LMFDB - Embedded newform 460.2.s.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	460.29
Dual form			460.2.s.a.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.244021 + 0.831059i) q^{3} +(-1.24767 + 1.85562i) q^{5} +(-3.43041 - 0.493219i) q^{7} +(1.89265 + 1.21633i) q^{9} +O(q^{10})$	\(q+(-0.244021 + 0.831059i) q^{3} +(-1.24767 + 1.85562i) q^{5} +(-3.43041 - 0.493219i) q^{7} +(1.89265 + 1.21633i) q^{9} +(-1.52714 - 3.34398i) q^{11} +(-2.38038 + 0.342247i) q^{13} +(-1.23767 - 1.48970i) q^{15} +(-1.63645 - 1.41799i) q^{17} +(-1.66143 - 1.91739i) q^{19} +(1.24699 - 2.73052i) q^{21} +(-4.72651 + 0.812440i) q^{23} +(-1.88664 - 4.63040i) q^{25} +(-3.43645 + 2.97770i) q^{27} +(-0.935897 + 1.08008i) q^{29} +(5.66634 - 1.66379i) q^{31} +(3.15169 - 0.453145i) q^{33} +(5.19525 - 5.75016i) q^{35} +(-5.75433 + 8.95391i) q^{37} +(0.296435 - 2.06175i) q^{39} +(-6.34046 + 4.07476i) q^{41} +(2.18560 - 7.44347i) q^{43} +(-4.61845 + 1.99445i) q^{45} +5.65346i q^{47} +(4.80801 + 1.41176i) q^{49} +(1.57777 - 1.01397i) q^{51} +(10.1842 + 1.46427i) q^{53} +(8.11051 + 1.33839i) q^{55} +(1.99889 - 0.912863i) q^{57} +(1.07878 + 7.50307i) q^{59} +(-12.0915 + 3.55039i) q^{61} +(-5.89264 - 5.10601i) q^{63} +(2.33485 - 4.84409i) q^{65} +(-10.3260 - 4.71572i) q^{67} +(0.478182 - 4.12626i) q^{69} +(-2.91461 + 6.38210i) q^{71} +(8.81110 - 7.63486i) q^{73} +(4.30851 - 0.437993i) q^{75} +(3.58942 + 12.2244i) q^{77} +(-0.176811 - 1.22975i) q^{79} +(1.16772 + 2.55694i) q^{81} +(-3.28103 + 5.10538i) q^{83} +(4.67301 - 1.26744i) q^{85} +(-0.669234 - 1.04135i) q^{87} +(3.85654 + 1.13238i) q^{89} +8.33448 q^{91} +5.11506i q^{93} +(5.63087 - 0.690707i) q^{95} +(1.80905 + 2.81494i) q^{97} +(1.17704 - 8.18648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{11}\right)$

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
$3$	−0.244021	+	0.831059i	−0.140886	+	0.479812i	−0.999459	−	0.0328779i	$-0.989533\pi$
$3$	−0.244021	+	0.831059i	−0.140886	+	0.479812i	0.858574	+	0.512690i	$0.171351\pi$
$4$		0			0
$5$	−1.24767	+	1.85562i	−0.557975	+	0.829858i
$5$	−1.24767	+	1.85562i	−0.557975	+	0.829858i
$6$		0			0
$7$	−3.43041	−	0.493219i	−1.29657	−	0.186419i	−0.540744	−	0.841187i	$-0.681857\pi$
$7$	−3.43041	−	0.493219i	−1.29657	−	0.186419i	−0.755830	+	0.654768i	$0.772766\pi$
$8$		0			0
$9$	1.89265	+	1.21633i	0.630883	+	0.405444i
$10$		0			0
$11$	−1.52714	−	3.34398i	−0.460451	−	1.00825i	−0.987385	−	0.158340i	$-0.949386\pi$
$11$	−1.52714	−	3.34398i	−0.460451	−	1.00825i	0.526934	−	0.849906i	$-0.323342\pi$
$12$		0			0
$13$	−2.38038	+	0.342247i	−0.660199	+	0.0949222i	−0.464267	−	0.885695i	$-0.653682\pi$
$13$	−2.38038	+	0.342247i	−0.660199	+	0.0949222i	−0.195932	+	0.980618i	$0.562773\pi$
$14$		0			0
$15$	−1.23767	−	1.48970i	−0.319565	−	0.384638i
$16$		0			0
$17$	−1.63645	−	1.41799i	−0.396898	−	0.343914i	0.433432	−	0.901186i	$-0.357303\pi$
$17$	−1.63645	−	1.41799i	−0.396898	−	0.343914i	−0.830330	+	0.557272i	$0.811848\pi$
$18$		0			0
$19$	−1.66143	−	1.91739i	−0.381158	−	0.439880i	0.532459	−	0.846456i	$-0.321268\pi$
$19$	−1.66143	−	1.91739i	−0.381158	−	0.439880i	−0.913617	+	0.406576i	$0.866723\pi$
$20$		0			0
$21$	1.24699	−	2.73052i	0.272115	−	0.595848i
$22$		0			0
$23$	−4.72651	+	0.812440i	−0.985546	+	0.169406i
$23$	−4.72651	+	0.812440i	−0.985546	+	0.169406i
$24$		0			0
$25$	−1.88664	−	4.63040i	−0.377328	−	0.926080i
$26$		0			0
$27$	−3.43645	+	2.97770i	−0.661345	+	0.573059i
$28$		0			0
$29$	−0.935897	+	1.08008i	−0.173792	+	0.200566i	−0.835962	−	0.548787i	$-0.815090\pi$
$29$	−0.935897	+	1.08008i	−0.173792	+	0.200566i	0.662171	+	0.749353i	$0.269635\pi$
$30$		0			0
$31$	5.66634	−	1.66379i	1.01770	−	0.298825i	0.270003	−	0.962860i	$-0.412975\pi$
$31$	5.66634	−	1.66379i	1.01770	−	0.298825i	0.747702	+	0.664034i	$0.231157\pi$
$32$		0			0
$33$	3.15169	−	0.453145i	0.548640	−	0.0788825i
$34$		0			0
$35$	5.19525	−	5.75016i	0.878157	−	0.971954i
$36$		0			0
$37$	−5.75433	+	8.95391i	−0.946006	+	1.47201i	−0.0655697	+	0.997848i	$0.520886\pi$
$37$	−5.75433	+	8.95391i	−0.946006	+	1.47201i	−0.880436	+	0.474165i	$0.842750\pi$
$38$		0			0
$39$	0.296435	−	2.06175i	0.0474676	−	0.330144i
$40$		0			0
$41$	−6.34046	+	4.07476i	−0.990213	+	0.636371i	−0.932200	−	0.361945i	$-0.882113\pi$
$41$	−6.34046	+	4.07476i	−0.990213	+	0.636371i	−0.0580133	+	0.998316i	$0.518477\pi$
$42$		0			0
$43$	2.18560	−	7.44347i	0.333301	−	1.13512i	−0.606980	−	0.794717i	$-0.707619\pi$
$43$	2.18560	−	7.44347i	0.333301	−	1.13512i	0.940280	−	0.340401i	$-0.110563\pi$
$44$		0			0
$45$	−4.61845	+	1.99445i	−0.688477	+	0.297315i
$46$		0			0
$47$			5.65346i			0.824642i	0.911039	+	0.412321i	$0.135282\pi$
$47$			5.65346i			0.824642i	−0.911039	+	0.412321i	$0.864718\pi$
$48$		0			0
$49$	4.80801	+	1.41176i	0.686858	+	0.201680i
$50$		0			0
$51$	1.57777	−	1.01397i	0.220931	−	0.141984i
$52$		0			0
$53$	10.1842	+	1.46427i	1.39891	+	0.201133i	0.800151	−	0.599798i	$-0.204753\pi$
$53$	10.1842	+	1.46427i	1.39891	+	0.201133i	0.598757	+	0.800931i	$0.295662\pi$
$54$		0			0
$55$	8.11051	+	1.33839i	1.09362	+	0.180468i
$56$		0			0
$57$	1.99889	−	0.912863i	0.264760	−	0.120912i
$58$		0			0
$59$	1.07878	+	7.50307i	0.140445	+	0.976817i	0.931154	+	0.364625i	$0.118803\pi$
$59$	1.07878	+	7.50307i	0.140445	+	0.976817i	−0.790709	+	0.612192i	$0.790288\pi$
$60$		0			0
$61$	−12.0915	+	3.55039i	−1.54816	+	0.454581i	−0.940551	−	0.339653i	$-0.889690\pi$
$61$	−12.0915	+	3.55039i	−1.54816	+	0.454581i	−0.607611	+	0.794235i	$0.707872\pi$
$62$		0			0
$63$	−5.89264	−	5.10601i	−0.742403	−	0.643296i
$64$		0			0
$65$	2.33485	−	4.84409i	0.289602	−	0.600835i
$66$		0			0
$67$	−10.3260	−	4.71572i	−1.26152	−	0.576116i	−0.331440	−	0.943476i	$-0.607535\pi$
$67$	−10.3260	−	4.71572i	−1.26152	−	0.576116i	−0.930079	+	0.367360i	$0.880262\pi$
$68$		0			0
$69$	0.478182	−	4.12626i	0.0575664	−	0.496744i
$70$		0			0
$71$	−2.91461	+	6.38210i	−0.345900	+	0.757415i	0.654099	+	0.756409i	$0.273048\pi$
$71$	−2.91461	+	6.38210i	−0.345900	+	0.757415i	−0.999999	+	0.00100688i	$0.999680\pi$
$72$		0			0
$73$	8.81110	−	7.63486i	1.03126	−	0.893593i	0.0368657	−	0.999320i	$-0.488263\pi$
$73$	8.81110	−	7.63486i	1.03126	−	0.893593i	0.994395	+	0.105728i	$0.0337172\pi$
$74$		0			0
$75$	4.30851	−	0.437993i	0.497504	−	0.0505750i
$76$		0			0
$77$	3.58942	+	12.2244i	0.409052	+	1.39310i
$78$		0			0
$79$	−0.176811	−	1.22975i	−0.0198928	−	0.138357i	0.977455	−	0.211146i	$-0.0677194\pi$
$79$	−0.176811	−	1.22975i	−0.0198928	−	0.138357i	−0.997347	+	0.0727882i	$0.976810\pi$
$80$		0			0
$81$	1.16772	+	2.55694i	0.129746	+	0.284105i
$82$		0			0
$83$	−3.28103	+	5.10538i	−0.360140	+	0.560388i	−0.973290	−	0.229578i	$-0.926265\pi$
$83$	−3.28103	+	5.10538i	−0.360140	+	0.560388i	0.613151	+	0.789966i	$0.289902\pi$
$84$		0			0
$85$	4.67301	−	1.26744i	0.506859	−	0.137473i
$86$		0			0
$87$	−0.669234	−	1.04135i	−0.0717494	−	0.111644i
$88$		0			0
$89$	3.85654	+	1.13238i	0.408793	+	0.120032i	0.479662	−	0.877453i	$-0.340759\pi$
$89$	3.85654	+	1.13238i	0.408793	+	0.120032i	−0.0708696	+	0.997486i	$0.522577\pi$
$90$		0			0
$91$	8.33448			0.873691
$92$		0			0
$93$			5.11506i			0.530407i
$94$		0			0
$95$	5.63087	−	0.690707i	0.577715	−	0.0708650i
$96$		0			0
$97$	1.80905	+	2.81494i	0.183682	+	0.285814i	0.920867	−	0.389876i	$-0.127482\pi$
$97$	1.80905	+	2.81494i	0.183682	+	0.285814i	−0.737186	+	0.675690i	$0.763846\pi$
$98$		0			0
$99$	1.17704	−	8.18648i	0.118297	−	0.822772i
$100$		0			0
$101$	8.74858	+	5.62237i	0.870516	+	0.559447i	0.897911	−	0.440178i	$-0.145085\pi$
$101$	8.74858	+	5.62237i	0.870516	+	0.559447i	−0.0273944	+	0.999625i	$0.508721\pi$
$102$		0			0
$103$	9.07669	−	4.14519i	0.894353	−	0.408437i	0.0854246	−	0.996345i	$-0.472775\pi$
$103$	9.07669	−	4.14519i	0.894353	−	0.408437i	0.808928	+	0.587907i	$0.200048\pi$
$104$		0			0
$105$	3.51097	+	5.72072i	0.342636	+	0.558285i
$106$		0			0
$107$	−1.35251	−	4.60622i	−0.130752	−	0.445300i	0.867927	−	0.496692i	$-0.165452\pi$
$107$	−1.35251	−	4.60622i	−0.130752	−	0.445300i	−0.998679	+	0.0513925i	$0.983634\pi$
$108$		0			0
$109$	−6.65576	+	7.68115i	−0.637506	+	0.735721i	−0.978932	−	0.204188i	$-0.934545\pi$
$109$	−6.65576	+	7.68115i	−0.637506	+	0.735721i	0.341426	+	0.939909i	$0.389090\pi$
$110$		0			0
$111$	−6.03705	−	6.96713i	−0.573011	−	0.661290i
$112$		0			0
$113$	14.2028	+	6.48621i	1.33609	+	0.610171i	0.949988	−	0.312286i	$-0.101095\pi$
$113$	14.2028	+	6.48621i	1.33609	+	0.610171i	0.386100	+	0.922457i	$0.373822\pi$
$114$		0			0
$115$	4.38955	−	9.78426i	0.409328	−	0.912387i
$116$		0			0
$117$	−4.92151	−	2.24758i	−0.454993	−	0.207789i
$118$		0			0
$119$	4.91433	+	5.67143i	0.450496	+	0.519900i
$120$		0			0
$121$	−1.64654	+	1.90021i	−0.149685	+	0.172746i
$122$		0			0
$123$	−1.83916	−	6.26362i	−0.165832	−	0.564772i
$124$		0			0
$125$	10.9462	+	2.27633i	0.979054	+	0.203601i
$126$		0			0
$127$	−0.147945	+	0.0675642i	−0.0131280	+	0.00599535i	−0.421968	−	0.906611i	$-0.638661\pi$
$127$	−0.147945	+	0.0675642i	−0.0131280	+	0.00599535i	0.408840	+	0.912606i	$0.365933\pi$
$128$		0			0
$129$	5.65263	+	3.63272i	0.497686	+	0.319843i
$130$		0			0
$131$	−1.33780	+	9.30458i	−0.116884	+	0.812945i	0.844069	+	0.536234i	$0.180154\pi$
$131$	−1.33780	+	9.30458i	−0.116884	+	0.812945i	−0.960953	+	0.276711i	$0.910756\pi$
$132$		0			0
$133$	4.75370	+	7.39690i	0.412198	+	0.641392i
$134$		0			0
$135$	−1.23792	−	10.0919i	−0.106543	−	0.868575i
$136$		0			0
$137$		−	2.13033i		−	0.182006i	−0.995851	−	0.0910032i	$-0.970993\pi$
$137$		−	2.13033i		−	0.182006i	0.995851	−	0.0910032i	$-0.0290074\pi$
$138$		0			0
$139$	−18.6125			−1.57869			−0.789344	−	0.613951i	$-0.789579\pi$
$139$	−18.6125			−1.57869			−0.789344	+	0.613951i	$0.789579\pi$
$140$		0			0
$141$	−4.69836	−	1.37956i	−0.395673	−	0.116180i
$142$		0			0
$143$	4.77964	+	7.43727i	0.399694	+	0.621936i
$144$		0			0
$145$	−0.836530	−	3.08425i	−0.0694700	−	0.256133i
$146$		0			0
$147$	−2.34651	+	3.65124i	−0.193537	+	0.301149i
$148$		0			0
$149$	−9.22584	−	20.2018i	−0.755810	−	1.65499i	−0.755634	−	0.654994i	$-0.772671\pi$
$149$	−9.22584	−	20.2018i	−0.755810	−	1.65499i	−0.000176361	−	1.00000i	$-0.500056\pi$
$150$		0			0
$151$	−1.56591	−	10.8912i	−0.127432	−	0.886311i	−0.948792	−	0.315901i	$-0.897693\pi$
$151$	−1.56591	−	10.8912i	−0.127432	−	0.886311i	0.821360	−	0.570410i	$-0.193216\pi$
$152$		0			0
$153$	−1.37248	−	4.67423i	−0.110958	−	0.377889i
$154$		0			0
$155$	−3.98237	+	12.5904i	−0.319872	+	1.01129i
$156$		0			0
$157$	−7.89229	+	6.83870i	−0.629873	+	0.545788i	−0.910228	−	0.414109i	$-0.864093\pi$
$157$	−7.89229	+	6.83870i	−0.629873	+	0.545788i	0.280355	+	0.959897i	$0.409548\pi$
$158$		0			0
$159$	−3.70205	+	8.10636i	−0.293592	+	0.642876i
$160$		0			0
$161$	16.6146	−	0.455800i	1.30941	−	0.0359221i
$162$		0			0
$163$	−16.3175	−	7.45196i	−1.27809	−	0.583682i	−0.343411	−	0.939185i	$-0.611582\pi$
$163$	−16.3175	−	7.45196i	−1.27809	−	0.583682i	−0.934675	+	0.355503i	$0.884310\pi$
$164$		0			0
$165$	−3.09141	+	6.41372i	−0.240666	+	0.499307i
$166$		0			0
$167$	10.8754	+	9.42359i	0.841564	+	0.729219i	0.964751	−	0.263164i	$-0.0847661\pi$
$167$	10.8754	+	9.42359i	0.841564	+	0.729219i	−0.123187	+	0.992383i	$0.539312\pi$
$168$		0			0
$169$	−6.92433	+	2.03317i	−0.532641	+	0.156398i
$170$		0			0
$171$	−0.812319	−	5.64980i	−0.0621196	−	0.432051i
$172$		0			0
$173$	−0.537965	+	0.245680i	−0.0409007	+	0.0186787i	−0.435760	−	0.900063i	$-0.643520\pi$
$173$	−0.537965	+	0.245680i	−0.0409007	+	0.0186787i	0.394860	+	0.918741i	$0.370793\pi$
$174$		0			0
$175$	4.18814	+	16.8147i	0.316594	+	1.27107i
$176$		0			0
$177$	−6.49874	−	0.934377i	−0.488475	−	0.0702321i
$178$		0			0
$179$	5.83725	−	3.75137i	0.436297	−	0.280391i	−0.303999	−	0.952672i	$-0.598322\pi$
$179$	5.83725	−	3.75137i	0.436297	−	0.280391i	0.740296	+	0.672281i	$0.234686\pi$
$180$		0			0
$181$	9.25242	+	2.71676i	0.687727	+	0.201935i	0.606882	−	0.794792i	$-0.292420\pi$
$181$	9.25242	+	2.71676i	0.687727	+	0.201935i	0.0808449	+	0.996727i	$0.474238\pi$
$182$		0			0
$183$		−	10.9151i		−	0.806871i
$184$		0			0
$185$	−9.43553	−	21.8494i	−0.693714	−	1.60640i
$186$		0			0
$187$	−2.24264	+	7.63774i	−0.163998	+	0.558527i
$188$		0			0
$189$	13.2571	−	8.51982i	0.964312	−	0.619726i
$190$		0			0
$191$	3.06025	−	21.2845i	0.221432	−	1.54009i	−0.511195	−	0.859465i	$-0.670797\pi$
$191$	3.06025	−	21.2845i	0.221432	−	1.54009i	0.732627	−	0.680630i	$-0.238294\pi$
$192$		0			0
$193$	−3.89796	+	6.06534i	−0.280581	+	0.436593i	−0.952728	−	0.303825i	$-0.901736\pi$
$193$	−3.89796	+	6.06534i	−0.280581	+	0.436593i	0.672147	+	0.740418i	$0.265372\pi$
$194$		0			0
$195$	3.45597	+	3.12246i	0.247487	+	0.223604i
$196$		0			0
$197$	−6.81727	+	0.980175i	−0.485710	+	0.0698346i	−0.380820	−	0.924649i	$-0.624358\pi$
$197$	−6.81727	+	0.980175i	−0.485710	+	0.0698346i	−0.104890	+	0.994484i	$0.533449\pi$
$198$		0			0
$199$	−1.96927	+	0.578228i	−0.139598	+	0.0409895i	−0.350785	−	0.936456i	$-0.614085\pi$
$199$	−1.96927	+	0.578228i	−0.139598	+	0.0409895i	0.211187	+	0.977446i	$0.432267\pi$
$200$		0			0
$201$	6.43879	−	7.43076i	0.454157	−	0.524126i
$202$		0			0
$203$	3.74323	−	3.24353i	0.262723	−	0.227651i
$204$		0			0
$205$	0.349593	−	16.8494i	0.0244166	−	1.17682i
$206$		0			0
$207$	−9.93382	−	4.21134i	−0.690449	−	0.292709i
$208$		0			0
$209$	−3.87447	+	8.48392i	−0.268003	+	0.586845i
$210$		0			0
$211$	5.89505	+	6.80325i	0.405832	+	0.468355i	0.921469	−	0.388452i	$-0.126990\pi$
$211$	5.89505	+	6.80325i	0.405832	+	0.468355i	−0.515637	+	0.856807i	$0.672445\pi$
$212$		0			0
$213$	−4.59267	−	3.97957i	−0.314685	−	0.272676i
$214$		0			0
$215$	11.0853	+	13.3426i	0.756013	+	0.909960i
$216$		0			0
$217$	−20.2585	+	2.91273i	−1.37524	+	0.197729i
$218$		0			0
$219$	4.19493	+	9.18560i	0.283467	+	0.620706i
$220$		0			0
$221$	4.38068	+	2.81529i	0.294677	+	0.189377i
$222$		0			0
$223$	−7.34424	−	1.05594i	−0.491807	−	0.0707111i	−0.108050	−	0.994145i	$-0.534461\pi$
$223$	−7.34424	−	1.05594i	−0.491807	−	0.0707111i	−0.383756	+	0.923434i	$0.625370\pi$
$224$		0			0
$225$	2.06136	−	11.0585i	0.137424	−	0.737233i
$226$		0			0
$227$	−3.85853	+	13.1409i	−0.256099	+	0.872195i	0.726612	+	0.687048i	$0.241094\pi$
$227$	−3.85853	+	13.1409i	−0.256099	+	0.872195i	−0.982711	+	0.185146i	$0.940724\pi$
$228$		0			0
$229$	−18.7739			−1.24062			−0.620308	−	0.784358i	$-0.712992\pi$
$229$	−18.7739			−1.24062			−0.620308	+	0.784358i	$0.712992\pi$
$230$		0			0
$231$	−11.0351			−0.726057
$232$		0			0
$233$	4.73766	−	16.1350i	0.310375	−	1.05704i	−0.645621	−	0.763658i	$-0.723401\pi$
$233$	4.73766	−	16.1350i	0.310375	−	1.05704i	0.955996	−	0.293381i	$-0.0947804\pi$
$234$		0			0
$235$	−10.4907	−	7.05366i	−0.684336	−	0.460130i
$236$		0			0
$237$	1.06514	+	0.153144i	0.0691881	+	0.00994775i
$238$		0			0
$239$	−8.13700	−	5.22933i	−0.526339	−	0.338257i	0.250336	−	0.968159i	$-0.419459\pi$
$239$	−8.13700	−	5.22933i	−0.526339	−	0.338257i	−0.776675	+	0.629902i	$0.783095\pi$
$240$		0			0
$241$	−6.34819	−	13.9006i	−0.408923	−	0.895415i	−0.996287	−	0.0860930i	$-0.972562\pi$
$241$	−6.34819	−	13.9006i	−0.408923	−	0.895415i	0.587365	−	0.809322i	$-0.300165\pi$
$242$		0			0
$243$	−15.9123	+	2.28784i	−1.02077	+	0.146765i
$244$		0			0
$245$	−8.61850	+	7.16042i	−0.550616	+	0.457462i
$246$		0			0
$247$	4.61106	+	3.99550i	0.293395	+	0.254228i
$248$		0			0
$249$	−3.44223	−	3.97255i	−0.218142	−	0.251750i
$250$		0			0
$251$	−11.6791	+	25.5736i	−0.737177	+	1.61419i	0.0509673	+	0.998700i	$0.483770\pi$
$251$	−11.6791	+	25.5736i	−0.737177	+	1.61419i	−0.788144	+	0.615491i	$0.788958\pi$
$252$		0			0
$253$	9.93484	+	14.5646i	0.624598	+	0.915671i
$254$		0			0
$255$	−0.0869931	+	4.19283i	−0.00544772	+	0.262565i
$256$		0			0
$257$	−2.40354	+	2.08268i	−0.149929	+	0.129914i	−0.726596	−	0.687065i	$-0.758899\pi$
$257$	−2.40354	+	2.08268i	−0.149929	+	0.129914i	0.576667	+	0.816979i	$0.304353\pi$
$258$		0			0
$259$	24.1559	−	27.8774i	1.50098	−	1.73222i
$260$		0			0
$261$	−3.08506	+	0.905856i	−0.190960	+	0.0560710i
$262$		0			0
$263$	−31.0694	+	4.46711i	−1.91582	+	0.275454i	−0.993756	−	0.111576i	$-0.964410\pi$
$263$	−31.0694	+	4.46711i	−1.91582	+	0.275454i	−0.922067	+	0.387029i	$0.873501\pi$
$264$		0			0
$265$	−15.4237	+	17.0711i	−0.947467	+	1.04867i
$266$		0			0
$267$	−1.88215	+	2.92869i	−0.115186	+	0.179233i
$268$		0			0
$269$	−1.88834	+	13.1337i	−0.115134	+	0.800774i	0.847661	+	0.530539i	$0.178010\pi$
$269$	−1.88834	+	13.1337i	−0.115134	+	0.800774i	−0.962794	+	0.270235i	$0.912899\pi$
$270$		0			0
$271$	−0.0246766	+	0.0158587i	−0.00149900	+	0.000963347i	−0.541390	−	0.840772i	$-0.682102\pi$
$271$	−0.0246766	+	0.0158587i	−0.00149900	+	0.000963347i	0.539891	+	0.841735i	$0.318465\pi$
$272$		0			0
$273$	−2.03379	+	6.92645i	−0.123090	+	0.419208i
$274$		0			0
$275$	−12.6028	+	13.3801i	−0.759976	+	0.806853i
$276$		0			0
$277$		−	29.6618i		−	1.78220i	−0.453805	−	0.891101i	$-0.649934\pi$
$277$		−	29.6618i		−	1.78220i	0.453805	−	0.891101i	$-0.350066\pi$
$278$		0			0
$279$	12.7481	+	3.74318i	0.763209	+	0.224098i
$280$		0			0
$281$	−8.70771	+	5.59611i	−0.519458	+	0.333836i	−0.773958	−	0.633237i	$-0.781726\pi$
$281$	−8.70771	+	5.59611i	−0.519458	+	0.333836i	0.254499	+	0.967073i	$0.418089\pi$
$282$		0			0
$283$	17.7577	+	2.55318i	1.05559	+	0.151771i	0.648189	−	0.761480i	$-0.275527\pi$
$283$	17.7577	+	2.55318i	1.05559	+	0.151771i	0.407399	+	0.913250i	$0.366436\pi$
$284$		0			0
$285$	−0.800032	+	4.84813i	−0.0473898	+	0.287178i
$286$		0			0
$287$	23.7601	−	10.8509i	1.40252	−	0.640508i
$288$		0			0
$289$	−1.75208	−	12.1860i	−0.103064	−	0.716824i
$290$		0			0
$291$	−2.78083	+	0.816525i	−0.163015	+	0.0478655i
$292$		0			0
$293$	3.62679	+	3.14263i	0.211879	+	0.183594i	0.754334	−	0.656490i	$-0.227960\pi$
$293$	3.62679	+	3.14263i	0.211879	+	0.183594i	−0.542455	+	0.840085i	$0.682505\pi$
$294$		0			0
$295$	−15.2688	−	7.35956i	−0.888984	−	0.428490i
$296$		0			0
$297$	15.2053	+	6.94403i	0.882302	+	0.402934i
$298$		0			0
$299$	10.9728	−	3.55155i	0.634576	−	0.205392i
$300$		0			0
$301$	−11.1688	+	24.4562i	−0.643757	+	1.40963i
$302$		0			0
$303$	−6.80736	+	5.89861i	−0.391072	+	0.338866i
$304$		0			0
$305$	8.49807	−	26.8670i	0.486598	−	1.53840i
$306$		0			0
$307$	−2.61972	−	8.92195i	−0.149515	−	0.509203i	0.850340	−	0.526234i	$-0.176397\pi$
$307$	−2.61972	−	8.92195i	−0.149515	−	0.509203i	−0.999855	+	0.0170318i	$0.994578\pi$
$308$		0			0
$309$	1.22999	+	8.55478i	0.0699718	+	0.486664i
$310$		0			0
$311$	−4.98800	−	10.9222i	−0.282844	−	0.619342i	0.713876	−	0.700272i	$-0.246938\pi$
$311$	−4.98800	−	10.9222i	−0.282844	−	0.619342i	−0.996720	+	0.0809307i	$0.974211\pi$
$312$		0			0
$313$	15.6183	−	24.3026i	0.882800	−	1.37366i	−0.0443665	−	0.999015i	$-0.514127\pi$
$313$	15.6183	−	24.3026i	0.882800	−	1.37366i	0.927167	−	0.374649i	$-0.122237\pi$
$314$		0			0
$315$	16.8269	−	4.56389i	0.948087	−	0.257146i
$316$		0			0
$317$	−10.3053	−	16.0353i	−0.578801	−	0.900631i	0.421179	−	0.906977i	$-0.361616\pi$
$317$	−10.3053	−	16.0353i	−0.578801	−	0.900631i	−0.999980	+	0.00634602i	$0.997980\pi$
$318$		0			0
$319$	5.04102	+	1.48018i	0.282243	+	0.0828739i
$320$		0			0
$321$	4.15808			0.232081
$322$		0			0
$323$			5.49362i			0.305673i
$324$		0			0
$325$	6.07565	+	10.3764i	0.337017	+	0.575580i
$326$		0			0
$327$	−4.75935	−	7.40569i	−0.263192	−	0.409536i
$328$		0			0
$329$	2.78839	−	19.3937i	0.153729	−	1.06921i
$330$		0			0
$331$	22.6022	+	14.5256i	1.24233	+	0.798398i	0.985765	−	0.168129i	$-0.0537726\pi$
$331$	22.6022	+	14.5256i	1.24233	+	0.798398i	0.256566	+	0.966527i	$0.417409\pi$
$332$		0			0
$333$	−21.7818	+	9.94743i	−1.19364	+	0.545116i
$334$		0			0
$335$	21.6340	−	13.2774i	1.18199	−	0.725423i
$336$		0			0
$337$	−1.36948	−	4.66403i	−0.0746005	−	0.254066i	0.913746	−	0.406285i	$-0.133176\pi$
$337$	−1.36948	−	4.66403i	−0.0746005	−	0.254066i	−0.988347	+	0.152219i	$0.951358\pi$
$338$		0			0
$339$	−8.85620	+	10.2206i	−0.481003	+	0.555107i
$340$		0			0
$341$	−14.2170	−	16.4073i	−0.769892	−	0.888503i
$342$		0			0
$343$	6.27036	+	2.86358i	0.338567	+	0.154619i
$344$		0			0
$345$	7.06016	+	6.03554i	0.380106	+	0.324943i
$346$		0			0
$347$	18.9989	+	8.67649i	1.01991	+	0.465779i	0.853951	−	0.520354i	$-0.174200\pi$
$347$	18.9989	+	8.67649i	1.01991	+	0.465779i	0.165962	+	0.986132i	$0.446927\pi$
$348$		0			0
$349$	9.43879	+	10.8929i	0.505247	+	0.583086i	0.949875	−	0.312629i	$-0.101210\pi$
$349$	9.43879	+	10.8929i	0.505247	+	0.583086i	−0.444628	+	0.895715i	$0.646664\pi$
$350$		0			0
$351$	7.16095	−	8.26418i	0.382223	−	0.441109i
$352$		0			0
$353$	−0.0485549	−	0.165363i	−0.00258432	−	0.00880137i	0.958191	−	0.286130i	$-0.0923690\pi$
$353$	−0.0485549	−	0.165363i	−0.00258432	−	0.00880137i	−0.960775	+	0.277329i	$0.910551\pi$
$354$		0			0
$355$	−8.20627	−	13.3711i	−0.435543	−	0.709667i
$356$		0			0
$357$	−5.91249	+	2.70015i	−0.312922	+	0.142907i
$358$		0			0
$359$	12.2412	+	7.86693i	0.646065	+	0.415200i	0.822226	−	0.569161i	$-0.192732\pi$
$359$	12.2412	+	7.86693i	0.646065	+	0.415200i	−0.176162	+	0.984361i	$0.556368\pi$
$360$		0			0
$361$	1.78794	−	12.4354i	0.0941019	−	0.654493i
$362$		0			0
$363$	−1.17739	−	1.83206i	−0.0617971	−	0.0961582i
$364$		0			0
$365$	3.17404	+	25.8758i	0.166137	+	1.35440i
$366$		0			0
$367$		−	12.9569i		−	0.676343i	−0.941085	−	0.338171i	$-0.890192\pi$
$367$		−	12.9569i		−	0.676343i	0.941085	−	0.338171i	$-0.109808\pi$
$368$		0			0
$369$	−16.9565			−0.882721
$370$		0			0
$371$	−34.2138	−	10.0461i	−1.77629	−	0.521567i
$372$		0			0
$373$	18.7666	+	29.2013i	0.971695	+	1.51199i	0.854875	+	0.518835i	$0.173634\pi$
$373$	18.7666	+	29.2013i	0.971695	+	1.51199i	0.116821	+	0.993153i	$0.462730\pi$
$374$		0			0
$375$	−4.56286	+	8.54143i	−0.235625	+	0.441077i
$376$		0			0
$377$	1.85813	−	2.89131i	0.0956988	−	0.148910i
$378$		0			0
$379$	1.34814	+	2.95202i	0.0692495	+	0.151635i	0.941092	−	0.338152i	$-0.109802\pi$
$379$	1.34814	+	2.95202i	0.0692495	+	0.151635i	−0.871842	+	0.489787i	$0.837074\pi$
$380$		0			0
$381$	−0.0200482	−	0.139438i	−0.00102710	−	0.00714363i
$382$		0			0
$383$	−0.151815	−	0.517034i	−0.00775738	−	0.0264192i	0.955523	−	0.294915i	$-0.0952915\pi$
$383$	−0.151815	−	0.517034i	−0.00775738	−	0.0264192i	−0.963281	+	0.268496i	$0.913473\pi$
$384$		0			0
$385$	−27.1623	−	8.59147i	−1.38432	−	0.437862i
$386$		0			0
$387$	13.1903	−	11.4294i	0.670500	−	0.580992i
$388$		0			0
$389$	2.05104	−	4.49114i	0.103992	−	0.227710i	−0.850483	−	0.526003i	$-0.823690\pi$
$389$	2.05104	−	4.49114i	0.103992	−	0.227710i	0.954474	+	0.298293i	$0.0964173\pi$
$390$		0			0
$391$	8.88675	+	5.37265i	0.449423	+	0.271707i
$392$		0			0
$393$	−7.40621	−	3.38230i	−0.373594	−	0.170615i
$394$		0			0
$395$	2.50254	+	1.20623i	0.125917	+	0.0606918i
$396$		0			0
$397$	5.56352	+	4.82082i	0.279225	+	0.241950i	0.783202	−	0.621767i	$-0.213585\pi$
$397$	5.56352	+	4.82082i	0.279225	+	0.241950i	−0.503977	+	0.863717i	$0.668130\pi$
$398$		0			0
$399$	−7.30726	+	2.14561i	−0.365821	+	0.107415i
$400$		0			0
$401$	5.03656	+	35.0301i	0.251514	+	1.74932i	0.589134	+	0.808036i	$0.299469\pi$
$401$	5.03656	+	35.0301i	0.251514	+	1.74932i	−0.337620	+	0.941283i	$0.609622\pi$
$402$		0			0
$403$	−12.9186	+	5.89973i	−0.643522	+	0.293887i
$404$		0			0
$405$	−6.20163	−	1.02338i	−0.308161	−	0.0508524i
$406$		0			0
$407$	38.7293	+	5.56844i	1.91974	+	0.276017i
$408$		0			0
$409$	4.76069	−	3.05951i	0.235401	−	0.151283i	−0.417623	−	0.908621i	$-0.637137\pi$
$409$	4.76069	−	3.05951i	0.235401	−	0.151283i	0.653024	+	0.757338i	$0.273500\pi$
$410$		0			0
$411$	1.77043	+	0.519845i	0.0873289	+	0.0256421i
$412$		0			0
$413$		−	26.2707i		−	1.29270i
$414$		0			0
$415$	−5.37999	−	12.4582i	−0.264093	−	0.611547i
$416$		0			0
$417$	4.54183	−	15.4680i	0.222414	−	0.757474i
$418$		0			0
$419$	−22.4013	+	14.3964i	−1.09437	+	0.703311i	−0.957834	−	0.287324i	$-0.907234\pi$
$419$	−22.4013	+	14.3964i	−1.09437	+	0.703311i	−0.136540	+	0.990635i	$0.543598\pi$
$420$		0			0
$421$	4.45408	−	30.9788i	0.217079	−	1.50982i	−0.531664	−	0.846955i	$-0.678433\pi$
$421$	4.45408	−	30.9788i	0.217079	−	1.50982i	0.748743	−	0.662860i	$-0.230658\pi$
$422$		0			0
$423$	−6.87648	+	10.7000i	−0.334346	+	0.520252i
$424$		0			0
$425$	−3.47849	+	10.2527i	−0.168731	+	0.497328i
$426$		0			0
$427$	43.2301	−	6.21554i	2.09205	−	0.300791i
$428$		0			0
$429$	−7.34714	+	2.15732i	−0.354723	+	0.104156i
$430$		0			0
$431$	−5.81941	+	6.71596i	−0.280311	+	0.323496i	−0.878393	−	0.477938i	$-0.841384\pi$
$431$	−5.81941	+	6.71596i	−0.280311	+	0.323496i	0.598082	+	0.801435i	$0.295930\pi$
$432$		0			0
$433$	22.7975	−	19.7542i	1.09558	−	0.949325i	0.0966374	−	0.995320i	$-0.469191\pi$
$433$	22.7975	−	19.7542i	1.09558	−	0.949325i	0.998942	+	0.0459950i	$0.0146458\pi$
$434$		0			0
$435$	2.76733	+	0.0574167i	0.132683	+	0.00275292i
$436$		0			0
$437$	9.41055	+	7.71277i	0.450167	+	0.368952i
$438$		0			0
$439$	−12.9842	+	28.4315i	−0.619704	+	1.35696i	0.296031	+	0.955178i	$0.404337\pi$
$439$	−12.9842	+	28.4315i	−0.619704	+	1.35696i	−0.915735	+	0.401784i	$0.868390\pi$
$440$		0			0
$441$	7.38270	+	8.52009i	0.351557	+	0.405719i
$442$		0			0
$443$	21.2044	+	18.3737i	1.00745	+	0.872961i	0.991913	−	0.126918i	$-0.0405085\pi$
$443$	21.2044	+	18.3737i	1.00745	+	0.872961i	0.0155379	+	0.999879i	$0.495054\pi$
$444$		0			0
$445$	−6.91296	+	5.74343i	−0.327706	+	0.272265i
$446$		0			0
$447$	19.0402	−	2.73756i	0.900569	−	0.129482i
$448$		0			0
$449$	12.2203	+	26.7586i	0.576710	+	1.26282i	0.943147	+	0.332375i	$0.107850\pi$
$449$	12.2203	+	26.7586i	0.576710	+	1.26282i	−0.366438	+	0.930443i	$0.619423\pi$
$450$		0			0
$451$	23.3087	+	14.9796i	1.09756	+	0.705361i
$452$		0			0
$453$	9.43332	+	1.35631i	0.443216	+	0.0637248i
$454$		0			0
$455$	−10.3987	+	15.4656i	−0.487498	+	0.725040i
$456$		0			0
$457$	3.62249	−	12.3371i	0.169453	−	0.577103i	−0.830350	−	0.557242i	$-0.811859\pi$
$457$	3.62249	−	12.3371i	0.169453	−	0.577103i	0.999803	−	0.0198611i	$-0.00632240\pi$
$458$		0			0
$459$	9.84596			0.459570
$460$		0			0
$461$	9.61771			0.447942			0.223971	−	0.974596i	$-0.428098\pi$
$461$	9.61771			0.447942			0.223971	+	0.974596i	$0.428098\pi$
$462$		0			0
$463$	0.109455	−	0.372771i	0.00508682	−	0.0173241i	−0.956910	−	0.290383i	$-0.906217\pi$
$463$	0.109455	−	0.372771i	0.00508682	−	0.0173241i	0.961997	+	0.273059i	$0.0880354\pi$
$464$		0			0
$465$	−9.49160	−	6.38191i	−0.440162	−	0.295954i
$466$		0			0
$467$	6.58603	+	0.946928i	0.304765	+	0.0438186i	0.293001	−	0.956112i	$-0.405346\pi$
$467$	6.58603	+	0.946928i	0.304765	+	0.0438186i	0.0117644	+	0.999931i	$0.496255\pi$
$468$		0			0
$469$	33.0965	+	21.2698i	1.52825	+	0.982149i
$470$		0			0
$471$	−3.75748	−	8.22774i	−0.173136	−	0.379114i
$472$		0			0
$473$	−28.2285	+	4.05864i	−1.29795	+	0.186617i
$474$		0			0
$475$	−5.74378	+	11.3105i	−0.263543	+	0.518962i
$476$		0			0
$477$	17.4941	+	15.1587i	0.800999	+	0.694069i
$478$		0			0
$479$	−1.61168	−	1.85998i	−0.0736396	−	0.0849846i	0.717734	−	0.696317i	$-0.245179\pi$
$479$	−1.61168	−	1.85998i	−0.0736396	−	0.0849846i	−0.791374	+	0.611333i	$0.790634\pi$
$480$		0			0
$481$	10.6330	−	23.2831i	0.484825	−	1.06162i
$482$		0			0
$483$	−3.67551	+	13.9189i	−0.167242	+	0.633334i
$484$		0			0
$485$	−7.48056	−	0.155207i	−0.339675	−	0.00704760i
$486$		0			0
$487$	−28.2900	+	24.5134i	−1.28194	+	1.11081i	−0.294030	+	0.955796i	$0.594996\pi$
$487$	−28.2900	+	24.5134i	−1.28194	+	1.11081i	−0.987912	+	0.155013i	$0.950458\pi$
$488$		0			0
$489$	10.1748	−	11.7424i	0.460122	−	0.531009i
$490$		0			0
$491$	33.0350	−	9.69995i	1.49085	−	0.437753i	0.568037	−	0.823003i	$-0.307703\pi$
$491$	33.0350	−	9.69995i	1.49085	−	0.437753i	0.922812	+	0.385251i	$0.125885\pi$
$492$		0			0
$493$	3.06310	−	0.440408i	0.137955	−	0.0198350i
$494$		0			0
$495$	13.7224	+	12.3982i	0.616777	+	0.557256i
$496$		0			0
$497$	13.1461	−	20.4557i	0.589682	−	0.917563i
$498$		0			0
$499$	4.53097	−	31.5136i	0.202834	−	1.41074i	−0.592987	−	0.805212i	$-0.702052\pi$
$499$	4.53097	−	31.5136i	0.202834	−	1.41074i	0.795822	−	0.605531i	$-0.207039\pi$
$500$		0			0
$501$	−10.4854	+	6.73855i	−0.468452	+	0.301056i
$502$		0			0
$503$	−2.97367	+	10.1274i	−0.132589	+	0.451558i	−0.998845	−	0.0480427i	$-0.984702\pi$
$503$	−2.97367	+	10.1274i	−0.132589	+	0.451558i	0.866256	+	0.499600i	$0.166520\pi$
$504$		0			0
$505$	−21.3483	+	9.21916i	−0.949988	+	0.410247i
$506$		0			0
$507$		−	6.25067i		−	0.277602i
$508$		0			0
$509$	−2.19380	−	0.644158i	−0.0972384	−	0.0285518i	0.232751	−	0.972536i	$-0.425227\pi$
$509$	−2.19380	−	0.644158i	−0.0972384	−	0.0285518i	−0.329990	+	0.943984i	$0.607045\pi$
$510$		0			0
$511$	−33.9913	+	21.8449i	−1.50369	+	0.966362i
$512$		0			0
$513$	11.4189	+	1.64178i	0.504155	+	0.0724865i
$514$		0			0
$515$	−3.63284	+	22.0147i	−0.160082	+	0.970083i
$516$		0			0
$517$	18.9050	−	8.63364i	0.831442	−	0.379707i
$518$		0			0
$519$	−0.0729002	−	0.507032i	−0.00319996	−	0.0222562i
$520$		0			0
$521$	3.80745	−	1.11797i	0.166807	−	0.0489791i	−0.197262	−	0.980351i	$-0.563205\pi$
$521$	3.80745	−	1.11797i	0.166807	−	0.0489791i	0.364070	+	0.931372i	$0.381387\pi$
$522$		0			0
$523$	−13.5772	−	11.7647i	−0.593691	−	0.514437i	0.305385	−	0.952229i	$-0.401215\pi$
$523$	−13.5772	−	11.7647i	−0.593691	−	0.514437i	−0.899076	+	0.437793i	$0.855760\pi$
$524$		0			0
$525$	−14.9960	−	0.622544i	−0.654479	−	0.0271701i
$526$		0			0
$527$	−11.6319	−	5.31213i	−0.506695	−	0.231400i
$528$		0			0
$529$	21.6799	−	7.68002i	0.942604	−	0.333914i
$530$		0			0
$531$	−7.08447	+	15.5128i	−0.307440	+	0.673199i
$532$		0			0
$533$	13.6981	−	11.8695i	0.593331	−	0.514124i
$534$		0			0
$535$	10.2349	+	3.23730i	0.442492	+	0.139961i
$536$		0			0
$537$	1.69320	+	5.76651i	0.0730670	+	0.248843i
$538$		0			0
$539$	−2.62163	−	18.2338i	−0.112921	−	0.785386i
$540$		0			0
$541$	−6.96925	−	15.2605i	−0.299631	−	0.656101i	0.698602	−	0.715510i	$-0.253806\pi$
$541$	−6.96925	−	15.2605i	−0.299631	−	0.656101i	−0.998234	+	0.0594088i	$0.981078\pi$
$542$		0			0
$543$	−4.51557	+	7.02636i	−0.193782	+	0.301530i
$544$		0			0
$545$	−5.94910	−	21.9341i	−0.254831	−	0.939553i
$546$		0			0
$547$	4.11084	+	6.39660i	0.175767	+	0.273499i	0.917948	−	0.396701i	$-0.129845\pi$
$547$	4.11084	+	6.39660i	0.175767	+	0.273499i	−0.742181	+	0.670199i	$0.766209\pi$
$548$		0			0
$549$	−27.2035	−	7.98766i	−1.16102	−	0.340905i
$550$		0			0
$551$	3.62587			0.154467
$552$		0			0
$553$			4.30575i			0.183099i
$554$		0			0
$555$	20.4606	−	2.50978i	0.868503	−	0.106534i
$556$		0			0
$557$	−24.3346	−	37.8654i	−1.03109	−	1.60441i	−0.768875	−	0.639400i	$-0.779183\pi$
$557$	−24.3346	−	37.8654i	−1.03109	−	1.60441i	−0.262216	−	0.965009i	$-0.584453\pi$
$558$		0			0
$559$	−2.65505	+	18.4663i	−0.112297	+	0.781041i
$560$		0			0
$561$	−5.80016	−	3.72754i	−0.244883	−	0.157377i
$562$		0			0
$563$	−10.8150	+	4.93903i	−0.455797	+	0.208155i	−0.630064	−	0.776543i	$-0.716972\pi$
$563$	−10.8150	+	4.93903i	−0.455797	+	0.208155i	0.174268	+	0.984698i	$0.444244\pi$
$564$		0			0
$565$	−29.7563	+	18.2623i	−1.25186	+	0.768303i
$566$		0			0
$567$	−2.74461	−	9.34730i	−0.115263	−	0.392550i
$568$		0			0
$569$	−3.57875	+	4.13010i	−0.150029	+	0.173143i	−0.825789	−	0.563979i	$-0.809270\pi$
$569$	−3.57875	+	4.13010i	−0.150029	+	0.173143i	0.675760	+	0.737121i	$0.263815\pi$
$570$		0			0
$571$	−15.6490	−	18.0599i	−0.654889	−	0.755782i	0.327044	−	0.945009i	$-0.393947\pi$
$571$	−15.6490	−	18.0599i	−0.654889	−	0.755782i	−0.981933	+	0.189227i	$0.939402\pi$
$572$		0			0
$573$	16.9419	+	7.73712i	0.707759	+	0.323223i
$574$		0			0
$575$	12.6791	+	20.3529i	0.528757	+	0.848773i
$576$		0			0
$577$	−10.9301	−	4.99163i	−0.455028	−	0.207804i	0.174697	−	0.984622i	$-0.444105\pi$
$577$	−10.9301	−	4.99163i	−0.455028	−	0.207804i	−0.629725	+	0.776818i	$0.716833\pi$
$578$		0			0
$579$	−4.08947	−	4.71950i	−0.169953	−	0.196136i
$580$		0			0
$581$	13.7733	−	15.8953i	0.571415	−	0.659448i
$582$		0			0
$583$	−10.6563	−	36.2919i	−0.441337	−	1.50306i
$584$		0			0
$585$	10.3111	−	6.32820i	0.426310	−	0.261639i
$586$		0			0
$587$	17.0611	−	7.79154i	0.704187	−	0.321591i	−0.0309398	−	0.999521i	$-0.509850\pi$
$587$	17.0611	−	7.79154i	0.704187	−	0.321591i	0.735127	+	0.677930i	$0.237123\pi$
$588$		0			0
$589$	−12.6044	−	8.10034i	−0.519354	−	0.333769i
$590$		0			0
$591$	0.848972	−	5.90473i	0.0349221	−	0.242888i
$592$		0			0
$593$	−15.7146	−	24.4523i	−0.645320	−	1.00414i	−0.997667	−	0.0682680i	$-0.978253\pi$
$593$	−15.7146	−	24.4523i	−0.645320	−	1.00414i	0.352347	−	0.935869i	$-0.385384\pi$
$594$		0			0
$595$	−16.6555	+	2.04303i	−0.682808	+	0.0837562i
$596$		0			0
$597$		−	1.77768i		−	0.0727554i
$598$		0			0
$599$	−32.8918			−1.34392			−0.671961	−	0.740587i	$-0.734548\pi$
$599$	−32.8918			−1.34392			−0.671961	+	0.740587i	$0.734548\pi$
$600$		0			0
$601$	−10.2433	−	3.00771i	−0.417834	−	0.122687i	0.0660560	−	0.997816i	$-0.478958\pi$
$601$	−10.2433	−	3.00771i	−0.417834	−	0.122687i	−0.483890	+	0.875129i	$0.660777\pi$
$602$		0			0
$603$	−13.8076	−	21.4850i	−0.562288	−	0.874937i
$604$		0			0
$605$	−1.47172	−	5.42618i	−0.0598339	−	0.220605i
$606$		0			0
$607$	7.95847	−	12.3836i	0.323024	−	0.502636i	−0.641325	−	0.767270i	$-0.721615\pi$
$607$	7.95847	−	12.3836i	0.323024	−	0.502636i	0.964349	+	0.264634i	$0.0852512\pi$
$608$		0			0
$609$	1.78213	+	3.90233i	0.0722157	+	0.158130i
$610$		0			0
$611$	−1.93488	−	13.4574i	−0.0782768	−	0.544427i
$612$		0			0
$613$	5.99700	+	20.4239i	0.242217	+	0.824914i	0.987426	+	0.158083i	$0.0505314\pi$
$613$	5.99700	+	20.4239i	0.242217	+	0.824914i	−0.745209	+	0.666831i	$0.767650\pi$
$614$		0			0
$615$	13.9176	+	4.40214i	0.561210	+	0.177512i
$616$		0			0
$617$	8.97629	−	7.77800i	0.361372	−	0.313131i	−0.455183	−	0.890398i	$-0.650426\pi$
$617$	8.97629	−	7.77800i	0.361372	−	0.313131i	0.816555	+	0.577267i	$0.195881\pi$
$618$		0			0
$619$	3.86836	−	8.47052i	0.155482	−	0.340459i	−0.815820	−	0.578305i	$-0.803714\pi$
$619$	3.86836	−	8.47052i	0.155482	−	0.340459i	0.971303	+	0.237847i	$0.0764415\pi$
$620$		0			0
$621$	13.8232	−	16.8661i	0.554707	−	0.676812i
$622$		0			0
$623$	−12.6710	−	5.78666i	−0.507653	−	0.231838i
$624$		0			0
$625$	−17.8812	+	17.4718i	−0.715248	+	0.698871i
$626$		0			0
$627$	−6.10518	−	5.29017i	−0.243817	−	0.211269i
$628$		0			0
$629$	22.1133	−	6.49304i	0.881714	−	0.258895i
$630$		0			0
$631$	4.70037	+	32.6918i	0.187119	+	1.30144i	0.839421	+	0.543481i	$0.182894\pi$
$631$	4.70037	+	32.6918i	0.187119	+	1.30144i	−0.652302	+	0.757959i	$0.726197\pi$
$632$		0			0
$633$	−7.09242	+	3.23900i	−0.281898	+	0.128739i
$634$		0			0
$635$	0.0592132	−	0.358827i	0.00234980	−	0.0142396i
$636$		0			0
$637$	−11.9281	−	1.71500i	−0.472607	−	0.0679506i
$638$		0			0
$639$	−13.2791	+	8.53394i	−0.525312	+	0.337597i
$640$		0			0
$641$	33.2014	+	9.74880i	1.31138	+	0.385055i	0.861373	−	0.507973i	$-0.169605\pi$
$641$	33.2014	+	9.74880i	1.31138	+	0.385055i	0.450002	+	0.893027i	$0.351423\pi$
$642$		0			0
$643$			34.1824i			1.34802i	0.738722	+	0.674010i	$0.235430\pi$
$643$			34.1824i			1.34802i	−0.738722	+	0.674010i	$0.764570\pi$
$644$		0			0
$645$	−13.7936	+	5.95668i	−0.543121	+	0.234544i
$646$		0			0
$647$	−9.11871	+	31.0555i	−0.358494	+	1.22092i	0.561001	+	0.827815i	$0.310416\pi$
$647$	−9.11871	+	31.0555i	−0.358494	+	1.22092i	−0.919495	+	0.393102i	$0.871402\pi$
$648$		0			0
$649$	23.4426	−	15.0657i	0.920204	−	0.591379i
$650$		0			0
$651$	2.52284	−	17.5468i	0.0988781	−	0.687712i
$652$		0			0
$653$	−12.3899	+	19.2791i	−0.484855	+	0.754449i	−0.994364	−	0.106016i	$-0.966191\pi$
$653$	−12.3899	+	19.2791i	−0.484855	+	0.754449i	0.509509	+	0.860465i	$0.329827\pi$
$654$		0			0
$655$	−15.5966	−	14.0915i	−0.609411	−	0.550600i
$656$		0			0
$657$	25.9628	−	3.73289i	1.01291	−	0.145634i
$658$		0			0
$659$	−18.4727	+	5.42407i	−0.719593	+	0.211292i	−0.620971	−	0.783833i	$-0.713262\pi$
$659$	−18.4727	+	5.42407i	−0.719593	+	0.211292i	−0.0986220	+	0.995125i	$0.531443\pi$
$660$		0			0
$661$	−28.2629	+	32.6171i	−1.09930	+	1.26866i	−0.138817	+	0.990318i	$0.544330\pi$
$661$	−28.2629	+	32.6171i	−1.09930	+	1.26866i	−0.960482	+	0.278341i	$0.910215\pi$
$662$		0			0
$663$	−3.40865	+	2.95362i	−0.132381	+	0.114709i
$664$		0			0
$665$	−19.6569	−	0.407842i	−0.762261	−	0.0158154i
$666$		0			0
$667$	3.54603	−	5.86539i	0.137303	−	0.227109i
$668$		0			0
$669$	2.66970	−	5.84582i	0.103216	−	0.226013i
$670$		0			0
$671$	30.3379	+	35.0118i	1.17118	+	1.35162i
$672$		0			0
$673$	21.7157	+	18.8168i	0.837079	+	0.725333i	0.963806	−	0.266605i	$-0.0859019\pi$
$673$	21.7157	+	18.8168i	0.837079	+	0.725333i	−0.126727	+	0.991938i	$0.540447\pi$
$674$		0			0
$675$	20.2713	+	10.2943i	0.780242	+	0.396228i
$676$		0			0
$677$	−17.5483	+	2.52307i	−0.674437	+	0.0969694i	−0.471020	−	0.882123i	$-0.656114\pi$
$677$	−17.5483	+	2.52307i	−0.674437	+	0.0969694i	−0.203417	+	0.979092i	$0.565205\pi$
$678$		0			0
$679$	−4.81742	−	10.5487i	−0.184875	−	0.404821i
$680$		0			0
$681$	−9.97933	−	6.41333i	−0.382409	−	0.245759i
$682$		0			0
$683$	−45.9940	−	6.61294i	−1.75991	−	0.253037i	−0.814790	−	0.579756i	$-0.803148\pi$
$683$	−45.9940	−	6.61294i	−1.75991	−	0.253037i	−0.945122	+	0.326719i	$0.894057\pi$
$684$		0			0
$685$	3.95308	+	2.65795i	0.151039	+	0.101555i
$686$		0			0
$687$	4.58123	−	15.6022i	0.174785	−	0.595262i
$688$		0			0
$689$	−24.7434			−0.942649
$690$		0			0
$691$	−6.09538			−0.231879			−0.115940	−	0.993256i	$-0.536988\pi$
$691$	−6.09538			−0.231879			−0.115940	+	0.993256i	$0.536988\pi$
$692$		0			0
$693$	−8.07545	+	27.5025i	−0.306761	+	1.04473i
$694$		0			0
$695$	23.2222	−	34.5376i	0.880869	−	1.31009i
$696$		0			0
$697$	16.1538	+	2.32257i	0.611871	+	0.0879737i
$698$		0			0
$699$	12.2530	+	7.87455i	0.463453	+	0.297843i
$700$		0			0
$701$	−11.1619	−	24.4411i	−0.421578	−	0.923128i	−0.994619	−	0.103601i	$-0.966964\pi$
$701$	−11.1619	−	24.4411i	−0.421578	−	0.923128i	0.573041	−	0.819527i	$-0.305764\pi$
$702$		0			0
$703$	26.7286	−	3.84299i	1.00809	−	0.144941i
$704$		0			0
$705$	8.42194	−	6.99712i	0.317189	−	0.263527i
$706$		0			0
$707$	−27.2382	−	23.6020i	−1.02440	−	0.887645i
$708$		0			0
$709$	−17.3923	−	20.0718i	−0.653183	−	0.753813i	0.328465	−	0.944516i	$-0.393469\pi$
$709$	−17.3923	−	20.0718i	−0.653183	−	0.753813i	−0.981648	+	0.190703i	$0.938923\pi$
$710$		0			0
$711$	1.16114	−	2.54254i	0.0435461	−	0.0953527i
$712$		0			0
$713$	−25.4303	+	12.4675i	−0.952373	+	0.466911i
$714$		0			0
$715$	−19.7642	−	0.410068i	−0.739137	−	0.0153357i
$716$		0			0
$717$	6.33148	−	5.48626i	0.236453	−	0.204888i
$718$		0			0
$719$	21.9188	−	25.2957i	0.817434	−	0.943369i	−0.181767	−	0.983342i	$-0.558182\pi$
$719$	21.9188	−	25.2957i	0.817434	−	0.943369i	0.999201	+	0.0399729i	$0.0127272\pi$
$720$		0			0
$721$	−33.1813	+	9.74290i	−1.23574	+	0.362845i
$722$		0			0
$723$	13.1013	−	1.88368i	0.487242	−	0.0700549i
$724$		0			0
$725$	6.76691	+	2.29585i	0.251317	+	0.0852658i
$726$		0			0
$727$	−13.5310	+	21.0546i	−0.501836	+	0.780872i	−0.996081	−	0.0884512i	$-0.971808\pi$
$727$	−13.5310	+	21.0546i	−0.501836	+	0.780872i	0.494245	+	0.869323i	$0.335445\pi$
$728$		0			0
$729$	0.781476	−	5.43529i	0.0289436	−	0.201307i
$730$		0			0
$731$	−14.1314	+	9.08171i	−0.522670	+	0.335899i
$732$		0			0
$733$	−0.110181	+	0.375243i	−0.00406963	+	0.0138599i	−0.961503	−	0.274795i	$-0.911390\pi$
$733$	−0.110181	+	0.375243i	−0.00406963	+	0.0138599i	0.957433	+	0.288655i	$0.0932081\pi$
$734$		0			0
$735$	−3.84764	−	8.90977i	−0.141922	−	0.328642i
$736$		0			0
$737$			41.7314i			1.53720i
$738$		0			0
$739$	−2.49528	−	0.732682i	−0.0917905	−	0.0269521i	0.235515	−	0.971871i	$-0.424322\pi$
$739$	−2.49528	−	0.732682i	−0.0917905	−	0.0269521i	−0.327305	+	0.944919i	$0.606141\pi$
$740$		0			0
$741$	−4.44569	+	2.85707i	−0.163317	+	0.104957i
$742$		0			0
$743$	−30.1702	−	4.33781i	−1.10684	−	0.159139i	−0.435426	−	0.900225i	$-0.643402\pi$
$743$	−30.1702	−	4.33781i	−1.10684	−	0.159139i	−0.671410	+	0.741086i	$0.734311\pi$
$744$		0			0
$745$	48.9976	+	8.08552i	1.79513	+	0.296230i
$746$		0			0
$747$	−12.4197	+	5.67187i	−0.454412	+	0.207523i
$748$		0			0
$749$	2.36778	+	16.4683i	0.0865169	+	0.601739i
$750$		0			0
$751$	0.810571	−	0.238005i	0.0295782	−	0.00868493i	−0.266910	−	0.963721i	$-0.586003\pi$
$751$	0.810571	−	0.238005i	0.0295782	−	0.00868493i	0.296488	+	0.955037i	$0.404184\pi$
$752$		0			0
$753$	−18.4032	−	15.9465i	−0.670651	−	0.581122i
$754$		0			0
$755$	22.1636	+	10.6828i	0.806616	+	0.388789i
$756$		0			0
$757$	−32.0703	−	14.6460i	−1.16561	−	0.532318i	−0.263858	−	0.964562i	$-0.584995\pi$
$757$	−32.0703	−	14.6460i	−1.16561	−	0.532318i	−0.901757	+	0.432243i	$0.857722\pi$
$758$		0			0
$759$	−14.5284	+	4.70236i	−0.527347	+	0.170685i
$760$		0			0
$761$	−1.69171	+	3.70432i	−0.0613243	+	0.134282i	−0.937813	−	0.347141i	$-0.887152\pi$
$761$	−1.69171	+	3.70432i	−0.0613243	+	0.134282i	0.876489	+	0.481423i	$0.159880\pi$
$762$		0			0
$763$	26.6205	−	23.0668i	0.963726	−	0.835073i
$764$		0			0
$765$	10.3860	+	3.28511i	0.375506	+	0.118773i
$766$		0			0
$767$	−5.13581	−	17.4909i	−0.185443	−	0.631561i
$768$		0			0
$769$	5.90618	+	41.0784i	0.212982	+	1.48132i	0.763123	+	0.646253i	$0.223665\pi$
$769$	5.90618	+	41.0784i	0.212982	+	1.48132i	−0.550141	+	0.835072i	$0.685426\pi$
$770$		0			0
$771$	−1.14432	−	2.50570i	−0.0412115	−	0.0902407i
$772$		0			0
$773$	−17.9267	+	27.8945i	−0.644778	+	1.00329i	0.352931	+	0.935649i	$0.385185\pi$
$773$	−17.9267	+	27.8945i	−0.644778	+	1.00329i	−0.997709	+	0.0676450i	$0.978451\pi$
$774$		0			0
$775$	−18.3943	−	23.0985i	−0.660744	−	0.829721i
$776$		0			0
$777$	17.2732	+	26.8777i	0.619674	+	0.964232i
$778$		0			0
$779$	18.3472	+	5.38721i	0.657355	+	0.193017i
$780$		0			0
$781$	25.7926			0.922931
$782$		0			0
$783$		−	6.49847i		−	0.232236i
$784$		0			0
$785$	−2.84305	−	23.1775i	−0.101473	−	0.827241i
$786$		0			0
$787$	14.2955	+	22.2442i	0.509580	+	0.792921i	0.996764	−	0.0803776i	$-0.0256126\pi$
$787$	14.2955	+	22.2442i	0.509580	+	0.792921i	−0.487185	+	0.873299i	$0.661976\pi$
$788$		0			0
$789$	3.86916	−	26.9106i	0.137746	−	0.958043i
$790$		0			0
$791$	−45.5224	−	29.2554i	−1.61859	−	1.04020i
$792$		0			0
$793$	27.5673	−	12.5896i	0.978944	−	0.447069i
$794$		0			0
$795$	−10.4234	−	16.9837i	−0.369679	−	0.602348i
$796$		0			0
$797$	−12.1456	−	41.3639i	−0.430217	−	1.46519i	−0.834733	−	0.550655i	$-0.814378\pi$
$797$	−12.1456	−	41.3639i	−0.430217	−	1.46519i	0.404515	−	0.914531i	$-0.367440\pi$
$798$		0			0
$799$	8.01658	−	9.25162i	0.283606	−	0.327299i
$800$		0			0
$801$	5.92172	+	6.83403i	0.209234	+	0.241469i
$802$		0			0
$803$	−38.9866	−	17.8046i	−1.37581	−	0.628310i
$804$		0			0
$805$	−19.8838	+	31.3990i	−0.700810	+	1.10667i
$806$		0			0
$807$	−10.4541	−	4.77421i	−0.368000	−	0.168060i
$808$		0			0
$809$	−16.5942	−	19.1508i	−0.583423	−	0.673306i	0.384914	−	0.922952i	$-0.374231\pi$
$809$	−16.5942	−	19.1508i	−0.583423	−	0.673306i	−0.968337	+	0.249647i	$0.919686\pi$
$810$		0			0
$811$	−12.1914	+	14.0696i	−0.428098	+	0.494051i	−0.928287	−	0.371865i	$-0.878718\pi$
$811$	−12.1914	+	14.0696i	−0.428098	+	0.494051i	0.500189	+	0.865916i	$0.333264\pi$
$812$		0			0
$813$	−0.00715790	−	0.0243776i	−0.000251038	−	0.000854958i
$814$		0			0
$815$	34.1869	−	20.9815i	1.19751	−	0.734949i
$816$		0			0
$817$	−17.9033	+	8.17615i	−0.626356	+	0.286047i
$818$		0			0
$819$	15.7742	+	10.1375i	0.551197	+	0.354233i
$820$		0			0
$821$	−5.65892	+	39.3586i	−0.197498	+	1.37363i	0.614017	+	0.789293i	$0.289553\pi$
$821$	−5.65892	+	39.3586i	−0.197498	+	1.37363i	−0.811514	+	0.584333i	$0.801356\pi$
$822$		0			0
$823$	22.5333	+	35.0624i	0.785460	+	1.22220i	0.970886	+	0.239542i	$0.0769972\pi$
$823$	22.5333	+	35.0624i	0.785460	+	1.22220i	−0.185426	+	0.982658i	$0.559366\pi$
$824$		0			0
$825$	−8.04435	−	13.7387i	−0.280068	−	0.478320i
$826$		0			0
$827$		−	17.8290i		−	0.619974i	−0.950741	−	0.309987i	$-0.899675\pi$
$827$		−	17.8290i		−	0.619974i	0.950741	−	0.309987i	$-0.100325\pi$
$828$		0			0
$829$	0.0203346			0.000706250			0.000353125	−	1.00000i	$-0.499888\pi$
$829$	0.0203346			0.000706250			0.000353125		1.00000i	$0.499888\pi$
$830$		0			0
$831$	24.6507	+	7.23809i	0.855122	+	0.251086i
$832$		0			0
$833$	−5.86621	−	9.12801i	−0.203252	−	0.316267i
$834$		0			0
$835$	−31.0555	+	8.42306i	−1.07472	+	0.291492i
$836$		0			0
$837$	−14.5178	+	22.5902i	−0.501810	+	0.780832i
$838$		0			0
$839$	−23.6111	−	51.7011i	−0.815146	−	1.78492i	−0.583485	−	0.812124i	$-0.698311\pi$
$839$	−23.6111	−	51.7011i	−0.815146	−	1.78492i	−0.231660	−	0.972797i	$-0.574416\pi$
$840$		0			0
$841$	3.83646	+	26.6831i	0.132292	+	0.920108i
$842$		0			0
$843$	−2.52583	−	8.60219i	−0.0869942	−	0.296275i
$844$		0			0
$845$	4.86650	−	15.3856i	0.167413	−	0.529282i
$846$		0			0
$847$	6.58552	−	5.70639i	0.226281	−	0.196074i
$848$		0			0
$849$	−6.45509	+	14.1347i	−0.221538	+	0.485101i
$850$		0			0
$851$	19.9234	−	46.9958i	0.682965	−	1.61100i
$852$		0			0
$853$	22.5746	+	10.3095i	0.772939	+	0.352989i	0.762527	−	0.646956i	$-0.223958\pi$
$853$	22.5746	+	10.3095i	0.772939	+	0.352989i	0.0104121	+	0.999946i	$0.496686\pi$
$854$		0			0
$855$	11.4974	+	5.54174i	0.393202	+	0.189523i
$856$		0			0
$857$	35.3895	+	30.6652i	1.20888	+	1.04750i	0.997541	+	0.0700899i	$0.0223286\pi$
$857$	35.3895	+	30.6652i	1.20888	+	1.04750i	0.211341	+	0.977412i	$0.432217\pi$
$858$		0			0
$859$	10.0959	−	2.96443i	0.344469	−	0.101145i	−0.104922	−	0.994480i	$-0.533459\pi$
$859$	10.0959	−	2.96443i	0.344469	−	0.101145i	0.449391	+	0.893335i	$0.351641\pi$
$860$		0			0
$861$	3.21976	+	22.3939i	0.109729	+	0.763182i
$862$		0			0
$863$	9.32429	−	4.25826i	0.317403	−	0.144953i	−0.250343	−	0.968157i	$-0.580543\pi$
$863$	9.32429	−	4.25826i	0.317403	−	0.144953i	0.567745	+	0.823204i	$0.307816\pi$
$864$		0			0
$865$	0.215314	−	1.30479i	0.00732090	−	0.0443641i
$866$		0			0
$867$	10.5548	+	1.51756i	0.358461	+	0.0515389i
$868$		0			0
$869$	−3.84223	+	2.46925i	−0.130339	+	0.0837636i
$870$		0			0
$871$	26.1937	+	7.69116i	0.887539	+	0.260605i
$872$		0			0
$873$			7.52810i			0.254788i
$874$		0			0
$875$	−36.4271	−	13.2076i	−1.23146	−	0.446499i
$876$		0			0
$877$	−8.60888	+	29.3191i	−0.290701	+	0.990037i	0.676588	+	0.736362i	$0.263458\pi$
$877$	−8.60888	+	29.3191i	−0.290701	+	0.990037i	−0.967289	+	0.253676i	$0.918360\pi$
$878$		0			0
$879$	−3.49672	+	2.24721i	−0.117941	+	0.0757964i
$880$		0			0
$881$	6.23640	−	43.3751i	0.210110	−	1.46134i	−0.562676	−	0.826677i	$-0.690228\pi$
$881$	6.23640	−	43.3751i	0.210110	−	1.46134i	0.772786	−	0.634667i	$-0.218863\pi$
$882$		0			0
$883$	4.36839	−	6.79735i	0.147008	−	0.228749i	−0.759938	−	0.649995i	$-0.774771\pi$
$883$	4.36839	−	6.79735i	0.147008	−	0.228749i	0.906946	+	0.421246i	$0.138407\pi$
$884$		0			0
$885$	9.84213	−	10.8934i	0.330840	−	0.366177i
$886$		0			0
$887$	−29.3567	+	4.22086i	−0.985702	+	0.141723i	−0.616270	−	0.787535i	$-0.711357\pi$
$887$	−29.3567	+	4.22086i	−0.985702	+	0.141723i	−0.369432	+	0.929258i	$0.620448\pi$
$888$		0			0
$889$	0.540836	−	0.158804i	0.0181391	−	0.00532611i
$890$		0			0
$891$	6.76708	−	7.80963i	0.226706	−	0.261632i
$892$		0			0
$893$	10.8399	−	9.39284i	0.362744	−	0.314319i
$894$		0			0
$895$	−0.321848	+	15.5122i	−0.0107582	+	0.518515i
$896$		0			0
$897$	0.273945	+	9.98573i	0.00914677	+	0.333414i
$898$		0			0
$899$	−3.50608	+	7.67725i	−0.116934	+	0.256051i
$900$		0			0
$901$	−14.5896	−	16.8374i	−0.486052	−	0.560933i
$902$		0			0
$903$	−17.5991	−	15.2497i	−0.585662	−	0.507479i
$904$		0			0
$905$	−16.5852	+	13.7793i	−0.551312	+	0.458041i
$906$		0			0
$907$	7.61245	−	1.09450i	0.252767	−	0.0363424i	−0.0147664	−	0.999891i	$-0.504700\pi$
$907$	7.61245	−	1.09450i	0.252767	−	0.0363424i	0.267534	+	0.963549i	$0.413791\pi$
$908$		0			0
$909$	9.71932	+	21.2823i	0.322369	+	0.705891i
$910$		0			0
$911$	33.5962	+	21.5909i	1.11309	+	0.715340i	0.961964	−	0.273175i	$-0.0880737\pi$
$911$	33.5962	+	21.5909i	1.11309	+	0.715340i	0.151126	+	0.988514i	$0.451710\pi$
$912$		0			0
$913$	22.0829	+	3.17503i	0.730836	+	0.105078i
$914$		0			0
$915$	20.2543	+	13.6185i	0.669588	+	0.450214i
$916$		0			0
$917$	9.17839	−	31.2587i	0.303097	−	1.03225i
$918$		0			0
$919$	−17.5368			−0.578485			−0.289242	−	0.957256i	$-0.593403\pi$
$919$	−17.5368			−0.578485			−0.289242	+	0.957256i	$0.593403\pi$
$920$		0			0
$921$	8.05393			0.265386
$922$		0			0
$923$	4.75361	−	16.1893i	0.156467	−	0.532878i
$924$		0			0
$925$	52.3165	+	9.75205i	1.72016	+	0.320646i
$926$		0			0
$927$	22.2209	+	3.19488i	0.729830	+	0.104934i
$928$		0			0
$929$	22.6661	+	14.5666i	0.743650	+	0.477915i	0.856791	−	0.515664i	$-0.172455\pi$
$929$	22.6661	+	14.5666i	0.743650	+	0.477915i	−0.113141	+	0.993579i	$0.536091\pi$
$930$		0			0
$931$	−5.28128	−	11.5644i	−0.173087	−	0.379007i
$932$		0			0
$933$	10.2942	−	1.48008i	0.337016	−	0.0484556i
$934$		0			0
$935$	−11.3746	−	13.6909i	−0.371991	−	0.447739i
$936$		0			0
$937$	29.4026	+	25.4775i	0.960542	+	0.832315i	0.985895	−	0.167364i	$-0.0535255\pi$
$937$	29.4026	+	25.4775i	0.960542	+	0.832315i	−0.0253529	+	0.999679i	$0.508071\pi$
$938$		0			0
$939$	16.3857	+	18.9101i	0.534727	+	0.617108i
$940$		0			0
$941$	5.83030	−	12.7666i	0.190062	−	0.416179i	−0.790479	−	0.612489i	$-0.790169\pi$
$941$	5.83030	−	12.7666i	0.190062	−	0.416179i	0.980542	+	0.196310i	$0.0628958\pi$
$942$		0			0
$943$	26.6578	−	24.4107i	0.868096	−	0.794921i
$944$		0			0
$945$	−0.730956	+	35.2301i	−0.0237780	+	1.14603i
$946$		0			0
$947$	−17.7717	+	15.3992i	−0.577502	+	0.500408i	−0.893929	−	0.448209i	$-0.852062\pi$
$947$	−17.7717	+	15.3992i	−0.577502	+	0.500408i	0.316427	+	0.948617i	$0.397517\pi$
$948$		0			0
$949$	−18.3607	+	21.1894i	−0.596015	+	0.687838i
$950$		0			0
$951$	15.8410	−	4.65133i	0.513678	−	0.150830i
$952$		0			0
$953$	24.1670	−	3.47469i	0.782846	−	0.112556i	0.260709	−	0.965418i	$-0.416044\pi$
$953$	24.1670	−	3.47469i	0.782846	−	0.112556i	0.522138	+	0.852861i	$0.325135\pi$
$954$		0			0
$955$	35.6778	+	32.2347i	1.15451	+	1.04309i
$956$		0			0
$957$	−2.46023	+	3.82819i	−0.0795278	+	0.123748i
$958$		0			0
$959$	−1.05072	+	7.30791i	−0.0339295	+	0.235985i
$960$		0			0
$961$	3.26036	−	2.09531i	0.105173	−	0.0675906i
$962$		0			0
$963$	3.04286	−	10.3630i	0.0980549	−	0.333944i
$964$		0			0
$965$	−6.39159	−	14.8007i	−0.205753	−	0.476450i
$966$		0			0
$967$			15.4686i			0.497438i	0.968576	+	0.248719i	$0.0800095\pi$
$967$			15.4686i			0.497438i	−0.968576	+	0.248719i	$0.919990\pi$
$968$		0			0
$969$	−4.56553	−	1.34056i	−0.146666	−	0.0430650i
$970$		0			0
$971$	−24.8185	+	15.9499i	−0.796463	+	0.511855i	−0.874460	−	0.485098i	$-0.838784\pi$
$971$	−24.8185	+	15.9499i	−0.796463	+	0.511855i	0.0779971	+	0.996954i	$0.475148\pi$
$972$		0			0
$973$	63.8484	+	9.18001i	2.04689	+	0.294298i
$974$		0			0
$975$	−10.1060	+	2.51716i	−0.323651	+	0.0806138i
$976$		0			0
$977$	−12.7053	+	5.80232i	−0.406479	+	0.185633i	−0.608153	−	0.793820i	$-0.708089\pi$
$977$	−12.7053	+	5.80232i	−0.406479	+	0.185633i	0.201674	+	0.979453i	$0.435362\pi$
$978$		0			0
$979$	−2.10283	−	14.6255i	−0.0672067	−	0.467433i
$980$		0			0
$981$	−21.9398	+	6.44212i	−0.700485	+	0.205681i
$982$		0			0
$983$	−2.74425	−	2.37791i	−0.0875281	−	0.0758435i	0.609998	−	0.792403i	$-0.291170\pi$
$983$	−2.74425	−	2.37791i	−0.0875281	−	0.0758435i	−0.697526	+	0.716560i	$0.745716\pi$
$984$		0			0
$985$	6.68687	−	13.8732i	0.213061	−	0.442036i
$986$		0			0
$987$	15.4369	+	7.04979i	0.491361	+	0.224397i
$988$		0			0
$989$	−4.28289	+	36.9573i	−0.136188	+	1.17517i
$990$		0			0
$991$	11.7366	−	25.6995i	0.372824	−	0.816370i	−0.626494	−	0.779427i	$-0.715511\pi$
$991$	11.7366	−	25.6995i	0.372824	−	0.816370i	0.999317	−	0.0369437i	$-0.0117622\pi$
$992$		0			0
$993$	−17.5870	+	15.2392i	−0.558107	+	0.483603i
$994$		0			0
$995$	1.38402	−	4.37564i	0.0438765	−	0.138717i
$996$		0			0
$997$	−17.5855	−	59.8908i	−0.556939	−	1.89676i	−0.424075	−	0.905627i	$-0.639401\pi$
$997$	−17.5855	−	59.8908i	−0.556939	−	1.89676i	−0.132865	−	0.991134i	$-0.542418\pi$
$998$		0			0
$999$	−6.88760	−	47.9043i	−0.217914	−	1.51563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.29.6	✓	120
5.4	even	2	inner	460.2.s.a.29.7	yes	120
23.4	even	11	inner	460.2.s.a.349.7	yes	120
115.4	even	22	inner	460.2.s.a.349.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.29.6	✓	120	1.1	even	1	trivial
460.2.s.a.29.7	yes	120	5.4	even	2	inner
460.2.s.a.349.6	yes	120	115.4	even	22	inner
460.2.s.a.349.7	yes	120	23.4	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.244021 + 0.831059i) q^{3} +(-1.24767 + 1.85562i) q^{5} +(-3.43041 - 0.493219i) q^{7} +(1.89265 + 1.21633i) q^{9} +O(q^{10})\)	\(q+(-0.244021 + 0.831059i) q^{3} +(-1.24767 + 1.85562i) q^{5} +(-3.43041 - 0.493219i) q^{7} +(1.89265 + 1.21633i) q^{9} +(-1.52714 - 3.34398i) q^{11} +(-2.38038 + 0.342247i) q^{13} +(-1.23767 - 1.48970i) q^{15} +(-1.63645 - 1.41799i) q^{17} +(-1.66143 - 1.91739i) q^{19} +(1.24699 - 2.73052i) q^{21} +(-4.72651 + 0.812440i) q^{23} +(-1.88664 - 4.63040i) q^{25} +(-3.43645 + 2.97770i) q^{27} +(-0.935897 + 1.08008i) q^{29} +(5.66634 - 1.66379i) q^{31} +(3.15169 - 0.453145i) q^{33} +(5.19525 - 5.75016i) q^{35} +(-5.75433 + 8.95391i) q^{37} +(0.296435 - 2.06175i) q^{39} +(-6.34046 + 4.07476i) q^{41} +(2.18560 - 7.44347i) q^{43} +(-4.61845 + 1.99445i) q^{45} +5.65346i q^{47} +(4.80801 + 1.41176i) q^{49} +(1.57777 - 1.01397i) q^{51} +(10.1842 + 1.46427i) q^{53} +(8.11051 + 1.33839i) q^{55} +(1.99889 - 0.912863i) q^{57} +(1.07878 + 7.50307i) q^{59} +(-12.0915 + 3.55039i) q^{61} +(-5.89264 - 5.10601i) q^{63} +(2.33485 - 4.84409i) q^{65} +(-10.3260 - 4.71572i) q^{67} +(0.478182 - 4.12626i) q^{69} +(-2.91461 + 6.38210i) q^{71} +(8.81110 - 7.63486i) q^{73} +(4.30851 - 0.437993i) q^{75} +(3.58942 + 12.2244i) q^{77} +(-0.176811 - 1.22975i) q^{79} +(1.16772 + 2.55694i) q^{81} +(-3.28103 + 5.10538i) q^{83} +(4.67301 - 1.26744i) q^{85} +(-0.669234 - 1.04135i) q^{87} +(3.85654 + 1.13238i) q^{89} +8.33448 q^{91} +5.11506i q^{93} +(5.63087 - 0.690707i) q^{95} +(1.80905 + 2.81494i) q^{97} +(1.17704 - 8.18648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more