LMFDB - Embedded newform 800.2.be.a.529.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

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

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

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.10
Character	$\chi$	$=$	800.529
Dual form			800.2.be.a.369.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06117 - 0.770982i) q^{3} +(-1.15605 + 1.91404i) q^{5} -2.31589i q^{7} +(-0.395392 - 1.21689i) q^{9} +O(q^{10})$	\(q+(-1.06117 - 0.770982i) q^{3} +(-1.15605 + 1.91404i) q^{5} -2.31589i q^{7} +(-0.395392 - 1.21689i) q^{9} +(0.219837 + 0.0714294i) q^{11} +(0.659008 + 2.02822i) q^{13} +(2.70245 - 1.13982i) q^{15} +(1.33923 + 1.84329i) q^{17} +(0.307368 + 0.423055i) q^{19} +(-1.78551 + 2.45754i) q^{21} +(-6.59576 - 2.14309i) q^{23} +(-2.32708 - 4.42546i) q^{25} +(-1.73461 + 5.33859i) q^{27} +(-5.13469 + 7.06729i) q^{29} +(-6.95750 + 5.05492i) q^{31} +(-0.178213 - 0.245289i) q^{33} +(4.43271 + 2.67729i) q^{35} +(-2.46601 - 7.58959i) q^{37} +(0.864403 - 2.66036i) q^{39} +(1.84490 + 5.67801i) q^{41} -9.74670 q^{43} +(2.78627 + 0.649995i) q^{45} +(0.657286 - 0.904676i) q^{47} +1.63664 q^{49} -2.98855i q^{51} +(-3.51671 - 2.55504i) q^{53} +(-0.390862 + 0.338200i) q^{55} -0.685906i q^{57} +(-4.66275 + 1.51502i) q^{59} +(-2.16726 - 0.704186i) q^{61} +(-2.81819 + 0.915685i) q^{63} +(-4.64393 - 1.08336i) q^{65} +(-2.55761 + 1.85821i) q^{67} +(5.34690 + 7.35938i) q^{69} +(5.30236 + 3.85239i) q^{71} +(-5.24971 - 1.70573i) q^{73} +(-0.942529 + 6.49028i) q^{75} +(0.165423 - 0.509119i) q^{77} +(10.1775 + 7.39438i) q^{79} +(2.85122 - 2.07153i) q^{81} +(-4.44876 + 3.23222i) q^{83} +(-5.07634 + 0.432393i) q^{85} +(10.8975 - 3.54081i) q^{87} +(-4.88895 + 15.0466i) q^{89} +(4.69713 - 1.52619i) q^{91} +11.2803 q^{93} +(-1.16508 + 0.0992390i) q^{95} +(7.50193 - 10.3255i) q^{97} -0.295760i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.06117	−	0.770982i	−0.612664	−	0.445127i	0.237687	−	0.971342i	$-0.423611\pi$
$3$	−1.06117	−	0.770982i	−0.612664	−	0.445127i	−0.850351	+	0.526215i	$0.823611\pi$
$4$		0			0
$5$	−1.15605	+	1.91404i	−0.517003	+	0.855984i
$5$	−1.15605	+	1.91404i	−0.517003	+	0.855984i
$6$		0			0
$7$		−	2.31589i		−	0.875325i	−0.899139	−	0.437662i	$-0.855806\pi$
$7$		−	2.31589i		−	0.875325i	0.899139	−	0.437662i	$-0.144194\pi$
$8$		0			0
$9$	−0.395392	−	1.21689i	−0.131797	−	0.405630i
$10$		0			0
$11$	0.219837	+	0.0714294i	0.0662834	+	0.0215368i	0.341971	−	0.939711i	$-0.388906\pi$
$11$	0.219837	+	0.0714294i	0.0662834	+	0.0215368i	−0.275688	+	0.961247i	$0.588906\pi$
$12$		0			0
$13$	0.659008	+	2.02822i	0.182776	+	0.562526i	0.999903	−	0.0139312i	$-0.00443460\pi$
$13$	0.659008	+	2.02822i	0.182776	+	0.562526i	−0.817127	+	0.576458i	$0.804435\pi$
$14$		0			0
$15$	2.70245	−	1.13982i	0.697770	−	0.294299i
$16$		0			0
$17$	1.33923	+	1.84329i	0.324810	+	0.447063i	0.939928	−	0.341372i	$-0.110892\pi$
$17$	1.33923	+	1.84329i	0.324810	+	0.447063i	−0.615118	+	0.788435i	$0.710892\pi$
$18$		0			0
$19$	0.307368	+	0.423055i	0.0705150	+	0.0970555i	0.842818	−	0.538199i	$-0.180895\pi$
$19$	0.307368	+	0.423055i	0.0705150	+	0.0970555i	−0.772303	+	0.635255i	$0.780895\pi$
$20$		0			0
$21$	−1.78551	+	2.45754i	−0.389630	+	0.536280i
$22$		0			0
$23$	−6.59576	−	2.14309i	−1.37531	−	0.446865i	−0.474185	−	0.880425i	$-0.657257\pi$
$23$	−6.59576	−	2.14309i	−1.37531	−	0.446865i	−0.901125	+	0.433560i	$0.857257\pi$
$24$		0			0
$25$	−2.32708	−	4.42546i	−0.465417	−	0.885092i
$26$		0			0
$27$	−1.73461	+	5.33859i	−0.333826	+	1.02741i
$28$		0			0
$29$	−5.13469	+	7.06729i	−0.953487	+	1.31236i	−0.00352661	+	0.999994i	$0.501123\pi$
$29$	−5.13469	+	7.06729i	−0.953487	+	1.31236i	−0.949961	+	0.312369i	$0.898877\pi$
$30$		0			0
$31$	−6.95750	+	5.05492i	−1.24960	+	0.907890i	−0.998199	−	0.0599915i	$-0.980893\pi$
$31$	−6.95750	+	5.05492i	−1.24960	+	0.907890i	−0.251405	+	0.967882i	$0.580893\pi$
$32$		0			0
$33$	−0.178213	−	0.245289i	−0.0310228	−	0.0426993i
$34$		0			0
$35$	4.43271	+	2.67729i	0.749264	+	0.452545i
$36$		0			0
$37$	−2.46601	−	7.58959i	−0.405409	−	1.24772i	−0.920553	−	0.390617i	$-0.872262\pi$
$37$	−2.46601	−	7.58959i	−0.405409	−	1.24772i	0.515144	−	0.857104i	$-0.327738\pi$
$38$		0			0
$39$	0.864403	−	2.66036i	0.138415	−	0.425998i
$40$		0			0
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	0.985445	+	0.169996i	$0.0543756\pi$
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	−0.697320	+	0.716760i	$0.745624\pi$
$42$		0			0
$43$	−9.74670			−1.48636			−0.743179	−	0.669093i	$-0.766683\pi$
$43$	−9.74670			−1.48636			−0.743179	+	0.669093i	$0.766683\pi$
$44$		0			0
$45$	2.78627	+	0.649995i	0.415352	+	0.0968956i
$46$		0			0
$47$	0.657286	−	0.904676i	0.0958750	−	0.131961i	−0.758384	−	0.651807i	$-0.774011\pi$
$47$	0.657286	−	0.904676i	0.0958750	−	0.131961i	0.854259	+	0.519847i	$0.174011\pi$
$48$		0			0
$49$	1.63664			0.233806
$50$		0			0
$51$		−	2.98855i		−	0.418481i
$52$		0			0
$53$	−3.51671	−	2.55504i	−0.483057	−	0.350962i	0.319451	−	0.947603i	$-0.396502\pi$
$53$	−3.51671	−	2.55504i	−0.483057	−	0.350962i	−0.802508	+	0.596641i	$0.796502\pi$
$54$		0			0
$55$	−0.390862	+	0.338200i	−0.0527038	+	0.0456029i
$56$		0			0
$57$		−	0.685906i		−	0.0908505i
$58$		0			0
$59$	−4.66275	+	1.51502i	−0.607038	+	0.197239i	−0.596377	−	0.802705i	$-0.703394\pi$
$59$	−4.66275	+	1.51502i	−0.607038	+	0.197239i	−0.0106611	+	0.999943i	$0.503394\pi$
$60$		0			0
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	0.166966	−	0.985963i	$-0.446603\pi$
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	−0.444456	+	0.895801i	$0.646603\pi$
$62$		0			0
$63$	−2.81819	+	0.915685i	−0.355058	+	0.115365i
$64$		0			0
$65$	−4.64393	−	1.08336i	−0.576009	−	0.134374i
$66$		0			0
$67$	−2.55761	+	1.85821i	−0.312462	+	0.227017i	−0.732952	−	0.680280i	$-0.761858\pi$
$67$	−2.55761	+	1.85821i	−0.312462	+	0.227017i	0.420490	+	0.907297i	$0.361858\pi$
$68$		0			0
$69$	5.34690	+	7.35938i	0.643692	+	0.885966i
$70$		0			0
$71$	5.30236	+	3.85239i	0.629274	+	0.457194i	0.856149	−	0.516730i	$-0.172851\pi$
$71$	5.30236	+	3.85239i	0.629274	+	0.457194i	−0.226875	+	0.973924i	$0.572851\pi$
$72$		0			0
$73$	−5.24971	−	1.70573i	−0.614432	−	0.199641i	−0.0147656	−	0.999891i	$-0.504700\pi$
$73$	−5.24971	−	1.70573i	−0.614432	−	0.199641i	−0.599667	+	0.800250i	$0.704700\pi$
$74$		0			0
$75$	−0.942529	+	6.49028i	−0.108834	+	0.749433i
$76$		0			0
$77$	0.165423	−	0.509119i	0.0188517	−	0.0580195i
$78$		0			0
$79$	10.1775	+	7.39438i	1.14506	+	0.831933i	0.987816	−	0.155628i	$-0.0497400\pi$
$79$	10.1775	+	7.39438i	1.14506	+	0.831933i	0.157241	+	0.987560i	$0.449740\pi$
$80$		0			0
$81$	2.85122	−	2.07153i	0.316802	−	0.230170i
$82$		0			0
$83$	−4.44876	+	3.23222i	−0.488315	+	0.354782i	−0.804536	−	0.593904i	$-0.797586\pi$
$83$	−4.44876	+	3.23222i	−0.488315	+	0.354782i	0.316221	+	0.948686i	$0.397586\pi$
$84$		0			0
$85$	−5.07634	+	0.432393i	−0.550606	+	0.0468996i
$86$		0			0
$87$	10.8975	−	3.54081i	1.16834	−	0.379615i
$88$		0			0
$89$	−4.88895	+	15.0466i	−0.518227	+	1.59494i	0.259105	+	0.965849i	$0.416573\pi$
$89$	−4.88895	+	15.0466i	−0.518227	+	1.59494i	−0.777332	+	0.629091i	$0.783427\pi$
$90$		0			0
$91$	4.69713	−	1.52619i	0.492393	−	0.159988i
$92$		0			0
$93$	11.2803			1.16971
$94$		0			0
$95$	−1.16508	+	0.0992390i	−0.119534	+	0.0101817i
$96$		0			0
$97$	7.50193	−	10.3255i	0.761706	−	1.04840i	−0.235364	−	0.971907i	$-0.575628\pi$
$97$	7.50193	−	10.3255i	0.761706	−	1.04840i	0.997070	−	0.0764911i	$-0.0243717\pi$
$98$		0			0
$99$		−	0.295760i		−	0.0297250i
$100$		0			0
$101$		−	11.5894i		−	1.15318i	−0.817032	−	0.576592i	$-0.804382\pi$
$101$		−	11.5894i		−	1.15318i	0.817032	−	0.576592i	$-0.195618\pi$
$102$		0			0
$103$	3.94133	−	5.42478i	0.388351	−	0.534519i	−0.569422	−	0.822045i	$-0.692833\pi$
$103$	3.94133	−	5.42478i	0.388351	−	0.534519i	0.957773	+	0.287526i	$0.0928329\pi$
$104$		0			0
$105$	−2.63969	−	6.25859i	−0.257607	−	0.610776i
$106$		0			0
$107$	7.65011			0.739564			0.369782	−	0.929119i	$-0.379432\pi$
$107$	7.65011			0.739564			0.369782	+	0.929119i	$0.379432\pi$
$108$		0			0
$109$	−6.41848	+	2.08549i	−0.614779	+	0.199754i	−0.599821	−	0.800134i	$-0.704761\pi$
$109$	−6.41848	+	2.08549i	−0.614779	+	0.199754i	−0.0149580	+	0.999888i	$0.504761\pi$
$110$		0			0
$111$	−3.23459	+	9.95506i	−0.307014	+	0.944892i
$112$		0			0
$113$	−14.4512	+	4.69549i	−1.35946	+	0.441714i	−0.895862	−	0.444333i	$-0.853441\pi$
$113$	−14.4512	+	4.69549i	−1.35946	+	0.441714i	−0.463595	+	0.886047i	$0.653441\pi$
$114$		0			0
$115$	11.7270	−	10.1470i	1.09355	−	0.946213i
$116$		0			0
$117$	2.20755	−	1.60388i	0.204088	−	0.148279i
$118$		0			0
$119$	4.26886	−	3.10151i	0.391325	−	0.284315i
$120$		0			0
$121$	−8.85596	−	6.43423i	−0.805087	−	0.584930i
$122$		0			0
$123$	2.41990	−	7.44769i	0.218195	−	0.671536i
$124$		0			0
$125$	11.1607	+	0.661940i	0.998246	+	0.0592057i
$126$		0			0
$127$	4.34009	+	1.41018i	0.385121	+	0.125133i	0.495177	−	0.868792i	$-0.335103\pi$
$127$	4.34009	+	1.41018i	0.385121	+	0.125133i	−0.110056	+	0.993925i	$0.535103\pi$
$128$		0			0
$129$	10.3429	+	7.51453i	0.910638	+	0.661618i
$130$		0			0
$131$	9.12255	+	12.5561i	0.797041	+	1.09703i	0.993195	+	0.116460i	$0.0371547\pi$
$131$	9.12255	+	12.5561i	0.797041	+	1.09703i	−0.196154	+	0.980573i	$0.562845\pi$
$132$		0			0
$133$	0.979750	−	0.711830i	0.0849551	−	0.0617235i
$134$		0			0
$135$	−8.21295	−	9.49180i	−0.706859	−	0.816924i
$136$		0			0
$137$	13.9802	−	4.54244i	1.19441	−	0.388087i	0.356708	−	0.934216i	$-0.383899\pi$
$137$	13.9802	−	4.54244i	1.19441	−	0.388087i	0.837701	+	0.546129i	$0.183899\pi$
$138$		0			0
$139$	−5.61357	−	1.82396i	−0.476137	−	0.154706i	0.0611104	−	0.998131i	$-0.480536\pi$
$139$	−5.61357	−	1.82396i	−0.476137	−	0.154706i	−0.537247	+	0.843425i	$0.680536\pi$
$140$		0			0
$141$	−1.39498	+	0.453256i	−0.117478	+	0.0381710i
$142$		0			0
$143$			0.492950i			0.0412225i
$144$		0			0
$145$	−7.59109	−	17.9981i	−0.630406	−	1.49466i
$146$		0			0
$147$	−1.73675	−	1.26182i	−0.143245	−	0.104073i
$148$		0			0
$149$		−	9.14052i		−	0.748820i	−0.927263	−	0.374410i	$-0.877845\pi$
$149$		−	9.14052i		−	0.748820i	0.927263	−	0.374410i	$-0.122155\pi$
$150$		0			0
$151$	−8.59512			−0.699461			−0.349730	−	0.936850i	$-0.613727\pi$
$151$	−8.59512			−0.699461			−0.349730	+	0.936850i	$0.613727\pi$
$152$		0			0
$153$	1.71356	−	2.35851i	0.138533	−	0.190675i
$154$		0			0
$155$	−1.63207	−	19.1607i	−0.131091	−	1.53902i
$156$		0			0
$157$	4.64663			0.370842			0.185421	−	0.982659i	$-0.440635\pi$
$157$	4.64663			0.370842			0.185421	+	0.982659i	$0.440635\pi$
$158$		0			0
$159$	1.76192	+	5.42264i	0.139730	+	0.430043i
$160$		0			0
$161$	−4.96317	+	15.2751i	−0.391152	+	1.20384i
$162$		0			0
$163$	−4.05889	−	12.4920i	−0.317917	−	0.978448i	−0.974537	−	0.224226i	$-0.928015\pi$
$163$	−4.05889	−	12.4920i	−0.317917	−	0.978448i	0.656620	−	0.754221i	$-0.271985\pi$
$164$		0			0
$165$	0.675515	−	0.0575391i	0.0525888	−	0.00447941i
$166$		0			0
$167$	−12.2739	−	16.8935i	−0.949780	−	1.30726i	−0.951625	−	0.307261i	$-0.900587\pi$
$167$	−12.2739	−	16.8935i	−0.949780	−	1.30726i	0.00184537	−	0.999998i	$-0.499413\pi$
$168$		0			0
$169$	6.83785	−	4.96799i	0.525988	−	0.382153i
$170$		0			0
$171$	0.393281	−	0.541305i	0.0300750	−	0.0413947i
$172$		0			0
$173$	2.43455	−	7.49277i	0.185095	−	0.569664i	−0.814855	−	0.579665i	$-0.803183\pi$
$173$	2.43455	−	7.49277i	0.185095	−	0.569664i	0.999950	+	0.0100007i	$0.00318338\pi$
$174$		0			0
$175$	−10.2489	+	5.38927i	−0.774743	+	0.407391i
$176$		0			0
$177$	6.11600	+	1.98721i	0.459706	+	0.149368i
$178$		0			0
$179$	9.43646	−	12.9882i	0.705314	−	0.970782i	−0.294571	−	0.955630i	$-0.595177\pi$
$179$	9.43646	−	12.9882i	0.705314	−	0.970782i	0.999885	−	0.0151522i	$-0.00482327\pi$
$180$		0			0
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	−0.998029	−	0.0627560i	$-0.980011\pi$
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	0.248723	−	0.968575i	$-0.419989\pi$
$182$		0			0
$183$	1.75691	+	2.41818i	0.129874	+	0.178757i
$184$		0			0
$185$	17.3776	+	4.05394i	1.27763	+	0.298051i
$186$		0			0
$187$	0.162747	+	0.500883i	0.0119012	+	0.0366282i
$188$		0			0
$189$	12.3636	+	4.01717i	0.899319	+	0.292206i
$190$		0			0
$191$	0.923572	+	2.84246i	0.0668273	+	0.205673i	0.978894	−	0.204369i	$-0.0655141\pi$
$191$	0.923572	+	2.84246i	0.0668273	+	0.205673i	−0.912067	+	0.410042i	$0.865514\pi$
$192$		0			0
$193$			14.9349i			1.07504i	0.843252	+	0.537518i	$0.180638\pi$
$193$			14.9349i			1.07504i	−0.843252	+	0.537518i	$0.819362\pi$
$194$		0			0
$195$	4.09273	+	4.73001i	0.293087	+	0.338723i
$196$		0			0
$197$	22.2749	+	16.1837i	1.58702	+	1.15304i	0.908039	+	0.418887i	$0.137580\pi$
$197$	22.2749	+	16.1837i	1.58702	+	1.15304i	0.678984	+	0.734153i	$0.262420\pi$
$198$		0			0
$199$	11.3822			0.806862			0.403431	−	0.915010i	$-0.367818\pi$
$199$	11.3822			0.806862			0.403431	+	0.915010i	$0.367818\pi$
$200$		0			0
$201$	4.14670			0.292485
$202$		0			0
$203$	16.3671	+	11.8914i	1.14874	+	0.834611i
$204$		0			0
$205$	−13.0007	−	3.03288i	−0.908010	−	0.211825i
$206$		0			0
$207$			8.87368i			0.616763i
$208$		0			0
$209$	0.0373522	+	0.114958i	0.00258371	+	0.00795183i
$210$		0			0
$211$	−15.0746	−	4.89802i	−1.03778	−	0.337194i	−0.259916	−	0.965631i	$-0.583695\pi$
$211$	−15.0746	−	4.89802i	−1.03778	−	0.337194i	−0.777860	+	0.628438i	$0.783695\pi$
$212$		0			0
$213$	−2.65656	−	8.17604i	−0.182024	−	0.560213i
$214$		0			0
$215$	11.2677	−	18.6556i	0.768451	−	1.27230i
$216$		0			0
$217$	11.7066	+	16.1128i	0.794699	+	1.09381i
$218$		0			0
$219$	4.25572	+	5.85750i	0.287575	+	0.395813i
$220$		0			0
$221$	−2.85603	+	3.93099i	−0.192117	+	0.264427i
$222$		0			0
$223$	−22.1415	−	7.19420i	−1.48270	−	0.481759i	−0.547783	−	0.836620i	$-0.684528\pi$
$223$	−22.1415	−	7.19420i	−1.48270	−	0.481759i	−0.934919	+	0.354861i	$0.884528\pi$
$224$		0			0
$225$	−4.46519	+	4.58160i	−0.297679	+	0.305440i
$226$		0			0
$227$	−1.38398	+	4.25947i	−0.0918583	+	0.282711i	−0.986422	−	0.164229i	$-0.947486\pi$
$227$	−1.38398	+	4.25947i	−0.0918583	+	0.282711i	0.894564	+	0.446940i	$0.147486\pi$
$228$		0			0
$229$	2.99987	−	4.12897i	0.198237	−	0.272850i	−0.698313	−	0.715793i	$-0.746066\pi$
$229$	2.99987	−	4.12897i	0.198237	−	0.272850i	0.896550	+	0.442943i	$0.146066\pi$
$230$		0			0
$231$	−0.568062	+	0.412721i	−0.0373757	+	0.0271551i
$232$		0			0
$233$	−2.05646	−	2.83047i	−0.134723	−	0.185430i	0.736325	−	0.676628i	$-0.236559\pi$
$233$	−2.05646	−	2.83047i	−0.134723	−	0.185430i	−0.871048	+	0.491197i	$0.836559\pi$
$234$		0			0
$235$	0.971727	+	2.30392i	0.0633885	+	0.150291i
$236$		0			0
$237$	−5.09907	−	15.6933i	−0.331220	−	1.01939i
$238$		0			0
$239$	−6.27635	+	19.3166i	−0.405983	+	1.24949i	0.514088	+	0.857738i	$0.328131\pi$
$239$	−6.27635	+	19.3166i	−0.405983	+	1.24949i	−0.920071	+	0.391751i	$0.871869\pi$
$240$		0			0
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	0.936068	+	0.351819i	$0.114437\pi$
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	−0.550501	+	0.834835i	$0.685563\pi$
$242$		0			0
$243$	12.2172			0.783736
$244$		0			0
$245$	−1.89205	+	3.13260i	−0.120879	+	0.200134i
$246$		0			0
$247$	−0.655490	+	0.902205i	−0.0417079	+	0.0574059i
$248$		0			0
$249$	7.21286			0.457096
$250$		0			0
$251$		−	4.56980i		−	0.288443i	−0.989545	−	0.144222i	$-0.953932\pi$
$251$		−	4.56980i		−	0.288443i	0.989545	−	0.144222i	$-0.0460679\pi$
$252$		0			0
$253$	−1.29691	−	0.942261i	−0.0815361	−	0.0592395i
$254$		0			0
$255$	5.72020	+	3.45493i	0.358213	+	0.216356i
$256$		0			0
$257$		−	27.4389i		−	1.71159i	−0.517312	−	0.855797i	$-0.673067\pi$
$257$		−	27.4389i		−	1.71159i	0.517312	−	0.855797i	$-0.326933\pi$
$258$		0			0
$259$	−17.5767	+	5.71101i	−1.09216	+	0.354865i
$260$		0			0
$261$	10.6303	+	3.45400i	0.658001	+	0.213798i
$262$		0			0
$263$	−12.2444	+	3.97845i	−0.755022	+	0.245322i	−0.661141	−	0.750262i	$-0.729927\pi$
$263$	−12.2444	+	3.97845i	−0.755022	+	0.245322i	−0.0938814	+	0.995583i	$0.529927\pi$
$264$		0			0
$265$	8.95595	−	3.77736i	0.550160	−	0.232041i
$266$		0			0
$267$	16.7887	−	12.1977i	1.02745	−	0.746486i
$268$		0			0
$269$	0.897279	+	1.23500i	0.0547081	+	0.0752992i	0.835495	−	0.549499i	$-0.185181\pi$
$269$	0.897279	+	1.23500i	0.0547081	+	0.0752992i	−0.780786	+	0.624798i	$0.785181\pi$
$270$		0			0
$271$	19.8030	+	14.3877i	1.20294	+	0.873990i	0.994571	−	0.104059i	$-0.0331830\pi$
$271$	19.8030	+	14.3877i	1.20294	+	0.873990i	0.208373	+	0.978049i	$0.433183\pi$
$272$		0			0
$273$	−6.16110	−	2.00186i	−0.372887	−	0.121158i
$274$		0			0
$275$	−0.195471	−	1.13910i	−0.0117874	−	0.0686904i
$276$		0			0
$277$	−8.46626	+	26.0565i	−0.508689	+	1.56558i	0.285791	+	0.958292i	$0.407744\pi$
$277$	−8.46626	+	26.0565i	−0.508689	+	1.56558i	−0.794480	+	0.607290i	$0.792256\pi$
$278$		0			0
$279$	8.90222	+	6.46784i	0.532962	+	0.387220i
$280$		0			0
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.408116	+	0.912930i	$0.633814\pi$
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.994363	+	0.106031i	$0.966186\pi$
$282$		0			0
$283$	8.02169	−	5.82810i	0.476840	−	0.346444i	−0.323261	−	0.946310i	$-0.604779\pi$
$283$	8.02169	−	5.82810i	0.476840	−	0.346444i	0.800101	+	0.599865i	$0.204779\pi$
$284$		0			0
$285$	1.31285	+	0.792944i	0.0777666	+	0.0469700i
$286$		0			0
$287$	13.1497	−	4.27258i	0.776200	−	0.252203i
$288$		0			0
$289$	3.64911	−	11.2308i	0.214653	−	0.660635i
$290$		0			0
$291$	−15.9216	+	5.17324i	−0.933340	+	0.303261i
$292$		0			0
$293$	−6.22226			−0.363508			−0.181754	−	0.983344i	$-0.558177\pi$
$293$	−6.22226			−0.363508			−0.181754	+	0.983344i	$0.558177\pi$
$294$		0			0
$295$	2.49058	−	10.6761i	0.145007	−	0.621587i
$296$		0			0
$297$	−0.762664	+	1.04972i	−0.0442542	+	0.0609107i
$298$		0			0
$299$		−	14.7899i		−	0.855324i
$300$		0			0
$301$			22.5723i			1.30105i
$302$		0			0
$303$	−8.93519	+	12.2982i	−0.513313	+	0.706515i
$304$		0			0
$305$	3.85331	−	3.33415i	0.220640	−	0.190913i
$306$		0			0
$307$	−29.6136			−1.69014			−0.845070	−	0.534656i	$-0.820441\pi$
$307$	−29.6136			−1.69014			−0.845070	+	0.534656i	$0.820441\pi$
$308$		0			0
$309$	−8.36481	+	2.71789i	−0.475857	+	0.154615i
$310$		0			0
$311$	1.32670	−	4.08315i	0.0752301	−	0.231534i	−0.906369	−	0.422486i	$-0.861157\pi$
$311$	1.32670	−	4.08315i	0.0752301	−	0.231534i	0.981599	+	0.190952i	$0.0611575\pi$
$312$		0			0
$313$	−13.0617	+	4.24400i	−0.738290	+	0.239885i	−0.653935	−	0.756551i	$-0.726883\pi$
$313$	−13.0617	+	4.24400i	−0.738290	+	0.239885i	−0.0843552	+	0.996436i	$0.526883\pi$
$314$		0			0
$315$	1.50532	−	6.45270i	0.0848151	−	0.363568i
$316$		0			0
$317$	−10.3334	+	7.50769i	−0.580384	+	0.421674i	−0.838863	−	0.544343i	$-0.816779\pi$
$317$	−10.3334	+	7.50769i	−0.580384	+	0.421674i	0.258478	+	0.966017i	$0.416779\pi$
$318$		0			0
$319$	−1.63361	+	1.18688i	−0.0914644	+	0.0664528i
$320$		0			0
$321$	−8.11803	−	5.89809i	−0.453104	−	0.329200i
$322$		0			0
$323$	−0.368178	+	1.13313i	−0.0204859	+	0.0630493i
$324$		0			0
$325$	7.44223	−	7.63624i	0.412821	−	0.423583i
$326$		0			0
$327$	8.41894	+	2.73548i	0.465569	+	0.151272i
$328$		0			0
$329$	−2.09513	−	1.52220i	−0.115508	−	0.0839217i
$330$		0			0
$331$	−2.79298	−	3.84421i	−0.153516	−	0.211297i	0.725331	−	0.688400i	$-0.241687\pi$
$331$	−2.79298	−	3.84421i	−0.153516	−	0.211297i	−0.878847	+	0.477103i	$0.841687\pi$
$332$		0			0
$333$	−8.26066	+	6.00172i	−0.452682	+	0.328892i
$334$		0			0
$335$	−0.599957	−	7.04356i	−0.0327791	−	0.384831i
$336$		0			0
$337$	−28.1678	+	9.15228i	−1.53440	+	0.498556i	−0.949824	−	0.312784i	$-0.898739\pi$
$337$	−28.1678	+	9.15228i	−1.53440	+	0.498556i	−0.584574	+	0.811340i	$0.698739\pi$
$338$		0			0
$339$	18.9553	+	6.15894i	1.02951	+	0.334508i
$340$		0			0
$341$	−1.89059	+	0.614289i	−0.102381	+	0.0332656i
$342$		0			0
$343$		−	20.0015i		−	1.07998i
$344$		0			0
$345$	−20.2674	+	1.72634i	−1.09116	+	0.0929431i
$346$		0			0
$347$	15.6090	+	11.3406i	0.837937	+	0.608797i	0.921794	−	0.387681i	$-0.126724\pi$
$347$	15.6090	+	11.3406i	0.837937	+	0.608797i	−0.0838564	+	0.996478i	$0.526724\pi$
$348$		0			0
$349$		−	33.1221i		−	1.77299i	−0.462742	−	0.886493i	$-0.653134\pi$
$349$		−	33.1221i		−	1.77299i	0.462742	−	0.886493i	$-0.346866\pi$
$350$		0			0
$351$	−11.9709			−0.638961
$352$		0			0
$353$	7.81083	−	10.7507i	0.415729	−	0.572202i	−0.548875	−	0.835904i	$-0.684944\pi$
$353$	7.81083	−	10.7507i	0.415729	−	0.572202i	0.964604	+	0.263703i	$0.0849438\pi$
$354$		0			0
$355$	−13.5034	+	5.69535i	−0.716687	+	0.302278i
$356$		0			0
$357$	−6.92117			−0.366307
$358$		0			0
$359$	−5.23366	−	16.1076i	−0.276222	−	0.850124i	−0.988893	−	0.148626i	$-0.952515\pi$
$359$	−5.23366	−	16.1076i	−0.276222	−	0.850124i	0.712671	−	0.701498i	$-0.247485\pi$
$360$		0			0
$361$	5.78682	−	17.8100i	0.304570	−	0.937369i
$362$		0			0
$363$	4.43696	+	13.6556i	0.232880	+	0.716732i
$364$		0			0
$365$	9.33379	−	8.07623i	0.488553	−	0.422729i
$366$		0			0
$367$	5.13516	+	7.06794i	0.268053	+	0.368944i	0.921731	−	0.387829i	$-0.126775\pi$
$367$	5.13516	+	7.06794i	0.268053	+	0.368944i	−0.653678	+	0.756773i	$0.726775\pi$
$368$		0			0
$369$	6.18006	−	4.49008i	0.321721	−	0.233744i
$370$		0			0
$371$	−5.91720	+	8.14432i	−0.307206	+	0.422832i
$372$		0			0
$373$	0.310042	−	0.954212i	0.0160534	−	0.0494072i	−0.942709	−	0.333616i	$-0.891731\pi$
$373$	0.310042	−	0.954212i	0.0160534	−	0.0494072i	0.958762	+	0.284209i	$0.0917310\pi$
$374$		0			0
$375$	−11.3330	−	9.30715i	−0.585235	−	0.480619i
$376$		0			0
$377$	−17.7178	−	5.75686i	−0.912513	−	0.296494i
$378$		0			0
$379$	−21.2264	+	29.2157i	−1.09033	+	1.50071i	−0.242712	+	0.970098i	$0.578037\pi$
$379$	−21.2264	+	29.2157i	−1.09033	+	1.50071i	−0.847616	+	0.530610i	$0.821963\pi$
$380$		0			0
$381$	−3.51833	−	4.84257i	−0.180250	−	0.248092i
$382$		0			0
$383$	18.1528	+	24.9852i	0.927565	+	1.27668i	0.960802	+	0.277236i	$0.0894183\pi$
$383$	18.1528	+	24.9852i	0.927565	+	1.27668i	−0.0332373	+	0.999447i	$0.510582\pi$
$384$		0			0
$385$	0.783235	+	0.905194i	0.0399174	+	0.0461329i
$386$		0			0
$387$	3.85377	+	11.8607i	0.195898	+	0.602912i
$388$		0			0
$389$	−1.26254	−	0.410223i	−0.0640132	−	0.0207991i	0.276835	−	0.960917i	$-0.410714\pi$
$389$	−1.26254	−	0.410223i	−0.0640132	−	0.0207991i	−0.340849	+	0.940118i	$0.610714\pi$
$390$		0			0
$391$	−4.88288	−	15.0280i	−0.246938	−	0.759997i
$392$		0			0
$393$		−	20.3574i		−	1.02690i
$394$		0			0
$395$	−25.9188	+	10.9318i	−1.30412	+	0.550039i
$396$		0			0
$397$	7.80606	+	5.67144i	0.391775	+	0.284641i	0.766182	−	0.642623i	$-0.222154\pi$
$397$	7.80606	+	5.67144i	0.391775	+	0.284641i	−0.374407	+	0.927264i	$0.622154\pi$
$398$		0			0
$399$	−1.58849			−0.0795237
$400$		0			0
$401$	11.7737			0.587953			0.293976	−	0.955813i	$-0.405021\pi$
$401$	11.7737			0.587953			0.293976	+	0.955813i	$0.405021\pi$
$402$		0			0
$403$	−14.8375	−	10.7801i	−0.739110	−	0.536995i
$404$		0			0
$405$	0.668830	+	7.85214i	0.0332344	+	0.390176i
$406$		0			0
$407$		−	1.84462i		−	0.0914343i
$408$		0			0
$409$	−0.0454622	−	0.139918i	−0.00224796	−	0.00691851i	0.949926	−	0.312474i	$-0.101158\pi$
$409$	−0.0454622	−	0.139918i	−0.00224796	−	0.00691851i	−0.952174	+	0.305556i	$0.901158\pi$
$410$		0			0
$411$	−18.3375	−	5.95820i	−0.904520	−	0.293896i
$412$		0			0
$413$	3.50862	+	10.7984i	0.172648	+	0.531355i
$414$		0			0
$415$	−1.04358	−	12.2517i	−0.0512272	−	0.601413i
$416$		0			0
$417$	4.55069	+	6.26349i	0.222848	+	0.306724i
$418$		0			0
$419$	20.0431	+	27.5869i	0.979168	+	1.34771i	0.937277	+	0.348587i	$0.113338\pi$
$419$	20.0431	+	27.5869i	0.979168	+	1.34771i	0.0418913	+	0.999122i	$0.486662\pi$
$420$		0			0
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	−0.884423	−	0.466686i	$-0.845448\pi$
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	0.717146	+	0.696923i	$0.245448\pi$
$422$		0			0
$423$	−1.36078	−	0.442143i	−0.0661633	−	0.0214977i
$424$		0			0
$425$	5.04090	−	10.2162i	0.244520	−	0.495557i
$426$		0			0
$427$	−1.63082	+	5.01915i	−0.0789209	+	0.242894i
$428$		0			0
$429$	0.380055	−	0.523101i	0.0183492	−	0.0252556i
$430$		0			0
$431$	3.30954	−	2.40452i	0.159415	−	0.115822i	−0.505218	−	0.862992i	$-0.668588\pi$
$431$	3.30954	−	2.40452i	0.159415	−	0.115822i	0.664633	+	0.747170i	$0.268588\pi$
$432$		0			0
$433$	2.79701	+	3.84976i	0.134416	+	0.185008i	0.870919	−	0.491427i	$-0.163524\pi$
$433$	2.79701	+	3.84976i	0.134416	+	0.185008i	−0.736503	+	0.676434i	$0.763524\pi$
$434$		0			0
$435$	−5.82084	+	24.9516i	−0.279088	+	1.19634i
$436$		0			0
$437$	−1.12068	−	3.44909i	−0.0536092	−	0.164992i
$438$		0			0
$439$	−0.541600	+	1.66687i	−0.0258492	+	0.0795556i	−0.963149	−	0.268969i	$-0.913317\pi$
$439$	−0.541600	+	1.66687i	−0.0258492	+	0.0795556i	0.937300	+	0.348524i	$0.113317\pi$
$440$		0			0
$441$	−0.647116	−	1.99162i	−0.0308150	−	0.0948389i
$442$		0			0
$443$	3.43488			0.163196			0.0815981	−	0.996665i	$-0.473998\pi$
$443$	3.43488			0.163196			0.0815981	+	0.996665i	$0.473998\pi$
$444$		0			0
$445$	−23.1479	−	26.7523i	−1.09732	−	1.26818i
$446$		0			0
$447$	−7.04717	+	9.69960i	−0.333320	+	0.458775i
$448$		0			0
$449$	5.54236			0.261560			0.130780	−	0.991411i	$-0.458252\pi$
$449$	5.54236			0.261560			0.130780	+	0.991411i	$0.458252\pi$
$450$		0			0
$451$			1.38002i			0.0649825i
$452$		0			0
$453$	9.12084	+	6.62668i	0.428534	+	0.311348i
$454$		0			0
$455$	−2.50895	+	10.7548i	−0.117621	+	0.504195i
$456$		0			0
$457$		−	3.02813i		−	0.141650i	−0.997489	−	0.0708250i	$-0.977437\pi$
$457$		−	3.02813i		−	0.141650i	0.997489	−	0.0708250i	$-0.0225632\pi$
$458$		0			0
$459$	−12.1636	+	3.95219i	−0.567748	+	0.184472i
$460$		0			0
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	0.574377	−	0.818591i	$-0.305244\pi$
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	−0.0164747	+	0.999864i	$0.505244\pi$
$462$		0			0
$463$	4.16641	−	1.35375i	0.193629	−	0.0629140i	−0.210597	−	0.977573i	$-0.567541\pi$
$463$	4.16641	−	1.35375i	0.193629	−	0.0629140i	0.404226	+	0.914659i	$0.367541\pi$
$464$		0			0
$465$	−13.0406	+	21.5909i	−0.604745	+	1.00126i
$466$		0			0
$467$	18.3661	−	13.3438i	0.849883	−	0.617476i	−0.0752308	−	0.997166i	$-0.523969\pi$
$467$	18.3661	−	13.3438i	0.849883	−	0.617476i	0.925114	+	0.379690i	$0.123969\pi$
$468$		0			0
$469$	4.30342	+	5.92315i	0.198714	+	0.273506i
$470$		0			0
$471$	−4.93085	−	3.58247i	−0.227201	−	0.165072i
$472$		0			0
$473$	−2.14269	−	0.696201i	−0.0985208	−	0.0320113i
$474$		0			0
$475$	1.15694	−	2.34473i	0.0530842	−	0.107583i
$476$		0			0
$477$	−1.71873	+	5.28970i	−0.0786951	+	0.242199i
$478$		0			0
$479$	−5.58405	−	4.05705i	−0.255142	−	0.185371i	0.452861	−	0.891581i	$-0.350403\pi$
$479$	−5.58405	−	4.05705i	−0.255142	−	0.185371i	−0.708002	+	0.706210i	$0.750403\pi$
$480$		0			0
$481$	13.7682	−	10.0032i	0.627777	−	0.456107i
$482$		0			0
$483$	17.0435	−	12.3829i	0.775508	−	0.563439i
$484$		0			0
$485$	11.0908	+	26.2958i	0.503608	+	1.19403i
$486$		0			0
$487$	34.1041	−	11.0811i	1.54540	−	0.502132i	0.592543	−	0.805539i	$-0.298124\pi$
$487$	34.1041	−	11.0811i	1.54540	−	0.502132i	0.952861	+	0.303407i	$0.0981242\pi$
$488$		0			0
$489$	−5.32394	+	16.3854i	−0.240757	+	0.740973i
$490$		0			0
$491$	7.36748	−	2.39384i	0.332490	−	0.108032i	−0.138014	−	0.990430i	$-0.544072\pi$
$491$	7.36748	−	2.39384i	0.332490	−	0.108032i	0.470504	+	0.882398i	$0.344072\pi$
$492$		0			0
$493$	−19.9036			−0.896411
$494$		0			0
$495$	0.566096	+	0.341914i	0.0254441	+	0.0153679i
$496$		0			0
$497$	8.92171	−	12.2797i	0.400194	−	0.550819i
$498$		0			0
$499$		−	36.4452i		−	1.63151i	−0.578396	−	0.815756i	$-0.696321\pi$
$499$		−	36.4452i		−	1.63151i	0.578396	−	0.815756i	$-0.303679\pi$
$500$		0			0
$501$			27.3897i			1.22368i
$502$		0			0
$503$	7.52915	−	10.3630i	0.335708	−	0.462063i	−0.607473	−	0.794340i	$-0.707817\pi$
$503$	7.52915	−	10.3630i	0.335708	−	0.462063i	0.943182	+	0.332277i	$0.107817\pi$
$504$		0			0
$505$	22.1825	+	13.3979i	0.987107	+	0.596199i
$506$		0			0
$507$	−11.0863			−0.492360
$508$		0			0
$509$	−40.6350	+	13.2031i	−1.80111	+	0.585217i	−0.999913	−	0.0131803i	$-0.995804\pi$
$509$	−40.6350	+	13.2031i	−1.80111	+	0.585217i	−0.801200	+	0.598397i	$0.795804\pi$
$510$		0			0
$511$	−3.95030	+	12.1578i	−0.174751	+	0.537828i
$512$		0			0
$513$	−2.79168	+	0.907072i	−0.123256	+	0.0400482i
$514$		0			0
$515$	5.82684	+	13.8152i	0.256761	+	0.608770i
$516$		0			0
$517$	0.209116	−	0.151932i	0.00919692	−	0.00668195i
$518$		0			0
$519$	−8.36024	+	6.07407i	−0.366974	+	0.266622i
$520$		0			0
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	0.550179	−	0.835047i	$-0.314560\pi$
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	−0.624162	+	0.781295i	$0.714560\pi$
$522$		0			0
$523$	−10.0536	+	30.9419i	−0.439615	+	1.35300i	0.448668	+	0.893699i	$0.351899\pi$
$523$	−10.0536	+	30.9419i	−0.439615	+	1.35300i	−0.888283	+	0.459297i	$0.848101\pi$
$524$		0			0
$525$	15.0308	+	2.18279i	0.655998	+	0.0952650i
$526$		0			0
$527$	−18.6353	−	6.05499i	−0.811768	−	0.263760i
$528$		0			0
$529$	20.3038	+	14.7515i	0.882772	+	0.641372i
$530$		0			0
$531$	3.68722	+	5.07503i	0.160012	+	0.220237i
$532$		0			0
$533$	−10.3004	+	7.48371i	−0.446162	+	0.324155i
$534$		0			0
$535$	−8.84393	+	14.6426i	−0.382356	+	0.633055i
$536$		0			0
$537$	−20.0273	+	6.50726i	−0.864242	+	0.280809i
$538$		0			0
$539$	0.359795	+	0.116904i	0.0154975	+	0.00503543i
$540$		0			0
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	−0.414872	−	0.909880i	$-0.636174\pi$
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	0.199176	+	0.979964i	$0.436174\pi$
$542$		0			0
$543$			22.4960i			0.965395i
$544$		0			0
$545$	3.42839	−	14.6962i	0.146856	−	0.629514i
$546$		0			0
$547$	−12.2753	−	8.91852i	−0.524854	−	0.381329i	0.293575	−	0.955936i	$-0.405155\pi$
$547$	−12.2753	−	8.91852i	−0.524854	−	0.381329i	−0.818429	+	0.574607i	$0.805155\pi$
$548$		0			0
$549$			2.91575i			0.124441i
$550$		0			0
$551$	−4.56809			−0.194607
$552$		0			0
$553$	17.1246	−	23.5700i	0.728211	−	1.00230i
$554$		0			0
$555$	−15.3150	−	17.6997i	−0.650085	−	0.751311i
$556$		0			0
$557$	−21.0806			−0.893213			−0.446606	−	0.894731i	$-0.647368\pi$
$557$	−21.0806			−0.893213			−0.446606	+	0.894731i	$0.647368\pi$
$558$		0			0
$559$	−6.42315	−	19.7684i	−0.271670	−	0.836116i
$560$		0			0
$561$	0.213470	−	0.656995i	0.00901273	−	0.0277383i
$562$		0			0
$563$	−5.40722	−	16.6417i	−0.227887	−	0.701365i	−0.997986	−	0.0634396i	$-0.979793\pi$
$563$	−5.40722	−	16.6417i	−0.227887	−	0.701365i	0.770099	−	0.637925i	$-0.220207\pi$
$564$		0			0
$565$	7.71904	−	33.0884i	0.324743	−	1.39204i
$566$		0			0
$567$	−4.79744	−	6.60311i	−0.201474	−	0.277305i
$568$		0			0
$569$	−26.4646	+	19.2277i	−1.10945	+	0.806065i	−0.982578	−	0.185853i	$-0.940495\pi$
$569$	−26.4646	+	19.2277i	−1.10945	+	0.806065i	−0.126876	+	0.991919i	$0.540495\pi$
$570$		0			0
$571$	17.4500	−	24.0179i	0.730261	−	1.00512i	−0.268860	−	0.963179i	$-0.586647\pi$
$571$	17.4500	−	24.0179i	0.730261	−	1.00512i	0.999120	−	0.0419380i	$-0.0133532\pi$
$572$		0			0
$573$	1.21142	−	3.72838i	0.0506080	−	0.155755i
$574$		0			0
$575$	5.86471	+	34.1764i	0.244575	+	1.42525i
$576$		0			0
$577$	−7.08229	−	2.30117i	−0.294839	−	0.0957992i	0.157862	−	0.987461i	$-0.449540\pi$
$577$	−7.08229	−	2.30117i	−0.294839	−	0.0957992i	−0.452702	+	0.891662i	$0.649540\pi$
$578$		0			0
$579$	11.5145	−	15.8484i	0.478527	−	0.658636i
$580$		0			0
$581$	7.48546	+	10.3029i	0.310549	+	0.427435i
$582$		0			0
$583$	−0.590598	−	0.812889i	−0.0244601	−	0.0336664i
$584$		0			0
$585$	0.517841	+	6.07951i	0.0214101	+	0.251357i
$586$		0			0
$587$	−4.32742	−	13.3184i	−0.178612	−	0.549710i	0.821168	−	0.570686i	$-0.193323\pi$
$587$	−4.32742	−	13.3184i	−0.178612	−	0.549710i	−0.999780	+	0.0209758i	$0.993323\pi$
$588$		0			0
$589$	−4.27702	−	1.38969i	−0.176232	−	0.0572611i
$590$		0			0
$591$	−11.1601	−	34.3471i	−0.459063	−	1.41285i
$592$		0			0
$593$			10.4531i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$593$			10.4531i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$594$		0			0
$595$	1.00138	+	11.7563i	0.0410524	+	0.481960i
$596$		0			0
$597$	−12.0784	−	8.77546i	−0.494335	−	0.359156i
$598$		0			0
$599$	−25.1691			−1.02838			−0.514191	−	0.857676i	$-0.671908\pi$
$599$	−25.1691			−1.02838			−0.514191	+	0.857676i	$0.671908\pi$
$600$		0			0
$601$	−9.80217			−0.399839			−0.199919	−	0.979812i	$-0.564068\pi$
$601$	−9.80217			−0.399839			−0.199919	+	0.979812i	$0.564068\pi$
$602$		0			0
$603$	3.27250	+	2.37761i	0.133267	+	0.0968238i
$604$		0			0
$605$	22.5533	−	9.51233i	0.916923	−	0.386731i
$606$		0			0
$607$			2.47771i			0.100567i	0.998735	+	0.0502836i	$0.0160125\pi$
$607$			2.47771i			0.100567i	−0.998735	+	0.0502836i	$0.983987\pi$
$608$		0			0
$609$	−8.20014	−	25.2374i	−0.332287	−	1.02267i
$610$		0			0
$611$	2.26804	+	0.736930i	0.0917549	+	0.0298130i
$612$		0			0
$613$	0.797806	+	2.45539i	0.0322231	+	0.0991725i	0.965875	−	0.259010i	$-0.0833964\pi$
$613$	0.797806	+	2.45539i	0.0322231	+	0.0991725i	−0.933651	+	0.358183i	$0.883396\pi$
$614$		0			0
$615$	11.4576	+	13.2417i	0.462016	+	0.533957i
$616$		0			0
$617$	10.4128	+	14.3320i	0.419205	+	0.576986i	0.965433	−	0.260650i	$-0.0839369\pi$
$617$	10.4128	+	14.3320i	0.419205	+	0.576986i	−0.546228	+	0.837636i	$0.683937\pi$
$618$		0			0
$619$	12.1197	+	16.6813i	0.487130	+	0.670477i	0.979855	−	0.199708i	$-0.0639993\pi$
$619$	12.1197	+	16.6813i	0.487130	+	0.670477i	−0.492726	+	0.870185i	$0.663999\pi$
$620$		0			0
$621$	22.8822	−	31.4946i	0.918229	−	1.26383i
$622$		0			0
$623$	34.8464	+	11.3223i	1.39609	+	0.453617i
$624$		0			0
$625$	−14.1694	+	20.5968i	−0.566775	+	0.823873i
$626$		0			0
$627$	0.0489939	−	0.150788i	0.00195663	−	0.00602188i
$628$		0			0
$629$	10.6873	−	14.7097i	0.426129	−	0.586516i
$630$		0			0
$631$	26.5548	−	19.2932i	1.05713	−	0.768050i	0.0835747	−	0.996502i	$-0.473366\pi$
$631$	26.5548	−	19.2932i	1.05713	−	0.768050i	0.973555	+	0.228452i	$0.0733663\pi$
$632$		0			0
$633$	12.2203	+	16.8198i	0.485714	+	0.668528i
$634$		0			0
$635$	−7.71651	+	6.67685i	−0.306221	+	0.264963i
$636$		0			0
$637$	1.07856	+	3.31947i	0.0427342	+	0.131522i
$638$		0			0
$639$	2.59143	−	7.97559i	0.102515	−	0.315510i
$640$		0			0
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	0.996258	+	0.0864316i	$0.0275464\pi$
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	−0.755186	+	0.655510i	$0.772454\pi$
$642$		0			0
$643$	−21.0042			−0.828324			−0.414162	−	0.910203i	$-0.635925\pi$
$643$	−21.0042			−0.828324			−0.414162	+	0.910203i	$0.635925\pi$
$644$		0			0
$645$	−26.3400	+	11.1094i	−1.03714	+	0.437434i
$646$		0			0
$647$	−19.4638	+	26.7896i	−0.765202	+	1.05321i	0.231562	+	0.972820i	$0.425616\pi$
$647$	−19.4638	+	26.7896i	−0.765202	+	1.05321i	−0.996764	+	0.0803896i	$0.974384\pi$
$648$		0			0
$649$	−1.13326			−0.0444844
$650$		0			0
$651$		−	26.1240i		−	1.02388i
$652$		0			0
$653$	0.267998	+	0.194712i	0.0104876	+	0.00761966i	0.593017	−	0.805190i	$-0.297937\pi$
$653$	0.267998	+	0.194712i	0.0104876	+	0.00761966i	−0.582529	+	0.812810i	$0.697937\pi$
$654$		0			0
$655$	−34.5790	+	2.94538i	−1.35111	+	0.115085i
$656$		0			0
$657$			7.06276i			0.275545i
$658$		0			0
$659$	2.06861	−	0.672132i	0.0805816	−	0.0261826i	−0.268449	−	0.963294i	$-0.586511\pi$
$659$	2.06861	−	0.672132i	0.0805816	−	0.0261826i	0.349030	+	0.937111i	$0.386511\pi$
$660$		0			0
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	0.575658	−	0.817691i	$-0.304746\pi$
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	−0.0149097	+	0.999889i	$0.504746\pi$
$662$		0			0
$663$	6.06144	−	1.96948i	0.235407	−	0.0764883i
$664$		0			0
$665$	0.229827	+	2.69819i	0.00891230	+	0.104631i
$666$		0			0
$667$	49.0130	−	35.6100i	1.89779	−	1.37883i
$668$		0			0
$669$	17.9492	+	24.7049i	0.693955	+	0.955147i
$670$		0			0
$671$	−0.426145	−	0.309612i	−0.0164511	−	0.0119525i
$672$		0			0
$673$	3.94041	+	1.28032i	0.151892	+	0.0493526i	0.383976	−	0.923343i	$-0.374555\pi$
$673$	3.94041	+	1.28032i	0.151892	+	0.0493526i	−0.232084	+	0.972696i	$0.574555\pi$
$674$		0			0
$675$	27.6623	−	4.74688i	1.06472	−	0.182707i
$676$		0			0
$677$	6.92852	−	21.3238i	0.266285	−	0.819540i	−0.725110	−	0.688633i	$-0.758211\pi$
$677$	6.92852	−	21.3238i	0.266285	−	0.819540i	0.991395	−	0.130907i	$-0.0417890\pi$
$678$		0			0
$679$	−23.9128	−	17.3737i	−0.917689	−	0.666740i
$680$		0			0
$681$	4.75261	−	3.45297i	0.182120	−	0.132318i
$682$		0			0
$683$	−26.5359	+	19.2795i	−1.01537	+	0.737709i	−0.965328	−	0.261038i	$-0.915935\pi$
$683$	−26.5359	+	19.2795i	−1.01537	+	0.737709i	−0.0500406	+	0.998747i	$0.515935\pi$
$684$		0			0
$685$	−7.46745	+	32.0100i	−0.285317	+	1.22304i
$686$		0			0
$687$	−6.36672	+	2.06867i	−0.242905	+	0.0789247i
$688$		0			0
$689$	2.86464	−	8.81645i	0.109134	−	0.335880i
$690$		0			0
$691$	35.7160	−	11.6048i	1.35870	−	0.441468i	0.463090	−	0.886311i	$-0.346741\pi$
$691$	35.7160	−	11.6048i	1.35870	−	0.441468i	0.895609	+	0.444843i	$0.146741\pi$
$692$		0			0
$693$	−0.684949			−0.0260190
$694$		0			0
$695$	9.98072	−	8.63600i	0.378590	−	0.327582i
$696$		0			0
$697$	−7.99547	+	11.0048i	−0.302850	+	0.416837i
$698$		0			0
$699$			4.58909i			0.173575i
$700$		0			0
$701$		−	23.3655i		−	0.882503i	−0.897383	−	0.441252i	$-0.854535\pi$
$701$		−	23.3655i		−	0.882503i	0.897383	−	0.441252i	$-0.145465\pi$
$702$		0			0
$703$	2.45284	−	3.37605i	0.0925108	−	0.127330i
$704$		0			0
$705$	0.745120	−	3.19403i	0.0280628	−	0.120294i
$706$		0			0
$707$	−26.8397			−1.00941
$708$		0			0
$709$	−12.3034	+	3.99762i	−0.462064	+	0.150134i	−0.530793	−	0.847502i	$-0.678106\pi$
$709$	−12.3034	+	3.99762i	−0.462064	+	0.150134i	0.0687289	+	0.997635i	$0.478106\pi$
$710$		0			0
$711$	4.97406	−	15.3086i	0.186542	−	0.574116i
$712$		0			0
$713$	56.7231	−	18.4305i	2.12430	−	0.690226i
$714$		0			0
$715$	−0.943525	−	0.569876i	−0.0352858	−	0.0213122i
$716$		0			0
$717$	21.5530	−	15.6592i	0.804912	−	0.584803i
$718$		0			0
$719$	1.77973	−	1.29305i	0.0663726	−	0.0482225i	−0.554104	−	0.832447i	$-0.686939\pi$
$719$	1.77973	−	1.29305i	0.0663726	−	0.0482225i	0.620477	+	0.784225i	$0.286939\pi$
$720$		0			0
$721$	−12.5632	−	9.12770i	−0.467878	−	0.339933i
$722$		0			0
$723$	7.85116	−	24.1634i	0.291988	−	0.898646i
$724$		0			0
$725$	43.2248	+	6.27718i	1.60533	+	0.233128i
$726$		0			0
$727$	−4.25417	−	1.38226i	−0.157778	−	0.0512653i	0.229063	−	0.973412i	$-0.426434\pi$
$727$	−4.25417	−	1.38226i	−0.157778	−	0.0512653i	−0.386841	+	0.922146i	$0.626434\pi$
$728$		0			0
$729$	−21.5182	−	15.6339i	−0.796969	−	0.579032i
$730$		0			0
$731$	−13.0530	−	17.9660i	−0.482784	−	0.664496i
$732$		0			0
$733$	10.5599	−	7.67219i	0.390037	−	0.283379i	−0.375433	−	0.926849i	$-0.622506\pi$
$733$	10.5599	−	7.67219i	0.390037	−	0.283379i	0.765471	+	0.643471i	$0.222506\pi$
$734$		0			0
$735$	4.42295	−	1.86547i	0.163143	−	0.0688090i
$736$		0			0
$737$	−0.694989	+	0.225815i	−0.0256002	+	0.00831802i
$738$		0			0
$739$	29.8146	+	9.68735i	1.09675	+	0.356355i	0.800850	−	0.598865i	$-0.204381\pi$
$739$	29.8146	+	9.68735i	1.09675	+	0.356355i	0.295898	+	0.955220i	$0.404381\pi$
$740$		0			0
$741$	1.39117	−	0.452018i	0.0511058	−	0.0166053i
$742$		0			0
$743$			28.1541i			1.03287i	0.856325	+	0.516437i	$0.172742\pi$
$743$			28.1541i			1.03287i	−0.856325	+	0.516437i	$0.827258\pi$
$744$		0			0
$745$	17.4953	+	10.5669i	0.640978	+	0.387142i
$746$		0			0
$747$	5.69226	+	4.13567i	0.208269	+	0.151316i
$748$		0			0
$749$		−	17.7168i		−	0.647359i
$750$		0			0
$751$	12.9756			0.473487			0.236743	−	0.971572i	$-0.423920\pi$
$751$	12.9756			0.473487			0.236743	+	0.971572i	$0.423920\pi$
$752$		0			0
$753$	−3.52324	+	4.84932i	−0.128394	+	0.176719i
$754$		0			0
$755$	9.93641	−	16.4514i	0.361623	−	0.598727i
$756$		0			0
$757$	−16.0395			−0.582965			−0.291482	−	0.956576i	$-0.594149\pi$
$757$	−16.0395			−0.582965			−0.291482	+	0.956576i	$0.594149\pi$
$758$		0			0
$759$	0.649771	+	1.99979i	0.0235852	+	0.0725878i
$760$		0			0
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	−0.867518	−	0.497405i	$-0.834286\pi$
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	0.994205	+	0.107505i	$0.0342863\pi$
$762$		0			0
$763$	4.82977	+	14.8645i	0.174849	+	0.538131i
$764$		0			0
$765$	2.53332	+	6.00639i	0.0915923	+	0.217161i
$766$		0			0
$767$	−6.14557	−	8.45866i	−0.221904	−	0.305424i
$768$		0			0
$769$	3.25219	−	2.36285i	0.117277	−	0.0852066i	−0.527601	−	0.849492i	$-0.676908\pi$
$769$	3.25219	−	2.36285i	0.117277	−	0.0852066i	0.644878	+	0.764286i	$0.276908\pi$
$770$		0			0
$771$	−21.1549	+	29.1173i	−0.761876	+	1.04863i
$772$		0			0
$773$	0.759693	−	2.33810i	0.0273243	−	0.0840955i	−0.936464	−	0.350763i	$-0.885922\pi$
$773$	0.759693	−	2.33810i	0.0273243	−	0.0840955i	0.963789	+	0.266667i	$0.0859224\pi$
$774$		0			0
$775$	38.5610	+	19.0269i	1.38515	+	0.683467i
$776$		0			0
$777$	23.0548	+	7.49097i	0.827088	+	0.268737i
$778$		0			0
$779$	−1.83505	+	2.52573i	−0.0657475	+	0.0904937i
$780$		0			0
$781$	0.890481	+	1.22564i	0.0318639	+	0.0438569i
$782$		0			0
$783$	−28.8227	−	39.6710i	−1.03004	−	1.41773i
$784$		0			0
$785$	−5.37175	+	8.89383i	−0.191726	+	0.317435i
$786$		0			0
$787$	−9.27720	−	28.5523i	−0.330697	−	1.01778i	−0.968803	−	0.247831i	$-0.920282\pi$
$787$	−9.27720	−	28.5523i	−0.330697	−	1.01778i	0.638107	−	0.769948i	$-0.279718\pi$
$788$		0			0
$789$	16.0606	+	5.21842i	0.571774	+	0.185781i
$790$		0			0
$791$	10.8742	+	33.4675i	0.386644	+	1.18997i
$792$		0			0
$793$		−	4.85974i		−	0.172575i
$794$		0			0
$795$	−12.4160	−	2.89647i	−0.440351	−	0.102727i
$796$		0			0
$797$	17.9888	+	13.0696i	0.637196	+	0.462950i	0.858886	−	0.512167i	$-0.171157\pi$
$797$	17.9888	+	13.0696i	0.637196	+	0.462950i	−0.221690	+	0.975117i	$0.571157\pi$
$798$		0			0
$799$	2.54783			0.0901359
$800$		0			0
$801$	20.2432			0.715257
$802$		0			0
$803$	−1.03224	−	0.749967i	−0.0364270	−	0.0264658i
$804$		0			0
$805$	−23.4994	−	27.1585i	−0.828243	−	0.957210i
$806$		0			0
$807$		−	2.00232i		−	0.0704852i
$808$		0			0
$809$	−10.2871	−	31.6605i	−0.361676	−	1.11313i	−0.952036	−	0.305985i	$-0.901014\pi$
$809$	−10.2871	−	31.6605i	−0.361676	−	1.11313i	0.590360	−	0.807140i	$-0.298986\pi$
$810$		0			0
$811$	41.7447	+	13.5637i	1.46585	+	0.476285i	0.929853	−	0.367932i	$-0.119934\pi$
$811$	41.7447	+	13.5637i	1.46585	+	0.476285i	0.536002	+	0.844217i	$0.319934\pi$
$812$		0			0
$813$	−9.92157	−	30.5355i	−0.347965	−	1.07093i
$814$		0			0
$815$	28.6024	+	6.67252i	1.00190	+	0.233728i
$816$		0			0
$817$	−2.99582	−	4.12339i	−0.104810	−	0.144259i
$818$		0			0
$819$	−3.71442	−	5.11245i	−0.129792	−	0.178644i
$820$		0			0
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	−0.396107	−	0.918205i	$-0.629639\pi$
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	0.995668	+	0.0929790i	$0.0296390\pi$
$822$		0			0
$823$	12.8489	+	4.17485i	0.447883	+	0.145526i	0.524270	−	0.851552i	$-0.324338\pi$
$823$	12.8489	+	4.17485i	0.447883	+	0.145526i	−0.0763866	+	0.997078i	$0.524338\pi$
$824$		0			0
$825$	−0.670799	+	1.35948i	−0.0233542	+	0.0473310i
$826$		0			0
$827$	−8.92624	+	27.4721i	−0.310396	+	0.955300i	0.667213	+	0.744867i	$0.267487\pi$
$827$	−8.92624	+	27.4721i	−0.310396	+	0.955300i	−0.977608	+	0.210433i	$0.932513\pi$
$828$		0			0
$829$	21.9589	−	30.2238i	0.762663	−	1.04972i	−0.234325	−	0.972158i	$-0.575288\pi$
$829$	21.9589	−	30.2238i	0.762663	−	1.04972i	0.996988	−	0.0775572i	$-0.0247120\pi$
$830$		0			0
$831$	29.0732	−	21.1229i	1.00854	−	0.732745i
$832$		0			0
$833$	2.19184	+	3.01681i	0.0759427	+	0.104526i
$834$		0			0
$835$	46.5241	−	3.96283i	1.61003	−	0.137139i
$836$		0			0
$837$	−14.9176	−	45.9115i	−0.515627	−	1.58694i
$838$		0			0
$839$	−2.47513	+	7.61767i	−0.0854510	+	0.262991i	−0.984648	−	0.174553i	$-0.944152\pi$
$839$	−2.47513	+	7.61767i	−0.0854510	+	0.262991i	0.899197	+	0.437545i	$0.144152\pi$
$840$		0			0
$841$	−14.6201	−	44.9960i	−0.504141	−	1.55159i
$842$		0			0
$843$	38.1169			1.31282
$844$		0			0
$845$	1.60400	+	18.8312i	0.0551793	+	0.647811i
$846$		0			0
$847$	−14.9010	+	20.5094i	−0.512004	+	0.704713i
$848$		0			0
$849$	−13.0057			−0.446354
$850$		0			0
$851$			55.3440i			1.89717i
$852$		0			0
$853$	13.5745	+	9.86242i	0.464780	+	0.337683i	0.795404	−	0.606080i	$-0.207259\pi$
$853$	13.5745	+	9.86242i	0.464780	+	0.337683i	−0.330623	+	0.943763i	$0.607259\pi$
$854$		0			0
$855$	0.581425	+	1.37853i	0.0198843	+	0.0471448i
$856$		0			0
$857$			12.0516i			0.411675i	0.978586	+	0.205837i	$0.0659918\pi$
$857$			12.0516i			0.411675i	−0.978586	+	0.205837i	$0.934008\pi$
$858$		0			0
$859$	−53.1530	+	17.2704i	−1.81356	+	0.589260i	−0.813587	+	0.581443i	$0.802488\pi$
$859$	−53.1530	+	17.2704i	−1.81356	+	0.589260i	−0.999969	+	0.00781665i	$0.997512\pi$
$860$		0			0
$861$	−17.2481	−	5.60423i	−0.587812	−	0.190992i
$862$		0			0
$863$	27.1681	−	8.82744i	0.924812	−	0.300490i	0.192373	−	0.981322i	$-0.438382\pi$
$863$	27.1681	−	8.82744i	0.924812	−	0.300490i	0.732439	+	0.680832i	$0.238382\pi$
$864$		0			0
$865$	11.5270	+	13.3218i	0.391929	+	0.452956i
$866$		0			0
$867$	−12.5310	+	9.10434i	−0.425577	+	0.309200i
$868$		0			0
$869$	1.70921	+	2.35253i	0.0579811	+	0.0798041i
$870$		0			0
$871$	−5.45435	−	3.96281i	−0.184813	−	0.134275i
$872$		0			0
$873$	−15.5312	−	5.04641i	−0.525653	−	0.170795i
$874$		0			0
$875$	1.53298	−	25.8470i	0.0518243	−	0.873789i
$876$		0			0
$877$	1.52668	−	4.69863i	0.0515522	−	0.158661i	−0.921966	−	0.387271i	$-0.873418\pi$
$877$	1.52668	−	4.69863i	0.0515522	−	0.158661i	0.973518	+	0.228609i	$0.0734178\pi$
$878$		0			0
$879$	6.60284	+	4.79725i	0.222708	+	0.161807i
$880$		0			0
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	−0.597021	−	0.802225i	$-0.703649\pi$
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	0.578472	+	0.815702i	$0.303649\pi$
$882$		0			0
$883$	1.43973	−	1.04603i	0.0484509	−	0.0352017i	−0.563296	−	0.826255i	$-0.690467\pi$
$883$	1.43973	−	1.04603i	0.0484509	−	0.0352017i	0.611747	+	0.791053i	$0.290467\pi$
$884$		0			0
$885$	−10.8740	+	9.40893i	−0.365526	+	0.316278i
$886$		0			0
$887$	−42.8681	+	13.9287i	−1.43937	+	0.467680i	−0.921701	−	0.387901i	$-0.873200\pi$
$887$	−42.8681	+	13.9287i	−1.43937	+	0.467680i	−0.517669	+	0.855581i	$0.673200\pi$
$888$		0			0
$889$	3.26583	−	10.0512i	0.109532	−	0.337106i
$890$		0			0
$891$	0.774771	−	0.251738i	0.0259558	−	0.00843355i
$892$		0			0
$893$	0.584756			0.0195681
$894$		0			0
$895$	13.9508	+	33.0768i	0.466324	+	1.10563i
$896$		0			0
$897$	−11.4028	+	15.6946i	−0.380728	+	0.524027i
$898$		0			0
$899$		−	75.1261i		−	2.50560i
$900$		0			0
$901$		−	9.90409i		−	0.329953i
$902$		0			0
$903$	17.4028	−	23.9530i	0.579130	−	0.797104i
$904$		0			0
$905$	38.2116	−	3.25479i	1.27020	−	0.108193i
$906$		0			0
$907$	−22.9525			−0.762127			−0.381063	−	0.924549i	$-0.624442\pi$
$907$	−22.9525			−0.762127			−0.381063	+	0.924549i	$0.624442\pi$
$908$		0			0
$909$	−14.1030	+	4.58234i	−0.467766	+	0.151987i
$910$		0			0
$911$	−1.55833	+	4.79606i	−0.0516299	+	0.158900i	−0.973547	−	0.228487i	$-0.926622\pi$
$911$	−1.55833	+	4.79606i	−0.0516299	+	0.158900i	0.921917	+	0.387387i	$0.126622\pi$
$912$		0			0
$913$	−1.20888	+	0.392788i	−0.0400080	+	0.0129994i
$914$		0			0
$915$	−6.65957	+	0.567249i	−0.220158	+	0.0187527i
$916$		0			0
$917$	29.0786	−	21.1268i	0.960260	−	0.697670i
$918$		0			0
$919$	0.772993	−	0.561613i	0.0254987	−	0.0185259i	−0.574963	−	0.818179i	$-0.694984\pi$
$919$	0.772993	−	0.561613i	0.0254987	−	0.0185259i	0.600462	+	0.799654i	$0.294984\pi$
$920$		0			0
$921$	31.4250	+	22.8316i	1.03549	+	0.752326i
$922$		0			0
$923$	−4.31919	+	13.2931i	−0.142168	+	0.437547i
$924$		0			0
$925$	−27.8488	+	28.5748i	−0.915663	+	0.939534i
$926$		0			0
$927$	−8.15973	−	2.65126i	−0.268001	−	0.0870787i
$928$		0			0
$929$	−46.5656	−	33.8319i	−1.52777	−	1.10999i	−0.957463	−	0.288555i	$-0.906825\pi$
$929$	−46.5656	−	33.8319i	−1.52777	−	1.10999i	−0.570304	−	0.821433i	$-0.693175\pi$
$930$		0			0
$931$	0.503052	+	0.692391i	0.0164868	+	0.0226922i
$932$		0			0
$933$	−4.55588	+	3.31004i	−0.149153	+	0.108366i
$934$		0			0
$935$	−1.14685	−	0.267544i	−0.0375061	−	0.00874962i
$936$		0			0
$937$	−33.6886	+	10.9461i	−1.10056	+	0.357593i	−0.802317	−	0.596898i	$-0.796400\pi$
$937$	−33.6886	+	10.9461i	−1.10056	+	0.357593i	−0.298240	+	0.954491i	$0.596400\pi$
$938$		0			0
$939$	17.1327	+	5.56674i	0.559103	+	0.181664i
$940$		0			0
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	−0.312314	−	0.949979i	$-0.601104\pi$
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	0.305716	+	0.952123i	$0.401104\pi$
$942$		0			0
$943$		−	41.4046i		−	1.34832i
$944$		0			0
$945$	−21.9820	+	19.0203i	−0.715074	+	0.618731i
$946$		0			0
$947$	−4.78799	−	3.47868i	−0.155589	−	0.113042i	0.507267	−	0.861789i	$-0.330656\pi$
$947$	−4.78799	−	3.47868i	−0.155589	−	0.113042i	−0.662856	+	0.748747i	$0.730656\pi$
$948$		0			0
$949$		−	11.7717i		−	0.382124i
$950$		0			0
$951$	16.7538			0.543279
$952$		0			0
$953$	−30.3932	+	41.8326i	−0.984531	+	1.35509i	−0.0501787	+	0.998740i	$0.515979\pi$
$953$	−30.3932	+	41.8326i	−0.984531	+	1.35509i	−0.934352	+	0.356351i	$0.884021\pi$
$954$		0			0
$955$	−6.50828	−	1.51829i	−0.210603	−	0.0491306i
$956$		0			0
$957$	2.64859			0.0856169
$958$		0			0
$959$	−10.5198	−	32.3766i	−0.339702	−	1.04550i
$960$		0			0
$961$	13.2751	−	40.8565i	0.428228	−	1.31795i
$962$		0			0
$963$	−3.02479	−	9.30935i	−0.0974725	−	0.299989i
$964$		0			0
$965$	−28.5859	−	17.2655i	−0.920214	−	0.555797i
$966$		0			0
$967$	11.6201	+	15.9937i	0.373677	+	0.514323i	0.953896	−	0.300138i	$-0.0970328\pi$
$967$	11.6201	+	15.9937i	0.373677	+	0.514323i	−0.580218	+	0.814461i	$0.697033\pi$
$968$		0			0
$969$	1.26432	−	0.918585i	0.0406159	−	0.0295092i
$970$		0			0
$971$	11.7741	−	16.2057i	0.377850	−	0.520065i	−0.577164	−	0.816628i	$-0.695841\pi$
$971$	11.7741	−	16.2057i	0.377850	−	0.520065i	0.955013	+	0.296563i	$0.0958405\pi$
$972$		0			0
$973$	−4.22409	+	13.0004i	−0.135418	+	0.416775i
$974$		0			0
$975$	−13.7848	+	2.36549i	−0.441468	+	0.0757564i
$976$		0			0
$977$	−44.2455	−	14.3762i	−1.41554	−	0.459937i	−0.501357	−	0.865240i	$-0.667166\pi$
$977$	−44.2455	−	14.3762i	−1.41554	−	0.459937i	−0.914182	+	0.405304i	$0.867166\pi$
$978$		0			0
$979$	−2.14954	+	2.95859i	−0.0686997	+	0.0945570i
$980$		0			0
$981$	5.07563	+	6.98600i	0.162052	+	0.223046i
$982$		0			0
$983$	18.2599	+	25.1326i	0.582401	+	0.801606i	0.993956	−	0.109779i	$-0.0350142\pi$
$983$	18.2599	+	25.1326i	0.582401	+	0.801606i	−0.411555	+	0.911385i	$0.635014\pi$
$984$		0			0
$985$	−56.7272	+	23.9259i	−1.80748	+	0.762341i
$986$		0			0
$987$	1.04969	+	3.23062i	0.0334120	+	0.102832i
$988$		0			0
$989$	64.2869	+	20.8881i	2.04420	+	0.664202i
$990$		0			0
$991$	−4.56887	−	14.0615i	−0.145135	−	0.446679i	0.851893	−	0.523715i	$-0.175454\pi$
$991$	−4.56887	−	14.0615i	−0.145135	−	0.446679i	−0.997028	+	0.0770360i	$0.975454\pi$
$992$		0			0
$993$			6.23268i			0.197788i
$994$		0			0
$995$	−13.1584	+	21.7859i	−0.417150	+	0.690661i
$996$		0			0
$997$	21.0204	+	15.2722i	0.665723	+	0.483676i	0.868591	−	0.495530i	$-0.165026\pi$
$997$	21.0204	+	15.2722i	0.665723	+	0.483676i	−0.202868	+	0.979206i	$0.565026\pi$
$998$		0			0
$999$	44.7952			1.41726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.529.10		112
4.3	odd	2		200.2.o.a.29.15	✓	112
8.3	odd	2		200.2.o.a.29.20	yes	112
8.5	even	2	inner	800.2.be.a.529.19		112
20.3	even	4		1000.2.t.b.101.56		224
20.7	even	4		1000.2.t.b.101.1		224
20.19	odd	2		1000.2.o.a.149.14		112
25.19	even	10	inner	800.2.be.a.369.19		112
40.3	even	4		1000.2.t.b.101.11		224
40.19	odd	2		1000.2.o.a.149.9		112
40.27	even	4		1000.2.t.b.101.46		224
100.19	odd	10		200.2.o.a.69.20	yes	112
100.31	odd	10		1000.2.o.a.349.9		112
100.67	even	20		1000.2.t.b.901.46		224
100.83	even	20		1000.2.t.b.901.11		224
200.19	odd	10		200.2.o.a.69.15	yes	112
200.67	even	20		1000.2.t.b.901.1		224
200.69	even	10	inner	800.2.be.a.369.10		112
200.83	even	20		1000.2.t.b.901.56		224
200.131	odd	10		1000.2.o.a.349.14		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.15	✓	112	4.3	odd	2
200.2.o.a.29.20	yes	112	8.3	odd	2
200.2.o.a.69.15	yes	112	200.19	odd	10
200.2.o.a.69.20	yes	112	100.19	odd	10
800.2.be.a.369.10		112	200.69	even	10	inner
800.2.be.a.369.19		112	25.19	even	10	inner
800.2.be.a.529.10		112	1.1	even	1	trivial
800.2.be.a.529.19		112	8.5	even	2	inner
1000.2.o.a.149.9		112	40.19	odd	2
1000.2.o.a.149.14		112	20.19	odd	2
1000.2.o.a.349.9		112	100.31	odd	10
1000.2.o.a.349.14		112	200.131	odd	10
1000.2.t.b.101.1		224	20.7	even	4
1000.2.t.b.101.11		224	40.3	even	4
1000.2.t.b.101.46		224	40.27	even	4
1000.2.t.b.101.56		224	20.3	even	4
1000.2.t.b.901.1		224	200.67	even	20
1000.2.t.b.901.11		224	100.83	even	20
1000.2.t.b.901.46		224	100.67	even	20
1000.2.t.b.901.56		224	200.83	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06117 - 0.770982i) q^{3} +(-1.15605 + 1.91404i) q^{5} -2.31589i q^{7} +(-0.395392 - 1.21689i) q^{9} +O(q^{10})\)	\(q+(-1.06117 - 0.770982i) q^{3} +(-1.15605 + 1.91404i) q^{5} -2.31589i q^{7} +(-0.395392 - 1.21689i) q^{9} +(0.219837 + 0.0714294i) q^{11} +(0.659008 + 2.02822i) q^{13} +(2.70245 - 1.13982i) q^{15} +(1.33923 + 1.84329i) q^{17} +(0.307368 + 0.423055i) q^{19} +(-1.78551 + 2.45754i) q^{21} +(-6.59576 - 2.14309i) q^{23} +(-2.32708 - 4.42546i) q^{25} +(-1.73461 + 5.33859i) q^{27} +(-5.13469 + 7.06729i) q^{29} +(-6.95750 + 5.05492i) q^{31} +(-0.178213 - 0.245289i) q^{33} +(4.43271 + 2.67729i) q^{35} +(-2.46601 - 7.58959i) q^{37} +(0.864403 - 2.66036i) q^{39} +(1.84490 + 5.67801i) q^{41} -9.74670 q^{43} +(2.78627 + 0.649995i) q^{45} +(0.657286 - 0.904676i) q^{47} +1.63664 q^{49} -2.98855i q^{51} +(-3.51671 - 2.55504i) q^{53} +(-0.390862 + 0.338200i) q^{55} -0.685906i q^{57} +(-4.66275 + 1.51502i) q^{59} +(-2.16726 - 0.704186i) q^{61} +(-2.81819 + 0.915685i) q^{63} +(-4.64393 - 1.08336i) q^{65} +(-2.55761 + 1.85821i) q^{67} +(5.34690 + 7.35938i) q^{69} +(5.30236 + 3.85239i) q^{71} +(-5.24971 - 1.70573i) q^{73} +(-0.942529 + 6.49028i) q^{75} +(0.165423 - 0.509119i) q^{77} +(10.1775 + 7.39438i) q^{79} +(2.85122 - 2.07153i) q^{81} +(-4.44876 + 3.23222i) q^{83} +(-5.07634 + 0.432393i) q^{85} +(10.8975 - 3.54081i) q^{87} +(-4.88895 + 15.0466i) q^{89} +(4.69713 - 1.52619i) q^{91} +11.2803 q^{93} +(-1.16508 + 0.0992390i) q^{95} +(7.50193 - 10.3255i) q^{97} -0.295760i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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