LMFDB - Embedded newform 800.2.be.a.529.4

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			529.4
Character	$\chi$	$=$	800.529
Dual form			800.2.be.a.369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03813 - 1.48079i) q^{3} +(-2.19360 - 0.433703i) q^{5} -3.58786i q^{7} +(1.03418 + 3.18289i) q^{9} +O(q^{10})$	\(q+(-2.03813 - 1.48079i) q^{3} +(-2.19360 - 0.433703i) q^{5} -3.58786i q^{7} +(1.03418 + 3.18289i) q^{9} +(2.49567 + 0.810891i) q^{11} +(-2.11444 - 6.50757i) q^{13} +(3.82862 + 4.13220i) q^{15} +(-1.14335 - 1.57369i) q^{17} +(-3.00859 - 4.14097i) q^{19} +(-5.31285 + 7.31251i) q^{21} +(0.737902 + 0.239759i) q^{23} +(4.62380 + 1.90275i) q^{25} +(0.269899 - 0.830663i) q^{27} +(-3.28631 + 4.52322i) q^{29} +(-1.72253 + 1.25149i) q^{31} +(-3.88573 - 5.34825i) q^{33} +(-1.55607 + 7.87034i) q^{35} +(2.73986 + 8.43241i) q^{37} +(-5.32683 + 16.3943i) q^{39} +(1.12308 + 3.45647i) q^{41} +0.652170 q^{43} +(-0.888162 - 7.43054i) q^{45} +(-0.541317 + 0.745059i) q^{47} -5.87273 q^{49} +4.90045i q^{51} +(-1.48529 - 1.07913i) q^{53} +(-5.12282 - 2.86115i) q^{55} +12.8949i q^{57} +(3.74706 - 1.21749i) q^{59} +(6.21266 + 2.01862i) q^{61} +(11.4198 - 3.71051i) q^{63} +(1.81589 + 15.1921i) q^{65} +(3.97847 - 2.89052i) q^{67} +(-1.14891 - 1.58133i) q^{69} +(-4.48762 - 3.26045i) q^{71} +(-14.1026 - 4.58222i) q^{73} +(-6.60634 - 10.7249i) q^{75} +(2.90936 - 8.95410i) q^{77} +(-7.65406 - 5.56100i) q^{79} +(6.34247 - 4.60807i) q^{81} +(-6.50869 + 4.72884i) q^{83} +(1.82555 + 3.94794i) q^{85} +(13.3958 - 4.35257i) q^{87} +(3.35636 - 10.3298i) q^{89} +(-23.3483 + 7.58631i) q^{91} +5.36393 q^{93} +(4.80370 + 10.3885i) q^{95} +(-3.31560 + 4.56353i) q^{97} +8.78205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.03813	−	1.48079i	−1.17671	−	0.854932i	−0.184916	−	0.982754i	$-0.559201\pi$
$3$	−2.03813	−	1.48079i	−1.17671	−	0.854932i	−0.991797	+	0.127822i	$0.959201\pi$
$4$		0			0
$5$	−2.19360	−	0.433703i	−0.981010	−	0.193958i
$5$	−2.19360	−	0.433703i	−0.981010	−	0.193958i
$6$		0			0
$7$		−	3.58786i		−	1.35608i	−0.735024	−	0.678042i	$-0.762829\pi$
$7$		−	3.58786i		−	1.35608i	0.735024	−	0.678042i	$-0.237171\pi$
$8$		0			0
$9$	1.03418	+	3.18289i	0.344728	+	1.06096i
$10$		0			0
$11$	2.49567	+	0.810891i	0.752472	+	0.244493i	0.660044	−	0.751227i	$-0.270537\pi$
$11$	2.49567	+	0.810891i	0.752472	+	0.244493i	0.0924272	+	0.995719i	$0.470537\pi$
$12$		0			0
$13$	−2.11444	−	6.50757i	−0.586440	−	1.80488i	−0.593410	−	0.804900i	$-0.702219\pi$
$13$	−2.11444	−	6.50757i	−0.586440	−	1.80488i	0.00697033	−	0.999976i	$-0.497781\pi$
$14$		0			0
$15$	3.82862	+	4.13220i	0.988547	+	1.06693i
$16$		0			0
$17$	−1.14335	−	1.57369i	−0.277304	−	0.381677i	0.647534	−	0.762036i	$-0.275800\pi$
$17$	−1.14335	−	1.57369i	−0.277304	−	0.381677i	−0.924839	+	0.380360i	$0.875800\pi$
$18$		0			0
$19$	−3.00859	−	4.14097i	−0.690218	−	0.950003i	0.309782	−	0.950808i	$-0.399744\pi$
$19$	−3.00859	−	4.14097i	−0.690218	−	0.950003i	−1.00000		0.000804663i	$0.999744\pi$
$20$		0			0
$21$	−5.31285	+	7.31251i	−1.15936	+	1.59572i
$22$		0			0
$23$	0.737902	+	0.239759i	0.153863	+	0.0499932i	0.384936	−	0.922943i	$-0.374224\pi$
$23$	0.737902	+	0.239759i	0.153863	+	0.0499932i	−0.231073	+	0.972936i	$0.574224\pi$
$24$		0			0
$25$	4.62380	+	1.90275i	0.924761	+	0.380549i
$26$		0			0
$27$	0.269899	−	0.830663i	0.0519421	−	0.159861i
$28$		0			0
$29$	−3.28631	+	4.52322i	−0.610252	+	0.839940i	−0.996598	−	0.0824137i	$-0.973737\pi$
$29$	−3.28631	+	4.52322i	−0.610252	+	0.839940i	0.386346	+	0.922354i	$0.373737\pi$
$30$		0			0
$31$	−1.72253	+	1.25149i	−0.309376	+	0.224775i	−0.731629	−	0.681704i	$-0.761239\pi$
$31$	−1.72253	+	1.25149i	−0.309376	+	0.224775i	0.422253	+	0.906478i	$0.361239\pi$
$32$		0			0
$33$	−3.88573	−	5.34825i	−0.676419	−	0.931010i
$34$		0			0
$35$	−1.55607	+	7.87034i	−0.263023	+	1.33033i
$36$		0			0
$37$	2.73986	+	8.43241i	0.450430	+	1.38628i	0.876418	+	0.481551i	$0.159926\pi$
$37$	2.73986	+	8.43241i	0.450430	+	1.38628i	−0.425988	+	0.904729i	$0.640074\pi$
$38$		0			0
$39$	−5.32683	+	16.3943i	−0.852975	+	2.62519i
$40$		0			0
$41$	1.12308	+	3.45647i	0.175395	+	0.539811i	0.999651	−	0.0264065i	$-0.00840642\pi$
$41$	1.12308	+	3.45647i	0.175395	+	0.539811i	−0.824256	+	0.566217i	$0.808406\pi$
$42$		0			0
$43$	0.652170			0.0994550			0.0497275	−	0.998763i	$-0.484165\pi$
$43$	0.652170			0.0994550			0.0497275	+	0.998763i	$0.484165\pi$
$44$		0			0
$45$	−0.888162	−	7.43054i	−0.132399	−	1.10768i
$46$		0			0
$47$	−0.541317	+	0.745059i	−0.0789592	+	0.108678i	−0.846670	−	0.532119i	$-0.821396\pi$
$47$	−0.541317	+	0.745059i	−0.0789592	+	0.108678i	0.767710	+	0.640797i	$0.221396\pi$
$48$		0			0
$49$	−5.87273			−0.838962
$50$		0			0
$51$			4.90045i			0.686201i
$52$		0			0
$53$	−1.48529	−	1.07913i	−0.204020	−	0.148229i	0.481084	−	0.876675i	$-0.340243\pi$
$53$	−1.48529	−	1.07913i	−0.204020	−	0.148229i	−0.685104	+	0.728445i	$0.740243\pi$
$54$		0			0
$55$	−5.12282	−	2.86115i	−0.690761	−	0.385798i
$56$		0			0
$57$			12.8949i			1.70797i
$58$		0			0
$59$	3.74706	−	1.21749i	0.487826	−	0.158504i	−0.0547685	−	0.998499i	$-0.517442\pi$
$59$	3.74706	−	1.21749i	0.487826	−	0.158504i	0.542594	+	0.839995i	$0.317442\pi$
$60$		0			0
$61$	6.21266	+	2.01862i	0.795449	+	0.258457i	0.678423	−	0.734672i	$-0.262664\pi$
$61$	6.21266	+	2.01862i	0.795449	+	0.258457i	0.117027	+	0.993129i	$0.462664\pi$
$62$		0			0
$63$	11.4198	−	3.71051i	1.43876	−	0.467480i
$64$		0			0
$65$	1.81589	+	15.1921i	0.225233	+	1.88435i
$66$		0			0
$67$	3.97847	−	2.89052i	0.486047	−	0.353134i	−0.317615	−	0.948220i	$-0.602882\pi$
$67$	3.97847	−	2.89052i	0.486047	−	0.353134i	0.803662	+	0.595086i	$0.202882\pi$
$68$		0			0
$69$	−1.14891	−	1.58133i	−0.138312	−	0.190370i
$70$		0			0
$71$	−4.48762	−	3.26045i	−0.532582	−	0.386944i	0.288740	−	0.957407i	$-0.406764\pi$
$71$	−4.48762	−	3.26045i	−0.532582	−	0.386944i	−0.821323	+	0.570464i	$0.806764\pi$
$72$		0			0
$73$	−14.1026	−	4.58222i	−1.65059	−	0.536309i	−0.671721	−	0.740804i	$-0.734445\pi$
$73$	−14.1026	−	4.58222i	−1.65059	−	0.536309i	−0.978868	+	0.204496i	$0.934445\pi$
$74$		0			0
$75$	−6.60634	−	10.7249i	−0.762835	−	1.23841i
$76$		0			0
$77$	2.90936	−	8.95410i	0.331553	−	1.02041i
$78$		0			0
$79$	−7.65406	−	5.56100i	−0.861148	−	0.625661i	0.0670487	−	0.997750i	$-0.478642\pi$
$79$	−7.65406	−	5.56100i	−0.861148	−	0.625661i	−0.928197	+	0.372089i	$0.878642\pi$
$80$		0			0
$81$	6.34247	−	4.60807i	0.704719	−	0.512008i
$82$		0			0
$83$	−6.50869	+	4.72884i	−0.714422	+	0.519058i	−0.884597	−	0.466356i	$-0.845567\pi$
$83$	−6.50869	+	4.72884i	−0.714422	+	0.519058i	0.170176	+	0.985414i	$0.445567\pi$
$84$		0			0
$85$	1.82555	+	3.94794i	0.198009	+	0.428214i
$86$		0			0
$87$	13.3958	−	4.35257i	1.43618	−	0.466645i
$88$		0			0
$89$	3.35636	−	10.3298i	0.355773	−	1.09496i	−0.599787	−	0.800160i	$-0.704748\pi$
$89$	3.35636	−	10.3298i	0.355773	−	1.09496i	0.955560	−	0.294797i	$-0.0952521\pi$
$90$		0			0
$91$	−23.3483	+	7.58631i	−2.44756	+	0.795261i
$92$		0			0
$93$	5.36393			0.556213
$94$		0			0
$95$	4.80370	+	10.3885i	0.492850	+	1.06584i
$96$		0			0
$97$	−3.31560	+	4.56353i	−0.336648	+	0.463356i	−0.943459	−	0.331490i	$-0.892449\pi$
$97$	−3.31560	+	4.56353i	−0.336648	+	0.463356i	0.606811	+	0.794846i	$0.292449\pi$
$98$		0			0
$99$			8.78205i			0.882629i
$100$		0			0
$101$		−	0.202935i		−	0.0201928i	−0.999949	−	0.0100964i	$-0.996786\pi$
$101$		−	0.202935i		−	0.0201928i	0.999949	−	0.0100964i	$-0.00321383\pi$
$102$		0			0
$103$	−7.76000	+	10.6807i	−0.764616	+	1.05240i	0.232201	+	0.972668i	$0.425407\pi$
$103$	−7.76000	+	10.6807i	−0.764616	+	1.05240i	−0.996816	+	0.0797351i	$0.974593\pi$
$104$		0			0
$105$	14.8258	−	13.7366i	1.44685	−	1.34055i
$106$		0			0
$107$	14.9185			1.44222			0.721111	−	0.692819i	$-0.243632\pi$
$107$	14.9185			1.44222			0.721111	+	0.692819i	$0.243632\pi$
$108$		0			0
$109$	8.22423	−	2.67221i	0.787738	−	0.255952i	0.112598	−	0.993641i	$-0.464083\pi$
$109$	8.22423	−	2.67221i	0.787738	−	0.255952i	0.675141	+	0.737689i	$0.264083\pi$
$110$		0			0
$111$	6.90242	−	21.2435i	0.655149	−	2.01634i
$112$		0			0
$113$	5.61964	−	1.82593i	0.528652	−	0.171769i	−0.0325164	−	0.999471i	$-0.510352\pi$
$113$	5.61964	−	1.82593i	0.528652	−	0.171769i	0.561168	+	0.827702i	$0.310352\pi$
$114$		0			0
$115$	−1.51468	−	0.845966i	−0.141245	−	0.0788867i
$116$		0			0
$117$	18.5262	−	13.4601i	1.71275	−	1.24438i
$118$		0			0
$119$	−5.64619	+	4.10220i	−0.517585	+	0.376048i
$120$		0			0
$121$	−3.32838	−	2.41821i	−0.302580	−	0.219837i
$122$		0			0
$123$	2.82933	−	8.70777i	0.255112	−	0.785153i
$124$		0			0
$125$	−9.31757	−	6.17923i	−0.833389	−	0.552687i
$126$		0			0
$127$	−3.36061	−	1.09193i	−0.298206	−	0.0968930i	0.156093	−	0.987742i	$-0.450110\pi$
$127$	−3.36061	−	1.09193i	−0.298206	−	0.0968930i	−0.454299	+	0.890849i	$0.650110\pi$
$128$		0			0
$129$	−1.32921	−	0.965725i	−0.117030	−	0.0850273i
$130$		0			0
$131$	3.96559	+	5.45817i	0.346475	+	0.476883i	0.946319	−	0.323235i	$-0.104770\pi$
$131$	3.96559	+	5.45817i	0.346475	+	0.476883i	−0.599843	+	0.800118i	$0.704770\pi$
$132$		0			0
$133$	−14.8572	+	10.7944i	−1.28828	+	0.935992i
$134$		0			0
$135$	−0.952313	+	1.70509i	−0.0819620	+	0.146751i
$136$		0			0
$137$	7.83872	−	2.54696i	0.669707	−	0.217601i	0.0456237	−	0.998959i	$-0.485472\pi$
$137$	7.83872	−	2.54696i	0.669707	−	0.217601i	0.624084	+	0.781358i	$0.285472\pi$
$138$		0			0
$139$	−1.29543	−	0.420910i	−0.109877	−	0.0357011i	0.253563	−	0.967319i	$-0.418398\pi$
$139$	−1.29543	−	0.420910i	−0.109877	−	0.0357011i	−0.363439	+	0.931618i	$0.618398\pi$
$140$		0			0
$141$	2.20655	−	0.716950i	0.185825	−	0.0603781i
$142$		0			0
$143$		−	17.9553i		−	1.50150i
$144$		0			0
$145$	9.17060	−	8.49687i	0.761577	−	0.705626i
$146$		0			0
$147$	11.9694	+	8.69626i	0.987218	+	0.717256i
$148$		0			0
$149$			9.46274i			0.775218i	0.921824	+	0.387609i	$0.126699\pi$
$149$			9.46274i			0.775218i	−0.921824	+	0.387609i	$0.873301\pi$
$150$		0			0
$151$	−7.99542			−0.650658			−0.325329	−	0.945601i	$-0.605475\pi$
$151$	−7.99542			−0.650658			−0.325329	+	0.945601i	$0.605475\pi$
$152$		0			0
$153$	3.82646	−	5.26667i	0.309351	−	0.425785i
$154$		0			0
$155$	4.32133	−	1.99821i	0.347097	−	0.160500i
$156$		0			0
$157$	−7.78075			−0.620971			−0.310486	−	0.950578i	$-0.600492\pi$
$157$	−7.78075			−0.620971			−0.310486	+	0.950578i	$0.600492\pi$
$158$		0			0
$159$	1.42926	+	4.39880i	0.113347	+	0.348847i
$160$		0			0
$161$	0.860221	−	2.64749i	0.0677949	−	0.208651i
$162$		0			0
$163$	−7.10008	−	21.8518i	−0.556121	−	1.71157i	−0.692964	−	0.720973i	$-0.743695\pi$
$163$	−7.10008	−	21.8518i	−0.556121	−	1.71157i	0.136842	−	0.990593i	$-0.456305\pi$
$164$		0			0
$165$	6.20420	+	13.4172i	0.482997	+	1.04453i
$166$		0			0
$167$	7.10896	+	9.78464i	0.550108	+	0.757158i	0.990027	−	0.140879i	$-0.0449929\pi$
$167$	7.10896	+	9.78464i	0.550108	+	0.757158i	−0.439919	+	0.898037i	$0.644993\pi$
$168$		0			0
$169$	−27.3604	+	19.8785i	−2.10465	+	1.52912i
$170$		0			0
$171$	10.0688	−	13.8585i	0.769982	−	1.05979i
$172$		0			0
$173$	4.88649	−	15.0391i	0.371513	−	1.14340i	−0.574288	−	0.818653i	$-0.694721\pi$
$173$	4.88649	−	15.0391i	0.371513	−	1.14340i	0.945801	−	0.324747i	$-0.105279\pi$
$174$		0			0
$175$	6.82678	−	16.5896i	0.516056	−	1.25405i
$176$		0			0
$177$	−9.43984	−	3.06719i	−0.709542	−	0.230544i
$178$		0			0
$179$	−8.68076	+	11.9480i	−0.648830	+	0.893038i	−0.999048	−	0.0436301i	$-0.986108\pi$
$179$	−8.68076	+	11.9480i	−0.648830	+	0.893038i	0.350217	+	0.936668i	$0.386108\pi$
$180$		0			0
$181$	−3.16443	−	4.35546i	−0.235210	−	0.323739i	0.675053	−	0.737769i	$-0.264121\pi$
$181$	−3.16443	−	4.35546i	−0.235210	−	0.323739i	−0.910263	+	0.414030i	$0.864121\pi$
$182$		0			0
$183$	−9.67305	−	13.3138i	−0.715053	−	0.984186i
$184$		0			0
$185$	−2.35300	−	19.6857i	−0.172996	−	1.44732i
$186$		0			0
$187$	−1.57734	−	4.85455i	−0.115346	−	0.355000i
$188$		0			0
$189$	−2.98030	−	0.968359i	−0.216785	−	0.0704378i
$190$		0			0
$191$	−3.20367	−	9.85988i	−0.231809	−	0.713436i	−0.997529	−	0.0702610i	$-0.977617\pi$
$191$	−3.20367	−	9.85988i	−0.231809	−	0.713436i	0.765719	−	0.643175i	$-0.222383\pi$
$192$		0			0
$193$		−	0.720451i		−	0.0518592i	−0.999664	−	0.0259296i	$-0.991745\pi$
$193$		−	0.720451i		−	0.0518592i	0.999664	−	0.0259296i	$-0.00825458\pi$
$194$		0			0
$195$	18.7952	−	33.6523i	1.34595	−	2.40989i
$196$		0			0
$197$	−4.83357	−	3.51179i	−0.344377	−	0.250205i	0.402129	−	0.915583i	$-0.368270\pi$
$197$	−4.83357	−	3.51179i	−0.344377	−	0.250205i	−0.746506	+	0.665378i	$0.768270\pi$
$198$		0			0
$199$	13.1660			0.933311			0.466655	−	0.884439i	$-0.345459\pi$
$199$	13.1660			0.933311			0.466655	+	0.884439i	$0.345459\pi$
$200$		0			0
$201$	−12.3889			−0.873843
$202$		0			0
$203$	16.2287	+	11.7908i	1.13903	+	0.827553i
$204$		0			0
$205$	−0.964503	−	8.06922i	−0.0673638	−	0.563579i
$206$		0			0
$207$			2.59662i			0.180477i
$208$		0			0
$209$	−4.15056	−	12.7741i	−0.287100	−	0.883603i
$210$		0			0
$211$	5.22662	+	1.69823i	0.359816	+	0.116911i	0.483346	−	0.875430i	$-0.339421\pi$
$211$	5.22662	+	1.69823i	0.359816	+	0.116911i	−0.123530	+	0.992341i	$0.539421\pi$
$212$		0			0
$213$	4.31832	+	13.2904i	0.295886	+	0.910644i
$214$		0			0
$215$	−1.43060	−	0.282848i	−0.0975664	−	0.0192901i
$216$		0			0
$217$	4.49018	+	6.18020i	0.304813	+	0.419539i
$218$		0			0
$219$	21.9577	+	30.2221i	1.48376	+	2.04222i
$220$		0			0
$221$	−7.82337	+	10.7679i	−0.526257	+	0.724330i
$222$		0			0
$223$	19.3706	+	6.29390i	1.29715	+	0.421471i	0.874590	−	0.484862i	$-0.161130\pi$
$223$	19.3706	+	6.29390i	1.29715	+	0.421471i	0.422564	+	0.906333i	$0.361130\pi$
$224$		0			0
$225$	−1.27437	+	16.6849i	−0.0849581	+	1.11232i
$226$		0			0
$227$	4.89137	−	15.0541i	0.324652	−	0.999175i	−0.646946	−	0.762536i	$-0.723954\pi$
$227$	4.89137	−	15.0541i	0.324652	−	0.999175i	0.971598	−	0.236639i	$-0.0760460\pi$
$228$		0			0
$229$	3.76598	−	5.18342i	0.248863	−	0.342530i	−0.666250	−	0.745729i	$-0.732102\pi$
$229$	3.76598	−	5.18342i	0.248863	−	0.342530i	0.915113	+	0.403198i	$0.132102\pi$
$230$		0			0
$231$	−19.1888	+	13.9414i	−1.26253	+	0.917280i
$232$		0			0
$233$	−10.3375	−	14.2284i	−0.677234	−	0.932133i	0.322662	−	0.946514i	$-0.395422\pi$
$233$	−10.3375	−	14.2284i	−0.677234	−	0.932133i	−0.999897	+	0.0143813i	$0.995422\pi$
$234$		0			0
$235$	1.51057	−	1.39959i	0.0985387	−	0.0912994i
$236$		0			0
$237$	7.36529	+	22.6680i	0.478427	+	1.47245i
$238$		0			0
$239$	2.60748	−	8.02498i	0.168664	−	0.519093i	−0.830624	−	0.556834i	$-0.812016\pi$
$239$	2.60748	−	8.02498i	0.168664	−	0.519093i	0.999288	+	0.0377406i	$0.0120161\pi$
$240$		0			0
$241$	1.07674	+	3.31387i	0.0693591	+	0.213465i	0.979728	−	0.200332i	$-0.0642022\pi$
$241$	1.07674	+	3.31387i	0.0693591	+	0.213465i	−0.910369	+	0.413797i	$0.864202\pi$
$242$		0			0
$243$	−22.3706			−1.43507
$244$		0			0
$245$	12.8825	+	2.54702i	0.823030	+	0.162723i
$246$		0			0
$247$	−20.5862	+	28.3344i	−1.30987	+	1.80288i
$248$		0			0
$249$	20.2679			1.28443
$250$		0			0
$251$			16.8769i			1.06526i	0.846347	+	0.532632i	$0.178797\pi$
$251$			16.8769i			1.06526i	−0.846347	+	0.532632i	$0.821203\pi$
$252$		0			0
$253$	1.64714	+	1.19672i	0.103555	+	0.0752369i
$254$		0			0
$255$	2.12534	−	10.7497i	0.133094	−	0.673169i
$256$		0			0
$257$			4.42621i			0.276099i	0.990425	+	0.138050i	$0.0440833\pi$
$257$			4.42621i			0.276099i	−0.990425	+	0.138050i	$0.955917\pi$
$258$		0			0
$259$	30.2543	−	9.83022i	1.87991	−	0.610820i
$260$		0			0
$261$	−17.7956	−	5.78213i	−1.10152	−	0.357905i
$262$		0			0
$263$	11.6771	−	3.79412i	0.720041	−	0.233956i	0.0740002	−	0.997258i	$-0.476423\pi$
$263$	11.6771	−	3.79412i	0.720041	−	0.233956i	0.646041	+	0.763303i	$0.276423\pi$
$264$		0			0
$265$	2.79012	+	3.01135i	0.171396	+	0.184986i
$266$		0			0
$267$	−22.1369	+	16.0834i	−1.35476	+	0.984289i
$268$		0			0
$269$	16.8702	+	23.2198i	1.02859	+	1.41573i	0.906000	+	0.423277i	$0.139120\pi$
$269$	16.8702	+	23.2198i	1.02859	+	1.41573i	0.122591	+	0.992457i	$0.460880\pi$
$270$		0			0
$271$	2.96640	+	2.15522i	0.180196	+	0.130920i	0.674227	−	0.738524i	$-0.264477\pi$
$271$	2.96640	+	2.15522i	0.180196	+	0.130920i	−0.494031	+	0.869444i	$0.664477\pi$
$272$		0			0
$273$	58.8204	+	19.1119i	3.55997	+	1.15671i
$274$		0			0
$275$	9.99655	+	8.49802i	0.602815	+	0.512450i
$276$		0			0
$277$	−1.23158	+	3.79042i	−0.0739986	+	0.227744i	−0.981214	−	0.192922i	$-0.938204\pi$
$277$	−1.23158	+	3.79042i	−0.0739986	+	0.227744i	0.907216	+	0.420666i	$0.138204\pi$
$278$		0			0
$279$	−5.76478	−	4.18836i	−0.345128	−	0.250750i
$280$		0			0
$281$	−23.0045	+	16.7138i	−1.37234	+	0.997060i	−0.374785	+	0.927112i	$0.622283\pi$
$281$	−23.0045	+	16.7138i	−1.37234	+	0.997060i	−0.997551	+	0.0699483i	$0.977717\pi$
$282$		0			0
$283$	−10.5601	+	7.67233i	−0.627730	+	0.456073i	−0.855613	−	0.517616i	$-0.826820\pi$
$283$	−10.5601	+	7.67233i	−0.627730	+	0.456073i	0.227883	+	0.973689i	$0.426820\pi$
$284$		0			0
$285$	5.59256	−	28.2863i	0.331274	−	1.67554i
$286$		0			0
$287$	12.4013	−	4.02944i	0.732028	−	0.237850i
$288$		0			0
$289$	4.08404	−	12.5694i	0.240238	−	0.739375i
$290$		0			0
$291$	13.5152	−	4.39136i	0.792277	−	0.257426i
$292$		0			0
$293$	−27.0373			−1.57954			−0.789769	−	0.613404i	$-0.789800\pi$
$293$	−27.0373			−1.57954			−0.789769	+	0.613404i	$0.789800\pi$
$294$		0			0
$295$	−8.74760	+	1.04559i	−0.509305	+	0.0608765i
$296$		0			0
$297$	1.34715	−	1.85420i	0.0781698	−	0.107592i
$298$		0			0
$299$		−	5.30890i		−	0.307022i
$300$		0			0
$301$		−	2.33989i		−	0.134869i
$302$		0			0
$303$	−0.300503	+	0.413607i	−0.0172635	+	0.0237611i
$304$		0			0
$305$	−12.7526	−	7.12249i	−0.730214	−	0.407833i
$306$		0			0
$307$	−23.1194			−1.31949			−0.659747	−	0.751488i	$-0.729336\pi$
$307$	−23.1194			−1.31949			−0.659747	+	0.751488i	$0.729336\pi$
$308$		0			0
$309$	31.6317	−	10.2778i	1.79947	−	0.584682i
$310$		0			0
$311$	−3.30515	+	10.1722i	−0.187418	+	0.576813i	−0.999982	−	0.00605932i	$-0.998071\pi$
$311$	−3.30515	+	10.1722i	−0.187418	+	0.576813i	0.812564	+	0.582872i	$0.198071\pi$
$312$		0			0
$313$	6.62056	−	2.15115i	0.374216	−	0.121590i	−0.115870	−	0.993264i	$-0.536965\pi$
$313$	6.62056	−	2.15115i	0.374216	−	0.121590i	0.490086	+	0.871674i	$0.336965\pi$
$314$		0			0
$315$	−26.6597	+	3.18660i	−1.50211	+	0.179545i
$316$		0			0
$317$	−2.26671	+	1.64686i	−0.127311	+	0.0924971i	−0.649619	−	0.760260i	$-0.725071\pi$
$317$	−2.26671	+	1.64686i	−0.127311	+	0.0924971i	0.522307	+	0.852757i	$0.325071\pi$
$318$		0			0
$319$	−11.8694	+	8.62360i	−0.664557	+	0.482829i
$320$		0			0
$321$	−30.4057	−	22.0911i	−1.69708	−	1.23300i
$322$		0			0
$323$	−3.07673	+	9.46919i	−0.171194	+	0.526880i
$324$		0			0
$325$	2.60551	−	34.1130i	0.144528	−	1.89225i
$326$		0			0
$327$	−20.7190	−	6.73201i	−1.14576	−	0.372281i
$328$		0			0
$329$	2.67317	+	1.94217i	0.147376	+	0.107075i
$330$		0			0
$331$	−15.6066	−	21.4807i	−0.857819	−	1.18069i	−0.982085	−	0.188437i	$-0.939658\pi$
$331$	−15.6066	−	21.4807i	−0.857819	−	1.18069i	0.124266	−	0.992249i	$-0.460342\pi$
$332$		0			0
$333$	−24.0060	+	17.4413i	−1.31552	+	0.955780i
$334$		0			0
$335$	−9.98081	+	4.61520i	−0.545310	+	0.252155i
$336$		0			0
$337$	−18.1528	+	5.89820i	−0.988845	+	0.321295i	−0.758400	−	0.651790i	$-0.774018\pi$
$337$	−18.1528	+	5.89820i	−0.988845	+	0.321295i	−0.230446	+	0.973085i	$0.574018\pi$
$338$		0			0
$339$	−14.1574	−	4.60001i	−0.768923	−	0.249838i
$340$		0			0
$341$	−5.31368	+	1.72652i	−0.287752	+	0.0934963i
$342$		0			0
$343$		−	4.04448i		−	0.218381i
$344$		0			0
$345$	1.83442	+	3.96711i	0.0987617	+	0.213582i
$346$		0			0
$347$	−15.5716	−	11.3134i	−0.835926	−	0.607336i	0.0853039	−	0.996355i	$-0.472814\pi$
$347$	−15.5716	−	11.3134i	−0.835926	−	0.607336i	−0.921230	+	0.389019i	$0.872814\pi$
$348$		0			0
$349$			0.0595710i			0.00318876i	0.999999	+	0.00159438i	$0.000507507\pi$
$349$			0.0595710i			0.00318876i	−0.999999	+	0.00159438i	$0.999492\pi$
$350$		0			0
$351$	−5.97629			−0.318991
$352$		0			0
$353$	−11.4459	+	15.7539i	−0.609203	+	0.838497i	−0.996512	−	0.0834537i	$-0.973405\pi$
$353$	−11.4459	+	15.7539i	−0.609203	+	0.838497i	0.387308	+	0.921950i	$0.373405\pi$
$354$		0			0
$355$	8.43000	+	9.09842i	0.447418	+	0.482894i
$356$		0			0
$357$	17.5821			0.930545
$358$		0			0
$359$	−7.90364	−	24.3249i	−0.417138	−	1.28382i	−0.910324	−	0.413896i	$-0.864168\pi$
$359$	−7.90364	−	24.3249i	−0.417138	−	1.28382i	0.493186	−	0.869924i	$-0.335832\pi$
$360$		0			0
$361$	−2.22468	+	6.84685i	−0.117088	+	0.360361i
$362$		0			0
$363$	3.20281	+	9.85725i	0.168104	+	0.517371i
$364$		0			0
$365$	28.9483	+	16.1679i	1.51522	+	0.846269i
$366$		0			0
$367$	16.9820	+	23.3737i	0.886453	+	1.22010i	0.974592	+	0.223990i	$0.0719082\pi$
$367$	16.9820	+	23.3737i	0.886453	+	1.22010i	−0.0881385	+	0.996108i	$0.528092\pi$
$368$		0			0
$369$	−9.84012	+	7.14927i	−0.512256	+	0.372176i
$370$		0			0
$371$	−3.87175	+	5.32901i	−0.201011	+	0.276669i
$372$		0			0
$373$	7.68840	−	23.6625i	0.398090	−	1.22520i	−0.528438	−	0.848972i	$-0.677222\pi$
$373$	7.68840	−	23.6625i	0.398090	−	1.22520i	0.926529	−	0.376224i	$-0.122778\pi$
$374$		0			0
$375$	9.84028	+	26.3914i	0.508150	+	1.36285i
$376$		0			0
$377$	36.3839	+	11.8218i	1.87386	+	0.608855i
$378$		0			0
$379$	−3.80553	+	5.23786i	−0.195477	+	0.269051i	−0.895492	−	0.445077i	$-0.853176\pi$
$379$	−3.80553	+	5.23786i	−0.195477	+	0.269051i	0.700016	+	0.714128i	$0.253176\pi$
$380$		0			0
$381$	5.23244	+	7.20183i	0.268066	+	0.368961i
$382$		0			0
$383$	−1.79838	−	2.47525i	−0.0918928	−	0.126480i	0.760595	−	0.649227i	$-0.224907\pi$
$383$	−1.79838	−	2.47525i	−0.0918928	−	0.126480i	−0.852488	+	0.522747i	$0.824907\pi$
$384$		0			0
$385$	−10.2654	+	18.3799i	−0.523174	+	0.936729i
$386$		0			0
$387$	0.674465	+	2.07579i	0.0342850	+	0.105518i
$388$		0			0
$389$	−26.7250	−	8.68349i	−1.35501	−	0.440270i	−0.460637	−	0.887588i	$-0.652379\pi$
$389$	−26.7250	−	8.68349i	−1.35501	−	0.440270i	−0.894375	+	0.447318i	$0.852379\pi$
$390$		0			0
$391$	−0.466377	−	1.43536i	−0.0235857	−	0.0725893i
$392$		0			0
$393$		−	16.9966i		−	0.857367i
$394$		0			0
$395$	14.3782	+	15.5182i	0.723443	+	0.780806i
$396$		0			0
$397$	−28.3014	−	20.5622i	−1.42041	−	1.03199i	−0.991704	−	0.128539i	$-0.958971\pi$
$397$	−28.3014	−	20.5622i	−1.42041	−	1.03199i	−0.428701	−	0.903446i	$-0.641029\pi$
$398$		0			0
$399$	46.2651			2.31615
$400$		0			0
$401$	13.3727			0.667799			0.333900	−	0.942609i	$-0.391635\pi$
$401$	13.3727			0.667799			0.333900	+	0.942609i	$0.391635\pi$
$402$		0			0
$403$	11.7864	+	8.56329i	0.587120	+	0.426568i
$404$		0			0
$405$	−15.9114	+	7.35755i	−0.790644	+	0.365599i
$406$		0			0
$407$			23.2662i			1.15326i
$408$		0			0
$409$	8.50186	+	26.1660i	0.420390	+	1.29383i	0.907340	+	0.420397i	$0.138109\pi$
$409$	8.50186	+	26.1660i	0.420390	+	1.29383i	−0.486950	+	0.873430i	$0.661891\pi$
$410$		0			0
$411$	−19.7478	−	6.41645i	−0.974088	−	0.316500i
$412$		0			0
$413$	−4.36820	−	13.4439i	−0.214945	−	0.661533i
$414$		0			0
$415$	16.3284	−	7.55037i	0.801530	−	0.370633i
$416$		0			0
$417$	2.01697	+	2.77612i	0.0987713	+	0.135947i
$418$		0			0
$419$	−23.3551	−	32.1455i	−1.14097	−	1.57041i	−0.765321	−	0.643648i	$-0.777420\pi$
$419$	−23.3551	−	32.1455i	−1.14097	−	1.57041i	−0.375649	−	0.926762i	$-0.622580\pi$
$420$		0			0
$421$	−2.75042	+	3.78563i	−0.134047	+	0.184500i	−0.870764	−	0.491701i	$-0.836375\pi$
$421$	−2.75042	+	3.78563i	−0.134047	+	0.184500i	0.736717	+	0.676202i	$0.236375\pi$
$422$		0			0
$423$	−2.93127	−	0.952426i	−0.142523	−	0.0463085i
$424$		0			0
$425$	−2.29231	−	9.45196i	−0.111193	−	0.458487i
$426$		0			0
$427$	7.24251	−	22.2901i	0.350489	−	1.07870i
$428$		0			0
$429$	−26.5880	+	36.5952i	−1.28368	+	1.76683i
$430$		0			0
$431$	16.2735	−	11.8234i	0.783869	−	0.569514i	−0.122269	−	0.992497i	$-0.539017\pi$
$431$	16.2735	−	11.8234i	0.783869	−	0.569514i	0.906138	+	0.422983i	$0.139017\pi$
$432$		0			0
$433$	−0.827085	−	1.13838i	−0.0397472	−	0.0547073i	0.788681	−	0.614803i	$-0.210764\pi$
$433$	−0.827085	−	1.13838i	−0.0397472	−	0.0547073i	−0.828428	+	0.560096i	$0.810764\pi$
$434$		0			0
$435$	−31.2729	+	3.73801i	−1.49942	+	0.179224i
$436$		0			0
$437$	−1.22721	−	3.77696i	−0.0587054	−	0.180677i
$438$		0			0
$439$	4.33963	−	13.3560i	0.207119	−	0.637447i	−0.792500	−	0.609871i	$-0.791221\pi$
$439$	4.33963	−	13.3560i	0.207119	−	0.637447i	0.999620	−	0.0275762i	$-0.00877888\pi$
$440$		0			0
$441$	−6.07349	−	18.6923i	−0.289214	−	0.890109i
$442$		0			0
$443$	−9.37158			−0.445257			−0.222629	−	0.974903i	$-0.571464\pi$
$443$	−9.37158			−0.445257			−0.222629	+	0.974903i	$0.571464\pi$
$444$		0			0
$445$	−11.8426	+	21.2039i	−0.561393	+	1.00516i
$446$		0			0
$447$	14.0123	−	19.2863i	0.662759	−	0.912210i
$448$		0			0
$449$	27.0993			1.27889			0.639447	−	0.768835i	$-0.279163\pi$
$449$	27.0993			1.27889			0.639447	+	0.768835i	$0.279163\pi$
$450$		0			0
$451$			9.53690i			0.449075i
$452$		0			0
$453$	16.2957	+	11.8395i	0.765638	+	0.556269i
$454$		0			0
$455$	54.5070	−	6.51515i	2.55533	−	0.305435i
$456$		0			0
$457$		−	32.1890i		−	1.50574i	−0.658170	−	0.752869i	$-0.728669\pi$
$457$		−	32.1890i		−	1.50574i	0.658170	−	0.752869i	$-0.271331\pi$
$458$		0			0
$459$	−1.61580	+	0.525005i	−0.0754190	+	0.0245051i
$460$		0			0
$461$	−2.49963	−	0.812178i	−0.116419	−	0.0378269i	0.250228	−	0.968187i	$-0.419494\pi$
$461$	−2.49963	−	0.812178i	−0.116419	−	0.0378269i	−0.366647	+	0.930360i	$0.619494\pi$
$462$		0			0
$463$	−28.7725	+	9.34875i	−1.33717	+	0.434473i	−0.888358	−	0.459152i	$-0.848153\pi$
$463$	−28.7725	+	9.34875i	−1.33717	+	0.434473i	−0.448814	+	0.893625i	$0.648153\pi$
$464$		0			0
$465$	−11.7663	−	2.32635i	−0.545651	−	0.107882i
$466$		0			0
$467$	−33.3692	+	24.2441i	−1.54414	+	1.12188i	−0.596471	+	0.802635i	$0.703431\pi$
$467$	−33.3692	+	24.2441i	−1.54414	+	1.12188i	−0.947671	+	0.319250i	$0.896569\pi$
$468$		0			0
$469$	−10.3708	−	14.2742i	−0.478879	−	0.659120i
$470$		0			0
$471$	15.8582	+	11.5216i	0.730705	+	0.530889i
$472$		0			0
$473$	1.62760	+	0.528839i	0.0748371	+	0.0243160i
$474$		0			0
$475$	−6.03191	−	24.8716i	−0.276763	−	1.14119i
$476$		0			0
$477$	1.89868	−	5.84354i	0.0869346	−	0.267557i
$478$		0			0
$479$	−12.7715	−	9.27902i	−0.583544	−	0.423969i	0.256456	−	0.966556i	$-0.417445\pi$
$479$	−12.7715	−	9.27902i	−0.583544	−	0.423969i	−0.840000	+	0.542586i	$0.817445\pi$
$480$		0			0
$481$	49.0813	−	35.6596i	2.23791	−	1.62594i
$482$		0			0
$483$	−5.67360	+	4.12211i	−0.258158	+	0.187563i
$484$		0			0
$485$	9.25233	−	8.57260i	0.420127	−	0.389262i
$486$		0			0
$487$	−34.0773	+	11.0724i	−1.54419	+	0.501738i	−0.952529	−	0.304449i	$-0.901528\pi$
$487$	−34.0773	+	11.0724i	−1.54419	+	0.501738i	−0.591661	+	0.806187i	$0.701528\pi$
$488$		0			0
$489$	−17.8870	+	55.0505i	−0.808877	+	2.48947i
$490$		0			0
$491$	−7.10672	+	2.30911i	−0.320722	+	0.104209i	−0.464954	−	0.885335i	$-0.653929\pi$
$491$	−7.10672	+	2.30911i	−0.320722	+	0.104209i	0.144232	+	0.989544i	$0.453929\pi$
$492$		0			0
$493$	10.8756			0.489811
$494$		0			0
$495$	3.80880	−	19.2643i	0.171193	−	0.865868i
$496$		0			0
$497$	−11.6980	+	16.1009i	−0.524728	+	0.722226i
$498$		0			0
$499$			1.61567i			0.0723272i	0.999346	+	0.0361636i	$0.0115137\pi$
$499$			1.61567i			0.0723272i	−0.999346	+	0.0361636i	$0.988486\pi$
$500$		0			0
$501$		−	30.4692i		−	1.36126i
$502$		0			0
$503$	−17.4576	+	24.0283i	−0.778395	+	1.07137i	0.217062	+	0.976158i	$0.430353\pi$
$503$	−17.4576	+	24.0283i	−0.778395	+	1.07137i	−0.995457	+	0.0952114i	$0.969647\pi$
$504$		0			0
$505$	−0.0880134	+	0.445159i	−0.00391655	+	0.0198093i
$506$		0			0
$507$	85.1999			3.78386
$508$		0			0
$509$	1.21315	−	0.394177i	0.0537721	−	0.0174716i	−0.282007	−	0.959412i	$-0.591000\pi$
$509$	1.21315	−	0.394177i	0.0537721	−	0.0174716i	0.335780	+	0.941941i	$0.391000\pi$
$510$		0			0
$511$	−16.4404	+	50.5983i	−0.727279	+	2.23834i
$512$		0			0
$513$	−4.25176	+	1.38148i	−0.187720	+	0.0609939i
$514$		0			0
$515$	21.6546	−	20.0638i	0.954217	−	0.884114i
$516$		0			0
$517$	−1.95511	+	1.42047i	−0.0859855	+	0.0624722i
$518$		0			0
$519$	−32.2290	+	23.4157i	−1.41469	+	1.02784i
$520$		0			0
$521$	9.44563	+	6.86265i	0.413821	+	0.300658i	0.775147	−	0.631781i	$-0.217676\pi$
$521$	9.44563	+	6.86265i	0.413821	+	0.300658i	−0.361326	+	0.932440i	$0.617676\pi$
$522$		0			0
$523$	6.21617	−	19.1314i	0.271814	−	0.836558i	−0.718230	−	0.695805i	$-0.755048\pi$
$523$	6.21617	−	19.1314i	0.271814	−	0.836558i	0.990045	−	0.140753i	$-0.0449524\pi$
$524$		0			0
$525$	−38.4794	+	23.7026i	−1.67938	+	1.03447i
$526$		0			0
$527$	3.93893	+	1.27984i	0.171582	+	0.0557505i
$528$		0			0
$529$	−18.1204	−	13.1652i	−0.787842	−	0.572401i
$530$		0			0
$531$	7.75031	+	10.6674i	0.336335	+	0.462925i
$532$		0			0
$533$	20.1186	−	14.6170i	0.871432	−	0.633133i
$534$		0			0
$535$	−32.7252	−	6.47018i	−1.41483	−	0.279730i
$536$		0			0
$537$	35.3850	−	11.4973i	1.52697	−	0.496144i
$538$		0			0
$539$	−14.6564	−	4.76215i	−0.631295	−	0.205120i
$540$		0			0
$541$	19.0637	−	6.19417i	0.819612	−	0.266308i	0.130949	−	0.991389i	$-0.458198\pi$
$541$	19.0637	−	6.19417i	0.819612	−	0.266308i	0.688664	+	0.725081i	$0.258198\pi$
$542$		0			0
$543$			13.5628i			0.582036i
$544$		0			0
$545$	−19.1997	+	2.29491i	−0.822423	+	0.0983031i
$546$		0			0
$547$	31.1058	+	22.5997i	1.32999	+	0.966293i	0.999749	+	0.0223953i	$0.00712924\pi$
$547$	31.1058	+	22.5997i	1.32999	+	0.966293i	0.330239	+	0.943897i	$0.392871\pi$
$548$		0			0
$549$			21.8619i			0.933041i
$550$		0			0
$551$	28.6176			1.21915
$552$		0			0
$553$	−19.9521	+	27.4617i	−0.848448	+	1.16779i
$554$		0			0
$555$	−24.3545	+	43.6062i	−1.03379	+	1.85098i
$556$		0			0
$557$	10.9707			0.464844			0.232422	−	0.972615i	$-0.425335\pi$
$557$	10.9707			0.464844			0.232422	+	0.972615i	$0.425335\pi$
$558$		0			0
$559$	−1.37897	−	4.24405i	−0.0583244	−	0.179504i
$560$		0			0
$561$	−3.97373	+	12.2299i	−0.167771	+	0.516346i
$562$		0			0
$563$	0.325391	+	1.00145i	0.0137136	+	0.0422061i	0.957679	−	0.287838i	$-0.0929364\pi$
$563$	0.325391	+	1.00145i	0.0137136	+	0.0422061i	−0.943966	+	0.330044i	$0.892936\pi$
$564$		0			0
$565$	−13.1192	+	1.56812i	−0.551929	+	0.0659713i
$566$		0			0
$567$	−16.5331	−	22.7559i	−0.694326	−	0.955658i
$568$		0			0
$569$	16.4403	−	11.9446i	0.689213	−	0.500743i	−0.187188	−	0.982324i	$-0.559937\pi$
$569$	16.4403	−	11.9446i	0.689213	−	0.500743i	0.876401	+	0.481581i	$0.159937\pi$
$570$		0			0
$571$	8.81803	−	12.1370i	0.369023	−	0.507917i	−0.583612	−	0.812033i	$-0.698361\pi$
$571$	8.81803	−	12.1370i	0.369023	−	0.507917i	0.952635	+	0.304116i	$0.0983610\pi$
$572$		0			0
$573$	−8.07089	+	24.8396i	−0.337166	+	1.03769i
$574$		0			0
$575$	2.95571	+	2.51264i	0.123262	+	0.104784i
$576$		0			0
$577$	−27.0844	−	8.80026i	−1.12754	−	0.366360i	−0.314899	−	0.949125i	$-0.601971\pi$
$577$	−27.0844	−	8.80026i	−1.12754	−	0.366360i	−0.812640	+	0.582765i	$0.801971\pi$
$578$		0			0
$579$	−1.06683	+	1.46837i	−0.0443361	+	0.0610235i
$580$		0			0
$581$	16.9664	+	23.3523i	0.703885	+	0.968815i
$582$		0			0
$583$	−2.83173	−	3.89755i	−0.117278	−	0.161420i
$584$		0			0
$585$	−46.4768	+	21.4912i	−1.92158	+	0.888552i
$586$		0			0
$587$	−10.7007	−	32.9333i	−0.441664	−	1.35930i	−0.886101	−	0.463491i	$-0.846597\pi$
$587$	−10.7007	−	32.9333i	−0.441664	−	1.35930i	0.444438	−	0.895810i	$-0.353403\pi$
$588$		0			0
$589$	10.3648	+	3.36772i	0.427073	+	0.138764i
$590$		0			0
$591$	4.65121	+	14.3150i	0.191325	+	0.588839i
$592$		0			0
$593$			34.9925i			1.43697i	0.695543	+	0.718484i	$0.255164\pi$
$593$			34.9925i			1.43697i	−0.695543	+	0.718484i	$0.744836\pi$
$594$		0			0
$595$	14.1646	−	6.54983i	0.580694	−	0.268517i
$596$		0			0
$597$	−26.8339	−	19.4960i	−1.09824	−	0.797918i
$598$		0			0
$599$	−17.7341			−0.724596			−0.362298	−	0.932062i	$-0.618008\pi$
$599$	−17.7341			−0.724596			−0.362298	+	0.932062i	$0.618008\pi$
$600$		0			0
$601$	−2.01505			−0.0821957			−0.0410979	−	0.999155i	$-0.513086\pi$
$601$	−2.01505			−0.0821957			−0.0410979	+	0.999155i	$0.513086\pi$
$602$		0			0
$603$	13.3147	+	9.67370i	0.542217	+	0.393943i
$604$		0			0
$605$	6.25237	+	6.74813i	0.254195	+	0.274351i
$606$		0			0
$607$		−	39.1971i		−	1.59096i	−0.605979	−	0.795481i	$-0.707218\pi$
$607$		−	39.1971i		−	1.59096i	0.605979	−	0.795481i	$-0.292782\pi$
$608$		0			0
$609$	−15.6164	−	48.0624i	−0.632809	−	1.94759i
$610$		0			0
$611$	5.99311	+	1.94728i	0.242455	+	0.0787785i
$612$		0			0
$613$	−6.65786	−	20.4908i	−0.268909	−	0.827615i	−0.990767	−	0.135575i	$-0.956712\pi$
$613$	−6.65786	−	20.4908i	−0.268909	−	0.827615i	0.721859	−	0.692041i	$-0.243288\pi$
$614$		0			0
$615$	−9.98301	+	17.8743i	−0.402554	+	0.720762i
$616$		0			0
$617$	17.5267	+	24.1235i	0.705600	+	0.971175i	0.999881	+	0.0154563i	$0.00492007\pi$
$617$	17.5267	+	24.1235i	0.705600	+	0.971175i	−0.294280	+	0.955719i	$0.595080\pi$
$618$		0			0
$619$	2.86875	+	3.94849i	0.115305	+	0.158703i	0.862768	−	0.505599i	$-0.168729\pi$
$619$	2.86875	+	3.94849i	0.115305	+	0.158703i	−0.747464	+	0.664303i	$0.768729\pi$
$620$		0			0
$621$	0.398318	−	0.548237i	0.0159839	−	0.0220000i
$622$		0			0
$623$	−37.0619	−	12.0421i	−1.48485	−	0.482458i
$624$		0			0
$625$	17.7591	+	17.5958i	0.710365	+	0.703834i
$626$		0			0
$627$	−10.4564	+	32.1813i	−0.417587	+	1.28520i
$628$		0			0
$629$	10.1374	−	13.9529i	0.404205	−	0.556340i
$630$		0			0
$631$	12.3860	−	8.99897i	0.493080	−	0.358243i	−0.313288	−	0.949658i	$-0.601430\pi$
$631$	12.3860	−	8.99897i	0.493080	−	0.358243i	0.806367	+	0.591415i	$0.201430\pi$
$632$		0			0
$633$	−8.13781	−	11.2007i	−0.323449	−	0.445189i
$634$		0			0
$635$	6.89828	+	3.85277i	0.273750	+	0.152892i
$636$		0			0
$637$	12.4175	+	38.2172i	0.492001	+	1.51422i
$638$		0			0
$639$	5.73663	−	17.6555i	0.226937	−	0.698442i
$640$		0			0
$641$	−2.46226	−	7.57805i	−0.0972533	−	0.299315i	0.890581	−	0.454825i	$-0.150298\pi$
$641$	−2.46226	−	7.57805i	−0.0972533	−	0.299315i	−0.987834	+	0.155510i	$0.950298\pi$
$642$		0			0
$643$	6.46830			0.255085			0.127542	−	0.991833i	$-0.459291\pi$
$643$	6.46830			0.255085			0.127542	+	0.991833i	$0.459291\pi$
$644$		0			0
$645$	2.49692	+	2.69490i	0.0983159	+	0.106112i
$646$		0			0
$647$	8.81321	−	12.1303i	0.346483	−	0.476893i	−0.599838	−	0.800122i	$-0.704768\pi$
$647$	8.81321	−	12.1303i	0.346483	−	0.476893i	0.946321	+	0.323229i	$0.104768\pi$
$648$		0			0
$649$	10.3387			0.405828
$650$		0			0
$651$		−	19.2450i		−	0.754272i
$652$		0			0
$653$	31.2404	+	22.6975i	1.22253	+	0.888220i	0.996308	−	0.0858552i	$-0.0273622\pi$
$653$	31.2404	+	22.6975i	1.22253	+	0.888220i	0.226223	+	0.974076i	$0.427362\pi$
$654$		0			0
$655$	−6.33172	−	13.6930i	−0.247401	−	0.535028i
$656$		0			0
$657$		−	49.6261i		−	1.93610i
$658$		0			0
$659$	32.1885	−	10.4587i	1.25389	−	0.407412i	0.394574	−	0.918864i	$-0.370892\pi$
$659$	32.1885	−	10.4587i	1.25389	−	0.407412i	0.859312	+	0.511452i	$0.170892\pi$
$660$		0			0
$661$	1.06103	+	0.344750i	0.0412693	+	0.0134092i	0.329579	−	0.944128i	$-0.393093\pi$
$661$	1.06103	+	0.344750i	0.0412693	+	0.0134092i	−0.288310	+	0.957537i	$0.593093\pi$
$662$		0			0
$663$	31.8900	−	10.3617i	1.23851	−	0.402415i
$664$		0			0
$665$	37.2724	−	17.2350i	1.44536	−	0.668345i
$666$		0			0
$667$	−3.50945	+	2.54977i	−0.135887	+	0.0987274i
$668$		0			0
$669$	−30.1599	−	41.5116i	−1.16605	−	1.60493i
$670$		0			0
$671$	13.8678	+	10.0756i	0.535362	+	0.388963i
$672$		0			0
$673$	−25.0129	−	8.12719i	−0.964177	−	0.313280i	−0.215714	−	0.976457i	$-0.569208\pi$
$673$	−25.0129	−	8.12719i	−0.964177	−	0.313280i	−0.748463	+	0.663177i	$0.769208\pi$
$674$		0			0
$675$	2.82850	−	3.32727i	0.108869	−	0.128067i
$676$		0			0
$677$	−5.47038	+	16.8361i	−0.210244	+	0.647064i	0.789213	+	0.614119i	$0.210489\pi$
$677$	−5.47038	+	16.8361i	−0.210244	+	0.647064i	−0.999457	+	0.0329450i	$0.989511\pi$
$678$		0			0
$679$	16.3733	+	11.8959i	0.628350	+	0.456523i
$680$		0			0
$681$	−32.2611	+	23.4391i	−1.23625	+	0.898188i
$682$		0			0
$683$	37.0207	−	26.8971i	1.41656	−	1.02919i	0.424230	−	0.905554i	$-0.360545\pi$
$683$	37.0207	−	26.8971i	1.41656	−	1.02919i	0.992328	−	0.123635i	$-0.0394553\pi$
$684$		0			0
$685$	−18.2997	+	2.18734i	−0.699195	+	0.0835738i
$686$		0			0
$687$	−15.3511	+	4.98787i	−0.585680	+	0.190299i
$688$		0			0
$689$	−3.88194	+	11.9474i	−0.147890	+	0.455159i
$690$		0			0
$691$	−5.90130	+	1.91745i	−0.224496	+	0.0729432i	−0.419105	−	0.907938i	$-0.637656\pi$
$691$	−5.90130	+	1.91745i	−0.224496	+	0.0729432i	0.194609	+	0.980881i	$0.437656\pi$
$692$		0			0
$693$	31.5088			1.19692
$694$		0			0
$695$	2.65910	+	1.48514i	0.100866	+	0.0563346i
$696$		0			0
$697$	4.15535	−	5.71935i	0.157395	−	0.216636i
$698$		0			0
$699$			44.3069i			1.67584i
$700$		0			0
$701$			21.2933i			0.804238i	0.915587	+	0.402119i	$0.131726\pi$
$701$			21.2933i			0.804238i	−0.915587	+	0.402119i	$0.868274\pi$
$702$		0			0
$703$	26.6752	−	36.7153i	1.00608	−	1.38474i
$704$		0			0
$705$	−5.15123	+	0.615720i	−0.194007	+	0.0231894i
$706$		0			0
$707$	−0.728101			−0.0273831
$708$		0			0
$709$	10.0050	−	3.25084i	0.375747	−	0.122088i	−0.115054	−	0.993359i	$-0.536704\pi$
$709$	10.0050	−	3.25084i	0.375747	−	0.122088i	0.490801	+	0.871272i	$0.336704\pi$
$710$		0			0
$711$	9.78435	−	30.1131i	0.366942	−	1.12933i
$712$		0			0
$713$	−1.57111	+	0.510486i	−0.0588387	+	0.0191178i
$714$		0			0
$715$	−7.78727	+	39.3868i	−0.291227	+	1.47298i
$716$		0			0
$717$	−17.1977	+	12.4948i	−0.642258	+	0.466628i
$718$		0			0
$719$	−5.42565	+	3.94197i	−0.202343	+	0.147011i	−0.684342	−	0.729161i	$-0.739911\pi$
$719$	−5.42565	+	3.94197i	−0.202343	+	0.147011i	0.482000	+	0.876171i	$0.339911\pi$
$720$		0			0
$721$	38.3209	+	27.8418i	1.42715	+	1.03688i
$722$		0			0
$723$	2.71260	−	8.34852i	0.100883	−	0.310485i
$724$		0			0
$725$	−23.8018	+	14.6615i	−0.883976	+	0.544513i
$726$		0			0
$727$	40.2119	+	13.0656i	1.49138	+	0.484578i	0.937490	−	0.348013i	$-0.113143\pi$
$727$	40.2119	+	13.0656i	1.49138	+	0.484578i	0.553888	+	0.832591i	$0.313143\pi$
$728$		0			0
$729$	26.5667	+	19.3018i	0.983951	+	0.714882i
$730$		0			0
$731$	−0.745662	−	1.02632i	−0.0275793	−	0.0379597i
$732$		0			0
$733$	21.7381	−	15.7936i	0.802914	−	0.583351i	−0.108854	−	0.994058i	$-0.534718\pi$
$733$	21.7381	−	15.7936i	0.802914	−	0.583351i	0.911768	+	0.410707i	$0.134718\pi$
$734$		0			0
$735$	−22.4845	−	24.2673i	−0.829353	−	0.895113i
$736$		0			0
$737$	12.2728	−	3.98768i	0.452075	−	0.146888i
$738$		0			0
$739$	−13.3854	−	4.34919i	−0.492391	−	0.159988i	0.0522881	−	0.998632i	$-0.483349\pi$
$739$	−13.3854	−	4.34919i	−0.492391	−	0.159988i	−0.544679	+	0.838644i	$0.683349\pi$
$740$		0			0
$741$	83.9145	−	27.2655i	3.08268	−	1.00162i
$742$		0			0
$743$			43.2190i			1.58555i	0.609513	+	0.792776i	$0.291365\pi$
$743$			43.2190i			1.58555i	−0.609513	+	0.792776i	$0.708635\pi$
$744$		0			0
$745$	4.10402	−	20.7575i	0.150360	−	0.760497i
$746$		0			0
$747$	−21.7826	−	15.8260i	−0.796983	−	0.579042i
$748$		0			0
$749$		−	53.5254i		−	1.95577i
$750$		0			0
$751$	3.24240			0.118317			0.0591584	−	0.998249i	$-0.481158\pi$
$751$	3.24240			0.118317			0.0591584	+	0.998249i	$0.481158\pi$
$752$		0			0
$753$	24.9912	−	34.3974i	0.910728	−	1.25351i
$754$		0			0
$755$	17.5388	+	3.46764i	0.638302	+	0.126200i
$756$		0			0
$757$	−25.4279			−0.924193			−0.462096	−	0.886830i	$-0.652903\pi$
$757$	−25.4279			−0.924193			−0.462096	+	0.886830i	$0.652903\pi$
$758$		0			0
$759$	−1.58500	−	4.87812i	−0.0575317	−	0.177064i
$760$		0			0
$761$	5.54324	−	17.0603i	0.200942	−	0.618437i	−0.798913	−	0.601446i	$-0.794591\pi$
$761$	5.54324	−	17.0603i	0.200942	−	0.618437i	0.999856	−	0.0169909i	$-0.00540862\pi$
$762$		0			0
$763$	−9.58753	−	29.5074i	−0.347092	−	1.06824i
$764$		0			0
$765$	−10.6779	+	9.89344i	−0.386060	+	0.357698i
$766$		0			0
$767$	−15.8459	−	21.8100i	−0.572161	−	0.787512i
$768$		0			0
$769$	−9.85987	+	7.16362i	−0.355556	+	0.258327i	−0.751196	−	0.660079i	$-0.770523\pi$
$769$	−9.85987	+	7.16362i	−0.355556	+	0.258327i	0.395640	+	0.918406i	$0.370523\pi$
$770$		0			0
$771$	6.55427	−	9.02118i	0.236046	−	0.324890i
$772$		0			0
$773$	−6.29718	+	19.3807i	−0.226494	+	0.697076i	0.771643	+	0.636056i	$0.219435\pi$
$773$	−6.29718	+	19.3807i	−0.226494	+	0.697076i	−0.998137	+	0.0610199i	$0.980565\pi$
$774$		0			0
$775$	−10.3459	+	2.50911i	−0.371636	+	0.0901300i
$776$		0			0
$777$	−76.2186	−	24.7649i	−2.73433	−	0.888437i
$778$		0			0
$779$	10.9343	−	15.0497i	0.391761	−	0.539213i
$780$		0			0
$781$	−8.55573	−	11.7760i	−0.306148	−	0.421377i
$782$		0			0
$783$	2.87030	+	3.95063i	0.102576	+	0.141184i
$784$		0			0
$785$	17.0679	+	3.37453i	0.609179	+	0.120442i
$786$		0			0
$787$	0.608835	+	1.87380i	0.0217026	+	0.0667938i	0.961321	−	0.275430i	$-0.0888201\pi$
$787$	0.608835	+	1.87380i	0.0217026	+	0.0667938i	−0.939619	+	0.342223i	$0.888820\pi$
$788$		0			0
$789$	−29.4177	−	9.55840i	−1.04730	−	0.340288i
$790$		0			0
$791$	−6.55119	−	20.1625i	−0.232934	−	0.716896i
$792$		0			0
$793$		−	44.6976i		−	1.58726i
$794$		0			0
$795$	−1.22745	−	10.2691i	−0.0435332	−	0.364207i
$796$		0			0
$797$	18.3873	+	13.3592i	0.651313	+	0.473206i	0.863718	−	0.503975i	$-0.168130\pi$
$797$	18.3873	+	13.3592i	0.651313	+	0.473206i	−0.212405	+	0.977182i	$0.568130\pi$
$798$		0			0
$799$	1.79141			0.0633756
$800$		0			0
$801$	36.3498			1.28436
$802$		0			0
$803$	−31.4798	−	22.8714i	−1.11090	−	0.807114i
$804$		0			0
$805$	−3.03521	+	5.43446i	−0.106977	+	0.191540i
$806$		0			0
$807$		−	72.3059i		−	2.54529i
$808$		0			0
$809$	−15.7618	−	48.5099i	−0.554156	−	1.70552i	−0.698163	−	0.715939i	$-0.745999\pi$
$809$	−15.7618	−	48.5099i	−0.554156	−	1.70552i	0.144007	−	0.989577i	$-0.454001\pi$
$810$		0			0
$811$	42.6096	+	13.8447i	1.49622	+	0.486153i	0.938914	−	0.344152i	$-0.111834\pi$
$811$	42.6096	+	13.8447i	1.49622	+	0.486153i	0.557310	+	0.830305i	$0.311834\pi$
$812$		0			0
$813$	−2.85449	−	8.78521i	−0.100111	−	0.308111i
$814$		0			0
$815$	6.09758	+	51.0136i	0.213589	+	1.78693i
$816$		0			0
$817$	−1.96211	−	2.70061i	−0.0686456	−	0.0944826i
$818$		0			0
$819$	−48.2928	−	66.4694i	−1.68749	−	2.32263i
$820$		0			0
$821$	−16.5666	+	22.8020i	−0.578180	+	0.795796i	−0.993494	−	0.113881i	$-0.963672\pi$
$821$	−16.5666	+	22.8020i	−0.578180	+	0.795796i	0.415314	+	0.909678i	$0.363672\pi$
$822$		0			0
$823$	3.43957	+	1.11758i	0.119896	+	0.0389565i	0.368350	−	0.929687i	$-0.379923\pi$
$823$	3.43957	+	1.11758i	0.119896	+	0.0389565i	−0.248455	+	0.968644i	$0.579923\pi$
$824$		0			0
$825$	−7.79049	−	32.1228i	−0.271230	−	1.11837i
$826$		0			0
$827$	8.71857	−	26.8330i	0.303174	−	0.933075i	−0.677178	−	0.735819i	$-0.736797\pi$
$827$	8.71857	−	26.8330i	0.303174	−	0.933075i	0.980352	−	0.197255i	$-0.0632028\pi$
$828$		0			0
$829$	31.0042	−	42.6736i	1.07682	−	1.48212i	0.213846	−	0.976867i	$-0.431401\pi$
$829$	31.0042	−	42.6736i	1.07682	−	1.48212i	0.862974	−	0.505248i	$-0.168599\pi$
$830$		0			0
$831$	8.12292	−	5.90165i	0.281781	−	0.204726i
$832$		0			0
$833$	6.71462	+	9.24188i	0.232648	+	0.320212i
$834$		0			0
$835$	−11.3506	−	24.5468i	−0.392804	−	0.849477i
$836$		0			0
$837$	0.574659	+	1.76862i	0.0198631	+	0.0611324i
$838$		0			0
$839$	−2.76644	+	8.51422i	−0.0955081	+	0.293944i	−0.987386	−	0.158333i	$-0.949388\pi$
$839$	−2.76644	+	8.51422i	−0.0955081	+	0.293944i	0.891878	+	0.452277i	$0.149388\pi$
$840$		0			0
$841$	−0.698169	−	2.14874i	−0.0240748	−	0.0740946i
$842$		0			0
$843$	71.6357			2.46726
$844$		0			0
$845$	68.6394	−	31.7393i	2.36127	−	1.09187i
$846$		0			0
$847$	−8.67620	+	11.9418i	−0.298118	+	0.410324i
$848$		0			0
$849$	32.8838			1.12857
$850$		0			0
$851$			6.87919i			0.235816i
$852$		0			0
$853$	−25.4769	−	18.5100i	−0.872312	−	0.633772i	0.0588942	−	0.998264i	$-0.481243\pi$
$853$	−25.4769	−	18.5100i	−0.872312	−	0.633772i	−0.931206	+	0.364492i	$0.881243\pi$
$854$		0			0
$855$	−28.0975	+	26.0333i	−0.960914	+	0.890320i
$856$		0			0
$857$		−	47.9238i		−	1.63705i	−0.574473	−	0.818523i	$-0.694793\pi$
$857$		−	47.9238i		−	1.63705i	0.574473	−	0.818523i	$-0.305207\pi$
$858$		0			0
$859$	−25.9430	+	8.42940i	−0.885164	+	0.287607i	−0.716100	−	0.697998i	$-0.754075\pi$
$859$	−25.9430	+	8.42940i	−0.885164	+	0.287607i	−0.169064	+	0.985605i	$0.554075\pi$
$860$		0			0
$861$	−31.2423	−	10.1512i	−1.06473	−	0.345953i
$862$		0			0
$863$	−40.6471	+	13.2070i	−1.38364	+	0.449573i	−0.903865	−	0.427817i	$-0.859283\pi$
$863$	−40.6471	+	13.2070i	−1.38364	+	0.449573i	−0.479778	+	0.877390i	$0.659283\pi$
$864$		0			0
$865$	−17.2415	+	30.8705i	−0.586230	+	1.04963i
$866$		0			0
$867$	−26.9364	+	19.5704i	−0.914807	+	0.664646i
$868$		0			0
$869$	−14.5926	−	20.0850i	−0.495020	−	0.681337i
$870$		0			0
$871$	−27.2225	−	19.7783i	−0.922400	−	0.670163i
$872$		0			0
$873$	−17.9542	−	5.83367i	−0.607657	−	0.197440i
$874$		0			0
$875$	−22.1702	+	33.4301i	−0.749490	+	1.13014i
$876$		0			0
$877$	17.9202	−	55.1526i	0.605121	−	1.86237i	0.109168	−	0.994023i	$-0.465181\pi$
$877$	17.9202	−	55.1526i	0.605121	−	1.86237i	0.495953	−	0.868349i	$-0.334819\pi$
$878$		0			0
$879$	55.1055	+	40.0365i	1.85866	+	1.35040i
$880$		0			0
$881$	14.3649	−	10.4367i	0.483965	−	0.351621i	−0.318894	−	0.947790i	$-0.603311\pi$
$881$	14.3649	−	10.4367i	0.483965	−	0.351621i	0.802859	+	0.596169i	$0.203311\pi$
$882$		0			0
$883$	−34.4318	+	25.0162i	−1.15872	+	0.841861i	−0.989616	−	0.143736i	$-0.954088\pi$
$883$	−34.4318	+	25.0162i	−1.15872	+	0.841861i	−0.169107	+	0.985598i	$0.554088\pi$
$884$		0			0
$885$	19.3770	+	10.8223i	0.651352	+	0.363787i
$886$		0			0
$887$	37.7360	−	12.2612i	1.26705	−	0.411689i	0.403048	−	0.915179i	$-0.367951\pi$
$887$	37.7360	−	12.2612i	1.26705	−	0.411689i	0.864001	+	0.503489i	$0.167951\pi$
$888$		0			0
$889$	−3.91768	+	12.0574i	−0.131395	+	0.404392i
$890$		0			0
$891$	19.5653	−	6.35716i	0.655463	−	0.212973i
$892$		0			0
$893$	4.71386			0.157743
$894$		0			0
$895$	24.2241	−	22.4444i	0.809721	−	0.750234i
$896$		0			0
$897$	−7.86135	+	10.8202i	−0.262483	+	0.361277i
$898$		0			0
$899$		−	11.9042i		−	0.397026i
$900$		0			0
$901$			3.57122i			0.118974i
$902$		0			0
$903$	−3.46488	+	4.76900i	−0.115304	+	0.158703i
$904$		0			0
$905$	5.05252	+	10.9266i	0.167952	+	0.363212i
$906$		0			0
$907$	−34.9093			−1.15914			−0.579571	−	0.814921i	$-0.696780\pi$
$907$	−34.9093			−1.15914			−0.579571	+	0.814921i	$0.696780\pi$
$908$		0			0
$909$	0.645920	−	0.209872i	0.0214238	−	0.00696102i
$910$		0			0
$911$	7.05588	−	21.7158i	0.233772	−	0.719476i	−0.763510	−	0.645796i	$-0.776526\pi$
$911$	7.05588	−	21.7158i	0.233772	−	0.719476i	0.997282	−	0.0736799i	$-0.0234743\pi$
$912$		0			0
$913$	−20.0781	+	6.52377i	−0.664488	+	0.215905i
$914$		0			0
$915$	15.4446	+	33.4005i	0.510583	+	1.10419i
$916$		0			0
$917$	19.5831	−	14.2280i	0.646692	−	0.469850i
$918$		0			0
$919$	44.3337	−	32.2104i	1.46244	−	1.06252i	0.479715	−	0.877424i	$-0.340740\pi$
$919$	44.3337	−	32.2104i	1.46244	−	1.06252i	0.982720	−	0.185097i	$-0.0592600\pi$
$920$		0			0
$921$	47.1203	+	34.2349i	1.55267	+	1.12808i
$922$		0			0
$923$	−11.7288	+	36.0975i	−0.386058	+	1.18816i
$924$		0			0
$925$	−3.37618	+	44.2031i	−0.111008	+	1.45339i
$926$		0			0
$927$	−42.0209	−	13.6534i	−1.38015	−	0.448437i
$928$		0			0
$929$	−26.3740	−	19.1618i	−0.865301	−	0.628678i	0.0640206	−	0.997949i	$-0.479608\pi$
$929$	−26.3740	−	19.1618i	−0.865301	−	0.628678i	−0.929322	+	0.369270i	$0.879608\pi$
$930$		0			0
$931$	17.6686	+	24.3188i	0.579066	+	0.797016i
$932$		0			0
$933$	21.7992	−	15.8380i	0.713673	−	0.518514i
$934$		0			0
$935$	1.35462	+	11.3331i	0.0443010	+	0.370631i
$936$		0			0
$937$	7.69340	−	2.49974i	0.251332	−	0.0816628i	−0.180641	−	0.983549i	$-0.557817\pi$
$937$	7.69340	−	2.49974i	0.251332	−	0.0816628i	0.431974	+	0.901886i	$0.357817\pi$
$938$		0			0
$939$	−16.6789	−	5.41932i	−0.544297	−	0.176853i
$940$		0			0
$941$	−34.7042	+	11.2761i	−1.13133	+	0.367590i	−0.814080	−	0.580753i	$-0.802758\pi$
$941$	−34.7042	+	11.2761i	−1.13133	+	0.367590i	−0.317246	+	0.948343i	$0.602758\pi$
$942$		0			0
$943$			2.81981i			0.0918255i
$944$		0			0
$945$	6.11763	+	3.41676i	0.199006	+	0.111147i
$946$		0			0
$947$	−12.2602	−	8.90757i	−0.398404	−	0.289457i	0.370487	−	0.928838i	$-0.379191\pi$
$947$	−12.2602	−	8.90757i	−0.398404	−	0.289457i	−0.768890	+	0.639380i	$0.779191\pi$
$948$		0			0
$949$			101.463i			3.29362i
$950$		0			0
$951$	7.05851			0.228888
$952$		0			0
$953$	−32.0176	+	44.0685i	−1.03715	+	1.42752i	−0.137714	+	0.990472i	$0.543976\pi$
$953$	−32.0176	+	44.0685i	−1.03715	+	1.42752i	−0.899439	+	0.437047i	$0.856024\pi$
$954$		0			0
$955$	2.75132	+	23.0181i	0.0890308	+	0.744849i
$956$		0			0
$957$	36.9610			1.19478
$958$		0			0
$959$	−9.13812	−	28.1242i	−0.295085	−	0.908179i
$960$		0			0
$961$	−8.17865	+	25.1713i	−0.263827	+	0.811977i
$962$		0			0
$963$	15.4285	+	47.4839i	0.497175	+	1.53015i
$964$		0			0
$965$	−0.312462	+	1.58039i	−0.0100585	+	0.0508744i
$966$		0			0
$967$	12.9780	+	17.8627i	0.417344	+	0.574424i	0.964990	−	0.262285i	$-0.0844762\pi$
$967$	12.9780	+	17.8627i	0.417344	+	0.574424i	−0.547647	+	0.836710i	$0.684476\pi$
$968$		0			0
$969$	20.2926	−	14.7434i	0.651892	−	0.473628i
$970$		0			0
$971$	−5.05516	+	6.95783i	−0.162228	+	0.223287i	−0.882390	−	0.470518i	$-0.844067\pi$
$971$	−5.05516	+	6.95783i	−0.162228	+	0.223287i	0.720163	+	0.693805i	$0.244067\pi$
$972$		0			0
$973$	−1.51016	+	4.64781i	−0.0484137	+	0.149002i
$974$		0			0
$975$	−55.8244	+	65.6684i	−1.78781	+	2.10307i
$976$		0			0
$977$	−18.1117	−	5.88484i	−0.579444	−	0.188273i	0.00460737	−	0.999989i	$-0.498533\pi$
$977$	−18.1117	−	5.88484i	−0.579444	−	0.188273i	−0.584052	+	0.811717i	$0.698533\pi$
$978$		0			0
$979$	16.7527	−	23.0581i	0.535418	−	0.736940i
$980$		0			0
$981$	17.0107	+	23.4133i	0.543111	+	0.747529i
$982$		0			0
$983$	−12.0848	−	16.6333i	−0.385446	−	0.530521i	0.571571	−	0.820553i	$-0.306334\pi$
$983$	−12.0848	−	16.6333i	−0.385446	−	0.530521i	−0.957017	+	0.290032i	$0.906334\pi$
$984$		0			0
$985$	9.07986	+	9.79982i	0.289308	+	0.312248i
$986$		0			0
$987$	−2.57232	−	7.91678i	−0.0818777	−	0.251994i
$988$		0			0
$989$	0.481237	+	0.156364i	0.0153025	+	0.00497207i
$990$		0			0
$991$	7.98983	+	24.5902i	0.253805	+	0.781132i	0.994063	+	0.108809i	$0.0347036\pi$
$991$	7.98983	+	24.5902i	0.253805	+	0.781132i	−0.740258	+	0.672323i	$0.765296\pi$
$992$		0			0
$993$			66.8905i			2.12271i
$994$		0			0
$995$	−28.8809	−	5.71012i	−0.915587	−	0.181023i
$996$		0			0
$997$	15.5099	+	11.2686i	0.491204	+	0.356881i	0.805647	−	0.592396i	$-0.201818\pi$
$997$	15.5099	+	11.2686i	0.491204	+	0.356881i	−0.314443	+	0.949276i	$0.601818\pi$
$998$		0			0
$999$	7.74398			0.245009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.529.4		112
4.3	odd	2		200.2.o.a.29.24	yes	112
8.3	odd	2		200.2.o.a.29.19	✓	112
8.5	even	2	inner	800.2.be.a.529.25		112
20.3	even	4		1000.2.t.b.101.20		224
20.7	even	4		1000.2.t.b.101.37		224
20.19	odd	2		1000.2.o.a.149.5		112
25.19	even	10	inner	800.2.be.a.369.25		112
40.3	even	4		1000.2.t.b.101.48		224
40.19	odd	2		1000.2.o.a.149.10		112
40.27	even	4		1000.2.t.b.101.9		224
100.19	odd	10		200.2.o.a.69.19	yes	112
100.31	odd	10		1000.2.o.a.349.10		112
100.67	even	20		1000.2.t.b.901.9		224
100.83	even	20		1000.2.t.b.901.48		224
200.19	odd	10		200.2.o.a.69.24	yes	112
200.67	even	20		1000.2.t.b.901.37		224
200.69	even	10	inner	800.2.be.a.369.4		112
200.83	even	20		1000.2.t.b.901.20		224
200.131	odd	10		1000.2.o.a.349.5		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.19	✓	112	8.3	odd	2
200.2.o.a.29.24	yes	112	4.3	odd	2
200.2.o.a.69.19	yes	112	100.19	odd	10
200.2.o.a.69.24	yes	112	200.19	odd	10
800.2.be.a.369.4		112	200.69	even	10	inner
800.2.be.a.369.25		112	25.19	even	10	inner
800.2.be.a.529.4		112	1.1	even	1	trivial
800.2.be.a.529.25		112	8.5	even	2	inner
1000.2.o.a.149.5		112	20.19	odd	2
1000.2.o.a.149.10		112	40.19	odd	2
1000.2.o.a.349.5		112	200.131	odd	10
1000.2.o.a.349.10		112	100.31	odd	10
1000.2.t.b.101.9		224	40.27	even	4
1000.2.t.b.101.20		224	20.3	even	4
1000.2.t.b.101.37		224	20.7	even	4
1000.2.t.b.101.48		224	40.3	even	4
1000.2.t.b.901.9		224	100.67	even	20
1000.2.t.b.901.20		224	200.83	even	20
1000.2.t.b.901.37		224	200.67	even	20
1000.2.t.b.901.48		224	100.83	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)

\(f(q)\)	\(=\)	\(q+(-2.03813 - 1.48079i) q^{3} +(-2.19360 - 0.433703i) q^{5} -3.58786i q^{7} +(1.03418 + 3.18289i) q^{9} +O(q^{10})\)	\(q+(-2.03813 - 1.48079i) q^{3} +(-2.19360 - 0.433703i) q^{5} -3.58786i q^{7} +(1.03418 + 3.18289i) q^{9} +(2.49567 + 0.810891i) q^{11} +(-2.11444 - 6.50757i) q^{13} +(3.82862 + 4.13220i) q^{15} +(-1.14335 - 1.57369i) q^{17} +(-3.00859 - 4.14097i) q^{19} +(-5.31285 + 7.31251i) q^{21} +(0.737902 + 0.239759i) q^{23} +(4.62380 + 1.90275i) q^{25} +(0.269899 - 0.830663i) q^{27} +(-3.28631 + 4.52322i) q^{29} +(-1.72253 + 1.25149i) q^{31} +(-3.88573 - 5.34825i) q^{33} +(-1.55607 + 7.87034i) q^{35} +(2.73986 + 8.43241i) q^{37} +(-5.32683 + 16.3943i) q^{39} +(1.12308 + 3.45647i) q^{41} +0.652170 q^{43} +(-0.888162 - 7.43054i) q^{45} +(-0.541317 + 0.745059i) q^{47} -5.87273 q^{49} +4.90045i q^{51} +(-1.48529 - 1.07913i) q^{53} +(-5.12282 - 2.86115i) q^{55} +12.8949i q^{57} +(3.74706 - 1.21749i) q^{59} +(6.21266 + 2.01862i) q^{61} +(11.4198 - 3.71051i) q^{63} +(1.81589 + 15.1921i) q^{65} +(3.97847 - 2.89052i) q^{67} +(-1.14891 - 1.58133i) q^{69} +(-4.48762 - 3.26045i) q^{71} +(-14.1026 - 4.58222i) q^{73} +(-6.60634 - 10.7249i) q^{75} +(2.90936 - 8.95410i) q^{77} +(-7.65406 - 5.56100i) q^{79} +(6.34247 - 4.60807i) q^{81} +(-6.50869 + 4.72884i) q^{83} +(1.82555 + 3.94794i) q^{85} +(13.3958 - 4.35257i) q^{87} +(3.35636 - 10.3298i) q^{89} +(-23.3483 + 7.58631i) q^{91} +5.36393 q^{93} +(4.80370 + 10.3885i) q^{95} +(-3.31560 + 4.56353i) q^{97} +8.78205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 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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