LMFDB - Embedded newform 882.2.u.c.505.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(127,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.u (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,1,0,-1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			505.1
Root			$0.222521 + 0.974928i$ of defining polynomial
Character	$\chi$	$=$	882.505
Dual form			882.2.u.c.379.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.554958 + 0.695895i) q^{5} +(-2.57942 - 0.588735i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.554958 + 0.695895i) q^{10} +(-0.198062 + 0.867767i) q^{11} +(-0.881355 + 3.86147i) q^{13} +(-1.14795 + 2.38374i) q^{14} +(0.623490 + 0.781831i) q^{16} +(4.04892 - 1.94986i) q^{17} +4.44504 q^{19} +(0.801938 - 0.386193i) q^{20} +(0.801938 + 0.386193i) q^{22} +(8.29590 + 3.99509i) q^{23} +(0.936313 + 4.10225i) q^{25} +(3.56853 + 1.71851i) q^{26} +(2.06853 + 1.64960i) q^{28} +(4.85086 - 2.33605i) q^{29} -4.47219 q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.00000 - 4.38129i) q^{34} +(1.84117 - 1.46828i) q^{35} +(-9.47434 + 4.56260i) q^{37} +(0.989115 - 4.33360i) q^{38} +(-0.198062 - 0.867767i) q^{40} +(-4.74094 + 5.94495i) q^{41} +(2.83244 + 3.55176i) q^{43} +(0.554958 - 0.695895i) q^{44} +(5.74094 - 7.19891i) q^{46} +(1.09783 - 4.80993i) q^{47} +(6.30678 + 3.03719i) q^{49} +4.20775 q^{50} +(2.46950 - 3.09666i) q^{52} +(10.1860 + 4.90531i) q^{53} +(-0.493959 - 0.619405i) q^{55} +(2.06853 - 1.64960i) q^{56} +(-1.19806 - 5.24905i) q^{58} +(5.10992 + 6.40763i) q^{59} +(-11.0782 + 5.33499i) q^{61} +(-0.995156 + 4.36006i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(-2.19806 - 2.75628i) q^{65} +6.13706 q^{67} -4.49396 q^{68} +(-1.02177 - 2.12173i) q^{70} +(-12.3448 - 5.94495i) q^{71} +(-1.29105 - 5.65647i) q^{73} +(2.33997 + 10.2521i) q^{74} +(-4.00484 - 1.92863i) q^{76} +(1.02177 - 2.12173i) q^{77} +3.67994 q^{79} -0.890084 q^{80} +(4.74094 + 5.94495i) q^{82} +(-0.493959 - 2.16418i) q^{83} +(-0.890084 + 3.89971i) q^{85} +(4.09299 - 1.97108i) q^{86} +(-0.554958 - 0.695895i) q^{88} +(2.86831 + 12.5669i) q^{89} +(4.54676 - 9.44145i) q^{91} +(-5.74094 - 7.19891i) q^{92} +(-4.44504 - 2.14062i) q^{94} +(-2.46681 + 3.09328i) q^{95} -15.7506 q^{97} +(4.36443 - 5.47282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} + 4 q^{10} - 10 q^{11} + 12 q^{13} + 7 q^{14} - q^{16} + 6 q^{17} + 26 q^{19} - 4 q^{20} - 4 q^{22} + 22 q^{23} - 11 q^{25} + 16 q^{26} + 7 q^{28} + 2 q^{29}+ \cdots - 7 q^{98}+O(q^{100}) $ 6 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 + 4 * q^10 - 10 * q^11 + 12 * q^13 + 7 * q^14 - q^16 + 6 * q^17 + 26 * q^19 - 4 * q^20 - 4 * q^22 + 22 * q^23 - 11 * q^25 + 16 * q^26 + 7 * q^28 + 2 * q^29 - 14 * q^31 + q^32 - 6 * q^34 + 28 * q^35 - 25 * q^37 + 9 * q^38 - 10 * q^40 + 18 * q^43 + 4 * q^44 + 6 * q^46 - 30 * q^47 + 7 * q^49 - 10 * q^50 + 5 * q^52 + 32 * q^53 + 16 * q^55 + 7 * q^56 - 16 * q^58 + 32 * q^59 - 17 * q^61 - 28 * q^62 - q^64 - 22 * q^65 + 26 * q^67 - 8 * q^68 - 28 * q^71 - 2 * q^73 - 10 * q^74 - 2 * q^76 - 26 * q^79 - 4 * q^80 + 16 * q^83 - 4 * q^85 + 10 * q^86 - 4 * q^88 + 22 * q^89 + 28 * q^91 - 6 * q^92 - 26 * q^94 - 8 * q^95 - 22 * q^97 - 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$		0			0
$3$		0			0
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.554958	+	0.695895i	−0.248185	+	0.311214i	−0.890282	−	0.455409i	$-0.849493\pi$
$5$	−0.554958	+	0.695895i	−0.248185	+	0.311214i	0.642097	+	0.766623i	$0.278064\pi$
$6$		0			0
$7$	−2.57942	−	0.588735i	−0.974928	−	0.222521i
$7$	−2.57942	−	0.588735i	−0.974928	−	0.222521i
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$		0			0
$10$	0.554958	+	0.695895i	0.175493	+	0.220061i
$11$	−0.198062	+	0.867767i	−0.0597180	+	0.261642i	−0.995970	−	0.0896876i	$-0.971413\pi$
$11$	−0.198062	+	0.867767i	−0.0597180	+	0.261642i	0.936252	+	0.351329i	$0.114270\pi$
$12$		0			0
$13$	−0.881355	+	3.86147i	−0.244444	+	1.07098i	0.692478	+	0.721439i	$0.256519\pi$
$13$	−0.881355	+	3.86147i	−0.244444	+	1.07098i	−0.936922	+	0.349539i	$0.886338\pi$
$14$	−1.14795	+	2.38374i	−0.306802	+	0.637081i
$15$		0			0
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	4.04892	−	1.94986i	0.982007	−	0.472910i	0.127212	−	0.991876i	$-0.459397\pi$
$17$	4.04892	−	1.94986i	0.982007	−	0.472910i	0.854795	+	0.518966i	$0.173683\pi$
$18$		0			0
$19$	4.44504			1.01976			0.509881	−	0.860245i	$-0.329689\pi$
$19$	4.44504			1.01976			0.509881	+	0.860245i	$0.329689\pi$
$20$	0.801938	−	0.386193i	0.179319	−	0.0863553i
$21$		0			0
$22$	0.801938	+	0.386193i	0.170974	+	0.0823366i
$23$	8.29590	+	3.99509i	1.72981	+	0.833035i	0.986433	+	0.164167i	$0.0524936\pi$
$23$	8.29590	+	3.99509i	1.72981	+	0.833035i	0.743382	+	0.668868i	$0.233221\pi$
$24$		0			0
$25$	0.936313	+	4.10225i	0.187263	+	0.820451i
$26$	3.56853	+	1.71851i	0.699847	+	0.337028i
$27$		0			0
$28$	2.06853	+	1.64960i	0.390916	+	0.311745i
$29$	4.85086	−	2.33605i	0.900781	−	0.433793i	0.0746102	−	0.997213i	$-0.476229\pi$
$29$	4.85086	−	2.33605i	0.900781	−	0.433793i	0.826171	+	0.563419i	$0.190514\pi$
$30$		0			0
$31$	−4.47219			−0.803229			−0.401614	−	0.915809i	$-0.631551\pi$
$31$	−4.47219			−0.803229			−0.401614	+	0.915809i	$0.631551\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$		0			0
$34$	−1.00000	−	4.38129i	−0.171499	−	0.751384i
$35$	1.84117	−	1.46828i	0.311214	−	0.248185i
$36$		0			0
$37$	−9.47434	+	4.56260i	−1.55757	+	0.750087i	−0.996954	−	0.0779869i	$-0.975151\pi$
$37$	−9.47434	+	4.56260i	−1.55757	+	0.750087i	−0.560618	+	0.828074i	$0.689436\pi$
$38$	0.989115	−	4.33360i	0.160456	−	0.703002i
$39$		0			0
$40$	−0.198062	−	0.867767i	−0.0313164	−	0.137206i
$41$	−4.74094	+	5.94495i	−0.740410	+	0.928445i	−0.999298	−	0.0374623i	$-0.988073\pi$
$41$	−4.74094	+	5.94495i	−0.740410	+	0.928445i	0.258888	+	0.965907i	$0.416644\pi$
$42$		0			0
$43$	2.83244	+	3.55176i	0.431943	+	0.541639i	0.949400	−	0.314070i	$-0.101693\pi$
$43$	2.83244	+	3.55176i	0.431943	+	0.541639i	−0.517457	+	0.855709i	$0.673121\pi$
$44$	0.554958	−	0.695895i	0.0836631	−	0.104910i
$45$		0			0
$46$	5.74094	−	7.19891i	0.846455	−	1.06142i
$47$	1.09783	−	4.80993i	0.160136	−	0.701600i	−0.829561	−	0.558417i	$-0.811409\pi$
$47$	1.09783	−	4.80993i	0.160136	−	0.701600i	0.989696	−	0.143183i	$-0.0457339\pi$
$48$		0			0
$49$	6.30678	+	3.03719i	0.900969	+	0.433884i
$50$	4.20775			0.595066
$51$		0			0
$52$	2.46950	−	3.09666i	0.342458	−	0.429429i
$53$	10.1860	+	4.90531i	1.39915	+	0.673796i	0.972989	−	0.230850i	$-0.0741508\pi$
$53$	10.1860	+	4.90531i	1.39915	+	0.673796i	0.426163	+	0.904646i	$0.359865\pi$
$54$		0			0
$55$	−0.493959	−	0.619405i	−0.0666054	−	0.0835206i
$56$	2.06853	−	1.64960i	0.276419	−	0.220437i
$57$		0			0
$58$	−1.19806	−	5.24905i	−0.157313	−	0.689235i
$59$	5.10992	+	6.40763i	0.665254	+	0.834203i	0.993904	−	0.110249i	$-0.0351649\pi$
$59$	5.10992	+	6.40763i	0.665254	+	0.834203i	−0.328650	+	0.944452i	$0.606593\pi$
$60$		0			0
$61$	−11.0782	+	5.33499i	−1.41842	+	0.683075i	−0.976805	−	0.214129i	$-0.931309\pi$
$61$	−11.0782	+	5.33499i	−1.41842	+	0.683075i	−0.441615	+	0.897204i	$0.645594\pi$
$62$	−0.995156	+	4.36006i	−0.126385	+	0.553728i
$63$		0			0
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−2.19806	−	2.75628i	−0.272636	−	0.341875i
$66$		0			0
$67$	6.13706			0.749762			0.374881	−	0.927073i	$-0.377684\pi$
$67$	6.13706			0.749762			0.374881	+	0.927073i	$0.377684\pi$
$68$	−4.49396			−0.544973
$69$		0			0
$70$	−1.02177	−	2.12173i	−0.122125	−	0.253595i
$71$	−12.3448	−	5.94495i	−1.46506	−	0.705536i	−0.479924	−	0.877310i	$-0.659336\pi$
$71$	−12.3448	−	5.94495i	−1.46506	−	0.705536i	−0.985136	+	0.171775i	$0.945050\pi$
$72$		0			0
$73$	−1.29105	−	5.65647i	−0.151106	−	0.662040i	−0.992565	−	0.121718i	$-0.961160\pi$
$73$	−1.29105	−	5.65647i	−0.151106	−	0.662040i	0.841458	−	0.540322i	$-0.181698\pi$
$74$	2.33997	+	10.2521i	0.272016	+	1.19178i
$75$		0			0
$76$	−4.00484	−	1.92863i	−0.459387	−	0.221229i
$77$	1.02177	−	2.12173i	0.116442	−	0.241793i
$78$		0			0
$79$	3.67994			0.414026			0.207013	−	0.978338i	$-0.433626\pi$
$79$	3.67994			0.414026			0.207013	+	0.978338i	$0.433626\pi$
$80$	−0.890084			−0.0995144
$81$		0			0
$82$	4.74094	+	5.94495i	0.523549	+	0.656510i
$83$	−0.493959	−	2.16418i	−0.0542191	−	0.237549i	0.940556	−	0.339638i	$-0.110305\pi$
$83$	−0.493959	−	2.16418i	−0.0542191	−	0.237549i	−0.994775	+	0.102089i	$0.967447\pi$
$84$		0			0
$85$	−0.890084	+	3.89971i	−0.0965431	+	0.422983i
$86$	4.09299	−	1.97108i	0.441358	−	0.212547i
$87$		0			0
$88$	−0.554958	−	0.695895i	−0.0591587	−	0.0741827i
$89$	2.86831	+	12.5669i	0.304041	+	1.33209i	0.863968	+	0.503547i	$0.167972\pi$
$89$	2.86831	+	12.5669i	0.304041	+	1.33209i	−0.559927	+	0.828542i	$0.689171\pi$
$90$		0			0
$91$	4.54676	−	9.44145i	0.476630	−	0.989733i
$92$	−5.74094	−	7.19891i	−0.598534	−	0.750538i
$93$		0			0
$94$	−4.44504	−	2.14062i	−0.458471	−	0.220788i
$95$	−2.46681	+	3.09328i	−0.253090	+	0.317364i
$96$		0			0
$97$	−15.7506			−1.59923			−0.799617	−	0.600510i	$-0.794964\pi$
$97$	−15.7506			−1.59923			−0.799617	+	0.600510i	$0.794964\pi$
$98$	4.36443	−	5.47282i	0.440874	−	0.552838i
$99$		0			0
$100$	0.936313	−	4.10225i	0.0936313	−	0.410225i
$101$	4.46681	−	5.60121i	0.444464	−	0.557341i	−0.508249	−	0.861210i	$-0.669707\pi$
$101$	4.46681	−	5.60121i	0.444464	−	0.557341i	0.952714	+	0.303869i	$0.0982786\pi$
$102$		0			0
$103$	5.77144	−	7.23715i	0.568677	−	0.713098i	−0.411458	−	0.911428i	$-0.634980\pi$
$103$	5.77144	−	7.23715i	0.568677	−	0.713098i	0.980135	+	0.198330i	$0.0635519\pi$
$104$	−2.46950	−	3.09666i	−0.242154	−	0.303652i
$105$		0			0
$106$	7.04892	−	8.83906i	0.684651	−	0.858526i
$107$	−2.24698	−	9.84466i	−0.217224	−	0.951719i	−0.959518	−	0.281646i	$-0.909120\pi$
$107$	−2.24698	−	9.84466i	−0.217224	−	0.951719i	0.742295	−	0.670074i	$-0.233737\pi$
$108$		0			0
$109$	0.820356	−	3.59421i	0.0785758	−	0.344263i	−0.920324	−	0.391157i	$-0.872075\pi$
$109$	0.820356	−	3.59421i	0.0785758	−	0.344263i	0.998900	+	0.0468936i	$0.0149322\pi$
$110$	−0.713792	+	0.343744i	−0.0680574	+	0.0327747i
$111$		0			0
$112$	−1.14795	−	2.38374i	−0.108471	−	0.225242i
$113$	−1.29052	−	5.65414i	−0.121402	−	0.531897i	−0.998654	−	0.0518666i	$-0.983483\pi$
$113$	−1.29052	−	5.65414i	−0.121402	−	0.531897i	0.877252	−	0.480030i	$-0.159374\pi$
$114$		0			0
$115$	−7.38404	+	3.55597i	−0.688566	+	0.331596i
$116$	−5.38404			−0.499896
$117$		0			0
$118$	7.38404	−	3.55597i	0.679756	−	0.327353i
$119$	−11.5918	+	2.64575i	−1.06262	+	0.242536i
$120$		0			0
$121$	9.19687	+	4.42898i	0.836079	+	0.402634i
$122$	2.73609	+	11.9876i	0.247714	+	1.08531i
$123$		0			0
$124$	4.02930	+	1.94041i	0.361842	+	0.174254i
$125$	−7.38404	−	3.55597i	−0.660449	−	0.318055i
$126$		0			0
$127$	−1.36174	+	0.655780i	−0.120835	+	0.0581910i	−0.493325	−	0.869845i	$-0.664218\pi$
$127$	−1.36174	+	0.655780i	−0.120835	+	0.0581910i	0.372490	+	0.928036i	$0.378504\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−3.17629	+	1.52962i	−0.278579	+	0.134157i
$131$	10.4819	+	13.1439i	0.915806	+	1.14838i	0.988529	+	0.151032i	$0.0482597\pi$
$131$	10.4819	+	13.1439i	0.915806	+	1.14838i	−0.0727230	+	0.997352i	$0.523169\pi$
$132$		0			0
$133$	−11.4656	−	2.61695i	−0.994195	−	0.226919i
$134$	1.36563	−	5.98319i	0.117972	−	0.516869i
$135$		0			0
$136$	−1.00000	+	4.38129i	−0.0857493	+	0.375692i
$137$	4.80194	+	6.02144i	0.410257	+	0.514446i	0.943435	−	0.331557i	$-0.107574\pi$
$137$	4.80194	+	6.02144i	0.410257	+	0.514446i	−0.533178	+	0.846003i	$0.679002\pi$
$138$		0			0
$139$	−0.496648	+	0.622776i	−0.0421251	+	0.0528232i	−0.802448	−	0.596722i	$-0.796469\pi$
$139$	−0.496648	+	0.622776i	−0.0421251	+	0.0528232i	0.760323	+	0.649546i	$0.225041\pi$
$140$	−2.29590	+	0.524023i	−0.194039	+	0.0442881i
$141$		0			0
$142$	−8.54288	+	10.7124i	−0.716902	+	0.898967i
$143$	−3.17629	−	1.52962i	−0.265615	−	0.127913i
$144$		0			0
$145$	−1.06638	+	4.67210i	−0.0885577	+	0.387997i
$146$	−5.80194			−0.480172
$147$		0			0
$148$	10.5157			0.864388
$149$	−0.850855	+	3.72784i	−0.0697048	+	0.305397i	−0.997748	−	0.0670763i	$-0.978633\pi$
$149$	−0.850855	+	3.72784i	−0.0697048	+	0.305397i	0.928043	+	0.372473i	$0.121490\pi$
$150$		0			0
$151$	10.2518	+	4.93702i	0.834282	+	0.401769i	0.801719	−	0.597701i	$-0.203919\pi$
$151$	10.2518	+	4.93702i	0.834282	+	0.401769i	0.0325624	+	0.999470i	$0.489633\pi$
$152$	−2.77144	+	3.47527i	−0.224793	+	0.281882i
$153$		0			0
$154$	−1.84117	−	1.46828i	−0.148365	−	0.118317i
$155$	2.48188	−	3.11218i	0.199349	−	0.249976i
$156$		0			0
$157$	−5.30529	−	6.65262i	−0.423408	−	0.530937i	0.523678	−	0.851916i	$-0.324559\pi$
$157$	−5.30529	−	6.65262i	−0.423408	−	0.530937i	−0.947086	+	0.320979i	$0.895988\pi$
$158$	0.818864	−	3.58768i	0.0651453	−	0.285420i
$159$		0			0
$160$	−0.198062	+	0.867767i	−0.0156582	+	0.0686030i
$161$	−19.0465	−	15.1891i	−1.50108	−	1.19707i
$162$		0			0
$163$	3.38135	+	4.24008i	0.264848	+	0.332109i	0.896418	−	0.443210i	$-0.146160\pi$
$163$	3.38135	+	4.24008i	0.264848	+	0.332109i	−0.631570	+	0.775319i	$0.717589\pi$
$164$	6.85086	−	3.29920i	0.534962	−	0.257624i
$165$		0			0
$166$	−2.21983			−0.172292
$167$	−18.1250	+	8.72853i	−1.40255	+	0.675434i	−0.973678	−	0.227930i	$-0.926804\pi$
$167$	−18.1250	+	8.72853i	−1.40255	+	0.675434i	−0.428876	+	0.903364i	$0.641090\pi$
$168$		0			0
$169$	−2.42154	−	1.16615i	−0.186273	−	0.0897041i
$170$	3.60388	+	1.73553i	0.276405	+	0.133109i
$171$		0			0
$172$	−1.01089	−	4.42898i	−0.0770793	−	0.337706i
$173$	−16.8780	−	8.12802i	−1.28321	−	0.617962i	−0.336998	−	0.941506i	$-0.609411\pi$
$173$	−16.8780	−	8.12802i	−1.28321	−	0.617962i	−0.946213	+	0.323544i	$0.895126\pi$
$174$		0			0
$175$		−	11.1327i		−	0.841550i
$176$	−0.801938	+	0.386193i	−0.0604483	+	0.0291104i
$177$		0			0
$178$	12.8901			0.966153
$179$	−4.02715	+	1.93937i	−0.301003	+	0.144955i	−0.578289	−	0.815832i	$-0.696279\pi$
$179$	−4.02715	+	1.93937i	−0.301003	+	0.144955i	0.277286	+	0.960787i	$0.410565\pi$
$180$		0			0
$181$	4.86390	+	21.3101i	0.361531	+	1.58397i	0.749312	+	0.662217i	$0.230384\pi$
$181$	4.86390	+	21.3101i	0.361531	+	1.58397i	−0.387781	+	0.921751i	$0.626758\pi$
$182$	−8.19298	−	6.53368i	−0.607304	−	0.484309i
$183$		0			0
$184$	−8.29590	+	3.99509i	−0.611582	+	0.294522i
$185$	2.08277	−	9.12521i	0.153128	−	0.670899i
$186$		0			0
$187$	0.890084	+	3.89971i	0.0650894	+	0.285175i
$188$	−3.07606	+	3.85726i	−0.224345	+	0.281320i
$189$		0			0
$190$	2.46681	+	3.09328i	0.178961	+	0.224410i
$191$	13.7778	−	17.2768i	0.996925	−	1.25010i	0.0288132	−	0.999585i	$-0.490827\pi$
$191$	13.7778	−	17.2768i	0.996925	−	1.25010i	0.968112	−	0.250519i	$-0.0806014\pi$
$192$		0			0
$193$	−0.386731	+	0.484946i	−0.0278375	+	0.0349072i	−0.795555	−	0.605881i	$-0.792821\pi$
$193$	−0.386731	+	0.484946i	−0.0278375	+	0.0349072i	0.767718	+	0.640788i	$0.221392\pi$
$194$	−3.50484	+	15.3557i	−0.251633	+	1.10248i
$195$		0			0
$196$	−4.36443	−	5.47282i	−0.311745	−	0.390916i
$197$	−10.2983			−0.733723			−0.366861	−	0.930276i	$-0.619568\pi$
$197$	−10.2983			−0.733723			−0.366861	+	0.930276i	$0.619568\pi$
$198$		0			0
$199$	2.94235	−	3.68959i	0.208578	−	0.261548i	−0.666528	−	0.745480i	$-0.732220\pi$
$199$	2.94235	−	3.68959i	0.208578	−	0.261548i	0.875106	+	0.483932i	$0.160792\pi$
$200$	−3.79105	−	1.82567i	−0.268068	−	0.129095i
$201$		0			0
$202$	−4.46681	−	5.60121i	−0.314284	−	0.394099i
$203$	−13.8877	+	3.16977i	−0.974725	+	0.222475i
$204$		0			0
$205$	−1.50604	−	6.59840i	−0.105186	−	0.460852i
$206$	−5.77144	−	7.23715i	−0.402115	−	0.504236i
$207$		0			0
$208$	−3.56853	+	1.71851i	−0.247433	+	0.119158i
$209$	−0.880395	+	3.85726i	−0.0608982	+	0.266812i
$210$		0			0
$211$	3.25182	+	14.2472i	0.223865	+	0.980816i	0.954538	+	0.298089i	$0.0963491\pi$
$211$	3.25182	+	14.2472i	0.223865	+	0.980816i	−0.730673	+	0.682727i	$0.760794\pi$
$212$	−7.04892	−	8.83906i	−0.484122	−	0.607069i
$213$		0			0
$214$	−10.0978			−0.690274
$215$	−4.04354			−0.275767
$216$		0			0
$217$	11.5356	+	2.63293i	0.783090	+	0.178735i
$218$	−3.32155	−	1.59958i	−0.224964	−	0.108337i
$219$		0			0
$220$	0.176292	+	0.772386i	0.0118856	+	0.0520742i
$221$	3.96077	+	17.3533i	0.266430	+	1.16731i
$222$		0			0
$223$	−13.2371	−	6.37463i	−0.886419	−	0.426877i	−0.0654539	−	0.997856i	$-0.520850\pi$
$223$	−13.2371	−	6.37463i	−0.886419	−	0.426877i	−0.820965	+	0.570979i	$0.806564\pi$
$224$	−2.57942	+	0.588735i	−0.172345	+	0.0393365i
$225$		0			0
$226$	−5.79954			−0.385780
$227$	20.0000			1.32745			0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000			1.32745			0.663723	+	0.747978i	$0.268975\pi$
$228$		0			0
$229$	5.83244	+	7.31364i	0.385418	+	0.483299i	0.936259	−	0.351311i	$-0.114264\pi$
$229$	5.83244	+	7.31364i	0.385418	+	0.483299i	−0.550840	+	0.834611i	$0.685693\pi$
$230$	1.82371	+	7.99019i	0.120252	+	0.526857i
$231$		0			0
$232$	−1.19806	+	5.24905i	−0.0786566	+	0.344617i
$233$	19.1347	−	9.21477i	1.25355	−	0.603680i	0.315092	−	0.949061i	$-0.397965\pi$
$233$	19.1347	−	9.21477i	1.25355	−	0.603680i	0.938462	+	0.345382i	$0.112250\pi$
$234$		0			0
$235$	2.73795	+	3.43329i	0.178604	+	0.223963i
$236$	−1.82371	−	7.99019i	−0.118713	−	0.520117i
$237$		0			0
$238$			11.8899i			0.770708i
$239$	−4.70709	−	5.90250i	−0.304476	−	0.381801i	0.605929	−	0.795519i	$-0.292802\pi$
$239$	−4.70709	−	5.90250i	−0.304476	−	0.381801i	−0.910405	+	0.413718i	$0.864230\pi$
$240$		0			0
$241$	−5.19418	−	2.50138i	−0.334586	−	0.161128i	0.259045	−	0.965865i	$-0.416592\pi$
$241$	−5.19418	−	2.50138i	−0.334586	−	0.161128i	−0.593632	+	0.804737i	$0.702306\pi$
$242$	6.36443	−	7.98074i	0.409121	−	0.513021i
$243$		0			0
$244$	12.2959			0.787164
$245$	−5.61356	+	2.70335i	−0.358637	+	0.172711i
$246$		0			0
$247$	−3.91766	+	17.1644i	−0.249275	+	1.09214i
$248$	2.78836	−	3.49650i	0.177061	−	0.222028i
$249$		0			0
$250$	−5.10992	+	6.40763i	−0.323179	+	0.405254i
$251$	−7.86592	−	9.86355i	−0.496493	−	0.622582i	0.468942	−	0.883229i	$-0.344635\pi$
$251$	−7.86592	−	9.86355i	−0.496493	−	0.622582i	−0.965434	+	0.260647i	$0.916064\pi$
$252$		0			0
$253$	−5.10992	+	6.40763i	−0.321258	+	0.402844i
$254$	0.336322	+	1.47352i	0.0211027	+	0.0924571i
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−10.4155	+	5.01584i	−0.649701	+	0.312880i	−0.729550	−	0.683927i	$-0.760270\pi$
$257$	−10.4155	+	5.01584i	−0.649701	+	0.312880i	0.0798489	+	0.996807i	$0.474556\pi$
$258$		0			0
$259$	27.1244	−	6.19098i	1.68543	−	0.384689i
$260$	0.784479	+	3.43703i	0.0486513	+	0.213155i
$261$		0			0
$262$	15.1468	−	7.29429i	0.935769	−	0.450643i
$263$	3.40342			0.209864			0.104932	−	0.994479i	$-0.466538\pi$
$263$	3.40342			0.209864			0.104932	+	0.994479i	$0.466538\pi$
$264$		0			0
$265$	−9.06638	+	4.36614i	−0.556943	+	0.268210i
$266$	−5.10268	+	10.5958i	−0.312865	+	0.649672i
$267$		0			0
$268$	−5.52930	−	2.66277i	−0.337756	−	0.162655i
$269$	5.92931	+	25.9780i	0.361517	+	1.58391i	0.749347	+	0.662177i	$0.230367\pi$
$269$	5.92931	+	25.9780i	0.361517	+	1.58391i	−0.387831	+	0.921731i	$0.626776\pi$
$270$		0			0
$271$	−15.5782	−	7.50208i	−0.946309	−	0.455719i	−0.103919	−	0.994586i	$-0.533138\pi$
$271$	−15.5782	−	7.50208i	−0.946309	−	0.455719i	−0.842391	+	0.538867i	$0.818852\pi$
$272$	4.04892	+	1.94986i	0.245502	+	0.118227i
$273$		0			0
$274$	6.93900	−	3.34165i	0.419200	−	0.201876i
$275$	−3.74525			−0.225847
$276$		0			0
$277$	4.13318	−	1.99043i	0.248339	−	0.119594i	−0.305574	−	0.952168i	$-0.598848\pi$
$277$	4.13318	−	1.99043i	0.248339	−	0.119594i	0.553913	+	0.832575i	$0.313134\pi$
$278$	0.496648	+	0.622776i	0.0297869	+	0.0373516i
$279$		0			0
$280$			2.35494i			0.140735i
$281$	4.15644	−	18.2106i	0.247952	−	1.08635i	−0.685619	−	0.727960i	$-0.740469\pi$
$281$	4.15644	−	18.2106i	0.247952	−	1.08635i	0.933572	−	0.358390i	$-0.116674\pi$
$282$		0			0
$283$	1.60441	−	7.02937i	0.0953722	−	0.417853i	−0.904592	−	0.426278i	$-0.859825\pi$
$283$	1.60441	−	7.02937i	0.0953722	−	0.417853i	0.999965	+	0.00842499i	$0.00268179\pi$
$284$	8.54288	+	10.7124i	0.506926	+	0.635666i
$285$		0			0
$286$	−2.19806	+	2.75628i	−0.129974	+	0.162982i
$287$	15.7289	−	12.5433i	0.928445	−	0.740410i
$288$		0			0
$289$	1.99247	−	2.49847i	0.117204	−	0.146969i
$290$	4.31767	+	2.07928i	0.253542	+	0.122099i
$291$		0			0
$292$	−1.29105	+	5.65647i	−0.0755531	+	0.331020i
$293$	−19.0858			−1.11500			−0.557501	−	0.830176i	$-0.688240\pi$
$293$	−19.0858			−1.11500			−0.557501	+	0.830176i	$0.688240\pi$
$294$		0			0
$295$	−7.29483			−0.424722
$296$	2.33997	−	10.2521i	0.136008	−	0.595890i
$297$		0			0
$298$	3.44504	+	1.65904i	0.199566	+	0.0961059i
$299$	−22.7385	+	28.5132i	−1.31500	+	1.64896i
$300$		0			0
$301$	−5.21499	−	10.8290i	−0.300587	−	0.624175i
$302$	7.09448	−	8.89620i	0.408242	−	0.511919i
$303$		0			0
$304$	2.77144	+	3.47527i	0.158953	+	0.199321i
$305$	2.43535	−	10.6700i	0.139448	−	0.610961i
$306$		0			0
$307$	6.29709	−	27.5894i	0.359394	−	1.57461i	−0.395313	−	0.918547i	$-0.629364\pi$
$307$	6.29709	−	27.5894i	0.359394	−	1.57461i	0.754707	−	0.656062i	$-0.227779\pi$
$308$	−1.84117	+	1.46828i	−0.104910	+	0.0836631i
$309$		0			0
$310$	−2.48188	−	3.11218i	−0.140961	−	0.176760i
$311$	10.9487	−	5.27261i	0.620843	−	0.298982i	−0.0968958	−	0.995295i	$-0.530891\pi$
$311$	10.9487	−	5.27261i	0.620843	−	0.298982i	0.717739	+	0.696312i	$0.245177\pi$
$312$		0			0
$313$	3.18598			0.180082			0.0900411	−	0.995938i	$-0.471300\pi$
$313$	3.18598			0.180082			0.0900411	+	0.995938i	$0.471300\pi$
$314$	−7.66637	+	3.69193i	−0.432638	+	0.208348i
$315$		0			0
$316$	−3.31551	−	1.59667i	−0.186512	−	0.0898195i
$317$	−15.5133	−	7.47083i	−0.871316	−	0.419604i	−0.0558707	−	0.998438i	$-0.517793\pi$
$317$	−15.5133	−	7.47083i	−0.871316	−	0.419604i	−0.815445	+	0.578834i	$0.803508\pi$
$318$		0			0
$319$	1.06638	+	4.67210i	0.0597056	+	0.261587i
$320$	0.801938	+	0.386193i	0.0448297	+	0.0215888i
$321$		0			0
$322$	−19.0465	+	15.1891i	−1.06142	+	0.846455i
$323$	17.9976	−	8.66719i	1.00141	−	0.482255i
$324$		0			0
$325$	−16.6659			−0.924460
$326$	4.88620	−	2.35307i	0.270622	−	0.130324i
$327$		0			0
$328$	−1.69202	−	7.41323i	−0.0934263	−	0.409327i
$329$	−5.66355	+	11.7605i	−0.312241	+	0.648376i
$330$		0			0
$331$	21.9807	−	10.5853i	1.20817	−	0.581823i	0.282174	−	0.959363i	$-0.408944\pi$
$331$	21.9807	−	10.5853i	1.20817	−	0.581823i	0.925993	+	0.377540i	$0.123230\pi$
$332$	−0.493959	+	2.16418i	−0.0271095	+	0.118775i
$333$		0			0
$334$	4.47650	+	19.6128i	0.244943	+	1.07317i
$335$	−3.40581	+	4.27075i	−0.186079	+	0.233336i
$336$		0			0
$337$	−9.88740	−	12.3984i	−0.538601	−	0.675384i	0.435841	−	0.900024i	$-0.356451\pi$
$337$	−9.88740	−	12.3984i	−0.538601	−	0.675384i	−0.974442	+	0.224640i	$0.927880\pi$
$338$	−1.67576	+	2.10134i	−0.0911493	+	0.114298i
$339$		0			0
$340$	2.49396	−	3.12733i	0.135254	−	0.169603i
$341$	0.885772	−	3.88082i	0.0479672	−	0.210158i
$342$		0			0
$343$	−14.4797	−	11.5472i	−0.781831	−	0.623490i
$344$	−4.54288			−0.244935
$345$		0			0
$346$	−11.6799	+	14.6462i	−0.627917	+	0.787384i
$347$	8.50365	+	4.09514i	0.456500	+	0.219839i	0.647979	−	0.761658i	$-0.275614\pi$
$347$	8.50365	+	4.09514i	0.456500	+	0.219839i	−0.191480	+	0.981497i	$0.561329\pi$
$348$		0			0
$349$	10.4852	+	13.1481i	0.561261	+	0.703800i	0.978790	−	0.204864i	$-0.0656752\pi$
$349$	10.4852	+	13.1481i	0.561261	+	0.703800i	−0.417529	+	0.908664i	$0.637104\pi$
$350$	−10.8535	−	2.47725i	−0.580146	−	0.132415i
$351$		0			0
$352$	0.198062	+	0.867767i	0.0105568	+	0.0462522i
$353$	0.905149	+	1.13502i	0.0481762	+	0.0604111i	0.805336	−	0.592819i	$-0.201985\pi$
$353$	0.905149	+	1.13502i	0.0481762	+	0.0604111i	−0.757160	+	0.653230i	$0.773414\pi$
$354$		0			0
$355$	10.9879	−	5.29150i	0.583178	−	0.280844i
$356$	2.86831	−	12.5669i	0.152020	−	0.666044i
$357$		0			0
$358$	0.994623	+	4.35773i	0.0525675	+	0.230313i
$359$	8.83877	+	11.0835i	0.466493	+	0.584963i	0.958308	−	0.285736i	$-0.0922381\pi$
$359$	8.83877	+	11.0835i	0.466493	+	0.584963i	−0.491816	+	0.870699i	$0.663667\pi$
$360$		0			0
$361$	0.758397			0.0399156
$362$	21.8582			1.14884
$363$		0			0
$364$	−8.19298	+	6.53368i	−0.429429	+	0.342458i
$365$	4.65279	+	2.24067i	0.243538	+	0.117282i
$366$		0			0
$367$	−1.95204	−	8.55246i	−0.101896	−	0.446435i	−0.999978	−	0.00660730i	$-0.997897\pi$
$367$	−1.95204	−	8.55246i	−0.101896	−	0.446435i	0.898082	−	0.439827i	$-0.144960\pi$
$368$	2.04892	+	8.97689i	0.106807	+	0.467953i
$369$		0			0
$370$	−8.43296	−	4.06110i	−0.438409	−	0.211127i
$371$	−23.3860	−	18.6497i	−1.21414	−	0.968243i
$372$		0			0
$373$	22.0006			1.13915			0.569574	−	0.821940i	$-0.307108\pi$
$373$	22.0006			1.13915			0.569574	+	0.821940i	$0.307108\pi$
$374$	4.00000			0.206835
$375$		0			0
$376$	3.07606	+	3.85726i	0.158636	+	0.198923i
$377$	4.74525	+	20.7903i	0.244393	+	1.07076i
$378$		0			0
$379$	7.44816	−	32.6325i	0.382586	−	1.67622i	−0.306760	−	0.951787i	$-0.599245\pi$
$379$	7.44816	−	32.6325i	0.382586	−	1.67622i	0.689346	−	0.724432i	$-0.257898\pi$
$380$	3.56465	−	1.71664i	0.182863	−	0.0880619i
$381$		0			0
$382$	−13.7778	−	17.2768i	−0.704932	−	0.883957i
$383$	5.00000	+	21.9064i	0.255488	+	1.11937i	0.926017	+	0.377483i	$0.123210\pi$
$383$	5.00000	+	21.9064i	0.255488	+	1.11937i	−0.670529	+	0.741884i	$0.733933\pi$
$384$		0			0
$385$	0.909461	+	1.88852i	0.0463504	+	0.0962477i
$386$	0.386731	+	0.484946i	0.0196841	+	0.0246831i
$387$		0			0
$388$	14.1908	+	6.83394i	0.720430	+	0.346941i
$389$	8.09783	−	10.1544i	0.410577	−	0.514847i	−0.532949	−	0.846148i	$-0.678916\pi$
$389$	8.09783	−	10.1544i	0.410577	−	0.514847i	0.943525	+	0.331301i	$0.107488\pi$
$390$		0			0
$391$	41.3793			2.09264
$392$	−6.30678	+	3.03719i	−0.318541	+	0.153401i
$393$		0			0
$394$	−2.29159	+	10.0401i	−0.115448	+	0.505812i
$395$	−2.04221	+	2.56085i	−0.102755	+	0.128851i
$396$		0			0
$397$	1.91036	−	2.39552i	0.0958783	−	0.120228i	−0.731578	−	0.681758i	$-0.761216\pi$
$397$	1.91036	−	2.39552i	0.0958783	−	0.120228i	0.827456	+	0.561530i	$0.189787\pi$
$398$	−2.94235	−	3.68959i	−0.147487	−	0.184943i
$399$		0			0
$400$	−2.62349	+	3.28975i	−0.131174	+	0.164488i
$401$	−2.07606	−	9.09583i	−0.103674	−	0.454224i	−0.999943	−	0.0107131i	$-0.996590\pi$
$401$	−2.07606	−	9.09583i	−0.103674	−	0.454224i	0.896269	−	0.443511i	$-0.146267\pi$
$402$		0			0
$403$	3.94158	−	17.2692i	0.196344	−	0.860241i
$404$	−6.45473	+	3.10843i	−0.321135	+	0.154650i
$405$		0			0
$406$			14.2448i			0.706959i
$407$	−2.08277	−	9.12521i	−0.103239	−	0.452320i
$408$		0			0
$409$	−4.73341	+	2.27949i	−0.234052	+	0.112713i	−0.547234	−	0.836980i	$-0.684319\pi$
$409$	−4.73341	+	2.27949i	−0.234052	+	0.112713i	0.313182	+	0.949693i	$0.398605\pi$
$410$	−6.76809			−0.334252
$411$		0			0
$412$	−8.33997	+	4.01632i	−0.410881	+	0.197870i
$413$	−9.40821	−	19.5363i	−0.462948	−	0.961321i
$414$		0			0
$415$	1.78017	+	0.857283i	0.0873850	+	0.0420824i
$416$	0.881355	+	3.86147i	0.0432120	+	0.189324i
$417$		0			0
$418$	3.56465	+	1.71664i	0.174353	+	0.0839638i
$419$	17.6310	+	8.49065i	0.861332	+	0.414796i	0.811771	−	0.583976i	$-0.198504\pi$
$419$	17.6310	+	8.49065i	0.861332	+	0.414796i	0.0495606	+	0.998771i	$0.484218\pi$
$420$		0			0
$421$	−32.5758	+	15.6877i	−1.58765	+	0.764571i	−0.999038	−	0.0438456i	$-0.986039\pi$
$421$	−32.5758	+	15.6877i	−1.58765	+	0.764571i	−0.588610	+	0.808417i	$0.700325\pi$
$422$	14.6136			0.711377
$423$		0			0
$424$	−10.1860	+	4.90531i	−0.494675	+	0.238223i
$425$	11.7899	+	14.7840i	0.571892	+	0.717130i
$426$		0			0
$427$	31.7162	−	7.23903i	1.53486	−	0.350321i
$428$	−2.24698	+	9.84466i	−0.108612	+	0.475860i
$429$		0			0
$430$	−0.899772	+	3.94216i	−0.0433909	+	0.190108i
$431$	25.5743	+	32.0692i	1.23187	+	1.54472i	0.737267	+	0.675601i	$0.236116\pi$
$431$	25.5743	+	32.0692i	1.23187	+	1.54472i	0.494605	+	0.869118i	$0.335313\pi$
$432$		0			0
$433$	−19.4852	+	24.4337i	−0.936400	+	1.17421i	0.0481028	+	0.998842i	$0.484682\pi$
$433$	−19.4852	+	24.4337i	−0.936400	+	1.17421i	−0.984503	+	0.175367i	$0.943889\pi$
$434$	5.13384	−	10.6605i	0.246432	−	0.511722i
$435$		0			0
$436$	−2.29859	+	2.88233i	−0.110082	+	0.138039i
$437$	36.8756	+	17.7584i	1.76400	+	0.849497i
$438$		0			0
$439$	8.81604	−	38.6256i	0.420767	−	1.84350i	−0.107204	−	0.994237i	$-0.534190\pi$
$439$	8.81604	−	38.6256i	0.420767	−	1.84350i	0.527970	−	0.849263i	$-0.322953\pi$
$440$	0.792249			0.0377690
$441$		0			0
$442$	17.7995			0.846638
$443$	4.68963	−	20.5466i	0.222811	−	0.976199i	−0.732540	−	0.680724i	$-0.761665\pi$
$443$	4.68963	−	20.5466i	0.222811	−	0.976199i	0.955351	−	0.295474i	$-0.0954777\pi$
$444$		0			0
$445$	−10.3370	−	4.97806i	−0.490023	−	0.235983i
$446$	−9.16033	+	11.4867i	−0.433754	+	0.543910i
$447$		0			0
$448$			2.64575i			0.125000i
$449$	5.63102	−	7.06108i	0.265744	−	0.333233i	−0.630999	−	0.775784i	$-0.717355\pi$
$449$	5.63102	−	7.06108i	0.265744	−	0.333233i	0.896744	+	0.442551i	$0.145926\pi$
$450$		0			0
$451$	−4.21983	−	5.29150i	−0.198704	−	0.249167i
$452$	−1.29052	+	5.65414i	−0.0607010	+	0.265948i
$453$		0			0
$454$	4.45042	−	19.4986i	0.208868	−	0.915113i
$455$	4.04700	+	8.40368i	0.189726	+	0.393971i
$456$		0			0
$457$	−13.1942	−	16.5450i	−0.617198	−	0.773941i	0.370750	−	0.928733i	$-0.379101\pi$
$457$	−13.1942	−	16.5450i	−0.617198	−	0.773941i	−0.987947	+	0.154792i	$0.950529\pi$
$458$	8.42812	−	4.05877i	0.393820	−	0.189654i
$459$		0			0
$460$	8.19567			0.382125
$461$	32.8853	−	15.8367i	1.53162	−	0.737590i	0.537238	−	0.843431i	$-0.319468\pi$
$461$	32.8853	−	15.8367i	1.53162	−	0.737590i	0.994383	+	0.105841i	$0.0337534\pi$
$462$		0			0
$463$	9.35839	+	4.50676i	0.434921	+	0.209447i	0.638517	−	0.769608i	$-0.279548\pi$
$463$	9.35839	+	4.50676i	0.434921	+	0.209447i	−0.203595	+	0.979055i	$0.565263\pi$
$464$	4.85086	+	2.33605i	0.225195	+	0.108448i
$465$		0			0
$466$	−4.72587	−	20.7054i	−0.218922	−	0.959159i
$467$	−0.660563	−	0.318110i	−0.0305672	−	0.0147204i	0.418538	−	0.908199i	$-0.362543\pi$
$467$	−0.660563	−	0.318110i	−0.0305672	−	0.0147204i	−0.449105	+	0.893479i	$0.648257\pi$
$468$		0			0
$469$	−15.8300	−	3.61310i	−0.730964	−	0.166838i
$470$	3.95646	−	1.90533i	0.182498	−	0.0878863i
$471$		0			0
$472$	−8.19567			−0.377236
$473$	−3.64310	+	1.75443i	−0.167510	+	0.0806686i
$474$		0			0
$475$	4.16195	+	18.2347i	0.190963	+	0.836665i
$476$	11.5918	+	2.64575i	0.531309	+	0.121268i
$477$		0			0
$478$	−6.80194	+	3.27564i	−0.311113	+	0.149824i
$479$	5.62565	−	24.6476i	0.257042	−	1.12618i	−0.667353	−	0.744741i	$-0.732573\pi$
$479$	5.62565	−	24.6476i	0.257042	−	1.12618i	0.924396	−	0.381435i	$-0.124570\pi$
$480$		0			0
$481$	−9.26809	−	40.6061i	−0.422588	−	1.85148i
$482$	−3.59448	+	4.50734i	−0.163724	+	0.205304i
$483$		0			0
$484$	−6.36443	−	7.98074i	−0.289292	−	0.362761i
$485$	8.74094	−	10.9608i	0.396906	−	0.497704i
$486$		0			0
$487$	−14.8319	+	18.5986i	−0.672098	+	0.842784i	−0.994600	−	0.103785i	$-0.966905\pi$
$487$	−14.8319	+	18.5986i	−0.672098	+	0.842784i	0.322502	+	0.946569i	$0.395476\pi$
$488$	2.73609	−	11.9876i	0.123857	−	0.542654i
$489$		0			0
$490$	1.38644	+	6.07437i	0.0626328	+	0.274412i
$491$	4.69441			0.211856			0.105928	−	0.994374i	$-0.466219\pi$
$491$	4.69441			0.211856			0.105928	+	0.994374i	$0.466219\pi$
$492$		0			0
$493$	15.0858	−	18.9169i	0.679428	−	0.851976i
$494$	15.8623	+	7.63887i	0.713677	+	0.343689i
$495$		0			0
$496$	−2.78836	−	3.49650i	−0.125201	−	0.156997i
$497$	28.3424	+	22.6023i	1.27133	+	1.01385i
$498$		0			0
$499$	−1.64795	−	7.22013i	−0.0737723	−	0.323218i	0.924554	−	0.381051i	$-0.124438\pi$
$499$	−1.64795	−	7.22013i	−0.0737723	−	0.323218i	−0.998326	+	0.0578336i	$0.981581\pi$
$500$	5.10992	+	6.40763i	0.228522	+	0.286558i
$501$		0			0
$502$	−11.3666	+	5.47386i	−0.507315	+	0.244310i
$503$	−0.496352	+	2.17466i	−0.0221312	+	0.0969633i	−0.984787	−	0.173764i	$-0.944407\pi$
$503$	−0.496352	+	2.17466i	−0.0221312	+	0.0969633i	0.962656	+	0.270727i	$0.0872642\pi$
$504$		0			0
$505$	1.41896	+	6.21687i	0.0631429	+	0.276647i
$506$	5.10992	+	6.40763i	0.227163	+	0.284854i
$507$		0			0
$508$	1.51142			0.0670583
$509$	27.2620			1.20837			0.604184	−	0.796844i	$-0.293499\pi$
$509$	27.2620			1.20837			0.604184	+	0.796844i	$0.293499\pi$
$510$		0			0
$511$			15.3505i			0.679065i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$		0			0
$514$	2.57242	+	11.2705i	0.113464	+	0.497120i
$515$	1.83340	+	8.03264i	0.0807891	+	0.353960i
$516$		0			0
$517$	3.95646	+	1.90533i	0.174005	+	0.0837963i
$518$		−	27.8220i		−	1.22243i
$519$		0			0
$520$	3.52542			0.154600
$521$	−12.7138			−0.557001			−0.278501	−	0.960436i	$-0.589837\pi$
$521$	−12.7138			−0.557001			−0.278501	+	0.960436i	$0.589837\pi$
$522$		0			0
$523$	−8.79672	−	11.0307i	−0.384654	−	0.482341i	0.551378	−	0.834255i	$-0.314102\pi$
$523$	−8.79672	−	11.0307i	−0.384654	−	0.482341i	−0.936032	+	0.351915i	$0.885531\pi$
$524$	−3.74094	−	16.3901i	−0.163424	−	0.716006i
$525$		0			0
$526$	0.757332	−	3.31809i	0.0330213	−	0.144676i
$527$	−18.1075	+	8.72012i	−0.788776	+	0.379855i
$528$		0			0
$529$	38.5209	+	48.3036i	1.67482	+	2.10016i
$530$	2.23921	+	9.81062i	0.0972651	+	0.426146i
$531$		0			0
$532$	9.19471	+	7.33254i	0.398641	+	0.317906i
$533$	−18.7778	−	23.5466i	−0.813356	−	1.01992i
$534$		0			0
$535$	8.09783	+	3.89971i	0.350100	+	0.168599i
$536$	−3.82640	+	4.79815i	−0.165275	+	0.207248i
$537$		0			0
$538$	26.6461			1.14879
$539$	−3.88471	+	4.87127i	−0.167326	+	0.209820i
$540$		0			0
$541$	5.96197	−	26.1211i	0.256325	−	1.12303i	−0.668821	−	0.743423i	$-0.733201\pi$
$541$	5.96197	−	26.1211i	0.256325	−	1.12303i	0.925147	−	0.379610i	$-0.123942\pi$
$542$	−10.7805	+	13.5183i	−0.463061	+	0.580660i
$543$		0			0
$544$	2.80194	−	3.51352i	0.120132	−	0.150641i
$545$	2.04593	+	2.56552i	0.0876382	+	0.109895i
$546$		0			0
$547$	−6.59030	+	8.26398i	−0.281781	+	0.353342i	−0.902499	−	0.430692i	$-0.858270\pi$
$547$	−6.59030	+	8.26398i	−0.281781	+	0.353342i	0.620718	+	0.784034i	$0.286841\pi$
$548$	−1.71379	−	7.50861i	−0.0732096	−	0.320752i
$549$		0			0
$550$	−0.833397	+	3.65135i	−0.0355362	+	0.155694i
$551$	21.5623	−	10.3838i	0.918583	−	0.442366i
$552$		0			0
$553$	−9.49210	−	2.16651i	−0.403645	−	0.0921294i
$554$	−1.02081	−	4.47246i	−0.0433701	−	0.190017i
$555$		0			0
$556$	0.717677	−	0.345615i	0.0304363	−	0.0146573i
$557$	−10.2500			−0.434305			−0.217152	−	0.976138i	$-0.569677\pi$
$557$	−10.2500			−0.434305			−0.217152	+	0.976138i	$0.569677\pi$
$558$		0			0
$559$	−16.2114	+	7.80700i	−0.685669	+	0.330201i
$560$	2.29590	+	0.524023i	0.0970194	+	0.0221440i
$561$		0			0
$562$	−16.8291	−	8.10446i	−0.709892	−	0.341866i
$563$	0.442649	+	1.93937i	0.0186554	+	0.0817348i	0.983399	−	0.181458i	$-0.0580816\pi$
$563$	0.442649	+	1.93937i	0.0186554	+	0.0817348i	−0.964743	+	0.263193i	$0.915224\pi$
$564$		0			0
$565$	4.65087	+	2.23974i	0.195664	+	0.0942267i
$566$	−6.49612	−	3.12836i	−0.273052	−	0.131495i
$567$		0			0
$568$	12.3448	−	5.94495i	0.517977	−	0.249445i
$569$	27.5797			1.15620			0.578101	−	0.815965i	$-0.303794\pi$
$569$	27.5797			1.15620			0.578101	+	0.815965i	$0.303794\pi$
$570$		0			0
$571$	1.78232	−	0.858322i	0.0745879	−	0.0359196i	−0.396218	−	0.918157i	$-0.629678\pi$
$571$	1.78232	−	0.858322i	0.0745879	−	0.0359196i	0.470806	+	0.882237i	$0.343963\pi$
$572$	2.19806	+	2.75628i	0.0919056	+	0.115246i
$573$		0			0
$574$	−8.72886	−	18.1257i	−0.364335	−	0.756550i
$575$	−8.62133	+	37.7725i	−0.359534	+	1.57522i
$576$		0			0
$577$	−2.97189	+	13.0207i	−0.123722	+	0.542059i	0.874637	+	0.484779i	$0.161100\pi$
$577$	−2.97189	+	13.0207i	−0.123722	+	0.542059i	−0.998358	+	0.0572803i	$0.981757\pi$
$578$	−1.99247	−	2.49847i	−0.0828757	−	0.103923i
$579$		0			0
$580$	2.98792	−	3.74673i	0.124067	−	0.155575i
$581$			5.87312i			0.243658i
$582$		0			0
$583$	−6.27413	+	7.86751i	−0.259848	+	0.325839i
$584$	5.22737	+	2.51737i	0.216310	+	0.104169i
$585$		0			0
$586$	−4.24698	+	18.6072i	−0.175441	+	0.768658i
$587$	−11.7259			−0.483979			−0.241989	−	0.970279i	$-0.577800\pi$
$587$	−11.7259			−0.483979			−0.241989	+	0.970279i	$0.577800\pi$
$588$		0			0
$589$	−19.8791			−0.819103
$590$	−1.62325	+	7.11194i	−0.0668283	+	0.292794i
$591$		0			0
$592$	−9.47434	−	4.56260i	−0.389393	−	0.187522i
$593$	−11.5278	+	14.4554i	−0.473390	+	0.593613i	−0.959998	−	0.280008i	$-0.909663\pi$
$593$	−11.5278	+	14.4554i	−0.473390	+	0.593613i	0.486607	+	0.873621i	$0.338234\pi$
$594$		0			0
$595$	4.59179	−	9.53496i	0.188245	−	0.390895i
$596$	2.38404	−	2.98950i	0.0976542	−	0.122454i
$597$		0			0
$598$	22.7385	+	28.5132i	0.929848	+	1.16599i
$599$	−0.594187	+	2.60330i	−0.0242778	+	0.106368i	−0.985615	−	0.169006i	$-0.945944\pi$
$599$	−0.594187	+	2.60330i	−0.0242778	+	0.106368i	0.961337	+	0.275374i	$0.0888016\pi$
$600$		0			0
$601$	4.07308	−	17.8453i	0.166144	−	0.727926i	−0.821370	−	0.570396i	$-0.806790\pi$
$601$	4.07308	−	17.8453i	0.166144	−	0.727926i	0.987514	−	0.157530i	$-0.0503531\pi$
$602$	−11.7180	+	2.67455i	−0.477589	+	0.109007i
$603$		0			0
$604$	−7.09448	−	8.89620i	−0.288670	−	0.361981i
$605$	−8.18598	+	3.94216i	−0.332807	+	0.160272i
$606$		0			0
$607$	−33.2707			−1.35041			−0.675207	−	0.737628i	$-0.735946\pi$
$607$	−33.2707			−1.35041			−0.675207	+	0.737628i	$0.735946\pi$
$608$	4.00484	−	1.92863i	0.162418	−	0.0782163i
$609$		0			0
$610$	−9.86054	−	4.74859i	−0.399242	−	0.192265i
$611$	17.6058	+	8.47850i	0.712254	+	0.343004i
$612$		0			0
$613$	2.78070	+	12.1830i	0.112311	+	0.492068i	0.999528	+	0.0307156i	$0.00977862\pi$
$613$	2.78070	+	12.1830i	0.112311	+	0.492068i	−0.887217	+	0.461353i	$0.847364\pi$
$614$	−25.4964	−	12.2784i	−1.02895	−	0.495517i
$615$		0			0
$616$	1.02177	+	2.12173i	0.0411683	+	0.0854868i
$617$	2.92154	−	1.40694i	0.117617	−	0.0566413i	−0.374150	−	0.927368i	$-0.622065\pi$
$617$	2.92154	−	1.40694i	0.117617	−	0.0566413i	0.491767	+	0.870727i	$0.336351\pi$
$618$		0			0
$619$	22.6595			0.910762			0.455381	−	0.890297i	$-0.349503\pi$
$619$	22.6595			0.910762			0.455381	+	0.890297i	$0.349503\pi$
$620$	−3.58642	+	1.72713i	−0.144034	+	0.0693631i
$621$		0			0
$622$	−2.70410	−	11.8474i	−0.108425	−	0.475039i
$623$		−	34.1040i		−	1.36635i
$624$		0			0
$625$	−12.3828	+	5.96326i	−0.495314	+	0.238531i
$626$	0.708947	−	3.10610i	0.0283352	−	0.124145i
$627$		0			0
$628$	1.89344	+	8.29569i	0.0755563	+	0.331034i
$629$	−29.4644	+	36.9472i	−1.17482	+	1.47318i
$630$		0			0
$631$	7.55645	+	9.47549i	0.300818	+	0.377213i	0.909150	−	0.416469i	$-0.136733\pi$
$631$	7.55645	+	9.47549i	0.300818	+	0.377213i	−0.608332	+	0.793682i	$0.708161\pi$
$632$	−2.29440	+	2.87709i	−0.0912665	+	0.114445i
$633$		0			0
$634$	−10.7356	+	13.4620i	−0.426364	+	0.534643i
$635$	0.299355	−	1.31156i	0.0118795	−	0.0520476i
$636$		0			0
$637$	−17.2865	+	21.6766i	−0.684916	+	0.858858i
$638$	4.79225			0.189727
$639$		0			0
$640$	0.554958	−	0.695895i	0.0219366	−	0.0275077i
$641$	−37.1269	−	17.8794i	−1.46642	−	0.706193i	−0.481065	−	0.876685i	$-0.659750\pi$
$641$	−37.1269	−	17.8794i	−1.46642	−	0.706193i	−0.985359	+	0.170492i	$0.945464\pi$
$642$		0			0
$643$	6.93631	+	8.69786i	0.273541	+	0.343010i	0.899559	−	0.436799i	$-0.143888\pi$
$643$	6.93631	+	8.69786i	0.273541	+	0.343010i	−0.626018	+	0.779809i	$0.715316\pi$
$644$	10.5700	+	21.9489i	0.416517	+	0.864907i
$645$		0			0
$646$	−4.44504	−	19.4750i	−0.174888	−	0.766234i
$647$	−26.9584	−	33.8047i	−1.05984	−	1.32900i	−0.941867	−	0.335985i	$-0.890931\pi$
$647$	−26.9584	−	33.8047i	−1.05984	−	1.32900i	−0.117976	−	0.993016i	$-0.537641\pi$
$648$		0			0
$649$	−6.57242	+	3.16511i	−0.257990	+	0.124241i
$650$	−3.70852	+	16.2481i	−0.145460	+	0.637303i
$651$		0			0
$652$	−1.20679	−	5.28730i	−0.0472616	−	0.207067i
$653$	−4.28919	−	5.37848i	−0.167849	−	0.210476i	0.690792	−	0.723054i	$-0.257262\pi$
$653$	−4.28919	−	5.37848i	−0.167849	−	0.210476i	−0.858641	+	0.512578i	$0.828691\pi$
$654$		0			0
$655$	−14.9638			−0.584682
$656$	−7.60388			−0.296881
$657$		0			0
$658$	10.2054	+	8.13850i	0.397846	+	0.317272i
$659$	−5.97046	−	2.87522i	−0.232576	−	0.112003i	0.313966	−	0.949434i	$-0.398342\pi$
$659$	−5.97046	−	2.87522i	−0.232576	−	0.112003i	−0.546543	+	0.837431i	$0.684056\pi$
$660$		0			0
$661$	2.13600	+	9.35842i	0.0830807	+	0.364000i	0.999330	−	0.0366090i	$-0.0116556\pi$
$661$	2.13600	+	9.35842i	0.0830807	+	0.364000i	−0.916249	+	0.400609i	$0.868798\pi$
$662$	−5.42878	−	23.7850i	−0.210996	−	0.924432i
$663$		0			0
$664$	2.00000	+	0.963149i	0.0776151	+	0.0373774i
$665$	8.18406	−	6.52657i	0.317364	−	0.253090i
$666$		0			0
$667$	49.5749			1.91955
$668$	20.1172			0.778358
$669$		0			0
$670$	3.40581	+	4.27075i	0.131578	+	0.164994i
$671$	−2.43535	−	10.6700i	−0.0940158	−	0.411910i
$672$		0			0
$673$	−1.14819	+	5.03053i	−0.0442593	+	0.193913i	−0.992224	−	0.124461i	$-0.960280\pi$
$673$	−1.14819	+	5.03053i	−0.0442593	+	0.193913i	0.947965	+	0.318374i	$0.103137\pi$
$674$	−14.2877	+	6.88059i	−0.550342	+	0.265031i
$675$		0			0
$676$	1.67576	+	2.10134i	0.0644523	+	0.0808206i
$677$	−3.32736	−	14.5781i	−0.127881	−	0.560282i	−0.997753	−	0.0670043i	$-0.978656\pi$
$677$	−3.32736	−	14.5781i	−0.127881	−	0.560282i	0.869872	−	0.493277i	$-0.164201\pi$
$678$		0			0
$679$	40.6274	+	9.27295i	1.55914	+	0.355863i
$680$	−2.49396	−	3.12733i	−0.0956390	−	0.119927i
$681$		0			0
$682$	−3.58642	−	1.72713i	−0.137331	−	0.0661351i
$683$	32.2543	−	40.4456i	1.23418	−	1.54761i	0.505336	−	0.862923i	$-0.331369\pi$
$683$	32.2543	−	40.4456i	1.23418	−	1.54761i	0.728840	−	0.684685i	$-0.240060\pi$
$684$		0			0
$685$	−6.85517			−0.261922
$686$	−14.4797	+	11.5472i	−0.552838	+	0.440874i
$687$		0			0
$688$	−1.01089	+	4.42898i	−0.0385396	+	0.168853i
$689$	−27.9191	+	35.0095i	−1.06363	+	1.33376i
$690$		0			0
$691$	24.2634	−	30.4253i	0.923022	−	1.15743i	−0.0641766	−	0.997939i	$-0.520442\pi$
$691$	24.2634	−	30.4253i	0.923022	−	1.15743i	0.987199	−	0.159495i	$-0.0509865\pi$
$692$	11.6799	+	14.6462i	0.444005	+	0.556764i
$693$		0			0
$694$	5.88471	−	7.37919i	0.223380	−	0.280110i
$695$	−0.157769	−	0.691230i	−0.00598451	−	0.0262198i
$696$		0			0
$697$	−7.60388	+	33.3148i	−0.288017	+	1.26189i
$698$	15.1516	−	7.29662i	0.573496	−	0.276181i
$699$		0			0
$700$	−4.83028	+	10.0302i	−0.182567	+	0.379105i
$701$	3.38165	+	14.8160i	0.127723	+	0.559592i	0.997777	+	0.0666357i	$0.0212265\pi$
$701$	3.38165	+	14.8160i	0.127723	+	0.559592i	−0.870054	+	0.492956i	$0.835916\pi$
$702$		0			0
$703$	−42.1139	+	20.2810i	−1.58835	+	0.764911i
$704$	0.890084			0.0335463
$705$		0			0
$706$	1.30798	−	0.629889i	0.0492264	−	0.0237062i
$707$	−14.8194	+	11.8181i	−0.557341	+	0.444464i
$708$		0			0
$709$	42.5550	+	20.4934i	1.59819	+	0.769646i	0.999509	−	0.0313430i	$-0.00997843\pi$
$709$	42.5550	+	20.4934i	1.59819	+	0.769646i	0.598679	+	0.800989i	$0.295693\pi$
$710$	−2.71379	−	11.8899i	−0.101847	−	0.446220i
$711$		0			0
$712$	−11.6136	−	5.59280i	−0.435237	−	0.209599i
$713$	−37.1008	−	17.8668i	−1.38944	−	0.669117i
$714$		0			0
$715$	2.82717	−	1.36149i	0.105730	−	0.0509169i
$716$	4.46980			0.167044
$717$		0			0
$718$	12.7724	−	6.15086i	0.476662	−	0.229548i
$719$	−16.9571	−	21.2635i	−0.632391	−	0.792994i	0.357637	−	0.933861i	$-0.383582\pi$
$719$	−16.9571	−	21.2635i	−0.632391	−	0.792994i	−0.990029	+	0.140867i	$0.955011\pi$
$720$		0			0
$721$	−19.1477	+	15.2698i	−0.713098	+	0.568677i
$722$	0.168759	−	0.739383i	0.00628057	−	0.0275170i
$723$		0			0
$724$	4.86390	−	21.3101i	0.180765	−	0.791984i
$725$	14.1250	+	17.7122i	0.524589	+	0.657813i
$726$		0			0
$727$	−17.3056	+	21.7005i	−0.641829	+	0.804828i	−0.991230	−	0.132145i	$-0.957813\pi$
$727$	−17.3056	+	21.7005i	−0.641829	+	0.804828i	0.349402	+	0.936973i	$0.386385\pi$
$728$	4.54676	+	9.44145i	0.168514	+	0.349923i
$729$		0			0
$730$	3.21983	−	4.03754i	0.119171	−	0.149436i
$731$	18.3937	+	8.85795i	0.680317	+	0.327623i
$732$		0			0
$733$	−3.12379	+	13.6862i	−0.115380	+	0.505511i	0.883904	+	0.467668i	$0.154906\pi$
$733$	−3.12379	+	13.6862i	−0.115380	+	0.505511i	−0.999284	+	0.0378430i	$0.987951\pi$
$734$	−8.77240			−0.323795
$735$		0			0
$736$	9.20775			0.339402
$737$	−1.21552	+	5.32554i	−0.0447743	+	0.196169i
$738$		0			0
$739$	−17.8034	−	8.57368i	−0.654910	−	0.315388i	0.0767576	−	0.997050i	$-0.475543\pi$
$739$	−17.8034	−	8.57368i	−0.654910	−	0.315388i	−0.731667	+	0.681662i	$0.761258\pi$
$740$	−5.83579	+	7.31785i	−0.214528	+	0.269009i
$741$		0			0
$742$	−23.3860	+	18.6497i	−0.858526	+	0.684651i
$743$	15.3177	−	19.2077i	0.561951	−	0.704664i	−0.416966	−	0.908922i	$-0.636907\pi$
$743$	15.3177	−	19.2077i	0.561951	−	0.704664i	0.978917	+	0.204258i	$0.0654782\pi$
$744$		0			0
$745$	−2.12200	−	2.66090i	−0.0777440	−	0.0974879i
$746$	4.89559	−	21.4490i	0.179240	−	0.785303i
$747$		0			0
$748$	0.890084	−	3.89971i	0.0325447	−	0.142588i
$749$			26.7164i			0.976195i
$750$		0			0
$751$	19.9972	+	25.0757i	0.729710	+	0.915027i	0.998844	−	0.0480758i	$-0.0153089\pi$
$751$	19.9972	+	25.0757i	0.729710	+	0.915027i	−0.269134	+	0.963103i	$0.586737\pi$
$752$	4.44504	−	2.14062i	0.162094	−	0.0780604i
$753$		0			0
$754$	21.3250			0.776609
$755$	−9.12498	+	4.39436i	−0.332092	+	0.159927i
$756$		0			0
$757$	−18.7327	−	9.02121i	−0.680853	−	0.327882i	0.0612929	−	0.998120i	$-0.480478\pi$
$757$	−18.7327	−	9.02121i	−0.680853	−	0.327882i	−0.742146	+	0.670238i	$0.766192\pi$
$758$	−30.1570	−	14.5228i	−1.09535	−	0.527493i
$759$		0			0
$760$	−0.880395	−	3.85726i	−0.0319353	−	0.139918i
$761$	−32.3599	−	15.5837i	−1.17304	−	0.564909i	−0.257167	−	0.966367i	$-0.582789\pi$
$761$	−32.3599	−	15.5837i	−1.17304	−	0.564909i	−0.915877	+	0.401458i	$0.868503\pi$
$762$		0			0
$763$	−4.23208	+	8.78800i	−0.153212	+	0.318147i
$764$	−19.9095	+	9.58789i	−0.720299	+	0.346878i
$765$		0			0
$766$	22.4698			0.811867
$767$	−29.2465	+	14.0844i	−1.05603	+	0.508557i
$768$		0			0
$769$	1.35450	+	5.93447i	0.0488446	+	0.214002i	0.993461	−	0.114176i	$-0.0364226\pi$
$769$	1.35450	+	5.93447i	0.0488446	+	0.214002i	−0.944616	+	0.328178i	$0.893565\pi$
$770$	2.04354	−	0.466425i	0.0736441	−	0.0168088i
$771$		0			0
$772$	0.558843	−	0.269125i	0.0201132	−	0.00968601i
$773$	11.1612	−	48.9005i	0.401441	−	1.75883i	−0.220128	−	0.975471i	$-0.570648\pi$
$773$	11.1612	−	48.9005i	0.401441	−	1.75883i	0.621570	−	0.783359i	$-0.286495\pi$
$774$		0			0
$775$	−4.18737	−	18.3461i	−0.150415	−	0.659010i
$776$	9.82036	−	12.3143i	0.352530	−	0.442059i
$777$		0			0
$778$	−8.09783	−	10.1544i	−0.290321	−	0.364052i
$779$	−21.0737	+	26.4255i	−0.755043	+	0.946794i
$780$		0			0
$781$	7.60388	−	9.53496i	0.272088	−	0.341188i
$782$	9.20775	−	40.3418i	0.329269	−	1.44262i
$783$		0			0
$784$	1.55765	+	6.82450i	0.0556302	+	0.243732i
$785$	7.57374			0.270319
$786$		0			0
$787$	−25.3614	+	31.8022i	−0.904035	+	1.13362i	0.0864844	+	0.996253i	$0.472437\pi$
$787$	−25.3614	+	31.8022i	−0.904035	+	1.13362i	−0.990520	+	0.137371i	$0.956135\pi$
$788$	9.27844	+	4.46826i	0.330531	+	0.159175i
$789$		0			0
$790$	2.04221	+	2.56085i	0.0726587	+	0.0911111i
$791$			15.3442i			0.545575i
$792$		0			0
$793$	−10.8370	−	47.4802i	−0.384835	−	1.68607i
$794$	−1.91036	−	2.39552i	−0.0677962	−	0.0850138i
$795$		0			0
$796$	−4.25182	+	2.04757i	−0.150702	+	0.0725742i
$797$	5.59179	−	24.4992i	0.198072	−	0.867808i	−0.774012	−	0.633171i	$-0.781753\pi$
$797$	5.59179	−	24.4992i	0.198072	−	0.867808i	0.972083	−	0.234637i	$-0.0753900\pi$
$798$		0			0
$799$	−4.93362	−	21.6156i	−0.174539	−	0.764706i
$800$	2.62349	+	3.28975i	0.0927544	+	0.116310i
$801$		0			0
$802$	−9.32975			−0.329445
$803$	5.16421			0.182241
$804$		0			0
$805$	21.1400	−	4.82508i	0.745089	−	0.170062i
$806$	−15.9591	−	7.68552i	−0.562137	−	0.270711i
$807$		0			0
$808$	1.59419	+	6.98459i	0.0560833	+	0.245717i
$809$	8.01208	+	35.1032i	0.281690	+	1.23416i	0.895626	+	0.444808i	$0.146728\pi$
$809$	8.01208	+	35.1032i	0.281690	+	1.23416i	−0.613936	+	0.789356i	$0.710415\pi$
$810$		0			0
$811$	4.25086	+	2.04711i	0.149268	+	0.0718837i	0.507027	−	0.861930i	$-0.330745\pi$
$811$	4.25086	+	2.04711i	0.149268	+	0.0718837i	−0.357758	+	0.933814i	$0.616459\pi$
$812$	13.8877	+	3.16977i	0.487362	+	0.111237i
$813$		0			0
$814$	−9.35988			−0.328064
$815$	−4.82717			−0.169088
$816$		0			0
$817$	12.5903	+	15.7877i	0.440479	+	0.552343i
$818$	1.16905	+	5.12196i	0.0408750	+	0.179085i
$819$		0			0
$820$	−1.50604	+	6.59840i	−0.0525932	+	0.230426i
$821$	1.68664	−	0.812245i	0.0588643	−	0.0283476i	−0.404220	−	0.914662i	$-0.632457\pi$
$821$	1.68664	−	0.812245i	0.0588643	−	0.0283476i	0.463084	+	0.886314i	$0.346743\pi$
$822$		0			0
$823$	−30.6132	−	38.3877i	−1.06711	−	1.33811i	−0.938060	−	0.346474i	$-0.887379\pi$
$823$	−30.6132	−	38.3877i	−1.06711	−	1.33811i	−0.129049	−	0.991638i	$-0.541193\pi$
$824$	2.05980	+	9.02458i	0.0717566	+	0.314386i
$825$		0			0
$826$	−21.1400	+	4.82508i	−0.735556	+	0.167886i
$827$	8.28083	+	10.3838i	0.287953	+	0.361081i	0.904677	−	0.426098i	$-0.140112\pi$
$827$	8.28083	+	10.3838i	0.287953	+	0.361081i	−0.616724	+	0.787179i	$0.711541\pi$
$828$		0			0
$829$	−13.4351	−	6.47001i	−0.466621	−	0.224713i	0.185773	−	0.982593i	$-0.440521\pi$
$829$	−13.4351	−	6.47001i	−0.466621	−	0.224713i	−0.652394	+	0.757880i	$0.726235\pi$
$830$	1.23191	−	1.54477i	0.0427604	−	0.0536198i
$831$		0			0
$832$	3.96077			0.137315
$833$	31.4577			1.08995
$834$		0			0
$835$	3.98446	−	17.4571i	0.137888	−	0.604127i
$836$	2.46681	−	3.09328i	0.0853165	−	0.106983i
$837$		0			0
$838$	12.2010	−	15.2996i	0.421478	−	0.528517i
$839$	2.07979	+	2.60797i	0.0718022	+	0.0900371i	0.816435	−	0.577437i	$-0.195947\pi$
$839$	2.07979	+	2.60797i	0.0718022	+	0.0900371i	−0.744633	+	0.667474i	$0.767376\pi$
$840$		0			0
$841$	−0.00753275	+	0.00944576i	−0.000259750	+	0.000325716i
$842$	8.04556	+	35.2499i	0.277268	+	1.21479i
$843$		0			0
$844$	3.25182	−	14.2472i	0.111932	−	0.490408i
$845$	2.15538	−	1.03797i	0.0741472	−	0.0357074i
$846$		0			0
$847$	−21.1151	−	16.8387i	−0.725522	−	0.578584i
$848$	2.51573	+	11.0221i	0.0863905	+	0.378502i
$849$		0			0
$850$	17.0368	−	8.20451i	0.584359	−	0.281412i
$851$	−96.8262			−3.31916
$852$		0			0
$853$	20.7458	−	9.99064i	0.710322	−	0.342073i	−0.0435890	−	0.999050i	$-0.513879\pi$
$853$	20.7458	−	9.99064i	0.710322	−	0.342073i	0.753911	+	0.656976i	$0.228165\pi$
$854$		−	32.5319i		−	1.11322i
$855$		0			0
$856$	9.09783	+	4.38129i	0.310958	+	0.149749i
$857$	−0.473517	−	2.07461i	−0.0161750	−	0.0708674i	0.966196	−	0.257808i	$-0.0830001\pi$
$857$	−0.473517	−	2.07461i	−0.0161750	−	0.0708674i	−0.982371	+	0.186940i	$0.940143\pi$
$858$		0			0
$859$	−20.6848	−	9.96127i	−0.705756	−	0.339874i	0.0463420	−	0.998926i	$-0.485244\pi$
$859$	−20.6848	−	9.96127i	−0.705756	−	0.339874i	−0.752098	+	0.659052i	$0.770958\pi$
$860$	3.64310	+	1.75443i	0.124229	+	0.0598254i
$861$		0			0
$862$	36.9560	−	17.7971i	1.25873	−	0.606170i
$863$	−24.1172			−0.820959			−0.410480	−	0.911870i	$-0.634639\pi$
$863$	−24.1172			−0.820959			−0.410480	+	0.911870i	$0.634639\pi$
$864$		0			0
$865$	15.0228	−	7.23462i	0.510792	−	0.245984i
$866$	19.4852	+	24.4337i	0.662135	+	0.830291i
$867$		0			0
$868$	−9.25086	−	7.37732i	−0.313995	−	0.250402i
$869$	−0.728857	+	3.19333i	−0.0247248	+	0.108326i
$870$		0			0
$871$	−5.40893	+	23.6981i	−0.183275	+	0.802978i
$872$	2.29859	+	2.88233i	0.0778399	+	0.0976082i
$873$		0			0
$874$	25.5187	−	31.9995i	0.863183	−	1.08240i
$875$	16.9530	+	13.5196i	0.573116	+	0.457045i
$876$		0			0
$877$	−12.0281	+	15.0828i	−0.406160	+	0.509309i	−0.942277	−	0.334835i	$-0.891319\pi$
$877$	−12.0281	+	15.0828i	−0.406160	+	0.509309i	0.536116	+	0.844144i	$0.319891\pi$
$878$	−35.6954	−	17.1900i	−1.20466	−	0.580135i
$879$		0			0
$880$	0.176292	−	0.772386i	0.00594280	−	0.0260371i
$881$	21.7232			0.731874			0.365937	−	0.930640i	$-0.380749\pi$
$881$	21.7232			0.731874			0.365937	+	0.930640i	$0.380749\pi$
$882$		0			0
$883$	−29.6276			−0.997047			−0.498523	−	0.866876i	$-0.666124\pi$
$883$	−29.6276			−0.997047			−0.498523	+	0.866876i	$0.666124\pi$
$884$	3.96077	−	17.3533i	0.133215	−	0.583654i
$885$		0			0
$886$	−18.9879	−	9.14410i	−0.637912	−	0.307202i
$887$	−5.74094	+	7.19891i	−0.192762	+	0.241716i	−0.868815	−	0.495137i	$-0.835118\pi$
$887$	−5.74094	+	7.19891i	−0.192762	+	0.241716i	0.676053	+	0.736853i	$0.263689\pi$
$888$		0			0
$889$	3.89858	−	0.889825i	0.130754	−	0.0298438i
$890$	−7.15346	+	8.97015i	−0.239784	+	0.300680i
$891$		0			0
$892$	9.16033	+	11.4867i	0.306710	+	0.384603i
$893$	4.87992	−	21.3803i	0.163300	−	0.715466i
$894$		0			0
$895$	0.885298	−	3.87874i	0.0295922	−	0.129652i
$896$	2.57942	+	0.588735i	0.0861723	+	0.0196683i
$897$		0			0
$898$	−5.63102	−	7.06108i	−0.187910	−	0.235631i
$899$	−21.6939	+	10.4473i	−0.723533	+	0.348435i
$900$		0			0
$901$	50.8068			1.69262
$902$	−6.09783	+	2.93656i	−0.203036	+	0.0977768i
$903$		0			0
$904$	5.22521	+	2.51633i	0.173788	+	0.0836918i
$905$	−17.5289	−	8.44146i	−0.582680	−	0.280604i
$906$		0			0
$907$	4.43200	+	19.4179i	0.147162	+	0.644760i	0.993666	+	0.112376i	$0.0358463\pi$
$907$	4.43200	+	19.4179i	0.147162	+	0.644760i	−0.846504	+	0.532383i	$0.821297\pi$
$908$	−18.0194	−	8.67767i	−0.597994	−	0.287979i
$909$		0			0
$910$	9.09352	−	2.07554i	0.301447	−	0.0688034i
$911$	−22.6625	+	10.9137i	−0.750842	+	0.361586i	−0.769843	−	0.638233i	$-0.779666\pi$
$911$	−22.6625	+	10.9137i	−0.750842	+	0.361586i	0.0190015	+	0.999819i	$0.493951\pi$
$912$		0			0
$913$	1.97584			0.0653907
$914$	−19.0661	+	9.18177i	−0.630652	+	0.303706i
$915$		0			0
$916$	−2.08157	−	9.11997i	−0.0687771	−	0.301332i
$917$	−19.2989	−	40.0745i	−0.637305	−	1.32338i
$918$		0			0
$919$	−25.7032	+	12.3780i	−0.847870	+	0.408313i	−0.806787	−	0.590843i	$-0.798795\pi$
$919$	−25.7032	+	12.3780i	−0.847870	+	0.408313i	−0.0410837	+	0.999156i	$0.513081\pi$
$920$	1.82371	−	7.99019i	0.0601259	−	0.263429i
$921$		0			0
$922$	−8.12200	−	35.5848i	−0.267484	−	1.17192i
$923$	33.8364	−	42.4295i	1.11374	−	1.39658i
$924$		0			0
$925$	−27.5879	−	34.5941i	−0.907085	−	1.13745i
$926$	6.47621	−	8.12090i	0.212821	−	0.266869i
$927$		0			0
$928$	3.35690	−	4.20941i	0.110196	−	0.138181i
$929$	8.59312	−	37.6489i	0.281931	−	1.23522i	−0.613383	−	0.789786i	$-0.710192\pi$
$929$	8.59312	−	37.6489i	0.281931	−	1.23522i	0.895314	−	0.445436i	$-0.146951\pi$
$930$		0			0
$931$	28.0339	+	13.5004i	0.918774	+	0.442458i
$932$	−21.2379			−0.695670
$933$		0			0
$934$	−0.457123	+	0.573215i	−0.0149575	+	0.0187562i
$935$	−3.20775	−	1.54477i	−0.104905	−	0.0505194i
$936$		0			0
$937$	11.7661	+	14.7542i	0.384380	+	0.481998i	0.935951	−	0.352130i	$-0.114543\pi$
$937$	11.7661	+	14.7542i	0.384380	+	0.481998i	−0.551570	+	0.834128i	$0.685971\pi$
$938$	−7.04503	+	14.6292i	−0.230028	+	0.477659i
$939$		0			0
$940$	−0.977165	−	4.28124i	−0.0318716	−	0.139639i
$941$	−17.2091	−	21.5795i	−0.561000	−	0.703472i	0.417742	−	0.908566i	$-0.362821\pi$
$941$	−17.2091	−	21.5795i	−0.561000	−	0.703472i	−0.978742	+	0.205094i	$0.934250\pi$
$942$		0			0
$943$	−63.0810	+	30.3782i	−2.05420	+	0.989250i
$944$	−1.82371	+	7.99019i	−0.0593566	+	0.260058i
$945$		0			0
$946$	0.899772	+	3.94216i	0.0292541	+	0.128171i
$947$	4.19269	+	5.25746i	0.136244	+	0.170845i	0.845273	−	0.534335i	$-0.179438\pi$
$947$	4.19269	+	5.25746i	0.136244	+	0.170845i	−0.709029	+	0.705179i	$0.750866\pi$
$948$		0			0
$949$	22.9801			0.745967
$950$	18.7036			0.606826
$951$		0			0
$952$	5.15883	−	10.7124i	0.167199	−	0.347192i
$953$	−26.4403	−	12.7330i	−0.856484	−	0.412461i	−0.0465037	−	0.998918i	$-0.514808\pi$
$953$	−26.4403	−	12.7330i	−0.856484	−	0.412461i	−0.809980	+	0.586457i	$0.800522\pi$
$954$		0			0
$955$	4.37675	+	19.1758i	0.141628	+	0.620514i
$956$	1.67994	+	7.36030i	0.0543331	+	0.238049i
$957$		0			0
$958$	−22.7778	−	10.9692i	−0.735916	−	0.354399i
$959$	−8.84117	−	18.3589i	−0.285496	−	0.592839i
$960$		0			0
$961$	−10.9995			−0.354823
$962$	−41.6504			−1.34286
$963$		0			0
$964$	3.59448	+	4.50734i	0.115770	+	0.145172i
$965$	−0.122852	−	0.538249i	−0.00395474	−	0.0173269i
$966$		0			0
$967$	−7.68545	+	33.6721i	−0.247147	+	1.08282i	0.687202	+	0.726466i	$0.258839\pi$
$967$	−7.68545	+	33.6721i	−0.247147	+	1.08282i	−0.934350	+	0.356357i	$0.884019\pi$
$968$	−9.19687	+	4.42898i	−0.295598	+	0.142353i
$969$		0			0
$970$	−8.74094	−	10.9608i	−0.280655	−	0.351930i
$971$	−11.6998	−	51.2601i	−0.375464	−	1.64502i	−0.711149	−	0.703042i	$-0.751825\pi$
$971$	−11.6998	−	51.2601i	−0.375464	−	1.64502i	0.335685	−	0.941974i	$-0.391032\pi$
$972$		0			0
$973$	1.64771	−	1.31401i	0.0528232	−	0.0421251i
$974$	14.8319	+	18.5986i	0.475245	+	0.595938i
$975$		0			0
$976$	−11.0782	−	5.33499i	−0.354605	−	0.170769i
$977$	29.9788	−	37.5923i	0.959107	−	1.20268i	−0.0200952	−	0.999798i	$-0.506397\pi$
$977$	29.9788	−	37.5923i	0.959107	−	1.20268i	0.979203	−	0.202885i	$-0.0650316\pi$
$978$		0			0
$979$	−11.4733			−0.366687
$980$	6.23059			0.199029
$981$		0			0
$982$	1.04461	−	4.57672i	0.0333347	−	0.146049i
$983$	−35.1444	+	44.0696i	−1.12093	+	1.40560i	−0.217930	+	0.975964i	$0.569930\pi$
$983$	−35.1444	+	44.0696i	−1.12093	+	1.40560i	−0.903001	+	0.429639i	$0.858641\pi$
$984$		0			0
$985$	5.71512	−	7.16653i	0.182099	−	0.228345i
$986$	−15.0858	−	18.9169i	−0.480428	−	0.602438i
$987$		0			0
$988$	10.9770	−	13.7648i	0.349226	−	0.437915i
$989$	9.30798	+	40.7809i	0.295976	+	1.29676i
$990$		0			0
$991$	−8.39062	+	36.7617i	−0.266537	+	1.16777i	0.647475	+	0.762086i	$0.275825\pi$
$991$	−8.39062	+	36.7617i	−0.266537	+	1.16777i	−0.914012	+	0.405687i	$0.867032\pi$
$992$	−4.02930	+	1.94041i	−0.127930	+	0.0616081i
$993$		0			0
$994$	28.3424	−	22.6023i	0.898967	−	0.716902i
$995$	0.934689	+	4.09514i	0.0296316	+	0.129825i
$996$		0			0
$997$	54.9614	−	26.4680i	1.74064	−	0.838250i	0.758119	−	0.652116i	$-0.226118\pi$
$997$	54.9614	−	26.4680i	1.74064	−	0.838250i	0.982524	−	0.186134i	$-0.0595959\pi$
$998$	−7.40581			−0.234427
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.u.c.505.1	yes	6
3.2	odd	2		882.2.u.a.505.1	yes	6
49.36	even	7	inner	882.2.u.c.379.1	yes	6
147.134	odd	14		882.2.u.a.379.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.u.a.379.1	✓	6	147.134	odd	14
882.2.u.a.505.1	yes	6	3.2	odd	2
882.2.u.c.379.1	yes	6	49.36	even	7	inner
882.2.u.c.505.1	yes	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.554958 + 0.695895i) q^{5} +(-2.57942 - 0.588735i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.554958 + 0.695895i) q^{10} +(-0.198062 + 0.867767i) q^{11} +(-0.881355 + 3.86147i) q^{13} +(-1.14795 + 2.38374i) q^{14} +(0.623490 + 0.781831i) q^{16} +(4.04892 - 1.94986i) q^{17} +4.44504 q^{19} +(0.801938 - 0.386193i) q^{20} +(0.801938 + 0.386193i) q^{22} +(8.29590 + 3.99509i) q^{23} +(0.936313 + 4.10225i) q^{25} +(3.56853 + 1.71851i) q^{26} +(2.06853 + 1.64960i) q^{28} +(4.85086 - 2.33605i) q^{29} -4.47219 q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.00000 - 4.38129i) q^{34} +(1.84117 - 1.46828i) q^{35} +(-9.47434 + 4.56260i) q^{37} +(0.989115 - 4.33360i) q^{38} +(-0.198062 - 0.867767i) q^{40} +(-4.74094 + 5.94495i) q^{41} +(2.83244 + 3.55176i) q^{43} +(0.554958 - 0.695895i) q^{44} +(5.74094 - 7.19891i) q^{46} +(1.09783 - 4.80993i) q^{47} +(6.30678 + 3.03719i) q^{49} +4.20775 q^{50} +(2.46950 - 3.09666i) q^{52} +(10.1860 + 4.90531i) q^{53} +(-0.493959 - 0.619405i) q^{55} +(2.06853 - 1.64960i) q^{56} +(-1.19806 - 5.24905i) q^{58} +(5.10992 + 6.40763i) q^{59} +(-11.0782 + 5.33499i) q^{61} +(-0.995156 + 4.36006i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(-2.19806 - 2.75628i) q^{65} +6.13706 q^{67} -4.49396 q^{68} +(-1.02177 - 2.12173i) q^{70} +(-12.3448 - 5.94495i) q^{71} +(-1.29105 - 5.65647i) q^{73} +(2.33997 + 10.2521i) q^{74} +(-4.00484 - 1.92863i) q^{76} +(1.02177 - 2.12173i) q^{77} +3.67994 q^{79} -0.890084 q^{80} +(4.74094 + 5.94495i) q^{82} +(-0.493959 - 2.16418i) q^{83} +(-0.890084 + 3.89971i) q^{85} +(4.09299 - 1.97108i) q^{86} +(-0.554958 - 0.695895i) q^{88} +(2.86831 + 12.5669i) q^{89} +(4.54676 - 9.44145i) q^{91} +(-5.74094 - 7.19891i) q^{92} +(-4.44504 - 2.14062i) q^{94} +(-2.46681 + 3.09328i) q^{95} -15.7506 q^{97} +(4.36443 - 5.47282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} + 4 q^{10} - 10 q^{11} + 12 q^{13} + 7 q^{14} - q^{16} + 6 q^{17} + 26 q^{19} - 4 q^{20} - 4 q^{22} + 22 q^{23} - 11 q^{25} + 16 q^{26} + 7 q^{28} + 2 q^{29}+ \cdots - 7 q^{98}+O(q^{100}) \) 6 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 + 4 * q^10 - 10 * q^11 + 12 * q^13 + 7 * q^14 - q^16 + 6 * q^17 + 26 * q^19 - 4 * q^20 - 4 * q^22 + 22 * q^23 - 11 * q^25 + 16 * q^26 + 7 * q^28 + 2 * q^29 - 14 * q^31 + q^32 - 6 * q^34 + 28 * q^35 - 25 * q^37 + 9 * q^38 - 10 * q^40 + 18 * q^43 + 4 * q^44 + 6 * q^46 - 30 * q^47 + 7 * q^49 - 10 * q^50 + 5 * q^52 + 32 * q^53 + 16 * q^55 + 7 * q^56 - 16 * q^58 + 32 * q^59 - 17 * q^61 - 28 * q^62 - q^64 - 22 * q^65 + 26 * q^67 - 8 * q^68 - 28 * q^71 - 2 * q^73 - 10 * q^74 - 2 * q^76 - 26 * q^79 - 4 * q^80 + 16 * q^83 - 4 * q^85 + 10 * q^86 - 4 * q^88 + 22 * q^89 + 28 * q^91 - 6 * q^92 - 26 * q^94 - 8 * q^95 - 22 * q^97 - 7 * q^98

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