LMFDB - Embedded newform 820.2.bo.b.21.6

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			21.6
Character	$\chi$	$=$	820.21
Dual form			820.2.bo.b.781.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.901610 + 0.901610i) q^{3} +(0.587785 - 0.809017i) q^{5} +(-4.93870e-6 + 9.69274e-6i) q^{7} -1.37420i q^{9} +(2.30019 + 0.364315i) q^{11} +(3.08580 - 1.57229i) q^{13} +(1.25937 - 0.199465i) q^{15} +(-0.986892 + 6.23099i) q^{17} +(-1.02270 - 0.521092i) q^{19} +(-1.31918e-5 + 4.28629e-6i) q^{21} +(2.63248 - 8.10194i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(3.94382 - 3.94382i) q^{27} +(0.446858 + 2.82135i) q^{29} +(2.29721 - 1.66902i) q^{31} +(1.74541 + 2.40235i) q^{33} +(4.93870e-6 + 9.69274e-6i) q^{35} +(6.84323 + 4.97190i) q^{37} +(4.19978 + 1.36459i) q^{39} +(-3.81801 - 5.14031i) q^{41} +(-0.267806 - 0.0870154i) q^{43} +(-1.11175 - 0.807734i) q^{45} +(1.68269 + 3.30246i) q^{47} +(4.11450 + 5.66312i) q^{49} +(-6.50772 + 4.72813i) q^{51} +(1.06518 + 6.72527i) q^{53} +(1.64676 - 1.64676i) q^{55} +(-0.452255 - 1.39190i) q^{57} +(-0.325718 + 1.00246i) q^{59} +(-7.43430 + 2.41555i) q^{61} +(1.33197e-5 + 6.78675e-6i) q^{63} +(0.541776 - 3.42064i) q^{65} +(-10.6530 + 1.68727i) q^{67} +(9.67826 - 4.93132i) q^{69} +(-0.388333 - 0.0615060i) q^{71} -14.0096i q^{73} +(0.578869 - 1.13609i) q^{75} +(-1.48912e-5 + 2.04959e-5i) q^{77} +(-3.38127 - 3.38127i) q^{79} +2.98898 q^{81} +5.94200 q^{83} +(4.46090 + 4.46090i) q^{85} +(-2.14087 + 2.94665i) q^{87} +(-7.18184 + 14.0952i) q^{89} +3.76749e-5i q^{91} +(3.57600 + 0.566382i) q^{93} +(-1.02270 + 0.521092i) q^{95} +(2.31166 - 0.366131i) q^{97} +(0.500641 - 3.16092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.901610	+	0.901610i	0.520545	+	0.520545i	0.917736	−	0.397191i	$-0.130015\pi$
$3$	0.901610	+	0.901610i	0.520545	+	0.520545i	−0.397191	+	0.917736i	$0.630015\pi$
$4$		0			0
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$6$		0			0
$7$	−4.93870e−6	0	9.69274e-6i	−1.86665e−6	0	3.66351e-6i	−0.891007	−	0.453989i	$-0.850001\pi$
$7$	−4.93870e−6	0	9.69274e-6i	−1.86665e−6	0	3.66351e-6i	0.891006	+	0.453992i	$0.150001\pi$
$8$		0			0
$9$		−	1.37420i		−	0.458066i
$10$		0			0
$11$	2.30019	+	0.364315i	0.693534	+	0.109845i	0.493243	−	0.869891i	$-0.335811\pi$
$11$	2.30019	+	0.364315i	0.693534	+	0.109845i	0.200291	+	0.979736i	$0.435811\pi$
$12$		0			0
$13$	3.08580	−	1.57229i	0.855847	−	0.436076i	0.0297190	−	0.999558i	$-0.490539\pi$
$13$	3.08580	−	1.57229i	0.855847	−	0.436076i	0.826128	+	0.563482i	$0.190539\pi$
$14$		0			0
$15$	1.25937	−	0.199465i	0.325168	−	0.0515016i
$16$		0			0
$17$	−0.986892	+	6.23099i	−0.239357	+	1.51124i	0.516378	+	0.856360i	$0.327280\pi$
$17$	−0.986892	+	6.23099i	−0.239357	+	1.51124i	−0.755735	+	0.654878i	$0.772720\pi$
$18$		0			0
$19$	−1.02270	−	0.521092i	−0.234623	−	0.119547i	0.332727	−	0.943023i	$-0.392031\pi$
$19$	−1.02270	−	0.521092i	−0.234623	−	0.119547i	−0.567350	+	0.823477i	$0.692031\pi$
$20$		0			0
$21$	−1.31918e−5	0	4.28629e-6i	−2.87870e−6	0	9.35345e-7i
$22$		0			0
$23$	2.63248	−	8.10194i	0.548910	−	1.68937i	−0.162598	−	0.986692i	$-0.551987\pi$
$23$	2.63248	−	8.10194i	0.548910	−	1.68937i	0.711508	−	0.702678i	$-0.248013\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	3.94382	−	3.94382i	0.758989	−	0.758989i
$28$		0			0
$29$	0.446858	+	2.82135i	0.0829795	+	0.523912i	0.993807	+	0.111124i	$0.0354450\pi$
$29$	0.446858	+	2.82135i	0.0829795	+	0.523912i	−0.910827	+	0.412788i	$0.864555\pi$
$30$		0			0
$31$	2.29721	−	1.66902i	0.412591	−	0.299765i	−0.362059	−	0.932155i	$-0.617926\pi$
$31$	2.29721	−	1.66902i	0.412591	−	0.299765i	0.774650	+	0.632390i	$0.217926\pi$
$32$		0			0
$33$	1.74541	+	2.40235i	0.303836	+	0.418195i
$34$		0			0
$35$	4.93870e−6	0	9.69274e-6i	8.34792e−7	0	1.63837e-6i
$36$		0			0
$37$	6.84323	+	4.97190i	1.12502	+	0.817375i	0.984962	−	0.172769i	$-0.0552714\pi$
$37$	6.84323	+	4.97190i	1.12502	+	0.817375i	0.140057	+	0.990143i	$0.455271\pi$
$38$		0			0
$39$	4.19978	+	1.36459i	0.672504	+	0.218510i
$40$		0			0
$41$	−3.81801	−	5.14031i	−0.596273	−	0.802781i
$41$	−3.81801	−	5.14031i	−0.596273	−	0.802781i
$42$		0			0
$43$	−0.267806	−	0.0870154i	−0.0408400	−	0.0132697i	0.288526	−	0.957472i	$-0.406835\pi$
$43$	−0.267806	−	0.0870154i	−0.0408400	−	0.0132697i	−0.329366	+	0.944202i	$0.606835\pi$
$44$		0			0
$45$	−1.11175	−	0.807734i	−0.165730	−	0.120410i
$46$		0			0
$47$	1.68269	+	3.30246i	0.245445	+	0.481713i	0.980557	−	0.196232i	$-0.0628706\pi$
$47$	1.68269	+	3.30246i	0.245445	+	0.481713i	−0.735112	+	0.677945i	$0.762871\pi$
$48$		0			0
$49$	4.11450	+	5.66312i	0.587785	+	0.809017i
$50$		0			0
$51$	−6.50772	+	4.72813i	−0.911263	+	0.662071i
$52$		0			0
$53$	1.06518	+	6.72527i	0.146314	+	0.923787i	0.946187	+	0.323619i	$0.104900\pi$
$53$	1.06518	+	6.72527i	0.146314	+	0.923787i	−0.799874	+	0.600168i	$0.795100\pi$
$54$		0			0
$55$	1.64676	−	1.64676i	0.222049	−	0.222049i
$56$		0			0
$57$	−0.452255	−	1.39190i	−0.0599027	−	0.184361i
$58$		0			0
$59$	−0.325718	+	1.00246i	−0.0424049	+	0.130509i	−0.970018	−	0.243034i	$-0.921857\pi$
$59$	−0.325718	+	1.00246i	−0.0424049	+	0.130509i	0.927613	+	0.373543i	$0.121857\pi$
$60$		0			0
$61$	−7.43430	+	2.41555i	−0.951865	+	0.309280i	−0.743473	−	0.668766i	$-0.766823\pi$
$61$	−7.43430	+	2.41555i	−0.951865	+	0.309280i	−0.208392	+	0.978045i	$0.566823\pi$
$62$		0			0
$63$	1.33197e−5	0	6.78675e-6i	1.67813e−6	0	8.55050e-7i
$64$		0			0
$65$	0.541776	−	3.42064i	0.0671990	−	0.424278i
$66$		0			0
$67$	−10.6530	+	1.68727i	−1.30147	+	0.206133i	−0.768419	−	0.639947i	$-0.778956\pi$
$67$	−10.6530	+	1.68727i	−1.30147	+	0.206133i	−0.533056	+	0.846080i	$0.678956\pi$
$68$		0			0
$69$	9.67826	−	4.93132i	1.16513	−	0.593661i
$70$		0			0
$71$	−0.388333	−	0.0615060i	−0.0460867	−	0.00729941i	0.133349	−	0.991069i	$-0.457427\pi$
$71$	−0.388333	−	0.0615060i	−0.0460867	−	0.00729941i	−0.179435	+	0.983770i	$0.557427\pi$
$72$		0			0
$73$		−	14.0096i		−	1.63970i	−0.572578	−	0.819850i	$-0.694057\pi$
$73$		−	14.0096i		−	1.63970i	0.572578	−	0.819850i	$-0.305943\pi$
$74$		0			0
$75$	0.578869	−	1.13609i	0.0668421	−	0.131185i
$76$		0			0
$77$	−1.48912e−5	0	2.04959e-5i	−1.69701e−6	0	2.33573e-6i
$78$		0			0
$79$	−3.38127	−	3.38127i	−0.380423	−	0.380423i	0.490832	−	0.871254i	$-0.336693\pi$
$79$	−3.38127	−	3.38127i	−0.380423	−	0.380423i	−0.871254	+	0.490832i	$0.836693\pi$
$80$		0			0
$81$	2.98898			0.332109
$82$		0			0
$83$	5.94200			0.652219			0.326109	−	0.945332i	$-0.394262\pi$
$83$	5.94200			0.652219			0.326109	+	0.945332i	$0.394262\pi$
$84$		0			0
$85$	4.46090	+	4.46090i	0.483852	+	0.483852i
$86$		0			0
$87$	−2.14087	+	2.94665i	−0.229525	+	0.315914i
$88$		0			0
$89$	−7.18184	+	14.0952i	−0.761274	+	1.49408i	0.104977	+	0.994475i	$0.466523\pi$
$89$	−7.18184	+	14.0952i	−0.761274	+	1.49408i	−0.866251	+	0.499609i	$0.833477\pi$
$90$		0			0
$91$		0	3.76749e-5i		0	3.94941e-6i
$92$		0			0
$93$	3.57600	+	0.566382i	0.370814	+	0.0587311i
$94$		0			0
$95$	−1.02270	+	0.521092i	−0.104927	+	0.0534629i
$96$		0			0
$97$	2.31166	−	0.366131i	0.234713	−	0.0371750i	−0.0379695	−	0.999279i	$-0.512089\pi$
$97$	2.31166	−	0.366131i	0.234713	−	0.0371750i	0.272683	+	0.962104i	$0.412089\pi$
$98$		0			0
$99$	0.500641	−	3.16092i	0.0503163	−	0.317685i
$100$		0			0
$101$	8.65902	+	4.41199i	0.861604	+	0.439009i	0.828200	−	0.560433i	$-0.189365\pi$
$101$	8.65902	+	4.41199i	0.861604	+	0.439009i	0.0334042	+	0.999442i	$0.489365\pi$
$102$		0			0
$103$	−6.04370	+	1.96372i	−0.595503	+	0.193491i	−0.591234	−	0.806500i	$-0.701359\pi$
$103$	−6.04370	+	1.96372i	−0.595503	+	0.193491i	−0.00426940	+	0.999991i	$0.501359\pi$
$104$		0			0
$105$	−4.28629e−6	0	1.31918e-5i	−4.18299e−7	0	1.28739e-6i
$106$		0			0
$107$	2.21776	+	6.82558i	0.214399	+	0.659853i	0.999196	+	0.0400996i	$0.0127675\pi$
$107$	2.21776	+	6.82558i	0.214399	+	0.659853i	−0.784796	+	0.619754i	$0.787232\pi$
$108$		0			0
$109$	−1.86474	+	1.86474i	−0.178609	+	0.178609i	−0.790749	−	0.612140i	$-0.790309\pi$
$109$	−1.86474	+	1.86474i	−0.178609	+	0.178609i	0.612140	+	0.790749i	$0.290309\pi$
$110$		0			0
$111$	1.68721	+	10.6526i	0.160143	+	1.01110i
$112$		0			0
$113$	8.06278	−	5.85795i	0.758483	−	0.551070i	−0.139962	−	0.990157i	$-0.544698\pi$
$113$	8.06278	−	5.85795i	0.758483	−	0.551070i	0.898445	+	0.439087i	$0.144698\pi$
$114$		0			0
$115$	−5.00727	−	6.89192i	−0.466931	−	0.642675i
$116$		0			0
$117$	−2.16064	−	4.24050i	−0.199752	−	0.392035i
$118$		0			0
$119$	−5.55214e−5	0	4.03387e-5i	−5.08964e−6	0	3.69784e-6i
$120$		0			0
$121$	−5.30346	−	1.72320i	−0.482132	−	0.156654i
$122$		0			0
$123$	1.19220	−	8.07691i	0.107497	−	0.728271i
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.0850651	−	0.0276393i
$126$		0			0
$127$	−7.68351	−	5.58240i	−0.681801	−	0.495358i	0.192153	−	0.981365i	$-0.438453\pi$
$127$	−7.68351	−	5.58240i	−0.681801	−	0.495358i	−0.873955	+	0.486007i	$0.838453\pi$
$128$		0			0
$129$	−0.163003	−	0.319910i	−0.0143516	−	0.0281665i
$130$		0			0
$131$	−9.65337	−	13.2867i	−0.843419	−	1.16087i	−0.985275	−	0.170979i	$-0.945307\pi$
$131$	−9.65337	−	13.2867i	−0.843419	−	1.16087i	0.141856	−	0.989887i	$-0.454693\pi$
$132$		0			0
$133$	1.01016e−5	0	7.33925e-6i	8.75920e−7	0	6.36393e-7i
$134$		0			0
$135$	−0.872498	−	5.50874i	−0.0750927	−	0.474117i
$136$		0			0
$137$	−10.6699	+	10.6699i	−0.911588	+	0.911588i	−0.996397	−	0.0848094i	$-0.972972\pi$
$137$	−10.6699	+	10.6699i	−0.911588	+	0.911588i	0.0848094	+	0.996397i	$0.472972\pi$
$138$		0			0
$139$	−7.14003	−	21.9748i	−0.605610	−	1.86388i	−0.492543	−	0.870288i	$-0.663933\pi$
$139$	−7.14003	−	21.9748i	−0.605610	−	1.86388i	−0.113066	−	0.993587i	$-0.536067\pi$
$140$		0			0
$141$	−1.46040	+	4.49466i	−0.122988	+	0.378518i
$142$		0			0
$143$	7.67075	−	2.49238i	0.641460	−	0.208423i
$144$		0			0
$145$	2.54518	+	1.29683i	0.211366	+	0.107696i
$146$		0			0
$147$	−1.39625	+	8.81560i	−0.115161	+	0.727098i
$148$		0			0
$149$	−18.2315	+	2.88759i	−1.49358	+	0.236560i	−0.849171	−	0.528118i	$-0.822898\pi$
$149$	−18.2315	+	2.88759i	−1.49358	+	0.236560i	−0.644412	+	0.764679i	$0.722898\pi$
$150$		0			0
$151$	−8.59238	+	4.37803i	−0.699238	+	0.356279i	−0.767200	−	0.641409i	$-0.778350\pi$
$151$	−8.59238	+	4.37803i	−0.699238	+	0.356279i	0.0679619	+	0.997688i	$0.478350\pi$
$152$		0			0
$153$	8.56262	+	1.35619i	0.692247	+	0.109641i
$154$		0			0
$155$		−	2.83951i		−	0.228075i
$156$		0			0
$157$	6.41636	−	12.5928i	0.512081	−	1.00502i	−0.479743	−	0.877409i	$-0.659270\pi$
$157$	6.41636	−	12.5928i	0.512081	−	1.00502i	0.991825	−	0.127608i	$-0.0407298\pi$
$158$		0			0
$159$	−5.10320	+	7.02395i	−0.404710	+	0.557035i
$160$		0			0
$161$	6.55289e−5	0	6.55289e-5i	5.16440e−6	0	5.16440e-6i
$162$		0			0
$163$	2.37069			0.185687			0.0928436	−	0.995681i	$-0.470404\pi$
$163$	2.37069			0.185687			0.0928436	+	0.995681i	$0.470404\pi$
$164$		0			0
$165$	2.96946			0.231173
$166$		0			0
$167$	−5.51446	−	5.51446i	−0.426721	−	0.426721i	0.460789	−	0.887510i	$-0.347567\pi$
$167$	−5.51446	−	5.51446i	−0.426721	−	0.426721i	−0.887510	+	0.460789i	$0.847567\pi$
$168$		0			0
$169$	−0.591151	+	0.813650i	−0.0454732	+	0.0625884i
$170$		0			0
$171$	−0.716083	+	1.40539i	−0.0547603	+	0.107473i
$172$		0			0
$173$		−	13.6231i		−	1.03575i	−0.855457	−	0.517873i	$-0.826724\pi$
$173$		−	13.6231i		−	1.03575i	0.855457	−	0.517873i	$-0.173276\pi$
$174$		0			0
$175$	1.07445e−5	0	1.70176e-6i	8.12206e−7	0	1.28641e-7i
$176$		0			0
$177$	−1.19750	+	0.610155i	−0.0900094	+	0.0458621i
$178$		0			0
$179$	0.497029	−	0.0787217i	0.0371497	−	0.00588394i	−0.137832	−	0.990456i	$-0.544013\pi$
$179$	0.497029	−	0.0787217i	0.0371497	−	0.00588394i	0.174982	+	0.984572i	$0.444013\pi$
$180$		0			0
$181$	−2.88304	+	18.2028i	−0.214295	+	1.35300i	0.612487	+	0.790481i	$0.290169\pi$
$181$	−2.88304	+	18.2028i	−0.214295	+	1.35300i	−0.826781	+	0.562523i	$0.809831\pi$
$182$		0			0
$183$	−8.88073	−	4.52496i	−0.656482	−	0.334494i
$184$		0			0
$185$	8.04470	−	2.61388i	0.591458	−	0.192176i
$186$		0			0
$187$	−4.54009	+	13.9730i	−0.332004	+	1.02180i
$188$		0			0
$189$	1.87491e−5	0	5.77038e-5i	1.36380e−6	0	4.19733e-6i
$190$		0			0
$191$	−16.1176	+	16.1176i	−1.16623	+	1.16623i	−0.183140	+	0.983087i	$0.558626\pi$
$191$	−16.1176	+	16.1176i	−1.16623	+	1.16623i	−0.983087	+	0.183140i	$0.941374\pi$
$192$		0			0
$193$	−1.94325	−	12.2692i	−0.139878	−	0.883156i	−0.953419	−	0.301649i	$-0.902463\pi$
$193$	−1.94325	−	12.2692i	−0.139878	−	0.883156i	0.813541	−	0.581508i	$-0.197537\pi$
$194$		0			0
$195$	3.57255	−	2.59561i	0.255836	−	0.185875i
$196$		0			0
$197$	8.60874	+	11.8489i	0.613348	+	0.844201i	0.996848	−	0.0793403i	$-0.0252814\pi$
$197$	8.60874	+	11.8489i	0.613348	+	0.844201i	−0.383500	+	0.923541i	$0.625281\pi$
$198$		0			0
$199$	8.44530	+	16.5748i	0.598671	+	1.17496i	0.969232	+	0.246150i	$0.0791656\pi$
$199$	8.44530	+	16.5748i	0.598671	+	1.17496i	−0.370561	+	0.928808i	$0.620834\pi$
$200$		0			0
$201$	−11.1261	−	8.08362i	−0.784778	−	0.570174i
$202$		0			0
$203$	−2.95535e−5	0	9.60252e-6i	−2.07425e−6	0	6.73965e-7i
$204$		0			0
$205$	−6.40277	+	0.0674385i	−0.447189	+	0.00471011i
$206$		0			0
$207$	−11.1337	−	3.61755i	−0.773843	−	0.251437i
$208$		0			0
$209$	−2.16257	−	1.57120i	−0.149588	−	0.108682i
$210$		0			0
$211$	−8.25858	−	16.2084i	−0.568544	−	1.11583i	−0.978983	−	0.203943i	$-0.934624\pi$
$211$	−8.25858	−	16.2084i	−0.568544	−	1.11583i	0.410438	−	0.911888i	$-0.365376\pi$
$212$		0			0
$213$	−0.294671	−	0.405580i	−0.0201905	−	0.0277899i
$214$		0			0
$215$	−0.227809	+	0.165513i	−0.0155365	+	0.0112879i
$216$		0			0
$217$	4.83216e−6	0	3.05091e-5i	3.28028e−7	0	2.07109e-6i
$218$		0			0
$219$	12.6312	−	12.6312i	0.853538	−	0.853538i
$220$		0			0
$221$	6.75160	+	20.7793i	0.454162	+	1.39777i
$222$		0			0
$223$	7.24009	−	22.2827i	0.484832	−	1.49216i	−0.347391	−	0.937720i	$-0.612932\pi$
$223$	7.24009	−	22.2827i	0.484832	−	1.49216i	0.832224	−	0.554440i	$-0.187068\pi$
$224$		0			0
$225$	−1.30694	+	0.424651i	−0.0871294	+	0.0283100i
$226$		0			0
$227$	−12.0991	−	6.16481i	−0.803047	−	0.409173i	0.00375662	−	0.999993i	$-0.498804\pi$
$227$	−12.0991	−	6.16481i	−0.803047	−	0.409173i	−0.806803	+	0.590820i	$0.798804\pi$
$228$		0			0
$229$	−0.463349	+	2.92547i	−0.0306190	+	0.193320i	−0.998257	−	0.0590233i	$-0.981201\pi$
$229$	−0.463349	+	2.92547i	−0.0306190	+	0.193320i	0.967638	+	0.252344i	$0.0812014\pi$
$230$		0			0
$231$	−3.19054e−5	0	5.05331e-6i	−2.09922e−6	0	3.32484e-7i
$232$		0			0
$233$	−18.3209	+	9.33499i	−1.20024	+	0.611555i	−0.935693	−	0.352816i	$-0.885224\pi$
$233$	−18.3209	+	9.33499i	−1.20024	+	0.611555i	−0.264552	+	0.964371i	$0.585224\pi$
$234$		0			0
$235$	3.66080	+	0.579814i	0.238804	+	0.0378229i
$236$		0			0
$237$		−	6.09718i		−	0.396054i
$238$		0			0
$239$	−1.88496	+	3.69945i	−0.121928	+	0.239297i	−0.943901	−	0.330230i	$-0.892874\pi$
$239$	−1.88496	+	3.69945i	−0.121928	+	0.239297i	0.821972	+	0.569527i	$0.192874\pi$
$240$		0			0
$241$	1.30796	−	1.80025i	0.0842528	−	0.115964i	−0.764810	−	0.644256i	$-0.777167\pi$
$241$	1.30796	−	1.80025i	0.0842528	−	0.115964i	0.849063	+	0.528292i	$0.177167\pi$
$242$		0			0
$243$	−9.13657	−	9.13657i	−0.586111	−	0.586111i
$244$		0			0
$245$	7.00000			0.447214
$246$		0			0
$247$	−3.97516			−0.252933
$248$		0			0
$249$	5.35736	+	5.35736i	0.339509	+	0.339509i
$250$		0			0
$251$	−17.5167	+	24.1097i	−1.10564	+	1.52179i	−0.277960	+	0.960593i	$0.589658\pi$
$251$	−17.5167	+	24.1097i	−1.10564	+	1.52179i	−0.827683	+	0.561195i	$0.810342\pi$
$252$		0			0
$253$	9.00687	−	17.6770i	0.566257	−	1.11134i
$254$		0			0
$255$			8.04398i			0.503734i
$256$		0			0
$257$	−3.35955	−	0.532100i	−0.209563	−	0.0331915i	0.0507703	−	0.998710i	$-0.483832\pi$
$257$	−3.35955	−	0.532100i	−0.209563	−	0.0331915i	−0.260333	+	0.965519i	$0.583832\pi$
$258$		0			0
$259$	−8.19879e−5	0	4.17749e-5i	−5.09448e−6	0	2.59577e-6i
$260$		0			0
$261$	3.87710	−	0.614072i	0.239986	−	0.0380101i
$262$		0			0
$263$	−3.06634	+	19.3601i	−0.189079	+	1.19380i	0.692379	+	0.721534i	$0.256563\pi$
$263$	−3.06634	+	19.3601i	−0.189079	+	1.19380i	−0.881458	+	0.472263i	$0.843437\pi$
$264$		0			0
$265$	6.06696	+	3.09127i	0.372690	+	0.189895i
$266$		0			0
$267$	−19.1836	+	6.23312i	−1.17401	+	0.381460i
$268$		0			0
$269$	−4.33524	+	13.3425i	−0.264324	+	0.813506i	0.727524	+	0.686082i	$0.240671\pi$
$269$	−4.33524	+	13.3425i	−0.264324	+	0.813506i	−0.991848	+	0.127424i	$0.959329\pi$
$270$		0			0
$271$	3.89698	+	11.9937i	0.236725	+	0.728563i	0.996888	+	0.0788313i	$0.0251188\pi$
$271$	3.89698	+	11.9937i	0.236725	+	0.728563i	−0.760163	+	0.649732i	$0.774881\pi$
$272$		0			0
$273$	−3.39681e−5	0	3.39681e-5i	−2.05584e−6	0	2.05584e-6i
$274$		0			0
$275$	−0.364315	−	2.30019i	−0.0219690	−	0.138707i
$276$		0			0
$277$	10.9492	−	7.95508i	0.657876	−	0.477975i	−0.208069	−	0.978114i	$-0.566718\pi$
$277$	10.9492	−	7.95508i	0.657876	−	0.477975i	0.865945	+	0.500139i	$0.166718\pi$
$278$		0			0
$279$	−2.29357	−	3.15683i	−0.137312	−	0.188994i
$280$		0			0
$281$	12.1064	+	23.7602i	0.722209	+	1.41741i	0.901129	+	0.433551i	$0.142740\pi$
$281$	12.1064	+	23.7602i	0.722209	+	1.41741i	−0.178920	+	0.983864i	$0.557260\pi$
$282$		0			0
$283$	−0.469995	−	0.341471i	−0.0279383	−	0.0202984i	0.573728	−	0.819046i	$-0.305496\pi$
$283$	−0.469995	−	0.341471i	−0.0279383	−	0.0202984i	−0.601667	+	0.798747i	$0.705496\pi$
$284$		0			0
$285$	−1.39190	−	0.452255i	−0.0824489	−	0.0267893i
$286$		0			0
$287$	6.86797e−5	0	1.16206e-5i	4.05403e−6	0	6.85940e-7i
$288$		0			0
$289$	−21.6834	−	7.04535i	−1.27549	−	0.414433i
$290$		0			0
$291$	2.41432	+	1.75411i	0.141530	+	0.102828i
$292$		0			0
$293$	1.69300	+	3.32271i	0.0989063	+	0.194115i	0.935158	−	0.354232i	$-0.115258\pi$
$293$	1.69300	+	3.32271i	0.0989063	+	0.194115i	−0.836251	+	0.548346i	$0.815258\pi$
$294$		0			0
$295$	0.619553	+	0.852742i	0.0360718	+	0.0496485i
$296$		0			0
$297$	10.5083	−	7.63476i	0.609756	−	0.443014i
$298$		0			0
$299$	−4.61532	−	29.1400i	−0.266911	−	1.68521i
$300$		0			0
$301$	2.16603e−6	0	2.16603e-6i	1.24848e−7	0	1.24848e-7i
$302$		0			0
$303$	3.82916	+	11.7849i	0.219980	+	0.677028i
$304$		0			0
$305$	−2.41555	+	7.43430i	−0.138314	+	0.425687i
$306$		0			0
$307$	11.4813	−	3.73051i	0.655275	−	0.212912i	0.0375362	−	0.999295i	$-0.488049\pi$
$307$	11.4813	−	3.73051i	0.655275	−	0.212912i	0.617738	+	0.786384i	$0.288049\pi$
$308$		0			0
$309$	−7.21957	−	3.67855i	−0.410707	−	0.209266i
$310$		0			0
$311$	−0.631071	+	3.98442i	−0.0357847	+	0.225936i	−0.999099	−	0.0424399i	$-0.986487\pi$
$311$	−0.631071	+	3.98442i	−0.0357847	+	0.225936i	0.963314	+	0.268376i	$0.0864869\pi$
$312$		0			0
$313$	24.6748	−	3.90810i	1.39470	−	0.220899i	0.586569	−	0.809899i	$-0.300478\pi$
$313$	24.6748	−	3.90810i	1.39470	−	0.220899i	0.808133	+	0.589000i	$0.200478\pi$
$314$		0			0
$315$	1.33197e−5	0	6.78675e-6i	7.50483e−7	0	3.82390e-7i
$316$		0			0
$317$	23.4754	+	3.71814i	1.31851	+	0.208831i	0.775741	−	0.631051i	$-0.217376\pi$
$317$	23.4754	+	3.71814i	1.31851	+	0.208831i	0.542768	+	0.839883i	$0.317376\pi$
$318$		0			0
$319$			6.65246i			0.372466i
$320$		0			0
$321$	−4.15445	+	8.15357i	−0.231879	+	0.455088i
$322$		0			0
$323$	4.25621	−	5.85818i	0.236822	−	0.325958i
$324$		0			0
$325$	−2.44891	−	2.44891i	−0.135841	−	0.135841i
$326$		0			0
$327$	−3.36253			−0.185948
$328$		0			0
$329$	−4.03201e−5	0		−2.22292e−6	0
$330$		0			0
$331$	−7.74845	−	7.74845i	−0.425893	−	0.425893i	0.461333	−	0.887227i	$-0.347371\pi$
$331$	−7.74845	−	7.74845i	−0.425893	−	0.425893i	−0.887227	+	0.461333i	$0.847371\pi$
$332$		0			0
$333$	6.83237	−	9.40395i	0.374412	−	0.515333i
$334$		0			0
$335$	−4.89666	+	9.61024i	−0.267533	+	0.525063i
$336$		0			0
$337$		−	5.76908i		−	0.314262i	−0.987578	−	0.157131i	$-0.949776\pi$
$337$		−	5.76908i		−	0.314262i	0.987578	−	0.157131i	$-0.0502244\pi$
$338$		0			0
$339$	12.5511	+	1.98789i	0.681681	+	0.107968i
$340$		0			0
$341$	5.89208	−	3.00217i	0.319074	−	0.162576i
$342$		0			0
$343$	−0.000150423	0	2.38246e-5i	−8.12206e−6	0	1.28641e-6i
$344$		0			0
$345$	1.69922	−	10.7284i	0.0914827	−	0.577599i
$346$		0			0
$347$	−22.8730	−	11.6544i	−1.22789	−	0.625641i	−0.284930	−	0.958548i	$-0.591970\pi$
$347$	−22.8730	−	11.6544i	−1.22789	−	0.625641i	−0.942959	+	0.332908i	$0.891970\pi$
$348$		0			0
$349$	−6.01795	+	1.95535i	−0.322134	+	0.104668i	−0.465620	−	0.884985i	$-0.654169\pi$
$349$	−6.01795	+	1.95535i	−0.322134	+	0.104668i	0.143486	+	0.989652i	$0.454169\pi$
$350$		0			0
$351$	5.96900	−	18.3707i	0.318602	−	0.980555i
$352$		0			0
$353$	8.33205	+	25.6434i	0.443470	+	1.36486i	0.884153	+	0.467198i	$0.154736\pi$
$353$	8.33205	+	25.6434i	0.443470	+	1.36486i	−0.440683	+	0.897663i	$0.645264\pi$
$354$		0			0
$355$	−0.278016	+	0.278016i	−0.0147556	+	0.0147556i
$356$		0			0
$357$	−1.36889e−5	0	8.64284e-5i	−7.24494e−7	0	4.57428e-6i
$358$		0			0
$359$	19.6380	−	14.2679i	1.03646	−	0.753029i	0.0668655	−	0.997762i	$-0.478700\pi$
$359$	19.6380	−	14.2679i	1.03646	−	0.753029i	0.969591	+	0.244732i	$0.0787001\pi$
$360$		0			0
$361$	−10.3935	−	14.3055i	−0.547028	−	0.752920i
$362$		0			0
$363$	−3.22800	−	6.33530i	−0.169426	−	0.332517i
$364$		0			0
$365$	−11.3340	−	8.23464i	−0.593249	−	0.431021i
$366$		0			0
$367$	21.2026	+	6.88914i	1.10677	+	0.359610i	0.804703	−	0.593678i	$-0.202325\pi$
$367$	21.2026	+	6.88914i	1.10677	+	0.359610i	0.302064	+	0.953288i	$0.402325\pi$
$368$		0			0
$369$	−7.06381	+	5.24671i	−0.367727	+	0.273133i
$370$		0			0
$371$	−7.04469e−5	0	2.28896e-5i	−3.65742e−6	0	1.18837e-6i
$372$		0			0
$373$	9.69979	+	7.04731i	0.502236	+	0.364896i	0.809871	−	0.586609i	$-0.199537\pi$
$373$	9.69979	+	7.04731i	0.502236	+	0.364896i	−0.307634	+	0.951505i	$0.599537\pi$
$374$		0			0
$375$	−0.578869	−	1.13609i	−0.0298927	−	0.0586677i
$376$		0			0
$377$	5.81491	+	8.00354i	0.299483	+	0.412203i
$378$		0			0
$379$	28.0413	−	20.3732i	1.44038	−	1.04650i	0.452421	−	0.891804i	$-0.350560\pi$
$379$	28.0413	−	20.3732i	1.44038	−	1.04650i	0.987962	−	0.154696i	$-0.0494397\pi$
$380$		0			0
$381$	−1.89439	−	11.9607i	−0.0970523	−	0.612764i
$382$		0			0
$383$	7.44908	−	7.44908i	0.380630	−	0.380630i	−0.490699	−	0.871329i	$-0.663259\pi$
$383$	7.44908	−	7.44908i	0.380630	−	0.380630i	0.871329	+	0.490699i	$0.163259\pi$
$384$		0			0
$385$	7.82875e−6	0	2.40944e-5i	3.98990e−7	0	1.22796e-6i
$386$		0			0
$387$	−0.119576	+	0.368018i	−0.00607841	+	0.0187074i
$388$		0			0
$389$	19.0004	−	6.17359i	0.963356	−	0.313013i	0.215225	−	0.976564i	$-0.430951\pi$
$389$	19.0004	−	6.17359i	0.963356	−	0.313013i	0.748131	+	0.663551i	$0.230951\pi$
$390$		0			0
$391$	47.8851	+	24.3987i	2.42166	+	1.23390i
$392$		0			0
$393$	3.27587	−	20.6830i	0.165246	−	1.04332i
$394$		0			0
$395$	−4.72297	+	0.748045i	−0.237638	+	0.0376382i
$396$		0			0
$397$	6.44121	−	3.28196i	0.323275	−	0.164717i	−0.284820	−	0.958581i	$-0.591934\pi$
$397$	6.44121	−	3.28196i	0.323275	−	0.164717i	0.608095	+	0.793864i	$0.291934\pi$
$398$		0			0
$399$	1.57249e−5	0	2.49057e-6i	7.87227e−7	0	1.24685e-7i
$400$		0			0
$401$			15.4651i			0.772291i	0.922438	+	0.386146i	$0.126194\pi$
$401$			15.4651i			0.772291i	−0.922438	+	0.386146i	$0.873806\pi$
$402$		0			0
$403$	4.46454	−	8.76216i	0.222395	−	0.436474i
$404$		0			0
$405$	1.75688	−	2.41814i	0.0873001	−	0.120158i
$406$		0			0
$407$	13.9294	+	13.9294i	0.690455	+	0.690455i
$408$		0			0
$409$	−37.1371			−1.83631			−0.918156	−	0.396220i	$-0.870322\pi$
$409$	−37.1371			−1.83631			−0.918156	+	0.396220i	$0.870322\pi$
$410$		0			0
$411$	−19.2401			−0.949045
$412$		0			0
$413$	−8.10794e−6	0	8.10794e-6i	−3.98966e−7	0	3.98966e-7i
$414$		0			0
$415$	3.49262	−	4.80718i	0.171446	−	0.235975i
$416$		0			0
$417$	13.3751	−	26.2502i	0.654984	−	1.28548i
$418$		0			0
$419$			23.3890i			1.14263i	0.820732	+	0.571314i	$0.193566\pi$
$419$			23.3890i			1.14263i	−0.820732	+	0.571314i	$0.806434\pi$
$420$		0			0
$421$	−11.5003	−	1.82147i	−0.560492	−	0.0887732i	−0.130241	−	0.991482i	$-0.541575\pi$
$421$	−11.5003	−	1.82147i	−0.560492	−	0.0887732i	−0.430251	+	0.902709i	$0.641575\pi$
$422$		0			0
$423$	4.53823	−	2.31235i	0.220656	−	0.112430i
$424$		0			0
$425$	6.23099	−	0.986892i	0.302248	−	0.0478713i
$426$		0			0
$427$	1.33025e−5	0	8.39884e-5i	6.43751e−7	0	4.06448e-6i
$428$		0			0
$429$	9.16318	+	4.66887i	0.442402	+	0.225415i
$430$		0			0
$431$	20.7245	−	6.73379i	0.998263	−	0.324355i	0.236092	−	0.971731i	$-0.424133\pi$
$431$	20.7245	−	6.73379i	0.998263	−	0.324355i	0.762171	+	0.647375i	$0.224133\pi$
$432$		0			0
$433$	−4.60496	+	14.1726i	−0.221300	+	0.681092i	0.777346	+	0.629073i	$0.216565\pi$
$433$	−4.60496	+	14.1726i	−0.221300	+	0.681092i	−0.998646	+	0.0520184i	$0.983435\pi$
$434$		0			0
$435$	1.12552	+	3.46400i	0.0539646	+	0.166086i
$436$		0			0
$437$	−6.91409	+	6.91409i	−0.330746	+	0.330746i
$438$		0			0
$439$	0.525516	+	3.31798i	0.0250815	+	0.158358i	0.997050	−	0.0767518i	$-0.0244549\pi$
$439$	0.525516	+	3.31798i	0.0250815	+	0.158358i	−0.971969	+	0.235110i	$0.924455\pi$
$440$		0			0
$441$	7.78225	−	5.65414i	0.370583	−	0.269245i
$442$		0			0
$443$	16.4174	+	22.5966i	0.780015	+	1.07360i	0.995280	+	0.0970428i	$0.0309384\pi$
$443$	16.4174	+	22.5966i	0.780015	+	1.07360i	−0.215265	+	0.976556i	$0.569062\pi$
$444$		0			0
$445$	7.18184	+	14.0952i	0.340452	+	0.668175i
$446$		0			0
$447$	−19.0412	−	13.8342i	−0.900617	−	0.654336i
$448$		0			0
$449$	21.2447	+	6.90281i	1.00260	+	0.325764i	0.763903	−	0.645331i	$-0.223280\pi$
$449$	21.2447	+	6.90281i	1.00260	+	0.325764i	0.238695	+	0.971095i	$0.423280\pi$
$450$		0			0
$451$	−6.90948	−	13.2147i	−0.325354	−	0.622254i
$452$		0			0
$453$	−11.6943	−	3.79969i	−0.549444	−	0.178525i
$454$		0			0
$455$	3.04797e−5	0	2.21448e-5i	1.42891e−6	0	1.03816e-6i
$456$		0			0
$457$	4.55314	+	8.93603i	0.212987	+	0.418010i	0.972640	−	0.232319i	$-0.0746312\pi$
$457$	4.55314	+	8.93603i	0.212987	+	0.418010i	−0.759653	+	0.650329i	$0.774631\pi$
$458$		0			0
$459$	20.6818	+	28.4661i	0.965344	+	1.32868i
$460$		0			0
$461$	−13.7696	+	10.0042i	−0.641316	+	0.465943i	−0.860302	−	0.509785i	$-0.829725\pi$
$461$	−13.7696	+	10.0042i	−0.641316	+	0.465943i	0.218986	+	0.975728i	$0.429725\pi$
$462$		0			0
$463$	0.291925	+	1.84314i	0.0135669	+	0.0856579i	0.993543	−	0.113458i	$-0.0361929\pi$
$463$	0.291925	+	1.84314i	0.0135669	+	0.0856579i	−0.979976	+	0.199116i	$0.936193\pi$
$464$		0			0
$465$	2.56013	−	2.56013i	0.118723	−	0.118723i
$466$		0			0
$467$	−11.9055	−	36.6415i	−0.550922	−	1.69557i	−0.706476	−	0.707737i	$-0.749716\pi$
$467$	−11.9055	−	36.6415i	−0.550922	−	1.69557i	0.155553	−	0.987828i	$-0.450284\pi$
$468$		0			0
$469$	3.62578e−5	0	0.000111590i	1.67423e−6	0	5.15275e-6i
$470$		0			0
$471$	17.1389	−	5.56876i	0.789718	−	0.256595i
$472$		0			0
$473$	−0.584304	−	0.297718i	−0.0268663	−	0.0136891i
$474$		0			0
$475$	−0.179556	+	1.13367i	−0.00823859	+	0.0520164i
$476$		0			0
$477$	9.24186	−	1.46377i	0.423156	−	0.0670213i
$478$		0			0
$479$	10.2379	−	5.21647i	0.467781	−	0.238347i	−0.204179	−	0.978934i	$-0.565452\pi$
$479$	10.2379	−	5.21647i	0.467781	−	0.238347i	0.671960	+	0.740587i	$0.265452\pi$
$480$		0			0
$481$	28.9341	+	4.58271i	1.31928	+	0.208954i
$482$		0			0
$483$		0	0.000118163i		0	5.37661e-6i
$484$		0			0
$485$	1.06255	−	2.08538i	0.0482481	−	0.0946922i
$486$		0			0
$487$	−21.6385	+	29.7829i	−0.980536	+	1.34959i	−0.0439956	+	0.999032i	$0.514009\pi$
$487$	−21.6385	+	29.7829i	−0.980536	+	1.34959i	−0.936540	+	0.350560i	$0.885991\pi$
$488$		0			0
$489$	2.13744	+	2.13744i	0.0966585	+	0.0966585i
$490$		0			0
$491$	24.9509			1.12602			0.563008	−	0.826451i	$-0.309644\pi$
$491$	24.9509			1.12602			0.563008	+	0.826451i	$0.309644\pi$
$492$		0			0
$493$	−18.0208			−0.811618
$494$		0			0
$495$	−2.26297	−	2.26297i	−0.101713	−	0.101713i
$496$		0			0
$497$	2.51402e−6	0	3.46025e-6i	1.12769e−7	0	1.55214e-7i
$498$		0			0
$499$	4.25690	−	8.35464i	0.190565	−	0.374005i	−0.775879	−	0.630882i	$-0.782693\pi$
$499$	4.25690	−	8.35464i	0.190565	−	0.374005i	0.966444	+	0.256876i	$0.0826933\pi$
$500$		0			0
$501$		−	9.94378i		−	0.444255i
$502$		0			0
$503$	6.71008	+	1.06277i	0.299187	+	0.0473866i	0.304224	−	0.952601i	$-0.401603\pi$
$503$	6.71008	+	1.06277i	0.299187	+	0.0473866i	−0.00503604	+	0.999987i	$0.501603\pi$
$504$		0			0
$505$	8.65902	−	4.41199i	0.385321	−	0.196331i
$506$		0			0
$507$	−1.26658	+	0.200607i	−0.0562509	+	0.00890927i
$508$		0			0
$509$	−0.841871	+	5.31536i	−0.0373153	+	0.235599i	−0.999296	−	0.0375182i	$-0.988055\pi$
$509$	−0.841871	+	5.31536i	−0.0373153	+	0.235599i	0.961981	+	0.273117i	$0.0880548\pi$
$510$		0			0
$511$	0.000135791	0	6.91892e-5i	6.00706e−6	0	3.06075e-6i
$512$		0			0
$513$	−6.08844	+	1.97825i	−0.268811	+	0.0873420i
$514$		0			0
$515$	−1.96372	+	6.04370i	−0.0865317	+	0.266317i
$516$		0			0
$517$	2.66737	+	8.20932i	0.117311	+	0.361045i
$518$		0			0
$519$	12.2827	−	12.2827i	0.539153	−	0.539153i
$520$		0			0
$521$	−2.06522	−	13.0393i	−0.0904790	−	0.571262i	−0.990725	−	0.135881i	$-0.956614\pi$
$521$	−2.06522	−	13.0393i	−0.0904790	−	0.571262i	0.900246	−	0.435381i	$-0.143386\pi$
$522$		0			0
$523$	5.95290	−	4.32504i	0.260302	−	0.189121i	−0.449978	−	0.893040i	$-0.648568\pi$
$523$	5.95290	−	4.32504i	0.260302	−	0.189121i	0.710280	+	0.703919i	$0.248568\pi$
$524$		0			0
$525$	8.15301e−6	0	1.12217e-5i	3.55826e−7	0	4.89753e-7i
$526$		0			0
$527$	8.13257	+	15.9611i	0.354260	+	0.695275i
$528$		0			0
$529$	−40.1040	−	29.1373i	−1.74365	−	1.26684i
$530$		0			0
$531$	1.37758	+	0.447602i	0.0597817	+	0.0194243i
$532$		0			0
$533$	−19.8637	−	9.85893i	−0.860392	−	0.427038i
$534$		0			0
$535$	6.82558	+	2.21776i	0.295095	+	0.0958823i
$536$		0			0
$537$	0.519103	+	0.377150i	0.0224009	+	0.0162752i
$538$		0			0
$539$	7.40098	+	14.5252i	0.318783	+	0.625646i
$540$		0			0
$541$	−2.07618	−	2.85761i	−0.0892618	−	0.122858i	0.762051	−	0.647518i	$-0.224193\pi$
$541$	−2.07618	−	2.85761i	−0.0892618	−	0.122858i	−0.851312	+	0.524659i	$0.824193\pi$
$542$		0			0
$543$	−19.0112	+	13.8125i	−0.815849	+	0.592749i
$544$		0			0
$545$	0.412539	+	2.60467i	0.0176712	+	0.111572i
$546$		0			0
$547$	−9.15743	+	9.15743i	−0.391543	+	0.391543i	−0.875237	−	0.483694i	$-0.839295\pi$
$547$	−9.15743	+	9.15743i	−0.391543	+	0.391543i	0.483694	+	0.875237i	$0.339295\pi$
$548$		0			0
$549$	3.31945	+	10.2162i	0.141671	+	0.436017i
$550$		0			0
$551$	1.01318	−	3.11825i	0.0431630	−	0.132842i
$552$		0			0
$553$	4.94729e−5	0	1.60747e-5i	2.10380e−6	0	6.83566e-7i
$554$		0			0
$555$	9.60988	+	4.89648i	0.407917	+	0.207844i
$556$		0			0
$557$	3.86053	−	24.3744i	0.163576	−	1.03278i	−0.760157	−	0.649739i	$-0.774878\pi$
$557$	3.86053	−	24.3744i	0.163576	−	1.03278i	0.923733	−	0.383037i	$-0.125122\pi$
$558$		0			0
$559$	−0.963209	+	0.152557i	−0.0407394	+	0.00645249i
$560$		0			0
$561$	−16.6915	+	8.50477i	−0.704717	+	0.359071i
$562$		0			0
$563$	35.8375	+	5.67611i	1.51037	+	0.239219i	0.856009	−	0.516961i	$-0.172937\pi$
$563$	35.8375	+	5.67611i	1.51037	+	0.239219i	0.654363	+	0.756181i	$0.272937\pi$
$564$		0			0
$565$		−	9.96615i		−	0.419279i
$566$		0			0
$567$	−1.47617e−5	0	2.89714e-5i	−6.19932e−7	0	1.21669e-6i
$568$		0			0
$569$	−1.36999	+	1.88563i	−0.0574329	+	0.0790496i	−0.836767	−	0.547559i	$-0.815557\pi$
$569$	−1.36999	+	1.88563i	−0.0574329	+	0.0790496i	0.779334	+	0.626608i	$0.215557\pi$
$570$		0			0
$571$	−6.90664	−	6.90664i	−0.289034	−	0.289034i	0.547664	−	0.836698i	$-0.315517\pi$
$571$	−6.90664	−	6.90664i	−0.289034	−	0.289034i	−0.836698	+	0.547664i	$0.815517\pi$
$572$		0			0
$573$	−29.0635			−1.21415
$574$		0			0
$575$	−8.51888			−0.355262
$576$		0			0
$577$	3.78061	+	3.78061i	0.157389	+	0.157389i	0.781409	−	0.624020i	$-0.214502\pi$
$577$	3.78061	+	3.78061i	0.157389	+	0.157389i	−0.624020	+	0.781409i	$0.714502\pi$
$578$		0			0
$579$	9.30998	−	12.8141i	0.386909	−	0.532535i
$580$		0			0
$581$	−2.93457e−5	0	5.75942e-5i	−1.21747e−6	0	2.38941e-6i
$582$		0			0
$583$			15.8575i			0.656750i
$584$		0			0
$585$	−4.70063	−	0.744507i	−0.194347	−	0.0307816i
$586$		0			0
$587$	11.2140	−	5.71384i	0.462853	−	0.235835i	−0.206983	−	0.978345i	$-0.566364\pi$
$587$	11.2140	−	5.71384i	0.462853	−	0.235835i	0.669836	+	0.742509i	$0.266364\pi$
$588$		0			0
$589$	−3.21907	+	0.509851i	−0.132640	+	0.0210080i
$590$		0			0
$591$	−2.92138	+	18.4448i	−0.120169	+	0.758719i
$592$		0			0
$593$	−19.2951	−	9.83134i	−0.792354	−	0.403725i	0.0104663	−	0.999945i	$-0.496668\pi$
$593$	−19.2951	−	9.83134i	−0.792354	−	0.403725i	−0.802821	+	0.596220i	$0.796668\pi$
$594$		0			0
$595$	−6.52693e−5	0	2.12073e-5i	−2.67578e−6	0	8.69414e-7i
$596$		0			0
$597$	−7.32967	+	22.5584i	−0.299983	+	0.923254i
$598$		0			0
$599$	8.97179	+	27.6123i	0.366578	+	1.12821i	0.948987	+	0.315314i	$0.102110\pi$
$599$	8.97179	+	27.6123i	0.366578	+	1.12821i	−0.582410	+	0.812895i	$0.697890\pi$
$600$		0			0
$601$	22.7305	−	22.7305i	0.927198	−	0.927198i	−0.0703257	−	0.997524i	$-0.522404\pi$
$601$	22.7305	−	22.7305i	0.927198	−	0.927198i	0.997524	+	0.0703257i	$0.0224038\pi$
$602$		0			0
$603$	2.31865	+	14.6394i	0.0944227	+	0.596162i
$604$		0			0
$605$	−4.51139	+	3.27772i	−0.183414	+	0.133258i
$606$		0			0
$607$	6.11656	+	8.41872i	0.248263	+	0.341705i	0.914902	−	0.403676i	$-0.132268\pi$
$607$	6.11656	+	8.41872i	0.248263	+	0.341705i	−0.666639	+	0.745381i	$0.732268\pi$
$608$		0			0
$609$	−1.79880e−5	0	3.53035e-5i	−7.28912e−7	0	1.43057e-6i
$610$		0			0
$611$	10.3849	+	7.54505i	0.420127	+	0.305240i
$612$		0			0
$613$	−20.1479	−	6.54646i	−0.813768	−	0.264409i	−0.127575	−	0.991829i	$-0.540719\pi$
$613$	−20.1479	−	6.54646i	−0.813768	−	0.264409i	−0.686193	+	0.727420i	$0.740719\pi$
$614$		0			0
$615$	−5.83360	−	5.71200i	−0.235234	−	0.230330i
$616$		0			0
$617$	−13.7384	−	4.46387i	−0.553087	−	0.179709i	0.0191216	−	0.999817i	$-0.493913\pi$
$617$	−13.7384	−	4.46387i	−0.553087	−	0.179709i	−0.572208	+	0.820108i	$0.693913\pi$
$618$		0			0
$619$	−36.2448	−	26.3334i	−1.45680	−	1.05843i	−0.984181	−	0.177164i	$-0.943308\pi$
$619$	−36.2448	−	26.3334i	−1.45680	−	1.05843i	−0.472622	−	0.881265i	$-0.656692\pi$
$620$		0			0
$621$	−21.5706	−	42.3346i	−0.865597	−	1.69883i
$622$		0			0
$623$	−0.000101152	0	0.000139223i	−4.05256e−6	0	5.57787e-6i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−0.533185	−	3.36640i	−0.0212934	−	0.134441i
$628$		0			0
$629$	−37.7334	+	37.7334i	−1.50453	+	1.50453i
$630$		0			0
$631$	3.54293	+	10.9040i	0.141042	+	0.434082i	0.996481	−	0.0838215i	$-0.0267125\pi$
$631$	3.54293	+	10.9040i	0.141042	+	0.434082i	−0.855439	+	0.517904i	$0.826713\pi$
$632$		0			0
$633$	7.16762	−	22.0597i	0.284887	−	0.876793i
$634$		0			0
$635$	−9.03251	+	2.93484i	−0.358444	+	0.116466i
$636$		0			0
$637$	21.6006	+	11.0061i	0.855847	+	0.436076i
$638$		0			0
$639$	−0.0845214	+	0.533647i	−0.00334362	+	0.0211108i
$640$		0			0
$641$	−26.5737	+	4.20885i	−1.04960	+	0.166240i	−0.657323	−	0.753609i	$-0.728311\pi$
$641$	−26.5737	+	4.20885i	−1.04960	+	0.166240i	−0.392273	+	0.919849i	$0.628311\pi$
$642$		0			0
$643$	3.48186	−	1.77410i	0.137311	−	0.0699635i	−0.383985	−	0.923339i	$-0.625449\pi$
$643$	3.48186	−	1.77410i	0.137311	−	0.0699635i	0.521296	+	0.853376i	$0.325449\pi$
$644$		0			0
$645$	−0.354623	−	0.0561668i	−0.0139633	−	0.00221157i
$646$		0			0
$647$			11.0015i			0.432512i	0.976337	+	0.216256i	$0.0693845\pi$
$647$			11.0015i			0.432512i	−0.976337	+	0.216256i	$0.930615\pi$
$648$		0			0
$649$	−1.11443	+	2.18718i	−0.0437450	+	0.0858545i
$650$		0			0
$651$	−2.31506e−5	0	3.18640e-5i	−9.07342e−7	0	1.24885e-6i
$652$		0			0
$653$	13.7335	+	13.7335i	0.537432	+	0.537432i	0.922774	−	0.385342i	$-0.125916\pi$
$653$	13.7335	+	13.7335i	0.537432	+	0.537432i	−0.385342	+	0.922774i	$0.625916\pi$
$654$		0			0
$655$	−16.4233			−0.641711
$656$		0			0
$657$	−19.2520			−0.751091
$658$		0			0
$659$	−8.08834	−	8.08834i	−0.315077	−	0.315077i	0.531796	−	0.846873i	$-0.321517\pi$
$659$	−8.08834	−	8.08834i	−0.315077	−	0.315077i	−0.846873	+	0.531796i	$0.821517\pi$
$660$		0			0
$661$	12.4458	−	17.1301i	0.484084	−	0.666284i	−0.495199	−	0.868779i	$-0.664905\pi$
$661$	12.4458	−	17.1301i	0.484084	−	0.666284i	0.979283	+	0.202495i	$0.0649050\pi$
$662$		0			0
$663$	−12.6475	+	24.8221i	−0.491188	+	0.964012i
$664$		0			0
$665$		0	1.24863e-5i		0	4.84197e-7i
$666$		0			0
$667$	24.0348	+	3.80673i	0.930630	+	0.147397i
$668$		0			0
$669$	26.6181	−	13.5626i	1.02911	−	0.524359i
$670$		0			0
$671$	−17.9804	+	2.84781i	−0.694124	+	0.109938i
$672$		0			0
$673$	−6.74228	+	42.5691i	−0.259896	+	1.64092i	0.419938	+	0.907553i	$0.362052\pi$
$673$	−6.74228	+	42.5691i	−0.259896	+	1.64092i	−0.679834	+	0.733366i	$0.737948\pi$
$674$		0			0
$675$	−4.96950	−	2.53209i	−0.191276	−	0.0974602i
$676$		0			0
$677$	−11.9692	+	3.88901i	−0.460012	+	0.149467i	−0.529850	−	0.848091i	$-0.677752\pi$
$677$	−11.9692	+	3.88901i	−0.460012	+	0.149467i	0.0698380	+	0.997558i	$0.477752\pi$
$678$		0			0
$679$	−7.86777e−6	0	2.42145e-5i	−3.01937e−7	0	9.29268e-7i
$680$		0			0
$681$	−5.35043	−	16.4669i	−0.205029	−	0.631014i
$682$		0			0
$683$	13.8942	−	13.8942i	0.531645	−	0.531645i	−0.389417	−	0.921062i	$-0.627323\pi$
$683$	13.8942	−	13.8942i	0.531645	−	0.531645i	0.921062	+	0.389417i	$0.127323\pi$
$684$		0			0
$685$	2.36051	+	14.9037i	0.0901905	+	0.569441i
$686$		0			0
$687$	−3.05539	+	2.21987i	−0.116570	+	0.0846934i
$688$		0			0
$689$	13.8610	+	19.0781i	0.528063	+	0.726817i
$690$		0			0
$691$	−13.4210	−	26.3402i	−0.510559	−	1.00203i	−0.992082	−	0.125595i	$-0.959916\pi$
$691$	−13.4210	−	26.3402i	−0.510559	−	1.00203i	0.481523	−	0.876434i	$-0.340084\pi$
$692$		0			0
$693$	2.81655e−5	0	2.04634e-5i	1.06992e−6	0	7.77341e-7i
$694$		0			0
$695$	−21.9748	−	7.14003i	−0.833550	−	0.270837i
$696$		0			0
$697$	35.7972	−	18.7171i	1.35592	−	0.708960i
$698$		0			0
$699$	−24.9349	−	8.10183i	−0.943123	−	0.306439i
$700$		0			0
$701$	−32.2279	−	23.4150i	−1.21723	−	0.884371i	−0.221365	−	0.975191i	$-0.571051\pi$
$701$	−32.2279	−	23.4150i	−1.21723	−	0.884371i	−0.995867	+	0.0908201i	$0.971051\pi$
$702$		0			0
$703$	−4.40775	−	8.65071i	−0.166242	−	0.326268i
$704$		0			0
$705$	2.77785	+	3.82338i	0.104620	+	0.143997i
$706$		0			0
$707$	−8.55285e−5	0	6.21401e-5i	−3.21663e−6	0	2.33702e-6i
$708$		0			0
$709$	−2.55392	−	16.1248i	−0.0959144	−	0.605580i	−0.988088	−	0.153888i	$-0.950821\pi$
$709$	−2.55392	−	16.1248i	−0.0959144	−	0.605580i	0.892174	−	0.451692i	$-0.149179\pi$
$710$		0			0
$711$	−4.64654	+	4.64654i	−0.174259	+	0.174259i
$712$		0			0
$713$	−7.47495	−	23.0055i	−0.279939	−	0.861564i
$714$		0			0
$715$	2.49238	−	7.67075i	0.0932096	−	0.286870i
$716$		0			0
$717$	−5.03496	+	1.63596i	−0.188034	+	0.0610959i
$718$		0			0
$719$	−1.63576	−	0.833463i	−0.0610037	−	0.0310829i	0.423223	−	0.906026i	$-0.360899\pi$
$719$	−1.63576	−	0.833463i	−0.0610037	−	0.0310829i	−0.484226	+	0.874943i	$0.660899\pi$
$720$		0			0
$721$	1.08142e−5	0	6.82782e-5i	4.02742e−7	0	2.54281e-6i
$722$		0			0
$723$	2.80239	−	0.443854i	0.104222	−	0.0165071i
$724$		0			0
$725$	2.54518	−	1.29683i	0.0945256	−	0.0481632i
$726$		0			0
$727$	31.4494	+	4.98110i	1.16640	+	0.184739i	0.709450	−	0.704756i	$-0.248943\pi$
$727$	31.4494	+	4.98110i	1.16640	+	0.184739i	0.456945	+	0.889495i	$0.348943\pi$
$728$		0			0
$729$		−	25.4422i		−	0.942303i
$730$		0			0
$731$	0.806488	−	1.58282i	0.0298290	−	0.0585428i
$732$		0			0
$733$	−20.8429	+	28.6878i	−0.769849	+	1.05961i	0.226481	+	0.974016i	$0.427278\pi$
$733$	−20.8429	+	28.6878i	−0.769849	+	1.05961i	−0.996330	+	0.0855911i	$0.972722\pi$
$734$		0			0
$735$	6.31127	+	6.31127i	0.232795	+	0.232795i
$736$		0			0
$737$	−25.1187			−0.925260
$738$		0			0
$739$	−2.15732			−0.0793582			−0.0396791	−	0.999212i	$-0.512634\pi$
$739$	−2.15732			−0.0793582			−0.0396791	+	0.999212i	$0.512634\pi$
$740$		0			0
$741$	−3.58404	−	3.58404i	−0.131663	−	0.131663i
$742$		0			0
$743$	−29.6150	+	40.7616i	−1.08647	+	1.49540i	−0.234276	+	0.972170i	$0.575272\pi$
$743$	−29.6150	+	40.7616i	−1.08647	+	1.49540i	−0.852193	+	0.523227i	$0.824728\pi$
$744$		0			0
$745$	−8.38010	+	16.4469i	−0.307023	+	0.602567i
$746$		0			0
$747$		−	8.16548i		−	0.298759i
$748$		0			0
$749$	−7.71114e−5	0	1.22132e-5i	−2.81759e−6	0	4.46262e-7i
$750$		0			0
$751$	20.5231	−	10.4571i	0.748900	−	0.381584i	−0.0375037	−	0.999296i	$-0.511941\pi$
$751$	20.5231	−	10.4571i	0.748900	−	0.381584i	0.786404	+	0.617713i	$0.211941\pi$
$752$		0			0
$753$	−37.5307	+	5.94428i	−1.36770	+	0.216622i
$754$		0			0
$755$	−1.50857	+	9.52472i	−0.0549024	+	0.346640i
$756$		0			0
$757$	−11.2659	−	5.74029i	−0.409468	−	0.208634i	0.237109	−	0.971483i	$-0.423800\pi$
$757$	−11.2659	−	5.74029i	−0.409468	−	0.208634i	−0.646577	+	0.762849i	$0.723800\pi$
$758$		0			0
$759$	24.0584	−	7.81705i	0.873265	−	0.283741i
$760$		0			0
$761$	4.77234	−	14.6878i	0.172997	−	0.532431i	−0.826539	−	0.562879i	$-0.809694\pi$
$761$	4.77234	−	14.6878i	0.172997	−	0.532431i	0.999536	+	0.0304484i	$0.00969353\pi$
$762$		0			0
$763$	−8.86504e−6	0	2.72838e-5i	−3.20936e−7	0	9.87739e-7i
$764$		0			0
$765$	6.13016	−	6.13016i	0.221636	−	0.221636i
$766$		0			0
$767$	0.571057	+	3.60551i	0.0206197	+	0.130187i
$768$		0			0
$769$	11.1339	−	8.08925i	0.401499	−	0.291706i	−0.368653	−	0.929567i	$-0.620181\pi$
$769$	11.1339	−	8.08925i	0.401499	−	0.291706i	0.770151	+	0.637862i	$0.220181\pi$
$770$		0			0
$771$	−2.54925	−	3.50875i	−0.0918092	−	0.126364i
$772$		0			0
$773$	14.3511	+	28.1657i	0.516175	+	1.01305i	0.991112	+	0.133031i	$0.0424708\pi$
$773$	14.3511	+	28.1657i	0.516175	+	1.01305i	−0.474937	+	0.880020i	$0.657529\pi$
$774$		0			0
$775$	−2.29721	−	1.66902i	−0.0825183	−	0.0599530i
$776$		0			0
$777$	−0.000111586	0	3.62564e-5i	−4.00312e−6	0	1.30069e-6i
$778$		0			0
$779$	1.22611	+	7.24653i	0.0439299	+	0.259634i
$780$		0			0
$781$	−0.870834	−	0.282951i	−0.0311609	−	0.0101248i
$782$		0			0
$783$	12.8892	+	9.36458i	0.460624	+	0.334663i
$784$		0			0
$785$	−6.41636	−	12.5928i	−0.229010	−	0.449457i
$786$		0			0
$787$	11.2359	+	15.4649i	0.400518	+	0.551265i	0.960874	−	0.276987i	$-0.0893358\pi$
$787$	11.2359	+	15.4649i	0.400518	+	0.551265i	−0.560356	+	0.828252i	$0.689336\pi$
$788$		0			0
$789$	−20.2199	+	14.6906i	−0.719849	+	0.523001i
$790$		0			0
$791$	1.69600e−5	0	0.000107081i	6.03027e−7	0	3.80736e-6i
$792$		0			0
$793$	−19.1428	+	19.1428i	−0.679782	+	0.679782i
$794$		0			0
$795$	2.68291	+	8.25715i	0.0951530	+	0.292851i
$796$		0			0
$797$	12.2599	−	37.7320i	0.434267	−	1.33654i	−0.459569	−	0.888142i	$-0.651996\pi$
$797$	12.2599	−	37.7320i	0.434267	−	1.33654i	0.893836	−	0.448394i	$-0.148004\pi$
$798$		0			0
$799$	−22.2382	+	7.22564i	−0.786732	+	0.255625i
$800$		0			0
$801$	19.3695	+	9.86928i	0.684389	+	0.348714i
$802$		0			0
$803$	5.10391	−	32.2248i	0.180113	−	1.13719i
$804$		0			0
$805$	9.15309e−5	0	1.44971e-5i	3.22604e−6	0	5.10955e-7i
$806$		0			0
$807$	−15.9384	+	8.12103i	−0.561059	+	0.285874i
$808$		0			0
$809$	−10.8611	−	1.72023i	−0.381856	−	0.0604800i	−0.0374440	−	0.999299i	$-0.511922\pi$
$809$	−10.8611	−	1.72023i	−0.381856	−	0.0604800i	−0.344412	+	0.938819i	$0.611922\pi$
$810$		0			0
$811$		−	44.1060i		−	1.54877i	−0.632713	−	0.774386i	$-0.718059\pi$
$811$		−	44.1060i		−	1.54877i	0.632713	−	0.774386i	$-0.281941\pi$
$812$		0			0
$813$	−7.30005	+	14.3272i	−0.256024	+	0.502475i
$814$		0			0
$815$	1.39346	−	1.91793i	0.0488108	−	0.0671822i
$816$		0			0
$817$	0.228542	+	0.228542i	0.00799568	+	0.00799568i
$818$		0			0
$819$	5.17728e−5	0		1.80909e−6	0
$820$		0			0
$821$	12.4025			0.432852			0.216426	−	0.976299i	$-0.430560\pi$
$821$	12.4025			0.432852			0.216426	+	0.976299i	$0.430560\pi$
$822$		0			0
$823$	0.441578	+	0.441578i	0.0153924	+	0.0153924i	0.714761	−	0.699369i	$-0.246535\pi$
$823$	0.441578	+	0.441578i	0.0153924	+	0.0153924i	−0.699369	+	0.714761i	$0.746535\pi$
$824$		0			0
$825$	1.74541	−	2.40235i	0.0607673	−	0.0836390i
$826$		0			0
$827$	5.68865	−	11.1646i	0.197814	−	0.388232i	−0.770697	−	0.637201i	$-0.780092\pi$
$827$	5.68865	−	11.1646i	0.197814	−	0.388232i	0.968511	+	0.248970i	$0.0800920\pi$
$828$		0			0
$829$		−	12.1114i		−	0.420647i	−0.977632	−	0.210323i	$-0.932548\pi$
$829$		−	12.1114i		−	0.420647i	0.977632	−	0.210323i	$-0.0674517\pi$
$830$		0			0
$831$	17.0443	+	2.69956i	0.591261	+	0.0936465i
$832$		0			0
$833$	−39.3474	+	20.0485i	−1.36331	+	0.694640i
$834$		0			0
$835$	−7.70260	+	1.21997i	−0.266560	+	0.0422189i
$836$		0			0
$837$	2.47747	−	15.6421i	0.0856338	−	0.540671i
$838$		0			0
$839$	17.4004	+	8.86594i	0.600728	+	0.306086i	0.727781	−	0.685810i	$-0.240552\pi$
$839$	17.4004	+	8.86594i	0.600728	+	0.306086i	−0.127053	+	0.991896i	$0.540552\pi$
$840$		0			0
$841$	19.8203	−	6.44000i	0.683458	−	0.222069i
$842$		0			0
$843$	−10.5072	+	32.3377i	−0.361886	+	1.11377i
$844$		0			0
$845$	0.310787	+	0.956503i	0.0106914	+	0.0329047i
$846$		0			0
$847$	4.28947e−5	0	4.28947e-5i	1.47388e−6	0	1.47388e-6i
$848$		0			0
$849$	−0.115878	−	0.731626i	−0.00397693	−	0.0251093i
$850$		0			0
$851$	58.2966	−	42.3550i	1.99838	−	1.45191i
$852$		0			0
$853$	−8.14895	−	11.2161i	−0.279015	−	0.384031i	0.646392	−	0.763005i	$-0.276277\pi$
$853$	−8.14895	−	11.2161i	−0.279015	−	0.384031i	−0.925407	+	0.378974i	$0.876277\pi$
$854$		0			0
$855$	0.716083	+	1.40539i	0.0244895	+	0.0480634i
$856$		0			0
$857$	7.16572	+	5.20620i	0.244776	+	0.177840i	0.703409	−	0.710786i	$-0.251660\pi$
$857$	7.16572	+	5.20620i	0.244776	+	0.177840i	−0.458632	+	0.888626i	$0.651660\pi$
$858$		0			0
$859$	−6.12452	−	1.98998i	−0.208966	−	0.0678971i	0.202664	−	0.979248i	$-0.435040\pi$
$859$	−6.12452	−	1.98998i	−0.208966	−	0.0678971i	−0.411629	+	0.911351i	$0.635040\pi$
$860$		0			0
$861$	7.23995e−5	0	5.14451e-5i	2.46737e−6	0	1.75324e-6i
$862$		0			0
$863$	12.7974	+	4.15814i	0.435630	+	0.141545i	0.518619	−	0.855006i	$-0.326446\pi$
$863$	12.7974	+	4.15814i	0.435630	+	0.141545i	−0.0829885	+	0.996551i	$0.526446\pi$
$864$		0			0
$865$	−11.0213	−	8.00747i	−0.374737	−	0.272262i
$866$		0			0
$867$	−13.1978	−	25.9021i	−0.448220	−	0.879682i
$868$		0			0
$869$	−6.54573	−	9.00943i	−0.222049	−	0.305624i
$870$		0			0
$871$	−30.2202	+	21.9563i	−1.02397	+	0.743960i
$872$		0			0
$873$	−0.503137	−	3.17668i	−0.0170286	−	0.107514i
$874$		0			0
$875$	7.69220e−6	0	7.69220e-6i	2.60044e−7	0	2.60044e-7i
$876$		0			0
$877$	3.80199	+	11.7013i	0.128384	+	0.395125i	0.994502	−	0.104714i	$-0.0333926\pi$
$877$	3.80199	+	11.7013i	0.128384	+	0.395125i	−0.866118	+	0.499839i	$0.833393\pi$
$878$		0			0
$879$	−1.46936	+	4.52221i	−0.0495602	+	0.152530i
$880$		0			0
$881$	19.7024	−	6.40171i	0.663792	−	0.215679i	0.0423065	−	0.999105i	$-0.486529\pi$
$881$	19.7024	−	6.40171i	0.663792	−	0.215679i	0.621486	+	0.783426i	$0.286529\pi$
$882$		0			0
$883$	−28.5401	−	14.5419i	−0.960451	−	0.489374i	−0.0978182	−	0.995204i	$-0.531186\pi$
$883$	−28.5401	−	14.5419i	−0.960451	−	0.489374i	−0.862633	+	0.505830i	$0.831186\pi$
$884$		0			0
$885$	−0.210245	+	1.32744i	−0.00706732	+	0.0446213i
$886$		0			0
$887$	−42.0552	+	6.66090i	−1.41208	+	0.223651i	−0.815431	−	0.578854i	$-0.803500\pi$
$887$	−42.0552	+	6.66090i	−1.41208	+	0.223651i	−0.596646	+	0.802505i	$0.703500\pi$
$888$		0			0
$889$	9.20552e−5	0	4.69045e-5i	3.08743e−6	0	1.57313e-6i
$890$		0			0
$891$	6.87524	+	1.08893i	0.230329	+	0.0364806i
$892$		0			0
$893$		−	4.25426i		−	0.142363i
$894$		0			0
$895$	0.228459	−	0.448377i	0.00763655	−	0.0149876i
$896$		0			0
$897$	22.1117	−	30.4341i	0.738288	−	1.01617i
$898$		0			0
$899$	5.73543	+	5.73543i	0.191287	+	0.191287i
$900$		0			0
$901$	−42.9563			−1.43108
$902$		0			0
$903$	3.90583e−6	0		1.29978e−7	0
$904$		0			0
$905$	13.0318	+	13.0318i	0.433191	+	0.433191i
$906$		0			0
$907$	−25.8966	+	35.6436i	−0.859882	+	1.18353i	0.121716	+	0.992565i	$0.461160\pi$
$907$	−25.8966	+	35.6436i	−0.859882	+	1.18353i	−0.981598	+	0.190961i	$0.938840\pi$
$908$		0			0
$909$	6.06295	−	11.8992i	0.201095	−	0.394672i
$910$		0			0
$911$		−	55.1976i		−	1.82878i	−0.404836	−	0.914389i	$-0.632671\pi$
$911$		−	55.1976i		−	1.82878i	0.404836	−	0.914389i	$-0.367329\pi$
$912$		0			0
$913$	13.6677	+	2.16476i	0.452336	+	0.0716430i
$914$		0			0
$915$	−8.88073	+	4.52496i	−0.293588	+	0.149590i
$916$		0			0
$917$	0.000176460	0	2.79485e-5i	5.82721e−6	0	9.22940e-7i
$918$		0			0
$919$	−2.92807	+	18.4871i	−0.0965881	+	0.609833i	0.891150	+	0.453710i	$0.149900\pi$
$919$	−2.92807	+	18.4871i	−0.0965881	+	0.609833i	−0.987738	+	0.156123i	$0.950100\pi$
$920$		0			0
$921$	13.7152	+	6.98822i	0.451930	+	0.230270i
$922$		0			0
$923$	−1.29502	+	0.420779i	−0.0426263	+	0.0138501i
$924$		0			0
$925$	2.61388	−	8.04470i	0.0859438	−	0.264508i
$926$		0			0
$927$	2.69854	+	8.30524i	0.0886316	+	0.272780i
$928$		0			0
$929$	−17.5578	+	17.5578i	−0.576053	+	0.576053i	−0.933813	−	0.357761i	$-0.883540\pi$
$929$	−17.5578	+	17.5578i	−0.576053	+	0.576053i	0.357761	+	0.933813i	$0.383540\pi$
$930$		0			0
$931$	−1.25689	−	7.93570i	−0.0411930	−	0.260082i
$932$		0			0
$933$	−4.16138	+	3.02342i	−0.136237	+	0.0989822i
$934$		0			0
$935$	8.63576	+	11.8861i	0.282420	+	0.388717i
$936$		0			0
$937$	−4.10045	−	8.04758i	−0.133956	−	0.262903i	0.814279	−	0.580474i	$-0.197133\pi$
$937$	−4.10045	−	8.04758i	−0.133956	−	0.262903i	−0.948234	+	0.317571i	$0.897133\pi$
$938$		0			0
$939$	25.7706	+	18.7235i	0.840993	+	0.611017i
$940$		0			0
$941$	18.1330	+	5.89178i	0.591120	+	0.192067i	0.589276	−	0.807932i	$-0.299413\pi$
$941$	18.1330	+	5.89178i	0.591120	+	0.192067i	0.00184405	+	0.999998i	$0.499413\pi$
$942$		0			0
$943$	−51.6973	+	17.4015i	−1.68350	+	0.566672i
$944$		0			0
$945$	5.77038e−5	0	1.87491e-5i	1.87710e−6	0	6.09908e-7i
$946$		0			0
$947$	−29.1060	−	21.1468i	−0.945818	−	0.687177i	0.00399584	−	0.999992i	$-0.498728\pi$
$947$	−29.1060	−	21.1468i	−0.945818	−	0.687177i	−0.949814	+	0.312815i	$0.898728\pi$
$948$		0			0
$949$	−22.0272	−	43.2309i	−0.715034	−	1.40333i
$950$		0			0
$951$	17.8133	+	24.5180i	0.577637	+	0.795049i
$952$		0			0
$953$	−7.66971	+	5.57237i	−0.248446	+	0.180507i	−0.705038	−	0.709170i	$-0.749070\pi$
$953$	−7.66971	+	5.57237i	−0.248446	+	0.180507i	0.456592	+	0.889676i	$0.349070\pi$
$954$		0			0
$955$	3.56572	+	22.5131i	0.115384	+	0.728505i
$956$		0			0
$957$	−5.99792	+	5.99792i	−0.193885	+	0.193885i
$958$		0			0
$959$	−5.07250e−5	0	0.000156115i	−1.63799e−6	0	5.04123e-6i
$960$		0			0
$961$	−7.08798	+	21.8146i	−0.228644	+	0.703695i
$962$		0			0
$963$	9.37970	−	3.04765i	0.302257	−	0.0982091i
$964$		0			0
$965$	−11.0682	−	5.63953i	−0.356298	−	0.181543i
$966$		0			0
$967$	−4.81429	+	30.3962i	−0.154817	+	0.977477i	0.780882	+	0.624678i	$0.214770\pi$
$967$	−4.81429	+	30.3962i	−0.154817	+	0.977477i	−0.935699	+	0.352798i	$0.885230\pi$
$968$		0			0
$969$	9.11924	−	1.44435i	0.292952	−	0.0463990i
$970$		0			0
$971$	42.9764	−	21.8975i	1.37918	−	0.702726i	0.402097	−	0.915597i	$-0.368282\pi$
$971$	42.9764	−	21.8975i	1.37918	−	0.702726i	0.977080	+	0.212871i	$0.0682815\pi$
$972$		0			0
$973$	0.000248258	0	3.93202e-5i	7.95879e−6	0	1.26055e-6i
$974$		0			0
$975$		−	4.41592i		−	0.141422i
$976$		0			0
$977$	−17.5600	+	34.4634i	−0.561793	+	1.10258i	0.419083	+	0.907948i	$0.362352\pi$
$977$	−17.5600	+	34.4634i	−0.561793	+	1.10258i	−0.980876	+	0.194633i	$0.937648\pi$
$978$		0			0
$979$	−21.6547	+	29.8051i	−0.692087	+	0.952576i
$980$		0			0
$981$	2.56252	+	2.56252i	0.0818150	+	0.0818150i
$982$		0			0
$983$	8.94642			0.285347			0.142673	−	0.989770i	$-0.454430\pi$
$983$	8.94642			0.285347			0.142673	+	0.989770i	$0.454430\pi$
$984$		0			0
$985$	14.6461			0.466663
$986$		0			0
$987$	−3.63530e−5	0	3.63530e-5i	−1.15713e−6	0	1.15713e-6i
$988$		0			0
$989$	−1.40999	+	1.94068i	−0.0448350	+	0.0617100i
$990$		0			0
$991$	−7.94721	+	15.5973i	−0.252451	+	0.495464i	−0.982100	−	0.188358i	$-0.939683\pi$
$991$	−7.94721	+	15.5973i	−0.252451	+	0.495464i	0.729649	+	0.683822i	$0.239683\pi$
$992$		0			0
$993$		−	13.9722i		−	0.443393i
$994$		0			0
$995$	18.3733	+	2.91005i	0.582474	+	0.0922548i
$996$		0			0
$997$	45.1209	−	22.9902i	1.42899	−	0.728109i	0.443255	−	0.896395i	$-0.353823\pi$
$997$	45.1209	−	22.9902i	1.42899	−	0.728109i	0.985738	+	0.168287i	$0.0538235\pi$
$998$		0			0
$999$	46.5967	−	7.38020i	1.47426	−	0.233499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bo.b.21.6	✓	64
41.2	even	20	inner	820.2.bo.b.781.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bo.b.21.6	✓	64	1.1	even	1	trivial
820.2.bo.b.781.6	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)

\(f(q)\)	\(=\)	\(q+(0.901610 + 0.901610i) q^{3} +(0.587785 - 0.809017i) q^{5} +(-4.93870e-6 + 9.69274e-6i) q^{7} -1.37420i q^{9} +(2.30019 + 0.364315i) q^{11} +(3.08580 - 1.57229i) q^{13} +(1.25937 - 0.199465i) q^{15} +(-0.986892 + 6.23099i) q^{17} +(-1.02270 - 0.521092i) q^{19} +(-1.31918e-5 + 4.28629e-6i) q^{21} +(2.63248 - 8.10194i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(3.94382 - 3.94382i) q^{27} +(0.446858 + 2.82135i) q^{29} +(2.29721 - 1.66902i) q^{31} +(1.74541 + 2.40235i) q^{33} +(4.93870e-6 + 9.69274e-6i) q^{35} +(6.84323 + 4.97190i) q^{37} +(4.19978 + 1.36459i) q^{39} +(-3.81801 - 5.14031i) q^{41} +(-0.267806 - 0.0870154i) q^{43} +(-1.11175 - 0.807734i) q^{45} +(1.68269 + 3.30246i) q^{47} +(4.11450 + 5.66312i) q^{49} +(-6.50772 + 4.72813i) q^{51} +(1.06518 + 6.72527i) q^{53} +(1.64676 - 1.64676i) q^{55} +(-0.452255 - 1.39190i) q^{57} +(-0.325718 + 1.00246i) q^{59} +(-7.43430 + 2.41555i) q^{61} +(1.33197e-5 + 6.78675e-6i) q^{63} +(0.541776 - 3.42064i) q^{65} +(-10.6530 + 1.68727i) q^{67} +(9.67826 - 4.93132i) q^{69} +(-0.388333 - 0.0615060i) q^{71} -14.0096i q^{73} +(0.578869 - 1.13609i) q^{75} +(-1.48912e-5 + 2.04959e-5i) q^{77} +(-3.38127 - 3.38127i) q^{79} +2.98898 q^{81} +5.94200 q^{83} +(4.46090 + 4.46090i) q^{85} +(-2.14087 + 2.94665i) q^{87} +(-7.18184 + 14.0952i) q^{89} +3.76749e-5i q^{91} +(3.57600 + 0.566382i) q^{93} +(-1.02270 + 0.521092i) q^{95} +(2.31166 - 0.366131i) q^{97} +(0.500641 - 3.16092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) \) 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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