LMFDB - Embedded newform 460.2.x.a.333.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			333.4
Character	$\chi$	$=$	460.333
Dual form			460.2.x.a.297.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26823 + 0.949384i) q^{3} +(-2.13237 - 0.673046i) q^{5} +(0.0711105 - 0.994255i) q^{7} +(-0.138124 + 0.470407i) q^{9} +O(q^{10})$	\(q+(-1.26823 + 0.949384i) q^{3} +(-2.13237 - 0.673046i) q^{5} +(0.0711105 - 0.994255i) q^{7} +(-0.138124 + 0.470407i) q^{9} +(0.617875 - 0.961432i) q^{11} +(3.39836 - 0.243056i) q^{13} +(3.34331 - 1.17086i) q^{15} +(1.77564 - 4.76067i) q^{17} +(1.26196 - 2.76331i) q^{19} +(0.853746 + 1.32845i) q^{21} +(-1.13272 - 4.66014i) q^{23} +(4.09402 + 2.87037i) q^{25} +(-1.93230 - 5.18070i) q^{27} +(6.85806 - 3.13197i) q^{29} +(1.12545 + 7.82767i) q^{31} +(0.129162 + 1.80592i) q^{33} +(-0.820814 + 2.07226i) q^{35} +(-0.503406 - 0.921920i) q^{37} +(-4.07915 + 3.53460i) q^{39} +(7.46831 - 2.19289i) q^{41} +(-2.62696 - 3.50921i) q^{43} +(0.611137 - 0.910118i) q^{45} +(2.09561 - 2.09561i) q^{47} +(5.94526 + 0.854800i) q^{49} +(2.26779 + 7.72338i) q^{51} +(-8.42570 - 0.602618i) q^{53} +(-1.96463 + 1.63427i) q^{55} +(1.02299 + 4.70260i) q^{57} +(-5.56138 - 4.81897i) q^{59} +(-4.66129 + 0.670192i) q^{61} +(0.457882 + 0.170781i) q^{63} +(-7.41016 - 1.76897i) q^{65} +(-13.2854 - 2.89006i) q^{67} +(5.86081 + 4.83474i) q^{69} +(-8.50284 + 5.46444i) q^{71} +(10.2183 - 3.81123i) q^{73} +(-7.91723 + 0.246511i) q^{75} +(-0.911971 - 0.682693i) q^{77} +(-0.257462 + 0.297127i) q^{79} +(6.13176 + 3.94065i) q^{81} +(5.27778 - 2.88188i) q^{83} +(-6.99047 + 8.95643i) q^{85} +(-5.72414 + 10.4830i) q^{87} +(1.05389 - 7.32998i) q^{89} -3.39612i q^{91} +(-8.85880 - 8.85880i) q^{93} +(-4.55081 + 5.04305i) q^{95} +(4.66488 + 2.54722i) q^{97} +(0.366921 + 0.423449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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
$3$	−1.26823	+	0.949384i	−0.732212	+	0.548127i	−0.899044	−	0.437858i	$-0.855737\pi$
$3$	−1.26823	+	0.949384i	−0.732212	+	0.548127i	0.166832	+	0.985985i	$0.446646\pi$
$4$		0			0
$5$	−2.13237	−	0.673046i	−0.953626	−	0.300995i
$5$	−2.13237	−	0.673046i	−0.953626	−	0.300995i
$6$		0			0
$7$	0.0711105	−	0.994255i	0.0268773	−	0.375793i	−0.966156	−	0.257959i	$-0.916950\pi$
$7$	0.0711105	−	0.994255i	0.0268773	−	0.375793i	0.993033	−	0.117835i	$-0.0375953\pi$
$8$		0			0
$9$	−0.138124	+	0.470407i	−0.0460413	+	0.156802i
$10$		0			0
$11$	0.617875	−	0.961432i	0.186296	−	0.289883i	−0.735525	−	0.677497i	$-0.763065\pi$
$11$	0.617875	−	0.961432i	0.186296	−	0.289883i	0.921821	+	0.387615i	$0.126701\pi$
$12$		0			0
$13$	3.39836	−	0.243056i	0.942537	−	0.0674116i	0.408394	−	0.912806i	$-0.366089\pi$
$13$	3.39836	−	0.243056i	0.942537	−	0.0674116i	0.534143	+	0.845394i	$0.320634\pi$
$14$		0			0
$15$	3.34331	−	1.17086i	0.863240	−	0.302316i
$16$		0			0
$17$	1.77564	−	4.76067i	0.430656	−	1.15463i	−0.522629	−	0.852560i	$-0.675049\pi$
$17$	1.77564	−	4.76067i	0.430656	−	1.15463i	0.953285	−	0.302072i	$-0.0976785\pi$
$18$		0			0
$19$	1.26196	−	2.76331i	0.289514	−	0.633947i	−0.707861	−	0.706351i	$-0.750340\pi$
$19$	1.26196	−	2.76331i	0.289514	−	0.633947i	0.997375	+	0.0724043i	$0.0230672\pi$
$20$		0			0
$21$	0.853746	+	1.32845i	0.186303	+	0.289892i
$22$		0			0
$23$	−1.13272	−	4.66014i	−0.236188	−	0.971707i
$23$	−1.13272	−	4.66014i	−0.236188	−	0.971707i
$24$		0			0
$25$	4.09402	+	2.87037i	0.818804	+	0.574074i
$26$		0			0
$27$	−1.93230	−	5.18070i	−0.371872	−	0.997027i
$28$		0			0
$29$	6.85806	−	3.13197i	1.27351	−	0.581592i	0.340094	−	0.940391i	$-0.389541\pi$
$29$	6.85806	−	3.13197i	1.27351	−	0.581592i	0.933415	+	0.358799i	$0.116814\pi$
$30$		0			0
$31$	1.12545	+	7.82767i	0.202137	+	1.40589i	0.797928	+	0.602752i	$0.205929\pi$
$31$	1.12545	+	7.82767i	0.202137	+	1.40589i	−0.595792	+	0.803139i	$0.703162\pi$
$32$		0			0
$33$	0.129162	+	1.80592i	0.0224842	+	0.314370i
$34$		0			0
$35$	−0.820814	+	2.07226i	−0.138743	+	0.350276i
$36$		0			0
$37$	−0.503406	−	0.921920i	−0.0827595	−	0.151563i	0.833022	−	0.553241i	$-0.186609\pi$
$37$	−0.503406	−	0.921920i	−0.0827595	−	0.151563i	−0.915781	+	0.401678i	$0.868427\pi$
$38$		0			0
$39$	−4.07915	+	3.53460i	−0.653187	+	0.565989i
$40$		0			0
$41$	7.46831	−	2.19289i	1.16635	−	0.342472i	0.359455	−	0.933162i	$-0.382963\pi$
$41$	7.46831	−	2.19289i	1.16635	−	0.342472i	0.806898	+	0.590690i	$0.201144\pi$
$42$		0			0
$43$	−2.62696	−	3.50921i	−0.400608	−	0.535150i	0.554196	−	0.832386i	$-0.313026\pi$
$43$	−2.62696	−	3.50921i	−0.400608	−	0.535150i	−0.954804	+	0.297237i	$0.903935\pi$
$44$		0			0
$45$	0.611137	−	0.910118i	0.0911029	−	0.135672i
$46$		0			0
$47$	2.09561	−	2.09561i	0.305676	−	0.305676i	−0.537554	−	0.843230i	$-0.680651\pi$
$47$	2.09561	−	2.09561i	0.305676	−	0.305676i	0.843230	+	0.537554i	$0.180651\pi$
$48$		0			0
$49$	5.94526	+	0.854800i	0.849323	+	0.122114i
$50$		0			0
$51$	2.26779	+	7.72338i	0.317554	+	1.08149i
$52$		0			0
$53$	−8.42570	−	0.602618i	−1.15736	−	0.0827760i	−0.520574	−	0.853817i	$-0.674282\pi$
$53$	−8.42570	−	0.602618i	−1.15736	−	0.0827760i	−0.636786	+	0.771041i	$0.719736\pi$
$54$		0			0
$55$	−1.96463	+	1.63427i	−0.264910	+	0.220365i
$56$		0			0
$57$	1.02299	+	4.70260i	0.135498	+	0.622874i
$58$		0			0
$59$	−5.56138	−	4.81897i	−0.724031	−	0.627376i	0.212826	−	0.977090i	$-0.431733\pi$
$59$	−5.56138	−	4.81897i	−0.724031	−	0.627376i	−0.936856	+	0.349714i	$0.886279\pi$
$60$		0			0
$61$	−4.66129	+	0.670192i	−0.596817	+	0.0858093i	−0.434102	−	0.900864i	$-0.642934\pi$
$61$	−4.66129	+	0.670192i	−0.596817	+	0.0858093i	−0.162715	+	0.986673i	$0.552025\pi$
$62$		0			0
$63$	0.457882	+	0.170781i	0.0576877	+	0.0215164i
$64$		0			0
$65$	−7.41016	−	1.76897i	−0.919118	−	0.219414i
$66$		0			0
$67$	−13.2854	−	2.89006i	−1.62307	−	0.353077i	−0.693138	−	0.720805i	$-0.743772\pi$
$67$	−13.2854	−	2.89006i	−1.62307	−	0.353077i	−0.929933	+	0.367728i	$0.880136\pi$
$68$		0			0
$69$	5.86081	+	4.83474i	0.705559	+	0.582035i
$70$		0			0
$71$	−8.50284	+	5.46444i	−1.00910	+	0.648510i	−0.937160	−	0.348899i	$-0.886556\pi$
$71$	−8.50284	+	5.46444i	−1.00910	+	0.648510i	−0.0719411	+	0.997409i	$0.522919\pi$
$72$		0			0
$73$	10.2183	−	3.81123i	1.19596	−	0.446071i	0.328944	−	0.944349i	$-0.393307\pi$
$73$	10.2183	−	3.81123i	1.19596	−	0.446071i	0.867017	+	0.498279i	$0.166034\pi$
$74$		0			0
$75$	−7.91723	+	0.246511i	−0.914203	+	0.0284647i
$76$		0			0
$77$	−0.911971	−	0.682693i	−0.103929	−	0.0778001i
$78$		0			0
$79$	−0.257462	+	0.297127i	−0.0289667	+	0.0334294i	−0.770048	−	0.637986i	$-0.779768\pi$
$79$	−0.257462	+	0.297127i	−0.0289667	+	0.0334294i	0.741081	+	0.671415i	$0.234313\pi$
$80$		0			0
$81$	6.13176	+	3.94065i	0.681307	+	0.437849i
$82$		0			0
$83$	5.27778	−	2.88188i	0.579311	−	0.316328i	−0.162742	−	0.986669i	$-0.552034\pi$
$83$	5.27778	−	2.88188i	0.579311	−	0.316328i	0.742053	+	0.670341i	$0.233852\pi$
$84$		0			0
$85$	−6.99047	+	8.95643i	−0.758223	+	0.971462i
$86$		0			0
$87$	−5.72414	+	10.4830i	−0.613692	+	1.12389i
$88$		0			0
$89$	1.05389	−	7.32998i	0.111712	−	0.776976i	−0.854541	−	0.519384i	$-0.826162\pi$
$89$	1.05389	−	7.32998i	0.111712	−	0.776976i	0.966254	−	0.257593i	$-0.0829293\pi$
$90$		0			0
$91$		−	3.39612i		−	0.356011i
$92$		0			0
$93$	−8.85880	−	8.85880i	−0.918614	−	0.918614i
$94$		0			0
$95$	−4.55081	+	5.04305i	−0.466903	+	0.517406i
$96$		0			0
$97$	4.66488	+	2.54722i	0.473647	+	0.258631i	0.698296	−	0.715809i	$-0.253942\pi$
$97$	4.66488	+	2.54722i	0.473647	+	0.258631i	−0.224649	+	0.974440i	$0.572124\pi$
$98$		0			0
$99$	0.366921	+	0.423449i	0.0368769	+	0.0425582i
$100$		0			0
$101$	−10.0900	−	2.96270i	−1.00399	−	0.294799i	−0.261900	−	0.965095i	$-0.584349\pi$
$101$	−10.0900	−	2.96270i	−1.00399	−	0.294799i	−0.742094	+	0.670296i	$0.766167\pi$
$102$		0			0
$103$	5.62751	−	1.22419i	0.554495	−	0.120623i	0.0734178	−	0.997301i	$-0.476609\pi$
$103$	5.62751	−	1.22419i	0.554495	−	0.120623i	0.481077	+	0.876678i	$0.340246\pi$
$104$		0			0
$105$	−0.926392	−	3.40737i	−0.0904066	−	0.332525i
$106$		0			0
$107$	−5.71506	+	7.63443i	−0.552496	+	0.738048i	−0.986662	−	0.162785i	$-0.947952\pi$
$107$	−5.71506	+	7.63443i	−0.552496	+	0.738048i	0.434166	+	0.900833i	$0.357043\pi$
$108$		0			0
$109$	3.37921	+	7.39943i	0.323669	+	0.708737i	0.999602	−	0.0282267i	$-0.00898605\pi$
$109$	3.37921	+	7.39943i	0.323669	+	0.708737i	−0.675932	+	0.736964i	$0.736259\pi$
$110$		0			0
$111$	1.51369	+	0.691279i	0.143673	+	0.0656133i
$112$		0			0
$113$	3.03767	−	13.9639i	0.285760	−	1.31362i	−0.580597	−	0.814191i	$-0.697181\pi$
$113$	3.03767	−	13.9639i	0.285760	−	1.31362i	0.866357	−	0.499425i	$-0.166455\pi$
$114$		0			0
$115$	−0.721112	+	10.6995i	−0.0672441	+	0.997737i
$116$		0			0
$117$	−0.355060	+	1.63218i	−0.0328253	+	0.150896i
$118$		0			0
$119$	−4.60706	−	2.10397i	−0.422328	−	0.192871i
$120$		0			0
$121$	4.02698	+	8.81786i	0.366089	+	0.801624i
$122$		0			0
$123$	−7.38962	+	9.87138i	−0.666300	+	0.890072i
$124$		0			0
$125$	−6.79808	−	8.87616i	−0.608038	−	0.793908i
$126$		0			0
$127$	−0.140168	+	0.0304916i	−0.0124379	+	0.00270569i	−0.218780	−	0.975774i	$-0.570208\pi$
$127$	−0.140168	+	0.0304916i	−0.0124379	+	0.00270569i	0.206342	+	0.978480i	$0.433844\pi$
$128$		0			0
$129$	6.66318	+	1.95649i	0.586660	+	0.172259i
$130$		0			0
$131$	12.7649	+	14.7315i	1.11528	+	1.28710i	0.953874	+	0.300207i	$0.0970559\pi$
$131$	12.7649	+	14.7315i	1.11528	+	1.28710i	0.161401	+	0.986889i	$0.448399\pi$
$132$		0			0
$133$	−2.65770	−	1.45121i	−0.230452	−	0.125836i
$134$		0			0
$135$	0.633535	+	12.3477i	0.0545260	+	1.06272i
$136$		0			0
$137$	2.67930	+	2.67930i	0.228908	+	0.228908i	0.812236	−	0.583329i	$-0.198250\pi$
$137$	2.67930	+	2.67930i	0.228908	+	0.228908i	−0.583329	+	0.812236i	$0.698250\pi$
$138$		0			0
$139$		−	14.2670i		−	1.21011i	−0.796183	−	0.605056i	$-0.793151\pi$
$139$		−	14.2670i		−	1.21011i	0.796183	−	0.605056i	$-0.206849\pi$
$140$		0			0
$141$	−0.668173	+	4.64725i	−0.0562703	+	0.391369i
$142$		0			0
$143$	1.86608	−	3.41747i	0.156050	−	0.285783i
$144$		0			0
$145$	−16.7319	+	2.06273i	−1.38951	+	0.171301i
$146$		0			0
$147$	−8.35149	+	4.56026i	−0.688819	+	0.376124i
$148$		0			0
$149$	5.81945	+	3.73993i	0.476748	+	0.306387i	0.756857	−	0.653581i	$-0.226734\pi$
$149$	5.81945	+	3.73993i	0.476748	+	0.306387i	−0.280109	+	0.959968i	$0.590371\pi$
$150$		0			0
$151$	7.81020	−	9.01345i	0.635585	−	0.733504i	−0.343003	−	0.939334i	$-0.611444\pi$
$151$	7.81020	−	9.01345i	0.635585	−	0.733504i	0.978588	+	0.205830i	$0.0659896\pi$
$152$		0			0
$153$	1.99419	+	1.49283i	0.161221	+	0.120689i
$154$		0			0
$155$	2.86851	−	17.4490i	0.230404	−	1.40154i
$156$		0			0
$157$	−10.5924	+	3.95075i	−0.845364	+	0.315304i	−0.734565	−	0.678538i	$-0.762614\pi$
$157$	−10.5924	+	3.95075i	−0.845364	+	0.315304i	−0.110799	+	0.993843i	$0.535341\pi$
$158$		0			0
$159$	11.2578	−	7.23497i	0.892804	−	0.573770i
$160$		0			0
$161$	−4.71392	+	0.794827i	−0.371509	+	0.0626412i
$162$		0			0
$163$	6.90677	+	1.50248i	0.540980	+	0.117683i	0.474749	−	0.880121i	$-0.342539\pi$
$163$	6.90677	+	1.50248i	0.540980	+	0.117683i	0.0662312	+	0.997804i	$0.478903\pi$
$164$		0			0
$165$	0.940044	−	3.93781i	0.0731823	−	0.306558i
$166$		0			0
$167$	6.49927	+	2.42410i	0.502928	+	0.187583i	0.588107	−	0.808783i	$-0.299873\pi$
$167$	6.49927	+	2.42410i	0.502928	+	0.187583i	−0.0851786	+	0.996366i	$0.527146\pi$
$168$		0			0
$169$	−1.37788	+	0.198109i	−0.105990	+	0.0152391i
$170$		0			0
$171$	1.12557	+	0.975314i	0.0860747	+	0.0745842i
$172$		0			0
$173$	−0.188326	−	0.865721i	−0.0143182	−	0.0658196i	0.969433	−	0.245354i	$-0.0789044\pi$
$173$	−0.188326	−	0.865721i	−0.0143182	−	0.0658196i	−0.983752	+	0.179535i	$0.942541\pi$
$174$		0			0
$175$	3.14501	−	3.86638i	0.237740	−	0.292271i
$176$		0			0
$177$	11.6282	+	0.831662i	0.874026	+	0.0625116i
$178$		0			0
$179$	−3.27750	−	11.1621i	−0.244972	−	0.834297i	−0.986554	−	0.163435i	$-0.947743\pi$
$179$	−3.27750	−	11.1621i	−0.244972	−	0.834297i	0.741583	−	0.670862i	$-0.234076\pi$
$180$		0			0
$181$	7.98078	+	1.14746i	0.593207	+	0.0852903i	0.432379	−	0.901692i	$-0.357674\pi$
$181$	7.98078	+	1.14746i	0.593207	+	0.0852903i	0.160828	+	0.986982i	$0.448583\pi$
$182$		0			0
$183$	5.27531	−	5.27531i	0.389962	−	0.389962i
$184$		0			0
$185$	0.452955	+	2.30469i	0.0333019	+	0.169444i
$186$		0			0
$187$	−3.47994	−	4.64865i	−0.254478	−	0.339943i
$188$		0			0
$189$	−5.28835	+	1.55280i	−0.384671	+	0.112949i
$190$		0			0
$191$	−10.0576	+	8.71495i	−0.727742	+	0.630592i	−0.937832	−	0.347090i	$-0.887170\pi$
$191$	−10.0576	+	8.71495i	−0.727742	+	0.630592i	0.210090	+	0.977682i	$0.432624\pi$
$192$		0			0
$193$	7.59180	+	13.9034i	0.546470	+	1.00079i	0.994295	+	0.106664i	$0.0340169\pi$
$193$	7.59180	+	13.9034i	0.546470	+	1.00079i	−0.447825	+	0.894121i	$0.647801\pi$
$194$		0			0
$195$	11.0772	−	4.79163i	0.793256	−	0.343136i
$196$		0			0
$197$	−0.671085	−	9.38300i	−0.0478129	−	0.668511i	−0.963685	−	0.267041i	$-0.913954\pi$
$197$	−0.671085	−	9.38300i	−0.0478129	−	0.668511i	0.915872	−	0.401470i	$-0.131501\pi$
$198$		0			0
$199$	0.106903	+	0.743525i	0.00757813	+	0.0527071i	0.993260	−	0.115911i	$-0.0369787\pi$
$199$	0.106903	+	0.743525i	0.00757813	+	0.0527071i	−0.985681	+	0.168618i	$0.946070\pi$
$200$		0			0
$201$	19.5927	−	8.94769i	1.38196	−	0.631122i
$202$		0			0
$203$	−2.62630	−	7.04137i	−0.184330	−	0.494208i
$204$		0			0
$205$	−17.4011	−	0.350453i	−1.21535	−	0.0244767i
$206$		0			0
$207$	2.34862	+	0.110838i	0.163240	+	0.00770378i
$208$		0			0
$209$	−1.87700	−	2.92067i	−0.129835	−	0.202027i
$210$		0			0
$211$	8.18656	−	17.9261i	0.563586	−	1.23408i	−0.386556	−	0.922266i	$-0.626335\pi$
$211$	8.18656	−	17.9261i	0.563586	−	1.23408i	0.950143	−	0.311816i	$-0.100937\pi$
$212$		0			0
$213$	5.59569	−	15.0026i	0.383410	−	1.02796i
$214$		0			0
$215$	3.23980	+	9.25101i	0.220953	+	0.630914i
$216$		0			0
$217$	7.86274	−	0.562354i	0.533757	−	0.0381751i
$218$		0			0
$219$	−9.34082	+	14.5346i	−0.631194	+	0.982157i
$220$		0			0
$221$	4.87716	−	16.6101i	0.328073	−	1.11731i
$222$		0			0
$223$	−1.11661	+	15.6122i	−0.0747736	+	1.04547i	0.812118	+	0.583493i	$0.198315\pi$
$223$	−1.11661	+	15.6122i	−0.0747736	+	1.04547i	−0.886892	+	0.461978i	$0.847140\pi$
$224$		0			0
$225$	−1.91572	+	1.52939i	−0.127715	+	0.101959i
$226$		0			0
$227$	3.73527	−	2.79619i	0.247919	−	0.185590i	−0.468090	−	0.883681i	$-0.655058\pi$
$227$	3.73527	−	2.79619i	0.247919	−	0.185590i	0.716009	+	0.698091i	$0.245967\pi$
$228$		0			0
$229$	−0.694283			−0.0458795			−0.0229398	−	0.999737i	$-0.507303\pi$
$229$	−0.694283			−0.0458795			−0.0229398	+	0.999737i	$0.507303\pi$
$230$		0			0
$231$	1.80473			0.118742
$232$		0			0
$233$	−18.1613	+	13.5954i	−1.18979	+	0.890665i	−0.995909	−	0.0903599i	$-0.971198\pi$
$233$	−18.1613	+	13.5954i	−1.18979	+	0.890665i	−0.193880	+	0.981025i	$0.562107\pi$
$234$		0			0
$235$	−5.87906	+	3.05817i	−0.383507	+	0.199493i
$236$		0			0
$237$	0.0444330	−	0.621255i	0.00288623	−	0.0403548i
$238$		0			0
$239$	3.08249	−	10.4980i	0.199389	−	0.679058i	−0.797716	−	0.603033i	$-0.793959\pi$
$239$	3.08249	−	10.4980i	0.199389	−	0.679058i	0.997106	−	0.0760254i	$-0.0242230\pi$
$240$		0			0
$241$	9.97443	−	15.5205i	0.642510	−	0.999765i	−0.355373	−	0.934725i	$-0.615646\pi$
$241$	9.97443	−	15.5205i	0.642510	−	0.999765i	0.997883	−	0.0650402i	$-0.0207176\pi$
$242$		0			0
$243$	5.02806	−	0.359614i	0.322550	−	0.0230692i
$244$		0			0
$245$	−12.1022	−	5.82419i	−0.773181	−	0.372094i
$246$		0			0
$247$	3.61697	−	9.69746i	0.230142	−	0.617035i
$248$		0			0
$249$	−3.95741	+	8.66553i	−0.250791	+	0.549155i
$250$		0			0
$251$	0.488630	+	0.760323i	0.0308420	+	0.0479912i	0.856332	−	0.516425i	$-0.172738\pi$
$251$	0.488630	+	0.760323i	0.0308420	+	0.0479912i	−0.825490	+	0.564416i	$0.809101\pi$
$252$		0			0
$253$	−5.18029	−	1.79035i	−0.325682	−	0.112558i
$254$		0			0
$255$	0.362422	−	17.9955i	0.0226958	−	1.12692i
$256$		0			0
$257$	−4.86779	−	13.0510i	−0.303644	−	0.814102i	−0.995732	−	0.0922885i	$-0.970582\pi$
$257$	−4.86779	−	13.0510i	−0.303644	−	0.814102i	0.692088	−	0.721813i	$-0.256691\pi$
$258$		0			0
$259$	−0.952421	+	0.434956i	−0.0591805	+	0.0270269i
$260$		0			0
$261$	0.526038	+	3.65868i	0.0325609	+	0.226466i
$262$		0			0
$263$	−0.874603	−	12.2285i	−0.0539303	−	0.754045i	−0.950418	−	0.310976i	$-0.899344\pi$
$263$	−0.874603	−	12.2285i	−0.0539303	−	0.754045i	0.896488	−	0.443069i	$-0.146110\pi$
$264$		0			0
$265$	17.5611	+	6.95589i	1.07877	+	0.427297i
$266$		0			0
$267$	5.62239	+	10.2966i	0.344085	+	0.630144i
$268$		0			0
$269$	−0.665821	+	0.576937i	−0.0405958	+	0.0351765i	−0.674922	−	0.737889i	$-0.735823\pi$
$269$	−0.665821	+	0.576937i	−0.0405958	+	0.0351765i	0.634327	+	0.773065i	$0.281277\pi$
$270$		0			0
$271$	−16.9515	+	4.97740i	−1.02973	+	0.302356i	−0.752601	−	0.658477i	$-0.771201\pi$
$271$	−16.9515	+	4.97740i	−1.02973	+	0.302356i	−0.277128	+	0.960833i	$0.589383\pi$
$272$		0			0
$273$	3.22423	+	4.30706i	0.195139	+	0.260675i
$274$		0			0
$275$	5.28925	−	2.16259i	0.318954	−	0.130409i
$276$		0			0
$277$	−11.7981	+	11.7981i	−0.708877	+	0.708877i	−0.966299	−	0.257422i	$-0.917127\pi$
$277$	−11.7981	+	11.7981i	−0.708877	+	0.708877i	0.257422	+	0.966299i	$0.417127\pi$
$278$		0			0
$279$	−3.83764	−	0.551769i	−0.229754	−	0.0330336i
$280$		0			0
$281$	8.42457	+	28.6914i	0.502568	+	1.71159i	0.685154	+	0.728398i	$0.259735\pi$
$281$	8.42457	+	28.6914i	0.502568	+	1.71159i	−0.182586	+	0.983190i	$0.558447\pi$
$282$		0			0
$283$	18.8540	+	1.34846i	1.12075	+	0.0801578i	0.619393	−	0.785081i	$-0.287379\pi$
$283$	18.8540	+	1.34846i	1.12075	+	0.0801578i	0.501360	+	0.865239i	$0.332833\pi$
$284$		0			0
$285$	0.983675	−	10.7162i	0.0582679	−	0.634773i
$286$		0			0
$287$	−1.64922	−	7.58134i	−0.0973503	−	0.447512i
$288$		0			0
$289$	−6.66336	−	5.77383i	−0.391962	−	0.339637i
$290$		0			0
$291$	−8.33442	+	1.19831i	−0.488573	+	0.0702461i
$292$		0			0
$293$	26.2974	+	9.80841i	1.53631	+	0.573014i	0.968252	−	0.249976i	$-0.0804227\pi$
$293$	26.2974	+	9.80841i	1.53631	+	0.573014i	0.568057	+	0.822989i	$0.307695\pi$
$294$		0			0
$295$	8.61555	+	14.0189i	0.501617	+	0.816212i
$296$		0			0
$297$	−6.17481	−	1.34325i	−0.358299	−	0.0779432i
$298$		0			0
$299$	−4.98207	−	15.5616i	−0.288121	−	0.899948i
$300$		0			0
$301$	−3.67586	+	2.36233i	−0.211873	+	0.136162i
$302$		0			0
$303$	15.6092	−	5.82192i	0.896724	−	0.334461i
$304$		0			0
$305$	10.3907	+	1.70816i	0.594968	+	0.0978092i
$306$		0			0
$307$	11.7942	+	8.82904i	0.673131	+	0.503900i	0.880307	−	0.474404i	$-0.157336\pi$
$307$	11.7942	+	8.82904i	0.673131	+	0.503900i	−0.207176	+	0.978304i	$0.566427\pi$
$308$		0			0
$309$	−5.97474	+	6.89522i	−0.339891	+	0.392255i
$310$		0			0
$311$	9.13782	+	5.87252i	0.518158	+	0.333000i	0.773443	−	0.633866i	$-0.218533\pi$
$311$	9.13782	+	5.87252i	0.518158	+	0.333000i	−0.255285	+	0.966866i	$0.582169\pi$
$312$		0			0
$313$	−28.4301	+	15.5240i	−1.60696	+	0.877468i	−0.610629	+	0.791917i	$0.709083\pi$
$313$	−28.4301	+	15.5240i	−1.60696	+	0.877468i	−0.996334	+	0.0855511i	$0.972735\pi$
$314$		0			0
$315$	−0.861431	−	0.672345i	−0.0485362	−	0.0378823i
$316$		0			0
$317$	13.3787	−	24.5012i	0.751421	−	1.37612i	−0.169167	−	0.985587i	$-0.554108\pi$
$317$	13.3787	−	24.5012i	0.751421	−	1.37612i	0.920587	−	0.390537i	$-0.127711\pi$
$318$		0			0
$319$	1.22624	−	8.52872i	0.0686565	−	0.477517i
$320$		0			0
$321$		−	15.1080i		−	0.843245i
$322$		0			0
$323$	−10.9144	−	10.9144i	−0.607295	−	0.607295i
$324$		0			0
$325$	14.6106	+	8.75948i	0.810452	+	0.485889i
$326$		0			0
$327$	−11.3105	−	6.17601i	−0.625473	−	0.341534i
$328$		0			0
$329$	−1.93455	−	2.23259i	−0.106655	−	0.123087i
$330$		0			0
$331$	−30.9396	−	9.08468i	−1.70059	−	0.499339i	−0.719766	−	0.694217i	$-0.755751\pi$
$331$	−30.9396	−	9.08468i	−1.70059	−	0.499339i	−0.980828	+	0.194878i	$0.937569\pi$
$332$		0			0
$333$	0.503210	−	0.109467i	0.0275757	−	0.00599873i
$334$		0			0
$335$	26.3843	+	15.1044i	1.44153	+	0.825241i
$336$		0			0
$337$	9.21032	−	12.3036i	0.501718	−	0.670217i	−0.476168	−	0.879354i	$-0.657975\pi$
$337$	9.21032	−	12.3036i	0.501718	−	0.670217i	0.977886	+	0.209137i	$0.0670655\pi$
$338$		0			0
$339$	9.40468	+	20.5934i	0.510792	+	1.11848i
$340$		0			0
$341$	8.22116	+	3.75448i	0.445201	+	0.203316i
$342$		0			0
$343$	2.75585	−	12.6684i	0.148802	−	0.684031i
$344$		0			0
$345$	−9.24343	−	14.2541i	−0.497650	−	0.767413i
$346$		0			0
$347$	−5.21245	+	23.9613i	−0.279819	+	1.28631i	0.595732	+	0.803183i	$0.296862\pi$
$347$	−5.21245	+	23.9613i	−0.279819	+	1.28631i	−0.875552	+	0.483125i	$0.839502\pi$
$348$		0			0
$349$	31.7859	+	14.5161i	1.70146	+	0.777031i	0.997786	+	0.0665073i	$0.0211856\pi$
$349$	31.7859	+	14.5161i	1.70146	+	0.777031i	0.703674	+	0.710523i	$0.251542\pi$
$350$		0			0
$351$	−7.82587	−	17.1363i	−0.417714	−	0.914666i
$352$		0			0
$353$	−5.50119	+	7.34873i	−0.292799	+	0.391134i	−0.922685	−	0.385554i	$-0.874010\pi$
$353$	−5.50119	+	7.34873i	−0.292799	+	0.391134i	0.629887	+	0.776687i	$0.283101\pi$
$354$		0			0
$355$	21.8090	−	5.92942i	1.15750	−	0.314701i
$356$		0			0
$357$	7.84028	−	1.70555i	0.414951	−	0.0902672i
$358$		0			0
$359$	−14.2430	−	4.18211i	−0.751715	−	0.220723i	−0.116640	−	0.993174i	$-0.537213\pi$
$359$	−14.2430	−	4.18211i	−0.751715	−	0.220723i	−0.635075	+	0.772451i	$0.719031\pi$
$360$		0			0
$361$	6.39901	+	7.38486i	0.336790	+	0.388677i
$362$		0			0
$363$	−13.4787	−	7.35991i	−0.707447	−	0.386295i
$364$		0			0
$365$	−24.3543	+	1.24957i	−1.27476	+	0.0654054i
$366$		0			0
$367$	1.40836	+	1.40836i	0.0735159	+	0.0735159i	0.742909	−	0.669393i	$-0.233446\pi$
$367$	1.40836	+	1.40836i	0.0735159	+	0.0735159i	−0.669393	+	0.742909i	$0.733446\pi$
$368$		0			0
$369$			3.81603i			0.198655i
$370$		0			0
$371$	−1.19831	+	8.33445i	−0.0622133	+	0.432703i
$372$		0			0
$373$	−5.85501	+	10.7227i	−0.303161	+	0.555198i	−0.984202	−	0.177047i	$-0.943346\pi$
$373$	−5.85501	+	10.7227i	−0.303161	+	0.555198i	0.681041	+	0.732245i	$0.261527\pi$
$374$		0			0
$375$	17.0484	+	4.80301i	0.880375	+	0.248026i
$376$		0			0
$377$	22.5449	−	12.3105i	1.16112	−	0.634021i
$378$		0			0
$379$	16.6422	+	10.6953i	0.854852	+	0.549380i	0.893085	−	0.449889i	$-0.148536\pi$
$379$	16.6422	+	10.6953i	0.854852	+	0.549380i	−0.0382327	+	0.999269i	$0.512173\pi$
$380$		0			0
$381$	0.148816	−	0.171743i	0.00762409	−	0.00879867i
$382$		0			0
$383$	−7.58927	−	5.68125i	−0.387793	−	0.290299i	0.387537	−	0.921854i	$-0.373326\pi$
$383$	−7.58927	−	5.68125i	−0.387793	−	0.290299i	−0.775331	+	0.631556i	$0.782417\pi$
$384$		0			0
$385$	1.48518	+	2.06955i	0.0756916	+	0.105474i
$386$		0			0
$387$	2.01360	−	0.751035i	0.102357	−	0.0381773i
$388$		0			0
$389$	−30.4198	+	19.5496i	−1.54234	+	0.991204i	−0.555137	+	0.831759i	$0.687334\pi$
$389$	−30.4198	+	19.5496i	−1.54234	+	0.991204i	−0.987207	+	0.159445i	$0.949030\pi$
$390$		0			0
$391$	−24.1967	−	2.88223i	−1.22368	−	0.145760i
$392$		0			0
$393$	−30.1747	−	6.56410i	−1.52211	−	0.331115i
$394$		0			0
$395$	0.748984	−	0.460301i	0.0376855	−	0.0231602i
$396$		0			0
$397$	−21.0561	−	7.85351i	−1.05677	−	0.394156i	−0.239795	−	0.970824i	$-0.577080\pi$
$397$	−21.0561	−	7.85351i	−1.05677	−	0.394156i	−0.816979	+	0.576667i	$0.804353\pi$
$398$		0			0
$399$	4.74833	−	0.682706i	0.237714	−	0.0341781i
$400$		0			0
$401$	−28.4361	−	24.6400i	−1.42003	−	1.23046i	−0.934366	−	0.356316i	$-0.884033\pi$
$401$	−28.4361	−	24.6400i	−1.42003	−	1.23046i	−0.485663	−	0.874146i	$-0.661422\pi$
$402$		0			0
$403$	5.72725	+	26.3277i	0.285295	+	1.31148i
$404$		0			0
$405$	−10.4230	−	12.5299i	−0.517921	−	0.622615i
$406$		0			0
$407$	−1.19740	−	0.0856401i	−0.0593531	−	0.00424502i
$408$		0			0
$409$	−1.81126	−	6.16860i	−0.0895612	−	0.305018i	0.902514	−	0.430660i	$-0.141719\pi$
$409$	−1.81126	−	6.16860i	−0.0895612	−	0.305018i	−0.992076	+	0.125642i	$0.959901\pi$
$410$		0			0
$411$	−5.94164	−	0.854279i	−0.293079	−	0.0421385i
$412$		0			0
$413$	−5.18676	+	5.18676i	−0.255224	+	0.255224i
$414$		0			0
$415$	−13.1938	+	2.59306i	−0.647659	+	0.127288i
$416$		0			0
$417$	13.5449	+	18.0938i	0.663296	+	0.886059i
$418$		0			0
$419$	10.7679	−	3.16175i	0.526048	−	0.154462i	−0.00791628	−	0.999969i	$-0.502520\pi$
$419$	10.7679	−	3.16175i	0.526048	−	0.154462i	0.533964	+	0.845507i	$0.320702\pi$
$420$		0			0
$421$	−15.5362	+	13.4622i	−0.757187	+	0.656106i	−0.945360	−	0.326030i	$-0.894289\pi$
$421$	−15.5362	+	13.4622i	−0.757187	+	0.656106i	0.188172	+	0.982136i	$0.439744\pi$
$422$		0			0
$423$	0.696335	+	1.27524i	0.0338569	+	0.0620044i
$424$		0			0
$425$	20.9344	−	14.3935i	1.01547	−	0.698189i
$426$		0			0
$427$	0.334875	+	4.68217i	0.0162057	+	0.226586i
$428$		0			0
$429$	0.877876	+	6.10577i	0.0423843	+	0.294789i
$430$		0			0
$431$	−22.8062	+	10.4152i	−1.09853	+	0.501684i	−0.880398	−	0.474235i	$-0.842725\pi$
$431$	−22.8062	+	10.4152i	−1.09853	+	0.501684i	−0.218135	+	0.975919i	$0.569997\pi$
$432$		0			0
$433$	3.32111	+	8.90424i	0.159602	+	0.427910i	0.991995	−	0.126276i	$-0.0403024\pi$
$433$	3.32111	+	8.90424i	0.159602	+	0.427910i	−0.832393	+	0.554186i	$0.813030\pi$
$434$		0			0
$435$	19.2615	−	18.5010i	0.923520	−	0.887055i
$436$		0			0
$437$	−14.3069	−	2.75087i	−0.684391	−	0.131592i
$438$		0			0
$439$	7.61022	+	11.8417i	0.363216	+	0.565175i	0.973979	−	0.226638i	$-0.0727736\pi$
$439$	7.61022	+	11.8417i	0.363216	+	0.565175i	−0.610763	+	0.791813i	$0.709137\pi$
$440$		0			0
$441$	−1.22329	+	2.67862i	−0.0582517	+	0.127553i
$442$		0			0
$443$	−6.50356	+	17.4367i	−0.308993	+	0.828443i	0.685917	+	0.727680i	$0.259401\pi$
$443$	−6.50356	+	17.4367i	−0.308993	+	0.828443i	−0.994910	+	0.100764i	$0.967871\pi$
$444$		0			0
$445$	−7.18070	+	14.9209i	−0.340398	+	0.707320i
$446$		0			0
$447$	−10.9310	+	0.781802i	−0.517020	+	0.0369780i
$448$		0			0
$449$	−5.36515	+	8.34833i	−0.253197	+	0.393982i	−0.944463	−	0.328618i	$-0.893417\pi$
$449$	−5.36515	+	8.34833i	−0.253197	+	0.393982i	0.691266	+	0.722600i	$0.257053\pi$
$450$		0			0
$451$	2.50616	−	8.53520i	0.118010	−	0.401907i
$452$		0			0
$453$	−1.34789	+	18.8460i	−0.0633295	+	0.885462i
$454$		0			0
$455$	−2.28575	+	7.24180i	−0.107158	+	0.339501i
$456$		0			0
$457$	−9.38082	+	7.02240i	−0.438816	+	0.328494i	−0.795739	−	0.605640i	$-0.792917\pi$
$457$	−9.38082	+	7.02240i	−0.438816	+	0.328494i	0.356922	+	0.934134i	$0.383826\pi$
$458$		0			0
$459$	−28.0947			−1.31135
$460$		0			0
$461$	−21.3448			−0.994129			−0.497064	−	0.867714i	$-0.665589\pi$
$461$	−21.3448			−0.994129			−0.497064	+	0.867714i	$0.665589\pi$
$462$		0			0
$463$	−32.5153	+	24.3406i	−1.51111	+	1.13120i	−0.557497	+	0.830179i	$0.688238\pi$
$463$	−32.5153	+	24.3406i	−1.51111	+	1.13120i	−0.953616	+	0.301026i	$0.902671\pi$
$464$		0			0
$465$	12.9279	+	24.8526i	0.599515	+	1.15251i
$466$		0			0
$467$	−1.93794	+	27.0960i	−0.0896774	+	1.25385i	0.730967	+	0.682413i	$0.239070\pi$
$467$	−1.93794	+	27.0960i	−0.0896774	+	1.25385i	−0.820644	+	0.571440i	$0.806385\pi$
$468$		0			0
$469$	−3.81819	+	13.0036i	−0.176308	+	0.600449i
$470$		0			0
$471$	9.68278	−	15.0667i	0.446159	−	0.694237i
$472$		0			0
$473$	−4.99700	+	0.357393i	−0.229762	+	0.0164329i
$474$		0			0
$475$	13.0982	−	7.69075i	0.600987	−	0.352876i
$476$		0			0
$477$	1.44727	−	3.88027i	0.0662658	−	0.177665i
$478$		0			0
$479$	−3.09229	+	6.77118i	−0.141290	+	0.309383i	−0.967027	−	0.254673i	$-0.918032\pi$
$479$	−3.09229	+	6.77118i	−0.141290	+	0.309383i	0.825737	+	0.564055i	$0.190760\pi$
$480$		0			0
$481$	−1.93484	−	3.01066i	−0.0882209	−	0.137274i
$482$		0			0
$483$	5.22373	−	5.48334i	0.237688	−	0.249501i
$484$		0			0
$485$	−8.23286	−	8.57129i	−0.373835	−	0.389202i
$486$		0			0
$487$	−7.39314	−	19.8218i	−0.335015	−	0.898211i	−0.989809	−	0.142403i	$-0.954517\pi$
$487$	−7.39314	−	19.8218i	−0.335015	−	0.898211i	0.654793	−	0.755808i	$-0.272756\pi$
$488$		0			0
$489$	−10.1858	+	4.65170i	−0.460618	+	0.210357i
$490$		0			0
$491$	−2.46928	−	17.1742i	−0.111437	−	0.775060i	−0.966524	−	0.256576i	$-0.917406\pi$
$491$	−2.46928	−	17.1742i	−0.111437	−	0.775060i	0.855087	−	0.518484i	$-0.173504\pi$
$492$		0			0
$493$	−2.73285	−	38.2102i	−0.123081	−	1.72090i
$494$		0			0
$495$	−0.497410	−	1.14991i	−0.0223569	−	0.0516844i
$496$		0			0
$497$	4.82841	+	8.84257i	0.216584	+	0.396644i
$498$		0			0
$499$	27.6075	−	23.9220i	1.23588	−	1.07090i	0.240929	−	0.970543i	$-0.422548\pi$
$499$	27.6075	−	23.9220i	1.23588	−	1.07090i	0.994952	−	0.100354i	$-0.0319975\pi$
$500$		0			0
$501$	−10.5440	+	3.09599i	−0.471069	+	0.138318i
$502$		0			0
$503$	17.2602	+	23.0569i	0.769593	+	1.02806i	0.998508	+	0.0546092i	$0.0173913\pi$
$503$	17.2602	+	23.0569i	0.769593	+	1.02806i	−0.228915	+	0.973446i	$0.573518\pi$
$504$		0			0
$505$	19.5216	+	13.1086i	0.868701	+	0.583326i
$506$		0			0
$507$	1.55938	−	1.55938i	0.0692545	−	0.0692545i
$508$		0			0
$509$	−33.5635	−	4.82571i	−1.48768	−	0.213896i	−0.649947	−	0.759979i	$-0.725209\pi$
$509$	−33.5635	−	4.82571i	−1.48768	−	0.213896i	−0.837731	+	0.546083i	$0.816118\pi$
$510$		0			0
$511$	−3.06270	−	10.4306i	−0.135486	−	0.461423i
$512$		0			0
$513$	−16.7544	−	1.19830i	−0.739724	−	0.0529061i
$514$		0			0
$515$	−12.8239	−	1.17715i	−0.565088	−	0.0518712i
$516$		0			0
$517$	−0.719961	−	3.30961i	−0.0316638	−	0.145556i
$518$		0			0
$519$	1.06074	+	0.919139i	0.0465614	+	0.0403457i
$520$		0			0
$521$	−2.94197	+	0.422991i	−0.128890	+	0.0185316i	−0.206458	−	0.978456i	$-0.566194\pi$
$521$	−2.94197	+	0.422991i	−0.128890	+	0.0185316i	0.0775680	+	0.996987i	$0.475285\pi$
$522$		0			0
$523$	22.5357	+	8.40539i	0.985418	+	0.367542i	0.789952	−	0.613168i	$-0.210105\pi$
$523$	22.5357	+	8.40539i	0.985418	+	0.367542i	0.195466	+	0.980710i	$0.437378\pi$
$524$		0			0
$525$	−0.317904	+	7.88928i	−0.0138745	+	0.344316i
$526$		0			0
$527$	39.2634	+	8.54122i	1.71034	+	0.372062i
$528$		0			0
$529$	−20.4339	+	10.5573i	−0.888430	+	0.459012i
$530$		0			0
$531$	3.03503	−	1.95050i	0.131709	−	0.0846444i
$532$		0			0
$533$	24.8470	−	9.26746i	1.07624	−	0.401418i
$534$		0			0
$535$	17.3250	−	12.4329i	0.749023	−	0.537523i
$536$		0			0
$537$	14.7538	+	11.0445i	0.636672	+	0.476607i
$538$		0			0
$539$	4.49526	−	5.18781i	0.193625	−	0.223455i
$540$		0			0
$541$	−12.0348	−	7.73429i	−0.517416	−	0.332523i	0.255733	−	0.966747i	$-0.417683\pi$
$541$	−12.0348	−	7.73429i	−0.517416	−	0.332523i	−0.773149	+	0.634224i	$0.781320\pi$
$542$		0			0
$543$	−11.2108	+	6.12158i	−0.481103	+	0.262702i
$544$		0			0
$545$	−2.22557	−	18.0527i	−0.0953328	−	0.773293i
$546$		0			0
$547$	−15.0796	+	27.6162i	−0.644756	+	1.18078i	0.327052	+	0.945006i	$0.393945\pi$
$547$	−15.0796	+	27.6162i	−0.644756	+	1.18078i	−0.971808	+	0.235775i	$0.924237\pi$
$548$		0			0
$549$	0.328572	−	2.28527i	0.0140231	−	0.0975330i
$550$		0			0
$551$		−	22.9034i		−	0.975716i
$552$		0			0
$553$	0.277111	+	0.277111i	0.0117840	+	0.0117840i
$554$		0			0
$555$	−2.76249	−	2.49285i	−0.117261	−	0.105815i
$556$		0			0
$557$	−13.8009	−	7.53585i	−0.584762	−	0.319304i	0.159494	−	0.987199i	$-0.449014\pi$
$557$	−13.8009	−	7.53585i	−0.584762	−	0.319304i	−0.744256	+	0.667895i	$0.767196\pi$
$558$		0			0
$559$	−9.78031	−	11.2871i	−0.413663	−	0.477393i
$560$		0			0
$561$	8.82672	+	2.59176i	0.372664	+	0.109424i
$562$		0			0
$563$	34.9887	−	7.61133i	1.47460	−	0.320780i	0.597804	−	0.801642i	$-0.296040\pi$
$563$	34.9887	−	7.61133i	1.47460	−	0.320780i	0.876796	+	0.480863i	$0.159677\pi$
$564$		0			0
$565$	−15.8758	+	27.7318i	−0.667900	+	1.16669i
$566$		0			0
$567$	4.35404	−	5.81632i	0.182852	−	0.244262i
$568$		0			0
$569$	12.2439	+	26.8104i	0.513291	+	1.12395i	0.971918	+	0.235322i	$0.0756143\pi$
$569$	12.2439	+	26.8104i	0.513291	+	1.12395i	−0.458626	+	0.888629i	$0.651658\pi$
$570$		0			0
$571$	41.4122	+	18.9123i	1.73305	+	0.791456i	0.992892	+	0.119020i	$0.0379752\pi$
$571$	41.4122	+	18.9123i	1.73305	+	0.791456i	0.740155	+	0.672436i	$0.234752\pi$
$572$		0			0
$573$	4.48149	−	20.6011i	0.187217	−	0.860622i
$574$		0			0
$575$	8.73896	−	22.3300i	0.364440	−	0.931227i
$576$		0			0
$577$	5.75160	−	26.4397i	0.239442	−	1.10070i	−0.687702	−	0.725993i	$-0.741380\pi$
$577$	5.75160	−	26.4397i	0.239442	−	1.10070i	0.927144	−	0.374705i	$-0.122256\pi$
$578$		0			0
$579$	−22.8278	−	10.4251i	−0.948690	−	0.433252i
$580$		0			0
$581$	−2.49002	−	5.45239i	−0.103304	−	0.226203i
$582$		0			0
$583$	−5.78540	+	7.72839i	−0.239607	+	0.320077i
$584$		0			0
$585$	1.85566	−	3.24145i	0.0767219	−	0.134018i
$586$		0			0
$587$	14.0493	−	3.05624i	0.579877	−	0.126145i	0.0869463	−	0.996213i	$-0.472289\pi$
$587$	14.0493	−	3.05624i	0.579877	−	0.126145i	0.492931	+	0.870068i	$0.335926\pi$
$588$		0			0
$589$	23.0506	+	6.76826i	0.949782	+	0.278881i
$590$		0			0
$591$	9.75916	+	11.2627i	0.401438	+	0.463284i
$592$		0			0
$593$	−15.6616	−	8.55186i	−0.643143	−	0.351183i	0.124351	−	0.992238i	$-0.460315\pi$
$593$	−15.6616	−	8.55186i	−0.643143	−	0.351183i	−0.767495	+	0.641055i	$0.778497\pi$
$594$		0			0
$595$	8.40789	+	7.58721i	0.344690	+	0.311045i
$596$		0			0
$597$	−0.841468	−	0.841468i	−0.0344390	−	0.0344390i
$598$		0			0
$599$			3.12300i			0.127602i	0.997963	+	0.0638012i	$0.0203224\pi$
$599$			3.12300i			0.127602i	−0.997963	+	0.0638012i	$0.979678\pi$
$600$		0			0
$601$	5.94976	−	41.3815i	0.242696	−	1.68799i	−0.395781	−	0.918345i	$-0.629526\pi$
$601$	5.94976	−	41.3815i	0.242696	−	1.68799i	0.638477	−	0.769641i	$-0.279565\pi$
$602$		0			0
$603$	3.19454	−	5.85036i	0.130092	−	0.238245i
$604$		0			0
$605$	−2.65220	−	21.5133i	−0.107827	−	0.874640i
$606$		0			0
$607$	14.3033	−	7.81018i	0.580552	−	0.317005i	−0.162003	−	0.986790i	$-0.551796\pi$
$607$	14.3033	−	7.81018i	0.580552	−	0.317005i	0.742555	+	0.669785i	$0.233614\pi$
$608$		0			0
$609$	10.0157	+	6.43671i	0.405857	+	0.260829i
$610$		0			0
$611$	6.61229	−	7.63099i	0.267505	−	0.308717i
$612$		0			0
$613$	−21.3281	−	15.9660i	−0.861432	−	0.644860i	0.0744299	−	0.997226i	$-0.476286\pi$
$613$	−21.3281	−	15.9660i	−0.861432	−	0.644860i	−0.935862	+	0.352366i	$0.885377\pi$
$614$		0			0
$615$	22.4013	−	16.0759i	0.903308	−	0.648243i
$616$		0			0
$617$	16.0308	−	5.97918i	0.645376	−	0.240713i	−0.00539668	−	0.999985i	$-0.501718\pi$
$617$	16.0308	−	5.97918i	0.645376	−	0.240713i	0.650773	+	0.759273i	$0.274445\pi$
$618$		0			0
$619$	28.4929	−	18.3113i	1.14522	−	0.735991i	0.176542	−	0.984293i	$-0.443509\pi$
$619$	28.4929	−	18.3113i	1.14522	−	0.735991i	0.968683	+	0.248302i	$0.0798724\pi$
$620$		0			0
$621$	−21.9541	+	14.8731i	−0.880986	+	0.596837i
$622$		0			0
$623$	−7.21293	−	1.56908i	−0.288980	−	0.0628637i
$624$		0			0
$625$	8.52196	+	23.5027i	0.340879	+	0.940107i
$626$		0			0
$627$	5.15330	+	1.92208i	0.205803	+	0.0767606i
$628$		0			0
$629$	−5.28282	+	0.759555i	−0.210640	+	0.0302855i
$630$		0			0
$631$	−23.0538	−	19.9762i	−0.917757	−	0.795241i	0.0614486	−	0.998110i	$-0.480428\pi$
$631$	−23.0538	−	19.9762i	−0.917757	−	0.795241i	−0.979206	+	0.202869i	$0.934973\pi$
$632$		0			0
$633$	6.63629	+	30.5066i	0.263769	+	1.21253i
$634$		0			0
$635$	0.319412	+	0.0293199i	0.0126755	+	0.00116352i
$636$		0			0
$637$	20.4119	+	1.45989i	0.808750	+	0.0578430i
$638$		0			0
$639$	−1.39607	−	4.75456i	−0.0552275	−	0.188088i
$640$		0			0
$641$	44.6142	+	6.41455i	1.76215	+	0.253360i	0.945929	−	0.324374i	$-0.105154\pi$
$641$	44.6142	+	6.41455i	1.76215	+	0.253360i	0.816226	+	0.577733i	$0.196063\pi$
$642$		0			0
$643$	−2.24803	+	2.24803i	−0.0886538	+	0.0886538i	−0.750043	−	0.661389i	$-0.769967\pi$
$643$	−2.24803	+	2.24803i	−0.0886538	+	0.0886538i	0.661389	+	0.750043i	$0.269967\pi$
$644$		0			0
$645$	−12.8916	−	8.65658i	−0.507605	−	0.340853i
$646$		0			0
$647$	24.4183	+	32.6191i	0.959984	+	1.28239i	0.959300	+	0.282389i	$0.0911269\pi$
$647$	24.4183	+	32.6191i	0.959984	+	1.28239i	0.000684195		1.00000i	$0.499782\pi$
$648$		0			0
$649$	−8.06935	+	2.36937i	−0.316750	+	0.0930060i
$650$		0			0
$651$	−9.43786	+	8.17795i	−0.369899	+	0.320519i
$652$		0			0
$653$	19.6446	+	35.9764i	0.768752	+	1.40786i	0.908590	+	0.417689i	$0.137160\pi$
$653$	19.6446	+	35.9764i	0.768752	+	1.40786i	−0.139838	+	0.990174i	$0.544658\pi$
$654$		0			0
$655$	−17.3046	−	40.0044i	−0.676145	−	1.56310i
$656$		0			0
$657$	0.381436	+	5.33318i	0.0148812	+	0.208067i
$658$		0			0
$659$	4.87538	+	33.9090i	0.189918	+	1.32091i	0.832215	+	0.554453i	$0.187072\pi$
$659$	4.87538	+	33.9090i	0.189918	+	1.32091i	−0.642297	+	0.766456i	$0.722018\pi$
$660$		0			0
$661$	16.8452	−	7.69292i	0.655200	−	0.299220i	−0.0599388	−	0.998202i	$-0.519091\pi$
$661$	16.8452	−	7.69292i	0.655200	−	0.299220i	0.715139	+	0.698982i	$0.246363\pi$
$662$		0			0
$663$	9.58399	+	25.6957i	0.372211	+	0.997937i
$664$		0			0
$665$	4.69047	+	4.88328i	0.181888	+	0.189365i
$666$		0			0
$667$	−22.3637	−	28.4119i	−0.865926	−	1.10011i
$668$		0			0
$669$	−13.4059	−	20.8599i	−0.518301	−	0.806492i
$670$		0			0
$671$	−2.23575	+	4.89561i	−0.0863101	+	0.188993i
$672$		0			0
$673$	4.29646	−	11.5192i	0.165616	−	0.444034i	−0.827457	−	0.561529i	$-0.810213\pi$
$673$	4.29646	−	11.5192i	0.165616	−	0.444034i	0.993074	+	0.117494i	$0.0374862\pi$
$674$		0			0
$675$	6.95965	−	26.7563i	0.267877	−	1.02985i
$676$		0			0
$677$	−9.03601	+	0.646268i	−0.347282	+	0.0248381i	−0.243891	−	0.969803i	$-0.578424\pi$
$677$	−9.03601	+	0.646268i	−0.347282	+	0.0248381i	−0.103391	+	0.994641i	$0.532969\pi$
$678$		0			0
$679$	2.86431	−	4.45695i	0.109922	−	0.171042i
$680$		0			0
$681$	−2.08252	+	7.09241i	−0.0798023	+	0.271782i
$682$		0			0
$683$	−2.33666	+	32.6708i	−0.0894100	+	1.25011i	0.732607	+	0.680652i	$0.238303\pi$
$683$	−2.33666	+	32.6708i	−0.0894100	+	1.25011i	−0.822017	+	0.569463i	$0.807151\pi$
$684$		0			0
$685$	−3.90996	−	7.51654i	−0.149392	−	0.287192i
$686$		0			0
$687$	0.880510	−	0.659141i	0.0335935	−	0.0251478i
$688$		0			0
$689$	−28.7801			−1.09643
$690$		0			0
$691$	−21.0450			−0.800588			−0.400294	−	0.916387i	$-0.631092\pi$
$691$	−21.0450			−0.800588			−0.400294	+	0.916387i	$0.631092\pi$
$692$		0			0
$693$	0.447108	−	0.334701i	0.0169842	−	0.0127142i
$694$		0			0
$695$	−9.60236	+	30.4226i	−0.364238	+	1.15399i
$696$		0			0
$697$	2.82137	−	39.4479i	0.106867	−	1.49420i
$698$		0			0
$699$	10.1255	−	34.4842i	0.382981	−	1.30431i
$700$		0			0
$701$	22.5769	−	35.1303i	0.852717	−	1.32685i	−0.0909152	−	0.995859i	$-0.528979\pi$
$701$	22.5769	−	35.1303i	0.852717	−	1.32685i	0.943632	−	0.330995i	$-0.107384\pi$
$702$		0			0
$703$	−3.18283	+	0.227640i	−0.120043	+	0.00858562i
$704$		0			0
$705$	4.55261	−	9.45995i	0.171461	−	0.356282i
$706$		0			0
$707$	−3.66318	+	9.82137i	−0.137768	+	0.369371i
$708$		0			0
$709$	12.0839	−	26.4601i	0.453821	−	0.993728i	−0.535032	−	0.844832i	$-0.679701\pi$
$709$	12.0839	−	26.4601i	0.453821	−	0.993728i	0.988853	−	0.148897i	$-0.0475722\pi$
$710$		0			0
$711$	−0.104209	−	0.162152i	−0.00390813	−	0.00608117i
$712$		0			0
$713$	35.2033	−	14.1113i	1.31837	−	0.528473i
$714$		0			0
$715$	−6.27930	+	6.03136i	−0.234832	+	0.225560i
$716$		0			0
$717$	6.05732	+	16.2403i	0.226215	+	0.606506i
$718$		0			0
$719$	−35.6906	+	16.2994i	−1.33104	+	0.607864i	−0.948705	−	0.316162i	$-0.897606\pi$
$719$	−35.6906	+	16.2994i	−1.33104	+	0.607864i	−0.382331	+	0.924025i	$0.624879\pi$
$720$		0			0
$721$	−0.816982	−	5.68223i	−0.0304260	−	0.211617i
$722$		0			0
$723$	2.08507	+	29.1531i	0.0775447	+	1.08422i
$724$		0			0
$725$	37.0669	+	6.86281i	1.37663	+	0.254879i
$726$		0			0
$727$	−2.23446	−	4.09212i	−0.0828717	−	0.151768i	0.832957	−	0.553338i	$-0.186646\pi$
$727$	−2.23446	−	4.09212i	−0.0828717	−	0.151768i	−0.915828	+	0.401570i	$0.868465\pi$
$728$		0			0
$729$	−22.5609	+	19.5492i	−0.835590	+	0.724043i
$730$		0			0
$731$	−21.3707	+	6.27502i	−0.790426	+	0.232090i
$732$		0			0
$733$	−4.83718	−	6.46171i	−0.178665	−	0.238669i	0.702264	−	0.711916i	$-0.252173\pi$
$733$	−4.83718	−	6.46171i	−0.178665	−	0.238669i	−0.880929	+	0.473248i	$0.843082\pi$
$734$		0			0
$735$	20.8777	−	4.10323i	0.770087	−	0.151350i
$736$		0			0
$737$	−10.9873	+	10.9873i	−0.404723	+	0.404723i
$738$		0			0
$739$	−37.0090	−	5.32109i	−1.36140	−	0.195740i	−0.577379	−	0.816476i	$-0.695925\pi$
$739$	−37.0090	−	5.32109i	−1.36140	−	0.195740i	−0.784019	+	0.620736i	$0.786834\pi$
$740$		0			0
$741$	4.61948	+	15.7325i	0.169701	+	0.577948i
$742$		0			0
$743$	14.4516	+	1.03360i	0.530177	+	0.0379190i	0.333862	−	0.942622i	$-0.391648\pi$
$743$	14.4516	+	1.03360i	0.530177	+	0.0379190i	0.196315	+	0.980541i	$0.437103\pi$
$744$		0			0
$745$	−9.89208	−	11.8917i	−0.362418	−	0.435678i
$746$		0			0
$747$	0.626671	+	2.88076i	0.0229287	+	0.105401i
$748$		0			0
$749$	7.18417	+	6.22511i	0.262504	+	0.227461i
$750$		0			0
$751$	41.3429	−	5.94422i	1.50862	−	0.216907i	0.662164	−	0.749359i	$-0.269638\pi$
$751$	41.3429	−	5.94422i	1.50862	−	0.216907i	0.846461	+	0.532451i	$0.178729\pi$
$752$		0			0
$753$	−1.34153	−	0.500366i	−0.0488882	−	0.0182343i
$754$		0			0
$755$	−22.7207	+	13.9634i	−0.826891	+	0.508180i
$756$		0			0
$757$	−38.8055	−	8.44161i	−1.41041	−	0.306816i	−0.558065	−	0.829798i	$-0.688456\pi$
$757$	−38.8055	−	8.44161i	−1.41041	−	0.306816i	−0.852344	+	0.522982i	$0.824820\pi$
$758$		0			0
$759$	8.26952	−	2.64751i	0.300165	−	0.0960985i
$760$		0			0
$761$	30.7202	−	19.7427i	1.11361	−	0.715671i	0.151530	−	0.988453i	$-0.451580\pi$
$761$	30.7202	−	19.7427i	1.11361	−	0.715671i	0.962076	+	0.272782i	$0.0879436\pi$
$762$		0			0
$763$	7.59722	−	2.83362i	0.275038	−	0.102584i
$764$		0			0
$765$	−3.24762	−	4.52546i	−0.117418	−	0.163618i
$766$		0			0
$767$	−20.0709	−	15.0249i	−0.724718	−	0.542517i
$768$		0			0
$769$	27.0051	−	31.1656i	0.973830	−	1.12386i	−0.0184482	−	0.999830i	$-0.505873\pi$
$769$	27.0051	−	31.1656i	0.973830	−	1.12386i	0.992278	−	0.124030i	$-0.0395820\pi$
$770$		0			0
$771$	18.5639	+	11.9303i	0.668563	+	0.429659i
$772$		0			0
$773$	15.2043	−	8.30219i	0.546862	−	0.298609i	−0.181968	−	0.983305i	$-0.558247\pi$
$773$	15.2043	−	8.30219i	0.546862	−	0.298609i	0.728829	+	0.684695i	$0.240065\pi$
$774$		0			0
$775$	−17.8607	+	35.2771i	−0.641575	+	1.26719i
$776$		0			0
$777$	0.794947	−	1.45584i	0.0285186	−	0.0522279i
$778$		0			0
$779$	3.36507	−	23.4046i	0.120566	−	0.838557i
$780$		0			0
$781$			11.5512i			0.413336i
$782$		0			0
$783$	−29.4776	−	29.4776i	−1.05344	−	1.05344i
$784$		0			0
$785$	25.2459	−	1.29531i	0.901066	−	0.0462318i
$786$		0			0
$787$	−10.3418	−	5.64708i	−0.368647	−	0.201296i	0.284238	−	0.958754i	$-0.408260\pi$
$787$	−10.3418	−	5.64708i	−0.368647	−	0.201296i	−0.652885	+	0.757457i	$0.726441\pi$
$788$		0			0
$789$	12.7188	+	14.6783i	0.452801	+	0.522560i
$790$		0			0
$791$	−13.6677	−	4.01320i	−0.485967	−	0.142693i
$792$		0			0
$793$	−15.6779	+	3.41051i	−0.556737	+	0.121111i
$794$		0			0
$795$	−28.8754	+	7.85060i	−1.02410	+	0.278432i
$796$		0			0
$797$	−24.4356	+	32.6422i	−0.865554	+	1.15624i	0.120975	+	0.992656i	$0.461398\pi$
$797$	−24.4356	+	32.6422i	−0.865554	+	1.15624i	−0.986529	+	0.163589i	$0.947693\pi$
$798$		0			0
$799$	−6.25546	−	13.6975i	−0.221302	−	0.484584i
$800$		0			0
$801$	3.30250	+	1.50820i	0.116688	+	0.0532897i
$802$		0			0
$803$	2.64939	−	12.1791i	0.0934950	−	0.429790i
$804$		0			0
$805$	10.5868	+	1.47782i	0.373135	+	0.0520863i
$806$		0			0
$807$	0.296678	−	1.36381i	0.0104436	−	0.0480083i
$808$		0			0
$809$	16.3143	+	7.45049i	0.573580	+	0.261945i	0.681018	−	0.732267i	$-0.261537\pi$
$809$	16.3143	+	7.45049i	0.573580	+	0.261945i	−0.107438	+	0.994212i	$0.534265\pi$
$810$		0			0
$811$	−9.44316	−	20.6776i	−0.331594	−	0.726090i	0.668246	−	0.743940i	$-0.267045\pi$
$811$	−9.44316	−	20.6776i	−0.331594	−	0.726090i	−0.999841	+	0.0178498i	$0.994318\pi$
$812$		0			0
$813$	16.7729	−	22.4059i	0.588251	−	0.785811i
$814$		0			0
$815$	−13.7166	−	7.85241i	−0.480470	−	0.275058i
$816$		0			0
$817$	−13.0122	+	2.83062i	−0.455238	+	0.0990310i
$818$		0			0
$819$	1.59756	+	0.469086i	0.0558233	+	0.0163912i
$820$		0			0
$821$	8.54811	+	9.86504i	0.298331	+	0.344292i	0.885048	−	0.465500i	$-0.154125\pi$
$821$	8.54811	+	9.86504i	0.298331	+	0.344292i	−0.586717	+	0.809792i	$0.699580\pi$
$822$		0			0
$823$	26.7717	+	14.6185i	0.933203	+	0.509568i	0.872514	−	0.488589i	$-0.162488\pi$
$823$	26.7717	+	14.6185i	0.933203	+	0.509568i	0.0606893	+	0.998157i	$0.480670\pi$
$824$		0			0
$825$	−4.65485	+	7.76419i	−0.162061	+	0.270314i
$826$		0			0
$827$	8.20921	+	8.20921i	0.285462	+	0.285462i	0.835283	−	0.549821i	$-0.185304\pi$
$827$	8.20921	+	8.20921i	0.285462	+	0.285462i	−0.549821	+	0.835283i	$0.685304\pi$
$828$		0			0
$829$		−	3.98248i		−	0.138317i	−0.997606	−	0.0691587i	$-0.977969\pi$
$829$		−	3.98248i		−	0.138317i	0.997606	−	0.0691587i	$-0.0220315\pi$
$830$		0			0
$831$	3.76175	−	26.1635i	0.130494	−	0.907603i
$832$		0			0
$833$	14.6261	−	26.7856i	0.506763	−	0.928067i
$834$		0			0
$835$	−12.2273	−	9.54339i	−0.423144	−	0.330263i
$836$		0			0
$837$	38.3781	−	20.9560i	1.32654	−	0.724347i
$838$		0			0
$839$	13.0187	+	8.36662i	0.449456	+	0.288848i	0.745721	−	0.666258i	$-0.232105\pi$
$839$	13.0187	+	8.36662i	0.449456	+	0.288848i	−0.296266	+	0.955106i	$0.595741\pi$
$840$		0			0
$841$	18.2328	−	21.0417i	0.628716	−	0.725576i
$842$		0			0
$843$	−37.9235	−	28.3892i	−1.30615	−	0.977775i
$844$		0			0
$845$	3.07148	+	0.504933i	0.105662	+	0.0173702i
$846$		0			0
$847$	9.05357	−	3.37681i	0.311084	−	0.116028i
$848$		0			0
$849$	−25.1914	+	16.1895i	−0.864566	+	0.555623i
$850$		0			0
$851$	−3.72606	+	3.39022i	−0.127728	+	0.116215i
$852$		0			0
$853$	12.3199	+	2.68003i	0.421825	+	0.0917625i	0.418467	−	0.908232i	$-0.362567\pi$
$853$	12.3199	+	2.68003i	0.421825	+	0.0917625i	0.00335813	+	0.999994i	$0.498931\pi$
$854$		0			0
$855$	−1.74371	−	2.83730i	−0.0596336	−	0.0970334i
$856$		0			0
$857$	11.5365	+	4.30288i	0.394078	+	0.146983i	0.538688	−	0.842505i	$-0.318920\pi$
$857$	11.5365	+	4.30288i	0.394078	+	0.146983i	−0.144610	+	0.989489i	$0.546193\pi$
$858$		0			0
$859$	−29.4578	+	4.23539i	−1.00509	+	0.144510i	−0.625151	−	0.780504i	$-0.714963\pi$
$859$	−29.4578	+	4.23539i	−1.00509	+	0.144510i	−0.379935	+	0.925013i	$0.624054\pi$
$860$		0			0
$861$	9.28919	+	8.04913i	0.316575	+	0.274314i
$862$		0			0
$863$	−3.42201	−	15.7307i	−0.116487	−	0.535481i	−0.997994	−	0.0633102i	$-0.979834\pi$
$863$	−3.42201	−	15.7307i	−0.116487	−	0.535481i	0.881507	−	0.472171i	$-0.156529\pi$
$864$		0			0
$865$	−0.181089	+	1.97279i	−0.00615721	+	0.0670769i
$866$		0			0
$867$	13.9323	+	0.996454i	0.473164	+	0.0338414i
$868$		0			0
$869$	0.126588	+	0.431119i	0.00429420	+	0.0146247i
$870$		0			0
$871$	−45.8511	−	6.59239i	−1.55361	−	0.223375i
$872$		0			0
$873$	−1.84256	+	1.84256i	−0.0623612	+	0.0623612i
$874$		0			0
$875$	−9.30858	+	6.12783i	−0.314687	+	0.207159i
$876$		0			0
$877$	17.4317	+	23.2861i	0.588628	+	0.786314i	0.991661	−	0.128871i	$-0.0411352\pi$
$877$	17.4317	+	23.2861i	0.588628	+	0.786314i	−0.403034	+	0.915185i	$0.632044\pi$
$878$		0			0
$879$	−42.6630	+	12.5270i	−1.43899	+	0.422525i
$880$		0			0
$881$	−2.14996	+	1.86295i	−0.0724339	+	0.0627644i	−0.690325	−	0.723499i	$-0.742533\pi$
$881$	−2.14996	+	1.86295i	−0.0724339	+	0.0627644i	0.617891	+	0.786263i	$0.287987\pi$
$882$		0			0
$883$	27.1804	+	49.7771i	0.914692	+	1.67513i	0.719647	+	0.694340i	$0.244303\pi$
$883$	27.1804	+	49.7771i	0.914692	+	1.67513i	0.195045	+	0.980794i	$0.437515\pi$
$884$		0			0
$885$	−24.2358	−	9.59970i	−0.814678	−	0.322690i
$886$		0			0
$887$	2.43743	+	34.0797i	0.0818408	+	1.14428i	0.857967	+	0.513706i	$0.171728\pi$
$887$	2.43743	+	34.0797i	0.0818408	+	1.14428i	−0.776126	+	0.630578i	$0.782818\pi$
$888$		0			0
$889$	0.0203490	+	0.141531i	0.000682485	+	0.00474679i
$890$		0			0
$891$	7.57732	−	3.46045i	0.253850	−	0.115929i
$892$		0			0
$893$	−3.14624	−	8.43539i	−0.105285	−	0.282280i
$894$		0			0
$895$	−0.523786	+	26.0077i	−0.0175082	+	0.869342i
$896$		0			0
$897$	21.0923	+	15.0057i	0.704251	+	0.501026i
$898$		0			0
$899$	32.2344	+	50.1578i	1.07508	+	1.67285i
$900$		0			0
$901$	−17.8299	+	39.0420i	−0.593999	+	1.30068i
$902$		0			0
$903$	2.41907	−	6.48577i	0.0805016	−	0.215833i
$904$		0			0
$905$	−16.2457	−	7.81825i	−0.540025	−	0.259887i
$906$		0			0
$907$	−38.5156	+	2.75469i	−1.27889	+	0.0914681i	−0.694197	−	0.719785i	$-0.744240\pi$
$907$	−38.5156	+	2.75469i	−1.27889	+	0.0914681i	−0.584695	+	0.811254i	$0.698786\pi$
$908$		0			0
$909$	2.78734	−	4.33719i	0.0924503	−	0.143856i
$910$		0			0
$911$	−4.97032	+	16.9274i	−0.164674	+	0.560828i	0.835266	+	0.549847i	$0.185314\pi$
$911$	−4.97032	+	16.9274i	−0.164674	+	0.560828i	−0.999940	+	0.0109816i	$0.996504\pi$
$912$		0			0
$913$	0.490270	−	6.85487i	0.0162256	−	0.226863i
$914$		0			0
$915$	−14.7994	+	7.69839i	−0.489255	+	0.254501i
$916$		0			0
$917$	15.5546	−	11.6440i	0.513657	−	0.384519i
$918$		0			0
$919$	56.1938			1.85366			0.926831	−	0.375478i	$-0.122521\pi$
$919$	56.1938			1.85366			0.926831	+	0.375478i	$0.122521\pi$
$920$		0			0
$921$	−23.3399			−0.769076
$922$		0			0
$923$	−27.5676	+	20.6368i	−0.907398	+	0.679270i
$924$		0			0
$925$	0.585295	−	5.21932i	0.0192444	−	0.171610i
$926$		0			0
$927$	−0.201426	+	2.81631i	−0.00661571	+	0.0924997i
$928$		0			0
$929$	−0.278685	+	0.949114i	−0.00914336	+	0.0311394i	−0.963938	−	0.266126i	$-0.914256\pi$
$929$	−0.278685	+	0.949114i	−0.00914336	+	0.0311394i	0.954795	+	0.297265i	$0.0960745\pi$
$930$		0			0
$931$	9.86477	−	15.3499i	0.323305	−	0.503072i
$932$		0			0
$933$	−17.1641	+	1.22760i	−0.561928	+	0.0401899i
$934$		0			0
$935$	4.29176	+	12.2548i	0.140356	+	0.400775i
$936$		0			0
$937$	−16.4105	+	43.9982i	−0.536107	+	1.43736i	0.333091	+	0.942895i	$0.391908\pi$
$937$	−16.4105	+	43.9982i	−0.536107	+	1.43736i	−0.869198	+	0.494464i	$0.835364\pi$
$938$		0			0
$939$	21.3176	−	46.6790i	0.695674	−	1.52331i
$940$		0			0
$941$	28.0232	+	43.6049i	0.913529	+	1.42148i	0.906828	+	0.421501i	$0.138497\pi$
$941$	28.0232	+	43.6049i	0.913529	+	1.42148i	0.00670133	+	0.999978i	$0.497867\pi$
$942$		0			0
$943$	−18.6787	−	32.3194i	−0.608262	−	1.05247i
$944$		0			0
$945$	12.3218	+	0.248157i	0.400829	+	0.00807256i
$946$		0			0
$947$	−9.35597	−	25.0843i	−0.304028	−	0.815131i	−0.995676	−	0.0928960i	$-0.970388\pi$
$947$	−9.35597	−	25.0843i	−0.304028	−	0.815131i	0.691648	−	0.722235i	$-0.256885\pi$
$948$		0			0
$949$	33.7992	−	15.4356i	1.09717	−	0.501059i
$950$		0			0
$951$	6.29384	+	43.7746i	0.204092	+	1.41949i
$952$		0			0
$953$	−0.485869	−	6.79333i	−0.0157388	−	0.220058i	−0.999234	−	0.0391250i	$-0.987543\pi$
$953$	−0.485869	−	6.79333i	−0.0157388	−	0.220058i	0.983495	−	0.180933i	$-0.0579116\pi$
$954$		0			0
$955$	27.3121	−	11.8143i	0.883798	−	0.382302i
$956$		0			0
$957$	6.54187	+	11.9805i	0.211469	+	0.387276i
$958$		0			0
$959$	2.85443	−	2.47338i	0.0921743	−	0.0798695i
$960$		0			0
$961$	−30.2616	+	8.88559i	−0.976179	+	0.286632i
$962$		0			0
$963$	−2.80190	−	3.74290i	−0.0902899	−	0.120613i
$964$		0			0
$965$	−6.83095	−	34.7567i	−0.219896	−	1.11886i
$966$		0			0
$967$	8.28884	−	8.28884i	0.266551	−	0.266551i	−0.561158	−	0.827709i	$-0.689644\pi$
$967$	8.28884	−	8.28884i	0.266551	−	0.266551i	0.827709	+	0.561158i	$0.189644\pi$
$968$		0			0
$969$	24.2040	+	3.48001i	0.777544	+	0.111794i
$970$		0			0
$971$	8.43955	+	28.7425i	0.270838	+	0.922390i	0.976802	+	0.214143i	$0.0686957\pi$
$971$	8.43955	+	28.7425i	0.270838	+	0.922390i	−0.705964	+	0.708247i	$0.749486\pi$
$972$		0			0
$973$	−14.1851	−	1.01454i	−0.454752	−	0.0325245i
$974$		0			0
$975$	−26.8457	+	2.76206i	−0.859751	+	0.0884569i
$976$		0			0
$977$	−4.59883	−	21.1405i	−0.147130	−	0.676344i	−0.990329	−	0.138742i	$-0.955694\pi$
$977$	−4.59883	−	21.1405i	−0.147130	−	0.676344i	0.843199	−	0.537602i	$-0.180670\pi$
$978$		0			0
$979$	−6.39610	−	5.54225i	−0.204420	−	0.177131i
$980$		0			0
$981$	−3.94749	+	0.567564i	−0.126034	+	0.0181209i
$982$		0			0
$983$	−43.9107	−	16.3778i	−1.40053	−	0.522372i	−0.468088	−	0.883682i	$-0.655057\pi$
$983$	−43.9107	−	16.3778i	−1.40053	−	0.522372i	−0.932446	+	0.361310i	$0.882330\pi$
$984$		0			0
$985$	−4.88419	+	20.4597i	−0.155623	+	0.651901i
$986$		0			0
$987$	4.57304	+	0.994803i	0.145561	+	0.0316649i
$988$		0			0
$989$	−13.3778	+	16.2170i	−0.425390	+	0.515670i
$990$		0			0
$991$	−25.9403	+	16.6708i	−0.824021	+	0.529566i	−0.883373	−	0.468671i	$-0.844733\pi$
$991$	−25.9403	+	16.6708i	−0.824021	+	0.529566i	0.0593517	+	0.998237i	$0.481097\pi$
$992$		0			0
$993$	47.8633	−	17.8521i	1.51890	−	0.566519i
$994$		0			0
$995$	0.272470	−	1.65742i	0.00863789	−	0.0525438i
$996$		0			0
$997$	−25.6389	−	19.1931i	−0.811993	−	0.607851i	0.110494	−	0.993877i	$-0.464757\pi$
$997$	−25.6389	−	19.1931i	−0.811993	−	0.607851i	−0.922488	+	0.386026i	$0.873847\pi$
$998$		0			0
$999$	−3.80346	+	4.38942i	−0.120336	+	0.138875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.333.4	yes	240
5.2	odd	4	inner	460.2.x.a.57.9	✓	240
23.21	odd	22	inner	460.2.x.a.113.9	yes	240
115.67	even	44	inner	460.2.x.a.297.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.57.9	✓	240	5.2	odd	4	inner
460.2.x.a.113.9	yes	240	23.21	odd	22	inner
460.2.x.a.297.4	yes	240	115.67	even	44	inner
460.2.x.a.333.4	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26823 + 0.949384i) q^{3} +(-2.13237 - 0.673046i) q^{5} +(0.0711105 - 0.994255i) q^{7} +(-0.138124 + 0.470407i) q^{9} +O(q^{10})\)	\(q+(-1.26823 + 0.949384i) q^{3} +(-2.13237 - 0.673046i) q^{5} +(0.0711105 - 0.994255i) q^{7} +(-0.138124 + 0.470407i) q^{9} +(0.617875 - 0.961432i) q^{11} +(3.39836 - 0.243056i) q^{13} +(3.34331 - 1.17086i) q^{15} +(1.77564 - 4.76067i) q^{17} +(1.26196 - 2.76331i) q^{19} +(0.853746 + 1.32845i) q^{21} +(-1.13272 - 4.66014i) q^{23} +(4.09402 + 2.87037i) q^{25} +(-1.93230 - 5.18070i) q^{27} +(6.85806 - 3.13197i) q^{29} +(1.12545 + 7.82767i) q^{31} +(0.129162 + 1.80592i) q^{33} +(-0.820814 + 2.07226i) q^{35} +(-0.503406 - 0.921920i) q^{37} +(-4.07915 + 3.53460i) q^{39} +(7.46831 - 2.19289i) q^{41} +(-2.62696 - 3.50921i) q^{43} +(0.611137 - 0.910118i) q^{45} +(2.09561 - 2.09561i) q^{47} +(5.94526 + 0.854800i) q^{49} +(2.26779 + 7.72338i) q^{51} +(-8.42570 - 0.602618i) q^{53} +(-1.96463 + 1.63427i) q^{55} +(1.02299 + 4.70260i) q^{57} +(-5.56138 - 4.81897i) q^{59} +(-4.66129 + 0.670192i) q^{61} +(0.457882 + 0.170781i) q^{63} +(-7.41016 - 1.76897i) q^{65} +(-13.2854 - 2.89006i) q^{67} +(5.86081 + 4.83474i) q^{69} +(-8.50284 + 5.46444i) q^{71} +(10.2183 - 3.81123i) q^{73} +(-7.91723 + 0.246511i) q^{75} +(-0.911971 - 0.682693i) q^{77} +(-0.257462 + 0.297127i) q^{79} +(6.13176 + 3.94065i) q^{81} +(5.27778 - 2.88188i) q^{83} +(-6.99047 + 8.95643i) q^{85} +(-5.72414 + 10.4830i) q^{87} +(1.05389 - 7.32998i) q^{89} -3.39612i q^{91} +(-8.85880 - 8.85880i) q^{93} +(-4.55081 + 5.04305i) q^{95} +(4.66488 + 2.54722i) q^{97} +(0.366921 + 0.423449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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