LMFDB - Embedded newform 252.2.bi.c.139.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.10
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13617 - 0.842090i) q^{2} +(1.59413 + 0.677299i) q^{3} +(0.581768 + 1.91352i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-1.24086 - 2.11193i) q^{6} +(-0.0302588 + 2.64558i) q^{7} +(0.950366 - 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +O(q^{10})$	\(q+(-1.13617 - 0.842090i) q^{2} +(1.59413 + 0.677299i) q^{3} +(0.581768 + 1.91352i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-1.24086 - 2.11193i) q^{6} +(-0.0302588 + 2.64558i) q^{7} +(0.950366 - 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +(0.931077 + 2.14589i) q^{10} +(4.24842 - 2.45282i) q^{11} +(-0.368607 + 3.44443i) q^{12} +(0.876334 + 0.505952i) q^{13} +(2.26220 - 2.98035i) q^{14} +(-1.72337 - 2.28859i) q^{15} +(-3.32309 + 2.22644i) q^{16} +7.66107i q^{17} +(-0.547691 - 4.20714i) q^{18} +2.85119 q^{19} +(0.749173 - 3.22215i) q^{20} +(-1.84008 + 4.19691i) q^{21} +(-6.89242 - 0.790723i) q^{22} +(1.98118 + 1.14384i) q^{23} +(3.31933 - 3.60307i) q^{24} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 - 1.31280i) q^{26} +(1.85727 + 4.85289i) q^{27} +(-5.07996 + 1.48121i) q^{28} +(-4.19857 - 7.27213i) q^{29} +(0.0308507 + 4.05146i) q^{30} +(-0.348784 + 0.604112i) q^{31} +(5.65047 + 0.268722i) q^{32} +(8.43384 - 1.03268i) q^{33} +(6.45131 - 8.70428i) q^{34} +(2.23130 - 3.76463i) q^{35} +(-2.92052 + 5.24124i) q^{36} +3.97490 q^{37} +(-3.23944 - 2.40096i) q^{38} +(1.05431 + 1.40010i) q^{39} +(-3.56453 + 3.03004i) q^{40} +(-6.69947 - 3.86794i) q^{41} +(5.62483 - 3.21889i) q^{42} +(6.70811 - 3.87293i) q^{43} +(7.16511 + 6.70244i) q^{44} +(-1.19723 - 4.81555i) q^{45} +(-1.28775 - 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(-6.80543 + 1.29853i) q^{48} +(-6.99817 - 0.160104i) q^{49} +(-0.364945 + 3.18108i) q^{50} +(-5.18884 + 12.2128i) q^{51} +(-0.458324 + 1.97123i) q^{52} -8.61878 q^{53} +(1.97640 - 7.07770i) q^{54} -8.11418 q^{55} +(7.01902 + 2.59488i) q^{56} +(4.54518 + 1.93111i) q^{57} +(-1.35350 + 11.7980i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(3.37664 - 4.62913i) q^{60} +(-5.12759 + 2.96042i) q^{61} +(0.904996 - 0.392667i) q^{62} +(-5.77591 + 5.44416i) q^{63} +(-6.19361 - 5.06352i) q^{64} +(-0.836869 - 1.44950i) q^{65} +(-10.4519 - 5.92875i) q^{66} +(-2.18590 - 1.26203i) q^{67} +(-14.6596 + 4.45696i) q^{68} +(2.38355 + 3.16528i) q^{69} +(-5.70530 + 2.39830i) q^{70} -1.00362i q^{71} +(7.73181 - 3.49559i) q^{72} -5.89658i q^{73} +(-4.51617 - 3.34723i) q^{74} +(-0.476618 - 3.89250i) q^{75} +(1.65873 + 5.45580i) q^{76} +(6.36058 + 11.3137i) q^{77} +(-0.0188736 - 2.47857i) q^{78} +(-4.90752 + 2.83336i) q^{79} +(6.60149 - 0.440989i) q^{80} +(-0.326126 + 8.99409i) q^{81} +(4.35458 + 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(-9.10137 - 1.07940i) q^{84} +(6.33589 - 10.9741i) q^{85} +(-10.8829 - 1.24853i) q^{86} +(-1.76767 - 14.4364i) q^{87} +(-2.49673 - 13.6488i) q^{88} -8.19734i q^{89} +(-2.69487 + 6.47947i) q^{90} +(-1.36505 + 2.30310i) q^{91} +(-1.03616 + 4.45647i) q^{92} +(-0.965174 + 0.726805i) q^{93} +(-1.19511 + 10.4173i) q^{94} +(-4.08418 - 2.35800i) q^{95} +(8.82560 + 4.25544i) q^{96} +(8.82136 - 5.09301i) q^{97} +(7.81629 + 6.07500i) q^{98} +(14.1441 + 4.06600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.13617	−	0.842090i	−0.803394	−	0.595448i
$2$	−1.13617	−	0.842090i	−0.803394	−	0.595448i
$3$	1.59413	+	0.677299i	0.920374	+	0.391039i
$3$	1.59413	+	0.677299i	0.920374	+	0.391039i
$4$	0.581768	+	1.91352i	0.290884	+	0.956758i
$5$	−1.43245	−	0.827025i	−0.640611	−	0.369857i	0.144239	−	0.989543i	$-0.453927\pi$
$5$	−1.43245	−	0.827025i	−0.640611	−	0.369857i	−0.784850	+	0.619686i	$0.787260\pi$
$6$	−1.24086	−	2.11193i	−0.506580	−	0.862193i
$7$	−0.0302588	+	2.64558i	−0.0114368	+	0.999935i
$7$	−0.0302588	+	2.64558i	−0.0114368	+	0.999935i
$8$	0.950366	−	2.66398i	0.336005	−	0.941860i
$9$	2.08253	+	2.15941i	0.694177	+	0.719804i
$10$	0.931077	+	2.14589i	0.294432	+	0.678591i
$11$	4.24842	−	2.45282i	1.28095	−	0.739554i	0.303924	−	0.952696i	$-0.401703\pi$
$11$	4.24842	−	2.45282i	1.28095	−	0.739554i	0.977021	+	0.213142i	$0.0683697\pi$
$12$	−0.368607	+	3.44443i	−0.106408	+	0.994323i
$13$	0.876334	+	0.505952i	0.243051	+	0.140326i	0.616578	−	0.787294i	$-0.288518\pi$
$13$	0.876334	+	0.505952i	0.243051	+	0.140326i	−0.373527	+	0.927619i	$0.621852\pi$
$14$	2.26220	−	2.98035i	0.604597	−	0.796531i
$15$	−1.72337	−	2.28859i	−0.444973	−	0.590910i
$16$	−3.32309	+	2.22644i	−0.830773	+	0.556611i
$17$			7.66107i			1.85808i	0.369976	+	0.929041i	$0.379366\pi$
$17$			7.66107i			1.85808i	−0.369976	+	0.929041i	$0.620634\pi$
$18$	−0.547691	−	4.20714i	−0.129092	−	0.991633i
$19$	2.85119			0.654108			0.327054	−	0.945006i	$-0.393944\pi$
$19$	2.85119			0.654108			0.327054	+	0.945006i	$0.393944\pi$
$20$	0.749173	−	3.22215i	0.167520	−	0.720495i
$21$	−1.84008	+	4.19691i	−0.401539	+	0.915842i
$22$	−6.89242	−	0.790723i	−1.46947	−	0.168583i
$23$	1.98118	+	1.14384i	0.413105	+	0.238506i	0.692123	−	0.721780i	$-0.256676\pi$
$23$	1.98118	+	1.14384i	0.413105	+	0.238506i	−0.279018	+	0.960286i	$0.590009\pi$
$24$	3.31933	−	3.60307i	0.677554	−	0.735473i
$25$	−1.13206	−	1.96079i	−0.226412	−	0.392157i
$26$	−0.569608	−	1.31280i	−0.111709	−	0.257461i
$27$	1.85727	+	4.85289i	0.357431	+	0.933939i
$28$	−5.07996	+	1.48121i	−0.960023	+	0.279923i
$29$	−4.19857	−	7.27213i	−0.779654	−	1.35040i	−0.932141	−	0.362096i	$-0.882061\pi$
$29$	−4.19857	−	7.27213i	−0.779654	−	1.35040i	0.152486	−	0.988306i	$-0.451272\pi$
$30$	0.0308507	+	4.05146i	0.00563254	+	0.739692i
$31$	−0.348784	+	0.604112i	−0.0626435	+	0.108502i	−0.895646	−	0.444767i	$-0.853286\pi$
$31$	−0.348784	+	0.604112i	−0.0626435	+	0.108502i	0.833003	+	0.553269i	$0.186620\pi$
$32$	5.65047	+	0.268722i	0.998871	+	0.0475038i
$33$	8.43384	−	1.03268i	1.46814	−	0.179767i
$34$	6.45131	−	8.70428i	1.10639	−	1.49277i
$35$	2.23130	−	3.76463i	0.377159	−	0.636339i
$36$	−2.92052	+	5.24124i	−0.486754	+	0.873539i
$37$	3.97490			0.653470			0.326735	−	0.945116i	$-0.394051\pi$
$37$	3.97490			0.653470			0.326735	+	0.945116i	$0.394051\pi$
$38$	−3.23944	−	2.40096i	−0.525506	−	0.389487i
$39$	1.05431	+	1.40010i	0.168825	+	0.224195i
$40$	−3.56453	+	3.03004i	−0.563602	+	0.479092i
$41$	−6.69947	−	3.86794i	−1.04628	−	0.604071i	−0.124675	−	0.992198i	$-0.539789\pi$
$41$	−6.69947	−	3.86794i	−1.04628	−	0.604071i	−0.921606	+	0.388127i	$0.873122\pi$
$42$	5.62483	−	3.21889i	0.867930	−	0.496686i
$43$	6.70811	−	3.87293i	1.02298	−	0.590617i	0.108013	−	0.994150i	$-0.465551\pi$
$43$	6.70811	−	3.87293i	1.02298	−	0.590617i	0.914965	+	0.403533i	$0.132218\pi$
$44$	7.16511	+	6.70244i	1.08018	+	1.01043i
$45$	−1.19723	−	4.81555i	−0.178473	−	0.717860i
$46$	−1.28775	−	2.96793i	−0.189868	−	0.437597i
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	−0.998861	−	0.0477158i	$-0.984806\pi$
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	0.458107	−	0.888897i	$-0.348528\pi$
$48$	−6.80543	+	1.29853i	−0.982279	+	0.187426i
$49$	−6.99817	−	0.160104i	−0.999738	−	0.0228720i
$50$	−0.364945	+	3.18108i	−0.0516110	+	0.449873i
$51$	−5.18884	+	12.2128i	−0.726582	+	1.71013i
$52$	−0.458324	+	1.97123i	−0.0635581	+	0.273360i
$53$	−8.61878			−1.18388			−0.591940	−	0.805982i	$-0.701638\pi$
$53$	−8.61878			−1.18388			−0.591940	+	0.805982i	$0.701638\pi$
$54$	1.97640	−	7.07770i	0.268954	−	0.963153i
$55$	−8.11418			−1.09412
$56$	7.01902	+	2.59488i	0.937956	+	0.346755i
$57$	4.54518	+	1.93111i	0.602024	+	0.255782i
$58$	−1.35350	+	11.7980i	−0.177724	+	1.54915i
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	−0.982742	−	0.184981i	$-0.940778\pi$
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	0.651570	+	0.758589i	$0.274111\pi$
$60$	3.37664	−	4.62913i	0.435923	−	0.597618i
$61$	−5.12759	+	2.96042i	−0.656521	+	0.379042i	−0.790950	−	0.611881i	$-0.790413\pi$
$61$	−5.12759	+	2.96042i	−0.656521	+	0.379042i	0.134429	+	0.990923i	$0.457080\pi$
$62$	0.904996	−	0.392667i	0.114935	−	0.0498687i
$63$	−5.77591	+	5.44416i	−0.727696	+	0.685900i
$64$	−6.19361	−	5.06352i	−0.774201	−	0.632940i
$65$	−0.836869	−	1.44950i	−0.103801	−	0.179788i
$66$	−10.4519	−	5.92875i	−1.28654	−	0.729779i
$67$	−2.18590	−	1.26203i	−0.267051	−	0.154182i	0.360496	−	0.932761i	$-0.382607\pi$
$67$	−2.18590	−	1.26203i	−0.267051	−	0.154182i	−0.627547	+	0.778579i	$0.715941\pi$
$68$	−14.6596	+	4.45696i	−1.77774	+	0.540486i
$69$	2.38355	+	3.16528i	0.286946	+	0.381055i
$70$	−5.70530	+	2.39830i	−0.681914	+	0.286652i
$71$		−	1.00362i		−	0.119108i	−0.998225	−	0.0595539i	$-0.981032\pi$
$71$		−	1.00362i		−	0.119108i	0.998225	−	0.0595539i	$-0.0189678\pi$
$72$	7.73181	−	3.49559i	0.911202	−	0.411960i
$73$		−	5.89658i		−	0.690142i	−0.938577	−	0.345071i	$-0.887855\pi$
$73$		−	5.89658i		−	0.690142i	0.938577	−	0.345071i	$-0.112145\pi$
$74$	−4.51617	−	3.34723i	−0.524994	−	0.389107i
$75$	−0.476618	−	3.89250i	−0.0550351	−	0.449467i
$76$	1.65873	+	5.45580i	0.190269	+	0.625823i
$77$	6.36058	+	11.3137i	0.724856	+	1.28932i
$78$	−0.0188736	−	2.47857i	−0.00213702	−	0.280643i
$79$	−4.90752	+	2.83336i	−0.552139	+	0.318778i	−0.749984	−	0.661456i	$-0.769939\pi$
$79$	−4.90752	+	2.83336i	−0.552139	+	0.318778i	0.197845	+	0.980233i	$0.436606\pi$
$80$	6.60149	−	0.440989i	0.738069	−	0.0493041i
$81$	−0.326126	+	8.99409i	−0.0362362	+	0.999343i
$82$	4.35458	+	10.0362i	0.480883	+	1.10831i
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	0.924649	−	0.380820i	$-0.124358\pi$
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	−0.792125	+	0.610359i	$0.791025\pi$
$84$	−9.10137	−	1.07940i	−0.993041	−	0.117773i
$85$	6.33589	−	10.9741i	0.687224	−	1.19031i
$86$	−10.8829	−	1.24853i	−1.17354	−	0.134632i
$87$	−1.76767	−	14.4364i	−0.189514	−	1.54775i
$88$	−2.49673	−	13.6488i	−0.266152	−	1.45497i
$89$		−	8.19734i		−	0.868916i	−0.900692	−	0.434458i	$-0.856940\pi$
$89$		−	8.19734i		−	0.868916i	0.900692	−	0.434458i	$-0.143060\pi$
$90$	−2.69487	+	6.47947i	−0.284064	+	0.682996i
$91$	−1.36505	+	2.30310i	−0.143096	+	0.241431i
$92$	−1.03616	+	4.45647i	−0.108027	+	0.464619i
$93$	−0.965174	+	0.726805i	−0.100084	+	0.0753662i
$94$	−1.19511	+	10.4173i	−0.123266	+	1.07446i
$95$	−4.08418	−	2.35800i	−0.419028	−	0.241926i
$96$	8.82560	+	4.25544i	0.900759	+	0.434319i
$97$	8.82136	−	5.09301i	0.895673	−	0.517117i	0.0198794	−	0.999802i	$-0.493672\pi$
$97$	8.82136	−	5.09301i	0.895673	−	0.517117i	0.875794	+	0.482685i	$0.160338\pi$
$98$	7.81629	+	6.07500i	0.789565	+	0.613667i
$99$	14.1441	+	4.06600i	1.42154	+	0.408648i
$100$	3.09340	−	3.30694i	0.309340	−	0.330694i
$101$	−0.846450	+	0.488698i	−0.0842249	+	0.0486273i	−0.541521	−	0.840687i	$-0.682151\pi$
$101$	−0.846450	+	0.488698i	−0.0842249	+	0.0486273i	0.457296	+	0.889315i	$0.348818\pi$
$102$	16.1797	−	9.50633i	1.60203	−	0.941267i
$103$	6.53514	−	11.3192i	0.643926	−	1.11531i	−0.340622	−	0.940200i	$-0.610638\pi$
$103$	6.53514	−	11.3192i	0.643926	−	1.11531i	0.984548	−	0.175113i	$-0.0560290\pi$
$104$	2.18068	−	1.85370i	0.213834	−	0.181770i
$105$	6.10678	−	4.49007i	0.595961	−	0.438186i
$106$	9.79241	+	7.25779i	0.951122	+	0.704939i
$107$		−	1.03143i		−	0.0997116i	−0.998756	−	0.0498558i	$-0.984124\pi$
$107$		−	1.03143i		−	0.0997116i	0.998756	−	0.0498558i	$-0.0158762\pi$
$108$	−8.20559	+	6.37717i	−0.789583	+	0.613643i
$109$	−0.842410			−0.0806882			−0.0403441	−	0.999186i	$-0.512845\pi$
$109$	−0.842410			−0.0806882			−0.0403441	+	0.999186i	$0.512845\pi$
$110$	9.21910	+	6.83288i	0.879007	+	0.651489i
$111$	6.33653	+	2.69220i	0.601437	+	0.255532i
$112$	−5.78968	−	8.85887i	−0.547073	−	0.837085i
$113$	3.19162	−	5.52804i	0.300242	−	0.520035i	−0.675949	−	0.736949i	$-0.736266\pi$
$113$	3.19162	−	5.52804i	0.300242	−	0.520035i	0.976191	+	0.216914i	$0.0695992\pi$
$114$	−3.53793	−	6.02152i	−0.331358	−	0.563967i
$115$	−1.89196	−	3.27697i	−0.176426	−	0.305579i
$116$	11.4728	−	12.2647i	1.06522	−	1.13875i
$117$	0.732435	+	2.94603i	0.0677136	+	0.272360i
$118$	6.60039	−	2.86383i	0.607615	−	0.263637i
$119$	−20.2680	−	0.231815i	−1.85796	−	0.0212505i
$120$	−7.73459	+	2.41604i	−0.706068	+	0.220553i
$121$	6.53269	−	11.3149i	0.593881	−	1.02863i
$122$	8.31875	+	0.954356i	0.753145	+	0.0864034i
$123$	−8.06010	−	10.7036i	−0.726755	−	0.965108i
$124$	−1.35889	−	0.315952i	−0.122032	−	0.0283733i
$125$			12.0152i			1.07467i
$126$	11.1469	−	1.32166i	0.993044	−	0.117742i
$127$			17.9070i			1.58899i	0.607272	+	0.794494i	$0.292264\pi$
$127$			17.9070i			1.58899i	−0.607272	+	0.794494i	$0.707736\pi$
$128$	2.77306	+	10.9686i	0.245106	+	0.969496i
$129$	13.3168	−	1.63057i	1.17248	−	0.143564i
$130$	−0.269784	+	2.35160i	−0.0236616	+	0.206249i
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	−0.997605	−	0.0691675i	$-0.977966\pi$
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	0.558703	+	0.829368i	$0.311299\pi$
$132$	6.88259	+	15.5375i	0.599053	+	1.35237i
$133$	−0.0862737	+	7.54305i	−0.00748088	+	0.654065i
$134$	1.42081	+	3.27461i	0.122740	+	0.282883i
$135$	1.35302	−	8.48753i	0.116450	−	0.730490i
$136$	20.4090	+	7.28082i	1.75005	+	0.624325i
$137$	1.97707	+	3.42439i	0.168913	+	0.292566i	0.938038	−	0.346533i	$-0.112641\pi$
$137$	1.97707	+	3.42439i	0.168913	+	0.292566i	−0.769125	+	0.639098i	$0.779308\pi$
$138$	−0.0426688	−	5.60347i	−0.00363221	−	0.476999i
$139$	4.85060	−	8.40148i	0.411422	−	0.712605i	−0.583623	−	0.812025i	$-0.698365\pi$
$139$	4.85060	−	8.40148i	0.411422	−	0.712605i	0.995046	+	0.0994201i	$0.0316988\pi$
$140$	8.50178	+	2.07949i	0.718532	+	0.175749i
$141$	−1.56081	−	12.7470i	−0.131444	−	1.07349i
$142$	−0.845139	+	1.14028i	−0.0709225	+	0.0956905i
$143$	4.96404			0.415114
$144$	−11.7283	−	2.53929i	−0.977355	−	0.211607i
$145$			13.8893i			1.15344i
$146$	−4.96545	+	6.69952i	−0.410944	+	0.554456i
$147$	−11.0476	−	4.99508i	−0.911190	−	0.411987i
$148$	2.31247	+	7.60605i	0.190084	+	0.625213i
$149$	−3.46856	+	6.00773i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$149$	−3.46856	+	6.00773i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$150$	−2.73632	+	4.82390i	−0.223419	+	0.393870i
$151$	10.8500	−	6.26427i	0.882964	−	0.509779i	0.0113294	−	0.999936i	$-0.496394\pi$
$151$	10.8500	−	6.26427i	0.882964	−	0.509779i	0.871635	+	0.490156i	$0.163060\pi$
$152$	2.70967	−	7.59552i	0.219784	−	0.616078i
$153$	−16.5434	+	15.9544i	−1.33746	+	1.28984i
$154$	2.30048	−	18.2105i	0.185378	−	1.46745i
$155$	0.999232	−	0.576907i	0.0802602	−	0.0463383i
$156$	−2.06574	+	2.83198i	−0.165392	+	0.226740i
$157$	−1.44619	−	0.834956i	−0.115418	−	0.0666367i	0.441180	−	0.897419i	$-0.354560\pi$
$157$	−1.44619	−	0.834956i	−0.115418	−	0.0666367i	−0.556598	+	0.830782i	$0.687894\pi$
$158$	7.96173	+	0.913397i	0.633401	+	0.0726659i
$159$	−13.7395	−	5.83749i	−1.08961	−	0.462943i
$160$	−7.87177	−	5.05801i	−0.622318	−	0.399871i
$161$	−3.08606	+	5.20676i	−0.243215	+	0.410350i
$162$	7.94437	−	9.94419i	0.624169	−	0.781290i
$163$		−	7.06914i		−	0.553698i	−0.960913	−	0.276849i	$-0.910710\pi$
$163$		−	7.06914i		−	0.553698i	0.960913	−	0.276849i	$-0.0892901\pi$
$164$	3.50383	−	15.0698i	0.273603	−	1.17675i
$165$	−12.9351	−	5.49573i	−1.00700	−	0.427842i
$166$	0.389218	−	3.39266i	0.0302092	−	0.263322i
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	−0.842770	−	0.538274i	$-0.819076\pi$
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	0.887544	+	0.460723i	$0.152410\pi$
$168$	9.43175	+	8.89056i	0.727675	+	0.685922i
$169$	−5.98803	−	10.3716i	−0.460617	−	0.797813i
$170$	−16.4398	+	7.13305i	−1.26088	+	0.547080i
$171$	5.93769	+	6.15689i	0.454067	+	0.470830i
$172$	11.3135	+	10.5829i	0.862645	+	0.806942i
$173$	1.30347	−	0.752561i	0.0991013	−	0.0572162i	−0.449630	−	0.893215i	$-0.648444\pi$
$173$	1.30347	−	0.752561i	0.0991013	−	0.0572162i	0.548732	+	0.835999i	$0.315111\pi$
$174$	−10.1484	+	17.8908i	−0.769349	+	1.35630i
$175$	5.22167	−	2.93562i	0.394721	−	0.221912i
$176$	−8.65680	+	17.6098i	−0.652531	+	1.32739i
$177$	−7.03929	+	5.30080i	−0.529105	+	0.398432i
$178$	−6.90290	+	9.31357i	−0.517394	+	0.698082i
$179$		−	1.28088i		−	0.0957374i	−0.998854	−	0.0478687i	$-0.984757\pi$
$179$		−	1.28088i		−	0.0957374i	0.998854	−	0.0478687i	$-0.0152429\pi$
$180$	8.51813	−	5.09246i	0.634904	−	0.379569i
$181$		−	26.6202i		−	1.97866i	−0.145683	−	0.989331i	$-0.546538\pi$
$181$		−	26.6202i		−	1.97866i	0.145683	−	0.989331i	$-0.453462\pi$
$182$	3.49035	−	1.46722i	0.258722	−	0.108757i
$183$	−10.1792	+	1.24639i	−0.752465	+	0.0921357i
$184$	4.93001	−	4.19077i	0.363445	−	0.308948i
$185$	−5.69385	−	3.28734i	−0.418620	−	0.241690i
$186$	1.70864	−	0.0130108i	0.125283	−	0.000953996i
$187$	18.7913	+	32.5474i	1.37415	+	2.38010i
$188$	10.1301	−	10.8294i	0.738815	−	0.789816i
$189$	−12.8949	+	4.76670i	−0.937966	+	0.346727i
$190$	2.65468	+	6.11835i	0.192591	+	0.443872i
$191$	7.44229	−	4.29681i	0.538506	−	0.310906i	−0.205968	−	0.978559i	$-0.566034\pi$
$191$	7.44229	−	4.29681i	0.538506	−	0.310906i	0.744473	+	0.667653i	$0.232701\pi$
$192$	−6.44393	−	12.2669i	−0.465050	−	0.885284i
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	−0.969882	−	0.243573i	$-0.921680\pi$
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	0.695882	+	0.718156i	$0.255014\pi$
$194$	−14.3113	−	1.64185i	−1.02749	−	0.117878i
$195$	−0.352337	−	2.87751i	−0.0252314	−	0.206063i
$196$	−3.76495	−	13.4843i	−0.268925	−	0.963161i
$197$	14.3946			1.02557			0.512786	−	0.858517i	$-0.328614\pi$
$197$	14.3946			1.02557			0.512786	+	0.858517i	$0.328614\pi$
$198$	−12.6462	−	16.5303i	−0.898726	−	1.17476i
$199$	−21.9194			−1.55382			−0.776911	−	0.629610i	$-0.783215\pi$
$199$	−21.9194			−1.55382			−0.776911	+	0.629610i	$0.783215\pi$
$200$	−6.29937	+	1.15232i	−0.445433	+	0.0814816i
$201$	−2.62985	−	3.49236i	−0.185495	−	0.246332i
$202$	1.37324	+	0.157543i	0.0966208	+	0.0110847i
$203$	19.3660	−	10.8876i	1.35923	−	0.764159i
$204$	−26.3881	−	2.82392i	−1.84753	−	0.197714i
$205$	6.39776	+	11.0813i	0.446839	+	0.773948i
$206$	−16.9568	+	7.35736i	−1.18144	+	0.512611i
$207$	1.65586	+	6.66026i	0.115090	+	0.462920i
$208$	−4.03861	+	0.269785i	−0.280027	+	0.0187062i
$209$	12.1130	−	6.99347i	0.837876	−	0.483748i
$210$	−10.7194	−	0.0409746i	−0.739708	−	0.00282752i
$211$	−1.45464	−	0.839838i	−0.100142	−	0.0578168i	0.449093	−	0.893485i	$-0.351747\pi$
$211$	−1.45464	−	0.839838i	−0.100142	−	0.0578168i	−0.549234	+	0.835668i	$0.685081\pi$
$212$	−5.01413	−	16.4922i	−0.344372	−	1.13269i
$213$	0.679751	−	1.59991i	0.0465758	−	0.109624i
$214$	−0.868553	+	1.17188i	−0.0593731	+	0.0801077i
$215$	−12.8120			−0.873774
$216$	14.6931	−	0.335703i	0.999739	−	0.0228417i
$217$	−1.58767	−	0.941016i	−0.107778	−	0.0638803i
$218$	0.957121	+	0.709385i	0.0648244	+	0.0480456i
$219$	3.99375	−	9.39994i	0.269873	−	0.635189i
$220$	−4.72057	−	15.5266i	−0.318261	−	1.04680i
$221$	−3.87613	+	6.71366i	−0.260737	+	0.451609i
$222$	−4.93231	−	8.39473i	−0.331035	−	0.563418i
$223$	−4.09002	−	7.08413i	−0.273888	−	0.474388i	0.695966	−	0.718075i	$-0.254977\pi$
$223$	−4.09002	−	7.08413i	−0.273888	−	0.474388i	−0.969854	+	0.243687i	$0.921643\pi$
$224$	−0.881903	+	14.9406i	−0.0589246	+	0.998262i
$225$	1.87659	−	6.52798i	0.125106	−	0.435199i
$226$	−8.28133	+	3.59317i	−0.550866	+	0.239014i
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.832000	+	0.554776i	$0.187196\pi$
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.0644498	+	0.997921i	$0.479471\pi$
$228$	−1.05097	+	9.82074i	−0.0696021	+	0.650394i
$229$	10.4216	+	6.01689i	0.688677	+	0.397608i	0.803116	−	0.595823i	$-0.203174\pi$
$229$	10.4216	+	6.01689i	0.688677	+	0.397608i	−0.114439	+	0.993430i	$0.536507\pi$
$230$	−0.609916	+	5.31640i	−0.0402167	+	0.350553i
$231$	2.47685	+	22.3436i	0.162964	+	1.47010i
$232$	−23.3630	+	4.27372i	−1.53386	+	0.280584i
$233$	12.9746			0.849992			0.424996	−	0.905195i	$-0.360276\pi$
$233$	12.9746			0.849992			0.424996	+	0.905195i	$0.360276\pi$
$234$	1.64865	−	3.96397i	0.107776	−	0.259133i
$235$			12.2639i			0.800005i
$236$	−9.91077	−	2.30433i	−0.645136	−	0.149999i
$237$	−9.74228	+	1.19290i	−0.632829	+	0.0774869i
$238$	22.8327	+	17.3308i	1.48002	+	1.12339i
$239$	5.65067	+	3.26242i	0.365512	+	0.211028i	0.671496	−	0.741008i	$-0.265652\pi$
$239$	5.65067	+	3.26242i	0.365512	+	0.211028i	−0.305984	+	0.952037i	$0.598985\pi$
$240$	10.8223	+	3.76819i	0.698579	+	0.243235i
$241$	−20.0162	+	11.5564i	−1.28936	+	0.744410i	−0.978539	−	0.206059i	$-0.933936\pi$
$241$	−20.0162	+	11.5564i	−1.28936	+	0.744410i	−0.310817	+	0.950470i	$0.600603\pi$
$242$	−16.9505	+	7.35460i	−1.08962	+	0.472772i
$243$	−6.61158	+	14.1169i	−0.424133	+	0.905600i
$244$	−8.64787	−	8.08945i	−0.553623	−	0.517874i
$245$	9.89211	+	6.01700i	0.631984	+	0.384412i
$246$	0.144287	+	18.9484i	0.00919937	+	1.20811i
$247$	2.49859	+	1.44256i	0.158982	+	0.0917881i
$248$	1.27787	+	1.50328i	0.0811449	+	0.0954586i
$249$	0.508319	+	4.15140i	0.0322134	+	0.263084i
$250$	10.1179	−	13.6513i	0.639912	−	0.863386i
$251$	5.55147			0.350406			0.175203	−	0.984532i	$-0.443942\pi$
$251$	5.55147			0.350406			0.175203	+	0.984532i	$0.443942\pi$
$252$	−13.7777	−	7.88506i	−0.867915	−	0.496712i
$253$	11.2225			0.705553
$254$	15.0793	−	20.3454i	0.946159	−	1.27658i
$255$	17.5330	−	13.2029i	1.09796	−	0.826797i
$256$	6.08589	−	14.7974i	0.380368	−	0.924835i
$257$	−16.9652	−	9.79486i	−1.05826	−	0.610987i	−0.133309	−	0.991074i	$-0.542560\pi$
$257$	−16.9652	−	9.79486i	−1.05826	−	0.610987i	−0.924950	+	0.380088i	$0.875894\pi$
$258$	−16.5032	−	9.36131i	−1.02745	−	0.582810i
$259$	−0.120276	+	10.5159i	−0.00747359	+	0.653428i
$260$	2.28678	−	2.44464i	0.141820	−	0.151610i
$261$	6.95989	−	24.2109i	0.430806	−	1.49862i
$262$	13.0344	−	5.65549i	0.805270	−	0.349397i
$263$	−11.4745	+	6.62480i	−0.707548	+	0.408503i	−0.810152	−	0.586219i	$-0.800616\pi$
$263$	−11.4745	+	6.62480i	−0.707548	+	0.408503i	0.102605	+	0.994722i	$0.467282\pi$
$264$	5.26419	−	23.4490i	0.323988	−	1.44319i
$265$	12.3460	+	7.12794i	0.758406	+	0.437866i
$266$	6.44995	−	8.49754i	0.395472	−	0.521017i
$267$	5.55205	−	13.0677i	0.339780	−	0.799728i
$268$	1.14323	−	4.91697i	0.0698339	−	0.300352i
$269$		−	23.5318i		−	1.43476i	−0.696683	−	0.717379i	$-0.745342\pi$
$269$		−	23.5318i		−	1.43476i	0.696683	−	0.717379i	$-0.254658\pi$
$270$	−8.68453	+	8.50391i	−0.528523	+	0.517532i
$271$	20.2947			1.23281			0.616406	−	0.787428i	$-0.288588\pi$
$271$	20.2947			1.23281			0.616406	+	0.787428i	$0.288588\pi$
$272$	−17.0569	−	25.4584i	−1.03423	−	1.54364i
$273$	−3.73596	+	2.74690i	−0.226111	+	0.166250i
$274$	0.637354	−	5.55557i	0.0385040	−	0.335624i
$275$	−9.61892	−	5.55349i	−0.580043	−	0.334888i
$276$	−4.67015	+	6.40243i	−0.281110	+	0.385381i
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	0.996789	+	0.0800689i	$0.0255140\pi$
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	−0.429053	+	0.903279i	$0.641153\pi$
$278$	−12.5859	+	5.46088i	−0.754853	+	0.327522i
$279$	−2.03088	+	0.504913i	−0.121586	+	0.0302284i
$280$	−7.90836	−	9.52193i	−0.472615	−	0.569044i
$281$	−1.06714	−	1.84834i	−0.0636602	−	0.110263i	0.832439	−	0.554117i	$-0.186944\pi$
$281$	−1.06714	−	1.84834i	−0.0636602	−	0.110263i	−0.896099	+	0.443854i	$0.853611\pi$
$282$	−8.96077	+	15.7971i	−0.533606	+	0.940703i
$283$	0.122715	−	0.212549i	0.00729468	−	0.0126347i	−0.862355	−	0.506304i	$-0.831011\pi$
$283$	0.122715	−	0.212549i	0.00729468	−	0.0126347i	0.869650	+	0.493669i	$0.164345\pi$
$284$	1.92044	−	0.583874i	0.113957	−	0.0346465i
$285$	−4.91366	−	6.52519i	−0.291060	−	0.386519i
$286$	−5.64000	−	4.18017i	−0.333500	−	0.247179i
$287$	10.4357	−	17.6069i	0.615997	−	1.03930i
$288$	11.1870	+	12.7613i	0.659200	+	0.751968i
$289$	−41.6920			−2.45247
$290$	11.6960	−	15.7806i	0.686814	−	0.926668i
$291$	17.5119	−	2.14425i	1.02657	−	0.125698i
$292$	11.2832	−	3.43044i	0.660299	−	0.200751i
$293$	9.64296	+	5.56736i	0.563347	+	0.325249i	0.754488	−	0.656314i	$-0.227885\pi$
$293$	9.64296	+	5.56736i	0.563347	+	0.325249i	−0.191141	+	0.981563i	$0.561219\pi$
$294$	8.34563	+	14.9783i	0.486727	+	0.873554i
$295$	7.28768	−	4.20754i	0.424305	−	0.244973i
$296$	3.77762	−	10.5891i	0.219569	−	0.615478i
$297$	19.7937	+	16.0616i	1.14855	+	0.931986i
$298$	8.99993	−	3.90496i	0.521352	−	0.226208i
$299$	1.15745	+	2.00476i	0.0669371	+	0.115939i
$300$	7.17108	−	3.17655i	0.414023	−	0.183398i
$301$	10.0432	+	17.8640i	0.578878	+	1.02967i
$302$	−17.6026	−	2.01943i	−1.01291	−	0.116205i
$303$	−1.68035	+	0.205751i	−0.0965336	+	0.0118201i
$304$	−9.47477	+	6.34802i	−0.543415	+	0.364084i
$305$	9.79335			0.560765
$306$	32.2312	−	4.19590i	1.84254	−	0.239863i
$307$	−23.3864			−1.33473			−0.667366	−	0.744730i	$-0.732578\pi$
$307$	−23.3864			−1.33473			−0.667366	+	0.744730i	$0.732578\pi$
$308$	−17.9486	+	18.7531i	−1.02272	+	1.06855i
$309$	18.0844	−	13.6181i	1.02878	−	0.774705i
$310$	−1.62111	−	0.185979i	−0.0920726	−	0.0105629i
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.00684678	+	0.999977i	$0.502179\pi$
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.862582	+	0.505918i	$0.831154\pi$
$312$	4.73181	−	1.47807i	0.267886	−	0.0836792i
$313$	−13.6566	+	7.88467i	−0.771919	+	0.445668i	−0.833559	−	0.552431i	$-0.813700\pi$
$313$	−13.6566	+	7.88467i	−0.771919	+	0.445668i	0.0616396	+	0.998098i	$0.480367\pi$
$314$	0.940006	+	2.16647i	0.0530476	+	0.122261i
$315$	12.7762	−	3.02166i	0.719855	−	0.170251i
$316$	−8.27672	−	7.74227i	−0.465602	−	0.435537i
$317$	−3.31354	−	5.73923i	−0.186107	−	0.322347i	0.757842	−	0.652438i	$-0.226254\pi$
$317$	−3.31354	−	5.73923i	−0.186107	−	0.322347i	−0.943949	+	0.330091i	$0.892920\pi$
$318$	10.6947	+	18.2023i	0.599730	+	1.02073i
$319$	−35.6745	−	20.5967i	−1.99739	−	1.15319i
$320$	4.68437	+	12.3755i	0.261864	+	0.691811i
$321$	0.698583	−	1.64423i	0.0389911	−	0.0917720i
$322$	7.89085	−	3.31703i	0.439740	−	0.184851i
$323$			21.8432i			1.21539i
$324$	−17.4001	+	4.60842i	−0.966671	+	0.256024i
$325$		−	2.29107i		−	0.127086i
$326$	−5.95285	+	8.03175i	−0.329698	+	0.444837i
$327$	−1.34291	−	0.570563i	−0.0742633	−	0.0315522i
$328$	−16.6711	+	14.1713i	−0.920506	+	0.782479i
$329$	17.0997	−	9.61345i	0.942736	−	0.530006i
$330$	10.0686	+	17.1366i	0.554257	+	0.943339i
$331$	6.89178	−	3.97897i	0.378807	−	0.218704i	−0.298492	−	0.954412i	$-0.596484\pi$
$331$	6.89178	−	3.97897i	0.378807	−	0.218704i	0.677299	+	0.735708i	$0.263150\pi$
$332$	−3.29915	+	3.52689i	−0.181064	+	0.193563i
$333$	8.27786	+	8.58346i	0.453624	+	0.470371i
$334$	−1.50134	+	0.651413i	−0.0821496	+	0.0356437i
$335$	2.08746	+	3.61559i	0.114050	+	0.197541i
$336$	−3.22943	−	18.0436i	−0.176180	−	0.984358i
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.0139542	+	0.999903i	$0.504442\pi$
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.858964	+	0.512036i	$0.828891\pi$
$338$	−1.93037	+	16.8263i	−0.104999	+	0.915232i
$339$	8.83201	−	6.65077i	0.479689	−	0.361220i
$340$	24.6851	+	5.73947i	1.33874	+	0.311266i
$341$			3.42203i			0.185313i
$342$	−1.56157	−	11.9954i	−0.0844400	−	0.648635i
$343$	0.635325	−	18.5094i	0.0343043	−	0.999411i
$344$	−3.94226	−	21.5510i	−0.212552	−	1.16195i
$345$	−0.796550	−	6.50536i	−0.0428848	−	0.350237i
$346$	−2.11469	−	0.242605i	−0.113687	−	0.0130425i
$347$	2.35072	+	1.35719i	0.126193	+	0.0728576i	0.561768	−	0.827295i	$-0.310121\pi$
$347$	2.35072	+	1.35719i	0.126193	+	0.0728576i	−0.435575	+	0.900153i	$0.643455\pi$
$348$	26.5960	−	11.7811i	1.42570	−	0.631535i
$349$	−0.192902	+	0.111372i	−0.0103258	+	0.00596160i	−0.505154	−	0.863029i	$-0.668564\pi$
$349$	−0.192902	+	0.111372i	−0.0103258	+	0.00596160i	0.494828	+	0.868991i	$0.335231\pi$
$350$	−8.40476	−	1.06175i	−0.449253	−	0.0567527i
$351$	−0.827742	+	5.19244i	−0.0441816	+	0.277152i
$352$	24.6647	−	12.7180i	1.31463	−	0.677869i
$353$	−24.5385	+	14.1673i	−1.30605	+	0.754049i	−0.981435	−	0.191796i	$-0.938569\pi$
$353$	−24.5385	+	14.1673i	−1.30605	+	0.754049i	−0.324617	+	0.945846i	$0.605235\pi$
$354$	12.4616	−	0.0948913i	0.662326	−	0.00504341i
$355$	−0.830019	+	1.43763i	−0.0440528	+	0.0763017i
$356$	15.6857	−	4.76895i	0.831343	−	0.252754i
$357$	−32.1529	−	14.0970i	−1.70171	−	0.746093i
$358$	−1.07862	+	1.45530i	−0.0570066	+	0.0769148i
$359$			21.8680i			1.15415i	0.816691	+	0.577075i	$0.195806\pi$
$359$			21.8680i			1.15415i	−0.816691	+	0.577075i	$0.804194\pi$
$360$	−13.9664	−	1.38713i	−0.736092	−	0.0731084i
$361$	−10.8707			−0.572143
$362$	−22.4166	+	30.2451i	−1.17819	+	1.58965i
$363$	18.0776	−	13.6130i	0.948827	−	0.714495i
$364$	−5.20116	−	1.27218i	−0.272615	−	0.0666803i
$365$	−4.87662	+	8.44655i	−0.255254	+	0.442113i
$366$	12.6148	+	7.15566i	0.659388	+	0.374032i
$367$	−3.75833	−	6.50962i	−0.196183	−	0.339800i	0.751104	−	0.660183i	$-0.229521\pi$
$367$	−3.75833	−	6.50962i	−0.196183	−	0.339800i	−0.947288	+	0.320384i	$0.896188\pi$
$368$	−9.13034	+	0.609920i	−0.475952	+	0.0317943i
$369$	−5.59937	−	22.5220i	−0.291492	−	1.17245i
$370$	3.70094	+	8.52972i	0.192403	+	0.443439i
$371$	0.260794	−	22.8017i	0.0135398	−	1.18380i
$372$	−1.95226	−	1.42404i	−0.101220	−	0.0738333i
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	−0.705393	−	0.708816i	$-0.749230\pi$
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	0.966549	+	0.256480i	$0.0825629\pi$
$374$	6.05778	−	52.8033i	0.313240	−	2.73040i
$375$	−8.13790	+	19.1539i	−0.420239	+	0.989102i
$376$	−20.6289	+	3.77358i	−1.06385	+	0.194607i
$377$		−	8.49709i		−	0.437622i
$378$	18.6648	+	5.44289i	0.960014	+	0.279952i
$379$		−	20.7129i		−	1.06395i	−0.846761	−	0.531974i	$-0.821450\pi$
$379$		−	20.7129i		−	1.06395i	0.846761	−	0.531974i	$-0.178550\pi$
$380$	2.13603	−	9.18696i	0.109576	−	0.471281i
$381$	−12.1284	+	28.5462i	−0.621356	+	1.46246i
$382$	−12.0740	−	1.38517i	−0.617761	−	0.0708716i
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	−0.334926	−	0.942245i	$-0.608711\pi$
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	0.983471	−	0.181068i	$-0.0579555\pi$
$384$	−3.00840	+	19.3636i	−0.153522	+	0.988145i
$385$	0.245526	−	21.4667i	0.0125132	−	1.09404i
$386$	9.87688	−	4.28546i	0.502720	−	0.218124i
$387$	22.3331	+	6.42009i	1.13526	+	0.326351i
$388$	14.8776	+	13.9169i	0.755293	+	0.706522i
$389$	15.9336	+	27.5978i	0.807865	+	1.39926i	0.914340	+	0.404947i	$0.132710\pi$
$389$	15.9336	+	27.5978i	0.807865	+	1.39926i	−0.106475	+	0.994315i	$0.533957\pi$
$390$	−2.02281	+	3.56604i	−0.102429	+	0.180573i
$391$	−8.76301	+	15.1780i	−0.443164	+	0.767583i
$392$	−7.07734	+	18.4908i	−0.357460	+	0.933929i
$393$	−13.9012	+	10.4680i	−0.701222	+	0.528041i
$394$	−16.3547	−	12.1215i	−0.823938	−	0.610674i
$395$	9.37303			0.471608
$396$	0.448235	+	29.4305i	0.0225246	+	1.47894i
$397$			10.3571i			0.519806i	0.965635	+	0.259903i	$0.0836906\pi$
$397$			10.3571i			0.519806i	−0.965635	+	0.259903i	$0.916309\pi$
$398$	24.9041	+	18.4581i	1.24833	+	0.925220i
$399$	−5.24643	+	11.9662i	−0.262650	+	0.599059i
$400$	8.12752	+	3.99540i	0.406376	+	0.199770i
$401$	9.69923	−	16.7996i	0.484356	−	0.838930i	−0.515482	−	0.856900i	$-0.672387\pi$
$401$	9.69923	−	16.7996i	0.484356	−	0.838930i	0.999839	+	0.0179704i	$0.00572046\pi$
$402$	0.0470778	+	6.18249i	0.00234803	+	0.308354i
$403$	−0.611303	+	0.352936i	−0.0304512	+	0.0175810i
$404$	−1.42757	−	1.33539i	−0.0710242	−	0.0664380i
$405$	7.90549	−	12.6139i	0.392827	−	0.626788i
$406$	−31.1715	−	3.93779i	−1.54701	−	0.195429i
$407$	16.8870	−	9.74974i	0.837060	−	0.483277i
$408$	27.6033	+	25.4296i	1.36657	+	1.25895i
$409$	14.1825	+	8.18830i	0.701282	+	0.404885i	0.807825	−	0.589423i	$-0.200645\pi$
$409$	14.1825	+	8.18830i	0.701282	+	0.404885i	−0.106543	+	0.994308i	$0.533978\pi$
$410$	2.06246	−	17.9777i	0.101858	−	0.887855i
$411$	0.832384	+	6.79801i	0.0410585	+	0.335321i
$412$	25.4614	+	5.91995i	1.25439	+	0.291655i
$413$	−11.5793	−	6.86310i	−0.569782	−	0.337711i
$414$	3.72720	−	8.96158i	0.183182	−	0.440438i
$415$		−	3.99405i		−	0.196060i
$416$	4.81574	+	3.09435i	0.236111	+	0.151713i
$417$	13.4228	−	10.1078i	0.657319	−	0.494981i
$418$	−19.6516	−	2.25450i	−0.961192	−	0.110271i
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	−0.489722	−	0.871879i	$-0.662902\pi$
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	0.999930	−	0.0118282i	$-0.00376511\pi$
$420$	12.1446	+	9.07325i	0.592593	+	0.442729i
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	0.793061	−	0.609143i	$-0.208486\pi$
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	−0.924063	+	0.382239i	$0.875153\pi$
$422$	0.945502	+	2.17914i	0.0460263	+	0.106079i
$423$	6.14539	−	21.3775i	0.298799	−	1.03941i
$424$	−8.19100	+	22.9603i	−0.397790	+	1.11505i
$425$	15.0217	−	8.67279i	0.728660	−	0.420692i
$426$	−2.11958	+	1.24535i	−0.102694	+	0.0603376i
$427$	−7.67685	−	13.6550i	−0.371509	−	0.660813i
$428$	1.97365	−	0.600050i	0.0953999	−	0.0290045i
$429$	7.91335	+	3.36214i	0.382060	+	0.162326i
$430$	14.5567	+	10.7889i	0.701985	+	0.520287i
$431$			0.569062i			0.0274108i	0.999906	+	0.0137054i	$0.00436270\pi$
$431$			0.569062i			0.0274108i	−0.999906	+	0.0137054i	$0.995637\pi$
$432$	−16.9766	−	11.9915i	−0.816785	−	0.576942i
$433$			29.1119i			1.39903i	0.714619	+	0.699514i	$0.246600\pi$
$433$			29.1119i			1.39903i	−0.714619	+	0.699514i	$0.753400\pi$
$434$	1.01145	+	2.40612i	0.0485510	+	0.115497i
$435$	−9.40720	+	22.1414i	−0.451041	+	1.06160i
$436$	−0.490087	−	1.61196i	−0.0234709	−	0.0771991i
$437$	5.64873	+	3.26129i	0.270215	+	0.156009i
$438$	−12.4532	+	7.31684i	−0.595036	+	0.349612i
$439$	−0.679870	−	1.17757i	−0.0324484	−	0.0562023i	0.849345	−	0.527838i	$-0.176997\pi$
$439$	−0.679870	−	1.17757i	−0.0324484	−	0.0562023i	−0.881794	+	0.471636i	$0.843664\pi$
$440$	−7.71145	+	21.6160i	−0.367629	+	1.03050i
$441$	−14.2282	−	15.4454i	−0.677532	−	0.735493i
$442$	10.0575	−	4.36381i	0.478384	−	0.207565i
$443$	3.04716	−	1.75928i	0.144775	−	0.0835858i	−0.425863	−	0.904788i	$-0.640029\pi$
$443$	3.04716	−	1.75928i	0.144775	−	0.0835858i	0.570638	+	0.821202i	$0.306696\pi$
$444$	−1.46518	+	13.6913i	−0.0695343	+	0.649760i
$445$	−6.77940	+	11.7423i	−0.321374	+	0.556637i
$446$	−1.31851	+	11.4929i	−0.0624333	+	0.544207i
$447$	−9.59839	+	7.22787i	−0.453988	+	0.341867i
$448$	13.5833	−	16.2325i	0.641753	−	0.766912i
$449$	13.2772			0.626591			0.313295	−	0.949656i	$-0.398567\pi$
$449$	13.2772			0.626591			0.313295	+	0.949656i	$0.398567\pi$
$450$	−7.62928	+	5.83664i	−0.359648	+	0.275142i
$451$	−37.9495			−1.78697
$452$	12.4348	+	2.89118i	0.584883	+	0.135989i
$453$	21.5392	−	2.63737i	1.01200	−	0.123915i
$454$	4.35408	−	37.9529i	0.204347	−	1.78122i
$455$	3.86009	−	2.17014i	0.180964	−	0.101738i
$456$	9.46403	−	10.2730i	0.443194	−	0.481078i
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	0.998301	+	0.0582701i	$0.0185584\pi$
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	−0.448687	+	0.893689i	$0.648108\pi$
$458$	−6.77391	−	15.6121i	−0.316524	−	0.729507i
$459$	−37.1783	+	14.2287i	−1.73534	+	0.664137i
$460$	5.16986	−	5.52674i	0.241046	−	0.257685i
$461$	−13.3984	+	7.73555i	−0.624024	+	0.360280i	−0.778434	−	0.627726i	$-0.783986\pi$
$461$	−13.3984	+	7.73555i	−0.624024	+	0.360280i	0.154410	+	0.988007i	$0.450652\pi$
$462$	16.0012	−	27.4719i	0.744445	−	1.27811i
$463$	−18.2044	−	10.5103i	−0.846031	−	0.488456i	0.0132786	−	0.999912i	$-0.495773\pi$
$463$	−18.2044	−	10.5103i	−0.846031	−	0.488456i	−0.859310	+	0.511456i	$0.829106\pi$
$464$	30.1432	+	14.8181i	1.39936	+	0.687913i
$465$	1.98365	−	0.242888i	0.0919895	−	0.0112637i
$466$	−14.7413	−	10.9258i	−0.682878	−	0.506126i
$467$	−29.6578			−1.37240			−0.686199	−	0.727414i	$-0.740722\pi$
$467$	−29.6578			−1.37240			−0.686199	+	0.727414i	$0.740722\pi$
$468$	−5.21116	+	3.11543i	−0.240886	+	0.144011i
$469$	3.40495	−	5.74479i	0.157226	−	0.265270i
$470$	10.3273	−	13.9338i	0.476361	−	0.642720i
$471$	−1.73990	−	2.31053i	−0.0801703	−	0.106464i
$472$	9.31988	+	10.9639i	0.428982	+	0.504653i
$473$	18.9992	−	32.9076i	0.873586	−	1.51310i
$474$	12.0734	+	6.84855i	0.554551	+	0.314564i
$475$	−3.22772	−	5.59057i	−0.148098	−	0.256513i
$476$	−11.3477	−	38.9179i	−0.520119	−	1.78380i
$477$	−17.9489	−	18.6115i	−0.821823	−	0.852162i
$478$	−3.67288	−	8.46504i	−0.167994	−	0.387182i
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	0.911246	−	0.411863i	$-0.135122\pi$
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	−0.812307	+	0.583231i	$0.801788\pi$
$480$	−9.12287	−	13.3947i	−0.416400	−	0.611381i
$481$	3.48334	+	2.01111i	0.158827	+	0.0916987i
$482$	32.4733	+	3.72545i	1.47912	+	0.169690i
$483$	−8.44612	+	6.21010i	−0.384312	+	0.282569i
$484$	25.4518	+	5.91773i	1.15690	+	0.268988i
$485$	−16.8482			−0.765037
$486$	19.3996	−	10.4717i	0.879983	−	0.475005i
$487$			33.3117i			1.50950i	0.656015	+	0.754748i	$0.272241\pi$
$487$			33.3117i			1.50950i	−0.656015	+	0.754748i	$0.727759\pi$
$488$	3.01341	+	16.4733i	0.136411	+	0.745711i
$489$	4.78792	−	11.2692i	0.216517	−	0.509609i
$490$	−6.17227	−	15.1664i	−0.278835	−	0.685148i
$491$	−27.8604	−	16.0852i	−1.25732	−	0.725916i	−0.284770	−	0.958596i	$-0.591917\pi$
$491$	−27.8604	−	16.0852i	−1.25732	−	0.725916i	−0.972553	+	0.232680i	$0.925250\pi$
$492$	15.7923	−	21.6501i	0.711973	−	0.976063i
$493$	55.7123	−	32.1655i	2.50916	−	1.44866i
$494$	−1.62406	−	3.74304i	−0.0730699	−	0.168407i
$495$	−16.8980	−	17.5219i	−0.759511	−	0.787550i
$496$	−0.185980	−	2.78407i	−0.00835075	−	0.125008i
$497$	2.65516	+	0.0303684i	0.119100	+	0.00136221i
$498$	2.91832	−	5.14475i	0.130773	−	0.230542i
$499$	29.5577	+	17.0652i	1.32319	+	0.763941i	0.984235	−	0.176863i	$-0.0565950\pi$
$499$	29.5577	+	17.0652i	1.32319	+	0.763941i	0.338950	+	0.940805i	$0.389928\pi$
$500$	−22.9913	+	6.99007i	−1.02820	+	0.312605i
$501$	1.60117	−	1.20573i	0.0715351	−	0.0538681i
$502$	−6.30742	−	4.67484i	−0.281514	−	0.208648i
$503$	9.76180			0.435257			0.217629	−	0.976032i	$-0.430168\pi$
$503$	9.76180			0.435257			0.217629	+	0.976032i	$0.430168\pi$
$504$	9.01391	+	20.5609i	0.401512	+	0.915854i
$505$	1.61666			0.0719405
$506$	−12.7507	−	9.45037i	−0.566837	−	0.420120i
$507$	−2.52107	−	20.5894i	−0.111965	−	0.914405i
$508$	−34.2653	+	10.4177i	−1.52028	+	0.462211i
$509$	12.0256	+	6.94300i	0.533027	+	0.307743i	0.742248	−	0.670125i	$-0.233760\pi$
$509$	12.0256	+	6.94300i	0.533027	+	0.307743i	−0.209221	+	0.977868i	$0.567093\pi$
$510$	−31.0385	+	0.236349i	−1.37441	+	0.0104657i
$511$	15.5999	+	0.178424i	0.690097	+	0.00789300i
$512$	−19.3753	+	11.6875i	−0.856276	+	0.516518i
$513$	5.29542	+	13.8365i	0.233799	+	0.610897i
$514$	11.0272	+	25.4149i	0.486389	+	1.12100i
$515$	−18.7225	+	10.8094i	−0.825012	+	0.476321i
$516$	10.8674	+	24.5333i	0.478411	+	1.08002i
$517$	−31.4996	−	18.1863i	−1.38535	−	0.799833i
$518$	8.99201	−	11.8466i	0.395086	−	0.520510i
$519$	2.58762	−	0.316842i	0.113584	−	0.0139078i
$520$	−4.65677	+	0.851849i	−0.204213	+	0.0373561i
$521$		−	15.9160i		−	0.697291i	−0.937255	−	0.348646i	$-0.886642\pi$
$521$		−	15.9160i		−	0.697291i	0.937255	−	0.348646i	$-0.113358\pi$
$522$	−28.2954	+	21.6468i	−1.23845	+	0.947457i
$523$	28.0511			1.22659			0.613294	−	0.789855i	$-0.289844\pi$
$523$	28.0511			1.22659			0.613294	+	0.789855i	$0.289844\pi$
$524$	−19.5718	−	4.55058i	−0.854997	−	0.198793i
$525$	10.3123	−	1.14315i	0.450067	−	0.0498910i
$526$	18.6157	+	2.13565i	0.811682	+	0.0931189i
$527$	−4.62815	−	2.67206i	−0.201605	−	0.116397i
$528$	−25.7272	+	22.2092i	−1.11963	+	0.966531i
$529$	−8.88328	−	15.3863i	−0.386229	−	0.668969i
$530$	−8.02475	−	18.4950i	−0.348573	−	0.803370i
$531$	−14.8118	+	3.68248i	−0.642777	+	0.159806i
$532$	−14.4839	+	4.22321i	−0.627958	+	0.183100i
$533$	−3.91398	−	6.77921i	−0.169533	−	0.293640i
$534$	−17.3122	+	10.1718i	−0.749173	+	0.440175i
$535$	−0.853014	+	1.47746i	−0.0368790	+	0.0638763i
$536$	−5.43944	+	4.62382i	−0.234948	+	0.199718i
$537$	0.867538	−	2.04189i	0.0374370	−	0.0881142i
$538$	−19.8159	+	26.7361i	−0.854324	+	1.15268i
$539$	−30.1238	+	16.4851i	−1.29753	+	0.710063i
$540$	17.0282	−	2.34874i	0.732776	−	0.101074i
$541$	4.98478			0.214313			0.107156	−	0.994242i	$-0.465825\pi$
$541$	4.98478			0.214313			0.107156	+	0.994242i	$0.465825\pi$
$542$	−23.0582	−	17.0899i	−0.990434	−	0.734076i
$543$	18.0298	−	42.4362i	0.773734	−	1.82111i
$544$	−2.05870	+	43.2886i	−0.0882661	+	1.85598i
$545$	1.20671	+	0.696694i	0.0516897	+	0.0298431i
$546$	6.55783	+	0.0250672i	0.280649	+	0.00107278i
$547$	−24.9146	+	14.3844i	−1.06527	+	0.615034i	−0.926885	−	0.375345i	$-0.877524\pi$
$547$	−24.9146	+	14.3844i	−1.06527	+	0.615034i	−0.138384	+	0.990379i	$0.544191\pi$
$548$	−5.40243	+	5.77536i	−0.230780	+	0.246711i
$549$	−17.0711	−	4.90742i	−0.728578	−	0.209444i
$550$	6.25220	+	14.4097i	0.266595	+	0.614432i
$551$	−11.9709	−	20.7342i	−0.509978	−	0.883308i
$552$	10.6975	−	3.34156i	0.455316	−	0.142226i
$553$	−7.34738	−	13.0690i	−0.312442	−	0.555749i
$554$	3.04610	−	26.5517i	0.129417	−	1.12807i
$555$	−6.85025	−	9.09691i	−0.290777	−	0.386142i
$556$	18.8983	+	4.39399i	0.801467	+	0.186347i
$557$	−24.8923			−1.05472			−0.527360	−	0.849642i	$-0.676818\pi$
$557$	−24.8923			−1.05472			−0.527360	+	0.849642i	$0.676818\pi$
$558$	2.73261	+	1.13652i	0.115681	+	0.0481127i
$559$	7.83806			0.331515
$560$	0.966917	+	17.4781i	0.0408597	+	0.738584i
$561$	7.91146	+	64.6123i	0.334022	+	2.72793i
$562$	−0.344017	+	2.99866i	−0.0145115	+	0.126491i
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	−0.963687	−	0.267036i	$-0.913956\pi$
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	0.713103	+	0.701059i	$0.247289\pi$
$564$	23.4835	−	10.4024i	0.988835	−	0.438021i
$565$	−9.14366	+	5.27909i	−0.384677	+	0.222093i
$566$	−0.318411	+	0.138155i	−0.0133838	+	0.00580708i
$567$	−23.7847	−	1.13494i	−0.998863	−	0.0476631i
$568$	−2.67363	−	0.953807i	−0.112183	−	0.0400208i
$569$	2.96159	+	5.12962i	0.124156	+	0.215045i	0.921403	−	0.388609i	$-0.127044\pi$
$569$	2.96159	+	5.12962i	0.124156	+	0.215045i	−0.797247	+	0.603654i	$0.793711\pi$
$570$	0.0879611	+	11.5515i	0.00368429	+	0.483838i
$571$	28.8922	+	16.6809i	1.20910	+	0.698074i	0.962563	−	0.271059i	$-0.0873739\pi$
$571$	28.8922	+	16.6809i	1.20910	+	0.698074i	0.246537	+	0.969133i	$0.420707\pi$
$572$	2.88792	+	9.49877i	0.120750	+	0.397164i
$573$	14.7742	−	1.80903i	0.617203	−	0.0755735i
$574$	−26.6833	+	11.2167i	−1.11374	+	0.468176i
$575$		−	5.17956i		−	0.216003i
$576$	−1.96416	−	23.9195i	−0.0818399	−	0.996645i
$577$		−	29.0803i		−	1.21063i	−0.795987	−	0.605314i	$-0.793048\pi$
$577$		−	29.0803i		−	1.21063i	0.795987	−	0.605314i	$-0.206952\pi$
$578$	47.3692	+	35.1084i	1.97030	+	1.46032i
$579$	−10.5336	+	7.93215i	−0.437763	+	0.329649i
$580$	−26.5774	+	8.08034i	−1.10357	+	0.335518i
$581$	−5.56897	+	3.13088i	−0.231040	+	0.129891i
$582$	−21.7022	−	12.3104i	−0.899585	−	0.510282i
$583$	−36.6162	+	21.1403i	−1.51649	+	0.875544i
$584$	−15.7084	−	5.60391i	−0.650018	−	0.231891i
$585$	1.38726	−	4.82577i	0.0573562	−	0.199521i
$586$	−6.26782	−	14.4457i	−0.258921	−	0.596747i
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	0.978066	−	0.208297i	$-0.0667921\pi$
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	−0.669423	+	0.742881i	$0.733459\pi$
$588$	3.13104	−	24.0457i	0.129122	−	0.991629i
$589$	−0.994450	+	1.72244i	−0.0409756	+	0.0709718i
$590$	−11.8232	−	1.35640i	−0.486753	−	0.0558420i
$591$	22.9469	+	9.74944i	0.943910	+	0.401038i
$592$	−13.2090	+	8.84991i	−0.542886	+	0.363729i
$593$		−	15.6604i		−	0.643096i	−0.946893	−	0.321548i	$-0.895797\pi$
$593$		−	15.6604i		−	0.643096i	0.946893	−	0.321548i	$-0.104203\pi$
$594$	−8.96378	−	34.9168i	−0.367788	−	1.43265i
$595$	28.8411	+	17.0942i	1.18237	+	0.700793i
$596$	−13.5138	−	3.14205i	−0.553546	−	0.128703i
$597$	−34.9424	−	14.8460i	−1.43010	−	0.607605i
$598$	0.373130	−	3.25243i	0.0152584	−	0.133002i
$599$	33.5225	+	19.3542i	1.36969	+	0.790791i	0.990888	−	0.134686i	$-0.0430026\pi$
$599$	33.5225	+	19.3542i	1.36969	+	0.790791i	0.378803	+	0.925477i	$0.376336\pi$
$600$	−10.8225	−	2.42960i	−0.441827	−	0.0991880i
$601$	−22.3109	+	12.8812i	−0.910081	+	0.525435i	−0.880457	−	0.474126i	$-0.842764\pi$
$601$	−22.3109	+	12.8812i	−0.910081	+	0.525435i	−0.0296235	+	0.999561i	$0.509431\pi$
$602$	3.63238	−	28.7538i	0.148045	−	1.17192i
$603$	−1.82696	−	7.34849i	−0.0743997	−	0.299254i
$604$	18.2990	+	17.1174i	0.744576	+	0.696496i
$605$	−18.7155	+	10.8054i	−0.760893	+	0.439302i
$606$	2.08242	+	1.18124i	0.0845927	+	0.0479845i
$607$	3.14595	−	5.44895i	0.127690	−	0.221166i	−0.795091	−	0.606490i	$-0.792577\pi$
$607$	3.14595	−	5.44895i	0.127690	−	0.221166i	0.922781	+	0.385324i	$0.125910\pi$
$608$	16.1106	+	0.766178i	0.653369	+	0.0310726i
$609$	38.2462	−	4.23969i	1.54982	−	0.171801i
$610$	−11.1269	−	8.24688i	−0.450516	−	0.333906i
$611$		−	7.50270i		−	0.303527i
$612$	−40.1535	−	22.3743i	−1.62311	−	0.904428i
$613$	22.1645			0.895217			0.447608	−	0.894230i	$-0.352276\pi$
$613$	22.1645			0.895217			0.447608	+	0.894230i	$0.352276\pi$
$614$	26.5710	+	19.6935i	1.07232	+	0.794764i
$615$	2.69357	+	21.9982i	0.108615	+	0.887053i
$616$	36.1845	−	6.19230i	1.45791	−	0.249495i
$617$	−20.1769	+	34.9474i	−0.812291	+	1.40693i	0.0989666	+	0.995091i	$0.468446\pi$
$617$	−20.1769	+	34.9474i	−0.812291	+	1.40693i	−0.911257	+	0.411838i	$0.864887\pi$
$618$	−32.0146	+	0.243782i	−1.28782	+	0.00980633i
$619$	−19.4800	−	33.7403i	−0.782966	−	1.35614i	−0.930207	−	0.367035i	$-0.880373\pi$
$619$	−19.4800	−	33.7403i	−0.782966	−	1.35614i	0.147241	−	0.989101i	$-0.452961\pi$
$620$	1.68524	+	1.57642i	0.0676809	+	0.0633106i
$621$	−1.87133	+	11.7389i	−0.0750938	+	0.471065i
$622$	39.7836	−	17.2616i	1.59518	−	0.692127i
$623$	21.6867	+	0.248042i	0.868859	+	0.00993759i
$624$	−6.62082	−	2.30527i	−0.265045	−	0.0922849i
$625$	4.27658	−	7.40725i	0.171063	−	0.296290i
$626$	22.1559	+	2.54180i	0.885527	+	0.101591i
$627$	24.0465	−	2.94438i	0.960324	−	0.117587i
$628$	0.756357	−	3.25305i	0.0301819	−	0.129811i
$629$			30.4520i			1.21420i
$630$	−17.0604	−	7.32555i	−0.679703	−	0.291857i
$631$			1.06032i			0.0422108i	0.999777	+	0.0211054i	$0.00671856\pi$
$631$			1.06032i			0.0422108i	−0.999777	+	0.0211054i	$0.993281\pi$
$632$	2.88408	+	15.7663i	0.114722	+	0.627149i
$633$	−1.75007	−	2.32404i	−0.0695592	−	0.0923724i
$634$	−1.06820	+	9.31104i	−0.0424235	+	0.369789i
$635$	14.8095	−	25.6508i	0.587698	−	1.01792i
$636$	3.17694	−	29.6868i	0.125974	−	1.17716i
$637$	−6.05173	−	3.68104i	−0.239778	−	0.145848i
$638$	23.1881	+	53.4425i	0.918024	+	2.11581i
$639$	2.16723	−	2.09007i	0.0857343	−	0.0826819i
$640$	5.09904	−	18.0053i	0.201557	−	0.711724i
$641$	−13.7294	−	23.7800i	−0.542278	−	0.939253i	−0.998773	−	0.0495272i	$-0.984229\pi$
$641$	−13.7294	−	23.7800i	−0.542278	−	0.939253i	0.456495	−	0.889726i	$-0.349105\pi$
$642$	−2.17830	+	1.27986i	−0.0859707	+	0.0505119i
$643$	−0.0203966	+	0.0353280i	−0.000804364	+	0.00139320i	−0.866427	−	0.499303i	$-0.833589\pi$
$643$	−0.0203966	+	0.0353280i	−0.000804364	+	0.00139320i	0.865623	+	0.500696i	$0.166923\pi$
$644$	−11.7586	−	2.87609i	−0.463353	−	0.113334i
$645$	−20.4241	−	8.67759i	−0.804199	−	0.341680i
$646$	18.3939	−	24.8176i	0.723699	−	0.976434i
$647$	−12.6901			−0.498899			−0.249449	−	0.968388i	$-0.580250\pi$
$647$	−12.6901			−0.498899			−0.249449	+	0.968388i	$0.580250\pi$
$648$	23.6502	+	9.41647i	0.929066	+	0.369914i
$649$			24.9578i			0.979680i
$650$	−1.92929	+	2.60305i	−0.0756729	+	0.102100i
$651$	−1.89361	−	2.57544i	−0.0742166	−	0.100939i
$652$	13.5269	−	4.11260i	0.529755	−	0.161062i
$653$	−3.40787	+	5.90260i	−0.133360	+	0.230987i	−0.924970	−	0.380041i	$-0.875910\pi$
$653$	−3.40787	+	5.90260i	−0.133360	+	0.230987i	0.791610	+	0.611027i	$0.209243\pi$
$654$	1.04531	+	1.77911i	0.0408750	+	0.0695688i
$655$	14.3917	−	8.30905i	0.562330	−	0.324661i
$656$	30.8747	−	2.06248i	1.20545	−	0.0805261i
$657$	12.7331	−	12.2798i	0.496767	−	0.479081i
$658$	−27.5235	−	3.47696i	−1.07298	−	0.135546i
$659$	21.9583	−	12.6776i	0.855375	−	0.493851i	−0.00708581	−	0.999975i	$-0.502256\pi$
$659$	21.9583	−	12.6776i	0.855375	−	0.493851i	0.862461	+	0.506124i	$0.168922\pi$
$660$	2.99095	−	27.9488i	0.116422	−	1.08790i
$661$	−27.4120	−	15.8263i	−1.06620	−	0.615572i	−0.139061	−	0.990284i	$-0.544408\pi$
$661$	−27.4120	−	15.8263i	−1.06620	−	0.615572i	−0.927141	+	0.374712i	$0.877742\pi$
$662$	−11.1809	−	1.28271i	−0.434558	−	0.0498540i
$663$	−10.7262	+	8.07717i	−0.416572	+	0.313691i
$664$	6.71835	−	1.22897i	0.260723	−	0.0476932i
$665$	6.36187	−	10.7337i	0.246703	−	0.416234i
$666$	−2.17702	−	16.7230i	−0.0843578	−	0.648002i
$667$		−	19.2099i		−	0.743810i
$668$	2.25433	+	0.524147i	0.0872225	+	0.0202798i
$669$	−1.72197	−	14.0632i	−0.0665754	−	0.543716i
$670$	0.672941	−	5.86576i	0.0259980	−	0.226614i
$671$	−14.5228	+	25.1541i	−0.560645	+	0.971065i
$672$	−11.5251	+	23.2201i	−0.444592	+	0.895733i
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	0.820047	−	0.572297i	$-0.193947\pi$
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	−0.905647	+	0.424033i	$0.860614\pi$
$674$	41.5794	−	18.0408i	1.60158	−	0.694905i
$675$	7.41294	−	9.13547i	0.285324	−	0.351624i
$676$	16.3625	−	17.4920i	0.629328	−	0.672770i
$677$	5.61421	−	3.24137i	0.215772	−	0.124576i	−0.388219	−	0.921567i	$-0.626910\pi$
$677$	5.61421	−	3.24137i	0.215772	−	0.124576i	0.603991	+	0.796991i	$0.293576\pi$
$678$	−15.6352	+	0.119058i	−0.600467	+	0.00457238i
$679$	13.2070	+	23.4917i	0.506840	+	0.901529i
$680$	−23.2134	−	27.3081i	−0.890192	−	1.04722i
$681$	5.68643	+	46.4406i	0.217904	+	1.77961i
$682$	2.88165	−	3.88801i	0.110344	−	0.148879i
$683$		−	28.5921i		−	1.09405i	−0.837117	−	0.547024i	$-0.815761\pi$
$683$		−	28.5921i		−	1.09405i	0.837117	−	0.547024i	$-0.184239\pi$
$684$	−8.32696	+	14.9438i	−0.318389	+	0.571389i
$685$		−	6.54035i		−	0.249894i
$686$	−16.3084	+	20.4948i	−0.622657	+	0.782495i
$687$	12.5381	+	16.6503i	0.478360	+	0.635247i
$688$	−13.6688	+	27.8054i	−0.521119	+	1.06007i
$689$	−7.55293	−	4.36069i	−0.287744	−	0.166129i
$690$	−4.57309	+	8.06197i	−0.174094	+	0.306914i
$691$	−4.98156	−	8.62831i	−0.189507	−	0.328236i	0.755579	−	0.655058i	$-0.227356\pi$
$691$	−4.98156	−	8.62831i	−0.189507	−	0.328236i	−0.945086	+	0.326822i	$0.894022\pi$
$692$	2.19836	+	2.05640i	0.0835690	+	0.0781728i
$693$	−11.1849	+	37.2963i	−0.424879	+	1.41677i
$694$	−1.52794	−	3.52151i	−0.0579999	−	0.133675i
$695$	−13.8965	+	8.02313i	−0.527123	+	0.304335i
$696$	−40.1384	−	9.01086i	−1.52144	−	0.341556i
$697$	29.6326	−	51.3251i	1.12241	−	1.94408i
$698$	0.312954	+	0.0359032i	0.0118455	+	0.00135896i
$699$	20.6832	+	8.78766i	0.782311	+	0.332380i
$700$	8.65516	+	8.28389i	0.327134	+	0.313102i
$701$	−13.0365			−0.492382			−0.246191	−	0.969221i	$-0.579179\pi$
$701$	−13.0365			−0.492382			−0.246191	+	0.969221i	$0.579179\pi$
$702$	5.31296	−	5.20247i	0.200525	−	0.196354i
$703$	11.3332			0.427440
$704$	−38.7329	−	6.32010i	−1.45980	−	0.238198i
$705$	−8.30630	+	19.5502i	−0.312833	+	0.736304i
$706$	39.8101	+	4.56715i	1.49827	+	0.171887i
$707$	−1.26728	−	2.25414i	−0.0476608	−	0.0847755i
$708$	−14.2384	−	10.3860i	−0.535112	−	0.390328i
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	0.837113	−	0.547031i	$-0.184242\pi$
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	−0.892299	+	0.451445i	$0.850909\pi$
$710$	2.15366	−	0.934447i	0.0808254	−	0.0350692i
$711$	−16.3385	−	4.69680i	−0.612740	−	0.176144i
$712$	−21.8376	−	7.79047i	−0.818397	−	0.291960i
$713$	−1.38201	+	0.797904i	−0.0517567	+	0.0298817i
$714$	24.6602	+	43.0922i	0.922883	+	1.61269i
$715$	−7.11073	−	4.10538i	−0.265926	−	0.153533i
$716$	2.45098	−	0.745174i	0.0915975	−	0.0278485i
$717$	6.79830	+	9.02793i	0.253887	+	0.337154i
$718$	18.4148	−	24.8458i	0.687235	−	0.927236i
$719$	52.8108			1.96951			0.984754	−	0.173951i	$-0.0556534\pi$
$719$	52.8108			1.96951			0.984754	+	0.173951i	$0.0556534\pi$
$720$	14.7001	+	13.3370i	0.547840	+	0.497039i
$721$	29.7481	+	17.6317i	1.10788	+	0.656640i
$722$	12.3510	+	9.15413i	0.459656	+	0.340681i
$723$	−39.7356	+	4.86543i	−1.47778	+	0.180947i
$724$	50.9382	−	15.4868i	1.89310	−	0.575561i
$725$	−9.50606	+	16.4650i	−0.353046	+	0.611494i
$726$	−32.0026	+	0.243690i	−1.18773	+	0.00904419i
$727$	13.3309	+	23.0897i	0.494414	+	0.856351i	0.999979	−	0.00643778i	$-0.00204922\pi$
$727$	13.3309	+	23.0897i	0.494414	+	0.856351i	−0.505565	+	0.862789i	$0.668716\pi$
$728$	4.83812	+	5.82526i	0.179313	+	0.215899i
$729$	−20.1011	+	18.0262i	−0.744486	+	0.667638i
$730$	12.6534	−	5.49017i	0.468324	−	0.203200i
$731$	29.6708	+	51.3913i	1.09741	+	1.90078i
$732$	−8.30689	−	18.7529i	−0.307031	−	0.693126i
$733$	−23.6033	−	13.6274i	−0.871807	−	0.503338i	−0.00385894	−	0.999993i	$-0.501228\pi$
$733$	−23.6033	−	13.6274i	−0.871807	−	0.503338i	−0.867948	+	0.496654i	$0.834562\pi$
$734$	−1.21158	+	10.5609i	−0.0447203	+	0.389810i
$735$	11.6940	+	16.2918i	0.431341	+	0.600933i
$736$	10.8872	+	6.99560i	0.401309	+	0.257861i
$737$	−12.3822			−0.456103
$738$	−12.6037	+	30.3040i	−0.463950	+	1.11551i
$739$		−	42.7029i		−	1.57085i	−0.618957	−	0.785425i	$-0.712444\pi$
$739$		−	42.7029i		−	1.57085i	0.618957	−	0.785425i	$-0.287556\pi$
$740$	2.97789	−	12.8077i	0.109469	−	0.470822i
$741$	3.00605	+	3.99194i	0.110430	+	0.146647i
$742$	−19.4974	+	25.6870i	−0.715771	+	0.942998i
$743$	−31.9011	−	18.4181i	−1.17034	−	0.675695i	−0.216578	−	0.976265i	$-0.569490\pi$
$743$	−31.9011	−	18.4181i	−1.17034	−	0.675695i	−0.953760	+	0.300571i	$0.902823\pi$
$744$	1.01893	+	3.26194i	0.0373557	+	0.119588i
$745$	9.93708	−	5.73718i	0.364067	−	0.210194i
$746$	−13.0871	+	5.67835i	−0.479154	+	0.207899i
$747$	−2.00141	+	6.96217i	−0.0732278	+	0.254733i
$748$	−51.3479	+	54.8924i	−1.87746	+	2.00707i
$749$	2.72872	+	0.0312097i	0.0997051	+	0.00114038i
$750$	25.3753	−	14.9092i	0.926576	−	0.544408i
$751$	20.8062	+	12.0125i	0.759228	+	0.438341i	0.829019	−	0.559221i	$-0.188900\pi$
$751$	20.8062	+	12.0125i	0.759228	+	0.438341i	−0.0697904	+	0.997562i	$0.522233\pi$
$752$	26.6156	+	13.0840i	0.970573	+	0.477123i
$753$	8.84979	+	3.76001i	0.322504	+	0.137022i
$754$	−7.15532	+	9.65414i	−0.260581	+	0.351583i
$755$	−20.7228			−0.754181
$756$	−16.6230	−	21.9015i	−0.604573	−	0.796550i
$757$	45.4741			1.65279			0.826393	−	0.563094i	$-0.190389\pi$
$757$	45.4741			1.65279			0.826393	+	0.563094i	$0.190389\pi$
$758$	−17.4421	+	23.5333i	−0.633525	+	0.854769i
$759$	17.8902	+	7.60100i	0.649373	+	0.275899i
$760$	−10.1632	+	8.63923i	−0.368656	+	0.313378i
$761$	33.8844	+	19.5632i	1.22831	+	0.709164i	0.966676	−	0.256003i	$-0.0824057\pi$
$761$	33.8844	+	19.5632i	1.22831	+	0.709164i	0.261633	+	0.965167i	$0.415739\pi$
$762$	37.8184	−	22.2201i	1.37001	−	0.804949i
$763$	0.0254903	−	2.22866i	0.000922812	−	0.0806829i
$764$	12.5517	+	11.7412i	0.454105	+	0.424782i
$765$	36.8923	−	9.17208i	1.33384	−	0.331617i
$766$	−32.9328	+	14.2892i	−1.18991	+	0.516288i
$767$	−4.45841	+	2.57406i	−0.160984	+	0.0929440i
$768$	19.7240	−	19.4670i	0.711727	−	0.702456i
$769$	−14.2130	−	8.20587i	−0.512534	−	0.295911i	0.221341	−	0.975196i	$-0.428957\pi$
$769$	−14.2130	−	8.20587i	−0.512534	−	0.295911i	−0.733874	+	0.679285i	$0.762290\pi$
$770$	−18.3559	+	24.1831i	−0.661500	+	0.871498i
$771$	−20.4108	−	27.1048i	−0.735075	−	0.976157i
$772$	−14.8306	−	3.44821i	−0.533763	−	0.124104i
$773$			43.6024i			1.56827i	0.620591	+	0.784134i	$0.286893\pi$
$773$			43.6024i			1.56827i	−0.620591	+	0.784134i	$0.713107\pi$
$774$	−19.9679	−	26.1008i	−0.717733	−	0.938174i
$775$	1.57938			0.0567330
$776$	−5.18418	−	28.3402i	−0.186101	−	1.01735i
$777$	−7.31416	+	16.6823i	−0.262394	+	0.598475i
$778$	5.13655	−	44.7733i	0.184154	−	1.60520i
$779$	−19.1015	−	11.0282i	−0.684380	−	0.395127i
$780$	5.30118	−	2.34824i	0.189813	−	0.0840807i
$781$	−2.46170	−	4.26379i	−0.0880866	−	0.152571i
$782$	22.7375	−	9.86553i	0.813091	−	0.352790i
$783$	27.4930	−	33.8815i	0.982520	−	1.21083i
$784$	23.6120	−	15.0490i	0.843287	−	0.537464i
$785$	1.38106	+	2.39206i	0.0492921	+	0.0853764i
$786$	24.6091	−	0.187391i	0.877778	−	0.00668402i
$787$	2.89125	−	5.00779i	0.103062	−	0.178508i	−0.809883	−	0.586592i	$-0.800469\pi$
$787$	2.89125	−	5.00779i	0.103062	−	0.178508i	0.912945	+	0.408083i	$0.133803\pi$
$788$	8.37431	+	27.5443i	0.298322	+	0.981224i
$789$	−22.7789	+	2.78916i	−0.810949	+	0.0992968i
$790$	−10.6494	−	7.89294i	−0.378887	−	0.280818i
$791$	14.5283	+	8.61095i	0.516567	+	0.306170i
$792$	24.2738	−	33.8155i	0.862533	−	1.20158i
$793$	−5.99131			−0.212758
$794$	8.72159	−	11.7674i	0.309517	−	0.417609i
$795$	14.8534	+	19.7248i	0.526795	+	0.699567i
$796$	−12.7520	−	41.9431i	−0.451982	−	1.48663i
$797$	11.1404	+	6.43191i	0.394613	+	0.227830i	0.684157	−	0.729335i	$-0.260170\pi$
$797$	11.1404	+	6.43191i	0.394613	+	0.227830i	−0.289544	+	0.957165i	$0.593504\pi$
$798$	16.0375	−	9.17767i	0.567720	−	0.324886i
$799$	49.1924	−	28.4013i	1.74030	−	1.00476i
$800$	−5.86976	−	11.3836i	−0.207527	−	0.402470i
$801$	17.7014	−	17.0712i	0.625449	−	0.603182i
$802$	−25.1667	+	10.9195i	−0.888668	+	0.385582i
$803$	−14.4633	−	25.0511i	−0.510398	−	0.884035i
$804$	5.15272	−	7.06401i	0.181723	−	0.249128i
$805$	8.72674	−	4.90617i	0.307577	−	0.172920i
$806$	0.991749	+	0.113777i	0.0349329	+	0.00400762i
$807$	15.9381	−	37.5128i	0.561046	−	1.32051i
$808$	0.497446	+	2.71937i	0.0175001	+	0.0956671i
$809$	11.6895			0.410980			0.205490	−	0.978659i	$-0.434121\pi$
$809$	11.6895			0.410980			0.205490	+	0.978659i	$0.434121\pi$
$810$	−19.6040	+	7.67436i	−0.688814	+	0.269649i
$811$	23.0355			0.808885			0.404443	−	0.914563i	$-0.367466\pi$
$811$	23.0355			0.808885			0.404443	+	0.914563i	$0.367466\pi$
$812$	32.1001	+	30.7232i	1.12649	+	1.07817i
$813$	32.3524	+	13.7456i	1.13465	+	0.482078i
$814$	−27.3967	−	3.14305i	−0.960255	−	0.110164i
$815$	−5.84635	+	10.1262i	−0.204789	+	0.354705i
$816$	−9.94809	−	52.1368i	−0.348253	−	1.82515i
$817$	19.1261	−	11.0425i	0.669138	−	0.386327i
$818$	−9.21851	−	21.2463i	−0.322318	−	0.742859i
$819$	−7.81611	+	1.84857i	−0.273117	+	0.0645943i
$820$	−17.4821	+	18.6889i	−0.610503	+	0.652646i
$821$	5.85488	+	10.1410i	0.204337	+	0.353922i	0.949921	−	0.312489i	$-0.101163\pi$
$821$	5.85488	+	10.1410i	0.204337	+	0.353922i	−0.745584	+	0.666411i	$0.767830\pi$
$822$	4.77881	−	8.42464i	0.166680	−	0.293843i
$823$	30.7319	+	17.7431i	1.07125	+	0.618484i	0.928521	−	0.371279i	$-0.121081\pi$
$823$	30.7319	+	17.7431i	1.07125	+	0.618484i	0.142724	+	0.989763i	$0.454414\pi$
$824$	−23.9434	−	28.1669i	−0.834106	−	0.981239i
$825$	−11.5725	−	15.3679i	−0.402902	−	0.535041i
$826$	7.37677	+	17.5485i	0.256671	+	0.610591i
$827$			28.8739i			1.00405i	0.864854	+	0.502023i	$0.167411\pi$
$827$			28.8739i			1.00405i	−0.864854	+	0.502023i	$0.832589\pi$
$828$	−11.7812	+	7.04324i	−0.409425	+	0.244770i
$829$			31.4981i			1.09397i	0.837141	+	0.546987i	$0.184225\pi$
$829$			31.4981i			1.09397i	−0.837141	+	0.546987i	$0.815775\pi$
$830$	−3.36335	+	4.53793i	−0.116744	+	0.157514i
$831$	3.97821	+	32.4897i	0.138002	+	1.12706i
$832$	−2.86577	−	7.57100i	−0.0993528	−	0.262477i
$833$	1.22657	−	53.6135i	0.0424981	−	1.85760i
$834$	−23.7623	+	0.180943i	−0.822821	+	0.00626554i
$835$	−1.65767	+	0.957057i	−0.0573661	+	0.0331203i
$836$	20.4291	+	19.1099i	0.706555	+	0.660931i
$837$	−3.57948	−	0.570615i	−0.123725	−	0.0197233i
$838$	−27.0984	+	11.7577i	−0.936100	+	0.406162i
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	0.967868	−	0.251458i	$-0.0809102\pi$
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	−0.701703	+	0.712469i	$0.747577\pi$
$840$	−6.15779	−	20.5356i	−0.212464	−	0.708544i
$841$	−20.7559	+	35.9503i	−0.715722	+	1.23967i
$842$	−0.866522	+	7.55314i	−0.0298623	+	0.260298i
$843$	−0.449285	−	3.66928i	−0.0154742	−	0.126377i
$844$	0.760780	−	3.27207i	0.0261871	−	0.112629i
$845$			19.8090i			0.681450i
$846$	−24.9840	+	19.1136i	−0.858969	+	0.657138i
$847$	29.7369	+	17.6251i	1.02177	+	0.605606i
$848$	28.6410	−	19.1892i	0.983536	−	0.658961i
$849$	0.339584	−	0.255717i	0.0116545	−	0.00877619i
$850$	−24.3705	−	2.79587i	−0.835901	−	0.0958975i
$851$	7.87501	+	4.54664i	0.269952	+	0.155857i
$852$	3.45690	+	0.369941i	0.118432	+	0.0126740i
$853$	9.82218	−	5.67084i	0.336305	−	0.194166i	−0.322332	−	0.946627i	$-0.604467\pi$
$853$	9.82218	−	5.67084i	0.336305	−	0.194166i	0.658637	+	0.752461i	$0.271133\pi$
$854$	−2.77654	+	21.9790i	−0.0950112	+	0.752107i
$855$	−3.41354	−	13.7301i	−0.116740	−	0.469558i
$856$	−2.74770	−	0.980232i	−0.0939144	−	0.0335036i
$857$	−0.268417	+	0.154971i	−0.00916895	+	0.00529370i	−0.504577	−	0.863366i	$-0.668352\pi$
$857$	−0.268417	+	0.154971i	−0.00916895	+	0.00529370i	0.495409	+	0.868660i	$0.335018\pi$
$858$	−6.15969	−	10.4837i	−0.210288	−	0.357908i
$859$	−9.88124	+	17.1148i	−0.337144	+	0.583950i	−0.983894	−	0.178752i	$-0.942794\pi$
$859$	−9.88124	+	17.1148i	−0.337144	+	0.583950i	0.646751	+	0.762702i	$0.276127\pi$
$860$	−7.45363	−	24.5161i	−0.254167	−	0.835991i
$861$	28.5610	−	20.9998i	0.973356	−	0.715670i
$862$	0.479202	−	0.646552i	0.0163217	−	0.0220216i
$863$		−	23.9730i		−	0.816051i	−0.912970	−	0.408026i	$-0.866217\pi$
$863$		−	23.9730i		−	0.816051i	0.912970	−	0.408026i	$-0.133783\pi$
$864$	9.19035	+	27.9202i	0.312662	+	0.949864i
$865$	−2.48955			−0.0846472
$866$	24.5148	−	33.0761i	0.833048	−	1.12397i
$867$	−66.4626	−	28.2380i	−2.25719	−	0.959011i
$868$	0.876993	−	3.58549i	0.0297671	−	0.121699i
$869$	−13.8995	+	24.0746i	−0.471507	+	0.816674i
$870$	29.3332	−	17.2347i	0.994490	−	0.584310i
$871$	−1.27705	−	2.21192i	−0.0432713	−	0.0749481i
$872$	−0.800598	+	2.24416i	−0.0271117	+	0.0759970i
$873$	29.3687	+	8.44259i	0.993979	+	0.285738i
$874$	−3.67161	−	8.46212i	−0.124194	−	0.286236i
$875$	−31.7872	−	0.363567i	−1.07460	−	0.0122908i
$876$	20.3104	+	2.17352i	0.686224	+	0.0734365i
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	−0.469524	−	0.882919i	$-0.655575\pi$
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	0.999393	−	0.0348396i	$-0.0110920\pi$
$878$	−0.219171	+	1.91043i	−0.00739667	+	0.0644739i
$879$	11.6014	+	15.4063i	0.391305	+	0.519641i
$880$	26.9642	−	18.0658i	0.908962	−	0.608997i
$881$			2.85106i			0.0960548i	0.998846	+	0.0480274i	$0.0152935\pi$
$881$			2.85106i			0.0960548i	−0.998846	+	0.0480274i	$0.984707\pi$
$882$	3.15925	+	29.5300i	0.106378	+	0.994326i
$883$			58.5844i			1.97152i	0.168153	+	0.985761i	$0.446220\pi$
$883$			58.5844i			1.97152i	−0.168153	+	0.985761i	$0.553780\pi$
$884$	−15.1017	−	3.51125i	−0.507925	−	0.118096i
$885$	14.4673	−	1.77145i	0.486313	−	0.0595467i
$886$	−4.94356	−	0.567142i	−0.166082	−	0.0190535i
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	−0.993133	−	0.116987i	$-0.962676\pi$
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	0.597881	+	0.801585i	$0.296010\pi$
$888$	13.1940	−	14.3218i	0.442762	−	0.480610i
$889$	−47.3743	−	0.541845i	−1.58888	−	0.0181729i
$890$	17.5906	−	7.63235i	0.589638	−	0.255837i
$891$	20.6754	+	39.0106i	0.692652	+	1.30690i
$892$	11.1762	−	11.9476i	0.374205	−	0.400037i
$893$	−10.5700	−	18.3078i	−0.353711	−	0.612646i
$894$	16.9919	−	0.129389i	0.568295	−	0.00432740i
$895$	−1.05932	+	1.83479i	−0.0354091	+	0.0613304i
$896$	−29.1022	+	7.00444i	−0.972236	+	0.234002i
$897$	0.487308	+	3.97981i	0.0162707	+	0.132882i
$898$	−15.0852	−	11.1806i	−0.503399	−	0.373102i
$899$	5.85758			0.195361
$900$	13.5831	−	0.206875i	0.452771	−	0.00689584i
$901$		−	66.0291i		−	2.19975i
$902$	43.1171	+	31.9569i	1.43564	+	1.06405i
$903$	3.91086	+	35.2799i	0.130145	+	1.17404i
$904$	−11.6934	−	13.7561i	−0.388917	−	0.457520i
$905$	−22.0156	+	38.1321i	−0.731822	+	1.26755i
$906$	−26.6931	−	15.1415i	−0.886820	−	0.503041i
$907$	−16.2312	+	9.37107i	−0.538947	+	0.311161i	−0.744652	−	0.667453i	$-0.767385\pi$
$907$	−16.2312	+	9.37107i	−0.538947	+	0.311161i	0.205705	+	0.978614i	$0.434051\pi$
$908$	−36.9067	+	39.4544i	−1.22479	+	1.30934i
$909$	−2.81806	−	0.810105i	−0.0934691	−	0.0268695i
$910$	−6.21317	−	0.784890i	−0.205965	−	0.0260189i
$911$	−27.7633	+	16.0291i	−0.919838	+	0.531069i	−0.883583	−	0.468274i	$-0.844876\pi$
$911$	−27.7633	+	16.0291i	−0.919838	+	0.531069i	−0.0362544	+	0.999343i	$0.511543\pi$
$912$	−19.4036	+	3.70234i	−0.642516	+	0.122597i
$913$	10.2587	+	5.92286i	0.339513	+	0.196018i
$914$	3.78768	−	33.0158i	0.125285	−	1.09206i
$915$	15.6119	+	6.63303i	0.516114	+	0.219281i
$916$	−5.45050	+	23.4423i	−0.180089	+	0.774555i
$917$	−22.8669	−	13.5532i	−0.755131	−	0.447567i
$918$	54.2228	+	15.1413i	1.78962	+	0.499739i
$919$		−	40.9560i		−	1.35101i	−0.737354	−	0.675507i	$-0.763925\pi$
$919$		−	40.9560i		−	1.35101i	0.737354	−	0.675507i	$-0.236075\pi$
$920$	−10.5279	+	1.92583i	−0.347093	+	0.0634927i
$921$	−37.2811	−	15.8396i	−1.22845	−	0.521932i
$922$	21.7369	+	2.49373i	0.715865	+	0.0821265i
$923$	0.507783	−	0.879506i	0.0167139	−	0.0289493i
$924$	−41.3140	+	17.7383i	−1.35913	+	0.583547i
$925$	−4.49983	−	7.79394i	−0.147954	−	0.256263i
$926$	11.8327	+	27.2713i	0.388846	+	0.896190i
$927$	38.0524	−	9.46051i	1.24981	−	0.310724i
$928$	−21.7697	−	42.2192i	−0.714625	−	1.38591i
$929$	−20.6442	+	11.9189i	−0.677314	+	0.391047i	−0.798842	−	0.601540i	$-0.794554\pi$
$929$	−20.6442	+	11.9189i	−0.677314	+	0.391047i	0.121528	+	0.992588i	$0.461221\pi$
$930$	−2.45830	−	1.39445i	−0.0806107	−	0.0457258i
$931$	−19.9531	−	0.456488i	−0.653937	−	0.0149608i
$932$	7.54818	+	24.8270i	0.247249	+	0.813237i
$933$	−42.4290	+	31.9503i	−1.38906	+	1.04601i
$934$	33.6963	+	24.9745i	1.10258	+	0.817191i
$935$		−	62.1633i		−	2.03296i
$936$	8.54425	+	0.848611i	0.279277	+	0.0277377i
$937$		−	28.7675i		−	0.939794i	−0.882721	−	0.469897i	$-0.844291\pi$
$937$		−	28.7675i		−	0.939794i	0.882721	−	0.469897i	$-0.155709\pi$
$938$	−8.70623	+	3.65979i	−0.284269	+	0.119496i
$939$	−27.1108	+	3.31959i	−0.884728	+	0.108331i
$940$	−23.4671	+	7.13471i	−0.765412	+	0.232709i
$941$	−35.9743	−	20.7698i	−1.17273	−	0.677075i	−0.218407	−	0.975858i	$-0.570086\pi$
$941$	−35.9743	−	20.7698i	−1.17273	−	0.677075i	−0.954321	+	0.298783i	$0.903419\pi$
$942$	0.0311465	+	4.09031i	0.00101481	+	0.133270i
$943$	−8.84858	−	15.3262i	−0.288149	−	0.499089i
$944$	−1.35640	−	20.3050i	−0.0441472	−	0.660872i
$945$	22.4135	+	3.83635i	0.729110	+	0.124796i
$946$	−49.2976	+	21.3896i	−1.60280	+	0.695437i
$947$	11.5666	−	6.67800i	0.375865	−	0.217006i	−0.300152	−	0.953891i	$-0.597038\pi$
$947$	11.5666	−	6.67800i	0.375865	−	0.217006i	0.676018	+	0.736885i	$0.263704\pi$
$948$	−7.95037	−	17.9480i	−0.258216	−	0.582925i
$949$	2.98338	−	5.16737i	0.0968447	−	0.167740i
$950$	−1.04053	+	9.06987i	−0.0337592	+	0.294266i
$951$	−1.39506	−	11.3934i	−0.0452380	−	0.369455i
$952$	−19.8795	+	53.7732i	−0.644299	+	1.74280i
$953$	−6.70188			−0.217095			−0.108548	−	0.994091i	$-0.534620\pi$
$953$	−6.70188			−0.217095			−0.108548	+	0.994091i	$0.534620\pi$
$954$	4.72043	+	36.2604i	0.152829	+	1.17397i
$955$	−14.2143			−0.459963
$956$	−2.95531	+	12.7106i	−0.0955815	+	0.411091i
$957$	−42.9199	−	56.9962i	−1.38740	−	1.84243i
$958$	0.698063	−	6.08475i	0.0225534	−	0.196589i
$959$	−9.11932	+	5.12688i	−0.294478	+	0.165556i
$960$	−0.914397	+	22.9009i	−0.0295120	+	0.739125i
$961$	15.2567	+	26.4254i	0.492152	+	0.852432i
$962$	−2.26414	−	5.21825i	−0.0729987	−	0.168243i
$963$	2.22727	−	2.14798i	0.0717729	−	0.0692175i
$964$	−33.7581	−	31.5782i	−1.08727	−	1.01707i
$965$	10.9053	−	6.29620i	0.351055	−	0.202682i
$966$	14.8257	+	0.0566709i	0.477009	+	0.00182336i
$967$	18.7298	+	10.8137i	0.602311	+	0.347744i	0.769950	−	0.638104i	$-0.220281\pi$
$967$	18.7298	+	10.8137i	0.602311	+	0.347744i	−0.167639	+	0.985848i	$0.553614\pi$
$968$	−23.9344	−	28.1563i	−0.769280	−	0.904978i
$969$	−14.7944	+	34.8209i	−0.475263	+	1.11861i
$970$	19.1424	+	14.1877i	0.614626	+	0.455540i
$971$	−25.7885			−0.827592			−0.413796	−	0.910370i	$-0.635797\pi$
$971$	−25.7885			−0.827592			−0.413796	+	0.910370i	$0.635797\pi$
$972$	−30.8593	−	4.43860i	−0.989814	−	0.142368i
$973$	22.0800	+	13.0869i	0.707853	+	0.419545i
$974$	28.0514	−	37.8478i	0.898826	−	1.21272i
$975$	1.55174	−	3.65228i	0.0496955	−	0.116966i
$976$	10.4483	−	21.2540i	0.334440	−	0.680325i
$977$	18.8498	−	32.6488i	0.603058	−	1.04453i	−0.389298	−	0.921112i	$-0.627282\pi$
$977$	18.8498	−	32.6488i	0.603058	−	1.04453i	0.992355	−	0.123414i	$-0.0393844\pi$
$978$	−14.9295	+	8.77183i	−0.477394	+	0.280492i
$979$	−20.1066	−	34.8257i	−0.642610	−	1.11303i
$980$	−5.75872	+	22.4292i	−0.183956	+	0.716475i
$981$	−1.75434	−	1.81911i	−0.0560119	−	0.0580797i
$982$	18.1090	+	41.7365i	0.577881	+	1.33187i
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	−0.953240	−	0.302214i	$-0.902274\pi$
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	0.214895	−	0.976637i	$-0.431059\pi$
$984$	−36.1741	+	11.2997i	−1.15319	+	0.360220i
$985$	−20.6195	−	11.9047i	−0.656992	−	0.379315i
$986$	−90.3850	−	10.3693i	−2.87844	−	0.330225i
$987$	33.7704	−	3.74353i	1.07492	−	0.119158i
$988$	−1.30677	+	5.62034i	−0.0415738	+	0.178807i
$989$	17.7200			0.563463
$990$	4.44406	+	34.1375i	0.141242	+	1.08496i
$991$		−	12.6519i		−	0.401900i	−0.979602	−	0.200950i	$-0.935597\pi$
$991$		−	12.6519i		−	0.401900i	0.979602	−	0.200950i	$-0.0644028\pi$
$992$	−2.13313	+	3.31979i	−0.0677270	+	0.105403i
$993$	13.6814	−	1.67522i	0.434166	−	0.0531615i
$994$	−2.99114	−	2.27038i	−0.0948731	−	0.0720122i
$995$	31.3984	+	18.1279i	0.995395	+	0.574692i
$996$	−7.64805	+	3.38783i	−0.242338	+	0.107347i
$997$	−12.9778	+	7.49276i	−0.411012	+	0.237298i	−0.691225	−	0.722640i	$-0.742928\pi$
$997$	−12.9778	+	7.49276i	−0.411012	+	0.237298i	0.280212	+	0.959938i	$0.409595\pi$
$998$	−19.2122	−	44.2792i	−0.608152	−	1.40163i
$999$	7.38246	+	19.2898i	0.233571	+	0.610302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.10	yes	80
3.2	odd	2		756.2.bi.c.307.32		80
4.3	odd	2	inner	252.2.bi.c.139.19	yes	80
7.6	odd	2	inner	252.2.bi.c.139.9	✓	80
9.2	odd	6		756.2.bi.c.559.21		80
9.7	even	3	inner	252.2.bi.c.223.20	yes	80
12.11	even	2		756.2.bi.c.307.22		80
21.20	even	2		756.2.bi.c.307.31		80
28.27	even	2	inner	252.2.bi.c.139.20	yes	80
36.7	odd	6	inner	252.2.bi.c.223.9	yes	80
36.11	even	6		756.2.bi.c.559.31		80
63.20	even	6		756.2.bi.c.559.22		80
63.34	odd	6	inner	252.2.bi.c.223.19	yes	80
84.83	odd	2		756.2.bi.c.307.21		80
252.83	odd	6		756.2.bi.c.559.32		80
252.223	even	6	inner	252.2.bi.c.223.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.9	✓	80	7.6	odd	2	inner
252.2.bi.c.139.10	yes	80	1.1	even	1	trivial
252.2.bi.c.139.19	yes	80	4.3	odd	2	inner
252.2.bi.c.139.20	yes	80	28.27	even	2	inner
252.2.bi.c.223.9	yes	80	36.7	odd	6	inner
252.2.bi.c.223.10	yes	80	252.223	even	6	inner
252.2.bi.c.223.19	yes	80	63.34	odd	6	inner
252.2.bi.c.223.20	yes	80	9.7	even	3	inner
756.2.bi.c.307.21		80	84.83	odd	2
756.2.bi.c.307.22		80	12.11	even	2
756.2.bi.c.307.31		80	21.20	even	2
756.2.bi.c.307.32		80	3.2	odd	2
756.2.bi.c.559.21		80	9.2	odd	6
756.2.bi.c.559.22		80	63.20	even	6
756.2.bi.c.559.31		80	36.11	even	6
756.2.bi.c.559.32		80	252.83	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13617 - 0.842090i) q^{2} +(1.59413 + 0.677299i) q^{3} +(0.581768 + 1.91352i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-1.24086 - 2.11193i) q^{6} +(-0.0302588 + 2.64558i) q^{7} +(0.950366 - 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +O(q^{10})\)	\(q+(-1.13617 - 0.842090i) q^{2} +(1.59413 + 0.677299i) q^{3} +(0.581768 + 1.91352i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-1.24086 - 2.11193i) q^{6} +(-0.0302588 + 2.64558i) q^{7} +(0.950366 - 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +(0.931077 + 2.14589i) q^{10} +(4.24842 - 2.45282i) q^{11} +(-0.368607 + 3.44443i) q^{12} +(0.876334 + 0.505952i) q^{13} +(2.26220 - 2.98035i) q^{14} +(-1.72337 - 2.28859i) q^{15} +(-3.32309 + 2.22644i) q^{16} +7.66107i q^{17} +(-0.547691 - 4.20714i) q^{18} +2.85119 q^{19} +(0.749173 - 3.22215i) q^{20} +(-1.84008 + 4.19691i) q^{21} +(-6.89242 - 0.790723i) q^{22} +(1.98118 + 1.14384i) q^{23} +(3.31933 - 3.60307i) q^{24} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 - 1.31280i) q^{26} +(1.85727 + 4.85289i) q^{27} +(-5.07996 + 1.48121i) q^{28} +(-4.19857 - 7.27213i) q^{29} +(0.0308507 + 4.05146i) q^{30} +(-0.348784 + 0.604112i) q^{31} +(5.65047 + 0.268722i) q^{32} +(8.43384 - 1.03268i) q^{33} +(6.45131 - 8.70428i) q^{34} +(2.23130 - 3.76463i) q^{35} +(-2.92052 + 5.24124i) q^{36} +3.97490 q^{37} +(-3.23944 - 2.40096i) q^{38} +(1.05431 + 1.40010i) q^{39} +(-3.56453 + 3.03004i) q^{40} +(-6.69947 - 3.86794i) q^{41} +(5.62483 - 3.21889i) q^{42} +(6.70811 - 3.87293i) q^{43} +(7.16511 + 6.70244i) q^{44} +(-1.19723 - 4.81555i) q^{45} +(-1.28775 - 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(-6.80543 + 1.29853i) q^{48} +(-6.99817 - 0.160104i) q^{49} +(-0.364945 + 3.18108i) q^{50} +(-5.18884 + 12.2128i) q^{51} +(-0.458324 + 1.97123i) q^{52} -8.61878 q^{53} +(1.97640 - 7.07770i) q^{54} -8.11418 q^{55} +(7.01902 + 2.59488i) q^{56} +(4.54518 + 1.93111i) q^{57} +(-1.35350 + 11.7980i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(3.37664 - 4.62913i) q^{60} +(-5.12759 + 2.96042i) q^{61} +(0.904996 - 0.392667i) q^{62} +(-5.77591 + 5.44416i) q^{63} +(-6.19361 - 5.06352i) q^{64} +(-0.836869 - 1.44950i) q^{65} +(-10.4519 - 5.92875i) q^{66} +(-2.18590 - 1.26203i) q^{67} +(-14.6596 + 4.45696i) q^{68} +(2.38355 + 3.16528i) q^{69} +(-5.70530 + 2.39830i) q^{70} -1.00362i q^{71} +(7.73181 - 3.49559i) q^{72} -5.89658i q^{73} +(-4.51617 - 3.34723i) q^{74} +(-0.476618 - 3.89250i) q^{75} +(1.65873 + 5.45580i) q^{76} +(6.36058 + 11.3137i) q^{77} +(-0.0188736 - 2.47857i) q^{78} +(-4.90752 + 2.83336i) q^{79} +(6.60149 - 0.440989i) q^{80} +(-0.326126 + 8.99409i) q^{81} +(4.35458 + 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(-9.10137 - 1.07940i) q^{84} +(6.33589 - 10.9741i) q^{85} +(-10.8829 - 1.24853i) q^{86} +(-1.76767 - 14.4364i) q^{87} +(-2.49673 - 13.6488i) q^{88} -8.19734i q^{89} +(-2.69487 + 6.47947i) q^{90} +(-1.36505 + 2.30310i) q^{91} +(-1.03616 + 4.45647i) q^{92} +(-0.965174 + 0.726805i) q^{93} +(-1.19511 + 10.4173i) q^{94} +(-4.08418 - 2.35800i) q^{95} +(8.82560 + 4.25544i) q^{96} +(8.82136 - 5.09301i) q^{97} +(7.81629 + 6.07500i) q^{98} +(14.1441 + 4.06600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more