LMFDB - Embedded newform 378.2.z.a.83.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.20
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.419652 - 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.95067 + 1.63681i) q^{5} +(0.705083 - 1.58204i) q^{6} +(1.19511 - 2.36045i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.419652 - 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.95067 + 1.63681i) q^{5} +(0.705083 - 1.58204i) q^{6} +(1.19511 - 2.36045i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +(-2.20527 + 1.27321i) q^{10} +(3.38986 - 4.03988i) q^{11} +(0.969090 - 1.43557i) q^{12} +(4.61346 - 0.813477i) q^{13} +(1.58685 - 2.11706i) q^{14} +(1.93196 + 3.96488i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.45690 - 4.25548i) q^{17} +(-2.36264 - 1.84876i) q^{18} +(3.75220 + 2.16633i) q^{19} +(-2.39285 + 0.870927i) q^{20} +(-3.46506 - 2.99889i) q^{21} +(4.03988 - 3.38986i) q^{22} +(-2.80443 + 7.70512i) q^{23} +(1.20365 - 1.24548i) q^{24} +(0.257739 - 1.46171i) q^{25} +4.68463 q^{26} +(-3.48125 + 3.85757i) q^{27} +(1.93036 - 1.80934i) q^{28} +(-6.32009 - 1.11440i) q^{29} +(1.21411 + 4.24013i) q^{30} +(-2.00923 + 5.52031i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-5.36622 - 7.39181i) q^{33} +(-1.68062 - 4.61746i) q^{34} +(1.53232 + 6.56063i) q^{35} +(-2.00572 - 2.23094i) q^{36} +(0.448119 + 0.776165i) q^{37} +(3.31901 + 2.78498i) q^{38} +(0.569046 - 8.09404i) q^{39} +(-2.50773 + 0.442181i) q^{40} +(0.918246 + 5.20763i) q^{41} +(-2.89167 - 3.55503i) q^{42} +(-3.13499 - 2.63057i) q^{43} +(4.56714 - 2.63684i) q^{44} +(7.47352 - 1.58268i) q^{45} +(-4.09981 + 7.10107i) q^{46} +(2.09624 - 0.762970i) q^{47} +(1.40164 - 1.01755i) q^{48} +(-4.14340 - 5.64200i) q^{49} +(0.507646 - 1.39475i) q^{50} +(-8.18213 + 2.34286i) q^{51} +(4.61346 + 0.813477i) q^{52} +9.42246i q^{53} +(-4.09823 + 3.19445i) q^{54} +13.4290i q^{55} +(2.21522 - 1.44665i) q^{56} +(5.21502 - 5.39625i) q^{57} +(-6.03056 - 2.19494i) q^{58} +(0.881790 - 0.739910i) q^{59} +(0.459378 + 4.38654i) q^{60} +(2.05855 + 5.65582i) q^{61} +(-2.93730 + 5.08755i) q^{62} +(-6.49359 + 4.56435i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.66784 + 9.13817i) q^{65} +(-4.00112 - 8.21135i) q^{66} +(-1.26064 - 7.14945i) q^{67} +(-0.853272 - 4.83915i) q^{68} +(11.7711 + 7.94616i) q^{69} +(0.369799 + 6.72704i) q^{70} +(7.78966 - 4.49736i) q^{71} +(-1.58785 - 2.54534i) q^{72} +(7.53439 + 4.34998i) q^{73} +(0.306531 + 0.842188i) q^{74} +(-2.34816 - 1.04653i) q^{75} +(2.78498 + 3.31901i) q^{76} +(-5.48464 - 12.8297i) q^{77} +(1.96592 - 7.87226i) q^{78} +(1.83651 - 10.4153i) q^{79} -2.54642 q^{80} +(5.02152 + 7.46889i) q^{81} +5.28797i q^{82} +(-2.18909 + 12.4150i) q^{83} +(-2.23041 - 4.00316i) q^{84} +(11.7580 + 4.27956i) q^{85} +(-2.63057 - 3.13499i) q^{86} +(-4.52493 + 10.1529i) q^{87} +(4.95564 - 1.80371i) q^{88} +(4.96625 - 8.60180i) q^{89} +(7.63481 - 0.260870i) q^{90} +(3.59344 - 11.8620i) q^{91} +(-5.27061 + 6.28127i) q^{92} +(8.43339 + 5.69301i) q^{93} +(2.19688 - 0.387370i) q^{94} +(-10.8652 + 1.91582i) q^{95} +(1.55704 - 0.758696i) q^{96} +(4.09086 - 4.87530i) q^{97} +(-3.10073 - 6.27578i) q^{98} +(-14.6735 + 5.91565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.419652	−	1.68044i	0.242286	−	0.970205i
$3$	0.419652	−	1.68044i	0.242286	−	0.970205i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−1.95067	+	1.63681i	−0.872367	+	0.732003i	−0.964595	−	0.263735i	$-0.915045\pi$
$5$	−1.95067	+	1.63681i	−0.872367	+	0.732003i	0.0922283	+	0.995738i	$0.470601\pi$
$6$	0.705083	−	1.58204i	0.287849	−	0.645866i
$7$	1.19511	−	2.36045i	0.451711	−	0.892164i
$7$	1.19511	−	2.36045i	0.451711	−	0.892164i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.64778	−	1.41040i	−0.882595	−	0.470135i
$10$	−2.20527	+	1.27321i	−0.697366	+	0.402624i
$11$	3.38986	−	4.03988i	1.02208	−	1.21807i	0.0463888	−	0.998923i	$-0.485229\pi$
$11$	3.38986	−	4.03988i	1.02208	−	1.21807i	0.975692	−	0.219145i	$-0.0703269\pi$
$12$	0.969090	−	1.43557i	0.279752	−	0.414414i
$13$	4.61346	−	0.813477i	1.27954	−	0.225618i	0.507757	−	0.861500i	$-0.330475\pi$
$13$	4.61346	−	0.813477i	1.27954	−	0.225618i	0.771786	+	0.635882i	$0.219364\pi$
$14$	1.58685	−	2.11706i	0.424102	−	0.565807i
$15$	1.93196	+	3.96488i	0.498830	+	1.02373i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.45690	−	4.25548i	−0.595886	−	1.03210i	−0.993421	−	0.114518i	$-0.963468\pi$
$17$	−2.45690	−	4.25548i	−0.595886	−	1.03210i	0.397535	−	0.917587i	$-0.369866\pi$
$18$	−2.36264	−	1.84876i	−0.556880	−	0.435757i
$19$	3.75220	+	2.16633i	0.860813	+	0.496991i	0.864285	−	0.503003i	$-0.167772\pi$
$19$	3.75220	+	2.16633i	0.860813	+	0.496991i	−0.00347113	+	0.999994i	$0.501105\pi$
$20$	−2.39285	+	0.870927i	−0.535058	+	0.194745i
$21$	−3.46506	−	2.99889i	−0.756139	−	0.654411i
$22$	4.03988	−	3.38986i	0.861305	−	0.722720i
$23$	−2.80443	+	7.70512i	−0.584765	+	1.60663i	0.195172	+	0.980769i	$0.437474\pi$
$23$	−2.80443	+	7.70512i	−0.584765	+	1.60663i	−0.779937	+	0.625859i	$0.784749\pi$
$24$	1.20365	−	1.24548i	0.245694	−	0.254233i
$25$	0.257739	−	1.46171i	0.0515478	−	0.292342i
$26$	4.68463			0.918731
$27$	−3.48125	+	3.85757i	−0.669968	+	0.742390i
$28$	1.93036	−	1.80934i	0.364804	−	0.341933i
$29$	−6.32009	−	1.11440i	−1.17361	−	0.206939i	−0.447351	−	0.894359i	$-0.647632\pi$
$29$	−6.32009	−	1.11440i	−1.17361	−	0.206939i	−0.726261	+	0.687419i	$0.758743\pi$
$30$	1.21411	+	4.24013i	0.221666	+	0.774138i
$31$	−2.00923	+	5.52031i	−0.360868	+	0.991477i	0.617855	+	0.786292i	$0.288002\pi$
$31$	−2.00923	+	5.52031i	−0.360868	+	0.991477i	−0.978723	+	0.205185i	$0.934220\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−5.36622	−	7.39181i	−0.934140	−	1.28675i
$34$	−1.68062	−	4.61746i	−0.288224	−	0.791888i
$35$	1.53232	+	6.56063i	0.259009	+	1.10895i
$36$	−2.00572	−	2.23094i	−0.334286	−	0.371824i
$37$	0.448119	+	0.776165i	0.0736703	+	0.127601i	0.900507	−	0.434841i	$-0.143195\pi$
$37$	0.448119	+	0.776165i	0.0736703	+	0.127601i	−0.826837	+	0.562442i	$0.809862\pi$
$38$	3.31901	+	2.78498i	0.538415	+	0.451784i
$39$	0.569046	−	8.09404i	0.0911203	−	1.29608i
$40$	−2.50773	+	0.442181i	−0.396508	+	0.0699150i
$41$	0.918246	+	5.20763i	0.143406	+	0.813296i	0.968633	+	0.248495i	$0.0799359\pi$
$41$	0.918246	+	5.20763i	0.143406	+	0.813296i	−0.825227	+	0.564801i	$0.808953\pi$
$42$	−2.89167	−	3.55503i	−0.446194	−	0.548553i
$43$	−3.13499	−	2.63057i	−0.478082	−	0.401158i	0.371650	−	0.928373i	$-0.378792\pi$
$43$	−3.13499	−	2.63057i	−0.478082	−	0.401158i	−0.849732	+	0.527214i	$0.823236\pi$
$44$	4.56714	−	2.63684i	0.688523	−	0.397519i
$45$	7.47352	−	1.58268i	1.11409	−	0.235932i
$46$	−4.09981	+	7.10107i	−0.604483	+	1.04700i
$47$	2.09624	−	0.762970i	0.305768	−	0.111291i	−0.184579	−	0.982818i	$-0.559092\pi$
$47$	2.09624	−	0.762970i	0.305768	−	0.111291i	0.490347	+	0.871527i	$0.336870\pi$
$48$	1.40164	−	1.01755i	0.202309	−	0.146870i
$49$	−4.14340	−	5.64200i	−0.591915	−	0.806001i
$50$	0.507646	−	1.39475i	0.0717920	−	0.197247i
$51$	−8.18213	+	2.34286i	−1.14573	+	0.328066i
$52$	4.61346	+	0.813477i	0.639772	+	0.112809i
$53$			9.42246i			1.29427i	0.762373	+	0.647137i	$0.224034\pi$
$53$			9.42246i			1.29427i	−0.762373	+	0.647137i	$0.775966\pi$
$54$	−4.09823	+	3.19445i	−0.557698	+	0.434710i
$55$			13.4290i			1.81077i
$56$	2.21522	−	1.44665i	0.296022	−	0.193316i
$57$	5.21502	−	5.39625i	0.690746	−	0.714751i
$58$	−6.03056	−	2.19494i	−0.791851	−	0.288210i
$59$	0.881790	−	0.739910i	0.114799	−	0.0963281i	−0.583581	−	0.812055i	$-0.698349\pi$
$59$	0.881790	−	0.739910i	0.114799	−	0.0963281i	0.698380	+	0.715727i	$0.253904\pi$
$60$	0.459378	+	4.38654i	0.0593054	+	0.566300i
$61$	2.05855	+	5.65582i	0.263570	+	0.724153i	0.998920	+	0.0464655i	$0.0147957\pi$
$61$	2.05855	+	5.65582i	0.263570	+	0.724153i	−0.735350	+	0.677688i	$0.762982\pi$
$62$	−2.93730	+	5.08755i	−0.373037	+	0.646119i
$63$	−6.49359	+	4.56435i	−0.818115	+	0.575054i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−7.66784	+	9.13817i	−0.951078	+	1.13345i
$66$	−4.00112	−	8.21135i	−0.492504	−	1.01075i
$67$	−1.26064	−	7.14945i	−0.154012	−	0.873444i	−0.959684	−	0.281082i	$-0.909307\pi$
$67$	−1.26064	−	7.14945i	−0.154012	−	0.873444i	0.805672	−	0.592362i	$-0.201804\pi$
$68$	−0.853272	−	4.83915i	−0.103474	−	0.586833i
$69$	11.7711	+	7.94616i	1.41708	+	0.956605i
$70$	0.369799	+	6.72704i	0.0441994	+	0.804035i
$71$	7.78966	−	4.49736i	0.924463	−	0.533739i	0.0394068	−	0.999223i	$-0.487453\pi$
$71$	7.78966	−	4.49736i	0.924463	−	0.533739i	0.885056	+	0.465484i	$0.154120\pi$
$72$	−1.58785	−	2.54534i	−0.187129	−	0.299971i
$73$	7.53439	+	4.34998i	0.881834	+	0.509127i	0.871263	−	0.490817i	$-0.163302\pi$
$73$	7.53439	+	4.34998i	0.881834	+	0.509127i	0.0105711	+	0.999944i	$0.496635\pi$
$74$	0.306531	+	0.842188i	0.0356335	+	0.0979024i
$75$	−2.34816	−	1.04653i	−0.271142	−	0.120842i
$76$	2.78498	+	3.31901i	0.319460	+	0.380717i
$77$	−5.48464	−	12.8297i	−0.625032	−	1.46208i
$78$	1.96592	−	7.87226i	0.222596	−	0.891357i
$79$	1.83651	−	10.4153i	0.206623	−	1.17182i	−0.688242	−	0.725481i	$-0.741617\pi$
$79$	1.83651	−	10.4153i	0.206623	−	1.17182i	0.894865	−	0.446337i	$-0.147272\pi$
$80$	−2.54642			−0.284698
$81$	5.02152	+	7.46889i	0.557946	+	0.829877i
$82$			5.28797i			0.583959i
$83$	−2.18909	+	12.4150i	−0.240284	+	1.36272i	0.590910	+	0.806737i	$0.298769\pi$
$83$	−2.18909	+	12.4150i	−0.240284	+	1.36272i	−0.831194	+	0.555982i	$0.812342\pi$
$84$	−2.23041	−	4.00316i	−0.243358	−	0.436780i
$85$	11.7580	+	4.27956i	1.27533	+	0.464184i
$86$	−2.63057	−	3.13499i	−0.283662	−	0.338055i
$87$	−4.52493	+	10.1529i	−0.485124	+	1.08850i
$88$	4.95564	−	1.80371i	0.528273	−	0.192276i
$89$	4.96625	−	8.60180i	0.526422	−	0.911789i	−0.473104	−	0.881006i	$-0.656867\pi$
$89$	4.96625	−	8.60180i	0.526422	−	0.911789i	0.999526	−	0.0307827i	$-0.00979998\pi$
$90$	7.63481	−	0.260870i	0.804779	−	0.0274981i
$91$	3.59344	−	11.8620i	0.376695	−	1.24348i
$92$	−5.27061	+	6.28127i	−0.549499	+	0.654867i
$93$	8.43339	+	5.69301i	0.874502	+	0.590337i
$94$	2.19688	−	0.387370i	0.226591	−	0.0399542i
$95$	−10.8652	+	1.91582i	−1.11474	+	0.196559i
$96$	1.55704	−	0.758696i	0.158915	−	0.0774341i
$97$	4.09086	−	4.87530i	0.415364	−	0.495012i	−0.517276	−	0.855818i	$-0.673054\pi$
$97$	4.09086	−	4.87530i	0.415364	−	0.495012i	0.932641	+	0.360806i	$0.117498\pi$
$98$	−3.10073	−	6.27578i	−0.313221	−	0.633950i
$99$	−14.6735	+	5.91565i	−1.47474	+	0.594545i
$100$	0.742129	−	1.28541i	0.0742129	−	0.128541i
$101$	−10.0462	+	3.65652i	−0.999636	+	0.363838i	−0.789444	−	0.613823i	$-0.789631\pi$
$101$	−10.0462	+	3.65652i	−0.999636	+	0.363838i	−0.210192	+	0.977660i	$0.567409\pi$
$102$	−8.46466	+	0.886457i	−0.838126	+	0.0877723i
$103$	−1.54935	−	1.84644i	−0.152662	−	0.181935i	0.684293	−	0.729207i	$-0.260111\pi$
$103$	−1.54935	−	1.84644i	−0.152662	−	0.181935i	−0.836955	+	0.547272i	$0.815666\pi$
$104$	4.40211	+	1.60224i	0.431662	+	0.157112i
$105$	11.6678	+	0.178206i	1.13866	+	0.0173912i
$106$	−1.63619	+	9.27931i	−0.158921	+	0.901287i
$107$			8.64382i			0.835630i	0.908532	+	0.417815i	$0.137204\pi$
$107$			8.64382i			0.835630i	−0.908532	+	0.417815i	$0.862796\pi$
$108$	−4.59068	+	2.43427i	−0.441738	+	0.234238i
$109$	−10.0711			−0.964636			−0.482318	−	0.875996i	$-0.660205\pi$
$109$	−10.0711			−0.964636			−0.482318	+	0.875996i	$0.660205\pi$
$110$	−2.33192	+	13.2250i	−0.222340	+	1.26095i
$111$	1.49236	−	0.427319i	0.141648	−	0.0405593i
$112$	2.43278	−	1.04000i	0.229876	−	0.0982709i
$113$	−0.126205	−	0.150405i	−0.0118724	−	0.0141489i	0.760076	−	0.649835i	$-0.225162\pi$
$113$	−0.126205	−	0.150405i	−0.0118724	−	0.0141489i	−0.771948	+	0.635686i	$0.780717\pi$
$114$	6.07284	−	4.40869i	0.568774	−	0.412912i
$115$	−7.14127	−	19.6205i	−0.665926	−	1.82962i
$116$	−5.55779	−	3.20879i	−0.516028	−	0.297929i
$117$	−13.3628	−	4.35293i	−1.23539	−	0.402429i
$118$	0.996878	−	0.575548i	0.0917701	−	0.0529835i
$119$	−12.9811	+	0.713596i	−1.18997	+	0.0654153i
$120$	−0.309316	+	4.39967i	−0.0282366	+	0.401633i
$121$	−2.91933	−	16.5563i	−0.265394	−	1.50512i
$122$	1.04515	+	5.92736i	0.0946237	+	0.536638i
$123$	9.13648	+	0.642334i	0.823809	+	0.0579173i
$124$	−3.77611	+	4.50020i	−0.339105	+	0.404130i
$125$	−4.47628	−	7.75314i	−0.400370	−	0.693462i
$126$	−7.18753	+	3.36741i	−0.640316	+	0.299993i
$127$	−9.42794	+	16.3297i	−0.836595	+	1.44902i	0.0561306	+	0.998423i	$0.482124\pi$
$127$	−9.42794	+	16.3297i	−0.836595	+	1.44902i	−0.892725	+	0.450601i	$0.851210\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−5.73614	+	4.16425i	−0.505039	+	0.366642i
$130$	−9.13817	+	7.66784i	−0.801471	+	0.672514i
$131$	−8.02081	−	2.91934i	−0.700781	−	0.255064i	−0.0330369	−	0.999454i	$-0.510518\pi$
$131$	−8.02081	−	2.91934i	−0.700781	−	0.255064i	−0.667744	+	0.744391i	$0.732740\pi$
$132$	−2.51445	−	8.78139i	−0.218855	−	0.764322i
$133$	9.59782	−	6.26784i	0.832236	−	0.543491i
$134$		−	7.25974i		−	0.627146i
$135$	0.476679	−	13.2230i	0.0410260	−	1.13805i
$136$		−	4.91380i		−	0.421355i
$137$	−5.88182	−	1.03712i	−0.502518	−	0.0886075i	−0.0833577	−	0.996520i	$-0.526564\pi$
$137$	−5.88182	−	1.03712i	−0.502518	−	0.0886075i	−0.419160	+	0.907912i	$0.637676\pi$
$138$	10.2125	+	9.86948i	0.869342	+	0.840146i
$139$	−0.558807	+	1.53531i	−0.0473974	+	0.130223i	−0.961133	−	0.276087i	$-0.910962\pi$
$139$	−0.558807	+	1.53531i	−0.0473974	+	0.130223i	0.913735	+	0.406310i	$0.133185\pi$
$140$	−0.803958	+	6.68906i	−0.0679468	+	0.565328i
$141$	−0.402435	−	3.84280i	−0.0338911	−	0.323622i
$142$	8.45228	−	3.07638i	0.709299	−	0.258164i
$143$	12.3526	−	21.3954i	1.03298	−	1.78917i
$144$	−1.12173	−	2.78240i	−0.0934775	−	0.231866i
$145$	14.1525	−	8.17094i	1.17530	−	0.678560i
$146$	6.66456	+	5.59223i	0.551563	+	0.462816i
$147$	−11.2199	+	4.59507i	−0.925399	+	0.378995i
$148$	0.155630	+	0.882622i	0.0127927	+	0.0725511i
$149$	20.7850	−	3.66496i	1.70278	−	0.300246i	0.764114	−	0.645081i	$-0.223176\pi$
$149$	20.7850	−	3.66496i	1.70278	−	0.300246i	0.938663	+	0.344835i	$0.112065\pi$
$150$	−2.13076	−	1.43838i	−0.173976	−	0.117443i
$151$	16.8405	+	14.1309i	1.37046	+	1.14995i	0.972594	+	0.232511i	$0.0746942\pi$
$151$	16.8405	+	14.1309i	1.37046	+	1.14995i	0.397868	+	0.917443i	$0.369750\pi$
$152$	2.16633	+	3.75220i	0.175713	+	0.304344i
$153$	0.503398	+	14.7328i	0.0406973	+	1.19108i
$154$	−3.17346	−	13.5872i	−0.255725	−	1.09489i
$155$	−5.11634	−	14.0570i	−0.410954	−	1.12909i
$156$	3.30305	−	7.41128i	0.264456	−	0.593377i
$157$	−6.33840	−	7.55381i	−0.505859	−	0.602860i	0.451318	−	0.892363i	$-0.350954\pi$
$157$	−6.33840	−	7.55381i	−0.505859	−	0.602860i	−0.957177	+	0.289504i	$0.906510\pi$
$158$	3.61721	−	9.93821i	0.287770	−	0.790641i
$159$	15.8339	+	3.95416i	1.25571	+	0.313585i
$160$	−2.50773	−	0.442181i	−0.198254	−	0.0349575i
$161$	14.8359	+	15.8282i	1.16923	+	1.24744i
$162$	3.64827	+	8.22740i	0.286635	+	0.646406i
$163$	−6.19088			−0.484907			−0.242454	−	0.970163i	$-0.577952\pi$
$163$	−6.19088			−0.484907			−0.242454	+	0.970163i	$0.577952\pi$
$164$	−0.918246	+	5.20763i	−0.0717030	+	0.406648i
$165$	22.5667	+	5.63552i	1.75682	+	0.438725i
$166$	−4.31167	+	11.8462i	−0.334651	+	0.919445i
$167$	−3.15479	+	2.64718i	−0.244125	+	0.204845i	−0.756638	−	0.653835i	$-0.773159\pi$
$167$	−3.15479	+	2.64718i	−0.244125	+	0.204845i	0.512513	+	0.858680i	$0.328715\pi$
$168$	−1.50139	−	4.32965i	−0.115835	−	0.334039i
$169$	8.40625	−	3.05962i	0.646635	−	0.235356i
$170$	10.8362	+	6.25630i	0.831101	+	0.479836i
$171$	−6.87961	−	11.0281i	−0.526097	−	0.843340i
$172$	−2.04622	−	3.54416i	−0.156023	−	0.270240i
$173$	−5.13237	−	4.30657i	−0.390207	−	0.327423i	0.426487	−	0.904494i	$-0.359751\pi$
$173$	−5.13237	−	4.30657i	−0.390207	−	0.327423i	−0.816694	+	0.577071i	$0.804195\pi$
$174$	−6.21922	+	9.21290i	−0.471478	+	0.698428i
$175$	−3.14226	−	2.35529i	−0.237532	−	0.178043i
$176$	5.19357	−	0.915766i	0.391480	−	0.0690284i
$177$	−0.873332	−	1.79230i	−0.0656436	−	0.134718i
$178$	6.38449	−	7.60874i	0.478538	−	0.570299i
$179$	−0.794596	+	0.458760i	−0.0593909	+	0.0342893i	−0.529401	−	0.848371i	$-0.677583\pi$
$179$	−0.794596	+	0.458760i	−0.0593909	+	0.0342893i	0.470011	+	0.882661i	$0.344250\pi$
$180$	7.56412	+	1.06886i	0.563796	+	0.0796684i
$181$	6.84551	+	3.95226i	0.508823	+	0.293769i	0.732350	−	0.680929i	$-0.238424\pi$
$181$	6.84551	+	3.95226i	0.508823	+	0.293769i	−0.223527	+	0.974698i	$0.571757\pi$
$182$	5.59867	−	11.0578i	0.415001	−	0.819659i
$183$	10.3682	−	1.08580i	0.766437	−	0.0802646i
$184$	−6.28127	+	5.27061i	−0.463061	+	0.388554i
$185$	−2.14456	−	0.780558i	−0.157672	−	0.0573877i
$186$	7.31669	+	7.07096i	0.536486	+	0.518468i
$187$	−25.5201	−	4.49989i	−1.86622	−	0.329065i
$188$	2.23078			0.162696
$189$	4.94509	+	12.8276i	0.359702	+	0.933067i
$190$	−11.0328			−0.800403
$191$	13.9436	+	2.45864i	1.00893	+	0.177901i	0.653598	−	0.756841i	$-0.273259\pi$
$191$	13.9436	+	2.45864i	1.00893	+	0.177901i	0.355327	+	0.934742i	$0.384370\pi$
$192$	1.66513	−	0.476792i	0.120171	−	0.0344095i
$193$	−6.23166	−	2.26814i	−0.448565	−	0.163264i	0.107853	−	0.994167i	$-0.465602\pi$
$193$	−6.23166	−	2.26814i	−0.448565	−	0.163264i	−0.556418	+	0.830903i	$0.687825\pi$
$194$	4.87530	−	4.09086i	0.350026	−	0.293707i
$195$	12.1384	+	16.7202i	0.869246	+	1.19736i
$196$	−1.96384	−	6.71888i	−0.140275	−	0.479920i
$197$	0.128455	+	0.0741633i	0.00915201	+	0.00528392i	0.504569	−	0.863371i	$-0.331651\pi$
$197$	0.128455	+	0.0741633i	0.00915201	+	0.00528392i	−0.495417	+	0.868655i	$0.664985\pi$
$198$	−15.4778	+	3.27775i	−1.09996	+	0.232940i
$199$	1.74511	−	1.00754i	0.123708	−	0.0714226i	−0.436869	−	0.899525i	$-0.643913\pi$
$199$	1.74511	−	1.00754i	0.123708	−	0.0714226i	0.560577	+	0.828102i	$0.310579\pi$
$200$	0.954063	−	1.13701i	0.0674625	−	0.0803986i
$201$	−12.5433	−	0.881847i	−0.884735	−	0.0622007i
$202$	−10.5285	+	1.85647i	−0.740785	+	0.130620i
$203$	−10.1837	+	13.5864i	−0.714757	+	0.953577i
$204$	−8.48999	−	0.596884i	−0.594419	−	0.0417902i
$205$	−10.3151	−	8.65539i	−0.720437	−	0.604519i
$206$	−1.20518	−	2.08743i	−0.0839687	−	0.145438i
$207$	18.2929	−	16.4461i	1.27144	−	1.14308i
$208$	4.05701	+	2.34231i	0.281303	+	0.162410i
$209$	21.4711	−	7.81486i	1.48519	−	0.540565i
$210$	11.4596	+	2.20159i	0.790788	+	0.151924i
$211$	−7.67430	+	6.43950i	−0.528320	+	0.443314i	−0.867521	−	0.497401i	$-0.834288\pi$
$211$	−7.67430	+	6.43950i	−0.528320	+	0.443314i	0.339201	+	0.940714i	$0.389843\pi$
$212$	−3.22267	+	8.85422i	−0.221334	+	0.608110i
$213$	−4.28862	−	14.9774i	−0.293851	−	1.02624i
$214$	−1.50098	+	8.51250i	−0.102605	+	0.581903i
$215$	10.4211			0.710712
$216$	−4.94364	+	1.60013i	−0.336372	+	0.108875i
$217$	10.6291	+	11.3401i	0.721552	+	0.769815i
$218$	−9.91809	−	1.74883i	−0.671738	−	0.118445i
$219$	10.4717	−	10.8356i	0.707614	−	0.732205i
$220$	−4.59300	+	12.6192i	−0.309660	+	0.850783i
$221$	−14.7965	−	17.6338i	−0.995323	−	1.18618i
$222$	1.54389	−	0.161683i	0.103619	−	0.0108514i
$223$	6.12585	+	16.8306i	0.410217	+	1.12706i	0.957076	+	0.289837i	$0.0936012\pi$
$223$	6.12585	+	16.8306i	0.410217	+	1.12706i	−0.546859	+	0.837225i	$0.684177\pi$
$224$	2.57641	−	0.601754i	0.172144	−	0.0402064i
$225$	−2.74404	+	3.50677i	−0.182936	+	0.233785i
$226$	−0.0981700	−	0.170035i	−0.00653017	−	0.0113106i
$227$	−3.31314	−	2.78006i	−0.219901	−	0.184519i	0.526182	−	0.850372i	$-0.323623\pi$
$227$	−3.31314	−	2.78006i	−0.219901	−	0.184519i	−0.746083	+	0.665853i	$0.768068\pi$
$228$	6.74614	−	3.28718i	0.446774	−	0.217699i
$229$	11.5039	−	2.02846i	0.760202	−	0.134044i	0.219908	−	0.975521i	$-0.429424\pi$
$229$	11.5039	−	2.02846i	0.760202	−	0.134044i	0.540294	+	0.841476i	$0.318313\pi$
$230$	−3.62572	−	20.5625i	−0.239073	−	1.35585i
$231$	−23.8612	+	3.83261i	−1.56995	+	0.252168i
$232$	−4.91616	−	4.12515i	−0.322762	−	0.270829i
$233$	−5.83805	+	3.37060i	−0.382464	+	0.220816i	−0.678890	−	0.734240i	$-0.737539\pi$
$233$	−5.83805	+	3.37060i	−0.382464	+	0.220816i	0.296426	+	0.955056i	$0.404205\pi$
$234$	−12.4039	−	6.60722i	−0.810867	−	0.431928i
$235$	−2.84025	+	4.91945i	−0.185277	+	0.320910i
$236$	1.08168	−	0.393698i	0.0704111	−	0.0256275i
$237$	−16.7317	−	7.45697i	−1.08684	−	0.484382i
$238$	−12.9078	−	1.55139i	−0.836688	−	0.100562i
$239$	6.92882	−	19.0368i	0.448188	−	1.23139i	−0.485796	−	0.874072i	$-0.661470\pi$
$239$	6.92882	−	19.0368i	0.448188	−	1.23139i	0.933984	−	0.357315i	$-0.116308\pi$
$240$	−1.06861	+	4.27912i	−0.0689786	+	0.276216i
$241$	−1.77571	−	0.313105i	−0.114383	−	0.0201689i	0.116163	−	0.993230i	$-0.462940\pi$
$241$	−1.77571	−	0.313105i	−0.114383	−	0.0201689i	−0.230547	+	0.973061i	$0.574051\pi$
$242$		−	16.8118i		−	1.08070i
$243$	14.6583	−	5.30404i	0.940333	−	0.340254i
$244$			6.01880i			0.385314i
$245$	17.3173	+	4.22375i	1.10636	+	0.269845i
$246$	8.88614	+	2.21911i	0.566559	+	0.141485i
$247$	19.0729	+	6.94196i	1.21358	+	0.441706i
$248$	−4.50020	+	3.77611i	−0.285763	+	0.239784i
$249$	19.9440	+	8.88862i	1.26390	+	0.563293i
$250$	−3.06195	−	8.41265i	−0.193655	−	0.532063i
$251$	−2.51607	+	4.35797i	−0.158813	+	0.275073i	−0.934441	−	0.356118i	$-0.884100\pi$
$251$	−2.51607	+	4.35797i	−0.158813	+	0.275073i	0.775628	+	0.631191i	$0.217433\pi$
$252$	−7.66308	+	2.06815i	−0.482728	+	0.130281i
$253$	21.6211	+	37.4488i	1.35931	+	2.35439i
$254$	−12.1203	+	14.4444i	−0.760497	+	0.906325i
$255$	12.1258	−	17.9627i	0.759349	−	1.12487i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−3.84339	−	21.7969i	−0.239744	−	1.35966i	−0.832389	−	0.554192i	$-0.813027\pi$
$257$	−3.84339	−	21.7969i	−0.239744	−	1.35966i	0.592645	−	0.805464i	$-0.298084\pi$
$258$	−6.37211	+	3.10492i	−0.396710	+	0.193304i
$259$	2.36765	−	0.130154i	0.147118	−	0.00808739i
$260$	−10.3308	+	5.96452i	−0.640692	+	0.369904i
$261$	15.1625	+	11.8646i	0.938534	+	0.734399i
$262$	−7.39202	−	4.26778i	−0.456680	−	0.263665i
$263$	−4.76860	−	13.1016i	−0.294045	−	0.807881i	−0.995465	−	0.0951329i	$-0.969672\pi$
$263$	−4.76860	−	13.1016i	−0.294045	−	0.807881i	0.701420	−	0.712748i	$-0.252550\pi$
$264$	−0.951380	−	9.08461i	−0.0585534	−	0.559119i
$265$	−15.4228	−	18.3801i	−0.947413	−	1.12908i
$266$	10.5404	−	4.50598i	0.646274	−	0.276279i
$267$	−12.3707	−	11.9553i	−0.757077	−	0.731651i
$268$	1.26064	−	7.14945i	0.0770059	−	0.436722i
$269$	5.96085			0.363440			0.181720	−	0.983350i	$-0.441834\pi$
$269$	5.96085			0.363440			0.181720	+	0.983350i	$0.441834\pi$
$270$	2.76559	−	12.9393i	0.168308	−	0.787463i
$271$		−	28.5645i		−	1.73517i	−0.497287	−	0.867586i	$-0.665670\pi$
$271$		−	28.5645i		−	1.73517i	0.497287	−	0.867586i	$-0.334330\pi$
$272$	0.853272	−	4.83915i	0.0517372	−	0.293416i
$273$	−18.4255	−	11.0165i	−1.11516	−	0.666749i
$274$	−5.61237	−	2.04274i	−0.339056	−	0.123406i
$275$	−5.03143	−	5.99622i	−0.303407	−	0.361586i
$276$	8.34349	+	11.4929i	0.502219	+	0.691792i
$277$	−19.9590	+	7.26448i	−1.19922	+	0.436480i	−0.862952	−	0.505286i	$-0.831387\pi$
$277$	−19.9590	+	7.26448i	−1.19922	+	0.436480i	−0.336268	+	0.941766i	$0.609165\pi$
$278$	−0.816921	+	1.41495i	−0.0489957	+	0.0848630i
$279$	13.1059	−	11.7828i	0.784628	−	0.705416i
$280$	−1.95329	+	6.44783i	−0.116731	+	0.385331i
$281$	0.144779	−	0.172541i	0.00863681	−	0.0102930i	−0.761709	−	0.647920i	$-0.775639\pi$
$281$	0.144779	−	0.172541i	0.00863681	−	0.0102930i	0.770346	+	0.637627i	$0.220084\pi$
$282$	0.270974	−	3.85430i	0.0161363	−	0.229520i
$283$	−20.6570	+	3.64238i	−1.22793	+	0.216517i	−0.749735	−	0.661738i	$-0.769819\pi$
$283$	−20.6570	+	3.64238i	−1.22793	+	0.216517i	−0.478193	+	0.878255i	$0.658708\pi$
$284$	8.85808	−	1.56192i	0.525630	−	0.0926828i
$285$	−1.34016	+	19.0623i	−0.0793844	+	1.12915i
$286$	15.8802	−	18.9253i	0.939018	−	1.11908i
$287$	13.3897	+	4.05625i	0.790372	+	0.239433i
$288$	−0.621530	−	2.93491i	−0.0366240	−	0.172941i
$289$	−3.57271	+	6.18812i	−0.210160	+	0.364007i
$290$	15.3563	−	5.58925i	0.901755	−	0.328212i
$291$	−6.47593	−	8.92040i	−0.379626	−	0.522923i
$292$	5.59223	+	6.66456i	0.327260	+	0.390014i
$293$	7.26899	+	2.64570i	0.424659	+	0.154563i	0.545504	−	0.838108i	$-0.316338\pi$
$293$	7.26899	+	2.64570i	0.424659	+	0.154563i	−0.120845	+	0.992671i	$0.538560\pi$
$294$	−11.8473	+	2.57696i	−0.690950	+	0.150291i
$295$	−0.508993	+	2.88664i	−0.0296347	+	0.168067i
$296$			0.896238i			0.0520928i
$297$	3.78316	+	27.1405i	0.219521	+	1.57485i
$298$	21.1057			1.22262
$299$	−6.67020	+	37.8286i	−0.385748	+	2.18768i
$300$	−1.84862	−	1.78653i	−0.106730	−	0.103145i
$301$	−9.95600	+	4.25614i	−0.573854	+	0.245320i
$302$	14.1309	+	16.8405i	0.813140	+	0.969063i
$303$	1.92866	+	18.4166i	0.110799	+	1.05800i
$304$	1.48186	+	4.07137i	0.0849904	+	0.233509i
$305$	−13.2730	−	7.66319i	−0.760012	−	0.438793i
$306$	−2.06257	+	14.5964i	−0.117910	+	0.834420i
$307$	−20.6696	+	11.9336i	−1.17968	+	0.681087i	−0.955940	−	0.293562i	$-0.905159\pi$
$307$	−20.6696	+	11.9336i	−1.17968	+	0.681087i	−0.223737	+	0.974649i	$0.571826\pi$
$308$	−0.765860	−	13.9318i	−0.0436389	−	0.793839i
$309$	−3.75303	+	1.82873i	−0.213502	+	0.104033i
$310$	−2.59763	−	14.7319i	−0.147536	−	0.836717i
$311$	−0.0614824	−	0.348684i	−0.00348634	−	0.0197720i	0.983015	−	0.183525i	$-0.0587510\pi$
$311$	−0.0614824	−	0.348684i	−0.00348634	−	0.0197720i	−0.986501	+	0.163753i	$0.947640\pi$
$312$	4.53983	−	6.72512i	0.257017	−	0.380735i
$313$	6.73049	−	8.02108i	0.380430	−	0.453378i	−0.541520	−	0.840688i	$-0.682151\pi$
$313$	6.73049	−	8.02108i	0.380430	−	0.453378i	0.921950	+	0.387309i	$0.126595\pi$
$314$	−4.93040	−	8.53970i	−0.278239	−	0.481923i
$315$	5.19589	−	19.5323i	0.292755	−	1.10052i
$316$	5.28801	−	9.15910i	0.297474	−	0.515240i
$317$	−3.47766	−	9.55480i	−0.195325	−	0.536651i	0.802906	−	0.596106i	$-0.203286\pi$
$317$	−3.47766	−	9.55480i	−0.195325	−	0.536651i	−0.998231	+	0.0594545i	$0.981064\pi$
$318$	14.9067	+	6.64362i	0.835928	+	0.372556i
$319$	−25.9263	+	21.7547i	−1.45159	+	1.21803i
$320$	−2.39285	−	0.870927i	−0.133765	−	0.0486863i
$321$	14.5255	+	3.62740i	0.810732	+	0.202462i
$322$	11.8620	+	18.1640i	0.661041	+	1.01224i
$323$		−	21.2899i		−	1.18460i
$324$	2.16417	+	8.73592i	0.120232	+	0.485329i
$325$		−	6.95320i		−	0.385694i
$326$	−6.09683	−	1.07503i	−0.337672	−	0.0595407i
$327$	−4.22636	+	16.9239i	−0.233718	+	0.935894i
$328$	−1.80859	+	4.96907i	−0.0998628	+	0.274371i
$329$	0.704302	−	5.85990i	0.0388294	−	0.323067i
$330$	21.2453	+	9.46857i	1.16951	+	0.521228i
$331$	−16.3609	+	5.95487i	−0.899276	+	0.327310i	−0.749962	−	0.661480i	$-0.769928\pi$
$331$	−16.3609	+	5.95487i	−0.899276	+	0.327310i	−0.149313	+	0.988790i	$0.547706\pi$
$332$	−6.30324	+	10.9175i	−0.345935	+	0.599178i
$333$	−0.0918157	−	2.68714i	−0.00503147	−	0.147255i
$334$	−3.56654	+	2.05914i	−0.195152	+	0.112671i
$335$	14.1614	+	11.8828i	0.773718	+	0.649227i
$336$	−0.726743	−	4.52458i	−0.0396471	−	0.246836i
$337$	−5.51923	−	31.3011i	−0.300652	−	1.70508i	−0.643298	−	0.765616i	$-0.722435\pi$
$337$	−5.51923	−	31.3011i	−0.300652	−	1.70508i	0.342647	−	0.939464i	$-0.388677\pi$
$338$	8.80984	−	1.55341i	0.479192	−	0.0844945i
$339$	−0.305710	+	0.148962i	−0.0166039	+	0.00809053i
$340$	9.58521	+	8.04295i	0.519831	+	0.436190i
$341$	15.4904	+	26.8301i	0.838851	+	1.45293i
$342$	−4.86008	−	12.0552i	−0.262803	−	0.651870i
$343$	−18.2695	+	3.03743i	−0.986459	+	0.164006i
$344$	−1.39970	−	3.84564i	−0.0754666	−	0.207343i
$345$	−35.9679	+	3.76672i	−1.93645	+	0.202793i
$346$	−4.30657	−	5.13237i	−0.231523	−	0.275918i
$347$	5.65025	−	15.5239i	0.303321	−	0.833369i	−0.690596	−	0.723241i	$-0.742652\pi$
$347$	5.65025	−	15.5239i	0.303321	−	0.833369i	0.993917	−	0.110128i	$-0.0351261\pi$
$348$	−7.72454	+	7.99298i	−0.414079	+	0.428469i
$349$	−22.1665	−	3.90856i	−1.18655	−	0.209220i	−0.454672	−	0.890659i	$-0.650244\pi$
$349$	−22.1665	−	3.90856i	−1.18655	−	0.209220i	−0.731875	+	0.681439i	$0.761355\pi$
$350$	−2.68553	−	2.86515i	−0.143548	−	0.153149i
$351$	−12.9226	+	20.6287i	−0.689756	+	1.10108i
$352$	5.27368			0.281088
$353$	6.42145	−	36.4179i	0.341779	−	1.93833i	−0.00394896	−	0.999992i	$-0.501257\pi$
$353$	6.42145	−	36.4179i	0.341779	−	1.93833i	0.345728	−	0.938335i	$-0.387632\pi$
$354$	−0.548834	−	1.91673i	−0.0291702	−	0.101873i
$355$	−7.83375	+	21.5231i	−0.415772	+	1.14233i
$356$	7.60874	−	6.38449i	0.403262	−	0.338377i
$357$	−4.24839	+	22.1135i	−0.224849	+	1.17037i
$358$	−0.862187	+	0.313810i	−0.0455680	+	0.0165854i
$359$	15.1046	+	8.72065i	0.797191	+	0.460258i	0.842488	−	0.538715i	$-0.181090\pi$
$359$	15.1046	+	8.72065i	0.797191	+	0.460258i	−0.0452971	+	0.998974i	$0.514423\pi$
$360$	7.26359	+	2.36612i	0.382825	+	0.124705i
$361$	−0.114002	−	0.197457i	−0.00600009	−	0.0103925i
$362$	6.05521	+	5.08092i	0.318255	+	0.267047i
$363$	−29.0471	−	2.04214i	−1.52458	−	0.107184i
$364$	7.43378	−	9.91762i	0.389636	−	0.519824i
$365$	−21.8172	+	3.84696i	−1.14196	+	0.201359i
$366$	10.3992	+	0.731109i	0.543575	+	0.0382157i
$367$	−10.2418	+	12.2057i	−0.534617	+	0.637131i	−0.963972	−	0.266005i	$-0.914296\pi$
$367$	−10.2418	+	12.2057i	−0.534617	+	0.637131i	0.429355	+	0.903136i	$0.358741\pi$
$368$	−7.10107	+	4.09981i	−0.370169	+	0.213717i
$369$	4.91355	−	15.0838i	0.255789	−	0.785231i
$370$	−1.97644	−	1.14110i	−0.102750	−	0.0593229i
$371$	22.2412	+	11.2609i	1.15471	+	0.584638i
$372$	5.97768	+	8.23407i	0.309928	+	0.426917i
$373$	17.5072	−	14.6903i	0.906490	−	0.760636i	−0.0649577	−	0.997888i	$-0.520691\pi$
$373$	17.5072	−	14.6903i	0.906490	−	0.760636i	0.971448	+	0.237252i	$0.0762468\pi$
$374$	−24.3510	−	8.86305i	−1.25916	−	0.458298i
$375$	−14.9072	+	4.26851i	−0.769805	+	0.220425i
$376$	2.19688	+	0.387370i	0.113296	+	0.0199771i
$377$	−30.0640			−1.54838
$378$	2.64248	+	13.4914i	0.135915	+	0.693922i
$379$	−4.48039			−0.230142			−0.115071	−	0.993357i	$-0.536710\pi$
$379$	−4.48039			−0.230142			−0.115071	+	0.993357i	$0.536710\pi$
$380$	−10.8652	−	1.91582i	−0.557372	−	0.0982797i
$381$	23.4847	+	22.6959i	1.20316	+	1.16275i
$382$	13.3048	+	4.84257i	0.680735	+	0.247767i
$383$	−5.35178	+	4.49067i	−0.273463	+	0.229463i	−0.769197	−	0.639012i	$-0.779344\pi$
$383$	−5.35178	+	4.49067i	−0.273463	+	0.229463i	0.495734	+	0.868474i	$0.334899\pi$
$384$	1.72263	−	0.180401i	0.0879076	−	0.00920607i
$385$	31.6985	+	16.0492i	1.61550	+	0.817944i
$386$	−5.74313	−	3.31580i	−0.292318	−	0.168770i
$387$	4.59061	+	11.3868i	0.233354	+	0.578823i
$388$	5.51161	−	3.18213i	0.279809	−	0.161548i
$389$	−8.41647	+	10.0304i	−0.426732	+	0.508559i	−0.935976	−	0.352062i	$-0.885480\pi$
$389$	−8.41647	+	10.0304i	−0.426732	+	0.508559i	0.509244	+	0.860622i	$0.329925\pi$
$390$	9.05051	+	18.5740i	0.458291	+	0.940532i
$391$	39.6791	−	6.99650i	2.00666	−	0.353828i
$392$	−0.767289	−	6.95782i	−0.0387539	−	0.351423i
$393$	−8.27173	+	12.2534i	−0.417254	+	0.618103i
$394$	0.113625	+	0.0953425i	0.00572434	+	0.00480329i
$395$	13.4655	+	23.3229i	0.677523	+	1.17350i
$396$	−15.8118	+	0.540266i	−0.794574	+	0.0271494i
$397$	−2.44969	−	1.41433i	−0.122946	−	0.0709830i	0.437266	−	0.899332i	$-0.355947\pi$
$397$	−2.44969	−	1.41433i	−0.122946	−	0.0709830i	−0.560212	+	0.828349i	$0.689280\pi$
$398$	1.89356	−	0.689198i	0.0949154	−	0.0345464i
$399$	−6.50501	−	18.7589i	−0.325658	−	0.939120i
$400$	1.13701	−	0.954063i	0.0568504	−	0.0477032i
$401$	−8.93683	+	24.5537i	−0.446284	+	1.22616i	0.489008	+	0.872279i	$0.337359\pi$
$401$	−8.93683	+	24.5537i	−0.446284	+	1.22616i	−0.935292	+	0.353876i	$0.884863\pi$
$402$	−12.1996	−	3.04657i	−0.608460	−	0.151949i
$403$	−4.77885	+	27.1022i	−0.238051	+	1.35006i
$404$	−10.6910			−0.531895
$405$	−22.0205	−	6.35010i	−1.09421	−	0.315539i
$406$	−12.3883	+	11.6116i	−0.614819	+	0.576274i
$407$	4.65467	+	0.820744i	0.230723	+	0.0406828i
$408$	−8.25736	−	2.06209i	−0.408800	−	0.102089i
$409$	−0.298506	+	0.820139i	−0.0147602	+	0.0405533i	−0.946854	−	0.321664i	$-0.895758\pi$
$409$	−0.298506	+	0.820139i	−0.0147602	+	0.0405533i	0.932094	+	0.362217i	$0.117980\pi$
$410$	−8.65539	−	10.3151i	−0.427459	−	0.509426i
$411$	−4.21115	+	9.44884i	−0.207721	+	0.466077i
$412$	−0.824390	−	2.26499i	−0.0406148	−	0.111588i
$413$	−0.692676	−	2.96569i	−0.0340844	−	0.145932i
$414$	20.8708	−	13.0197i	1.02574	−	0.639884i
$415$	−16.0507	−	27.8006i	−0.787898	−	1.36468i
$416$	3.58863	+	3.01122i	0.175947	+	0.147637i
$417$	2.34550	+	1.58334i	0.114859	+	0.0775365i
$418$	22.5020	−	3.96771i	1.10061	−	0.194067i
$419$	3.55710	+	20.1733i	0.173776	+	0.985532i	0.939547	+	0.342419i	$0.111246\pi$
$419$	3.55710	+	20.1733i	0.173776	+	0.985532i	−0.765772	+	0.643113i	$0.777643\pi$
$420$	10.9032	+	4.15808i	0.532022	+	0.202894i
$421$	3.29401	+	2.76400i	0.160540	+	0.134709i	0.719519	−	0.694473i	$-0.244362\pi$
$421$	3.29401	+	2.76400i	0.160540	+	0.134709i	−0.558979	+	0.829182i	$0.688807\pi$
$422$	−8.67592	+	5.00904i	−0.422337	+	0.243836i
$423$	−6.62649	−	0.936371i	−0.322191	−	0.0455279i
$424$	−4.71123	+	8.16009i	−0.228798	+	0.396289i
$425$	−6.85351	+	2.49447i	−0.332444	+	0.121000i
$426$	−1.62266	−	15.4946i	−0.0786182	−	0.750715i
$427$	15.8105	+	1.90026i	0.765121	+	0.0919599i
$428$	−2.95636	+	8.12254i	−0.142901	+	0.392618i
$429$	−30.7699	−	29.7365i	−1.48559	−	1.43569i
$430$	10.2628	+	1.80960i	0.494914	+	0.0872667i
$431$			5.00891i			0.241271i	0.992697	+	0.120635i	$0.0384932\pi$
$431$			5.00891i			0.241271i	−0.992697	+	0.120635i	$0.961507\pi$
$432$	−5.14640	+	0.717365i	−0.247606	+	0.0345142i
$433$			23.3737i			1.12327i	0.827386	+	0.561633i	$0.189827\pi$
$433$			23.3737i			1.12327i	−0.827386	+	0.561633i	$0.810173\pi$
$434$	8.49847	+	13.0135i	0.407939	+	0.624669i
$435$	−7.79168	−	27.2114i	−0.373583	−	1.30469i
$436$	−9.46373	−	3.44452i	−0.453231	−	0.164962i
$437$	−27.2146	+	22.8358i	−1.30185	+	1.09238i
$438$	12.1942	−	8.85263i	0.582663	−	0.422995i
$439$	−7.67296	−	21.0813i	−0.366210	−	1.00615i	−0.976790	−	0.214200i	$-0.931286\pi$
$439$	−7.67296	−	21.0813i	−0.366210	−	1.00615i	0.610580	−	0.791955i	$-0.290937\pi$
$440$	−6.71451	+	11.6299i	−0.320102	+	0.554432i
$441$	3.01332	+	20.7827i	0.143492	+	0.989652i
$442$	−11.5097	−	19.9353i	−0.547459	−	0.948227i
$443$	14.4266	−	17.1930i	0.685429	−	0.816863i	−0.305366	−	0.952235i	$-0.598779\pi$
$443$	14.4266	−	17.1930i	0.685429	−	0.816863i	0.990795	+	0.135373i	$0.0432232\pi$
$444$	1.54851	+	0.108867i	0.0734889	+	0.00516659i
$445$	4.39197	+	24.9081i	0.208199	+	1.18076i
$446$	3.11017	+	17.6387i	0.147271	+	0.835216i
$447$	2.56373	−	36.4661i	0.121260	−	1.72479i
$448$	2.64176	−	0.145223i	0.124812	−	0.00686114i
$449$	16.7414	−	9.66565i	0.790075	−	0.456150i	−0.0499138	−	0.998754i	$-0.515895\pi$
$449$	16.7414	−	9.66565i	0.790075	−	0.456150i	0.839989	+	0.542603i	$0.182561\pi$
$450$	−3.31130	+	2.97700i	−0.156096	+	0.140337i
$451$	24.1509	+	13.9435i	1.13722	+	0.656576i
$452$	−0.0671522	−	0.184499i	−0.00315858	−	0.00867811i
$453$	30.8133	−	22.3695i	1.44773	−	1.05101i
$454$	−2.78006	−	3.31314i	−0.130475	−	0.155494i
$455$	12.4062	+	29.0207i	0.581612	+	1.36051i
$456$	7.21447	−	2.06578i	0.337848	−	0.0967391i
$457$	−0.271050	+	1.53720i	−0.0126792	+	0.0719073i	−0.990491	−	0.137579i	$-0.956068\pi$
$457$	−0.271050	+	1.53720i	−0.0126792	+	0.0719073i	0.977812	+	0.209486i	$0.0671791\pi$
$458$	11.6814			0.545837
$459$	24.9689	+	5.33672i	1.16545	+	0.249097i
$460$		−	20.8797i		−	0.973519i
$461$	6.66828	−	37.8177i	0.310573	−	1.76135i	−0.285465	−	0.958389i	$-0.592148\pi$
$461$	6.66828	−	37.8177i	0.310573	−	1.76135i	0.596037	−	0.802957i	$-0.296741\pi$
$462$	−24.1642	−	0.369069i	−1.12422	−	0.0171706i
$463$	23.6904	+	8.62262i	1.10099	+	0.400727i	0.827681	−	0.561200i	$-0.189660\pi$
$463$	23.6904	+	8.62262i	1.10099	+	0.400727i	0.273308	+	0.961927i	$0.411882\pi$
$464$	−4.12515	−	4.91616i	−0.191505	−	0.228227i
$465$	−25.7691	+	2.69866i	−1.19502	+	0.125147i
$466$	−6.33466	+	2.30563i	−0.293447	+	0.106806i
$467$	15.5985	−	27.0174i	0.721813	−	1.25022i	−0.238459	−	0.971152i	$-0.576642\pi$
$467$	15.5985	−	27.0174i	0.721813	−	1.25022i	0.960272	−	0.279064i	$-0.0900243\pi$
$468$	−11.0681	−	8.66075i	−0.511624	−	0.400344i
$469$	−18.3825	−	5.56874i	−0.848825	−	0.257140i
$470$	−3.65135	+	4.35151i	−0.168424	+	0.200720i
$471$	−15.3537	+	7.48135i	−0.707460	+	0.344722i
$472$	1.13361	−	0.199886i	0.0521785	−	0.00920048i
$473$	−21.2544	+	3.74772i	−0.977277	+	0.172320i
$474$	−15.1826	−	10.2491i	−0.697361	−	0.470757i
$475$	4.13364	−	4.92628i	0.189664	−	0.226033i
$476$	−12.4423	−	3.76923i	−0.570292	−	0.172763i
$477$	13.2895	−	24.9486i	0.608484	−	1.14232i
$478$	10.1293	−	17.5444i	0.463302	−	0.802462i
$479$	−24.8417	+	9.04163i	−1.13504	+	0.413123i	−0.840121	−	0.542398i	$-0.817516\pi$
$479$	−24.8417	+	9.04163i	−1.13504	+	0.413123i	−0.294923	+	0.955521i	$0.595294\pi$
$480$	−1.79544	+	4.02855i	−0.0819502	+	0.183877i
$481$	2.69877	+	3.21627i	0.123053	+	0.146649i
$482$	−1.69436	−	0.616696i	−0.0771759	−	0.0280897i
$483$	32.8243	−	18.2885i	1.49356	−	0.832157i
$484$	2.91933	−	16.5563i	0.132697	−	0.752561i
$485$			16.2061i			0.735880i
$486$	15.3567	−	2.67807i	0.696594	−	0.121479i
$487$	−6.11954			−0.277303			−0.138651	−	0.990341i	$-0.544277\pi$
$487$	−6.11954			−0.277303			−0.138651	+	0.990341i	$0.544277\pi$
$488$	−1.04515	+	5.92736i	−0.0473119	+	0.268319i
$489$	−2.59802	+	10.4034i	−0.117486	+	0.470459i
$490$	16.3208	+	7.16669i	0.737297	+	0.323758i
$491$	12.1413	+	14.4695i	0.547930	+	0.652998i	0.966946	−	0.254981i	$-0.0820693\pi$
$491$	12.1413	+	14.4695i	0.547930	+	0.652998i	−0.419016	+	0.907979i	$0.637625\pi$
$492$	8.36579	+	3.72846i	0.377159	+	0.168092i
$493$	10.7855	+	29.6330i	0.485755	+	1.33460i
$494$	17.5777	+	10.1485i	0.790856	+	0.456601i
$495$	18.9404	−	35.5571i	0.851306	−	1.59817i
$496$	−5.08755	+	2.93730i	−0.228438	+	0.131888i
$497$	−1.30624	−	23.7619i	−0.0585929	−	1.06587i
$498$	18.0975	+	12.2168i	0.810969	+	0.547449i
$499$	−0.224409	−	1.27269i	−0.0100459	−	0.0569733i	0.979373	−	0.202062i	$-0.0647643\pi$
$499$	−0.224409	−	1.27269i	−0.0100459	−	0.0569733i	−0.989419	+	0.145089i	$0.953653\pi$
$500$	−1.55460	−	8.81655i	−0.0695236	−	0.394288i
$501$	3.12453	+	6.41235i	0.139594	+	0.286482i
$502$	−3.23460	+	3.85485i	−0.144367	+	0.172050i
$503$	−1.03602	−	1.79445i	−0.0461941	−	0.0800105i	0.842004	−	0.539471i	$-0.181376\pi$
$503$	−1.03602	−	1.79445i	−0.0461941	−	0.0800105i	−0.888198	+	0.459461i	$0.848043\pi$
$504$	−7.90579	+	0.706052i	−0.352152	+	0.0314500i
$505$	13.6118	−	23.5764i	0.605719	−	1.04914i
$506$	14.7897	+	40.6343i	0.657482	+	1.80642i
$507$	−1.61383	−	15.4102i	−0.0716725	−	0.684391i
$508$	−14.4444	+	12.1203i	−0.640869	+	0.537753i
$509$	−26.3345	−	9.58496i	−1.16725	−	0.424846i	−0.315571	−	0.948902i	$-0.602196\pi$
$509$	−26.3345	−	9.58496i	−1.16725	−	0.424846i	−0.851684	+	0.524056i	$0.824418\pi$
$510$	15.0608	−	15.5842i	0.666904	−	0.690080i
$511$	19.2724	−	12.5858i	0.852559	−	0.556762i
$512$			1.00000i			0.0441942i
$513$	−21.4191	+	6.93282i	−0.945678	+	0.306092i
$514$		−	22.1332i		−	0.976254i
$515$	6.04453	+	1.06581i	0.266354	+	0.0469654i
$516$	−6.81446	+	1.95125i	−0.299990	+	0.0858988i
$517$	4.02366	−	11.0549i	0.176961	−	0.486195i
$518$	2.35428	+	0.282961i	0.103441	+	0.0124326i
$519$	−9.39076	+	6.81740i	−0.412209	+	0.299251i
$520$	−11.2096	+	4.07997i	−0.491575	+	0.178919i
$521$	−8.50594	+	14.7327i	−0.372652	+	0.645452i	−0.989973	−	0.141260i	$-0.954885\pi$
$521$	−8.50594	+	14.7327i	−0.372652	+	0.645452i	0.617321	+	0.786712i	$0.288218\pi$
$522$	12.8719	+	14.3173i	0.563386	+	0.626650i
$523$	−22.5596	+	13.0248i	−0.986461	+	0.569533i	−0.904214	−	0.427079i	$-0.859543\pi$
$523$	−22.5596	+	13.0248i	−0.986461	+	0.569533i	−0.0822461	+	0.996612i	$0.526209\pi$
$524$	−6.53862	−	5.48656i	−0.285641	−	0.239681i
$525$	−5.27659	+	4.29199i	−0.230289	+	0.187318i
$526$	−2.42108	−	13.7306i	−0.105564	−	0.598685i
$527$	28.4280	−	5.01263i	1.23834	−	0.218353i
$528$	0.640599	−	9.11180i	0.0278785	−	0.396540i
$529$	−33.8849	−	28.4328i	−1.47326	−	1.23621i
$530$	−11.9968	−	20.7790i	−0.521107	−	0.902583i
$531$	−3.37836	+	0.715440i	−0.146608	+	0.0310475i
$532$	11.1627	−	2.60720i	0.483966	−	0.113036i
$533$	8.47258	+	23.2782i	0.366988	+	1.00829i
$534$	−10.1068	−	13.9218i	−0.437364	−	0.602455i
$535$	−14.1483	−	16.8613i	−0.611683	−	0.728976i
$536$	2.48298	−	6.82193i	0.107248	−	0.294662i
$537$	0.437467	+	1.52779i	0.0188781	+	0.0659291i
$538$	5.87030	+	1.03509i	0.253086	+	0.0446260i
$539$	−36.8386	−	2.38677i	−1.58675	−	0.102805i
$540$	4.97046	−	12.2625i	0.213895	−	0.527695i
$541$	4.76276			0.204767			0.102384	−	0.994745i	$-0.467353\pi$
$541$	4.76276			0.204767			0.102384	+	0.994745i	$0.467353\pi$
$542$	4.96018	−	28.1306i	0.213058	−	1.20831i
$543$	9.51428	−	9.84492i	0.408297	−	0.422486i
$544$	1.68062	−	4.61746i	0.0720559	−	0.197972i
$545$	19.6454	−	16.4844i	0.841516	−	0.706116i
$546$	−16.2325	−	14.0487i	−0.694688	−	0.601228i
$547$	−9.23709	+	3.36202i	−0.394949	+	0.143750i	−0.531857	−	0.846834i	$-0.678506\pi$
$547$	−9.23709	+	3.36202i	−0.394949	+	0.143750i	0.136908	+	0.990584i	$0.456284\pi$
$548$	−5.17239	−	2.98628i	−0.220953	−	0.127568i
$549$	2.52640	−	17.8788i	0.107824	−	0.763047i
$550$	−3.91376	−	6.77882i	−0.166883	−	0.289050i
$551$	−21.3001	−	17.8729i	−0.907413	−	0.761410i
$552$	6.22101	+	12.7671i	0.264784	+	0.543406i
$553$	−22.3900	−	16.7825i	−0.952120	−	0.713665i
$554$	−20.9172	+	3.68827i	−0.888688	+	0.156700i
$555$	−2.21166	+	3.27626i	−0.0938795	+	0.139069i
$556$	−1.05021	+	1.25160i	−0.0445390	+	0.0530795i
$557$	−18.1232	+	10.4635i	−0.767906	+	0.443351i	−0.832127	−	0.554585i	$-0.812877\pi$
$557$	−18.1232	+	10.4635i	−0.767906	+	0.443351i	0.0642211	+	0.997936i	$0.479544\pi$
$558$	14.9528	−	9.32794i	0.633003	−	0.394883i
$559$	−16.6031	−	9.58579i	−0.702235	−	0.405436i
$560$	−3.04326	+	6.01069i	−0.128601	+	0.253998i
$561$	−18.2714	+	40.9968i	−0.771419	+	1.73089i
$562$	0.172541	−	0.144779i	0.00727822	−	0.00610715i
$563$	17.7561	+	6.46269i	0.748330	+	0.272370i	0.687903	−	0.725803i	$-0.258531\pi$
$563$	17.7561	+	6.46269i	0.748330	+	0.272370i	0.0604272	+	0.998173i	$0.480754\pi$
$564$	0.936150	−	3.74869i	0.0394190	−	0.157848i
$565$	0.492369	+	0.0868179i	0.0207141	+	0.00365246i
$566$	−20.9756			−0.881671
$567$	23.6312	−	2.92683i	0.992417	−	0.122915i
$568$	8.99473			0.377410
$569$	9.63394	+	1.69872i	0.403876	+	0.0712142i	0.371896	−	0.928274i	$-0.378708\pi$
$569$	9.63394	+	1.69872i	0.403876	+	0.0712142i	0.0319797	+	0.999489i	$0.489819\pi$
$570$	−4.62994	+	18.5400i	−0.193927	+	0.776555i
$571$	20.3261	+	7.39809i	0.850620	+	0.309601i	0.730293	−	0.683134i	$-0.239383\pi$
$571$	20.3261	+	7.39809i	0.850620	+	0.309601i	0.120327	+	0.992734i	$0.461606\pi$
$572$	18.9253	−	15.8802i	0.791307	−	0.663986i
$573$	9.98308	−	22.3997i	0.417049	−	0.935761i
$574$	12.4820	+	6.31973i	0.520987	+	0.263780i
$575$	10.5398	+	6.08517i	0.439541	+	0.253769i
$576$	−0.102446	−	2.99825i	−0.00426857	−	0.124927i
$577$	32.7558	−	18.9115i	1.36364	−	0.787298i	0.373534	−	0.927617i	$-0.378146\pi$
$577$	32.7558	−	18.9115i	1.36364	−	0.787298i	0.990106	+	0.140319i	$0.0448127\pi$
$578$	−4.59299	+	5.47371i	−0.191043	+	0.227677i
$579$	−6.42661	+	9.52013i	−0.267081	+	0.395643i
$580$	16.0936	−	2.83774i	0.668251	−	0.117831i
$581$	26.6886	+	20.0045i	1.10723	+	0.829928i
$582$	−4.82854	−	9.90941i	−0.200149	−	0.410758i
$583$	38.0656	+	31.9408i	1.57652	+	1.32285i
$584$	4.34998	+	7.53439i	0.180004	+	0.311775i
$585$	33.1913	−	13.3812i	1.37229	−	0.553242i
$586$	6.69914	+	3.86775i	0.276739	+	0.159775i
$587$	−23.0197	+	8.37850i	−0.950127	+	0.345818i	−0.770157	−	0.637854i	$-0.779822\pi$
$587$	−23.0197	+	8.37850i	−0.950127	+	0.345818i	−0.179970	+	0.983672i	$0.557600\pi$
$588$	−12.1148	+	0.480539i	−0.499607	+	0.0198171i
$589$	−19.4979	+	16.3606i	−0.803395	+	0.674129i
$590$	−1.00252	+	2.75440i	−0.0412731	+	0.113397i
$591$	0.178534	−	0.184738i	0.00734389	−	0.00759911i
$592$	−0.155630	+	0.882622i	−0.00639635	+	0.0362755i
$593$	−0.129923			−0.00533529			−0.00266765	−	0.999996i	$-0.500849\pi$
$593$	−0.129923			−0.00533529			−0.00266765	+	0.999996i	$0.500849\pi$
$594$	−0.987212	+	27.3851i	−0.0405058	+	1.12362i
$595$	24.1538	−	22.6395i	0.990210	−	0.928131i
$596$	20.7850	+	3.66496i	0.851389	+	0.150123i
$597$	−0.960775	−	3.35538i	−0.0393219	−	0.137326i
$598$	−13.1377	+	36.0956i	−0.537242	+	1.47606i
$599$	17.6534	+	21.0385i	0.721297	+	0.859608i	0.994756	−	0.102276i	$-0.0326124\pi$
$599$	17.6534	+	21.0385i	0.721297	+	0.859608i	−0.273459	+	0.961884i	$0.588168\pi$
$600$	−1.51030	−	2.08040i	−0.0616579	−	0.0849319i
$601$	−4.87437	−	13.3922i	−0.198830	−	0.546280i	0.799705	−	0.600393i	$-0.204989\pi$
$601$	−4.87437	−	13.3922i	−0.198830	−	0.546280i	−0.998535	+	0.0541131i	$0.982767\pi$
$602$	−10.5438	+	2.46264i	−0.429734	+	0.100370i
$603$	−6.74571	+	20.7082i	−0.274707	+	0.843304i
$604$	10.9919	+	19.0385i	0.447253	+	0.774664i
$605$	32.7942	+	27.5176i	1.33327	+	1.11875i
$606$	−1.29864	+	18.4717i	−0.0527536	+	0.750361i
$607$	21.3829	−	3.77039i	0.867907	−	0.153035i	0.278073	−	0.960560i	$-0.410304\pi$
$607$	21.3829	−	3.77039i	0.867907	−	0.153035i	0.589834	+	0.807525i	$0.299193\pi$
$608$	0.752360	+	4.26684i	0.0305122	+	0.173043i
$609$	18.5575	+	22.8147i	0.751989	+	0.924499i
$610$	−11.7407	−	9.85161i	−0.475367	−	0.398880i
$611$	9.05027	−	5.22518i	0.366135	−	0.211388i
$612$	−4.56588	+	14.0165i	−0.184565	+	0.566582i
$613$	4.50406	−	7.80126i	0.181917	−	0.315090i	−0.760616	−	0.649202i	$-0.775103\pi$
$613$	4.50406	−	7.80126i	0.181917	−	0.315090i	0.942533	+	0.334112i	$0.108436\pi$
$614$	−22.4278	+	8.16307i	−0.905114	+	0.329435i
$615$	−18.8737	+	13.7017i	−0.761059	+	0.552505i
$616$	1.66501	−	13.8532i	0.0670852	−	0.558160i
$617$	8.72811	−	23.9803i	0.351380	−	0.965410i	−0.630547	−	0.776151i	$-0.717169\pi$
$617$	8.72811	−	23.9803i	0.351380	−	0.965410i	0.981927	−	0.189259i	$-0.0606084\pi$
$618$	−4.01356	+	1.14924i	−0.161449	+	0.0462292i
$619$	27.0379	+	4.76752i	1.08675	+	0.191623i	0.688197	−	0.725524i	$-0.258403\pi$
$619$	27.0379	+	4.76752i	1.08675	+	0.191623i	0.398549	+	0.917147i	$0.369514\pi$
$620$		−	14.9592i		−	0.600775i
$621$	−19.9601	−	37.6418i	−0.800971	−	1.51051i
$622$		−	0.354063i		−	0.0141966i
$623$	−14.3688	−	22.0027i	−0.575675	−	0.881520i
$624$	5.63866	−	5.83462i	0.225727	−	0.233572i
$625$	28.3959	+	10.3353i	1.13584	+	0.413410i
$626$	8.02108	−	6.73049i	0.320587	−	0.269004i
$627$	−4.12201	−	39.3606i	−0.164617	−	1.57191i
$628$	−3.37259	−	9.26612i	−0.134581	−	0.369758i
$629$	2.20197	−	3.81392i	0.0877981	−	0.152071i
$630$	8.50870	−	18.3333i	0.338995	−	0.730417i
$631$	12.0161	+	20.8125i	0.478354	+	0.828533i	0.999692	−	0.0248169i	$-0.00790027\pi$
$631$	12.0161	+	20.8125i	0.478354	+	0.828533i	−0.521338	+	0.853350i	$0.674567\pi$
$632$	6.79813	−	8.10170i	0.270415	−	0.322268i
$633$	7.60068	+	15.5986i	0.302100	+	0.619988i
$634$	−1.76566	−	10.0135i	−0.0701232	−	0.397688i
$635$	−8.33772	−	47.2856i	−0.330872	−	1.87647i
$636$	13.5266	+	9.13121i	0.536365	+	0.362076i
$637$	−23.7051	−	22.6586i	−0.939229	−	0.897766i
$638$	−29.3101	+	16.9222i	−1.16040	+	0.669955i
$639$	−26.9684	+	0.921471i	−1.06686	+	0.0364528i
$640$	−2.20527	−	1.27321i	−0.0871708	−	0.0503281i
$641$	−6.87187	−	18.8803i	−0.271423	−	0.745728i	−0.998263	−	0.0589209i	$-0.981234\pi$
$641$	−6.87187	−	18.8803i	−0.271423	−	0.745728i	0.726840	−	0.686807i	$-0.240988\pi$
$642$	13.6749	+	6.09461i	0.539705	+	0.240535i
$643$	−25.3998	−	30.2703i	−1.00167	−	1.19374i	−0.981010	−	0.193958i	$-0.937867\pi$
$643$	−25.3998	−	30.2703i	−1.00167	−	1.19374i	−0.0206609	−	0.999787i	$-0.506577\pi$
$644$	8.52761	+	19.9478i	0.336035	+	0.786054i
$645$	4.37323	−	17.5120i	0.172196	−	0.689536i
$646$	3.69694	−	20.9664i	0.145454	−	0.824912i
$647$	10.2344			0.402357			0.201178	−	0.979555i	$-0.435523\pi$
$647$	10.2344			0.402357			0.201178	+	0.979555i	$0.435523\pi$
$648$	0.614316	+	8.97901i	0.0241326	+	0.352729i
$649$		−	6.07051i		−	0.238289i
$650$	1.20741	−	6.84757i	0.0473585	−	0.268584i
$651$	23.5169	−	13.1028i	0.921700	−	0.513538i
$652$	−5.81752	−	2.11741i	−0.227832	−	0.0829240i
$653$	1.38321	+	1.64844i	0.0541290	+	0.0645085i	0.792430	−	0.609963i	$-0.208816\pi$
$653$	1.38321	+	1.64844i	0.0541290	+	0.0645085i	−0.738301	+	0.674472i	$0.764371\pi$
$654$	−7.10096	+	15.9329i	−0.277669	+	0.623025i
$655$	20.4244	−	7.43386i	0.798046	−	0.290465i
$656$	−2.64399	+	4.57952i	−0.103230	+	0.178800i
$657$	−13.8142	−	22.1444i	−0.538943	−	0.863933i
$658$	1.71116	−	5.64858i	0.0667081	−	0.220204i
$659$	8.04128	−	9.58322i	0.313244	−	0.373309i	−0.586334	−	0.810069i	$-0.699430\pi$
$659$	8.04128	−	9.58322i	0.313244	−	0.373309i	0.899578	+	0.436760i	$0.143874\pi$
$660$	19.2783	+	13.0139i	0.750407	+	0.506566i
$661$	30.0972	−	5.30694i	1.17064	−	0.206416i	0.445673	−	0.895196i	$-0.352964\pi$
$661$	30.0972	−	5.30694i	1.17064	−	0.206416i	0.724971	+	0.688779i	$0.241853\pi$
$662$	−17.1464	+	3.02337i	−0.666413	+	0.117507i
$663$	−35.8421	+	17.4647i	−1.39199	+	0.678272i
$664$	−8.10329	+	9.65713i	−0.314469	+	0.374769i
$665$	−8.46294	+	27.9363i	−0.328179	+	1.08332i
$666$	0.376197	−	2.66226i	0.0145773	−	0.103161i
$667$	26.3109	−	45.5718i	1.01876	−	1.76455i
$668$	−3.86992	+	1.40854i	−0.149732	+	0.0544979i
$669$	30.8537	−	3.23113i	1.19287	−	0.124923i
$670$	11.8828	+	14.1614i	0.459073	+	0.547101i
$671$	29.8270	+	10.8561i	1.15146	+	0.419097i
$672$	0.0699831	−	4.58204i	0.00269966	−	0.176756i
$673$	−2.38731	+	13.5391i	−0.0920239	+	0.521893i	0.903595	+	0.428388i	$0.140918\pi$
$673$	−2.38731	+	13.5391i	−0.0920239	+	0.521893i	−0.995619	+	0.0935053i	$0.970193\pi$
$674$		−	31.7840i		−	1.22427i
$675$	4.74140	+	6.08283i	0.182496	+	0.234128i
$676$	8.94574			0.344067
$677$	−4.78160	+	27.1178i	−0.183772	+	1.04222i	0.743751	+	0.668457i	$0.233045\pi$
$677$	−4.78160	+	27.1178i	−0.183772	+	1.04222i	−0.927523	+	0.373766i	$0.878066\pi$
$678$	−0.326932	+	0.0936134i	−0.0125558	+	0.00359520i
$679$	−6.61883	−	15.4828i	−0.254007	−	0.594176i
$680$	8.04295	+	9.58521i	0.308433	+	0.367576i
$681$	−6.06210	+	4.40089i	−0.232300	+	0.168643i
$682$	10.5960	+	29.1124i	0.405743	+	1.11477i
$683$	−23.1093	−	13.3421i	−0.884251	−	0.510523i	−0.0121934	−	0.999926i	$-0.503881\pi$
$683$	−23.1093	−	13.3421i	−0.884251	−	0.510523i	−0.872058	+	0.489403i	$0.837215\pi$
$684$	−2.69288	−	12.7160i	−0.102965	−	0.486208i
$685$	13.1711	−	7.60432i	0.503241	−	0.290546i
$686$	−18.5194	−	0.181177i	−0.707073	−	0.00691739i
$687$	1.41895	−	20.1830i	0.0541364	−	0.770029i
$688$	−0.710645	−	4.03027i	−0.0270931	−	0.153653i
$689$	7.66496	+	43.4701i	0.292012	+	1.65608i
$690$	−36.0756	−	2.53627i	−1.37337	−	0.0965542i
$691$	−25.9753	+	30.9562i	−0.988148	+	1.17763i	−0.00405194	+	0.999992i	$0.501290\pi$
$691$	−25.9753	+	30.9562i	−0.988148	+	1.17763i	−0.984096	+	0.177637i	$0.943155\pi$
$692$	−3.34992	−	5.80223i	−0.127345	−	0.220568i
$693$	−3.57292	+	41.7058i	−0.135724	+	1.58427i
$694$	8.26012	−	14.3069i	0.313550	−	0.543084i
$695$	−1.42296	−	3.90954i	−0.0539758	−	0.148297i
$696$	−8.99515	+	6.53020i	−0.340960	+	0.247527i
$697$	19.9049	−	16.7022i	0.753953	−	0.632641i
$698$	−21.1511	−	7.69836i	−0.800579	−	0.291387i
$699$	3.21416	+	11.2250i	0.121571	+	0.424569i
$700$	−2.14720	−	3.28796i	−0.0811565	−	0.124273i
$701$		−	2.80042i		−	0.105770i	−0.998601	−	0.0528851i	$-0.983158\pi$
$701$		−	2.80042i		−	0.105770i	0.998601	−	0.0528851i	$-0.0168417\pi$
$702$	−16.3084	+	18.0713i	−0.615520	+	0.682057i
$703$			3.88310i			0.146454i
$704$	5.19357	+	0.915766i	0.195740	+	0.0345142i
$705$	7.07494	+	6.83733i	0.266458	+	0.257509i
$706$	12.6478	−	34.7495i	0.476006	−	1.30782i
$707$	−3.37536	+	28.0835i	−0.126943	+	1.05619i
$708$	−0.207659	−	1.98291i	−0.00780431	−	0.0745224i
$709$	−1.69734	+	0.617781i	−0.0637450	+	0.0232013i	−0.373696	−	0.927551i	$-0.621910\pi$
$709$	−1.69734	+	0.617781i	−0.0637450	+	0.0232013i	0.309951	+	0.950753i	$0.399687\pi$
$710$	−11.4522	+	19.8358i	−0.429793	+	0.744423i
$711$	−19.5525	+	24.9874i	−0.733277	+	0.937100i
$712$	8.60180	−	4.96625i	0.322366	−	0.186118i
$713$	−36.8999	−	30.9627i	−1.38191	−	1.15956i
$714$	−8.02381	+	21.0398i	−0.300283	+	0.787394i
$715$	10.9242	+	61.9542i	0.408542	+	2.31696i
$716$	−0.903581	+	0.159326i	−0.0337684	+	0.00595428i
$717$	−29.0826	−	19.6323i	−1.08611	−	0.733183i
$718$	13.3608	+	11.2111i	0.498621	+	0.418393i
$719$	−1.87236	−	3.24302i	−0.0698272	−	0.120944i	0.828998	−	0.559252i	$-0.188911\pi$
$719$	−1.87236	−	3.24302i	−0.0698272	−	0.120944i	−0.898825	+	0.438307i	$0.855578\pi$
$720$	6.74237	+	3.59148i	0.251273	+	0.133847i
$721$	−6.21007	+	1.45044i	−0.231275	+	0.0540173i
$722$	−0.0779817	−	0.214253i	−0.00290218	−	0.00797367i
$723$	−1.27133	+	2.85258i	−0.0472814	+	0.106089i
$724$	5.08092	+	6.05521i	0.188831	+	0.225040i
$725$	−3.25787	+	8.95091i	−0.120994	+	0.332428i
$726$	−28.2512	−	7.05509i	−1.04850	−	0.261839i
$727$	23.0697	+	4.06780i	0.855607	+	0.150867i	0.584211	−	0.811602i	$-0.301404\pi$
$727$	23.0697	+	4.06780i	0.855607	+	0.150867i	0.271395	+	0.962468i	$0.412515\pi$
$728$	9.04302	−	8.47608i	0.335157	−	0.314145i
$729$	−2.76173	−	26.8584i	−0.102286	−	0.994755i
$730$	−22.1538			−0.819948
$731$	−3.49197	+	19.8039i	−0.129155	+	0.732475i
$732$	10.1143	+	2.52580i	0.373833	+	0.0933563i
$733$	−14.2849	+	39.2474i	−0.527624	+	1.44964i	0.334236	+	0.942490i	$0.391522\pi$
$733$	−14.2849	+	39.2474i	−0.527624	+	1.44964i	−0.861860	+	0.507146i	$0.830700\pi$
$734$	−12.2057	+	10.2418i	−0.450520	+	0.378031i
$735$	14.3650	−	27.3282i	0.529861	−	1.00802i
$736$	−7.70512	+	2.80443i	−0.284014	+	0.103373i
$737$	−33.1563	−	19.1428i	−1.22133	−	0.705134i
$738$	7.45818	−	14.0014i	0.274539	−	0.515399i
$739$	12.1995	+	21.1302i	0.448766	+	0.777286i	0.998306	−	0.0581818i	$-0.0185303\pi$
$739$	12.1995	+	21.1302i	0.448766	+	0.777286i	−0.549540	+	0.835467i	$0.685197\pi$
$740$	−1.74827	−	1.46697i	−0.0642675	−	0.0539268i
$741$	19.6696	−	29.1377i	0.722579	−	1.07040i
$742$	19.9479	+	14.9520i	0.732309	+	0.548905i
$743$	5.60455	−	0.988234i	0.205611	−	0.0362548i	−0.0698939	−	0.997554i	$-0.522266\pi$
$743$	5.60455	−	0.988234i	0.205611	−	0.0362548i	0.275505	+	0.961300i	$0.411155\pi$
$744$	4.45703	+	9.14699i	0.163403	+	0.335345i
$745$	−34.5460	+	41.1703i	−1.26567	+	1.50836i
$746$	19.7922	−	11.4270i	0.724644	−	0.418374i
$747$	23.3064	−	29.7846i	0.852735	−	1.08976i
$748$	−22.4420	−	12.9569i	−0.820562	−	0.473752i
$749$	20.4033	+	10.3304i	0.745519	+	0.377463i
$750$	−15.4219	+	1.61505i	−0.563130	+	0.0589734i
$751$	−31.5031	+	26.4342i	−1.14956	+	0.964599i	−0.999709	−	0.0241096i	$-0.992325\pi$
$751$	−31.5031	+	26.4342i	−1.14956	+	0.964599i	−0.149854	+	0.988708i	$0.547881\pi$
$752$	2.09624	+	0.762970i	0.0764421	+	0.0278227i
$753$	6.26745	+	6.05695i	0.228398	+	0.220728i
$754$	−29.6073	−	5.22056i	−1.07823	−	0.190122i
$755$	−55.9798			−2.03731
$756$	0.259584	+	13.7453i	0.00944096	+	0.499911i
$757$	−49.1050			−1.78475			−0.892376	−	0.451292i	$-0.850963\pi$
$757$	−49.1050			−1.78475			−0.892376	+	0.451292i	$0.850963\pi$
$758$	−4.41232	−	0.778011i	−0.160263	−	0.0282586i
$759$	72.0040	−	20.6175i	2.61358	−	0.748369i
$760$	−10.3674	−	3.77344i	−0.376066	−	0.136877i
$761$	7.94534	−	6.66693i	0.288018	−	0.241676i	−0.487318	−	0.873225i	$-0.662025\pi$
$761$	7.94534	−	6.66693i	0.288018	−	0.241676i	0.775336	+	0.631548i	$0.217580\pi$
$762$	19.1868	+	26.4292i	0.695063	+	0.957428i
$763$	−12.0361	+	23.7723i	−0.435736	+	0.860614i
$764$	12.2618	+	7.07936i	0.443617	+	0.256122i
$765$	−25.0967	−	27.9149i	−0.907374	−	1.00926i
$766$	−6.05027	+	3.49313i	−0.218605	+	0.126212i
$767$	3.46620	−	4.13086i	0.125157	−	0.149157i
$768$	1.72779	+	0.121471i	0.0623461	+	0.00438320i
$769$	18.7911	−	3.31338i	0.677626	−	0.119484i	0.175765	−	0.984432i	$-0.443760\pi$
$769$	18.7911	−	3.31338i	0.677626	−	0.119484i	0.501861	+	0.864948i	$0.332649\pi$
$770$	28.4300	+	21.3098i	1.02455	+	0.767951i
$771$	−38.2414	−	2.68854i	−1.37723	−	0.0968254i
$772$	−5.08010	−	4.26271i	−0.182837	−	0.153418i
$773$	−4.01335	−	6.95132i	−0.144350	−	0.250022i	0.784780	−	0.619774i	$-0.212776\pi$
$773$	−4.01335	−	6.95132i	−0.144350	−	0.250022i	−0.929130	+	0.369753i	$0.879442\pi$
$774$	2.54358	+	12.0110i	0.0914269	+	0.431725i
$775$	7.55123	+	4.35971i	0.271248	+	0.156605i
$776$	5.98044	−	2.17670i	0.214685	−	0.0781391i
$777$	0.774872	−	4.03332i	0.0277984	−	0.144694i
$778$	−10.0304	+	8.41647i	−0.359606	+	0.301745i
$779$	−7.83603	+	21.5293i	−0.280755	+	0.771367i
$780$	5.68767	+	19.8634i	0.203651	+	0.711225i
$781$	8.23706	−	46.7147i	0.294745	−	1.67158i
$782$	40.2913			1.44081
$783$	26.3007	−	20.5007i	0.939911	−	0.732635i
$784$	0.452581	−	6.98535i	0.0161636	−	0.249477i
$785$	24.7283	+	4.36026i	0.882590	+	0.155624i
$786$	−10.2738	+	10.6309i	−0.366456	+	0.379191i
$787$	6.52266	−	17.9209i	0.232508	−	0.638809i	−0.767490	−	0.641061i	$-0.778495\pi$
$787$	6.52266	−	17.9209i	0.232508	−	0.638809i	0.999997	+	0.00225167i	$0.000716728\pi$
$788$	0.0953425	+	0.113625i	0.00339644	+	0.00404772i
$789$	−24.0177	+	2.51524i	−0.855053	+	0.0895449i
$790$	9.21094	+	25.3069i	0.327711	+	0.900378i
$791$	−0.505852	+	0.118148i	−0.0179860	+	0.00420087i
$792$	−15.6654	−	2.21364i	−0.556647	−	0.0786581i
$793$	14.0979	+	24.4183i	0.500632	+	0.867119i
$794$	−2.16687	−	1.81822i	−0.0768995	−	0.0645263i
$795$	−37.3590	+	18.2038i	−1.32499	+	0.645623i
$796$	1.98447	−	0.349915i	0.0703376	−	0.0124024i
$797$	0.0788175	+	0.446997i	0.00279186	+	0.0158334i	0.986172	−	0.165726i	$-0.0529967\pi$
$797$	0.0788175	+	0.446997i	0.00279186	+	0.0158334i	−0.983380	+	0.181559i	$0.941886\pi$
$798$	−3.14874	−	19.6035i	−0.111464	−	0.693957i
$799$	−8.39706	−	7.04597i	−0.297067	−	0.249268i
$800$	1.28541	−	0.742129i	0.0454460	−	0.0262382i
$801$	−25.2816	+	15.7713i	−0.893281	+	0.557251i
$802$	−13.0648	+	22.6288i	−0.461333	+	0.799052i
$803$	43.1139	−	15.6922i	1.52146	−	0.553765i
$804$	−11.4852	−	5.11872i	−0.405052	−	0.180523i
$805$	−54.8477	−	6.59214i	−1.93313	−	0.232342i
$806$	−9.41249	+	25.8606i	−0.331541	+	0.910901i
$807$	2.50149	−	10.0169i	0.0880565	−	0.352611i
$808$	−10.5285	−	1.85647i	−0.370393	−	0.0653102i
$809$			11.4927i			0.404062i	0.979379	+	0.202031i	$0.0647542\pi$
$809$			11.4927i			0.404062i	−0.979379	+	0.202031i	$0.935246\pi$
$810$	−20.5832	−	10.0774i	−0.723222	−	0.354085i
$811$			30.4408i			1.06892i	0.845193	+	0.534461i	$0.179485\pi$
$811$			30.4408i			1.06892i	−0.845193	+	0.534461i	$0.820515\pi$
$812$	−14.2164	+	9.28399i	−0.498897	+	0.325804i
$813$	−48.0011	−	11.9872i	−1.68347	−	0.420409i
$814$	4.44143	+	1.61655i	0.155672	+	0.0566600i
$815$	12.0764	−	10.1333i	0.423017	−	0.354953i
$816$	−7.77384	−	3.46464i	−0.272139	−	0.121287i
$817$	−6.06442	−	16.6619i	−0.212167	−	0.582925i
$818$	−0.436387	+	0.755844i	−0.0152579	+	0.0264275i
$819$	−26.2449	+	26.3398i	−0.917071	+	0.920388i
$820$	−6.73270	−	11.6614i	−0.235116	−	0.407233i
$821$	27.6443	−	32.9452i	0.964793	−	1.14980i	−0.0238802	−	0.999715i	$-0.507602\pi$
$821$	27.6443	−	32.9452i	0.964793	−	1.14980i	0.988674	−	0.150081i	$-0.0479535\pi$
$822$	−5.78795	+	8.57403i	−0.201878	+	0.299054i
$823$	−3.48262	−	19.7509i	−0.121396	−	0.688473i	−0.983383	−	0.181542i	$-0.941891\pi$
$823$	−3.48262	−	19.7509i	−0.121396	−	0.688473i	0.861987	−	0.506931i	$-0.169220\pi$
$824$	−0.418554	−	2.37374i	−0.0145810	−	0.0826931i
$825$	−12.1878	+	5.93870i	−0.424324	+	0.206759i
$826$	−0.167165	−	3.04092i	−0.00581643	−	0.105807i
$827$	−5.62389	+	3.24696i	−0.195562	+	0.112908i	−0.594584	−	0.804034i	$-0.702683\pi$
$827$	−5.62389	+	3.24696i	−0.195562	+	0.112908i	0.399022	+	0.916941i	$0.369350\pi$
$828$	22.8146	−	9.19775i	0.792861	−	0.319644i
$829$	−23.5097	−	13.5733i	−0.816525	−	0.471421i	0.0326915	−	0.999465i	$-0.489592\pi$
$829$	−23.5097	−	13.5733i	−0.816525	−	0.471421i	−0.849217	+	0.528044i	$0.822925\pi$
$830$	−10.9793	−	30.1655i	−0.381098	−	1.04706i
$831$	3.83171	+	36.5885i	0.132921	+	1.26924i
$832$	3.01122	+	3.58863i	0.104395	+	0.124413i
$833$	−13.8295	+	31.4940i	−0.479163	+	1.09120i
$834$	2.03492	+	1.96658i	0.0704635	+	0.0680970i
$835$	1.82103	−	10.3276i	0.0630193	−	0.357400i
$836$	22.8491			0.790253
$837$	−14.3004	−	26.9684i	−0.494293	−	0.932163i
$838$			20.4845i			0.707627i
$839$	−1.52905	+	8.67169i	−0.0527888	+	0.299380i	−0.999759	−	0.0219405i	$-0.993016\pi$
$839$	−1.52905	+	8.67169i	−0.0527888	+	0.299380i	0.946971	+	0.321320i	$0.104127\pi$
$840$	10.0155	+	5.98823i	0.345568	+	0.206614i
$841$	11.4506	+	4.16766i	0.394847	+	0.143712i
$842$	2.76400	+	3.29401i	0.0952538	+	0.113519i
$843$	−0.229189	−	0.315701i	−0.00789369	−	0.0108733i
$844$	−9.41392	+	3.42639i	−0.324041	+	0.117941i
$845$	−11.3898	+	19.7277i	−0.391822	+	0.678655i
$846$	−6.36322	−	2.07282i	−0.218772	−	0.0712652i
$847$	−42.5693	−	12.8958i	−1.46270	−	0.443105i
$848$	−6.05664	+	7.21802i	−0.207986	+	0.247868i
$849$	−2.54793	+	36.2414i	−0.0874446	+	1.24380i
$850$	−7.18255	+	1.26648i	−0.246359	+	0.0434398i
$851$	−7.23716	+	1.27611i	−0.248087	+	0.0437443i
$852$	1.09260	−	15.5410i	0.0374318	−	0.532425i
$853$	−16.3019	+	19.4278i	−0.558166	+	0.665196i	−0.969157	−	0.246443i	$-0.920738\pi$
$853$	−16.3019	+	19.4278i	−0.558166	+	0.665196i	0.410991	+	0.911639i	$0.365183\pi$
$854$	15.2403	+	4.61685i	0.521512	+	0.157985i
$855$	31.4707	+	10.2516i	1.07628	+	0.350598i
$856$	−4.32191	+	7.48577i	−0.147720	+	0.255858i
$857$	−40.2291	+	14.6422i	−1.37420	+	0.500168i	−0.920415	−	0.390942i	$-0.872149\pi$
$857$	−40.2291	+	14.6422i	−1.37420	+	0.500168i	−0.453786	+	0.891111i	$0.649927\pi$
$858$	−25.1388	−	34.6279i	−0.858223	−	1.18218i
$859$	27.9961	+	33.3644i	0.955213	+	1.13838i	0.990293	+	0.138994i	$0.0443870\pi$
$859$	27.9961	+	33.3644i	0.955213	+	1.13838i	−0.0350797	+	0.999385i	$0.511169\pi$
$860$	9.79261	+	3.56422i	0.333925	+	0.121539i
$861$	12.4353	−	20.7985i	0.423795	−	0.708811i
$862$	−0.869789	+	4.93282i	−0.0296251	+	0.168012i
$863$		−	2.17856i		−	0.0741589i	−0.999312	−	0.0370795i	$-0.988195\pi$
$863$		−	2.17856i		−	0.0741589i	0.999312	−	0.0370795i	$-0.0118055\pi$
$864$	−5.19278	−	0.187196i	−0.176662	−	0.00636853i
$865$	17.0606			0.580078
$866$	−4.05880	+	23.0186i	−0.137923	+	0.782203i
$867$	8.89949	+	8.60060i	0.302243	+	0.292092i
$868$	6.10958	+	14.2916i	0.207373	+	0.485087i
$869$	−35.8512	−	42.7258i	−1.21617	−	1.44937i
$870$	−2.94810	−	28.1510i	−0.0999499	−	0.954409i
$871$	−11.6318	−	31.9582i	−0.394129	−	1.08286i
$872$	−8.72182	−	5.03555i	−0.295358	−	0.170525i
$873$	−17.7079	+	7.13897i	−0.599321	+	0.241618i
$874$	−30.7666	+	17.7631i	−1.04070	+	0.600846i
$875$	−23.6505	+	1.30012i	−0.799534	+	0.0439520i
$876$	13.5462	−	6.60063i	0.457684	−	0.223015i
$877$	2.89582	+	16.4230i	0.0977848	+	0.554565i	0.993858	+	0.110660i	$0.0352964\pi$
$877$	2.89582	+	16.4230i	0.0977848	+	0.554565i	−0.896074	+	0.443906i	$0.853593\pi$
$878$	−3.89566	−	22.0934i	−0.131472	−	0.745616i
$879$	7.49639	−	11.1049i	0.252847	−	0.374557i
$880$	−8.63201	+	10.2872i	−0.290985	+	0.346782i
$881$	−0.915202	−	1.58518i	−0.0308340	−	0.0534060i	0.850197	−	0.526465i	$-0.176483\pi$
$881$	−0.915202	−	1.58518i	−0.0308340	−	0.0534060i	−0.881031	+	0.473059i	$0.843150\pi$
$882$	−0.641331	+	20.9902i	−0.0215947	+	0.706777i
$883$	20.8174	−	36.0567i	0.700560	−	1.21341i	−0.267710	−	0.963499i	$-0.586267\pi$
$883$	20.8174	−	36.0567i	0.700560	−	1.21341i	0.968270	−	0.249906i	$-0.0803997\pi$
$884$	−7.87307	−	21.6311i	−0.264800	−	0.727532i
$885$	4.63724	+	2.06672i	0.155879	+	0.0694720i
$886$	17.1930	−	14.4266i	0.577609	−	0.484672i
$887$	46.5492	+	16.9425i	1.56297	+	0.568874i	0.971414	−	0.237391i	$-0.0762922\pi$
$887$	46.5492	+	16.9425i	1.56297	+	0.568874i	0.591555	+	0.806265i	$0.298514\pi$
$888$	1.50608	+	0.376108i	0.0505406	+	0.0126214i
$889$	27.2778	+	41.7700i	0.914869	+	1.40092i
$890$			25.2923i			0.847801i
$891$	47.1956	+	5.03218i	1.58111	+	0.168584i
$892$			17.9108i			0.599697i
$893$	9.51837	+	1.67835i	0.318520	+	0.0561637i
$894$	8.85705	−	35.4669i	0.296224	−	1.18619i
$895$	0.799093	−	2.19549i	0.0267107	−	0.0733872i
$896$	2.62685	+	0.315721i	0.0877568	+	0.0105475i
$897$	60.7696	+	27.0837i	2.02904	+	0.904300i
$898$	18.1655	−	6.61169i	0.606190	−	0.220635i
$899$	18.8504	−	32.6498i	0.628694	−	1.08893i
$900$	−3.77794	+	2.35677i	−0.125931	+	0.0785591i
$901$	40.0971	−	23.1500i	1.33583	−	0.771240i
$902$	21.3627	+	17.9255i	0.711302	+	0.596853i
$903$	2.97415	+	18.5166i	0.0989737	+	0.616194i
$904$	−0.0340941	−	0.193357i	−0.00113395	−	0.00643096i
$905$	−19.8224	+	3.49523i	−0.658920	+	0.116185i
$906$	34.2296	−	16.6790i	1.13720	−	0.554122i
$907$	−30.4725	−	25.5694i	−1.01182	−	0.849019i	−0.0232438	−	0.999730i	$-0.507399\pi$
$907$	−30.4725	−	25.5694i	−1.01182	−	0.849019i	−0.988578	+	0.150711i	$0.951844\pi$
$908$	−2.16250	−	3.74556i	−0.0717651	−	0.124301i
$909$	31.7574	+	4.48754i	1.05333	+	0.148842i
$910$	7.17834	+	30.7341i	0.237960	+	1.01883i
$911$	−5.87526	−	16.1421i	−0.194656	−	0.534813i	0.803514	−	0.595286i	$-0.202961\pi$
$911$	−5.87526	−	16.1421i	−0.194656	−	0.534813i	−0.998170	+	0.0604732i	$0.980739\pi$
$912$	7.46358	−	0.781619i	0.247144	−	0.0258820i
$913$	42.7342	+	50.9286i	1.41430	+	1.68549i
$914$	−0.533865	+	1.46678i	−0.0176587	+	0.0485168i
$915$	−18.4476	+	19.0887i	−0.609860	+	0.631054i
$916$	11.5039	+	2.02846i	0.380101	+	0.0670221i
$917$	−16.4767	+	15.4437i	−0.544109	+	0.509997i
$918$	23.6629	+	9.59145i	0.780991	+	0.316565i
$919$	30.8418			1.01738			0.508688	−	0.860951i	$-0.330131\pi$
$919$	30.8418			1.01738			0.508688	+	0.860951i	$0.330131\pi$
$920$	3.62572	−	20.5625i	0.119536	−	0.677924i
$921$	11.3797	+	39.7421i	0.374974	+	1.30955i
$922$	13.1339	−	36.0852i	0.432544	−	1.18840i
$923$	32.2788	−	27.0851i	1.06247	−	0.891517i
$924$	−23.7330	−	4.55954i	−0.780760	−	0.149998i
$925$	1.25002	−	0.454972i	0.0411006	−	0.0149594i
$926$	21.8332	+	12.6054i	0.717485	+	0.414240i
$927$	1.49811	+	7.07418i	0.0492043	+	0.232347i
$928$	−3.20879	−	5.55779i	−0.105334	−	0.182444i
$929$	23.3958	+	19.6314i	0.767592	+	0.644086i	0.940091	−	0.340923i	$-0.110740\pi$
$929$	23.3958	+	19.6314i	0.767592	+	0.644086i	−0.172499	+	0.985010i	$0.555184\pi$
$930$	−25.8463	−	1.81710i	−0.847532	−	0.0595852i
$931$	−3.32441	−	30.1459i	−0.108953	−	0.987992i
$932$	−6.63879	+	1.17060i	−0.217461	+	0.0383442i
$933$	−0.611745	−	0.0430083i	−0.0200276	−	0.00140803i
$934$	20.0531	−	23.8983i	0.656156	−	0.781976i
$935$	57.1469	−	32.9938i	1.86890	−	1.07901i
$936$	−9.39603	−	10.4511i	−0.307119	−	0.341606i
$937$	2.37693	+	1.37232i	0.0776510	+	0.0448318i	0.538323	−	0.842739i	$-0.319058\pi$
$937$	2.37693	+	1.37232i	0.0776510	+	0.0448318i	−0.460672	+	0.887571i	$0.652391\pi$
$938$	−17.1362	−	8.67622i	−0.559517	−	0.283289i
$939$	−10.6545	−	14.6763i	−0.347697	−	0.478942i
$940$	−4.35151	+	3.65135i	−0.141931	+	0.119094i
$941$	18.7249	+	6.81530i	0.610414	+	0.222173i	0.628684	−	0.777661i	$-0.283594\pi$
$941$	18.7249	+	6.81530i	0.610414	+	0.222173i	−0.0182704	+	0.999833i	$0.505816\pi$
$942$	−16.4195	+	4.70155i	−0.534978	+	0.153185i
$943$	−42.7006	−	7.52926i	−1.39052	−	0.245187i
$944$	1.15110			0.0374650
$945$	−30.6425	−	16.9282i	−0.996800	−	0.550674i
$946$	−21.5823			−0.701700
$947$	−5.62577	−	0.991976i	−0.182813	−	0.0322349i	0.0814920	−	0.996674i	$-0.474031\pi$
$947$	−5.62577	−	0.991976i	−0.182813	−	0.0322349i	−0.264305	+	0.964439i	$0.585143\pi$
$948$	−13.1722	−	12.7298i	−0.427814	−	0.413446i
$949$	38.2982	+	13.9394i	1.24321	+	0.452492i
$950$	4.92628	−	4.13364i	0.159830	−	0.134113i
$951$	−17.5157	+	1.83432i	−0.567986	+	0.0594820i
$952$	−11.5988	−	5.87255i	−0.375918	−	0.190331i
$953$	−28.4693	−	16.4368i	−0.922211	−	0.532439i	−0.0378713	−	0.999283i	$-0.512058\pi$
$953$	−28.4693	−	16.4368i	−0.922211	−	0.532439i	−0.884340	+	0.466844i	$0.845391\pi$
$954$	17.4199	−	22.2619i	0.563989	−	0.720756i
$955$	−31.2237	+	18.0270i	−1.01038	+	0.583341i
$956$	13.0219	−	15.5189i	0.421159	−	0.501918i
$957$	25.6776	+	52.6971i	0.830038	+	1.70345i
$958$	−26.0343	+	4.59056i	−0.841131	+	0.148314i
$959$	−9.47753	+	12.6442i	−0.306045	+	0.408304i
$960$	−2.46771	+	3.65557i	−0.0796450	+	0.117983i
$961$	−2.68945	−	2.25671i	−0.0867563	−	0.0727972i
$962$	2.09927	+	3.63604i	0.0676832	+	0.117231i
$963$	12.1913	−	22.8870i	0.392859	−	0.737522i
$964$	−1.56153	−	0.901550i	−0.0502935	−	0.0290370i
$965$	15.8684	−	5.77564i	0.510823	−	0.185924i
$966$	35.5014	−	12.3108i	1.14224	−	0.396093i
$967$	2.62559	−	2.20313i	0.0844332	−	0.0708479i	−0.599594	−	0.800304i	$-0.704671\pi$
$967$	2.62559	−	2.20313i	0.0844332	−	0.0708479i	0.684027	+	0.729456i	$0.260227\pi$
$968$	5.74996	−	15.7979i	0.184811	−	0.507763i
$969$	−35.7764	−	8.93434i	−1.14930	−	0.287012i
$970$	−2.81416	+	15.9599i	−0.0903571	+	0.512440i
$971$	47.4770			1.52361			0.761805	−	0.647806i	$-0.224313\pi$
$971$	47.4770			1.52361			0.761805	+	0.647806i	$0.224313\pi$
$972$	15.5884	+	0.0292822i	0.499999	+	0.000939227i
$973$	2.95617	+	3.15390i	0.0947706	+	0.101109i
$974$	−6.02657	−	1.06265i	−0.193104	−	0.0340494i
$975$	−11.6845	−	2.91793i	−0.374202	−	0.0934485i
$976$	−2.05855	+	5.65582i	−0.0658926	+	0.181038i
$977$	31.3920	+	37.4115i	1.00432	+	1.19690i	0.980366	+	0.197188i	$0.0631808\pi$
$977$	31.3920	+	37.4115i	1.00432	+	1.19690i	0.0239533	+	0.999713i	$0.492375\pi$
$978$	−4.36508	+	9.79423i	−0.139580	+	0.313185i
$979$	−17.9153	−	49.2219i	−0.572576	−	1.57314i
$980$	14.8283	+	9.89189i	0.473674	+	0.315985i
$981$	26.6661	+	14.2043i	0.851382	+	0.453509i
$982$	9.44427	+	16.3580i	0.301379	+	0.522003i
$983$	−18.3269	−	15.3781i	−0.584537	−	0.490484i	0.301897	−	0.953341i	$-0.402380\pi$
$983$	−18.3269	−	15.3781i	−0.584537	−	0.490484i	−0.886433	+	0.462856i	$0.846825\pi$
$984$	7.59126	+	5.12452i	0.242000	+	0.163364i
$985$	−0.371964	+	0.0655873i	−0.0118518	+	0.00208978i
$986$	5.47595	+	31.0557i	0.174390	+	0.989014i
$987$	−9.55168	−	3.64266i	−0.304033	−	0.115947i
$988$	15.5484	+	13.0466i	0.494659	+	0.415068i
$989$	29.0607	−	16.7782i	0.924078	−	0.533516i
$990$	24.8270	−	31.7280i	0.789055	−	1.00838i
$991$	−23.9239	+	41.4373i	−0.759966	+	1.31630i	0.182901	+	0.983131i	$0.441451\pi$
$991$	−23.9239	+	41.4373i	−0.759966	+	1.31630i	−0.942867	+	0.333169i	$0.891882\pi$
$992$	−5.52031	+	2.00923i	−0.175270	+	0.0637931i
$993$	3.14095	+	29.9925i	0.0996750	+	0.951784i
$994$	2.83982	−	23.6278i	0.0900737	−	0.749427i
$995$	−1.75499	+	4.82179i	−0.0556369	+	0.152861i
$996$	15.7011	+	15.1738i	0.497510	+	0.480801i
$997$	−58.9417	−	10.3930i	−1.86670	−	0.329150i	−0.877954	−	0.478746i	$-0.841092\pi$
$997$	−58.9417	−	10.3930i	−1.86670	−	0.329150i	−0.988747	+	0.149596i	$0.952203\pi$
$998$		−	1.29232i		−	0.0409077i
$999$	−4.55413	−	0.973376i	−0.144086	−	0.0307962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.83.20	yes	144
7.6	odd	2	inner	378.2.z.a.83.17	yes	144
27.14	odd	18	inner	378.2.z.a.41.17	✓	144
189.41	even	18	inner	378.2.z.a.41.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.17	✓	144	27.14	odd	18	inner
378.2.z.a.41.20	yes	144	189.41	even	18	inner
378.2.z.a.83.17	yes	144	7.6	odd	2	inner
378.2.z.a.83.20	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.419652 - 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.95067 + 1.63681i) q^{5} +(0.705083 - 1.58204i) q^{6} +(1.19511 - 2.36045i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.419652 - 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.95067 + 1.63681i) q^{5} +(0.705083 - 1.58204i) q^{6} +(1.19511 - 2.36045i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +(-2.20527 + 1.27321i) q^{10} +(3.38986 - 4.03988i) q^{11} +(0.969090 - 1.43557i) q^{12} +(4.61346 - 0.813477i) q^{13} +(1.58685 - 2.11706i) q^{14} +(1.93196 + 3.96488i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.45690 - 4.25548i) q^{17} +(-2.36264 - 1.84876i) q^{18} +(3.75220 + 2.16633i) q^{19} +(-2.39285 + 0.870927i) q^{20} +(-3.46506 - 2.99889i) q^{21} +(4.03988 - 3.38986i) q^{22} +(-2.80443 + 7.70512i) q^{23} +(1.20365 - 1.24548i) q^{24} +(0.257739 - 1.46171i) q^{25} +4.68463 q^{26} +(-3.48125 + 3.85757i) q^{27} +(1.93036 - 1.80934i) q^{28} +(-6.32009 - 1.11440i) q^{29} +(1.21411 + 4.24013i) q^{30} +(-2.00923 + 5.52031i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-5.36622 - 7.39181i) q^{33} +(-1.68062 - 4.61746i) q^{34} +(1.53232 + 6.56063i) q^{35} +(-2.00572 - 2.23094i) q^{36} +(0.448119 + 0.776165i) q^{37} +(3.31901 + 2.78498i) q^{38} +(0.569046 - 8.09404i) q^{39} +(-2.50773 + 0.442181i) q^{40} +(0.918246 + 5.20763i) q^{41} +(-2.89167 - 3.55503i) q^{42} +(-3.13499 - 2.63057i) q^{43} +(4.56714 - 2.63684i) q^{44} +(7.47352 - 1.58268i) q^{45} +(-4.09981 + 7.10107i) q^{46} +(2.09624 - 0.762970i) q^{47} +(1.40164 - 1.01755i) q^{48} +(-4.14340 - 5.64200i) q^{49} +(0.507646 - 1.39475i) q^{50} +(-8.18213 + 2.34286i) q^{51} +(4.61346 + 0.813477i) q^{52} +9.42246i q^{53} +(-4.09823 + 3.19445i) q^{54} +13.4290i q^{55} +(2.21522 - 1.44665i) q^{56} +(5.21502 - 5.39625i) q^{57} +(-6.03056 - 2.19494i) q^{58} +(0.881790 - 0.739910i) q^{59} +(0.459378 + 4.38654i) q^{60} +(2.05855 + 5.65582i) q^{61} +(-2.93730 + 5.08755i) q^{62} +(-6.49359 + 4.56435i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.66784 + 9.13817i) q^{65} +(-4.00112 - 8.21135i) q^{66} +(-1.26064 - 7.14945i) q^{67} +(-0.853272 - 4.83915i) q^{68} +(11.7711 + 7.94616i) q^{69} +(0.369799 + 6.72704i) q^{70} +(7.78966 - 4.49736i) q^{71} +(-1.58785 - 2.54534i) q^{72} +(7.53439 + 4.34998i) q^{73} +(0.306531 + 0.842188i) q^{74} +(-2.34816 - 1.04653i) q^{75} +(2.78498 + 3.31901i) q^{76} +(-5.48464 - 12.8297i) q^{77} +(1.96592 - 7.87226i) q^{78} +(1.83651 - 10.4153i) q^{79} -2.54642 q^{80} +(5.02152 + 7.46889i) q^{81} +5.28797i q^{82} +(-2.18909 + 12.4150i) q^{83} +(-2.23041 - 4.00316i) q^{84} +(11.7580 + 4.27956i) q^{85} +(-2.63057 - 3.13499i) q^{86} +(-4.52493 + 10.1529i) q^{87} +(4.95564 - 1.80371i) q^{88} +(4.96625 - 8.60180i) q^{89} +(7.63481 - 0.260870i) q^{90} +(3.59344 - 11.8620i) q^{91} +(-5.27061 + 6.28127i) q^{92} +(8.43339 + 5.69301i) q^{93} +(2.19688 - 0.387370i) q^{94} +(-10.8652 + 1.91582i) q^{95} +(1.55704 - 0.758696i) q^{96} +(4.09086 - 4.87530i) q^{97} +(-3.10073 - 6.27578i) q^{98} +(-14.6735 + 5.91565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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