LMFDB - Embedded newform 296.2.q.a.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [296,2,Mod(85,296)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(296, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("296.85"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 296 = 2^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	296.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.36357189983$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	296.101
Dual form			296.2.q.a.85.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39280 + 0.245152i) q^{2} +(-0.0574215 + 0.0331523i) q^{3} +(1.87980 - 0.682898i) q^{4} +(-0.0588225 - 0.101884i) q^{5} +(0.0718494 - 0.0602516i) q^{6} +(1.40284 + 2.42979i) q^{7} +(-2.45078 + 1.41198i) q^{8} +(-1.49780 + 2.59427i) q^{9} +(0.106905 + 0.127483i) q^{10} -1.77206i q^{11} +(-0.0853013 + 0.101533i) q^{12} +(-0.666698 - 1.15475i) q^{13} +(-2.54954 - 3.04030i) q^{14} +(0.00675535 + 0.00390021i) q^{15} +(3.06730 - 2.56742i) q^{16} +(3.86149 + 2.22943i) q^{17} +(1.45015 - 3.98050i) q^{18} +(3.11573 + 5.39660i) q^{19} +(-0.180151 - 0.151351i) q^{20} +(-0.161106 - 0.0930146i) q^{21} +(0.434426 + 2.46814i) q^{22} +6.03806i q^{23} +(0.0939168 - 0.162327i) q^{24} +(2.49308 - 4.31814i) q^{25} +(1.21167 + 1.44490i) q^{26} -0.397536i q^{27} +(4.29635 + 3.60952i) q^{28} -8.43088 q^{29} +(-0.0103650 - 0.00377613i) q^{30} +7.13978i q^{31} +(-3.64273 + 4.32787i) q^{32} +(0.0587480 + 0.101754i) q^{33} +(-5.92485 - 2.15851i) q^{34} +(0.165037 - 0.285852i) q^{35} +(-1.04395 + 5.89955i) q^{36} +(2.72190 + 5.43979i) q^{37} +(-5.66258 - 6.75257i) q^{38} +(0.0765655 + 0.0442051i) q^{39} +(0.288019 + 0.166638i) q^{40} +(-2.42678 - 4.20331i) q^{41} +(0.247192 + 0.0900555i) q^{42} +11.6336 q^{43} +(-1.21014 - 3.33113i) q^{44} +0.352418 q^{45} +(-1.48024 - 8.40982i) q^{46} +6.45491 q^{47} +(-0.0910128 + 0.249113i) q^{48} +(-0.435906 + 0.755012i) q^{49} +(-2.41377 + 6.62550i) q^{50} -0.295643 q^{51} +(-2.04184 - 1.71542i) q^{52} +(-2.82675 - 1.63202i) q^{53} +(0.0974570 + 0.553689i) q^{54} +(-0.180544 + 0.104237i) q^{55} +(-6.86885 - 3.97409i) q^{56} +(-0.357819 - 0.206587i) q^{57} +(11.7426 - 2.06685i) q^{58} +(5.06132 - 8.76647i) q^{59} +(0.0153622 + 0.00271839i) q^{60} +(-4.77411 - 8.26900i) q^{61} +(-1.75033 - 9.94431i) q^{62} -8.40469 q^{63} +(4.01262 - 6.92090i) q^{64} +(-0.0784337 + 0.135851i) q^{65} +(-0.106770 - 0.127322i) q^{66} +(-6.61343 + 3.81827i) q^{67} +(8.78131 + 1.55388i) q^{68} +(-0.200175 - 0.346714i) q^{69} +(-0.159787 + 0.438595i) q^{70} +(-4.84512 - 8.39199i) q^{71} +(0.00772217 - 8.47284i) q^{72} -5.41038 q^{73} +(-5.12464 - 6.90927i) q^{74} +0.330605i q^{75} +(9.54227 + 8.01680i) q^{76} +(4.30573 - 2.48592i) q^{77} +(-0.117478 - 0.0427988i) q^{78} +(-5.20265 + 3.00375i) q^{79} +(-0.442005 - 0.161485i) q^{80} +(-4.48023 - 7.75998i) q^{81} +(4.41048 + 5.25945i) q^{82} +(0.309739 + 0.178828i) q^{83} +(-0.366367 - 0.0648299i) q^{84} -0.524564i q^{85} +(-16.2033 + 2.85200i) q^{86} +(0.484113 - 0.279503i) q^{87} +(2.50212 + 4.34293i) q^{88} +(3.23848 + 1.86974i) q^{89} +(-0.490849 + 0.0863962i) q^{90} +(1.87054 - 3.23987i) q^{91} +(4.12338 + 11.3503i) q^{92} +(-0.236700 - 0.409977i) q^{93} +(-8.99042 + 1.58244i) q^{94} +(0.366550 - 0.634883i) q^{95} +(0.0656922 - 0.369278i) q^{96} -15.7030i q^{97} +(0.422038 - 1.15845i) q^{98} +(4.59721 + 2.65420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 6 q^{2} - 2 q^{4} + 2 q^{7} + 30 q^{9} - 12 q^{12} - 6 q^{15} - 6 q^{16} - 12 q^{17} - 48 q^{18} + 18 q^{20} - 12 q^{22} - 6 q^{24} - 32 q^{25} - 16 q^{26} + 10 q^{28} - 14 q^{30} - 6 q^{32} + 4 q^{33}+ \cdots + 48 q^{98}+O(q^{100}) $ 72 * q - 6 * q^2 - 2 * q^4 + 2 * q^7 + 30 * q^9 - 12 * q^12 - 6 * q^15 - 6 * q^16 - 12 * q^17 - 48 * q^18 + 18 * q^20 - 12 * q^22 - 6 * q^24 - 32 * q^25 - 16 * q^26 + 10 * q^28 - 14 * q^30 - 6 * q^32 + 4 * q^33 + 8 * q^34 + 4 * q^36 - 24 * q^38 - 6 * q^39 - 18 * q^40 + 6 * q^42 - 10 * q^44 - 8 * q^46 + 32 * q^47 + 20 * q^48 - 18 * q^49 + 12 * q^50 + 42 * q^52 + 30 * q^54 + 24 * q^55 - 24 * q^56 - 6 * q^57 - 8 * q^58 + 32 * q^62 + 8 * q^63 - 68 * q^64 + 6 * q^65 + 20 * q^70 + 18 * q^71 + 18 * q^72 - 64 * q^73 - 12 * q^74 - 72 * q^76 + 54 * q^78 + 54 * q^79 - 16 * q^81 - 12 * q^84 + 48 * q^86 - 108 * q^87 - 36 * q^89 + 24 * q^90 - 120 * q^92 - 72 * q^94 + 50 * q^95 + 36 * q^96 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/296\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−1.39280	+	0.245152i	−0.984860	+	0.173349i
$2$	−1.39280	+	0.245152i	−0.984860	+	0.173349i
$3$	−0.0574215	+	0.0331523i	−0.0331523	+	0.0191405i	−0.516485	−	0.856297i	$-0.672760\pi$
$3$	−0.0574215	+	0.0331523i	−0.0331523	+	0.0191405i	0.483332	+	0.875437i	$0.339426\pi$
$4$	1.87980	−	0.682898i	0.939900	−	0.341449i
$5$	−0.0588225	−	0.101884i	−0.0263062	−	0.0455638i	0.852573	−	0.522609i	$-0.175041\pi$
$5$	−0.0588225	−	0.101884i	−0.0263062	−	0.0455638i	−0.878879	+	0.477045i	$0.841708\pi$
$6$	0.0718494	−	0.0602516i	0.0293324	−	0.0245976i
$7$	1.40284	+	2.42979i	0.530223	+	0.918373i	0.999378	+	0.0352572i	$0.0112250\pi$
$7$	1.40284	+	2.42979i	0.530223	+	0.918373i	−0.469156	+	0.883116i	$0.655442\pi$
$8$	−2.45078	+	1.41198i	−0.866481	+	0.499210i
$9$	−1.49780	+	2.59427i	−0.499267	+	0.864756i
$10$	0.106905	+	0.127483i	0.0338064	+	0.0403138i
$11$		−	1.77206i		−	0.534297i	−0.963655	−	0.267149i	$-0.913919\pi$
$11$		−	1.77206i		−	0.534297i	0.963655	−	0.267149i	$-0.0860815\pi$
$12$	−0.0853013	+	0.101533i	−0.0246244	+	0.0293100i
$13$	−0.666698	−	1.15475i	−0.184909	−	0.320271i	0.758637	−	0.651513i	$-0.225866\pi$
$13$	−0.666698	−	1.15475i	−0.184909	−	0.320271i	−0.943546	+	0.331242i	$0.892532\pi$
$14$	−2.54954	−	3.04030i	−0.681394	−	0.812555i
$15$	0.00675535	+	0.00390021i	0.00174422	+	0.00100703i
$16$	3.06730	−	2.56742i	0.766825	−	0.641856i
$17$	3.86149	+	2.22943i	0.936549	+	0.540717i	0.888877	−	0.458146i	$-0.151486\pi$
$17$	3.86149	+	2.22943i	0.936549	+	0.540717i	0.0476722	+	0.998863i	$0.484820\pi$
$18$	1.45015	−	3.98050i	0.341804	−	0.938212i
$19$	3.11573	+	5.39660i	0.714797	+	1.23806i	0.963038	+	0.269366i	$0.0868141\pi$
$19$	3.11573	+	5.39660i	0.714797	+	1.23806i	−0.248241	+	0.968698i	$0.579853\pi$
$20$	−0.180151	−	0.151351i	−0.0402829	−	0.0338431i
$21$	−0.161106	−	0.0930146i	−0.0351562	−	0.0202974i
$22$	0.434426	+	2.46814i	0.0926199	+	0.526208i
$23$			6.03806i			1.25902i	0.776992	+	0.629511i	$0.216745\pi$
$23$			6.03806i			1.25902i	−0.776992	+	0.629511i	$0.783255\pi$
$24$	0.0939168	−	0.162327i	0.0191707	−	0.0331348i
$25$	2.49308	−	4.31814i	0.498616	−	0.863628i
$26$	1.21167	+	1.44490i	0.237628	+	0.283369i
$27$		−	0.397536i		−	0.0765059i
$28$	4.29635	+	3.60952i	0.811934	+	0.682135i
$29$	−8.43088			−1.56558			−0.782788	−	0.622289i	$-0.786203\pi$
$29$	−8.43088			−1.56558			−0.782788	+	0.622289i	$0.786203\pi$
$30$	−0.0103650	−	0.00377613i	−0.00189239	−	0.000689423i
$31$			7.13978i			1.28234i	0.767398	+	0.641171i	$0.221551\pi$
$31$			7.13978i			1.28234i	−0.767398	+	0.641171i	$0.778449\pi$
$32$	−3.64273	+	4.32787i	−0.643950	+	0.765067i
$33$	0.0587480	+	0.101754i	0.0102267	+	0.0177132i
$34$	−5.92485	−	2.15851i	−1.01610	−	0.370181i
$35$	0.165037	−	0.285852i	0.0278963	−	0.0483179i
$36$	−1.04395	+	5.89955i	−0.173991	+	0.983259i
$37$	2.72190	+	5.43979i	0.447477	+	0.894295i
$37$	2.72190	+	5.43979i	0.447477	+	0.894295i
$38$	−5.66258	−	6.75257i	−0.918592	−	1.09541i
$39$	0.0765655	+	0.0442051i	0.0122603	+	0.00707849i
$40$	0.288019	+	0.166638i	0.0455398	+	0.0263478i
$41$	−2.42678	−	4.20331i	−0.379000	−	0.656447i	0.611917	−	0.790922i	$-0.290399\pi$
$41$	−2.42678	−	4.20331i	−0.379000	−	0.656447i	−0.990917	+	0.134475i	$0.957065\pi$
$42$	0.247192	+	0.0900555i	0.0381425	+	0.0138959i
$43$	11.6336			1.77410			0.887051	−	0.461671i	$-0.152750\pi$
$43$	11.6336			1.77410			0.887051	+	0.461671i	$0.152750\pi$
$44$	−1.21014	−	3.33113i	−0.182435	−	0.502186i
$45$	0.352418			0.0525354
$46$	−1.48024	−	8.40982i	−0.218250	−	1.23996i
$47$	6.45491			0.941546			0.470773	−	0.882254i	$-0.343975\pi$
$47$	6.45491			0.941546			0.470773	+	0.882254i	$0.343975\pi$
$48$	−0.0910128	+	0.249113i	−0.0131366	+	0.0359564i
$49$	−0.435906	+	0.755012i	−0.0622723	+	0.107859i
$50$	−2.41377	+	6.62550i	−0.341358	+	0.936988i
$51$	−0.295643			−0.0413983
$52$	−2.04184	−	1.71542i	−0.283152	−	0.237886i
$53$	−2.82675	−	1.63202i	−0.388284	−	0.224176i	0.293133	−	0.956072i	$-0.405302\pi$
$53$	−2.82675	−	1.63202i	−0.388284	−	0.224176i	−0.681416	+	0.731896i	$0.738636\pi$
$54$	0.0974570	+	0.553689i	0.0132622	+	0.0753476i
$55$	−0.180544	+	0.104237i	−0.0243446	+	0.0140554i
$56$	−6.86885	−	3.97409i	−0.917889	−	0.531060i
$57$	−0.357819	−	0.206587i	−0.0473943	−	0.0273631i
$58$	11.7426	−	2.06685i	1.54187	−	0.271391i
$59$	5.06132	−	8.76647i	0.658928	−	1.14130i	−0.321965	−	0.946751i	$-0.604343\pi$
$59$	5.06132	−	8.76647i	0.658928	−	1.14130i	0.980894	−	0.194545i	$-0.0623232\pi$
$60$	0.0153622	+	0.00271839i	0.00198325	+	0.000350942i
$61$	−4.77411	−	8.26900i	−0.611262	−	1.05874i	−0.991028	−	0.133654i	$-0.957329\pi$
$61$	−4.77411	−	8.26900i	−0.611262	−	1.05874i	0.379766	−	0.925082i	$-0.376004\pi$
$62$	−1.75033	−	9.94431i	−0.222293	−	1.26293i
$63$	−8.40469			−1.05889
$64$	4.01262	−	6.92090i	0.501578	−	0.865113i
$65$	−0.0784337	+	0.135851i	−0.00972851	+	0.0168503i
$66$	−0.106770	−	0.127322i	−0.0131424	−	0.0156722i
$67$	−6.61343	+	3.81827i	−0.807959	+	0.466475i	−0.846247	−	0.532791i	$-0.821143\pi$
$67$	−6.61343	+	3.81827i	−0.807959	+	0.466475i	0.0382876	+	0.999267i	$0.487810\pi$
$68$	8.78131	+	1.55388i	1.06489	+	0.188436i
$69$	−0.200175	−	0.346714i	−0.0240983	−	0.0417395i
$70$	−0.159787	+	0.438595i	−0.0190981	+	0.0524222i
$71$	−4.84512	−	8.39199i	−0.575010	−	0.995946i	−0.996041	−	0.0888995i	$-0.971665\pi$
$71$	−4.84512	−	8.39199i	−0.575010	−	0.995946i	0.421031	−	0.907046i	$-0.361668\pi$
$72$	0.00772217	−	8.47284i	0.000910066	−	0.998534i
$73$	−5.41038			−0.633237			−0.316619	−	0.948553i	$-0.602548\pi$
$73$	−5.41038			−0.633237			−0.316619	+	0.948553i	$0.602548\pi$
$74$	−5.12464	−	6.90927i	−0.595728	−	0.803187i
$75$			0.330605i			0.0381750i
$76$	9.54227	+	8.01680i	1.09457	+	0.919590i
$77$	4.30573	−	2.48592i	0.490684	−	0.283297i
$78$	−0.117478	−	0.0427988i	−0.0133017	−	0.00484601i
$79$	−5.20265	+	3.00375i	−0.585344	+	0.337948i	−0.763254	−	0.646098i	$-0.776400\pi$
$79$	−5.20265	+	3.00375i	−0.585344	+	0.337948i	0.177910	+	0.984047i	$0.443066\pi$
$80$	−0.442005	−	0.161485i	−0.0494177	−	0.0180546i
$81$	−4.48023	−	7.75998i	−0.497803	−	0.862220i
$82$	4.41048	+	5.25945i	0.487056	+	0.580809i
$83$	0.309739	+	0.178828i	0.0339983	+	0.0196289i	0.516903	−	0.856044i	$-0.327085\pi$
$83$	0.309739	+	0.178828i	0.0339983	+	0.0196289i	−0.482905	+	0.875673i	$0.660418\pi$
$84$	−0.366367	−	0.0648299i	−0.0399739	−	0.00707352i
$85$		−	0.524564i		−	0.0568969i
$86$	−16.2033	+	2.85200i	−1.74724	+	0.307539i
$87$	0.484113	−	0.279503i	0.0519024	−	0.0299659i
$88$	2.50212	+	4.34293i	0.266727	+	0.462958i
$89$	3.23848	+	1.86974i	0.343279	+	0.198192i	0.661721	−	0.749750i	$-0.269826\pi$
$89$	3.23848	+	1.86974i	0.343279	+	0.198192i	−0.318442	+	0.947942i	$0.603160\pi$
$90$	−0.490849	+	0.0863962i	−0.0517400	+	0.00910696i
$91$	1.87054	−	3.23987i	0.196086	−	0.339630i
$92$	4.12338	+	11.3503i	0.429892	+	1.18336i
$93$	−0.236700	−	0.409977i	−0.0245447	−	0.0425126i
$94$	−8.99042	+	1.58244i	−0.927291	+	0.163216i
$95$	0.366550	−	0.634883i	0.0376072	−	0.0651376i
$96$	0.0656922	−	0.369278i	0.00670468	−	0.0376893i
$97$		−	15.7030i		−	1.59440i	−0.603718	−	0.797198i	$-0.706315\pi$
$97$		−	15.7030i		−	1.59440i	0.603718	−	0.797198i	$-0.293685\pi$
$98$	0.422038	−	1.15845i	0.0426323	−	0.117021i
$99$	4.59721	+	2.65420i	0.462037	+	0.266757i
$100$	1.73764	−	9.81976i	0.173764	−	0.981976i
$101$		−	4.24740i		−	0.422632i	−0.977418	−	0.211316i	$-0.932225\pi$
$101$		−	4.24740i		−	0.422632i	0.977418	−	0.211316i	$-0.0677749\pi$
$102$	0.411773	−	0.0724777i	0.0407716	−	0.00717636i
$103$		−	6.89690i		−	0.679571i	−0.940503	−	0.339786i	$-0.889645\pi$
$103$		−	6.89690i		−	0.679571i	0.940503	−	0.339786i	$-0.110355\pi$
$104$	3.26442	+	1.88868i	0.320103	+	0.185201i
$105$			0.0218854i			0.00213580i
$106$	4.33720	+	1.58010i	0.421266	+	0.153473i
$107$	−3.95844	+	2.28541i	−0.382677	+	0.220939i	−0.678982	−	0.734155i	$-0.737579\pi$
$107$	−3.95844	+	2.28541i	−0.382677	+	0.220939i	0.296305	+	0.955093i	$0.404245\pi$
$108$	−0.271477	−	0.747289i	−0.0261229	−	0.0719079i
$109$	−4.71964	+	8.17466i	−0.452060	+	0.782991i	−0.998514	−	0.0544985i	$-0.982644\pi$
$109$	−4.71964	+	8.17466i	−0.452060	+	0.782991i	0.546454	+	0.837489i	$0.315977\pi$
$110$	0.225909	−	0.189443i	0.0215395	−	0.0180627i
$111$	−0.336637	−	0.222123i	−0.0319521	−	0.0210830i
$112$	10.5412	+	3.85120i	0.996051	+	0.363904i
$113$	0.495059	+	0.285823i	0.0465713	+	0.0268879i	0.523105	−	0.852268i	$-0.324774\pi$
$113$	0.495059	+	0.285823i	0.0465713	+	0.0268879i	−0.476534	+	0.879156i	$0.658107\pi$
$114$	0.549017	+	0.200015i	0.0514201	+	0.0187331i
$115$	0.615179	−	0.355174i	0.0573658	−	0.0331201i
$116$	−15.8484	+	5.75743i	−1.47148	+	0.534564i
$117$	3.99432			0.369275
$118$	−4.90030	+	13.4508i	−0.451110	+	1.23824i
$119$			12.5101i			1.14680i
$120$	−0.0220629		2.01082e-5i	−0.00201406		1.83562e-6i
$121$	7.85979			0.714526
$122$	8.67656	+	10.3467i	0.785539	+	0.936746i
$123$	0.278699	+	0.160907i	0.0251294	+	0.0145085i
$124$	4.87574	+	13.4214i	0.437855	+	1.20527i
$125$	−1.17482			−0.105079
$126$	11.7061	−	2.06043i	1.04286	−	0.183558i
$127$	7.13838	−	12.3640i	0.633429	−	1.09713i	−0.353416	−	0.935466i	$-0.614980\pi$
$127$	7.13838	−	12.3640i	0.633429	−	1.09713i	0.986846	−	0.161665i	$-0.0516865\pi$
$128$	−3.89212	+	10.6232i	−0.344018	+	0.938963i
$129$	−0.668016	+	0.385679i	−0.0588156	+	0.0339572i
$130$	0.0759385	−	0.208442i	0.00666024	−	0.0182816i
$131$	−7.99319	+	13.8446i	−0.698368	+	1.20961i	0.270664	+	0.962674i	$0.412757\pi$
$131$	−7.99319	+	13.8446i	−0.698368	+	1.20961i	−0.969032	+	0.246935i	$0.920576\pi$
$132$	0.179922	+	0.151159i	0.0156602	+	0.0131567i
$133$	−8.74172	+	15.1411i	−0.758003	+	1.31290i
$134$	8.27515	−	6.93939i	0.714864	−	0.599472i
$135$	−0.0405024	+	0.0233841i	−0.00348589	+	0.00201258i
$136$	−12.6116	−	0.0114942i	−1.08143	−	0.000985621i
$137$	12.4630			1.06478			0.532392	−	0.846498i	$-0.321293\pi$
$137$	12.4630			1.06478			0.532392	+	0.846498i	$0.321293\pi$
$138$	0.363803	+	0.433831i	0.0309690	+	0.0369301i
$139$	2.35322	+	1.35863i	0.199597	+	0.115238i	0.596468	−	0.802637i	$-0.296570\pi$
$139$	2.35322	+	1.35863i	0.199597	+	0.115238i	−0.396870	+	0.917875i	$0.629904\pi$
$140$	0.115028	−	0.650049i	0.00972168	−	0.0549392i
$141$	−0.370651	+	0.213995i	−0.0312144	+	0.0180216i
$142$	8.80561	+	10.5006i	0.738950	+	0.881190i
$143$	−2.04630	+	1.18143i	−0.171120	+	0.0987962i
$144$	2.06638	+	11.8029i	0.172199	+	0.983575i
$145$	0.495926	+	0.858969i	0.0411844	+	0.0713335i
$146$	7.53559	−	1.32637i	0.623650	−	0.109771i
$147$		−	0.0578052i		−	0.00476769i
$148$	8.83144	+	8.36694i	0.725940	+	0.687758i
$149$		−	14.1276i		−	1.15738i	−0.815549	−	0.578688i	$-0.803565\pi$
$149$		−	14.1276i		−	1.15738i	0.815549	−	0.578688i	$-0.196435\pi$
$150$	−0.0810487	−	0.460468i	−0.00661760	−	0.0375971i
$151$	−2.99047	−	5.17964i	−0.243361	−	0.421513i	0.718309	−	0.695725i	$-0.244917\pi$
$151$	−2.99047	−	5.17964i	−0.243361	−	0.421513i	−0.961669	+	0.274211i	$0.911583\pi$
$152$	−15.2558	−	8.82651i	−1.23741	−	0.715925i
$153$	−11.5675	+	6.67850i	−0.935177	+	0.539924i
$154$	−5.38761	+	4.51795i	−0.434146	+	0.364067i
$155$	0.727427	−	0.419980i	0.0584283	−	0.0337336i
$156$	0.174116	+	0.0308104i	0.0139404	+	0.00246680i
$157$	−0.353494	−	0.204090i	−0.0282119	−	0.0162882i	0.485828	−	0.874055i	$-0.338518\pi$
$157$	−0.353494	−	0.204090i	−0.0282119	−	0.0162882i	−0.514040	+	0.857766i	$0.671852\pi$
$158$	6.50989	−	5.45908i	0.517899	−	0.434301i
$159$	0.216421			0.0171633
$160$	0.655214	+	0.116558i	0.0517992	+	0.00921476i
$161$	−14.6712	+	8.47041i	−1.15625	+	0.667562i
$162$	8.14245	+	9.70978i	0.639731	+	0.762873i
$163$	2.69163	−	4.66203i	0.210824	−	0.365159i	−0.741148	−	0.671341i	$-0.765718\pi$
$163$	2.69163	−	4.66203i	0.210824	−	0.365159i	0.951973	+	0.306183i	$0.0990518\pi$
$164$	−7.43230	−	6.24414i	−0.580365	−	0.487586i
$165$	0.00691141	−	0.0119709i	0.000538053	−	0.000931935i
$166$	−0.475246	−	0.173139i	−0.0368862	−	0.0134382i
$167$	5.60294	−	3.23486i	0.433569	−	0.250321i	−0.267297	−	0.963614i	$-0.586130\pi$
$167$	5.60294	−	3.23486i	0.433569	−	0.250321i	0.700866	+	0.713293i	$0.252797\pi$
$168$	0.526170		0.000479552i	0.0405949		3.69983e-5i
$169$	5.61103	−	9.71859i	0.431618	−	0.747584i
$170$	0.128598	+	0.730614i	0.00986302	+	0.0560355i
$171$	−18.6670			−1.42750
$172$	21.8688	−	7.94454i	1.66748	−	0.605766i
$173$	16.5631	+	9.56268i	1.25927	+	0.727037i	0.972932	−	0.231093i	$-0.0742300\pi$
$173$	16.5631	+	9.56268i	1.25927	+	0.727037i	0.286334	+	0.958130i	$0.407563\pi$
$174$	−0.605754	+	0.507974i	−0.0459221	+	0.0385094i
$175$	13.9895			1.05751
$176$	−4.54964	−	5.43545i	−0.342942	−	0.409712i
$177$			0.671178i			0.0504488i
$178$	−4.96894	−	1.81026i	−0.372438	−	0.135684i
$179$	−4.06143			−0.303565			−0.151783	−	0.988414i	$-0.548501\pi$
$179$	−4.06143			−0.303565			−0.151783	+	0.988414i	$0.548501\pi$
$180$	0.662476	−	0.240666i	0.0493780	−	0.0179382i
$181$	−15.7641	+	9.10138i	−1.17173	+	0.676500i	−0.954088	−	0.299528i	$-0.903171\pi$
$181$	−15.7641	+	9.10138i	−1.17173	+	0.676500i	−0.217645	+	0.976028i	$0.569838\pi$
$182$	−1.81103	+	4.97106i	−0.134242	+	0.368480i
$183$	0.548272	+	0.316545i	0.0405295	+	0.0233997i
$184$	−8.52562	−	14.7979i	−0.628517	−	1.09092i
$185$	0.394116	−	0.597299i	0.0289760	−	0.0439143i
$186$	0.430183	+	0.512989i	0.0315426	+	0.0376142i
$187$	3.95070	−	6.84281i	0.288904	−	0.500396i
$188$	12.1340	−	4.40805i	0.884959	−	0.321490i
$189$	0.965928	−	0.557679i	0.0702609	−	0.0405651i
$190$	−0.354889	+	0.974128i	−0.0257463	+	0.0706707i
$191$		−	6.17125i		−	0.446536i	−0.974757	−	0.223268i	$-0.928327\pi$
$191$		−	6.17125i		−	0.446536i	0.974757	−	0.223268i	$-0.0716725\pi$
$192$	−0.000966882		0.530436i	−6.97787e−5		0.0382809i
$193$			2.30955i			0.166245i	0.996539	+	0.0831225i	$0.0264893\pi$
$193$			2.30955i			0.166245i	−0.996539	+	0.0831225i	$0.973511\pi$
$194$	3.84962	+	21.8711i	0.276387	+	1.57026i
$195$		−	0.0104010i		−	0.000744833i
$196$	−0.303821	+	1.71695i	−0.0217015	+	0.122639i
$197$	14.5131	+	8.37915i	1.03402	+	0.596990i	0.918133	−	0.396273i	$-0.129697\pi$
$197$	14.5131	+	8.37915i	1.03402	+	0.596990i	0.115884	+	0.993263i	$0.463030\pi$
$198$	−7.05369	−	2.56976i	−0.501284	−	0.182625i
$199$			1.85153i			0.131251i	0.997844	+	0.0656257i	$0.0209043\pi$
$199$			1.85153i			0.131251i	−0.997844	+	0.0656257i	$0.979096\pi$
$200$	−0.0128535	+	14.1030i	−0.000908879	+	0.997232i
$201$	0.253169	−	0.438501i	0.0178571	−	0.0309295i
$202$	1.04126	+	5.91579i	0.0732628	+	0.416233i
$203$	−11.8272	−	20.4852i	−0.830103	−	1.43778i
$204$	−0.555750	+	0.201894i	−0.0389103	+	0.0141354i
$205$	−0.285499	+	0.494499i	−0.0199401	+	0.0345373i
$206$	1.69079	+	9.60602i	0.117803	+	0.669283i
$207$	−15.6643	−	9.04381i	−1.08875	−	0.628589i
$208$	−5.00971	−	1.83028i	−0.347361	−	0.126907i
$209$	9.56311	−	5.52127i	0.661494	−	0.381914i
$210$	−0.00536526	−	0.0304821i	−0.000370238	−	0.00210346i
$211$		−	5.19026i		−	0.357312i	−0.983912	−	0.178656i	$-0.942825\pi$
$211$		−	5.19026i		−	0.357312i	0.983912	−	0.178656i	$-0.0571749\pi$
$212$	−6.42823	−	1.13750i	−0.441492	−	0.0781236i
$213$	0.556427	+	0.321253i	0.0381258	+	0.0220119i
$214$	4.95305	−	4.15354i	0.338584	−	0.283930i
$215$	−0.684316	−	1.18527i	−0.0466700	−	0.0808347i
$216$	0.561313	+	0.974273i	0.0381925	+	0.0662909i
$217$	−17.3481	+	10.0160i	−1.17767	+	0.679927i
$218$	4.56949	−	12.5427i	0.309485	−	0.849501i
$219$	0.310672	−	0.179367i	0.0209933	−	0.0121205i
$220$	−0.268204	+	0.319239i	−0.0180823	+	0.0215231i
$221$		−	5.94543i		−	0.399933i
$222$	0.523323	+	0.226847i	0.0351231	+	0.0152250i
$223$	4.24585			0.284323			0.142162	−	0.989843i	$-0.454595\pi$
$223$	4.24585			0.284323			0.142162	+	0.989843i	$0.454595\pi$
$224$	−15.6260	−	2.77976i	−1.04405	−	0.185731i
$225$	7.46828	+	12.9354i	0.497885	+	0.862363i
$226$	−0.759590	−	0.276730i	−0.0505272	−	0.0184078i
$227$	12.0135	+	20.8081i	0.797366	+	1.38108i	0.921326	+	0.388792i	$0.127107\pi$
$227$	12.0135	+	20.8081i	0.797366	+	1.38108i	−0.123959	+	0.992287i	$0.539559\pi$
$228$	−0.813707	−	0.143988i	−0.0538890	−	0.00953585i
$229$	21.9615	−	12.6795i	1.45126	−	0.837883i	0.452704	−	0.891661i	$-0.350460\pi$
$229$	21.9615	−	12.6795i	1.45126	−	0.837883i	0.998553	+	0.0537776i	$0.0171262\pi$
$230$	−0.769752	+	0.645500i	−0.0507559	+	0.0425630i
$231$	−0.164828	+	0.285490i	−0.0108449	+	0.0187839i
$232$	20.6622	−	11.9042i	1.35654	−	0.781551i
$233$	−6.80335			−0.445702			−0.222851	−	0.974853i	$-0.571536\pi$
$233$	−6.80335			−0.445702			−0.222851	+	0.974853i	$0.571536\pi$
$234$	−5.56331	+	0.979219i	−0.363685	+	0.0640135i
$235$	−0.379694	−	0.657650i	−0.0247685	−	0.0429004i
$236$	3.52767	−	19.9356i	0.229632	−	1.29770i
$237$	0.199162	−	0.344960i	0.0129370	−	0.0224075i
$238$	−3.06689	−	17.4241i	−0.198797	−	1.12944i
$239$	5.66461	+	3.27046i	0.366413	+	0.211549i	0.671890	−	0.740651i	$-0.265483\pi$
$239$	5.66461	+	3.27046i	0.366413	+	0.211549i	−0.305477	+	0.952199i	$0.598816\pi$
$240$	0.0307342	−	0.00538076i	0.00198388	−	0.000347327i
$241$	−18.6710	+	10.7797i	−1.20271	+	0.694383i	−0.961156	−	0.276006i	$-0.910989\pi$
$241$	−18.6710	+	10.7797i	−1.20271	+	0.694383i	−0.241550	+	0.970388i	$0.577656\pi$
$242$	−10.9471	+	1.92685i	−0.703709	+	0.123862i
$243$	1.54735	+	0.893364i	0.0992626	+	0.0573093i
$244$	−14.6213	−	12.2838i	−0.936030	−	0.786392i
$245$	0.102564			0.00655260
$246$	−0.427619	−	0.155788i	−0.0272640	−	0.00993267i
$247$	4.15450	−	7.19580i	0.264344	−	0.457858i
$248$	−10.0812	−	17.4980i	−0.640159	−	1.11112i
$249$	−0.0237142			−0.00150283
$250$	1.63630	−	0.288011i	0.103488	−	0.0182154i
$251$	−12.9386			−0.816679			−0.408340	−	0.912830i	$-0.633892\pi$
$251$	−12.9386			−0.816679			−0.408340	+	0.912830i	$0.633892\pi$
$252$	−15.7991	+	5.73955i	−0.995252	+	0.361558i
$253$	10.6998			0.672692
$254$	−6.91129	+	18.9707i	−0.433653	+	1.19033i
$255$	0.0173905	+	0.0301212i	0.00108903	+	0.00188626i
$256$	2.81666	−	15.7501i	0.176041	−	0.984383i
$257$	22.7103	+	13.1118i	1.41663	+	0.817893i	0.996001	−	0.0893384i	$-0.0284753\pi$
$257$	22.7103	+	13.1118i	1.41663	+	0.817893i	0.420631	+	0.907232i	$0.361809\pi$
$258$	0.835865	−	0.700941i	0.0520387	−	0.0436387i
$259$	−9.39914	+	14.2448i	−0.584034	+	0.885126i
$260$	−0.0546672	+	0.308935i	−0.00339032	+	0.0191594i
$261$	12.6278	−	21.8720i	0.781640	−	1.35384i
$262$	7.73890	−	21.2424i	0.478111	−	1.31236i
$263$	−1.44551	−	2.50369i	−0.0891338	−	0.154384i	0.818011	−	0.575202i	$-0.195077\pi$
$263$	−1.44551	−	2.50369i	−0.0891338	−	0.154384i	−0.907145	+	0.420818i	$0.861743\pi$
$264$	−0.287654	−	0.166427i	−0.0177039	−	0.0102428i
$265$			0.383999i			0.0235889i
$266$	8.46361	−	23.2316i	0.518937	−	1.42442i
$267$	−0.247945			−0.0151740
$268$	−9.82444	+	11.6939i	−0.600123	+	0.714317i
$269$		−	14.0116i		−	0.854305i	−0.904180	−	0.427153i	$-0.859517\pi$
$269$		−	14.0116i		−	0.854305i	0.904180	−	0.427153i	$-0.140483\pi$
$270$	0.0506792	−	0.0424987i	0.00308424	−	0.00258639i
$271$	−9.06115	+	15.6944i	−0.550426	+	0.953365i	0.447818	+	0.894125i	$0.352201\pi$
$271$	−9.06115	+	15.6944i	−0.550426	+	0.953365i	−0.998244	+	0.0592405i	$0.981132\pi$
$272$	17.5683	−	3.07575i	1.06523	−	0.186495i
$273$			0.248050i			0.0150127i
$274$	−17.3585	+	3.05533i	−1.04866	+	0.184579i
$275$	−7.65202	−	4.41790i	−0.461434	−	0.266409i
$276$	−0.613060	−	0.515054i	−0.0369019	−	0.0310026i
$277$	−0.722938	−	1.25217i	−0.0434372	−	0.0752354i	0.843489	−	0.537146i	$-0.180497\pi$
$277$	−0.722938	−	1.25217i	−0.0434372	−	0.0752354i	−0.886927	+	0.461910i	$0.847164\pi$
$278$	−3.61064	−	1.31541i	−0.216552	−	0.0788930i
$279$	−18.5225	−	10.6940i	−1.10891	−	0.640232i
$280$	−0.000850876		0.933590i	−5.08495e−5		0.0557927i
$281$	25.7216	+	14.8504i	1.53442	+	0.885901i	0.999150	+	0.0412228i	$0.0131254\pi$
$281$	25.7216	+	14.8504i	1.53442	+	0.885901i	0.535275	+	0.844678i	$0.320208\pi$
$282$	0.463782	−	0.388919i	0.0276178	−	0.0231598i
$283$	−14.9986	−	25.9783i	−0.891575	−	1.54425i	−0.837988	−	0.545689i	$-0.816268\pi$
$283$	−14.9986	−	25.9783i	−0.891575	−	1.54425i	−0.0535871	−	0.998563i	$-0.517065\pi$
$284$	−14.8387	−	12.4665i	−0.880516	−	0.739753i
$285$			0.0486079i			0.00287928i
$286$	2.56046	−	2.14716i	0.151403	−	0.126964i
$287$	6.80877	−	11.7931i	0.401909	−	0.696126i
$288$	−5.77157	−	15.9325i	−0.340093	−	0.938833i
$289$	1.44074	+	2.49544i	0.0847495	+	0.146790i
$290$	−0.901305	−	1.07480i	−0.0529265	−	0.0631142i
$291$	0.520590	+	0.901688i	0.0305175	+	0.0528579i
$292$	−10.1704	+	3.69474i	−0.595180	+	0.216218i
$293$	−7.96315	+	4.59753i	−0.465212	+	0.268591i	−0.714233	−	0.699908i	$-0.753225\pi$
$293$	−7.96315	+	4.59753i	−0.465212	+	0.268591i	0.249021	+	0.968498i	$0.419891\pi$
$294$	0.0141711	+	0.0805112i	0.000826474	+	0.00469551i
$295$	−1.19088			−0.0693357
$296$	−14.3516	−	9.48844i	−0.834172	−	0.551505i
$297$	−0.704459			−0.0408769
$298$	3.46341	+	19.6769i	0.200630	+	1.13985i
$299$	6.97247	−	4.02556i	0.403229	−	0.232804i
$300$	0.225770	+	0.621472i	0.0130348	+	0.0358807i
$301$	16.3200	+	28.2671i	0.940669	+	1.62929i
$302$	5.43493	+	6.48110i	0.312745	+	0.372945i
$303$	0.140811	+	0.243892i	0.00808938	+	0.0140112i
$304$	23.4122	+	8.55359i	1.34278	+	0.490582i
$305$	−0.561650	+	0.972807i	−0.0321600	+	0.0557028i
$306$	14.4740	−	12.1376i	0.827423	−	0.693862i
$307$			5.95372i			0.339797i	0.985462	+	0.169898i	$0.0543440\pi$
$307$			5.95372i			0.339797i	−0.985462	+	0.169898i	$0.945656\pi$
$308$	6.39629	−	7.61341i	0.364463	−	0.433814i
$309$	0.228648	+	0.396030i	0.0130073	+	0.0225293i
$310$	−0.910203	+	0.763280i	−0.0516961	+	0.0433514i
$311$	2.22987	+	1.28742i	0.126444	+	0.0730027i	0.561888	−	0.827213i	$-0.310075\pi$
$311$	2.22987	+	1.28742i	0.126444	+	0.0730027i	−0.435444	+	0.900216i	$0.643408\pi$
$312$	−0.250062		0.000227907i	−0.0141570		1.29027e-5i
$313$	−27.5687	−	15.9168i	−1.55828	−	0.899671i	−0.997422	−	0.0717560i	$-0.977140\pi$
$313$	−27.5687	−	15.9168i	−1.55828	−	0.899671i	−0.560854	−	0.827915i	$-0.689527\pi$
$314$	0.542381	+	0.197597i	0.0306083	+	0.0111511i
$315$	0.494385	+	0.856300i	0.0278555	+	0.0482471i
$316$	−7.72869	+	9.19933i	−0.434773	+	0.517503i
$317$	11.0688	+	6.39059i	0.621687	+	0.358931i	0.777526	−	0.628851i	$-0.216475\pi$
$317$	11.0688	+	6.39059i	0.621687	+	0.358931i	−0.155838	+	0.987783i	$0.549808\pi$
$318$	−0.301432	+	0.0530562i	−0.0169035	+	0.00297524i
$319$			14.9401i			0.836482i
$320$	−0.941159	−	0.00171555i	−0.0526124	−	9.59022e-5i
$321$	0.151533	−	0.262463i	0.00845774	−	0.0146492i
$322$	18.3575	−	15.3943i	1.02303	−	0.857891i
$323$			27.7852i			1.54601i
$324$	−13.7212	−	11.5277i	−0.762289	−	0.640426i
$325$	−6.64852			−0.368794
$326$	−2.60600	+	7.15315i	−0.144333	+	0.396177i
$327$		−	0.625868i		−	0.0346106i
$328$	11.8825	+	6.87481i	0.656101	+	0.379598i
$329$	9.05520	+	15.6841i	0.499229	+	0.864690i
$330$	−0.00669153	+	0.0183675i	−0.000368357	+	0.00101110i
$331$	11.3265	−	19.6180i	0.622558	−	1.07830i	−0.366450	−	0.930438i	$-0.619427\pi$
$331$	11.3265	−	19.6180i	0.622558	−	1.07830i	0.989008	−	0.147864i	$-0.0472399\pi$
$332$	0.704369	+	0.124641i	0.0386573	+	0.00684054i
$333$	−18.1891	−	1.08639i	−0.996758	−	0.0595339i
$334$	−7.01076	+	5.87910i	−0.383612	+	0.321690i
$335$	0.778038	+	0.449200i	0.0425087	+	0.0245424i
$336$	−0.732968	+	0.128324i	−0.0399867	+	0.00700064i
$337$	1.51804	+	2.62932i	0.0826928	+	0.143228i	0.904406	−	0.426674i	$-0.140315\pi$
$337$	1.51804	+	2.62932i	0.0826928	+	0.143228i	−0.821713	+	0.569902i	$0.806981\pi$
$338$	−5.43252	+	14.9116i	−0.295490	+	0.811086i
$339$	−0.0379027			−0.00205859
$340$	−0.358224	−	0.986075i	−0.0194274	−	0.0534774i
$341$	12.6521			0.685152
$342$	25.9994	−	4.57625i	1.40589	−	0.247455i
$343$	17.1937			0.928373
$344$	−28.5113	+	16.4264i	−1.53723	+	0.885650i
$345$	−0.0235497	+	0.0407892i	−0.00126787	+	0.00219602i
$346$	−25.4134	−	9.25846i	−1.36623	−	0.497738i
$347$	24.7590			1.32913			0.664566	−	0.747229i	$-0.268616\pi$
$347$	24.7590			1.32913			0.664566	+	0.747229i	$0.268616\pi$
$348$	0.719165	−	0.856010i	0.0385513	−	0.0458870i
$349$	7.68820	+	4.43878i	0.411540	+	0.237603i	0.691451	−	0.722423i	$-0.256972\pi$
$349$	7.68820	+	4.43878i	0.411540	+	0.237603i	−0.279911	+	0.960026i	$0.590305\pi$
$350$	−19.4847	+	3.42957i	−1.04150	+	0.183318i
$351$	−0.459057	+	0.265036i	−0.0245026	+	0.0141466i
$352$	7.66927	+	6.45516i	0.408773	+	0.344061i
$353$	−21.5013	−	12.4138i	−1.14440	−	0.660718i	−0.196881	−	0.980427i	$-0.563081\pi$
$353$	−21.5013	−	12.4138i	−1.14440	−	0.660718i	−0.947516	+	0.319710i	$0.896415\pi$
$354$	−0.164541	−	0.934819i	−0.00874525	−	0.0496850i
$355$	−0.570004	+	0.987276i	−0.0302527	+	0.0523992i
$356$	7.36455	+	1.30318i	0.390320	+	0.0690685i
$357$	−0.414739	−	0.718350i	−0.0219503	−	0.0380191i
$358$	5.65677	−	0.995669i	0.298969	−	0.0526227i
$359$	29.8646			1.57619			0.788095	−	0.615553i	$-0.211067\pi$
$359$	29.8646			1.57619			0.788095	+	0.615553i	$0.211067\pi$
$360$	−0.863698	+	0.497607i	−0.0455209	+	0.0262262i
$361$	−9.91550	+	17.1742i	−0.521869	+	0.903903i
$362$	19.7250	−	16.5410i	1.03672	−	0.869377i
$363$	−0.451321	+	0.260570i	−0.0236882	+	0.0136764i
$364$	1.30374	−	7.36769i	0.0683345	−	0.386172i
$365$	0.318252	+	0.551229i	0.0166581	+	0.0288527i
$366$	−0.841237	−	0.306475i	−0.0439722	−	0.0160197i
$367$	−2.35547	−	4.07979i	−0.122954	−	0.212963i	0.797977	−	0.602688i	$-0.205904\pi$
$367$	−2.35547	−	4.07979i	−0.122954	−	0.212963i	−0.920931	+	0.389724i	$0.872570\pi$
$368$	15.5023	+	18.5205i	0.808111	+	0.965450i
$369$	14.5394			0.756889
$370$	−0.402497	+	0.928538i	−0.0209248	+	0.0482724i
$371$		−	9.15785i		−	0.475452i
$372$	−0.724921	−	0.609032i	−0.0375854	−	0.0315768i
$373$	−30.0078	+	17.3250i	−1.55375	+	0.897056i	−0.555915	+	0.831239i	$0.687632\pi$
$373$	−30.0078	+	17.3250i	−1.55375	+	0.897056i	−0.997832	+	0.0658166i	$0.979035\pi$
$374$	−3.82501	+	10.4992i	−0.197787	+	0.542901i
$375$	0.0674600	−	0.0389481i	0.00348362	−	0.00201127i
$376$	−15.8196	+	9.11421i	−0.815831	+	0.470030i
$377$	5.62085	+	9.73560i	0.289488	+	0.501409i
$378$	−1.20863	+	1.01354i	−0.0621652	+	0.0521307i
$379$	−24.0330	−	13.8755i	−1.23449	−	0.712735i	−0.266531	−	0.963826i	$-0.585877\pi$
$379$	−24.0330	−	13.8755i	−1.23449	−	0.712735i	−0.967963	+	0.251091i	$0.919211\pi$
$380$	0.255480	−	1.44377i	0.0131059	−	0.0740638i
$381$			0.946615i			0.0484966i
$382$	1.51290	+	8.59534i	0.0774066	+	0.439776i
$383$	−11.9736	+	6.91297i	−0.611823	+	0.353236i	−0.773679	−	0.633578i	$-0.781585\pi$
$383$	−11.9736	+	6.91297i	−0.611823	+	0.353236i	0.161856	+	0.986814i	$0.448252\pi$
$384$	−0.128691	−	0.739030i	−0.00656724	−	0.0377135i
$385$	−0.506549	−	0.292456i	−0.0258161	−	0.0149049i
$386$	−0.566192	−	3.21675i	−0.0288184	−	0.163728i
$387$	−17.4248	+	30.1806i	−0.885751	+	1.53417i
$388$	−10.7235	−	29.5185i	−0.544405	−	1.49857i
$389$	−12.4342	−	21.5366i	−0.630438	−	1.09195i	−0.987462	−	0.157855i	$-0.949542\pi$
$389$	−12.4342	−	21.5366i	−0.630438	−	1.09195i	0.357025	−	0.934095i	$-0.383791\pi$
$390$	0.00254984	+	0.0144866i	0.000129116	+	0.000733557i
$391$	−13.4614	+	23.3159i	−0.680774	+	1.17914i
$392$	0.00224739	−	2.46586i	0.000113510	−	0.124545i
$393$		−	1.05997i		−	0.0534684i
$394$	−22.2681	−	8.11258i	−1.12185	−	0.408706i
$395$	0.612066	+	0.353377i	0.0307964	+	0.0177803i
$396$	10.4544	+	1.84994i	0.525353	+	0.0929630i
$397$			5.96597i			0.299423i	0.988730	+	0.149712i	$0.0478345\pi$
$397$			5.96597i			0.299423i	−0.988730	+	0.149712i	$0.952165\pi$
$398$	−0.453907	−	2.57881i	−0.0227523	−	0.129264i
$399$		−	1.15923i		−	0.0580342i
$400$	−3.43948	−	19.6458i	−0.171974	−	0.982291i
$401$			14.3923i			0.718718i	0.933199	+	0.359359i	$0.117005\pi$
$401$			14.3923i			0.718718i	−0.933199	+	0.359359i	$0.882995\pi$
$402$	−0.245114	+	0.672810i	−0.0122252	+	0.0335567i
$403$	8.24469	−	4.76008i	0.410697	−	0.237116i
$404$	−2.90054	−	7.98426i	−0.144307	−	0.397232i
$405$	−0.527077	+	0.912924i	−0.0261906	+	0.0453635i
$406$	21.4949	+	25.6324i	1.06677	+	1.27212i
$407$	9.63965	−	4.82337i	0.477820	−	0.239086i
$408$	0.724556	−	0.417443i	0.0358709	−	0.0206665i
$409$	0.418816	+	0.241804i	0.0207091	+	0.0119564i	0.510319	−	0.859985i	$-0.329527\pi$
$409$	0.418816	+	0.241804i	0.0207091	+	0.0119564i	−0.489610	+	0.871942i	$0.662861\pi$
$410$	0.276416	−	0.758731i	0.0136512	−	0.0374710i
$411$	−0.715643	+	0.413176i	−0.0353000	+	0.0203805i
$412$	−4.70988	−	12.9648i	−0.232039	−	0.638729i
$413$	28.4009			1.39751
$414$	24.0345	+	8.75610i	1.18123	+	0.430339i
$415$		−	0.0420765i		−	0.00206545i
$416$	7.42623	+	1.32108i	0.364101	+	0.0647713i
$417$	−0.180167			−0.00882282
$418$	−11.9660	+	10.0345i	−0.585275	+	0.490801i
$419$	6.21203	+	3.58652i	0.303478	+	0.175213i	0.644004	−	0.765022i	$-0.277272\pi$
$419$	6.21203	+	3.58652i	0.303478	+	0.175213i	−0.340527	+	0.940235i	$0.610605\pi$
$420$	0.0149455	+	0.0411402i	0.000729266	+	0.00200744i
$421$	28.9608			1.41146			0.705732	−	0.708479i	$-0.250618\pi$
$421$	28.9608			1.41146			0.705732	+	0.708479i	$0.250618\pi$
$422$	1.27240	+	7.22901i	0.0619397	+	0.351902i
$423$	−9.66818	+	16.7458i	−0.470083	+	0.814208i
$424$	9.23211	+	0.00841417i	0.448351	+	0.000408628i
$425$	19.2540	−	11.1163i	0.933957	−	0.539220i
$426$	−0.853750	−	0.311033i	−0.0413643	−	0.0150696i
$427$	13.3946	−	23.2001i	0.648210	−	1.12273i
$428$	−5.88038	+	6.99932i	−0.284239	+	0.338325i
$429$	0.0783343	−	0.135679i	0.00378202	−	0.00655064i
$430$	1.24369	+	1.48309i	0.0599760	+	0.0715208i
$431$	24.5328	−	14.1640i	1.18170	−	0.682257i	0.225296	−	0.974290i	$-0.427665\pi$
$431$	24.5328	−	14.1640i	1.18170	−	0.682257i	0.956408	+	0.292034i	$0.0943319\pi$
$432$	−1.02064	−	1.21936i	−0.0491058	−	0.0586666i
$433$	−9.60818			−0.461740			−0.230870	−	0.972985i	$-0.574157\pi$
$433$	−9.60818			−0.461740			−0.230870	+	0.972985i	$0.574157\pi$
$434$	21.7071	−	18.2032i	1.04197	−	0.873781i
$435$	−0.0569536	−	0.0328822i	−0.00273071	−	0.00157658i
$436$	−3.28953	+	18.5898i	−0.157540	+	0.890289i
$437$	−32.5850	+	18.8129i	−1.55875	+	0.899945i
$438$	−0.388733	+	0.325984i	−0.0185744	+	0.0155761i
$439$	4.93381	−	2.84854i	0.235478	−	0.135953i	−0.377619	−	0.925961i	$-0.623257\pi$
$439$	4.93381	−	2.84854i	0.235478	−	0.135953i	0.613097	+	0.790008i	$0.289924\pi$
$440$	0.295293	−	0.510387i	0.0140775	−	0.0243318i
$441$	−1.30580	−	2.26172i	−0.0621811	−	0.107701i
$442$	1.45754	+	8.28082i	0.0693280	+	0.393878i
$443$		−	17.5297i		−	0.832863i	−0.909167	−	0.416432i	$-0.863281\pi$
$443$		−	17.5297i		−	0.832863i	0.909167	−	0.416432i	$-0.136719\pi$
$444$	−0.784498	−	0.187659i	−0.0372306	−	0.00890590i
$445$		−	0.439931i		−	0.0208547i
$446$	−5.91363	+	1.04088i	−0.280019	+	0.0492871i
$447$	0.468361	+	0.811226i	0.0221527	+	0.0383697i
$448$	22.4454	+	0.0409135i	1.06044	+	0.00193298i
$449$	12.7067	−	7.33619i	0.599664	−	0.346216i	−0.169245	−	0.985574i	$-0.554133\pi$
$449$	12.7067	−	7.33619i	0.599664	−	0.346216i	0.768910	+	0.639358i	$0.220800\pi$
$450$	−13.5730	−	16.1857i	−0.639837	−	0.762999i
$451$	−7.44854	+	4.30041i	−0.350738	+	0.202499i
$452$	1.12580	+	0.199214i	0.0529532	+	0.00937026i
$453$	0.343434	+	0.198282i	0.0161359	+	0.00931609i
$454$	−21.8336	−	26.0364i	−1.02470	−	1.22195i
$455$	−0.440119			−0.0206331
$456$	1.16863	+	0.00106509i	0.0547262	+	4.98776e-5i
$457$	3.35122	−	1.93483i	0.156764	−	0.0905075i	−0.419566	−	0.907725i	$-0.637818\pi$
$457$	3.35122	−	1.93483i	0.156764	−	0.0905075i	0.576330	+	0.817217i	$0.304484\pi$
$458$	−27.4796	+	23.0439i	−1.28404	+	1.07677i
$459$	0.886280	−	1.53508i	0.0413680	−	0.0716515i
$460$	0.913867	−	1.08776i	0.0426093	−	0.0507171i
$461$	7.09406	−	12.2873i	0.330403	−	0.572275i	−0.652188	−	0.758058i	$-0.726149\pi$
$461$	7.09406	−	12.2873i	0.330403	−	0.572275i	0.982591	+	0.185782i	$0.0594819\pi$
$462$	0.159584	−	0.438039i	0.00742452	−	0.0203794i
$463$	10.3602	−	5.98146i	0.481479	−	0.277982i	−0.239554	−	0.970883i	$-0.577001\pi$
$463$	10.3602	−	5.98146i	0.481479	−	0.277982i	0.721033	+	0.692901i	$0.243668\pi$
$464$	−25.8600	+	21.6457i	−1.20052	+	1.00487i
$465$	−0.0278466	+	0.0482317i	−0.00129136	+	0.00223669i
$466$	9.47572	−	1.66786i	0.438954	−	0.0772620i
$467$	−40.6459			−1.88087			−0.940433	−	0.339979i	$-0.889580\pi$
$467$	−40.6459			−1.88087			−0.940433	+	0.339979i	$0.889580\pi$
$468$	7.50853	−	2.72772i	0.347082	−	0.126089i
$469$	−18.5551	−	10.7128i	−0.856797	−	0.494672i
$470$	0.690064	+	0.822894i	0.0318303	+	0.0379573i
$471$	0.0270642			0.00124705
$472$	−0.0260945	+	28.6312i	−0.00120110	+	1.31786i
$473$		−	20.6154i		−	0.947898i
$474$	−0.192826	+	0.529286i	−0.00885681	+	0.0243109i
$475$	31.0710			1.42564
$476$	8.54314	+	23.5165i	0.391574	+	1.07788i
$477$	8.46781	−	4.88889i	0.387715	−	0.223847i
$478$	−8.69145	−	3.16642i	−0.397537	−	0.144829i
$479$	−25.1217	−	14.5040i	−1.14784	−	0.662705i	−0.199479	−	0.979902i	$-0.563925\pi$
$479$	−25.1217	−	14.5040i	−1.14784	−	0.662705i	−0.948360	+	0.317197i	$0.897258\pi$
$480$	−0.0414876	+	0.0150289i	−0.00189364	+	0.000685973i
$481$	4.46694	−	6.76982i	0.203675	−	0.308677i
$482$	23.3624	−	19.5913i	1.06413	−	0.892358i
$483$	0.561627	−	0.972767i	0.0255549	−	0.0442624i
$484$	14.7748	−	5.36744i	0.671584	−	0.243974i
$485$	−1.59988	+	0.923689i	−0.0726466	+	0.0419426i
$486$	−2.37417	−	0.864943i	−0.107694	−	0.0392346i
$487$			35.6137i			1.61381i	0.590679	+	0.806906i	$0.298860\pi$
$487$			35.6137i			1.61381i	−0.590679	+	0.806906i	$0.701140\pi$
$488$	23.3759	+	13.5245i	1.05818	+	0.612227i
$489$			0.356934i			0.0161411i
$490$	−0.142852	+	0.0251439i	−0.00645340	+	0.00113589i
$491$			21.5105i			0.970754i	0.874305	+	0.485377i	$0.161318\pi$
$491$			21.5105i			0.970754i	−0.874305	+	0.485377i	$0.838682\pi$
$492$	0.633781	+	0.112150i	0.0285731	+	0.00505611i
$493$	−32.5558	−	18.7961i	−1.46624	−	0.846533i
$494$	−4.02233	+	11.0408i	−0.180973	+	0.496750i
$495$		−	0.624507i		−	0.0280695i
$496$	18.3308	+	21.8998i	0.823079	+	0.983332i
$497$	13.5938	−	23.5452i	0.609766	−	1.05615i
$498$	0.0330293	−	0.00581360i	0.00148008	−	0.000260514i
$499$	6.38910	+	11.0662i	0.286015	+	0.495393i	0.972855	−	0.231416i	$-0.0743358\pi$
$499$	6.38910	+	11.0662i	0.286015	+	0.495393i	−0.686840	+	0.726809i	$0.741002\pi$
$500$	−2.20843	+	0.802284i	−0.0987641	+	0.0358792i
$501$	−0.214486	+	0.371501i	−0.00958253	+	0.0165974i
$502$	18.0210	−	3.17194i	0.804315	−	0.141570i
$503$	−19.4096	−	11.2061i	−0.865430	−	0.499656i	0.000396621	−	1.00000i	$-0.499874\pi$
$503$	−19.4096	−	11.2061i	−0.865430	−	0.499656i	−0.865827	+	0.500343i	$0.833207\pi$
$504$	20.5980	−	11.8673i	0.917509	−	0.528610i
$505$	−0.432740	+	0.249843i	−0.0192567	+	0.0111179i
$506$	−14.9027	+	2.62309i	−0.662508	+	0.116610i
$507$			0.744074i			0.0330455i
$508$	4.97535	−	28.1167i	0.220746	−	1.24748i
$509$	−4.18109	−	2.41396i	−0.185324	−	0.106997i	0.404468	−	0.914552i	$-0.367457\pi$
$509$	−4.18109	−	2.41396i	−0.185324	−	0.106997i	−0.589792	+	0.807556i	$0.700790\pi$
$510$	−0.0316058	−	0.0376896i	−0.00139953	−	0.00166892i
$511$	−7.58988	−	13.1461i	−0.335757	−	0.581548i
$512$	−0.0618679	+	22.6273i	−0.00273420	+	0.999996i
$513$	2.14534	−	1.23861i	0.0947192	−	0.0546861i
$514$	−34.8454	−	12.6947i	−1.53697	−	0.559939i
$515$	−0.702681	+	0.405693i	−0.0309638	+	0.0178770i
$516$	−0.992358	+	1.18119i	−0.0436861	+	0.0519989i
$517$		−	11.4385i		−	0.503065i
$518$	9.59901	−	22.1444i	0.421756	−	0.972968i
$519$	−1.26810			−0.0556634
$520$	0.000404378	−	0.443688i	1.77332e−5	−	0.0194570i
$521$	−4.23916	−	7.34245i	−0.185721	−	0.321678i	0.758098	−	0.652140i	$-0.226129\pi$
$521$	−4.23916	−	7.34245i	−0.185721	−	0.321678i	−0.943819	+	0.330462i	$0.892795\pi$
$522$	−12.2261	+	33.5591i	−0.535120	+	1.46884i
$523$	13.5054	+	23.3921i	0.590550	+	1.02286i	0.994158	+	0.107931i	$0.0344226\pi$
$523$	13.5054	+	23.3921i	0.590550	+	1.02286i	−0.403608	+	0.914932i	$0.632244\pi$
$524$	−5.57114	+	31.4836i	−0.243377	+	1.37537i
$525$	−0.803300	+	0.463786i	−0.0350589	+	0.0202413i
$526$	2.62709	+	3.13278i	0.114547	+	0.136596i
$527$	−15.9177	+	27.5702i	−0.693384	+	1.20098i
$528$	0.441445	+	0.161280i	0.0192114	+	0.00701883i
$529$	−13.4581			−0.585136
$530$	−0.0941383	−	0.534835i	−0.00408911	−	0.0232317i
$531$	15.1617	+	26.2609i	0.657962	+	1.13962i
$532$	−6.09285	+	34.4319i	−0.264159	+	1.49281i
$533$	−3.23586	+	5.60468i	−0.140161	+	0.242766i
$534$	0.345338	−	0.0607843i	0.0149442	−	0.00263039i
$535$	0.465691	+	0.268867i	0.0201336	+	0.0116241i
$536$	10.8167	−	18.6958i	0.467212	−	0.807534i
$537$	0.233213	−	0.134646i	0.0100639	−	0.00581039i
$538$	3.43499	+	19.5155i	0.148093	+	0.841371i
$539$	1.33793	+	0.772453i	0.0576287	+	0.0332719i
$540$	−0.0601675	+	0.0716165i	−0.00258920	+	0.00308188i
$541$	−39.0532			−1.67903			−0.839514	−	0.543338i	$-0.817160\pi$
$541$	−39.0532			−1.67903			−0.839514	+	0.543338i	$0.817160\pi$
$542$	8.77288	−	24.0805i	0.376828	−	1.03435i
$543$	0.603463	−	1.04523i	0.0258971	−	0.0448551i
$544$	−23.7151	+	8.59081i	−1.01678	+	0.368328i
$545$	1.11049			0.0475680
$546$	−0.0608102	−	0.345485i	−0.00260244	−	0.0147854i
$547$	0.788689			0.0337219			0.0168610	−	0.999858i	$-0.494633\pi$
$547$	0.788689			0.0337219			0.0168610	+	0.999858i	$0.494633\pi$
$548$	23.4279	−	8.51095i	1.00079	−	0.363570i
$549$	28.6027			1.22073
$550$	11.7408	+	4.27735i	0.500630	+	0.182387i
$551$	−26.2683	−	45.4981i	−1.11907	−	1.93828i
$552$	0.980139	+	0.567075i	0.0417175	+	0.0241363i
$553$	−14.5969	−	8.42755i	−0.620725	−	0.358376i
$554$	1.31388	+	1.56679i	0.0558215	+	0.0665665i
$555$	−0.00282891	+	0.0473636i	−0.000120081	+	0.00201047i
$556$	5.35139	+	0.946948i	0.226950	+	0.0401595i
$557$	−3.62812	+	6.28408i	−0.153728	+	0.266265i	−0.932595	−	0.360924i	$-0.882461\pi$
$557$	−3.62812	+	6.28408i	−0.153728	+	0.266265i	0.778867	+	0.627189i	$0.215795\pi$
$558$	28.4199	+	10.3538i	1.20311	+	0.438310i
$559$	−7.75607	−	13.4339i	−0.328047	−	0.568194i
$560$	−0.227687	−	1.30052i	−0.00962152	−	0.0549568i
$561$			0.523899i			0.0221190i
$562$	−39.4658	−	14.3780i	−1.66476	−	0.606498i
$563$	14.9236			0.628954			0.314477	−	0.949265i	$-0.398171\pi$
$563$	14.9236			0.628954			0.314477	+	0.949265i	$0.398171\pi$
$564$	−0.550612	+	0.655385i	−0.0231850	+	0.0275967i
$565$		−	0.0672513i		−	0.00282928i
$566$	27.2588	+	32.5058i	1.14577	+	1.36632i
$567$	12.5701	−	21.7720i	0.527893	−	0.914337i
$568$	23.7236	+	13.7257i	0.995421	+	0.575917i
$569$			5.07491i			0.212751i	0.994326	+	0.106376i	$0.0339246\pi$
$569$			5.07491i			0.212751i	−0.994326	+	0.106376i	$0.966075\pi$
$570$	−0.0119163	−	0.0677012i	−0.000499121	−	0.00283569i
$571$	12.2321	+	7.06218i	0.511896	+	0.295543i	0.733612	−	0.679568i	$-0.237833\pi$
$571$	12.2321	+	7.06218i	0.511896	+	0.295543i	−0.221717	+	0.975111i	$0.571166\pi$
$572$	−3.03984	+	3.61827i	−0.127102	+	0.151287i
$573$	0.204591	+	0.354362i	0.00854692	+	0.0148037i
$574$	−6.59215	+	18.0947i	−0.275151	+	0.755258i
$575$	26.0732	+	15.0534i	1.08733	+	0.627768i
$576$	11.9446	+	20.7760i	0.497690	+	0.865665i
$577$	−23.9337	−	13.8181i	−0.996374	−	0.575257i	−0.0892008	−	0.996014i	$-0.528431\pi$
$577$	−23.9337	−	13.8181i	−0.996374	−	0.575257i	−0.907174	+	0.420757i	$0.861765\pi$
$578$	−2.61843	−	3.12245i	−0.108912	−	0.129877i
$579$	−0.0765669	−	0.132618i	−0.00318201	−	0.00551140i
$580$	1.51883	+	1.27602i	0.0630660	+	0.0529840i
$581$			1.00347i			0.0416308i
$582$	−0.946130	−	1.12825i	−0.0392183	−	0.0467674i
$583$	−2.89205	+	5.00917i	−0.119776	+	0.207459i
$584$	13.2596	−	7.63935i	0.548688	−	0.316119i
$585$	−0.234956	−	0.406956i	−0.00971425	−	0.0168256i
$586$	9.96401	−	8.35564i	0.411609	−	0.345168i
$587$	7.50930	+	13.0065i	0.309942	+	0.536835i	0.978349	−	0.206960i	$-0.0663571\pi$
$587$	7.50930	+	13.0065i	0.309942	+	0.536835i	−0.668407	+	0.743795i	$0.733024\pi$
$588$	−0.0394750	−	0.108662i	−0.00162792	−	0.00448115i
$589$	−38.5305	+	22.2456i	−1.58762	+	0.916614i
$590$	1.65866	−	0.291947i	0.0682860	−	0.0120193i
$591$	−1.11115			−0.0457067
$592$	22.3151	+	9.69719i	0.917146	+	0.398552i
$593$	−2.62264			−0.107699			−0.0538494	−	0.998549i	$-0.517149\pi$
$593$	−2.62264			−0.107699			−0.0538494	+	0.998549i	$0.517149\pi$
$594$	0.981173	−	0.172700i	0.0402580	−	0.00708596i
$595$	1.27458	−	0.735878i	0.0522526	−	0.0301680i
$596$	−9.64769	−	26.5570i	−0.395185	−	1.08782i
$597$	−0.0613824	−	0.106317i	−0.00251222	−	0.00435128i
$598$	−8.72441	+	7.31613i	−0.356768	+	0.299179i
$599$	15.0486	+	26.0650i	0.614870	+	1.06499i	0.990407	+	0.138179i	$0.0441250\pi$
$599$	15.0486	+	26.0650i	0.614870	+	1.06499i	−0.375537	+	0.926807i	$0.622542\pi$
$600$	−0.466808	−	0.810240i	−0.0190574	−	0.0330779i
$601$	20.5049	−	35.5155i	0.836413	−	1.44871i	−0.0564625	−	0.998405i	$-0.517982\pi$
$601$	20.5049	−	35.5155i	0.836413	−	1.44871i	0.892875	−	0.450304i	$-0.148685\pi$
$602$	−29.6603	−	35.3696i	−1.20886	−	1.44156i
$603$		−	22.8760i		−	0.931584i
$604$	−9.15865	−	7.69451i	−0.372660	−	0.313085i
$605$	−0.462333	−	0.800784i	−0.0187965	−	0.0325565i
$606$	−0.255913	−	0.305173i	−0.0103957	−	0.0123968i
$607$	−1.23016	−	0.710232i	−0.0499306	−	0.0288274i	0.474827	−	0.880079i	$-0.342511\pi$
$607$	−1.23016	−	0.710232i	−0.0499306	−	0.0288274i	−0.524757	+	0.851252i	$0.675844\pi$
$608$	−34.7056	−	6.17390i	−1.40750	−	0.250385i
$609$	1.35827	+	0.784195i	0.0550397	+	0.0317772i
$610$	0.543782	−	1.49262i	0.0220171	−	0.0604344i
$611$	−4.30348	−	7.45384i	−0.174100	−	0.301550i
$612$	−17.1839	+	20.4537i	−0.694616	+	0.826790i
$613$	22.8358	+	13.1843i	0.922331	+	0.532508i	0.884378	−	0.466772i	$-0.154583\pi$
$613$	22.8358	+	13.1843i	0.922331	+	0.532508i	0.0379529	+	0.999280i	$0.487916\pi$
$614$	−1.45957	−	8.29236i	−0.0589034	−	0.334652i
$615$		−	0.0378598i		−	0.00152665i
$616$	−7.04233	+	12.1720i	−0.283744	+	0.490426i
$617$	−1.14008	+	1.97467i	−0.0458978	+	0.0794973i	−0.888062	−	0.459724i	$-0.847948\pi$
$617$	−1.14008	+	1.97467i	−0.0458978	+	0.0794973i	0.842164	+	0.539222i	$0.181282\pi$
$618$	−0.415549	−	0.495538i	−0.0167158	−	0.0199335i
$619$		−	35.7164i		−	1.43557i	−0.696267	−	0.717783i	$-0.745157\pi$
$619$		−	35.7164i		−	1.43557i	0.696267	−	0.717783i	$-0.254843\pi$
$620$	1.08061	−	1.28624i	0.0433985	−	0.0516565i
$621$	2.40035			0.0963226
$622$	−3.42138	−	1.24646i	−0.137185	−	0.0499785i
$623$			10.4918i			0.420344i
$624$	0.348343	−	0.0609859i	0.0139449	−	0.00244139i
$625$	−12.3963	−	21.4710i	−0.495852	−	0.858840i
$626$	42.2998	+	15.4104i	1.69064	+	0.615925i
$627$	−0.366085	+	0.634078i	−0.0146200	+	0.0253226i
$628$	−0.803871	−	0.142248i	−0.0320780	−	0.00567631i
$629$	−1.61706	+	27.0740i	−0.0644764	+	1.07951i
$630$	−0.898506	−	1.07146i	−0.0357973	−	0.0426879i
$631$	−17.0288	−	9.83160i	−0.677907	−	0.391390i	0.121159	−	0.992633i	$-0.461339\pi$
$631$	−17.0288	−	9.83160i	−0.677907	−	0.391390i	−0.799066	+	0.601243i	$0.794672\pi$
$632$	8.50930	−	14.7076i	0.338482	−	0.585035i
$633$	0.172069	+	0.298032i	0.00683913	+	0.0118457i
$634$	−16.9834	−	6.18728i	−0.674496	−	0.245728i
$635$	−1.67959			−0.0666526
$636$	0.406829	−	0.147794i	0.0161318	−	0.00586040i
$637$	1.16247			0.0460588
$638$	−3.66259	−	20.8086i	−0.145003	−	0.823818i
$639$	29.0281			1.14833
$640$	1.31127	−	0.228338i	0.0518325	−	0.00902586i
$641$	5.10552	−	8.84303i	0.201656	−	0.349278i	−0.747406	−	0.664367i	$-0.768701\pi$
$641$	5.10552	−	8.84303i	0.201656	−	0.349278i	0.949062	+	0.315089i	$0.102034\pi$
$642$	−0.146712	+	0.402708i	−0.00579027	+	0.0158936i
$643$	14.5558			0.574023			0.287012	−	0.957927i	$-0.407338\pi$
$643$	14.5558			0.574023			0.287012	+	0.957927i	$0.407338\pi$
$644$	−21.7945	+	25.9416i	−0.858823	+	1.02224i
$645$	0.0785888	+	0.0453733i	0.00309443	+	0.00178657i
$646$	−6.81161	−	38.6993i	−0.267999	−	1.52260i
$647$	−35.7149	+	20.6200i	−1.40410	+	0.810656i	−0.994810	−	0.101750i	$-0.967556\pi$
$647$	−35.7149	+	20.6200i	−1.40410	+	0.810656i	−0.409287	+	0.912406i	$0.634222\pi$
$648$	21.9370	+	12.6920i	0.861766	+	0.498589i
$649$	−15.5347	−	8.96898i	−0.609792	−	0.352063i
$650$	9.26008	−	1.62990i	0.363210	−	0.0639300i
$651$	0.664104	−	1.15026i	0.0260283	−	0.0450823i
$652$	1.87603	−	10.6018i	0.0734709	−	0.415199i
$653$	−19.5700	−	33.8962i	−0.765832	−	1.32646i	−0.939806	−	0.341709i	$-0.888994\pi$
$653$	−19.5700	−	33.8962i	−0.765832	−	1.32646i	0.173974	−	0.984750i	$-0.444339\pi$
$654$	0.153433	+	0.871711i	0.00599971	+	0.0340866i
$655$	1.88072			0.0734858
$656$	−18.2354	−	6.66223i	−0.711971	−	0.260117i
$657$	8.10368	−	14.0360i	0.316155	−	0.547596i
$658$	−16.4571	−	19.6249i	−0.641564	−	0.765058i
$659$	−29.1716	+	16.8423i	−1.13637	+	0.656081i	−0.945528	−	0.325540i	$-0.894454\pi$
$659$	−29.1716	+	16.8423i	−1.13637	+	0.656081i	−0.190838	+	0.981622i	$0.561120\pi$
$660$	0.00481716	−	0.0272227i	0.000187508	−	0.00105964i
$661$	−10.0236	−	17.3614i	−0.389874	−	0.675281i	0.602559	−	0.798075i	$-0.294148\pi$
$661$	−10.0236	−	17.3614i	−0.389874	−	0.675281i	−0.992432	+	0.122794i	$0.960815\pi$
$662$	−10.9661	+	30.1007i	−0.426210	+	1.16990i
$663$	0.197105	+	0.341395i	0.00765491	+	0.0132587i
$664$	−1.01160		0.000921978i	−0.0392578		3.57797e-5i
$665$	2.05684			0.0797608
$666$	25.6002	−	2.94598i	0.991988	−	0.114154i
$667$		−	50.9061i		−	1.97109i
$668$	8.32334	−	9.90713i	0.322040	−	0.383319i
$669$	−0.243803	+	0.140760i	−0.00942596	+	0.00544208i
$670$	−1.19378	−	0.434910i	−0.0461196	−	0.0168020i
$671$	−14.6532	+	8.46002i	−0.565680	+	0.326595i
$672$	0.989422	−	0.358419i	0.0381678	−	0.0138263i
$673$	−9.91171	−	17.1676i	−0.382068	−	0.661761i	0.609290	−	0.792948i	$-0.291455\pi$
$673$	−9.91171	−	17.1676i	−0.382068	−	0.661761i	−0.991358	+	0.131186i	$0.958121\pi$
$674$	−2.75891	−	3.28997i	−0.106269	−	0.126725i
$675$	−1.71662	−	0.991089i	−0.0660726	−	0.0381470i
$676$	3.91081	−	22.1008i	0.150416	−	0.850029i
$677$		−	34.6863i		−	1.33310i	−0.745459	−	0.666551i	$-0.767770\pi$
$677$		−	34.6863i		−	1.33310i	0.745459	−	0.666551i	$-0.232230\pi$
$678$	0.0527910	−	0.00929195i	0.00202743	−	0.000356855i
$679$	38.1549	−	22.0287i	1.46425	−	0.845385i
$680$	0.740674	+	1.28559i	0.0284035	+	0.0493001i
$681$	−1.37967	−	0.796553i	−0.0528691	−	0.0305240i
$682$	−17.6219	+	3.10170i	−0.674779	+	0.118770i
$683$	6.85996	−	11.8818i	0.262489	−	0.454645i	−0.704414	−	0.709790i	$-0.748790\pi$
$683$	6.85996	−	11.8818i	0.262489	−	0.454645i	0.966903	+	0.255145i	$0.0821233\pi$
$684$	−35.0902	+	12.7476i	−1.34171	+	0.487418i
$685$	−0.733104	−	1.26977i	−0.0280105	−	0.0485156i
$686$	−23.9474	+	4.21508i	−0.914318	+	0.160932i
$687$	−0.840708	+	1.45615i	−0.0320750	+	0.0555555i
$688$	35.6836	−	29.8683i	1.36043	−	1.13872i
$689$			4.35226i			0.165808i
$690$	0.0228005	−	0.0625846i	0.000867999	−	0.00238256i
$691$	33.1616	+	19.1458i	1.26153	+	0.728342i	0.973370	−	0.229241i	$-0.0736245\pi$
$691$	33.1616	+	19.1458i	1.26153	+	0.728342i	0.288156	+	0.957584i	$0.406958\pi$
$692$	37.6656	+	6.66506i	1.43183	+	0.253367i
$693$			14.8936i			0.565763i
$694$	−34.4844	+	6.06973i	−1.30901	+	0.230404i
$695$		−	0.319673i		−	0.0121259i
$696$	−0.791802	+	1.36856i	−0.0300132	+	0.0518751i
$697$		−	21.6414i		−	0.819727i
$698$	−11.7963	−	4.29757i	−0.446497	−	0.162665i
$699$	0.390658	−	0.225547i	0.0147760	−	0.00853096i
$700$	26.2976	−	9.55343i	0.993954	−	0.361086i
$701$	12.3847	−	21.4509i	0.467763	−	0.810188i	−0.531559	−	0.847021i	$-0.678394\pi$
$701$	12.3847	−	21.4509i	0.467763	−	0.810188i	0.999321	+	0.0368329i	$0.0117269\pi$
$702$	0.574401	−	0.481682i	0.0216794	−	0.0181799i
$703$	−20.8756	+	31.6379i	−0.787340	+	1.19324i
$704$	−12.2643	−	7.11062i	−0.462227	−	0.267992i
$705$	0.0436052	+	0.0251755i	0.00164227	+	0.000948164i
$706$	32.9903	+	12.0188i	1.24161	+	0.452335i
$707$	10.3203	−	5.95841i	0.388134	−	0.224089i
$708$	0.458346	+	1.26168i	0.0172257	+	0.0474169i
$709$	33.6022			1.26196			0.630979	−	0.775800i	$-0.282654\pi$
$709$	33.6022			1.26196			0.630979	+	0.775800i	$0.282654\pi$
$710$	0.551870	−	1.51482i	0.0207113	−	0.0568502i
$711$		−	17.9961i		−	0.674906i
$712$	−10.5768	−	0.00963976i	−0.396384	−	0.000361265i
$713$	−43.1104			−1.61450
$714$	0.753756	+	0.898845i	0.0282086	+	0.0336384i
$715$	0.240737	+	0.138990i	0.00900305	+	0.00519791i
$716$	−7.63467	+	2.77354i	−0.285321	+	0.103652i
$717$	−0.433693			−0.0161966
$718$	−41.5954	+	7.32137i	−1.55233	+	0.273231i
$719$	8.33594	−	14.4383i	0.310878	−	0.538456i	−0.667675	−	0.744453i	$-0.732710\pi$
$719$	8.33594	−	14.4383i	0.310878	−	0.538456i	0.978553	+	0.205997i	$0.0660436\pi$
$720$	1.08097	−	0.904807i	0.0402854	−	0.0337202i
$721$	16.7580	−	9.67522i	0.624100	−	0.360324i
$722$	9.60006	−	26.3510i	0.357277	−	0.980684i
$723$	0.714745	−	1.23797i	0.0265816	−	0.0460408i
$724$	−23.4180	+	27.8740i	−0.870322	+	1.03593i
$725$	−21.0189	+	36.4057i	−0.780621	+	1.35207i
$726$	0.564721	−	0.473565i	0.0209588	−	0.0175757i
$727$	−14.4106	+	8.31995i	−0.534458	+	0.308570i	−0.742830	−	0.669480i	$-0.766517\pi$
$727$	−14.4106	+	8.31995i	−0.534458	+	0.308570i	0.208372	+	0.978050i	$0.433184\pi$
$728$	−0.00964387	+	10.5814i	−0.000357426	+	0.392171i
$729$	26.7629			0.991218
$730$	−0.578398	−	0.689733i	−0.0214075	−	0.0255282i
$731$	44.9229	+	25.9363i	1.66153	+	0.959287i
$732$	1.24681	+	0.220628i	0.0460835	+	0.00815463i
$733$	−37.0218	+	21.3745i	−1.36743	+	0.789486i	−0.990599	−	0.136796i	$-0.956320\pi$
$733$	−37.0218	+	21.3745i	−1.36743	+	0.789486i	−0.376831	+	0.926282i	$0.622986\pi$
$734$	4.28087	+	5.10490i	0.158010	+	0.188425i
$735$	−0.00588940	+	0.00340025i	−0.000217234	+	0.000125420i
$736$	−26.1319	−	21.9950i	−0.963236	−	0.810748i
$737$	6.76621	+	11.7194i	0.249236	+	0.431690i
$738$	−20.2505	+	3.56436i	−0.745430	+	0.131206i
$739$		−	9.95512i		−	0.366205i	−0.983094	−	0.183103i	$-0.941386\pi$
$739$		−	9.95512i		−	0.366205i	0.983094	−	0.183103i	$-0.0586140\pi$
$740$	0.332966	−	1.39194i	0.0122401	−	0.0511689i
$741$			0.550924i			0.0202387i
$742$	2.24507	+	12.7551i	0.0824191	+	0.468254i
$743$	6.26254	+	10.8470i	0.229750	+	0.397939i	0.957734	−	0.287655i	$-0.0928757\pi$
$743$	6.26254	+	10.8470i	0.229750	+	0.397939i	−0.727984	+	0.685594i	$0.759542\pi$
$744$	1.15898	+	0.670546i	0.0424902	+	0.0245834i
$745$	−1.43937	+	0.831019i	−0.0527344	+	0.0304462i
$746$	37.5477	−	31.4868i	1.37472	−	1.15282i
$747$	−0.927856	+	0.535698i	−0.0339485	+	0.0196002i
$748$	2.75358	−	15.5610i	0.100681	−	0.568968i
$749$	−11.1061	−	6.41211i	−0.405808	−	0.234293i
$750$	−0.0844103	+	0.0707850i	−0.00308223	+	0.00258470i
$751$	−36.9461			−1.34818			−0.674092	−	0.738647i	$-0.735465\pi$
$751$	−36.9461			−1.34818			−0.674092	+	0.738647i	$0.735465\pi$
$752$	19.7992	−	16.5725i	0.722001	−	0.604337i
$753$	0.742955	−	0.428945i	0.0270748	−	0.0156316i
$754$	−10.2154	−	12.1818i	−0.372024	−	0.443635i
$755$	−0.351814	+	0.609359i	−0.0128038	+	0.0221769i
$756$	1.43491	−	1.70795i	0.0521873	−	0.0621177i
$757$	2.35067	−	4.07149i	0.0854367	−	0.147981i	−0.820141	−	0.572162i	$-0.806105\pi$
$757$	2.35067	−	4.07149i	0.0854367	−	0.147981i	0.905577	+	0.424181i	$0.139438\pi$
$758$	36.8749	+	13.4341i	1.33936	+	0.487947i
$759$	−0.614399	+	0.354724i	−0.0223013	+	0.0128757i
$760$	−0.00188981	+	2.07352i	−6.85506e−5	+	0.0752144i
$761$	−15.6146	+	27.0452i	−0.566027	+	0.980388i	0.430926	+	0.902387i	$0.358187\pi$
$761$	−15.6146	+	27.0452i	−0.566027	+	0.980388i	−0.996953	+	0.0780005i	$0.975146\pi$
$762$	−0.232065	−	1.31845i	−0.00840683	−	0.0477624i
$763$	−26.4836			−0.958770
$764$	−4.21434	−	11.6007i	−0.152469	−	0.419699i
$765$	1.36086	+	0.785692i	0.0492020	+	0.0284068i
$766$	14.9821	−	12.5638i	0.541327	−	0.453947i
$767$	−13.4975			−0.487366
$768$	0.360416	+	0.997774i	0.0130054	+	0.0360041i
$769$			29.9901i			1.08147i	0.841193	+	0.540735i	$0.181854\pi$
$769$			29.9901i			1.08147i	−0.841193	+	0.540735i	$0.818146\pi$
$770$	0.777219	+	0.283152i	0.0280090	+	0.0102041i
$771$	−1.73875			−0.0626195
$772$	1.57719	+	4.34149i	0.0567642	+	0.156254i
$773$	−0.804044	+	0.464215i	−0.0289195	+	0.0166967i	−0.514390	−	0.857556i	$-0.671982\pi$
$773$	−0.804044	+	0.464215i	−0.0289195	+	0.0166967i	0.485471	+	0.874253i	$0.338648\pi$
$774$	16.8704	−	46.3074i	0.606395	−	1.66448i
$775$	30.8306	+	17.8000i	1.10747	+	0.639396i
$776$	22.1723	+	38.4845i	0.795939	+	1.38151i
$777$	0.0674657	−	1.12956i	0.00242032	−	0.0405227i
$778$	22.5981	+	26.9480i	0.810182	+	0.966133i
$779$	15.1224	−	26.1927i	0.541816	−	0.938452i
$780$	−0.00710285	−	0.0195519i	−0.000254323	−	0.000700069i
$781$	−14.8711	+	8.58585i	−0.532131	+	0.307226i
$782$	13.0332	−	35.7746i	0.466066	−	1.27930i
$783$			3.35158i			0.119776i
$784$	0.601381	+	3.43500i	0.0214779	+	0.122679i
$785$			0.0480204i			0.00171392i
$786$	0.259854	+	1.47633i	0.00926870	+	0.0526590i
$787$			34.1150i			1.21607i	0.793910	+	0.608035i	$0.208042\pi$
$787$			34.1150i			1.21607i	−0.793910	+	0.608035i	$0.791958\pi$
$788$	33.0039	+	5.84015i	1.17571	+	0.208047i
$789$	0.166006	+	0.0958437i	0.00590998	+	0.00341213i
$790$	−0.939119	−	0.342134i	−0.0334123	−	0.0121726i
$791$			1.60385i			0.0570264i
$792$	−15.0144	−	0.0136842i	−0.533514	−	0.000486246i
$793$	−6.36577	+	11.0258i	−0.226055	+	0.391539i
$794$	−1.46257	−	8.30942i	−0.0519047	−	0.294890i
$795$	−0.0127304	−	0.0220498i	−0.000451503	−	0.000782025i
$796$	1.26441	+	3.48050i	0.0448157	+	0.123363i
$797$	22.3658	−	38.7387i	0.792238	−	1.37220i	−0.132340	−	0.991204i	$-0.542249\pi$
$797$	22.3658	−	38.7387i	0.792238	−	1.37220i	0.924578	−	0.380992i	$-0.124418\pi$
$798$	0.284189	+	1.61458i	0.0100602	+	0.0571556i
$799$	24.9256	+	14.3908i	0.881804	+	0.509110i
$800$	9.60674	+	26.5196i	0.339650	+	0.937608i
$801$	−9.70122	+	5.60100i	−0.342776	+	0.197902i
$802$	−3.52831	−	20.0457i	−0.124589	−	0.707837i
$803$			9.58754i			0.338337i
$804$	0.176455	−	0.997182i	0.00622309	−	0.0351679i
$805$	1.72599	+	0.996503i	0.0608333	+	0.0351221i
$806$	−10.3163	+	8.65105i	−0.363376	+	0.304720i
$807$	0.464518	+	0.804569i	0.0163518	+	0.0283222i
$808$	5.99724	+	10.4094i	0.210982	+	0.366202i
$809$	−4.23943	+	2.44764i	−0.149050	+	0.0860543i	−0.572670	−	0.819786i	$-0.694093\pi$
$809$	−4.23943	+	2.44764i	−0.149050	+	0.0860543i	0.423620	+	0.905840i	$0.360759\pi$
$810$	0.510308	−	1.40074i	0.0179304	−	0.0492169i
$811$	−28.7819	+	16.6172i	−1.01067	+	0.583510i	−0.911387	−	0.411550i	$-0.864988\pi$
$811$	−28.7819	+	16.6172i	−1.01067	+	0.583510i	−0.0992810	+	0.995059i	$0.531654\pi$
$812$	−36.2220	−	30.4314i	−1.27114	−	1.06793i
$813$		−	1.20159i		−	0.0421417i
$814$	−12.2437	+	9.08119i	−0.429140	+	0.318296i
$815$	−0.633313			−0.0221840
$816$	−0.906827	+	0.759042i	−0.0317453	+	0.0265718i
$817$	36.2470	+	62.7817i	1.26812	+	2.19645i
$818$	−0.642608	−	0.234111i	−0.0224682	−	0.00818551i
$819$	5.60339	+	9.70535i	0.195798	+	0.339133i
$820$	−0.198989	+	1.12453i	−0.00694900	+	0.0392702i
$821$	2.33361	−	1.34731i	0.0814437	−	0.0470215i	−0.458725	−	0.888578i	$-0.651694\pi$
$821$	2.33361	−	1.34731i	0.0814437	−	0.0470215i	0.540169	+	0.841557i	$0.318360\pi$
$822$	0.895458	−	0.750915i	0.0312327	−	0.0261912i
$823$	−9.16810	+	15.8796i	−0.319580	+	0.553529i	−0.980400	−	0.197015i	$-0.936875\pi$
$823$	−9.16810	+	15.8796i	−0.319580	+	0.553529i	0.660821	+	0.750544i	$0.270208\pi$
$824$	9.73828	+	16.9028i	0.339249	+	0.588835i
$825$	0.585854			0.0203968
$826$	−39.5568	+	6.96254i	−1.37636	+	0.242258i
$827$	5.76131	+	9.97889i	0.200341	+	0.347000i	0.948638	−	0.316363i	$-0.102462\pi$
$827$	5.76131	+	9.97889i	0.200341	+	0.347000i	−0.748298	+	0.663363i	$0.769128\pi$
$828$	−35.6218	−	6.30341i	−1.23794	−	0.219059i
$829$	23.7205	−	41.0851i	0.823847	−	1.42694i	−0.0789503	−	0.996879i	$-0.525157\pi$
$829$	23.7205	−	41.0851i	0.823847	−	1.42694i	0.902797	−	0.430066i	$-0.141510\pi$
$830$	0.0103152	+	0.0586042i	0.000358044	+	0.00203418i
$831$	0.0830244	+	0.0479341i	0.00288008	+	0.00166282i
$832$	−10.6671	−	0.0194441i	−0.369817	−	0.000674104i
$833$	−3.36650	+	1.94365i	−0.116642	+	0.0673434i
$834$	0.250937	−	0.0441684i	0.00868925	−	0.00152943i
$835$	−0.659159	−	0.380566i	−0.0228111	−	0.0131700i
$836$	14.2063	−	16.9095i	0.491334	−	0.584828i
$837$	2.83832			0.0981067
$838$	−9.53138	−	3.47242i	−0.329256	−	0.119953i
$839$	−0.161050	+	0.278947i	−0.00556007	+	0.00963033i	−0.868792	−	0.495177i	$-0.835103\pi$
$839$	−0.161050	+	0.278947i	−0.00556007	+	0.00963033i	0.863232	+	0.504807i	$0.168437\pi$
$840$	−0.0309018	−	0.0536363i	−0.00106621	−	0.00185063i
$841$	42.0797			1.45103
$842$	−40.3367	+	7.09981i	−1.39009	+	0.244676i
$843$	−1.96930			−0.0678263
$844$	−3.54442	−	9.75665i	−0.122004	−	0.335838i
$845$	−1.32022			−0.0454169
$846$	9.36060	−	25.6938i	0.321824	−	0.883369i
$847$	11.0260	+	19.0976i	0.378858	+	0.656202i
$848$	−12.8606	+	2.25156i	−0.441634	+	0.0773188i
$849$	1.72248	+	0.994477i	0.0591155	+	0.0341303i
$850$	−24.0919	+	20.2030i	−0.826344	+	0.692957i
$851$	−32.8457	+	16.4350i	−1.12594	+	0.563383i
$852$	1.26536	+	0.223909i	0.0433504	+	0.00767100i
$853$	−0.939582	+	1.62740i	−0.0321707	+	0.0557212i	−0.881662	−	0.471881i	$-0.843575\pi$
$853$	−0.939582	+	1.62740i	−0.0321707	+	0.0557212i	0.849492	+	0.527602i	$0.176909\pi$
$854$	−12.9685	+	35.5969i	−0.443772	+	1.21810i
$855$	1.09804	+	1.90186i	0.0375521	+	0.0650422i
$856$	6.47431	−	11.1903i	0.221287	−	0.382475i
$857$		−	22.1967i		−	0.758225i	−0.925351	−	0.379112i	$-0.876229\pi$
$857$		−	22.1967i		−	0.758225i	0.925351	−	0.379112i	$-0.123771\pi$
$858$	−0.0758422	+	0.208178i	−0.00258921	+	0.00710708i
$859$	−6.66292			−0.227336			−0.113668	−	0.993519i	$-0.536260\pi$
$859$	−6.66292			−0.227336			−0.113668	+	0.993519i	$0.536260\pi$
$860$	−2.09580	−	1.76075i	−0.0714661	−	0.0600412i
$861$			0.902905i			0.0307709i
$862$	−30.6970	+	25.7420i	−1.04554	+	0.876775i
$863$	19.1729	−	33.2084i	0.652652	−	1.13043i	−0.329824	−	0.944042i	$-0.606990\pi$
$863$	19.1729	−	33.2084i	0.652652	−	1.13043i	0.982477	−	0.186385i	$-0.0596771\pi$
$864$	1.72049	+	1.44812i	0.0585321	+	0.0492660i
$865$		−	2.25001i		−	0.0765025i
$866$	13.3823	−	2.35547i	0.454749	−	0.0800421i
$867$	−0.165459	−	0.0955278i	−0.00561928	−	0.00324429i
$868$	−25.7712	+	30.6750i	−0.874730	+	1.04118i
$869$	5.32284	+	9.21942i	0.180565	+	0.312748i
$870$	0.0873863	+	0.0318361i	0.00296267	+	0.00107934i
$871$	8.81832	+	5.09126i	0.298797	+	0.172511i
$872$	0.0243329	−	26.6983i	0.000824016	−	0.904119i
$873$	40.7377	+	23.5199i	1.37876	+	0.796029i
$874$	40.7724	−	34.1910i	1.37915	−	1.15653i
$875$	−1.64809	−	2.85457i	−0.0557155	−	0.0965020i
$876$	0.461512	−	0.549331i	0.0155931	−	0.0185602i
$877$			22.3937i			0.756182i	0.925768	+	0.378091i	$0.123419\pi$
$877$			22.3937i			0.756182i	−0.925768	+	0.378091i	$0.876581\pi$
$878$	−6.17350	+	5.17699i	−0.208346	+	0.174715i
$879$	0.304837	−	0.527994i	0.0102819	−	0.0178088i
$880$	−0.286162	+	0.783261i	−0.00964652	+	0.0264037i
$881$	1.89824	+	3.28784i	0.0639532	+	0.110770i	0.896229	−	0.443591i	$-0.146296\pi$
$881$	1.89824	+	3.28784i	0.0639532	+	0.110770i	−0.832276	+	0.554362i	$0.812962\pi$
$882$	2.37319	+	2.83000i	0.0799095	+	0.0952912i
$883$	16.6281	+	28.8007i	0.559581	+	0.969222i	0.997531	+	0.0702232i	$0.0223712\pi$
$883$	16.6281	+	28.8007i	0.559581	+	0.969222i	−0.437951	+	0.898999i	$0.644296\pi$
$884$	−4.06012	−	11.1762i	−0.136557	−	0.375897i
$885$	0.0683820	−	0.0394804i	0.00229864	−	0.00132712i
$886$	4.29746	+	24.4155i	0.144376	+	0.820254i
$887$	−16.6114			−0.557756			−0.278878	−	0.960327i	$-0.589962\pi$
$887$	−16.6114			−0.557756			−0.278878	+	0.960327i	$0.589962\pi$
$888$	1.13866	+	0.0690506i	0.0382108	+	0.00231718i
$889$	40.0560			1.34343
$890$	0.107850	+	0.612738i	0.00361515	+	0.0205390i
$891$	−13.7512	+	7.93925i	−0.460682	+	0.265975i
$892$	7.98135	−	2.89948i	0.267235	−	0.0970818i
$893$	20.1117	+	34.8346i	0.673014	+	1.16569i
$894$	−0.851209	−	1.01506i	−0.0284687	−	0.0339486i
$895$	0.238903	+	0.413793i	0.00798566	+	0.0138316i
$896$	−31.2720	+	5.44555i	−1.04472	+	0.181923i
$897$	−0.266913	+	0.462307i	−0.00891197	+	0.0154360i
$898$	−15.8994	+	13.3329i	−0.530569	+	0.444926i
$899$		−	60.1946i		−	2.00760i
$900$	22.8725	+	19.2160i	0.762415	+	0.640532i
$901$	−7.27697	−	12.6041i	−0.242431	−	0.419903i
$902$	9.32009	−	7.81566i	0.310325	−	0.260233i
$903$	−1.87424	−	1.08209i	−0.0623707	−	0.0360097i
$904$	−1.61686	−	0.00147361i	−0.0537759	−	4.90114e-5i
$905$	1.85456	+	1.07073i	0.0616478	+	0.0355924i
$906$	−0.526945	−	0.191974i	−0.0175066	−	0.00637790i
$907$	−6.18617	−	10.7148i	−0.205409	−	0.355778i	0.744854	−	0.667227i	$-0.232519\pi$
$907$	−6.18617	−	10.7148i	−0.205409	−	0.355778i	−0.950263	+	0.311449i	$0.899186\pi$
$908$	36.7928	+	30.9110i	1.22101	+	1.02582i
$909$	11.0189	+	6.36176i	0.365474	+	0.211006i
$910$	0.612999	−	0.107896i	0.0203207	−	0.00357673i
$911$			7.60836i			0.252076i	0.992025	+	0.126038i	$0.0402262\pi$
$911$			7.60836i			0.252076i	−0.992025	+	0.126038i	$0.959774\pi$
$912$	−1.62794	+	0.285010i	−0.0539063	+	0.00943761i
$913$	0.316895	−	0.548877i	0.0104877	−	0.0181652i
$914$	−4.19326	+	3.51640i	−0.138701	+	0.116312i
$915$		−	0.0744800i		−	0.00246223i
$916$	32.6244	−	38.8324i	1.07794	−	1.28306i
$917$	−44.8526			−1.48116
$918$	−0.858084	+	2.35534i	−0.0283210	+	0.0777378i
$919$			28.8584i			0.951950i	0.879459	+	0.475975i	$0.157905\pi$
$919$			28.8584i			0.951950i	−0.879459	+	0.475975i	$0.842095\pi$
$920$	−1.00617	+	1.73907i	−0.0331724	+	0.0573356i
$921$	−0.197380	−	0.341871i	−0.00650388	−	0.0112650i
$922$	−6.86837	+	18.8529i	−0.226198	+	0.620887i
$923$	−6.46046	+	11.1898i	−0.212649	+	0.368318i
$924$	−0.114883	+	0.649225i	−0.00377936	+	0.0213579i
$925$	30.2757	+	1.80829i	0.995458	+	0.0594562i
$926$	−12.9633	+	10.8708i	−0.426002	+	0.357237i
$927$	17.8924	+	10.3302i	0.587664	+	0.339288i
$928$	30.7115	−	36.4878i	1.00815	−	1.19777i
$929$	28.2239	+	48.8852i	0.925995	+	1.60387i	0.789953	+	0.613167i	$0.210105\pi$
$929$	28.2239	+	48.8852i	0.925995	+	1.60387i	0.136042	+	0.990703i	$0.456562\pi$
$930$	0.0269607	−	0.0740040i	0.000884076	−	0.00242669i
$931$	−5.43266			−0.178048
$932$	−12.7889	+	4.64599i	−0.418916	+	0.152185i
$933$	−0.170723			−0.00558923
$934$	56.6117	−	9.96443i	1.85239	−	0.326046i
$935$	−0.929560			−0.0303999
$936$	−9.78920	+	5.63991i	−0.319970	+	0.184346i
$937$	−19.8799	+	34.4331i	−0.649449	+	1.12488i	0.333806	+	0.942642i	$0.391667\pi$
$937$	−19.8799	+	34.4331i	−0.649449	+	1.12488i	−0.983255	+	0.182237i	$0.941666\pi$
$938$	28.4699	+	10.3720i	0.929576	+	0.338658i
$939$	2.11071			0.0688806
$940$	−1.16286	−	0.976958i	−0.0379282	−	0.0318649i
$941$	25.3211	+	14.6191i	0.825443	+	0.476570i	0.852290	−	0.523070i	$-0.175213\pi$
$941$	25.3211	+	14.6191i	0.825443	+	0.476570i	−0.0268470	+	0.999640i	$0.508547\pi$
$942$	−0.0376951	+	0.00663486i	−0.00122817	+	0.000216175i
$943$	25.3798	−	14.6531i	0.826481	−	0.477169i
$944$	−6.98265	−	39.8840i	−0.227266	−	1.29811i
$945$	−0.113637	−	0.0656081i	−0.00369660	−	0.00213423i
$946$	5.05392	+	28.7132i	0.164317	+	0.933547i
$947$	−13.5486	+	23.4669i	−0.440272	+	0.762573i	−0.997709	−	0.0676457i	$-0.978451\pi$
$947$	−13.5486	+	23.4669i	−0.440272	+	0.762573i	0.557438	+	0.830219i	$0.311785\pi$
$948$	0.138813	−	0.784463i	0.00450845	−	0.0254782i
$949$	3.60709	+	6.24766i	0.117091	+	0.202808i
$950$	−43.2758	+	7.61714i	−1.40405	+	0.247133i
$951$	−0.847451			−0.0274805
$952$	−17.6641	−	30.6595i	−0.572495	−	0.993681i
$953$	−4.67199	+	8.09212i	−0.151341	+	0.262130i	−0.931721	−	0.363176i	$-0.881692\pi$
$953$	−4.67199	+	8.09212i	−0.151341	+	0.262130i	0.780380	+	0.625306i	$0.215026\pi$
$954$	−10.5955	+	8.88517i	−0.343041	+	0.287668i
$955$	−0.628750	+	0.363009i	−0.0203459	+	0.0117467i
$956$	12.8817	+	2.27947i	0.416625	+	0.0737232i
$957$	−0.495297	−	0.857880i	−0.0160107	−	0.0277313i
$958$	38.5452	+	14.0426i	1.24534	+	0.453695i
$959$	17.4835	+	30.2824i	0.564573	+	0.977869i
$960$	0.0540996	−	0.0311031i	0.00174606	−	0.00100385i
$961$	−19.9764			−0.644402
$962$	−4.56192	+	10.5241i	−0.147082	+	0.339311i
$963$		−	13.6923i		−	0.441230i
$964$	−27.7363	+	33.0141i	−0.893327	+	1.06331i
$965$	0.235305	−	0.135854i	0.00757475	−	0.00437328i
$966$	−0.543760	+	1.49256i	−0.0174952	+	0.0480222i
$967$	48.6874	−	28.1097i	1.56568	−	0.903947i	0.569018	−	0.822325i	$-0.307323\pi$
$967$	48.6874	−	28.1097i	1.56568	−	0.903947i	0.996663	−	0.0816217i	$-0.0260099\pi$
$968$	−19.2626	+	11.0979i	−0.619123	+	0.356699i
$969$	−0.921144	−	1.59547i	−0.0295914	−	0.0512538i
$970$	2.00187	−	1.67873i	0.0642761	−	0.0539008i
$971$	−46.6750	−	26.9478i	−1.49787	−	0.864796i	−0.497874	−	0.867249i	$-0.665886\pi$
$971$	−46.6750	−	26.9478i	−1.49787	−	0.864796i	−0.999997	+	0.00245303i	$0.999219\pi$
$972$	3.51879	+	0.622662i	0.112865	+	0.0199719i
$973$			7.62376i			0.244407i
$974$	−8.73080	−	49.6029i	−0.279753	−	1.58938i
$975$	0.381768	−	0.220414i	0.0122264	−	0.00705889i
$976$	−35.8736	−	13.1063i	−1.14829	−	0.419523i
$977$	−41.6623	−	24.0537i	−1.33289	−	0.769547i	−0.347152	−	0.937809i	$-0.612851\pi$
$977$	−41.6623	−	24.0537i	−1.33289	−	0.769547i	−0.985742	+	0.168262i	$0.946185\pi$
$978$	−0.0875034	−	0.497139i	−0.00279805	−	0.0158968i
$979$	3.31330	−	5.73880i	0.105893	−	0.183413i
$980$	0.192801	−	0.0700411i	0.00615879	−	0.00223738i
$981$	−14.1382	−	24.4880i	−0.451397	−	0.781843i
$982$	−5.27335	−	29.9599i	−0.168279	−	0.956057i
$983$	−0.144476	+	0.250239i	−0.00460806	+	0.00798139i	−0.868320	−	0.496004i	$-0.834800\pi$
$983$	−0.144476	+	0.250239i	−0.00460806	+	0.00798139i	0.863712	+	0.503985i	$0.168133\pi$
$984$	−0.910226		0.000829582i	−0.0290170		2.64461e-5i
$985$		−	1.97153i		−	0.0628183i
$986$	49.9517	+	18.1981i	1.59079	+	0.579546i
$987$	−1.03993	−	0.600401i	−0.0331012	−	0.0191110i
$988$	2.89563	−	16.3638i	0.0921221	−	0.520601i
$989$			70.2441i			2.23363i
$990$	0.153099	+	0.869816i	0.00486582	+	0.0276446i
$991$			14.7001i			0.466964i	0.972361	+	0.233482i	$0.0750121\pi$
$991$			14.7001i			0.466964i	−0.972361	+	0.233482i	$0.924988\pi$
$992$	−30.9001	−	26.0083i	−0.981078	−	0.825765i
$993$			1.50199i			0.0476643i
$994$	−13.1614	+	36.1264i	−0.417453	+	1.14586i
$995$	0.188640	−	0.108912i	0.00598031	−	0.00345273i
$996$	−0.0445780	+	0.0161944i	−0.00141251	+	0.000513139i
$997$	−4.47953	+	7.75877i	−0.141868	+	0.245723i	−0.928200	−	0.372081i	$-0.878644\pi$
$997$	−4.47953	+	7.75877i	−0.141868	+	0.245723i	0.786332	+	0.617804i	$0.211978\pi$
$998$	−11.6117	−	13.8468i	−0.367561	−	0.438313i
$999$	2.16251	−	1.08205i	0.0684188	−	0.0342346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	296.2.q.a.101.1	yes	72
4.3	odd	2		1184.2.y.a.1137.19		72
8.3	odd	2		1184.2.y.a.1137.18		72
8.5	even	2	inner	296.2.q.a.101.14	yes	72
37.11	even	6	inner	296.2.q.a.85.14	yes	72
148.11	odd	6		1184.2.y.a.529.18		72
296.11	odd	6		1184.2.y.a.529.19		72
296.85	even	6	inner	296.2.q.a.85.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.1	✓	72	296.85	even	6	inner
296.2.q.a.85.14	yes	72	37.11	even	6	inner
296.2.q.a.101.1	yes	72	1.1	even	1	trivial
296.2.q.a.101.14	yes	72	8.5	even	2	inner
1184.2.y.a.529.18		72	148.11	odd	6
1184.2.y.a.529.19		72	296.11	odd	6
1184.2.y.a.1137.18		72	8.3	odd	2
1184.2.y.a.1137.19		72	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39280 + 0.245152i) q^{2} +(-0.0574215 + 0.0331523i) q^{3} +(1.87980 - 0.682898i) q^{4} +(-0.0588225 - 0.101884i) q^{5} +(0.0718494 - 0.0602516i) q^{6} +(1.40284 + 2.42979i) q^{7} +(-2.45078 + 1.41198i) q^{8} +(-1.49780 + 2.59427i) q^{9} +(0.106905 + 0.127483i) q^{10} -1.77206i q^{11} +(-0.0853013 + 0.101533i) q^{12} +(-0.666698 - 1.15475i) q^{13} +(-2.54954 - 3.04030i) q^{14} +(0.00675535 + 0.00390021i) q^{15} +(3.06730 - 2.56742i) q^{16} +(3.86149 + 2.22943i) q^{17} +(1.45015 - 3.98050i) q^{18} +(3.11573 + 5.39660i) q^{19} +(-0.180151 - 0.151351i) q^{20} +(-0.161106 - 0.0930146i) q^{21} +(0.434426 + 2.46814i) q^{22} +6.03806i q^{23} +(0.0939168 - 0.162327i) q^{24} +(2.49308 - 4.31814i) q^{25} +(1.21167 + 1.44490i) q^{26} -0.397536i q^{27} +(4.29635 + 3.60952i) q^{28} -8.43088 q^{29} +(-0.0103650 - 0.00377613i) q^{30} +7.13978i q^{31} +(-3.64273 + 4.32787i) q^{32} +(0.0587480 + 0.101754i) q^{33} +(-5.92485 - 2.15851i) q^{34} +(0.165037 - 0.285852i) q^{35} +(-1.04395 + 5.89955i) q^{36} +(2.72190 + 5.43979i) q^{37} +(-5.66258 - 6.75257i) q^{38} +(0.0765655 + 0.0442051i) q^{39} +(0.288019 + 0.166638i) q^{40} +(-2.42678 - 4.20331i) q^{41} +(0.247192 + 0.0900555i) q^{42} +11.6336 q^{43} +(-1.21014 - 3.33113i) q^{44} +0.352418 q^{45} +(-1.48024 - 8.40982i) q^{46} +6.45491 q^{47} +(-0.0910128 + 0.249113i) q^{48} +(-0.435906 + 0.755012i) q^{49} +(-2.41377 + 6.62550i) q^{50} -0.295643 q^{51} +(-2.04184 - 1.71542i) q^{52} +(-2.82675 - 1.63202i) q^{53} +(0.0974570 + 0.553689i) q^{54} +(-0.180544 + 0.104237i) q^{55} +(-6.86885 - 3.97409i) q^{56} +(-0.357819 - 0.206587i) q^{57} +(11.7426 - 2.06685i) q^{58} +(5.06132 - 8.76647i) q^{59} +(0.0153622 + 0.00271839i) q^{60} +(-4.77411 - 8.26900i) q^{61} +(-1.75033 - 9.94431i) q^{62} -8.40469 q^{63} +(4.01262 - 6.92090i) q^{64} +(-0.0784337 + 0.135851i) q^{65} +(-0.106770 - 0.127322i) q^{66} +(-6.61343 + 3.81827i) q^{67} +(8.78131 + 1.55388i) q^{68} +(-0.200175 - 0.346714i) q^{69} +(-0.159787 + 0.438595i) q^{70} +(-4.84512 - 8.39199i) q^{71} +(0.00772217 - 8.47284i) q^{72} -5.41038 q^{73} +(-5.12464 - 6.90927i) q^{74} +0.330605i q^{75} +(9.54227 + 8.01680i) q^{76} +(4.30573 - 2.48592i) q^{77} +(-0.117478 - 0.0427988i) q^{78} +(-5.20265 + 3.00375i) q^{79} +(-0.442005 - 0.161485i) q^{80} +(-4.48023 - 7.75998i) q^{81} +(4.41048 + 5.25945i) q^{82} +(0.309739 + 0.178828i) q^{83} +(-0.366367 - 0.0648299i) q^{84} -0.524564i q^{85} +(-16.2033 + 2.85200i) q^{86} +(0.484113 - 0.279503i) q^{87} +(2.50212 + 4.34293i) q^{88} +(3.23848 + 1.86974i) q^{89} +(-0.490849 + 0.0863962i) q^{90} +(1.87054 - 3.23987i) q^{91} +(4.12338 + 11.3503i) q^{92} +(-0.236700 - 0.409977i) q^{93} +(-8.99042 + 1.58244i) q^{94} +(0.366550 - 0.634883i) q^{95} +(0.0656922 - 0.369278i) q^{96} -15.7030i q^{97} +(0.422038 - 1.15845i) q^{98} +(4.59721 + 2.65420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 6 q^{2} - 2 q^{4} + 2 q^{7} + 30 q^{9} - 12 q^{12} - 6 q^{15} - 6 q^{16} - 12 q^{17} - 48 q^{18} + 18 q^{20} - 12 q^{22} - 6 q^{24} - 32 q^{25} - 16 q^{26} + 10 q^{28} - 14 q^{30} - 6 q^{32} + 4 q^{33}+ \cdots + 48 q^{98}+O(q^{100}) \) 72 * q - 6 * q^2 - 2 * q^4 + 2 * q^7 + 30 * q^9 - 12 * q^12 - 6 * q^15 - 6 * q^16 - 12 * q^17 - 48 * q^18 + 18 * q^20 - 12 * q^22 - 6 * q^24 - 32 * q^25 - 16 * q^26 + 10 * q^28 - 14 * q^30 - 6 * q^32 + 4 * q^33 + 8 * q^34 + 4 * q^36 - 24 * q^38 - 6 * q^39 - 18 * q^40 + 6 * q^42 - 10 * q^44 - 8 * q^46 + 32 * q^47 + 20 * q^48 - 18 * q^49 + 12 * q^50 + 42 * q^52 + 30 * q^54 + 24 * q^55 - 24 * q^56 - 6 * q^57 - 8 * q^58 + 32 * q^62 + 8 * q^63 - 68 * q^64 + 6 * q^65 + 20 * q^70 + 18 * q^71 + 18 * q^72 - 64 * q^73 - 12 * q^74 - 72 * q^76 + 54 * q^78 + 54 * q^79 - 16 * q^81 - 12 * q^84 + 48 * q^86 - 108 * q^87 - 36 * q^89 + 24 * q^90 - 120 * q^92 - 72 * q^94 + 50 * q^95 + 36 * q^96 + 48 * q^98

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