LMFDB - Embedded newform 820.2.bo.b.21.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(21,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bo (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	820.21
Dual form			820.2.bo.b.781.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.39269 - 2.39269i) q^{3} +(0.587785 - 0.809017i) q^{5} +(0.802599 - 1.57519i) q^{7} +8.44996i q^{9} +(-4.02598 - 0.637652i) q^{11} +(-1.54720 + 0.788337i) q^{13} +(-3.34212 + 0.529340i) q^{15} +(-0.103370 + 0.652655i) q^{17} +(-3.61693 - 1.84292i) q^{19} +(-5.68932 + 1.84857i) q^{21} +(-0.980979 + 3.01914i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(13.0401 - 13.0401i) q^{27} +(-0.264069 - 1.66727i) q^{29} +(-5.76817 + 4.19082i) q^{31} +(8.10723 + 11.1586i) q^{33} +(-0.802599 - 1.57519i) q^{35} +(6.28689 + 4.56769i) q^{37} +(5.58822 + 1.81572i) q^{39} +(-5.51297 + 3.25686i) q^{41} +(6.76633 + 2.19851i) q^{43} +(6.83616 + 4.96676i) q^{45} +(-1.29835 - 2.54816i) q^{47} +(2.27744 + 3.13463i) q^{49} +(1.80894 - 1.31427i) q^{51} +(-0.0802020 - 0.506376i) q^{53} +(-2.88228 + 2.88228i) q^{55} +(4.24466 + 13.0637i) q^{57} +(-1.35075 + 4.15719i) q^{59} +(-4.70688 + 1.52936i) q^{61} +(13.3103 + 6.78193i) q^{63} +(-0.271642 + 1.71508i) q^{65} +(-0.0427763 + 0.00677510i) q^{67} +(9.57106 - 4.87670i) q^{69} +(9.96152 + 1.57775i) q^{71} -14.2833i q^{73} +(-1.53620 + 3.01497i) q^{75} +(-4.23567 + 5.82990i) q^{77} +(5.60539 + 5.60539i) q^{79} -37.0520 q^{81} -13.5812 q^{83} +(0.467249 + 0.467249i) q^{85} +(-3.35742 + 4.62109i) q^{87} +(-7.88376 + 15.4727i) q^{89} +3.06985i q^{91} +(23.8288 + 3.77412i) q^{93} +(-3.61693 + 1.84292i) q^{95} +(-14.0220 + 2.22087i) q^{97} +(5.38814 - 34.0194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) $ 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.39269	−	2.39269i	−1.38142	−	1.38142i	−0.842099	−	0.539324i	$-0.818680\pi$
$3$	−2.39269	−	2.39269i	−1.38142	−	1.38142i	−0.539324	−	0.842099i	$-0.681320\pi$
$4$		0			0
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$6$		0			0
$7$	0.802599	−	1.57519i	0.303354	−	0.595366i	−0.688131	−	0.725586i	$-0.741569\pi$
$7$	0.802599	−	1.57519i	0.303354	−	0.595366i	0.991485	+	0.130221i	$0.0415686\pi$
$8$		0			0
$9$			8.44996i			2.81665i
$10$		0			0
$11$	−4.02598	−	0.637652i	−1.21388	−	0.192259i	−0.483526	−	0.875330i	$-0.660644\pi$
$11$	−4.02598	−	0.637652i	−1.21388	−	0.192259i	−0.730352	+	0.683071i	$0.760644\pi$
$12$		0			0
$13$	−1.54720	+	0.788337i	−0.429116	+	0.218645i	−0.655189	−	0.755465i	$-0.727411\pi$
$13$	−1.54720	+	0.788337i	−0.429116	+	0.218645i	0.226073	+	0.974110i	$0.427411\pi$
$14$		0			0
$15$	−3.34212	+	0.529340i	−0.862932	+	0.136675i
$16$		0			0
$17$	−0.103370	+	0.652655i	−0.0250710	+	0.158292i	−0.997048	−	0.0767853i	$-0.975534\pi$
$17$	−0.103370	+	0.652655i	−0.0250710	+	0.158292i	0.971977	+	0.235077i	$0.0755344\pi$
$18$		0			0
$19$	−3.61693	−	1.84292i	−0.829780	−	0.422794i	−0.0131203	−	0.999914i	$-0.504176\pi$
$19$	−3.61693	−	1.84292i	−0.829780	−	0.422794i	−0.816659	+	0.577120i	$0.804176\pi$
$20$		0			0
$21$	−5.68932	+	1.84857i	−1.24151	+	0.403391i
$22$		0			0
$23$	−0.980979	+	3.01914i	−0.204548	+	0.629535i	0.795183	+	0.606369i	$0.207375\pi$
$23$	−0.980979	+	3.01914i	−0.204548	+	0.629535i	−0.999732	+	0.0231656i	$0.992625\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	13.0401	−	13.0401i	2.50957	−	2.50957i
$28$		0			0
$29$	−0.264069	−	1.66727i	−0.0490364	−	0.309603i	−1.00000		0.000300582i	$-0.999904\pi$
$29$	−0.264069	−	1.66727i	−0.0490364	−	0.309603i	0.950964	−	0.309303i	$-0.100096\pi$
$30$		0			0
$31$	−5.76817	+	4.19082i	−1.03599	+	0.752694i	−0.969500	−	0.245093i	$-0.921182\pi$
$31$	−5.76817	+	4.19082i	−1.03599	+	0.752694i	−0.0664948	+	0.997787i	$0.521182\pi$
$32$		0			0
$33$	8.10723	+	11.1586i	1.41129	+	1.94247i
$34$		0			0
$35$	−0.802599	−	1.57519i	−0.135664	−	0.266256i
$36$		0			0
$37$	6.28689	+	4.56769i	1.03356	+	0.750924i	0.969018	−	0.246991i	$-0.0794419\pi$
$37$	6.28689	+	4.56769i	1.03356	+	0.750924i	0.0645402	+	0.997915i	$0.479442\pi$
$38$		0			0
$39$	5.58822	+	1.81572i	0.894832	+	0.290748i
$40$		0			0
$41$	−5.51297	+	3.25686i	−0.860982	+	0.508636i
$41$	−5.51297	+	3.25686i	−0.860982	+	0.508636i
$42$		0			0
$43$	6.76633	+	2.19851i	1.03186	+	0.335270i	0.775523	−	0.631319i	$-0.217486\pi$
$43$	6.76633	+	2.19851i	1.03186	+	0.335270i	0.256332	+	0.966589i	$0.417486\pi$
$44$		0			0
$45$	6.83616	+	4.96676i	1.01908	+	0.740401i
$46$		0			0
$47$	−1.29835	−	2.54816i	−0.189384	−	0.371688i	0.776717	−	0.629849i	$-0.216883\pi$
$47$	−1.29835	−	2.54816i	−0.189384	−	0.371688i	−0.966102	+	0.258162i	$0.916883\pi$
$48$		0			0
$49$	2.27744	+	3.13463i	0.325349	+	0.447804i
$50$		0			0
$51$	1.80894	−	1.31427i	0.253302	−	0.184035i
$52$		0			0
$53$	−0.0802020	−	0.506376i	−0.0110166	−	0.0695561i	0.981568	−	0.191115i	$-0.0612105\pi$
$53$	−0.0802020	−	0.506376i	−0.0110166	−	0.0695561i	−0.992584	+	0.121559i	$0.961210\pi$
$54$		0			0
$55$	−2.88228	+	2.88228i	−0.388647	+	0.388647i
$56$		0			0
$57$	4.24466	+	13.0637i	0.562219	+	1.73033i
$58$		0			0
$59$	−1.35075	+	4.15719i	−0.175853	+	0.541220i	−0.999671	−	0.0256340i	$-0.991840\pi$
$59$	−1.35075	+	4.15719i	−0.175853	+	0.541220i	0.823818	+	0.566854i	$0.191840\pi$
$60$		0			0
$61$	−4.70688	+	1.52936i	−0.602654	+	0.195814i	−0.594424	−	0.804152i	$-0.702620\pi$
$61$	−4.70688	+	1.52936i	−0.602654	+	0.195814i	−0.00823036	+	0.999966i	$0.502620\pi$
$62$		0			0
$63$	13.3103	+	6.78193i	1.67694	+	0.854443i
$64$		0			0
$65$	−0.271642	+	1.71508i	−0.0336931	+	0.212730i
$66$		0			0
$67$	−0.0427763	+	0.00677510i	−0.00522596	+	0.000827710i	−0.159047	−	0.987271i	$-0.550842\pi$
$67$	−0.0427763	+	0.00677510i	−0.00522596	+	0.000827710i	0.153821	+	0.988099i	$0.450842\pi$
$68$		0			0
$69$	9.57106	−	4.87670i	1.15222	−	0.587086i
$70$		0			0
$71$	9.96152	+	1.57775i	1.18222	+	0.187245i	0.716434	−	0.697655i	$-0.245773\pi$
$71$	9.96152	+	1.57775i	1.18222	+	0.187245i	0.465782	+	0.884900i	$0.345773\pi$
$72$		0			0
$73$		−	14.2833i		−	1.67173i	−0.548933	−	0.835866i	$-0.684966\pi$
$73$		−	14.2833i		−	1.67173i	0.548933	−	0.835866i	$-0.315034\pi$
$74$		0			0
$75$	−1.53620	+	3.01497i	−0.177386	+	0.348139i
$76$		0			0
$77$	−4.23567	+	5.82990i	−0.482699	+	0.664379i
$78$		0			0
$79$	5.60539	+	5.60539i	0.630656	+	0.630656i	0.948233	−	0.317577i	$-0.102869\pi$
$79$	5.60539	+	5.60539i	0.630656	+	0.630656i	−0.317577	+	0.948233i	$0.602869\pi$
$80$		0			0
$81$	−37.0520			−4.11689
$82$		0			0
$83$	−13.5812			−1.49073			−0.745367	−	0.666654i	$-0.767726\pi$
$83$	−13.5812			−1.49073			−0.745367	+	0.666654i	$0.767726\pi$
$84$		0			0
$85$	0.467249	+	0.467249i	0.0506803	+	0.0506803i
$86$		0			0
$87$	−3.35742	+	4.62109i	−0.359953	+	0.495433i
$88$		0			0
$89$	−7.88376	+	15.4727i	−0.835676	+	1.64011i	−0.0694067	+	0.997588i	$0.522111\pi$
$89$	−7.88376	+	15.4727i	−0.835676	+	1.64011i	−0.766270	+	0.642519i	$0.777889\pi$
$90$		0			0
$91$			3.06985i			0.321808i
$92$		0			0
$93$	23.8288	+	3.77412i	2.47093	+	0.391357i
$94$		0			0
$95$	−3.61693	+	1.84292i	−0.371089	+	0.189079i
$96$		0			0
$97$	−14.0220	+	2.22087i	−1.42372	+	0.225495i	−0.820301	−	0.571931i	$-0.806194\pi$
$97$	−14.0220	+	2.22087i	−1.42372	+	0.225495i	−0.603417	+	0.797426i	$0.706194\pi$
$98$		0			0
$99$	5.38814	−	34.0194i	0.541528	−	3.41908i
$100$		0			0
$101$	−8.60273	−	4.38331i	−0.856004	−	0.436156i	−0.0298193	−	0.999555i	$-0.509493\pi$
$101$	−8.60273	−	4.38331i	−0.856004	−	0.436156i	−0.826185	+	0.563400i	$0.809493\pi$
$102$		0			0
$103$	3.43152	−	1.11497i	0.338118	−	0.109861i	−0.135037	−	0.990841i	$-0.543115\pi$
$103$	3.43152	−	1.11497i	0.338118	−	0.109861i	0.473155	+	0.880979i	$0.343115\pi$
$104$		0			0
$105$	−1.84857	+	5.68932i	−0.180402	+	0.555221i
$106$		0			0
$107$	−0.685989	−	2.11126i	−0.0663171	−	0.204103i	0.912407	−	0.409284i	$-0.134222\pi$
$107$	−0.685989	−	2.11126i	−0.0663171	−	0.204103i	−0.978724	+	0.205181i	$0.934222\pi$
$108$		0			0
$109$	14.5102	−	14.5102i	1.38982	−	1.38982i	0.564156	−	0.825668i	$-0.309202\pi$
$109$	14.5102	−	14.5102i	1.38982	−	1.38982i	0.825668	−	0.564156i	$-0.190798\pi$
$110$		0			0
$111$	−4.11351	−	25.9717i	−0.390437	−	2.46512i
$112$		0			0
$113$	−2.32564	+	1.68968i	−0.218778	+	0.158951i	−0.691776	−	0.722112i	$-0.743172\pi$
$113$	−2.32564	+	1.68968i	−0.218778	+	0.158951i	0.472999	+	0.881063i	$0.343172\pi$
$114$		0			0
$115$	1.86593	+	2.56824i	0.173999	+	0.239489i
$116$		0			0
$117$	−6.66142	−	13.0738i	−0.615849	−	1.20867i
$118$		0			0
$119$	0.945091	+	0.686648i	0.0866363	+	0.0629450i
$120$		0			0
$121$	5.34028	+	1.73516i	0.485480	+	0.157742i
$122$		0			0
$123$	20.9835	+	5.39818i	1.89202	+	0.486738i
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.0850651	−	0.0276393i
$126$		0			0
$127$	7.29199	+	5.29794i	0.647060	+	0.470116i	0.862268	−	0.506452i	$-0.169043\pi$
$127$	7.29199	+	5.29794i	0.647060	+	0.470116i	−0.215209	+	0.976568i	$0.569043\pi$
$128$		0			0
$129$	−10.9294	−	21.4501i	−0.962278	−	1.88858i
$130$		0			0
$131$	−2.53322	−	3.48668i	−0.221329	−	0.304633i	0.683885	−	0.729590i	$-0.260289\pi$
$131$	−2.53322	−	3.48668i	−0.221329	−	0.304633i	−0.905213	+	0.424957i	$0.860289\pi$
$132$		0			0
$133$	−5.80588	+	4.21822i	−0.503434	+	0.365766i
$134$		0			0
$135$	−2.88488	−	18.2144i	−0.248291	−	1.56765i
$136$		0			0
$137$	6.07795	−	6.07795i	0.519274	−	0.519274i	−0.398077	−	0.917352i	$-0.630322\pi$
$137$	6.07795	−	6.07795i	0.519274	−	0.519274i	0.917352	+	0.398077i	$0.130322\pi$
$138$		0			0
$139$	−3.93667	−	12.1158i	−0.333904	−	1.02765i	−0.967260	−	0.253789i	$-0.918323\pi$
$139$	−3.93667	−	12.1158i	−0.333904	−	1.02765i	0.633356	−	0.773861i	$-0.281677\pi$
$140$		0			0
$141$	−2.99041	+	9.20353i	−0.251838	+	0.775077i
$142$		0			0
$143$	6.73167	−	2.18725i	0.562931	−	0.182907i
$144$		0			0
$145$	−1.50406	−	0.766358i	−0.124906	−	0.0636426i
$146$		0			0
$147$	2.05099	−	12.9494i	0.169162	−	1.06805i
$148$		0			0
$149$	4.23633	−	0.670968i	0.347054	−	0.0549679i	0.0195255	−	0.999809i	$-0.493784\pi$
$149$	4.23633	−	0.670968i	0.347054	−	0.0549679i	0.327528	+	0.944841i	$0.393784\pi$
$150$		0			0
$151$	−17.5669	+	8.95078i	−1.42957	+	0.728404i	−0.985830	−	0.167749i	$-0.946350\pi$
$151$	−17.5669	+	8.95078i	−1.42957	+	0.728404i	−0.443744	+	0.896153i	$0.646350\pi$
$152$		0			0
$153$	−5.51491	−	0.873476i	−0.445854	−	0.0706164i
$154$		0			0
$155$			7.12985i			0.572684i
$156$		0			0
$157$	−10.1418	+	19.9044i	−0.809402	+	1.58854i	−0.000934298		1.00000i	$0.500297\pi$
$157$	−10.1418	+	19.9044i	−0.809402	+	1.58854i	−0.808467	+	0.588541i	$0.799703\pi$
$158$		0			0
$159$	−1.01970	+	1.40350i	−0.0808677	+	0.111305i
$160$		0			0
$161$	3.96839	+	3.96839i	0.312753	+	0.312753i
$162$		0			0
$163$	−18.2099			−1.42631			−0.713155	−	0.701007i	$-0.752734\pi$
$163$	−18.2099			−1.42631			−0.713155	+	0.701007i	$0.752734\pi$
$164$		0			0
$165$	13.7928			1.07377
$166$		0			0
$167$	−16.0818	−	16.0818i	−1.24445	−	1.24445i	−0.958138	−	0.286308i	$-0.907572\pi$
$167$	−16.0818	−	16.0818i	−1.24445	−	1.24445i	−0.286308	−	0.958138i	$-0.592428\pi$
$168$		0			0
$169$	−5.86886	+	8.07779i	−0.451451	+	0.621369i
$170$		0			0
$171$	15.5726	−	30.5629i	1.19086	−	2.33720i
$172$		0			0
$173$			6.27081i			0.476761i	0.971172	+	0.238381i	$0.0766165\pi$
$173$			6.27081i			0.476761i	−0.971172	+	0.238381i	$0.923383\pi$
$174$		0			0
$175$	−1.74611	−	0.276557i	−0.131994	−	0.0209057i
$176$		0			0
$177$	13.1788	−	6.71494i	0.990580	−	0.504726i
$178$		0			0
$179$	−24.3201	+	3.85192i	−1.81777	+	0.287906i	−0.970114	−	0.242648i	$-0.921984\pi$
$179$	−24.3201	+	3.85192i	−1.81777	+	0.287906i	−0.847651	+	0.530554i	$0.821984\pi$
$180$		0			0
$181$	3.68279	−	23.2522i	0.273740	−	1.72832i	−0.341411	−	0.939914i	$-0.610905\pi$
$181$	3.68279	−	23.2522i	0.273740	−	1.72832i	0.615150	−	0.788410i	$-0.289095\pi$
$182$		0			0
$183$	14.9214	+	7.60284i	1.10302	+	0.562018i
$184$		0			0
$185$	7.39068	−	2.40138i	0.543374	−	0.176553i
$186$		0			0
$187$	0.832334	−	2.56166i	0.0608663	−	0.187327i
$188$		0			0
$189$	−10.0747	−	31.0066i	−0.732823	−	2.25540i
$190$		0			0
$191$	−6.71941	+	6.71941i	−0.486199	+	0.486199i	−0.907105	−	0.420905i	$-0.861712\pi$
$191$	−6.71941	+	6.71941i	−0.486199	+	0.486199i	0.420905	+	0.907105i	$0.361712\pi$
$192$		0			0
$193$	−0.255981	−	1.61620i	−0.0184259	−	0.116336i	0.976761	−	0.214331i	$-0.0687572\pi$
$193$	−0.255981	−	1.61620i	−0.0184259	−	0.116336i	−0.995187	+	0.0979947i	$0.968757\pi$
$194$		0			0
$195$	4.75362	−	3.45371i	0.340414	−	0.247325i
$196$		0			0
$197$	−6.33184	−	8.71504i	−0.451125	−	0.620921i	0.521514	−	0.853243i	$-0.325368\pi$
$197$	−6.33184	−	8.71504i	−0.451125	−	0.620921i	−0.972639	+	0.232322i	$0.925368\pi$
$198$		0			0
$199$	8.46565	+	16.6148i	0.600114	+	1.17779i	0.968709	+	0.248200i	$0.0798389\pi$
$199$	8.46565	+	16.6148i	0.600114	+	1.17779i	−0.368595	+	0.929590i	$0.620161\pi$
$200$		0			0
$201$	0.118561	+	0.0861398i	0.00836267	+	0.00607583i
$202$		0			0
$203$	−2.83820	−	0.922187i	−0.199203	−	0.0647249i
$204$		0			0
$205$	−0.605588	+	6.37442i	−0.0422961	+	0.445209i
$206$		0			0
$207$	−25.5116	−	8.28923i	−1.77318	−	0.576142i
$208$		0			0
$209$	13.3865	+	9.72588i	0.925965	+	0.672753i
$210$		0			0
$211$	0.294891	+	0.578756i	0.0203011	+	0.0398432i	0.900934	−	0.433955i	$-0.142882\pi$
$211$	0.294891	+	0.578756i	0.0203011	+	0.0398432i	−0.880633	+	0.473799i	$0.842882\pi$
$212$		0			0
$213$	−20.0598	−	27.6099i	−1.37447	−	1.89180i
$214$		0			0
$215$	5.75578	−	4.18182i	0.392541	−	0.285198i
$216$		0			0
$217$	1.97181	+	12.4495i	0.133855	+	0.845128i
$218$		0			0
$219$	−34.1755	+	34.1755i	−2.30937	+	2.30937i
$220$		0			0
$221$	−0.354578	−	1.09128i	−0.0238515	−	0.0734073i
$222$		0			0
$223$	1.95880	−	6.02858i	0.131171	−	0.403703i	−0.863804	−	0.503829i	$-0.831924\pi$
$223$	1.95880	−	6.02858i	0.131171	−	0.403703i	0.994975	+	0.100125i	$0.0319243\pi$
$224$		0			0
$225$	8.03639	−	2.61118i	0.535760	−	0.174079i
$226$		0			0
$227$	−9.08778	−	4.63046i	−0.603177	−	0.307334i	0.125604	−	0.992080i	$-0.459913\pi$
$227$	−9.08778	−	4.63046i	−0.603177	−	0.307334i	−0.728782	+	0.684746i	$0.759913\pi$
$228$		0			0
$229$	−1.98434	+	12.5286i	−0.131129	+	0.827916i	0.831189	+	0.555990i	$0.187661\pi$
$229$	−1.98434	+	12.5286i	−0.131129	+	0.827916i	−0.962318	+	0.271926i	$0.912339\pi$
$230$		0			0
$231$	24.0838	−	3.81450i	1.58460	−	0.250976i
$232$		0			0
$233$	−23.5699	+	12.0094i	−1.54411	+	0.786765i	−0.998679	−	0.0513889i	$-0.983635\pi$
$233$	−23.5699	+	12.0094i	−1.54411	+	0.786765i	−0.545434	+	0.838154i	$0.683635\pi$
$234$		0			0
$235$	−2.82466	−	0.447382i	−0.184260	−	0.0291840i
$236$		0			0
$237$		−	26.8240i		−	1.74240i
$238$		0			0
$239$	−8.40305	+	16.4919i	−0.543548	+	1.06677i	0.441943	+	0.897043i	$0.354289\pi$
$239$	−8.40305	+	16.4919i	−0.543548	+	1.06677i	−0.985491	+	0.169730i	$0.945711\pi$
$240$		0			0
$241$	9.28787	−	12.7837i	0.598284	−	0.823467i	−0.397266	−	0.917704i	$-0.630041\pi$
$241$	9.28787	−	12.7837i	0.598284	−	0.823467i	0.995550	+	0.0942362i	$0.0300409\pi$
$242$		0			0
$243$	49.5338	+	49.5338i	3.17759	+	3.17759i
$244$		0			0
$245$	3.87461			0.247540
$246$		0			0
$247$	7.04894			0.448513
$248$		0			0
$249$	32.4957	+	32.4957i	2.05933	+	2.05933i
$250$		0			0
$251$	−4.65017	+	6.40041i	−0.293516	+	0.403990i	−0.930152	−	0.367174i	$-0.880325\pi$
$251$	−4.65017	+	6.40041i	−0.293516	+	0.403990i	0.636636	+	0.771164i	$0.280325\pi$
$252$		0			0
$253$	5.87456	−	11.5295i	0.369331	−	0.724852i
$254$		0			0
$255$		−	2.23597i		−	0.140022i
$256$		0			0
$257$	14.3461	+	2.27219i	0.894882	+	0.141735i	0.586903	−	0.809658i	$-0.300347\pi$
$257$	14.3461	+	2.27219i	0.894882	+	0.141735i	0.307980	+	0.951393i	$0.400347\pi$
$258$		0			0
$259$	12.2408	−	6.23701i	0.760608	−	0.387549i
$260$		0			0
$261$	14.0883	−	2.23137i	0.872046	−	0.138119i
$262$		0			0
$263$	3.04933	−	19.2527i	0.188030	−	1.18717i	−0.695404	−	0.718619i	$-0.744775\pi$
$263$	3.04933	−	19.2527i	0.188030	−	1.18717i	0.883434	−	0.468556i	$-0.155225\pi$
$264$		0			0
$265$	−0.456808	−	0.232755i	−0.0280615	−	0.0142980i
$266$		0			0
$267$	55.8849	−	18.1581i	3.42010	−	1.11126i
$268$		0			0
$269$	−8.65545	+	26.6387i	−0.527732	+	1.62419i	0.231116	+	0.972926i	$0.425762\pi$
$269$	−8.65545	+	26.6387i	−0.527732	+	1.62419i	−0.758849	+	0.651267i	$0.774238\pi$
$270$		0			0
$271$	1.01832	+	3.13407i	0.0618586	+	0.190381i	0.977210	−	0.212275i	$-0.0680872\pi$
$271$	1.01832	+	3.13407i	0.0618586	+	0.190381i	−0.915351	+	0.402656i	$0.868087\pi$
$272$		0			0
$273$	7.34521	−	7.34521i	0.444552	−	0.444552i
$274$		0			0
$275$	0.637652	+	4.02598i	0.0384519	+	0.242776i
$276$		0			0
$277$	13.9711	−	10.1506i	0.839443	−	0.609891i	−0.0827718	−	0.996569i	$-0.526377\pi$
$277$	13.9711	−	10.1506i	0.839443	−	0.609891i	0.922215	+	0.386677i	$0.126377\pi$
$278$		0			0
$279$	−35.4123	−	48.7409i	−2.12008	−	2.91804i
$280$		0			0
$281$	−8.70368	−	17.0819i	−0.519218	−	1.01902i	−0.990561	−	0.137072i	$-0.956231\pi$
$281$	−8.70368	−	17.0819i	−0.519218	−	1.01902i	0.471343	−	0.881950i	$-0.343769\pi$
$282$		0			0
$283$	18.3790	+	13.3532i	1.09252	+	0.793762i	0.979823	−	0.199867i	$-0.0640510\pi$
$283$	18.3790	+	13.3532i	1.09252	+	0.793762i	0.112697	+	0.993629i	$0.464051\pi$
$284$		0			0
$285$	13.0637	+	4.24466i	0.773828	+	0.251432i
$286$		0			0
$287$	0.705467	+	11.2979i	0.0416424	+	0.666896i
$288$		0			0
$289$	15.7527	+	5.11836i	0.926629	+	0.301080i
$290$		0			0
$291$	38.8642	+	28.2365i	2.27826	+	1.65525i
$292$		0			0
$293$	−9.29021	−	18.2331i	−0.542740	−	1.06519i	−0.985679	−	0.168635i	$-0.946064\pi$
$293$	−9.29021	−	18.2331i	−0.542740	−	1.06519i	0.442938	−	0.896552i	$-0.353936\pi$
$294$		0			0
$295$	2.56928	+	3.53631i	0.149589	+	0.205892i
$296$		0			0
$297$	−60.8142	+	44.1841i	−3.52880	+	2.56382i
$298$		0			0
$299$	−0.862333	−	5.44455i	−0.0498700	−	0.314867i
$300$		0			0
$301$	8.89372	−	8.89372i	0.512626	−	0.512626i
$302$		0			0
$303$	10.0958	+	31.0716i	0.579988	+	1.78502i
$304$		0			0
$305$	−1.52936	+	4.70688i	−0.0875708	+	0.269515i
$306$		0			0
$307$	−8.93928	+	2.90455i	−0.510192	+	0.165771i	−0.552789	−	0.833321i	$-0.686437\pi$
$307$	−8.93928	+	2.90455i	−0.510192	+	0.165771i	0.0425977	+	0.999092i	$0.486437\pi$
$308$		0			0
$309$	−10.8784	−	5.54280i	−0.618848	−	0.315319i
$310$		0			0
$311$	−2.04991	+	12.9426i	−0.116240	+	0.733909i	0.858871	+	0.512192i	$0.171166\pi$
$311$	−2.04991	+	12.9426i	−0.116240	+	0.733909i	−0.975111	+	0.221717i	$0.928834\pi$
$312$		0			0
$313$	11.6722	−	1.84870i	0.659755	−	0.104495i	0.182426	−	0.983220i	$-0.441605\pi$
$313$	11.6722	−	1.84870i	0.659755	−	0.104495i	0.477329	+	0.878725i	$0.341605\pi$
$314$		0			0
$315$	13.3103	−	6.78193i	0.749950	−	0.382119i
$316$		0			0
$317$	−32.9866	−	5.22457i	−1.85271	−	0.293441i	−0.872091	−	0.489344i	$-0.837236\pi$
$317$	−32.9866	−	5.22457i	−1.85271	−	0.293441i	−0.980623	+	0.195902i	$0.937236\pi$
$318$		0			0
$319$			6.88076i			0.385249i
$320$		0			0
$321$	−3.41023	+	6.69295i	−0.190341	+	0.373564i
$322$		0			0
$323$	1.57667	−	2.17010i	0.0877283	−	0.120748i
$324$		0			0
$325$	1.22786	+	1.22786i	0.0681096	+	0.0681096i
$326$		0			0
$327$	−69.4369			−3.83987
$328$		0			0
$329$	−5.05590			−0.278741
$330$		0			0
$331$	−13.6326	−	13.6326i	−0.749313	−	0.749313i	0.225037	−	0.974350i	$-0.427750\pi$
$331$	−13.6326	−	13.6326i	−0.749313	−	0.749313i	−0.974350	+	0.225037i	$0.927750\pi$
$332$		0			0
$333$	−38.5968	+	53.1240i	−2.11509	+	2.91118i
$334$		0			0
$335$	−0.0196621	+	0.0385890i	−0.00107426	+	0.00210834i
$336$		0			0
$337$		−	11.9233i		−	0.649505i	−0.945799	−	0.324752i	$-0.894719\pi$
$337$		−	11.9233i		−	0.649505i	0.945799	−	0.324752i	$-0.105281\pi$
$338$		0			0
$339$	9.60742	+	1.52167i	0.521803	+	0.0826455i
$340$		0			0
$341$	25.8948	−	13.1941i	1.40228	−	0.714499i
$342$		0			0
$343$	18.9883	−	3.00745i	1.02527	−	0.162387i
$344$		0			0
$345$	1.68040	−	10.6096i	0.0904695	−	0.571202i
$346$		0			0
$347$	29.9817	+	15.2764i	1.60950	+	0.820082i	0.999619	+	0.0275891i	$0.00878299\pi$
$347$	29.9817	+	15.2764i	1.60950	+	0.820082i	0.609882	+	0.792493i	$0.291217\pi$
$348$		0			0
$349$	4.27006	−	1.38743i	0.228571	−	0.0742672i	−0.192492	−	0.981298i	$-0.561657\pi$
$349$	4.27006	−	1.38743i	0.228571	−	0.0742672i	0.421063	+	0.907031i	$0.361657\pi$
$350$		0			0
$351$	−9.89563	+	30.4556i	−0.528189	+	1.62560i
$352$		0			0
$353$	2.35199	+	7.23868i	0.125184	+	0.385276i	0.993935	−	0.109973i	$-0.0350766\pi$
$353$	2.35199	+	7.23868i	0.125184	+	0.385276i	−0.868751	+	0.495250i	$0.835077\pi$
$354$		0			0
$355$	7.13166	−	7.13166i	0.378509	−	0.378509i
$356$		0			0
$357$	−0.618373	−	3.90425i	−0.0327278	−	0.206635i
$358$		0			0
$359$	−8.71876	+	6.33455i	−0.460159	+	0.334325i	−0.793594	−	0.608448i	$-0.791792\pi$
$359$	−8.71876	+	6.33455i	−0.460159	+	0.334325i	0.333435	+	0.942773i	$0.391792\pi$
$360$		0			0
$361$	−1.48211	−	2.03995i	−0.0780057	−	0.107366i
$362$		0			0
$363$	−8.62595	−	16.9294i	−0.452745	−	0.888562i
$364$		0			0
$365$	−11.5554	−	8.39550i	−0.604838	−	0.439441i
$366$		0			0
$367$	−21.9142	−	7.12035i	−1.14391	−	0.371679i	−0.325064	−	0.945692i	$-0.605386\pi$
$367$	−21.9142	−	7.12035i	−1.14391	−	0.371679i	−0.818846	+	0.574013i	$0.805386\pi$
$368$		0			0
$369$	−27.5204	−	46.5844i	−1.43265	−	2.42509i
$370$		0			0
$371$	−0.862008	−	0.280083i	−0.0447532	−	0.0145412i
$372$		0			0
$373$	−26.4430	−	19.2120i	−1.36917	−	0.994757i	−0.997802	−	0.0662703i	$-0.978890\pi$
$373$	−26.4430	−	19.2120i	−1.36917	−	0.994757i	−0.371364	−	0.928487i	$-0.621110\pi$
$374$		0			0
$375$	1.53620	+	3.01497i	0.0793292	+	0.155692i
$376$		0			0
$377$	1.72293	+	2.37142i	0.0887356	+	0.122134i
$378$		0			0
$379$	−0.399826	+	0.290490i	−0.0205377	+	0.0149215i	−0.598007	−	0.801491i	$-0.704040\pi$
$379$	−0.399826	+	0.290490i	−0.0205377	+	0.0149215i	0.577469	+	0.816413i	$0.304040\pi$
$380$		0			0
$381$	−4.77115	−	30.1239i	−0.244433	−	1.54329i
$382$		0			0
$383$	11.0408	−	11.0408i	0.564161	−	0.564161i	−0.366326	−	0.930487i	$-0.619384\pi$
$383$	11.0408	−	11.0408i	0.564161	−	0.564161i	0.930487	+	0.366326i	$0.119384\pi$
$384$		0			0
$385$	2.22682	+	6.85346i	0.113489	+	0.349285i
$386$		0			0
$387$	−18.5774	+	57.1752i	−0.944340	+	2.90638i
$388$		0			0
$389$	−8.42482	+	2.73739i	−0.427155	+	0.138791i	−0.514702	−	0.857369i	$-0.672097\pi$
$389$	−8.42482	+	2.73739i	−0.427155	+	0.138791i	0.0875465	+	0.996160i	$0.472097\pi$
$390$		0			0
$391$	−1.86905	−	0.952331i	−0.0945221	−	0.0481614i
$392$		0			0
$393$	−2.28134	+	14.4038i	−0.115078	+	0.726575i
$394$		0			0
$395$	7.82963	−	1.24009i	0.393951	−	0.0623957i
$396$		0			0
$397$	15.3365	−	7.81432i	0.769715	−	0.392189i	−0.0245986	−	0.999697i	$-0.507831\pi$
$397$	15.3365	−	7.81432i	0.769715	−	0.392189i	0.794313	+	0.607508i	$0.207831\pi$
$398$		0			0
$399$	23.9846	+	3.79879i	1.20073	+	0.190177i
$400$		0			0
$401$		−	29.4688i		−	1.47160i	−0.677198	−	0.735801i	$-0.736806\pi$
$401$		−	29.4688i		−	1.47160i	0.677198	−	0.735801i	$-0.263194\pi$
$402$		0			0
$403$	5.62073	−	11.0313i	0.279988	−	0.549508i
$404$		0			0
$405$	−21.7786	+	29.9757i	−1.08219	+	1.48950i
$406$		0			0
$407$	−22.3983	−	22.3983i	−1.11024	−	1.11024i
$408$		0			0
$409$	32.7527			1.61952			0.809758	−	0.586764i	$-0.199598\pi$
$409$	32.7527			1.61952			0.809758	+	0.586764i	$0.199598\pi$
$410$		0			0
$411$	−29.0853			−1.43467
$412$		0			0
$413$	5.46425	+	5.46425i	0.268878	+	0.268878i
$414$		0			0
$415$	−7.98285	+	10.9875i	−0.391863	+	0.539353i
$416$		0			0
$417$	−19.5702	+	38.4087i	−0.958356	+	1.88088i
$418$		0			0
$419$			13.3916i			0.654224i	0.944986	+	0.327112i	$0.106075\pi$
$419$			13.3916i			0.654224i	−0.944986	+	0.327112i	$0.893925\pi$
$420$		0			0
$421$	28.3759	+	4.49430i	1.38296	+	0.219039i	0.803179	−	0.595737i	$-0.203140\pi$
$421$	28.3759	+	4.49430i	1.38296	+	0.219039i	0.579776	+	0.814776i	$0.303140\pi$
$422$		0			0
$423$	21.5319	−	10.9710i	1.04692	−	0.533430i
$424$		0			0
$425$	0.652655	−	0.103370i	0.0316584	−	0.00501420i
$426$		0			0
$427$	−1.36871	+	8.64169i	−0.0662365	+	0.418201i
$428$		0			0
$429$	−21.3403	−	10.8734i	−1.03032	−	0.524973i
$430$		0			0
$431$	−27.9031	+	9.06627i	−1.34405	+	0.436707i	−0.890685	−	0.454620i	$-0.849775\pi$
$431$	−27.9031	+	9.06627i	−1.34405	+	0.436707i	−0.453361	+	0.891327i	$0.649775\pi$
$432$		0			0
$433$	5.38042	−	16.5592i	0.258567	−	0.795786i	−0.734539	−	0.678566i	$-0.762602\pi$
$433$	5.38042	−	16.5592i	0.258567	−	0.795786i	0.993106	−	0.117220i	$-0.0373982\pi$
$434$		0			0
$435$	1.76510	+	5.43242i	0.0846301	+	0.260465i
$436$		0			0
$437$	9.11215	−	9.11215i	0.435893	−	0.435893i
$438$		0			0
$439$	−2.22558	−	14.0518i	−0.106221	−	0.670654i	−0.982134	−	0.188184i	$-0.939740\pi$
$439$	−2.22558	−	14.0518i	−0.106221	−	0.670654i	0.875912	−	0.482470i	$-0.160260\pi$
$440$		0			0
$441$	−26.4875	+	19.2443i	−1.26131	+	0.916395i
$442$		0			0
$443$	−4.31764	−	5.94272i	−0.205137	−	0.282347i	0.694036	−	0.719941i	$-0.255831\pi$
$443$	−4.31764	−	5.94272i	−0.205137	−	0.282347i	−0.899173	+	0.437593i	$0.855831\pi$
$444$		0			0
$445$	7.88376	+	15.4727i	0.373726	+	0.733478i
$446$		0			0
$447$	−11.7417	−	8.53081i	−0.555361	−	0.403494i
$448$		0			0
$449$	−17.5855	−	5.71387i	−0.829910	−	0.269654i	−0.136903	−	0.990585i	$-0.543715\pi$
$449$	−17.5855	−	5.71387i	−0.829910	−	0.269654i	−0.693007	+	0.720930i	$0.743715\pi$
$450$		0			0
$451$	24.2719	−	9.59669i	1.14292	−	0.451891i
$452$		0			0
$453$	63.4487	+	20.6157i	2.98108	+	0.968611i
$454$		0			0
$455$	2.48356	+	1.80441i	0.116431	+	0.0845922i
$456$		0			0
$457$	16.2947	+	31.9802i	0.762235	+	1.49597i	0.865278	+	0.501293i	$0.167142\pi$
$457$	16.2947	+	31.9802i	0.762235	+	1.49597i	−0.103043	+	0.994677i	$0.532858\pi$
$458$		0			0
$459$	7.16272	+	9.85864i	0.334327	+	0.460162i
$460$		0			0
$461$	0.691140	−	0.502143i	0.0321896	−	0.0233871i	−0.571574	−	0.820550i	$-0.693667\pi$
$461$	0.691140	−	0.502143i	0.0321896	−	0.0233871i	0.603764	+	0.797163i	$0.293667\pi$
$462$		0			0
$463$	−1.53437	−	9.68761i	−0.0713081	−	0.450222i	−0.997347	−	0.0727936i	$-0.976809\pi$
$463$	−1.53437	−	9.68761i	−0.0713081	−	0.450222i	0.926039	−	0.377428i	$-0.123191\pi$
$464$		0			0
$465$	17.0596	−	17.0596i	0.791118	−	0.791118i
$466$		0			0
$467$	3.72634	+	11.4685i	0.172435	+	0.530699i	0.999507	−	0.0313963i	$-0.00999540\pi$
$467$	3.72634	+	11.4685i	0.172435	+	0.530699i	−0.827072	+	0.562095i	$0.809995\pi$
$468$		0			0
$469$	−0.0236602	+	0.0728185i	−0.00109252	+	0.00336244i
$470$		0			0
$471$	71.8912	−	23.3589i	3.31257	−	1.07632i
$472$		0			0
$473$	−25.8392	−	13.1657i	−1.18809	−	0.605361i
$474$		0			0
$475$	−0.635025	+	4.00939i	−0.0291370	+	0.183964i
$476$		0			0
$477$	4.27886	−	0.677704i	0.195915	−	0.0310299i
$478$		0			0
$479$	7.08425	−	3.60961i	0.323688	−	0.164927i	−0.284594	−	0.958648i	$-0.591859\pi$
$479$	7.08425	−	3.60961i	0.323688	−	0.164927i	0.608282	+	0.793721i	$0.291859\pi$
$480$		0			0
$481$	−13.3279	−	2.11094i	−0.607702	−	0.0962505i
$482$		0			0
$483$		−	18.9903i		−	0.864087i
$484$		0			0
$485$	−6.44520	+	12.6494i	−0.292662	+	0.574381i
$486$		0			0
$487$	−0.551957	+	0.759703i	−0.0250115	+	0.0344254i	−0.821340	−	0.570439i	$-0.806773\pi$
$487$	−0.551957	+	0.759703i	−0.0250115	+	0.0344254i	0.796328	+	0.604865i	$0.206773\pi$
$488$		0			0
$489$	43.5707	+	43.5707i	1.97034	+	1.97034i
$490$		0			0
$491$	−5.59955			−0.252704			−0.126352	−	0.991985i	$-0.540327\pi$
$491$	−5.59955			−0.252704			−0.126352	+	0.991985i	$0.540327\pi$
$492$		0			0
$493$	1.11545			0.0502372
$494$		0			0
$495$	−24.3552	−	24.3552i	−1.09468	−	1.09468i
$496$		0			0
$497$	10.4804	−	14.4250i	0.470109	−	0.647049i
$498$		0			0
$499$	−5.54357	+	10.8799i	−0.248164	+	0.487050i	−0.981163	−	0.193180i	$-0.938120\pi$
$499$	−5.54357	+	10.8799i	−0.248164	+	0.487050i	0.732999	+	0.680230i	$0.238120\pi$
$500$		0			0
$501$			76.9575i			3.43821i
$502$		0			0
$503$	−24.3763	−	3.86082i	−1.08688	−	0.172146i	−0.412816	−	0.910814i	$-0.635455\pi$
$503$	−24.3763	−	3.86082i	−1.08688	−	0.172146i	−0.674068	+	0.738669i	$0.735455\pi$
$504$		0			0
$505$	−8.60273	+	4.38331i	−0.382817	+	0.195055i
$506$		0			0
$507$	33.3701	−	5.28530i	1.48202	−	0.234728i
$508$		0			0
$509$	−1.60418	+	10.1284i	−0.0711039	+	0.448933i	0.926292	+	0.376807i	$0.122978\pi$
$509$	−1.60418	+	10.1284i	−0.0711039	+	0.448933i	−0.997396	+	0.0721252i	$0.977022\pi$
$510$		0			0
$511$	−22.4989	−	11.4638i	−0.995292	−	0.507127i
$512$		0			0
$513$	−71.1968	+	23.1333i	−3.14342	+	1.02136i
$514$		0			0
$515$	1.11497	−	3.43152i	0.0491314	−	0.151211i
$516$		0			0
$517$	3.60230	+	11.0867i	0.158429	+	0.487595i
$518$		0			0
$519$	15.0041	−	15.0041i	0.658608	−	0.658608i
$520$		0			0
$521$	−2.03124	−	12.8247i	−0.0889900	−	0.561861i	−0.991388	−	0.130957i	$-0.958195\pi$
$521$	−2.03124	−	12.8247i	−0.0889900	−	0.561861i	0.902398	−	0.430904i	$-0.141805\pi$
$522$		0			0
$523$	−13.2860	+	9.65284i	−0.580956	+	0.422089i	−0.839069	−	0.544026i	$-0.816899\pi$
$523$	−13.2860	+	9.65284i	−0.580956	+	0.422089i	0.258113	+	0.966115i	$0.416899\pi$
$524$		0			0
$525$	3.51619	+	4.83962i	0.153459	+	0.211219i
$526$		0			0
$527$	−2.13890	−	4.19783i	−0.0931721	−	0.182861i
$528$		0			0
$529$	10.4545	+	7.59563i	0.454543	+	0.330245i
$530$		0			0
$531$	−35.1281	−	11.4138i	−1.52443	−	0.495317i
$532$		0			0
$533$	5.96216	−	9.38509i	0.258250	−	0.406513i
$534$		0			0
$535$	−2.11126	−	0.685989i	−0.0912776	−	0.0296579i
$536$		0			0
$537$	67.4069	+	48.9740i	2.90882	+	2.11338i
$538$		0			0
$539$	−7.17012	−	14.0722i	−0.308839	−	0.606131i
$540$		0			0
$541$	21.8657	+	30.0955i	0.940079	+	1.29391i	0.955796	+	0.294031i	$0.0949969\pi$
$541$	21.8657	+	30.0955i	0.940079	+	1.29391i	−0.0157171	+	0.999876i	$0.505003\pi$
$542$		0			0
$543$	−64.4472	+	46.8237i	−2.76570	+	2.00940i
$544$		0			0
$545$	−3.21011	−	20.2679i	−0.137506	−	0.868180i
$546$		0			0
$547$	16.5147	−	16.5147i	0.706116	−	0.706116i	−0.259600	−	0.965716i	$-0.583591\pi$
$547$	16.5147	−	16.5147i	0.706116	−	0.706116i	0.965716	+	0.259600i	$0.0835907\pi$
$548$		0			0
$549$	−12.9230	−	39.7730i	−0.551541	−	1.69747i
$550$		0			0
$551$	−2.11751	+	6.51703i	−0.0902090	+	0.277635i
$552$		0			0
$553$	13.3284	−	4.33067i	0.566783	−	0.184159i
$554$		0			0
$555$	−23.4294	−	11.9379i	−0.994522	−	0.506734i
$556$		0			0
$557$	0.324479	−	2.04868i	0.0137486	−	0.0868053i	−0.979860	−	0.199686i	$-0.936008\pi$
$557$	0.324479	−	2.04868i	0.0137486	−	0.0868053i	0.993609	+	0.112881i	$0.0360078\pi$
$558$		0			0
$559$	−12.2020	+	1.93261i	−0.516090	+	0.0817407i
$560$		0			0
$561$	−8.12079	+	4.13775i	−0.342860	+	0.174696i
$562$		0			0
$563$	5.16258	+	0.817672i	0.217577	+	0.0344608i	0.264271	−	0.964448i	$-0.414869\pi$
$563$	5.16258	+	0.817672i	0.217577	+	0.0344608i	−0.0466943	+	0.998909i	$0.514869\pi$
$564$		0			0
$565$			2.87465i			0.120937i
$566$		0			0
$567$	−29.7379	+	58.3639i	−1.24887	+	2.45105i
$568$		0			0
$569$	24.1797	−	33.2805i	1.01367	−	1.39519i	0.0971157	−	0.995273i	$-0.469038\pi$
$569$	24.1797	−	33.2805i	1.01367	−	1.39519i	0.916551	−	0.399919i	$-0.130962\pi$
$570$		0			0
$571$	−2.84546	−	2.84546i	−0.119079	−	0.119079i	0.645056	−	0.764135i	$-0.276834\pi$
$571$	−2.84546	−	2.84546i	−0.119079	−	0.119079i	−0.764135	+	0.645056i	$0.776834\pi$
$572$		0			0
$573$	32.1550			1.34329
$574$		0			0
$575$	3.17451			0.132386
$576$		0			0
$577$	−17.2992	−	17.2992i	−0.720175	−	0.720175i	0.248465	−	0.968641i	$-0.420074\pi$
$577$	−17.2992	−	17.2992i	−0.720175	−	0.720175i	−0.968641	+	0.248465i	$0.920074\pi$
$578$		0			0
$579$	−3.25458	+	4.47955i	−0.135256	+	0.186164i
$580$		0			0
$581$	−10.9003	+	21.3930i	−0.452220	+	0.887532i
$582$		0			0
$583$			2.08980i			0.0865506i
$584$		0			0
$585$	−14.4924	−	2.29537i	−0.599187	−	0.0949018i
$586$		0			0
$587$	9.38915	−	4.78401i	0.387532	−	0.197457i	−0.249359	−	0.968411i	$-0.580220\pi$
$587$	9.38915	−	4.78401i	0.387532	−	0.197457i	0.636891	+	0.770954i	$0.280220\pi$
$588$		0			0
$589$	28.5864	−	4.52764i	1.17788	−	0.186558i
$590$		0			0
$591$	−5.70225	+	36.0026i	−0.234559	+	1.48095i
$592$		0			0
$593$	−10.5451	−	5.37298i	−0.433034	−	0.220642i	0.223865	−	0.974620i	$-0.428132\pi$
$593$	−10.5451	−	5.37298i	−0.433034	−	0.220642i	−0.656899	+	0.753978i	$0.728132\pi$
$594$		0			0
$595$	1.11102	−	0.360992i	0.0455474	−	0.0147992i
$596$		0			0
$597$	19.4983	−	60.0098i	0.798014	−	2.45604i
$598$		0			0
$599$	−1.54349	−	4.75037i	−0.0630653	−	0.194095i	0.914559	−	0.404451i	$-0.132538\pi$
$599$	−1.54349	−	4.75037i	−0.0630653	−	0.194095i	−0.977625	+	0.210357i	$0.932538\pi$
$600$		0			0
$601$	8.63295	−	8.63295i	0.352145	−	0.352145i	−0.508762	−	0.860907i	$-0.669897\pi$
$601$	8.63295	−	8.63295i	0.352145	−	0.352145i	0.860907	+	0.508762i	$0.169897\pi$
$602$		0			0
$603$	−0.0572493	−	0.361458i	−0.00233137	−	0.0147197i
$604$		0			0
$605$	4.54272	−	3.30048i	0.184688	−	0.134183i
$606$		0			0
$607$	−1.59647	−	2.19735i	−0.0647987	−	0.0891878i	0.775388	−	0.631486i	$-0.217554\pi$
$607$	−1.59647	−	2.19735i	−0.0647987	−	0.0891878i	−0.840186	+	0.542298i	$0.817554\pi$
$608$		0			0
$609$	4.58443	+	8.99746i	0.185771	+	0.364595i
$610$		0			0
$611$	4.01762	+	2.91897i	0.162536	+	0.118089i
$612$		0			0
$613$	14.2615	+	4.63383i	0.576015	+	0.187159i	0.582515	−	0.812820i	$-0.302069\pi$
$613$	14.2615	+	4.63383i	0.576015	+	0.187159i	−0.00649962	+	0.999979i	$0.502069\pi$
$614$		0			0
$615$	16.7010	−	13.8031i	0.673450	−	0.556593i
$616$		0			0
$617$	28.6802	+	9.31877i	1.15462	+	0.375159i	0.822883	−	0.568212i	$-0.192364\pi$
$617$	28.6802	+	9.31877i	1.15462	+	0.375159i	0.331740	+	0.943371i	$0.392364\pi$
$618$		0			0
$619$	−32.4588	−	23.5827i	−1.30463	−	0.947870i	−0.304641	−	0.952467i	$-0.598537\pi$
$619$	−32.4588	−	23.5827i	−1.30463	−	0.947870i	−0.999989	+	0.00459753i	$0.998537\pi$
$620$		0			0
$621$	26.5778	+	52.1619i	1.06653	+	2.09319i
$622$		0			0
$623$	18.0450	+	24.8368i	0.722958	+	0.995066i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−8.75880	−	55.3009i	−0.349793	−	2.20851i
$628$		0			0
$629$	−3.63100	+	3.63100i	−0.144778	+	0.144778i
$630$		0			0
$631$	−2.95847	−	9.10522i	−0.117775	−	0.362473i	0.874741	−	0.484591i	$-0.161031\pi$
$631$	−2.95847	−	9.10522i	−0.117775	−	0.362473i	−0.992516	+	0.122118i	$0.961031\pi$
$632$		0			0
$633$	0.679202	−	2.09037i	0.0269959	−	0.0830848i
$634$		0			0
$635$	8.57225	−	2.78529i	0.340179	−	0.110531i
$636$		0			0
$637$	−5.99479	−	3.05450i	−0.237522	−	0.121024i
$638$		0			0
$639$	−13.3319	+	84.1745i	−0.527403	+	3.32989i
$640$		0			0
$641$	9.86828	−	1.56298i	0.389774	−	0.0617341i	0.0415279	−	0.999137i	$-0.486777\pi$
$641$	9.86828	−	1.56298i	0.389774	−	0.0617341i	0.348246	+	0.937403i	$0.386777\pi$
$642$		0			0
$643$	6.09230	−	3.10418i	0.240257	−	0.122417i	−0.329717	−	0.944080i	$-0.606953\pi$
$643$	6.09230	−	3.10418i	0.240257	−	0.122417i	0.569974	+	0.821663i	$0.306953\pi$
$644$		0			0
$645$	−23.7776	−	3.76601i	−0.936243	−	0.148286i
$646$		0			0
$647$		−	14.3747i		−	0.565129i	−0.959248	−	0.282565i	$-0.908815\pi$
$647$		−	14.3747i		−	0.565129i	0.959248	−	0.282565i	$-0.0911852\pi$
$648$		0			0
$649$	8.08894	−	15.8754i	0.317519	−	0.623165i
$650$		0			0
$651$	25.0699	−	34.5058i	0.982569	−	1.35239i
$652$		0			0
$653$	−1.20547	−	1.20547i	−0.0471735	−	0.0471735i	0.683127	−	0.730300i	$-0.260620\pi$
$653$	−1.20547	−	1.20547i	−0.0471735	−	0.0471735i	−0.730300	+	0.683127i	$0.760620\pi$
$654$		0			0
$655$	−4.30978			−0.168397
$656$		0			0
$657$	120.693			4.70869
$658$		0			0
$659$	16.7820	+	16.7820i	0.653735	+	0.653735i	0.953890	−	0.300155i	$-0.0970385\pi$
$659$	16.7820	+	16.7820i	0.653735	+	0.653735i	−0.300155	+	0.953890i	$0.597038\pi$
$660$		0			0
$661$	3.00586	−	4.13721i	0.116914	−	0.160919i	−0.746549	−	0.665330i	$-0.768291\pi$
$661$	3.00586	−	4.13721i	0.116914	−	0.160919i	0.863463	+	0.504412i	$0.168291\pi$
$662$		0			0
$663$	−1.76270	+	3.45949i	−0.0684575	+	0.134355i
$664$		0			0
$665$			7.17647i			0.278291i
$666$		0			0
$667$	5.29276	+	0.838290i	0.204936	+	0.0324587i
$668$		0			0
$669$	−19.1114	+	9.73772i	−0.738887	+	0.376482i
$670$		0			0
$671$	19.9250	−	3.15581i	0.769196	−	0.121829i
$672$		0			0
$673$	−1.65899	+	10.4745i	−0.0639494	+	0.403761i	0.934862	+	0.355012i	$0.115523\pi$
$673$	−1.65899	+	10.4745i	−0.0639494	+	0.403761i	−0.998811	+	0.0487485i	$0.984477\pi$
$674$		0			0
$675$	−16.4315	−	8.37226i	−0.632448	−	0.322248i
$676$		0			0
$677$	−30.3214	+	9.85203i	−1.16535	+	0.378644i	−0.826904	−	0.562343i	$-0.809900\pi$
$677$	−30.3214	+	9.85203i	−1.16535	+	0.378644i	−0.338443	+	0.940987i	$0.609900\pi$
$678$		0			0
$679$	−7.75576	+	23.8698i	−0.297639	+	0.916038i
$680$		0			0
$681$	10.6650	+	32.8235i	0.408684	+	1.25780i
$682$		0			0
$683$	31.6371	−	31.6371i	1.21056	−	1.21056i	0.239717	−	0.970843i	$-0.422945\pi$
$683$	31.6371	−	31.6371i	1.21056	−	1.21056i	0.970843	−	0.239717i	$-0.0770546\pi$
$684$		0			0
$685$	−1.34464	−	8.48970i	−0.0513759	−	0.324375i
$686$		0			0
$687$	34.7251	−	25.2293i	1.32485	−	0.962557i
$688$		0			0
$689$	0.523283	+	0.720238i	0.0199355	+	0.0274389i
$690$		0			0
$691$	1.93783	+	3.80320i	0.0737183	+	0.144680i	0.924924	−	0.380152i	$-0.124128\pi$
$691$	1.93783	+	3.80320i	0.0737183	+	0.144680i	−0.851206	+	0.524832i	$0.824128\pi$
$692$		0			0
$693$	−49.2625	−	35.7913i	−1.87133	−	1.35960i
$694$		0			0
$695$	−12.1158	−	3.93667i	−0.459579	−	0.149326i
$696$		0			0
$697$	−1.55573	−	3.93473i	−0.0589274	−	0.149039i
$698$		0			0
$699$	85.1304	+	27.6605i	3.21993	+	1.04622i
$700$		0			0
$701$	−19.7799	−	14.3709i	−0.747075	−	0.542782i	0.147844	−	0.989011i	$-0.452767\pi$
$701$	−19.7799	−	14.3709i	−0.747075	−	0.542782i	−0.894919	+	0.446229i	$0.852767\pi$
$702$		0			0
$703$	−14.3213	−	28.1072i	−0.540139	−	1.06008i
$704$		0			0
$705$	5.68810	+	7.82899i	0.214226	+	0.294857i
$706$		0			0
$707$	−13.8091	+	10.0329i	−0.519344	+	0.377326i
$708$		0			0
$709$	−1.06108	−	6.69937i	−0.0398495	−	0.251600i	0.959719	−	0.280960i	$-0.0906530\pi$
$709$	−1.06108	−	6.69937i	−0.0398495	−	0.251600i	−0.999569	+	0.0293604i	$0.990653\pi$
$710$		0			0
$711$	−47.3654	+	47.3654i	−1.77634	+	1.77634i
$712$		0			0
$713$	−6.99423	−	21.5260i	−0.261936	−	0.806156i
$714$		0			0
$715$	2.18725	−	6.73167i	0.0817986	−	0.251750i
$716$		0			0
$717$	59.5660	−	19.3542i	2.22453	−	0.722795i
$718$		0			0
$719$	38.9670	+	19.8547i	1.45322	+	0.740455i	0.989365	−	0.145454i	$-0.0464642\pi$
$719$	38.9670	+	19.8547i	1.45322	+	0.740455i	0.463860	+	0.885909i	$0.346464\pi$
$720$		0			0
$721$	0.997849	−	6.30017i	0.0371618	−	0.234631i
$722$		0			0
$723$	−52.8104	+	8.36434i	−1.96404	+	0.311073i
$724$		0			0
$725$	−1.50406	+	0.766358i	−0.0558595	+	0.0284618i
$726$		0			0
$727$	8.99562	+	1.42477i	0.333629	+	0.0528417i	0.321002	−	0.947079i	$-0.395980\pi$
$727$	8.99562	+	1.42477i	0.333629	+	0.0528417i	0.0126274	+	0.999920i	$0.495980\pi$
$728$		0			0
$729$		−	125.882i		−	4.66231i
$730$		0			0
$731$	−2.13431	+	4.18882i	−0.0789402	+	0.154929i
$732$		0			0
$733$	5.09559	−	7.01347i	0.188210	−	0.259049i	−0.704476	−	0.709727i	$-0.748818\pi$
$733$	5.09559	−	7.01347i	0.188210	−	0.259049i	0.892686	+	0.450679i	$0.148818\pi$
$734$		0			0
$735$	−9.27076	−	9.27076i	−0.341957	−	0.341957i
$736$		0			0
$737$	0.176537			0.00650281
$738$		0			0
$739$	−18.4634			−0.679188			−0.339594	−	0.940572i	$-0.610290\pi$
$739$	−18.4634			−0.679188			−0.339594	+	0.940572i	$0.610290\pi$
$740$		0			0
$741$	−16.8660	−	16.8660i	−0.619586	−	0.619586i
$742$		0			0
$743$	8.64510	−	11.8990i	0.317158	−	0.436531i	−0.620439	−	0.784255i	$-0.713045\pi$
$743$	8.64510	−	11.8990i	0.317158	−	0.436531i	0.937597	+	0.347724i	$0.113045\pi$
$744$		0			0
$745$	1.94723	−	3.82165i	0.0713408	−	0.140014i
$746$		0			0
$747$		−	114.761i		−	4.19888i
$748$		0			0
$749$	−3.87621	−	0.613931i	−0.141633	−	0.0224325i
$750$		0			0
$751$	−22.8627	+	11.6491i	−0.834270	+	0.425082i	−0.818301	−	0.574791i	$-0.805084\pi$
$751$	−22.8627	+	11.6491i	−0.834270	+	0.425082i	−0.0159697	+	0.999872i	$0.505084\pi$
$752$		0			0
$753$	26.4407	−	4.18779i	0.963551	−	0.152612i
$754$		0			0
$755$	−3.08423	+	19.4731i	−0.112247	+	0.708697i
$756$		0			0
$757$	−10.6476	−	5.42522i	−0.386993	−	0.197183i	0.249659	−	0.968334i	$-0.419681\pi$
$757$	−10.6476	−	5.42522i	−0.386993	−	0.197183i	−0.636652	+	0.771151i	$0.719681\pi$
$758$		0			0
$759$	−41.6425	+	13.5305i	−1.51153	+	0.491125i
$760$		0			0
$761$	3.71369	−	11.4296i	0.134621	−	0.414321i	−0.860910	−	0.508758i	$-0.830105\pi$
$761$	3.71369	−	11.4296i	0.134621	−	0.414321i	0.995531	+	0.0944363i	$0.0301049\pi$
$762$		0			0
$763$	−11.2104	−	34.5022i	−0.405845	−	1.24906i
$764$		0			0
$765$	−3.94824	+	3.94824i	−0.142749	+	0.142749i
$766$		0			0
$767$	−1.18738	−	7.49684i	−0.0428739	−	0.270695i
$768$		0			0
$769$	−27.9899	+	20.3359i	−1.00934	+	0.733331i	−0.964071	−	0.265644i	$-0.914415\pi$
$769$	−27.9899	+	20.3359i	−1.00934	+	0.733331i	−0.0452720	+	0.998975i	$0.514415\pi$
$770$		0			0
$771$	−28.8890	−	39.7624i	−1.04041	−	1.43201i
$772$		0			0
$773$	−17.7192	−	34.7758i	−0.637314	−	1.25080i	−0.953297	−	0.302035i	$-0.902334\pi$
$773$	−17.7192	−	34.7758i	−0.637314	−	1.25080i	0.315983	−	0.948765i	$-0.397666\pi$
$774$		0			0
$775$	5.76817	+	4.19082i	0.207199	+	0.150539i
$776$		0			0
$777$	−44.2118	−	14.3653i	−1.58609	−	0.515352i
$778$		0			0
$779$	25.9421	−	1.61988i	0.929473	−	0.0580383i
$780$		0			0
$781$	−39.0988	−	12.7040i	−1.39907	−	0.454584i
$782$		0			0
$783$	−25.1848	−	18.2978i	−0.900031	−	0.653911i
$784$		0			0
$785$	10.1418	+	19.9044i	0.361975	+	0.710417i
$786$		0			0
$787$	−2.83953	−	3.90828i	−0.101218	−	0.139315i	0.755403	−	0.655260i	$-0.227441\pi$
$787$	−2.83953	−	3.90828i	−0.101218	−	0.139315i	−0.856622	+	0.515945i	$0.827441\pi$
$788$		0			0
$789$	−53.3620	+	38.7698i	−1.89974	+	1.38024i
$790$		0			0
$791$	0.795004	+	5.01946i	0.0282671	+	0.178471i
$792$		0			0
$793$	6.07683	−	6.07683i	0.215795	−	0.215795i
$794$		0			0
$795$	0.536090	+	1.64991i	0.0190131	+	0.0585164i
$796$		0			0
$797$	2.83509	−	8.72550i	0.100424	−	0.309073i	−0.888205	−	0.459447i	$-0.848048\pi$
$797$	2.83509	−	8.72550i	0.100424	−	0.309073i	0.988629	+	0.150374i	$0.0480477\pi$
$798$		0			0
$799$	1.79728	−	0.583973i	0.0635833	−	0.0206595i
$800$		0			0
$801$	−130.744	−	66.6175i	−4.61962	−	2.35381i
$802$		0			0
$803$	−9.10777	+	57.5042i	−0.321406	+	2.02928i
$804$		0			0
$805$	5.54305	−	0.877933i	0.195367	−	0.0309431i
$806$		0			0
$807$	84.4482	−	43.0285i	2.97272	−	1.51468i
$808$		0			0
$809$	11.8976	+	1.88440i	0.418298	+	0.0662519i	0.362036	−	0.932164i	$-0.382082\pi$
$809$	11.8976	+	1.88440i	0.418298	+	0.0662519i	0.0562622	+	0.998416i	$0.482082\pi$
$810$		0			0
$811$			27.4062i			0.962360i	0.876622	+	0.481180i	$0.159792\pi$
$811$			27.4062i			0.962360i	−0.876622	+	0.481180i	$0.840208\pi$
$812$		0			0
$813$	5.06234	−	9.93540i	0.177544	−	0.348450i
$814$		0			0
$815$	−10.7035	+	14.7321i	−0.374928	+	0.516044i
$816$		0			0
$817$	−20.4216	−	20.4216i	−0.714462	−	0.714462i
$818$		0			0
$819$	−25.9401			−0.906421
$820$		0			0
$821$	−9.88006			−0.344816			−0.172408	−	0.985026i	$-0.555155\pi$
$821$	−9.88006			−0.344816			−0.172408	+	0.985026i	$0.555155\pi$
$822$		0			0
$823$	25.5879	+	25.5879i	0.891938	+	0.891938i	0.994705	−	0.102767i	$-0.0327696\pi$
$823$	25.5879	+	25.5879i	0.891938	+	0.891938i	−0.102767	+	0.994705i	$0.532770\pi$
$824$		0			0
$825$	8.10723	−	11.1586i	0.282257	−	0.388494i
$826$		0			0
$827$	−4.08849	+	8.02412i	−0.142171	+	0.279026i	−0.951102	−	0.308878i	$-0.900047\pi$
$827$	−4.08849	+	8.02412i	−0.142171	+	0.279026i	0.808931	+	0.587904i	$0.200047\pi$
$828$		0			0
$829$		−	4.64122i		−	0.161196i	−0.996747	−	0.0805980i	$-0.974317\pi$
$829$		−	4.64122i		−	0.161196i	0.996747	−	0.0805980i	$-0.0256830\pi$
$830$		0			0
$831$	−57.7159	−	9.14130i	−2.00214	−	0.317108i
$832$		0			0
$833$	−2.28125	+	1.16236i	−0.0790406	+	0.0402732i
$834$		0			0
$835$	−22.4631	+	3.55780i	−0.777366	+	0.123123i
$836$		0			0
$837$	−20.5688	+	129.866i	−0.710961	+	4.48883i
$838$		0			0
$839$	24.7299	+	12.6005i	0.853771	+	0.435018i	0.825379	−	0.564579i	$-0.190961\pi$
$839$	24.7299	+	12.6005i	0.853771	+	0.435018i	0.0283921	+	0.999597i	$0.490961\pi$
$840$		0			0
$841$	24.8706	−	8.08095i	0.857607	−	0.278653i
$842$		0			0
$843$	−20.0466	+	61.6970i	−0.690441	+	2.12496i
$844$		0			0
$845$	3.08544	+	9.49601i	0.106142	+	0.326673i
$846$		0			0
$847$	7.01932	−	7.01932i	0.241187	−	0.241187i
$848$		0			0
$849$	−12.0254	−	75.9254i	−0.412711	−	2.60575i
$850$		0			0
$851$	−19.9578	+	14.5002i	−0.684145	+	0.497060i
$852$		0			0
$853$	−10.9430	−	15.0618i	−0.374683	−	0.515706i	0.579483	−	0.814984i	$-0.303254\pi$
$853$	−10.9430	−	15.0618i	−0.374683	−	0.515706i	−0.954166	+	0.299278i	$0.903254\pi$
$854$		0			0
$855$	−15.5726	−	30.5629i	−0.532571	−	1.04523i
$856$		0			0
$857$	17.3492	+	12.6049i	0.592637	+	0.430576i	0.843258	−	0.537509i	$-0.180635\pi$
$857$	17.3492	+	12.6049i	0.592637	+	0.430576i	−0.250621	+	0.968085i	$0.580635\pi$
$858$		0			0
$859$	29.6193	+	9.62391i	1.01060	+	0.328363i	0.767093	−	0.641536i	$-0.221702\pi$
$859$	29.6193	+	9.62391i	1.01060	+	0.328363i	0.243506	+	0.969899i	$0.421702\pi$
$860$		0			0
$861$	25.3445	−	28.7204i	0.863739	−	0.978790i
$862$		0			0
$863$	−31.9914	−	10.3946i	−1.08900	−	0.353837i	−0.291139	−	0.956681i	$-0.594034\pi$
$863$	−31.9914	−	10.3946i	−1.08900	−	0.353837i	−0.797859	+	0.602844i	$0.794034\pi$
$864$		0			0
$865$	5.07319	+	3.68589i	0.172494	+	0.125324i
$866$		0			0
$867$	−25.4447	−	49.9380i	−0.864147	−	1.69598i
$868$		0			0
$869$	−18.9929	−	26.1415i	−0.644290	−	0.886789i
$870$		0			0
$871$	0.0608424	−	0.0442046i	0.00206156	−	0.00149781i
$872$		0			0
$873$	−18.7662	−	118.485i	−0.635141	−	4.01012i
$874$		0			0
$875$	−1.25008	+	1.25008i	−0.0422603	+	0.0422603i
$876$		0			0
$877$	14.2311	+	43.7988i	0.480550	+	1.47898i	0.838324	+	0.545172i	$0.183536\pi$
$877$	14.2311	+	43.7988i	0.480550	+	1.47898i	−0.357774	+	0.933808i	$0.616464\pi$
$878$		0			0
$879$	−21.3975	+	65.8548i	−0.721720	+	2.22123i
$880$		0			0
$881$	19.3164	−	6.27627i	0.650785	−	0.211453i	0.0350246	−	0.999386i	$-0.488849\pi$
$881$	19.3164	−	6.27627i	0.650785	−	0.211453i	0.615760	+	0.787934i	$0.288849\pi$
$882$		0			0
$883$	−13.1918	−	6.72154i	−0.443939	−	0.226198i	0.217708	−	0.976014i	$-0.430142\pi$
$883$	−13.1918	−	6.72154i	−0.443939	−	0.226198i	−0.661646	+	0.749816i	$0.730142\pi$
$884$		0			0
$885$	2.31381	−	14.6088i	0.0777779	−	0.491070i
$886$		0			0
$887$	−6.59552	+	1.04463i	−0.221456	+	0.0350752i	−0.266176	−	0.963924i	$-0.585760\pi$
$887$	−6.59552	+	1.04463i	−0.221456	+	0.0350752i	0.0447204	+	0.999000i	$0.485760\pi$
$888$		0			0
$889$	14.1978	−	7.23415i	0.476179	−	0.242625i
$890$		0			0
$891$	149.171	+	23.6263i	4.99740	+	0.791511i
$892$		0			0
$893$			11.6093i			0.388489i
$894$		0			0
$895$	−11.1787	+	21.9394i	−0.373663	+	0.733354i
$896$		0			0
$897$	−10.9639	+	15.0904i	−0.366072	+	0.503855i
$898$		0			0
$899$	8.51041	+	8.51041i	0.283838	+	0.283838i
$900$		0			0
$901$	0.338779			0.0112864
$902$		0			0
$903$	−42.5599			−1.41630
$904$		0			0
$905$	−16.6468	−	16.6468i	−0.553357	−	0.553357i
$906$		0			0
$907$	−25.7736	+	35.4743i	−0.855797	+	1.17790i	0.126758	+	0.991934i	$0.459543\pi$
$907$	−25.7736	+	35.4743i	−0.855797	+	1.17790i	−0.982555	+	0.185970i	$0.940457\pi$
$908$		0			0
$909$	37.0388	−	72.6928i	1.22850	−	2.41107i
$910$		0			0
$911$		−	50.8258i		−	1.68393i	−0.539528	−	0.841967i	$-0.681397\pi$
$911$		−	50.8258i		−	1.68393i	0.539528	−	0.841967i	$-0.318603\pi$
$912$		0			0
$913$	54.6778	+	8.66011i	1.80957	+	0.286608i
$914$		0			0
$915$	14.9214	−	7.60284i	0.493286	−	0.251342i
$916$		0			0
$917$	−7.52535	+	1.19190i	−0.248509	+	0.0393599i
$918$		0			0
$919$	7.02011	−	44.3232i	0.231572	−	1.46209i	−0.548370	−	0.836236i	$-0.684751\pi$
$919$	7.02011	−	44.3232i	0.231572	−	1.46209i	0.779942	−	0.625852i	$-0.215249\pi$
$920$		0			0
$921$	28.3387	+	14.4393i	0.933790	+	0.475790i
$922$		0			0
$923$	−16.6563	+	5.41195i	−0.548247	+	0.178136i
$924$		0			0
$925$	2.40138	−	7.39068i	0.0789568	−	0.243004i
$926$		0			0
$927$	9.42145	+	28.9962i	0.309441	+	0.952361i
$928$		0			0
$929$	−38.6148	+	38.6148i	−1.26691	+	1.26691i	−0.319233	+	0.947676i	$0.603425\pi$
$929$	−38.6148	+	38.6148i	−1.26691	+	1.26691i	−0.947676	+	0.319233i	$0.896575\pi$
$930$		0			0
$931$	−2.46048	−	15.5348i	−0.0806389	−	0.509134i
$932$		0			0
$933$	35.8726	−	26.0629i	1.17441	−	0.853262i
$934$		0			0
$935$	−1.58319	−	2.17908i	−0.0517760	−	0.0712635i
$936$		0			0
$937$	6.36478	+	12.4916i	0.207928	+	0.408082i	0.971293	−	0.237885i	$-0.0764542\pi$
$937$	6.36478	+	12.4916i	0.207928	+	0.408082i	−0.763365	+	0.645967i	$0.776454\pi$
$938$		0			0
$939$	−32.3515	−	23.5047i	−1.05575	−	0.767048i
$940$		0			0
$941$	4.80343	+	1.56073i	0.156587	+	0.0508783i	0.386262	−	0.922389i	$-0.373766\pi$
$941$	4.80343	+	1.56073i	0.156587	+	0.0508783i	−0.229674	+	0.973268i	$0.573766\pi$
$942$		0			0
$943$	−4.42482	−	19.8394i	−0.144092	−	0.646058i
$944$		0			0
$945$	−31.0066	−	10.0747i	−1.00864	−	0.327728i
$946$		0			0
$947$	2.82086	+	2.04948i	0.0916657	+	0.0665990i	0.632674	−	0.774418i	$-0.281957\pi$
$947$	2.82086	+	2.04948i	0.0916657	+	0.0665990i	−0.541008	+	0.841017i	$0.681957\pi$
$948$		0			0
$949$	11.2600	+	22.0991i	0.365517	+	0.717367i
$950$		0			0
$951$	66.4261	+	91.4277i	2.15401	+	2.96475i
$952$		0			0
$953$	23.6101	−	17.1538i	0.764808	−	0.555665i	−0.135573	−	0.990767i	$-0.543288\pi$
$953$	23.6101	−	17.1538i	0.764808	−	0.555665i	0.900381	+	0.435102i	$0.143288\pi$
$954$		0			0
$955$	1.48655	+	9.38568i	0.0481035	+	0.303714i
$956$		0			0
$957$	16.4635	−	16.4635i	0.532191	−	0.532191i
$958$		0			0
$959$	−4.69577	−	14.4521i	−0.151634	−	0.466682i
$960$		0			0
$961$	6.12930	−	18.8640i	0.197719	−	0.608517i
$962$		0			0
$963$	17.8401	−	5.79658i	0.574888	−	0.186792i
$964$		0			0
$965$	−1.45799	−	0.742884i	−0.0469344	−	0.0239143i
$966$		0			0
$967$	−8.27441	+	52.2426i	−0.266087	+	1.68001i	0.386496	+	0.922291i	$0.373685\pi$
$967$	−8.27441	+	52.2426i	−0.266087	+	1.68001i	−0.652583	+	0.757717i	$0.726315\pi$
$968$		0			0
$969$	−8.96488	+	1.41990i	−0.287993	+	0.0456137i
$970$		0			0
$971$	−15.2297	+	7.75992i	−0.488744	+	0.249028i	−0.680954	−	0.732326i	$-0.738435\pi$
$971$	−15.2297	+	7.75992i	−0.488744	+	0.249028i	0.192210	+	0.981354i	$0.438435\pi$
$972$		0			0
$973$	−22.2443	−	3.52315i	−0.713118	−	0.112947i
$974$		0			0
$975$		−	5.87580i		−	0.188176i
$976$		0			0
$977$	−18.4062	+	36.1241i	−0.588866	+	1.15571i	0.383781	+	0.923424i	$0.374622\pi$
$977$	−18.4062	+	36.1241i	−0.588866	+	1.15571i	−0.972647	+	0.232290i	$0.925378\pi$
$978$		0			0
$979$	41.6061	−	57.2658i	1.32974	−	1.83022i
$980$		0			0
$981$	122.611	+	122.611i	3.91465	+	3.91465i
$982$		0			0
$983$	43.3890			1.38390			0.691948	−	0.721948i	$-0.256753\pi$
$983$	43.3890			1.38390			0.691948	+	0.721948i	$0.256753\pi$
$984$		0			0
$985$	−10.7724			−0.343236
$986$		0			0
$987$	12.0972	+	12.0972i	0.385058	+	0.385058i
$988$		0			0
$989$	−13.2752	+	18.2718i	−0.422128	+	0.581010i
$990$		0			0
$991$	12.8670	−	25.2529i	0.408733	−	0.802184i	−0.591257	−	0.806483i	$-0.701368\pi$
$991$	12.8670	−	25.2529i	0.408733	−	0.802184i	0.999991	+	0.00429859i	$0.00136829\pi$
$992$		0			0
$993$			65.2371i			2.07024i
$994$		0			0
$995$	18.4176	+	2.91706i	0.583878	+	0.0924771i
$996$		0			0
$997$	−31.4721	+	16.0358i	−0.996730	+	0.507860i	−0.874699	−	0.484667i	$-0.838941\pi$
$997$	−31.4721	+	16.0358i	−0.996730	+	0.507860i	−0.122032	+	0.992526i	$0.538941\pi$
$998$		0			0
$999$	141.545	−	22.4185i	4.47828	−	0.709289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bo.b.21.1	✓	64
41.2	even	20	inner	820.2.bo.b.781.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bo.b.21.1	✓	64	1.1	even	1	trivial
820.2.bo.b.781.1	yes	64	41.2	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bo (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39269 - 2.39269i) q^{3} +(0.587785 - 0.809017i) q^{5} +(0.802599 - 1.57519i) q^{7} +8.44996i q^{9} +(-4.02598 - 0.637652i) q^{11} +(-1.54720 + 0.788337i) q^{13} +(-3.34212 + 0.529340i) q^{15} +(-0.103370 + 0.652655i) q^{17} +(-3.61693 - 1.84292i) q^{19} +(-5.68932 + 1.84857i) q^{21} +(-0.980979 + 3.01914i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(13.0401 - 13.0401i) q^{27} +(-0.264069 - 1.66727i) q^{29} +(-5.76817 + 4.19082i) q^{31} +(8.10723 + 11.1586i) q^{33} +(-0.802599 - 1.57519i) q^{35} +(6.28689 + 4.56769i) q^{37} +(5.58822 + 1.81572i) q^{39} +(-5.51297 + 3.25686i) q^{41} +(6.76633 + 2.19851i) q^{43} +(6.83616 + 4.96676i) q^{45} +(-1.29835 - 2.54816i) q^{47} +(2.27744 + 3.13463i) q^{49} +(1.80894 - 1.31427i) q^{51} +(-0.0802020 - 0.506376i) q^{53} +(-2.88228 + 2.88228i) q^{55} +(4.24466 + 13.0637i) q^{57} +(-1.35075 + 4.15719i) q^{59} +(-4.70688 + 1.52936i) q^{61} +(13.3103 + 6.78193i) q^{63} +(-0.271642 + 1.71508i) q^{65} +(-0.0427763 + 0.00677510i) q^{67} +(9.57106 - 4.87670i) q^{69} +(9.96152 + 1.57775i) q^{71} -14.2833i q^{73} +(-1.53620 + 3.01497i) q^{75} +(-4.23567 + 5.82990i) q^{77} +(5.60539 + 5.60539i) q^{79} -37.0520 q^{81} -13.5812 q^{83} +(0.467249 + 0.467249i) q^{85} +(-3.35742 + 4.62109i) q^{87} +(-7.88376 + 15.4727i) q^{89} +3.06985i q^{91} +(23.8288 + 3.77412i) q^{93} +(-3.61693 + 1.84292i) q^{95} +(-14.0220 + 2.22087i) q^{97} +(5.38814 - 34.0194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) \) 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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