LMFDB - Embedded newform 950.2.w.a.37.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.20
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.966230 - 1.89633i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.684737 + 2.12865i) q^{5} +(-0.657682 + 2.02414i) q^{6} +(0.498269 + 0.498269i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.899122 - 1.23753i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.966230 - 1.89633i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.684737 + 2.12865i) q^{5} +(-0.657682 + 2.02414i) q^{6} +(0.498269 + 0.498269i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.899122 - 1.23753i) q^{9} +(-1.00930 - 1.99532i) q^{10} +(0.540220 + 0.392493i) q^{11} +(0.332940 - 2.10210i) q^{12} +(-1.46471 - 0.231987i) q^{13} +(-0.570081 - 0.414188i) q^{14} +(4.69823 + 0.758272i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.34377 + 0.684683i) q^{17} +(1.08165 + 1.08165i) q^{18} +(4.24374 - 0.995342i) q^{19} +(1.30901 + 1.81287i) q^{20} +(1.42633 - 0.463442i) q^{21} +(-0.594968 - 0.303152i) q^{22} +(4.89088 - 0.774640i) q^{23} +2.12830i q^{24} +(-4.06227 + 2.91513i) q^{25} +1.48297 q^{26} +(3.09077 - 0.489529i) q^{27} +(0.627856 + 0.319909i) q^{28} +(-0.348859 - 1.07368i) q^{29} +(-4.75901 - 0.0139707i) q^{30} +(7.42534 + 2.41264i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.26627 - 0.645199i) q^{33} +(1.22011 - 0.886465i) q^{34} +(-0.719456 + 1.40182i) q^{35} +(-1.23753 - 0.899122i) q^{36} +(-0.0798496 + 0.504151i) q^{37} +(-4.03578 + 1.64695i) q^{38} +(-1.85517 + 2.55343i) q^{39} +(-1.57649 - 1.58577i) q^{40} +(5.84064 + 8.03895i) q^{41} +(-1.33627 + 0.680863i) q^{42} +(-0.0475267 + 0.0475267i) q^{43} +(0.635067 + 0.206346i) q^{44} +(2.01861 - 2.76130i) q^{45} +(-4.70949 + 1.53021i) q^{46} +(-4.09127 + 8.02956i) q^{47} +(-0.332940 - 2.10210i) q^{48} -6.50346i q^{49} +(3.55623 - 3.51472i) q^{50} +3.20979i q^{51} +(-1.46471 + 0.231987i) q^{52} +(-1.42019 + 2.78728i) q^{53} +(-2.97614 + 0.967005i) q^{54} +(-0.465570 + 1.41869i) q^{55} +(-0.670171 - 0.217752i) q^{56} +(2.21292 - 9.00926i) q^{57} +(0.512524 + 1.00589i) q^{58} +(2.06738 - 1.50204i) q^{59} +(4.70261 - 0.730675i) q^{60} +(2.88327 + 2.09481i) q^{61} +(-7.71135 - 1.22136i) q^{62} +(0.168621 - 1.06463i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.509123 - 3.27670i) q^{65} +(-1.14975 + 0.835344i) q^{66} +(-7.00229 - 13.7428i) q^{67} +(-1.06642 + 1.06642i) q^{68} +(3.25674 - 10.0232i) q^{69} +(0.491305 - 1.49711i) q^{70} +(-0.536900 + 0.174450i) q^{71} +(1.36295 + 0.694459i) q^{72} +(12.7705 - 2.02264i) q^{73} -0.510435i q^{74} +(1.60296 + 10.5201i) q^{75} +(3.72846 - 2.25801i) q^{76} +(0.0736079 + 0.464742i) q^{77} +(1.43289 - 2.81220i) q^{78} +(0.380416 + 1.17080i) q^{79} +(1.80515 + 1.31963i) q^{80} +(3.47617 - 10.6985i) q^{81} +(-7.02630 - 7.02630i) q^{82} +(-1.88607 - 3.70161i) q^{83} +(1.21331 - 0.881518i) q^{84} +(-2.37757 - 2.39157i) q^{85} +(0.0395068 - 0.0543764i) q^{86} +(-2.37313 - 0.375867i) q^{87} +(-0.659528 - 0.104459i) q^{88} +(5.94240 + 4.31740i) q^{89} +(-1.56180 + 3.04308i) q^{90} +(-0.614228 - 0.845413i) q^{91} +(4.41213 - 2.24809i) q^{92} +(11.7498 - 11.7498i) q^{93} +(2.78480 - 8.57072i) q^{94} +(5.02457 + 8.35187i) q^{95} +(0.657682 + 2.02414i) q^{96} +(-10.8283 - 5.51730i) q^{97} +(1.01736 + 6.42339i) q^{98} -1.02144i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.966230	−	1.89633i	0.557853	−	1.09485i	−0.424081	−	0.905624i	$-0.639403\pi$
$3$	0.966230	−	1.89633i	0.557853	−	1.09485i	0.981934	−	0.189224i	$-0.0605972\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	0.684737	+	2.12865i	0.306224	+	0.951960i
$5$	0.684737	+	2.12865i	0.306224	+	0.951960i
$6$	−0.657682	+	2.02414i	−0.268498	+	0.826351i
$7$	0.498269	+	0.498269i	0.188328	+	0.188328i	0.794973	−	0.606645i	$-0.207485\pi$
$7$	0.498269	+	0.498269i	0.188328	+	0.188328i	−0.606645	+	0.794973i	$0.707485\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−0.899122	−	1.23753i	−0.299707	−	0.412512i
$10$	−1.00930	−	1.99532i	−0.319169	−	0.630976i
$11$	0.540220	+	0.392493i	0.162882	+	0.118341i	0.666241	−	0.745737i	$-0.267902\pi$
$11$	0.540220	+	0.392493i	0.162882	+	0.118341i	−0.503358	+	0.864078i	$0.667902\pi$
$12$	0.332940	−	2.10210i	0.0961115	−	0.606824i
$13$	−1.46471	−	0.231987i	−0.406238	−	0.0643417i	−0.0500281	−	0.998748i	$-0.515931\pi$
$13$	−1.46471	−	0.231987i	−0.406238	−	0.0643417i	−0.356210	+	0.934406i	$0.615931\pi$
$14$	−0.570081	−	0.414188i	−0.152361	−	0.110696i
$15$	4.69823	+	0.758272i	1.21308	+	0.195785i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.34377	+	0.684683i	−0.325911	+	0.166060i	−0.609289	−	0.792948i	$-0.708545\pi$
$17$	−1.34377	+	0.684683i	−0.325911	+	0.166060i	0.283378	+	0.959008i	$0.408545\pi$
$18$	1.08165	+	1.08165i	0.254946	+	0.254946i
$19$	4.24374	−	0.995342i	0.973580	−	0.228347i
$19$	4.24374	−	0.995342i	0.973580	−	0.228347i
$20$	1.30901	+	1.81287i	0.292704	+	0.405370i
$21$	1.42633	−	0.463442i	0.311250	−	0.101131i
$22$	−0.594968	−	0.303152i	−0.126848	−	0.0646321i
$23$	4.89088	−	0.774640i	1.01982	−	0.161524i	0.375935	−	0.926646i	$-0.377322\pi$
$23$	4.89088	−	0.774640i	1.01982	−	0.161524i	0.643885	+	0.765122i	$0.277322\pi$
$24$			2.12830i			0.434438i
$25$	−4.06227	+	2.91513i	−0.812454	+	0.583025i
$26$	1.48297			0.290834
$27$	3.09077	−	0.489529i	0.594818	−	0.0942100i
$28$	0.627856	+	0.319909i	0.118654	+	0.0604570i
$29$	−0.348859	−	1.07368i	−0.0647815	−	0.199377i	0.913427	−	0.407003i	$-0.133426\pi$
$29$	−0.348859	−	1.07368i	−0.0647815	−	0.199377i	−0.978208	+	0.207626i	$0.933426\pi$
$30$	−4.75901	−	0.0139707i	−0.868873	−	0.00255069i
$31$	7.42534	+	2.41264i	1.33363	+	0.433323i	0.887155	−	0.461472i	$-0.152679\pi$
$31$	7.42534	+	2.41264i	1.33363	+	0.433323i	0.446476	+	0.894795i	$0.352679\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.26627	−	0.645199i	0.220430	−	0.112315i
$34$	1.22011	−	0.886465i	0.209248	−	0.152027i
$35$	−0.719456	+	1.40182i	−0.121610	+	0.236951i
$36$	−1.23753	−	0.899122i	−0.206256	−	0.149854i
$37$	−0.0798496	+	0.504151i	−0.0131272	+	0.0828818i	−0.993382	−	0.114856i	$-0.963359\pi$
$37$	−0.0798496	+	0.504151i	−0.0131272	+	0.0828818i	0.980255	+	0.197738i	$0.0633594\pi$
$38$	−4.03578	+	1.64695i	−0.654690	+	0.267171i
$39$	−1.85517	+	2.55343i	−0.297065	+	0.408875i
$40$	−1.57649	−	1.58577i	−0.249265	−	0.250733i
$41$	5.84064	+	8.03895i	0.912155	+	1.25547i	0.966426	+	0.256947i	$0.0827166\pi$
$41$	5.84064	+	8.03895i	0.912155	+	1.25547i	−0.0542709	+	0.998526i	$0.517283\pi$
$42$	−1.33627	+	0.680863i	−0.206191	+	0.105059i
$43$	−0.0475267	+	0.0475267i	−0.00724776	+	0.00724776i	−0.710721	−	0.703474i	$-0.751631\pi$
$43$	−0.0475267	+	0.0475267i	−0.00724776	+	0.00724776i	0.703474	+	0.710721i	$0.251631\pi$
$44$	0.635067	+	0.206346i	0.0957399	+	0.0311078i
$45$	2.01861	−	2.76130i	0.300917	−	0.411630i
$46$	−4.70949	+	1.53021i	−0.694376	+	0.225617i
$47$	−4.09127	+	8.02956i	−0.596773	+	1.17123i	0.373139	+	0.927775i	$0.378281\pi$
$47$	−4.09127	+	8.02956i	−0.596773	+	1.17123i	−0.969912	+	0.243457i	$0.921719\pi$
$48$	−0.332940	−	2.10210i	−0.0480558	−	0.303412i
$49$		−	6.50346i		−	0.929065i
$50$	3.55623	−	3.51472i	0.502927	−	0.497056i
$51$			3.20979i			0.449460i
$52$	−1.46471	+	0.231987i	−0.203119	+	0.0321709i
$53$	−1.42019	+	2.78728i	−0.195078	+	0.382862i	−0.967738	−	0.251958i	$-0.918926\pi$
$53$	−1.42019	+	2.78728i	−0.195078	+	0.382862i	0.772660	+	0.634820i	$0.218926\pi$
$54$	−2.97614	+	0.967005i	−0.405001	+	0.131593i
$55$	−0.465570	+	1.41869i	−0.0627774	+	0.191296i
$56$	−0.670171	−	0.217752i	−0.0895553	−	0.0290983i
$57$	2.21292	−	9.00926i	0.293109	−	1.19331i
$58$	0.512524	+	1.00589i	0.0672977	+	0.132079i
$59$	2.06738	−	1.50204i	0.269150	−	0.195549i	−0.445021	−	0.895520i	$-0.646804\pi$
$59$	2.06738	−	1.50204i	0.269150	−	0.195549i	0.714171	+	0.699971i	$0.246804\pi$
$60$	4.70261	−	0.730675i	0.607104	−	0.0943297i
$61$	2.88327	+	2.09481i	0.369164	+	0.268214i	0.756864	−	0.653572i	$-0.226730\pi$
$61$	2.88327	+	2.09481i	0.369164	+	0.268214i	−0.387700	+	0.921786i	$0.626730\pi$
$62$	−7.71135	−	1.22136i	−0.979342	−	0.155113i
$63$	0.168621	−	1.06463i	0.0212442	−	0.134131i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−0.509123	−	3.27670i	−0.0631489	−	0.406425i
$66$	−1.14975	+	0.835344i	−0.141525	+	0.102824i
$67$	−7.00229	−	13.7428i	−0.855465	−	1.67895i	−0.726360	−	0.687314i	$-0.758790\pi$
$67$	−7.00229	−	13.7428i	−0.855465	−	1.67895i	−0.129105	−	0.991631i	$-0.541210\pi$
$68$	−1.06642	+	1.06642i	−0.129322	+	0.129322i
$69$	3.25674	−	10.0232i	0.392066	−	1.20665i
$70$	0.491305	−	1.49711i	0.0587221	−	0.178939i
$71$	−0.536900	+	0.174450i	−0.0637184	+	0.0207033i	−0.340703	−	0.940171i	$-0.610665\pi$
$71$	−0.536900	+	0.174450i	−0.0637184	+	0.0207033i	0.276984	+	0.960874i	$0.410665\pi$
$72$	1.36295	+	0.694459i	0.160625	+	0.0818428i
$73$	12.7705	−	2.02264i	1.49467	−	0.236733i	0.645055	−	0.764136i	$-0.276834\pi$
$73$	12.7705	−	2.02264i	1.49467	−	0.236733i	0.849615	+	0.527403i	$0.176834\pi$
$74$		−	0.510435i		−	0.0593369i
$75$	1.60296	+	10.5201i	0.185094	+	1.21476i
$76$	3.72846	−	2.25801i	0.427683	−	0.259012i
$77$	0.0736079	+	0.464742i	0.00838840	+	0.0529623i
$78$	1.43289	−	2.81220i	0.162243	−	0.318419i
$79$	0.380416	+	1.17080i	0.0428001	+	0.131725i	0.970173	−	0.242413i	$-0.0779387\pi$
$79$	0.380416	+	1.17080i	0.0428001	+	0.131725i	−0.927373	+	0.374138i	$0.877939\pi$
$80$	1.80515	+	1.31963i	0.201822	+	0.147539i
$81$	3.47617	−	10.6985i	0.386241	−	1.18873i
$82$	−7.02630	−	7.02630i	−0.775925	−	0.775925i
$83$	−1.88607	−	3.70161i	−0.207023	−	0.406305i	0.764026	−	0.645185i	$-0.223220\pi$
$83$	−1.88607	−	3.70161i	−0.207023	−	0.406305i	−0.971049	+	0.238880i	$0.923220\pi$
$84$	1.21331	−	0.881518i	0.132383	−	0.0961815i
$85$	−2.37757	−	2.39157i	−0.257884	−	0.259403i
$86$	0.0395068	−	0.0543764i	0.00426012	−	0.00586356i
$87$	−2.37313	−	0.375867i	−0.254426	−	0.0402971i
$88$	−0.659528	−	0.104459i	−0.0703059	−	0.0111354i
$89$	5.94240	+	4.31740i	0.629893	+	0.457644i	0.856363	−	0.516374i	$-0.172719\pi$
$89$	5.94240	+	4.31740i	0.629893	+	0.457644i	−0.226470	+	0.974018i	$0.572719\pi$
$90$	−1.56180	+	3.04308i	−0.164628	+	0.320769i
$91$	−0.614228	−	0.845413i	−0.0643886	−	0.0886233i
$92$	4.41213	−	2.24809i	0.459996	−	0.234380i
$93$	11.7498	−	11.7498i	1.21839	−	1.21839i
$94$	2.78480	−	8.57072i	0.287230	−	0.884003i
$95$	5.02457	+	8.35187i	0.515510	+	0.856883i
$96$	0.657682	+	2.02414i	0.0671244	+	0.206588i
$97$	−10.8283	−	5.51730i	−1.09945	−	0.560197i	−0.192440	−	0.981309i	$-0.561640\pi$
$97$	−10.8283	−	5.51730i	−1.09945	−	0.560197i	−0.907009	+	0.421112i	$0.861640\pi$
$98$	1.01736	+	6.42339i	0.102769	+	0.648860i
$99$		−	1.02144i		−	0.102659i
$100$	−2.96263	+	4.02776i	−0.296263	+	0.402776i
$101$	9.96157			0.991214			0.495607	−	0.868547i	$-0.334946\pi$
$101$	9.96157			0.991214			0.495607	+	0.868547i	$0.334946\pi$
$102$	−0.502121	−	3.17027i	−0.0497174	−	0.313903i
$103$	3.87883	−	7.61263i	0.382192	−	0.750095i	−0.617132	−	0.786860i	$-0.711705\pi$
$103$	3.87883	−	7.61263i	0.382192	−	0.750095i	0.999324	+	0.0367652i	$0.0117054\pi$
$104$	1.41039	−	0.458263i	0.138300	−	0.0449363i
$105$	1.96316	+	2.71881i	0.191585	+	0.265329i
$106$	0.966678	−	2.97513i	0.0938920	−	0.288970i
$107$	−4.43684	+	4.43684i	−0.428926	+	0.428926i	−0.888262	−	0.459337i	$-0.848087\pi$
$107$	−4.43684	+	4.43684i	−0.428926	+	0.428926i	0.459337	+	0.888262i	$0.348087\pi$
$108$	2.78822	−	1.42067i	0.268297	−	0.136704i
$109$	−8.53638	+	6.20205i	−0.817637	+	0.594048i	−0.916035	−	0.401099i	$-0.868628\pi$
$109$	−8.53638	+	6.20205i	−0.817637	+	0.594048i	0.0983975	+	0.995147i	$0.468628\pi$
$110$	0.237906	−	1.47406i	0.0226834	−	0.140546i
$111$	0.878884	+	0.638547i	0.0834200	+	0.0606082i
$112$	0.695984	+	0.110233i	0.0657643	+	0.0104160i
$113$	−8.06240	−	1.27696i	−0.758447	−	0.120126i	−0.234779	−	0.972049i	$-0.575437\pi$
$113$	−8.06240	−	1.27696i	−0.758447	−	0.120126i	−0.523668	+	0.851923i	$0.675437\pi$
$114$	−0.776320	+	9.24452i	−0.0727091	+	0.865829i
$115$	4.99790	+	9.88054i	0.466057	+	0.921365i
$116$	−0.663569	−	0.913325i	−0.0616109	−	0.0848001i
$117$	1.02986	+	2.02122i	0.0952107	+	0.186861i
$118$	−1.80695	+	1.80695i	−0.166344	+	0.166344i
$119$	−1.01071	−	0.328401i	−0.0926520	−	0.0301044i
$120$	−4.53041	+	1.45733i	−0.413568	+	0.133035i
$121$	−3.26140	−	10.0376i	−0.296491	−	0.912505i
$122$	−3.17547	−	1.61798i	−0.287493	−	0.146485i
$123$	20.8879	−	3.30832i	1.88340	−	0.298301i
$124$	7.80747			0.701131
$125$	−8.98686	−	6.65104i	−0.803809	−	0.594887i
$126$			1.07790i			0.0960270i
$127$	−7.75203	+	1.22780i	−0.687881	+	0.108950i	−0.490584	−	0.871394i	$-0.663216\pi$
$127$	−7.75203	+	1.22780i	−0.687881	+	0.108950i	−0.197297	+	0.980344i	$0.563216\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	0.0442047	+	0.136048i	0.00389201	+	0.0119784i
$130$	1.01544	+	3.15672i	0.0890603	+	0.276862i
$131$	−1.79311	+	5.51862i	−0.156665	+	0.482164i	−0.998326	−	0.0578419i	$-0.981578\pi$
$131$	−1.79311	+	5.51862i	−0.156665	+	0.482164i	0.841661	+	0.540006i	$0.181578\pi$
$132$	1.00492	−	1.00492i	0.0874671	−	0.0874671i
$133$	2.61047	+	1.61857i	0.226357	+	0.140348i
$134$	9.06592	+	12.4782i	0.783176	+	1.07795i
$135$	3.15840	+	6.24395i	0.271832	+	0.537394i
$136$	0.886465	−	1.22011i	0.0760137	−	0.104624i
$137$	7.47781	+	1.18437i	0.638872	+	0.101187i	0.467463	−	0.884013i	$-0.345168\pi$
$137$	7.47781	+	1.18437i	0.638872	+	0.101187i	0.171409	+	0.985200i	$0.445168\pi$
$138$	−1.64867	+	10.4093i	−0.140344	+	0.886097i
$139$	−6.84086	+	9.41564i	−0.580234	+	0.798624i	−0.993721	−	0.111886i	$-0.964311\pi$
$139$	−6.84086	+	9.41564i	−0.580234	+	0.798624i	0.413487	+	0.910510i	$0.364311\pi$
$140$	−0.251056	+	1.55554i	−0.0212181	+	0.131467i
$141$	11.2736	+	15.5168i	0.949410	+	1.30675i
$142$	0.503000	−	0.256291i	0.0422109	−	0.0215075i
$143$	−0.700213	−	0.700213i	−0.0585547	−	0.0585547i
$144$	−1.45481	−	0.472696i	−0.121234	−	0.0393914i
$145$	2.04660	−	1.47778i	0.169961	−	0.122723i
$146$	−12.2968	+	3.99548i	−1.01769	+	0.330669i
$147$	−12.3327	−	6.28383i	−1.01719	−	0.518282i
$148$	0.0798496	+	0.504151i	0.00656360	+	0.0414409i
$149$		−	6.92520i		−	0.567334i	−0.958923	−	0.283667i	$-0.908449\pi$
$149$		−	6.92520i		−	0.567334i	0.958923	−	0.283667i	$-0.0915511\pi$
$150$	−3.22893	−	10.1398i	−0.263641	−	0.827913i
$151$			16.2597i			1.32319i	0.749860	+	0.661596i	$0.230121\pi$
$151$			16.2597i			1.32319i	−0.749860	+	0.661596i	$0.769879\pi$
$152$	−3.32932	+	2.81347i	−0.270044	+	0.228203i
$153$	2.05553	+	1.04734i	0.166180	+	0.0846727i
$154$	−0.145403	−	0.447506i	−0.0117169	−	0.0360610i
$155$	−0.0512501	+	17.4580i	−0.00411651	+	1.40226i
$156$	−0.975322	+	3.00173i	−0.0780883	+	0.240331i
$157$	−4.50020	−	4.50020i	−0.359155	−	0.359155i	0.504347	−	0.863501i	$-0.331733\pi$
$157$	−4.50020	−	4.50020i	−0.359155	−	0.359155i	−0.863501	+	0.504347i	$0.831733\pi$
$158$	−0.558886	−	1.09687i	−0.0444625	−	0.0872627i
$159$	3.91338	+	5.38630i	0.310351	+	0.427161i
$160$	−1.98936	−	1.02100i	−0.157273	−	0.0807170i
$161$	2.82296	+	2.05100i	0.222480	+	0.161641i
$162$	−1.75975	+	11.1106i	−0.138259	+	0.872933i
$163$	1.78645	−	11.2792i	0.139925	−	0.883453i	−0.813443	−	0.581644i	$-0.802410\pi$
$163$	1.78645	−	11.2792i	0.139925	−	0.883453i	0.953368	−	0.301809i	$-0.0975905\pi$
$164$	8.03895	+	5.84064i	0.627737	+	0.456077i
$165$	2.24046	+	2.25366i	0.174420	+	0.175447i
$166$	2.44190	+	3.36099i	0.189529	+	0.260864i
$167$	−2.20259	−	4.32282i	−0.170441	−	0.334510i	0.789947	−	0.613175i	$-0.210108\pi$
$167$	−2.20259	−	4.32282i	−0.170441	−	0.334510i	−0.960388	+	0.278665i	$0.910108\pi$
$168$	−1.06047	+	1.06047i	−0.0818169	+	0.0818169i
$169$	−10.2722	−	3.33763i	−0.790167	−	0.256741i
$170$	2.72243	+	1.99020i	0.208801	+	0.152641i
$171$	−5.04740	−	4.35684i	−0.385985	−	0.333176i
$172$	−0.0305140	+	0.0598871i	−0.00232667	+	0.00456635i
$173$	0.415495	+	2.62333i	0.0315895	+	0.199448i	0.998436	−	0.0559109i	$-0.0178063\pi$
$173$	0.415495	+	2.62333i	0.0315895	+	0.199448i	−0.966846	+	0.255359i	$0.917806\pi$
$174$	2.40271			0.182149
$175$	−3.47662	−	0.571587i	−0.262808	−	0.0432079i
$176$	0.667749			0.0503335
$177$	−0.850801	−	5.37175i	−0.0639501	−	0.403765i
$178$	−6.54463	−	3.33465i	−0.490541	−	0.249943i
$179$	2.87715	+	8.85495i	0.215048	+	0.661850i	0.999150	+	0.0412182i	$0.0131239\pi$
$179$	2.87715	+	8.85495i	0.215048	+	0.661850i	−0.784102	+	0.620632i	$0.786876\pi$
$180$	1.06653	−	3.24994i	0.0794942	−	0.242236i
$181$	−20.7249	−	6.73394i	−1.54047	−	0.500530i	−0.588966	−	0.808158i	$-0.700465\pi$
$181$	−20.7249	−	6.73394i	−1.54047	−	0.500530i	−0.951507	+	0.307628i	$0.900465\pi$
$182$	0.738918	+	0.738918i	0.0547722	+	0.0547722i
$183$	6.75836	−	3.44356i	0.499593	−	0.254555i
$184$	−4.00613	+	2.91062i	−0.295336	+	0.214574i
$185$	−1.12783	+	0.175239i	−0.0829200	+	0.0128838i
$186$	−9.76703	+	13.4432i	−0.716153	+	0.985701i
$187$	−0.994662	−	0.157539i	−0.0727369	−	0.0115204i
$188$	−1.40975	+	8.90084i	−0.102817	+	0.649161i
$189$	1.78395	+	1.29612i	0.129763	+	0.0942786i
$190$	−6.26923	−	7.46302i	−0.454818	−	0.541425i
$191$	13.7198	−	9.96802i	0.992730	−	0.721261i	0.0322127	−	0.999481i	$-0.489745\pi$
$191$	13.7198	−	9.96802i	0.992730	−	0.721261i	0.960517	+	0.278221i	$0.0897446\pi$
$192$	−0.966230	−	1.89633i	−0.0697316	−	0.136856i
$193$	−9.49564	−	9.49564i	−0.683511	−	0.683511i	0.277278	−	0.960790i	$-0.410568\pi$
$193$	−9.49564	−	9.49564i	−0.683511	−	0.683511i	−0.960790	+	0.277278i	$0.910568\pi$
$194$	11.5581	+	3.75545i	0.829823	+	0.269626i
$195$	−6.70565	−	2.20058i	−0.480201	−	0.157587i
$196$	−2.00968	−	6.18515i	−0.143548	−	0.441797i
$197$	0.570534	−	1.11974i	0.0406489	−	0.0797779i	−0.869789	−	0.493424i	$-0.835745\pi$
$197$	0.570534	−	1.11974i	0.0406489	−	0.0797779i	0.910438	+	0.413646i	$0.135745\pi$
$198$	0.159788	+	1.00886i	0.0113557	+	0.0716969i
$199$			11.9008i			0.843624i	0.906683	+	0.421812i	$0.138606\pi$
$199$			11.9008i			0.843624i	−0.906683	+	0.421812i	$0.861394\pi$
$200$	2.29607	−	4.44163i	0.162357	−	0.314071i
$201$	−32.8267			−2.31541
$202$	−9.83893	+	1.55833i	−0.692265	+	0.109644i
$203$	0.361155	−	0.708806i	0.0253481	−	0.0497484i
$204$	0.991879	+	3.05269i	0.0694454	+	0.213731i
$205$	−13.1128	+	17.9372i	−0.915836	+	1.25279i
$206$	−2.64020	+	8.12569i	−0.183951	+	0.566144i
$207$	−5.35614	−	5.35614i	−0.372278	−	0.372278i
$208$	−1.32134	+	0.673254i	−0.0916181	+	0.0466818i
$209$	2.68322	+	1.12793i	0.185602	+	0.0780207i
$210$	−2.36431	−	2.37823i	−0.163153	−	0.164113i
$211$	−9.18477	+	12.6417i	−0.632306	+	0.870294i	−0.998176	−	0.0603719i	$-0.980771\pi$
$211$	−9.18477	+	12.6417i	−0.632306	+	0.870294i	0.365870	+	0.930666i	$0.380771\pi$
$212$	−0.489364	+	3.08972i	−0.0336096	+	0.212203i
$213$	−0.187955	+	1.18670i	−0.0128785	+	0.0813113i
$214$	3.68814	−	5.07629i	0.252116	−	0.347008i
$215$	−0.133711	−	0.0686243i	−0.00911900	−	0.00468014i
$216$	−2.53165	+	1.83935i	−0.172257	+	0.125152i
$217$	2.49768	+	4.90196i	0.169553	+	0.332767i
$218$	7.46107	−	7.46107i	0.505328	−	0.505328i
$219$	8.50360	−	26.1714i	0.574620	−	1.76850i
$220$	−0.00438326	+	1.49313i	−0.000295519	+	0.100666i
$221$	2.12707	−	0.691126i	0.143082	−	0.0464902i
$222$	−0.967954	−	0.493197i	−0.0649648	−	0.0331012i
$223$	−1.76803	−	11.1629i	−0.118396	−	0.747523i	−0.973436	−	0.228960i	$-0.926467\pi$
$223$	−1.76803	−	11.1629i	−0.118396	−	0.747523i	0.855040	−	0.518562i	$-0.173533\pi$
$224$	−0.704659			−0.0470820
$225$	7.26004	+	2.40615i	0.484003	+	0.160410i
$226$	8.16290			0.542988
$227$	−9.34922	+	1.48077i	−0.620530	+	0.0982823i	−0.458781	−	0.888550i	$-0.651714\pi$
$227$	−9.34922	+	1.48077i	−0.620530	+	0.0982823i	−0.161749	+	0.986832i	$0.551714\pi$
$228$	−0.679399	−	9.25215i	−0.0449943	−	0.612739i
$229$	25.6749	−	8.34229i	1.69665	−	0.551274i	0.708624	−	0.705586i	$-0.249316\pi$
$229$	25.6749	−	8.34229i	1.69665	−	0.551274i	0.988022	+	0.154312i	$0.0493161\pi$
$230$	−6.48203	−	8.97705i	−0.427412	−	0.591929i
$231$	0.952428	+	0.309463i	0.0626651	+	0.0203611i
$232$	0.798275	+	0.798275i	0.0524093	+	0.0524093i
$233$	−10.7406	−	21.0796i	−0.703641	−	1.38097i	−0.914955	−	0.403555i	$-0.867774\pi$
$233$	−10.7406	−	21.0796i	−0.703641	−	1.38097i	0.211314	−	0.977418i	$-0.432226\pi$
$234$	−1.33337	−	1.83523i	−0.0871651	−	0.119972i
$235$	−19.8935	−	3.21072i	−1.29771	−	0.209444i
$236$	1.50204	−	2.06738i	0.0977743	−	0.134575i
$237$	2.58779	+	0.409866i	0.168095	+	0.0266237i
$238$	1.04964	+	0.166247i	0.0680383	+	0.0107762i
$239$	−12.6072	+	17.3523i	−0.815490	+	1.12243i	0.174963	+	0.984575i	$0.444020\pi$
$239$	−12.6072	+	17.3523i	−0.815490	+	1.12243i	−0.990453	+	0.137851i	$0.955980\pi$
$240$	4.24665	−	2.14810i	0.274120	−	0.138659i
$241$	−4.99026	−	6.86850i	−0.321451	−	0.442439i	0.617459	−	0.786603i	$-0.288162\pi$
$241$	−4.99026	−	6.86850i	−0.321451	−	0.442439i	−0.938909	+	0.344164i	$0.888162\pi$
$242$	4.79147	+	9.40378i	0.308007	+	0.604498i
$243$	−10.2910	−	10.2910i	−0.660167	−	0.660167i
$244$	3.38948	+	1.10131i	0.216989	+	0.0705041i
$245$	13.8436	−	4.45316i	0.884432	−	0.284502i
$246$	−20.1132	+	6.53518i	−1.28237	+	0.416668i
$247$	−6.44675	+	0.473395i	−0.410197	+	0.0301214i
$248$	−7.71135	+	1.22136i	−0.489671	+	0.0775563i
$249$	−8.84186			−0.560330
$250$	9.91667	+	5.16330i	0.627185	+	0.326556i
$251$	−28.7400			−1.81405			−0.907025	−	0.421077i	$-0.861652\pi$
$251$	−28.7400			−1.81405			−0.907025	+	0.421077i	$0.861652\pi$
$252$	−0.168621	−	1.06463i	−0.0106221	−	0.0670654i
$253$	2.94619	+	1.50116i	0.185226	+	0.0943772i
$254$	7.46451	−	2.42537i	0.468365	−	0.152181i
$255$	−6.83250	+	2.19786i	−0.427868	+	0.137635i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.50592	+	8.50592i	−0.530585	+	0.530585i	−0.920746	−	0.390162i	$-0.872419\pi$
$257$	−8.50592	+	8.50592i	−0.530585	+	0.530585i	0.390162	+	0.920746i	$0.372419\pi$
$258$	−0.0649431	−	0.127458i	−0.00404318	−	0.00793519i
$259$	−0.290989	+	0.211416i	−0.0180812	+	0.0131368i
$260$	−1.49676	−	2.95900i	−0.0928252	−	0.183509i
$261$	−1.01505	+	1.39709i	−0.0628298	+	0.0864778i
$262$	0.907730	−	5.73118i	0.0560798	−	0.354074i
$263$	−3.55427	+	22.4408i	−0.219166	+	1.38376i	0.595280	+	0.803519i	$0.297041\pi$
$263$	−3.55427	+	22.4408i	−0.219166	+	1.38376i	−0.814445	+	0.580240i	$0.802959\pi$
$264$	−0.835344	+	1.14975i	−0.0514119	+	0.0707624i
$265$	−6.90558	−	1.11453i	−0.424207	−	0.0684649i
$266$	−2.83153	−	1.19028i	−0.173612	−	0.0729807i
$267$	13.9290	−	7.09716i	0.852438	−	0.434339i
$268$	−10.9063	−	10.9063i	−0.666209	−	0.666209i
$269$	4.81192	−	14.8096i	0.293388	−	0.902955i	−0.690370	−	0.723456i	$-0.742552\pi$
$269$	4.81192	−	14.8096i	0.293388	−	0.902955i	0.983758	−	0.179499i	$-0.0574476\pi$
$270$	−4.09628	−	5.67300i	−0.249292	−	0.345248i
$271$	−6.14184	−	18.9027i	−0.373090	−	1.14825i	−0.944758	−	0.327769i	$-0.893703\pi$
$271$	−6.14184	−	18.9027i	−0.373090	−	1.14825i	0.571667	−	0.820485i	$-0.306297\pi$
$272$	−0.684683	+	1.34377i	−0.0415150	+	0.0814778i
$273$	−2.19667	+	0.347918i	−0.132948	+	0.0210570i
$274$	−7.57102			−0.457382
$275$	−3.33869	−	0.0196025i	−0.201330	−	0.00118207i
$276$		−	10.5390i		−	0.634376i
$277$	−0.170716	−	1.07786i	−0.0102573	−	0.0647623i	0.982029	−	0.188732i	$-0.0604376\pi$
$277$	−0.170716	−	1.07786i	−0.0102573	−	0.0647623i	−0.992286	+	0.123969i	$0.960438\pi$
$278$	5.28371	−	10.3699i	0.316896	−	0.621943i
$279$	−3.69056	−	11.3584i	−0.220948	−	0.680008i
$280$	0.00462555	−	1.57566i	0.000276430	−	0.0941636i
$281$	2.71283	+	0.881452i	0.161834	+	0.0525830i	0.388813	−	0.921317i	$-0.372885\pi$
$281$	2.71283	+	0.881452i	0.161834	+	0.0525830i	−0.226980	+	0.973900i	$0.572885\pi$
$282$	−13.5622	−	13.5622i	−0.807616	−	0.807616i
$283$	0.0590089	+	0.115812i	0.00350772	+	0.00688428i	0.892754	−	0.450545i	$-0.148770\pi$
$283$	0.0590089	+	0.115812i	0.00350772	+	0.00688428i	−0.889246	+	0.457429i	$0.848770\pi$
$284$	−0.456715	+	0.331823i	−0.0271010	+	0.0196901i
$285$	20.6928	−	1.45844i	1.22574	−	0.0863907i
$286$	0.801130	+	0.582055i	0.0473718	+	0.0344176i
$287$	−1.09535	+	6.91577i	−0.0646565	+	0.408225i
$288$	1.51084	+	0.239294i	0.0890273	+	0.0141005i
$289$	−8.65543	+	11.9132i	−0.509143	+	0.700775i
$290$	−1.79023	+	1.77975i	−0.105126	+	0.104510i
$291$	−20.9253	+	15.2031i	−1.22666	+	0.891221i
$292$	11.5204	−	5.86994i	0.674181	−	0.343512i
$293$	10.6606	+	10.6606i	0.622796	+	0.622796i	0.946246	−	0.323449i	$-0.104842\pi$
$293$	10.6606	+	10.6606i	0.622796	+	0.622796i	−0.323449	+	0.946246i	$0.604842\pi$
$294$	13.1639	+	4.27721i	0.767733	+	0.249452i
$295$	4.61292	+	3.37221i	0.268574	+	0.196338i
$296$	−0.157733	−	0.485452i	−0.00916805	−	0.0282163i
$297$	1.86183	+	0.948650i	0.108034	+	0.0550463i
$298$	1.08334	+	6.83994i	0.0627562	+	0.396227i
$299$	−7.34344			−0.424682
$300$	4.77540	+	9.50986i	0.275708	+	0.549052i
$301$	−0.0473622			−0.00272991
$302$	−2.54357	−	16.0595i	−0.146366	−	0.924119i
$303$	9.62517	−	18.8905i	0.552951	−	1.08523i
$304$	2.84821	−	3.29965i	0.163356	−	0.189248i
$305$	−2.48484	+	7.57185i	−0.142282	+	0.433563i
$306$	−2.19406	−	0.712894i	−0.125426	−	0.0407534i
$307$	−0.0915209	+	0.0915209i	−0.00522337	+	0.00522337i	−0.709714	−	0.704490i	$-0.751176\pi$
$307$	−0.0915209	+	0.0915209i	−0.00522337	+	0.00522337i	0.704490	+	0.709714i	$0.251176\pi$
$308$	0.213619	+	0.419250i	0.0121720	+	0.0238890i
$309$	−10.6882	−	14.7111i	−0.608033	−	0.836885i
$310$	−2.68041	−	17.2510i	−0.152237	−	0.979793i
$311$	−8.25804	−	5.99981i	−0.468270	−	0.340218i	0.328497	−	0.944505i	$-0.393458\pi$
$311$	−8.25804	−	5.99981i	−0.468270	−	0.340218i	−0.796767	+	0.604287i	$0.793458\pi$
$312$	0.493740	−	3.11735i	0.0279525	−	0.176485i
$313$	−1.10403	+	6.97059i	−0.0624036	+	0.394001i	0.936641	+	0.350292i	$0.113918\pi$
$313$	−1.10403	+	6.97059i	−0.0624036	+	0.394001i	−0.999044	+	0.0437092i	$0.986082\pi$
$314$	5.14878	+	3.74081i	0.290562	+	0.211106i
$315$	2.38168	−	0.370058i	0.134193	−	0.0208504i
$316$	0.723594	+	0.995941i	0.0407053	+	0.0560261i
$317$	5.41600	+	10.6295i	0.304193	+	0.597013i	0.991612	−	0.129248i	$-0.0412564\pi$
$317$	5.41600	+	10.6295i	0.304193	+	0.597013i	−0.687419	+	0.726261i	$0.741256\pi$
$318$	−4.70780	−	4.70780i	−0.264000	−	0.264000i
$319$	0.232950	−	0.716947i	0.0130427	−	0.0401413i
$320$	2.12459	+	0.697223i	0.118768	+	0.0389760i
$321$	4.12672	+	12.7007i	0.230331	+	0.708886i
$322$	−3.10905	−	1.58414i	−0.173260	−	0.0882806i
$323$	−5.02109	+	4.24312i	−0.279381	+	0.236093i
$324$		−	11.2491i		−	0.624951i
$325$	6.62633	−	3.32742i	0.367562	−	0.184572i
$326$			11.4198i			0.632483i
$327$	3.51303	+	22.1804i	0.194271	+	1.22658i
$328$	−8.85366	−	4.51116i	−0.488861	−	0.249087i
$329$	−6.03944	+	1.96233i	−0.332965	+	0.108187i
$330$	−2.56543	−	1.87543i	−0.141222	−	0.103239i
$331$	−5.70375	−	1.85326i	−0.313506	−	0.101864i	0.148038	−	0.988982i	$-0.452704\pi$
$331$	−5.70375	−	1.85326i	−0.313506	−	0.101864i	−0.461544	+	0.887117i	$0.652704\pi$
$332$	−2.93762	−	2.93762i	−0.161223	−	0.161223i
$333$	0.695698	−	0.354476i	0.0381240	−	0.0194252i
$334$	2.85171	+	3.92504i	0.156038	+	0.214768i
$335$	24.4587	−	24.3156i	1.33632	−	1.32850i
$336$	0.881518	−	1.21331i	0.0480908	−	0.0661913i
$337$	−0.334714	+	2.11330i	−0.0182330	+	0.115119i	−0.995126	−	0.0986092i	$-0.968561\pi$
$337$	−0.334714	+	2.11330i	−0.0182330	+	0.115119i	0.976893	+	0.213728i	$0.0685606\pi$
$338$	10.6678	+	1.68962i	0.580253	+	0.0919031i
$339$	−10.2117	+	14.0552i	−0.554622	+	0.763371i
$340$	−3.00024	−	1.53981i	−0.162711	−	0.0835080i
$341$	3.06438	+	4.21775i	0.165945	+	0.228404i
$342$	5.66682	+	3.51361i	0.306427	+	0.189994i
$343$	6.72836	−	6.72836i	0.363297	−	0.363297i
$344$	0.0207699	−	0.0639233i	0.00111984	−	0.00344651i
$345$	23.5659	+	0.0691808i	1.26875	+	0.00372457i
$346$	−0.820760	−	2.52604i	−0.0441243	−	0.135801i
$347$	−2.40159	+	4.71340i	−0.128924	+	0.253028i	−0.946441	−	0.322877i	$-0.895350\pi$
$347$	−2.40159	+	4.71340i	−0.128924	+	0.253028i	0.817517	+	0.575905i	$0.195350\pi$
$348$	−2.37313	+	0.375867i	−0.127213	+	0.0201486i
$349$		−	12.9796i		−	0.694782i	−0.937720	−	0.347391i	$-0.887068\pi$
$349$		−	12.9796i		−	0.694782i	0.937720	−	0.347391i	$-0.112932\pi$
$350$	3.52323	+	0.0206860i	0.188325	+	0.00110571i
$351$	−4.64065			−0.247699
$352$	−0.659528	+	0.104459i	−0.0351529	+	0.00556768i
$353$	−16.9073	−	8.61468i	−0.899883	−	0.458513i	−0.0580886	−	0.998311i	$-0.518501\pi$
$353$	−16.9073	−	8.61468i	−0.899883	−	0.458513i	−0.841795	+	0.539798i	$0.818501\pi$
$354$	1.68065	+	5.17252i	0.0893257	+	0.274916i
$355$	−0.738977	−	1.02342i	−0.0392208	−	0.0543174i
$356$	6.98571	+	2.26979i	0.370242	+	0.120299i
$357$	−1.59934	+	1.59934i	−0.0846460	+	0.0846460i
$358$	−4.22695	−	8.29585i	−0.223401	−	0.438449i
$359$	19.1159	+	26.3108i	1.00890	+	1.38863i	0.919702	+	0.392618i	$0.128430\pi$
$359$	19.1159	+	26.3108i	1.00890	+	1.38863i	0.0891980	+	0.996014i	$0.471570\pi$
$360$	−0.544993	+	3.37676i	−0.0287237	+	0.177971i
$361$	17.0186	−	8.44794i	0.895715	−	0.444628i
$362$	21.5232	+	3.40894i	1.13123	+	0.179170i
$363$	−22.1858	−	3.51389i	−1.16445	−	0.184431i
$364$	−0.845413	−	0.614228i	−0.0443117	−	0.0321943i
$365$	13.0499	+	25.7988i	0.683063	+	1.35037i
$366$	−6.13646	+	4.45840i	−0.320758	+	0.233044i
$367$	−6.63317	+	3.37977i	−0.346249	+	0.176422i	−0.618463	−	0.785814i	$-0.712244\pi$
$367$	−6.63317	+	3.37977i	−0.346249	+	0.176422i	0.272214	+	0.962237i	$0.412244\pi$
$368$	3.50149	−	3.50149i	0.182528	−	0.182528i
$369$	4.69704	−	14.4560i	0.244518	−	0.752549i
$370$	1.08654	−	0.349514i	0.0564863	−	0.0181704i
$371$	−2.09645	+	0.681178i	−0.108842	+	0.0353650i
$372$	7.54381	−	14.8056i	0.391128	−	0.767632i
$373$	1.90003	+	11.9963i	0.0983798	+	0.621145i	0.986779	+	0.162073i	$0.0518181\pi$
$373$	1.90003	+	11.9963i	0.0983798	+	0.621145i	−0.888399	+	0.459072i	$0.848182\pi$
$374$	1.00706			0.0520739
$375$	−21.2960	+	10.6156i	−1.09972	+	0.548189i
$376$		−	9.01179i		−	0.464748i
$377$	0.261898	+	1.65356i	0.0134884	+	0.0851626i
$378$	−1.96475	−	1.00109i	−0.101056	−	0.0514904i
$379$	−0.633259	−	1.94897i	−0.0325283	−	0.100112i	0.933474	−	0.358645i	$-0.116761\pi$
$379$	−0.633259	−	1.94897i	−0.0325283	−	0.100112i	−0.966002	+	0.258533i	$0.916761\pi$
$380$	7.35952	+	6.39042i	0.377536	+	0.327821i
$381$	−5.16192	+	15.8868i	−0.264453	+	0.813903i
$382$	−11.9915	+	11.9915i	−0.613541	+	0.613541i
$383$	23.6524	−	12.0515i	1.20858	−	0.615802i	0.270666	−	0.962673i	$-0.412756\pi$
$383$	23.6524	−	12.0515i	1.20858	−	0.615802i	0.937913	+	0.346872i	$0.112756\pi$
$384$	1.25099	+	1.72183i	0.0638391	+	0.0878670i
$385$	−0.938870	+	0.474911i	−0.0478492	+	0.0242037i
$386$	10.8642	+	7.89329i	0.552972	+	0.401758i
$387$	0.101548	+	0.0160837i	0.00516199	+	0.000817578i
$388$	−12.0033	−	1.90113i	−0.609374	−	0.0965153i
$389$	−13.0132	+	17.9111i	−0.659794	+	0.908129i	−0.999475	−	0.0324123i	$-0.989681\pi$
$389$	−13.0132	+	17.9111i	−0.659794	+	0.908129i	0.339681	+	0.940541i	$0.389681\pi$
$390$	6.96734	+	1.12449i	0.352805	+	0.0569410i
$391$	−6.04182	+	4.38964i	−0.305548	+	0.221994i
$392$	2.95251	+	5.79462i	0.149124	+	0.292673i
$393$	8.73259	+	8.73259i	0.440501	+	0.440501i
$394$	−0.388345	+	1.19520i	−0.0195645	+	0.0602134i
$395$	−2.23173	+	1.61146i	−0.112291	+	0.0810814i
$396$	−0.315642	−	0.971447i	−0.0158616	−	0.0488171i
$397$	5.01634	−	9.84513i	0.251763	−	0.494113i	−0.730188	−	0.683246i	$-0.760568\pi$
$397$	5.01634	−	9.84513i	0.251763	−	0.494113i	0.981951	+	0.189133i	$0.0605677\pi$
$398$	−1.86169	−	11.7543i	−0.0933182	−	0.589188i
$399$	5.59167	−	3.38641i	0.279934	−	0.169532i
$400$	−1.57298	+	4.74613i	−0.0786489	+	0.237306i
$401$			2.44863i			0.122279i	0.998129	+	0.0611393i	$0.0194734\pi$
$401$			2.44863i			0.122279i	−0.998129	+	0.0611393i	$0.980527\pi$
$402$	32.4225	−	5.13522i	1.61709	−	0.256122i
$403$	−10.3163	−	5.25641i	−0.513891	−	0.261840i
$404$	9.47402	−	3.07830i	0.471350	−	0.153151i
$405$	25.1537	+	0.0738419i	1.24990	+	0.00366923i
$406$	−0.245827	+	0.756577i	−0.0122002	+	0.0375483i
$407$	−0.241012	+	0.241012i	−0.0119465	+	0.0119465i
$408$	−1.45721	−	2.85994i	−0.0721428	−	0.141588i
$409$	−14.1470	+	10.2784i	−0.699522	+	0.508232i	−0.879776	−	0.475388i	$-0.842308\pi$
$409$	−14.1470	+	10.2784i	−0.699522	+	0.508232i	0.180255	+	0.983620i	$0.442308\pi$
$410$	10.1453	−	19.7677i	0.501043	−	0.976256i
$411$	9.47124	−	13.0360i	0.467182	−	0.643020i
$412$	1.33655	−	8.43867i	0.0658473	−	0.415743i
$413$	1.77853	+	0.281691i	0.0875157	+	0.0138611i
$414$	6.12809	+	4.45231i	0.301179	+	0.218819i
$415$	6.58796	−	6.54940i	0.323390	−	0.321497i
$416$	1.19975	−	0.871667i	0.0588224	−	0.0427370i
$417$	11.2453	+	22.0702i	0.550687	+	1.08078i
$418$	−2.82663	−	0.694298i	−0.138255	−	0.0339592i
$419$	11.9883	+	3.89522i	0.585665	+	0.190294i	0.586837	−	0.809705i	$-0.300373\pi$
$419$	11.9883	+	3.89522i	0.585665	+	0.190294i	−0.00117207	+	0.999999i	$0.500373\pi$
$420$	2.70724	+	1.97909i	0.132100	+	0.0965697i
$421$	26.1265	−	8.48900i	1.27333	−	0.413728i	0.407101	−	0.913383i	$-0.366540\pi$
$421$	26.1265	−	8.48900i	1.27333	−	0.413728i	0.866225	+	0.499655i	$0.166540\pi$
$422$	7.09408	−	13.9229i	0.345335	−	0.677757i
$423$	13.6154	−	2.15647i	0.662004	−	0.104851i
$424$		−	3.12823i		−	0.151921i
$425$	3.46280	−	6.69861i	0.167971	−	0.324930i
$426$		−	1.20149i		−	0.0582125i
$427$	0.392861	+	2.48042i	0.0190119	+	0.120036i
$428$	−2.84863	+	5.59075i	−0.137694	+	0.270239i
$429$	−2.00440	+	0.651270i	−0.0967735	+	0.0314436i
$430$	0.142800	+	0.0468624i	0.00688642	+	0.00225991i
$431$	−23.0475	−	7.48860i	−1.11016	−	0.360713i	−0.304156	−	0.952622i	$-0.598374\pi$
$431$	−23.0475	−	7.48860i	−1.11016	−	0.360713i	−0.806005	+	0.591909i	$0.798374\pi$
$432$	2.21274	−	2.21274i	0.106461	−	0.106461i
$433$	−14.0245	+	7.14582i	−0.673973	+	0.343406i	−0.757255	−	0.653120i	$-0.773460\pi$
$433$	−14.0245	+	7.14582i	−0.673973	+	0.343406i	0.0832820	+	0.996526i	$0.473460\pi$
$434$	−3.23376	−	4.45089i	−0.155226	−	0.213650i
$435$	−0.824882	−	5.30892i	−0.0395501	−	0.254543i
$436$	−6.20205	+	8.53638i	−0.297024	+	0.408819i
$437$	19.9846	−	8.15547i	0.955993	−	0.390129i
$438$	−4.30480	+	27.1794i	−0.205691	+	1.29868i
$439$	17.8616	+	12.9772i	0.852490	+	0.619370i	0.925831	−	0.377937i	$-0.123366\pi$
$439$	17.8616	+	12.9772i	0.852490	+	0.619370i	−0.0733416	+	0.997307i	$0.523366\pi$
$440$	−0.229247	−	1.47543i	−0.0109289	−	0.0703383i
$441$	−8.04825	+	5.84740i	−0.383250	+	0.278447i
$442$	−1.99276	+	1.01536i	−0.0947861	+	0.0482959i
$443$	4.34566	−	4.34566i	0.206468	−	0.206468i	−0.596296	−	0.802765i	$-0.703362\pi$
$443$	4.34566	−	4.34566i	0.206468	−	0.206468i	0.802765	+	0.596296i	$0.203362\pi$
$444$	1.03319	+	0.335704i	0.0490330	+	0.0159318i
$445$	−5.12125	+	15.6055i	−0.242770	+	0.739774i
$446$	3.49252	+	10.7489i	0.165376	+	0.508974i
$447$	−13.1325	−	6.69133i	−0.621145	−	0.316489i
$448$	0.695984	−	0.110233i	0.0328821	−	0.00520802i
$449$	19.7113			0.930232			0.465116	−	0.885250i	$-0.346013\pi$
$449$	19.7113			0.930232			0.465116	+	0.885250i	$0.346013\pi$
$450$	−7.54707	−	1.24080i	−0.355772	−	0.0584920i
$451$			6.63521i			0.312440i
$452$	−8.06240	+	1.27696i	−0.379223	+	0.0600631i
$453$	30.8337	+	15.7106i	1.44869	+	0.738147i
$454$	9.00248	−	2.92508i	0.422507	−	0.137281i
$455$	1.37900	−	1.88636i	0.0646485	−	0.0884339i
$456$	2.11839	+	9.03196i	0.0992027	+	0.422960i
$457$	20.6620	+	20.6620i	0.966527	+	0.966527i	0.999458	−	0.0329308i	$-0.0104841\pi$
$457$	20.6620	+	20.6620i	0.966527	+	0.966527i	−0.0329308	+	0.999458i	$0.510484\pi$
$458$	−24.0538	+	12.2560i	−1.12396	+	0.572686i
$459$	−3.81809	+	2.77401i	−0.178213	+	0.129480i
$460$	7.80654	+	7.85251i	0.363982	+	0.366125i
$461$	−20.0570	−	14.5723i	−0.934147	−	0.678697i	0.0128577	−	0.999917i	$-0.495907\pi$
$461$	−20.0570	−	14.5723i	−0.934147	−	0.678697i	−0.947005	+	0.321220i	$0.895907\pi$
$462$	−0.989112	−	0.156660i	−0.0460177	−	0.00728848i
$463$	1.74191	−	10.9980i	0.0809533	−	0.511119i	−0.913577	−	0.406667i	$-0.866691\pi$
$463$	1.74191	−	10.9980i	0.0809533	−	0.511119i	0.994530	−	0.104452i	$-0.0333090\pi$
$464$	−0.913325	−	0.663569i	−0.0424000	−	0.0308054i
$465$	33.0566	+	16.9656i	1.53296	+	0.786760i
$466$	13.9060	+	19.1399i	0.644181	+	0.886640i
$467$	3.42193	−	1.74356i	0.158348	−	0.0806823i	−0.373021	−	0.927823i	$-0.621678\pi$
$467$	3.42193	−	1.74356i	0.158348	−	0.0806823i	0.531369	+	0.847141i	$0.321678\pi$
$468$	1.60405	+	1.60405i	0.0741471	+	0.0741471i
$469$	3.35857	−	10.3366i	0.155084	−	0.477301i
$470$	20.1509	+	0.0591556i	0.929491	+	0.00272864i
$471$	−12.8821	+	4.18565i	−0.593576	+	0.192864i
$472$	−1.16014	+	2.27689i	−0.0533996	+	0.104803i
$473$	−0.0443288	+	0.00702099i	−0.00203824	+	0.000322825i
$474$	−2.62005			−0.120343
$475$	−14.3377	+	16.4144i	−0.657857	+	0.753143i
$476$	−1.06273			−0.0487100
$477$	4.72627	−	0.748568i	0.216401	−	0.0342746i
$478$	9.73746	−	19.1108i	0.445381	−	0.874110i
$479$	6.37798	−	2.07233i	0.291417	−	0.0946873i	−0.159660	−	0.987172i	$-0.551040\pi$
$479$	6.37798	−	2.07233i	0.291417	−	0.0946873i	0.451077	+	0.892485i	$0.351040\pi$
$480$	−3.85833	+	2.78597i	−0.176108	+	0.127162i
$481$	0.233913	−	0.719911i	0.0106655	−	0.0328251i
$482$	6.00329	+	6.00329i	0.273442	+	0.273442i
$483$	6.61700	−	3.37153i	0.301084	−	0.153410i
$484$	−6.20355	−	8.53846i	−0.281980	−	0.388112i
$485$	4.32983	−	26.8275i	0.196608	−	1.21818i
$486$	11.7742	+	8.55443i	0.534087	+	0.388037i
$487$	−0.0837452	+	0.528746i	−0.00379486	+	0.0239598i	−0.989513	−	0.144443i	$-0.953861\pi$
$487$	−0.0837452	+	0.528746i	−0.00379486	+	0.0239598i	0.985718	+	0.168403i	$0.0538609\pi$
$488$	−3.52003	−	0.557519i	−0.159344	−	0.0252377i
$489$	−19.6630	−	14.2860i	−0.889190	−	0.646034i
$490$	−12.9765	+	6.56394i	−0.586218	+	0.296529i
$491$	14.0600	−	10.2152i	0.634520	−	0.461006i	−0.223443	−	0.974717i	$-0.571730\pi$
$491$	14.0600	−	10.2152i	0.634520	−	0.461006i	0.857963	+	0.513711i	$0.171730\pi$
$492$	18.8433	−	9.60112i	0.849520	−	0.432852i
$493$	1.20391	+	1.20391i	0.0542215	+	0.0542215i
$494$	6.29333	−	1.47606i	0.283150	−	0.0664111i
$495$	2.17428	−	0.699418i	0.0977268	−	0.0314365i
$496$	7.42534	−	2.41264i	0.333408	−	0.108331i
$497$	−0.354444	−	0.180598i	−0.0158990	−	0.00810093i
$498$	8.73300	−	1.38317i	0.391335	−	0.0619814i
$499$		−	23.4078i		−	1.04788i	−0.851756	−	0.523939i	$-0.824462\pi$
$499$		−	23.4078i		−	1.04788i	0.851756	−	0.523939i	$-0.175538\pi$
$500$	−10.6023	−	3.54842i	−0.474149	−	0.158690i
$501$	−10.3257			−0.461318
$502$	28.3861	−	4.49592i	1.26693	−	0.200663i
$503$	−7.66692	−	3.90649i	−0.341851	−	0.174182i	0.274633	−	0.961549i	$-0.411444\pi$
$503$	−7.66692	−	3.90649i	−0.341851	−	0.174182i	−0.616484	+	0.787367i	$0.711444\pi$
$504$	0.333090	+	1.02514i	0.0148370	+	0.0456636i
$505$	6.82106	+	21.2047i	0.303533	+	0.943595i
$506$	−3.14476	−	1.02179i	−0.139801	−	0.0454242i
$507$	−16.2545	+	16.2545i	−0.721889	+	0.721889i
$508$	−6.99320	+	3.56321i	−0.310273	+	0.158092i
$509$	−11.4546	+	8.32226i	−0.507716	+	0.368877i	−0.811957	−	0.583718i	$-0.801597\pi$
$509$	−11.4546	+	8.32226i	−0.507716	+	0.368877i	0.304240	+	0.952595i	$0.401597\pi$
$510$	6.40456	−	3.23964i	0.283599	−	0.143454i
$511$	7.37095	+	5.35531i	0.326072	+	0.236905i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	12.6292	−	5.15380i	0.557591	−	0.227546i
$514$	7.07058	−	9.73181i	0.311870	−	0.429252i
$515$	18.8606	+	3.04401i	0.831096	+	0.134135i
$516$	0.0840824	+	0.115729i	0.00370152	+	0.00509471i
$517$	−5.36173	+	2.73194i	−0.235809	+	0.120151i
$518$	0.254334	−	0.254334i	0.0111748	−	0.0111748i
$519$	5.37618	+	1.74683i	0.235988	+	0.0766771i
$520$	1.94122	+	2.68843i	0.0851283	+	0.117895i
$521$	33.3180	−	10.8257i	1.45969	−	0.474282i	0.531715	−	0.846924i	$-0.321548\pi$
$521$	33.3180	−	10.8257i	1.45969	−	0.474282i	0.927975	+	0.372641i	$0.121548\pi$
$522$	0.783996	−	1.53868i	0.0343146	−	0.0673462i
$523$	1.49962	+	9.46824i	0.0655739	+	0.414017i	0.998538	+	0.0540485i	$0.0172126\pi$
$523$	1.49962	+	9.46824i	0.0655739	+	0.414017i	−0.932964	+	0.359969i	$0.882787\pi$
$524$			5.80262i			0.253489i
$525$	−4.44313	+	6.04055i	−0.193914	+	0.263631i
$526$		−	22.7205i		−	0.990662i
$527$	−11.6298	+	1.84198i	−0.506603	+	0.0802380i
$528$	0.645199	−	1.26627i	0.0280787	−	0.0551075i
$529$	1.44638	−	0.469958i	0.0628861	−	0.0204329i
$530$	6.99492	+	0.0205345i	0.303840	+	0.000891961i
$531$	−3.71765	−	1.20794i	−0.161332	−	0.0524200i
$532$	2.98287	+	0.732676i	0.129324	+	0.0317655i
$533$	−6.68991	−	13.1297i	−0.289772	−	0.568710i
$534$	−12.6472	+	9.18875i	−0.547299	+	0.397636i
$535$	−12.4825	−	6.40640i	−0.539667	−	0.276973i
$536$	12.4782	+	9.06592i	0.538975	+	0.391588i
$537$	19.5719	+	3.09989i	0.844591	+	0.133770i
$538$	−2.43595	+	15.3800i	−0.105021	+	0.663078i
$539$	2.55256	−	3.51330i	0.109947	−	0.151328i
$540$	4.93330	+	4.96235i	0.212296	+	0.213546i
$541$	16.4610	−	11.9596i	0.707715	−	0.514185i	−0.174721	−	0.984618i	$-0.555902\pi$
$541$	16.4610	−	11.9596i	0.707715	−	0.514185i	0.882436	+	0.470433i	$0.155902\pi$
$542$	9.02325	+	17.7091i	0.387582	+	0.760672i
$543$	−32.7948	+	32.7948i	−1.40736	+	1.40736i
$544$	0.466042	−	1.43433i	0.0199814	−	0.0614964i
$545$	−19.0471	−	13.9242i	−0.815890	−	0.596446i
$546$	2.11520	−	0.687270i	0.0905221	−	0.0294124i
$547$	−31.6281	−	16.1153i	−1.35232	−	0.689041i	−0.380503	−	0.924780i	$-0.624249\pi$
$547$	−31.6281	−	16.1153i	−1.35232	−	0.689041i	−0.971817	+	0.235738i	$0.924249\pi$
$548$	7.47781	−	1.18437i	0.319436	−	0.0505937i
$549$		−	5.45163i		−	0.232670i
$550$	3.30065	−	0.502924i	0.140740	−	0.0214448i
$551$	−2.54914	−	4.20917i	−0.108597	−	0.179317i
$552$	1.64867	+	10.4093i	0.0701720	+	0.443049i
$553$	−0.393824	+	0.772923i	−0.0167471	+	0.0328680i
$554$	0.337229	+	1.03788i	0.0143275	+	0.0440954i
$555$	−0.757436	+	2.30807i	−0.0321513	+	0.0979721i
$556$	−3.59645	+	11.0687i	−0.152524	+	0.469420i
$557$	−25.5983	−	25.5983i	−1.08463	−	1.08463i	−0.996070	−	0.0885644i	$-0.971772\pi$
$557$	−25.5983	−	25.5983i	−1.08463	−	1.08463i	−0.0885644	−	0.996070i	$-0.528228\pi$
$558$	5.42197	+	10.6412i	0.229530	+	0.450478i
$559$	0.0806385	−	0.0585873i	0.00341065	−	0.00247798i
$560$	0.241919	+	1.55698i	0.0102229	+	0.0657946i
$561$	−1.25982	+	1.73399i	−0.0531896	+	0.0732092i
$562$	−2.81732	−	0.446219i	−0.118841	−	0.0188226i
$563$	−17.8862	−	2.83289i	−0.753813	−	0.119392i	−0.232310	−	0.972642i	$-0.574628\pi$
$563$	−17.8862	−	2.83289i	−0.753813	−	0.119392i	−0.521503	+	0.853249i	$0.674628\pi$
$564$	15.5168	+	11.2736i	0.653375	+	0.474705i
$565$	−2.80243	−	18.0364i	−0.117899	−	0.758796i
$566$	−0.0763993	−	0.105155i	−0.00321130	−	0.00441998i
$567$	7.06283	−	3.59869i	0.296611	−	0.151131i
$568$	0.399183	−	0.399183i	0.0167494	−	0.0167494i
$569$	11.0321	−	33.9535i	0.462492	−	1.42340i	−0.399618	−	0.916682i	$-0.630857\pi$
$569$	11.0321	−	33.9535i	0.462492	−	1.42340i	0.862110	−	0.506721i	$-0.169143\pi$
$570$	−20.2099	+	4.67756i	−0.846499	+	0.195921i
$571$	−6.75873	−	20.8012i	−0.282844	−	0.870504i	−0.987037	−	0.160495i	$-0.948691\pi$
$571$	−6.75873	−	20.8012i	−0.282844	−	0.870504i	0.704193	−	0.710009i	$-0.251309\pi$
$572$	−0.882320	−	0.449564i	−0.0368916	−	0.0187972i
$573$	−5.64620	−	35.6487i	−0.235873	−	1.48925i
$574$		−	7.00198i		−	0.292257i
$575$	−17.6099	+	17.4043i	−0.734384	+	0.725811i
$576$	−1.52968			−0.0637365
$577$	3.31942	+	20.9580i	0.138189	+	0.872492i	0.955220	+	0.295897i	$0.0956187\pi$
$577$	3.31942	+	20.9580i	0.138189	+	0.872492i	−0.817031	+	0.576594i	$0.804381\pi$
$578$	6.68524	−	13.1205i	0.278069	−	0.545742i
$579$	−27.1819	+	8.83192i	−1.12964	+	0.367042i
$580$	1.48977	−	2.03789i	0.0618595	−	0.0846188i
$581$	0.904631	−	2.78417i	0.0375304	−	0.115507i
$582$	18.2894	−	18.2894i	0.758118	−	0.758118i
$583$	−1.86120	+	0.948329i	−0.0770831	+	0.0392758i
$584$	−10.4603	+	7.59986i	−0.432851	+	0.314484i
$585$	−3.59727	+	3.57621i	−0.148729	+	0.147858i
$586$	−12.1970	−	8.86163i	−0.503853	−	0.366071i
$587$	−6.35799	−	1.00701i	−0.262422	−	0.0415636i	0.0238369	−	0.999716i	$-0.492412\pi$
$587$	−6.35799	−	1.00701i	−0.262422	−	0.0415636i	−0.286259	+	0.958152i	$0.592412\pi$
$588$	−13.6709	−	2.16526i	−0.563779	−	0.0892939i
$589$	33.9126	+	2.84785i	1.39734	+	0.117344i
$590$	−5.08365	−	2.60908i	−0.209291	−	0.107414i
$591$	−1.57213	−	2.16385i	−0.0646686	−	0.0890087i
$592$	0.231733	+	0.454801i	0.00952415	+	0.0186922i
$593$	−19.2660	+	19.2660i	−0.791161	+	0.791161i	−0.981683	−	0.190522i	$-0.938982\pi$
$593$	−19.2660	+	19.2660i	−0.791161	+	0.791161i	0.190522	+	0.981683i	$0.438982\pi$
$594$	−1.98731	−	0.645716i	−0.0815403	−	0.0264941i
$595$	0.00697599	−	2.37632i	0.000285988	−	0.0974196i
$596$	−2.14000	−	6.58625i	−0.0876580	−	0.269783i
$597$	22.5678	+	11.4989i	0.923641	+	0.470618i
$598$	7.25303	−	1.14877i	0.296598	−	0.0469766i
$599$	45.1641			1.84535			0.922677	−	0.385574i	$-0.125996\pi$
$599$	45.1641			1.84535			0.922677	+	0.385574i	$0.125996\pi$
$600$	−6.20427	−	8.64575i	−0.253288	−	0.352961i
$601$		−	16.0466i		−	0.654556i	−0.944928	−	0.327278i	$-0.893869\pi$
$601$		−	16.0466i		−	0.654556i	0.944928	−	0.327278i	$-0.106131\pi$
$602$	0.0467791	−	0.00740908i	0.00190657	−	0.000301972i
$603$	−10.7112	+	21.0220i	−0.436195	+	0.856081i
$604$	5.02451	+	15.4639i	0.204444	+	0.629215i
$605$	19.1332	−	13.8155i	0.777875	−	0.561678i
$606$	−6.55155	+	20.1636i	−0.266138	+	0.819090i
$607$	4.25801	−	4.25801i	0.172827	−	0.172827i	−0.615393	−	0.788220i	$-0.711003\pi$
$607$	4.25801	−	4.25801i	0.172827	−	0.172827i	0.788220	+	0.615393i	$0.211003\pi$
$608$	−2.29696	+	3.70459i	−0.0931541	+	0.150241i
$609$	−0.995174	−	1.36974i	−0.0403265	−	0.0555046i
$610$	1.26975	−	7.86734i	0.0514107	−	0.318539i
$611$	7.85528	−	10.8119i	0.317791	−	0.437401i
$612$	2.27857	+	0.360890i	0.0921057	+	0.0145881i
$613$	−1.39254	+	8.79214i	−0.0562441	+	0.355111i	0.943476	+	0.331442i	$0.107535\pi$
$613$	−1.39254	+	8.79214i	−0.0562441	+	0.355111i	−0.999720	+	0.0236697i	$0.992465\pi$
$614$	0.0760771	−	0.104711i	0.00307022	−	0.00422580i
$615$	21.3450	+	42.1977i	0.860713	+	1.70157i
$616$	−0.276574	−	0.380671i	−0.0111435	−	0.0153377i
$617$	−21.5448	+	10.9776i	−0.867360	+	0.441942i	−0.830264	−	0.557370i	$-0.811811\pi$
$617$	−21.5448	+	10.9776i	−0.867360	+	0.441942i	−0.0370956	+	0.999312i	$0.511811\pi$
$618$	12.8580	+	12.8580i	0.517224	+	0.517224i
$619$	2.36719	+	0.769148i	0.0951455	+	0.0309147i	0.356203	−	0.934409i	$-0.384071\pi$
$619$	2.36719	+	0.769148i	0.0951455	+	0.0309147i	−0.261057	+	0.965323i	$0.584071\pi$
$620$	5.34606	+	16.6193i	0.214703	+	0.667449i
$621$	14.7374	−	4.78846i	0.591390	−	0.192154i
$622$	9.09494	+	4.63411i	0.364674	+	0.185811i
$623$	0.809684	+	5.11214i	0.0324393	+	0.204814i
$624$			3.15621i			0.126349i
$625$	8.00408	−	23.6841i	0.320163	−	0.947362i
$626$		−	7.05748i		−	0.282073i
$627$	4.73154	−	3.99843i	0.188959	−	0.159682i
$628$	−5.67058	−	2.88930i	−0.226281	−	0.115296i
$629$	−0.237884	−	0.732132i	−0.00948506	−	0.0291920i
$630$	−2.29447	+	0.738079i	−0.0914139	+	0.0294058i
$631$	10.2853	−	31.6549i	0.409452	−	1.26016i	−0.507668	−	0.861553i	$-0.669492\pi$
$631$	10.2853	−	31.6549i	0.409452	−	1.26016i	0.917120	−	0.398611i	$-0.130508\pi$
$632$	−0.870485	−	0.870485i	−0.0346260	−	0.0346260i
$633$	15.0984	+	29.6322i	0.600106	+	1.17777i
$634$	−7.01214	−	9.65139i	−0.278488	−	0.383306i
$635$	−7.92165	−	15.6606i	−0.314361	−	0.621472i
$636$	5.38630	+	3.91338i	0.213581	+	0.155175i
$637$	−1.50872	+	9.52568i	−0.0597777	+	0.377421i
$638$	−0.117927	+	0.744562i	−0.00466877	+	0.0294775i
$639$	0.698626	+	0.507582i	0.0276372	+	0.0200796i
$640$	−2.20750	−	0.356280i	−0.0872592	−	0.0140832i
$641$	−23.7049	−	32.6270i	−0.936288	−	1.28869i	−0.957356	−	0.288912i	$-0.906706\pi$
$641$	−23.7049	−	32.6270i	−0.936288	−	1.28869i	0.0210675	−	0.999778i	$-0.493294\pi$
$642$	−6.06275	−	11.8988i	−0.239277	−	0.469609i
$643$	28.0302	−	28.0302i	1.10540	−	1.10540i	0.111655	−	0.993747i	$-0.464385\pi$
$643$	28.0302	−	28.0302i	1.10540	−	1.10540i	0.993747	−	0.111655i	$-0.0356153\pi$
$644$	3.31858	+	1.07827i	0.130771	+	0.0424899i
$645$	−0.259330	+	0.187253i	−0.0102111	+	0.00737310i
$646$	4.29551	−	4.97635i	0.169004	−	0.195792i
$647$	−4.51223	+	8.85575i	−0.177394	+	0.348155i	−0.962533	−	0.271164i	$-0.912591\pi$
$647$	−4.51223	+	8.85575i	−0.177394	+	0.348155i	0.785139	+	0.619319i	$0.212591\pi$
$648$	1.75975	+	11.1106i	0.0691295	+	0.436467i
$649$	1.70638			0.0669812
$650$	−6.02422	+	4.32304i	−0.236289	+	0.169564i
$651$	11.7091			0.458915
$652$	−1.78645	−	11.2792i	−0.0699626	−	0.441727i
$653$	−21.7803	−	11.0976i	−0.852330	−	0.434284i	−0.0274712	−	0.999623i	$-0.508745\pi$
$653$	−21.7803	−	11.0976i	−0.852330	−	0.434284i	−0.824859	+	0.565339i	$0.808745\pi$
$654$	−6.93957	−	21.3578i	−0.271358	−	0.835156i
$655$	−12.9750	−	0.0380898i	−0.506975	−	0.00148829i
$656$	9.45035	+	3.07061i	0.368974	+	0.119887i
$657$	−13.9853	−	13.9853i	−0.545618	−	0.545618i
$658$	5.65811	−	2.88295i	0.220576	−	0.112389i
$659$	−14.6498	+	10.6437i	−0.570676	+	0.414620i	−0.835351	−	0.549717i	$-0.814735\pi$
$659$	−14.6498	+	10.6437i	−0.570676	+	0.414620i	0.264675	+	0.964338i	$0.414735\pi$
$660$	2.82723	+	1.45101i	0.110050	+	0.0564806i
$661$	4.70053	−	6.46973i	0.182829	−	0.251643i	−0.707758	−	0.706455i	$-0.750293\pi$
$661$	4.70053	−	6.46973i	0.182829	−	0.251643i	0.890588	+	0.454812i	$0.150293\pi$
$662$	5.92344	+	0.938181i	0.230221	+	0.0364634i
$663$	0.744630	−	4.70141i	0.0289191	−	0.182588i
$664$	3.36099	+	2.44190i	0.130432	+	0.0947643i
$665$	−1.65789	+	6.66507i	−0.0642901	+	0.258460i
$666$	−0.631681	+	0.458943i	−0.0244771	+	0.0177837i
$667$	−2.53794	−	4.98099i	−0.0982695	−	0.192865i
$668$	−3.43061	−	3.43061i	−0.132734	−	0.132734i
$669$	−22.8769	−	7.43315i	−0.884471	−	0.287382i
$670$	−20.3538	+	27.8424i	−0.786337	+	1.07565i
$671$	0.735398	+	2.26332i	0.0283897	+	0.0873746i
$672$	−0.680863	+	1.33627i	−0.0262648	+	0.0515477i
$673$	0.772932	+	4.88010i	0.0297943	+	0.188114i	0.998097	−	0.0616666i	$-0.0196415\pi$
$673$	0.772932	+	4.88010i	0.0297943	+	0.188114i	−0.968302	+	0.249780i	$0.919642\pi$
$674$		−	2.13964i		−	0.0824159i
$675$	−11.1285	+	10.9986i	−0.428336	+	0.423335i
$676$	−10.8008			−0.415416
$677$	19.1237	−	3.02889i	0.734983	−	0.116410i	0.222288	−	0.974981i	$-0.428647\pi$
$677$	19.1237	−	3.02889i	0.734983	−	0.116410i	0.512695	+	0.858571i	$0.328647\pi$
$678$	7.88724	−	15.4796i	0.302907	−	0.594489i
$679$	−2.64631	−	8.14451i	−0.101556	−	0.312558i
$680$	3.20419	+	1.05151i	0.122875	+	0.0403237i
$681$	−6.22546	+	19.1600i	−0.238560	+	0.734213i
$682$	−3.68645	−	3.68645i	−0.141161	−	0.141161i
$683$	17.7789	−	9.05880i	0.680290	−	0.346625i	−0.0794618	−	0.996838i	$-0.525320\pi$
$683$	17.7789	−	9.05880i	0.680290	−	0.346625i	0.759752	+	0.650213i	$0.225320\pi$
$684$	−6.14670	−	2.58386i	−0.235025	−	0.0987965i
$685$	2.59923	+	16.7286i	0.0993115	+	0.639167i
$686$	−5.59297	+	7.69807i	−0.213541	+	0.293914i
$687$	8.98812	−	56.7488i	0.342918	−	2.16510i
$688$	−0.0105144	+	0.0663854i	−0.000400858	+	0.00253092i
$689$	2.72678	−	3.75309i	0.103882	−	0.142981i
$690$	−23.2866	+	3.61819i	−0.886506	+	0.137742i
$691$	37.1198	−	26.9691i	1.41210	−	1.02595i	0.419093	−	0.907944i	$-0.362348\pi$
$691$	37.1198	−	26.9691i	1.41210	−	1.02595i	0.993012	−	0.118011i	$-0.0376517\pi$
$692$	1.20581	+	2.36654i	0.0458382	+	0.0899625i
$693$	0.508952	−	0.508952i	0.0193335	−	0.0193335i
$694$	1.63469	−	5.03106i	0.0620520	−	0.190976i
$695$	−24.7268	−	8.11454i	−0.937939	−	0.307802i
$696$	2.28511	−	0.742478i	0.0866170	−	0.0281436i
$697$	−13.3526	−	6.80348i	−0.505765	−	0.257700i
$698$	2.03046	+	12.8198i	0.0768540	+	0.485237i
$699$	−50.3519			−1.90448
$700$	−3.48309	+	0.530724i	−0.131649	+	0.0200595i
$701$	−5.37116			−0.202866			−0.101433	−	0.994842i	$-0.532343\pi$
$701$	−5.37116			−0.202866			−0.101433	+	0.994842i	$0.532343\pi$
$702$	4.58351	−	0.725957i	0.172994	−	0.0273995i
$703$	0.162942	+	2.21896i	0.00614546	+	0.0836896i
$704$	0.635067	−	0.206346i	0.0239350	−	0.00777695i
$705$	−25.3103	+	34.6225i	−0.953242	+	1.30396i
$706$	18.0467	+	5.86374i	0.679198	+	0.220685i
$707$	4.96355	+	4.96355i	0.186673	+	0.186673i
$708$	−2.46912	−	4.84592i	−0.0927952	−	0.182121i
$709$	−18.0876	−	24.8955i	−0.679294	−	0.934969i	0.320631	−	0.947204i	$-0.396105\pi$
$709$	−18.0876	−	24.8955i	−0.679294	−	0.934969i	−0.999925	+	0.0122357i	$0.996105\pi$
$710$	0.889977	+	0.895218i	0.0334002	+	0.0335969i
$711$	1.10686	−	1.52347i	0.0415107	−	0.0571345i
$712$	−7.25478	−	1.14904i	−0.271884	−	0.0430622i
$713$	38.1854	+	6.04798i	1.43006	+	0.226499i
$714$	1.32946	−	1.82984i	0.0497537	−	0.0684800i
$715$	1.01104	−	1.96997i	0.0378109	−	0.0736726i
$716$	5.47266	+	7.53247i	0.204523	+	0.281502i
$717$	20.7243	+	40.6737i	0.773962	+	1.51899i
$718$	−22.9965	−	22.9965i	−0.858221	−	0.858221i
$719$	−34.1479	−	11.0953i	−1.27350	−	0.413785i	−0.407214	−	0.913333i	$-0.633500\pi$
$719$	−34.1479	−	11.0953i	−1.27350	−	0.413785i	−0.866286	+	0.499548i	$0.833500\pi$
$720$	0.0100412	−	3.42045i	0.000374212	−	0.127473i
$721$	5.72584	−	1.86044i	0.213241	−	0.0692864i
$722$	−15.4875	+	11.0062i	−0.576386	+	0.409609i
$723$	−17.8467	+	2.82664i	−0.663726	+	0.105124i
$724$	−21.7915			−0.809874
$725$	4.54707	+	3.34460i	0.168874	+	0.124215i
$726$	22.4624			0.833656
$727$	7.52151	+	47.4890i	0.278957	+	1.76127i	0.586706	+	0.809800i	$0.300425\pi$
$727$	7.52151	+	47.4890i	0.278957	+	1.76127i	−0.307748	+	0.951468i	$0.599575\pi$
$728$	0.931091	+	0.474414i	0.0345085	+	0.0175830i
$729$	2.63704	−	0.856825i	0.0976680	−	0.0317343i
$730$	−16.9251	−	23.4398i	−0.626425	−	0.867544i
$731$	0.0313240	−	0.0964055i	0.00115856	−	0.00356569i
$732$	5.36347	−	5.36347i	0.198239	−	0.198239i
$733$	−4.65469	−	9.13534i	−0.171925	−	0.337422i	0.788926	−	0.614489i	$-0.210638\pi$
$733$	−4.65469	−	9.13534i	−0.171925	−	0.337422i	−0.960851	+	0.277067i	$0.910638\pi$
$734$	6.02279	−	4.37581i	0.222305	−	0.161514i
$735$	4.93139	−	30.5548i	0.181897	−	1.12703i
$736$	−2.91062	+	4.00613i	−0.107287	+	0.147668i
$737$	1.61116	−	10.1725i	0.0593478	−	0.374707i
$738$	−2.37779	+	15.0128i	−0.0875277	+	0.552628i
$739$	−24.1311	+	33.2137i	−0.887679	+	1.22178i	0.0865558	+	0.996247i	$0.472414\pi$
$739$	−24.1311	+	33.2137i	−0.887679	+	1.22178i	−0.974234	+	0.225538i	$0.927586\pi$
$740$	−1.01848	+	0.515182i	−0.0374402	+	0.0189385i
$741$	−5.33133	+	12.6826i	−0.195851	+	0.465907i
$742$	1.96408	−	1.00075i	0.0721037	−	0.0367386i
$743$	12.7668	+	12.7668i	0.468370	+	0.468370i	0.901386	−	0.433016i	$-0.142551\pi$
$743$	12.7668	+	12.7668i	0.468370	+	0.468370i	−0.433016	+	0.901386i	$0.642551\pi$
$744$	−5.13483	+	15.8034i	−0.188252	+	0.579380i
$745$	14.7413	−	4.74194i	0.540079	−	0.173731i
$746$	−3.75327	−	11.5514i	−0.137417	−	0.422926i
$747$	−2.88507	+	5.66227i	−0.105559	+	0.207172i
$748$	−0.994662	+	0.157539i	−0.0363685	+	0.00576020i
$749$	−4.42148			−0.161557
$750$	19.3731	−	13.8164i	0.707406	−	0.504502i
$751$			14.9246i			0.544608i	0.962211	+	0.272304i	$0.0877856\pi$
$751$			14.9246i			0.544608i	−0.962211	+	0.272304i	$0.912214\pi$
$752$	1.40975	+	8.90084i	0.0514085	+	0.324580i
$753$	−27.7694	+	54.5005i	−1.01197	+	1.98611i
$754$	−0.517347	−	1.59223i	−0.0188407	−	0.0579856i
$755$	−34.6111	+	11.1336i	−1.25963	+	0.405193i
$756$	2.09716	+	0.681409i	0.0762730	+	0.0247826i
$757$	−33.6106	−	33.6106i	−1.22160	−	1.22160i	−0.967063	−	0.254535i	$-0.918078\pi$
$757$	−33.6106	−	33.6106i	−1.22160	−	1.22160i	−0.254535	−	0.967063i	$-0.581922\pi$
$758$	0.930348	+	1.82591i	0.0337918	+	0.0663201i
$759$	5.69340	−	4.13650i	0.206657	−	0.150145i
$760$	−8.26860	−	5.16046i	−0.299933	−	0.187189i
$761$	−21.9705	−	15.9625i	−0.796431	−	0.578641i	0.113434	−	0.993546i	$-0.463815\pi$
$761$	−21.9705	−	15.9625i	−0.796431	−	0.578641i	−0.909865	+	0.414905i	$0.863815\pi$
$762$	2.61313	−	16.4987i	0.0946638	−	0.597684i
$763$	−7.34371	−	1.16313i	−0.265860	−	0.0421081i
$764$	9.96802	−	13.7198i	0.360630	−	0.496365i
$765$	−0.821928	+	5.09265i	−0.0297169	+	0.184125i
$766$	−21.4759	+	15.6031i	−0.775955	+	0.563765i
$767$	−3.37656	+	1.72045i	−0.121921	+	0.0621217i
$768$	−1.50494	−	1.50494i	−0.0543048	−	0.0543048i
$769$	−37.0654	−	12.0433i	−1.33661	−	0.434292i	−0.448446	−	0.893810i	$-0.648022\pi$
$769$	−37.0654	−	12.0433i	−1.33661	−	0.434292i	−0.888169	+	0.459518i	$0.848022\pi$
$770$	0.853018	−	0.615936i	0.0307406	−	0.0221968i
$771$	7.91138	+	24.3487i	0.284921	+	0.876898i
$772$	−11.9652	−	6.09658i	−0.430637	−	0.219421i
$773$	4.48408	+	28.3113i	0.161281	+	1.01829i	0.926986	+	0.375096i	$0.122390\pi$
$773$	4.48408	+	28.3113i	0.161281	+	1.01829i	−0.765705	+	0.643192i	$0.777610\pi$
$774$	−0.102814			−0.00369557
$775$	−37.1969	+	11.8450i	−1.33615	+	0.425485i
$776$	12.1529			0.436264
$777$	0.119753	+	0.756089i	0.00429611	+	0.0271245i
$778$	10.0510	−	19.7263i	0.360347	−	0.707222i
$779$	32.7876	+	28.3018i	1.17474	+	1.01402i
$780$	−7.05747	−	0.0207181i	−0.252698	−	0.000741827i
$781$	−0.358515	−	0.116488i	−0.0128287	−	0.00416828i
$782$	5.28074	−	5.28074i	0.188839	−	0.188839i
$783$	−1.60384	−	3.14771i	−0.0573165	−	0.112490i
$784$	−3.82264	−	5.26141i	−0.136523	−	0.187907i
$785$	6.49788	−	12.6608i	0.231919	−	0.451883i
$786$	−9.99115	−	7.25900i	−0.356373	−	0.258920i
$787$	6.86080	−	43.3174i	0.244561	−	1.54410i	−0.493729	−	0.869616i	$-0.664367\pi$
$787$	6.86080	−	43.3174i	0.244561	−	1.54410i	0.738290	−	0.674483i	$-0.235633\pi$
$788$	0.196593	−	1.24124i	0.00700333	−	0.0442173i
$789$	39.1210	+	28.4230i	1.39274	+	1.01189i
$790$	1.95217	−	1.94074i	0.0694550	−	0.0690484i
$791$	−3.38098	−	4.65352i	−0.120214	−	0.165460i
$792$	0.463724	+	0.910110i	0.0164777	+	0.0323393i
$793$	−3.73718	−	3.73718i	−0.132711	−	0.132711i
$794$	−3.41447	+	10.5086i	−0.121175	+	0.372938i
$795$	−8.78589	+	12.0184i	−0.311604	+	0.426249i
$796$	3.67755	+	11.3183i	0.130347	+	0.401167i
$797$	−15.2307	−	7.76041i	−0.539498	−	0.274888i	0.162936	−	0.986637i	$-0.447903\pi$
$797$	−15.2307	−	7.76041i	−0.539498	−	0.274888i	−0.702434	+	0.711749i	$0.747903\pi$
$798$	−4.99308	+	4.21944i	−0.176753	+	0.149367i
$799$		−	13.5911i		−	0.480818i
$800$	0.811153	−	4.93376i	0.0286786	−	0.174435i
$801$		−	11.2358i		−	0.396997i
$802$	−0.383050	−	2.41848i	−0.0135260	−	0.0853995i
$803$	7.69274	+	3.91965i	0.271471	+	0.138321i
$804$	−31.2200	+	10.1440i	−1.10104	+	0.357751i
$805$	−2.43287	+	7.41347i	−0.0857473	+	0.261290i
$806$	11.0116	+	3.57787i	0.387865	+	0.126025i
$807$	−23.4344	−	23.4344i	−0.824931	−	0.824931i
$808$	−8.87583	+	4.52246i	−0.312250	+	0.159100i
$809$	−6.05846	−	8.33876i	−0.213004	−	0.293175i	0.689124	−	0.724644i	$-0.257996\pi$
$809$	−6.05846	−	8.33876i	−0.213004	−	0.293175i	−0.902128	+	0.431468i	$0.857996\pi$
$810$	−24.8556	+	3.86197i	−0.873335	+	0.135696i
$811$	−18.0065	+	24.7839i	−0.632295	+	0.870280i	−0.998175	−	0.0603822i	$-0.980768\pi$
$811$	−18.0065	+	24.7839i	−0.632295	+	0.870280i	0.365880	+	0.930662i	$0.380768\pi$
$812$	0.124445	−	0.785718i	0.00436718	−	0.0275733i
$813$	−41.7801	−	6.61733i	−1.46529	−	0.232080i
$814$	0.200342	−	0.275747i	0.00702199	−	0.00966493i
$815$	25.2326	−	3.92056i	0.883860	−	0.137331i
$816$	1.88667	+	2.59677i	0.0660465	+	0.0909052i
$817$	−0.154385	+	0.248996i	−0.00540126	+	0.00871127i
$818$	12.3649	−	12.3649i	0.432328	−	0.432328i
$819$	−0.493962	+	1.52026i	−0.0172604	+	0.0531221i
$820$	−6.92809	+	21.1114i	−0.241939	+	0.737242i
$821$	−9.22420	−	28.3892i	−0.321927	−	0.990789i	−0.972809	−	0.231610i	$-0.925601\pi$
$821$	−9.22420	−	28.3892i	−0.321927	−	0.990789i	0.650882	−	0.759179i	$-0.274399\pi$
$822$	−7.31534	+	14.3572i	−0.255152	+	0.500764i
$823$	33.9855	−	5.38278i	1.18466	−	0.187632i	0.467150	−	0.884178i	$-0.345281\pi$
$823$	33.9855	−	5.38278i	1.18466	−	0.187632i	0.717512	+	0.696546i	$0.245281\pi$
$824$			8.54386i			0.297639i
$825$	−3.26311	+	6.31232i	−0.113607	+	0.219767i
$826$	−1.80070			−0.0626543
$827$	−18.8790	+	2.99014i	−0.656486	+	0.103977i	−0.475786	−	0.879561i	$-0.657836\pi$
$827$	−18.8790	+	2.99014i	−0.656486	+	0.103977i	−0.180700	+	0.983538i	$0.557836\pi$
$828$	−6.74913	−	3.43886i	−0.234549	−	0.119508i
$829$	−7.76856	−	23.9092i	−0.269813	−	0.830399i	−0.990545	−	0.137186i	$-0.956194\pi$
$829$	−7.76856	−	23.9092i	−0.269813	−	0.830399i	0.720732	−	0.693214i	$-0.243806\pi$
$830$	−5.48230	+	7.49935i	−0.190294	+	0.260306i
$831$	−2.20893	−	0.717725i	−0.0766269	−	0.0248976i
$832$	−1.04862	+	1.04862i	−0.0363543	+	0.0363543i
$833$	4.45280	+	8.73912i	0.154281	+	0.302793i
$834$	−14.5594	−	20.0393i	−0.504152	−	0.693906i
$835$	7.69356	−	7.64852i	0.266247	−	0.264688i
$836$	2.90044	+	0.243568i	0.100314	+	0.00842398i
$837$	24.1311	+	3.82199i	0.834092	+	0.132107i
$838$	−12.4500	−	1.97189i	−0.430078	−	0.0681177i
$839$	−7.07392	−	5.13951i	−0.244219	−	0.177435i	0.458942	−	0.888466i	$-0.348229\pi$
$839$	−7.07392	−	5.13951i	−0.244219	−	0.177435i	−0.703161	+	0.711031i	$0.748229\pi$
$840$	−2.98350	−	1.53122i	−0.102941	−	0.0528321i
$841$	22.4304	−	16.2966i	0.773462	−	0.561953i
$842$	−24.4768	+	12.4716i	−0.843527	+	0.429798i
$843$	4.29274	−	4.29274i	0.147850	−	0.147850i
$844$	−4.82872	+	14.8613i	−0.166211	+	0.511546i
$845$	0.0708991	−	24.1512i	0.00243900	−	0.830827i
$846$	−13.1104	+	4.25984i	−0.450746	+	0.146456i
$847$	3.37635	−	6.62646i	0.116013	−	0.227688i
$848$	0.489364	+	3.08972i	0.0168048	+	0.106101i
$849$	0.276633			0.00949403
$850$	−2.37228	+	7.15784i	−0.0813684	+	0.245512i
$851$			2.52760i			0.0866449i
$852$	0.187955	+	1.18670i	0.00643923	+	0.0406557i
$853$	26.3529	+	13.4275i	0.902305	+	0.459747i	0.842644	−	0.538471i	$-0.180998\pi$
$853$	26.3529	+	13.4275i	0.902305	+	0.459747i	0.0596612	+	0.998219i	$0.480998\pi$
$854$	−0.776048	−	2.38843i	−0.0265558	−	0.0817304i
$855$	5.81802	−	13.7274i	0.198972	−	0.469468i
$856$	1.93897	−	5.96754i	0.0662727	−	0.203966i
$857$	−29.0167	+	29.0167i	−0.991193	+	0.991193i	−0.999962	−	0.00876876i	$-0.997209\pi$
$857$	−29.0167	+	29.0167i	−0.991193	+	0.991193i	0.00876876	+	0.999962i	$0.497209\pi$
$858$	1.87784	−	0.956810i	0.0641086	−	0.0326649i
$859$	−16.0975	−	22.1563i	−0.549240	−	0.755963i	0.440669	−	0.897670i	$-0.354741\pi$
$859$	−16.0975	−	22.1563i	−0.549240	−	0.755963i	−0.989909	+	0.141706i	$0.954741\pi$
$860$	−0.148373	−	0.0239466i	−0.00505947	−	0.000816573i
$861$	12.0562	+	8.75937i	0.410876	+	0.298519i
$862$	23.9353	+	3.79097i	0.815238	+	0.129121i
$863$	35.5663	+	5.63314i	1.21069	+	0.191754i	0.728954	−	0.684562i	$-0.240007\pi$
$863$	35.5663	+	5.63314i	1.21069	+	0.191754i	0.481735	+	0.876317i	$0.340007\pi$
$864$	−1.83935	+	2.53165i	−0.0625761	+	0.0861285i
$865$	−5.29964	+	2.68074i	−0.180193	+	0.0911478i
$866$	12.7339	−	9.25175i	0.432717	−	0.314387i
$867$	14.2282	+	27.9245i	0.483216	+	0.948364i
$868$	3.89022	+	3.89022i	0.132043	+	0.132043i
$869$	−0.254022	+	0.781800i	−0.00861711	+	0.0265207i
$870$	1.64522	+	5.11452i	0.0557783	+	0.173398i
$871$	7.06818	+	21.7536i	0.239496	+	0.737093i
$872$	4.79030	−	9.40150i	0.162220	−	0.318375i
$873$	2.90812	+	18.3611i	0.0984249	+	0.621430i
$874$	−18.4627	+	11.1813i	−0.624512	+	0.378214i
$875$	−1.16387	−	7.79188i	−0.0393459	−	0.263414i
$876$		−	27.5182i		−	0.929755i
$877$	33.1556	−	5.25132i	1.11958	−	0.177325i	0.430909	−	0.902395i	$-0.358193\pi$
$877$	33.1556	−	5.25132i	1.11958	−	0.177325i	0.688674	+	0.725071i	$0.258193\pi$
$878$	−19.6718	−	10.0233i	−0.663892	−	0.338270i
$879$	30.5165	−	9.91541i	1.02930	−	0.334439i
$880$	0.457232	+	1.42140i	0.0154133	+	0.0479154i
$881$	4.66122	−	14.3458i	0.157040	−	0.483321i	−0.841321	−	0.540535i	$-0.818222\pi$
$881$	4.66122	−	14.3458i	0.157040	−	0.483321i	0.998362	+	0.0572143i	$0.0182218\pi$
$882$	7.03443	−	7.03443i	0.236862	−	0.236862i
$883$	11.2773	+	22.1329i	0.379510	+	0.744831i	0.999199	−	0.0400169i	$-0.0127412\pi$
$883$	11.2773	+	22.1329i	0.379510	+	0.744831i	−0.619689	+	0.784848i	$0.712741\pi$
$884$	1.80939	−	1.31460i	0.0608564	−	0.0442148i
$885$	10.8520	−	5.48929i	0.364785	−	0.184520i
$886$	−3.61234	+	4.97196i	−0.121359	+	0.167036i
$887$	−8.70131	+	54.9379i	−0.292161	+	1.84463i	0.207274	+	0.978283i	$0.433541\pi$
$887$	−8.70131	+	54.9379i	−0.292161	+	1.84463i	−0.499435	+	0.866351i	$0.666459\pi$
$888$	−1.07299	−	0.169944i	−0.0360070	−	0.00570295i
$889$	−4.47437	−	3.25082i	−0.150066	−	0.109029i
$890$	2.61695	−	16.2146i	0.0877204	−	0.543513i
$891$	6.07700	−	4.41520i	0.203587	−	0.147915i
$892$	−5.13102	−	10.0702i	−0.171799	−	0.337175i
$893$	−9.37010	+	38.1476i	−0.313558	+	1.27656i
$894$	14.0175	+	4.55458i	0.468817	+	0.152328i
$895$	−16.8790	+	12.1877i	−0.564202	+	0.407391i
$896$	−0.670171	+	0.217752i	−0.0223888	+	0.00727457i
$897$	−7.09545	+	13.9256i	−0.236910	+	0.464962i
$898$	−19.4686	+	3.08352i	−0.649675	+	0.102898i
$899$		−	8.81410i		−	0.293967i
$900$	7.64825	+	0.0449053i	0.254942	+	0.00149684i
$901$		−	4.71783i		−	0.157174i
$902$	−1.03798	−	6.55352i	−0.0345608	−	0.218208i
$903$	−0.0457628	+	0.0898145i	−0.00152289	+	0.00298884i
$904$	7.76338	−	2.52247i	0.258206	−	0.0838963i
$905$	0.143045	−	48.7270i	0.00475496	−	1.61974i
$906$	−32.9118	−	10.6937i	−1.09342	−	0.355274i
$907$	28.3747	−	28.3747i	0.942165	−	0.942165i	−0.0562514	−	0.998417i	$-0.517915\pi$
$907$	28.3747	−	28.3747i	0.942165	−	0.942165i	0.998417	+	0.0562514i	$0.0179148\pi$
$908$	−8.43406	+	4.29737i	−0.279894	+	0.142613i
$909$	−8.95667	−	12.3278i	−0.297074	−	0.408887i
$910$	−1.06693	+	2.07886i	−0.0353684	+	0.0689135i
$911$	−9.80470	+	13.4950i	−0.324844	+	0.447110i	−0.939938	−	0.341344i	$-0.889118\pi$
$911$	−9.80470	+	13.4950i	−0.324844	+	0.447110i	0.615094	+	0.788454i	$0.289118\pi$
$912$	−3.50522	−	8.58937i	−0.116069	−	0.284423i
$913$	0.433966	−	2.73995i	0.0143622	−	0.0906792i
$914$	−23.6398	−	17.1754i	−0.781937	−	0.568110i
$915$	11.9578	+	12.0282i	0.395313	+	0.397641i
$916$	21.8404	−	15.8680i	0.721627	−	0.524293i
$917$	−3.64321	+	1.85631i	−0.120309	+	0.0613007i
$918$	3.33714	−	3.33714i	0.110142	−	0.110142i
$919$	33.1785	+	10.7804i	1.09446	+	0.355611i	0.799967	−	0.600043i	$-0.204850\pi$
$919$	33.1785	+	10.7804i	1.09446	+	0.355611i	0.294491	+	0.955654i	$0.404850\pi$
$920$	−8.93884	−	6.53462i	−0.294705	−	0.215440i
$921$	0.0851239	+	0.261984i	0.00280493	+	0.00863268i
$922$	22.0897	+	11.2552i	0.727484	+	0.370672i
$923$	0.826874	−	0.130964i	0.0272169	−	0.00431073i
$924$	1.00144			0.0329450
$925$	−1.14529	−	2.28077i	−0.0376570	−	0.0749912i
$926$			11.1351i			0.365921i
$927$	−12.9084	+	2.04450i	−0.423969	+	0.0671500i
$928$	1.00589	+	0.512524i	0.0330198	+	0.0168244i
$929$	6.26849	−	2.03676i	0.205663	−	0.0668238i	−0.204374	−	0.978893i	$-0.565516\pi$
$929$	6.26849	−	2.03676i	0.205663	−	0.0668238i	0.410037	+	0.912069i	$0.365516\pi$
$930$	−35.3036	−	11.5855i	−1.15765	−	0.379904i
$931$	−6.47316	−	27.5989i	−0.212149	−	0.904519i
$932$	−16.7289	−	16.7289i	−0.547973	−	0.547973i
$933$	−19.3568	+	9.86278i	−0.633713	+	0.322893i
$934$	−3.10705	+	2.25740i	−0.101666	+	0.0738644i
$935$	−0.345737	−	2.22516i	−0.0113068	−	0.0727704i
$936$	−1.83523	−	1.33337i	−0.0599862	−	0.0435825i
$937$	27.3415	+	4.33047i	0.893208	+	0.141470i	0.586133	−	0.810215i	$-0.300650\pi$
$937$	27.3415	+	4.33047i	0.893208	+	0.141470i	0.307075	+	0.951685i	$0.400650\pi$
$938$	−1.70022	+	10.7348i	−0.0555141	+	0.350502i
$939$	12.1518	+	8.82880i	0.396559	+	0.288117i
$940$	−19.9121	+	3.09387i	−0.649460	+	0.100911i
$941$	−29.3148	−	40.3484i	−0.955636	−	1.31532i	−0.948978	−	0.315342i	$-0.897881\pi$
$941$	−29.3148	−	40.3484i	−0.955636	−	1.31532i	−0.00665740	−	0.999978i	$-0.502119\pi$
$942$	12.0687	−	6.14932i	0.393220	−	0.200356i
$943$	34.7932	+	34.7932i	1.13302	+	1.13302i
$944$	0.789668	−	2.43035i	0.0257015	−	0.0791011i
$945$	−1.53744	+	4.68490i	−0.0500128	+	0.152400i
$946$	0.0426847	−	0.0138691i	0.00138780	−	0.000450923i
$947$	−14.3439	+	28.1514i	−0.466113	+	0.914797i	0.531587	+	0.847004i	$0.321596\pi$
$947$	−14.3439	+	28.1514i	−0.466113	+	0.914797i	−0.997699	+	0.0677936i	$0.978404\pi$
$948$	2.58779	−	0.409866i	0.0840476	−	0.0133118i
$949$	−19.1743			−0.622423
$950$	11.5934	−	18.4552i	0.376138	−	0.598765i
$951$	25.3902			0.823333
$952$	1.04964	−	0.166247i	0.0340191	−	0.00538810i
$953$	−8.89014	+	17.4479i	−0.287980	+	0.565192i	−0.988994	−	0.147955i	$-0.952731\pi$
$953$	−8.89014	+	17.4479i	−0.287980	+	0.565192i	0.701014	+	0.713147i	$0.252731\pi$
$954$	−4.55098	+	1.47870i	−0.147344	+	0.0478748i
$955$	30.6128	+	22.3791i	0.990608	+	0.724172i
$956$	−6.62798	+	20.3988i	−0.214364	+	0.659746i
$957$	−1.13449	−	1.13449i	−0.0366727	−	0.0366727i
$958$	−5.97527	+	3.04455i	−0.193052	+	0.0983651i
$959$	3.13583	+	4.31610i	0.101261	+	0.139374i
$960$	3.37501	−	3.35525i	0.108928	−	0.108290i
$961$	24.2354	+	17.6080i	0.781786	+	0.568001i
$962$	−0.118414	+	0.747640i	−0.00381784	+	0.0241049i
$963$	9.48001	+	1.50149i	0.305489	+	0.0483847i
$964$	−6.86850	−	4.99026i	−0.221219	−	0.160725i
$965$	13.7108	−	26.7149i	0.441368	−	0.859982i
$966$	−6.00811	+	4.36515i	−0.193308	+	0.140446i
$967$	−23.3012	+	11.8725i	−0.749315	+	0.381795i	−0.786562	−	0.617511i	$-0.788141\pi$
$967$	−23.3012	+	11.8725i	−0.749315	+	0.381795i	0.0372475	+	0.999306i	$0.488141\pi$
$968$	7.46288	+	7.46288i	0.239866	+	0.239866i
$969$	3.19484	+	13.6215i	0.102633	+	0.437585i
$970$	−0.0797745	+	27.1746i	−0.00256141	+	0.872523i
$971$	7.25050	−	2.35583i	0.232680	−	0.0756022i	−0.190356	−	0.981715i	$-0.560964\pi$
$971$	7.25050	−	2.35583i	0.232680	−	0.0756022i	0.423036	+	0.906113i	$0.360964\pi$
$972$	−12.9674	−	6.60722i	−0.415930	−	0.211927i
$973$	−8.10012	+	1.28293i	−0.259678	+	0.0411289i
$974$		−	0.535337i		−	0.0171533i
$975$	0.0926538	−	15.7808i	0.00296730	−	0.505389i
$976$	3.56391			0.114078
$977$	47.7031	−	7.55543i	1.52616	−	0.241719i	0.663757	−	0.747948i	$-0.268961\pi$
$977$	47.7031	−	7.55543i	1.52616	−	0.241719i	0.862399	+	0.506228i	$0.168961\pi$
$978$	21.6557	+	11.0341i	0.692473	+	0.352832i
$979$	1.51565	+	4.66470i	0.0484404	+	0.149084i
$980$	11.7899	−	8.51310i	0.376615	−	0.271941i
$981$	15.3505	+	4.98768i	0.490104	+	0.159244i
$982$	−12.2889	+	12.2889i	−0.392155	+	0.392155i
$983$	−26.7256	+	13.6174i	−0.852414	+	0.434327i	−0.824889	−	0.565294i	$-0.808763\pi$
$983$	−26.7256	+	13.6174i	−0.852414	+	0.434327i	−0.0275251	+	0.999621i	$0.508763\pi$
$984$	−17.1093	+	12.4307i	−0.545425	+	0.396275i
$985$	2.77419	+	0.447741i	0.0883930	+	0.0142662i
$986$	−1.37742	−	1.00076i	−0.0438661	−	0.0318706i
$987$	−2.11425	+	13.3488i	−0.0672973	+	0.424898i
$988$	−5.98494	+	2.44238i	−0.190406	+	0.0777025i
$989$	−0.195632	+	0.269264i	−0.00622072	+	0.00856209i
$990$	−2.03810	+	1.03094i	−0.0647751	+	0.0327654i
$991$	31.7078	+	43.6420i	1.00723	+	1.38633i	0.920782	+	0.390078i	$0.127552\pi$
$991$	31.7078	+	43.6420i	1.00723	+	1.38633i	0.0864487	+	0.996256i	$0.472448\pi$
$992$	−6.95650	+	3.54452i	−0.220869	+	0.112539i
$993$	−9.02553	+	9.02553i	−0.286416	+	0.286416i
$994$	0.378332	+	0.122927i	0.0120000	+	0.00389902i
$995$	−25.3326	+	8.14891i	−0.803096	+	0.258338i
$996$	−8.40911	+	2.73229i	−0.266453	+	0.0865758i
$997$	5.50989	−	10.8138i	0.174500	−	0.342475i	−0.787147	−	0.616765i	$-0.788443\pi$
$997$	5.50989	−	10.8138i	0.174500	−	0.342475i	0.961647	+	0.274290i	$0.0884428\pi$
$998$	3.66179	+	23.1196i	0.115912	+	0.731839i
$999$			1.59730i			0.0505364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.20	✓	400
19.18	odd	2	inner	950.2.w.a.37.31	yes	400
25.23	odd	20	inner	950.2.w.a.873.31	yes	400
475.398	even	20	inner	950.2.w.a.873.20	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.20	✓	400	1.1	even	1	trivial
950.2.w.a.37.31	yes	400	19.18	odd	2	inner
950.2.w.a.873.20	yes	400	475.398	even	20	inner
950.2.w.a.873.31	yes	400	25.23	odd	20	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.966230 - 1.89633i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.684737 + 2.12865i) q^{5} +(-0.657682 + 2.02414i) q^{6} +(0.498269 + 0.498269i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.899122 - 1.23753i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.966230 - 1.89633i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.684737 + 2.12865i) q^{5} +(-0.657682 + 2.02414i) q^{6} +(0.498269 + 0.498269i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.899122 - 1.23753i) q^{9} +(-1.00930 - 1.99532i) q^{10} +(0.540220 + 0.392493i) q^{11} +(0.332940 - 2.10210i) q^{12} +(-1.46471 - 0.231987i) q^{13} +(-0.570081 - 0.414188i) q^{14} +(4.69823 + 0.758272i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.34377 + 0.684683i) q^{17} +(1.08165 + 1.08165i) q^{18} +(4.24374 - 0.995342i) q^{19} +(1.30901 + 1.81287i) q^{20} +(1.42633 - 0.463442i) q^{21} +(-0.594968 - 0.303152i) q^{22} +(4.89088 - 0.774640i) q^{23} +2.12830i q^{24} +(-4.06227 + 2.91513i) q^{25} +1.48297 q^{26} +(3.09077 - 0.489529i) q^{27} +(0.627856 + 0.319909i) q^{28} +(-0.348859 - 1.07368i) q^{29} +(-4.75901 - 0.0139707i) q^{30} +(7.42534 + 2.41264i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.26627 - 0.645199i) q^{33} +(1.22011 - 0.886465i) q^{34} +(-0.719456 + 1.40182i) q^{35} +(-1.23753 - 0.899122i) q^{36} +(-0.0798496 + 0.504151i) q^{37} +(-4.03578 + 1.64695i) q^{38} +(-1.85517 + 2.55343i) q^{39} +(-1.57649 - 1.58577i) q^{40} +(5.84064 + 8.03895i) q^{41} +(-1.33627 + 0.680863i) q^{42} +(-0.0475267 + 0.0475267i) q^{43} +(0.635067 + 0.206346i) q^{44} +(2.01861 - 2.76130i) q^{45} +(-4.70949 + 1.53021i) q^{46} +(-4.09127 + 8.02956i) q^{47} +(-0.332940 - 2.10210i) q^{48} -6.50346i q^{49} +(3.55623 - 3.51472i) q^{50} +3.20979i q^{51} +(-1.46471 + 0.231987i) q^{52} +(-1.42019 + 2.78728i) q^{53} +(-2.97614 + 0.967005i) q^{54} +(-0.465570 + 1.41869i) q^{55} +(-0.670171 - 0.217752i) q^{56} +(2.21292 - 9.00926i) q^{57} +(0.512524 + 1.00589i) q^{58} +(2.06738 - 1.50204i) q^{59} +(4.70261 - 0.730675i) q^{60} +(2.88327 + 2.09481i) q^{61} +(-7.71135 - 1.22136i) q^{62} +(0.168621 - 1.06463i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.509123 - 3.27670i) q^{65} +(-1.14975 + 0.835344i) q^{66} +(-7.00229 - 13.7428i) q^{67} +(-1.06642 + 1.06642i) q^{68} +(3.25674 - 10.0232i) q^{69} +(0.491305 - 1.49711i) q^{70} +(-0.536900 + 0.174450i) q^{71} +(1.36295 + 0.694459i) q^{72} +(12.7705 - 2.02264i) q^{73} -0.510435i q^{74} +(1.60296 + 10.5201i) q^{75} +(3.72846 - 2.25801i) q^{76} +(0.0736079 + 0.464742i) q^{77} +(1.43289 - 2.81220i) q^{78} +(0.380416 + 1.17080i) q^{79} +(1.80515 + 1.31963i) q^{80} +(3.47617 - 10.6985i) q^{81} +(-7.02630 - 7.02630i) q^{82} +(-1.88607 - 3.70161i) q^{83} +(1.21331 - 0.881518i) q^{84} +(-2.37757 - 2.39157i) q^{85} +(0.0395068 - 0.0543764i) q^{86} +(-2.37313 - 0.375867i) q^{87} +(-0.659528 - 0.104459i) q^{88} +(5.94240 + 4.31740i) q^{89} +(-1.56180 + 3.04308i) q^{90} +(-0.614228 - 0.845413i) q^{91} +(4.41213 - 2.24809i) q^{92} +(11.7498 - 11.7498i) q^{93} +(2.78480 - 8.57072i) q^{94} +(5.02457 + 8.35187i) q^{95} +(0.657682 + 2.02414i) q^{96} +(-10.8283 - 5.51730i) q^{97} +(1.01736 + 6.42339i) q^{98} -1.02144i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

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Database

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