508.065i			1.26699i	−0.773745	+	0.633497i	$0.781619\pi$
$402$	390.019	+	398.891i	0.970196	+	0.992267i
$403$	−184.373	+	184.373i	−0.457501	+	0.457501i
$404$	−42.6943	+	42.1936i	−0.105679	+	0.104440i
$405$	−267.438	+	304.141i	−0.660341	+	0.750966i
$406$	489.397	−	201.026i	1.20541	−	0.495138i
$407$	587.555	−	587.555i	1.44362	−	1.44362i
$408$	−5.44205	+	317.389i	−0.0133384	+	0.777914i
$409$			583.921i			1.42768i	0.700309	+	0.713840i	$0.253046\pi$
$409$			583.921i			1.42768i	−0.700309	+	0.713840i	$0.746954\pi$
$410$	126.680	+	239.188i	0.308974	+	0.583384i
$411$	257.491	−	607.336i	0.626499	−	1.47770i
$412$	−56.8037	−	0.335045i	−0.137873	−	0.000813215i
$413$	−293.297	+	293.297i	−0.710162	+	0.710162i
$414$	−118.342	+	270.620i	−0.285851	+	0.653671i
$415$	8.75973	+	89.7297i	0.0211078	+	0.216216i
$416$	70.5351	+	177.652i	0.169556	+	0.427047i
$417$	−247.715	−	612.358i	−0.594040	−	1.46848i
$418$	13.7103	−	32.8254i	0.0327997	−	0.0785297i
$419$		−	283.902i		−	0.677571i	−0.940864	−	0.338786i	$-0.889984\pi$
$419$		−	283.902i		−	0.677571i	0.940864	−	0.338786i	$-0.110016\pi$
$420$	−384.019	−	122.834i	−0.914331	−	0.292462i
$421$	−468.185			−1.11208			−0.556039	−	0.831156i	$-0.687679\pi$
$421$	−468.185			−1.11208			−0.556039	+	0.831156i	$0.687679\pi$
$422$	499.853	+	208.775i	1.18449	+	0.494728i
$423$	3.16828	−	190.905i	0.00749003	−	0.451312i
$424$	−64.7066	+	152.388i	−0.152610	+	0.359406i
$425$	184.178	−	274.619i	0.433361	−	0.646163i
$426$	−85.6710	−	0.963531i	−0.201106	−	0.00226181i
$427$	401.989	+	401.989i	0.941425	+	0.941425i
$428$	−87.1293	−	0.513914i	−0.203573	−	0.00120073i
$429$	−83.5834	+	197.145i	−0.194833	+	0.459546i
$430$	−36.7745	+	119.588i	−0.0855222	+	0.278111i
$431$	−849.775			−1.97164			−0.985818	−	0.167821i	$-0.946327\pi$
$431$	−849.775			−1.97164			−0.985818	+	0.167821i	$0.946327\pi$
$432$	−179.848	+	392.783i	−0.416314	+	0.909221i
$433$	153.887	+	153.887i	0.355398	+	0.355398i	0.862113	−	0.506715i	$-0.169141\pi$
$433$	153.887	+	153.887i	0.355398	+	0.355398i	−0.506715	+	0.862113i	$0.669141\pi$
$434$	−222.907	−	542.667i	−0.513612	−	1.25039i
$435$	−176.582	+	563.486i	−0.405936	+	1.29537i
$436$	44.6556	−	44.1319i	0.102421	−	0.101220i
$437$	17.2708	+	17.2708i	0.0395214	+	0.0395214i
$438$	95.4499	+	97.6214i	0.217922	+	0.222880i
$439$	−55.5775			−0.126600			−0.0633001	−	0.997995i	$-0.520163\pi$
$439$	−55.5775			−0.126600			−0.0633001	+	0.997995i	$0.520163\pi$
$440$	−456.034	−	143.185i	−1.03644	−	0.325421i
$441$	24.0586	+	24.8706i	0.0545547	+	0.0563960i
$442$	−145.802	−	60.8975i	−0.329868	−	0.137777i
$443$	−543.074	−	543.074i	−1.22590	−	1.22590i	−0.965501	−	0.260398i	$-0.916146\pi$
$443$	−543.074	−	543.074i	−1.22590	−	1.22590i	−0.260398	−	0.965501i	$-0.583854\pi$
$444$	308.348	+	775.369i	0.694477	+	1.74633i
$445$	202.518	+	166.494i	0.455096	+	0.374143i
$446$	186.257	+	453.441i	0.417616	+	1.01668i
$447$	−27.3315	−	67.5643i	−0.0611443	−	0.151150i
$448$	−429.998	−	7.60946i	−0.959816	−	0.0169854i
$449$	−36.3462			−0.0809493			−0.0404746	−	0.999181i	$-0.512887\pi$
$449$	−36.3462			−0.0809493			−0.0404746	+	0.999181i	$0.512887\pi$
$450$	379.392	−	241.995i	0.843094	−	0.537766i
$451$			323.432i			0.717144i
$452$	−188.501	−	1.11183i	−0.417037	−	0.00245981i
$453$	335.857	−	135.863i	0.741407	−	0.299918i
$454$	−206.624	−	503.024i	−0.455118	−	1.10798i
$455$	127.451	−	155.028i	0.280112	−	0.340720i
$456$	24.8236	+	25.6897i	0.0544377	+	0.0563371i
$457$	465.155	−	465.155i	1.01784	−	1.01784i	0.0180061	−	0.999838i	$-0.494268\pi$
$457$	465.155	−	465.155i	1.01784	−	1.01784i	0.999838	−	0.0180061i	$-0.00573181\pi$
$458$	−137.797	−	57.5539i	−0.300866	−	0.125663i
$459$	−128.408	−	333.230i	−0.279756	−	0.725992i
$460$	209.906	−	252.276i	0.456318	−	0.548425i
$461$		−	69.6948i		−	0.151182i	−0.997139	−	0.0755909i	$-0.975916\pi$
$461$		−	69.6948i		−	0.151182i	0.997139	−	0.0755909i	$-0.0240843\pi$
$462$	−336.825	−	344.488i	−0.729059	−	0.745645i
$463$	453.386	−	453.386i	0.979236	−	0.979236i	−0.0205531	−	0.999789i	$-0.506543\pi$
$463$	453.386	−	453.386i	0.979236	−	0.979236i	0.999789	+	0.0205531i	$0.00654273\pi$
$464$	−7.43010	+	629.830i	−0.0160131	+	1.35739i
$465$	624.821	+	195.803i	1.34370	+	0.421082i
$466$	−159.889	−	389.249i	−0.343109	−	0.835298i
$467$	−434.371	+	434.371i	−0.930130	+	0.930130i	−0.997714	−	0.0675833i	$-0.978471\pi$
$467$	−434.371	+	434.371i	−0.930130	+	0.930130i	0.0675833	+	0.997714i	$0.478471\pi$
$468$	−148.594	−	155.434i	−0.317509	−	0.332124i
$469$		−	624.802i		−	1.33220i
$470$	−62.3554	+	202.775i	−0.132671	+	0.431436i
$471$	301.261	+	127.725i	0.639619	+	0.271178i
$472$	−184.929	−	457.873i	−0.391798	−	0.970071i
$473$	−105.717	+	105.717i	−0.223504	+	0.223504i
$474$	−55.9597	−	0.629373i	−0.118059	−	0.00132779i
$475$	−7.19695	−	36.5094i	−0.0151515	−	0.0768620i
$476$	252.866	−	249.900i	0.531230	−	0.525000i
$477$	3.09063	−	186.226i	0.00647930	−	0.390411i
$478$	395.324	+	165.116i	0.827038	+	0.345431i
$479$			307.039i			0.641000i	0.947248	+	0.320500i	$0.103851\pi$
$479$			307.039i			0.641000i	−0.947248	+	0.320500i	$0.896149\pi$
$480$	313.290	−	363.661i	0.652687	−	0.757628i
$481$	−415.351			−0.863516
$482$	−129.446	+	309.921i	−0.268559	+	0.642990i
$483$	306.656	−	124.050i	0.634898	−	0.256832i
$484$	−61.2763	−	62.0034i	−0.126604	−	0.128106i
$485$	−48.6192	+	4.74637i	−0.100246	+	0.00978634i
$486$	21.5886	−	485.520i	0.0444210	−	0.999013i
$487$	−250.434	−	250.434i	−0.514237	−	0.514237i	0.401585	−	0.915822i	$-0.368460\pi$
$487$	−250.434	−	250.434i	−0.514237	−	0.514237i	−0.915822	+	0.401585i	$0.868460\pi$
$488$	−627.555	+	253.461i	−1.28597	+	0.519386i
$489$	702.174	+	297.700i	1.43594	+	0.608793i
$490$	−17.9949	−	33.9767i	−0.0367242	−	0.0693401i
$491$	291.754			0.594203			0.297102	−	0.954846i	$-0.403980\pi$
$491$	291.754			0.594203			0.297102	+	0.954846i	$0.403980\pi$
$492$	−298.277	−	128.541i	−0.606255	−	0.261262i
$493$	−368.182	−	368.182i	−0.746819	−	0.746819i
$494$	−16.4484	+	6.75638i	−0.0332963	+	0.0136769i
$495$	535.982	−	43.3590i	1.08279	−	0.0875939i
$496$	698.386	+	8.23886i	1.40804	+	0.0166106i
$497$	67.8498	+	67.8498i	0.136519	+	0.136519i
$498$	−75.6350	−	77.3557i	−0.151877	−	0.155333i
$499$	−421.977			−0.845646			−0.422823	−	0.906212i	$-0.638961\pi$
$499$	−421.977			−0.845646			−0.422823	+	0.906212i	$0.638961\pi$
$500$	−479.683	+	141.081i	−0.959367	+	0.282162i
$501$	221.972	+	94.1089i	0.443057	+	0.187842i
$502$	−128.579	+	307.845i	−0.256133	+	0.613238i
$503$	288.062	+	288.062i	0.572688	+	0.572688i	0.932879	−	0.360191i	$-0.117288\pi$
$503$	288.062	+	288.062i	0.572688	+	0.572688i	−0.360191	+	0.932879i	$0.617288\pi$
$504$	451.560	−	173.720i	0.895952	−	0.344682i
$505$	−47.6498	+	57.9598i	−0.0943561	+	0.114772i
$506$	362.755	−	149.006i	0.716906	−	0.294478i
$507$	−370.775	+	149.988i	−0.731311	+	0.295834i
$508$	−0.399821	+	67.7859i	−0.000787049	+	0.133437i
$509$	808.790			1.58898			0.794489	−	0.607278i	$-0.207739\pi$
$509$	808.790			1.58898			0.794489	+	0.607278i	$0.207739\pi$
$510$	34.1094	+	395.326i	0.0668812	+	0.775148i
$511$		−	152.909i		−	0.299235i
$512$	208.418	−	467.660i	0.407067	−	0.913398i
$513$	−36.7355	−	16.2990i	−0.0716091	−	0.0317720i
$514$	42.6977	−	17.5386i	0.0830695	−	0.0341219i
$515$	−70.6699	+	6.89904i	−0.137223	+	0.0133962i
$516$	−55.4803	−	139.510i	−0.107520	−	0.270369i
$517$	−179.256	+	179.256i	−0.346723	+	0.346723i
$518$	360.174	−	862.335i	0.695316	−	1.66474i
$519$	−510.704	−	216.522i	−0.984015	−	0.417191i
$520$	110.579	+	211.799i	0.212652	+	0.407305i
$521$			105.970i			0.203397i	0.994815	+	0.101699i	$0.0324277\pi$
$521$			105.970i			0.203397i	−0.994815	+	0.101699i	$0.967572\pi$
$522$	−258.327	−	659.842i	−0.494879	−	1.26407i
$523$	−229.588	+	229.588i	−0.438982	+	0.438982i	−0.891669	−	0.452687i	$-0.850465\pi$
$523$	−229.588	+	229.588i	−0.438982	+	0.438982i	0.452687	+	0.891669i	$0.350465\pi$
$524$	−643.359	−	650.994i	−1.22778	−	1.24235i
$525$	−493.289	−	103.268i	−0.939598	−	0.196701i
$526$	−317.332	+	130.348i	−0.603294	+	0.247810i
$527$	−408.258	+	408.258i	−0.774684	+	0.774684i
$528$	534.224	−	208.809i	1.01179	−	0.395471i
$529$		−	259.741i		−	0.491004i
$530$	−60.8271	+	197.805i	−0.114768	+	0.373217i
$531$	386.250	+	399.286i	0.727400	+	0.751952i
$532$	0.235980	−	40.0083i	0.000443572	−	0.0752035i
$533$	114.319	−	114.319i	0.214483	−	0.214483i
$534$	−314.585	−	3.53811i	−0.589111	−	0.00662566i
$535$	−108.398	+	10.5822i	−0.202614	+	0.0197798i
$536$	684.672	+	290.724i	1.27737	+	0.542395i
$537$	−594.955	+	240.675i	−1.10792	+	0.448184i
$538$	−134.639	+	322.355i	−0.250258	+	0.599173i
$539$		−	45.9436i		−	0.0852385i
$540$	−173.027	+	511.529i	−0.320421	+	0.947275i
$541$	1053.67			1.94763			0.973816	−	0.227338i	$-0.0730021\pi$
$541$	1053.67			1.94763			0.973816	+	0.227338i	$0.0730021\pi$
$542$	−566.346	−	236.547i	−1.04492	−	0.436434i
$543$	−174.832	−	432.190i	−0.321975	−	0.795931i
$544$	156.186	+	393.375i	0.287107	+	0.723116i
$545$	49.8388	−	60.6224i	0.0914473	−	0.111234i
$546$	−2.70842	+	240.815i	−0.00496048	+	0.441054i
$547$	559.528	+	559.528i	1.02290	+	1.02290i	0.999732	+	0.0231709i	$0.00737620\pi$
$547$	559.528	+	559.528i	1.02290	+	1.02290i	0.0231709	+	0.999732i	$0.492624\pi$
$548$	5.18778	−	879.539i	0.00946675	−	1.60500i
$549$	547.256	−	529.388i	0.996824	−	0.964278i
$550$	−585.450	−	119.297i	−1.06445	−	0.216904i
$551$	−58.5972			−0.106347
$552$	−6.75155	+	393.761i	−0.0122311	+	0.713335i
$553$	44.3191	+	44.3191i	0.0801430	+	0.0801430i
$554$	30.7304	+	74.8131i	0.0554701	+	0.135042i
$555$	483.241	+	924.342i	0.870705	+	1.66548i
$556$	−619.101	−	626.448i	−1.11349	−	1.12671i
$557$	616.817	+	616.817i	1.10739	+	1.10739i	0.993492	+	0.113899i	$0.0363340\pi$
$557$	616.817	+	616.817i	1.10739	+	1.10739i	0.113899	+	0.993492i	$0.463666\pi$
$558$	−731.666	+	286.446i	−1.31123	+	0.513343i
$559$	74.7332			0.133691
$560$	−535.617	+	45.9172i	−0.956458	+	0.0819950i
$561$	−185.079	+	436.541i	−0.329910	+	0.778147i
$562$	78.1032	+	32.6216i	0.138974	+	0.0580455i
$563$	170.898	+	170.898i	0.303550	+	0.303550i	0.842401	−	0.538851i	$-0.181142\pi$
$563$	170.898	+	170.898i	0.303550	+	0.303550i	−0.538851	+	0.842401i	$0.681142\pi$
$564$	−94.0732	−	236.556i	−0.166796	−	0.419425i
$565$	−234.515	+	22.8942i	−0.415071	+	0.0405207i
$566$	367.362	+	894.342i	0.649050	+	1.58011i
$567$	−397.438	+	371.895i	−0.700949	+	0.655900i
$568$	−105.922	+	42.7805i	−0.186483	+	0.0753177i
$569$	−609.836			−1.07177			−0.535884	−	0.844291i	$-0.680022\pi$
$569$	−609.836			−1.07177			−0.535884	+	0.844291i	$0.680022\pi$
$570$	34.1729	+	28.7443i	0.0599524	+	0.0504285i
$571$		−	478.800i		−	0.838529i	−0.907864	−	0.419265i	$-0.862288\pi$
$571$		−	478.800i		−	0.838529i	0.907864	−	0.419265i	$-0.137712\pi$
$572$	−1.68399	+	285.504i	−0.00294404	+	0.499134i
$573$	−115.399	−	285.271i	−0.201395	−	0.497855i
$574$	138.212	+	336.478i	0.240788	+	0.586198i
$575$	228.496	−	340.700i	0.397385	−	0.592521i
$576$	−19.7467	+	575.661i	−0.0342826	+	0.999412i
$577$	−162.684	+	162.684i	−0.281947	+	0.281947i	−0.833885	−	0.551938i	$-0.813889\pi$
$577$	−162.684	+	162.684i	−0.281947	+	0.281947i	0.551938	+	0.833885i	$0.313889\pi$
$578$	210.498	+	87.9192i	0.364183	+	0.152109i
$579$	228.888	−	539.871i	0.395316	−	0.932419i
$580$	71.8761	+	784.054i	0.123924	+	1.35182i
$581$			121.166i			0.208547i
$582$	41.9144	−	40.9821i	0.0720179	−	0.0704159i
$583$	−174.862	+	174.862i	−0.299935	+	0.299935i
$584$	167.561	+	71.1493i	0.286919	+	0.121831i
$585$	−204.772	−	174.121i	−0.350038	−	0.297643i
$586$	271.807	+	661.712i	0.463834	+	1.12920i
$587$	785.786	−	785.786i	1.33865	−	1.33865i	0.441275	−	0.897372i	$-0.354526\pi$
$587$	785.786	−	785.786i	1.33865	−	1.33865i	0.897372	−	0.441275i	$-0.145474\pi$
$588$	42.3704	+	18.2593i	0.0720585	+	0.0310532i
$589$			64.9754i			0.110315i
$590$	−288.899	−	545.479i	−0.489659	−	0.924541i
$591$	−156.378	+	368.845i	−0.264600	+	0.624103i
$592$	777.374	+	795.935i	1.31313	+	1.34448i
$593$	646.718	−	646.718i	1.09059	−	1.09059i	0.0951217	−	0.995466i	$-0.469676\pi$
$593$	646.718	−	646.718i	1.09059	−	1.09059i	0.995466	−	0.0951217i	$-0.0303240\pi$
$594$	−468.806	+	443.403i	−0.789236	+	0.746470i
$595$	282.216	−	343.279i	0.474312	−	0.576939i
$596$	−68.3083	−	69.1189i	−0.114611	−	0.115971i
$597$	208.443	+	515.278i	0.349151	+	0.863112i
$598$	−180.886	−	75.5510i	−0.302484	−	0.126340i
$599$			300.352i			0.501423i	0.968062	+	0.250711i	$0.0806645\pi$
$599$			300.352i			0.501423i	−0.968062	+	0.250711i	$0.919336\pi$
$600$	342.693	−	492.505i	0.571155	−	0.820842i
$601$	7.74118			0.0128805			0.00644025	−	0.999979i	$-0.497950\pi$
$601$	7.74118			0.0128805			0.00644025	+	0.999979i	$0.497950\pi$
$602$	−64.8053	+	155.158i	−0.107650	+	0.257737i
$603$	−836.703	−	13.8860i	−1.38757	−	0.0230282i
$604$	343.585	−	339.556i	0.568850	−	0.562179i
$605$	−84.1730	−	69.2002i	−0.139129	−	0.114380i
$606$	1.01259	−	90.0331i	0.00167094	−	0.148569i
$607$	−424.929	−	424.929i	−0.700047	−	0.700047i	0.264373	−	0.964421i	$-0.414835\pi$
$607$	−424.929	−	424.929i	−0.700047	−	0.700047i	−0.964421	+	0.264373i	$0.914835\pi$
$608$	43.7321	+	18.8746i	0.0719278	+	0.0310438i
$609$	−309.775	+	730.657i	−0.508662	+	1.19977i
$610$	−747.626	+	395.961i	−1.22562	+	0.649116i
$611$	126.719			0.207396
$612$	−329.033	−	344.178i	−0.537636	−	0.562383i
$613$	714.397	+	714.397i	1.16541	+	1.16541i	0.983273	+	0.182138i	$0.0583017\pi$
$613$	714.397	+	714.397i	1.16541	+	1.16541i	0.182138	+	0.983273i	$0.441698\pi$
$614$	736.733	−	302.622i	1.19989	−	0.492870i
$615$	−387.417	−	121.407i	−0.629946	−	0.197409i
$616$	−591.292	−	251.073i	−0.959889	−	0.407586i
$617$	−464.917	−	464.917i	−0.753513	−	0.753513i	0.221620	−	0.975133i	$-0.428865\pi$
$617$	−464.917	−	464.917i	−0.753513	−	0.753513i	−0.975133	+	0.221620i	$0.928865\pi$
$618$	60.9242	−	59.5691i	0.0985829	−	0.0963901i
$619$	667.181			1.07784			0.538918	−	0.842358i	$-0.318833\pi$
$619$	667.181			1.07784			0.538918	+	0.842358i	$0.318833\pi$
$620$	869.398	−	79.6998i	1.40225	−	0.128548i
$621$	−159.306	−	413.414i	−0.256532	−	0.665724i
$622$	245.649	−	588.137i	0.394934	−	0.945558i
$623$	249.146	+	249.146i	0.399913	+	0.399913i
$624$	−262.630	−	115.020i	−0.420882	−	0.184328i
$625$	−578.244	+	237.190i	−0.925190	+	0.379504i
$626$	433.183	−	177.936i	0.691986	−	0.284242i
$627$	20.0104	+	49.4663i	0.0319145	+	0.0788936i
$628$	436.283	+	2.57333i	0.694718	+	0.00409765i
$629$	−919.715			−1.46219
$630$	539.073	−	274.150i	0.855671	−	0.435158i
$631$		−	736.830i		−	1.16772i	−0.811855	−	0.583859i	$-0.801542\pi$
$631$		−	736.830i		−	1.16772i	0.811855	−	0.583859i	$-0.198458\pi$
$632$	−69.1877	+	27.9439i	−0.109474	+	0.0442151i
$633$	−753.254	+	304.711i	−1.18997	+	0.481375i
$634$	17.6432	−	7.24718i	0.0278284	−	0.0114309i
$635$	8.23287	+	84.3329i	0.0129652	+	0.132808i
$636$	−91.7675	−	230.758i	−0.144288	−	0.362827i
$637$	−16.2391	+	16.2391i	−0.0254931	+	0.0254931i
$638$	−362.607	+	868.160i	−0.568350	+	1.36075i
$639$	92.3689	−	89.3531i	0.144552	−	0.139833i
$640$	198.908	−	608.306i	0.310793	−	0.950477i
$641$		−	367.670i		−	0.573588i	−0.957992	−	0.286794i	$-0.907410\pi$
$641$		−	367.670i		−	0.573588i	0.957992	−	0.286794i	$-0.0925895\pi$
$642$	93.4497	−	91.3710i	0.145560	−	0.142322i
$643$	−376.586	+	376.586i	−0.585670	+	0.585670i	−0.936456	−	0.350786i	$-0.885914\pi$
$643$	−376.586	+	376.586i	−0.585670	+	0.585670i	0.350786	+	0.936456i	$0.385914\pi$
$644$	313.712	−	310.033i	0.487130	−	0.481417i
$645$	−86.9485	−	166.315i	−0.134804	−	0.257852i
$646$	−36.4218	+	14.9607i	−0.0563805	+	0.0231590i
$647$	311.254	−	311.254i	0.481073	−	0.481073i	−0.424402	−	0.905474i	$-0.639515\pi$
$647$	311.254	−	311.254i	0.481073	−	0.481073i	0.905474	+	0.424402i	$0.139515\pi$
$648$	−222.601	−	608.566i	−0.343520	−	0.939145i
$649$		−	737.603i		−	1.13652i
$650$	164.765	+	249.098i	0.253485	+	0.383228i
$651$	810.189	+	343.494i	1.24453	+	0.527641i
$652$	1016.88	+	5.99787i	1.55964	+	0.00919919i
$653$	−47.7734	+	47.7734i	−0.0731598	+	0.0731598i	−0.742740	−	0.669580i	$-0.766474\pi$
$653$	−47.7734	+	47.7734i	−0.0731598	+	0.0731598i	0.669580	+	0.742740i	$0.266474\pi$
$654$	−1.05911	+	94.1690i	−0.00161943	+	0.143989i
$655$	−883.759	−	726.555i	−1.34925	−	1.10924i
$656$	−433.030	−	5.10846i	−0.660107	−	0.00778728i
$657$	−204.768	−	3.39835i	−0.311671	−	0.00517253i
$658$	−109.885	+	263.088i	−0.166998	+	0.399830i
$659$			471.784i			0.715909i	0.933739	+	0.357954i	$0.116526\pi$
$659$			471.784i			0.715909i	−0.933739	+	0.357954i	$0.883474\pi$
$660$	637.334	−	328.423i	0.965657	−	0.497611i
$661$	86.9863			0.131598			0.0657990	−	0.997833i	$-0.479040\pi$
$661$	86.9863			0.131598			0.0657990	+	0.997833i	$0.479040\pi$
$662$	513.796	+	214.599i	0.776127	+	0.324167i
$663$	219.716	−	88.8809i	0.331397	−	0.134059i
$664$	−132.776	−	56.3790i	−0.199964	−	0.0849082i
$665$	−4.85917	−	49.7746i	−0.00730702	−	0.0748490i
$666$	−1146.79	−	501.491i	−1.72191	−	0.752990i
$667$	−456.776	−	456.776i	−0.684822	−	0.684822i
$668$	321.458	+	1.89605i	0.481224	+	0.00283840i
$669$	−676.976	−	287.016i	−1.01192	−	0.429023i
$670$	888.727	+	273.293i	1.32646	+	0.407900i
$671$	−1010.95			−1.50663
$672$	466.542	−	445.521i	0.694259	−	0.662978i
$673$	561.901	+	561.901i	0.834920	+	0.834920i	0.988185	−	0.153265i	$-0.0489789\pi$
$673$	561.901	+	561.901i	0.834920	+	0.834920i	−0.153265	+	0.988185i	$0.548979\pi$
$674$	304.096	+	740.321i	0.451181	+	1.09840i
$675$	−149.255	+	658.292i	−0.221118	+	0.975247i
$676$	−379.306	+	374.858i	−0.561104	+	0.554524i
$677$	−429.992	−	429.992i	−0.635143	−	0.635143i	0.314210	−	0.949353i	$-0.398260\pi$
$677$	−429.992	−	429.992i	−0.635143	−	0.635143i	−0.949353	+	0.314210i	$0.898260\pi$
$678$	202.175	−	197.677i	0.298193	−	0.291560i
$679$	−65.6525			−0.0966900
$680$	244.856	+	468.987i	0.360082	+	0.689687i
$681$	751.003	+	318.401i	1.10279	+	0.467550i
$682$	962.659	+	402.077i	1.41152	+	0.589555i
$683$	371.280	+	371.280i	0.543602	+	0.543602i	0.924583	−	0.380981i	$-0.124414\pi$
$683$	371.280	+	371.280i	0.543602	+	0.543602i	−0.380981	+	0.924583i	$0.624414\pi$
$684$	−53.5718	−	1.20518i	−0.0783213	−	0.00176196i
$685$	−106.824	−	1094.24i	−0.155947	−	1.59743i
$686$	−269.849	−	656.946i	−0.393366	−	0.957647i
$687$	207.653	−	84.0008i	0.302260	−	0.122272i
$688$	−139.871	−	143.211i	−0.203301	−	0.208155i
$689$	123.613			0.179409
$690$	42.3171	+	490.451i	0.0613291	+	0.710799i
$691$			112.536i			0.162860i	0.996679	+	0.0814301i	$0.0259487\pi$
$691$			112.536i			0.162860i	−0.996679	+	0.0814301i	$0.974051\pi$
$692$	−739.597	−	4.36236i	−1.06878	−	0.00630398i
$693$	722.588	+	11.9922i	1.04270	+	0.0173047i
$694$	−38.7160	−	94.2540i	−0.0557868	−	0.135813i
$695$	−850.437	−	699.160i	−1.22365	−	1.00599i
$696$	−656.530	−	679.437i	−0.943290	−	0.976202i
$697$	253.138	−	253.138i	0.363183	−	0.363183i
$698$	−706.510	−	295.090i	−1.01219	−	0.422765i
$699$	581.139	+	246.384i	0.831386	+	0.352481i
$700$	−660.044	+	126.072i	−0.942920	+	0.180103i
$701$		−	525.802i		−	0.750074i	−0.927010	−	0.375037i	$-0.877630\pi$
$701$		−	525.802i		−	0.750074i	0.927010	−	0.375037i	$-0.122370\pi$
$702$	322.427	+	8.97902i	0.459298	+	0.0127906i
$703$	−73.1876	+	73.1876i	−0.104108	+	0.104108i
$704$	550.262	−	531.125i	0.781622	−	0.754439i
$705$	−147.431	−	282.006i	−0.209122	−	0.400008i
$706$	−231.836	−	564.405i	−0.328380	−	0.799440i
$707$	−71.3046	+	71.3046i	−0.100855	+	0.100855i
$708$	680.236	+	293.144i	0.960786	+	0.414045i
$709$			638.797i			0.900984i	0.892781	+	0.450492i	$0.148751\pi$
$709$			638.797i			0.900984i	−0.892781	+	0.450492i	$0.851249\pi$
$710$	−126.188	+	66.8325i	−0.177730	+	0.0941302i
$711$	60.3348	−	58.3649i	0.0848591	−	0.0820884i
$712$	−388.948	+	157.091i	−0.546275	+	0.220633i
$713$	−506.496	+	506.496i	−0.710373	+	0.710373i
$714$	−5.99728	+	533.239i	−0.00839955	+	0.746833i
$715$	34.6757	+	355.198i	0.0484975	+	0.496781i
$716$	−608.645	+	601.507i	−0.850063	+	0.840094i
$717$	−595.734	+	240.990i	−0.830871	+	0.336109i
$718$	−874.739	−	365.355i	−1.21830	−	0.508850i
$719$		−	313.578i		−	0.436131i	−0.975934	−	0.218065i	$-0.930025\pi$
$719$		−	313.578i		−	0.436131i	0.975934	−	0.218065i	$-0.0699746\pi$
$720$	49.5861	+	718.290i	0.0688695	+	0.997626i
$721$	−95.4285			−0.132356
$722$	276.556	−	662.134i	0.383041	−	0.917084i
$723$	−188.928	−	467.036i	−0.261311	−	0.645969i
$724$	−436.950	−	442.135i	−0.603522	−	0.610684i
$725$	190.344	+	965.595i	0.262543	+	1.33186i
$726$	130.752	+	1.47055i	0.180099	+	0.00202555i
$727$	−318.387	−	318.387i	−0.437946	−	0.437946i	0.453374	−	0.891320i	$-0.350220\pi$
$727$	−318.387	−	318.387i	−0.437946	−	0.437946i	−0.891320	+	0.453374i	$0.850220\pi$
$728$	120.253	+	297.740i	0.165183	+	0.408984i
$729$	489.190	+	540.494i	0.671043	+	0.741419i
$730$	217.500	+	66.8835i	0.297945	+	0.0916212i
$731$	165.482			0.226378
$732$	401.779	−	932.323i	0.548878	−	1.27366i
$733$	−120.156	−	120.156i	−0.163924	−	0.163924i	0.620379	−	0.784303i	$-0.286979\pi$
$733$	−120.156	−	120.156i	−0.163924	−	0.163924i	−0.784303	+	0.620379i	$0.786979\pi$
$734$	−652.305	+	267.942i	−0.888699	+	0.365044i
$735$	55.0327	+	17.2458i	0.0748744	+	0.0234637i
$736$	193.769	+	488.032i	0.263273	+	0.663086i
$737$	785.647	+	785.647i	1.06601	+	1.06601i
$738$	453.665	−	177.609i	0.614723	−	0.240663i
$739$	376.922			0.510043			0.255022	−	0.966935i	$-0.417917\pi$
$739$	376.922			0.510043			0.255022	+	0.966935i	$0.417917\pi$
$740$	1069.05	+	889.507i	1.44467	+	1.20204i
$741$	10.4114	−	24.5570i	0.0140505	−	0.0331404i
$742$	−107.191	+	256.640i	−0.144463	+	0.345876i
$743$	−139.469	−	139.469i	−0.187710	−	0.187710i	0.606995	−	0.794705i	$-0.292375\pi$
$743$	−139.469	−	139.469i	−0.187710	−	0.187710i	−0.794705	+	0.606995i	$0.792375\pi$
$744$	−753.393	+	727.993i	−1.01263	+	0.978485i
$745$	−93.8327	−	77.1416i	−0.125950	−	0.103546i
$746$	282.780	−	116.156i	0.379062	−	0.155705i
$747$	162.259	+	2.69287i	0.217214	+	0.00360491i
$748$	−3.72887	+	632.194i	−0.00498512	+	0.845180i
$749$	−146.375			−0.195427
$750$	362.658	−	656.490i	0.483544	−	0.875320i
$751$			387.240i			0.515633i	0.966194	+	0.257816i	$0.0830029\pi$
$751$			387.240i			0.515633i	−0.966194	+	0.257816i	$0.916997\pi$
$752$	−237.168	−	242.830i	−0.315382	−	0.322912i
$753$	−187.663	−	463.908i	−0.249220	−	0.616079i
$754$	435.024	−	178.692i	0.576955	−	0.236992i
$755$	383.466	−	466.436i	0.507901	−	0.617796i
$756$	−298.236	+	661.624i	−0.394492	+	0.875163i
$757$	−765.761	+	765.761i	−1.01157	+	1.01157i	−0.0116408	+	0.999932i	$0.503705\pi$
$757$	−765.761	+	765.761i	−1.01157	+	1.01157i	−0.999932	+	0.0116408i	$0.996295\pi$
$758$	−46.2993	+	110.851i	−0.0610809	+	0.146241i
$759$	−229.614	+	541.584i	−0.302522	+	0.713549i
$760$	56.8051	+	17.8356i	0.0747435	+	0.0234679i
$761$		−	1139.50i		−	1.49737i	−0.662925	−	0.748686i	$-0.730685\pi$
$761$		−	1139.50i		−	1.49737i	0.662925	−	0.748686i	$-0.269315\pi$
$762$	−71.0859	−	72.7031i	−0.0932886	−	0.0954108i
$763$	74.5802	−	74.5802i	0.0977460	−	0.0977460i
$764$	−288.412	−	291.835i	−0.377503	−	0.381983i
$765$	−453.429	−	385.558i	−0.592718	−	0.503997i
$766$	−982.088	+	403.405i	−1.28210	+	0.526639i
$767$	−260.711	+	260.711i	−0.339910	+	0.339910i
$768$	271.128	+	718.550i	0.353031	+	0.935612i
$769$		−	1312.74i		−	1.70708i	−0.521031	−	0.853538i	$-0.674452\pi$
$769$		−	1312.74i		−	1.70708i	0.521031	−	0.853538i	$-0.325548\pi$
$770$	−767.516	−	236.020i	−0.996775	−	0.306519i
$771$	−27.0266	+	63.7467i	−0.0350539	+	0.0826805i
$772$	4.61150	−	781.836i	0.00597345	−	1.01274i
$773$	−335.897	+	335.897i	−0.434537	+	0.434537i	−0.890168	−	0.455632i	$-0.849413\pi$
$773$	−335.897	+	335.897i	−0.434537	+	0.434537i	0.455632	+	0.890168i	$0.349413\pi$
$774$	206.339	+	90.2322i	0.266588	+	0.116579i
$775$	1070.70	−	211.062i	1.38155	−	0.272339i
$776$	30.5484	−	71.9434i	0.0393665	−	0.0927106i
$777$	525.680	+	1299.50i	0.676550	+	1.67245i
$778$	357.946	−	857.000i	0.460084	−	1.10154i
$779$		−	40.2877i		−	0.0517171i
$780$	−341.354	−	109.187i	−0.437633	−	0.139983i
$781$	−170.633			−0.218481
$782$	−400.536	−	167.293i	−0.512195	−	0.213930i
$783$	971.574	+	431.074i	1.24084	+	0.550541i
$784$	61.5121	+	0.725658i	0.0784593	+	0.000925584i
$785$	542.783	−	52.9884i	0.691443	−	0.0675011i
$786$	1372.81	+	15.4398i	1.74657	+	0.0196435i
$787$	168.467	+	168.467i	0.214063	+	0.214063i	0.805991	−	0.591928i	$-0.201633\pi$
$787$	168.467	+	168.467i	0.214063	+	0.214063i	−0.591928	+	0.805991i	$0.701633\pi$
$788$	−3.15062	+	534.158i	−0.00399825	+	0.677865i
$789$	200.863	−	473.770i	0.254580	−	0.600468i
$790$	−82.4255	+	43.6546i	−0.104336	+	0.0552589i
$791$	−316.676			−0.400348
$792$	−349.365	+	786.247i	−0.441117	+	0.992737i
$793$	357.327	+	357.327i	0.450602	+	0.450602i
$794$	−135.339	−	329.483i	−0.170453	−	0.414966i
$795$	−143.818	−	275.094i	−0.180903	−	0.346030i
$796$	520.952	+	527.134i	0.654463	+	0.662229i
$797$	639.400	+	639.400i	0.802258	+	0.802258i	0.983448	−	0.181190i	$-0.0579949\pi$
$797$	639.400	+	639.400i	0.802258	+	0.802258i	−0.181190	+	0.983448i	$0.557995\pi$
$798$	41.9560	+	42.9105i	0.0525764	+	0.0537725i
$799$	280.594			0.351182
$800$	168.969	−	781.952i	0.211212	−	0.977440i
$801$	339.180	−	328.106i	0.423446	−	0.409621i
$802$	−937.631	−	391.623i	−1.16912	−	0.488308i
$803$	192.273	+	192.273i	0.239443	+	0.239443i
$804$	−1036.78	+	412.306i	−1.28953	+	0.512819i
$805$	350.124	−	425.881i	0.434937	−	0.529044i
$806$	−198.142	−	482.376i	−0.245834	−	0.598482i
$807$	−196.508	−	485.773i	−0.243504	−	0.601949i
$808$	−44.9587	−	111.315i	−0.0556420	−	0.137767i
$809$	857.503			1.05995			0.529977	−	0.848012i	$-0.322200\pi$
$809$	857.503			1.05995			0.529977	+	0.848012i	$0.322200\pi$
$810$	−355.146	−	727.991i	−0.438452	−	0.898754i
$811$			1573.57i			1.94028i	0.242547	+	0.970140i	$0.422017\pi$
$811$			1573.57i			1.94028i	−0.242547	+	0.970140i	$0.577983\pi$
$812$	−6.24117	+	1058.13i	−0.00768617	+	1.30312i
$813$	853.456	−	345.245i	1.04976	−	0.424656i
$814$	631.434	+	1537.22i	0.775717	+	1.88848i
$815$	1265.11	−	123.505i	1.55228	−	0.151539i
$816$	−581.544	−	254.691i	−0.712677	−	0.312121i
$817$	13.1685	−	13.1685i	0.0161181	−	0.0161181i
$818$	−1077.62	−	450.094i	−1.31739	−	0.550237i
$819$	−251.165	−	259.643i	−0.306673	−	0.317024i
$820$	−539.065	+	49.4174i	−0.657397	+	0.0602652i
$821$			1040.55i			1.26742i	0.773571	+	0.633710i	$0.218469\pi$
$821$			1040.55i			1.26742i	−0.773571	+	0.633710i	$0.781531\pi$
$822$	922.357	+	943.341i	1.12209	+	1.14762i
$823$	−309.894	+	309.894i	−0.376542	+	0.376542i	−0.869853	−	0.493311i	$-0.835786\pi$
$823$	−309.894	+	309.894i	−0.376542	+	0.376542i	0.493311	+	0.869853i	$0.335786\pi$
$824$	44.4033	−	104.573i	0.0538875	−	0.126908i
$825$	750.131	−	490.425i	0.909249	−	0.594454i
$826$	−315.201	−	767.355i	−0.381599	−	0.929001i
$827$	−527.373	+	527.373i	−0.637694	+	0.637694i	−0.949986	−	0.312292i	$-0.898903\pi$
$827$	−527.373	+	527.373i	−0.637694	+	0.637694i	0.312292	+	0.949986i	$0.398903\pi$
$828$	−408.208	−	426.997i	−0.493004	−	0.515697i
$829$			1067.23i			1.28737i	0.765292	+	0.643683i	$0.222594\pi$
$829$			1067.23i			1.28737i	−0.765292	+	0.643683i	$0.777406\pi$
$830$	−172.348	−	52.9988i	−0.207648	−	0.0638540i
$831$	−111.694	−	47.3548i	−0.134409	−	0.0569853i
$832$	−382.224	−	6.76404i	−0.459404	−	0.00812986i
$833$	−35.9584	+	35.9584i	−0.0431673	+	0.0431673i
$834$	1321.04	+	14.8576i	1.58399	+	0.0178149i
$835$	399.928	−	39.0423i	0.478955	−	0.0467573i
$836$	50.0110	+	50.6045i	0.0598218	+	0.0605317i
$837$	477.996	−	1077.33i	0.571083	−	1.28713i
$838$	523.940	+	218.836i	0.625227	+	0.261140i
$839$			1290.47i			1.53811i	0.639182	+	0.769055i	$0.279273\pi$
$839$			1290.47i			1.53811i	−0.639182	+	0.769055i	$0.720727\pi$
$840$	522.696	−	614.023i	0.622257	−	0.730980i
$841$	708.767			0.842767
$842$	360.883	−	864.032i	0.428602	−	1.02617i
$843$	−117.698	+	47.6117i	−0.139618	+	0.0564789i
$844$	−770.586	+	761.549i	−0.913017	+	0.902309i
$845$	−423.333	+	514.929i	−0.500985	+	0.609383i
$846$	349.872	+	152.999i	0.413560	+	0.180850i
$847$	−103.553	−	103.553i	−0.122259	−	0.122259i
$848$	−231.355	−	236.878i	−0.272824	−	0.279338i
$849$	−1335.23	−	566.095i	−1.57271	−	0.666779i
$850$	364.841	+	551.580i	0.429225	+	0.648917i
$851$	−1141.02			−1.34080
$852$	67.8145	−	157.363i	0.0795944	−	0.184698i
$853$	−547.033	−	547.033i	−0.641305	−	0.641305i	0.309572	−	0.950876i	$-0.399814\pi$
$853$	−547.033	−	547.033i	−0.641305	−	0.641305i	−0.950876	+	0.309572i	$0.899814\pi$
$854$	−1051.73	+	432.010i	−1.23153	+	0.505866i
$855$	−66.7635	+	5.40093i	−0.0780860	+	0.00631687i
$856$	68.1088	−	160.400i	0.0795664	−	0.187384i
$857$	−29.4871	−	29.4871i	−0.0344074	−	0.0344074i	0.689694	−	0.724101i	$-0.257745\pi$
$857$	−29.4871	−	29.4871i	−0.0344074	−	0.0344074i	−0.724101	+	0.689694i	$0.757745\pi$
$858$	−299.404	−	306.215i	−0.348955	−	0.356894i
$859$	−1301.37			−1.51499			−0.757493	−	0.652843i	$-0.773576\pi$
$859$	−1301.37			−1.51499			−0.757493	+	0.652843i	$0.773576\pi$
$860$	−192.352	−	160.047i	−0.223666	−	0.186101i
$861$	−502.353	−	212.982i	−0.583453	−	0.247366i
$862$	655.017	−	1568.25i	0.759881	−	1.81932i
$863$	−7.00094	−	7.00094i	−0.00811233	−	0.00811233i	0.703039	−	0.711151i	$-0.251826\pi$
$863$	−7.00094	−	7.00094i	−0.00811233	−	0.00811233i	−0.711151	+	0.703039i	$0.751826\pi$
$864$	−586.251	−	634.670i	−0.678531	−	0.734572i
$865$	−920.138	+	89.8271i	−1.06374	+	0.103846i
$866$	−402.616	+	165.380i	−0.464915	+	0.190970i
$867$	−317.210	+	128.319i	−0.365870	+	0.148004i
$868$	1173.31	+	6.92052i	1.35174	+	0.00797295i
$869$	−111.457			−0.128258
$870$	−903.798	−	760.223i	−1.03885	−	0.873820i
$871$		−	555.386i		−	0.637642i
$872$	47.0240	+	116.429i	0.0539267	+	0.133520i
$873$	−1.45911	+	87.9184i	−0.00167137	+	0.100708i
$874$	−45.1858	+	18.5606i	−0.0517000	+	0.0212364i
$875$	−804.428	+	241.757i	−0.919346	+	0.276294i
$876$	−253.734	+	100.904i	−0.289650	+	0.115188i
$877$	−43.0680	+	43.0680i	−0.0491084	+	0.0491084i	−0.731235	−	0.682126i	$-0.761055\pi$
$877$	−43.0680	+	43.0680i	−0.0491084	+	0.0491084i	0.682126	+	0.731235i	$0.261055\pi$
$878$	42.8398	−	102.568i	0.0487925	−	0.116820i
$879$	−987.920	−	418.847i	−1.12391	−	0.476504i
$880$	615.764	−	731.240i	0.699732	−	0.830954i
$881$		−	648.829i		−	0.736469i	−0.929733	−	0.368235i	$-0.879962\pi$
$881$		−	648.829i		−	0.736469i	0.929733	−	0.368235i	$-0.120038\pi$
$882$	−64.4433	+	25.2294i	−0.0730650	+	0.0286048i
$883$	799.685	−	799.685i	0.905645	−	0.905645i	−0.0902718	−	0.995917i	$-0.528774\pi$
$883$	799.685	−	799.685i	0.905645	−	0.905645i	0.995917	+	0.0902718i	$0.0287736\pi$
$884$	224.772	−	222.136i	0.254267	−	0.251285i
$885$	883.524	+	276.874i	0.998332	+	0.312852i
$886$	1420.85	−	583.631i	1.60366	−	0.658726i
$887$	−103.964	+	103.964i	−0.117209	+	0.117209i	−0.763278	−	0.646070i	$-0.776412\pi$
$887$	−103.964	+	103.964i	−0.117209	+	0.117209i	0.646070	+	0.763278i	$0.276412\pi$
$888$	−1668.62	−	28.6106i	−1.87907	−	0.0322192i
$889$			113.878i			0.128097i
$890$	−463.366	+	245.410i	−0.520636	+	0.275742i
$891$	32.1186	−	967.386i	0.0360478	−	1.08573i
$892$	−980.391	−	5.78263i	−1.09909	−	0.00648277i
$893$	22.3287	−	22.3287i	0.0250041	−	0.0250041i
$894$	145.757	+	1.63931i	0.163039	+	0.00183368i
$895$	−679.290	+	826.268i	−0.758984	+	0.923205i
$896$	345.491	−	787.692i	0.385592	−	0.879121i
$897$	272.586	−	110.268i	0.303886	−	0.122930i
$898$	28.0161	−	67.0767i	0.0311984	−	0.0746957i
$899$		−	1718.46i		−	1.91152i
$900$	154.160	+	886.699i	0.171289	+	0.985221i
$901$	273.717			0.303792
$902$	−596.891	−	249.305i	−0.661742	−	0.276392i
$903$	−94.5843	−	233.815i	−0.104745	−	0.258932i
$904$	147.351	−	347.020i	0.162998	−	0.383872i
$905$	−600.222	−	493.454i	−0.663229	−	0.545253i
$906$	−8.14891	+	724.548i	−0.00899438	+	0.799722i
$907$	695.991	+	695.991i	0.767355	+	0.767355i	0.977640	−	0.210285i	$-0.0674393\pi$
$907$	695.991	+	695.991i	0.767355	+	0.767355i	−0.210285	+	0.977640i	$0.567439\pi$
$908$	1087.60	+	6.41496i	1.19779	+	0.00706494i
$909$	93.9027	+	97.0721i	0.103303	+	0.106790i
$910$	187.862	+	354.707i	0.206441	+	0.389788i
$911$	1074.43			1.17939			0.589696	−	0.807625i	$-0.299247\pi$
$911$	1074.43			1.17939			0.589696	+	0.807625i	$0.299247\pi$
$912$	−66.5445	+	26.0098i	−0.0729655	+	0.0285196i
$913$	−152.358	−	152.358i	−0.166876	−	0.166876i
$914$	499.893	+	1216.99i	0.546929	+	1.33150i
$915$	379.479	−	1210.95i	0.414731	−	1.32344i
$916$	212.431	−	209.939i	0.231911	−	0.229191i
$917$	−1087.24	−	1087.24i	−1.18565	−	1.18565i
$918$	713.953	+	19.8823i	0.777727	+	0.0216583i
$919$	1186.92			1.29153			0.645766	−	0.763535i	$-0.276538\pi$
$919$	1186.92			1.29153			0.645766	+	0.763535i	$0.276538\pi$
$920$	303.775	+	581.838i	0.330190	+	0.632433i
$921$	−466.333	+	1099.92i	−0.506333	+	1.19427i
$922$	128.621	+	53.7217i	0.139503	+	0.0582665i
$923$	60.3116	+	60.3116i	0.0653431	+	0.0653431i
$924$	895.380	−	356.073i	0.969026	−	0.385361i
$925$	1443.76	+	968.286i	1.56082	+	1.04680i
$926$	487.245	+	1186.20i	0.526183	+	1.28099i
$927$	−2.12087	+	127.793i	−0.00228788	+	0.137856i
$928$	−1156.62	−	499.193i	−1.24636	−	0.537923i
$929$	1085.41			1.16836			0.584182	−	0.811623i	$-0.301415\pi$
$929$	1085.41			1.16836			0.584182	+	0.811623i	$0.301415\pi$
$930$	−842.973	+	1002.18i	−0.906423	+	1.07761i
$931$			5.72287i			0.00614702i
$932$	841.600	+	4.96401i	0.903005	+	0.00532619i
$933$	358.528	+	886.293i	0.384275	+	0.949939i
$934$	−466.810	−	1136.45i	−0.499797	−	1.21675i
$935$	76.7826	+	786.518i	0.0821204	+	0.841195i
$936$	401.391	−	154.419i	0.428836	−	0.164978i
$937$	−302.640	+	302.640i	−0.322988	+	0.322988i	−0.849912	−	0.526924i	$-0.823345\pi$
$937$	−302.640	+	302.640i	−0.322988	+	0.322988i	0.526924	+	0.849912i	$0.323345\pi$
$938$	1153.07	+	481.606i	1.22928	+	0.513439i
$939$	−274.194	+	646.732i	−0.292006	+	0.688746i
$940$	−326.155	−	271.378i	−0.346974	−	0.288700i
$941$			193.039i			0.205142i	0.994726	+	0.102571i	$0.0327069\pi$
$941$			193.039i			0.205142i	−0.994726	+	0.102571i	$0.967293\pi$
$942$	−467.931	+	457.523i	−0.496742	+	0.485693i
$943$	314.050	−	314.050i	0.333033	−	0.333033i
$944$	987.548	+	11.6501i	1.04613	+	0.0123412i
$945$	−285.602	+	861.037i	−0.302225	+	0.911151i
$946$	−113.612	−	276.589i	−0.120098	−	0.292377i
$947$	508.522	−	508.522i	0.536982	−	0.536982i	−0.385659	−	0.922641i	$-0.626026\pi$
$947$	508.522	−	508.522i	0.536982	−	0.536982i	0.922641	+	0.385659i	$0.126026\pi$
$948$	44.2960	−	102.788i	0.0467257	−	0.108426i
$949$		−	135.921i		−	0.143225i
$950$	72.9254	+	14.8600i	0.0767636	+	0.0156421i
$951$	−11.1677	+	26.3409i	−0.0117431	+	0.0276981i
$952$	266.277	+	659.288i	0.279703	+	0.692529i
$953$	182.398	−	182.398i	0.191393	−	0.191393i	−0.604905	−	0.796298i	$-0.706789\pi$
$953$	182.398	−	182.398i	0.191393	−	0.191393i	0.796298	+	0.604905i	$0.206789\pi$
$954$	341.296	+	149.249i	0.357753	+	0.156446i
$955$	−396.182	−	325.708i	−0.414850	−	0.341056i
$956$	−609.442	+	602.295i	−0.637492	+	0.630015i
$957$	−529.231	−	1308.27i	−0.553010	−	1.36706i
$958$	−566.639	−	236.670i	−0.591481	−	0.247046i
$959$		−	1477.60i		−	1.54077i
$960$	429.647	+	858.489i	0.447549	+	0.894260i
$961$	−944.513			−0.982844
$962$	320.158	−	766.528i	0.332805	−	0.796807i
$963$	−3.25313	+	196.017i	−0.00337812	+	0.203549i
$964$	−472.179	−	477.782i	−0.489812	−	0.495625i
$965$	−94.9573	−	972.688i	−0.0984013	−	1.00797i
$966$	−7.44038	+	661.550i	−0.00770226	+	0.684835i
$967$	754.876	+	754.876i	0.780637	+	0.780637i	0.979938	−	0.199301i	$-0.0638673\pi$
$967$	754.876	+	754.876i	0.780637	+	0.780637i	−0.199301	+	0.979938i	$0.563867\pi$
$968$	161.659	−	65.2920i	0.167004	−	0.0674504i
$969$	23.0540	−	54.3768i	0.0237916	−	0.0561164i
$970$	28.7169	−	93.3850i	0.0296050	−	0.0962731i
$971$	670.107			0.690121			0.345060	−	0.938580i	$-0.387858\pi$
$971$	670.107			0.690121			0.345060	+	0.938580i	$0.387858\pi$
$972$	879.384	+	414.087i	0.904716	+	0.426015i
$973$	−1046.24	−	1046.24i	−1.07528	−	1.07528i
$974$	655.211	−	269.136i	0.672701	−	0.276321i
$975$	−438.484	−	91.7950i	−0.449727	−	0.0941487i
$976$	15.9675	−	1353.52i	0.0163601	−	1.38680i
$977$	−1030.12	−	1030.12i	−1.05437	−	1.05437i	−0.998435	−	0.0559325i	$-0.982187\pi$
$977$	−1030.12	−	1030.12i	−1.05437	−	1.05437i	−0.0559325	−	0.998435i	$-0.517813\pi$
$978$	−1090.65	+	1066.39i	−1.11518	+	1.09038i
$979$	−626.569			−0.640009
$980$	76.5744	−	7.01976i	0.0781371	−	0.00716302i
$981$	−98.2164	−	101.531i	−0.100119	−	0.103498i
$982$	−224.888	+	538.430i	−0.229010	+	0.548299i
$983$	−1099.04	−	1099.04i	−1.11804	−	1.11804i	−0.992028	−	0.126017i	$-0.959781\pi$
$983$	−1099.04	−	1099.04i	−1.11804	−	1.11804i	−0.126017	−	0.992028i	$-0.540219\pi$
$984$	467.137	−	451.388i	0.474733	−	0.458728i
$985$	64.8756	+	664.549i	0.0658636	+	0.674669i
$986$	963.277	−	395.678i	0.976954	−	0.401296i
$987$	−160.379	−	396.461i	−0.162491	−	0.401683i
$988$	0.209763	−	35.5633i	0.000212310	−	0.0359952i
$989$	205.302			0.207585
$990$	−333.123	+	1022.57i	−0.336488	+	1.03290i
$991$			893.875i			0.901993i	0.892526	+	0.450996i	$0.148931\pi$
$991$			893.875i			0.901993i	−0.892526	+	0.450996i	$0.851069\pi$
$992$	−553.530	+	1282.52i	−0.557994	+	1.29286i
$993$	−774.266	+	313.210i	−0.779724	+	0.315418i
$994$	−177.516	+	72.9169i	−0.178588	+	0.0733571i
$995$	715.613	+	588.319i	0.719209	+	0.591275i
$996$	201.060	−	79.9572i	0.201867	−	0.0802783i
$997$	465.597	−	465.597i	0.466998	−	0.466998i	−0.433943	−	0.900940i	$-0.642878\pi$
$997$	465.597	−	465.597i	0.466998	−	0.466998i	0.900940	+	0.433943i	$0.142878\pi$
$998$	325.266	−	778.757i	0.325917	−	0.780317i
$999$	1751.90	−	675.082i	1.75365	−	0.675758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.l.a.23.9	yes	40
3.2	odd	2	inner	60.3.l.a.23.12	yes	40
4.3	odd	2	inner	60.3.l.a.23.19	yes	40
5.2	odd	4	inner	60.3.l.a.47.2	yes	40
5.3	odd	4		300.3.l.g.107.19		40
5.4	even	2		300.3.l.g.143.12		40
12.11	even	2	inner	60.3.l.a.23.2	✓	40
15.2	even	4	inner	60.3.l.a.47.19	yes	40
15.8	even	4		300.3.l.g.107.2		40
15.14	odd	2		300.3.l.g.143.9		40
20.3	even	4		300.3.l.g.107.9		40
20.7	even	4	inner	60.3.l.a.47.12	yes	40
20.19	odd	2		300.3.l.g.143.2		40
60.23	odd	4		300.3.l.g.107.12		40
60.47	odd	4	inner	60.3.l.a.47.9	yes	40
60.59	even	2		300.3.l.g.143.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.2	✓	40	12.11	even	2	inner
60.3.l.a.23.9	yes	40	1.1	even	1	trivial
60.3.l.a.23.12	yes	40	3.2	odd	2	inner
60.3.l.a.23.19	yes	40	4.3	odd	2	inner
60.3.l.a.47.2	yes	40	5.2	odd	4	inner
60.3.l.a.47.9	yes	40	60.47	odd	4	inner
60.3.l.a.47.12	yes	40	20.7	even	4	inner
60.3.l.a.47.19	yes	40	15.2	even	4	inner
300.3.l.g.107.2		40	15.8	even	4
300.3.l.g.107.9		40	20.3	even	4
300.3.l.g.107.12		40	60.23	odd	4
300.3.l.g.107.19		40	5.3	odd	4
300.3.l.g.143.2		40	20.19	odd	2
300.3.l.g.143.9		40	15.14	odd	2
300.3.l.g.143.12		40	5.4	even	2
300.3.l.g.143.19		40	60.59	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770813 + 1.84549i) q^{2} +(-1.12501 - 2.78107i) q^{3} +(-2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 - 4.75159i) q^{7} +(7.41783 - 2.99596i) q^{8} +(-6.46869 + 6.25748i) q^{9} +O(q^{10})\)	\(q+(-0.770813 + 1.84549i) q^{2} +(-1.12501 - 2.78107i) q^{3} +(-2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 - 4.75159i) q^{7} +(7.41783 - 2.99596i) q^{8} +(-6.46869 + 6.25748i) q^{9} +(8.83710 - 4.68034i) q^{10} +11.9496 q^{11} +(-4.74911 + 11.0203i) q^{12} +(-4.22368 - 4.22368i) q^{13} +(12.4316 - 5.10644i) q^{14} +(-4.48553 + 14.3136i) q^{15} +(-0.188739 + 15.9989i) q^{16} +(-9.35253 - 9.35253i) q^{17} +(-6.56200 - 16.7613i) q^{18} -1.48848 q^{19} +(1.82579 + 19.9165i) q^{20} +(-7.86889 + 18.5601i) q^{21} +(-9.21092 + 22.0529i) q^{22} +(-11.6030 - 11.6030i) q^{23} +(-16.6771 - 17.2590i) q^{24} +(4.83510 + 24.5280i) q^{25} +(11.0504 - 4.53911i) q^{26} +(24.6799 + 10.9501i) q^{27} +(-0.158538 + 26.8786i) q^{28} +39.3671 q^{29} +(-22.9582 - 19.3111i) q^{30} -43.6522i q^{31} +(-29.3804 - 12.6805i) q^{32} +(-13.4435 - 33.2327i) q^{33} +(24.4691 - 10.0510i) q^{34} +(3.26452 + 33.4399i) q^{35} +(35.9909 + 0.809673i) q^{36} +(49.1693 - 49.1693i) q^{37} +(1.14734 - 2.74698i) q^{38} +(-6.99465 + 16.4981i) q^{39} +(-38.1631 - 11.9824i) q^{40} +27.0663i q^{41} +(-28.1871 - 28.8284i) q^{42} +(-8.84693 + 8.84693i) q^{43} +(-33.5987 - 33.9974i) q^{44} +(44.8535 - 3.62848i) q^{45} +(30.3570 - 12.4695i) q^{46} +(-15.0010 + 15.0010i) q^{47} +(44.7063 - 17.4741i) q^{48} -3.84477i q^{49} +(-48.9932 - 9.98334i) q^{50} +(-15.4883 + 36.5318i) q^{51} +(-0.140924 + 23.8923i) q^{52} +(-14.6333 + 14.6333i) q^{53} +(-39.2319 + 37.1060i) q^{54} +(-46.1533 - 37.9435i) q^{55} +(-49.4821 - 21.0109i) q^{56} +(1.67456 + 4.13957i) q^{57} +(-30.3447 + 72.6517i) q^{58} -61.7260i q^{59} +(53.3351 - 27.4840i) q^{60} -84.6009 q^{61} +(80.5598 + 33.6477i) q^{62} +(60.4695 + 1.00356i) q^{63} +(46.0485 - 44.4470i) q^{64} +(2.90182 + 29.7246i) q^{65} +(71.6932 + 0.806325i) q^{66} +(65.7467 + 65.7467i) q^{67} +(-0.312049 + 52.9050i) q^{68} +(-19.2152 + 45.3223i) q^{69} +(-64.2294 - 19.7512i) q^{70} -14.2794 q^{71} +(-29.2365 + 65.7969i) q^{72} +(16.0903 + 16.0903i) q^{73} +(52.8413 + 128.642i) q^{74} +(62.7745 - 41.0411i) q^{75} +(4.18516 + 4.23482i) q^{76} +(-56.7797 - 56.7797i) q^{77} +(-25.0555 - 25.6255i) q^{78} -9.32721 q^{79} +(51.5300 - 61.1936i) q^{80} +(2.68783 - 80.9554i) q^{81} +(-49.9507 - 20.8630i) q^{82} +(-12.7500 - 12.7500i) q^{83} +(74.9296 - 29.7979i) q^{84} +(6.42553 + 65.8195i) q^{85} +(-9.50762 - 23.1463i) q^{86} +(-44.2885 - 109.483i) q^{87} +(88.6403 - 35.8005i) q^{88} -52.4342 q^{89} +(-27.8773 + 85.5737i) q^{90} +40.1384i q^{91} +(-0.387136 + 65.6353i) q^{92} +(-121.400 + 49.1093i) q^{93} +(-16.1213 - 39.2471i) q^{94} +(5.74900 + 4.72636i) q^{95} +(-2.21192 + 95.9745i) q^{96} +(6.90848 - 6.90848i) q^{97} +(7.09551 + 2.96360i) q^{98} +(-77.2983 + 74.7745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Introduction

L-functions

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