LMFDB - Embedded newform 60.3.l.a.47.12

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			47.12
Character	$\chi$	$=$	60.47
Dual form			60.3.l.a.23.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.770813 + 1.84549i) q^{2} +(2.78107 - 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(-7.41783 - 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})$	\(q+(0.770813 + 1.84549i) q^{2} +(2.78107 - 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) 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} +(-4.61879 + 11.0755i) q^{12} +(-4.22368 + 4.22368i) q^{13} +(-12.4316 - 5.10644i) q^{14} +(7.16915 - 13.1759i) q^{15} +(-0.188739 - 15.9989i) q^{16} +(9.35253 - 9.35253i) q^{17} +(16.5343 + 7.11458i) 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} +(-24.0000 + 0.0132009i) q^{24} +(4.83510 - 24.5280i) q^{25} +(-11.0504 - 4.53911i) q^{26} +(10.9501 - 24.6799i) q^{27} +(-0.158538 - 26.8786i) q^{28} -39.3671 q^{29} +(29.8420 + 3.07449i) q^{30} +43.6522i q^{31} +(29.3804 - 12.6805i) q^{32} +(-33.2327 + 13.4435i) q^{33} +(24.4691 + 10.0510i) q^{34} +(-3.26452 + 33.4399i) q^{35} +(-0.385062 + 35.9979i) 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} +(-40.3180 - 0.215630i) q^{42} +(-8.84693 - 8.84693i) q^{43} +(33.5987 - 33.9974i) q^{44} +(5.11486 - 44.7084i) q^{45} +(30.3570 + 12.4695i) q^{46} +(15.0010 + 15.0010i) q^{47} +(-18.5239 - 44.2817i) 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} +(53.9870 + 1.18482i) q^{54} +(-46.1533 + 37.9435i) q^{55} +(49.4821 - 21.0109i) q^{56} +(-4.13957 + 1.67456i) q^{57} +(-30.3447 - 72.6517i) q^{58} -61.7260i q^{59} +(17.3287 + 57.4432i) q^{60} -84.6009 q^{61} +(-80.5598 + 33.6477i) q^{62} +(-1.00356 + 60.4695i) q^{63} +(46.0485 + 44.4470i) q^{64} +(-2.90182 + 29.7246i) q^{65} +(-50.4261 - 50.9683i) 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} +(-66.7308 + 27.0370i) q^{72} +(16.0903 - 16.0903i) q^{73} +(-52.8413 + 128.642i) q^{74} +(-14.1476 - 73.6536i) q^{75} +(4.18516 - 4.23482i) q^{76} +(56.7797 - 56.7797i) q^{77} +(-35.8386 - 0.191673i) 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} +(-30.6797 - 74.5728i) q^{84} +(6.42553 - 65.8195i) q^{85} +(9.50762 - 23.1463i) q^{86} +(-109.483 + 44.2885i) q^{87} +(88.6403 + 35.8005i) q^{88} +52.4342 q^{89} +(86.4516 - 25.0223i) q^{90} -40.1384i q^{91} +(0.387136 + 65.6353i) q^{92} +(49.1093 + 121.400i) q^{93} +(-16.1213 + 39.2471i) q^{94} +(-5.74900 + 4.72636i) q^{95} +(67.4431 - 68.3186i) 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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

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

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
$3$	2.78107	−	1.12501i	0.927023	−	0.375005i
$3$	2.78107	−	1.12501i	0.927023	−	0.375005i
$4$	−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
$6$	4.21989	+	4.26527i	0.703315	+	0.710878i
$7$	−4.75159	+	4.75159i	−0.678799	+	0.678799i	−0.959728	−	0.280930i	$-0.909357\pi$
$7$	−4.75159	+	4.75159i	−0.678799	+	0.678799i	0.280930	+	0.959728i	$0.409357\pi$
$8$	−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	$-0.682774\pi$
$11$	−11.9496			−1.08633			−0.543164	+	0.839626i	$0.682774\pi$
$12$	−4.61879	+	11.0755i	−0.384899	+	0.922959i
$13$	−4.22368	+	4.22368i	−0.324899	+	0.324899i	−0.850643	−	0.525744i	$-0.823787\pi$
$13$	−4.22368	+	4.22368i	−0.324899	+	0.324899i	0.525744	+	0.850643i	$0.323787\pi$
$14$	−12.4316	−	5.10644i	−0.887973	−	0.364746i
$15$	7.16915	−	13.1759i	0.477943	−	0.878391i
$16$	−0.188739	−	15.9989i	−0.0117962	−	0.999930i
$17$	9.35253	−	9.35253i	0.550149	−	0.550149i	−0.376335	−	0.926484i	$-0.622816\pi$
$17$	9.35253	−	9.35253i	0.550149	−	0.550149i	0.926484	+	0.376335i	$0.122816\pi$
$18$	16.5343	+	7.11458i	0.918572	+	0.395254i
$19$	−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	$-0.633895\pi$
$23$	11.6030	−	11.6030i	0.504478	−	0.504478i	0.912826	+	0.408348i	$0.133895\pi$
$24$	−24.0000	+	0.0132009i	−1.00000	+	0.000550037i
$25$	4.83510	−	24.5280i	0.193404	−	0.981119i
$26$	−11.0504	−	4.53911i	−0.425017	−	0.174581i
$27$	10.9501	−	24.6799i	0.405560	−	0.914069i
$28$	−0.158538	−	26.8786i	−0.00566206	−	0.959950i
$29$	−39.3671			−1.35749			−0.678743	−	0.734376i	$-0.737475\pi$
$29$	−39.3671			−1.35749			−0.678743	+	0.734376i	$0.737475\pi$
$30$	29.8420	+	3.07449i	0.994735	+	0.102483i
$31$			43.6522i			1.40813i	0.710133	+	0.704067i	$0.248635\pi$
$31$			43.6522i			1.40813i	−0.710133	+	0.704067i	$0.751365\pi$
$32$	29.3804	−	12.6805i	0.918136	−	0.396264i
$33$	−33.2327	+	13.4435i	−1.00705	+	0.407378i
$34$	24.4691	+	10.0510i	0.719679	+	0.295617i
$35$	−3.26452	+	33.4399i	−0.0932719	+	0.955424i
$36$	−0.385062	+	35.9979i	−0.0106962	+	0.999943i
$37$	49.1693	+	49.1693i	1.32890	+	1.32890i	0.906330	+	0.422571i	$0.138872\pi$
$37$	49.1693	+	49.1693i	1.32890	+	1.32890i	0.422571	+	0.906330i	$0.361128\pi$
$38$	−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	$0.892925\pi$
$42$	−40.3180	−	0.215630i	−0.959953	−	0.00513405i
$43$	−8.84693	−	8.84693i	−0.205742	−	0.205742i	0.596713	−	0.802455i	$-0.296473\pi$
$43$	−8.84693	−	8.84693i	−0.205742	−	0.205742i	−0.802455	+	0.596713i	$0.796473\pi$
$44$	33.5987	−	33.9974i	0.763606	−	0.772668i
$45$	5.11486	−	44.7084i	0.113664	−	0.993519i
$46$	30.3570	+	12.4695i	0.659935	+	0.271077i
$47$	15.0010	+	15.0010i	0.319170	+	0.319170i	0.848448	−	0.529278i	$-0.177537\pi$
$47$	15.0010	+	15.0010i	0.319170	+	0.319170i	−0.529278	+	0.848448i	$0.677537\pi$
$48$	−18.5239	−	44.2817i	−0.385914	−	0.922535i
$49$			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	$-0.187454\pi$
$53$	14.6333	+	14.6333i	0.276100	+	0.276100i	−0.555450	+	0.831550i	$0.687454\pi$
$54$	53.9870	+	1.18482i	0.999759	+	0.0219410i
$55$	−46.1533	+	37.9435i	−0.839151	+	0.689881i
$56$	49.4821	−	21.0109i	0.883608	−	0.375195i
$57$	−4.13957	+	1.67456i	−0.0726240	+	0.0293783i
$58$	−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	$-0.175225\pi$
$60$	17.3287	+	57.4432i	0.288811	+	0.957386i
$61$	−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
$63$	−1.00356	+	60.4695i	−0.0159295	+	0.959834i
$64$	46.0485	+	44.4470i	0.719507	+	0.694485i
$65$	−2.90182	+	29.7246i	−0.0446434	+	0.457302i
$66$	−50.4261	−	50.9683i	−0.764031	−	0.772248i
$67$	65.7467	−	65.7467i	0.981293	−	0.981293i	−0.0185347	−	0.999828i	$-0.505900\pi$
$67$	65.7467	−	65.7467i	0.981293	−	0.981293i	0.999828	+	0.0185347i	$0.00590012\pi$
$68$	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	$-0.467937\pi$
$71$	14.2794			0.201118			0.100559	+	0.994931i	$0.467937\pi$
$72$	−66.7308	+	27.0370i	−0.926817	+	0.375514i
$73$	16.0903	−	16.0903i	0.220415	−	0.220415i	−0.588258	−	0.808673i	$-0.700186\pi$
$73$	16.0903	−	16.0903i	0.220415	−	0.220415i	0.808673	+	0.588258i	$0.200186\pi$
$74$	−52.8413	+	128.642i	−0.714072	+	1.73841i
$75$	−14.1476	−	73.6536i	−0.188634	−	0.982047i
$76$	4.18516	−	4.23482i	0.0550678	−	0.0557213i
$77$	56.7797	−	56.7797i	0.737399	−	0.737399i
$78$	−35.8386	−	0.191673i	−0.459470	−	0.00245735i
$79$	−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	$-0.715356\pi$
$83$	12.7500	−	12.7500i	0.153615	−	0.153615i	0.779730	+	0.626116i	$0.215356\pi$
$84$	−30.6797	−	74.5728i	−0.365234	−	0.887772i
$85$	6.42553	−	65.8195i	0.0755945	−	0.774347i
$86$	9.50762	−	23.1463i	0.110554	−	0.269143i
$87$	−109.483	+	44.2885i	−1.25842	+	0.509063i
$88$	88.6403	+	35.8005i	1.00728	+	0.406824i
$89$	52.4342			0.589148			0.294574	−	0.955629i	$-0.404822\pi$
$89$	52.4342			0.589148			0.294574	+	0.955629i	$0.404822\pi$
$90$	86.4516	−	25.0223i	0.960574	−	0.278026i
$91$		−	40.1384i		−	0.441082i
$92$	0.387136	+	65.6353i	0.00420800	+	0.713427i
$93$	49.1093	+	121.400i	0.528057	+	1.30537i
$94$	−16.1213	+	39.2471i	−0.171503	+	0.417523i
$95$	−5.74900	+	4.72636i	−0.0605158	+	0.0497511i
$96$	67.4431	−	68.3186i	0.702533	−	0.711652i
$97$	6.90848	+	6.90848i	0.0712214	+	0.0712214i	0.741820	−	0.670599i	$-0.233963\pi$
$97$	6.90848	+	6.90848i	0.0712214	+	0.0712214i	−0.670599	+	0.741820i	$0.733963\pi$
$98$	−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	$-0.0236689\pi$
$102$	79.3577	+	0.424424i	0.778017	+	0.00416102i
$103$	10.0417	+	10.0417i	0.0974926	+	0.0974926i	0.754171	−	0.656678i	$-0.228039\pi$
$103$	10.0417	+	10.0417i	0.0974926	+	0.0974926i	−0.656678	+	0.754171i	$0.728039\pi$
$104$	43.9845	−	18.6766i	0.422928	−	0.179583i
$105$	28.5415	+	96.6712i	0.271823	+	0.920678i
$106$	−15.7261	+	38.2852i	−0.148360	+	0.361181i
$107$	−15.4027	−	15.4027i	−0.143950	−	0.143950i	0.631459	−	0.775409i	$-0.282456\pi$
$107$	−15.4027	−	15.4027i	−0.143950	−	0.143950i	−0.775409	+	0.631459i	$0.782456\pi$
$108$	39.4273	+	100.546i	0.365068	+	0.930981i
$109$		−	15.6958i		−	0.143998i	−0.997405	−	0.0719992i	$-0.977062\pi$
$109$		−	15.6958i		−	0.143998i	0.997405	−	0.0719992i	$-0.0229379\pi$
$110$	−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	$-0.316865\pi$
$113$	−33.3231	−	33.3231i	−0.294895	−	0.294895i	−0.839010	+	0.544116i	$0.816865\pi$
$114$	−6.28123	−	6.34877i	−0.0550985	−	0.0556910i
$115$	7.97168	−	81.6574i	0.0693190	−	0.710064i
$116$	110.688	−	112.002i	0.954209	−	0.965532i
$117$	−0.892063	+	53.7513i	−0.00762447	+	0.459413i
$118$	113.915	−	47.5792i	0.965382	−	0.403214i
$119$			88.8788i			0.746881i
$120$	−92.6538	+	76.2579i	−0.772115	+	0.635482i
$121$	21.7934			0.180110
$122$	−65.2114	−	156.130i	−0.534520	−	1.27976i
$123$	30.4500	+	75.2732i	0.247561	+	0.611977i
$124$	−124.193	−	122.737i	−1.00156	−	0.989812i
$125$	−59.2087	−	110.088i	−0.473670	−	0.880703i
$126$	−112.370	+	44.7586i	−0.891823	+	0.355227i
$127$	−11.9832	+	11.9832i	−0.0943557	+	0.0943557i	−0.752709	−	0.658353i	$-0.771253\pi$
$127$	−11.9832	+	11.9832i	−0.0943557	+	0.0943557i	0.658353	+	0.752709i	$0.271253\pi$
$128$	−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	$-0.838051\pi$
$131$	−228.815			−1.74668			−0.873341	+	0.487109i	$0.838051\pi$
$132$	55.1927	−	132.348i	0.418127	−	1.00264i
$133$	7.07265	−	7.07265i	0.0531778	−	0.0531778i
$134$	172.013	+	70.6567i	1.28368	+	0.527289i
$135$	−36.0728	−	130.091i	−0.267206	−	0.963640i
$136$	−97.3953	+	41.3557i	−0.716142	+	0.304086i
$137$	−155.485	+	155.485i	−1.13492	+	1.13492i	−0.145578	+	0.989347i	$0.546504\pi$
$137$	−155.485	+	155.485i	−1.13492	+	1.13492i	−0.989347	+	0.145578i	$0.953496\pi$
$138$	98.4533	+	0.526552i	0.713430	+	0.00381559i
$139$	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
$144$	−101.334	−	102.311i	−0.703706	−	0.710491i
$145$	−152.048	+	125.002i	−1.04861	+	0.862082i
$146$	42.0971	+	17.2919i	0.288337	+	0.118438i
$147$	4.32542	+	10.6926i	0.0294247	+	0.0727386i
$148$	−278.139	+	1.64054i	−1.87932	+	0.0110848i
$149$	−24.2943			−0.163049			−0.0815247	−	0.996671i	$-0.525979\pi$
$149$	−24.2943			−0.163049			−0.0815247	+	0.996671i	$0.525979\pi$
$150$	125.022	−	82.8824i	0.833480	−	0.552549i
$151$		−	120.766i		−	0.799772i	−0.916565	−	0.399886i	$-0.869050\pi$
$151$		−	120.766i		−	0.799772i	0.916565	−	0.399886i	$-0.130950\pi$
$152$	11.0413	+	4.45943i	0.0726402	+	0.0293383i
$153$	1.97530	−	119.022i	0.0129105	−	0.777921i
$154$	148.553	+	61.0201i	0.964630	+	0.396234i
$155$	138.608	+	168.599i	0.894247	+	1.08773i
$156$	−27.2711	−	66.2877i	−0.174815	−	0.424921i
$157$	−77.1260	−	77.1260i	−0.491249	−	0.491249i	0.417451	−	0.908700i	$-0.362924\pi$
$157$	−77.1260	−	77.1260i	−0.491249	−	0.491249i	−0.908700	+	0.417451i	$0.862924\pi$
$158$	−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
$162$	151.474	−	57.4411i	0.935028	−	0.354575i
$163$	−179.764	−	179.764i	−1.10285	−	1.10285i	−0.994065	−	0.108783i	$-0.965305\pi$
$163$	−179.764	−	179.764i	−1.10285	−	1.10285i	−0.108783	−	0.994065i	$-0.534695\pi$
$164$	−77.0052	−	76.1022i	−0.469544	−	0.464038i
$165$	−85.6686	+	157.447i	−0.519203	+	0.954221i
$166$	33.3580	+	13.7022i	0.200952	+	0.0825434i
$167$	56.8272	+	56.8272i	0.340283	+	0.340283i	0.856474	−	0.516191i	$-0.172651\pi$
$167$	56.8272	+	56.8272i	0.340283	+	0.340283i	−0.516191	+	0.856474i	$0.672651\pi$
$168$	113.975	−	114.101i	0.678425	−	0.679172i
$169$			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	$-0.429462\pi$
$173$	−130.746	−	130.746i	−0.755756	−	0.755756i	−0.975547	+	0.219791i	$0.929462\pi$
$174$	−166.125	−	167.911i	−0.954740	−	0.965007i
$175$	93.5725	+	139.521i	0.534700	+	0.797265i
$176$	2.25536	+	191.181i	0.0128145	+	1.08625i
$177$	−69.4427	−	171.664i	−0.392331	−	0.969855i
$178$	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	$-0.203867\pi$
$180$	112.817	+	140.258i	0.626759	+	0.779213i
$181$	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
$183$	−235.281	+	95.1771i	−1.28569	+	0.520094i
$184$	−120.831	+	51.3070i	−0.656691	+	0.278842i
$185$	346.035	+	33.7811i	1.87046	+	0.182601i
$186$	−186.188	+	184.207i	−1.00101	+	0.990362i
$187$	−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	$-0.586536\pi$
$191$	−102.576			−0.537047			−0.268524	+	0.963273i	$0.586536\pi$
$192$	178.068	+	71.8050i	0.927435	+	0.373985i
$193$	138.213	−	138.213i	0.716129	−	0.716129i	−0.251681	−	0.967810i	$-0.580983\pi$
$193$	138.213	−	138.213i	0.716129	−	0.716129i	0.967810	+	0.251681i	$0.0809835\pi$
$194$	−7.42441	+	18.0747i	−0.0382701	+	0.0931685i
$195$	25.3705	+	85.9309i	0.130105	+	0.440671i
$196$	−10.9386	−	10.8103i	−0.0558093	−	0.0551548i
$197$	94.4283	−	94.4283i	0.479331	−	0.479331i	−0.425586	−	0.904918i	$-0.639932\pi$
$197$	94.4283	−	94.4283i	0.479331	−	0.479331i	0.904918	+	0.425586i	$0.139932\pi$
$198$	−197.578	−	85.0165i	−0.997871	−	0.429376i
$199$	−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
$204$	60.3867	+	146.781i	0.296013	+	0.719516i
$205$	85.9433	+	104.539i	0.419235	+	0.509945i
$206$	−10.7917	+	26.2723i	−0.0523868	+	0.127535i
$207$	2.45061	−	147.662i	0.0118387	−	0.713342i
$208$	68.3714	+	66.7771i	0.328709	+	0.321044i
$209$	17.7868			0.0851042
$210$	−156.406	+	127.188i	−0.744790	+	0.605659i
$211$			270.850i			1.28365i	0.766850	+	0.641826i	$0.221823\pi$
$211$			270.850i			1.28365i	−0.766850	+	0.641826i	$0.778177\pi$
$212$	−82.7770	+	0.488243i	−0.390458	+	0.00230303i
$213$	39.7120	−	16.0645i	0.186441	−	0.0754203i
$214$	16.5530	−	40.2982i	0.0773504	−	0.188309i
$215$	−62.2612	−	6.07816i	−0.289587	−	0.0282705i
$216$	−155.166	+	150.265i	−0.718360	+	0.695671i
$217$	−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
$222$	−2.23134	+	417.210i	−0.0100511	+	1.87932i
$223$	173.313	+	173.313i	0.777190	+	0.777190i	0.979352	−	0.202162i	$-0.0647968\pi$
$223$	173.313	+	173.313i	0.777190	+	0.777190i	−0.202162	+	0.979352i	$0.564797\pi$
$224$	−79.3511	+	199.856i	−0.354246	+	0.892214i
$225$	−122.207	−	188.919i	−0.543141	−	0.839642i
$226$	35.8117	−	87.1835i	0.158459	−	0.385768i
$227$	192.265	+	192.265i	0.846983	+	0.846983i	0.989755	−	0.142773i	$-0.0456019\pi$
$227$	192.265	+	192.265i	0.846983	+	0.846983i	−0.142773	+	0.989755i	$0.545602\pi$
$228$	6.87497	−	16.4857i	0.0301534	−	0.0723056i
$229$		−	74.6665i		−	0.326054i	−0.986622	−	0.163027i	$-0.947874\pi$
$229$		−	74.6665i		−	0.326054i	0.986622	−	0.163027i	$-0.0521258\pi$
$230$	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	$-0.100885\pi$
$233$	148.778	+	148.778i	0.638532	+	0.638532i	−0.311661	+	0.950193i	$0.600885\pi$
$234$	−99.8853	+	39.7859i	−0.426860	+	0.170025i
$235$	105.571	+	10.3062i	0.449238	+	0.0438562i
$236$	175.614	+	173.555i	0.744128	+	0.735402i
$237$	−25.9396	+	10.4932i	−0.109450	+	0.0442753i
$238$	−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	$-0.147913\pi$
$240$	−212.152	−	112.212i	−0.883968	−	0.467548i
$241$	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
$243$	−83.6009	−	228.166i	−0.344037	−	0.938956i
$244$	237.872	−	240.695i	0.974885	−	0.986453i
$245$	12.2083	+	14.8498i	0.0498296	+	0.0606113i
$246$	−115.445	+	114.217i	−0.469289	+	0.464296i
$247$	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	$-0.607821\pi$
$251$	−166.809			−0.664578			−0.332289	+	0.943178i	$0.607821\pi$
$252$	−169.218	−	172.877i	−0.671499	−	0.686020i
$253$	−138.651	+	138.651i	−0.548029	+	0.548029i
$254$	−31.3516	−	12.8781i	−0.123432	−	0.0507011i
$255$	−56.1780	−	190.277i	−0.220306	−	0.746186i
$256$	−255.929	+	6.03922i	−0.999722	+	0.0235907i
$257$	16.3199	−	16.3199i	0.0635014	−	0.0635014i	−0.674643	−	0.738144i	$-0.735702\pi$
$257$	16.3199	−	16.3199i	0.0635014	−	0.0635014i	0.738144	+	0.674643i	$0.235702\pi$
$258$	0.401479	−	75.0676i	0.00155612	−	0.290960i
$259$	−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	$-0.855736\pi$
$263$	−121.290	+	121.290i	−0.461180	+	0.461180i	0.437862	+	0.899042i	$0.355736\pi$
$264$	286.791	−	0.157746i	1.08633	−	0.000597521i
$265$	102.984	+	10.0536i	0.388617	+	0.0379382i
$266$	18.5042	+	7.60085i	0.0695648	+	0.0285746i
$267$	145.823	−	58.9892i	0.546154	−	0.220933i
$268$	2.19365	+	371.913i	0.00818526	+	1.38773i
$269$	−174.671			−0.649336			−0.324668	−	0.945828i	$-0.605253\pi$
$269$	−174.671			−0.649336			−0.324668	+	0.945828i	$0.605253\pi$
$270$	212.277	−	166.848i	0.786213	−	0.617956i
$271$		−	306.881i		−	1.13240i	−0.824268	−	0.566200i	$-0.808413\pi$
$271$		−	306.881i		−	1.13240i	0.824268	−	0.566200i	$-0.191587\pi$
$272$	−151.395	−	147.865i	−0.556600	−	0.543621i
$273$	−45.1563	−	111.628i	−0.165408	−	0.408893i
$274$	−406.796	−	167.096i	−1.48466	−	0.609841i
$275$	−57.7775	+	293.100i	−0.210100	+	1.06582i
$276$	74.9173	+	182.101i	0.271439	+	0.659786i
$277$	28.5949	+	28.5949i	0.103231	+	0.103231i	0.756836	−	0.653605i	$-0.226744\pi$
$277$	28.5949	+	28.5949i	0.103231	+	0.103231i	−0.653605	+	0.756836i	$0.726744\pi$
$278$	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	$-0.0239928\pi$
$282$	−0.680754	+	127.286i	−0.00241402	+	0.451368i
$283$	341.834	+	341.834i	1.20789	+	1.20789i	0.971708	+	0.236185i	$0.0758971\pi$
$283$	341.834	+	341.834i	1.20789	+	1.20789i	0.236185	+	0.971708i	$0.424103\pi$
$284$	−40.1493	+	40.6257i	−0.141371	+	0.143048i
$285$	−10.6711	+	19.6120i	−0.0374426	+	0.0688141i
$286$	132.049	+	54.2407i	0.461709	+	0.189653i
$287$	−128.608	−	128.608i	−0.448111	−	0.448111i
$288$	110.705	−	265.873i	0.384391	−	0.923170i
$289$			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	$-0.458982\pi$
$293$	−252.918	−	252.918i	−0.863203	−	0.863203i	−0.991709	+	0.128506i	$0.958982\pi$
$294$	−16.3990	+	16.2245i	−0.0557789	+	0.0551854i
$295$	−195.998	−	238.406i	−0.664400	−	0.808156i
$296$	−217.421	−	512.039i	−0.734529	−	1.72986i
$297$	−130.850	+	294.915i	−0.440571	+	0.992979i
$298$	−18.7264	−	44.8351i	−0.0628403	−	0.150453i
$299$			98.0148i			0.327809i
$300$	249.328	+	166.841i	0.831092	+	0.556135i
$301$	84.0739			0.279315
$302$	222.872	−	93.0877i	0.737987	−	0.308237i
$303$	−16.8825	−	41.7340i	−0.0557177	−	0.137736i
$304$	0.280934	+	23.8140i	0.000924125	+	0.0783357i
$305$	−326.756	+	268.632i	−1.07133	+	0.880761i
$306$	221.177	−	88.0982i	0.722800	−	0.287903i
$307$	−281.593	+	281.593i	−0.917240	+	0.917240i	−0.996828	−	0.0795878i	$-0.974640\pi$
$307$	−281.593	+	281.593i	−0.917240	+	0.917240i	0.0795878	+	0.996828i	$0.474640\pi$
$308$	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	$-0.328771\pi$
$311$	318.688			1.02472			0.512360	+	0.858771i	$0.328771\pi$
$312$	101.313	−	101.424i	0.324720	−	0.325077i
$313$	−165.571	+	165.571i	−0.528979	+	0.528979i	−0.920268	−	0.391289i	$-0.872029\pi$
$313$	−165.571	+	165.571i	−0.528979	+	0.528979i	0.391289	+	0.920268i	$0.372029\pi$
$314$	82.8859	−	201.785i	0.263968	−	0.642629i
$315$	188.132	+	236.740i	0.597245	+	0.751554i
$316$	26.2253	−	26.5365i	0.0829914	−	0.0839762i
$317$	6.74356	−	6.74356i	0.0212731	−	0.0212731i	−0.696390	−	0.717663i	$-0.745212\pi$
$317$	6.74356	−	6.74356i	0.0212731	−	0.0212731i	0.717663	+	0.696390i	$0.245212\pi$
$318$	−0.664069	+	124.166i	−0.00208827	+	0.390459i
$319$	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
$324$	222.766	+	235.269i	0.687548	+	0.726139i
$325$	83.1765	+	124.020i	0.255928	+	0.381601i
$326$	193.189	−	470.319i	0.592605	−	1.44270i
$327$	−17.6580	−	43.6512i	−0.0540001	−	0.133490i
$328$	81.0894	−	200.773i	0.247224	−	0.612113i
$329$	−142.557			−0.433304
$330$	−356.601	−	36.7390i	−1.08061	−	0.111330i
$331$			278.406i			0.841105i	0.907268	+	0.420553i	$0.138164\pi$
$331$			278.406i			0.841105i	−0.907268	+	0.420553i	$0.861836\pi$
$332$	0.425407	+	72.1238i	0.00128135	+	0.217240i
$333$	625.737	+	10.3848i	1.87909	+	0.0311856i
$334$	−61.0711	+	148.677i	−0.182848	+	0.445142i
$335$	45.1704	−	462.700i	0.134837	−	1.38119i
$336$	298.426	+	122.391i	0.888173	+	0.364258i
$337$	282.964	+	282.964i	0.839656	+	0.839656i	0.988813	−	0.149157i	$-0.0476560\pi$
$337$	282.964	+	282.964i	0.839656	+	0.839656i	−0.149157	+	0.988813i	$0.547656\pi$
$338$	−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
$342$	−24.6110	−	10.5899i	−0.0719619	−	0.0309647i
$343$	−251.097	−	251.097i	−0.732060	−	0.732060i
$344$	39.1200	+	92.1300i	0.113721	+	0.267820i
$345$	−69.6959	−	236.063i	−0.202017	−	0.684241i
$346$	140.510	−	342.071i	0.406098	−	0.988644i
$347$	36.0256	+	36.0256i	0.103820	+	0.103820i	0.757109	−	0.653289i	$-0.226611\pi$
$347$	36.0256	+	36.0256i	0.103820	+	0.103820i	−0.653289	+	0.757109i	$0.726611\pi$
$348$	181.828	−	436.010i	0.522495	−	1.25290i
$349$		−	382.830i		−	1.09693i	−0.836173	−	0.548467i	$-0.815212\pi$
$349$		−	382.830i		−	1.09693i	0.836173	−	0.548467i	$-0.184788\pi$
$350$	−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	$-0.107763\pi$
$353$	215.726	+	215.726i	0.611121	+	0.611121i	−0.332117	+	0.943238i	$0.607763\pi$
$354$	263.278	−	260.477i	0.743724	−	0.735811i
$355$	55.1517	−	45.3412i	0.155357	−	0.127722i
$356$	−147.429	+	149.178i	−0.414126	+	0.419041i
$357$	99.9899	+	247.178i	0.280084	+	0.692375i
$358$	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	$0.770494\pi$
$360$	−171.886	+	316.315i	−0.477460	+	0.878654i
$361$	−358.784			−0.993863
$362$	119.788	+	286.798i	0.330905	+	0.792260i
$363$	60.6088	−	24.5178i	0.166966	−	0.0675422i
$364$	114.196	+	112.857i	0.313726	+	0.310047i
$365$	11.0546	−	113.237i	0.0302866	−	0.310239i
$366$	−357.006	−	360.846i	−0.975427	−	0.985917i
$367$	249.323	−	249.323i	0.679354	−	0.679354i	−0.280500	−	0.959854i	$-0.590500\pi$
$367$	249.323	−	249.323i	0.679354	−	0.679354i	0.959854	+	0.280500i	$0.0905004\pi$
$368$	−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
$372$	−483.470	−	201.620i	−1.29965	−	0.541989i
$373$	−108.084	+	108.084i	−0.289769	+	0.289769i	−0.836989	−	0.547220i	$-0.815686\pi$
$373$	−108.084	+	108.084i	−0.289769	+	0.289769i	0.547220	+	0.836989i	$0.315686\pi$
$374$	−292.396	−	120.105i	−0.781808	−	0.321138i
$375$	−288.514	−	239.551i	−0.769370	−	0.638803i
$376$	−66.3324	−	156.217i	−0.176416	−	0.415471i
$377$	166.274	−	166.274i	0.441045	−	0.441045i
$378$	−262.154	+	250.894i	−0.693529	+	0.663742i
$379$	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	$-0.993722\pi$
$383$	−375.372	+	375.372i	−0.980084	+	0.980084i	0.0197220	+	0.999806i	$0.493722\pi$
$384$	4.74093	+	383.971i	0.0123462	+	0.999924i
$385$	39.0097	−	399.593i	0.101324	−	1.03790i
$386$	361.607	+	148.535i	0.936806	+	0.384805i
$387$	−112.587	−	1.86852i	−0.290924	−	0.00482821i
$388$	−39.0796	+	0.230503i	−0.100721	+	0.000594079i
$389$	464.374			1.19376			0.596882	−	0.802329i	$-0.296406\pi$
$389$	464.374			1.19376			0.596882	+	0.802329i	$0.296406\pi$
$390$	−139.029	+	113.058i	−0.356485	+	0.289891i
$391$		−	217.035i		−	0.555076i
$392$	11.5188	−	28.5199i	0.0293846	−	0.0727548i
$393$	−636.351	+	257.421i	−1.61921	+	0.655014i
$394$	247.053	+	101.480i	0.627039	+	0.257564i
$395$	−36.0247	+	29.6166i	−0.0912018	+	0.0749787i
$396$	4.60135	−	430.162i	0.0116196	−	1.08627i
$397$	−125.935	−	125.935i	−0.317215	−	0.317215i	0.530481	−	0.847697i	$-0.322011\pi$
$397$	−125.935	−	125.935i	−0.317215	−	0.317215i	−0.847697	+	0.530481i	$0.822011\pi$
$398$	−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	$0.781619\pi$
$402$	557.871	+	2.98363i	1.38774	+	0.00742196i
$403$	−184.373	−	184.373i	−0.457501	−	0.457501i
$404$	42.6943	+	42.1936i	0.105679	+	0.104440i
$405$	−246.675	−	321.211i	−0.609075	−	0.793113i
$406$	489.397	+	201.026i	1.20541	+	0.495138i
$407$	−587.555	−	587.555i	−1.44362	−	1.44362i
$408$	−224.337	+	224.584i	−0.549846	+	0.550451i
$409$		−	583.921i		−	1.42768i	−0.700309	−	0.713840i	$-0.746954\pi$
$409$		−	583.921i		−	1.42768i	0.700309	−	0.713840i	$-0.253046\pi$
$410$	−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
$414$	274.398	−	109.297i	0.662796	−	0.264002i
$415$	8.75973	−	89.7297i	0.0211078	−	0.216216i
$416$	−70.5351	+	177.652i	−0.169556	+	0.427047i
$417$	612.358	−	247.715i	1.46848	−	0.594040i
$418$	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	$-0.110016\pi$
$420$	−355.285	−	190.608i	−0.845917	−	0.453828i
$421$	−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
$423$	190.905	+	3.16828i	0.451312	+	0.00749003i
$424$	−64.7066	−	152.388i	−0.152610	−	0.359406i
$425$	−184.178	−	274.619i	−0.433361	−	0.646163i
$426$	60.2575	+	60.9055i	0.141449	+	0.142971i
$427$	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	$-0.0536730\pi$
$431$	849.775			1.97164			0.985818	+	0.167821i	$0.0536730\pi$
$432$	−396.917	−	170.532i	−0.918789	−	0.394749i
$433$	153.887	−	153.887i	0.355398	−	0.355398i	−0.506715	−	0.862113i	$-0.669141\pi$
$433$	153.887	−	153.887i	0.355398	−	0.355398i	0.862113	+	0.506715i	$0.169141\pi$
$434$	222.907	−	542.667i	0.513612	−	1.25039i
$435$	−282.228	+	518.695i	−0.648801	+	1.19240i
$436$	44.6556	+	44.1319i	0.102421	+	0.101220i
$437$	−17.2708	+	17.2708i	−0.0395214	+	0.0395214i
$438$	136.529	+	0.730188i	0.311709	+	0.00166710i
$439$	−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	0.260398	−	0.965501i	$-0.416146\pi$
$443$	543.074	−	543.074i	1.22590	−	1.22590i	0.965501	−	0.260398i	$-0.0838539\pi$
$444$	−771.678	+	317.473i	−1.73801	+	0.715028i
$445$	202.518	−	166.494i	0.455096	−	0.374143i
$446$	−186.257	+	453.441i	−0.417616	+	1.01668i
$447$	−67.5643	+	27.3315i	−0.151150	+	0.0611443i
$448$	−429.998	+	7.60946i	−0.959816	+	0.0169854i
$449$	36.3462			0.0809493			0.0404746	−	0.999181i	$-0.487113\pi$
$449$	36.3462			0.0809493			0.0404746	+	0.999181i	$0.487113\pi$
$450$	254.451	−	371.153i	0.565447	−	0.824785i
$451$		−	323.432i		−	0.717144i
$452$	188.501	−	1.11183i	0.417037	−	0.00245981i
$453$	−135.863	−	335.857i	−0.299918	−	0.741407i
$454$	−206.624	+	503.024i	−0.455118	+	1.10798i
$455$	−127.451	−	155.028i	−0.280112	−	0.340720i
$456$	35.7235	−	0.0196493i	0.0783411	−	4.30905e-5i
$457$	465.155	+	465.155i	1.01784	+	1.01784i	0.999838	+	0.0180061i	$0.00573181\pi$
$457$	465.155	+	465.155i	1.01784	+	1.01784i	0.0180061	+	0.999838i	$0.494268\pi$
$458$	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	$-0.0240843\pi$
$462$	481.785	+	2.57670i	1.04282	+	0.00557727i
$463$	453.386	+	453.386i	0.979236	+	0.979236i	0.999789	−	0.0205531i	$-0.00654273\pi$
$463$	453.386	+	453.386i	0.979236	+	0.979236i	−0.0205531	+	0.999789i	$0.506543\pi$
$464$	7.43010	+	629.830i	0.0160131	+	1.35739i
$465$	575.155	+	312.949i	1.23689	+	0.673008i
$466$	−159.889	+	389.249i	−0.343109	+	0.835298i
$467$	434.371	+	434.371i	0.930130	+	0.930130i	0.997714	−	0.0675833i	$-0.0215288\pi$
$467$	434.371	+	434.371i	0.930130	+	0.930130i	−0.0675833	+	0.997714i	$0.521529\pi$
$468$	−150.418	−	153.670i	−0.321405	−	0.328355i
$469$			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
$474$	−39.3598	−	39.7831i	−0.0830376	−	0.0839305i
$475$	−7.19695	+	36.5094i	−0.0151515	+	0.0768620i
$476$	−252.866	−	249.900i	−0.531230	−	0.525000i
$477$	186.226	+	3.09063i	0.390411	+	0.00647930i
$478$	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	$0.896149\pi$
$480$	43.5561	−	478.020i	0.0907419	−	0.995874i
$481$	−415.351			−0.863516
$482$	129.446	+	309.921i	0.268559	+	0.642990i
$483$	124.050	+	306.656i	0.256832	+	0.634898i
$484$	−61.2763	+	62.0034i	−0.126604	+	0.128106i
$485$	48.6192	+	4.74637i	0.100246	+	0.00978634i
$486$	356.639	−	330.158i	0.733825	−	0.679338i
$487$	−250.434	+	250.434i	−0.514237	+	0.514237i	−0.915822	−	0.401585i	$-0.868460\pi$
$487$	−250.434	+	250.434i	−0.514237	+	0.514237i	0.401585	+	0.915822i	$0.368460\pi$
$488$	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	$-0.596020\pi$
$491$	−291.754			−0.594203			−0.297102	+	0.954846i	$0.596020\pi$
$492$	−299.773	−	125.013i	−0.609294	−	0.254092i
$493$	−368.182	+	368.182i	−0.746819	+	0.746819i
$494$	16.4484	+	6.75638i	0.0332963	+	0.0136769i
$495$	−61.1206	+	534.248i	−0.123476	+	1.07929i
$496$	698.386	−	8.23886i	1.40804	−	0.0166106i
$497$	−67.8498	+	67.8498i	−0.136519	+	0.136519i
$498$	108.186	+	0.578605i	0.217241	+	0.00116186i
$499$	−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	$-0.882712\pi$
$503$	−288.062	+	288.062i	−0.572688	+	0.572688i	0.360191	+	0.932879i	$0.382712\pi$
$504$	188.608	−	445.546i	0.374223	−	0.884021i
$505$	−47.6498	−	57.9598i	−0.0943561	−	0.114772i
$506$	−362.755	−	149.006i	−0.716906	−	0.294478i
$507$	149.988	+	370.775i	0.295834	+	0.731311i
$508$	−0.399821	−	67.7859i	−0.000787049	−	0.133437i
$509$	−808.790			−1.58898			−0.794489	−	0.607278i	$-0.792261\pi$
$509$	−808.790			−1.58898			−0.794489	+	0.607278i	$0.792261\pi$
$510$	307.853	−	250.344i	0.603633	−	0.490871i
$511$			152.909i			0.299235i
$512$	−208.418	−	467.660i	−0.407067	−	0.913398i
$513$	−16.2990	+	36.7355i	−0.0317720	+	0.0716091i
$514$	42.6977	+	17.5386i	0.0830695	+	0.0341219i
$515$	70.6699	+	6.89904i	0.137223	+	0.0133962i
$516$	138.846	−	57.1221i	0.269082	−	0.110702i
$517$	−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	$0.967572\pi$
$522$	−650.907	−	280.080i	−1.24695	−	0.536552i
$523$	−229.588	−	229.588i	−0.438982	−	0.438982i	0.452687	−	0.891669i	$-0.350465\pi$
$523$	−229.588	−	229.588i	−0.438982	−	0.438982i	−0.891669	+	0.452687i	$0.850465\pi$
$524$	643.359	−	650.994i	1.22778	−	1.24235i
$525$	417.195	+	282.748i	0.794657	+	0.538568i
$526$	−317.332	−	130.348i	−0.603294	−	0.247810i
$527$	408.258	+	408.258i	0.774684	+	0.774684i
$528$	221.353	+	529.149i	0.419229	+	1.00218i
$529$			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
$534$	221.267	+	223.646i	0.414357	+	0.418813i
$535$	−108.398	−	10.5822i	−0.202614	−	0.0197798i
$536$	−684.672	+	290.724i	−1.27737	+	0.542395i
$537$	−240.675	−	594.955i	−0.448184	−	1.10792i
$538$	−134.639	−	322.355i	−0.250258	−	0.599173i
$539$		−	45.9436i		−	0.0852385i
$540$	471.543	+	263.148i	0.873228	+	0.487311i
$541$	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
$543$	432.190	−	174.832i	0.795931	−	0.321975i
$544$	156.186	−	393.375i	0.287107	−	0.723116i
$545$	−49.8388	−	60.6224i	−0.0914473	−	0.111234i
$546$	171.201	−	169.380i	0.313555	−	0.310219i
$547$	559.528	−	559.528i	1.02290	−	1.02290i	0.0231709	−	0.999732i	$-0.492624\pi$
$547$	559.528	−	559.528i	1.02290	−	1.02290i	0.999732	−	0.0231709i	$-0.00737620\pi$
$548$	−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
$552$	−278.319	+	278.625i	−0.504201	+	0.504756i
$553$	44.3191	−	44.3191i	0.0801430	−	0.0801430i
$554$	−30.7304	+	74.8131i	−0.0554701	+	0.135042i
$555$	1000.35	−	295.346i	1.80243	−	0.532155i
$556$	−619.101	+	626.448i	−1.11349	+	1.12671i
$557$	−616.817	+	616.817i	−1.10739	+	1.10739i	−0.113899	+	0.993492i	$0.536334\pi$
$557$	−616.817	+	616.817i	−1.10739	+	1.10739i	−0.993492	+	0.113899i	$0.963666\pi$
$558$	−310.567	+	721.758i	−0.556571	+	1.29347i
$559$	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	$-0.818858\pi$
$563$	−170.898	+	170.898i	−0.303550	+	0.303550i	0.538851	+	0.842401i	$0.318858\pi$
$564$	−235.430	+	96.8571i	−0.417428	+	0.171732i
$565$	−234.515	−	22.8942i	−0.415071	−	0.0405207i
$566$	−367.362	+	894.342i	−0.649050	+	1.58011i
$567$	371.895	+	397.438i	0.655900	+	0.700949i
$568$	−105.922	−	42.7805i	−0.186483	−	0.0753177i
$569$	609.836			1.07177			0.535884	−	0.844291i	$-0.319978\pi$
$569$	609.836			1.07177			0.535884	+	0.844291i	$0.319978\pi$
$570$	−44.4193	−	4.57632i	−0.0779286	−	0.00802864i
$571$			478.800i			0.838529i	0.907864	+	0.419265i	$0.137712\pi$
$571$			478.800i			0.838529i	−0.907864	+	0.419265i	$0.862288\pi$
$572$	1.68399	+	285.504i	0.00294404	+	0.499134i
$573$	−285.271	+	115.399i	−0.497855	+	0.201395i
$574$	138.212	−	336.478i	0.240788	−	0.586198i
$575$	−228.496	−	340.700i	−0.397385	−	0.592521i
$576$	576.000	−	0.633642i	0.999999	−	0.00110007i
$577$	−162.684	−	162.684i	−0.281947	−	0.281947i	0.551938	−	0.833885i	$-0.313889\pi$
$577$	−162.684	−	162.684i	−0.281947	−	0.281947i	−0.833885	+	0.551938i	$0.813889\pi$
$578$	−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
$582$	−0.313511	+	58.6195i	−0.000538679	+	0.100721i
$583$	−174.862	−	174.862i	−0.299935	−	0.299935i
$584$	−167.561	+	71.1493i	−0.286919	+	0.121831i
$585$	167.230	+	210.438i	0.285864	+	0.359722i
$586$	271.807	−	661.712i	0.463834	−	1.12920i
$587$	−785.786	−	785.786i	−1.33865	−	1.33865i	−0.897372	−	0.441275i	$-0.854526\pi$
$587$	−785.786	−	785.786i	−1.33865	−	1.33865i	−0.441275	−	0.897372i	$-0.645474\pi$
$588$	−42.5828	−	17.7582i	−0.0724197	−	0.0302010i
$589$		−	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	−0.995466	−	0.0951217i	$-0.969676\pi$
$593$	−646.718	−	646.718i	−1.09059	−	1.09059i	−0.0951217	−	0.995466i	$-0.530324\pi$
$594$	−645.124	−	14.1581i	−1.08607	−	0.0238352i
$595$	282.216	+	343.279i	0.474312	+	0.576939i
$596$	68.3083	−	69.1189i	0.114611	−	0.115971i
$597$	−515.278	+	208.443i	−0.863112	+	0.349151i
$598$	−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	$0.919336\pi$
$600$	−115.718	+	588.735i	−0.192864	+	0.981225i
$601$	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
$603$	13.8860	−	836.703i	0.0230282	−	1.38757i
$604$	343.585	+	339.556i	0.568850	+	0.562179i
$605$	84.1730	−	69.2002i	0.139129	−	0.114380i
$606$	64.0066	−	63.3256i	0.105621	−	0.104498i
$607$	−424.929	+	424.929i	−0.700047	+	0.700047i	−0.964421	−	0.264373i	$-0.914835\pi$
$607$	−424.929	+	424.929i	−0.700047	+	0.700047i	0.264373	+	0.964421i	$0.414835\pi$
$608$	−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
$612$	333.071	+	340.273i	0.544233	+	0.556002i
$613$	714.397	−	714.397i	1.16541	−	1.16541i	0.182138	−	0.983273i	$-0.441698\pi$
$613$	714.397	−	714.397i	1.16541	−	1.16541i	0.983273	−	0.182138i	$-0.0583017\pi$
$614$	−736.733	−	302.622i	−1.19989	−	0.492870i
$615$	356.622	+	194.042i	0.579873	+	0.315516i
$616$	−591.292	+	251.073i	−0.959889	+	0.407586i
$617$	464.917	−	464.917i	0.753513	−	0.753513i	−0.221620	−	0.975133i	$-0.571135\pi$
$617$	464.917	−	464.917i	0.753513	−	0.753513i	0.975133	+	0.221620i	$0.0711345\pi$
$618$	−0.455701	+	85.2058i	−0.000737380	+	0.137873i
$619$	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
$624$	265.271	+	108.793i	0.425113	+	0.174347i
$625$	−578.244	−	237.190i	−0.925190	−	0.379504i
$626$	−433.183	−	177.936i	−0.691986	−	0.284242i
$627$	49.4663	−	20.0104i	0.0788936	−	0.0319145i
$628$	436.283	−	2.57333i	0.694718	−	0.00409765i
$629$	919.715			1.46219
$630$	−291.887	+	529.679i	−0.463312	+	0.840760i
$631$			736.830i			1.16772i	0.811855	+	0.583859i	$0.198458\pi$
$631$			736.830i			1.16772i	−0.811855	+	0.583859i	$0.801542\pi$
$632$	69.1877	+	27.9439i	0.109474	+	0.0442151i
$633$	304.711	+	753.254i	0.481375	+	1.18997i
$634$	17.6432	+	7.24718i	0.0278284	+	0.0114309i
$635$	−8.23287	+	84.3329i	−0.0129652	+	0.132808i
$636$	−229.659	+	94.4831i	−0.361100	+	0.148558i
$637$	−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	$-0.0925895\pi$
$642$	0.698985	−	130.694i	0.00108876	−	0.203574i
$643$	−376.586	−	376.586i	−0.585670	−	0.585670i	0.350786	−	0.936456i	$-0.385914\pi$
$643$	−376.586	−	376.586i	−0.585670	−	0.585670i	−0.936456	+	0.350786i	$0.885914\pi$
$644$	−313.712	−	310.033i	−0.487130	−	0.481417i
$645$	−179.991	+	53.1410i	−0.279055	+	0.0823891i
$646$	−36.4218	−	14.9607i	−0.0563805	−	0.0231590i
$647$	−311.254	−	311.254i	−0.481073	−	0.481073i	0.424402	−	0.905474i	$-0.360485\pi$
$647$	−311.254	−	311.254i	−0.481073	−	0.481073i	−0.905474	+	0.424402i	$0.860485\pi$
$648$	−262.477	+	592.461i	−0.405057	+	0.914292i
$649$			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	$-0.233526\pi$
$653$	47.7734	+	47.7734i	0.0731598	+	0.0731598i	−0.669580	+	0.742740i	$0.733526\pi$
$654$	66.9470	−	66.2347i	0.102365	−	0.101276i
$655$	−883.759	+	726.555i	−1.34925	+	1.10924i
$656$	433.030	−	5.10846i	0.660107	−	0.00778728i
$657$	3.39835	−	204.768i	0.00517253	−	0.311671i
$658$	−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	$0.883474\pi$
$660$	−207.071	−	686.424i	−0.313744	−	1.04004i
$661$	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
$663$	88.8809	+	219.716i	0.134059	+	0.331397i
$664$	−132.776	+	56.3790i	−0.199964	+	0.0849082i
$665$	4.85917	−	49.7746i	0.00730702	−	0.0748490i
$666$	463.161	+	1162.80i	0.695437	+	1.74594i
$667$	−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
$672$	4.15973	+	645.084i	0.00619007	+	0.959946i
$673$	561.901	−	561.901i	0.834920	−	0.834920i	−0.153265	−	0.988185i	$-0.548979\pi$
$673$	561.901	−	561.901i	0.834920	−	0.834920i	0.988185	+	0.153265i	$0.0489789\pi$
$674$	−304.096	+	740.321i	−0.451181	+	1.09840i
$675$	−552.402	−	387.914i	−0.818374	−	0.574687i
$676$	−379.306	−	374.858i	−0.561104	−	0.554524i
$677$	429.992	−	429.992i	0.635143	−	0.635143i	−0.314210	−	0.949353i	$-0.601740\pi$
$677$	429.992	−	429.992i	0.635143	−	0.635143i	0.949353	+	0.314210i	$0.101740\pi$
$678$	1.51222	−	282.752i	0.00223042	−	0.417038i
$679$	−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	$-0.875586\pi$
$683$	−371.280	+	371.280i	−0.543602	+	0.543602i	0.380981	+	0.924583i	$0.375586\pi$
$684$	0.573158	−	53.5823i	0.000837950	−	0.0783366i
$685$	−106.824	+	1094.24i	−0.155947	+	1.59743i
$686$	269.849	−	656.946i	0.393366	−	0.957647i
$687$	−84.0008	−	207.653i	−0.122272	−	0.302260i
$688$	−139.871	+	143.211i	−0.203301	+	0.208155i
$689$	−123.613			−0.179409
$690$	381.930	−	310.584i	0.553522	−	0.450121i
$691$		−	112.536i		−	0.162860i	−0.996679	−	0.0814301i	$-0.974051\pi$
$691$		−	112.536i		−	0.162860i	0.996679	−	0.0814301i	$-0.0259487\pi$
$692$	739.597	−	4.36236i	1.06878	−	0.00630398i
$693$	11.9922	−	722.588i	0.0173047	−	1.04270i
$694$	−38.7160	+	94.2540i	−0.0557868	+	0.135813i
$695$	850.437	−	699.160i	1.22365	−	1.00599i
$696$	944.810	−	0.519680i	1.35749	−	0.000746667i
$697$	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	$-0.122370\pi$
$702$	−233.028	+	223.020i	−0.331949	+	0.317692i
$703$	−73.1876	−	73.1876i	−0.104108	−	0.104108i
$704$	−550.262	−	531.125i	−0.781622	−	0.754439i
$705$	305.195	−	90.1066i	0.432901	−	0.127811i
$706$	−231.836	+	564.405i	−0.328380	+	0.799440i
$707$	71.3046	+	71.3046i	0.100855	+	0.100855i
$708$	683.647	+	285.099i	0.965603	+	0.402683i
$709$		−	638.797i		−	0.900984i	−0.892781	−	0.450492i	$-0.851249\pi$
$709$		−	638.797i		−	0.900984i	0.892781	−	0.450492i	$-0.148751\pi$
$710$	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
$714$	−379.092	+	375.059i	−0.530941	+	0.525292i
$715$	34.6757	−	355.198i	0.0484975	−	0.496781i
$716$	608.645	+	601.507i	0.850063	+	0.840094i
$717$	−240.990	−	595.734i	−0.336109	−	0.830871i
$718$	−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	$-0.0699746\pi$
$720$	−716.249	−	73.3939i	−0.994791	−	0.101936i
$721$	−95.4285			−0.132356
$722$	−276.556	−	662.134i	−0.383041	−	0.917084i
$723$	467.036	−	188.928i	0.645969	−	0.261311i
$724$	−436.950	+	442.135i	−0.603522	+	0.610684i
$725$	−190.344	+	965.595i	−0.262543	+	1.33186i
$726$	91.9656	+	92.9546i	0.126674	+	0.128037i
$727$	−318.387	+	318.387i	−0.437946	+	0.437946i	−0.891320	−	0.453374i	$-0.850220\pi$
$727$	−318.387	+	318.387i	−0.437946	+	0.437946i	0.453374	+	0.891320i	$0.350220\pi$
$728$	−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
$732$	390.753	−	936.997i	0.533816	−	1.28005i
$733$	−120.156	+	120.156i	−0.163924	+	0.163924i	−0.784303	−	0.620379i	$-0.786979\pi$
$733$	−120.156	+	120.156i	−0.163924	+	0.163924i	0.620379	+	0.784303i	$0.286979\pi$
$734$	652.305	+	267.942i	0.888699	+	0.365044i
$735$	50.6582	+	27.5637i	0.0689227	+	0.0375017i
$736$	193.769	−	488.032i	0.263273	−	0.663086i
$737$	−785.647	+	785.647i	−1.06601	+	1.06601i
$738$	−192.565	+	447.522i	−0.260928	+	0.606398i
$739$	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	$-0.707625\pi$
$743$	139.469	−	139.469i	0.187710	−	0.187710i	0.794705	+	0.606995i	$0.207625\pi$
$744$	−0.576247	−	1047.65i	−0.000774526	−	1.40813i
$745$	−93.8327	+	77.1416i	−0.125950	+	0.103546i
$746$	−282.780	−	116.156i	−0.379062	−	0.155705i
$747$	2.69287	−	162.259i	0.00360491	−	0.217214i
$748$	−3.72887	−	632.194i	−0.00498512	−	0.845180i
$749$	146.375			0.195427
$750$	219.700	−	717.100i	0.292934	−	0.956133i
$751$		−	387.240i		−	0.515633i	−0.966194	−	0.257816i	$-0.916997\pi$
$751$		−	387.240i		−	0.515633i	0.966194	−	0.257816i	$-0.0830029\pi$
$752$	237.168	−	242.830i	0.315382	−	0.322912i
$753$	−463.908	+	187.663i	−0.616079	+	0.249220i
$754$	435.024	+	178.692i	0.576955	+	0.236992i
$755$	−383.466	−	466.436i	−0.507901	−	0.617796i
$756$	−665.096	−	290.411i	−0.879756	−	0.384141i
$757$	−765.761	−	765.761i	−1.01157	−	1.01157i	−0.999932	−	0.0116408i	$-0.996295\pi$
$757$	−765.761	−	765.761i	−1.01157	−	1.01157i	−0.0116408	−	0.999932i	$-0.503705\pi$
$758$	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	$-0.269315\pi$
$762$	−101.679	−	0.543804i	−0.133437	−	0.000713654i
$763$	74.5802	+	74.5802i	0.0977460	+	0.0977460i
$764$	288.412	−	291.835i	0.377503	−	0.381983i
$765$	−370.300	−	465.973i	−0.484052	−	0.609115i
$766$	−982.088	−	403.405i	−1.28210	−	0.526639i
$767$	260.711	+	260.711i	0.339910	+	0.339910i
$768$	−704.961	+	304.719i	−0.917918	+	0.396769i
$769$			1312.74i			1.70708i	0.521031	+	0.853538i	$0.325548\pi$
$769$			1312.74i			1.70708i	−0.521031	+	0.853538i	$0.674452\pi$
$770$	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	$-0.150587\pi$
$773$	335.897	+	335.897i	0.434537	+	0.434537i	−0.455632	+	0.890168i	$0.650587\pi$
$774$	−83.3355	−	209.220i	−0.107669	−	0.270310i
$775$	1070.70	+	211.062i	1.38155	+	0.272339i
$776$	−30.5484	−	71.9434i	−0.0393665	−	0.0927106i
$777$	−1299.50	+	525.680i	−1.67245	+	0.676550i
$778$	357.946	+	857.000i	0.460084	+	1.10154i
$779$		−	40.2877i		−	0.0517171i
$780$	−315.813	−	169.431i	−0.404888	−	0.217219i
$781$	−170.633			−0.218481
$782$	400.536	−	167.293i	0.512195	−	0.213930i
$783$	−431.074	+	971.574i	−0.550541	+	1.24084i
$784$	61.5121	−	0.725658i	0.0784593	−	0.000925584i
$785$	−542.783	−	52.9884i	−0.691443	−	0.0675011i
$786$	−965.576	−	975.960i	−1.22847	−	1.24168i
$787$	168.467	−	168.467i	0.214063	−	0.214063i	−0.591928	−	0.805991i	$-0.701633\pi$
$787$	168.467	−	168.467i	0.214063	−	0.214063i	0.805991	+	0.591928i	$0.201633\pi$
$788$	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
$792$	797.407	−	323.082i	1.00683	−	0.407932i
$793$	357.327	−	357.327i	0.450602	−	0.450602i
$794$	135.339	−	329.483i	0.170453	−	0.414966i
$795$	297.715	−	87.8981i	0.374484	−	0.110564i
$796$	520.952	−	527.134i	0.654463	−	0.662229i
$797$	−639.400	+	639.400i	−0.802258	+	0.802258i	−0.983448	−	0.181190i	$-0.942005\pi$
$797$	−639.400	+	639.400i	−0.802258	+	0.802258i	0.181190	+	0.983448i	$0.442005\pi$
$798$	60.0126	+	0.320962i	0.0752037	+	0.000402208i
$799$	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
$804$	424.508	+	1031.85i	0.527995	+	1.28339i
$805$	350.124	+	425.881i	0.434937	+	0.529044i
$806$	198.142	−	482.376i	0.245834	−	0.598482i
$807$	−485.773	+	196.508i	−0.601949	+	0.243504i
$808$	−44.9587	+	111.315i	−0.0556420	+	0.137767i
$809$	−857.503			−1.05995			−0.529977	−	0.848012i	$-0.677800\pi$
$809$	−857.503			−1.05995			−0.529977	+	0.848012i	$0.677800\pi$
$810$	402.652	−	702.831i	0.497101	−	0.867693i
$811$		−	1573.57i		−	1.94028i	−0.242547	−	0.970140i	$-0.577983\pi$
$811$		−	1573.57i		−	1.94028i	0.242547	−	0.970140i	$-0.422017\pi$
$812$	6.24117	+	1058.13i	0.00768617	+	1.30312i
$813$	−345.245	−	853.456i	−0.424656	−	1.04976i
$814$	631.434	−	1537.22i	0.775717	−	1.88848i
$815$	−1265.11	−	123.505i	−1.55228	−	0.151539i
$816$	−587.391	−	240.901i	−0.719842	−	0.295221i
$817$	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	$0.781531\pi$
$822$	−1319.31	−	7.05600i	−1.60500	−	0.00858394i
$823$	−309.894	−	309.894i	−0.376542	−	0.376542i	0.493311	−	0.869853i	$-0.335786\pi$
$823$	−309.894	−	309.894i	−0.376542	−	0.376542i	−0.869853	+	0.493311i	$0.835786\pi$
$824$	−44.4033	−	104.573i	−0.0538875	−	0.126908i
$825$	169.058	+	880.132i	0.204919	+	1.06683i
$826$	−315.201	+	767.355i	−0.381599	+	0.929001i
$827$	527.373	+	527.373i	0.637694	+	0.637694i	0.949986	−	0.312292i	$-0.101097\pi$
$827$	527.373	+	527.373i	0.637694	+	0.637694i	−0.312292	+	0.949986i	$0.601097\pi$
$828$	413.216	+	422.152i	0.499053	+	0.509845i
$829$		−	1067.23i		−	1.28737i	−0.765292	−	0.643683i	$-0.777406\pi$
$829$		−	1067.23i		−	1.28737i	0.765292	−	0.643683i	$-0.222594\pi$
$830$	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
$834$	929.169	+	939.161i	1.11411	+	1.12609i
$835$	399.928	+	39.0423i	0.478955	+	0.0467573i
$836$	−50.0110	+	50.6045i	−0.0598218	+	0.0605317i
$837$	1077.33	+	477.996i	1.28713	+	0.571083i
$838$	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	$0.720727\pi$
$840$	77.9069	−	802.599i	0.0927463	−	0.955475i
$841$	708.767			0.842767
$842$	−360.883	−	864.032i	−0.428602	−	1.02617i
$843$	−47.6117	−	117.698i	−0.0564789	−	0.139618i
$844$	−770.586	−	761.549i	−0.913017	−	0.902309i
$845$	423.333	+	514.929i	0.500985	+	0.609383i
$846$	141.305	+	354.756i	0.167027	+	0.419333i
$847$	−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
$852$	−65.9535	+	158.152i	−0.0774102	+	0.185624i
$853$	−547.033	+	547.033i	−0.641305	+	0.641305i	−0.950876	−	0.309572i	$-0.899814\pi$
$853$	−547.033	+	547.033i	−0.641305	+	0.641305i	0.309572	+	0.950876i	$0.399814\pi$
$854$	1051.73	+	432.010i	1.23153	+	0.505866i
$855$	−7.61337	+	66.5476i	−0.00890453	+	0.0778334i
$856$	68.1088	+	160.400i	0.0795664	+	0.187384i
$857$	29.4871	−	29.4871i	0.0344074	−	0.0344074i	−0.689694	−	0.724101i	$-0.742255\pi$
$857$	29.4871	−	29.4871i	0.0344074	−	0.0344074i	0.724101	+	0.689694i	$0.242255\pi$
$858$	428.258	+	2.29043i	0.499135	+	0.00266949i
$859$	−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	$-0.748174\pi$
$863$	7.00094	−	7.00094i	0.00811233	−	0.00811233i	0.711151	+	0.703039i	$0.248174\pi$
$864$	8.76628	−	863.956i	0.0101462	−	0.999949i
$865$	−920.138	−	89.8271i	−1.06374	−	0.103846i
$866$	402.616	+	165.380i	0.464915	+	0.190970i
$867$	128.319	+	317.210i	0.148004	+	0.365870i
$868$	1173.31	−	6.92052i	1.35174	−	0.00797295i
$869$	111.457			0.128258
$870$	−1174.79	−	121.034i	−1.35034	−	0.139119i
$871$			555.386i			0.637642i
$872$	−47.0240	+	116.429i	−0.0539267	+	0.133520i
$873$	87.9184	+	1.45911i	0.100708	+	0.00167137i
$874$	−45.1858	−	18.5606i	−0.0517000	−	0.0212364i
$875$	804.428	+	241.757i	0.919346	+	0.276294i
$876$	103.891	+	252.526i	0.118596	+	0.288271i
$877$	−43.0680	−	43.0680i	−0.0491084	−	0.0491084i	0.682126	−	0.731235i	$-0.261055\pi$
$877$	−43.0680	−	43.0680i	−0.0491084	−	0.0491084i	−0.731235	+	0.682126i	$0.761055\pi$
$878$	−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	$-0.120038\pi$
$882$	−27.3539	+	63.5706i	−0.0310135	+	0.0720755i
$883$	799.685	+	799.685i	0.905645	+	0.905645i	0.995917	−	0.0902718i	$-0.0287736\pi$
$883$	799.685	+	799.685i	0.905645	+	0.905645i	−0.0902718	+	0.995917i	$0.528774\pi$
$884$	−224.772	−	222.136i	−0.254267	−	0.251285i
$885$	−813.294	−	442.523i	−0.918976	−	0.500026i
$886$	1420.85	+	583.631i	1.60366	+	0.658726i
$887$	103.964	+	103.964i	0.117209	+	0.117209i	0.763278	−	0.646070i	$-0.223588\pi$
$887$	103.964	+	103.964i	0.117209	+	0.117209i	−0.646070	+	0.763278i	$0.723588\pi$
$888$	−1180.71	−	1179.41i	−1.32963	−	1.32817i
$889$		−	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
$894$	−102.519	−	103.622i	−0.114675	−	0.115908i
$895$	−679.290	−	826.268i	−0.758984	−	0.923205i
$896$	−345.491	−	787.692i	−0.385592	−	0.879121i
$897$	110.268	+	272.586i	0.122930	+	0.303886i
$898$	28.0161	+	67.0767i	0.0311984	+	0.0746957i
$899$		−	1718.46i		−	1.91152i
$900$	881.095	+	183.498i	0.978994	+	0.203887i
$901$	273.717			0.303792
$902$	596.891	−	249.305i	0.661742	−	0.276392i
$903$	233.815	−	94.5843i	0.258932	−	0.104745i
$904$	147.351	+	347.020i	0.162998	+	0.383872i
$905$	600.222	−	493.454i	0.663229	−	0.545253i
$906$	515.098	−	509.618i	0.568541	−	0.562492i
$907$	695.991	−	695.991i	0.767355	−	0.767355i	−0.210285	−	0.977640i	$-0.567439\pi$
$907$	695.991	−	695.991i	0.767355	−	0.767355i	0.977640	+	0.210285i	$0.0674393\pi$
$908$	−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	$-0.700753\pi$
$911$	−1074.43			−1.17939			−0.589696	+	0.807625i	$0.700753\pi$
$912$	27.5724	+	65.9124i	0.0302329	+	0.0722724i
$913$	−152.358	+	152.358i	−0.166876	+	0.166876i
$914$	−499.893	+	1216.99i	−0.546929	+	1.33150i
$915$	−606.516	+	1114.69i	−0.662859	+	1.21824i
$916$	212.431	+	209.939i	0.231911	+	0.229191i
$917$	1087.24	−	1087.24i	1.18565	−	1.18565i
$918$	515.996	−	493.834i	0.562087	−	0.537946i
$919$	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
$924$	366.611	+	891.117i	0.396765	+	0.964412i
$925$	1443.76	−	968.286i	1.56082	−	1.04680i
$926$	−487.245	+	1186.20i	−0.526183	+	1.28099i
$927$	127.793	+	2.12087i	0.137856	+	0.00228788i
$928$	−1156.62	+	499.193i	−1.24636	+	0.537923i
$929$	−1085.41			−1.16836			−0.584182	−	0.811623i	$-0.698585\pi$
$929$	−1085.41			−1.16836			−0.584182	+	0.811623i	$0.698585\pi$
$930$	−134.208	+	1302.67i	−0.144310	+	1.40072i
$931$		−	5.72287i		−	0.00614702i
$932$	−841.600	+	4.96401i	−0.903005	+	0.00532619i
$933$	886.293	−	358.528i	0.949939	−	0.384275i
$934$	−466.810	+	1136.45i	−0.499797	+	1.21675i
$935$	−76.7826	+	786.518i	−0.0821204	+	0.841195i
$936$	167.654	−	396.046i	0.179117	−	0.423126i
$937$	−302.640	−	302.640i	−0.322988	−	0.322988i	0.526924	−	0.849912i	$-0.323345\pi$
$937$	−302.640	−	302.640i	−0.322988	−	0.322988i	−0.849912	+	0.526924i	$0.823345\pi$
$938$	−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	$0.967293\pi$
$942$	3.50003	−	654.427i	0.00371553	−	0.694721i
$943$	314.050	+	314.050i	0.333033	+	0.333033i
$944$	−987.548	+	11.6501i	−1.04613	+	0.0123412i
$945$	789.544	+	446.738i	0.835496	+	0.472738i
$946$	−113.612	+	276.589i	−0.120098	+	0.292377i
$947$	−508.522	−	508.522i	−0.536982	−	0.536982i	0.385659	−	0.922641i	$-0.373974\pi$
$947$	−508.522	−	508.522i	−0.536982	−	0.536982i	−0.922641	+	0.385659i	$0.873974\pi$
$948$	43.0804	−	103.304i	0.0454434	−	0.108970i
$949$			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	$-0.293211\pi$
$953$	−182.398	−	182.398i	−0.191393	−	0.191393i	−0.796298	+	0.604905i	$0.793211\pi$
$954$	137.842	+	346.061i	0.144488	+	0.362747i
$955$	−396.182	+	325.708i	−0.414850	+	0.341056i
$956$	609.442	+	602.295i	0.637492	+	0.630015i
$957$	1308.27	−	529.231i	1.36706	−	0.553010i
$958$	−566.639	+	236.670i	−0.591481	+	0.247046i
$959$		−	1477.60i		−	1.54077i
$960$	915.756	−	288.081i	0.953913	−	0.300085i
$961$	−944.513			−0.982844
$962$	−320.158	−	766.528i	−0.332805	−	0.796807i
$963$	−196.017	−	3.25313i	−0.203549	−	0.00337812i
$964$	−472.179	+	477.782i	−0.489812	+	0.495625i
$965$	94.9573	−	972.688i	0.0984013	−	1.00797i
$966$	−470.312	+	465.308i	−0.486865	+	0.481685i
$967$	754.876	−	754.876i	0.780637	−	0.780637i	−0.199301	−	0.979938i	$-0.563867\pi$
$967$	754.876	−	754.876i	0.780637	−	0.780637i	0.979938	+	0.199301i	$0.0638673\pi$
$968$	−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	$-0.612142\pi$
$971$	−670.107			−0.690121			−0.345060	+	0.938580i	$0.612142\pi$
$972$	884.207	+	403.685i	0.909678	+	0.415313i
$973$	−1046.24	+	1046.24i	−1.07528	+	1.07528i
$974$	−655.211	−	269.136i	−0.672701	−	0.276321i
$975$	370.844	+	251.334i	0.380353	+	0.257779i
$976$	15.9675	+	1353.52i	0.0163601	+	1.38680i
$977$	1030.12	−	1030.12i	1.05437	−	1.05437i	0.0559325	−	0.998435i	$-0.482187\pi$
$977$	1030.12	−	1030.12i	1.05437	−	1.05437i	0.998435	−	0.0559325i	$-0.0178132\pi$
$978$	8.15782	−	1525.33i	0.00834133	−	1.55964i
$979$	−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	0.126017	−	0.992028i	$-0.459781\pi$
$983$	1099.04	−	1099.04i	1.11804	−	1.11804i	0.992028	−	0.126017i	$-0.0402193\pi$
$984$	−0.357299	−	649.591i	−0.000363109	−	0.660153i
$985$	64.8756	−	664.549i	0.0658636	−	0.674669i
$986$	−963.277	−	395.678i	−0.976954	−	0.401296i
$987$	−396.461	+	160.379i	−0.401683	+	0.162491i
$988$	0.209763	+	35.5633i	0.000212310	+	0.0359952i
$989$	−205.302			−0.207585
$990$	−1033.06	+	299.007i	−1.04350	+	0.302028i
$991$		−	893.875i		−	0.901993i	−0.892526	−	0.450996i	$-0.851069\pi$
$991$		−	893.875i		−	0.901993i	0.892526	−	0.450996i	$-0.148931\pi$
$992$	553.530	+	1282.52i	0.557994	+	1.29286i
$993$	313.210	+	774.266i	0.315418	+	0.779724i
$994$	−177.516	−	72.9169i	−0.178588	−	0.0733571i
$995$	−715.613	+	588.319i	−0.719209	+	0.591275i
$996$	82.3233	+	200.103i	0.0826540	+	0.200906i
$997$	465.597	+	465.597i	0.466998	+	0.466998i	0.900940	−	0.433943i	$-0.142878\pi$
$997$	465.597	+	465.597i	0.466998	+	0.466998i	−0.433943	+	0.900940i	$0.642878\pi$
$998$	−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.47.12	yes	40
3.2	odd	2	inner	60.3.l.a.47.9	yes	40
4.3	odd	2	inner	60.3.l.a.47.2	yes	40
5.2	odd	4		300.3.l.g.143.2		40
5.3	odd	4	inner	60.3.l.a.23.19	yes	40
5.4	even	2		300.3.l.g.107.9		40
12.11	even	2	inner	60.3.l.a.47.19	yes	40
15.2	even	4		300.3.l.g.143.19		40
15.8	even	4	inner	60.3.l.a.23.2	✓	40
15.14	odd	2		300.3.l.g.107.12		40
20.3	even	4	inner	60.3.l.a.23.9	yes	40
20.7	even	4		300.3.l.g.143.12		40
20.19	odd	2		300.3.l.g.107.19		40
60.23	odd	4	inner	60.3.l.a.23.12	yes	40
60.47	odd	4		300.3.l.g.143.9		40
60.59	even	2		300.3.l.g.107.2		40

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

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)

\(f(q)\)	\(=\)	\(q+(0.770813 + 1.84549i) q^{2} +(2.78107 - 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(-7.41783 - 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})\)	\(q+(0.770813 + 1.84549i) q^{2} +(2.78107 - 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) 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} +(-4.61879 + 11.0755i) q^{12} +(-4.22368 + 4.22368i) q^{13} +(-12.4316 - 5.10644i) q^{14} +(7.16915 - 13.1759i) q^{15} +(-0.188739 - 15.9989i) q^{16} +(9.35253 - 9.35253i) q^{17} +(16.5343 + 7.11458i) 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} +(-24.0000 + 0.0132009i) q^{24} +(4.83510 - 24.5280i) q^{25} +(-11.0504 - 4.53911i) q^{26} +(10.9501 - 24.6799i) q^{27} +(-0.158538 - 26.8786i) q^{28} -39.3671 q^{29} +(29.8420 + 3.07449i) q^{30} +43.6522i q^{31} +(29.3804 - 12.6805i) q^{32} +(-33.2327 + 13.4435i) q^{33} +(24.4691 + 10.0510i) q^{34} +(-3.26452 + 33.4399i) q^{35} +(-0.385062 + 35.9979i) 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} +(-40.3180 - 0.215630i) q^{42} +(-8.84693 - 8.84693i) q^{43} +(33.5987 - 33.9974i) q^{44} +(5.11486 - 44.7084i) q^{45} +(30.3570 + 12.4695i) q^{46} +(15.0010 + 15.0010i) q^{47} +(-18.5239 - 44.2817i) 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} +(53.9870 + 1.18482i) q^{54} +(-46.1533 + 37.9435i) q^{55} +(49.4821 - 21.0109i) q^{56} +(-4.13957 + 1.67456i) q^{57} +(-30.3447 - 72.6517i) q^{58} -61.7260i q^{59} +(17.3287 + 57.4432i) q^{60} -84.6009 q^{61} +(-80.5598 + 33.6477i) q^{62} +(-1.00356 + 60.4695i) q^{63} +(46.0485 + 44.4470i) q^{64} +(-2.90182 + 29.7246i) q^{65} +(-50.4261 - 50.9683i) 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} +(-66.7308 + 27.0370i) q^{72} +(16.0903 - 16.0903i) q^{73} +(-52.8413 + 128.642i) q^{74} +(-14.1476 - 73.6536i) q^{75} +(4.18516 - 4.23482i) q^{76} +(56.7797 - 56.7797i) q^{77} +(-35.8386 - 0.191673i) 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} +(-30.6797 - 74.5728i) q^{84} +(6.42553 - 65.8195i) q^{85} +(9.50762 - 23.1463i) q^{86} +(-109.483 + 44.2885i) q^{87} +(88.6403 + 35.8005i) q^{88} +52.4342 q^{89} +(86.4516 - 25.0223i) q^{90} -40.1384i q^{91} +(0.387136 + 65.6353i) q^{92} +(49.1093 + 121.400i) q^{93} +(-16.1213 + 39.2471i) q^{94} +(-5.74900 + 4.72636i) q^{95} +(67.4431 - 68.3186i) 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

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