LMFDB - Embedded newform 605.2.m.d.578.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,6,0,-2,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			578.1
Character	$\chi$	$=$	605.578
Dual form			605.2.m.d.112.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690094 + 1.35439i) q^{2} +(-0.124714 - 0.787410i) q^{3} +(-0.182561 - 0.251273i) q^{4} +(0.543872 - 2.16892i) q^{5} +(1.15252 + 0.374477i) q^{6} +(0.189114 + 0.0299527i) q^{7} +(-2.53639 + 0.401725i) q^{8} +(2.24871 - 0.730650i) q^{9} +(2.56223 + 2.23337i) q^{10} +(-0.175087 + 0.175087i) q^{12} +(-2.75820 - 1.40537i) q^{13} +(-0.171074 + 0.235463i) q^{14} +(-1.77566 - 0.157757i) q^{15} +(1.39821 - 4.30326i) q^{16} +(3.30253 - 1.68272i) q^{17} +(-0.562239 + 3.54984i) q^{18} +(-0.601740 - 0.437190i) q^{19} +(-0.644280 + 0.259299i) q^{20} -0.152646i q^{21} +(-1.14886 - 1.14886i) q^{23} +(0.632645 + 1.94708i) q^{24} +(-4.40841 - 2.35923i) q^{25} +(3.80684 - 2.76583i) q^{26} +(-1.94156 - 3.81053i) q^{27} +(-0.0269984 - 0.0529874i) q^{28} +(7.72385 - 5.61170i) q^{29} +(1.43903 - 2.29606i) q^{30} +(0.108440 + 0.333745i) q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(0.167819 - 0.393882i) q^{35} +(-0.594118 - 0.431652i) q^{36} +(0.845584 - 5.33881i) q^{37} +(1.00738 - 0.513286i) q^{38} +(-0.762621 + 2.34710i) q^{39} +(-0.508163 + 5.71971i) q^{40} +(3.93579 - 5.41715i) q^{41} +(0.206741 + 0.105340i) q^{42} +(-3.72708 + 3.72708i) q^{43} +(-0.361710 - 5.27464i) q^{45} +(2.34882 - 0.763176i) q^{46} +(12.2119 - 1.93417i) q^{47} +(-3.56281 - 0.564293i) q^{48} +(-6.62253 - 2.15179i) q^{49} +(6.23752 - 4.34260i) q^{50} +(-1.73686 - 2.39059i) q^{51} +(0.150406 + 0.949628i) q^{52} +(-4.09968 + 8.04607i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(-0.269202 + 0.528339i) q^{57} +(2.27023 + 14.3337i) q^{58} +(5.65807 + 7.78767i) q^{59} +(0.284525 + 0.474975i) q^{60} +(5.60460 + 1.82105i) q^{61} +(-0.526853 - 0.0834454i) q^{62} +(0.447147 - 0.0708211i) q^{63} +(6.08841 - 1.97824i) q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-1.02573 - 0.522638i) q^{68} +(-0.761344 + 1.04790i) q^{69} +(0.417657 + 0.499106i) q^{70} +(-3.54186 + 10.9007i) q^{71} +(-5.41009 + 2.75658i) q^{72} +(-0.375734 + 2.37229i) q^{73} +(6.64727 + 4.82953i) q^{74} +(-1.30789 + 3.76545i) q^{75} +0.231015i q^{76} +(-2.65261 - 2.65261i) q^{78} +(-0.207191 - 0.637669i) q^{79} +(-8.57297 - 5.37303i) q^{80} +(2.98028 - 2.16530i) q^{81} +(4.62085 + 9.06892i) q^{82} +(-7.57393 - 14.8647i) q^{83} +(-0.0383557 + 0.0278671i) q^{84} +(-1.85353 - 8.07810i) q^{85} +(-2.47587 - 7.61994i) q^{86} +(-5.38198 - 5.38198i) q^{87} +7.92190i q^{89} +(7.39352 + 3.15010i) q^{90} +(-0.479519 - 0.348391i) q^{91} +(-0.0789408 + 0.498413i) q^{92} +(0.249270 - 0.127009i) q^{93} +(-5.80772 + 17.8743i) q^{94} +(-1.27550 + 1.06735i) q^{95} +(0.816218 - 1.12343i) q^{96} +(1.22869 + 0.626047i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) $ 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.690094	+	1.35439i	−0.487970	+	0.957695i	0.507412	+	0.861704i	$0.330602\pi$
$2$	−0.690094	+	1.35439i	−0.487970	+	0.957695i	−0.995382	+	0.0959918i	$0.969398\pi$
$3$	−0.124714	−	0.787410i	−0.0720034	−	0.454611i	−0.997178	−	0.0750703i	$-0.976082\pi$
$3$	−0.124714	−	0.787410i	−0.0720034	−	0.454611i	0.925175	−	0.379541i	$-0.123918\pi$
$4$	−0.182561	−	0.251273i	−0.0912803	−	0.125637i
$5$	0.543872	−	2.16892i	0.243227	−	0.969969i
$5$	0.543872	−	2.16892i	0.243227	−	0.969969i
$6$	1.15252	+	0.374477i	0.470515	+	0.152880i
$7$	0.189114	+	0.0299527i	0.0714783	+	0.0113210i	0.192071	−	0.981381i	$-0.438480\pi$
$7$	0.189114	+	0.0299527i	0.0714783	+	0.0113210i	−0.120593	+	0.992702i	$0.538480\pi$
$8$	−2.53639	+	0.401725i	−0.896750	+	0.142031i
$9$	2.24871	−	0.730650i	0.749569	−	0.243550i
$10$	2.56223	+	2.23337i	0.810248	+	0.706253i
$11$		0			0
$11$		0			0
$12$	−0.175087	+	0.175087i	−0.0505433	+	0.0505433i
$13$	−2.75820	−	1.40537i	−0.764988	−	0.389781i	0.0275369	−	0.999621i	$-0.491234\pi$
$13$	−2.75820	−	1.40537i	−0.764988	−	0.389781i	−0.792524	+	0.609840i	$0.791234\pi$
$14$	−0.171074	+	0.235463i	−0.0457214	+	0.0629301i
$15$	−1.77566	−	0.157757i	−0.458472	−	0.0407326i
$16$	1.39821	−	4.30326i	0.349553	−	1.07581i
$17$	3.30253	−	1.68272i	0.800981	−	0.408120i	−0.00505476	−	0.999987i	$-0.501609\pi$
$17$	3.30253	−	1.68272i	0.800981	−	0.408120i	0.806036	+	0.591867i	$0.201609\pi$
$18$	−0.562239	+	3.54984i	−0.132521	+	0.836704i
$19$	−0.601740	−	0.437190i	−0.138049	−	0.100298i	0.516618	−	0.856216i	$-0.327191\pi$
$19$	−0.601740	−	0.437190i	−0.138049	−	0.100298i	−0.654666	+	0.755918i	$0.727191\pi$
$20$	−0.644280	+	0.259299i	−0.144065	+	0.0579809i
$21$		−	0.152646i		−	0.0333100i
$22$		0			0
$23$	−1.14886	−	1.14886i	−0.239553	−	0.239553i	0.577112	−	0.816665i	$-0.304180\pi$
$23$	−1.14886	−	1.14886i	−0.239553	−	0.239553i	−0.816665	+	0.577112i	$0.804180\pi$
$24$	0.632645	+	1.94708i	0.129138	+	0.397446i
$25$	−4.40841	−	2.35923i	−0.881681	−	0.471845i
$26$	3.80684	−	2.76583i	0.746582	−	0.542424i
$27$	−1.94156	−	3.81053i	−0.373654	−	0.733337i
$28$	−0.0269984	−	0.0529874i	−0.00510222	−	0.0100137i
$29$	7.72385	−	5.61170i	1.43428	−	1.04207i	0.445084	−	0.895489i	$-0.353174\pi$
$29$	7.72385	−	5.61170i	1.43428	−	1.04207i	0.989199	−	0.146578i	$-0.0468261\pi$
$30$	1.43903	−	2.29606i	0.262730	−	0.419201i
$31$	0.108440	+	0.333745i	0.0194765	+	0.0599424i	0.960322	−	0.278892i	$-0.0899673\pi$
$31$	0.108440	+	0.333745i	0.0194765	+	0.0599424i	−0.940846	+	0.338835i	$0.889967\pi$
$32$	1.23166	+	1.23166i	0.217729	+	0.217729i
$33$		0			0
$34$			5.63413i			0.966246i
$35$	0.167819	−	0.393882i	0.0283665	−	0.0665782i
$36$	−0.594118	−	0.431652i	−0.0990197	−	0.0719420i
$37$	0.845584	−	5.33881i	0.139013	−	0.877694i	−0.815333	−	0.578992i	$-0.803446\pi$
$37$	0.845584	−	5.33881i	0.139013	−	0.877694i	0.954346	−	0.298702i	$-0.0965538\pi$
$38$	1.00738	−	0.513286i	0.163419	−	0.0832660i
$39$	−0.762621	+	2.34710i	−0.122117	+	0.375838i
$40$	−0.508163	+	5.71971i	−0.0803477	+	0.904366i
$41$	3.93579	−	5.41715i	0.614667	−	0.846017i	−0.382284	−	0.924045i	$-0.624862\pi$
$41$	3.93579	−	5.41715i	0.614667	−	0.846017i	0.996951	+	0.0780281i	$0.0248624\pi$
$42$	0.206741	+	0.105340i	0.0319008	+	0.0162543i
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	−0.931673	−	0.363299i	$-0.881650\pi$
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	0.363299	+	0.931673i	$0.381650\pi$
$44$		0			0
$45$	−0.361710	−	5.27464i	−0.0539205	−	0.786297i
$46$	2.34882	−	0.763176i	0.346314	−	0.112524i
$47$	12.2119	−	1.93417i	1.78128	−	0.282128i	0.823020	−	0.568013i	$-0.192287\pi$
$47$	12.2119	−	1.93417i	1.78128	−	0.282128i	0.958264	+	0.285885i	$0.0922875\pi$
$48$	−3.56281	−	0.564293i	−0.514247	−	0.0814487i
$49$	−6.62253	−	2.15179i	−0.946076	−	0.307399i
$50$	6.23752	−	4.34260i	0.882118	−	0.614136i
$51$	−1.73686	−	2.39059i	−0.243209	−	0.334749i
$52$	0.150406	+	0.949628i	0.0208576	+	0.131690i
$53$	−4.09968	+	8.04607i	−0.563134	+	1.10521i	0.417374	+	0.908735i	$0.362950\pi$
$53$	−4.09968	+	8.04607i	−0.563134	+	1.10521i	−0.980508	+	0.196478i	$0.937050\pi$
$54$	6.50079			0.884646
$55$		0			0
$56$	−0.491699			−0.0657061
$57$	−0.269202	+	0.528339i	−0.0356567	+	0.0699803i
$58$	2.27023	+	14.3337i	0.298096	+	1.88210i
$59$	5.65807	+	7.78767i	0.736618	+	1.01387i	0.998806	+	0.0488514i	$0.0155561\pi$
$59$	5.65807	+	7.78767i	0.736618	+	1.01387i	−0.262188	+	0.965017i	$0.584444\pi$
$60$	0.284525	+	0.474975i	0.0367320	+	0.0613190i
$61$	5.60460	+	1.82105i	0.717596	+	0.233161i	0.644980	−	0.764199i	$-0.276866\pi$
$61$	5.60460	+	1.82105i	0.717596	+	0.233161i	0.0726152	+	0.997360i	$0.476866\pi$
$62$	−0.526853	−	0.0834454i	−0.0669104	−	0.0105976i
$63$	0.447147	−	0.0708211i	0.0563352	−	0.00892261i
$64$	6.08841	−	1.97824i	0.761051	−	0.247281i
$65$	−4.54825	+	5.21797i	−0.564141	+	0.647209i
$66$		0			0
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	−0.407932	−	0.913012i	$-0.633750\pi$
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	0.913012	+	0.407932i	$0.133750\pi$
$68$	−1.02573	−	0.522638i	−0.124389	−	0.0633791i
$69$	−0.761344	+	1.04790i	−0.0916550	+	0.126152i
$70$	0.417657	+	0.499106i	0.0499196	+	0.0596546i
$71$	−3.54186	+	10.9007i	−0.420342	+	1.29368i	0.487043	+	0.873378i	$0.338075\pi$
$71$	−3.54186	+	10.9007i	−0.420342	+	1.29368i	−0.907385	+	0.420301i	$0.861925\pi$
$72$	−5.41009	+	2.75658i	−0.637585	+	0.324866i
$73$	−0.375734	+	2.37229i	−0.0439764	+	0.277656i	−0.999871	−	0.0160534i	$-0.994890\pi$
$73$	−0.375734	+	2.37229i	−0.0439764	+	0.277656i	0.955895	+	0.293709i	$0.0948898\pi$
$74$	6.64727	+	4.82953i	0.772730	+	0.561421i
$75$	−1.30789	+	3.76545i	−0.151022	+	0.434797i
$76$			0.231015i			0.0264992i
$77$		0			0
$78$	−2.65261	−	2.65261i	−0.300348	−	0.300348i
$79$	−0.207191	−	0.637669i	−0.0233108	−	0.0717434i	0.938724	−	0.344669i	$-0.112009\pi$
$79$	−0.207191	−	0.637669i	−0.0233108	−	0.0717434i	−0.962035	+	0.272925i	$0.912009\pi$
$80$	−8.57297	−	5.37303i	−0.958487	−	0.600723i
$81$	2.98028	−	2.16530i	0.331143	−	0.240589i
$82$	4.62085	+	9.06892i	0.510287	+	1.00149i
$83$	−7.57393	−	14.8647i	−0.831347	−	1.63161i	−0.773939	−	0.633260i	$-0.781716\pi$
$83$	−7.57393	−	14.8647i	−0.831347	−	1.63161i	−0.0574083	−	0.998351i	$-0.518284\pi$
$84$	−0.0383557	+	0.0278671i	−0.00418495	+	0.00304055i
$85$	−1.85353	−	8.07810i	−0.201044	−	0.876193i
$86$	−2.47587	−	7.61994i	−0.266980	−	0.821679i
$87$	−5.38198	−	5.38198i	−0.577009	−	0.577009i
$88$		0			0
$89$			7.92190i			0.839720i	0.907589	+	0.419860i	$0.137921\pi$
$89$			7.92190i			0.839720i	−0.907589	+	0.419860i	$0.862079\pi$
$90$	7.39352	+	3.15010i	0.779345	+	0.332050i
$91$	−0.479519	−	0.348391i	−0.0502673	−	0.0365213i
$92$	−0.0789408	+	0.498413i	−0.00823015	+	0.0519631i
$93$	0.249270	−	0.127009i	0.0258481	−	0.0131703i
$94$	−5.80772	+	17.8743i	−0.599021	+	1.84360i
$95$	−1.27550	+	1.06735i	−0.130863	+	0.109508i
$96$	0.816218	−	1.12343i	0.0833049	−	0.114659i
$97$	1.22869	+	0.626047i	0.124754	+	0.0635655i	0.515254	−	0.857038i	$-0.327698\pi$
$97$	1.22869	+	0.626047i	0.124754	+	0.0635655i	−0.390500	+	0.920603i	$0.627698\pi$
$98$	7.48452	−	7.48452i	0.756051	−	0.756051i
$99$		0			0
$100$	0.211991	+	1.53842i	0.0211991	+	0.153842i
$101$	4.58927	−	1.49114i	0.456649	−	0.148374i	−0.0716549	−	0.997429i	$-0.522828\pi$
$101$	4.58927	−	1.49114i	0.456649	−	0.148374i	0.528304	+	0.849055i	$0.322828\pi$
$102$	4.43637	−	0.702653i	0.439266	−	0.0695730i
$103$	−3.19748	−	0.506431i	−0.315057	−	0.0499001i	−0.00309638	−	0.999995i	$-0.500986\pi$
$103$	−3.19748	−	0.506431i	−0.315057	−	0.0499001i	−0.311960	+	0.950095i	$0.600986\pi$
$104$	7.56045	+	2.45654i	0.741364	+	0.240884i
$105$	−0.331076	−	0.0830196i	−0.0323097	−	0.00810188i
$106$	−8.06832	−	11.1051i	−0.783665	−	1.07862i
$107$	1.72947	+	10.9194i	0.167194	+	1.05562i	0.918429	+	0.395586i	$0.129458\pi$
$107$	1.72947	+	10.9194i	0.167194	+	1.05562i	−0.751235	+	0.660035i	$0.770542\pi$
$108$	−0.603031	+	1.18352i	−0.0580267	+	0.113884i
$109$	−9.54212			−0.913969			−0.456985	−	0.889475i	$-0.651071\pi$
$109$	−9.54212			−0.913969			−0.456985	+	0.889475i	$0.651071\pi$
$110$		0			0
$111$	−4.30929			−0.409019
$112$	0.393316	−	0.771925i	0.0371648	−	0.0729401i
$113$	−0.648841	−	4.09662i	−0.0610378	−	0.385378i	−0.999229	−	0.0392603i	$-0.987500\pi$
$113$	−0.648841	−	4.09662i	−0.0610378	−	0.385378i	0.938191	−	0.346117i	$-0.112500\pi$
$114$	−0.529801	−	0.729208i	−0.0496204	−	0.0682966i
$115$	−3.11661	+	1.86695i	−0.290625	+	0.174094i
$116$	−2.82014	−	0.916319i	−0.261843	−	0.0850781i
$117$	−7.22923	−	1.14500i	−0.668342	−	0.105855i
$118$	−14.4521	+	2.28899i	−1.33042	+	0.210719i
$119$	0.674956	−	0.219306i	0.0618731	−	0.0201038i
$120$	4.56713	−	0.313192i	0.416920	−	0.0285904i
$121$		0			0
$122$	−6.33410	+	6.33410i	−0.573462	+	0.573462i
$123$	−4.75636	−	2.42349i	−0.428867	−	0.218519i
$124$	0.0640642	−	0.0881768i	0.00575313	−	0.00791851i
$125$	−7.51457	+	8.27836i	−0.672124	+	0.740439i
$126$	−0.212654	+	0.654482i	−0.0189447	+	0.0583059i
$127$	−12.9795	+	6.61337i	−1.15174	+	0.586842i	−0.922298	−	0.386480i	$-0.873691\pi$
$127$	−12.9795	+	6.61337i	−1.15174	+	0.586842i	−0.229444	+	0.973322i	$0.573691\pi$
$128$	−2.06723	+	13.0520i	−0.182719	+	1.15365i
$129$	3.39956	+	2.46992i	0.299314	+	0.217465i
$130$	−3.92842	−	9.76097i	−0.344546	−	0.856094i
$131$		−	9.76926i		−	0.853544i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$		−	9.76926i		−	0.853544i	0.904359	−	0.426772i	$-0.140349\pi$
$132$		0			0
$133$	−0.100702	−	0.100702i	−0.00873200	−	0.00873200i
$134$	2.74636	+	8.45242i	0.237249	+	0.730178i
$135$	−9.32069	+	2.13865i	−0.802197	+	0.184066i
$136$	−7.70051	+	5.59475i	−0.660314	+	0.479746i
$137$	1.96583	+	3.85816i	0.167952	+	0.329625i	0.959607	−	0.281344i	$-0.0907801\pi$
$137$	1.96583	+	3.85816i	0.167952	+	0.329625i	−0.791655	+	0.610969i	$0.790780\pi$
$138$	−0.893862	−	1.75430i	−0.0760906	−	0.149336i
$139$	8.50321	−	6.17795i	0.721233	−	0.524007i	−0.165545	−	0.986202i	$-0.552938\pi$
$139$	8.50321	−	6.17795i	0.721233	−	0.524007i	0.886778	+	0.462196i	$0.152938\pi$
$140$	−0.129609	+	0.0297390i	−0.0109540	+	0.00251340i
$141$	−3.04597	−	9.37453i	−0.256517	−	0.789478i
$142$	−12.3196	−	12.3196i	−1.03384	−	1.03384i
$143$		0			0
$144$		−	10.6984i		−	0.891532i
$145$	−7.97054	−	19.8044i	−0.661918	−	1.64467i
$146$	−2.95371	−	2.14600i	−0.244451	−	0.177604i
$147$	−0.868422	+	5.48300i	−0.0716263	+	0.452230i
$148$	−1.49587	+	0.762183i	−0.122960	+	0.0626511i
$149$	1.78068	−	5.48038i	0.145879	−	0.448970i	−0.851244	−	0.524771i	$-0.824151\pi$
$149$	1.78068	−	5.48038i	0.145879	−	0.448970i	0.997123	+	0.0758003i	$0.0241511\pi$
$150$	−4.19731	−	4.36990i	−0.342709	−	0.356801i
$151$	−8.79574	+	12.1063i	−0.715787	+	0.985196i	0.283866	+	0.958864i	$0.408383\pi$
$151$	−8.79574	+	12.1063i	−0.715787	+	0.985196i	−0.999653	+	0.0263324i	$0.991617\pi$
$152$	1.70188	+	0.867150i	0.138041	+	0.0703352i
$153$	6.19694	−	6.19694i	0.500993	−	0.500993i
$154$		0			0
$155$	0.782843	−	0.0536836i	0.0628795	−	0.00431197i
$156$	0.728989	−	0.236863i	0.0583658	−	0.0189642i
$157$	−4.88720	+	0.774057i	−0.390041	+	0.0617765i	−0.348375	−	0.937355i	$-0.613267\pi$
$157$	−4.88720	+	0.774057i	−0.390041	+	0.0617765i	−0.0416659	+	0.999132i	$0.513267\pi$
$158$	1.00663	+	0.159435i	0.0800833	+	0.0126839i
$159$	6.84684	+	2.22467i	0.542990	+	0.176428i
$160$	3.34124	−	2.00151i	0.264148	−	0.158233i
$161$	−0.182853	−	0.251676i	−0.0144109	−	0.0198349i
$162$	0.875980	+	5.53072i	0.0688235	+	0.434534i
$163$	−4.54748	+	8.92492i	−0.356186	+	0.699054i	−0.997680	−	0.0680736i	$-0.978315\pi$
$163$	−4.54748	+	8.92492i	−0.356186	+	0.699054i	0.641494	+	0.767128i	$0.278315\pi$
$164$	−2.07970			−0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	−5.47615	+	10.7475i	−0.423757	+	0.831670i	0.576140	+	0.817351i	$0.304558\pi$
$167$	−5.47615	+	10.7475i	−0.423757	+	0.831670i	−0.999897	+	0.0143193i	$0.995442\pi$
$168$	0.0613215	+	0.387169i	0.00473106	+	0.0298707i
$169$	−2.00861	−	2.76461i	−0.154508	−	0.212662i
$170$	12.2200	+	3.06425i	0.937229	+	0.235017i
$171$	−1.67257	−	0.543451i	−0.127905	−	0.0415587i
$172$	1.61693	+	0.256097i	0.123290	+	0.0195272i
$173$	−12.3116	+	1.94997i	−0.936035	+	0.148253i	−0.605775	−	0.795636i	$-0.707137\pi$
$173$	−12.3116	+	1.94997i	−0.936035	+	0.148253i	−0.330261	+	0.943890i	$0.607137\pi$
$174$	11.0034	−	3.57521i	0.834162	−	0.271036i
$175$	−0.763025	−	0.578206i	−0.0576793	−	0.0437082i
$176$		0			0
$177$	5.42645	−	5.42645i	0.407877	−	0.407877i
$178$	−10.7293	−	5.46686i	−0.804196	−	0.409758i
$179$	11.8607	−	16.3248i	0.886507	−	1.22017i	−0.0880691	−	0.996114i	$-0.528070\pi$
$179$	11.8607	−	16.3248i	0.886507	−	1.22017i	0.974576	−	0.224058i	$-0.0719304\pi$
$180$	−1.25934	+	1.05383i	−0.0938658	+	0.0785478i
$181$	1.42448	−	4.38411i	0.105881	−	0.325868i	−0.884055	−	0.467383i	$-0.845197\pi$
$181$	1.42448	−	4.38411i	0.105881	−	0.325868i	0.989936	+	0.141514i	$0.0451971\pi$
$182$	0.802769	−	0.409031i	0.0595052	−	0.0303194i
$183$	0.734940	−	4.64023i	0.0543283	−	0.343016i
$184$	3.37548	+	2.45243i	0.248843	+	0.180795i
$185$	−11.1195	−	4.73763i	−0.817525	−	0.348317i
$186$			0.425256i			0.0311813i
$187$		0			0
$188$	−2.71541	−	2.71541i	−0.198042	−	0.198042i
$189$	−0.253041	−	0.778779i	−0.0184060	−	0.0566478i
$190$	−0.565389	−	2.46409i	−0.0410176	−	0.178764i
$191$	−5.11808	+	3.71850i	−0.370331	+	0.269062i	−0.757348	−	0.653011i	$-0.773505\pi$
$191$	−5.11808	+	3.71850i	−0.370331	+	0.269062i	0.387017	+	0.922073i	$0.373505\pi$
$192$	−2.31700	−	4.54736i	−0.167215	−	0.328178i
$193$	−2.69302	−	5.28534i	−0.193848	−	0.380447i	0.773540	−	0.633747i	$-0.218484\pi$
$193$	−2.69302	−	5.28534i	−0.193848	−	0.380447i	−0.967388	+	0.253300i	$0.918484\pi$
$194$	−1.69582	+	1.23208i	−0.121753	+	0.0884585i
$195$	4.67591	+	2.93059i	0.334849	+	0.209864i
$196$	0.668326	+	2.05690i	0.0477376	+	0.146921i
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	0.965631	−	0.259918i	$-0.0836955\pi$
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	−0.259918	+	0.965631i	$0.583696\pi$
$198$		0			0
$199$			13.3828i			0.948680i	0.880342	+	0.474340i	$0.157313\pi$
$199$			13.3828i			0.948680i	−0.880342	+	0.474340i	$0.842687\pi$
$200$	12.1292	+	4.21295i	0.857664	+	0.297901i
$201$	−3.77096	−	2.73976i	−0.265983	−	0.193248i
$202$	−1.14744	+	7.24467i	−0.0807338	+	0.509733i
$203$	1.62877	−	0.829901i	0.114317	−	0.0582476i
$204$	−0.283607	+	0.872853i	−0.0198565	+	0.0611120i
$205$	−9.60879	−	11.4826i	−0.671107	−	0.801982i
$206$	2.89246	−	3.98113i	0.201527	−	0.277379i
$207$	−3.42286	−	1.74403i	−0.237905	−	0.121219i
$208$	−9.90424	+	9.90424i	−0.686736	+	0.686736i
$209$		0			0
$210$	0.340914	−	0.391113i	0.0235253	−	0.0269893i
$211$	−5.64203	+	1.83321i	−0.388413	+	0.126203i	−0.496712	−	0.867915i	$-0.665460\pi$
$211$	−5.64203	+	1.83321i	−0.388413	+	0.126203i	0.108299	+	0.994118i	$0.465460\pi$
$212$	2.77020	−	0.438757i	0.190258	−	0.0301339i
$213$	9.02506	+	1.42943i	0.618387	+	0.0979429i
$214$	−15.9826	−	5.19306i	−1.09255	−	0.354990i
$215$	6.05667	+	10.1108i	0.413062	+	0.689549i
$216$	6.45535	+	8.88503i	0.439231	+	0.604550i
$217$	0.0105110	+	0.0663638i	0.000713533	+	0.00450507i
$218$	6.58496	−	12.9237i	0.445990	−	0.875304i
$219$	1.91483			0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$	2.97381	−	5.83644i	0.199589	−	0.391716i
$223$	3.32511	+	20.9939i	0.222666	+	1.40586i	0.805178	+	0.593034i	$0.202070\pi$
$223$	3.32511	+	20.9939i	0.222666	+	1.40586i	−0.582512	+	0.812822i	$0.697930\pi$
$224$	0.196033	+	0.269816i	0.0130980	+	0.0180278i
$225$	−11.6370	−	2.08421i	−0.775799	−	0.138947i
$226$	5.99617	+	1.94827i	0.398859	+	0.129597i
$227$	12.9092	+	2.04462i	0.856816	+	0.135706i	0.569361	−	0.822088i	$-0.307191\pi$
$227$	12.9092	+	2.04462i	0.856816	+	0.135706i	0.287455	+	0.957794i	$0.407191\pi$
$228$	0.181903	−	0.0288106i	0.0120468	−	0.00190803i
$229$	−15.6269	+	5.07749i	−1.03265	+	0.335530i	−0.775839	−	0.630931i	$-0.782673\pi$
$229$	−15.6269	+	5.07749i	−1.03265	+	0.335530i	−0.256816	+	0.966460i	$0.582673\pi$
$230$	−0.377812	−	5.50946i	−0.0249122	−	0.363283i
$231$		0			0
$232$	−17.3363	+	17.3363i	−1.13819	+	1.13819i
$233$	13.9385	+	7.10204i	0.913144	+	0.465270i	0.846429	−	0.532502i	$-0.178748\pi$
$233$	13.9385	+	7.10204i	0.913144	+	0.465270i	0.0667155	+	0.997772i	$0.478748\pi$
$234$	6.53961	−	9.00101i	0.427508	−	0.588414i
$235$	2.44663	−	27.5385i	0.159601	−	1.79641i
$236$	0.923891	−	2.84344i	0.0601402	−	0.185092i
$237$	−0.476268	+	0.242670i	−0.0309369	+	0.0157631i
$238$	−0.168757	+	1.06549i	−0.0109389	+	0.0690656i
$239$	4.27301	+	3.10452i	0.276398	+	0.200815i	0.717345	−	0.696718i	$-0.245357\pi$
$239$	4.27301	+	3.10452i	0.276398	+	0.200815i	−0.440947	+	0.897533i	$0.645357\pi$
$240$	−3.16161	+	7.42053i	−0.204081	+	0.478993i
$241$			16.1676i			1.04144i	0.853726	+	0.520722i	$0.174337\pi$
$241$			16.1676i			1.04144i	−0.853726	+	0.520722i	$0.825663\pi$
$242$		0			0
$243$	−11.1488	−	11.1488i	−0.715198	−	0.715198i
$244$	−0.565599	−	1.74074i	−0.0362088	−	0.111439i
$245$	−8.26886	+	13.1934i	−0.528278	+	0.842897i
$246$	6.56468	−	4.76952i	0.418549	−	0.304093i
$247$	1.04531	+	2.05153i	0.0665112	+	0.130536i
$248$	−0.409121	−	0.802945i	−0.0259792	−	0.0509870i
$249$	−10.7600	+	7.81762i	−0.681889	+	0.495421i
$250$	−6.02632	−	15.8905i	−0.381138	−	1.00500i
$251$	5.97722	+	18.3960i	0.377279	+	1.16114i	0.941928	+	0.335814i	$0.109011\pi$
$251$	5.97722	+	18.3960i	0.377279	+	1.16114i	−0.564649	+	0.825331i	$0.690989\pi$
$252$	−0.0994268	−	0.0994268i	−0.00626330	−	0.00626330i
$253$		0			0
$254$		−	22.1431i		−	1.38938i
$255$	−6.12961	+	2.46694i	−0.383851	+	0.154486i
$256$	−5.89265	−	4.28126i	−0.368290	−	0.267579i
$257$	0.736199	−	4.64818i	0.0459228	−	0.289945i	−0.954029	−	0.299713i	$-0.903109\pi$
$257$	0.736199	−	4.64818i	0.0459228	−	0.289945i	0.999952	+	0.00976747i	$0.00310913\pi$
$258$	−5.69124	+	2.89983i	−0.354321	+	0.180536i
$259$	0.319823	−	0.984314i	0.0198728	−	0.0611623i
$260$	2.14147	+	0.190257i	0.132808	+	0.0117992i
$261$	13.2685	−	18.2625i	0.821299	−	1.13042i
$262$	13.2313	+	6.74170i	0.817435	+	0.416504i
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	−0.270700	−	0.962664i	$-0.587255\pi$
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	0.962664	+	0.270700i	$0.0872550\pi$
$264$		0			0
$265$	15.2216	+	13.2679i	0.935053	+	0.815040i
$266$	0.205884	−	0.0668957i	0.0126235	−	0.00410164i
$267$	6.23779	−	0.987968i	0.381746	−	0.0604627i
$268$	−1.79358	−	0.284076i	−0.109560	−	0.0173527i
$269$	10.7587	+	3.49572i	0.655971	+	0.213138i	0.618045	−	0.786143i	$-0.287925\pi$
$269$	10.7587	+	3.49572i	0.655971	+	0.213138i	0.0379260	+	0.999281i	$0.487925\pi$
$270$	3.53560	−	14.0997i	0.215170	−	0.858079i
$271$	10.4791	+	14.4233i	0.636563	+	0.876153i	0.998426	−	0.0560778i	$-0.0178595\pi$
$271$	10.4791	+	14.4233i	0.636563	+	0.876153i	−0.361864	+	0.932231i	$0.617859\pi$
$272$	−2.62355	−	16.5644i	−0.159076	−	1.00437i
$273$	−0.214524	+	0.421027i	−0.0129836	+	0.0254817i
$274$	−6.58205			−0.397636
$275$		0			0
$276$	0.402300			0.0242156
$277$	2.12539	−	4.17132i	0.127703	−	0.250630i	−0.818299	−	0.574793i	$-0.805083\pi$
$277$	2.12539	−	4.17132i	0.127703	−	0.250630i	0.946001	+	0.324163i	$0.105083\pi$
$278$	2.49931	+	15.7800i	0.149898	+	0.946421i
$279$	0.487701	+	0.671263i	0.0291979	+	0.0401875i
$280$	−0.267421	+	1.06646i	−0.0159815	+	0.0637329i
$281$	12.5438	+	4.07572i	0.748298	+	0.243137i	0.658249	−	0.752800i	$-0.271297\pi$
$281$	12.5438	+	4.07572i	0.748298	+	0.243137i	0.0900496	+	0.995937i	$0.471297\pi$
$282$	14.7987	+	2.34389i	0.881252	+	0.139577i
$283$	22.5060	−	3.56460i	1.33784	−	0.211893i	0.553825	−	0.832633i	$-0.313168\pi$
$283$	22.5060	−	3.56460i	1.33784	−	0.211893i	0.784017	+	0.620740i	$0.213168\pi$
$284$	3.38566	−	1.10007i	0.200902	−	0.0652771i
$285$	0.999513	+	0.871227i	0.0592061	+	0.0516070i
$286$		0			0
$287$	0.906570	−	0.906570i	0.0535131	−	0.0535131i
$288$	3.66956	+	1.86974i	0.216231	+	0.110175i
$289$	−1.91721	+	2.63881i	−0.112777	+	0.155224i
$290$	32.3233	+	2.87174i	1.89809	+	0.168634i
$291$	0.339722	−	1.04556i	0.0199149	−	0.0612916i
$292$	0.664688	−	0.338675i	0.0388979	−	0.0198195i
$293$	1.13067	−	7.13875i	0.0660543	−	0.417050i	−0.932398	−	0.361433i	$-0.882287\pi$
$293$	1.13067	−	7.13875i	0.0660543	−	0.417050i	0.998452	−	0.0556168i	$-0.0177125\pi$
$294$	−6.82681	−	4.95997i	−0.398148	−	0.289271i
$295$	19.9681	−	8.03640i	1.16259	−	0.467897i
$296$			13.8810i			0.806817i
$297$		0			0
$298$	6.19371	+	6.19371i	0.358792	+	0.358792i
$299$	1.55421	+	4.78335i	0.0898821	+	0.276629i
$300$	1.18493	−	0.358785i	0.0684117	−	0.0207145i
$301$	−0.816478	+	0.593206i	−0.0470610	+	0.0341918i
$302$	−10.3267	−	20.2673i	−0.594235	−	1.16625i
$303$	−1.74649	−	3.42767i	−0.100333	−	0.196915i
$304$	−2.72270	+	1.97816i	−0.156158	+	0.113455i
$305$	6.99788	−	11.1655i	0.400697	−	0.639335i
$306$	4.11658	+	12.6695i	0.235329	+	0.724269i
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.986804	+	0.161918i	$0.0517681\pi$
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.161918	+	0.986804i	$0.448232\pi$
$308$		0			0
$309$			2.58088i			0.146821i
$310$	−0.467527	+	1.09732i	−0.0265537	+	0.0623235i
$311$	6.08048	+	4.41772i	0.344792	+	0.250506i	0.746681	−	0.665182i	$-0.231646\pi$
$311$	6.08048	+	4.41772i	0.344792	+	0.250506i	−0.401889	+	0.915688i	$0.631646\pi$
$312$	0.991414	−	6.25954i	0.0561278	−	0.354377i
$313$	1.19937	−	0.611109i	0.0677923	−	0.0345419i	−0.419766	−	0.907632i	$-0.637888\pi$
$313$	1.19937	−	0.611109i	0.0677923	−	0.0345419i	0.487558	+	0.873091i	$0.337888\pi$
$314$	2.32426	−	7.15333i	0.131165	−	0.403686i
$315$	0.0895853	−	1.00834i	0.00504756	−	0.0568136i
$316$	−0.122404	+	0.168475i	−0.00688577	+	0.00947745i
$317$	10.0968	+	5.14460i	0.567095	+	0.288949i	0.713936	−	0.700211i	$-0.246911\pi$
$317$	10.0968	+	5.14460i	0.567095	+	0.288949i	−0.146841	+	0.989160i	$0.546911\pi$
$318$	−7.73803	+	7.73803i	−0.433927	+	0.433927i
$319$		0			0
$320$	−0.979335	−	14.2812i	−0.0547465	−	0.798342i
$321$	8.38237	−	2.72360i	0.467859	−	0.152016i
$322$	0.467052	−	0.0739738i	0.0260278	−	0.00412240i
$323$	−2.72293	−	0.431270i	−0.151508	−	0.0239965i
$324$	−1.08816	−	0.353566i	−0.0604536	−	0.0196426i
$325$	8.84368	+	12.7027i	0.490559	+	0.704618i
$326$	−8.94960	−	12.3181i	−0.495673	−	0.682235i
$327$	1.19003	+	7.51356i	0.0658089	+	0.415501i
$328$	−7.80650	+	15.3211i	−0.431042	+	0.845967i
$329$	2.36737			0.130517
$330$		0			0
$331$	−17.7048			−0.973145			−0.486572	−	0.873640i	$-0.661753\pi$
$331$	−17.7048			−0.973145			−0.486572	+	0.873640i	$0.661753\pi$
$332$	−2.35239	+	4.61683i	−0.129104	+	0.253381i
$333$	−1.99933	−	12.6232i	−0.109562	−	0.691750i
$334$	−10.7773	−	14.8336i	−0.589706	−	0.811660i
$335$	−6.71837	−	11.2154i	−0.367064	−	0.612762i
$336$	−0.656873	−	0.213431i	−0.0358354	−	0.0116436i
$337$	7.52627	+	1.19204i	0.409982	+	0.0649348i	0.358019	−	0.933714i	$-0.383452\pi$
$337$	7.52627	+	1.19204i	0.409982	+	0.0649348i	0.0519628	+	0.998649i	$0.483452\pi$
$338$	5.13048	−	0.812588i	0.279061	−	0.0441989i
$339$	−3.14480	+	1.02181i	−0.170802	+	0.0554970i
$340$	−1.69143	+	1.94049i	−0.0917305	+	0.105238i
$341$		0			0
$342$	1.89027	−	1.89027i	0.102214	−	0.102214i
$343$	−2.38217	−	1.21378i	−0.128625	−	0.0655378i
$344$	7.95607	−	10.9506i	0.428963	−	0.590416i
$345$	1.85873	+	2.22121i	0.100071	+	0.119586i
$346$	5.85517	−	18.0203i	0.314776	−	0.968780i
$347$	8.31639	−	4.23741i	0.446447	−	0.227476i	−0.216289	−	0.976329i	$-0.569395\pi$
$347$	8.31639	−	4.23741i	0.446447	−	0.227476i	0.662736	+	0.748853i	$0.269395\pi$
$348$	−0.369809	+	2.33488i	−0.0198239	+	0.125163i
$349$	−1.21496	−	0.882720i	−0.0650353	−	0.0472509i	0.554793	−	0.831989i	$-0.312798\pi$
$349$	−1.21496	−	0.882720i	−0.0650353	−	0.0472509i	−0.619828	+	0.784738i	$0.712798\pi$
$350$	1.30967	−	0.634414i	0.0700049	−	0.0339109i
$351$			13.2388i			0.706637i
$352$		0			0
$353$	4.40229	+	4.40229i	0.234310	+	0.234310i	0.814489	−	0.580179i	$-0.197017\pi$
$353$	4.40229	+	4.40229i	0.234310	+	0.234310i	−0.580179	+	0.814489i	$0.697017\pi$
$354$	3.60475	+	11.0943i	0.191590	+	0.589654i
$355$	21.7165	+	13.6106i	1.15259	+	0.722376i
$356$	1.99056	−	1.44623i	0.105500	−	0.0766499i
$357$	−0.256860	−	0.504116i	−0.0135945	−	0.0266807i
$358$	13.9251	+	27.3295i	0.735964	+	1.44441i
$359$	−21.2806	+	15.4612i	−1.12315	+	0.816013i	−0.984683	−	0.174355i	$-0.944216\pi$
$359$	−21.2806	+	15.4612i	−1.12315	+	0.816013i	−0.138463	+	0.990368i	$0.544216\pi$
$360$	3.03639	+	13.2333i	0.160032	+	0.697454i
$361$	−5.70037	−	17.5439i	−0.300019	−	0.923364i
$362$	4.95475	+	4.95475i	0.260416	+	0.260416i
$363$		0			0
$364$			0.184093i			0.00964908i
$365$	4.94096	+	2.10516i	0.258622	+	0.110189i
$366$	5.77748	+	4.19759i	0.301994	+	0.219411i
$367$	−1.27793	+	8.06852i	−0.0667073	+	0.421173i	0.931624	+	0.363424i	$0.118392\pi$
$367$	−1.27793	+	8.06852i	−0.0667073	+	0.421173i	−0.998331	+	0.0577492i	$0.981608\pi$
$368$	−6.55018	+	3.33748i	−0.341452	+	0.173978i
$369$	4.89241	−	15.0573i	0.254688	−	0.783850i
$370$	14.0901	−	11.7907i	0.732510	−	0.612971i
$371$	−1.01631	+	1.39883i	−0.0527640	+	0.0726234i
$372$	−0.0774210	−	0.0394479i	−0.00401409	−	0.00204528i
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	−0.530536	−	0.847662i	$-0.678009\pi$
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	0.847662	+	0.530536i	$0.178009\pi$
$374$		0			0
$375$	7.45563	+	4.88463i	0.385007	+	0.252241i
$376$	−30.1971	+	9.81162i	−1.55730	+	0.505996i
$377$	−29.1905	+	4.62332i	−1.50339	+	0.238113i
$378$	1.22939	+	0.194716i	0.0632330	+	0.0100151i
$379$	0.588124	+	0.191093i	0.0302099	+	0.00981580i	0.324083	−	0.946029i	$-0.394944\pi$
$379$	0.588124	+	0.191093i	0.0302099	+	0.00981580i	−0.293873	+	0.955844i	$0.594944\pi$
$380$	0.501052	+	0.125642i	0.0257034	+	0.00644531i
$381$	6.82615	+	9.39539i	0.349714	+	0.481340i
$382$	−1.50433	−	9.49797i	−0.0769683	−	0.485959i
$383$	4.71192	−	9.24766i	0.240768	−	0.472533i	−0.738726	−	0.674005i	$-0.764572\pi$
$383$	4.71192	−	9.24766i	0.240768	−	0.472533i	0.979494	+	0.201472i	$0.0645725\pi$
$384$	10.5351			0.537617
$385$		0			0
$386$	9.01683			0.458945
$387$	−5.65792	+	11.1043i	−0.287608	+	0.564463i
$388$	−0.0670010	−	0.423027i	−0.00340146	−	0.0214760i
$389$	−13.0176	−	17.9172i	−0.660020	−	0.908440i	0.339462	−	0.940620i	$-0.389755\pi$
$389$	−13.0176	−	17.9172i	−0.660020	−	0.908440i	−0.999482	+	0.0321799i	$0.989755\pi$
$390$	−7.19596	+	4.31061i	−0.364382	+	0.218276i
$391$	−5.72734	−	1.86093i	−0.289644	−	0.0941111i
$392$	17.6618	+	2.79735i	0.892053	+	0.141287i
$393$	−7.69241	+	1.21836i	−0.388031	+	0.0614580i
$394$	−20.2509	+	6.57991i	−1.02022	+	0.331491i
$395$	−1.49574	+	0.102571i	−0.0752587	+	0.00516089i
$396$		0			0
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	−0.382910	−	0.923786i	$-0.625078\pi$
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	0.923786	+	0.382910i	$0.125078\pi$
$398$	−18.1254	−	9.23538i	−0.908547	−	0.462928i
$399$	−0.0667351	+	0.0918529i	−0.00334093	+	0.00459840i
$400$	−16.3163	+	15.6718i	−0.815813	+	0.783591i
$401$	−1.32312	+	4.07216i	−0.0660737	+	0.203354i	−0.978643	−	0.205569i	$-0.934096\pi$
$401$	−1.32312	+	4.07216i	−0.0660737	+	0.203354i	0.912569	+	0.408923i	$0.134096\pi$
$402$	6.31301	−	3.21664i	0.314864	−	0.160431i
$403$	0.169936	−	1.07294i	0.00846513	−	0.0534467i
$404$	−1.21250	−	0.880936i	−0.0603243	−	0.0438282i
$405$	−3.07547	−	7.64164i	−0.152821	−	0.379716i
$406$			2.77869i			0.137904i
$407$		0			0
$408$	5.36572	+	5.36572i	0.265643	+	0.265643i
$409$	−1.32742	−	4.08538i	−0.0656367	−	0.202009i	0.912859	−	0.408274i	$-0.133869\pi$
$409$	−1.32742	−	4.08538i	−0.0656367	−	0.202009i	−0.978496	+	0.206265i	$0.933869\pi$
$410$	22.1829	−	5.08990i	1.09553	−	0.251372i
$411$	2.79279	−	2.02908i	0.137758	−	0.100087i
$412$	0.456481	+	0.895894i	0.0224892	+	0.0441375i
$413$	0.836758	+	1.64223i	0.0411742	+	0.0808088i
$414$	4.72419	−	3.43232i	0.232181	−	0.168689i
$415$	−36.3595	+	8.34276i	−1.78482	+	0.409530i
$416$	−1.66623	−	5.12812i	−0.0816935	−	0.251427i
$417$	−5.92504	−	5.92504i	−0.290151	−	0.290151i
$418$		0			0
$419$		−	1.20241i		−	0.0587414i	−0.999569	−	0.0293707i	$-0.990650\pi$
$419$		−	1.20241i		−	0.0587414i	0.999569	−	0.0293707i	$-0.00935032\pi$
$420$	0.0395808	+	0.0983465i	0.00193134	+	0.00479882i
$421$	−25.3293	−	18.4028i	−1.23447	−	0.896898i	−0.237257	−	0.971447i	$-0.576248\pi$
$421$	−25.3293	−	18.4028i	−1.23447	−	0.896898i	−0.997217	+	0.0745484i	$0.976248\pi$
$422$	1.41066	−	8.90656i	0.0686699	−	0.433565i
$423$	26.0477	−	13.2720i	1.26648	−	0.645306i
$424$	7.16608	−	22.0549i	0.348016	−	1.07108i
$425$	−18.5288	−	0.373286i	−0.898779	−	0.0181070i
$426$	−8.16414	+	11.2370i	−0.395554	+	0.544433i
$427$	1.00536	+	0.512257i	0.0486529	+	0.0247899i
$428$	2.42802	−	2.42802i	0.117363	−	0.117363i
$429$		0			0
$430$	−17.8736	+	1.22568i	−0.861940	+	0.0591078i
$431$	9.40717	−	3.05658i	0.453128	−	0.147230i	−0.0735568	−	0.997291i	$-0.523435\pi$
$431$	9.40717	−	3.05658i	0.453128	−	0.147230i	0.526684	+	0.850061i	$0.323435\pi$
$432$	−19.1124	+	3.02711i	−0.919547	+	0.145642i
$433$	26.6501	+	4.22096i	1.28072	+	0.202846i	0.759462	−	0.650552i	$-0.225462\pi$
$433$	26.6501	+	4.22096i	1.28072	+	0.202846i	0.521260	+	0.853398i	$0.325462\pi$
$434$	−0.0971358	−	0.0315613i	−0.00466267	−	0.00151499i
$435$	−14.6002	+	8.74597i	−0.700025	+	0.419337i
$436$	1.74201	+	2.39768i	0.0834274	+	0.114828i
$437$	0.189045	+	1.19358i	0.00904324	+	0.0570968i
$438$	−1.32141	+	2.59342i	−0.0631395	+	0.123918i
$439$	−24.5862			−1.17344			−0.586718	−	0.809791i	$-0.699580\pi$
$439$	−24.5862			−1.17344			−0.586718	+	0.809791i	$0.699580\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$	7.91807	−	15.5401i	0.376624	−	0.739166i
$443$	−4.81773	−	30.4180i	−0.228897	−	1.44520i	−0.787781	−	0.615955i	$-0.788770\pi$
$443$	−4.81773	−	30.4180i	−0.228897	−	1.44520i	0.558884	−	0.829246i	$-0.311230\pi$
$444$	0.786706	+	1.08281i	0.0373354	+	0.0513878i
$445$	17.1820	+	4.30850i	0.814503	+	0.204242i
$446$	−30.7285	−	9.98429i	−1.45504	−	0.472770i
$447$	−4.53738	−	0.718651i	−0.214611	−	0.0339910i
$448$	1.21066	−	0.191749i	0.0571981	−	0.00905929i
$449$	6.96621	−	2.26346i	0.328756	−	0.106819i	−0.139988	−	0.990153i	$-0.544707\pi$
$449$	6.96621	−	2.26346i	0.328756	−	0.106819i	0.468744	+	0.883334i	$0.344707\pi$
$450$	10.8534	−	14.3227i	0.511636	−	0.675177i
$451$		0			0
$452$	−0.910918	+	0.910918i	−0.0428460	+	0.0428460i
$453$	10.6296	+	5.41603i	0.499421	+	0.254467i
$454$	−11.6778	+	16.0731i	−0.548066	+	0.754348i
$455$	−1.01643	+	0.850557i	−0.0476509	+	0.0398747i
$456$	0.470556	−	1.44822i	0.0220358	−	0.0678192i
$457$	6.00144	−	3.05789i	0.280736	−	0.143042i	−0.307954	−	0.951401i	$-0.599644\pi$
$457$	6.00144	−	3.05789i	0.280736	−	0.143042i	0.588689	+	0.808359i	$0.299644\pi$
$458$	3.90715	−	24.6688i	0.182569	−	1.15270i
$459$	−12.8241	−	9.31728i	−0.598579	−	0.434893i
$460$	1.03808	+	0.442289i	0.0484009	+	0.0206218i
$461$		−	29.0801i		−	1.35440i	−0.735801	−	0.677198i	$-0.763194\pi$
$461$		−	29.0801i		−	1.35440i	0.735801	−	0.677198i	$-0.236806\pi$
$462$		0			0
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	0.985227	−	0.171256i	$-0.0547826\pi$
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	−0.171256	+	0.985227i	$0.554783\pi$
$464$	−13.3490	−	41.0841i	−0.619713	−	1.90728i
$465$	−0.139902	−	0.609723i	−0.00648781	−	0.0282752i
$466$	−19.2378	+	13.9771i	−0.891174	+	0.647476i
$467$	−12.0115	−	23.5740i	−0.555828	−	1.09087i	−0.982464	−	0.186451i	$-0.940302\pi$
$467$	−12.0115	−	23.5740i	−0.555828	−	1.09087i	0.426636	−	0.904423i	$-0.359698\pi$
$468$	1.03206	+	2.02554i	0.0477072	+	0.0936307i
$469$	0.905678	−	0.658014i	0.0418203	−	0.0303842i
$470$	35.6093	+	22.3178i	1.64253	+	1.02944i
$471$	1.21900	+	3.75170i	0.0561686	+	0.172869i
$472$	−17.4796	−	17.4796i	−0.804563	−	0.804563i
$473$		0			0
$474$		−	0.812515i		−	0.0373201i
$475$	1.62129	+	3.34695i	0.0743897	+	0.153569i
$476$	−0.178326	−	0.129561i	−0.00817356	−	0.00593844i
$477$	−3.34012	+	21.0887i	−0.152934	+	0.965585i
$478$	−7.15350	+	3.64489i	−0.327194	+	0.166713i
$479$	−8.11328	+	24.9701i	−0.370705	+	1.14091i	0.575625	+	0.817714i	$0.304759\pi$
$479$	−8.11328	+	24.9701i	−0.370705	+	1.14091i	−0.946331	+	0.323200i	$0.895241\pi$
$480$	−1.99271	−	2.38131i	−0.0909541	−	0.108691i
$481$	−9.83531	+	13.5371i	−0.448452	+	0.617241i
$482$	−21.8971	−	11.1571i	−0.997386	−	0.508193i
$483$	−0.175368	+	0.175368i	−0.00797952	+	0.00797952i
$484$		0			0
$485$	2.02609	−	2.32443i	0.0920001	−	0.105547i
$486$	22.7936	−	7.40608i	1.03394	−	0.335946i
$487$	23.0478	−	3.65041i	1.04440	−	0.165416i	0.389416	−	0.921062i	$-0.372677\pi$
$487$	23.0478	−	3.65041i	1.04440	−	0.165416i	0.654980	+	0.755646i	$0.272677\pi$
$488$	−14.9470	−	2.36738i	−0.676620	−	0.107166i
$489$	7.59471	+	2.46767i	0.343445	+	0.111592i
$490$	−12.1627	−	20.3039i	−0.549454	−	0.917238i
$491$	10.7845	+	14.8436i	0.486697	+	0.669881i	0.979775	−	0.200104i	$-0.0641280\pi$
$491$	10.7845	+	14.8436i	0.486697	+	0.669881i	−0.493077	+	0.869985i	$0.664128\pi$
$492$	0.259367	+	1.63758i	0.0116932	+	0.0738278i
$493$	16.0653	−	31.5299i	0.723544	−	1.42004i
$494$	−3.49992			−0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	−0.996321	+	1.95539i	−0.0446911	+	0.0877112i
$498$	−3.16264	−	19.9681i	−0.141721	−	0.894793i
$499$	6.91112	+	9.51235i	0.309384	+	0.425831i	0.935189	−	0.354149i	$-0.115229\pi$
$499$	6.91112	+	9.51235i	0.309384	+	0.425831i	−0.625805	+	0.779980i	$0.715229\pi$
$500$	3.45199	+	0.376909i	0.154378	+	0.0168559i
$501$	9.14567	+	2.97161i	0.408599	+	0.132762i
$502$	−29.0401	−	4.59950i	−1.29612	−	0.205286i
$503$	−5.27489	+	0.835461i	−0.235196	+	0.0372514i	−0.272920	−	0.962037i	$-0.587989\pi$
$503$	−5.27489	+	0.835461i	−0.235196	+	0.0372514i	0.0377237	+	0.999288i	$0.487989\pi$
$504$	−1.10569	+	0.359260i	−0.0492513	+	0.0160027i
$505$	−0.738195	−	10.7647i	−0.0328492	−	0.479025i
$506$		0			0
$507$	−1.92638	+	1.92638i	−0.0855536	+	0.0855536i
$508$	4.03130	+	2.05405i	0.178860	+	0.0911337i
$509$	−11.5130	+	15.8462i	−0.510303	+	0.702371i	−0.983970	−	0.178332i	$-0.942930\pi$
$509$	−11.5130	+	15.8462i	−0.510303	+	0.702371i	0.473668	+	0.880704i	$0.342930\pi$
$510$	0.888823	−	10.0043i	0.0393577	−	0.442997i
$511$	−0.142113	+	0.437379i	−0.00628671	+	0.0193485i
$512$	−13.6838	+	6.97225i	−0.604745	+	0.308133i
$513$	−0.497609	+	3.14178i	−0.0219700	+	0.138713i
$514$	5.78738	+	4.20478i	0.255270	+	0.185465i
$515$	−2.83742	+	6.65963i	−0.125032	+	0.293458i
$516$		−	1.30513i		−	0.0574550i
$517$		0			0
$518$	1.11243	+	1.11243i	0.0488775	+	0.0488775i
$519$	3.07085	+	9.45111i	0.134795	+	0.414858i
$520$	9.43995	−	15.0620i	0.413969	−	0.660511i
$521$	−15.1561	+	11.0116i	−0.664003	+	0.482426i	−0.868012	−	0.496543i	$-0.834603\pi$
$521$	−15.1561	+	11.0116i	−0.664003	+	0.482426i	0.204010	+	0.978969i	$0.434603\pi$
$522$	15.5780	+	30.5735i	0.681830	+	1.33817i
$523$	1.17234	+	2.30085i	0.0512628	+	0.100609i	0.915217	−	0.402962i	$-0.132019\pi$
$523$	1.17234	+	2.30085i	0.0512628	+	0.100609i	−0.863954	+	0.503571i	$0.832019\pi$
$524$	−2.45475	+	1.78348i	−0.107236	+	0.0779117i
$525$	−0.360125	+	0.672924i	−0.0157172	+	0.0293688i
$526$	7.45453	+	22.9427i	0.325033	+	1.00035i
$527$	0.919727	+	0.919727i	0.0400639	+	0.0400639i
$528$		0			0
$529$		−	20.3603i		−	0.885228i
$530$	−28.4742	+	11.4598i	−1.23684	+	0.497781i
$531$	18.4134	+	13.3781i	0.799074	+	0.580561i
$532$	−0.00691951	+	0.0436880i	−0.000299999	+	0.00189412i
$533$	−18.4688	+	9.41034i	−0.799974	+	0.407607i
$534$	−2.96657	+	9.13016i	−0.128376	+	0.395101i
$535$	24.6239	+	2.18769i	1.06459	+	0.0945823i
$536$	−8.82527	+	12.1469i	−0.381194	+	0.524668i
$537$	−14.3335	−	7.30328i	−0.618536	−	0.315160i
$538$	−12.1591	+	12.1591i	−0.524216	+	0.524216i
$539$		0			0
$540$	2.23898	+	1.95161i	0.0963502	+	0.0839837i
$541$	−8.78315	+	2.85382i	−0.377617	+	0.122695i	−0.491675	−	0.870779i	$-0.663615\pi$
$541$	−8.78315	+	2.85382i	−0.377617	+	0.122695i	0.114058	+	0.993474i	$0.463615\pi$
$542$	−26.7663	+	4.23937i	−1.14971	+	0.182096i
$543$	−3.62974	−	0.574895i	−0.155767	−	0.0246711i
$544$	6.14015	+	1.99505i	0.263257	+	0.0855372i
$545$	−5.18969	+	20.6961i	−0.222302	+	0.886522i
$546$	−0.422192	−	0.581097i	−0.0180681	−	0.0248686i
$547$	−0.167546	−	1.05784i	−0.00716375	−	0.0452301i	0.983848	−	0.179009i	$-0.0572890\pi$
$547$	−0.167546	−	1.05784i	−0.00716375	−	0.0452301i	−0.991011	+	0.133778i	$0.957289\pi$
$548$	0.610569	−	1.19831i	0.0260822	−	0.0511892i
$549$	13.9337			0.594674
$550$		0			0
$551$	−7.10113			−0.302518
$552$	1.51010	−	2.96374i	0.0642741	−	0.126145i
$553$	−0.0200828	−	0.126798i	−0.000854008	−	0.00539200i
$554$	4.18286	+	5.75721i	0.177713	+	0.244600i
$555$	−2.34370	+	9.34649i	−0.0994845	+	0.396736i
$556$	−3.10470	−	1.00878i	−0.131669	−	0.0427818i
$557$	−42.5071	−	6.73247i	−1.80108	−	0.285264i	−0.836294	−	0.548282i	$-0.815282\pi$
$557$	−42.5071	−	6.73247i	−1.80108	−	0.285264i	−0.964791	+	0.263018i	$0.915282\pi$
$558$	−1.24571	+	0.197301i	−0.0527351	+	0.00835241i
$559$	15.5180	−	5.04210i	0.656340	−	0.213258i
$560$	−1.46033	−	1.27290i	−0.0617102	−	0.0537897i
$561$		0			0
$562$	−14.1765	+	14.1765i	−0.597998	+	0.597998i
$563$	23.0435	+	11.7412i	0.971166	+	0.494834i	0.866230	−	0.499645i	$-0.166536\pi$
$563$	23.0435	+	11.7412i	0.971166	+	0.494834i	0.104936	+	0.994479i	$0.466536\pi$
$564$	−1.79949	+	2.47679i	−0.0757723	+	0.104292i
$565$	−9.23812	−	0.820754i	−0.388651	−	0.0345294i
$566$	−10.7034	+	32.9417i	−0.449898	+	1.38464i
$567$	0.628469	−	0.320221i	0.0263932	−	0.0134480i
$568$	4.60445	−	29.0714i	0.193199	−	1.21981i
$569$	−21.9823	−	15.9711i	−0.921548	−	0.669544i	0.0223611	−	0.999750i	$-0.492882\pi$
$569$	−21.9823	−	15.9711i	−0.921548	−	0.669544i	−0.943909	+	0.330206i	$0.892882\pi$
$570$	−1.86974	+	0.752498i	−0.0783146	+	0.0315187i
$571$		−	40.5475i		−	1.69686i	−0.529308	−	0.848430i	$-0.677549\pi$
$571$		−	40.5475i		−	1.69686i	0.529308	−	0.848430i	$-0.322451\pi$
$572$		0			0
$573$	3.56628	+	3.56628i	0.148984	+	0.148984i
$574$	0.602227	+	1.85346i	0.0251365	+	0.0773621i
$575$	2.35422	+	7.77504i	0.0981776	+	0.324242i
$576$	12.2457	−	8.89699i	0.510236	−	0.370708i
$577$	15.3485	+	30.1231i	0.638965	+	1.25404i	0.952522	+	0.304470i	$0.0984795\pi$
$577$	15.3485	+	30.1231i	0.638965	+	1.25404i	−0.313556	+	0.949570i	$0.601521\pi$
$578$	−2.25092	−	4.41767i	−0.0936257	−	0.183751i
$579$	−3.82588	+	2.77966i	−0.158998	+	0.115519i
$580$	−3.52122	+	5.61829i	−0.146211	+	0.233287i
$581$	−0.987098	−	3.03798i	−0.0409517	−	0.126036i
$582$	1.18165	+	1.18165i	0.0489808	+	0.0489808i
$583$		0			0
$584$		−	6.16801i		−	0.255234i
$585$	−6.41518	+	15.0569i	−0.265235	+	0.622525i
$586$	8.88835	+	6.45777i	0.367175	+	0.266768i
$587$	−1.51493	+	9.56487i	−0.0625277	+	0.394784i	0.936499	+	0.350671i	$0.114046\pi$
$587$	−1.51493	+	9.56487i	−0.0625277	+	0.394784i	−0.999027	+	0.0441136i	$0.985954\pi$
$588$	1.53627	−	0.782769i	0.0633547	−	0.0322808i
$589$	0.0806570	−	0.248237i	0.00332341	−	0.0102284i
$590$	−2.89547	+	32.5904i	−0.119204	+	1.34172i
$591$	6.56411	−	9.03472i	0.270011	−	0.371639i
$592$	−21.7920	−	11.1036i	−0.895644	−	0.456353i
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	−0.934012	−	0.357243i	$-0.883717\pi$
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	0.357243	+	0.934012i	$0.383717\pi$
$594$		0			0
$595$	−0.108568	−	1.58320i	−0.00445086	−	0.0649048i
$596$	−1.70215	+	0.553064i	−0.0697230	+	0.0226544i
$597$	10.5377	−	1.66901i	0.431281	−	0.0683082i
$598$	−7.55106	−	1.19597i	−0.308786	−	0.0489068i
$599$	−4.29480	−	1.39547i	−0.175481	−	0.0570172i	0.219959	−	0.975509i	$-0.429408\pi$
$599$	−4.29480	−	1.39547i	−0.175481	−	0.0570172i	−0.395440	+	0.918492i	$0.629408\pi$
$600$	1.80465	−	10.0761i	0.0736744	−	0.411354i
$601$	−4.92416	−	6.77753i	−0.200861	−	0.276461i	0.696690	−	0.717372i	$-0.254655\pi$
$601$	−4.92416	−	6.77753i	−0.200861	−	0.276461i	−0.897551	+	0.440911i	$0.854655\pi$
$602$	−0.239983	−	1.51519i	−0.00978098	−	0.0617547i
$603$	6.27605	−	12.3174i	0.255581	−	0.501605i
$604$	4.64774			0.189114
$605$		0			0
$606$	5.84763			0.237544
$607$	3.48610	−	6.84185i	0.141496	−	0.277702i	−0.809373	−	0.587295i	$-0.800193\pi$
$607$	3.48610	−	6.84185i	0.141496	−	0.277702i	0.950869	+	0.309593i	$0.100193\pi$
$608$	−0.202670	−	1.27961i	−0.00821937	−	0.0518950i
$609$	−0.856602	−	1.17901i	−0.0347113	−	0.0477760i
$610$	10.2932	+	17.1831i	0.416760	+	0.695722i
$611$	−36.4010	−	11.8274i	−1.47263	−	0.478486i
$612$	−2.68844	−	0.425807i	−0.108674	−	0.0172122i
$613$	42.3979	−	6.71517i	1.71243	−	0.271223i	0.778235	−	0.627973i	$-0.216115\pi$
$613$	42.3979	−	6.71517i	1.71243	−	0.271223i	0.934200	+	0.356750i	$0.116115\pi$
$614$	−41.1497	+	13.3704i	−1.66067	+	0.539584i
$615$	−7.84320	+	8.99810i	−0.316268	+	0.362838i
$616$		0			0
$617$	33.4407	−	33.4407i	1.34627	−	1.34627i	0.456601	−	0.889671i	$-0.349067\pi$
$617$	33.4407	−	33.4407i	1.34627	−	1.34627i	0.889671	−	0.456601i	$-0.150933\pi$
$618$	−3.49551	−	1.78105i	−0.140610	−	0.0716444i
$619$	−12.4023	+	17.0703i	−0.498492	+	0.686115i	−0.981926	−	0.189266i	$-0.939389\pi$
$619$	−12.4023	+	17.0703i	−0.498492	+	0.686115i	0.483434	+	0.875381i	$0.339389\pi$
$620$	−0.156405	−	0.186907i	−0.00628140	−	0.00750636i
$621$	−2.14718	+	6.60834i	−0.0861633	+	0.265183i
$622$	−10.1794	+	5.18667i	−0.408157	+	0.207966i
$623$	−0.237282	+	1.49814i	−0.00950651	+	0.0600217i
$624$	9.03389	+	6.56351i	0.361645	+	0.262751i
$625$	13.8681	+	20.8009i	0.554724	+	0.832034i
$626$			2.04613i			0.0817798i
$627$		0			0
$628$	1.08671	+	1.08671i	0.0433645	+	0.0433645i
$629$	−6.19116	−	19.0544i	−0.246858	−	0.759750i
$630$	1.30386	+	0.817184i	0.0519471	+	0.0325574i
$631$	22.8304	−	16.5872i	0.908863	−	0.660327i	−0.0318642	−	0.999492i	$-0.510144\pi$
$631$	22.8304	−	16.5872i	0.908863	−	0.660327i	0.940727	+	0.339165i	$0.110144\pi$
$632$	0.781686	+	1.53414i	0.0310938	+	0.0610250i
$633$	2.14712	+	4.21396i	0.0853404	+	0.167490i
$634$	−13.9355	+	10.1248i	−0.553451	+	0.402106i
$635$	7.28469	+	31.7482i	0.289084	+	1.25989i
$636$	−0.690963	−	2.12656i	−0.0273985	−	0.0843238i
$637$	15.2422	+	15.2422i	0.603918	+	0.603918i
$638$		0			0
$639$			27.1004i			1.07208i
$640$	27.1844	+	11.5823i	1.07456	+	0.457830i
$641$	13.7037	+	9.95634i	0.541265	+	0.393252i	0.824554	−	0.565783i	$-0.191426\pi$
$641$	13.7037	+	9.95634i	0.541265	+	0.393252i	−0.283290	+	0.959034i	$0.591426\pi$
$642$	−2.09582	+	13.2325i	−0.0827156	+	0.522245i
$643$	−5.59164	+	2.84908i	−0.220513	+	0.112357i	−0.560758	−	0.827980i	$-0.689490\pi$
$643$	−5.59164	+	2.84908i	−0.220513	+	0.112357i	0.340245	+	0.940337i	$0.389490\pi$
$644$	−0.0298576	+	0.0918922i	−0.00117655	+	0.00362106i
$645$	7.20598	−	6.03004i	0.283735	−	0.237432i
$646$	2.46318	−	3.39028i	0.0969127	−	0.133389i
$647$	38.7473	+	19.7428i	1.52331	+	0.776168i	0.997238	−	0.0742694i	$-0.0236625\pi$
$647$	38.7473	+	19.7428i	1.52331	+	0.776168i	0.526077	+	0.850437i	$0.323662\pi$
$648$	−6.68931	+	6.68931i	−0.262781	+	0.262781i
$649$		0			0
$650$	−23.3073	+	3.21171i	−0.914188	+	0.125974i
$651$	0.0509447	−	0.0165529i	0.00199668	−	0.000648761i
$652$	3.07278	−	0.486681i	0.120339	−	0.0190599i
$653$	−9.61123	−	1.52227i	−0.376117	−	0.0595710i	−0.0344856	−	0.999405i	$-0.510979\pi$
$653$	−9.61123	−	1.52227i	−0.376117	−	0.0595710i	−0.341631	+	0.939834i	$0.610979\pi$
$654$	−10.9975	−	3.57330i	−0.430036	−	0.139727i
$655$	−21.1887	−	5.31322i	−0.827911	−	0.207605i
$656$	−17.8083	−	24.5111i	−0.695298	−	0.956996i
$657$	0.888399	+	5.60913i	0.0346597	+	0.218833i
$658$	−1.63370	+	3.20633i	−0.0636884	+	0.124996i
$659$	−3.37375			−0.131423			−0.0657113	−	0.997839i	$-0.520932\pi$
$659$	−3.37375			−0.131423			−0.0657113	+	0.997839i	$0.520932\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	12.2180	−	23.9792i	0.474866	−	0.931976i
$663$	1.43095	+	9.03466i	0.0555735	+	0.350877i
$664$	25.1820	+	34.6600i	0.977250	+	1.34507i
$665$	−0.273184	+	0.163646i	−0.0105936	+	0.00634591i
$666$	18.4765	+	6.00337i	0.715949	+	0.232626i
$667$	−15.3206	−	2.42655i	−0.593218	−	0.0939565i
$668$	3.70030	−	0.586069i	0.143169	−	0.0226757i
$669$	16.1161	−	5.23645i	0.623086	−	0.202453i
$670$	19.8263	−	1.35959i	0.765955	−	0.0525256i
$671$		0			0
$672$	0.188008	−	0.188008i	0.00725256	−	0.00725256i
$673$	34.0839	+	17.3666i	1.31384	+	0.669433i	0.963630	−	0.267239i	$-0.0861114\pi$
$673$	34.0839	+	17.3666i	1.31384	+	0.669433i	0.350207	+	0.936672i	$0.386111\pi$
$674$	−6.80832	+	9.37085i	−0.262247	+	0.360952i
$675$	−0.430706	+	21.3790i	−0.0165779	+	0.822877i
$676$	−0.327980	+	1.00942i	−0.0126146	+	0.0388238i
$677$	28.6832	−	14.6148i	1.10238	−	0.561693i	0.194495	−	0.980903i	$-0.437693\pi$
$677$	28.6832	−	14.6148i	1.10238	−	0.561693i	0.907889	+	0.419211i	$0.137693\pi$
$678$	0.786287	−	4.96442i	0.0301972	−	0.190657i
$679$	0.213610	+	0.155197i	0.00819759	+	0.00595590i
$680$	7.94646	+	19.7446i	0.304733	+	0.757171i
$681$		−	10.4198i		−	0.399289i
$682$		0			0
$683$	−28.7223	−	28.7223i	−1.09903	−	1.09903i	−0.994524	−	0.104505i	$-0.966674\pi$
$683$	−28.7223	−	28.7223i	−1.09903	−	1.09903i	−0.104505	−	0.994524i	$-0.533326\pi$
$684$	0.168791	+	0.519484i	0.00645388	+	0.0198630i
$685$	9.43720	−	2.16538i	0.360577	−	0.0827350i
$686$	3.28785	−	2.38876i	0.125531	−	0.0912033i
$687$	5.94695	+	11.6715i	0.226890	+	0.445297i
$688$	10.8273	+	21.2498i	0.412788	+	0.810142i
$689$	22.6155	−	16.4311i	0.861581	−	0.625975i
$690$	−4.29108	+	0.984597i	−0.163359	+	0.0374830i
$691$	−7.80728	−	24.0283i	−0.297003	−	0.914081i	−0.982541	−	0.186044i	$-0.940433\pi$
$691$	−7.80728	−	24.0283i	−0.297003	−	0.914081i	0.685538	−	0.728036i	$-0.259567\pi$
$692$	2.73759	+	2.73759i	0.104068	+	0.104068i
$693$		0			0
$694$			14.1878i			0.538562i
$695$	−8.77480	−	21.8028i	−0.332847	−	0.827027i
$696$	15.8129	+	11.4887i	0.599386	+	0.435479i
$697$	3.88250	−	24.5131i	0.147060	−	0.928501i
$698$	2.03398	−	1.03636i	0.0769873	−	0.0392270i
$699$	3.85390	−	11.8611i	0.145768	−	0.448627i
$700$	−0.00598918	+	0.297285i	−0.000226370	+	0.0112363i
$701$	16.5916	−	22.8364i	0.626657	−	0.862519i	−0.371160	−	0.928569i	$-0.621040\pi$
$701$	16.5916	−	22.8364i	0.626657	−	0.862519i	0.997816	+	0.0660500i	$0.0210397\pi$
$702$	−17.9305	−	9.13604i	−0.676743	−	0.344818i
$703$	−2.84289	+	2.84289i	−0.107222	+	0.107222i
$704$		0			0
$705$	−21.9892	+	1.50791i	−0.828161	+	0.0567914i
$706$	−9.00040	+	2.92441i	−0.338735	+	0.110062i
$707$	0.912558	−	0.144535i	0.0343203	−	0.00543580i
$708$	−2.35418	−	0.372865i	−0.0884754	−	0.0140131i
$709$	−7.76034	−	2.52149i	−0.291446	−	0.0946964i	0.159645	−	0.987174i	$-0.448965\pi$
$709$	−7.76034	−	2.52149i	−0.291446	−	0.0946964i	−0.451091	+	0.892478i	$0.648965\pi$
$710$	−33.4204	+	20.0199i	−1.25425	+	0.751333i
$711$	−0.931826	−	1.28255i	−0.0349462	−	0.0480993i
$712$	−3.18243	−	20.0930i	−0.119266	−	0.753019i
$713$	0.258843	−	0.508008i	0.00969374	−	0.0190250i
$714$	0.860026			0.0321856
$715$		0			0
$716$	−6.26727			−0.234219
$717$	1.91163	−	3.75179i	0.0713912	−	0.140113i
$718$	−6.25489	−	39.4918i	−0.233430	−	1.47382i
$719$	0.609910	+	0.839469i	0.0227458	+	0.0313069i	0.820238	−	0.572022i	$-0.193841\pi$
$719$	0.609910	+	0.839469i	0.0227458	+	0.0313069i	−0.797493	+	0.603329i	$0.793841\pi$
$720$	−23.2039	−	5.81855i	−0.864758	−	0.216844i
$721$	−0.589518	−	0.191546i	−0.0219548	−	0.00713354i
$722$	27.6950	+	4.38646i	1.03070	+	0.163247i
$723$	12.7305	−	2.01631i	0.473452	−	0.0749875i
$724$	−1.36166	+	0.442431i	−0.0506058	+	0.0164428i
$725$	−47.2892	+	6.51637i	−1.75627	+	0.242012i
$726$		0			0
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	−0.765294	−	0.643681i	$-0.777406\pi$
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	0.643681	+	0.765294i	$0.277406\pi$
$728$	1.35621	+	0.691021i	0.0502643	+	0.0256110i
$729$	−0.892381	+	1.22826i	−0.0330512	+	0.0454910i
$730$	−6.26093	+	5.23921i	−0.231727	+	0.193912i
$731$	−6.03714	+	18.5804i	−0.223292	+	0.687222i
$732$	−1.30014	+	0.662452i	−0.0480544	+	0.0244849i
$733$	−7.14516	+	45.1128i	−0.263912	+	1.66628i	0.398523	+	0.917158i	$0.369523\pi$
$733$	−7.14516	+	45.1128i	−0.263912	+	1.66628i	−0.662435	+	0.749119i	$0.730477\pi$
$734$	−10.0460	−	7.29884i	−0.370805	−	0.269405i
$735$	11.4199	+	4.86559i	0.421228	+	0.179470i
$736$		−	2.83001i		−	0.104315i
$737$		0			0
$738$	17.0171	+	17.0171i	0.626410	+	0.626410i
$739$	1.17326	+	3.61092i	0.0431591	+	0.132830i	0.970314	−	0.241848i	$-0.0777534\pi$
$739$	1.17326	+	3.61092i	0.0431591	+	0.132830i	−0.927155	+	0.374678i	$0.877753\pi$
$740$	0.839552	+	3.65895i	0.0308625	+	0.134506i
$741$	1.48503	−	1.07894i	0.0545539	−	0.0396357i
$742$	−1.19320	−	2.34179i	−0.0438039	−	0.0859699i
$743$	19.2624	+	37.8046i	0.706668	+	1.38691i	0.912807	+	0.408392i	$0.133910\pi$
$743$	19.2624	+	37.8046i	0.706668	+	1.38691i	−0.206138	+	0.978523i	$0.566090\pi$
$744$	−0.581224	+	0.422284i	−0.0213087	+	0.0154817i
$745$	−10.9180	−	6.84278i	−0.400006	−	0.250700i
$746$	4.06860	+	12.5219i	0.148962	+	0.458459i
$747$	−27.8924	−	27.8924i	−1.02053	−	1.02053i
$748$		0			0
$749$			2.11681i			0.0773467i
$750$	−11.7608	+	6.72694i	−0.429442	+	0.245633i
$751$	8.08383	+	5.87325i	0.294983	+	0.214318i	0.725426	−	0.688300i	$-0.241643\pi$
$751$	8.08383	+	5.87325i	0.294983	+	0.214318i	−0.430443	+	0.902618i	$0.641643\pi$
$752$	8.75157	−	55.2552i	0.319137	−	2.01495i
$753$	13.7398	−	7.00075i	0.500704	−	0.255122i
$754$	13.8824	−	42.7257i	0.505568	−	1.55598i
$755$	21.4738	+	25.6615i	0.781512	+	0.933918i
$756$	−0.149491	+	0.205757i	−0.00543693	+	0.00748330i
$757$	−26.1808	−	13.3398i	−0.951558	−	0.484843i	−0.0919310	−	0.995765i	$-0.529304\pi$
$757$	−26.1808	−	13.3398i	−0.951558	−	0.484843i	−0.859627	+	0.510922i	$0.829304\pi$
$758$	−0.664675	+	0.664675i	−0.0241421	+	0.0241421i
$759$		0			0
$760$	2.80638	−	3.21961i	0.101798	−	0.116788i
$761$	28.8663	−	9.37924i	1.04640	−	0.339997i	0.265147	−	0.964208i	$-0.414579\pi$
$761$	28.8663	−	9.37924i	1.04640	−	0.339997i	0.781256	+	0.624211i	$0.214579\pi$
$762$	−17.4357	+	2.76154i	−0.631627	+	0.100040i
$763$	−1.80455	−	0.285812i	−0.0653289	−	0.0103471i
$764$	1.86872	+	0.607184i	0.0676079	+	0.0219671i
$765$	−10.0703	−	16.8110i	−0.364093	−	0.607803i
$766$	9.27323	+	12.7635i	0.335056	+	0.461164i
$767$	−4.66152	−	29.4317i	−0.168318	−	1.06272i
$768$	−2.63621	+	5.17386i	−0.0951261	+	0.186696i
$769$	37.6421			1.35741			0.678705	−	0.734411i	$-0.262542\pi$
$769$	37.6421			1.35741			0.678705	+	0.734411i	$0.262542\pi$
$770$		0			0
$771$	−3.75184			−0.135119
$772$	−0.836426	+	1.64158i	−0.0301036	+	0.0590817i
$773$	−4.03803	−	25.4951i	−0.145238	−	0.916996i	−0.947438	−	0.319941i	$-0.896337\pi$
$773$	−4.03803	−	25.4951i	−0.145238	−	0.916996i	0.802200	−	0.597056i	$-0.203663\pi$
$774$	−11.1350	−	15.3260i	−0.400240	−	0.550883i
$775$	0.309331	−	1.72712i	0.0111115	−	0.0620399i
$776$	−3.36793	−	1.09431i	−0.120902	−	0.0392833i
$777$	−0.814945	−	0.129075i	−0.0292360	−	0.00463053i
$778$	33.2502	−	5.26632i	1.19208	−	0.188807i
$779$	−4.73664	+	1.53903i	−0.169708	+	0.0551414i
$780$	−0.117260	−	1.70994i	−0.00419856	−	0.0612257i
$781$		0			0
$782$	6.47282	−	6.47282i	0.231467	−	0.231467i
$783$	−36.3799	−	18.5365i	−1.30011	−	0.662440i
$784$	−18.5194	+	25.4898i	−0.661408	+	0.910350i
$785$	−0.979146	+	11.0209i	−0.0349472	+	0.393354i
$786$	3.65836	−	11.2593i	0.130489	−	0.401605i
$787$	15.3923	−	7.84278i	0.548677	−	0.279565i	−0.157597	−	0.987504i	$-0.550375\pi$
$787$	15.3923	−	7.84278i	0.548677	−	0.279565i	0.706274	+	0.707939i	$0.250375\pi$
$788$	0.680608	−	4.29719i	0.0242456	−	0.153081i
$789$	−10.2356	−	7.43663i	−0.364399	−	0.264751i
$790$	0.893279	−	2.09659i	0.0317815	−	0.0745933i
$791$		−	0.794162i		−	0.0282372i
$792$		0			0
$793$	−12.8994	−	12.8994i	−0.458070	−	0.458070i
$794$	7.15898	+	22.0331i	0.254063	+	0.781925i
$795$	8.54894	−	13.6403i	0.303200	−	0.483772i
$796$	3.36273	−	2.44317i	0.119189	−	0.0865958i
$797$	−20.2339	−	39.7113i	−0.716722	−	1.40665i	−0.905380	−	0.424603i	$-0.860414\pi$
$797$	−20.2339	−	39.7113i	−0.716722	−	1.40665i	0.188658	−	0.982043i	$-0.439586\pi$
$798$	−0.0783508	−	0.153772i	−0.00277359	−	0.00544348i
$799$	37.0754	−	26.9368i	1.31163	−	0.952957i
$800$	−2.52390	−	8.33544i	−0.0892333	−	0.294702i
$801$	5.78814	+	17.8140i	0.204514	+	0.629428i
$802$	−4.60219	−	4.60219i	−0.162509	−	0.162509i
$803$		0			0
$804$			1.44771i			0.0510569i
$805$	−0.645313	+	0.259714i	−0.0227443	+	0.00915373i
$806$	1.33590	+	0.970585i	0.0470549	+	0.0341874i
$807$	1.41081	−	8.90749i	0.0496628	−	0.313559i
$808$	−11.0412	+	5.62575i	−0.388427	+	0.197913i
$809$	−4.70791	+	14.4894i	−0.165521	+	0.509422i	−0.999074	−	0.0430175i	$-0.986303\pi$
$809$	−4.70791	+	14.4894i	−0.165521	+	0.509422i	0.833553	+	0.552439i	$0.186303\pi$
$810$	12.4721	+	1.10807i	0.438225	+	0.0389337i
$811$	−26.7779	+	36.8566i	−0.940299	+	1.29421i	0.0154047	+	0.999881i	$0.495096\pi$
$811$	−26.7779	+	36.8566i	−0.940299	+	1.29421i	−0.955704	+	0.294330i	$0.904904\pi$
$812$	−0.505881	−	0.257759i	−0.0177529	−	0.00904558i
$813$	10.0502	−	10.0502i	0.352475	−	0.352475i
$814$		0			0
$815$	16.8842	+	14.7171i	0.591427	+	0.515518i
$816$	−12.7158	+	4.13162i	−0.445143	+	0.144636i
$817$	3.87217	−	0.613292i	0.135470	−	0.0214564i
$818$	6.44923	+	1.02146i	0.225492	+	0.0357144i
$819$	−1.33285	−	0.433069i	−0.0465736	−	0.0151327i
$820$	−1.13109	+	4.51071i	−0.0394995	+	0.157521i
$821$	−16.8767	−	23.2288i	−0.589000	−	0.810690i	0.405646	−	0.914030i	$-0.367047\pi$
$821$	−16.8767	−	23.2288i	−0.589000	−	0.810690i	−0.994646	+	0.103341i	$0.967047\pi$
$822$	0.820871	+	5.18277i	0.0286312	+	0.180770i
$823$	−12.2383	+	24.0189i	−0.426599	+	0.837247i	0.573242	+	0.819386i	$0.305686\pi$
$823$	−12.2383	+	24.0189i	−0.426599	+	0.837247i	−0.999840	+	0.0178607i	$0.994314\pi$
$824$	8.31350			0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	−18.0157	+	35.3578i	−0.626467	+	1.22951i	0.331722	+	0.943377i	$0.392370\pi$
$827$	−18.0157	+	35.3578i	−0.626467	+	1.22951i	−0.958190	+	0.286134i	$0.907630\pi$
$828$	0.186650	+	1.17846i	0.00648655	+	0.0409544i
$829$	6.38756	+	8.79172i	0.221849	+	0.305349i	0.905405	−	0.424549i	$-0.139567\pi$
$829$	6.38756	+	8.79172i	0.221849	+	0.305349i	−0.683556	+	0.729898i	$0.739567\pi$
$830$	13.7922	−	55.0021i	0.478733	−	1.90915i
$831$	−3.54961	−	1.15334i	−0.123134	−	0.0400088i
$832$	−19.5732	−	3.10010i	−0.678580	−	0.107476i
$833$	−25.4920	+	4.03753i	−0.883244	+	0.139892i
$834$	12.1136	−	3.93596i	0.419461	−	0.136291i
$835$	20.3322	+	17.7226i	0.703625	+	0.613316i
$836$		0			0
$837$	1.06120	−	1.06120i	0.0366805	−	0.0366805i
$838$	1.62852	+	0.829773i	0.0562563	+	0.0286640i
$839$	−23.6970	+	32.6161i	−0.818112	+	1.12603i	0.171909	+	0.985113i	$0.445007\pi$
$839$	−23.6970	+	32.6161i	−0.818112	+	1.12603i	−0.990021	+	0.140922i	$0.954993\pi$
$840$	0.873089	+	0.0775689i	0.0301244	+	0.00267638i
$841$	19.2051	−	59.1073i	0.662246	−	2.03818i
$842$	42.4041	−	21.6060i	1.46134	−	0.744591i
$843$	1.64488	−	10.3854i	0.0566528	−	0.357692i
$844$	1.49065	+	1.08302i	0.0513102	+	0.0372790i
$845$	−7.08864	+	2.85291i	−0.243857	+	0.0981431i
$846$			44.4376i			1.52780i
$847$		0			0
$848$	28.8921	+	28.8921i	0.992159	+	0.992159i
$849$	−5.61360	−	17.2769i	−0.192658	−	0.592941i
$850$	13.2922	−	24.8376i	0.455919	−	0.851921i
$851$	−7.10498	+	5.16207i	−0.243556	+	0.176954i
$852$	−1.28844	−	2.52871i	−0.0441414	−	0.0866323i
$853$	−6.33606	−	12.4352i	−0.216942	−	0.425774i	0.756729	−	0.653728i	$-0.226796\pi$
$853$	−6.33606	−	12.4352i	−0.216942	−	0.425774i	−0.973672	+	0.227955i	$0.926796\pi$
$854$	−1.38759	+	1.00814i	−0.0474823	+	0.0344979i
$855$	−2.08836	+	3.33210i	−0.0714205	+	0.113955i
$856$	−8.77321	−	27.0012i	−0.299862	−	0.922881i
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	0.997005	−	0.0773373i	$-0.0246418\pi$
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	−0.0773373	+	0.997005i	$0.524642\pi$
$858$		0			0
$859$		−	18.3200i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$859$		−	18.3200i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$860$	1.43486	−	3.36771i	0.0489282	−	0.114838i
$861$	−0.826904	−	0.600781i	−0.0281808	−	0.0204746i
$862$	−2.35205	+	14.8503i	−0.0801112	+	0.505802i
$863$	10.8283	−	5.51731i	0.368601	−	0.187812i	−0.259872	−	0.965643i	$-0.583680\pi$
$863$	10.8283	−	5.51731i	0.368601	−	0.187812i	0.628473	+	0.777832i	$0.283680\pi$
$864$	2.30194	−	7.08464i	0.0783135	−	0.241024i
$865$	−2.46662	+	27.7634i	−0.0838676	+	0.943985i
$866$	−24.1079	+	33.1817i	−0.819219	+	1.12756i
$867$	2.31693	+	1.18053i	0.0786871	+	0.0400931i
$868$	0.0147565	−	0.0147565i	0.000500870	−	0.000500870i
$869$		0			0
$870$	−1.76991	−	25.8098i	−0.0600057	−	0.875035i
$871$	−17.2133	+	5.59295i	−0.583251	+	0.189510i
$872$	24.2026	−	3.83331i	0.819602	−	0.129812i
$873$	3.22038	+	0.510058i	0.108993	+	0.0172628i
$874$	−1.74703	−	0.567644i	−0.0590941	−	0.0192008i
$875$	−1.66907	+	1.34047i	−0.0564248	+	0.0453161i
$876$	−0.349572	−	0.481145i	−0.0118109	−	0.0162564i
$877$	2.00784	+	12.6770i	0.0677999	+	0.428072i	0.998118	+	0.0613187i	$0.0195306\pi$
$877$	2.00784	+	12.6770i	0.0677999	+	0.428072i	−0.930318	+	0.366753i	$0.880469\pi$
$878$	16.9668	−	33.2992i	0.572602	−	1.12379i
$879$	−5.76213			−0.194352
$880$		0			0
$881$	13.8380			0.466216			0.233108	−	0.972451i	$-0.425110\pi$
$881$	13.8380			0.466216			0.233108	+	0.972451i	$0.425110\pi$
$882$	11.3619	−	22.2991i	0.382577	−	0.750849i
$883$	−6.81876	−	43.0520i	−0.229470	−	1.44881i	−0.786123	−	0.618069i	$-0.787915\pi$
$883$	−6.81876	−	43.0520i	−0.229470	−	1.44881i	0.556654	−	0.830745i	$-0.312085\pi$
$884$	2.09468	+	2.88308i	0.0704517	+	0.0969685i
$885$	−8.81823	−	14.7208i	−0.296422	−	0.494835i
$886$	44.5223	+	14.4662i	1.49576	+	0.486001i
$887$	−10.2712	−	1.62679i	−0.344872	−	0.0546224i	−0.0184043	−	0.999831i	$-0.505859\pi$
$887$	−10.2712	−	1.62679i	−0.344872	−	0.0546224i	−0.326468	+	0.945208i	$0.605859\pi$
$888$	10.9300	−	1.73115i	0.366788	−	0.0580935i
$889$	−2.65268	+	0.861909i	−0.0889682	+	0.0289075i
$890$	−17.6925	+	20.2977i	−0.593055	+	0.680381i
$891$		0			0
$892$	4.66817	−	4.66817i	0.156302	−	0.156302i
$893$	−8.19397	−	4.17503i	−0.274201	−	0.139712i
$894$	4.10455	−	5.64943i	0.137277	−	0.188945i
$895$	−28.9564	−	34.6034i	−0.967907	−	1.15666i
$896$	−0.781885	+	2.40639i	−0.0261209	+	0.0803920i
$897$	3.57263	−	1.82035i	0.119287	−	0.0607796i
$898$	−1.74174	+	10.9969i	−0.0581228	+	0.366973i
$899$	2.71045	+	1.96926i	0.0903987	+	0.0656785i
$900$	1.60075	+	3.30456i	0.0533583	+	0.110152i
$901$			33.4710i			1.11508i
$902$		0			0
$903$	0.568922	+	0.568922i	0.0189325	+	0.0189325i
$904$	3.29143	+	10.1300i	0.109471	+	0.336918i
$905$	−8.73404	−	5.47398i	−0.290329	−	0.181961i
$906$	−14.6708	+	10.6590i	−0.487405	+	0.354120i
$907$	7.40321	+	14.5296i	0.245820	+	0.482448i	0.980641	−	0.195812i	$-0.0627343\pi$
$907$	7.40321	+	14.5296i	0.245820	+	0.482448i	−0.734822	+	0.678260i	$0.762734\pi$
$908$	−1.84296	−	3.61701i	−0.0611607	−	0.120035i
$909$	9.23043	−	6.70630i	0.306154	−	0.222434i
$910$	−0.450552	−	1.96360i	−0.0149356	−	0.0650927i
$911$	−5.47283	−	16.8436i	−0.181323	−	0.558055i	0.818543	−	0.574446i	$-0.194782\pi$
$911$	−5.47283	−	16.8436i	−0.181323	−	0.558055i	−0.999866	+	0.0163910i	$0.994782\pi$
$912$	1.89718	+	1.89718i	0.0628219	+	0.0628219i
$913$		0			0
$914$			10.2385i			0.338659i
$915$	−9.66456	−	4.11771i	−0.319500	−	0.136127i
$916$	4.12869	+	2.99967i	0.136416	+	0.0991119i
$917$	0.292615	−	1.84750i	0.00966301	−	0.0610098i
$918$	21.4691	−	10.9390i	0.708584	−	0.361042i
$919$	2.82132	−	8.68314i	0.0930669	−	0.286430i	−0.893678	−	0.448708i	$-0.851884\pi$
$919$	2.82132	−	8.68314i	0.0930669	−	0.286430i	0.986745	+	0.162278i	$0.0518842\pi$
$920$	7.15494	−	5.98732i	0.235891	−	0.197396i
$921$	13.3383	−	18.3585i	0.439510	−	0.604934i
$922$	39.3857	+	20.0680i	1.29710	+	0.660905i
$923$	25.0888	−	25.0888i	0.825807	−	0.825807i
$924$		0			0
$925$	−16.3231	+	21.5407i	−0.536701	+	0.708254i
$926$	−35.8082	+	11.6348i	−1.17673	+	0.382342i
$927$	−7.56022	+	1.19742i	−0.248310	+	0.0393284i
$928$	16.4249	+	2.60145i	0.539174	+	0.0853967i
$929$	−1.72368	−	0.560057i	−0.0565521	−	0.0183749i	0.280604	−	0.959824i	$-0.409465\pi$
$929$	−1.72368	−	0.560057i	−0.0565521	−	0.0183749i	−0.337156	+	0.941449i	$0.609465\pi$
$930$	0.922346	+	0.231285i	0.0302449	+	0.00758413i
$931$	3.04430	+	4.19012i	0.0997729	+	0.137326i
$932$	−0.760076	−	4.79893i	−0.0248971	−	0.157194i
$933$	2.72024	−	5.33878i	0.0890568	−	0.174784i
$934$	40.2174			1.31595
$935$		0			0
$936$	18.7961			0.614371
$937$	−6.88215	+	13.5070i	−0.224830	+	0.441254i	−0.975674	−	0.219226i	$-0.929647\pi$
$937$	−6.88215	+	13.5070i	−0.224830	+	0.441254i	0.750844	+	0.660479i	$0.229647\pi$
$938$	0.266201	+	1.68073i	0.00869178	+	0.0548777i
$939$	−0.630770	−	0.868181i	−0.0205844	−	0.0283320i
$940$	−7.36634	+	4.41267i	−0.240263	+	0.143925i
$941$	20.7606	+	6.74553i	0.676777	+	0.219898i	0.627184	−	0.778871i	$-0.284208\pi$
$941$	20.7606	+	6.74553i	0.676777	+	0.219898i	0.0495931	+	0.998770i	$0.484208\pi$
$942$	−5.92247	−	0.938027i	−0.192965	−	0.0305626i
$943$	−10.7452	+	1.70187i	−0.349912	+	0.0554206i
$944$	41.4236	−	13.4593i	1.34822	−	0.438064i
$945$	−1.82673	+	0.125268i	−0.0594235	+	0.00407498i
$946$		0			0
$947$	6.90662	−	6.90662i	0.224435	−	0.224435i	−0.585928	−	0.810363i	$-0.699270\pi$
$947$	6.90662	−	6.90662i	0.224435	−	0.224435i	0.810363	+	0.585928i	$0.199270\pi$
$948$	0.147924	+	0.0753712i	0.00480436	+	0.00244794i
$949$	4.37031	−	6.01522i	0.141866	−	0.195262i
$950$	−5.65190	−	0.113865i	−0.183372	−	0.00369425i
$951$	2.79170	−	8.59195i	0.0905269	−	0.278613i
$952$	−1.62385	+	0.827393i	−0.0526293	+	0.0268160i
$953$	2.04042	−	12.8827i	0.0660956	−	0.417311i	−0.932349	−	0.361560i	$-0.882244\pi$
$953$	2.04042	−	12.8827i	0.0660956	−	0.417311i	0.998445	−	0.0557519i	$-0.0177556\pi$
$954$	−26.2572	−	19.0770i	−0.850109	−	0.617641i
$955$	5.28155	+	13.1231i	0.170907	+	0.424653i
$956$		−	1.64046i		−	0.0530561i
$957$		0			0
$958$	−28.2202	−	28.2202i	−0.911755	−	0.911755i
$959$	0.256204	+	0.788514i	0.00827325	+	0.0254624i
$960$	−11.1230	+	2.55219i	−0.358993	+	0.0823717i
$961$	24.9799	−	18.1490i	0.805803	−	0.585450i
$962$	−11.5472	−	22.6627i	−0.372298	−	0.730675i
$963$	11.8673	+	23.2910i	0.382420	+	0.750541i
$964$	4.06247	−	2.95156i	0.130843	−	0.0950633i
$965$	−12.9281	+	2.96638i	−0.416171	+	0.0954913i
$966$	−0.116495	−	0.358536i	−0.00374818	−	0.0115357i
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	0.453092	−	0.891464i	$-0.350321\pi$
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	−0.891464	+	0.453092i	$0.850321\pi$
$968$		0			0
$969$			2.19785i			0.0706051i
$970$	1.74998	+	4.34819i	0.0561885	+	0.139612i
$971$	−3.32405	−	2.41506i	−0.106674	−	0.0775030i	0.533170	−	0.846008i	$-0.321001\pi$
$971$	−3.32405	−	2.41506i	−0.106674	−	0.0775030i	−0.639843	+	0.768505i	$0.721001\pi$
$972$	−0.766064	+	4.83674i	−0.0245715	+	0.155138i
$973$	1.79312	−	0.913641i	0.0574848	−	0.0292900i
$974$	−10.9611	+	33.7348i	−0.351216	+	1.08093i
$975$	8.89929	−	8.54780i	0.285005	−	0.273749i
$976$	15.6729	−	21.5718i	0.501676	−	0.690498i
$977$	−27.3623	−	13.9418i	−0.875398	−	0.446038i	−0.0422626	−	0.999107i	$-0.513457\pi$
$977$	−27.3623	−	13.9418i	−0.875398	−	0.446038i	−0.833136	+	0.553069i	$0.813457\pi$
$978$	−8.58324	+	8.58324i	−0.274462	+	0.274462i
$979$		0			0
$980$	4.82472	−	0.330856i	0.154120	−	0.0105688i
$981$	−21.4574	+	6.97195i	−0.685083	+	0.222597i
$982$	−27.5462	+	4.36290i	−0.879036	+	0.139226i
$983$	−27.3840	−	4.33721i	−0.873415	−	0.138335i	−0.296395	−	0.955065i	$-0.595785\pi$
$983$	−27.3840	−	4.33721i	−0.873415	−	0.138335i	−0.577020	+	0.816730i	$0.695785\pi$
$984$	13.0376	+	4.23617i	0.415623	+	0.135044i
$985$	26.8706	−	16.0963i	0.856168	−	0.512872i
$986$	31.6171	+	43.5172i	1.00689	+	1.38587i
$987$	−0.295242	−	1.86409i	−0.00939767	−	0.0593346i
$988$	0.324662	−	0.637185i	0.0103289	−	0.0202716i
$989$	8.56376			0.272312
$990$		0			0
$991$	9.10087			0.289099			0.144549	−	0.989498i	$-0.453827\pi$
$991$	9.10087			0.289099			0.144549	+	0.989498i	$0.453827\pi$
$992$	−0.277499	+	0.544623i	−0.00881061	+	0.0172918i
$993$	2.20803	+	13.9410i	0.0700697	+	0.442403i
$994$	−1.96080	−	2.69881i	−0.0621927	−	0.0856009i
$995$	29.0261	+	7.27852i	0.920191	+	0.230744i
$996$	3.92871	+	1.27652i	0.124486	+	0.0404480i
$997$	28.5152	+	4.51636i	0.903085	+	0.143035i	0.590672	−	0.806912i	$-0.298863\pi$
$997$	28.5152	+	4.51636i	0.903085	+	0.143035i	0.312413	+	0.949946i	$0.398863\pi$
$998$	−17.6527	+	2.79592i	−0.558787	+	0.0885031i
$999$	−21.9855	+	7.14351i	−0.695589	+	0.226011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.d.578.1		32
5.2	odd	4	inner	605.2.m.d.457.1		32
11.2	odd	10	inner	605.2.m.d.233.1		32
11.3	even	5		605.2.e.b.483.14		32
11.4	even	5		605.2.m.e.118.1		32
11.5	even	5		55.2.l.a.18.1	yes	32
11.6	odd	10		605.2.m.e.403.4		32
11.7	odd	10		55.2.l.a.8.4	yes	32
11.8	odd	10		605.2.e.b.483.3		32
11.9	even	5		605.2.m.c.233.4		32
11.10	odd	2		605.2.m.c.578.4		32
33.5	odd	10		495.2.bj.a.73.4		32
33.29	even	10		495.2.bj.a.118.1		32
44.7	even	10		880.2.cm.a.833.4		32
44.27	odd	10		880.2.cm.a.513.1		32
55.2	even	20	inner	605.2.m.d.112.1		32
55.7	even	20		55.2.l.a.52.1	yes	32
55.17	even	20		605.2.m.e.282.1		32
55.18	even	20		275.2.bm.b.107.4		32
55.27	odd	20		55.2.l.a.7.4	✓	32
55.29	odd	10		275.2.bm.b.118.1		32
55.32	even	4		605.2.m.c.457.4		32
55.37	odd	20		605.2.m.e.602.4		32
55.38	odd	20		275.2.bm.b.7.1		32
55.42	odd	20		605.2.m.c.112.4		32
55.47	odd	20		605.2.e.b.362.3		32
55.49	even	10		275.2.bm.b.18.4		32
55.52	even	20		605.2.e.b.362.14		32
165.62	odd	20		495.2.bj.a.217.4		32
165.137	even	20		495.2.bj.a.172.1		32
220.7	odd	20		880.2.cm.a.657.1		32
220.27	even	20		880.2.cm.a.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	55.27	odd	20
55.2.l.a.8.4	yes	32	11.7	odd	10
55.2.l.a.18.1	yes	32	11.5	even	5
55.2.l.a.52.1	yes	32	55.7	even	20
275.2.bm.b.7.1		32	55.38	odd	20
275.2.bm.b.18.4		32	55.49	even	10
275.2.bm.b.107.4		32	55.18	even	20
275.2.bm.b.118.1		32	55.29	odd	10
495.2.bj.a.73.4		32	33.5	odd	10
495.2.bj.a.118.1		32	33.29	even	10
495.2.bj.a.172.1		32	165.137	even	20
495.2.bj.a.217.4		32	165.62	odd	20
605.2.e.b.362.3		32	55.47	odd	20
605.2.e.b.362.14		32	55.52	even	20
605.2.e.b.483.3		32	11.8	odd	10
605.2.e.b.483.14		32	11.3	even	5
605.2.m.c.112.4		32	55.42	odd	20
605.2.m.c.233.4		32	11.9	even	5
605.2.m.c.457.4		32	55.32	even	4
605.2.m.c.578.4		32	11.10	odd	2
605.2.m.d.112.1		32	55.2	even	20	inner
605.2.m.d.233.1		32	11.2	odd	10	inner
605.2.m.d.457.1		32	5.2	odd	4	inner
605.2.m.d.578.1		32	1.1	even	1	trivial
605.2.m.e.118.1		32	11.4	even	5
605.2.m.e.282.1		32	55.17	even	20
605.2.m.e.403.4		32	11.6	odd	10
605.2.m.e.602.4		32	55.37	odd	20
880.2.cm.a.337.4		32	220.27	even	20
880.2.cm.a.513.1		32	44.27	odd	10
880.2.cm.a.657.1		32	220.7	odd	20
880.2.cm.a.833.4		32	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.690094 + 1.35439i) q^{2} +(-0.124714 - 0.787410i) q^{3} +(-0.182561 - 0.251273i) q^{4} +(0.543872 - 2.16892i) q^{5} +(1.15252 + 0.374477i) q^{6} +(0.189114 + 0.0299527i) q^{7} +(-2.53639 + 0.401725i) q^{8} +(2.24871 - 0.730650i) q^{9} +(2.56223 + 2.23337i) q^{10} +(-0.175087 + 0.175087i) q^{12} +(-2.75820 - 1.40537i) q^{13} +(-0.171074 + 0.235463i) q^{14} +(-1.77566 - 0.157757i) q^{15} +(1.39821 - 4.30326i) q^{16} +(3.30253 - 1.68272i) q^{17} +(-0.562239 + 3.54984i) q^{18} +(-0.601740 - 0.437190i) q^{19} +(-0.644280 + 0.259299i) q^{20} -0.152646i q^{21} +(-1.14886 - 1.14886i) q^{23} +(0.632645 + 1.94708i) q^{24} +(-4.40841 - 2.35923i) q^{25} +(3.80684 - 2.76583i) q^{26} +(-1.94156 - 3.81053i) q^{27} +(-0.0269984 - 0.0529874i) q^{28} +(7.72385 - 5.61170i) q^{29} +(1.43903 - 2.29606i) q^{30} +(0.108440 + 0.333745i) q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(0.167819 - 0.393882i) q^{35} +(-0.594118 - 0.431652i) q^{36} +(0.845584 - 5.33881i) q^{37} +(1.00738 - 0.513286i) q^{38} +(-0.762621 + 2.34710i) q^{39} +(-0.508163 + 5.71971i) q^{40} +(3.93579 - 5.41715i) q^{41} +(0.206741 + 0.105340i) q^{42} +(-3.72708 + 3.72708i) q^{43} +(-0.361710 - 5.27464i) q^{45} +(2.34882 - 0.763176i) q^{46} +(12.2119 - 1.93417i) q^{47} +(-3.56281 - 0.564293i) q^{48} +(-6.62253 - 2.15179i) q^{49} +(6.23752 - 4.34260i) q^{50} +(-1.73686 - 2.39059i) q^{51} +(0.150406 + 0.949628i) q^{52} +(-4.09968 + 8.04607i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(-0.269202 + 0.528339i) q^{57} +(2.27023 + 14.3337i) q^{58} +(5.65807 + 7.78767i) q^{59} +(0.284525 + 0.474975i) q^{60} +(5.60460 + 1.82105i) q^{61} +(-0.526853 - 0.0834454i) q^{62} +(0.447147 - 0.0708211i) q^{63} +(6.08841 - 1.97824i) q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-1.02573 - 0.522638i) q^{68} +(-0.761344 + 1.04790i) q^{69} +(0.417657 + 0.499106i) q^{70} +(-3.54186 + 10.9007i) q^{71} +(-5.41009 + 2.75658i) q^{72} +(-0.375734 + 2.37229i) q^{73} +(6.64727 + 4.82953i) q^{74} +(-1.30789 + 3.76545i) q^{75} +0.231015i q^{76} +(-2.65261 - 2.65261i) q^{78} +(-0.207191 - 0.637669i) q^{79} +(-8.57297 - 5.37303i) q^{80} +(2.98028 - 2.16530i) q^{81} +(4.62085 + 9.06892i) q^{82} +(-7.57393 - 14.8647i) q^{83} +(-0.0383557 + 0.0278671i) q^{84} +(-1.85353 - 8.07810i) q^{85} +(-2.47587 - 7.61994i) q^{86} +(-5.38198 - 5.38198i) q^{87} +7.92190i q^{89} +(7.39352 + 3.15010i) q^{90} +(-0.479519 - 0.348391i) q^{91} +(-0.0789408 + 0.498413i) q^{92} +(0.249270 - 0.127009i) q^{93} +(-5.80772 + 17.8743i) q^{94} +(-1.27550 + 1.06735i) q^{95} +(0.816218 - 1.12343i) q^{96} +(1.22869 + 0.626047i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) \) 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more