LMFDB - Embedded newform 864.2.v.b.325.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			325.12
Character	$\chi$	$=$	864.325
Dual form			864.2.v.b.109.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.479175 - 1.33056i) q^{2} +(-1.54078 + 1.27514i) q^{4} +(-0.855212 - 0.354240i) q^{5} +(-3.04155 - 3.04155i) q^{7} +(2.43496 + 1.43909i) q^{8} +O(q^{10})$	\(q+(-0.479175 - 1.33056i) q^{2} +(-1.54078 + 1.27514i) q^{4} +(-0.855212 - 0.354240i) q^{5} +(-3.04155 - 3.04155i) q^{7} +(2.43496 + 1.43909i) q^{8} +(-0.0615424 + 1.30765i) q^{10} +(1.47477 - 3.56040i) q^{11} +(-0.524396 + 0.217212i) q^{13} +(-2.58953 + 5.50440i) q^{14} +(0.748026 - 3.92943i) q^{16} +5.34789i q^{17} +(-4.09576 + 1.69652i) q^{19} +(1.76940 - 0.544709i) q^{20} +(-5.44400 - 0.256212i) q^{22} +(2.03658 - 2.03658i) q^{23} +(-2.92963 - 2.92963i) q^{25} +(0.540290 + 0.593658i) q^{26} +(8.56477 + 0.807961i) q^{28} +(3.31480 + 8.00262i) q^{29} +2.51477 q^{31} +(-5.58679 + 0.887591i) q^{32} +(7.11569 - 2.56257i) q^{34} +(1.52373 + 3.67861i) q^{35} +(-7.84910 - 3.25120i) q^{37} +(4.21990 + 4.63673i) q^{38} +(-1.57262 - 2.09329i) q^{40} +(-8.96180 + 8.96180i) q^{41} +(-4.72038 + 11.3960i) q^{43} +(2.26772 + 7.36634i) q^{44} +(-3.68566 - 1.73391i) q^{46} +3.46822i q^{47} +11.5020i q^{49} +(-2.49425 + 5.30186i) q^{50} +(0.531004 - 1.00335i) q^{52} +(3.31524 - 8.00369i) q^{53} +(-2.52248 + 2.52248i) q^{55} +(-3.02898 - 11.7831i) q^{56} +(9.05961 - 8.24519i) q^{58} +(0.0488541 + 0.0202360i) q^{59} +(-0.0218216 - 0.0526820i) q^{61} +(-1.20501 - 3.34605i) q^{62} +(3.85804 + 7.00825i) q^{64} +0.525415 q^{65} +(2.67338 + 6.45412i) q^{67} +(-6.81931 - 8.23993i) q^{68} +(4.16448 - 3.79011i) q^{70} +(-0.889622 - 0.889622i) q^{71} +(-4.73977 + 4.73977i) q^{73} +(-0.564834 + 12.0016i) q^{74} +(4.14737 - 7.83664i) q^{76} +(-15.3147 + 6.34356i) q^{77} -12.2691i q^{79} +(-2.03169 + 3.09552i) q^{80} +(16.2185 + 7.62995i) q^{82} +(2.42613 - 1.00493i) q^{83} +(1.89444 - 4.57358i) q^{85} +(17.4250 + 0.820074i) q^{86} +(8.71473 - 6.54710i) q^{88} +(-4.26786 - 4.26786i) q^{89} +(2.25563 + 0.934314i) q^{91} +(-0.540999 + 5.73485i) q^{92} +(4.61467 - 1.66188i) q^{94} +4.10372 q^{95} -6.74287 q^{97} +(15.3042 - 5.51149i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.479175	−	1.33056i	−0.338828	−	0.940848i
$2$	−0.479175	−	1.33056i	−0.338828	−	0.940848i
$3$		0			0
$3$		0			0
$4$	−1.54078	+	1.27514i	−0.770392	+	0.637571i
$5$	−0.855212	−	0.354240i	−0.382462	−	0.158421i	0.183165	−	0.983082i	$-0.441366\pi$
$5$	−0.855212	−	0.354240i	−0.382462	−	0.158421i	−0.565627	+	0.824661i	$0.691366\pi$
$6$		0			0
$7$	−3.04155	−	3.04155i	−1.14960	−	1.14960i	−0.986632	−	0.162966i	$-0.947894\pi$
$7$	−3.04155	−	3.04155i	−1.14960	−	1.14960i	−0.162966	−	0.986632i	$-0.552106\pi$
$8$	2.43496	+	1.43909i	0.860888	+	0.508795i
$9$		0			0
$10$	−0.0615424	+	1.30765i	−0.0194614	+	0.413517i
$11$	1.47477	−	3.56040i	0.444659	−	1.07350i	−0.529636	−	0.848225i	$-0.677672\pi$
$11$	1.47477	−	3.56040i	0.444659	−	1.07350i	0.974295	−	0.225276i	$-0.0723284\pi$
$12$		0			0
$13$	−0.524396	+	0.217212i	−0.145441	+	0.0602437i	−0.454217	−	0.890891i	$-0.650081\pi$
$13$	−0.524396	+	0.217212i	−0.145441	+	0.0602437i	0.308776	+	0.951135i	$0.400081\pi$
$14$	−2.58953	+	5.50440i	−0.692082	+	1.47111i
$15$		0			0
$16$	0.748026	−	3.92943i	0.187007	−	0.982359i
$17$			5.34789i			1.29705i	0.761192	+	0.648526i	$0.224614\pi$
$17$			5.34789i			1.29705i	−0.761192	+	0.648526i	$0.775386\pi$
$18$		0			0
$19$	−4.09576	+	1.69652i	−0.939631	+	0.389208i	−0.799324	−	0.600900i	$-0.794809\pi$
$19$	−4.09576	+	1.69652i	−0.939631	+	0.389208i	−0.140307	+	0.990108i	$0.544809\pi$
$20$	1.76940	−	0.544709i	0.395651	−	0.121801i
$21$		0			0
$22$	−5.44400	−	0.256212i	−1.16066	−	0.0546246i
$23$	2.03658	−	2.03658i	0.424656	−	0.424656i	−0.462148	−	0.886803i	$-0.652921\pi$
$23$	2.03658	−	2.03658i	0.424656	−	0.424656i	0.886803	+	0.462148i	$0.152921\pi$
$24$		0			0
$25$	−2.92963	−	2.92963i	−0.585927	−	0.585927i
$26$	0.540290	+	0.593658i	0.105960	+	0.116426i
$27$		0			0
$28$	8.56477	+	0.807961i	1.61859	+	0.152690i
$29$	3.31480	+	8.00262i	0.615542	+	1.48605i	0.856831	+	0.515597i	$0.172430\pi$
$29$	3.31480	+	8.00262i	0.615542	+	1.48605i	−0.241289	+	0.970453i	$0.577570\pi$
$30$		0			0
$31$	2.51477			0.451665			0.225833	−	0.974166i	$-0.427490\pi$
$31$	2.51477			0.451665			0.225833	+	0.974166i	$0.427490\pi$
$32$	−5.58679	+	0.887591i	−0.987614	+	0.156905i
$33$		0			0
$34$	7.11569	−	2.56257i	1.22033	−	0.439477i
$35$	1.52373	+	3.67861i	0.257557	+	0.621798i
$36$		0			0
$37$	−7.84910	−	3.25120i	−1.29038	−	0.534495i	−0.371285	−	0.928519i	$-0.621083\pi$
$37$	−7.84910	−	3.25120i	−1.29038	−	0.534495i	−0.919100	+	0.394024i	$0.871083\pi$
$38$	4.21990	+	4.63673i	0.684559	+	0.752176i
$39$		0			0
$40$	−1.57262	−	2.09329i	−0.248653	−	0.330978i
$41$	−8.96180	+	8.96180i	−1.39960	+	1.39960i	−0.598402	+	0.801196i	$0.704197\pi$
$41$	−8.96180	+	8.96180i	−1.39960	+	1.39960i	−0.801196	+	0.598402i	$0.795803\pi$
$42$		0			0
$43$	−4.72038	+	11.3960i	−0.719851	+	1.73787i	−0.0460752	+	0.998938i	$0.514671\pi$
$43$	−4.72038	+	11.3960i	−0.719851	+	1.73787i	−0.673776	+	0.738936i	$0.735329\pi$
$44$	2.26772	+	7.36634i	0.341872	+	1.11052i
$45$		0			0
$46$	−3.68566	−	1.73391i	−0.543422	−	0.255651i
$47$			3.46822i			0.505892i	0.967480	+	0.252946i	$0.0813994\pi$
$47$			3.46822i			0.505892i	−0.967480	+	0.252946i	$0.918601\pi$
$48$		0			0
$49$			11.5020i			1.64315i
$50$	−2.49425	+	5.30186i	−0.352740	+	0.749796i
$51$		0			0
$52$	0.531004	−	1.00335i	0.0736370	−	0.139140i
$53$	3.31524	−	8.00369i	0.455383	−	1.09939i	−0.514864	−	0.857272i	$-0.672158\pi$
$53$	3.31524	−	8.00369i	0.455383	−	1.09939i	0.970247	−	0.242119i	$-0.0778425\pi$
$54$		0			0
$55$	−2.52248	+	2.52248i	−0.340131	+	0.340131i
$56$	−3.02898	−	11.7831i	−0.404765	−	1.57458i
$57$		0			0
$58$	9.05961	−	8.24519i	1.18959	−	1.08265i
$59$	0.0488541	+	0.0202360i	0.00636027	+	0.00263451i	0.385861	−	0.922557i	$-0.373904\pi$
$59$	0.0488541	+	0.0202360i	0.00636027	+	0.00263451i	−0.379501	+	0.925191i	$0.623904\pi$
$60$		0			0
$61$	−0.0218216	−	0.0526820i	−0.00279397	−	0.00674523i	0.922476	−	0.386053i	$-0.126162\pi$
$61$	−0.0218216	−	0.0526820i	−0.00279397	−	0.00674523i	−0.925270	+	0.379308i	$0.876162\pi$
$62$	−1.20501	−	3.34605i	−0.153037	−	0.424949i
$63$		0			0
$64$	3.85804	+	7.00825i	0.482255	+	0.876031i
$65$	0.525415			0.0651696
$66$		0			0
$67$	2.67338	+	6.45412i	0.326606	+	0.788496i	0.998840	+	0.0481572i	$0.0153348\pi$
$67$	2.67338	+	6.45412i	0.326606	+	0.788496i	−0.672234	+	0.740339i	$0.734665\pi$
$68$	−6.81931	−	8.23993i	−0.826963	−	0.999239i
$69$		0			0
$70$	4.16448	−	3.79011i	0.497750	−	0.453005i
$71$	−0.889622	−	0.889622i	−0.105579	−	0.105579i	0.652344	−	0.757923i	$-0.273786\pi$
$71$	−0.889622	−	0.889622i	−0.105579	−	0.105579i	−0.757923	+	0.652344i	$0.773786\pi$
$72$		0			0
$73$	−4.73977	+	4.73977i	−0.554748	+	0.554748i	−0.927807	−	0.373060i	$-0.878309\pi$
$73$	−4.73977	+	4.73977i	−0.554748	+	0.554748i	0.373060	+	0.927807i	$0.378309\pi$
$74$	−0.564834	+	12.0016i	−0.0656606	+	1.39516i
$75$		0			0
$76$	4.14737	−	7.83664i	0.475736	−	0.898924i
$77$	−15.3147	+	6.34356i	−1.74527	+	0.722916i
$78$		0			0
$79$		−	12.2691i		−	1.38038i	−0.723630	−	0.690189i	$-0.757528\pi$
$79$		−	12.2691i		−	1.38038i	0.723630	−	0.690189i	$-0.242472\pi$
$80$	−2.03169	+	3.09552i	−0.227149	+	0.346090i
$81$		0			0
$82$	16.2185	+	7.62995i	1.79103	+	0.842587i
$83$	2.42613	−	1.00493i	0.266302	−	0.110306i	−0.245537	−	0.969387i	$-0.578964\pi$
$83$	2.42613	−	1.00493i	0.266302	−	0.110306i	0.511839	+	0.859081i	$0.328964\pi$
$84$		0			0
$85$	1.89444	−	4.57358i	0.205481	−	0.496074i
$86$	17.4250	+	0.820074i	1.87898	+	0.0884309i
$87$		0			0
$88$	8.71473	−	6.54710i	0.928993	−	0.697924i
$89$	−4.26786	−	4.26786i	−0.452392	−	0.452392i	0.443756	−	0.896148i	$-0.353646\pi$
$89$	−4.26786	−	4.26786i	−0.452392	−	0.452392i	−0.896148	+	0.443756i	$0.853646\pi$
$90$		0			0
$91$	2.25563	+	0.934314i	0.236455	+	0.0979428i
$92$	−0.540999	+	5.73485i	−0.0564030	+	0.597899i
$93$		0			0
$94$	4.61467	−	1.66188i	0.475967	−	0.171410i
$95$	4.10372			0.421032
$96$		0			0
$97$	−6.74287			−0.684635			−0.342317	−	0.939584i	$-0.611212\pi$
$97$	−6.74287			−0.684635			−0.342317	+	0.939584i	$0.611212\pi$
$98$	15.3042	−	5.51149i	1.54595	−	0.556744i
$99$		0			0
$100$	8.24963	+	0.778232i	0.824963	+	0.0778232i
$101$	−2.21585	−	0.917836i	−0.220485	−	0.0913281i	0.269706	−	0.962943i	$-0.413073\pi$
$101$	−2.21585	−	0.917836i	−0.220485	−	0.0913281i	−0.490192	+	0.871615i	$0.663073\pi$
$102$		0			0
$103$	−1.95787	−	1.95787i	−0.192914	−	0.192914i	0.604040	−	0.796954i	$-0.293557\pi$
$103$	−1.95787	−	1.95787i	−0.192914	−	0.192914i	−0.796954	+	0.604040i	$0.793557\pi$
$104$	−1.58947	−	0.225751i	−0.155860	−	0.0221367i
$105$		0			0
$106$	−12.2380	−	0.575958i	−1.18866	−	0.0559420i
$107$	2.70991	−	6.54229i	0.261977	−	0.632467i	−0.737084	−	0.675801i	$-0.763798\pi$
$107$	2.70991	−	6.54229i	0.261977	−	0.632467i	0.999061	+	0.0433336i	$0.0137978\pi$
$108$		0			0
$109$	1.40147	−	0.580509i	0.134237	−	0.0556027i	−0.314554	−	0.949240i	$-0.601855\pi$
$109$	1.40147	−	0.580509i	0.134237	−	0.0556027i	0.448791	+	0.893637i	$0.351855\pi$
$110$	4.56501	+	2.14760i	0.435257	+	0.204766i
$111$		0			0
$112$	−14.2267	+	9.67641i	−1.34430	+	0.914335i
$113$		−	8.10234i		−	0.762204i	−0.924533	−	0.381102i	$-0.875545\pi$
$113$		−	8.10234i		−	0.762204i	0.924533	−	0.381102i	$-0.124455\pi$
$114$		0			0
$115$	−2.46314	+	1.02027i	−0.229689	+	0.0951404i
$116$	−15.3119	−	8.10348i	−1.42167	−	0.752389i
$117$		0			0
$118$	0.00351562	−	0.0747000i	0.000323639	−	0.00687669i
$119$	16.2659	−	16.2659i	1.49109	−	1.49109i
$120$		0			0
$121$	−2.72334	−	2.72334i	−0.247576	−	0.247576i
$122$	−0.0596402	+	0.0542788i	−0.00539957	+	0.00491417i
$123$		0			0
$124$	−3.87471	+	3.20668i	−0.347959	+	0.287969i
$125$	3.23886	+	7.81931i	0.289693	+	0.699380i
$126$		0			0
$127$	−10.2316			−0.907909			−0.453955	−	0.891025i	$-0.649987\pi$
$127$	−10.2316			−0.907909			−0.453955	+	0.891025i	$0.649987\pi$
$128$	7.47622	−	8.49153i	0.660811	−	0.750552i
$129$		0			0
$130$	−0.251765	−	0.699096i	−0.0220813	−	0.0613148i
$131$	6.84888	+	16.5347i	0.598389	+	1.44464i	0.875222	+	0.483721i	$0.160715\pi$
$131$	6.84888	+	16.5347i	0.598389	+	1.44464i	−0.276833	+	0.960918i	$0.589285\pi$
$132$		0			0
$133$	17.6175	+	7.29740i	1.52763	+	0.632765i
$134$	7.30658	−	6.64975i	0.631192	−	0.574451i
$135$		0			0
$136$	−7.69609	+	13.0219i	−0.659934	+	1.11662i
$137$	9.25015	−	9.25015i	0.790294	−	0.790294i	−0.191248	−	0.981542i	$-0.561254\pi$
$137$	9.25015	−	9.25015i	0.790294	−	0.790294i	0.981542	+	0.191248i	$0.0612535\pi$
$138$		0			0
$139$	0.239980	−	0.579363i	0.0203548	−	0.0491409i	−0.913375	−	0.407119i	$-0.866534\pi$
$139$	0.239980	−	0.579363i	0.0203548	−	0.0491409i	0.933730	+	0.357978i	$0.116534\pi$
$140$	−7.03849	−	3.72497i	−0.594861	−	0.314817i
$141$		0			0
$142$	−0.757412	+	1.60998i	−0.0635606	+	0.135107i
$143$			2.18739i			0.182919i
$144$		0			0
$145$		−	8.01818i		−	0.665873i
$146$	8.57772	+	4.03537i	0.709897	+	0.333970i
$147$		0			0
$148$	16.2395	−	4.99932i	1.33488	−	0.410941i
$149$	−1.41140	+	3.40742i	−0.115626	+	0.279146i	−0.971089	−	0.238718i	$-0.923273\pi$
$149$	−1.41140	+	3.40742i	−0.115626	+	0.279146i	0.855463	+	0.517864i	$0.173273\pi$
$150$		0			0
$151$	9.73971	−	9.73971i	0.792606	−	0.792606i	−0.189311	−	0.981917i	$-0.560625\pi$
$151$	9.73971	−	9.73971i	0.792606	−	0.792606i	0.981917	+	0.189311i	$0.0606254\pi$
$152$	−12.4144	−	1.76321i	−1.00694	−	0.143015i
$153$		0			0
$154$	15.7789	+	17.3375i	1.27150	+	1.39709i
$155$	−2.15066	−	0.890832i	−0.172745	−	0.0715533i
$156$		0			0
$157$	3.33119	+	8.04219i	0.265858	+	0.641837i	0.999280	−	0.0379360i	$-0.0120783\pi$
$157$	3.33119	+	8.04219i	0.265858	+	0.641837i	−0.733423	+	0.679773i	$0.762078\pi$
$158$	−16.3247	+	5.87902i	−1.29873	+	0.467710i
$159$		0			0
$160$	5.09231	+	1.21999i	0.402582	+	0.0964484i
$161$	−12.3887			−0.976366
$162$		0			0
$163$	−5.38043	−	12.9895i	−0.421427	−	1.01742i	−0.981927	−	0.189261i	$-0.939391\pi$
$163$	−5.38043	−	12.9895i	−0.421427	−	1.01742i	0.560499	−	0.828155i	$-0.310609\pi$
$164$	2.38062	−	25.2358i	0.185896	−	1.97058i
$165$		0			0
$166$	−2.49967	−	2.74657i	−0.194012	−	0.213175i
$167$	−10.7945	−	10.7945i	−0.835305	−	0.835305i	0.152931	−	0.988237i	$-0.451129\pi$
$167$	−10.7945	−	10.7945i	−0.835305	−	0.835305i	−0.988237	+	0.152931i	$0.951129\pi$
$168$		0			0
$169$	−8.96458	+	8.96458i	−0.689583	+	0.689583i
$170$	−6.99319	−	0.329122i	−0.536353	−	0.0252425i
$171$		0			0
$172$	−7.25844	−	23.5779i	−0.553451	−	1.79780i
$173$	1.23615	−	0.512030i	0.0939827	−	0.0389289i	−0.335197	−	0.942148i	$-0.608803\pi$
$173$	1.23615	−	0.512030i	0.0939827	−	0.0389289i	0.429179	+	0.903219i	$0.358803\pi$
$174$		0			0
$175$			17.8212i			1.34716i
$176$	−12.8872	−	8.45827i	−0.971409	−	0.637566i
$177$		0			0
$178$	−3.63359	+	7.72369i	−0.272349	+	0.578915i
$179$	6.04611	−	2.50438i	0.451908	−	0.187186i	−0.145108	−	0.989416i	$-0.546353\pi$
$179$	6.04611	−	2.50438i	0.451908	−	0.187186i	0.597016	+	0.802230i	$0.296353\pi$
$180$		0			0
$181$	−0.246883	+	0.596027i	−0.0183506	+	0.0443023i	−0.932789	−	0.360422i	$-0.882633\pi$
$181$	−0.246883	+	0.596027i	−0.0183506	+	0.0443023i	0.914439	+	0.404725i	$0.132633\pi$
$182$	0.162319	−	3.44896i	0.0120319	−	0.255654i
$183$		0			0
$184$	7.88979	−	2.02816i	0.581643	−	0.149518i
$185$	5.56094	+	5.56094i	0.408848	+	0.408848i
$186$		0			0
$187$	19.0406	+	7.88688i	1.39239	+	0.576746i
$188$	−4.42247	−	5.34377i	−0.322542	−	0.389735i
$189$		0			0
$190$	−1.96640	−	5.46024i	−0.142657	−	0.396128i
$191$	−12.9033			−0.933653			−0.466827	−	0.884349i	$-0.654603\pi$
$191$	−12.9033			−0.933653			−0.466827	+	0.884349i	$0.654603\pi$
$192$		0			0
$193$	−23.5010			−1.69164			−0.845820	−	0.533469i	$-0.820888\pi$
$193$	−23.5010			−1.69164			−0.845820	+	0.533469i	$0.820888\pi$
$194$	3.23101	+	8.97180i	0.231973	+	0.644138i
$195$		0			0
$196$	−14.6667	−	17.7221i	−1.04762	−	1.26587i
$197$	−19.2884	−	7.98950i	−1.37424	−	0.569229i	−0.431305	−	0.902206i	$-0.641947\pi$
$197$	−19.2884	−	7.98950i	−1.37424	−	0.569229i	−0.942935	+	0.332978i	$0.891947\pi$
$198$		0			0
$199$	−11.3518	−	11.3518i	−0.804708	−	0.804708i	0.179119	−	0.983827i	$-0.442675\pi$
$199$	−11.3518	−	11.3518i	−0.804708	−	0.804708i	−0.983827	+	0.179119i	$0.942675\pi$
$200$	−2.91753	−	11.3495i	−0.206300	−	0.802533i
$201$		0			0
$202$	−0.159456	+	3.38813i	−0.0112193	+	0.238388i
$203$	14.2583	−	34.4225i	1.00073	−	2.41598i
$204$		0			0
$205$	10.8389	−	4.48961i	0.757020	−	0.313568i
$206$	−1.66690	+	3.54322i	−0.116139	+	0.246868i
$207$		0			0
$208$	0.461258	+	2.22306i	0.0319825	+	0.154141i
$209$			17.0845i			1.18176i
$210$		0			0
$211$	−2.32439	+	0.962795i	−0.160018	+	0.0662816i	−0.461255	−	0.887268i	$-0.652601\pi$
$211$	−2.32439	+	0.962795i	−0.160018	+	0.0662816i	0.301237	+	0.953549i	$0.402601\pi$
$212$	5.09778	+	16.5593i	0.350117	+	1.13730i
$213$		0			0
$214$	−10.0034	−	0.470794i	−0.683821	−	0.0321828i
$215$	8.07385	−	8.07385i	0.550632	−	0.550632i
$216$		0			0
$217$	−7.64878	−	7.64878i	−0.519233	−	0.519233i
$218$	−1.44395	−	1.58658i	−0.0977969	−	0.107457i
$219$		0			0
$220$	0.670074	−	7.10310i	0.0451764	−	0.478891i
$221$	−1.16162	−	2.80441i	−0.0781393	−	0.188645i
$222$		0			0
$223$	−27.9863			−1.87410			−0.937051	−	0.349193i	$-0.886456\pi$
$223$	−27.9863			−1.87410			−0.937051	+	0.349193i	$0.886456\pi$
$224$	19.6921	+	14.2928i	1.31574	+	0.954980i
$225$		0			0
$226$	−10.7807	+	3.88244i	−0.717118	+	0.258256i
$227$	−9.62412	−	23.2347i	−0.638776	−	1.54214i	−0.828312	−	0.560267i	$-0.810699\pi$
$227$	−9.62412	−	23.2347i	−0.638776	−	1.54214i	0.189537	−	0.981874i	$-0.439301\pi$
$228$		0			0
$229$	13.3775	+	5.54114i	0.884010	+	0.366169i	0.778051	−	0.628202i	$-0.216209\pi$
$229$	13.3775	+	5.54114i	0.884010	+	0.366169i	0.105959	+	0.994370i	$0.466209\pi$
$230$	2.53780	+	2.78847i	0.167338	+	0.183867i
$231$		0			0
$232$	−3.44511	+	24.2563i	−0.226182	+	1.59251i
$233$	−5.89713	+	5.89713i	−0.386334	+	0.386334i	−0.873378	−	0.487044i	$-0.838075\pi$
$233$	−5.89713	+	5.89713i	−0.386334	+	0.386334i	0.487044	+	0.873378i	$0.338075\pi$
$234$		0			0
$235$	1.22858	−	2.96606i	0.0801439	−	0.193485i
$236$	−0.101077	+	0.0311166i	−0.00657958	+	0.00202552i
$237$		0			0
$238$	−29.4369	−	13.8485i	−1.90811	−	0.897666i
$239$			6.07025i			0.392652i	0.980539	+	0.196326i	$0.0629010\pi$
$239$			6.07025i			0.392652i	−0.980539	+	0.196326i	$0.937099\pi$
$240$		0			0
$241$		−	1.35136i		−	0.0870490i	−0.999052	−	0.0435245i	$-0.986141\pi$
$241$		−	1.35136i		−	0.0870490i	0.999052	−	0.0435245i	$-0.0138587\pi$
$242$	−2.31861	+	4.92853i	−0.149046	+	0.316818i
$243$		0			0
$244$	0.100799	+	0.0533459i	0.00645301	+	0.00341512i
$245$	4.07449	−	9.83668i	0.260309	−	0.628443i
$246$		0			0
$247$	1.77929	−	1.77929i	0.113214	−	0.113214i
$248$	6.12335	+	3.61897i	0.388833	+	0.229805i
$249$		0			0
$250$	8.85209	−	8.05632i	0.559855	−	0.509527i
$251$	23.1337	+	9.58228i	1.46018	+	0.604828i	0.964597	−	0.263729i	$-0.0849526\pi$
$251$	23.1337	+	9.58228i	1.46018	+	0.604828i	0.495588	+	0.868558i	$0.334953\pi$
$252$		0			0
$253$	−4.24755	−	10.2545i	−0.267041	−	0.644695i
$254$	4.90273	+	13.6138i	0.307625	+	0.854205i
$255$		0			0
$256$	−14.8809	−	5.87864i	−0.930057	−	0.367415i
$257$	−22.9216			−1.42981			−0.714906	−	0.699220i	$-0.753531\pi$
$257$	−22.9216			−1.42981			−0.714906	+	0.699220i	$0.753531\pi$
$258$		0			0
$259$	13.9847	+	33.7621i	0.868969	+	2.09788i
$260$	−0.809550	+	0.669978i	−0.0502062	+	0.0415503i
$261$		0			0
$262$	18.7185	−	17.0358i	1.15644	−	1.05248i
$263$	−10.9350	−	10.9350i	−0.674278	−	0.674278i	0.284421	−	0.958699i	$-0.408199\pi$
$263$	−10.9350	−	10.9350i	−0.674278	−	0.674278i	−0.958699	+	0.284421i	$0.908199\pi$
$264$		0			0
$265$	−5.67046	+	5.67046i	−0.348334	+	0.348334i
$266$	1.26778	−	26.9379i	0.0777328	−	1.65167i
$267$		0			0
$268$	−12.3490	−	6.53545i	−0.754336	−	0.399216i
$269$	−23.8790	+	9.89099i	−1.45593	+	0.603065i	−0.963601	−	0.267346i	$-0.913853\pi$
$269$	−23.8790	+	9.89099i	−1.45593	+	0.603065i	−0.492326	+	0.870411i	$0.663853\pi$
$270$		0			0
$271$		−	17.4859i		−	1.06219i	−0.847311	−	0.531096i	$-0.821780\pi$
$271$		−	17.4859i		−	1.06219i	0.847311	−	0.531096i	$-0.178220\pi$
$272$	21.0142	+	4.00036i	1.27417	+	0.242557i
$273$		0			0
$274$	−16.7403	−	7.87545i	−1.01132	−	0.475773i
$275$	−14.7512	+	6.11014i	−0.889530	+	0.368455i
$276$		0			0
$277$	−1.93766	+	4.67793i	−0.116423	+	0.281069i	−0.971340	−	0.237695i	$-0.923608\pi$
$277$	−1.93766	+	4.67793i	−0.116423	+	0.281069i	0.854917	+	0.518765i	$0.173608\pi$
$278$	−0.885870	−	0.0416919i	−0.0531309	−	0.00250051i
$279$		0			0
$280$	−1.58363	+	11.1500i	−0.0946401	+	0.666342i
$281$	20.0932	+	20.0932i	1.19866	+	1.19866i	0.974568	+	0.224094i	$0.0719422\pi$
$281$	20.0932	+	20.0932i	1.19866	+	1.19866i	0.224094	+	0.974568i	$0.428058\pi$
$282$		0			0
$283$	1.09431	+	0.453279i	0.0650501	+	0.0269446i	0.414971	−	0.909835i	$-0.363792\pi$
$283$	1.09431	+	0.453279i	0.0650501	+	0.0269446i	−0.349921	+	0.936779i	$0.613792\pi$
$284$	2.50511	+	0.236321i	0.148651	+	0.0140230i
$285$		0			0
$286$	2.91046	−	1.04814i	0.172099	−	0.0619781i
$287$	54.5155			3.21795
$288$		0			0
$289$	−11.5999			−0.682346
$290$	−10.6687	+	3.84211i	−0.626486	+	0.225616i
$291$		0			0
$292$	1.25908	−	13.3468i	0.0736820	−	0.781064i
$293$	17.1536	+	7.10527i	1.00213	+	0.415094i	0.822577	−	0.568654i	$-0.192536\pi$
$293$	17.1536	+	7.10527i	1.00213	+	0.415094i	0.179550	+	0.983749i	$0.442536\pi$
$294$		0			0
$295$	−0.0346122	−	0.0346122i	−0.00201520	−	0.00201520i
$296$	−14.4335	−	19.2121i	−0.838928	−	1.11668i
$297$		0			0
$298$	5.21008	+	0.245203i	0.301812	+	0.0142042i
$299$	−0.625603	+	1.51034i	−0.0361796	+	0.0873452i
$300$		0			0
$301$	49.0188	−	20.3042i	2.82539	−	1.17032i
$302$	−17.6263	−	8.29225i	−1.01428	−	0.477166i
$303$		0			0
$304$	3.60262	+	17.3631i	0.206625	+	0.995839i
$305$			0.0527843i			0.00302242i
$306$		0			0
$307$	17.8200	−	7.38127i	1.01704	−	0.421271i	0.189021	−	0.981973i	$-0.439469\pi$
$307$	17.8200	−	7.38127i	1.01704	−	0.421271i	0.828018	+	0.560702i	$0.189469\pi$
$308$	15.5077	−	29.3025i	0.883633	−	1.66966i
$309$		0			0
$310$	−0.154765	+	3.28844i	−0.00879005	+	0.186771i
$311$	−14.1128	+	14.1128i	−0.800264	+	0.800264i	−0.983137	−	0.182873i	$-0.941460\pi$
$311$	−14.1128	+	14.1128i	−0.800264	+	0.800264i	0.182873	+	0.983137i	$0.441460\pi$
$312$		0			0
$313$	−5.88822	−	5.88822i	−0.332822	−	0.332822i	0.520835	−	0.853657i	$-0.325621\pi$
$313$	−5.88822	−	5.88822i	−0.332822	−	0.332822i	−0.853657	+	0.520835i	$0.825621\pi$
$314$	9.10441	−	8.28596i	0.513791	−	0.467604i
$315$		0			0
$316$	15.6448	+	18.9040i	0.880088	+	1.06343i
$317$	12.9292	+	31.2138i	0.726175	+	1.75314i	0.654937	+	0.755683i	$0.272695\pi$
$317$	12.9292	+	31.2138i	0.726175	+	1.75314i	0.0712382	+	0.997459i	$0.477305\pi$
$318$		0			0
$319$	33.3811			1.86898
$320$	−0.816838	−	7.36021i	−0.0456627	−	0.411448i
$321$		0			0
$322$	5.93635	+	16.4839i	0.330820	+	0.918612i
$323$	−9.07279	−	21.9036i	−0.504823	−	1.21875i
$324$		0			0
$325$	2.17264	+	0.899936i	0.120516	+	0.0499194i
$326$	−14.7051	+	13.3832i	−0.814443	+	0.741228i
$327$		0			0
$328$	−34.7184	+	8.92477i	−1.91701	+	0.492788i
$329$	10.5488	−	10.5488i	0.581572	−	0.581572i
$330$		0			0
$331$	0.203102	−	0.490332i	0.0111635	−	0.0269511i	−0.918199	−	0.396118i	$-0.870357\pi$
$331$	0.203102	−	0.490332i	0.0111635	−	0.0269511i	0.929363	+	0.369167i	$0.120357\pi$
$332$	−2.45670	+	4.64204i	−0.134829	+	0.254765i
$333$		0			0
$334$	−9.19031	+	19.5352i	−0.502871	+	1.06892i
$335$		−	6.46666i		−	0.353311i
$336$		0			0
$337$			3.29629i			0.179560i	0.995962	+	0.0897801i	$0.0286164\pi$
$337$			3.29629i			0.179560i	−0.995962	+	0.0897801i	$0.971384\pi$
$338$	16.2235	+	7.63232i	0.882443	+	0.415143i
$339$		0			0
$340$	2.91304	+	9.46257i	0.157982	+	0.513180i
$341$	3.70869	−	8.95357i	0.200837	−	0.484863i
$342$		0			0
$343$	13.6932	−	13.6932i	0.739362	−	0.739362i
$344$	−27.8938	+	20.9557i	−1.50393	+	1.12986i
$345$		0			0
$346$	−1.27362	−	1.39942i	−0.0684701	−	0.0752333i
$347$	−8.71908	−	3.61156i	−0.468065	−	0.193879i	0.136169	−	0.990686i	$-0.456521\pi$
$347$	−8.71908	−	3.61156i	−0.468065	−	0.193879i	−0.604234	+	0.796807i	$0.706521\pi$
$348$		0			0
$349$	0.660845	+	1.59542i	0.0353742	+	0.0854009i	0.940579	−	0.339574i	$-0.110283\pi$
$349$	0.660845	+	1.59542i	0.0353742	+	0.0854009i	−0.905205	+	0.424975i	$0.860283\pi$
$350$	23.7122	−	8.53949i	1.26747	−	0.456455i
$351$		0			0
$352$	−5.07902	+	21.2002i	−0.270713	+	1.12997i
$353$	−21.0472			−1.12023			−0.560114	−	0.828415i	$-0.689243\pi$
$353$	−21.0472			−1.12023			−0.560114	+	0.828415i	$0.689243\pi$
$354$		0			0
$355$	0.445676	+	1.07596i	0.0236540	+	0.0571058i
$356$	12.0180	+	1.13372i	0.636951	+	0.0600870i
$357$		0			0
$358$	−6.22937	−	6.84468i	−0.329233	−	0.361753i
$359$	3.16613	+	3.16613i	0.167102	+	0.167102i	0.785704	−	0.618602i	$-0.212301\pi$
$359$	3.16613	+	3.16613i	0.167102	+	0.167102i	−0.618602	+	0.785704i	$0.712301\pi$
$360$		0			0
$361$	0.462029	−	0.462029i	0.0243173	−	0.0243173i
$362$	0.911350	+	0.0428911i	0.0478995	+	0.00225430i
$363$		0			0
$364$	−4.66683	+	1.43668i	−0.244608	+	0.0753024i
$365$	5.73252	−	2.37449i	0.300054	−	0.124286i
$366$		0			0
$367$		−	17.1425i		−	0.894833i	−0.894326	−	0.447416i	$-0.852344\pi$
$367$		−	17.1425i		−	0.894833i	0.894326	−	0.447416i	$-0.147656\pi$
$368$	−6.47918	−	9.52601i	−0.337751	−	0.496577i
$369$		0			0
$370$	4.73451	−	10.0638i	0.246135	−	0.523193i
$371$	−34.4271	+	14.2602i	−1.78736	+	0.740350i
$372$		0			0
$373$	7.52495	−	18.1668i	0.389627	−	0.940643i	−0.600392	−	0.799706i	$-0.704989\pi$
$373$	7.52495	−	18.1668i	0.389627	−	0.940643i	0.990019	−	0.140937i	$-0.0450114\pi$
$374$	1.37019	−	29.1139i	0.0708510	−	1.50544i
$375$		0			0
$376$	−4.99108	+	8.44497i	−0.257395	+	0.435516i
$377$	−3.47653	−	3.47653i	−0.179050	−	0.179050i
$378$		0			0
$379$	−13.0553	−	5.40768i	−0.670605	−	0.277774i	0.0212882	−	0.999773i	$-0.493223\pi$
$379$	−13.0553	−	5.40768i	−0.670605	−	0.277774i	−0.691893	+	0.722000i	$0.743223\pi$
$380$	−6.32294	+	5.23282i	−0.324360	+	0.268438i
$381$		0			0
$382$	6.18295	+	17.1687i	0.316347	+	0.878426i
$383$	25.0479			1.27989			0.639943	−	0.768422i	$-0.278958\pi$
$383$	25.0479			1.27989			0.639943	+	0.768422i	$0.278958\pi$
$384$		0			0
$385$	15.3445			0.782026
$386$	11.2611	+	31.2695i	0.573174	+	1.59158i
$387$		0			0
$388$	10.3893	−	8.59812i	0.527437	−	0.436503i
$389$	−10.3585	−	4.29064i	−0.525198	−	0.217544i	0.104300	−	0.994546i	$-0.466740\pi$
$389$	−10.3585	−	4.29064i	−0.525198	−	0.217544i	−0.629499	+	0.777002i	$0.716740\pi$
$390$		0			0
$391$	10.8914	+	10.8914i	0.550801	+	0.550801i
$392$	−16.5525	+	28.0070i	−0.836026	+	1.41457i
$393$		0			0
$394$	−1.38802	+	29.4927i	−0.0699275	+	1.48582i
$395$	−4.34620	+	10.4926i	−0.218681	+	0.527942i
$396$		0			0
$397$	14.2652	−	5.90883i	0.715948	−	0.296555i	0.00518475	−	0.999987i	$-0.498350\pi$
$397$	14.2652	−	5.90883i	0.715948	−	0.296555i	0.710763	+	0.703431i	$0.248350\pi$
$398$	−9.66477	+	20.5438i	−0.484451	+	1.02977i
$399$		0			0
$400$	−13.7032	+	9.32036i	−0.685162	+	0.466018i
$401$		−	30.5445i		−	1.52532i	−0.646801	−	0.762659i	$-0.723894\pi$
$401$		−	30.5445i		−	1.52532i	0.646801	−	0.762659i	$-0.276106\pi$
$402$		0			0
$403$	−1.31873	+	0.546237i	−0.0656907	+	0.0272100i
$404$	4.58452	−	1.41134i	0.228088	−	0.0702167i
$405$		0			0
$406$	−52.6334	−	2.47710i	−2.61215	−	0.122936i
$407$	−23.1512	+	23.1512i	−1.14756	+	1.14756i
$408$		0			0
$409$	23.0606	+	23.0606i	1.14027	+	1.14027i	0.988400	+	0.151875i	$0.0485312\pi$
$409$	23.0606	+	23.0606i	1.14027	+	1.14027i	0.151875	+	0.988400i	$0.451469\pi$
$410$	−11.1674	−	12.2705i	−0.551519	−	0.605995i
$411$		0			0
$412$	5.51321	+	0.520091i	0.271616	+	0.0256230i
$413$	−0.0870433	−	0.210141i	−0.00428312	−	0.0103404i
$414$		0			0
$415$	−2.43084			−0.119325
$416$	2.73689	−	1.67896i	0.134187	−	0.0823180i
$417$		0			0
$418$	22.7320	−	8.18646i	1.11186	−	0.400413i
$419$	10.2186	+	24.6698i	0.499211	+	1.20520i	0.949910	+	0.312525i	$0.101175\pi$
$419$	10.2186	+	24.6698i	0.499211	+	1.20520i	−0.450699	+	0.892676i	$0.648825\pi$
$420$		0			0
$421$	−4.20371	−	1.74123i	−0.204876	−	0.0848625i	0.277886	−	0.960614i	$-0.410366\pi$
$421$	−4.20371	−	1.74123i	−0.204876	−	0.0848625i	−0.482762	+	0.875752i	$0.660366\pi$
$422$	2.39485	+	2.63140i	0.116579	+	0.128095i
$423$		0			0
$424$	19.5905	−	14.7177i	0.951398	−	0.714756i
$425$	15.6673	−	15.6673i	0.759978	−	0.759978i
$426$		0			0
$427$	−0.0938634	+	0.226606i	−0.00454237	+	0.0109662i
$428$	4.16697	+	13.5358i	0.201418	+	0.654276i
$429$		0			0
$430$	−14.6115	−	6.87396i	−0.704630	−	0.331492i
$431$			28.7138i			1.38309i	0.722332	+	0.691547i	$0.243070\pi$
$431$			28.7138i			1.38309i	−0.722332	+	0.691547i	$0.756930\pi$
$432$		0			0
$433$		−	6.26663i		−	0.301155i	−0.988598	−	0.150578i	$-0.951887\pi$
$433$		−	6.26663i		−	0.301155i	0.988598	−	0.150578i	$-0.0481133\pi$
$434$	−6.51207	+	13.8423i	−0.312589	+	0.664450i
$435$		0			0
$436$	−1.41914	+	2.68152i	−0.0679643	+	0.128421i
$437$	−4.88623	+	11.7964i	−0.233740	+	0.564299i
$438$		0			0
$439$	−0.329078	+	0.329078i	−0.0157060	+	0.0157060i	−0.714916	−	0.699210i	$-0.753535\pi$
$439$	−0.329078	+	0.329078i	−0.0157060	+	0.0157060i	0.699210	+	0.714916i	$0.253535\pi$
$440$	−9.77219	+	2.51205i	−0.465871	+	0.119757i
$441$		0			0
$442$	−3.17481	+	2.88941i	−0.151010	+	0.137435i
$443$	25.7914	+	10.6831i	1.22538	+	0.507571i	0.899118	−	0.437707i	$-0.144209\pi$
$443$	25.7914	+	10.6831i	1.22538	+	0.507571i	0.326267	+	0.945278i	$0.394209\pi$
$444$		0			0
$445$	2.13807	+	5.16177i	0.101354	+	0.244691i
$446$	13.4103	+	37.2375i	0.634998	+	1.76325i
$447$		0			0
$448$	9.58151	−	33.0503i	0.452684	−	1.56148i
$449$	−25.7331			−1.21442			−0.607209	−	0.794542i	$-0.707711\pi$
$449$	−25.7331			−1.21442			−0.607209	+	0.794542i	$0.707711\pi$
$450$		0			0
$451$	18.6910	+	45.1242i	0.880127	+	2.12481i
$452$	10.3316	+	12.4839i	0.485959	+	0.587196i
$453$		0			0
$454$	−26.3035	+	23.9390i	−1.23449	+	1.12351i
$455$	−1.59807	−	1.59807i	−0.0749189	−	0.0749189i
$456$		0			0
$457$	29.5529	−	29.5529i	1.38243	−	1.38243i	0.542138	−	0.840290i	$-0.317615\pi$
$457$	29.5529	−	29.5529i	1.38243	−	1.38243i	0.840290	−	0.542138i	$-0.182385\pi$
$458$	0.962666	−	20.4547i	0.0449824	−	0.955788i
$459$		0			0
$460$	2.49418	−	4.71287i	0.116292	−	0.219739i
$461$	30.7137	−	12.7220i	1.43048	−	0.592525i	0.473011	−	0.881056i	$-0.343167\pi$
$461$	30.7137	−	12.7220i	1.43048	−	0.592525i	0.957470	+	0.288532i	$0.0931670\pi$
$462$		0			0
$463$		−	34.2809i		−	1.59317i	−0.604529	−	0.796583i	$-0.706639\pi$
$463$		−	34.2809i		−	1.59317i	0.604529	−	0.796583i	$-0.293361\pi$
$464$	33.9253	−	7.03910i	1.57494	−	0.326782i
$465$		0			0
$466$	10.6722	+	5.02073i	0.494382	+	0.232581i
$467$	−21.7245	+	8.99857i	−1.00529	+	0.416404i	−0.823734	−	0.566976i	$-0.808113\pi$
$467$	−21.7245	+	8.99857i	−1.00529	+	0.416404i	−0.181555	+	0.983381i	$0.558113\pi$
$468$		0			0
$469$	11.4993	−	27.7617i	0.530988	−	1.28192i
$470$	−4.53523	−	0.213443i	−0.209195	−	0.00984537i
$471$		0			0
$472$	0.0898363	+	0.119579i	0.00413505	+	0.00550409i
$473$	33.6129	+	33.6129i	1.54552	+	1.54552i
$474$		0			0
$475$	16.9692	+	7.02889i	0.778602	+	0.322508i
$476$	−4.32088	+	45.8034i	−0.198047	+	2.09940i
$477$		0			0
$478$	8.07683	−	2.90871i	0.369426	−	0.133041i
$479$	−16.1430			−0.737592			−0.368796	−	0.929510i	$-0.620230\pi$
$479$	−16.1430			−0.737592			−0.368796	+	0.929510i	$0.620230\pi$
$480$		0			0
$481$	4.82223			0.219875
$482$	−1.79807	+	0.647540i	−0.0819000	+	0.0294946i
$483$		0			0
$484$	7.66872	+	0.723432i	0.348578	+	0.0328833i
$485$	5.76658	+	2.38860i	0.261847	+	0.108461i
$486$		0			0
$487$	−15.6630	−	15.6630i	−0.709760	−	0.709760i	0.256725	−	0.966485i	$-0.417357\pi$
$487$	−15.6630	−	15.6630i	−0.709760	−	0.709760i	−0.966485	+	0.256725i	$0.917357\pi$
$488$	0.0226794	−	0.159682i	0.00102665	−	0.00722845i
$489$		0			0
$490$	−15.0407	−	0.707863i	−0.679469	−	0.0319780i
$491$	−1.83009	+	4.41824i	−0.0825909	+	0.199392i	−0.959780	−	0.280753i	$-0.909416\pi$
$491$	−1.83009	+	4.41824i	−0.0825909	+	0.199392i	0.877189	+	0.480145i	$0.159416\pi$
$492$		0			0
$493$	−42.7971	+	17.7271i	−1.92749	+	0.798391i
$494$	−3.22005	−	1.51487i	−0.144877	−	0.0681570i
$495$		0			0
$496$	1.88111	−	9.88161i	0.0844644	−	0.443697i
$497$			5.41166i			0.242746i
$498$		0			0
$499$	2.18878	−	0.906622i	0.0979832	−	0.0405860i	−0.333153	−	0.942873i	$-0.608113\pi$
$499$	2.18878	−	0.906622i	0.0979832	−	0.0405860i	0.431137	+	0.902287i	$0.358113\pi$
$500$	−14.9611	−	7.91785i	−0.669082	−	0.354097i
$501$		0			0
$502$	1.66474	−	35.3723i	0.0743008	−	1.57875i
$503$	−17.6732	+	17.6732i	−0.788011	+	0.788011i	−0.981168	−	0.193157i	$-0.938127\pi$
$503$	−17.6732	+	17.6732i	−0.788011	+	0.788011i	0.193157	+	0.981168i	$0.438127\pi$
$504$		0			0
$505$	1.56989	+	1.56989i	0.0698591	+	0.0698591i
$506$	−11.6089	+	10.5653i	−0.516079	+	0.469686i
$507$		0			0
$508$	15.7647	−	13.0468i	0.699446	−	0.578857i
$509$	−10.2708	−	24.7960i	−0.455247	−	1.09906i	−0.970300	−	0.241905i	$-0.922228\pi$
$509$	−10.2708	−	24.7960i	−0.455247	−	1.09906i	0.515053	−	0.857158i	$-0.327772\pi$
$510$		0			0
$511$	28.8325			1.27547
$512$	−0.691331	+	22.6169i	−0.0305528	+	0.999533i
$513$		0			0
$514$	10.9835	+	30.4986i	0.484460	+	1.34524i
$515$	0.980836	+	2.36795i	0.0432208	+	0.104344i
$516$		0			0
$517$	12.3482	+	5.11481i	0.543075	+	0.224949i
$518$	38.2214	−	34.7855i	1.67935	−	1.52839i
$519$		0			0
$520$	1.27936	+	0.756119i	0.0561037	+	0.0331580i
$521$	15.0583	−	15.0583i	0.659715	−	0.659715i	−0.295598	−	0.955312i	$-0.595519\pi$
$521$	15.0583	−	15.0583i	0.659715	−	0.659715i	0.955312	+	0.295598i	$0.0955188\pi$
$522$		0			0
$523$	−16.4769	+	39.7788i	−0.720486	+	1.73941i	−0.0485224	+	0.998822i	$0.515451\pi$
$523$	−16.4769	+	39.7788i	−0.720486	+	1.73941i	−0.671963	+	0.740584i	$0.734549\pi$
$524$	−31.6367	−	16.7430i	−1.38205	−	0.731422i
$525$		0			0
$526$	−9.30987	+	19.7894i	−0.405930	+	0.862858i
$527$			13.4487i			0.585834i
$528$		0			0
$529$			14.7047i			0.639335i
$530$	10.2620	+	4.82775i	0.445754	+	0.209704i
$531$		0			0
$532$	−36.4500	+	11.2211i	−1.58031	+	0.486496i
$533$	2.75292	−	6.64614i	0.119242	−	0.287876i
$534$		0			0
$535$	−4.63509	+	4.63509i	−0.200392	+	0.200392i
$536$	−2.77848	+	19.5627i	−0.120012	+	0.844982i
$537$		0			0
$538$	24.6028	+	27.0329i	1.06070	+	1.16547i
$539$	40.9519	+	16.9628i	1.76392	+	0.730640i
$540$		0			0
$541$	2.79019	+	6.73611i	0.119959	+	0.289608i	0.972441	−	0.233150i	$-0.0749033\pi$
$541$	2.79019	+	6.73611i	0.119959	+	0.289608i	−0.852481	+	0.522758i	$0.824903\pi$
$542$	−23.2661	+	8.37880i	−0.999362	+	0.359900i
$543$		0			0
$544$	−4.74674	−	29.8775i	−0.203515	−	1.28099i
$545$	−1.40420			−0.0601492
$546$		0			0
$547$	−5.23404	−	12.6361i	−0.223792	−	0.540281i	0.771607	−	0.636099i	$-0.219453\pi$
$547$	−5.23404	−	12.6361i	−0.223792	−	0.540281i	−0.995399	+	0.0958187i	$0.969453\pi$
$548$	−2.45722	+	26.0477i	−0.104967	+	1.11270i
$549$		0			0
$550$	15.1983	+	16.6995i	0.648058	+	0.712070i
$551$	−27.1532	−	27.1532i	−1.15677	−	1.15677i
$552$		0			0
$553$	−37.3169	+	37.3169i	−1.58688	+	1.58688i
$554$	7.15274	+	0.336631i	0.303891	+	0.0143021i
$555$		0			0
$556$	0.369013	+	1.19868i	0.0156496	+	0.0508354i
$557$	−35.0039	+	14.4991i	−1.48316	+	0.614346i	−0.969816	−	0.243836i	$-0.921594\pi$
$557$	−35.0039	+	14.4991i	−1.48316	+	0.614346i	−0.513346	+	0.858182i	$0.671594\pi$
$558$		0			0
$559$		−	7.00133i		−	0.296125i
$560$	15.5946	−	3.23570i	0.658994	−	0.136733i
$561$		0			0
$562$	17.1071	−	36.3634i	0.721619	−	1.53390i
$563$	−3.78277	+	1.56687i	−0.159425	+	0.0660358i	−0.460969	−	0.887416i	$-0.652498\pi$
$563$	−3.78277	+	1.56687i	−0.159425	+	0.0660358i	0.301544	+	0.953452i	$0.402498\pi$
$564$		0			0
$565$	−2.87018	+	6.92922i	−0.120749	+	0.291514i
$566$	0.0787485	−	1.67325i	0.00331005	−	0.0703319i
$567$		0			0
$568$	−0.885947	−	3.44644i	−0.0371735	−	0.144609i
$569$	17.9967	+	17.9967i	0.754460	+	0.754460i	0.975308	−	0.220848i	$-0.0708826\pi$
$569$	17.9967	+	17.9967i	0.754460	+	0.754460i	−0.220848	+	0.975308i	$0.570883\pi$
$570$		0			0
$571$	−6.70495	−	2.77728i	−0.280593	−	0.116226i	0.237949	−	0.971278i	$-0.423525\pi$
$571$	−6.70495	−	2.77728i	−0.280593	−	0.116226i	−0.518542	+	0.855052i	$0.673525\pi$
$572$	−2.78924	−	3.37030i	−0.116624	−	0.140919i
$573$		0			0
$574$	−26.1224	−	72.5362i	−1.09033	−	3.02760i
$575$	−11.9328			−0.497634
$576$		0			0
$577$	−16.6125			−0.691589			−0.345794	−	0.938310i	$-0.612391\pi$
$577$	−16.6125			−0.691589			−0.345794	+	0.938310i	$0.612391\pi$
$578$	5.55837	+	15.4344i	0.231198	+	0.641985i
$579$		0			0
$580$	10.2243	+	12.3543i	0.424541	+	0.512983i
$581$	−10.4357	−	4.32263i	−0.432948	−	0.179333i
$582$		0			0
$583$	−23.6071	−	23.6071i	−0.977708	−	0.977708i
$584$	−18.3621	+	4.72018i	−0.759828	+	0.195323i
$585$		0			0
$586$	1.23440	−	26.2286i	0.0509927	−	1.08349i
$587$	1.79864	−	4.34230i	0.0742378	−	0.179226i	−0.882404	−	0.470492i	$-0.844076\pi$
$587$	1.79864	−	4.34230i	0.0742378	−	0.179226i	0.956642	+	0.291266i	$0.0940765\pi$
$588$		0			0
$589$	−10.2999	+	4.26635i	−0.424399	+	0.175792i
$590$	−0.0294684	+	0.0626390i	−0.00121319	+	0.00257880i
$591$		0			0
$592$	−18.6467	+	28.4106i	−0.766376	+	1.16767i
$593$		−	11.4622i		−	0.470697i	−0.971911	−	0.235348i	$-0.924377\pi$
$593$		−	11.4622i		−	0.470697i	0.971911	−	0.235348i	$-0.0756231\pi$
$594$		0			0
$595$	−19.6728	+	8.14873i	−0.806505	+	0.334065i
$596$	−2.17028	−	7.04982i	−0.0888982	−	0.288772i
$597$		0			0
$598$	2.30937	+	0.108686i	0.0944372	+	0.00444452i
$599$	26.2359	−	26.2359i	1.07197	−	1.07197i	0.0747702	−	0.997201i	$-0.476178\pi$
$599$	26.2359	−	26.2359i	1.07197	−	1.07197i	0.997201	−	0.0747702i	$-0.0238223\pi$
$600$		0			0
$601$	4.12728	+	4.12728i	0.168355	+	0.168355i	0.786256	−	0.617901i	$-0.212017\pi$
$601$	4.12728	+	4.12728i	0.168355	+	0.168355i	−0.617901	+	0.786256i	$0.712017\pi$
$602$	−50.5046	−	55.4932i	−2.05841	−	2.26173i
$603$		0			0
$604$	−2.58727	+	27.4263i	−0.105275	+	1.11596i
$605$	1.36432	+	3.29375i	0.0554673	+	0.133910i
$606$		0			0
$607$	−35.3912			−1.43649			−0.718243	−	0.695792i	$-0.755053\pi$
$607$	−35.3912			−1.43649			−0.718243	+	0.695792i	$0.755053\pi$
$608$	21.3763	−	13.1134i	0.866924	−	0.531820i
$609$		0			0
$610$	0.0702328	−	0.0252929i	0.00284364	−	0.00102408i
$611$	−0.753338	−	1.81872i	−0.0304768	−	0.0735775i
$612$		0			0
$613$	15.0061	+	6.21571i	0.606089	+	0.251050i	0.664555	−	0.747239i	$-0.268621\pi$
$613$	15.0061	+	6.21571i	0.606089	+	0.251050i	−0.0584665	+	0.998289i	$0.518621\pi$
$614$	−18.3601	−	20.1736i	−0.740953	−	0.814141i
$615$		0			0
$616$	−46.4196	−	6.59294i	−1.87030	−	0.265637i
$617$	17.0036	−	17.0036i	0.684540	−	0.684540i	−0.276480	−	0.961020i	$-0.589168\pi$
$617$	17.0036	−	17.0036i	0.684540	−	0.684540i	0.961020	+	0.276480i	$0.0891678\pi$
$618$		0			0
$619$	2.17702	−	5.25579i	0.0875018	−	0.211248i	−0.874071	−	0.485798i	$-0.838529\pi$
$619$	2.17702	−	5.25579i	0.0875018	−	0.211248i	0.961573	+	0.274550i	$0.0885290\pi$
$620$	4.44963	−	1.36982i	0.178702	−	0.0550131i
$621$		0			0
$622$	25.5404	+	12.0154i	1.02408	+	0.481775i
$623$			25.9618i			1.04014i
$624$		0			0
$625$			12.8811i			0.515245i
$626$	−5.01315	+	10.6561i	−0.200366	+	0.425904i
$627$		0			0
$628$	−15.3876	−	8.14354i	−0.614031	−	0.324963i
$629$	17.3871	−	41.9761i	0.693268	−	1.67370i
$630$		0			0
$631$	3.76171	−	3.76171i	0.149751	−	0.149751i	−0.628256	−	0.778007i	$-0.716231\pi$
$631$	3.76171	−	3.76171i	0.149751	−	0.149751i	0.778007	+	0.628256i	$0.216231\pi$
$632$	17.6563	−	29.8746i	0.702329	−	1.18835i
$633$		0			0
$634$	35.3365	−	32.1599i	1.40339	−	1.27723i
$635$	8.75020	+	3.62445i	0.347241	+	0.143832i
$636$		0			0
$637$	−2.49838	−	6.03162i	−0.0989893	−	0.238981i
$638$	−15.9954	−	44.4156i	−0.633263	−	1.75843i
$639$		0			0
$640$	−9.40180	+	4.61368i	−0.371639	+	0.182372i
$641$	−10.7295			−0.423791			−0.211896	−	0.977292i	$-0.567964\pi$
$641$	−10.7295			−0.423791			−0.211896	+	0.977292i	$0.567964\pi$
$642$		0			0
$643$	−11.2121	−	27.0684i	−0.442162	−	1.06747i	−0.975189	−	0.221375i	$-0.928945\pi$
$643$	−11.2121	−	27.0684i	−0.442162	−	1.06747i	0.533027	−	0.846099i	$-0.321055\pi$
$644$	19.0883	−	15.7973i	0.752184	−	0.622502i
$645$		0			0
$646$	−24.7967	+	22.5676i	−0.975612	+	0.887909i
$647$	−28.0825	−	28.0825i	−1.10404	−	1.10404i	−0.993918	−	0.110119i	$-0.964877\pi$
$647$	−28.0825	−	28.0825i	−1.10404	−	1.10404i	−0.110119	−	0.993918i	$-0.535123\pi$
$648$		0			0
$649$	0.144097	−	0.144097i	0.00565630	−	0.00565630i
$650$	0.156346	−	3.32205i	0.00613241	−	0.130302i
$651$		0			0
$652$	24.8535	+	13.1532i	0.973339	+	0.515119i
$653$	27.5948	−	11.4301i	1.07987	−	0.447296i	0.229405	−	0.973331i	$-0.426322\pi$
$653$	27.5948	−	11.4301i	1.07987	−	0.447296i	0.850463	+	0.526035i	$0.176322\pi$
$654$		0			0
$655$		−	16.5668i		−	0.647318i
$656$	28.5111	+	41.9185i	1.11317	+	1.63664i
$657$		0			0
$658$	−19.0905	−	8.98106i	−0.744223	−	0.350118i
$659$	−21.3865	+	8.85859i	−0.833101	+	0.345082i	−0.758130	−	0.652104i	$-0.773887\pi$
$659$	−21.3865	+	8.85859i	−0.833101	+	0.345082i	−0.0749715	+	0.997186i	$0.523887\pi$
$660$		0			0
$661$	10.5821	−	25.5475i	0.411597	−	0.993683i	−0.573112	−	0.819477i	$-0.694264\pi$
$661$	10.5821	−	25.5475i	0.411597	−	0.993683i	0.984709	−	0.174206i	$-0.0557358\pi$
$662$	−0.749738	−	0.0352851i	−0.0291394	−	0.00137139i
$663$		0			0
$664$	7.35371	+	1.04444i	0.285379	+	0.0405322i
$665$	−12.4817	−	12.4817i	−0.484018	−	0.484018i
$666$		0			0
$667$	23.0488	+	9.54712i	0.892453	+	0.369666i
$668$	30.3966	+	2.86747i	1.17608	+	0.110946i
$669$		0			0
$670$	−8.60428	+	3.09866i	−0.332412	+	0.119712i
$671$	−0.219751			−0.00848338
$672$		0			0
$673$	24.0201			0.925908			0.462954	−	0.886382i	$-0.346790\pi$
$673$	24.0201			0.925908			0.462954	+	0.886382i	$0.346790\pi$
$674$	4.38591	−	1.57950i	0.168939	−	0.0608400i
$675$		0			0
$676$	2.38136	−	25.2436i	0.0915909	−	0.970907i
$677$	31.7111	+	13.1352i	1.21876	+	0.504826i	0.897015	−	0.442001i	$-0.145731\pi$
$677$	31.7111	+	13.1352i	1.21876	+	0.504826i	0.321743	+	0.946827i	$0.395731\pi$
$678$		0			0
$679$	20.5088	+	20.5088i	0.787054	+	0.787054i
$680$	11.1947	−	8.41020i	0.429296	−	0.322516i
$681$		0			0
$682$	−13.6904	−	0.644313i	−0.524232	−	0.0246720i
$683$	−4.66467	+	11.2615i	−0.178489	+	0.430910i	−0.987650	−	0.156677i	$-0.949922\pi$
$683$	−4.66467	+	11.2615i	−0.178489	+	0.430910i	0.809161	+	0.587587i	$0.199922\pi$
$684$		0			0
$685$	−11.1876	+	4.63406i	−0.427457	+	0.177058i
$686$	−24.7810	−	11.6582i	−0.946144	−	0.445111i
$687$		0			0
$688$	41.2489	+	27.0729i	1.57260	+	1.03215i
$689$			4.91721i			0.187331i
$690$		0			0
$691$	21.3386	−	8.83876i	0.811760	−	0.336242i	0.0621042	−	0.998070i	$-0.480219\pi$
$691$	21.3386	−	8.83876i	0.811760	−	0.336242i	0.749656	+	0.661828i	$0.230219\pi$
$692$	−1.25173	+	2.36519i	−0.0475835	+	0.0899111i
$693$		0			0
$694$	−0.627439	+	13.3318i	−0.0238173	+	0.506070i
$695$	−0.410468	+	0.410468i	−0.0155699	+	0.0155699i
$696$		0			0
$697$	−47.9267	−	47.9267i	−1.81535	−	1.81535i
$698$	1.80614	−	1.64378i	0.0683636	−	0.0622180i
$699$		0			0
$700$	−22.7246	−	27.4587i	−0.858910	−	1.03784i
$701$	9.87590	+	23.8425i	0.373008	+	0.900520i	0.993238	+	0.116100i	$0.0370393\pi$
$701$	9.87590	+	23.8425i	0.373008	+	0.900520i	−0.620230	+	0.784420i	$0.712961\pi$
$702$		0			0
$703$	37.6638			1.42052
$704$	30.6419	−	3.40064i	1.15486	−	0.128167i
$705$		0			0
$706$	10.0853	+	28.0045i	0.379564	+	1.05397i
$707$	3.94798	+	9.53126i	0.148479	+	0.358460i
$708$		0			0
$709$	−35.5689	−	14.7331i	−1.33582	−	0.553315i	−0.403510	−	0.914975i	$-0.632210\pi$
$709$	−35.5689	−	14.7331i	−1.33582	−	0.553315i	−0.932310	+	0.361661i	$0.882210\pi$
$710$	1.21807	−	1.10857i	0.0457133	−	0.0416039i
$711$		0			0
$712$	−4.25022	−	16.5339i	−0.159284	−	0.619633i
$713$	5.12151	−	5.12151i	0.191802	−	0.191802i
$714$		0			0
$715$	0.774864	−	1.87069i	0.0289783	−	0.0699597i
$716$	−6.12231	+	11.5684i	−0.228801	+	0.432330i
$717$		0			0
$718$	2.69560	−	5.72986i	0.100599	−	0.213836i
$719$		−	12.5206i		−	0.466941i	−0.972364	−	0.233471i	$-0.924992\pi$
$719$		−	12.5206i		−	0.466941i	0.972364	−	0.233471i	$-0.0750083\pi$
$720$		0			0
$721$			11.9099i			0.443548i
$722$	−0.836150	−	0.393365i	−0.0311183	−	0.0146395i
$723$		0			0
$724$	−0.379627	−	1.23316i	−0.0141087	−	0.0458300i
$725$	13.7336	−	33.1559i	0.510054	−	1.23138i
$726$		0			0
$727$	−19.8374	+	19.8374i	−0.735729	+	0.735729i	−0.971748	−	0.236020i	$-0.924157\pi$
$727$	−19.8374	+	19.8374i	−0.735729	+	0.735729i	0.236020	+	0.971748i	$0.424157\pi$
$728$	4.14781	+	5.52108i	0.153728	+	0.204625i
$729$		0			0
$730$	−5.90628	−	6.48967i	−0.218601	−	0.240194i
$731$	−60.9445	−	25.2440i	−2.25411	−	0.933685i
$732$		0			0
$733$	−15.9981	−	38.6228i	−0.590903	−	1.42657i	−0.882632	−	0.470065i	$-0.844231\pi$
$733$	−15.9981	−	38.6228i	−0.590903	−	1.42657i	0.291729	−	0.956501i	$-0.405769\pi$
$734$	−22.8092	+	8.21426i	−0.841902	+	0.303194i
$735$		0			0
$736$	−9.57027	+	13.1856i	−0.352765	+	0.486026i
$737$	26.9219			0.991679
$738$		0			0
$739$	−6.18168	−	14.9239i	−0.227397	−	0.548984i	0.768462	−	0.639895i	$-0.221022\pi$
$739$	−6.18168	−	14.9239i	−0.227397	−	0.548984i	−0.995859	+	0.0909109i	$0.971022\pi$
$740$	−15.6592	−	1.47722i	−0.575643	−	0.0543035i
$741$		0			0
$742$	35.4706	+	38.9742i	1.30217	+	1.43079i
$743$	−3.18178	−	3.18178i	−0.116728	−	0.116728i	0.646330	−	0.763058i	$-0.276303\pi$
$743$	−3.18178	−	3.18178i	−0.116728	−	0.116728i	−0.763058	+	0.646330i	$0.776303\pi$
$744$		0			0
$745$	2.41409	−	2.41409i	0.0884454	−	0.0884454i
$746$	−27.7778	−	1.30731i	−1.01702	−	0.0478642i
$747$		0			0
$748$	−39.3944	+	12.1275i	−1.44040	+	0.443426i
$749$	−28.1410	+	11.6564i	−1.02825	+	0.425915i
$750$		0			0
$751$			41.5823i			1.51736i	0.651463	+	0.758681i	$0.274156\pi$
$751$			41.5823i			1.51736i	−0.651463	+	0.758681i	$0.725844\pi$
$752$	13.6281	+	2.59432i	0.496967	+	0.0946051i
$753$		0			0
$754$	−2.95987	+	6.29160i	−0.107792	+	0.229126i
$755$	−11.7797	+	4.87932i	−0.428708	+	0.177577i
$756$		0			0
$757$	−19.7593	+	47.7033i	−0.718166	+	1.73381i	−0.0396566	+	0.999213i	$0.512626\pi$
$757$	−19.7593	+	47.7033i	−0.718166	+	1.73381i	−0.678509	+	0.734592i	$0.737374\pi$
$758$	−0.939480	+	19.9621i	−0.0341234	+	0.725055i
$759$		0			0
$760$	9.99238	+	5.90562i	0.362462	+	0.214219i
$761$	5.44211	+	5.44211i	0.197276	+	0.197276i	0.798831	−	0.601555i	$-0.205452\pi$
$761$	5.44211	+	5.44211i	0.197276	+	0.197276i	−0.601555	+	0.798831i	$0.705452\pi$
$762$		0			0
$763$	−6.02830	−	2.49700i	−0.218239	−	0.0903976i
$764$	19.8813	−	16.4536i	0.719279	−	0.595270i
$765$		0			0
$766$	−12.0023	−	33.3277i	−0.433661	−	1.20418i
$767$	−0.0300144			−0.00108376
$768$		0			0
$769$	−3.21709			−0.116011			−0.0580056	−	0.998316i	$-0.518474\pi$
$769$	−3.21709			−0.116011			−0.0580056	+	0.998316i	$0.518474\pi$
$770$	−7.35268	−	20.4167i	−0.264972	−	0.735768i
$771$		0			0
$772$	36.2100	−	29.9671i	1.30322	−	1.07854i
$773$	1.06853	+	0.442600i	0.0384324	+	0.0159192i	0.401817	−	0.915720i	$-0.368379\pi$
$773$	1.06853	+	0.442600i	0.0384324	+	0.0159192i	−0.363384	+	0.931639i	$0.618379\pi$
$774$		0			0
$775$	−7.36734	−	7.36734i	−0.264643	−	0.264643i
$776$	−16.4186	−	9.70360i	−0.589394	−	0.348339i
$777$		0			0
$778$	−0.745416	+	15.8386i	−0.0267245	+	0.567842i
$779$	21.5015	−	51.9092i	0.770371	−	1.85984i
$780$		0			0
$781$	−4.47940	+	1.85543i	−0.160285	+	0.0663924i
$782$	9.27277	−	19.7105i	0.331593	−	0.704847i
$783$		0			0
$784$	45.1965	+	8.60383i	1.61416	+	0.307280i
$785$		−	8.05782i		−	0.287596i
$786$		0			0
$787$	−37.7933	+	15.6545i	−1.34719	+	0.558022i	−0.935507	−	0.353307i	$-0.885057\pi$
$787$	−37.7933	+	15.6545i	−1.34719	+	0.558022i	−0.411678	+	0.911329i	$0.635057\pi$
$788$	39.9069	−	12.2853i	1.42163	−	0.437646i
$789$		0			0
$790$	16.0437	+	0.755068i	0.570809	+	0.0268641i
$791$	−24.6437	+	24.6437i	−0.876228	+	0.876228i
$792$		0			0
$793$	0.0228863	+	0.0228863i	0.000812716	+	0.000812716i
$794$	−14.6976	−	16.1493i	−0.521597	−	0.573118i
$795$		0			0
$796$	31.9658	+	3.01551i	1.13300	+	0.106882i
$797$	14.9613	+	36.1198i	0.529956	+	1.27943i	0.931551	+	0.363610i	$0.118456\pi$
$797$	14.9613	+	36.1198i	0.529956	+	1.27943i	−0.401595	+	0.915817i	$0.631544\pi$
$798$		0			0
$799$	−18.5476			−0.656168
$800$	18.9675	+	13.7669i	0.670604	+	0.486734i
$801$		0			0
$802$	−40.6412	+	14.6361i	−1.43509	+	0.516820i
$803$	9.88542	+	23.8655i	0.348849	+	0.842196i
$804$		0			0
$805$	10.5950	+	4.38858i	0.373423	+	0.154677i
$806$	1.35870	+	1.49291i	0.0478583	+	0.0525855i
$807$		0			0
$808$	−4.07466	−	5.42370i	−0.143346	−	0.190805i
$809$	13.7295	−	13.7295i	0.482703	−	0.482703i	−0.423291	−	0.905994i	$-0.639125\pi$
$809$	13.7295	−	13.7295i	0.482703	−	0.482703i	0.905994	+	0.423291i	$0.139125\pi$
$810$		0			0
$811$	0.127753	−	0.308422i	0.00448600	−	0.0108302i	−0.921621	−	0.388092i	$-0.873134\pi$
$811$	0.127753	−	0.308422i	0.00448600	−	0.0108302i	0.926107	+	0.377262i	$0.123134\pi$
$812$	21.9247	+	71.2189i	0.769405	+	2.49929i
$813$		0			0
$814$	41.8975	+	19.7106i	1.46851	+	0.690856i
$815$			13.0147i			0.455886i
$816$		0			0
$817$		−	54.6835i		−	1.91313i
$818$	19.6335	−	41.7336i	0.686469	−	1.45918i
$819$		0			0
$820$	−10.9755	+	20.7386i	−0.383280	+	0.724224i
$821$	1.21500	−	2.93326i	0.0424037	−	0.102372i	−0.901259	−	0.433281i	$-0.857356\pi$
$821$	1.21500	−	2.93326i	0.0424037	−	0.102372i	0.943662	+	0.330910i	$0.107356\pi$
$822$		0			0
$823$	8.94437	−	8.94437i	0.311781	−	0.311781i	−0.533818	−	0.845599i	$-0.679243\pi$
$823$	8.94437	−	8.94437i	0.311781	−	0.311781i	0.845599	+	0.533818i	$0.179243\pi$
$824$	−1.94978	−	7.58487i	−0.0679237	−	0.264232i
$825$		0			0
$826$	−0.237897	+	0.216511i	−0.00827748	+	0.00753337i
$827$	−13.2609	−	5.49285i	−0.461128	−	0.191005i	0.140011	−	0.990150i	$-0.455286\pi$
$827$	−13.2609	−	5.49285i	−0.461128	−	0.191005i	−0.601139	+	0.799145i	$0.705286\pi$
$828$		0			0
$829$	11.9942	+	28.9565i	0.416575	+	1.00570i	0.983332	+	0.181817i	$0.0581978\pi$
$829$	11.9942	+	28.9565i	0.416575	+	1.00570i	−0.566757	+	0.823885i	$0.691802\pi$
$830$	1.16480	+	3.23438i	0.0404307	+	0.112267i
$831$		0			0
$832$	−3.54541	−	2.83708i	−0.122915	−	0.0983581i
$833$	−61.5116			−2.13125
$834$		0			0
$835$	5.40775	+	13.0555i	0.187143	+	0.451803i
$836$	−21.7852	−	26.3235i	−0.753456	−	0.910418i
$837$		0			0
$838$	27.9282	−	25.4176i	0.964765	−	0.878037i
$839$	−11.2535	−	11.2535i	−0.388514	−	0.388514i	0.485643	−	0.874157i	$-0.338586\pi$
$839$	−11.2535	−	11.2535i	−0.388514	−	0.388514i	−0.874157	+	0.485643i	$0.838586\pi$
$840$		0			0
$841$	−32.5480	+	32.5480i	−1.12235	+	1.12235i
$842$	−0.302506	+	6.42764i	−0.0104250	+	0.221511i
$843$		0			0
$844$	2.35369	−	4.44739i	0.0810172	−	0.153085i
$845$	10.8422	−	4.49100i	0.372984	−	0.154495i
$846$		0			0
$847$			16.5663i			0.569226i
$848$	−28.9701	−	19.0140i	−0.994837	−	0.652942i
$849$		0			0
$850$	−28.3537	−	13.3390i	−0.972525	−	0.457522i
$851$	−22.6066	+	9.36397i	−0.774945	+	0.320993i
$852$		0			0
$853$	−0.298105	+	0.719690i	−0.0102069	+	0.0246417i	−0.928901	−	0.370329i	$-0.879245\pi$
$853$	−0.298105	+	0.719690i	−0.0102069	+	0.0246417i	0.918694	+	0.394970i	$0.129245\pi$
$854$	0.346490	+	0.0163069i	0.0118567	+	0.000558012i
$855$		0			0
$856$	16.0135	−	12.0304i	0.547329	−	0.411191i
$857$	7.55324	+	7.55324i	0.258014	+	0.258014i	0.824246	−	0.566232i	$-0.191599\pi$
$857$	7.55324	+	7.55324i	0.258014	+	0.258014i	−0.566232	+	0.824246i	$0.691599\pi$
$858$		0			0
$859$	−42.2997	−	17.5211i	−1.44325	−	0.597812i	−0.482663	−	0.875806i	$-0.660330\pi$
$859$	−42.2997	−	17.5211i	−1.44325	−	0.597812i	−0.960583	+	0.277994i	$0.910330\pi$
$860$	−2.14475	+	22.7354i	−0.0731353	+	0.775269i
$861$		0			0
$862$	38.2054	−	13.7589i	1.30128	−	0.468630i
$863$	24.1788			0.823056			0.411528	−	0.911397i	$-0.364995\pi$
$863$	24.1788			0.823056			0.411528	+	0.911397i	$0.364995\pi$
$864$		0			0
$865$	−1.23855			−0.0421120
$866$	−8.33813	+	3.00281i	−0.283341	+	0.102040i
$867$		0			0
$868$	21.5384	+	2.03183i	0.731061	+	0.0689649i
$869$	−43.6828	−	18.0940i	−1.48184	−	0.613797i
$870$		0			0
$871$	−2.80382	−	2.80382i	−0.0950038	−	0.0950038i
$872$	4.24794	+	0.603331i	0.143853	+	0.0204314i
$873$		0			0
$874$	18.0372	+	0.848889i	0.610118	+	0.0287141i
$875$	13.9317	−	33.6340i	0.470976	−	1.13704i
$876$		0			0
$877$	−1.19559	+	0.495231i	−0.0403723	+	0.0167228i	−0.402778	−	0.915298i	$-0.631955\pi$
$877$	−1.19559	+	0.495231i	−0.0403723	+	0.0167228i	0.362406	+	0.932020i	$0.381955\pi$
$878$	0.595544	+	0.280172i	0.0200986	+	0.00945535i
$879$		0			0
$880$	8.02502	+	11.7988i	0.270524	+	0.397737i
$881$		−	11.6547i		−	0.392658i	−0.980538	−	0.196329i	$-0.937098\pi$
$881$		−	11.6547i		−	0.392658i	0.980538	−	0.196329i	$-0.0629020\pi$
$882$		0			0
$883$	28.1083	−	11.6428i	0.945919	−	0.391813i	0.144224	−	0.989545i	$-0.453932\pi$
$883$	28.1083	−	11.6428i	0.945919	−	0.391813i	0.801696	+	0.597733i	$0.203932\pi$
$884$	5.36583	+	2.83975i	0.180472	+	0.0955111i
$885$		0			0
$886$	1.85599	−	39.4360i	0.0623531	−	1.32488i
$887$	23.8571	−	23.8571i	0.801044	−	0.801044i	−0.182215	−	0.983259i	$-0.558327\pi$
$887$	23.8571	−	23.8571i	0.801044	−	0.801044i	0.983259	+	0.182215i	$0.0583267\pi$
$888$		0			0
$889$	31.1200	+	31.1200i	1.04373	+	1.04373i
$890$	5.84354	−	5.31823i	0.195876	−	0.178267i
$891$		0			0
$892$	43.1208	−	35.6865i	1.44379	−	1.19487i
$893$	−5.88390	−	14.2050i	−0.196897	−	0.475352i
$894$		0			0
$895$	−6.05786			−0.202492
$896$	−48.5667	+	3.08811i	−1.62250	+	0.103167i
$897$		0			0
$898$	12.3306	+	34.2394i	0.411479	+	1.14258i
$899$	8.33593	+	20.1247i	0.278019	+	0.671197i
$900$		0			0
$901$	42.8028	+	17.7295i	1.42597	+	0.590655i
$902$	51.0842	−	46.4919i	1.70092	−	1.54801i
$903$		0			0
$904$	11.6600	−	19.7289i	0.387806	−	0.656172i
$905$	0.422274	−	0.422274i	0.0140369	−	0.0140369i
$906$		0			0
$907$	4.40910	−	10.6445i	0.146402	−	0.353445i	−0.833619	−	0.552340i	$-0.813735\pi$
$907$	4.40910	−	10.6445i	0.146402	−	0.353445i	0.980021	+	0.198895i	$0.0637352\pi$
$908$	44.4562	+	23.5275i	1.47533	+	0.780787i
$909$		0			0
$910$	−1.36058	+	2.89209i	−0.0451027	+	0.0958719i
$911$			23.0572i			0.763918i	0.924179	+	0.381959i	$0.124750\pi$
$911$			23.0572i			0.763918i	−0.924179	+	0.381959i	$0.875250\pi$
$912$		0			0
$913$		−	10.1200i		−	0.334924i
$914$	−53.4830	−	25.1609i	−1.76906	−	0.832250i
$915$		0			0
$916$	−27.6776	+	8.52051i	−0.914493	+	0.281526i
$917$	29.4598	−	71.1221i	0.972847	−	2.34866i
$918$		0			0
$919$	−22.7215	+	22.7215i	−0.749514	+	0.749514i	−0.974388	−	0.224874i	$-0.927803\pi$
$919$	−22.7215	+	22.7215i	−0.749514	+	0.749514i	0.224874	+	0.974388i	$0.427803\pi$
$920$	−7.46590	−	1.06038i	−0.246144	−	0.0349596i
$921$		0			0
$922$	−31.6447	−	34.7704i	−1.04216	−	1.14510i
$923$	0.659750	+	0.273278i	0.0217160	+	0.00899504i
$924$		0			0
$925$	13.4702	+	32.5198i	0.442896	+	1.06925i
$926$	−45.6128	+	16.4265i	−1.49893	+	0.539809i
$927$		0			0
$928$	−25.6221	−	41.7668i	−0.841087	−	1.37106i
$929$	14.6491			0.480622			0.240311	−	0.970696i	$-0.422750\pi$
$929$	14.6491			0.480622			0.240311	+	0.970696i	$0.422750\pi$
$930$		0			0
$931$	−19.5134	−	47.1096i	−0.639527	−	1.54395i
$932$	1.56652	−	16.6059i	0.0513131	−	0.543944i
$933$		0			0
$934$	22.3830	+	24.5938i	0.732393	+	0.804735i
$935$	−13.4899	−	13.4899i	−0.441167	−	0.441167i
$936$		0			0
$937$	−14.4649	+	14.4649i	−0.472547	+	0.472547i	−0.902738	−	0.430191i	$-0.858446\pi$
$937$	−14.4649	+	14.4649i	−0.472547	+	0.472547i	0.430191	+	0.902738i	$0.358446\pi$
$938$	−42.4488	−	1.99778i	−1.38600	−	0.0652298i
$939$		0			0
$940$	1.88917	+	6.13668i	0.0616179	+	0.200156i
$941$	21.4888	−	8.90093i	0.700513	−	0.290162i	−0.00385932	−	0.999993i	$-0.501228\pi$
$941$	21.4888	−	8.90093i	0.700513	−	0.290162i	0.704373	+	0.709830i	$0.251228\pi$
$942$		0			0
$943$			36.5028i			1.18869i
$944$	0.116060	−	0.176832i	0.00377744	−	0.00575539i
$945$		0			0
$946$	28.6175	−	60.8304i	0.930436	−	1.97777i
$947$	−17.4353	+	7.22193i	−0.566570	+	0.234681i	−0.647535	−	0.762036i	$-0.724200\pi$
$947$	−17.4353	+	7.22193i	−0.566570	+	0.234681i	0.0809646	+	0.996717i	$0.474200\pi$
$948$		0			0
$949$	1.45598	−	3.51505i	0.0472631	−	0.114103i
$950$	1.22113	−	25.9467i	0.0396188	−	0.841821i
$951$		0			0
$952$	63.0147	−	16.1986i	2.04232	−	0.525001i
$953$	−16.1053	−	16.1053i	−0.521702	−	0.521702i	0.396383	−	0.918085i	$-0.370265\pi$
$953$	−16.1053	−	16.1053i	−0.521702	−	0.521702i	−0.918085	+	0.396383i	$0.870265\pi$
$954$		0			0
$955$	11.0351	+	4.57089i	0.357087	+	0.147910i
$956$	−7.74043	−	9.35294i	−0.250343	−	0.302496i
$957$		0			0
$958$	7.73531	+	21.4792i	0.249917	+	0.693962i
$959$	−56.2696			−1.81704
$960$		0			0
$961$	−24.6760			−0.795999
$962$	−2.31069	−	6.41627i	−0.0744997	−	0.206869i
$963$		0			0
$964$	1.72318	+	2.08216i	0.0554999	+	0.0670619i
$965$	20.0983	+	8.32501i	0.646989	+	0.267991i
$966$		0			0
$967$	25.2649	+	25.2649i	0.812466	+	0.812466i	0.985003	−	0.172537i	$-0.0551966\pi$
$967$	25.2649	+	25.2649i	0.812466	+	0.812466i	−0.172537	+	0.985003i	$0.555197\pi$
$968$	−2.71209	−	10.5504i	−0.0871698	−	0.339101i
$969$		0			0
$970$	0.414973	−	8.81734i	0.0133240	−	0.283108i
$971$	−9.38116	+	22.6481i	−0.301056	+	0.726813i	0.698877	+	0.715242i	$0.253683\pi$
$971$	−9.38116	+	22.6481i	−0.301056	+	0.726813i	−0.999933	+	0.0115714i	$0.996317\pi$
$972$		0			0
$973$	−2.49207	+	1.03225i	−0.0798921	+	0.0330924i
$974$	−13.3353	+	28.3460i	−0.427290	+	0.908263i
$975$		0			0
$976$	−0.223333	+	0.0463390i	−0.00714873	+	0.00148328i
$977$			8.85414i			0.283269i	0.989919	+	0.141634i	$0.0452358\pi$
$977$			8.85414i			0.283269i	−0.989919	+	0.141634i	$0.954764\pi$
$978$		0			0
$979$	−21.4894	+	8.90119i	−0.686803	+	0.284483i
$980$	6.26526	+	20.3517i	0.200137	+	0.650113i
$981$		0			0
$982$	6.75566	+	0.317943i	0.215582	+	0.0101460i
$983$	22.2597	−	22.2597i	0.709974	−	0.709974i	−0.256556	−	0.966529i	$-0.582588\pi$
$983$	22.2597	−	22.2597i	0.709974	−	0.709974i	0.966529	+	0.256556i	$0.0825877\pi$
$984$		0			0
$985$	13.6654	+	13.6654i	0.435417	+	0.435417i
$986$	44.0943	+	48.4498i	1.40425	+	1.54295i
$987$		0			0
$988$	−0.472654	+	5.01036i	−0.0150371	+	0.159401i
$989$	13.5954	+	32.8222i	0.432309	+	1.04369i
$990$		0			0
$991$	−44.3860			−1.40997			−0.704984	−	0.709224i	$-0.749046\pi$
$991$	−44.3860			−1.40997			−0.704984	+	0.709224i	$0.749046\pi$
$992$	−14.0495	+	2.23208i	−0.446071	+	0.0708687i
$993$		0			0
$994$	7.20054	−	2.59313i	0.228387	−	0.0822491i
$995$	5.68693	+	13.7295i	0.180288	+	0.435253i
$996$		0			0
$997$	−33.3914	−	13.8312i	−1.05752	−	0.438037i	−0.214946	−	0.976626i	$-0.568958\pi$
$997$	−33.3914	−	13.8312i	−1.05752	−	0.438037i	−0.842569	+	0.538589i	$0.818958\pi$
$998$	−2.25512	−	2.47787i	−0.0713847	−	0.0784357i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.325.12	yes	128
3.2	odd	2	inner	864.2.v.b.325.21	yes	128
32.13	even	8	inner	864.2.v.b.109.12	✓	128
96.77	odd	8	inner	864.2.v.b.109.21	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.12	✓	128	32.13	even	8	inner
864.2.v.b.109.21	yes	128	96.77	odd	8	inner
864.2.v.b.325.12	yes	128	1.1	even	1	trivial
864.2.v.b.325.21	yes	128	3.2	odd	2	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.479175 - 1.33056i) q^{2} +(-1.54078 + 1.27514i) q^{4} +(-0.855212 - 0.354240i) q^{5} +(-3.04155 - 3.04155i) q^{7} +(2.43496 + 1.43909i) q^{8} +O(q^{10})\)	\(q+(-0.479175 - 1.33056i) q^{2} +(-1.54078 + 1.27514i) q^{4} +(-0.855212 - 0.354240i) q^{5} +(-3.04155 - 3.04155i) q^{7} +(2.43496 + 1.43909i) q^{8} +(-0.0615424 + 1.30765i) q^{10} +(1.47477 - 3.56040i) q^{11} +(-0.524396 + 0.217212i) q^{13} +(-2.58953 + 5.50440i) q^{14} +(0.748026 - 3.92943i) q^{16} +5.34789i q^{17} +(-4.09576 + 1.69652i) q^{19} +(1.76940 - 0.544709i) q^{20} +(-5.44400 - 0.256212i) q^{22} +(2.03658 - 2.03658i) q^{23} +(-2.92963 - 2.92963i) q^{25} +(0.540290 + 0.593658i) q^{26} +(8.56477 + 0.807961i) q^{28} +(3.31480 + 8.00262i) q^{29} +2.51477 q^{31} +(-5.58679 + 0.887591i) q^{32} +(7.11569 - 2.56257i) q^{34} +(1.52373 + 3.67861i) q^{35} +(-7.84910 - 3.25120i) q^{37} +(4.21990 + 4.63673i) q^{38} +(-1.57262 - 2.09329i) q^{40} +(-8.96180 + 8.96180i) q^{41} +(-4.72038 + 11.3960i) q^{43} +(2.26772 + 7.36634i) q^{44} +(-3.68566 - 1.73391i) q^{46} +3.46822i q^{47} +11.5020i q^{49} +(-2.49425 + 5.30186i) q^{50} +(0.531004 - 1.00335i) q^{52} +(3.31524 - 8.00369i) q^{53} +(-2.52248 + 2.52248i) q^{55} +(-3.02898 - 11.7831i) q^{56} +(9.05961 - 8.24519i) q^{58} +(0.0488541 + 0.0202360i) q^{59} +(-0.0218216 - 0.0526820i) q^{61} +(-1.20501 - 3.34605i) q^{62} +(3.85804 + 7.00825i) q^{64} +0.525415 q^{65} +(2.67338 + 6.45412i) q^{67} +(-6.81931 - 8.23993i) q^{68} +(4.16448 - 3.79011i) q^{70} +(-0.889622 - 0.889622i) q^{71} +(-4.73977 + 4.73977i) q^{73} +(-0.564834 + 12.0016i) q^{74} +(4.14737 - 7.83664i) q^{76} +(-15.3147 + 6.34356i) q^{77} -12.2691i q^{79} +(-2.03169 + 3.09552i) q^{80} +(16.2185 + 7.62995i) q^{82} +(2.42613 - 1.00493i) q^{83} +(1.89444 - 4.57358i) q^{85} +(17.4250 + 0.820074i) q^{86} +(8.71473 - 6.54710i) q^{88} +(-4.26786 - 4.26786i) q^{89} +(2.25563 + 0.934314i) q^{91} +(-0.540999 + 5.73485i) q^{92} +(4.61467 - 1.66188i) q^{94} +4.10372 q^{95} -6.74287 q^{97} +(15.3042 - 5.51149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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