LMFDB - Embedded newform 864.2.y.d.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	864.97
Dual form			864.2.y.d.481.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.790581 - 1.54110i) q^{3} +(3.49481 + 1.27201i) q^{5} +(0.718530 - 4.07499i) q^{7} +(-1.74996 + 2.43673i) q^{9} +O(q^{10})$	\(q+(-0.790581 - 1.54110i) q^{3} +(3.49481 + 1.27201i) q^{5} +(0.718530 - 4.07499i) q^{7} +(-1.74996 + 2.43673i) q^{9} +(-3.82696 + 1.39290i) q^{11} +(4.06368 - 3.40983i) q^{13} +(-0.802644 - 6.39146i) q^{15} +(-2.18334 - 3.78166i) q^{17} +(2.06780 - 3.58154i) q^{19} +(-6.84801 + 2.11428i) q^{21} +(0.676087 + 3.83428i) q^{23} +(6.76546 + 5.67690i) q^{25} +(5.13872 + 0.770433i) q^{27} +(-2.28202 - 1.91484i) q^{29} +(1.09063 + 6.18526i) q^{31} +(5.17211 + 4.79651i) q^{33} +(7.69453 - 13.3273i) q^{35} +(-3.23710 - 5.60682i) q^{37} +(-8.46755 - 3.56678i) q^{39} +(-0.477092 + 0.400328i) q^{41} +(4.31111 - 1.56912i) q^{43} +(-9.21531 + 6.28993i) q^{45} +(-0.191373 + 1.08533i) q^{47} +(-9.51137 - 3.46186i) q^{49} +(-4.10180 + 6.35445i) q^{51} +2.61345 q^{53} -15.1463 q^{55} +(-7.15427 - 0.355188i) q^{57} +(-5.66002 - 2.06008i) q^{59} +(1.75064 - 9.92840i) q^{61} +(8.67222 + 8.88193i) q^{63} +(18.5391 - 6.74768i) q^{65} +(6.64142 - 5.57282i) q^{67} +(5.37450 - 4.07323i) q^{69} +(-2.91408 - 5.04733i) q^{71} +(-1.06936 + 1.85218i) q^{73} +(3.40000 - 14.9143i) q^{75} +(2.92626 + 16.5956i) q^{77} +(7.77819 + 6.52668i) q^{79} +(-2.87526 - 8.52836i) q^{81} +(-3.75731 - 3.15276i) q^{83} +(-2.82007 - 15.9934i) q^{85} +(-1.14684 + 5.03066i) q^{87} +(-3.99446 + 6.91860i) q^{89} +(-10.9751 - 19.0095i) q^{91} +(8.66985 - 6.57071i) q^{93} +(11.7823 - 9.88655i) q^{95} +(-3.00873 + 1.09509i) q^{97} +(3.30292 - 11.7628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−0.790581	−	1.54110i	−0.456442	−	0.889753i
$3$	−0.790581	−	1.54110i	−0.456442	−	0.889753i
$4$		0			0
$5$	3.49481	+	1.27201i	1.56293	+	0.568858i	0.971404	−	0.237431i	$-0.0763053\pi$
$5$	3.49481	+	1.27201i	1.56293	+	0.568858i	0.591521	+	0.806289i	$0.298528\pi$
$6$		0			0
$7$	0.718530	−	4.07499i	0.271579	−	1.54020i	−0.478045	−	0.878335i	$-0.658654\pi$
$7$	0.718530	−	4.07499i	0.271579	−	1.54020i	0.749624	−	0.661864i	$-0.230234\pi$
$8$		0			0
$9$	−1.74996	+	2.43673i	−0.583321	+	0.812242i
$10$		0			0
$11$	−3.82696	+	1.39290i	−1.15387	+	0.419975i	−0.846904	−	0.531746i	$-0.821536\pi$
$11$	−3.82696	+	1.39290i	−1.15387	+	0.419975i	−0.306967	+	0.951720i	$0.599314\pi$
$12$		0			0
$13$	4.06368	−	3.40983i	1.12706	−	0.945717i	0.128122	−	0.991758i	$-0.459105\pi$
$13$	4.06368	−	3.40983i	1.12706	−	0.945717i	0.998940	+	0.0460411i	$0.0146605\pi$
$14$		0			0
$15$	−0.802644	−	6.39146i	−0.207242	−	1.65027i
$16$		0			0
$17$	−2.18334	−	3.78166i	−0.529538	−	0.917187i	−0.999406	−	0.0344504i	$-0.989032\pi$
$17$	−2.18334	−	3.78166i	−0.529538	−	0.917187i	0.469868	−	0.882737i	$-0.344301\pi$
$18$		0			0
$19$	2.06780	−	3.58154i	0.474387	−	0.821662i	−0.525183	−	0.850989i	$-0.676003\pi$
$19$	2.06780	−	3.58154i	0.474387	−	0.821662i	0.999570	+	0.0293271i	$0.00933643\pi$
$20$		0			0
$21$	−6.84801	+	2.11428i	−1.49436	+	0.461374i
$22$		0			0
$23$	0.676087	+	3.83428i	0.140974	+	0.799503i	0.970512	+	0.241053i	$0.0774927\pi$
$23$	0.676087	+	3.83428i	0.140974	+	0.799503i	−0.829538	+	0.558450i	$0.811396\pi$
$24$		0			0
$25$	6.76546	+	5.67690i	1.35309	+	1.13538i
$26$		0			0
$27$	5.13872	+	0.770433i	0.988947	+	0.148270i
$28$		0			0
$29$	−2.28202	−	1.91484i	−0.423761	−	0.355578i	0.405831	−	0.913948i	$-0.366982\pi$
$29$	−2.28202	−	1.91484i	−0.423761	−	0.355578i	−0.829592	+	0.558371i	$0.811427\pi$
$30$		0			0
$31$	1.09063	+	6.18526i	0.195882	+	1.11090i	0.911156	+	0.412061i	$0.135191\pi$
$31$	1.09063	+	6.18526i	0.195882	+	1.11090i	−0.715274	+	0.698844i	$0.753698\pi$
$32$		0			0
$33$	5.17211	+	4.79651i	0.900349	+	0.834966i
$34$		0			0
$35$	7.69453	−	13.3273i	1.30061	−	2.25273i
$36$		0			0
$37$	−3.23710	−	5.60682i	−0.532176	−	0.921755i	−0.999294	−	0.0375605i	$-0.988041\pi$
$37$	−3.23710	−	5.60682i	−0.532176	−	0.921755i	0.467119	−	0.884195i	$-0.345292\pi$
$38$		0			0
$39$	−8.46755	−	3.56678i	−1.35589	−	0.571141i
$40$		0			0
$41$	−0.477092	+	0.400328i	−0.0745093	+	0.0625207i	−0.679282	−	0.733878i	$-0.737709\pi$
$41$	−0.477092	+	0.400328i	−0.0745093	+	0.0625207i	0.604772	+	0.796398i	$0.293264\pi$
$42$		0			0
$43$	4.31111	−	1.56912i	0.657438	−	0.239288i	0.00830830	−	0.999965i	$-0.497355\pi$
$43$	4.31111	−	1.56912i	0.657438	−	0.239288i	0.649130	+	0.760678i	$0.275133\pi$
$44$		0			0
$45$	−9.21531	+	6.28993i	−1.37374	+	0.937647i
$46$		0			0
$47$	−0.191373	+	1.08533i	−0.0279146	+	0.158312i	−0.995579	−	0.0939304i	$-0.970057\pi$
$47$	−0.191373	+	1.08533i	−0.0279146	+	0.158312i	0.967664	+	0.252242i	$0.0811680\pi$
$48$		0			0
$49$	−9.51137	−	3.46186i	−1.35877	−	0.494551i
$50$		0			0
$51$	−4.10180	+	6.35445i	−0.574366	+	0.889801i
$52$		0			0
$53$	2.61345			0.358984			0.179492	−	0.983759i	$-0.442555\pi$
$53$	2.61345			0.358984			0.179492	+	0.983759i	$0.442555\pi$
$54$		0			0
$55$	−15.1463			−2.04232
$56$		0			0
$57$	−7.15427	−	0.355188i	−0.947607	−	0.0470458i
$58$		0			0
$59$	−5.66002	−	2.06008i	−0.736871	−	0.268199i	−0.0538009	−	0.998552i	$-0.517134\pi$
$59$	−5.66002	−	2.06008i	−0.736871	−	0.268199i	−0.683071	+	0.730352i	$0.739356\pi$
$60$		0			0
$61$	1.75064	−	9.92840i	0.224147	−	1.27120i	−0.640162	−	0.768240i	$-0.721133\pi$
$61$	1.75064	−	9.92840i	0.224147	−	1.27120i	0.864309	−	0.502961i	$-0.167756\pi$
$62$		0			0
$63$	8.67222	+	8.88193i	1.09260	+	1.11902i
$64$		0			0
$65$	18.5391	−	6.74768i	2.29949	−	0.836947i
$66$		0			0
$67$	6.64142	−	5.57282i	0.811379	−	0.680828i	−0.139557	−	0.990214i	$-0.544568\pi$
$67$	6.64142	−	5.57282i	0.811379	−	0.680828i	0.950937	+	0.309386i	$0.100124\pi$
$68$		0			0
$69$	5.37450	−	4.07323i	0.647014	−	0.490359i
$70$		0			0
$71$	−2.91408	−	5.04733i	−0.345837	−	0.599008i	0.639668	−	0.768651i	$-0.279072\pi$
$71$	−2.91408	−	5.04733i	−0.345837	−	0.599008i	−0.985506	+	0.169643i	$0.945738\pi$
$72$		0			0
$73$	−1.06936	+	1.85218i	−0.125159	+	0.216781i	−0.921795	−	0.387678i	$-0.873277\pi$
$73$	−1.06936	+	1.85218i	−0.125159	+	0.216781i	0.796636	+	0.604459i	$0.206611\pi$
$74$		0			0
$75$	3.40000	−	14.9143i	0.392599	−	1.72215i
$76$		0			0
$77$	2.92626	+	16.5956i	0.333478	+	1.89125i
$78$		0			0
$79$	7.77819	+	6.52668i	0.875115	+	0.734309i	0.965169	−	0.261628i	$-0.0842595\pi$
$79$	7.77819	+	6.52668i	0.875115	+	0.734309i	−0.0900539	+	0.995937i	$0.528704\pi$
$80$		0			0
$81$	−2.87526	−	8.52836i	−0.319474	−	0.947595i
$82$		0			0
$83$	−3.75731	−	3.15276i	−0.412419	−	0.346060i	0.412852	−	0.910798i	$-0.364533\pi$
$83$	−3.75731	−	3.15276i	−0.412419	−	0.346060i	−0.825270	+	0.564738i	$0.808977\pi$
$84$		0			0
$85$	−2.82007	−	15.9934i	−0.305879	−	1.73473i
$86$		0			0
$87$	−1.14684	+	5.03066i	−0.122954	+	0.539343i
$88$		0			0
$89$	−3.99446	+	6.91860i	−0.423412	+	0.733371i	−0.996271	−	0.0862834i	$-0.972501\pi$
$89$	−3.99446	+	6.91860i	−0.423412	+	0.733371i	0.572859	+	0.819654i	$0.305834\pi$
$90$		0			0
$91$	−10.9751	−	19.0095i	−1.15051	−	1.99274i
$92$		0			0
$93$	8.66985	−	6.57071i	0.899022	−	0.681351i
$94$		0			0
$95$	11.7823	−	9.88655i	1.20884	−	1.01434i
$96$		0			0
$97$	−3.00873	+	1.09509i	−0.305490	+	0.111189i	−0.490216	−	0.871601i	$-0.663082\pi$
$97$	−3.00873	+	1.09509i	−0.305490	+	0.111189i	0.184727	+	0.982790i	$0.440860\pi$
$98$		0			0
$99$	3.30292	−	11.7628i	0.331956	−	1.18220i
$100$		0			0
$101$	−3.16978	+	17.9767i	−0.315405	+	1.78875i	0.254537	+	0.967063i	$0.418077\pi$
$101$	−3.16978	+	17.9767i	−0.315405	+	1.78875i	−0.569942	+	0.821685i	$0.693034\pi$
$102$		0			0
$103$	−11.9582	−	4.35242i	−1.17827	−	0.428857i	−0.322682	−	0.946508i	$-0.604584\pi$
$103$	−11.9582	−	4.35242i	−1.17827	−	0.428857i	−0.855592	+	0.517651i	$0.826807\pi$
$104$		0			0
$105$	−26.6218	−	1.32169i	−2.59803	−	0.128984i
$106$		0			0
$107$	18.3129			1.77038			0.885190	−	0.465230i	$-0.154028\pi$
$107$	18.3129			1.77038			0.885190	+	0.465230i	$0.154028\pi$
$108$		0			0
$109$	−5.09831			−0.488330			−0.244165	−	0.969734i	$-0.578514\pi$
$109$	−5.09831			−0.488330			−0.244165	+	0.969734i	$0.578514\pi$
$110$		0			0
$111$	−6.08146	+	9.42133i	−0.577227	+	0.894233i
$112$		0			0
$113$	11.5551	+	4.20570i	1.08701	+	0.395639i	0.822512	−	0.568748i	$-0.192572\pi$
$113$	11.5551	+	4.20570i	1.08701	+	0.395639i	0.264496	+	0.964387i	$0.414794\pi$
$114$		0			0
$115$	−2.51443	+	14.2601i	−0.234472	+	1.32976i
$116$		0			0
$117$	1.19754	+	15.8692i	0.110712	+	1.46710i
$118$		0			0
$119$	−16.9790	+	6.17985i	−1.55646	+	0.566506i
$120$		0			0
$121$	4.27894	−	3.59045i	0.388994	−	0.326405i
$122$		0			0
$123$	0.994125	+	0.418754i	0.0896372	+	0.0377578i
$124$		0			0
$125$	7.12520	+	12.3412i	0.637297	+	1.10383i
$126$		0			0
$127$	−5.54093	+	9.59718i	−0.491678	+	0.851612i	−0.999954	−	0.00958268i	$-0.996950\pi$
$127$	−5.54093	+	9.59718i	−0.491678	+	0.851612i	0.508276	+	0.861194i	$0.330283\pi$
$128$		0			0
$129$	−5.82644	−	5.40333i	−0.512990	−	0.475737i
$130$		0			0
$131$	0.475797	+	2.69838i	0.0415706	+	0.235758i	0.998513	−	0.0545205i	$-0.0173630\pi$
$131$	0.475797	+	2.69838i	0.0415706	+	0.235758i	−0.956942	+	0.290279i	$0.906252\pi$
$132$		0			0
$133$	−13.1090	−	10.9997i	−1.13669	−	0.953797i
$134$		0			0
$135$	16.9788	+	9.22900i	1.46131	+	0.794306i
$136$		0			0
$137$	2.86980	+	2.40805i	0.245184	+	0.205734i	0.757095	−	0.653305i	$-0.226618\pi$
$137$	2.86980	+	2.40805i	0.245184	+	0.205734i	−0.511911	+	0.859038i	$0.671062\pi$
$138$		0			0
$139$	3.00951	+	17.0678i	0.255263	+	1.44767i	0.795396	+	0.606090i	$0.207263\pi$
$139$	3.00951	+	17.0678i	0.255263	+	1.44767i	−0.540133	+	0.841580i	$0.681626\pi$
$140$		0			0
$141$	1.82390	−	0.563118i	0.153600	−	0.0474231i
$142$		0			0
$143$	−10.8020	+	18.7096i	−0.903306	+	1.56457i
$144$		0			0
$145$	−5.53954	−	9.59476i	−0.460033	−	0.796801i
$146$		0			0
$147$	2.18445	+	17.3948i	0.180171	+	1.43470i
$148$		0			0
$149$	1.98619	−	1.66661i	0.162715	−	0.136534i	−0.557795	−	0.829979i	$-0.688352\pi$
$149$	1.98619	−	1.66661i	0.162715	−	0.136534i	0.720510	+	0.693445i	$0.243908\pi$
$150$		0			0
$151$	9.81474	−	3.57227i	0.798712	−	0.290707i	0.0897593	−	0.995963i	$-0.471390\pi$
$151$	9.81474	−	3.57227i	0.798712	−	0.290707i	0.708953	+	0.705256i	$0.249168\pi$
$152$		0			0
$153$	13.0356	+	1.29756i	1.05387	+	0.104901i
$154$		0			0
$155$	−4.05615	+	23.0036i	−0.325798	+	1.84769i
$156$		0			0
$157$	15.8461	+	5.76749i	1.26465	+	0.460296i	0.885328	−	0.464967i	$-0.153934\pi$
$157$	15.8461	+	5.76749i	1.26465	+	0.460296i	0.379325	+	0.925263i	$0.376156\pi$
$158$		0			0
$159$	−2.06614	−	4.02758i	−0.163856	−	0.319408i
$160$		0			0
$161$	16.1104			1.26968
$162$		0			0
$163$	−8.19944			−0.642230			−0.321115	−	0.947040i	$-0.604058\pi$
$163$	−8.19944			−0.642230			−0.321115	+	0.947040i	$0.604058\pi$
$164$		0			0
$165$	11.9743	+	23.3418i	0.932201	+	1.81716i
$166$		0			0
$167$	−4.87891	−	1.77578i	−0.377542	−	0.137414i	0.146277	−	0.989244i	$-0.453271\pi$
$167$	−4.87891	−	1.77578i	−0.377542	−	0.137414i	−0.523819	+	0.851830i	$0.675493\pi$
$168$		0			0
$169$	2.62911	−	14.9104i	0.202239	−	1.14696i
$170$		0			0
$171$	5.10866	+	11.3062i	0.390669	+	0.864610i
$172$		0			0
$173$	14.3992	−	5.24087i	1.09475	−	0.398456i	0.269371	−	0.963036i	$-0.413184\pi$
$173$	14.3992	−	5.24087i	1.09475	−	0.398456i	0.825378	+	0.564580i	$0.190962\pi$
$174$		0			0
$175$	27.9945	−	23.4901i	2.11618	−	1.77569i
$176$		0			0
$177$	1.29992	+	10.3513i	0.0977082	+	0.778051i
$178$		0			0
$179$	8.42147	+	14.5864i	0.629451	+	1.09024i	0.987662	+	0.156600i	$0.0500533\pi$
$179$	8.42147	+	14.5864i	0.629451	+	1.09024i	−0.358212	+	0.933640i	$0.616613\pi$
$180$		0			0
$181$	0.504862	−	0.874446i	0.0375261	−	0.0649971i	−0.846652	−	0.532146i	$-0.821386\pi$
$181$	0.504862	−	0.874446i	0.0375261	−	0.0649971i	0.884178	+	0.467149i	$0.154719\pi$
$182$		0			0
$183$	−16.6847	+	5.15129i	−1.23337	+	0.380794i
$184$		0			0
$185$	−4.18113	−	23.7124i	−0.307403	−	1.74337i
$186$		0			0
$187$	13.6230	+	11.4311i	0.996214	+	0.835922i
$188$		0			0
$189$	6.83183	−	20.3866i	0.496942	−	1.48291i
$190$		0			0
$191$	3.94392	+	3.30934i	0.285372	+	0.239456i	0.774225	−	0.632911i	$-0.218140\pi$
$191$	3.94392	+	3.30934i	0.285372	+	0.239456i	−0.488853	+	0.872366i	$0.662584\pi$
$192$		0			0
$193$	2.91547	+	16.5345i	0.209860	+	1.19018i	0.889606	+	0.456729i	$0.150979\pi$
$193$	2.91547	+	16.5345i	0.209860	+	1.19018i	−0.679745	+	0.733448i	$0.737910\pi$
$194$		0			0
$195$	−25.0555	−	23.2360i	−1.79426	−	1.66396i
$196$		0			0
$197$	1.08277	−	1.87542i	0.0771443	−	0.133618i	−0.824872	−	0.565319i	$-0.808753\pi$
$197$	1.08277	−	1.87542i	0.0771443	−	0.133618i	0.902017	+	0.431701i	$0.142086\pi$
$198$		0			0
$199$	11.6272	+	20.1388i	0.824228	+	1.42760i	0.902508	+	0.430673i	$0.141724\pi$
$199$	11.6272	+	20.1388i	0.824228	+	1.42760i	−0.0782800	+	0.996931i	$0.524943\pi$
$200$		0			0
$201$	−13.8388	−	5.82932i	−0.976116	−	0.411168i
$202$		0			0
$203$	−9.44266	+	7.92333i	−0.662745	+	0.556109i
$204$		0			0
$205$	−2.17657	+	0.792205i	−0.152018	+	0.0553300i
$206$		0			0
$207$	−10.5262	−	5.06241i	−0.731623	−	0.351862i
$208$		0			0
$209$	−2.92467	+	16.5866i	−0.202304	+	1.14732i
$210$		0			0
$211$	5.06308	+	1.84281i	0.348557	+	0.126864i	0.510365	−	0.859958i	$-0.329510\pi$
$211$	5.06308	+	1.84281i	0.348557	+	0.126864i	−0.161808	+	0.986822i	$0.551733\pi$
$212$		0			0
$213$	−5.47461	+	8.48120i	−0.375114	+	0.581122i
$214$		0			0
$215$	17.0624			1.16365
$216$		0			0
$217$	25.9885			1.76421
$218$		0			0
$219$	3.69980	+	0.183684i	0.250009	+	0.0124122i
$220$		0			0
$221$	−21.7672	−	7.92262i	−1.46422	−	0.532933i
$222$		0			0
$223$	−3.66530	+	20.7869i	−0.245447	+	1.39200i	0.574007	+	0.818850i	$0.305388\pi$
$223$	−3.66530	+	20.7869i	−0.245447	+	1.39200i	−0.819453	+	0.573146i	$0.805723\pi$
$224$		0			0
$225$	−25.6723	+	6.55122i	−1.71149	+	0.436748i
$226$		0			0
$227$	2.65053	−	0.964714i	0.175922	−	0.0640303i	−0.252558	−	0.967582i	$-0.581272\pi$
$227$	2.65053	−	0.964714i	0.175922	−	0.0640303i	0.428479	+	0.903552i	$0.359049\pi$
$228$		0			0
$229$	−17.3556	+	14.5631i	−1.14689	+	0.962356i	−0.999642	−	0.0267436i	$-0.991486\pi$
$229$	−17.3556	+	14.5631i	−1.14689	+	0.962356i	−0.147249	+	0.989099i	$0.547042\pi$
$230$		0			0
$231$	23.2620	−	17.6298i	1.53053	−	1.15996i
$232$		0			0
$233$	9.23565	+	15.9966i	0.605047	+	1.04797i	0.992044	+	0.125892i	$0.0401792\pi$
$233$	9.23565	+	15.9966i	0.605047	+	1.04797i	−0.386997	+	0.922081i	$0.626487\pi$
$234$		0			0
$235$	−2.04936	+	3.54960i	−0.133686	+	0.231550i
$236$		0			0
$237$	3.90895	−	17.1468i	0.253914	−	1.11381i
$238$		0			0
$239$	−3.68055	−	20.8734i	−0.238075	−	1.35019i	−0.836041	−	0.548667i	$-0.815135\pi$
$239$	−3.68055	−	20.8734i	−0.238075	−	1.35019i	0.597966	−	0.801522i	$-0.295976\pi$
$240$		0			0
$241$	−0.298133	−	0.250163i	−0.0192044	−	0.0161144i	0.633135	−	0.774041i	$-0.281768\pi$
$241$	−0.298133	−	0.250163i	−0.0192044	−	0.0161144i	−0.652339	+	0.757927i	$0.726212\pi$
$242$		0			0
$243$	−10.8699	+	11.1734i	−0.697304	+	0.716775i
$244$		0			0
$245$	−28.8369	−	24.1970i	−1.84232	−	1.54589i
$246$		0			0
$247$	−3.80956	−	21.6051i	−0.242397	−	1.37470i
$248$		0			0
$249$	−1.88825	+	8.28290i	−0.119663	+	0.524907i
$250$		0			0
$251$	12.3296	−	21.3556i	0.778240	−	1.34795i	−0.154716	−	0.987959i	$-0.549446\pi$
$251$	12.3296	−	21.3556i	0.778240	−	1.34795i	0.932955	−	0.359992i	$-0.117221\pi$
$252$		0			0
$253$	−7.92812	−	13.7319i	−0.498437	−	0.863317i
$254$		0			0
$255$	−22.4179	+	16.9901i	−1.40386	+	1.06396i
$256$		0			0
$257$	10.2718	−	8.61908i	0.640738	−	0.537643i	−0.263507	−	0.964658i	$-0.584879\pi$
$257$	10.2718	−	8.61908i	0.640738	−	0.537643i	0.904245	+	0.427014i	$0.140435\pi$
$258$		0			0
$259$	−25.1736	+	9.16246i	−1.56421	+	0.569328i
$260$		0			0
$261$	8.65940	−	2.20976i	0.536003	−	0.136780i
$262$		0			0
$263$	−3.01475	+	17.0975i	−0.185897	+	1.05428i	0.738899	+	0.673816i	$0.235346\pi$
$263$	−3.01475	+	17.0975i	−0.185897	+	1.05428i	−0.924797	+	0.380461i	$0.875765\pi$
$264$		0			0
$265$	9.13349	+	3.32432i	0.561066	+	0.204211i
$266$		0			0
$267$	13.8202	+	0.686130i	0.845782	+	0.0419905i
$268$		0			0
$269$	−7.42802			−0.452894			−0.226447	−	0.974023i	$-0.572711\pi$
$269$	−7.42802			−0.452894			−0.226447	+	0.974023i	$0.572711\pi$
$270$		0			0
$271$	0.127126			0.00772233			0.00386116	−	0.999993i	$-0.498771\pi$
$271$	0.127126			0.00772233			0.00386116	+	0.999993i	$0.498771\pi$
$272$		0			0
$273$	−20.6188	+	31.9423i	−1.24790	+	1.93324i
$274$		0			0
$275$	−33.7985	−	12.3016i	−2.03812	−	0.741816i
$276$		0			0
$277$	−0.184320	+	1.04533i	−0.0110747	+	0.0628078i	−0.989844	−	0.142156i	$-0.954597\pi$
$277$	−0.184320	+	1.04533i	−0.0110747	+	0.0628078i	0.978770	+	0.204964i	$0.0657077\pi$
$278$		0			0
$279$	−16.9803	−	8.16641i	−1.01659	−	0.488910i
$280$		0			0
$281$	−5.96339	+	2.17050i	−0.355746	+	0.129481i	−0.513710	−	0.857964i	$-0.671729\pi$
$281$	−5.96339	+	2.17050i	−0.355746	+	0.129481i	0.157964	+	0.987445i	$0.449507\pi$
$282$		0			0
$283$	8.03928	−	6.74576i	0.477886	−	0.400994i	−0.371776	−	0.928323i	$-0.621251\pi$
$283$	8.03928	−	6.74576i	0.477886	−	0.400994i	0.849661	+	0.527329i	$0.176806\pi$
$284$		0			0
$285$	−24.5510	−	10.3416i	−1.45428	−	0.612583i
$286$		0			0
$287$	1.28853	+	2.23179i	0.0760593	+	0.131739i
$288$		0			0
$289$	−1.03396	+	1.79087i	−0.0608212	+	0.105345i
$290$		0			0
$291$	4.06628	+	3.77098i	0.238369	+	0.221059i
$292$		0			0
$293$	−0.903546	−	5.12426i	−0.0527857	−	0.299363i	0.946973	−	0.321312i	$-0.104124\pi$
$293$	−0.903546	−	5.12426i	−0.0527857	−	0.299363i	−0.999759	+	0.0219494i	$0.993013\pi$
$294$		0			0
$295$	−17.1602	−	14.3992i	−0.999108	−	0.838351i
$296$		0			0
$297$	−20.7388	+	4.20930i	−1.20339	+	0.244248i
$298$		0			0
$299$	15.8217	+	13.2759i	0.914990	+	0.767768i
$300$		0			0
$301$	−3.29646	−	18.6952i	−0.190005	−	1.07757i
$302$		0			0
$303$	30.2098	−	9.32711i	1.73551	−	0.535828i
$304$		0			0
$305$	18.7471	−	32.4710i	1.07346	−	1.85928i
$306$		0			0
$307$	−12.3396	−	21.3728i	−0.704259	−	1.21981i	−0.966958	−	0.254934i	$-0.917946\pi$
$307$	−12.3396	−	21.3728i	−0.704259	−	1.21981i	0.262700	−	0.964878i	$-0.415387\pi$
$308$		0			0
$309$	2.74641	+	21.8696i	0.156238	+	1.24412i
$310$		0			0
$311$	−6.87269	+	5.76687i	−0.389715	+	0.327009i	−0.816502	−	0.577343i	$-0.804090\pi$
$311$	−6.87269	+	5.76687i	−0.389715	+	0.327009i	0.426787	+	0.904352i	$0.359645\pi$
$312$		0			0
$313$	1.77911	−	0.647544i	0.100561	−	0.0366013i	−0.291250	−	0.956647i	$-0.594071\pi$
$313$	1.77911	−	0.647544i	0.100561	−	0.0366013i	0.391811	+	0.920046i	$0.371849\pi$
$314$		0			0
$315$	19.0099	+	42.0718i	1.07109	+	2.37048i
$316$		0			0
$317$	−5.67056	+	32.1594i	−0.318491	+	1.80625i	0.233452	+	0.972368i	$0.424998\pi$
$317$	−5.67056	+	32.1594i	−0.318491	+	1.80625i	−0.551943	+	0.833882i	$0.686113\pi$
$318$		0			0
$319$	11.4004	+	4.14940i	0.638299	+	0.232322i
$320$		0			0
$321$	−14.4779	−	28.2220i	−0.808076	−	1.57520i
$322$		0			0
$323$	−18.0589			−1.00482
$324$		0			0
$325$	46.8499			2.59877
$326$		0			0
$327$	4.03063	+	7.85699i	0.222894	+	0.434493i
$328$		0			0
$329$	4.28520	+	1.55969i	0.236251	+	0.0859883i
$330$		0			0
$331$	−2.57508	+	14.6040i	−0.141539	+	0.802707i	0.828542	+	0.559927i	$0.189171\pi$
$331$	−2.57508	+	14.6040i	−0.141539	+	0.802707i	−0.970081	+	0.242781i	$0.921940\pi$
$332$		0			0
$333$	19.3271	+	1.92380i	1.05912	+	0.105424i
$334$		0			0
$335$	30.2992	−	11.0280i	1.65542	−	0.602524i
$336$		0			0
$337$	11.3476	−	9.52176i	0.618143	−	0.518683i	−0.279076	−	0.960269i	$-0.590028\pi$
$337$	11.3476	−	9.52176i	0.618143	−	0.518683i	0.897219	+	0.441585i	$0.145584\pi$
$338$		0			0
$339$	−2.65382	−	21.1324i	−0.144136	−	1.14775i
$340$		0			0
$341$	−12.7892	−	22.1516i	−0.692575	−	1.19957i
$342$		0			0
$343$	−6.45875	+	11.1869i	−0.348740	+	0.604035i
$344$		0			0
$345$	23.9640	−	7.39875i	1.29018	−	0.398335i
$346$		0			0
$347$	−6.12313	−	34.7260i	−0.328707	−	1.86419i	−0.482230	−	0.876045i	$-0.660173\pi$
$347$	−6.12313	−	34.7260i	−0.328707	−	1.86419i	0.153523	−	0.988145i	$-0.450938\pi$
$348$		0			0
$349$	−3.44126	−	2.88756i	−0.184207	−	0.154568i	0.546021	−	0.837771i	$-0.316142\pi$
$349$	−3.44126	−	2.88756i	−0.184207	−	0.154568i	−0.730228	+	0.683204i	$0.760586\pi$
$350$		0			0
$351$	23.5092	−	14.3914i	1.25483	−	0.768155i
$352$		0			0
$353$	−13.5745	−	11.3903i	−0.722495	−	0.606246i	0.205579	−	0.978641i	$-0.434092\pi$
$353$	−13.5745	−	11.3903i	−0.722495	−	0.606246i	−0.928074	+	0.372395i	$0.878537\pi$
$354$		0			0
$355$	−3.76391	−	21.3462i	−0.199767	−	1.13294i
$356$		0			0
$357$	22.9470	+	21.2806i	1.21449	+	1.12629i
$358$		0			0
$359$	6.30140	−	10.9143i	0.332575	−	0.576037i	−0.650441	−	0.759557i	$-0.725416\pi$
$359$	6.30140	−	10.9143i	0.332575	−	0.576037i	0.983016	+	0.183520i	$0.0587492\pi$
$360$		0			0
$361$	0.948366	+	1.64262i	0.0499140	+	0.0864536i
$362$		0			0
$363$	−8.91608	−	3.75571i	−0.467973	−	0.197124i
$364$		0			0
$365$	−6.09317	+	5.11278i	−0.318931	+	0.267615i
$366$		0			0
$367$	−31.9195	+	11.6177i	−1.66618	+	0.606441i	−0.991316	−	0.131499i	$-0.958021\pi$
$367$	−31.9195	+	11.6177i	−1.66618	+	0.606441i	−0.674866	+	0.737940i	$0.735799\pi$
$368$		0			0
$369$	−0.140596	−	1.86310i	−0.00731912	−	0.0969892i
$370$		0			0
$371$	1.87784	−	10.6498i	0.0974926	−	0.552908i
$372$		0			0
$373$	−16.7089	−	6.08154i	−0.865153	−	0.314890i	−0.128950	−	0.991651i	$-0.541161\pi$
$373$	−16.7089	−	6.08154i	−0.865153	−	0.314890i	−0.736203	+	0.676761i	$0.763383\pi$
$374$		0			0
$375$	13.3860	−	20.7374i	0.691248	−	1.07087i
$376$		0			0
$377$	−15.8027			−0.813880
$378$		0			0
$379$	18.3633			0.943260			0.471630	−	0.881797i	$-0.343666\pi$
$379$	18.3633			0.943260			0.471630	+	0.881797i	$0.343666\pi$
$380$		0			0
$381$	19.1707	+	0.951769i	0.982147	+	0.0487606i
$382$		0			0
$383$	−5.04048	−	1.83458i	−0.257556	−	0.0937429i	0.210015	−	0.977698i	$-0.432649\pi$
$383$	−5.04048	−	1.83458i	−0.257556	−	0.0937429i	−0.467571	+	0.883955i	$0.654871\pi$
$384$		0			0
$385$	−10.8830	+	61.7207i	−0.554651	+	3.14558i
$386$		0			0
$387$	−3.72078	+	13.2509i	−0.189138	+	0.673581i
$388$		0			0
$389$	10.4800	−	3.81442i	0.531359	−	0.193399i	−0.0623858	−	0.998052i	$-0.519871\pi$
$389$	10.4800	−	3.81442i	0.531359	−	0.193399i	0.593745	+	0.804653i	$0.297649\pi$
$390$		0			0
$391$	13.0238	−	10.9283i	0.658643	−	0.552667i
$392$		0			0
$393$	3.78231	−	2.86654i	0.190792	−	0.144598i
$394$		0			0
$395$	18.8813	+	32.7034i	0.950022	+	1.64549i
$396$		0			0
$397$	−15.1368	+	26.2178i	−0.759696	+	1.31583i	0.183309	+	0.983055i	$0.441319\pi$
$397$	−15.1368	+	26.2178i	−0.759696	+	1.31583i	−0.943005	+	0.332777i	$0.892014\pi$
$398$		0			0
$399$	−6.58795	+	28.8984i	−0.329810	+	1.44673i
$400$		0			0
$401$	4.07267	+	23.0973i	0.203380	+	1.15342i	0.899969	+	0.435953i	$0.143589\pi$
$401$	4.07267	+	23.0973i	0.203380	+	1.15342i	−0.696590	+	0.717470i	$0.745300\pi$
$402$		0			0
$403$	25.5226	+	21.4160i	1.27137	+	1.06681i
$404$		0			0
$405$	0.799631	−	33.4623i	0.0397340	−	1.66276i
$406$		0			0
$407$	20.1980	+	16.9481i	1.00118	+	0.840086i
$408$		0			0
$409$	6.69332	+	37.9597i	0.330964	+	1.87699i	0.463937	+	0.885868i	$0.346436\pi$
$409$	6.69332	+	37.9597i	0.330964	+	1.87699i	−0.132974	+	0.991120i	$0.542453\pi$
$410$		0			0
$411$	1.44223	−	6.32641i	0.0711399	−	0.312059i
$412$		0			0
$413$	−12.4617	+	21.5843i	−0.613199	+	1.06209i
$414$		0			0
$415$	−9.12076	−	15.7976i	−0.447720	−	0.775475i
$416$		0			0
$417$	23.9238	−	18.1314i	1.17156	−	0.887899i
$418$		0			0
$419$	−3.32611	+	2.79094i	−0.162491	+	0.136346i	−0.720408	−	0.693551i	$-0.756045\pi$
$419$	−3.32611	+	2.79094i	−0.162491	+	0.136346i	0.557917	+	0.829897i	$0.311601\pi$
$420$		0			0
$421$	30.1360	−	10.9686i	1.46874	−	0.534577i	0.520980	−	0.853569i	$-0.325567\pi$
$421$	30.1360	−	10.9686i	1.46874	−	0.534577i	0.947757	+	0.318992i	$0.103344\pi$
$422$		0			0
$423$	−2.30976	−	2.36561i	−0.112304	−	0.115020i
$424$		0			0
$425$	6.69677	−	37.9793i	0.324841	−	1.84227i
$426$		0			0
$427$	−39.2002	−	14.2677i	−1.89703	−	0.690462i
$428$		0			0
$429$	37.3731	+	1.85546i	1.80439	+	0.0895825i
$430$		0			0
$431$	7.12897			0.343391			0.171695	−	0.985150i	$-0.445076\pi$
$431$	7.12897			0.343391			0.171695	+	0.985150i	$0.445076\pi$
$432$		0			0
$433$	−12.3858			−0.595226			−0.297613	−	0.954687i	$-0.596190\pi$
$433$	−12.3858			−0.595226			−0.297613	+	0.954687i	$0.596190\pi$
$434$		0			0
$435$	−10.4070	+	16.1224i	−0.498978	+	0.773010i
$436$		0			0
$437$	15.1307	+	5.50711i	0.723798	+	0.263441i
$438$		0			0
$439$	0.731071	−	4.14611i	0.0348921	−	0.197883i	−0.962379	−	0.271711i	$-0.912410\pi$
$439$	0.731071	−	4.14611i	0.0348921	−	0.197883i	0.997271	+	0.0738281i	$0.0235216\pi$
$440$		0			0
$441$	25.0801	−	17.1185i	1.19429	−	0.815166i
$442$		0			0
$443$	−31.2580	+	11.3770i	−1.48511	+	0.540537i	−0.952158	−	0.305607i	$-0.901141\pi$
$443$	−31.2580	+	11.3770i	−1.48511	+	0.540537i	−0.532955	+	0.846144i	$0.678918\pi$
$444$		0			0
$445$	−22.7604	+	19.0982i	−1.07895	+	0.905342i
$446$		0			0
$447$	−4.13866	−	1.74332i	−0.195752	−	0.0824563i
$448$		0			0
$449$	−2.67506	−	4.63334i	−0.126244	−	0.218661i	0.795975	−	0.605330i	$-0.206959\pi$
$449$	−2.67506	−	4.63334i	−0.126244	−	0.218661i	−0.922218	+	0.386669i	$0.873625\pi$
$450$		0			0
$451$	1.26820	−	2.19658i	0.0597170	−	0.103433i
$452$		0			0
$453$	−13.2646	−	12.3013i	−0.623224	−	0.577965i
$454$		0			0
$455$	−14.1758	−	80.3950i	−0.664572	−	3.76898i
$456$		0			0
$457$	−15.2928	−	12.8322i	−0.715366	−	0.600263i	0.210733	−	0.977544i	$-0.432415\pi$
$457$	−15.2928	−	12.8322i	−0.715366	−	0.600263i	−0.926099	+	0.377280i	$0.876859\pi$
$458$		0			0
$459$	−8.30606	−	21.1150i	−0.387694	−	0.985564i
$460$		0			0
$461$	21.5076	+	18.0471i	1.00171	+	0.840535i	0.987221	−	0.159360i	$-0.0509431\pi$
$461$	21.5076	+	18.0471i	1.00171	+	0.840535i	0.0144901	+	0.999895i	$0.495387\pi$
$462$		0			0
$463$	−5.72965	−	32.4944i	−0.266279	−	1.51014i	−0.765368	−	0.643593i	$-0.777443\pi$
$463$	−5.72965	−	32.4944i	−0.266279	−	1.51014i	0.499088	−	0.866551i	$-0.333668\pi$
$464$		0			0
$465$	38.6575	−	11.9353i	1.79270	−	0.553485i
$466$		0			0
$467$	−2.76592	+	4.79071i	−0.127991	+	0.221687i	−0.922898	−	0.385044i	$-0.874186\pi$
$467$	−2.76592	+	4.79071i	−0.127991	+	0.221687i	0.794907	+	0.606731i	$0.207520\pi$
$468$		0			0
$469$	−17.9371	−	31.0679i	−0.828258	−	1.43458i
$470$		0			0
$471$	−3.63933	−	28.9800i	−0.167691	−	1.33533i
$472$		0			0
$473$	−14.3128	+	12.0099i	−0.658104	+	0.552215i
$474$		0			0
$475$	34.3217	−	12.4921i	1.57479	−	0.573176i
$476$		0			0
$477$	−4.57343	+	6.36825i	−0.209403	+	0.291582i
$478$		0			0
$479$	−3.67542	+	20.8444i	−0.167934	+	0.952403i	0.778053	+	0.628199i	$0.216208\pi$
$479$	−3.67542	+	20.8444i	−0.167934	+	0.952403i	−0.945987	+	0.324204i	$0.894904\pi$
$480$		0			0
$481$	−32.2728	−	11.7464i	−1.47151	−	0.535587i
$482$		0			0
$483$	−12.7366	−	24.8277i	−0.579536	−	1.12970i
$484$		0			0
$485$	−11.9079			−0.540709
$486$		0			0
$487$	−14.4479			−0.654695			−0.327348	−	0.944904i	$-0.606155\pi$
$487$	−14.4479			−0.654695			−0.327348	+	0.944904i	$0.606155\pi$
$488$		0			0
$489$	6.48232	+	12.6361i	0.293141	+	0.571426i
$490$		0			0
$491$	9.93340	+	3.61546i	0.448288	+	0.163164i	0.556292	−	0.830987i	$-0.312224\pi$
$491$	9.93340	+	3.61546i	0.448288	+	0.163164i	−0.108004	+	0.994150i	$0.534446\pi$
$492$		0			0
$493$	−2.25885	+	12.8106i	−0.101734	+	0.576960i
$494$		0			0
$495$	26.5054	−	36.9073i	1.19133	−	1.65886i
$496$		0			0
$497$	−22.6616	+	8.24817i	−1.01651	+	0.369981i
$498$		0			0
$499$	1.57824	−	1.32430i	0.0706519	−	0.0592840i	−0.606778	−	0.794871i	$-0.707538\pi$
$499$	1.57824	−	1.32430i	0.0706519	−	0.0592840i	0.677430	+	0.735588i	$0.263094\pi$
$500$		0			0
$501$	1.12053	+	8.92278i	0.0500615	+	0.398640i
$502$		0			0
$503$	−12.5110	−	21.6698i	−0.557840	−	0.966207i	−0.997676	−	0.0681293i	$-0.978297\pi$
$503$	−12.5110	−	21.6698i	−0.557840	−	0.966207i	0.439837	−	0.898078i	$-0.355036\pi$
$504$		0			0
$505$	−33.9442	+	58.7931i	−1.51050	+	2.61626i
$506$		0			0
$507$	−25.0569	+	7.73619i	−1.11282	+	0.343576i
$508$		0			0
$509$	−2.04442	−	11.5945i	−0.0906174	−	0.513917i	−0.996002	−	0.0893254i	$-0.971529\pi$
$509$	−2.04442	−	11.5945i	−0.0906174	−	0.513917i	0.905385	−	0.424591i	$-0.139582\pi$
$510$		0			0
$511$	6.77923	+	5.68845i	0.299896	+	0.251642i
$512$		0			0
$513$	13.3852	−	16.8114i	0.590971	−	0.742243i
$514$		0			0
$515$	−36.2552	−	30.4217i	−1.59760	−	1.34054i
$516$		0			0
$517$	−0.779379	−	4.42008i	−0.0342770	−	0.194395i
$518$		0			0
$519$	−19.4604	−	18.0472i	−0.854218	−	0.792184i
$520$		0			0
$521$	0.916637	−	1.58766i	0.0401586	−	0.0695567i	−0.845247	−	0.534375i	$-0.820547\pi$
$521$	0.916637	−	1.58766i	0.0401586	−	0.0695567i	0.885406	+	0.464818i	$0.153880\pi$
$522$		0			0
$523$	10.2381	+	17.7329i	0.447680	+	0.775404i	0.998235	−	0.0593951i	$-0.0189172\pi$
$523$	10.2381	+	17.7329i	0.447680	+	0.775404i	−0.550555	+	0.834799i	$0.685584\pi$
$524$		0			0
$525$	−58.3325	−	24.5713i	−2.54584	−	1.07238i
$526$		0			0
$527$	21.0093	−	17.6289i	0.915180	−	0.767927i
$528$		0			0
$529$	7.36831	−	2.68184i	0.320361	−	0.116602i
$530$		0			0
$531$	14.9247	−	10.1868i	0.647675	−	0.442072i
$532$		0			0
$533$	−0.573699	+	3.25361i	−0.0248497	+	0.140929i
$534$		0			0
$535$	64.0002	+	23.2942i	2.76697	+	1.00710i
$536$		0			0
$537$	15.8212	−	24.5101i	0.682737	−	1.05769i
$538$		0			0
$539$	41.2216			1.77554
$540$		0			0
$541$	−22.8214			−0.981169			−0.490584	−	0.871394i	$-0.663217\pi$
$541$	−22.8214			−0.981169			−0.490584	+	0.871394i	$0.663217\pi$
$542$		0			0
$543$	−1.74674	−	0.0867204i	−0.0749598	−	0.00372153i
$544$		0			0
$545$	−17.8176	−	6.48508i	−0.763223	−	0.277790i
$546$		0			0
$547$	−1.76657	+	10.0187i	−0.0755332	+	0.428370i	0.923468	+	0.383676i	$0.125342\pi$
$547$	−1.76657	+	10.0187i	−0.0755332	+	0.428370i	−0.999001	+	0.0446934i	$0.985769\pi$
$548$		0			0
$549$	21.1292	+	21.6402i	0.901773	+	0.923580i
$550$		0			0
$551$	−11.5769	+	4.21364i	−0.493191	+	0.179507i
$552$		0			0
$553$	32.1850	−	27.0064i	1.36864	−	1.14843i
$554$		0			0
$555$	−33.2375	+	25.1901i	−1.41085	+	1.06926i
$556$		0			0
$557$	3.30359	+	5.72199i	0.139978	+	0.242448i	0.927488	−	0.373853i	$-0.121964\pi$
$557$	3.30359	+	5.72199i	0.139978	+	0.242448i	−0.787510	+	0.616302i	$0.788630\pi$
$558$		0			0
$559$	12.1686	−	21.0765i	0.514675	−	0.891443i
$560$		0			0
$561$	6.84629	−	30.0316i	0.289050	−	1.26793i
$562$		0			0
$563$	7.13543	+	40.4670i	0.300722	+	1.70548i	0.642986	+	0.765878i	$0.277695\pi$
$563$	7.13543	+	40.4670i	0.300722	+	1.70548i	−0.342264	+	0.939604i	$0.611194\pi$
$564$		0			0
$565$	35.0330	+	29.3962i	1.47385	+	1.23671i
$566$		0			0
$567$	−36.8189	+	5.58877i	−1.54625	+	0.234706i
$568$		0			0
$569$	−8.33625	−	6.99495i	−0.349474	−	0.293243i	0.451105	−	0.892471i	$-0.351030\pi$
$569$	−8.33625	−	6.99495i	−0.349474	−	0.293243i	−0.800579	+	0.599228i	$0.795474\pi$
$570$		0			0
$571$	−4.72897	−	26.8193i	−0.197901	−	1.12235i	−0.908226	−	0.418480i	$-0.862563\pi$
$571$	−4.72897	−	26.8193i	−0.197901	−	1.12235i	0.710324	−	0.703874i	$-0.248548\pi$
$572$		0			0
$573$	1.98203	−	8.69427i	0.0828005	−	0.363209i
$574$		0			0
$575$	−17.1928	+	29.7788i	−0.716988	+	1.24186i
$576$		0			0
$577$	2.97982	+	5.16120i	0.124052	+	0.214864i	0.921362	−	0.388706i	$-0.127078\pi$
$577$	2.97982	+	5.16120i	0.124052	+	0.214864i	−0.797310	+	0.603570i	$0.793744\pi$
$578$		0			0
$579$	23.1763	−	17.5649i	0.963175	−	0.729971i
$580$		0			0
$581$	−15.5472	+	13.0456i	−0.645006	+	0.541225i
$582$		0			0
$583$	−10.0015	+	3.64026i	−0.414222	+	0.150764i
$584$		0			0
$585$	−16.0005	+	56.9829i	−0.661539	+	2.35595i
$586$		0			0
$587$	6.77108	−	38.4007i	0.279473	−	1.58497i	−0.444914	−	0.895573i	$-0.646766\pi$
$587$	6.77108	−	38.4007i	0.279473	−	1.58497i	0.724386	−	0.689394i	$-0.242123\pi$
$588$		0			0
$589$	24.4080	+	8.88377i	1.00571	+	0.366049i
$590$		0			0
$591$	−3.74622	−	0.185988i	−0.154099	−	0.00765053i
$592$		0			0
$593$	−22.2104			−0.912070			−0.456035	−	0.889962i	$-0.650731\pi$
$593$	−22.2104			−0.912070			−0.456035	+	0.889962i	$0.650731\pi$
$594$		0			0
$595$	−67.1992			−2.75490
$596$		0			0
$597$	21.8437	−	33.8400i	0.894003	−	1.38498i
$598$		0			0
$599$	−14.0876	−	5.12746i	−0.575603	−	0.209502i	0.0377827	−	0.999286i	$-0.487971\pi$
$599$	−14.0876	−	5.12746i	−0.575603	−	0.209502i	−0.613385	+	0.789784i	$0.710193\pi$
$600$		0			0
$601$	5.38658	−	30.5488i	0.219723	−	1.24611i	−0.652796	−	0.757533i	$-0.726404\pi$
$601$	5.38658	−	30.5488i	0.219723	−	1.24611i	0.872520	−	0.488579i	$-0.162485\pi$
$602$		0			0
$603$	1.95718	+	25.9355i	0.0797026	+	1.05618i
$604$		0			0
$605$	19.5211	−	7.10511i	0.793647	−	0.288864i
$606$		0			0
$607$	16.2118	−	13.6033i	0.658017	−	0.552141i	−0.251475	−	0.967864i	$-0.580916\pi$
$607$	16.2118	−	13.6033i	0.658017	−	0.552141i	0.909492	+	0.415722i	$0.136471\pi$
$608$		0			0
$609$	19.6758	+	8.28802i	0.797304	+	0.335848i
$610$		0			0
$611$	2.92312	+	5.06299i	0.118257	+	0.204827i
$612$		0			0
$613$	−0.991914	+	1.71805i	−0.0400630	+	0.0693912i	−0.885362	−	0.464903i	$-0.846089\pi$
$613$	−0.991914	+	1.71805i	−0.0400630	+	0.0693912i	0.845299	+	0.534294i	$0.179423\pi$
$614$		0			0
$615$	2.94162	+	2.72800i	0.118617	+	0.110003i
$616$		0			0
$617$	−0.199631	−	1.13216i	−0.00803685	−	0.0455792i	0.980526	−	0.196391i	$-0.0629223\pi$
$617$	−0.199631	−	1.13216i	−0.00803685	−	0.0455792i	−0.988562	+	0.150812i	$0.951811\pi$
$618$		0			0
$619$	14.1141	+	11.8431i	0.567293	+	0.476015i	0.880746	−	0.473588i	$-0.157042\pi$
$619$	14.1141	+	11.8431i	0.567293	+	0.476015i	−0.313453	+	0.949604i	$0.601486\pi$
$620$		0			0
$621$	0.520165	+	20.2242i	0.0208735	+	0.811568i
$622$		0			0
$623$	25.3231	+	21.2486i	1.01455	+	0.851306i
$624$		0			0
$625$	1.53509	+	8.70592i	0.0614035	+	0.348237i
$626$		0			0
$627$	27.8738	−	8.60589i	1.11317	−	0.343686i
$628$		0			0
$629$	−14.1354	+	24.4832i	−0.563614	+	0.976209i
$630$		0			0
$631$	−2.19443	−	3.80086i	−0.0873588	−	0.151310i	0.819035	−	0.573743i	$-0.194509\pi$
$631$	−2.19443	−	3.80086i	−0.0873588	−	0.151310i	−0.906394	+	0.422434i	$0.861176\pi$
$632$		0			0
$633$	−1.16283	−	9.25958i	−0.0462181	−	0.368035i
$634$		0			0
$635$	−31.5722	+	26.4922i	−1.25290	+	1.05131i
$636$		0			0
$637$	−50.4555	+	18.3643i	−1.99912	+	0.727620i
$638$		0			0
$639$	17.3985	+	1.73183i	0.688273	+	0.0685102i
$640$		0			0
$641$	3.31302	−	18.7890i	0.130856	−	0.742123i	−0.846800	−	0.531912i	$-0.821474\pi$
$641$	3.31302	−	18.7890i	0.130856	−	0.742123i	0.977656	−	0.210211i	$-0.0674151\pi$
$642$		0			0
$643$	33.4844	+	12.1873i	1.32049	+	0.480621i	0.903617	−	0.428342i	$-0.140902\pi$
$643$	33.4844	+	12.1873i	1.32049	+	0.480621i	0.416878	+	0.908962i	$0.363124\pi$
$644$		0			0
$645$	−13.4892	−	26.2949i	−0.531138	−	1.03536i
$646$		0			0
$647$	4.64685			0.182687			0.0913434	−	0.995819i	$-0.470884\pi$
$647$	4.64685			0.182687			0.0913434	+	0.995819i	$0.470884\pi$
$648$		0			0
$649$	24.5301			0.962891
$650$		0			0
$651$	−20.5460	−	40.0508i	−0.805261	−	1.56971i
$652$		0			0
$653$	5.74640	+	2.09152i	0.224874	+	0.0818475i	0.452000	−	0.892018i	$-0.350711\pi$
$653$	5.74640	+	2.09152i	0.224874	+	0.0818475i	−0.227126	+	0.973865i	$0.572933\pi$
$654$		0			0
$655$	−1.76954	+	10.0355i	−0.0691415	+	0.392121i
$656$		0			0
$657$	−2.64192	−	5.84697i	−0.103071	−	0.228112i
$658$		0			0
$659$	−32.4589	+	11.8141i	−1.26442	+	0.460211i	−0.885250	−	0.465115i	$-0.846013\pi$
$659$	−32.4589	+	11.8141i	−1.26442	+	0.460211i	−0.379170	+	0.925327i	$0.623791\pi$
$660$		0			0
$661$	21.8307	−	18.3181i	0.849114	−	0.712492i	−0.110480	−	0.993878i	$-0.535239\pi$
$661$	21.8307	−	18.3181i	0.849114	−	0.712492i	0.959594	+	0.281387i	$0.0907944\pi$
$662$		0			0
$663$	4.99923	+	39.8089i	0.194154	+	1.54605i
$664$		0			0
$665$	−31.8216	−	55.1166i	−1.23399	−	2.13733i
$666$		0			0
$667$	5.79920	−	10.0445i	0.224546	−	0.388925i
$668$		0			0
$669$	34.9324	−	10.7852i	1.35057	−	0.416979i
$670$		0			0
$671$	7.12961	+	40.4340i	0.275235	+	1.56094i
$672$		0			0
$673$	1.91246	+	1.60474i	0.0737199	+	0.0618583i	0.678903	−	0.734228i	$-0.262456\pi$
$673$	1.91246	+	1.60474i	0.0737199	+	0.0618583i	−0.605183	+	0.796086i	$0.706900\pi$
$674$		0			0
$675$	30.3921	+	34.3843i	1.16979	+	1.32345i
$676$		0			0
$677$	−24.4592	−	20.5237i	−0.940042	−	0.788789i	0.0375506	−	0.999295i	$-0.488044\pi$
$677$	−24.4592	−	20.5237i	−0.940042	−	0.788789i	−0.977593	+	0.210506i	$0.932489\pi$
$678$		0			0
$679$	2.30060	+	13.0474i	0.0882890	+	0.500712i
$680$		0			0
$681$	−3.58218	−	3.32204i	−0.137269	−	0.127301i
$682$		0			0
$683$	12.7427	−	22.0711i	0.487587	−	0.844526i	−0.512311	−	0.858800i	$-0.671210\pi$
$683$	12.7427	−	22.0711i	0.487587	−	0.844526i	0.999898	+	0.0142741i	$0.00454374\pi$
$684$		0			0
$685$	6.96636	+	12.0661i	0.266171	+	0.461021i
$686$		0			0
$687$	36.1642	+	15.2334i	1.37975	+	0.581190i
$688$		0			0
$689$	10.6202	−	8.91141i	0.404598	−	0.339498i
$690$		0			0
$691$	33.4246	−	12.1656i	1.27153	−	0.462800i	0.383909	−	0.923371i	$-0.374578\pi$
$691$	33.4246	−	12.1656i	1.27153	−	0.462800i	0.887623	+	0.460571i	$0.152355\pi$
$692$		0			0
$693$	−45.5598	−	21.9112i	−1.73067	−	0.832339i
$694$		0			0
$695$	−11.1927	+	63.4767i	−0.424562	+	2.40781i
$696$		0			0
$697$	2.55556	+	0.930147i	0.0967987	+	0.0352318i
$698$		0			0
$699$	17.3508	−	26.8797i	0.656268	−	1.01668i
$700$		0			0
$701$	−2.71776			−0.102648			−0.0513242	−	0.998682i	$-0.516344\pi$
$701$	−2.71776			−0.102648			−0.0513242	+	0.998682i	$0.516344\pi$
$702$		0			0
$703$	−26.7747			−1.00983
$704$		0			0
$705$	7.09046	+	0.352020i	0.267042	+	0.0132578i
$706$		0			0
$707$	70.9772	+	25.8336i	2.66937	+	0.971572i
$708$		0			0
$709$	−5.01413	+	28.4365i	−0.188309	+	1.06796i	0.733320	+	0.679884i	$0.237970\pi$
$709$	−5.01413	+	28.4365i	−0.188309	+	1.06796i	−0.921629	+	0.388072i	$0.873141\pi$
$710$		0			0
$711$	−29.5153	+	7.53188i	−1.10691	+	0.282467i
$712$		0			0
$713$	−22.9787	+	8.36355i	−0.860557	+	0.313217i
$714$		0			0
$715$	−61.5495	+	51.6462i	−2.30182	+	1.93146i
$716$		0			0
$717$	−29.2582	+	22.1742i	−1.09267	+	0.828111i
$718$		0			0
$719$	−17.8472	−	30.9122i	−0.665588	−	1.15283i	−0.979126	−	0.203256i	$-0.934848\pi$
$719$	−17.8472	−	30.9122i	−0.665588	−	1.15283i	0.313538	−	0.949576i	$-0.398486\pi$
$720$		0			0
$721$	−26.3283	+	45.6020i	−0.980519	+	1.69831i
$722$		0			0
$723$	−0.149828	+	0.657226i	−0.00557215	+	0.0244425i
$724$		0			0
$725$	−4.56856	−	25.9096i	−0.169672	−	0.962259i
$726$		0			0
$727$	−10.6359	−	8.92461i	−0.394465	−	0.330996i	0.423884	−	0.905716i	$-0.360666\pi$
$727$	−10.6359	−	8.92461i	−0.394465	−	0.330996i	−0.818350	+	0.574721i	$0.805111\pi$
$728$		0			0
$729$	25.8129	+	7.91808i	0.956032	+	0.293262i
$730$		0			0
$731$	−15.3465	−	12.8772i	−0.567610	−	0.476282i
$732$		0			0
$733$	−0.354851	−	2.01246i	−0.0131067	−	0.0743320i	0.977553	−	0.210690i	$-0.0675712\pi$
$733$	−0.354851	−	2.01246i	−0.0131067	−	0.0743320i	−0.990660	+	0.136358i	$0.956460\pi$
$734$		0			0
$735$	−14.4921	+	63.5702i	−0.534548	+	2.34482i
$736$		0			0
$737$	−17.6541	+	30.5777i	−0.650296	+	1.12635i
$738$		0			0
$739$	−9.01775	−	15.6192i	−0.331723	−	0.574562i	0.651127	−	0.758969i	$-0.274297\pi$
$739$	−9.01775	−	15.6192i	−0.331723	−	0.574562i	−0.982850	+	0.184408i	$0.940963\pi$
$740$		0			0
$741$	−30.2838	+	22.9515i	−1.11250	+	0.843145i
$742$		0			0
$743$	−7.57525	+	6.35639i	−0.277909	+	0.233193i	−0.771079	−	0.636740i	$-0.780283\pi$
$743$	−7.57525	+	6.35639i	−0.277909	+	0.233193i	0.493170	+	0.869933i	$0.335838\pi$
$744$		0			0
$745$	9.06130	−	3.29805i	0.331981	−	0.120831i
$746$		0			0
$747$	14.2576	−	3.63833i	0.521657	−	0.133120i
$748$		0			0
$749$	13.1584	−	74.6250i	0.480797	−	2.72674i
$750$		0			0
$751$	25.5492	+	9.29916i	0.932305	+	0.339331i	0.763123	−	0.646254i	$-0.223665\pi$
$751$	25.5492	+	9.29916i	0.932305	+	0.339331i	0.169182	+	0.985585i	$0.445887\pi$
$752$		0			0
$753$	−42.6586	−	2.11787i	−1.55456	−	0.0771794i
$754$		0			0
$755$	38.8446			1.41370
$756$		0			0
$757$	27.5055			0.999703			0.499852	−	0.866111i	$-0.333388\pi$
$757$	27.5055			0.999703			0.499852	+	0.866111i	$0.333388\pi$
$758$		0			0
$759$	−14.8944	+	23.0742i	−0.540632	+	0.837540i
$760$		0			0
$761$	−47.7505	−	17.3798i	−1.73095	−	0.630016i	−0.732256	−	0.681030i	$-0.761532\pi$
$761$	−47.7505	−	17.3798i	−1.73095	−	0.630016i	−0.998698	+	0.0510142i	$0.983755\pi$
$762$		0			0
$763$	−3.66329	+	20.7755i	−0.132620	+	0.752125i
$764$		0			0
$765$	43.9065	+	21.1161i	1.58744	+	0.763455i
$766$		0			0
$767$	−30.0250	+	10.9282i	−1.08414	+	0.394595i
$768$		0			0
$769$	−35.1032	+	29.4551i	−1.26585	+	1.06218i	−0.270821	+	0.962630i	$0.587295\pi$
$769$	−35.1032	+	29.4551i	−1.26585	+	1.06218i	−0.995033	+	0.0995482i	$0.968260\pi$
$770$		0			0
$771$	−21.4035	−	9.01579i	−0.770830	−	0.324696i
$772$		0			0
$773$	−3.87109	−	6.70492i	−0.139233	−	0.241159i	0.787973	−	0.615709i	$-0.211130\pi$
$773$	−3.87109	−	6.70492i	−0.139233	−	0.241159i	−0.927207	+	0.374550i	$0.877797\pi$
$774$		0			0
$775$	−27.7345	+	48.0375i	−0.996251	+	1.72556i
$776$		0			0
$777$	34.0221	+	31.5514i	1.22053	+	1.13190i
$778$		0			0
$779$	0.447258	+	2.53653i	0.0160247	+	0.0908805i
$780$		0			0
$781$	18.1825	+	15.2569i	0.650620	+	0.545935i
$782$		0			0
$783$	−10.2514	−	11.5980i	−0.366355	−	0.414478i
$784$		0			0
$785$	48.0427	+	40.3126i	1.71472	+	1.43882i
$786$		0			0
$787$	−1.54793	−	8.77873i	−0.0551776	−	0.312928i	0.944710	−	0.327907i	$-0.106343\pi$
$787$	−1.54793	−	8.77873i	−0.0551776	−	0.312928i	−0.999888	+	0.0149786i	$0.995232\pi$
$788$		0			0
$789$	28.7323	−	8.87094i	1.02290	−	0.315814i
$790$		0			0
$791$	25.4408	−	44.0648i	0.904571	−	1.56676i
$792$		0			0
$793$	−26.7401	−	46.3152i	−0.949569	−	1.64470i
$794$		0			0
$795$	−2.09767	−	16.7037i	−0.0743966	−	0.592421i
$796$		0			0
$797$	17.0645	−	14.3188i	0.604455	−	0.507198i	−0.288419	−	0.957504i	$-0.593130\pi$
$797$	17.0645	−	14.3188i	0.604455	−	0.507198i	0.892874	+	0.450307i	$0.148685\pi$
$798$		0			0
$799$	4.52218	−	1.64594i	0.159983	−	0.0582292i
$800$		0			0
$801$	−9.86859	−	21.8407i	−0.348689	−	0.771703i
$802$		0			0
$803$	1.51248	−	8.57771i	0.0533743	−	0.302701i
$804$		0			0
$805$	56.3029	+	20.4926i	1.98442	+	0.722268i
$806$		0			0
$807$	5.87245	+	11.4473i	0.206720	+	0.402964i
$808$		0			0
$809$	29.7225			1.04499			0.522494	−	0.852643i	$-0.325002\pi$
$809$	29.7225			1.04499			0.522494	+	0.852643i	$0.325002\pi$
$810$		0			0
$811$	7.15882			0.251380			0.125690	−	0.992070i	$-0.459886\pi$
$811$	7.15882			0.251380			0.125690	+	0.992070i	$0.459886\pi$
$812$		0			0
$813$	−0.100503	−	0.195913i	−0.00352480	−	0.00687097i
$814$		0			0
$815$	−28.6555	−	10.4297i	−1.00376	−	0.365338i
$816$		0			0
$817$	3.29468	−	18.6851i	0.115266	−	0.653707i
$818$		0			0
$819$	65.5270	+	6.52251i	2.28970	+	0.227915i
$820$		0			0
$821$	−19.1617	+	6.97429i	−0.668748	+	0.243404i	−0.654009	−	0.756487i	$-0.726914\pi$
$821$	−19.1617	+	6.97429i	−0.668748	+	0.243404i	−0.0147393	+	0.999891i	$0.504692\pi$
$822$		0			0
$823$	−37.0587	+	31.0959i	−1.29178	+	1.08394i	−0.300282	+	0.953850i	$0.597081\pi$
$823$	−37.0587	+	31.0959i	−1.29178	+	1.08394i	−0.991503	+	0.130086i	$0.958475\pi$
$824$		0			0
$825$	7.76241	+	61.8122i	0.270253	+	2.15202i
$826$		0			0
$827$	−13.3505	−	23.1237i	−0.464242	−	0.804091i	0.534925	−	0.844900i	$-0.320340\pi$
$827$	−13.3505	−	23.1237i	−0.464242	−	0.804091i	−0.999167	+	0.0408087i	$0.987007\pi$
$828$		0			0
$829$	−16.8443	+	29.1752i	−0.585027	+	1.01330i	0.409845	+	0.912155i	$0.365583\pi$
$829$	−16.8443	+	29.1752i	−0.585027	+	1.01330i	−0.994872	+	0.101142i	$0.967750\pi$
$830$		0			0
$831$	1.75668	−	0.542364i	0.0609384	−	0.0188144i
$832$		0			0
$833$	7.67502	+	43.5272i	0.265924	+	1.50813i
$834$		0			0
$835$	−14.7921	−	12.4120i	−0.511901	−	0.429536i
$836$		0			0
$837$	0.839102	+	32.6245i	0.0290036	+	1.12767i
$838$		0			0
$839$	−8.81910	−	7.40010i	−0.304469	−	0.255480i	0.477732	−	0.878505i	$-0.341459\pi$
$839$	−8.81910	−	7.40010i	−0.304469	−	0.255480i	−0.782202	+	0.623025i	$0.785903\pi$
$840$		0			0
$841$	−3.49480	−	19.8200i	−0.120510	−	0.683448i
$842$		0			0
$843$	8.05949	+	7.47421i	0.277584	+	0.257426i
$844$		0			0
$845$	28.1544	−	48.7648i	0.968541	−	1.67756i
$846$		0			0
$847$	−11.5565	−	20.0164i	−0.397086	−	0.687773i
$848$		0			0
$849$	−16.7516	−	7.05624i	−0.574912	−	0.242170i
$850$		0			0
$851$	19.3096	−	16.2026i	0.661923	−	0.555419i
$852$		0			0
$853$	13.1062	−	4.77028i	0.448749	−	0.163331i	−0.107753	−	0.994178i	$-0.534365\pi$
$853$	13.1062	−	4.77028i	0.448749	−	0.163331i	0.556502	+	0.830846i	$0.312143\pi$
$854$		0			0
$855$	3.47217	+	46.0114i	0.118746	+	1.57356i
$856$		0			0
$857$	6.80072	−	38.5688i	0.232308	−	1.31749i	−0.615900	−	0.787824i	$-0.711208\pi$
$857$	6.80072	−	38.5688i	0.232308	−	1.31749i	0.848209	−	0.529662i	$-0.177681\pi$
$858$		0			0
$859$	−25.7913	−	9.38728i	−0.879989	−	0.320290i	−0.137784	−	0.990462i	$-0.543998\pi$
$859$	−25.7913	−	9.38728i	−0.879989	−	0.320290i	−0.742205	+	0.670173i	$0.766220\pi$
$860$		0			0
$861$	2.42072	−	3.75016i	0.0824981	−	0.127805i
$862$		0			0
$863$	−29.2657			−0.996215			−0.498108	−	0.867115i	$-0.665972\pi$
$863$	−29.2657			−0.996215			−0.498108	+	0.867115i	$0.665972\pi$
$864$		0			0
$865$	56.9888			1.93768
$866$		0			0
$867$	3.57734	+	0.177604i	0.121493	+	0.00603174i
$868$		0			0
$869$	−38.8578	−	14.1431i	−1.31816	−	0.479771i
$870$		0			0
$871$	7.98625	−	45.2923i	0.270604	−	1.53467i
$872$		0			0
$873$	2.59673	−	9.24780i	0.0878860	−	0.312991i
$874$		0			0
$875$	55.4099	−	20.1676i	1.87320	−	0.681788i
$876$		0			0
$877$	−41.0245	+	34.4236i	−1.38530	+	1.16240i	−0.418094	+	0.908404i	$0.637302\pi$
$877$	−41.0245	+	34.4236i	−1.38530	+	1.16240i	−0.967204	+	0.253999i	$0.918254\pi$
$878$		0			0
$879$	−7.18266	+	5.44360i	−0.242265	+	0.183608i
$880$		0			0
$881$	14.8443	+	25.7111i	0.500118	+	0.866230i	1.00000		0.000136425i	$4.34255e-5\pi$
$881$	14.8443	+	25.7111i	0.500118	+	0.866230i	−0.499882	+	0.866094i	$0.666623\pi$
$882$		0			0
$883$	12.8331	−	22.2276i	0.431870	−	0.748020i	−0.565165	−	0.824978i	$-0.691187\pi$
$883$	12.8331	−	22.2276i	0.431870	−	0.748020i	0.997034	+	0.0769581i	$0.0245208\pi$
$884$		0			0
$885$	−8.62393	+	37.8293i	−0.289890	+	1.27162i
$886$		0			0
$887$	1.07159	+	6.07726i	0.0359803	+	0.204055i	0.997499	−	0.0706865i	$-0.0225190\pi$
$887$	1.07159	+	6.07726i	0.0359803	+	0.204055i	−0.961518	+	0.274741i	$0.911408\pi$
$888$		0			0
$889$	35.1270	+	29.4751i	1.17812	+	0.988562i
$890$		0			0
$891$	22.8826	+	28.6327i	0.766597	+	0.959231i
$892$		0			0
$893$	3.49144	+	2.92966i	0.116837	+	0.0980375i
$894$		0			0
$895$	10.8774	+	61.6889i	0.363592	+	2.06203i
$896$		0			0
$897$	7.95122	−	34.8784i	0.265484	−	1.16456i
$898$		0			0
$899$	9.35496	−	16.2033i	0.312005	−	0.540409i
$900$		0			0
$901$	−5.70605	−	9.88316i	−0.190096	−	0.329256i
$902$		0			0
$903$	−26.2050	+	19.8602i	−0.872046	+	0.660907i
$904$		0			0
$905$	2.87670	−	2.41383i	0.0956246	−	0.0802386i
$906$		0			0
$907$	35.7794	−	13.0226i	1.18803	−	0.432409i	0.329001	−	0.944329i	$-0.393288\pi$
$907$	35.7794	−	13.0226i	1.18803	−	0.432409i	0.859033	+	0.511920i	$0.171066\pi$
$908$		0			0
$909$	−38.2573	−	39.1824i	−1.26891	−	1.29960i
$910$		0			0
$911$	0.564052	−	3.19890i	0.0186879	−	0.105984i	−0.974037	−	0.226389i	$-0.927308\pi$
$911$	0.564052	−	3.19890i	0.0186879	−	0.105984i	0.992725	+	0.120405i	$0.0384192\pi$
$912$		0			0
$913$	18.7705	+	6.83192i	0.621214	+	0.226104i
$914$		0			0
$915$	−64.8621	−	3.22021i	−2.14428	−	0.106457i
$916$		0			0
$917$	11.3377			0.374405
$918$		0			0
$919$	41.7773			1.37811			0.689053	−	0.724711i	$-0.258027\pi$
$919$	41.7773			1.37811			0.689053	+	0.724711i	$0.258027\pi$
$920$		0			0
$921$	−23.1821	+	35.9135i	−0.763878	+	1.18339i
$922$		0			0
$923$	−29.0524	−	10.5742i	−0.956272	−	0.348055i
$924$		0			0
$925$	9.92886	−	56.3094i	0.326459	−	1.85144i
$926$		0			0
$927$	31.5320	−	21.5222i	1.03565	−	0.706882i
$928$		0			0
$929$	−45.8090	+	16.6731i	−1.50295	+	0.547027i	−0.956821	−	0.290677i	$-0.906119\pi$
$929$	−45.8090	+	16.6731i	−1.50295	+	0.547027i	−0.546124	+	0.837704i	$0.683897\pi$
$930$		0			0
$931$	−32.0664	+	26.9069i	−1.05094	+	0.881839i
$932$		0			0
$933$	14.3207	+	6.03231i	0.468840	+	0.197489i
$934$		0			0
$935$	33.0694	+	57.2779i	1.08149	+	1.87319i
$936$		0			0
$937$	25.8742	−	44.8154i	0.845272	−	1.46405i	−0.0401130	−	0.999195i	$-0.512772\pi$
$937$	25.8742	−	44.8154i	0.845272	−	1.46405i	0.885385	−	0.464859i	$-0.153895\pi$
$938$		0			0
$939$	−2.40446	−	2.22985i	−0.0784666	−	0.0727683i
$940$		0			0
$941$	−6.33721	−	35.9401i	−0.206587	−	1.17161i	−0.894923	−	0.446221i	$-0.852769\pi$
$941$	−6.33721	−	35.9401i	−0.206587	−	1.17161i	0.688336	−	0.725392i	$-0.258342\pi$
$942$		0			0
$943$	−1.85753	−	1.55865i	−0.0604894	−	0.0507566i
$944$		0			0
$945$	49.8078	−	62.5572i	1.62025	−	2.03499i
$946$		0			0
$947$	−20.4955	−	17.1977i	−0.666013	−	0.558851i	0.245869	−	0.969303i	$-0.420927\pi$
$947$	−20.4955	−	17.1977i	−0.666013	−	0.558851i	−0.911882	+	0.410452i	$0.865371\pi$
$948$		0			0
$949$	1.97010	+	11.1730i	0.0639521	+	0.362690i
$950$		0			0
$951$	54.0438	−	16.6857i	1.75249	−	0.541071i
$952$		0			0
$953$	−11.6621	+	20.1993i	−0.377771	+	0.654319i	−0.990738	−	0.135790i	$-0.956643\pi$
$953$	−11.6621	+	20.1993i	−0.377771	+	0.654319i	0.612966	+	0.790109i	$0.289976\pi$
$954$		0			0
$955$	9.57375	+	16.5822i	0.309799	+	0.536588i
$956$		0			0
$957$	−2.61830	−	20.8495i	−0.0846376	−	0.673970i
$958$		0			0
$959$	11.8748	−	9.96415i	0.383458	−	0.321759i
$960$		0			0
$961$	−7.93744	+	2.88899i	−0.256047	+	0.0931933i
$962$		0			0
$963$	−32.0470	+	44.6236i	−1.03270	+	1.43798i
$964$		0			0
$965$	−10.8429	+	61.4933i	−0.349046	+	1.97954i
$966$		0			0
$967$	10.1127	+	3.68070i	0.325201	+	0.118363i	0.499461	−	0.866336i	$-0.333531\pi$
$967$	10.1127	+	3.68070i	0.325201	+	0.118363i	−0.174260	+	0.984700i	$0.555753\pi$
$968$		0			0
$969$	14.2770	+	27.8305i	0.458644	+	0.894045i
$970$		0			0
$971$	−52.2764			−1.67763			−0.838814	−	0.544418i	$-0.816751\pi$
$971$	−52.2764			−1.67763			−0.838814	+	0.544418i	$0.816751\pi$
$972$		0			0
$973$	71.7133			2.29902
$974$		0			0
$975$	−37.0387	−	72.2003i	−1.18619	−	2.31226i
$976$		0			0
$977$	55.9585	+	20.3672i	1.79027	+	0.651605i	0.999205	+	0.0398736i	$0.0126955\pi$
$977$	55.9585	+	20.3672i	1.79027	+	0.651605i	0.791065	+	0.611731i	$0.209527\pi$
$978$		0			0
$979$	5.64970	−	32.0411i	0.180565	−	1.02404i
$980$		0			0
$981$	8.92185	−	12.4232i	0.284853	−	0.396642i
$982$		0			0
$983$	7.56531	−	2.75355i	0.241296	−	0.0878246i	−0.218541	−	0.975828i	$-0.570130\pi$
$983$	7.56531	−	2.75355i	0.241296	−	0.0878246i	0.459837	+	0.888003i	$0.347908\pi$
$984$		0			0
$985$	6.16962	−	5.17693i	0.196580	−	0.164951i
$986$		0			0
$987$	−0.984172	−	7.83697i	−0.0313265	−	0.249454i
$988$		0			0
$989$	8.93112	+	15.4692i	0.283993	+	0.491890i
$990$		0			0
$991$	−9.43980	+	16.3502i	−0.299865	+	0.519382i	−0.976105	−	0.217300i	$-0.930275\pi$
$991$	−9.43980	+	16.3502i	−0.299865	+	0.519382i	0.676240	+	0.736682i	$0.263608\pi$
$992$		0			0
$993$	24.5420	−	7.57719i	0.778816	−	0.240455i
$994$		0			0
$995$	15.0180	+	85.1712i	0.476102	+	2.70011i
$996$		0			0
$997$	−36.4297	−	30.5681i	−1.15374	−	0.968103i	−0.153940	−	0.988080i	$-0.549196\pi$
$997$	−36.4297	−	30.5681i	−1.15374	−	0.968103i	−0.999800	+	0.0199773i	$0.993641\pi$
$998$		0			0
$999$	−12.3149	−	31.3058i	−0.389625	−	0.990472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.97.4	✓	60
4.3	odd	2	inner	864.2.y.d.97.7	yes	60
27.22	even	9	inner	864.2.y.d.481.4	yes	60
108.103	odd	18	inner	864.2.y.d.481.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.97.4	✓	60	1.1	even	1	trivial
864.2.y.d.97.7	yes	60	4.3	odd	2	inner
864.2.y.d.481.4	yes	60	27.22	even	9	inner
864.2.y.d.481.7	yes	60	108.103	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.790581 - 1.54110i) q^{3} +(3.49481 + 1.27201i) q^{5} +(0.718530 - 4.07499i) q^{7} +(-1.74996 + 2.43673i) q^{9} +O(q^{10})\)	\(q+(-0.790581 - 1.54110i) q^{3} +(3.49481 + 1.27201i) q^{5} +(0.718530 - 4.07499i) q^{7} +(-1.74996 + 2.43673i) q^{9} +(-3.82696 + 1.39290i) q^{11} +(4.06368 - 3.40983i) q^{13} +(-0.802644 - 6.39146i) q^{15} +(-2.18334 - 3.78166i) q^{17} +(2.06780 - 3.58154i) q^{19} +(-6.84801 + 2.11428i) q^{21} +(0.676087 + 3.83428i) q^{23} +(6.76546 + 5.67690i) q^{25} +(5.13872 + 0.770433i) q^{27} +(-2.28202 - 1.91484i) q^{29} +(1.09063 + 6.18526i) q^{31} +(5.17211 + 4.79651i) q^{33} +(7.69453 - 13.3273i) q^{35} +(-3.23710 - 5.60682i) q^{37} +(-8.46755 - 3.56678i) q^{39} +(-0.477092 + 0.400328i) q^{41} +(4.31111 - 1.56912i) q^{43} +(-9.21531 + 6.28993i) q^{45} +(-0.191373 + 1.08533i) q^{47} +(-9.51137 - 3.46186i) q^{49} +(-4.10180 + 6.35445i) q^{51} +2.61345 q^{53} -15.1463 q^{55} +(-7.15427 - 0.355188i) q^{57} +(-5.66002 - 2.06008i) q^{59} +(1.75064 - 9.92840i) q^{61} +(8.67222 + 8.88193i) q^{63} +(18.5391 - 6.74768i) q^{65} +(6.64142 - 5.57282i) q^{67} +(5.37450 - 4.07323i) q^{69} +(-2.91408 - 5.04733i) q^{71} +(-1.06936 + 1.85218i) q^{73} +(3.40000 - 14.9143i) q^{75} +(2.92626 + 16.5956i) q^{77} +(7.77819 + 6.52668i) q^{79} +(-2.87526 - 8.52836i) q^{81} +(-3.75731 - 3.15276i) q^{83} +(-2.82007 - 15.9934i) q^{85} +(-1.14684 + 5.03066i) q^{87} +(-3.99446 + 6.91860i) q^{89} +(-10.9751 - 19.0095i) q^{91} +(8.66985 - 6.57071i) q^{93} +(11.7823 - 9.88655i) q^{95} +(-3.00873 + 1.09509i) q^{97} +(3.30292 - 11.7628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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