LMFDB - Embedded newform 666.2.k.a.175.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.7
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-0.617040 + 1.61841i) q^{3} -1.00000 q^{4} -1.45509i q^{5} +(1.61841 + 0.617040i) q^{6} +(0.0208867 - 0.0361769i) q^{7} +1.00000i q^{8} +(-2.23852 - 1.99725i) q^{9} -1.45509 q^{10} +(2.61594 + 4.53095i) q^{11} +(0.617040 - 1.61841i) q^{12} +0.341207i q^{13} +(-0.0361769 - 0.0208867i) q^{14} +(2.35494 + 0.897851i) q^{15} +1.00000 q^{16} +(1.12437 + 0.649153i) q^{17} +(-1.99725 + 2.23852i) q^{18} +(0.568843 - 0.328422i) q^{19} +1.45509i q^{20} +(0.0456612 + 0.0561259i) q^{21} +(4.53095 - 2.61594i) q^{22} +(-0.205756 - 0.118793i) q^{23} +(-1.61841 - 0.617040i) q^{24} +2.88270 q^{25} +0.341207 q^{26} +(4.61364 - 2.39047i) q^{27} +(-0.0208867 + 0.0361769i) q^{28} +(-5.29661 + 3.05800i) q^{29} +(0.897851 - 2.35494i) q^{30} +(8.98698 + 5.18863i) q^{31} -1.00000i q^{32} +(-8.94709 + 1.43790i) q^{33} +(0.649153 - 1.12437i) q^{34} +(-0.0526407 - 0.0303921i) q^{35} +(2.23852 + 1.99725i) q^{36} +(3.97276 + 4.60621i) q^{37} +(-0.328422 - 0.568843i) q^{38} +(-0.552214 - 0.210538i) q^{39} +1.45509 q^{40} +0.500483 q^{41} +(0.0561259 - 0.0456612i) q^{42} +(3.75718 - 2.16921i) q^{43} +(-2.61594 - 4.53095i) q^{44} +(-2.90619 + 3.25726i) q^{45} +(-0.118793 + 0.205756i) q^{46} +(4.90128 + 8.48927i) q^{47} +(-0.617040 + 1.61841i) q^{48} +(3.49913 + 6.06067i) q^{49} -2.88270i q^{50} +(-1.74438 + 1.41914i) q^{51} -0.341207i q^{52} +(-0.326973 + 0.566334i) q^{53} +(-2.39047 - 4.61364i) q^{54} +(6.59296 - 3.80644i) q^{55} +(0.0361769 + 0.0208867i) q^{56} +(0.180523 + 1.12327i) q^{57} +(3.05800 + 5.29661i) q^{58} +(-2.26051 + 1.30511i) q^{59} +(-2.35494 - 0.897851i) q^{60} +(-6.04786 - 3.49174i) q^{61} +(5.18863 - 8.98698i) q^{62} +(-0.119010 + 0.0392667i) q^{63} -1.00000 q^{64} +0.496488 q^{65} +(1.43790 + 8.94709i) q^{66} +6.79289 q^{67} +(-1.12437 - 0.649153i) q^{68} +(0.319217 - 0.259698i) q^{69} +(-0.0303921 + 0.0526407i) q^{70} +(0.365314 + 0.632742i) q^{71} +(1.99725 - 2.23852i) q^{72} +4.44903 q^{73} +(4.60621 - 3.97276i) q^{74} +(-1.77874 + 4.66540i) q^{75} +(-0.568843 + 0.328422i) q^{76} +0.218554 q^{77} +(-0.210538 + 0.552214i) q^{78} +(-8.25102 - 4.76373i) q^{79} -1.45509i q^{80} +(1.02197 + 8.94179i) q^{81} -0.500483i q^{82} -5.71363 q^{83} +(-0.0456612 - 0.0561259i) q^{84} +(0.944579 - 1.63606i) q^{85} +(-2.16921 - 3.75718i) q^{86} +(-1.68089 - 10.4590i) q^{87} +(-4.53095 + 2.61594i) q^{88} +(-5.22746 - 3.01807i) q^{89} +(3.25726 + 2.90619i) q^{90} +(0.0123438 + 0.00712669i) q^{91} +(0.205756 + 0.118793i) q^{92} +(-13.9427 + 11.3430i) q^{93} +(8.48927 - 4.90128i) q^{94} +(-0.477884 - 0.827720i) q^{95} +(1.61841 + 0.617040i) q^{96} +(2.98127 - 1.72123i) q^{97} +(6.06067 - 3.49913i) q^{98} +(3.19359 - 15.3673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.617040	+	1.61841i	−0.356248	+	0.934391i
$3$	−0.617040	+	1.61841i	−0.356248	+	0.934391i
$4$	−1.00000			−0.500000
$5$		−	1.45509i		−	0.650738i	−0.945587	−	0.325369i	$-0.894512\pi$
$5$		−	1.45509i		−	0.650738i	0.945587	−	0.325369i	$-0.105488\pi$
$6$	1.61841	+	0.617040i	0.660714	+	0.251906i
$7$	0.0208867	−	0.0361769i	0.00789444	−	0.0136736i	−0.862051	−	0.506821i	$-0.830820\pi$
$7$	0.0208867	−	0.0361769i	0.00789444	−	0.0136736i	0.869946	+	0.493148i	$0.164154\pi$
$8$			1.00000i			0.353553i
$9$	−2.23852	−	1.99725i	−0.746174	−	0.665750i
$10$	−1.45509			−0.460141
$11$	2.61594	+	4.53095i	0.788737	+	1.36613i	0.926741	+	0.375701i	$0.122598\pi$
$11$	2.61594	+	4.53095i	0.788737	+	1.36613i	−0.138004	+	0.990432i	$0.544069\pi$
$12$	0.617040	−	1.61841i	0.178124	−	0.467196i
$13$			0.341207i			0.0946337i	0.998880	+	0.0473169i	$0.0150671\pi$
$13$			0.341207i			0.0946337i	−0.998880	+	0.0473169i	$0.984933\pi$
$14$	−0.0361769	−	0.0208867i	−0.00966867	−	0.00558221i
$15$	2.35494	+	0.897851i	0.608044	+	0.231824i
$16$	1.00000			0.250000
$17$	1.12437	+	0.649153i	0.272699	+	0.157443i	0.630114	−	0.776503i	$-0.283008\pi$
$17$	1.12437	+	0.649153i	0.272699	+	0.157443i	−0.357415	+	0.933946i	$0.616342\pi$
$18$	−1.99725	+	2.23852i	−0.470757	+	0.527625i
$19$	0.568843	−	0.328422i	0.130501	−	0.0753451i	−0.433328	−	0.901236i	$-0.642661\pi$
$19$	0.568843	−	0.328422i	0.130501	−	0.0753451i	0.563830	+	0.825891i	$0.309328\pi$
$20$			1.45509i			0.325369i
$21$	0.0456612	+	0.0561259i	0.00996408	+	0.0122477i
$22$	4.53095	−	2.61594i	0.966002	−	0.557721i
$23$	−0.205756	−	0.118793i	−0.0429031	−	0.0247701i	0.478395	−	0.878145i	$-0.341219\pi$
$23$	−0.205756	−	0.118793i	−0.0429031	−	0.0247701i	−0.521298	+	0.853375i	$0.674552\pi$
$24$	−1.61841	−	0.617040i	−0.330357	−	0.125953i
$25$	2.88270			0.576540
$26$	0.341207			0.0669161
$27$	4.61364	−	2.39047i	0.887895	−	0.460047i
$28$	−0.0208867	+	0.0361769i	−0.00394722	+	0.00683678i
$29$	−5.29661	+	3.05800i	−0.983556	+	0.567856i	−0.903342	−	0.428922i	$-0.858894\pi$
$29$	−5.29661	+	3.05800i	−0.983556	+	0.567856i	−0.0802138	+	0.996778i	$0.525560\pi$
$30$	0.897851	−	2.35494i	0.163924	−	0.429952i
$31$	8.98698	+	5.18863i	1.61411	+	0.931906i	0.988404	+	0.151846i	$0.0485217\pi$
$31$	8.98698	+	5.18863i	1.61411	+	0.931906i	0.625704	+	0.780060i	$0.284812\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−8.94709	+	1.43790i	−1.55749	+	0.250307i
$34$	0.649153	−	1.12437i	0.111329	−	0.192827i
$35$	−0.0526407	−	0.0303921i	−0.00889790	−	0.00513721i
$36$	2.23852	+	1.99725i	0.373087	+	0.332875i
$37$	3.97276	+	4.60621i	0.653118	+	0.757257i
$37$	3.97276	+	4.60621i	0.653118	+	0.757257i
$38$	−0.328422	−	0.568843i	−0.0532770	−	0.0922785i
$39$	−0.552214	−	0.210538i	−0.0884249	−	0.0337131i
$40$	1.45509			0.230071
$41$	0.500483			0.0781622			0.0390811	−	0.999236i	$-0.487557\pi$
$41$	0.500483			0.0781622			0.0390811	+	0.999236i	$0.487557\pi$
$42$	0.0561259	−	0.0456612i	0.00866042	−	0.00704567i
$43$	3.75718	−	2.16921i	0.572965	−	0.330802i	−0.185368	−	0.982669i	$-0.559348\pi$
$43$	3.75718	−	2.16921i	0.572965	−	0.330802i	0.758333	+	0.651868i	$0.226014\pi$
$44$	−2.61594	−	4.53095i	−0.394368	−	0.683066i
$45$	−2.90619	+	3.25726i	−0.433229	+	0.485564i
$46$	−0.118793	+	0.205756i	−0.0175151	+	0.0303371i
$47$	4.90128	+	8.48927i	0.714925	+	1.23829i	0.962988	+	0.269543i	$0.0868726\pi$
$47$	4.90128	+	8.48927i	0.714925	+	1.23829i	−0.248063	+	0.968744i	$0.579794\pi$
$48$	−0.617040	+	1.61841i	−0.0890621	+	0.233598i
$49$	3.49913	+	6.06067i	0.499875	+	0.865810i
$50$		−	2.88270i		−	0.407676i
$51$	−1.74438	+	1.41914i	−0.244262	+	0.198719i
$52$		−	0.341207i		−	0.0473169i
$53$	−0.326973	+	0.566334i	−0.0449132	+	0.0777920i	−0.887608	−	0.460599i	$-0.847634\pi$
$53$	−0.326973	+	0.566334i	−0.0449132	+	0.0777920i	0.842695	+	0.538391i	$0.180968\pi$
$54$	−2.39047	−	4.61364i	−0.325302	−	0.627836i
$55$	6.59296	−	3.80644i	0.888994	−	0.513261i
$56$	0.0361769	+	0.0208867i	0.00483434	+	0.00279110i
$57$	0.180523	+	1.12327i	0.0239109	+	0.148781i
$58$	3.05800	+	5.29661i	0.401535	+	0.695479i
$59$	−2.26051	+	1.30511i	−0.294294	+	0.169911i	−0.639877	−	0.768478i	$-0.721015\pi$
$59$	−2.26051	+	1.30511i	−0.294294	+	0.169911i	0.345583	+	0.938388i	$0.387681\pi$
$60$	−2.35494	−	0.897851i	−0.304022	−	0.115912i
$61$	−6.04786	−	3.49174i	−0.774350	−	0.447071i	0.0600745	−	0.998194i	$-0.480866\pi$
$61$	−6.04786	−	3.49174i	−0.774350	−	0.447071i	−0.834424	+	0.551123i	$0.814200\pi$
$62$	5.18863	−	8.98698i	0.658957	−	1.14135i
$63$	−0.119010	+	0.0392667i	−0.0149938	+	0.00494714i
$64$	−1.00000			−0.125000
$65$	0.496488			0.0615817
$66$	1.43790	+	8.94709i	0.176994	+	1.10131i
$67$	6.79289			0.829884			0.414942	−	0.909848i	$-0.363802\pi$
$67$	6.79289			0.829884			0.414942	+	0.909848i	$0.363802\pi$
$68$	−1.12437	−	0.649153i	−0.136349	−	0.0787214i
$69$	0.319217	−	0.259698i	0.0384292	−	0.0312640i
$70$	−0.0303921	+	0.0526407i	−0.00363255	+	0.00629177i
$71$	0.365314	+	0.632742i	0.0433547	+	0.0750926i	0.886888	−	0.461984i	$-0.152862\pi$
$71$	0.365314	+	0.632742i	0.0433547	+	0.0750926i	−0.843534	+	0.537076i	$0.819529\pi$
$72$	1.99725	−	2.23852i	0.235378	−	0.263813i
$73$	4.44903			0.520720			0.260360	−	0.965512i	$-0.416159\pi$
$73$	4.44903			0.520720			0.260360	+	0.965512i	$0.416159\pi$
$74$	4.60621	−	3.97276i	0.535461	−	0.461824i
$75$	−1.77874	+	4.66540i	−0.205391	+	0.538714i
$76$	−0.568843	+	0.328422i	−0.0652507	+	0.0376725i
$77$	0.218554			0.0249065
$78$	−0.210538	+	0.552214i	−0.0238388	+	0.0625259i
$79$	−8.25102	−	4.76373i	−0.928312	−	0.535961i	−0.0420350	−	0.999116i	$-0.513384\pi$
$79$	−8.25102	−	4.76373i	−0.928312	−	0.535961i	−0.886277	+	0.463155i	$0.846717\pi$
$80$		−	1.45509i		−	0.162684i
$81$	1.02197	+	8.94179i	0.113553	+	0.993532i
$82$		−	0.500483i		−	0.0552691i
$83$	−5.71363			−0.627152			−0.313576	−	0.949563i	$-0.601527\pi$
$83$	−5.71363			−0.627152			−0.313576	+	0.949563i	$0.601527\pi$
$84$	−0.0456612	−	0.0561259i	−0.00498204	−	0.00612384i
$85$	0.944579	−	1.63606i	0.102454	−	0.177455i
$86$	−2.16921	−	3.75718i	−0.233912	−	0.405147i
$87$	−1.68089	−	10.4590i	−0.180210	−	1.12132i
$88$	−4.53095	+	2.61594i	−0.483001	+	0.278861i
$89$	−5.22746	−	3.01807i	−0.554109	−	0.319915i	0.196669	−	0.980470i	$-0.436988\pi$
$89$	−5.22746	−	3.01807i	−0.554109	−	0.319915i	−0.750778	+	0.660555i	$0.770321\pi$
$90$	3.25726	+	2.90619i	0.343345	+	0.306339i
$91$	0.0123438	+	0.00712669i	0.00129398	+	0.000747080i
$92$	0.205756	+	0.118793i	0.0214516	+	0.0123851i
$93$	−13.9427	+	11.3430i	−1.44579	+	1.17622i
$94$	8.48927	−	4.90128i	0.875601	−	0.505528i
$95$	−0.477884	−	0.827720i	−0.0490299	−	0.0849222i
$96$	1.61841	+	0.617040i	0.165179	+	0.0629764i
$97$	2.98127	−	1.72123i	0.302702	−	0.174765i	−0.340954	−	0.940080i	$-0.610750\pi$
$97$	2.98127	−	1.72123i	0.302702	−	0.174765i	0.643656	+	0.765315i	$0.277417\pi$
$98$	6.06067	−	3.49913i	0.612220	−	0.353465i
$99$	3.19359	−	15.3673i	0.320968	−	1.54448i
$100$	−2.88270			−0.288270
$101$	−9.81680	−	17.0032i	−0.976808	−	1.69188i	−0.673834	−	0.738883i	$-0.735354\pi$
$101$	−9.81680	−	17.0032i	−0.976808	−	1.69188i	−0.302974	−	0.952999i	$-0.597980\pi$
$102$	1.41914	+	1.74438i	0.140515	+	0.172719i
$103$	−9.77566	−	5.64398i	−0.963224	−	0.556118i	−0.0660604	−	0.997816i	$-0.521043\pi$
$103$	−9.77566	−	5.64398i	−0.963224	−	0.556118i	−0.897164	+	0.441698i	$0.854376\pi$
$104$	−0.341207			−0.0334581
$105$	0.0816685	−	0.0664413i	0.00797003	−	0.00648400i
$106$	0.566334	+	0.326973i	0.0550072	+	0.0317584i
$107$	−6.64602	−	11.5112i	−0.642495	−	1.11283i	−0.984874	−	0.173272i	$-0.944566\pi$
$107$	−6.64602	−	11.5112i	−0.642495	−	1.11283i	0.342379	−	0.939562i	$-0.388767\pi$
$108$	−4.61364	+	2.39047i	−0.443947	+	0.230023i
$109$	−3.27345	−	1.88993i	−0.313540	−	0.181022i	0.334970	−	0.942229i	$-0.391274\pi$
$109$	−3.27345	−	1.88993i	−0.313540	−	0.181022i	−0.648509	+	0.761207i	$0.724607\pi$
$110$	−3.80644	−	6.59296i	−0.362930	−	0.628614i
$111$	−9.90611	+	3.58735i	−0.940246	+	0.340496i
$112$	0.0208867	−	0.0361769i	0.00197361	−	0.00341839i
$113$	−2.46731	+	1.42450i	−0.232105	+	0.134006i	−0.611543	−	0.791211i	$-0.709451\pi$
$113$	−2.46731	+	1.42450i	−0.232105	+	0.134006i	0.379438	+	0.925217i	$0.376117\pi$
$114$	1.12327	−	0.180523i	0.105204	−	0.0169075i
$115$	−0.172855	+	0.299395i	−0.0161189	+	0.0279187i
$116$	5.29661	−	3.05800i	0.491778	−	0.283928i
$117$	0.681476	−	0.763799i	0.0630024	−	0.0706133i
$118$	1.30511	+	2.26051i	0.120145	+	0.208097i
$119$	0.0469686	−	0.0271174i	0.00430561	−	0.00248584i
$120$	−0.897851	+	2.35494i	−0.0819622	+	0.214976i
$121$	−8.18633	+	14.1791i	−0.744212	+	1.28901i
$122$	−3.49174	+	6.04786i	−0.316127	+	0.547548i
$123$	−0.308818	+	0.809988i	−0.0278452	+	0.0730341i
$124$	−8.98698	−	5.18863i	−0.807054	−	0.465953i
$125$		−	11.4701i		−	1.02591i
$126$	0.0392667	+	0.119010i	0.00349816	+	0.0106022i
$127$	5.77648	−	10.0052i	0.512579	−	0.887814i	−0.487314	−	0.873227i	$-0.662023\pi$
$127$	5.77648	−	10.0052i	0.512579	−	0.887814i	0.999894	−	0.0145869i	$-0.00464332\pi$
$128$			1.00000i			0.0883883i
$129$	1.19235	+	7.41916i	0.104980	+	0.653221i
$130$		−	0.496488i		−	0.0435449i
$131$	3.87625	−	2.23795i	0.338670	−	0.195531i	−0.321014	−	0.947074i	$-0.604024\pi$
$131$	3.87625	−	2.23795i	0.338670	−	0.195531i	0.659684	+	0.751543i	$0.270690\pi$
$132$	8.94709	−	1.43790i	0.778744	−	0.125153i
$133$		−	0.0274386i		−	0.00237923i
$134$		−	6.79289i		−	0.586816i
$135$	−3.47836	−	6.71327i	−0.299370	−	0.577787i
$136$	−0.649153	+	1.12437i	−0.0556644	+	0.0964136i
$137$	3.84716	+	6.66347i	0.328685	+	0.569299i	0.982251	−	0.187570i	$-0.0600613\pi$
$137$	3.84716	+	6.66347i	0.328685	+	0.569299i	−0.653566	+	0.756869i	$0.726728\pi$
$138$	−0.259698	−	0.319217i	−0.0221070	−	0.0271735i
$139$	8.27271	+	14.3288i	0.701682	+	1.21535i	0.967876	+	0.251429i	$0.0809007\pi$
$139$	8.27271	+	14.3288i	0.701682	+	1.21535i	−0.266193	+	0.963920i	$0.585766\pi$
$140$	0.0526407	+	0.0303921i	0.00444895	+	0.00256860i
$141$	−16.7634	+	2.69408i	−1.41174	+	0.226882i
$142$	0.632742	−	0.365314i	0.0530985	−	0.0306564i
$143$	−1.54599	+	0.892578i	−0.129282	+	0.0746411i
$144$	−2.23852	−	1.99725i	−0.186544	−	0.166438i
$145$	4.44967	+	7.70706i	0.369525	+	0.640037i
$146$		−	4.44903i		−	0.368204i
$147$	−11.9678	+	1.92336i	−0.987085	+	0.158636i
$148$	−3.97276	−	4.60621i	−0.326559	−	0.378628i
$149$	−4.62276	+	8.00686i	−0.378711	+	0.655948i	−0.990875	−	0.134784i	$-0.956966\pi$
$149$	−4.62276	+	8.00686i	−0.378711	+	0.655948i	0.612164	+	0.790731i	$0.290299\pi$
$150$	4.66540	+	1.77874i	0.380929	+	0.145234i
$151$	8.52443	−	14.7648i	0.693709	−	1.20154i	−0.276906	−	0.960897i	$-0.589309\pi$
$151$	8.52443	−	14.7648i	0.693709	−	1.20154i	0.970614	−	0.240641i	$-0.0773577\pi$
$152$	0.328422	+	0.568843i	0.0266385	+	0.0461392i
$153$	−1.22040	−	3.69879i	−0.0986633	−	0.299029i
$154$		−	0.218554i		−	0.0176116i
$155$	7.54995	−	13.0769i	0.606426	−	1.05036i
$156$	0.552214	+	0.210538i	0.0442125	+	0.0168565i
$157$	6.30575	+	10.9219i	0.503253	+	0.871660i	0.999993	+	0.00376077i	$0.00119709\pi$
$157$	6.30575	+	10.9219i	0.503253	+	0.871660i	−0.496740	+	0.867900i	$0.665470\pi$
$158$	−4.76373	+	8.25102i	−0.378982	+	0.656416i
$159$	−0.714807	−	0.878629i	−0.0566879	−	0.0696798i
$160$	−1.45509			−0.115035
$161$	−0.00859514	+	0.00496241i	−0.000677392	+	0.000391092i
$162$	8.94179	−	1.02197i	0.702533	−	0.0802938i
$163$	−5.32607	−	3.07501i	−0.417170	−	0.240853i	0.276696	−	0.960958i	$-0.410761\pi$
$163$	−5.32607	−	3.07501i	−0.417170	−	0.240853i	−0.693866	+	0.720104i	$0.744094\pi$
$164$	−0.500483			−0.0390811
$165$	2.09228	+	13.0189i	0.162884	+	1.01352i
$166$			5.71363i			0.443463i
$167$			9.76764i			0.755843i	0.925838	+	0.377921i	$0.123361\pi$
$167$			9.76764i			0.755843i	−0.925838	+	0.377921i	$0.876639\pi$
$168$	−0.0561259	+	0.0456612i	−0.00433021	+	0.00352284i
$169$	12.8836			0.991044
$170$	−1.63606	−	0.944579i	−0.125480	−	0.0724459i
$171$	−1.92931	−	0.400943i	−0.147538	−	0.0306609i
$172$	−3.75718	+	2.16921i	−0.286483	+	0.165401i
$173$	−12.5805			−0.956480			−0.478240	−	0.878229i	$-0.658725\pi$
$173$	−12.5805			−0.956480			−0.478240	+	0.878229i	$0.658725\pi$
$174$	−10.4590	+	1.68089i	−0.792895	+	0.127428i
$175$	0.0602102	−	0.104287i	0.00455146	−	0.00788336i
$176$	2.61594	+	4.53095i	0.197184	+	0.341533i
$177$	−0.717377	−	4.46375i	−0.0539213	−	0.335516i
$178$	−3.01807	+	5.22746i	−0.226214	+	0.391814i
$179$			0.373026i			0.0278813i	0.999903	+	0.0139406i	$0.00443759\pi$
$179$			0.373026i			0.0278813i	−0.999903	+	0.0139406i	$0.995562\pi$
$180$	2.90619	−	3.25726i	0.216614	−	0.242782i
$181$	−3.79833	−	6.57891i	−0.282328	−	0.489006i	0.689630	−	0.724162i	$-0.257773\pi$
$181$	−3.79833	−	6.57891i	−0.282328	−	0.489006i	−0.971958	+	0.235156i	$0.924440\pi$
$182$	0.00712669	−	0.0123438i	0.000528265	−	0.000914982i
$183$	9.38284	−	7.63340i	0.693600	−	0.564277i
$184$	0.118793	−	0.205756i	0.00875756	−	0.0151685i
$185$	6.70247	−	5.78074i	0.492775	−	0.425008i
$186$	11.3430	+	13.9427i	0.831713	+	1.02233i
$187$			6.79260i			0.496724i
$188$	−4.90128	−	8.48927i	−0.357463	−	0.619143i
$189$	0.00988397	−	0.216836i	0.000718953	−	0.0157725i
$190$	−0.827720	+	0.477884i	−0.0600491	+	0.0346694i
$191$	−6.67602	+	3.85440i	−0.483060	+	0.278895i	−0.721691	−	0.692216i	$-0.756635\pi$
$191$	−6.67602	+	3.85440i	−0.483060	+	0.278895i	0.238631	+	0.971110i	$0.423301\pi$
$192$	0.617040	−	1.61841i	0.0445310	−	0.116799i
$193$	19.0833	+	11.0178i	1.37365	+	0.793076i	0.991385	−	0.130978i	$-0.0418118\pi$
$193$	19.0833	+	11.0178i	1.37365	+	0.793076i	0.382262	+	0.924054i	$0.375145\pi$
$194$	−1.72123	−	2.98127i	−0.123577	−	0.214042i
$195$	−0.306353	+	0.803522i	−0.0219384	+	0.0575414i
$196$	−3.49913	−	6.06067i	−0.249938	−	0.432905i
$197$	−8.30916	+	14.3919i	−0.592003	+	1.02538i	0.401959	+	0.915658i	$0.368329\pi$
$197$	−8.30916	+	14.3919i	−0.592003	+	1.02538i	−0.993962	+	0.109722i	$0.965004\pi$
$198$	−15.3673	−	3.19359i	−1.09211	−	0.226959i
$199$		−	20.0844i		−	1.42375i	−0.702308	−	0.711873i	$-0.747847\pi$
$199$		−	20.0844i		−	1.42375i	0.702308	−	0.711873i	$-0.252153\pi$
$200$			2.88270i			0.203838i
$201$	−4.19148	+	10.9937i	−0.295645	+	0.775436i
$202$	−17.0032	+	9.81680i	−1.19634	+	0.690708i
$203$			0.255486i			0.0179316i
$204$	1.74438	−	1.41914i	0.122131	−	0.0993594i
$205$		−	0.728249i		−	0.0508631i
$206$	−5.64398	+	9.77566i	−0.393235	+	0.681102i
$207$	0.223330	+	0.676869i	0.0155225	+	0.0470456i
$208$			0.341207i			0.0236584i
$209$	2.97612	+	1.71827i	0.205863	+	0.118855i
$210$	−0.0664413	−	0.0816685i	−0.00458488	−	0.00563566i
$211$	−0.411170	+	0.712168i	−0.0283061	+	0.0490276i	−0.879831	−	0.475286i	$-0.842345\pi$
$211$	−0.411170	+	0.712168i	−0.0283061	+	0.0490276i	0.851525	+	0.524313i	$0.175678\pi$
$212$	0.326973	−	0.566334i	0.0224566	−	0.0388960i
$213$	−1.24945	+	0.200801i	−0.0856109	+	0.0137587i
$214$	−11.5112	+	6.64602i	−0.786893	+	0.454313i
$215$	−3.15640	−	5.46705i	−0.215265	−	0.372850i
$216$	2.39047	+	4.61364i	0.162651	+	0.313918i
$217$	0.375417	−	0.216747i	0.0254850	−	0.0147137i
$218$	−1.88993	+	3.27345i	−0.128002	+	0.221706i
$219$	−2.74523	+	7.20037i	−0.185505	+	0.486556i
$220$	−6.59296	+	3.80644i	−0.444497	+	0.256630i
$221$	−0.221495	+	0.383641i	−0.0148994	+	0.0258065i
$222$	3.58735	+	9.90611i	0.240767	+	0.664854i
$223$	10.5539	+	18.2799i	0.706743	+	1.22411i	0.966059	+	0.258322i	$0.0831697\pi$
$223$	10.5539	+	18.2799i	0.706743	+	1.22411i	−0.259316	+	0.965793i	$0.583497\pi$
$224$	−0.0361769	−	0.0208867i	−0.00241717	−	0.00139555i
$225$	−6.45300	−	5.75748i	−0.430200	−	0.383832i
$226$	1.42450	+	2.46731i	0.0947564	+	0.164123i
$227$	12.1202	+	6.99762i	0.804448	+	0.464448i	0.845024	−	0.534728i	$-0.179586\pi$
$227$	12.1202	+	6.99762i	0.804448	+	0.464448i	−0.0405759	+	0.999176i	$0.512919\pi$
$228$	−0.180523	−	1.12327i	−0.0119554	−	0.0743905i
$229$	−25.0499			−1.65534			−0.827671	−	0.561213i	$-0.810335\pi$
$229$	−25.0499			−1.65534			−0.827671	+	0.561213i	$0.810335\pi$
$230$	0.299395	+	0.172855i	0.0197415	+	0.0113978i
$231$	−0.134857	+	0.353711i	−0.00887291	+	0.0232725i
$232$	−3.05800	−	5.29661i	−0.200767	−	0.347739i
$233$	−7.60849			−0.498448			−0.249224	−	0.968446i	$-0.580176\pi$
$233$	−7.60849			−0.498448			−0.249224	+	0.968446i	$0.580176\pi$
$234$	−0.763799	−	0.681476i	−0.0499311	−	0.0445495i
$235$	12.3527	−	7.13182i	0.805800	−	0.465229i
$236$	2.26051	−	1.30511i	0.147147	−	0.0849553i
$237$	12.8009	−	10.4142i	0.831507	−	0.676472i
$238$	−0.0271174	−	0.0469686i	−0.00175776	−	0.00304453i
$239$	−11.7346	+	6.77496i	−0.759047	+	0.438236i	−0.828953	−	0.559318i	$-0.811063\pi$
$239$	−11.7346	+	6.77496i	−0.759047	+	0.438236i	0.0699067	+	0.997554i	$0.477730\pi$
$240$	2.35494	+	0.897851i	0.152011	+	0.0579560i
$241$	−16.9545	−	9.78870i	−1.09214	−	0.630545i	−0.157992	−	0.987440i	$-0.550502\pi$
$241$	−16.9545	−	9.78870i	−1.09214	−	0.630545i	−0.934145	+	0.356895i	$0.883835\pi$
$242$	14.1791	+	8.18633i	0.911470	+	0.526237i
$243$	−15.1021	−	3.86347i	−0.968801	−	0.247841i
$244$	6.04786	+	3.49174i	0.387175	+	0.223535i
$245$	8.81884	−	5.09156i	0.563415	−	0.325288i
$246$	0.809988	+	0.308818i	0.0516429	+	0.0196895i
$247$	0.112060	+	0.194093i	0.00713018	+	0.0123498i
$248$	−5.18863	+	8.98698i	−0.329479	+	0.570674i
$249$	3.52554	−	9.24701i	0.223422	−	0.586005i
$250$	−11.4701			−0.725431
$251$		−	2.69186i		−	0.169909i	−0.996385	−	0.0849544i	$-0.972926\pi$
$251$		−	2.69186i		−	0.169909i	0.996385	−	0.0849544i	$-0.0270745\pi$
$252$	0.119010	−	0.0392667i	0.00749691	−	0.00247357i
$253$		−	1.24303i		−	0.0781485i
$254$	−10.0052	−	5.77648i	−0.627779	−	0.362448i
$255$	2.06498	+	2.53823i	0.129314	+	0.158950i
$256$	1.00000			0.0625000
$257$	18.8634	−	10.8908i	1.17666	−	0.679347i	0.221423	−	0.975178i	$-0.428930\pi$
$257$	18.8634	−	10.8908i	1.17666	−	0.679347i	0.955240	+	0.295831i	$0.0955965\pi$
$258$	7.41916	−	1.19235i	0.461897	−	0.0742323i
$259$	0.249616	−	0.0475133i	0.0155104	−	0.00295233i
$260$	−0.496488			−0.0307909
$261$	17.9642	+	3.73326i	1.11195	+	0.231083i
$262$	−2.23795	−	3.87625i	−0.138261	−	0.239476i
$263$	−6.32355	+	10.9527i	−0.389927	+	0.675373i	−0.992439	−	0.122736i	$-0.960833\pi$
$263$	−6.32355	+	10.9527i	−0.389927	+	0.675373i	0.602513	+	0.798109i	$0.294166\pi$
$264$	−1.43790	−	8.94709i	−0.0884968	−	0.550655i
$265$	0.824069	+	0.475777i	0.0506222	+	0.0292267i
$266$	−0.0274386			−0.00168237
$267$	8.11004	−	6.59791i	0.496326	−	0.403786i
$268$	−6.79289			−0.414942
$269$	14.1133			0.860500			0.430250	−	0.902710i	$-0.358425\pi$
$269$	14.1133			0.860500			0.430250	+	0.902710i	$0.358425\pi$
$270$	−6.71327	+	3.47836i	−0.408557	+	0.211686i
$271$	−3.83806	+	6.64771i	−0.233145	+	0.403820i	−0.958732	−	0.284311i	$-0.908235\pi$
$271$	−3.83806	+	6.64771i	−0.233145	+	0.403820i	0.725587	+	0.688131i	$0.241568\pi$
$272$	1.12437	+	0.649153i	0.0681747	+	0.0393607i
$273$	−0.0191505	+	0.0155799i	−0.00115904	+	0.000942938i
$274$	6.66347	−	3.84716i	0.402555	−	0.232415i
$275$	7.54099	+	13.0614i	0.454739	+	0.787631i
$276$	−0.319217	+	0.259698i	−0.0192146	+	0.0156320i
$277$	−8.13485	−	4.69666i	−0.488776	−	0.282195i	0.235291	−	0.971925i	$-0.424396\pi$
$277$	−8.13485	−	4.69666i	−0.488776	−	0.282195i	−0.724066	+	0.689730i	$0.757729\pi$
$278$	14.3288	−	8.27271i	0.859382	−	0.496164i
$279$	−9.75455	−	29.5641i	−0.583990	−	1.76996i
$280$	0.0303921	−	0.0526407i	0.00181628	−	0.00314588i
$281$		−	25.5202i		−	1.52241i	−0.648513	−	0.761203i	$-0.724609\pi$
$281$		−	25.5202i		−	1.52241i	0.648513	−	0.761203i	$-0.275391\pi$
$282$	2.69408	+	16.7634i	0.160430	+	0.998248i
$283$		−	14.7579i		−	0.877265i	−0.898667	−	0.438632i	$-0.855463\pi$
$283$		−	14.7579i		−	0.877265i	0.898667	−	0.438632i	$-0.144537\pi$
$284$	−0.365314	−	0.632742i	−0.0216774	−	0.0375463i
$285$	1.63447	−	0.262678i	0.0968174	−	0.0155597i
$286$	0.892578	+	1.54599i	0.0527792	+	0.0914163i
$287$	0.0104534	−	0.0181059i	0.000617047	−	0.00106876i
$288$	−1.99725	+	2.23852i	−0.117689	+	0.131906i
$289$	−7.65720	−	13.2627i	−0.450424	−	0.780156i
$290$	7.70706	−	4.44967i	0.452574	−	0.261294i
$291$	0.946109	+	5.88699i	0.0554619	+	0.345101i
$292$	−4.44903			−0.260360
$293$	20.9716			1.22517			0.612587	−	0.790404i	$-0.290129\pi$
$293$	20.9716			1.22517			0.612587	+	0.790404i	$0.290129\pi$
$294$	1.92336	+	11.9678i	0.112173	+	0.697974i
$295$	1.89905	+	3.28926i	0.110567	+	0.191508i
$296$	−4.60621	+	3.97276i	−0.267731	+	0.230912i
$297$	22.9001	+	14.6508i	1.32880	+	0.850126i
$298$	8.00686	+	4.62276i	0.463825	+	0.267789i
$299$	0.0405331	−	0.0702054i	0.00234409	−	0.00406008i
$300$	1.77874	−	4.66540i	0.102696	−	0.269357i
$301$		−	0.181231i		−	0.0104460i
$302$	−14.7648	−	8.52443i	−0.849616	−	0.490526i
$303$	33.5756	−	5.39599i	1.92887	−	0.309991i
$304$	0.568843	−	0.328422i	0.0326254	−	0.0188363i
$305$	−5.08080	+	8.80021i	−0.290926	+	0.503898i
$306$	−3.69879	+	1.22040i	−0.211446	+	0.0697655i
$307$	30.6335			1.74835			0.874173	−	0.485614i	$-0.161404\pi$
$307$	30.6335			1.74835			0.874173	+	0.485614i	$0.161404\pi$
$308$	−0.218554			−0.0124533
$309$	15.1663	−	12.3385i	0.862779	−	0.701912i
$310$	−13.0769	−	7.54995i	−0.742718	−	0.428808i
$311$	25.9144	−	14.9617i	1.46947	−	0.848401i	0.470059	−	0.882635i	$-0.344233\pi$
$311$	25.9144	−	14.9617i	1.46947	−	0.848401i	0.999414	+	0.0342345i	$0.0108993\pi$
$312$	0.210538	−	0.552214i	0.0119194	−	0.0312629i
$313$		−	18.9592i		−	1.07164i	−0.844334	−	0.535818i	$-0.820003\pi$
$313$		−	18.9592i		−	1.07164i	0.844334	−	0.535818i	$-0.179997\pi$
$314$	10.9219	−	6.30575i	0.616357	−	0.355854i
$315$	0.0571367	+	0.173170i	0.00321929	+	0.00975704i
$316$	8.25102	+	4.76373i	0.464156	+	0.267981i
$317$	8.21870			0.461608			0.230804	−	0.973000i	$-0.425864\pi$
$317$	8.21870			0.461608			0.230804	+	0.973000i	$0.425864\pi$
$318$	−0.878629	+	0.714807i	−0.0492710	+	0.0400844i
$319$	−27.7113	−	15.9991i	−1.55153	−	0.895778i
$320$			1.45509i			0.0813422i
$321$	22.7308	−	3.65311i	1.26871	−	0.203897i
$322$	0.00496241	+	0.00859514i	0.000276544	+	0.000478989i
$323$	0.852784			0.0474502
$324$	−1.02197	−	8.94179i	−0.0567763	−	0.496766i
$325$			0.983597i			0.0545602i
$326$	−3.07501	+	5.32607i	−0.170309	+	0.294984i
$327$	5.07854	−	4.13164i	0.280844	−	0.228480i
$328$			0.500483i			0.0276345i
$329$	0.409487			0.0225757
$330$	13.0189	−	2.09228i	0.716664	−	0.115176i
$331$			20.7737i			1.14182i	0.821011	+	0.570912i	$0.193410\pi$
$331$			20.7737i			1.14182i	−0.821011	+	0.570912i	$0.806590\pi$
$332$	5.71363			0.313576
$333$	0.306649	−	18.2457i	0.0168042	−	0.999859i
$334$	9.76764			0.534461
$335$		−	9.88429i		−	0.540037i
$336$	0.0456612	+	0.0561259i	0.00249102	+	0.00306192i
$337$	−5.68691			−0.309786			−0.154893	−	0.987931i	$-0.549503\pi$
$337$	−5.68691			−0.309786			−0.154893	+	0.987931i	$0.549503\pi$
$338$		−	12.8836i		−	0.700774i
$339$	−0.783003	−	4.87210i	−0.0425269	−	0.264616i
$340$	−0.944579	+	1.63606i	−0.0512270	+	0.0887277i
$341$			54.2927i			2.94012i
$342$	−0.400943	+	1.92931i	−0.0216805	+	0.104325i
$343$	0.584755			0.0315738
$344$	2.16921	+	3.75718i	0.116956	+	0.202574i
$345$	−0.377885	−	0.464490i	−0.0203447	−	0.0250073i
$346$			12.5805i			0.676334i
$347$	−20.3441	−	11.7457i	−1.09213	−	0.630540i	−0.157986	−	0.987441i	$-0.550500\pi$
$347$	−20.3441	−	11.7457i	−1.09213	−	0.630540i	−0.934142	+	0.356901i	$0.883833\pi$
$348$	1.68089	+	10.4590i	0.0901049	+	0.560662i
$349$	−21.1848			−1.13399			−0.566997	−	0.823720i	$-0.691895\pi$
$349$	−21.1848			−1.13399			−0.566997	+	0.823720i	$0.691895\pi$
$350$	−0.104287	−	0.0602102i	−0.00557438	−	0.00321837i
$351$	0.815645	+	1.57420i	0.0435359	+	0.0840248i
$352$	4.53095	−	2.61594i	0.241500	−	0.139430i
$353$			35.9435i			1.91308i	0.291606	+	0.956539i	$0.405811\pi$
$353$			35.9435i			1.91308i	−0.291606	+	0.956539i	$0.594189\pi$
$354$	−4.46375	+	0.717377i	−0.237245	+	0.0381281i
$355$	0.920698	−	0.531565i	0.0488656	−	0.0282126i
$356$	5.22746	+	3.01807i	0.277055	+	0.159958i
$357$	0.0149056	+	0.0927472i	0.000788886	+	0.00490870i
$358$	0.373026			0.0197150
$359$	9.15938			0.483414			0.241707	−	0.970349i	$-0.422293\pi$
$359$	9.15938			0.483414			0.241707	+	0.970349i	$0.422293\pi$
$360$	−3.25726	−	2.90619i	−0.171673	−	0.153170i
$361$	−9.28428	+	16.0808i	−0.488646	+	0.846360i
$362$	−6.57891	+	3.79833i	−0.345780	+	0.199636i
$363$	−17.8964	−	21.9980i	−0.939318	−	1.15459i
$364$	−0.0123438	−	0.00712669i	−0.000646990	−	0.000373540i
$365$		−	6.47376i		−	0.338852i
$366$	−7.63340	−	9.38284i	−0.399004	−	0.490449i
$367$	10.5665	−	18.3018i	0.551568	−	0.955344i	−0.446594	−	0.894737i	$-0.647363\pi$
$367$	10.5665	−	18.3018i	0.551568	−	0.955344i	0.998162	−	0.0606069i	$-0.0193036\pi$
$368$	−0.205756	−	0.118793i	−0.0107258	−	0.00619253i
$369$	−1.12034	−	0.999590i	−0.0583227	−	0.0520366i
$370$	−5.78074	−	6.70247i	−0.300526	−	0.348445i
$371$	0.0136588	+	0.0236577i	0.000709129	+	0.00122825i
$372$	13.9427	−	11.3430i	0.722894	−	0.588110i
$373$	0.943470			0.0488510			0.0244255	−	0.999702i	$-0.492224\pi$
$373$	0.943470			0.0488510			0.0244255	+	0.999702i	$0.492224\pi$
$374$	6.79260			0.351237
$375$	18.5633	+	7.07749i	0.958605	+	0.365480i
$376$	−8.48927	+	4.90128i	−0.437800	+	0.252764i
$377$	−1.04341	−	1.80724i	−0.0537383	−	0.0930775i
$378$	−0.216836	−	0.00988397i	−0.0111528	−	0.000508376i
$379$	3.24242	−	5.61603i	0.166552	−	0.288476i	−0.770654	−	0.637254i	$-0.780070\pi$
$379$	3.24242	−	5.61603i	0.166552	−	0.288476i	0.937205	+	0.348778i	$0.113403\pi$
$380$	0.477884	+	0.827720i	0.0245149	+	0.0424611i
$381$	12.6282	+	15.5223i	0.646960	+	0.795232i
$382$	3.85440	+	6.67602i	0.197208	+	0.341575i
$383$		−	16.7343i		−	0.855084i	−0.903995	−	0.427542i	$-0.859380\pi$
$383$		−	16.7343i		−	0.855084i	0.903995	−	0.427542i	$-0.140620\pi$
$384$	−1.61841	−	0.617040i	−0.0825893	−	0.0314882i
$385$		−	0.318017i		−	0.0162076i
$386$	11.0178	−	19.0833i	0.560789	−	0.971315i
$387$	−12.7430	−	2.64821i	−0.647763	−	0.134616i
$388$	−2.98127	+	1.72123i	−0.151351	+	0.0873824i
$389$	2.48344	+	1.43382i	0.125916	+	0.0726974i	0.561635	−	0.827385i	$-0.310173\pi$
$389$	2.48344	+	1.43382i	0.125916	+	0.0726974i	−0.435719	+	0.900083i	$0.643506\pi$
$390$	0.803522	+	0.306353i	0.0406879	+	0.0155128i
$391$	−0.154230	−	0.267135i	−0.00779976	−	0.0135096i
$392$	−6.06067	+	3.49913i	−0.306110	+	0.176733i
$393$	1.23013	+	7.65429i	0.0620520	+	0.386108i
$394$	14.3919	+	8.30916i	0.725053	+	0.418609i
$395$	−6.93167	+	12.0060i	−0.348770	+	0.604088i
$396$	−3.19359	+	15.3673i	−0.160484	+	0.772238i
$397$	−3.64104			−0.182738			−0.0913692	−	0.995817i	$-0.529124\pi$
$397$	−3.64104			−0.182738			−0.0913692	+	0.995817i	$0.529124\pi$
$398$	−20.0844			−1.00674
$399$	0.0444070	+	0.0169307i	0.00222313	+	0.000847596i
$400$	2.88270			0.144135
$401$	−9.62340	−	5.55607i	−0.480569	−	0.277457i	0.240084	−	0.970752i	$-0.422825\pi$
$401$	−9.62340	−	5.55607i	−0.480569	−	0.277457i	−0.720654	+	0.693295i	$0.756158\pi$
$402$	10.9937	+	4.19148i	0.548316	+	0.209052i
$403$	−1.77040	+	3.06642i	−0.0881897	+	0.152749i
$404$	9.81680	+	17.0032i	0.488404	+	0.845941i
$405$	13.0111	−	1.48707i	0.646529	−	0.0738929i
$406$	0.255486			0.0126796
$407$	−10.4780	+	30.0500i	−0.519375	+	1.48952i
$408$	−1.41914	−	1.74438i	−0.0702577	−	0.0863595i
$409$	27.6360	−	15.9557i	1.36651	−	0.788957i	0.376032	−	0.926607i	$-0.377288\pi$
$409$	27.6360	−	15.9557i	1.36651	−	0.788957i	0.990481	+	0.137650i	$0.0439550\pi$
$410$	−0.728249			−0.0359657
$411$	−13.1581	+	2.11466i	−0.649041	+	0.104309i
$412$	9.77566	+	5.64398i	0.481612	+	0.278059i
$413$			0.109038i			0.00536539i
$414$	0.676869	−	0.223330i	0.0332663	−	0.0109761i
$415$			8.31386i			0.408111i
$416$	0.341207			0.0167290
$417$	−28.2944	+	4.54725i	−1.38558	+	0.222680i
$418$	1.71827	−	2.97612i	0.0840431	−	0.145567i
$419$	13.1635	+	22.7999i	0.643079	+	1.11385i	0.984742	+	0.174023i	$0.0556767\pi$
$419$	13.1635	+	22.7999i	0.643079	+	1.11385i	−0.341663	+	0.939823i	$0.610990\pi$
$420$	−0.0816685	+	0.0664413i	−0.00398501	+	0.00324200i
$421$	−26.2369	+	15.1479i	−1.27871	+	0.738262i	−0.976611	−	0.215015i	$-0.931020\pi$
$421$	−26.2369	+	15.1479i	−1.27871	+	0.738262i	−0.302097	+	0.953277i	$0.597687\pi$
$422$	0.712168	+	0.411170i	0.0346678	+	0.0200155i
$423$	5.98357	−	28.7925i	0.290931	−	1.39994i
$424$	−0.566334	−	0.326973i	−0.0275036	−	0.0158792i
$425$	3.24121	+	1.87132i	0.157222	+	0.0907721i
$426$	0.200801	+	1.24945i	0.00972886	+	0.0605361i
$427$	−0.252640	+	0.145862i	−0.0122261	+	0.00705875i
$428$	6.64602	+	11.5112i	0.321248	+	0.556417i
$429$	−0.490622	−	3.05281i	−0.0236875	−	0.147391i
$430$	−5.46705	+	3.15640i	−0.263645	+	0.152215i
$431$	0.131345	−	0.0758322i	0.00632668	−	0.00365271i	−0.496833	−	0.867846i	$-0.665504\pi$
$431$	0.131345	−	0.0758322i	0.00632668	−	0.00365271i	0.503160	+	0.864193i	$0.332171\pi$
$432$	4.61364	−	2.39047i	0.221974	−	0.115012i
$433$	12.4357			0.597621			0.298810	−	0.954313i	$-0.403410\pi$
$433$	12.4357			0.597621			0.298810	+	0.954313i	$0.403410\pi$
$434$	−0.216747	−	0.375417i	−0.0104042	−	0.0180206i
$435$	−15.2188	+	2.44585i	−0.729687	+	0.117269i
$436$	3.27345	+	1.88993i	0.156770	+	0.0905112i
$437$	−0.156057			−0.00746523
$438$	7.20037	+	2.74523i	0.344047	+	0.131172i
$439$	−12.5896	−	7.26859i	−0.600867	−	0.346911i	0.168515	−	0.985699i	$-0.446103\pi$
$439$	−12.5896	−	7.26859i	−0.600867	−	0.346911i	−0.769383	+	0.638788i	$0.779436\pi$
$440$	3.80644	+	6.59296i	0.181465	+	0.314307i
$441$	4.27180	−	20.5556i	0.203419	−	0.978837i
$442$	0.383641	+	0.221495i	0.0182480	+	0.0105355i
$443$	4.01521	+	6.95455i	0.190768	+	0.330421i	0.945505	−	0.325607i	$-0.105569\pi$
$443$	4.01521	+	6.95455i	0.190768	+	0.330421i	−0.754737	+	0.656028i	$0.772235\pi$
$444$	9.90611	−	3.58735i	0.470123	−	0.170248i
$445$	−4.39158	+	7.60644i	−0.208181	+	0.360580i
$446$	18.2799	−	10.5539i	0.865580	−	0.499743i
$447$	−10.1060	−	12.4221i	−0.477996	−	0.587545i
$448$	−0.0208867	+	0.0361769i	−0.000986805	+	0.00170920i
$449$	−16.0685	+	9.27715i	−0.758319	+	0.437816i	−0.828692	−	0.559705i	$-0.810914\pi$
$449$	−16.0685	+	9.27715i	−0.758319	+	0.437816i	0.0703729	+	0.997521i	$0.477581\pi$
$450$	−5.75748	+	6.45300i	−0.271410	+	0.304197i
$451$	1.30923	+	2.26766i	0.0616495	+	0.106780i
$452$	2.46731	−	1.42450i	0.116052	−	0.0670029i
$453$	18.6356	+	22.9065i	0.875575	+	1.07624i
$454$	6.99762	−	12.1202i	0.328415	−	0.568831i
$455$	0.0103700	−	0.0179614i	0.000486153	−	0.000842042i
$456$	−1.12327	+	0.180523i	−0.0526020	+	0.00845377i
$457$	11.4952	+	6.63678i	0.537725	+	0.310456i	0.744156	−	0.668005i	$-0.232852\pi$
$457$	11.4952	+	6.63678i	0.537725	+	0.310456i	−0.206432	+	0.978461i	$0.566185\pi$
$458$			25.0499i			1.17050i
$459$	6.73920	+	0.307191i	0.314559	+	0.0143384i
$460$	0.172855	−	0.299395i	0.00805943	−	0.0139593i
$461$		−	22.6122i		−	1.05316i	−0.850127	−	0.526578i	$-0.823475\pi$
$461$		−	22.6122i		−	1.05316i	0.850127	−	0.526578i	$-0.176525\pi$
$462$	0.353711	+	0.134857i	0.0164561	+	0.00627409i
$463$		−	13.7267i		−	0.637932i	−0.947766	−	0.318966i	$-0.896664\pi$
$463$		−	13.7267i		−	0.637932i	0.947766	−	0.318966i	$-0.103336\pi$
$464$	−5.29661	+	3.05800i	−0.245889	+	0.141964i
$465$	16.5052	+	20.2879i	0.765410	+	0.940829i
$466$			7.60849i			0.352456i
$467$		−	14.5445i		−	0.673039i	−0.941677	−	0.336519i	$-0.890750\pi$
$467$		−	14.5445i		−	0.673039i	0.941677	−	0.336519i	$-0.109250\pi$
$468$	−0.681476	+	0.763799i	−0.0315012	+	0.0353066i
$469$	0.141881	−	0.245745i	0.00655146	−	0.0113475i
$470$	−7.13182	−	12.3527i	−0.328966	−	0.569787i
$471$	−21.5670	+	3.46607i	−0.993755	+	0.159708i
$472$	−1.30511	−	2.26051i	−0.0600724	−	0.104049i
$473$	19.6572	+	11.3491i	0.903837	+	0.521831i
$474$	−10.4142	−	12.8009i	−0.478338	−	0.587964i
$475$	1.63980	−	0.946741i	0.0752394	−	0.0434395i
$476$	−0.0469686	+	0.0271174i	−0.00215280	+	0.00124292i
$477$	1.86305	−	0.614705i	0.0853032	−	0.0281454i
$478$	6.77496	+	11.7346i	0.309879	+	0.536727i
$479$		−	7.43800i		−	0.339851i	−0.985457	−	0.169925i	$-0.945647\pi$
$479$		−	7.43800i		−	0.339851i	0.985457	−	0.169925i	$-0.0543527\pi$
$480$	0.897851	−	2.35494i	0.0409811	−	0.107488i
$481$	−1.57167	+	1.35553i	−0.0716620	+	0.0618070i
$482$	−9.78870	+	16.9545i	−0.445863	+	0.772257i
$483$	−0.00272768	−	0.0169725i	−0.000124114	−	0.000772275i
$484$	8.18633	−	14.1791i	0.372106	−	0.644507i
$485$	−2.50456	−	4.33802i	−0.113726	−	0.196979i
$486$	−3.86347	+	15.1021i	−0.175250	+	0.685045i
$487$		−	15.4519i		−	0.700193i	−0.936714	−	0.350096i	$-0.886149\pi$
$487$		−	15.4519i		−	0.700193i	0.936714	−	0.350096i	$-0.113851\pi$
$488$	3.49174	−	6.04786i	0.158063	−	0.273774i
$489$	8.26303	−	6.72238i	0.373667	−	0.303996i
$490$	−5.09156	−	8.81884i	−0.230013	−	0.398394i
$491$	−11.0179	+	19.0836i	−0.497231	+	0.861229i	−0.999995	−	0.00319433i	$-0.998983\pi$
$491$	−11.0179	+	19.0836i	−0.497231	+	0.861229i	0.502764	+	0.864424i	$0.332317\pi$
$492$	0.308818	−	0.809988i	0.0139226	−	0.0365171i
$493$	−7.94044			−0.357619
$494$	0.194093	−	0.112060i	0.00873266	−	0.00504180i
$495$	−22.3609	−	4.64697i	−1.00505	−	0.208866i
$496$	8.98698	+	5.18863i	0.403527	+	0.232977i
$497$	0.0305208			0.00136905
$498$	−9.24701	−	3.52554i	−0.414368	−	0.157983i
$499$			21.4031i			0.958134i	0.877778	+	0.479067i	$0.159025\pi$
$499$			21.4031i			0.958134i	−0.877778	+	0.479067i	$0.840975\pi$
$500$			11.4701i			0.512957i
$501$	−15.8081	−	6.02702i	−0.706253	−	0.269268i
$502$	−2.69186			−0.120144
$503$	−17.7548	−	10.2508i	−0.791649	−	0.457059i	0.0488937	−	0.998804i	$-0.484430\pi$
$503$	−17.7548	−	10.2508i	−0.791649	−	0.457059i	−0.840543	+	0.541745i	$0.817764\pi$
$504$	−0.0392667	−	0.119010i	−0.00174908	−	0.00530111i
$505$	−24.7412	+	14.2844i	−1.10097	+	0.635646i
$506$	−1.24303			−0.0552593
$507$	−7.94968	+	20.8510i	−0.353058	+	0.926023i
$508$	−5.77648	+	10.0052i	−0.256290	+	0.443907i
$509$	−15.3898	−	26.6560i	−0.682142	−	1.18150i	−0.974326	−	0.225142i	$-0.927715\pi$
$509$	−15.3898	−	26.6560i	−0.682142	−	1.18150i	0.292184	−	0.956362i	$-0.405618\pi$
$510$	2.53823	−	2.06498i	0.112395	−	0.0914387i
$511$	0.0929256	−	0.160952i	0.00411079	−	0.00712009i
$512$		−	1.00000i		−	0.0441942i
$513$	1.83935	−	2.87502i	0.0812094	−	0.126935i
$514$	−10.8908	−	18.8634i	−0.480371	−	0.832027i
$515$	−8.21252	+	14.2245i	−0.361887	+	0.626806i
$516$	−1.19235	−	7.41916i	−0.0524902	−	0.326611i
$517$	−25.6430	+	44.4149i	−1.12778	+	1.95336i
$518$	−0.0475133	−	0.249616i	−0.00208761	−	0.0109675i
$519$	7.76269	−	20.3605i	0.340744	−	0.893727i
$520$			0.496488i			0.0217724i
$521$	2.21973	+	3.84468i	0.0972480	+	0.168439i	0.910545	−	0.413411i	$-0.135663\pi$
$521$	2.21973	+	3.84468i	0.0972480	+	0.168439i	−0.813297	+	0.581849i	$0.802329\pi$
$522$	3.73326	−	17.9642i	0.163400	−	0.786271i
$523$	18.3747	−	10.6087i	0.803471	−	0.463884i	−0.0412122	−	0.999150i	$-0.513122\pi$
$523$	18.3747	−	10.6087i	0.803471	−	0.463884i	0.844684	+	0.535266i	$0.179789\pi$
$524$	−3.87625	+	2.23795i	−0.169335	+	0.0977655i
$525$	0.131628	+	0.161794i	0.00574470	+	0.00706128i
$526$	10.9527	+	6.32355i	0.477561	+	0.275720i
$527$	6.73644	+	11.6679i	0.293444	+	0.508260i
$528$	−8.94709	+	1.43790i	−0.389372	+	0.0625767i
$529$	−11.4718	−	19.8697i	−0.498773	−	0.863900i
$530$	0.475777	−	0.824069i	0.0206664	−	0.0357953i
$531$	7.66684	+	1.59330i	0.332712	+	0.0691433i
$532$			0.0274386i			0.00118961i
$533$			0.170768i			0.00739678i
$534$	−6.59791	−	8.11004i	−0.285520	−	0.350956i
$535$	−16.7499	+	9.67059i	−0.724163	+	0.418096i
$536$			6.79289i			0.293408i
$537$	−0.603710	−	0.230172i	−0.0260520	−	0.00993265i
$538$		−	14.1133i		−	0.608466i
$539$	−18.3070	+	31.7087i	−0.788540	+	1.36579i
$540$	3.47836	+	6.71327i	0.149685	+	0.288893i
$541$		−	21.4388i		−	0.921726i	−0.887471	−	0.460863i	$-0.847540\pi$
$541$		−	21.4388i		−	0.921726i	0.887471	−	0.460863i	$-0.152460\pi$
$542$	6.64771	+	3.83806i	0.285544	+	0.164859i
$543$	12.9911	−	2.08783i	0.557502	−	0.0895972i
$544$	0.649153	−	1.12437i	0.0278322	−	0.0482068i
$545$	−2.75002	+	4.76318i	−0.117798	+	0.204032i
$546$	0.0155799	+	0.0191505i	0.000666758	+	0.000819567i
$547$	−19.1184	+	11.0380i	−0.817446	+	0.471952i	−0.849535	−	0.527533i	$-0.823117\pi$
$547$	−19.1184	+	11.0380i	−0.817446	+	0.471952i	0.0320892	+	0.999485i	$0.489784\pi$
$548$	−3.84716	−	6.66347i	−0.164342	−	0.284649i
$549$	6.56441	+	19.8954i	0.280162	+	0.849116i
$550$	13.0614	−	7.54099i	0.556939	−	0.321549i
$551$	−2.00863	+	3.47904i	−0.0855703	+	0.148212i
$552$	0.259698	+	0.319217i	0.0110535	+	0.0135868i
$553$	−0.344673	+	0.198997i	−0.0146570	+	0.00846223i
$554$	−4.69666	+	8.13485i	−0.199542	+	0.345617i
$555$	5.21993	+	14.4143i	0.221574	+	0.611853i
$556$	−8.27271	−	14.3288i	−0.350841	−	0.607675i
$557$	3.00270	+	1.73361i	0.127229	+	0.0734555i	0.562264	−	0.826958i	$-0.309931\pi$
$557$	3.00270	+	1.73361i	0.127229	+	0.0734555i	−0.435035	+	0.900414i	$0.643264\pi$
$558$	−29.5641	+	9.75455i	−1.25155	+	0.412943i
$559$	0.740149	+	1.28198i	0.0313050	+	0.0542218i
$560$	−0.0526407	−	0.0303921i	−0.00222448	−	0.00128430i
$561$	−10.9932	−	4.19130i	−0.464134	−	0.176957i
$562$	−25.5202			−1.07650
$563$	30.1591	+	17.4123i	1.27105	+	0.733843i	0.975186	−	0.221386i	$-0.0710582\pi$
$563$	30.1591	+	17.4123i	1.27105	+	0.733843i	0.295867	+	0.955229i	$0.404392\pi$
$564$	16.7634	−	2.69408i	0.705868	−	0.113441i
$565$	2.07278	+	3.59016i	0.0872026	+	0.151039i
$566$	−14.7579			−0.620320
$567$	0.344831	+	0.149793i	0.0144816	+	0.00629071i
$568$	−0.632742	+	0.365314i	−0.0265492	+	0.0153282i
$569$	−4.68062	+	2.70236i	−0.196222	+	0.113289i	−0.594892	−	0.803806i	$-0.702805\pi$
$569$	−4.68062	+	2.70236i	−0.196222	+	0.113289i	0.398670	+	0.917094i	$0.369472\pi$
$570$	−0.262678	−	1.63447i	−0.0110024	−	0.0684602i
$571$	−10.1778	−	17.6285i	−0.425930	−	0.737732i	0.570577	−	0.821244i	$-0.306720\pi$
$571$	−10.1778	−	17.6285i	−0.425930	−	0.737732i	−0.996507	+	0.0835123i	$0.973386\pi$
$572$	1.54599	−	0.892578i	0.0646411	−	0.0373206i
$573$	−2.11864	−	13.1829i	−0.0885076	−	0.550723i
$574$	−0.0181059	−	0.0104534i	−0.000755725	−	0.000436318i
$575$	−0.593134	−	0.342446i	−0.0247354	−	0.0142810i
$576$	2.23852	+	1.99725i	0.0932718	+	0.0832188i
$577$	−7.43567	−	4.29299i	−0.309551	−	0.178719i	0.337175	−	0.941442i	$-0.390529\pi$
$577$	−7.43567	−	4.29299i	−0.309551	−	0.178719i	−0.646726	+	0.762723i	$0.723862\pi$
$578$	−13.2627	+	7.65720i	−0.551654	+	0.318498i
$579$	−29.6065	+	24.0863i	−1.23040	+	1.00099i
$580$	−4.44967	−	7.70706i	−0.184763	−	0.320018i
$581$	−0.119339	+	0.206701i	−0.00495101	+	0.00857540i
$582$	5.88699	−	0.946109i	0.244024	−	0.0392175i
$583$	−3.42138			−0.141699
$584$			4.44903i			0.184102i
$585$	−1.11140	−	0.991611i	−0.0459507	−	0.0409981i
$586$		−	20.9716i		−	0.866328i
$587$	39.3851	+	22.7390i	1.62560	+	0.938538i	0.985386	+	0.170337i	$0.0544857\pi$
$587$	39.3851	+	22.7390i	1.62560	+	0.938538i	0.640209	+	0.768201i	$0.278848\pi$
$588$	11.9678	−	1.92336i	0.493542	−	0.0793181i
$589$	6.81624			0.280858
$590$	3.28926	−	1.89905i	0.135417	−	0.0781828i
$591$	−18.1649	−	22.3280i	−0.747206	−	0.918452i
$592$	3.97276	+	4.60621i	0.163279	+	0.189314i
$593$	32.1558			1.32048			0.660240	−	0.751054i	$-0.270454\pi$
$593$	32.1558			1.32048			0.660240	+	0.751054i	$0.270454\pi$
$594$	14.6508	−	22.9001i	0.601130	−	0.939603i
$595$	−0.0394583	−	0.0683438i	−0.00161763	−	0.00280182i
$596$	4.62276	−	8.00686i	0.189356	−	0.327974i
$597$	32.5049	+	12.3929i	1.33034	+	0.507207i
$598$	−0.0702054	−	0.0405331i	−0.00287091	−	0.00165752i
$599$	0.523102			0.0213734			0.0106867	−	0.999943i	$-0.496598\pi$
$599$	0.523102			0.0213734			0.0106867	+	0.999943i	$0.496598\pi$
$600$	−4.66540	−	1.77874i	−0.190464	−	0.0726169i
$601$	18.6389			0.760295			0.380148	−	0.924926i	$-0.375873\pi$
$601$	18.6389			0.760295			0.380148	+	0.924926i	$0.375873\pi$
$602$	−0.181231			−0.00738641
$603$	−15.2060	−	13.5671i	−0.619238	−	0.552495i
$604$	−8.52443	+	14.7648i	−0.346854	+	0.600769i
$605$	20.6320	+	11.9119i	0.838809	+	0.484287i
$606$	−5.39599	−	33.5756i	−0.219197	−	1.36391i
$607$	36.0463	−	20.8114i	1.46308	−	0.844707i	0.463923	−	0.885875i	$-0.346441\pi$
$607$	36.0463	−	20.8114i	1.46308	−	0.844707i	0.999152	+	0.0411682i	$0.0131080\pi$
$608$	−0.328422	−	0.568843i	−0.0133193	−	0.0230696i
$609$	−0.413482	−	0.157645i	−0.0167551	−	0.00638811i
$610$	8.80021	+	5.08080i	0.356310	+	0.205716i
$611$	−2.89659	+	1.67235i	−0.117184	+	0.0676560i
$612$	1.22040	+	3.69879i	0.0493317	+	0.149515i
$613$	−0.993483	+	1.72076i	−0.0401264	+	0.0695009i	−0.885391	−	0.464847i	$-0.846109\pi$
$613$	−0.993483	+	1.72076i	−0.0401264	+	0.0695009i	0.845265	+	0.534348i	$0.179443\pi$
$614$		−	30.6335i		−	1.23627i
$615$	1.17861	+	0.449359i	0.0475261	+	0.0181199i
$616$			0.218554i			0.00880579i
$617$	−24.2924	−	42.0756i	−0.977975	−	1.69390i	−0.669747	−	0.742589i	$-0.733598\pi$
$617$	−24.2924	−	42.0756i	−0.977975	−	1.69390i	−0.308227	−	0.951313i	$-0.599736\pi$
$618$	−12.3385	−	15.1663i	−0.496327	−	0.610077i
$619$	0.972158	+	1.68383i	0.0390743	+	0.0676787i	0.884901	−	0.465779i	$-0.154226\pi$
$619$	0.972158	+	1.68383i	0.0390743	+	0.0676787i	−0.845827	+	0.533457i	$0.820892\pi$
$620$	−7.54995	+	13.0769i	−0.303213	+	0.525181i
$621$	−1.23326	−	0.0562152i	−0.0494889	−	0.00225584i
$622$	−14.9617	−	25.9144i	−0.599910	−	1.03907i
$623$	−0.218369	+	0.126075i	−0.00874876	+	0.00505110i
$624$	−0.552214	−	0.210538i	−0.0221062	−	0.00842827i
$625$	−2.27652			−0.0910607
$626$	−18.9592			−0.757761
$627$	−4.61725	+	3.75636i	−0.184395	+	0.150014i
$628$	−6.30575	−	10.9219i	−0.251627	−	0.435830i
$629$	1.47670	+	7.75800i	0.0588799	+	0.309332i
$630$	0.173170	−	0.0571367i	0.00689927	−	0.00227638i
$631$	32.4975	+	18.7624i	1.29370	+	0.746921i	0.979309	−	0.202371i	$-0.0648647\pi$
$631$	32.4975	+	18.7624i	1.29370	+	0.746921i	0.314396	+	0.949292i	$0.398198\pi$
$632$	4.76373	−	8.25102i	0.189491	−	0.328208i
$633$	−0.898873	−	1.10488i	−0.0357270	−	0.0439150i
$634$		−	8.21870i		−	0.326406i
$635$	−14.5584	−	8.40532i	−0.577734	−	0.333555i
$636$	0.714807	+	0.878629i	0.0283440	+	0.0348399i
$637$	−2.06794	+	1.19393i	−0.0819348	+	0.0473051i
$638$	−15.9991	+	27.7113i	−0.633411	+	1.09710i
$639$	0.445981	−	2.14603i	0.0176427	−	0.0848956i
$640$	1.45509			0.0575176
$641$	−30.8433			−1.21824			−0.609119	−	0.793079i	$-0.708477\pi$
$641$	−30.8433			−1.21824			−0.609119	+	0.793079i	$0.708477\pi$
$642$	−3.65311	−	22.7308i	−0.144177	−	0.897114i
$643$	3.92274	+	2.26480i	0.154698	+	0.0893149i	0.575351	−	0.817907i	$-0.304866\pi$
$643$	3.92274	+	2.26480i	0.154698	+	0.0893149i	−0.420653	+	0.907222i	$0.638199\pi$
$644$	0.00859514	−	0.00496241i	0.000338696	−	0.000195546i
$645$	10.7956	−	1.73498i	0.425076	−	0.0683146i
$646$		−	0.852784i		−	0.0335523i
$647$	12.7023	−	7.33365i	0.499377	−	0.288316i	−0.229079	−	0.973408i	$-0.573571\pi$
$647$	12.7023	−	7.33365i	0.499377	−	0.288316i	0.728456	+	0.685092i	$0.240238\pi$
$648$	−8.94179	+	1.02197i	−0.351267	+	0.0401469i
$649$	−11.8268	−	6.82818i	−0.464241	−	0.268029i
$650$	0.983597			0.0385799
$651$	0.119139	+	0.741321i	0.00466943	+	0.0290547i
$652$	5.32607	+	3.07501i	0.208585	+	0.120427i
$653$		−	15.2782i		−	0.597881i	−0.954272	−	0.298940i	$-0.903367\pi$
$653$		−	15.2782i		−	0.597881i	0.954272	−	0.298940i	$-0.0966332\pi$
$654$	−4.13164	−	5.07854i	−0.161560	−	0.198586i
$655$	−3.25643	−	5.64031i	−0.127239	−	0.220385i
$656$	0.500483			0.0195406
$657$	−9.95926	−	8.88583i	−0.388548	−	0.346669i
$658$		−	0.409487i		−	0.0159634i
$659$	−14.7887	+	25.6147i	−0.576084	+	0.997807i	0.419839	+	0.907599i	$0.362087\pi$
$659$	−14.7887	+	25.6147i	−0.576084	+	0.997807i	−0.995923	+	0.0902086i	$0.971247\pi$
$660$	−2.09228	−	13.0189i	−0.0814420	−	0.506758i
$661$			3.46463i			0.134759i	0.997727	+	0.0673793i	$0.0214638\pi$
$661$			3.46463i			0.134759i	−0.997727	+	0.0673793i	$0.978536\pi$
$662$	20.7737			0.807392
$663$	−0.484219	−	0.595193i	−0.0188055	−	0.0231154i
$664$		−	5.71363i		−	0.221732i
$665$	−0.0399257			−0.00154825
$666$	−18.2457	−	0.306649i	−0.707007	−	0.0118824i
$667$	1.45308			0.0562635
$668$		−	9.76764i		−	0.377921i
$669$	−36.0967	+	5.80116i	−1.39558	+	0.224286i
$670$	−9.88429			−0.381863
$671$		−	36.5367i		−	1.41049i
$672$	0.0561259	−	0.0456612i	0.00216510	−	0.00176142i
$673$	−1.67330	+	2.89824i	−0.0645009	+	0.111719i	−0.896472	−	0.443099i	$-0.853879\pi$
$673$	−1.67330	+	2.89824i	−0.0645009	+	0.111719i	0.831972	+	0.554818i	$0.187212\pi$
$674$			5.68691i			0.219051i
$675$	13.2997	−	6.89102i	0.511907	−	0.265235i
$676$	−12.8836			−0.495522
$677$	−4.91544	−	8.51379i	−0.188916	−	0.327212i	0.755973	−	0.654602i	$-0.227164\pi$
$677$	−4.91544	−	8.51379i	−0.188916	−	0.327212i	−0.944889	+	0.327391i	$0.893831\pi$
$678$	−4.87210	+	0.783003i	−0.187112	+	0.0300711i
$679$		−	0.143804i		−	0.00551868i
$680$	1.63606	+	0.944579i	0.0627400	+	0.0362229i
$681$	−18.8037	+	15.2977i	−0.720560	+	0.586211i
$682$	54.2927			2.07898
$683$	−38.6149	−	22.2943i	−1.47756	−	0.853067i	−0.477878	−	0.878426i	$-0.658594\pi$
$683$	−38.6149	−	22.2943i	−1.47756	−	0.853067i	−0.999678	+	0.0253588i	$0.991927\pi$
$684$	1.92931	+	0.400943i	0.0737689	+	0.0153304i
$685$	9.69598	−	5.59797i	0.370464	−	0.213888i
$686$		−	0.584755i		−	0.0223261i
$687$	15.4568	−	40.5411i	0.589713	−	1.54674i
$688$	3.75718	−	2.16921i	0.143241	−	0.0827004i
$689$	−0.193237	−	0.111565i	−0.00736175	−	0.00425031i
$690$	−0.464490	+	0.377885i	−0.0176828	+	0.0143858i
$691$	1.04953			0.0399260			0.0199630	−	0.999801i	$-0.493645\pi$
$691$	1.04953			0.0399260			0.0199630	+	0.999801i	$0.493645\pi$
$692$	12.5805			0.478240
$693$	−0.489238	−	0.436507i	−0.0185846	−	0.0165815i
$694$	−11.7457	+	20.3441i	−0.445859	+	0.772251i
$695$	20.8497	−	12.0376i	0.790873	−	0.456611i
$696$	10.4590	−	1.68089i	0.396448	−	0.0637138i
$697$	0.562726	+	0.324890i	0.0213148	+	0.0123061i
$698$			21.1848i			0.801855i
$699$	4.69474	−	12.3137i	0.177571	−	0.465746i
$700$	−0.0602102	+	0.104287i	−0.00227573	+	0.00394168i
$701$	−7.50171	−	4.33111i	−0.283336	−	0.163584i	0.351597	−	0.936151i	$-0.385639\pi$
$701$	−7.50171	−	4.33111i	−0.283336	−	0.163584i	−0.634932	+	0.772568i	$0.718972\pi$
$702$	1.57420	−	0.815645i	0.0594145	−	0.0307845i
$703$	3.77265	+	1.31547i	0.142288	+	0.0496139i
$704$	−2.61594	−	4.53095i	−0.0985921	−	0.170767i
$705$	3.92014	+	24.3924i	0.147641	+	0.918669i
$706$	35.9435			1.35275
$707$	−0.820163			−0.0308454
$708$	0.717377	+	4.46375i	0.0269607	+	0.167758i
$709$	−39.3142	+	22.6981i	−1.47648	+	0.852445i	−0.999647	−	0.0265509i	$-0.991548\pi$
$709$	−39.3142	+	22.6981i	−1.47648	+	0.852445i	−0.476830	+	0.878996i	$0.658214\pi$
$710$	−0.531565	−	0.920698i	−0.0199493	−	0.0345532i
$711$	8.95574	+	27.1431i	0.335866	+	1.01795i
$712$	3.01807	−	5.22746i	0.113107	−	0.195907i
$713$	−1.23275	−	2.13519i	−0.0461669	−	0.0799634i
$714$	0.0927472	−	0.0149056i	0.00347098	−	0.000557827i
$715$	1.29878	+	2.24956i	0.0485718	+	0.0841288i
$716$		−	0.373026i		−	0.0139406i
$717$	−3.72398	−	23.1718i	−0.139075	−	0.865367i
$718$		−	9.15938i		−	0.341825i
$719$	−10.5767	+	18.3194i	−0.394444	+	0.683197i	−0.993030	−	0.117861i	$-0.962396\pi$
$719$	−10.5767	+	18.3194i	−0.394444	+	0.683197i	0.598586	+	0.801059i	$0.295730\pi$
$720$	−2.90619	+	3.25726i	−0.108307	+	0.121391i
$721$	−0.408363	+	0.235768i	−0.0152082	+	0.00878047i
$722$	16.0808	+	9.28428i	0.598467	+	0.345525i
$723$	26.3038	−	21.3994i	0.978248	−	0.795852i
$724$	3.79833	+	6.57891i	0.141164	+	0.244503i
$725$	−15.2685	+	8.81530i	−0.567060	+	0.327392i
$726$	−21.9980	+	17.8964i	−0.816421	+	0.664198i
$727$	−11.1927	−	6.46209i	−0.415113	−	0.239666i	0.277871	−	0.960618i	$-0.410371\pi$
$727$	−11.1927	−	6.46209i	−0.415113	−	0.239666i	−0.692984	+	0.720953i	$0.743704\pi$
$728$	−0.00712669	+	0.0123438i	−0.000264133	+	0.000457491i
$729$	15.5713	−	22.0575i	0.576714	−	0.816946i
$730$	−6.47376			−0.239604
$731$	5.63260			0.208329
$732$	−9.38284	+	7.63340i	−0.346800	+	0.282139i
$733$	−7.42460			−0.274234			−0.137117	−	0.990555i	$-0.543784\pi$
$733$	−7.42460			−0.274234			−0.137117	+	0.990555i	$0.543784\pi$
$734$	−18.3018	−	10.5665i	−0.675530	−	0.390017i
$735$	2.79867	+	17.4142i	0.103231	+	0.642333i
$736$	−0.118793	+	0.205756i	−0.00437878	+	0.00758427i
$737$	17.7698	+	30.7782i	0.654560	+	1.13373i
$738$	−0.999590	+	1.12034i	−0.0367954	+	0.0412404i
$739$	−51.0637			−1.87841			−0.939203	−	0.343361i	$-0.888435\pi$
$739$	−51.0637			−1.87841			−0.939203	+	0.343361i	$0.888435\pi$
$740$	−6.70247	+	5.78074i	−0.246388	+	0.212504i
$741$	−0.383268	+	0.0615957i	−0.0140797	+	0.00226277i
$742$	0.0236577	−	0.0136588i	0.000868502	−	0.000501430i
$743$	−35.4616			−1.30096			−0.650479	−	0.759524i	$-0.725432\pi$
$743$	−35.4616			−1.30096			−0.650479	+	0.759524i	$0.725432\pi$
$744$	−11.3430	−	13.9427i	−0.415856	−	0.511163i
$745$	11.6507	+	6.72655i	0.426850	+	0.246442i
$746$		−	0.943470i		−	0.0345429i
$747$	12.7901	+	11.4115i	0.467965	+	0.417527i
$748$		−	6.79260i		−	0.248362i
$749$	−0.555254			−0.0202886
$750$	7.07749	−	18.5633i	0.258433	−	0.677836i
$751$	18.6773	−	32.3500i	0.681544	−	1.18047i	−0.292965	−	0.956123i	$-0.594642\pi$
$751$	18.6773	−	32.3500i	0.681544	−	1.18047i	0.974509	−	0.224346i	$-0.0720247\pi$
$752$	4.90128	+	8.48927i	0.178731	+	0.309572i
$753$	4.35655	+	1.66099i	0.158761	+	0.0605297i
$754$	−1.80724	+	1.04341i	−0.0658157	+	0.0379987i
$755$	−21.4841	−	12.4038i	−0.781886	−	0.451422i
$756$	−0.00988397	+	0.216836i	−0.000359476	+	0.00788625i
$757$	−40.0896	−	23.1458i	−1.45708	−	0.841247i	−0.458215	−	0.888841i	$-0.651511\pi$
$757$	−40.0896	−	23.1458i	−1.45708	−	0.841247i	−0.998867	+	0.0475947i	$0.984844\pi$
$758$	−5.61603	−	3.24242i	−0.203983	−	0.117770i
$759$	2.01173	+	0.766998i	0.0730213	+	0.0278403i
$760$	0.827720	−	0.477884i	0.0300245	−	0.0173347i
$761$	−24.2847	−	42.0624i	−0.880321	−	1.52476i	−0.850984	−	0.525192i	$-0.823994\pi$
$761$	−24.2847	−	42.0624i	−0.880321	−	1.52476i	−0.0293374	−	0.999570i	$-0.509340\pi$
$762$	15.5223	−	12.6282i	0.562314	−	0.457470i
$763$	−0.136743	+	0.0789488i	−0.00495044	+	0.00285814i
$764$	6.67602	−	3.85440i	0.241530	−	0.139447i
$765$	−5.38208	+	1.77579i	−0.194590	+	0.0642040i
$766$	−16.7343			−0.604636
$767$	−0.445312	−	0.771302i	−0.0160793	−	0.0278501i
$768$	−0.617040	+	1.61841i	−0.0222655	+	0.0583995i
$769$	−12.3639	−	7.13832i	−0.445855	−	0.257414i	0.260223	−	0.965548i	$-0.416204\pi$
$769$	−12.3639	−	7.13832i	−0.445855	−	0.257414i	−0.706078	+	0.708134i	$0.749537\pi$
$770$	−0.318017			−0.0114605
$771$	5.98631	+	37.2487i	0.215592	+	1.34148i
$772$	−19.0833	−	11.0178i	−0.686824	−	0.396538i
$773$	−7.92140	−	13.7203i	−0.284913	−	0.493484i	0.687675	−	0.726019i	$-0.258631\pi$
$773$	−7.92140	−	13.7203i	−0.284913	−	0.493484i	−0.972588	+	0.232535i	$0.925298\pi$
$774$	−2.64821	+	12.7430i	−0.0951880	+	0.458038i
$775$	25.9068	+	14.9573i	0.930599	+	0.537282i
$776$	1.72123	+	2.98127i	0.0617887	+	0.107021i
$777$	−0.0771270	+	0.433300i	−0.00276692	+	0.0155445i
$778$	1.43382	−	2.48344i	0.0514048	−	0.0890358i
$779$	0.284696	−	0.164369i	0.0102003	−	0.00588914i
$780$	0.306353	−	0.803522i	0.0109692	−	0.0287707i
$781$	−1.91128	+	3.31043i	−0.0683910	+	0.118457i
$782$	−0.267135	+	0.154230i	−0.00955271	+	0.00551526i
$783$	−17.1266	+	26.7699i	−0.612054	+	0.956678i
$784$	3.49913	+	6.06067i	0.124969	+	0.216452i
$785$	15.8924	−	9.17545i	0.567222	−	0.327486i
$786$	7.65429	−	1.23013i	0.273019	−	0.0438774i
$787$	−15.6124	+	27.0414i	−0.556521	+	0.963922i	0.441263	+	0.897378i	$0.354531\pi$
$787$	−15.6124	+	27.0414i	−0.556521	+	0.963922i	−0.997783	+	0.0665441i	$0.978803\pi$
$788$	8.30916	−	14.3919i	0.296002	−	0.512690i
$789$	−13.8241	−	16.9924i	−0.492152	−	0.604945i
$790$	12.0060	+	6.93167i	0.427155	+	0.246618i
$791$			0.119013i			0.00423160i
$792$	15.3673	+	3.19359i	0.546054	+	0.113479i
$793$	1.19140	−	2.06357i	0.0423080	−	0.0732796i
$794$			3.64104i			0.129216i
$795$	−1.27849	+	1.04011i	−0.0453433	+	0.0368890i
$796$			20.0844i			0.711873i
$797$	33.5001	−	19.3413i	1.18663	−	0.685104i	0.229095	−	0.973404i	$-0.426423\pi$
$797$	33.5001	−	19.3413i	1.18663	−	0.685104i	0.957540	+	0.288300i	$0.0930901\pi$
$798$	0.0169307	−	0.0444070i	0.000599341	−	0.00157199i
$799$			12.7267i			0.450239i
$800$		−	2.88270i		−	0.101919i
$801$	5.67393	+	17.1966i	0.200478	+	0.607611i
$802$	−5.55607	+	9.62340i	−0.196192	+	0.339814i
$803$	11.6384	+	20.1583i	0.410711	+	0.711372i
$804$	4.19148	−	10.9937i	0.147822	−	0.387718i
$805$	0.00722077	+	0.0125067i	0.000254499	+	0.000440805i
$806$	3.06642	+	1.77040i	0.108010	+	0.0623596i
$807$	−8.70844	+	22.8411i	−0.306552	+	0.804044i
$808$	17.0032	−	9.81680i	0.598170	−	0.345354i
$809$	27.7742	−	16.0355i	0.976490	−	0.563777i	0.0752813	−	0.997162i	$-0.476015\pi$
$809$	27.7742	−	16.0355i	0.976490	−	0.563777i	0.901209	+	0.433386i	$0.142681\pi$
$810$	−1.48707	−	13.0111i	−0.0522502	−	0.457165i
$811$	16.7743	+	29.0540i	0.589027	+	1.02022i	0.994360	+	0.106055i	$0.0338220\pi$
$811$	16.7743	+	29.0540i	0.589027	+	1.02022i	−0.405334	+	0.914169i	$0.632845\pi$
$812$		−	0.255486i		−	0.00896581i
$813$	−8.39051	−	10.3135i	−0.294268	−	0.361709i
$814$	30.0500	+	10.4780i	1.05325	+	0.367253i
$815$	−4.47442	+	7.74993i	−0.156732	+	0.271468i
$816$	−1.74438	+	1.41914i	−0.0610654	+	0.0496797i
$817$	1.42483	−	2.46788i	0.0498485	−	0.0863402i
$818$	−15.9557	−	27.6360i	−0.557877	−	0.966270i
$819$	−0.0133981	−	0.0406069i	−0.000468166	−	0.00141892i
$820$			0.728249i			0.0254316i
$821$	−1.93152	+	3.34550i	−0.0674106	+	0.116759i	−0.897761	−	0.440483i	$-0.854807\pi$
$821$	−1.93152	+	3.34550i	−0.0674106	+	0.116759i	0.830350	+	0.557242i	$0.188140\pi$
$822$	2.11466	+	13.1581i	0.0737573	+	0.458941i
$823$	2.74181	+	4.74895i	0.0955735	+	0.165538i	0.909848	−	0.414942i	$-0.136198\pi$
$823$	2.74181	+	4.74895i	0.0955735	+	0.165538i	−0.814274	+	0.580480i	$0.802865\pi$
$824$	5.64398	−	9.77566i	0.196617	−	0.340551i
$825$	−25.7918	+	4.14505i	−0.897955	+	0.144312i
$826$	0.109038			0.00379390
$827$	37.1675	−	21.4586i	1.29244	−	0.746190i	0.313353	−	0.949637i	$-0.398548\pi$
$827$	37.1675	−	21.4586i	1.29244	−	0.746190i	0.979086	+	0.203446i	$0.0652143\pi$
$828$	−0.223330	−	0.676869i	−0.00776124	−	0.0235228i
$829$	−24.3241	−	14.0435i	−0.844812	−	0.487752i	0.0140849	−	0.999901i	$-0.495516\pi$
$829$	−24.3241	−	14.0435i	−0.844812	−	0.487752i	−0.858897	+	0.512148i	$0.828850\pi$
$830$	8.31386			0.288578
$831$	12.6207	−	10.2675i	0.437806	−	0.356176i
$832$		−	0.341207i		−	0.0118292i
$833$			9.08588i			0.314807i
$834$	4.54725	+	28.2944i	0.157458	+	0.979756i
$835$	14.2128			0.491855
$836$	−2.97612	−	1.71827i	−0.102931	−	0.0594274i
$837$	53.8659	+	2.45535i	1.86188	+	0.0848695i
$838$	22.7999	−	13.1635i	0.787608	−	0.454726i
$839$	35.4866			1.22513			0.612567	−	0.790419i	$-0.290137\pi$
$839$	35.4866			1.22513			0.612567	+	0.790419i	$0.290137\pi$
$840$	0.0664413	+	0.0816685i	0.00229244	+	0.00281783i
$841$	4.20271	−	7.27930i	0.144921	−	0.251011i
$842$	15.1479	+	26.2369i	0.522030	+	0.904183i
$843$	41.3022	+	15.7470i	1.42252	+	0.542355i
$844$	0.411170	−	0.712168i	0.0141531	−	0.0245138i
$845$		−	18.7468i		−	0.644910i
$846$	−28.7925	−	5.98357i	−0.989907	−	0.205719i
$847$	0.341971	+	0.592312i	0.0117503	+	0.0203521i
$848$	−0.326973	+	0.566334i	−0.0112283	+	0.0194480i
$849$	23.8843	+	9.10620i	0.819709	+	0.312524i
$850$	1.87132	−	3.24121i	0.0641856	−	0.111173i
$851$	−0.270232	−	1.41969i	−0.00926344	−	0.0486665i
$852$	1.24945	−	0.200801i	0.0428055	−	0.00687934i
$853$		−	4.23010i		−	0.144836i	−0.997374	−	0.0724179i	$-0.976928\pi$
$853$		−	4.23010i		−	0.144836i	0.997374	−	0.0724179i	$-0.0230715\pi$
$854$	0.145862	+	0.252640i	0.00499129	+	0.00864516i
$855$	−0.583409	+	2.80732i	−0.0199522	+	0.0960085i
$856$	11.5112	−	6.64602i	0.393446	−	0.227156i
$857$	25.0874	−	14.4842i	0.856968	−	0.494771i	−0.00602795	−	0.999982i	$-0.501919\pi$
$857$	25.0874	−	14.4842i	0.856968	−	0.494771i	0.862996	+	0.505211i	$0.168585\pi$
$858$	−3.05281	+	0.490622i	−0.104221	+	0.0167496i
$859$	−19.9827	−	11.5370i	−0.681800	−	0.393637i	0.118733	−	0.992926i	$-0.462117\pi$
$859$	−19.9827	−	11.5370i	−0.681800	−	0.393637i	−0.800533	+	0.599289i	$0.795450\pi$
$860$	3.15640	+	5.46705i	0.107633	+	0.186425i
$861$	0.0228526	+	0.0280900i	0.000778815	+	0.000957306i
$862$	−0.0758322	−	0.131345i	−0.00258286	−	0.00447364i
$863$	−17.8847	+	30.9772i	−0.608801	+	1.05447i	0.382637	+	0.923899i	$0.375016\pi$
$863$	−17.8847	+	30.9772i	−0.608801	+	1.05447i	−0.991438	+	0.130576i	$0.958317\pi$
$864$	−2.39047	−	4.61364i	−0.0813255	−	0.156959i
$865$			18.3059i			0.622418i
$866$		−	12.4357i		−	0.422582i
$867$	26.1893	−	4.20892i	0.889434	−	0.142943i
$868$	−0.375417	+	0.216747i	−0.0127425	+	0.00735687i
$869$		−	49.8466i		−	1.69093i
$870$	2.44585	+	15.2188i	0.0829220	+	0.515967i
$871$			2.31778i			0.0785350i
$872$	1.88993	−	3.27345i	0.0640010	−	0.110853i
$873$	−10.1114	−	2.10131i	−0.342218	−	0.0711187i
$874$			0.156057i			0.00527871i
$875$	−0.414951	−	0.239572i	−0.0140279	−	0.00809902i
$876$	2.74523	−	7.20037i	0.0927527	−	0.243278i
$877$	4.50438	−	7.80181i	0.152102	−	0.263448i	−0.779898	−	0.625907i	$-0.784729\pi$
$877$	4.50438	−	7.80181i	0.152102	−	0.263448i	0.932000	+	0.362458i	$0.118062\pi$
$878$	−7.26859	+	12.5896i	−0.245303	+	0.424877i
$879$	−12.9403	+	33.9407i	−0.436466	+	1.14479i
$880$	6.59296	−	3.80644i	0.222248	−	0.128315i
$881$	−12.0005	−	20.7855i	−0.404308	−	0.700282i	0.589933	−	0.807453i	$-0.299154\pi$
$881$	−12.0005	−	20.7855i	−0.404308	−	0.700282i	−0.994241	+	0.107170i	$0.965821\pi$
$882$	−20.5556	−	4.27180i	−0.692142	−	0.143839i
$883$	−5.04030	+	2.91002i	−0.169619	+	0.0979299i	−0.582406	−	0.812898i	$-0.697889\pi$
$883$	−5.04030	+	2.91002i	−0.169619	+	0.0979299i	0.412787	+	0.910828i	$0.364555\pi$
$884$	0.221495	−	0.383641i	0.00744970	−	0.0129033i
$885$	−6.49517	+	1.04385i	−0.218333	+	0.0350886i
$886$	6.95455	−	4.01521i	0.233643	−	0.134894i
$887$	8.10162	−	14.0324i	0.272026	−	0.471162i	−0.697355	−	0.716726i	$-0.745640\pi$
$887$	8.10162	−	14.0324i	0.272026	−	0.471162i	0.969380	+	0.245564i	$0.0789731\pi$
$888$	−3.58735	−	9.90611i	−0.120384	−	0.332427i
$889$	−0.241303	−	0.417950i	−0.00809305	−	0.0140176i
$890$	7.60644	+	4.39158i	0.254968	+	0.147206i
$891$	−37.8414	+	28.0217i	−1.26773	+	0.938763i
$892$	−10.5539	−	18.2799i	−0.353372	−	0.612057i
$893$	5.57612	+	3.21937i	0.186598	+	0.107732i
$894$	−12.4221	+	10.1060i	−0.415457	+	0.337995i
$895$	0.542788			0.0181434
$896$	0.0361769	+	0.0208867i	0.00120858	+	0.000697776i
$897$	0.0886108	+	0.108919i	0.00295863	+	0.00363669i
$898$	9.27715	+	16.0685i	0.309582	+	0.536212i
$899$	−63.4673			−2.11675
$900$	6.45300	+	5.75748i	0.215100	+	0.191916i
$901$	−0.735275	+	0.424511i	−0.0244956	+	0.0141425i
$902$	2.26766	−	1.30923i	0.0755049	−	0.0435927i
$903$	0.293306	+	0.111827i	0.00976062	+	0.00372136i
$904$	−1.42450	−	2.46731i	−0.0473782	−	0.0820614i
$905$	−9.57293	+	5.52693i	−0.318215	+	0.183721i
$906$	22.9065	−	18.6356i	0.761017	−	0.619125i
$907$	−8.51658	−	4.91705i	−0.282788	−	0.163268i	0.351897	−	0.936039i	$-0.385537\pi$
$907$	−8.51658	−	4.91705i	−0.282788	−	0.163268i	−0.634685	+	0.772771i	$0.718870\pi$
$908$	−12.1202	−	6.99762i	−0.402224	−	0.232224i
$909$	−11.9845	+	57.6687i	−0.397502	+	1.91275i
$910$	−0.0179614	−	0.0103700i	−0.000595414	−	0.000343762i
$911$	9.52725	−	5.50056i	0.315652	−	0.182242i	−0.333801	−	0.942644i	$-0.608331\pi$
$911$	9.52725	−	5.50056i	0.315652	−	0.182242i	0.649453	+	0.760402i	$0.274998\pi$
$912$	0.180523	+	1.12327i	0.00597772	+	0.0371953i
$913$	−14.9465	−	25.8881i	−0.494658	−	0.856773i
$914$	6.63678	−	11.4952i	0.219525	−	0.380229i
$915$	−11.1073	−	13.6529i	−0.367197	−	0.451352i
$916$	25.0499			0.827671
$917$		−	0.186974i		−	0.00617443i
$918$	0.307191	−	6.73920i	0.0101388	−	0.222427i
$919$			57.2033i			1.88696i	0.331427	+	0.943481i	$0.392470\pi$
$919$			57.2033i			1.88696i	−0.331427	+	0.943481i	$0.607530\pi$
$920$	−0.299395	−	0.172855i	−0.00987074	−	0.00569888i
$921$	−18.9021	+	49.5777i	−0.622845	+	1.63364i
$922$	−22.6122			−0.744693
$923$	−0.215896	+	0.124647i	−0.00710629	+	0.00410282i
$924$	0.134857	−	0.353711i	0.00443645	−	0.0116362i
$925$	11.4523	+	13.2783i	0.376549	+	0.436589i
$926$	−13.7267			−0.451086
$927$	10.6106	+	32.1586i	0.348498	+	1.05623i
$928$	3.05800	+	5.29661i	0.100384	+	0.173870i
$929$	15.8149	−	27.3921i	0.518869	−	0.898707i	−0.480891	−	0.876780i	$-0.659687\pi$
$929$	15.8149	−	27.3921i	0.518869	−	0.898707i	0.999760	−	0.0219266i	$-0.00698000\pi$
$930$	20.2879	−	16.5052i	0.665267	−	0.541227i
$931$	3.98091	+	2.29838i	0.130469	+	0.0753263i
$932$	7.60849			0.249224
$933$	8.22398	+	51.1722i	0.269241	+	1.67530i
$934$	−14.5445			−0.475910
$935$	9.88386			0.323237
$936$	0.763799	+	0.681476i	0.0249656	+	0.0222747i
$937$	−16.6700	+	28.8732i	−0.544584	+	0.943247i	0.454049	+	0.890977i	$0.349979\pi$
$937$	−16.6700	+	28.8732i	−0.544584	+	0.943247i	−0.998633	+	0.0522702i	$0.983354\pi$
$938$	−0.245745	−	0.141881i	−0.00802387	−	0.00463258i
$939$	30.6838	+	11.6986i	1.00133	+	0.381768i
$940$	−12.3527	+	7.13182i	−0.402900	+	0.232614i
$941$	4.00575	+	6.93816i	0.130584	+	0.226177i	0.923902	−	0.382630i	$-0.124982\pi$
$941$	4.00575	+	6.93816i	0.130584	+	0.226177i	−0.793318	+	0.608807i	$0.791648\pi$
$942$	3.46607	+	21.5670i	0.112931	+	0.702691i
$943$	−0.102977	−	0.0594540i	−0.00335340	−	0.00193609i
$944$	−2.26051	+	1.30511i	−0.0735734	+	0.0424776i
$945$	−0.315517	−	0.0143821i	−0.0102638	−	0.000467850i
$946$	11.3491	−	19.6572i	0.368990	−	0.639110i
$947$			4.33549i			0.140885i	0.997516	+	0.0704423i	$0.0224411\pi$
$947$			4.33549i			0.140885i	−0.997516	+	0.0704423i	$0.977559\pi$
$948$	−12.8009	+	10.4142i	−0.415754	+	0.338236i
$949$			1.51804i			0.0492776i
$950$	−0.946741	−	1.63980i	−0.0307163	−	0.0532023i
$951$	−5.07127	+	13.3013i	−0.164447	+	0.431323i
$952$	0.0271174	+	0.0469686i	0.000878879	+	0.00152226i
$953$	26.3994	−	45.7252i	0.855162	−	1.48118i	−0.0213329	−	0.999772i	$-0.506791\pi$
$953$	26.3994	−	45.7252i	0.855162	−	1.48118i	0.876495	−	0.481411i	$-0.159876\pi$
$954$	−0.614705	−	1.86305i	−0.0199018	−	0.0603184i
$955$	5.60852	+	9.71423i	0.181487	+	0.314345i
$956$	11.7346	−	6.77496i	0.379523	−	0.219118i
$957$	42.9921	−	34.9762i	1.38974	−	1.13062i
$958$	−7.43800			−0.240311
$959$	0.321418			0.0103791
$960$	−2.35494	−	0.897851i	−0.0760055	−	0.0289780i
$961$	38.3438	+	66.4135i	1.23690	+	2.14237i
$962$	1.35553	+	1.57167i	0.0437041	+	0.0506727i
$963$	−8.11358	+	39.0420i	−0.261457	+	1.25811i
$964$	16.9545	+	9.78870i	0.546068	+	0.315273i
$965$	16.0319	−	27.7680i	0.516084	−	0.893884i
$966$	−0.0169725	+	0.00272768i	−0.000546081	+	8.77617e-5i
$967$		−	9.68277i		−	0.311377i	−0.987806	−	0.155688i	$-0.950240\pi$
$967$		−	9.68277i		−	0.311377i	0.987806	−	0.155688i	$-0.0497596\pi$
$968$	−14.1791	−	8.18633i	−0.455735	−	0.263119i
$969$	−0.526202	+	1.38016i	−0.0169040	+	0.0443370i
$970$	−4.33802	+	2.50456i	−0.139285	+	0.0804165i
$971$	1.59103	−	2.75574i	0.0510586	−	0.0884360i	−0.839367	−	0.543566i	$-0.817074\pi$
$971$	1.59103	−	2.75574i	0.0510586	−	0.0884360i	0.890425	+	0.455130i	$0.150407\pi$
$972$	15.1021	+	3.86347i	0.484400	+	0.123921i
$973$	0.691159			0.0221575
$974$	−15.4519			−0.495111
$975$	−1.59187	−	0.606919i	−0.0509806	−	0.0194370i
$976$	−6.04786	−	3.49174i	−0.193587	−	0.111768i
$977$	−50.3669	+	29.0793i	−1.61138	+	0.930330i	−0.622328	+	0.782757i	$0.713813\pi$
$977$	−50.3669	+	29.0793i	−1.61138	+	0.930330i	−0.989051	+	0.147573i	$0.952854\pi$
$978$	−6.72238	−	8.26303i	−0.214958	−	0.264223i
$979$		−	31.5804i		−	1.00932i
$980$	−8.81884	+	5.09156i	−0.281707	+	0.162644i
$981$	3.55304	+	10.7686i	0.113440	+	0.343814i
$982$	19.0836	+	11.0179i	0.608981	+	0.351595i
$983$	20.2438			0.645676			0.322838	−	0.946454i	$-0.395363\pi$
$983$	20.2438			0.645676			0.322838	+	0.946454i	$0.395363\pi$
$984$	−0.809988	−	0.308818i	−0.0258215	−	0.00984475i
$985$	20.9415	+	12.0906i	0.667253	+	0.385239i
$986$			7.94044i			0.252875i
$987$	−0.252670	+	0.662719i	−0.00804256	+	0.0210946i
$988$	−0.112060	−	0.194093i	−0.00356509	−	0.00617492i
$989$	−1.03075			−0.0327760
$990$	−4.64697	+	22.3609i	−0.147691	+	0.710676i
$991$			32.6050i			1.03573i	0.855462	+	0.517865i	$0.173273\pi$
$991$			32.6050i			1.03573i	−0.855462	+	0.517865i	$0.826727\pi$
$992$	5.18863	−	8.98698i	0.164739	−	0.285337i
$993$	−33.6204	−	12.8182i	−1.06691	−	0.406773i
$994$		−	0.0305208i		−	0.000968061i
$995$	−29.2247			−0.926486
$996$	−3.52554	+	9.24701i	−0.111711	+	0.293003i
$997$			33.1494i			1.04985i	0.851148	+	0.524926i	$0.175907\pi$
$997$			33.1494i			1.04985i	−0.851148	+	0.524926i	$0.824093\pi$
$998$	21.4031			0.677503
$999$	29.3399	+	11.7546i	0.928273	+	0.371900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.7	✓	76
3.2	odd	2		1998.2.k.a.1063.25		76
9.2	odd	6		1998.2.t.a.397.27		76
9.7	even	3		666.2.t.a.619.19	yes	76
37.11	even	6		666.2.t.a.85.19	yes	76
111.11	odd	6		1998.2.t.a.307.27		76
333.11	odd	6		1998.2.k.a.1639.14		76
333.196	even	6	inner	666.2.k.a.529.26	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.7	✓	76	1.1	even	1	trivial
666.2.k.a.529.26	yes	76	333.196	even	6	inner
666.2.t.a.85.19	yes	76	37.11	even	6
666.2.t.a.619.19	yes	76	9.7	even	3
1998.2.k.a.1063.25		76	3.2	odd	2
1998.2.k.a.1639.14		76	333.11	odd	6
1998.2.t.a.307.27		76	111.11	odd	6
1998.2.t.a.397.27		76	9.2	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.617040 + 1.61841i) q^{3} -1.00000 q^{4} -1.45509i q^{5} +(1.61841 + 0.617040i) q^{6} +(0.0208867 - 0.0361769i) q^{7} +1.00000i q^{8} +(-2.23852 - 1.99725i) q^{9} -1.45509 q^{10} +(2.61594 + 4.53095i) q^{11} +(0.617040 - 1.61841i) q^{12} +0.341207i q^{13} +(-0.0361769 - 0.0208867i) q^{14} +(2.35494 + 0.897851i) q^{15} +1.00000 q^{16} +(1.12437 + 0.649153i) q^{17} +(-1.99725 + 2.23852i) q^{18} +(0.568843 - 0.328422i) q^{19} +1.45509i q^{20} +(0.0456612 + 0.0561259i) q^{21} +(4.53095 - 2.61594i) q^{22} +(-0.205756 - 0.118793i) q^{23} +(-1.61841 - 0.617040i) q^{24} +2.88270 q^{25} +0.341207 q^{26} +(4.61364 - 2.39047i) q^{27} +(-0.0208867 + 0.0361769i) q^{28} +(-5.29661 + 3.05800i) q^{29} +(0.897851 - 2.35494i) q^{30} +(8.98698 + 5.18863i) q^{31} -1.00000i q^{32} +(-8.94709 + 1.43790i) q^{33} +(0.649153 - 1.12437i) q^{34} +(-0.0526407 - 0.0303921i) q^{35} +(2.23852 + 1.99725i) q^{36} +(3.97276 + 4.60621i) q^{37} +(-0.328422 - 0.568843i) q^{38} +(-0.552214 - 0.210538i) q^{39} +1.45509 q^{40} +0.500483 q^{41} +(0.0561259 - 0.0456612i) q^{42} +(3.75718 - 2.16921i) q^{43} +(-2.61594 - 4.53095i) q^{44} +(-2.90619 + 3.25726i) q^{45} +(-0.118793 + 0.205756i) q^{46} +(4.90128 + 8.48927i) q^{47} +(-0.617040 + 1.61841i) q^{48} +(3.49913 + 6.06067i) q^{49} -2.88270i q^{50} +(-1.74438 + 1.41914i) q^{51} -0.341207i q^{52} +(-0.326973 + 0.566334i) q^{53} +(-2.39047 - 4.61364i) q^{54} +(6.59296 - 3.80644i) q^{55} +(0.0361769 + 0.0208867i) q^{56} +(0.180523 + 1.12327i) q^{57} +(3.05800 + 5.29661i) q^{58} +(-2.26051 + 1.30511i) q^{59} +(-2.35494 - 0.897851i) q^{60} +(-6.04786 - 3.49174i) q^{61} +(5.18863 - 8.98698i) q^{62} +(-0.119010 + 0.0392667i) q^{63} -1.00000 q^{64} +0.496488 q^{65} +(1.43790 + 8.94709i) q^{66} +6.79289 q^{67} +(-1.12437 - 0.649153i) q^{68} +(0.319217 - 0.259698i) q^{69} +(-0.0303921 + 0.0526407i) q^{70} +(0.365314 + 0.632742i) q^{71} +(1.99725 - 2.23852i) q^{72} +4.44903 q^{73} +(4.60621 - 3.97276i) q^{74} +(-1.77874 + 4.66540i) q^{75} +(-0.568843 + 0.328422i) q^{76} +0.218554 q^{77} +(-0.210538 + 0.552214i) q^{78} +(-8.25102 - 4.76373i) q^{79} -1.45509i q^{80} +(1.02197 + 8.94179i) q^{81} -0.500483i q^{82} -5.71363 q^{83} +(-0.0456612 - 0.0561259i) q^{84} +(0.944579 - 1.63606i) q^{85} +(-2.16921 - 3.75718i) q^{86} +(-1.68089 - 10.4590i) q^{87} +(-4.53095 + 2.61594i) q^{88} +(-5.22746 - 3.01807i) q^{89} +(3.25726 + 2.90619i) q^{90} +(0.0123438 + 0.00712669i) q^{91} +(0.205756 + 0.118793i) q^{92} +(-13.9427 + 11.3430i) q^{93} +(8.48927 - 4.90128i) q^{94} +(-0.477884 - 0.827720i) q^{95} +(1.61841 + 0.617040i) q^{96} +(2.98127 - 1.72123i) q^{97} +(6.06067 - 3.49913i) q^{98} +(3.19359 - 15.3673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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