LMFDB - Embedded newform 800.2.be.a.369.27

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			369.27
Character	$\chi$	$=$	800.369
Dual form			800.2.be.a.529.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54275 - 1.84742i) q^{3} +(-1.08744 - 1.95384i) q^{5} -1.17589i q^{7} +(2.12559 - 6.54190i) q^{9} +O(q^{10})$	\(q+(2.54275 - 1.84742i) q^{3} +(-1.08744 - 1.95384i) q^{5} -1.17589i q^{7} +(2.12559 - 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(-0.280944 + 0.864656i) q^{13} +(-6.37465 - 2.95917i) q^{15} +(3.27511 - 4.50780i) q^{17} +(-2.64864 + 3.64555i) q^{19} +(-2.17235 - 2.98999i) q^{21} +(2.07468 - 0.674105i) q^{23} +(-2.63495 + 4.24936i) q^{25} +(-3.76703 - 11.5937i) q^{27} +(3.65841 + 5.03536i) q^{29} +(1.16778 + 0.848445i) q^{31} +(-7.33789 + 10.0997i) q^{33} +(-2.29749 + 1.27870i) q^{35} +(2.16303 - 6.65712i) q^{37} +(0.883011 + 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} -2.96089 q^{43} +(-15.0933 + 2.96086i) q^{45} +(3.12538 + 4.30172i) q^{47} +5.61729 q^{49} -17.5127i q^{51} +(10.5708 - 7.68016i) q^{53} +(6.50602 + 6.04601i) q^{55} +14.1629i q^{57} +(1.22277 + 0.397301i) q^{59} +(-14.7321 + 4.78675i) q^{61} +(-7.69253 - 2.49945i) q^{63} +(1.99491 - 0.391343i) q^{65} +(2.45652 + 1.78477i) q^{67} +(4.03005 - 5.54689i) q^{69} +(1.58201 - 1.14940i) q^{71} +(4.01616 - 1.30493i) q^{73} +(1.15031 + 15.6729i) q^{75} +(1.44329 + 4.44199i) q^{77} +(-2.23200 + 1.62164i) q^{79} +(-14.3025 - 10.3914i) q^{81} +(7.65878 + 5.56443i) q^{83} +(-12.3690 - 1.49707i) q^{85} +(18.6049 + 6.04509i) q^{87} +(0.806910 + 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +4.53682 q^{93} +(10.0030 + 1.21071i) q^{95} +(-0.171369 - 0.235869i) q^{97} +27.3214i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	2.54275	−	1.84742i	1.46806	−	1.06661i	0.486890	−	0.873463i	$-0.338131\pi$
$3$	2.54275	−	1.84742i	1.46806	−	1.06661i	0.981170	−	0.193145i	$-0.0618687\pi$
$4$		0			0
$5$	−1.08744	−	1.95384i	−0.486318	−	0.873782i
$5$	−1.08744	−	1.95384i	−0.486318	−	0.873782i
$6$		0			0
$7$		−	1.17589i		−	0.444443i	−0.974996	−	0.222222i	$-0.928669\pi$
$7$		−	1.17589i		−	0.444443i	0.974996	−	0.222222i	$-0.0713308\pi$
$8$		0			0
$9$	2.12559	−	6.54190i	0.708531	−	2.18063i
$10$		0			0
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.816981	−	0.576664i	$-0.804354\pi$
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.321997	+	0.946741i	$0.604354\pi$
$12$		0			0
$13$	−0.280944	+	0.864656i	−0.0779198	+	0.239812i	−0.982427	−	0.186645i	$-0.940239\pi$
$13$	−0.280944	+	0.864656i	−0.0779198	+	0.239812i	0.904508	+	0.426457i	$0.140239\pi$
$14$		0			0
$15$	−6.37465	−	2.95917i	−1.64593	−	0.764054i
$16$		0			0
$17$	3.27511	−	4.50780i	0.794331	−	1.09330i	−0.199225	−	0.979954i	$-0.563842\pi$
$17$	3.27511	−	4.50780i	0.794331	−	1.09330i	0.993555	−	0.113348i	$-0.0361576\pi$
$18$		0			0
$19$	−2.64864	+	3.64555i	−0.607641	+	0.836346i	−0.996381	−	0.0850017i	$-0.972910\pi$
$19$	−2.64864	+	3.64555i	−0.607641	+	0.836346i	0.388740	+	0.921348i	$0.372910\pi$
$20$		0			0
$21$	−2.17235	−	2.98999i	−0.474047	−	0.652469i
$22$		0			0
$23$	2.07468	−	0.674105i	0.432601	−	0.140561i	−0.0846183	−	0.996413i	$-0.526967\pi$
$23$	2.07468	−	0.674105i	0.432601	−	0.140561i	0.517220	+	0.855853i	$0.326967\pi$
$24$		0			0
$25$	−2.63495	+	4.24936i	−0.526990	+	0.849871i
$26$		0			0
$27$	−3.76703	−	11.5937i	−0.724966	−	2.23122i
$28$		0			0
$29$	3.65841	+	5.03536i	0.679349	+	0.935044i	0.999926	−	0.0121788i	$-0.00387674\pi$
$29$	3.65841	+	5.03536i	0.679349	+	0.935044i	−0.320577	+	0.947223i	$0.603877\pi$
$30$		0			0
$31$	1.16778	+	0.848445i	0.209740	+	0.152385i	0.687696	−	0.725999i	$-0.258622\pi$
$31$	1.16778	+	0.848445i	0.209740	+	0.152385i	−0.477956	+	0.878384i	$0.658622\pi$
$32$		0			0
$33$	−7.33789	+	10.0997i	−1.27736	+	1.75814i
$34$		0			0
$35$	−2.29749	+	1.27870i	−0.388347	+	0.216141i
$36$		0			0
$37$	2.16303	−	6.65712i	0.355600	−	1.09442i	−0.600061	−	0.799954i	$-0.704857\pi$
$37$	2.16303	−	6.65712i	0.355600	−	1.09442i	0.955661	−	0.294470i	$-0.0951431\pi$
$38$		0			0
$39$	0.883011	+	2.71763i	0.141395	+	0.435169i
$40$		0			0
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	−0.670868	−	0.741577i	$-0.734078\pi$
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	0.978632	−	0.205622i	$-0.0659216\pi$
$42$		0			0
$43$	−2.96089			−0.451532			−0.225766	−	0.974182i	$-0.572488\pi$
$43$	−2.96089			−0.451532			−0.225766	+	0.974182i	$0.572488\pi$
$44$		0			0
$45$	−15.0933	+	2.96086i	−2.24997	+	0.441379i
$46$		0			0
$47$	3.12538	+	4.30172i	0.455884	+	0.627470i	0.973649	−	0.228053i	$-0.0732359\pi$
$47$	3.12538	+	4.30172i	0.455884	+	0.627470i	−0.517765	+	0.855523i	$0.673236\pi$
$48$		0			0
$49$	5.61729			0.802470
$50$		0			0
$51$		−	17.5127i		−	2.45227i
$52$		0			0
$53$	10.5708	−	7.68016i	1.45202	−	1.05495i	0.466661	−	0.884436i	$-0.345457\pi$
$53$	10.5708	−	7.68016i	1.45202	−	1.05495i	0.985355	−	0.170515i	$-0.0545433\pi$
$54$		0			0
$55$	6.50602	+	6.04601i	0.877272	+	0.815244i
$56$		0			0
$57$			14.1629i			1.87592i
$58$		0			0
$59$	1.22277	+	0.397301i	0.159191	+	0.0517242i	0.387528	−	0.921858i	$-0.373329\pi$
$59$	1.22277	+	0.397301i	0.159191	+	0.0517242i	−0.228338	+	0.973582i	$0.573329\pi$
$60$		0			0
$61$	−14.7321	+	4.78675i	−1.88625	+	0.612881i	−0.903306	+	0.428996i	$0.858867\pi$
$61$	−14.7321	+	4.78675i	−1.88625	+	0.612881i	−0.982948	+	0.183885i	$0.941133\pi$
$62$		0			0
$63$	−7.69253	−	2.49945i	−0.969167	−	0.314902i
$64$		0			0
$65$	1.99491	−	0.391343i	0.247438	−	0.0485401i
$66$		0			0
$67$	2.45652	+	1.78477i	0.300112	+	0.218044i	0.727642	−	0.685957i	$-0.240616\pi$
$67$	2.45652	+	1.78477i	0.300112	+	0.218044i	−0.427530	+	0.904001i	$0.640616\pi$
$68$		0			0
$69$	4.03005	−	5.54689i	0.485161	−	0.667767i
$70$		0			0
$71$	1.58201	−	1.14940i	0.187750	−	0.136409i	−0.489940	−	0.871756i	$-0.662981\pi$
$71$	1.58201	−	1.14940i	0.187750	−	0.136409i	0.677690	+	0.735348i	$0.262981\pi$
$72$		0			0
$73$	4.01616	−	1.30493i	0.470056	−	0.152731i	−0.0644044	−	0.997924i	$-0.520515\pi$
$73$	4.01616	−	1.30493i	0.470056	−	0.152731i	0.534461	+	0.845193i	$0.320515\pi$
$74$		0			0
$75$	1.15031	+	15.6729i	0.132826	+	1.80975i
$76$		0			0
$77$	1.44329	+	4.44199i	0.164478	+	0.506211i
$78$		0			0
$79$	−2.23200	+	1.62164i	−0.251119	+	0.182449i	−0.706223	−	0.707990i	$-0.749602\pi$
$79$	−2.23200	+	1.62164i	−0.251119	+	0.182449i	0.455103	+	0.890439i	$0.349602\pi$
$80$		0			0
$81$	−14.3025	−	10.3914i	−1.58917	−	1.15460i
$82$		0			0
$83$	7.65878	+	5.56443i	0.840660	+	0.610775i	0.922555	−	0.385866i	$-0.126097\pi$
$83$	7.65878	+	5.56443i	0.840660	+	0.610775i	−0.0818950	+	0.996641i	$0.526097\pi$
$84$		0			0
$85$	−12.3690	−	1.49707i	−1.34160	−	0.162380i
$86$		0			0
$87$	18.6049	+	6.04509i	1.99465	+	0.648101i
$88$		0			0
$89$	0.806910	+	2.48341i	0.0855323	+	0.263241i	0.984671	−	0.174423i	$-0.0558059\pi$
$89$	0.806910	+	2.48341i	0.0855323	+	0.263241i	−0.899139	+	0.437664i	$0.855806\pi$
$90$		0			0
$91$	1.01674	+	0.330358i	0.106583	+	0.0346309i
$92$		0			0
$93$	4.53682			0.470447
$94$		0			0
$95$	10.0030	+	1.21071i	1.02629	+	0.124216i
$96$		0			0
$97$	−0.171369	−	0.235869i	−0.0173999	−	0.0239489i	0.800228	−	0.599695i	$-0.204712\pi$
$97$	−0.171369	−	0.235869i	−0.0173999	−	0.0239489i	−0.817628	+	0.575746i	$0.804712\pi$
$98$		0			0
$99$			27.3214i			2.74590i
$100$		0			0
$101$		−	7.84171i		−	0.780280i	−0.920756	−	0.390140i	$-0.872427\pi$
$101$		−	7.84171i		−	0.780280i	0.920756	−	0.390140i	$-0.127573\pi$
$102$		0			0
$103$	−7.73997	−	10.6532i	−0.762642	−	1.04969i	−0.996990	−	0.0775342i	$-0.975295\pi$
$103$	−7.73997	−	10.6532i	−0.762642	−	1.04969i	0.234347	−	0.972153i	$-0.424705\pi$
$104$		0			0
$105$	−3.47965	+	7.49586i	−0.339579	+	0.731521i
$106$		0			0
$107$	−7.00700			−0.677392			−0.338696	−	0.940896i	$-0.609986\pi$
$107$	−7.00700			−0.677392			−0.338696	+	0.940896i	$0.609986\pi$
$108$		0			0
$109$	2.56991	+	0.835013i	0.246152	+	0.0799797i	0.429495	−	0.903069i	$-0.358692\pi$
$109$	2.56991	+	0.835013i	0.246152	+	0.0799797i	−0.183342	+	0.983049i	$0.558692\pi$
$110$		0			0
$111$	−6.79844	−	20.9235i	−0.645280	−	1.98597i
$112$		0			0
$113$	4.34695	+	1.41241i	0.408926	+	0.132868i	0.506255	−	0.862384i	$-0.331030\pi$
$113$	4.34695	+	1.41241i	0.408926	+	0.132868i	−0.0973282	+	0.995252i	$0.531030\pi$
$114$		0			0
$115$	−3.57318	−	3.32054i	−0.333201	−	0.309642i
$116$		0			0
$117$	5.05932	+	3.67581i	0.467734	+	0.339829i
$118$		0			0
$119$	−5.30066	−	3.85116i	−0.485911	−	0.353035i
$120$		0			0
$121$	3.86428	−	2.80757i	0.351299	−	0.255233i
$122$		0			0
$123$	−6.19378	−	19.0625i	−0.558474	−	1.71881i
$124$		0			0
$125$	11.1679	+	0.527349i	0.998887	+	0.0471675i
$126$		0			0
$127$	8.20787	−	2.66690i	0.728330	−	0.236649i	0.0786992	−	0.996898i	$-0.474923\pi$
$127$	8.20787	−	2.66690i	0.728330	−	0.236649i	0.649631	+	0.760250i	$0.274923\pi$
$128$		0			0
$129$	−7.52882	+	5.47001i	−0.662876	+	0.481607i
$130$		0			0
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	−0.524999	−	0.851103i	$-0.675934\pi$
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	0.971680	+	0.236299i	$0.0759343\pi$
$132$		0			0
$133$	4.28675	+	3.11451i	0.371708	+	0.270062i
$134$		0			0
$135$	−18.5558	+	19.9677i	−1.59703	+	1.71854i
$136$		0			0
$137$	3.46540	+	1.12598i	0.296069	+	0.0961988i	0.453285	−	0.891365i	$-0.350252\pi$
$137$	3.46540	+	1.12598i	0.296069	+	0.0961988i	−0.157216	+	0.987564i	$0.550252\pi$
$138$		0			0
$139$	13.2832	−	4.31597i	1.12666	−	0.366075i	0.314357	−	0.949305i	$-0.398211\pi$
$139$	13.2832	−	4.31597i	1.12666	−	0.366075i	0.812307	+	0.583230i	$0.198211\pi$
$140$		0			0
$141$	15.8941	+	5.16432i	1.33853	+	0.434914i
$142$		0			0
$143$		−	3.61112i		−	0.301977i
$144$		0			0
$145$	5.85998	−	12.6236i	0.486645	−	1.04833i
$146$		0			0
$147$	14.2834	−	10.3775i	1.17807	−	0.855921i
$148$		0			0
$149$		−	2.61363i		−	0.214117i	−0.994253	−	0.107059i	$-0.965857\pi$
$149$		−	2.61363i		−	0.214117i	0.994253	−	0.107059i	$-0.0341433\pi$
$150$		0			0
$151$	−10.6178			−0.864067			−0.432034	−	0.901857i	$-0.642204\pi$
$151$	−10.6178			−0.864067			−0.432034	+	0.901857i	$0.642204\pi$
$152$		0			0
$153$	−22.5280	−	31.0072i	−1.82128	−	2.50678i
$154$		0			0
$155$	0.387828	−	3.20429i	0.0311511	−	0.257375i
$156$		0			0
$157$	−3.90358			−0.311539			−0.155770	−	0.987793i	$-0.549786\pi$
$157$	−3.90358			−0.311539			−0.155770	+	0.987793i	$0.549786\pi$
$158$		0			0
$159$	12.6906	−	39.0575i	1.00643	−	3.09746i
$160$		0			0
$161$	−0.792671	−	2.43959i	−0.0624712	−	0.192267i
$162$		0			0
$163$	−6.06584	+	18.6687i	−0.475114	+	1.46225i	0.370691	+	0.928756i	$0.379121\pi$
$163$	−6.06584	+	18.6687i	−0.475114	+	1.46225i	−0.845805	+	0.533493i	$0.820879\pi$
$164$		0			0
$165$	27.7127	+	3.35418i	2.15743	+	0.261123i
$166$		0			0
$167$	−9.89993	+	13.6261i	−0.766080	+	1.05442i	0.230604	+	0.973048i	$0.425930\pi$
$167$	−9.89993	+	13.6261i	−0.766080	+	1.05442i	−0.996684	+	0.0813708i	$0.974070\pi$
$168$		0			0
$169$	9.84852	+	7.15537i	0.757579	+	0.550413i
$170$		0			0
$171$	18.2189	+	25.0761i	1.39323	+	1.91762i
$172$		0			0
$173$	3.14623	+	9.68309i	0.239203	+	0.736192i	0.996536	+	0.0831625i	$0.0265020\pi$
$173$	3.14623	+	9.68309i	0.239203	+	0.736192i	−0.757333	+	0.653029i	$0.773498\pi$
$174$		0			0
$175$	4.99676	+	3.09840i	0.377719	+	0.234217i
$176$		0			0
$177$	3.84317	−	1.24872i	0.288871	−	0.0938598i
$178$		0			0
$179$	−8.87687	−	12.2180i	−0.663488	−	0.913214i	0.336102	−	0.941826i	$-0.390891\pi$
$179$	−8.87687	−	12.2180i	−0.663488	−	0.913214i	−0.999591	+	0.0286120i	$0.990891\pi$
$180$		0			0
$181$	−11.1217	+	15.3077i	−0.826668	+	1.13781i	0.161866	+	0.986813i	$0.448249\pi$
$181$	−11.1217	+	15.3077i	−0.826668	+	1.13781i	−0.988534	+	0.150998i	$0.951751\pi$
$182$		0			0
$183$	−28.6170	+	39.3879i	−2.11543	+	2.91164i
$184$		0			0
$185$	−15.3591	+	3.01301i	−1.12922	+	0.221521i
$186$		0			0
$187$	−6.83904	+	21.0484i	−0.500120	+	1.53921i
$188$		0			0
$189$	−13.6329	+	4.42960i	−0.991649	+	0.322206i
$190$		0			0
$191$	0.692493	−	2.13127i	0.0501070	−	0.154214i	−0.922872	−	0.385106i	$-0.874165\pi$
$191$	0.692493	−	2.13127i	0.0501070	−	0.154214i	0.972979	+	0.230893i	$0.0741647\pi$
$192$		0			0
$193$			22.6952i			1.63363i	0.576896	+	0.816817i	$0.304264\pi$
$193$			22.6952i			1.63363i	−0.576896	+	0.816817i	$0.695736\pi$
$194$		0			0
$195$	4.34958	−	4.68051i	0.311480	−	0.335179i
$196$		0			0
$197$	−10.5031	+	7.63095i	−0.748315	+	0.543682i	−0.895304	−	0.445456i	$-0.853042\pi$
$197$	−10.5031	+	7.63095i	−0.748315	+	0.543682i	0.146989	+	0.989138i	$0.453042\pi$
$198$		0			0
$199$	18.2166			1.29134			0.645672	−	0.763615i	$-0.276577\pi$
$199$	18.2166			1.29134			0.645672	+	0.763615i	$0.276577\pi$
$200$		0			0
$201$	9.54353			0.673149
$202$		0			0
$203$	5.92102	−	4.30187i	0.415574	−	0.301932i
$204$		0			0
$205$	−13.9930	+	2.74503i	−0.977316	+	0.191721i
$206$		0			0
$207$		−	15.0052i		−	1.04294i
$208$		0			0
$209$	5.53086	−	17.0222i	0.382578	−	1.17745i
$210$		0			0
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	−0.250933	−	0.968005i	$-0.580737\pi$
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	0.365970	+	0.930627i	$0.380737\pi$
$212$		0			0
$213$	1.89925	−	5.84528i	0.130134	−	0.400512i
$214$		0			0
$215$	3.21979	+	5.78510i	0.219588	+	0.394540i
$216$		0			0
$217$	0.997675	−	1.37318i	0.0677266	−	0.0932177i
$218$		0			0
$219$	7.80136	−	10.7377i	0.527167	−	0.725583i
$220$		0			0
$221$	2.97757	+	4.09828i	0.200293	+	0.275680i
$222$		0			0
$223$	1.48230	−	0.481630i	0.0992625	−	0.0322523i	−0.258965	−	0.965887i	$-0.583381\pi$
$223$	1.48230	−	0.481630i	0.0992625	−	0.0322523i	0.358227	+	0.933634i	$0.383381\pi$
$224$		0			0
$225$	22.1980	+	26.2700i	1.47987	+	1.75133i
$226$		0			0
$227$	2.84981	+	8.77081i	0.189148	+	0.582139i	0.999995	−	0.00311955i	$-0.000992986\pi$
$227$	2.84981	+	8.77081i	0.189148	+	0.582139i	−0.810847	+	0.585259i	$0.800993\pi$
$228$		0			0
$229$	6.64077	+	9.14023i	0.438834	+	0.604003i	0.969953	−	0.243294i	$-0.0782280\pi$
$229$	6.64077	+	9.14023i	0.438834	+	0.604003i	−0.531118	+	0.847298i	$0.678228\pi$
$230$		0			0
$231$	11.8761	+	8.62852i	0.781393	+	0.567715i
$232$		0			0
$233$	−7.30682	+	10.0570i	−0.478685	+	0.658854i	−0.978252	−	0.207422i	$-0.933493\pi$
$233$	−7.30682	+	10.0570i	−0.478685	+	0.658854i	0.499566	+	0.866276i	$0.333493\pi$
$234$		0			0
$235$	5.00619	−	10.7843i	0.326568	−	0.703492i
$236$		0			0
$237$	−2.67957	+	8.24687i	−0.174057	+	0.535692i
$238$		0			0
$239$	8.53966	+	26.2824i	0.552384	+	1.70006i	0.702752	+	0.711435i	$0.251954\pi$
$239$	8.53966	+	26.2824i	0.552384	+	1.70006i	−0.150368	+	0.988630i	$0.548046\pi$
$240$		0			0
$241$	−1.32369	+	4.07389i	−0.0852663	+	0.262423i	−0.984595	−	0.174851i	$-0.944056\pi$
$241$	−1.32369	+	4.07389i	−0.0852663	+	0.262423i	0.899329	+	0.437273i	$0.144056\pi$
$242$		0			0
$243$	−18.9940			−1.21846
$244$		0			0
$245$	−6.10846	−	10.9753i	−0.390255	−	0.701184i
$246$		0			0
$247$	−2.40802	−	3.31436i	−0.153219	−	0.210888i
$248$		0			0
$249$	29.7542			1.88560
$250$		0			0
$251$			13.4000i			0.845800i	0.906176	+	0.422900i	$0.138988\pi$
$251$			13.4000i			0.845800i	−0.906176	+	0.422900i	$0.861012\pi$
$252$		0			0
$253$	−7.00985	+	5.09295i	−0.440705	+	0.320191i
$254$		0			0
$255$	−34.2170	+	19.0440i	−2.14275	+	1.19258i
$256$		0			0
$257$		−	7.81899i		−	0.487735i	−0.969809	−	0.243868i	$-0.921584\pi$
$257$		−	7.81899i		−	0.487735i	0.969809	−	0.243868i	$-0.0784162\pi$
$258$		0			0
$259$	−7.82802	−	2.54348i	−0.486409	−	0.158044i
$260$		0			0
$261$	40.7171	−	13.2298i	2.52033	−	0.818904i
$262$		0			0
$263$	26.0980	+	8.47975i	1.60927	+	0.522884i	0.969377	−	0.245579i	$-0.0789781\pi$
$263$	26.0980	+	8.47975i	1.60927	+	0.522884i	0.639894	+	0.768463i	$0.278978\pi$
$264$		0			0
$265$	−26.5009	−	12.3020i	−1.62794	−	0.755704i
$266$		0			0
$267$	6.63968	+	4.82401i	0.406342	+	0.295225i
$268$		0			0
$269$	12.5408	−	17.2610i	0.764629	−	1.05242i	−0.232186	−	0.972671i	$-0.574588\pi$
$269$	12.5408	−	17.2610i	0.764629	−	1.05242i	0.996815	−	0.0797498i	$-0.0254121\pi$
$270$		0			0
$271$	−0.864363	+	0.627996i	−0.0525063	+	0.0381481i	−0.613729	−	0.789517i	$-0.710331\pi$
$271$	−0.864363	+	0.627996i	−0.0525063	+	0.0381481i	0.561223	+	0.827665i	$0.310331\pi$
$272$		0			0
$273$	3.19562	−	1.03832i	0.193408	−	0.0628420i
$274$		0			0
$275$	4.73802	−	19.2864i	0.285713	−	1.16301i
$276$		0			0
$277$	5.48602	+	16.8842i	0.329623	+	1.01448i	0.969310	+	0.245840i	$0.0790639\pi$
$277$	5.48602	+	16.8842i	0.329623	+	1.01448i	−0.639687	+	0.768635i	$0.720936\pi$
$278$		0			0
$279$	8.03268	−	5.83608i	0.480904	−	0.349397i
$280$		0			0
$281$	−8.77867	−	6.37807i	−0.523691	−	0.380484i	0.294301	−	0.955713i	$-0.404913\pi$
$281$	−8.77867	−	6.37807i	−0.523691	−	0.380484i	−0.817993	+	0.575229i	$0.804913\pi$
$282$		0			0
$283$	−18.7899	−	13.6517i	−1.11695	−	0.811509i	−0.133203	−	0.991089i	$-0.542526\pi$
$283$	−18.7899	−	13.6517i	−1.11695	−	0.811509i	−0.983743	+	0.179580i	$0.942526\pi$
$284$		0			0
$285$	27.6720	−	15.4013i	1.63915	−	0.912293i
$286$		0			0
$287$	−7.13178	−	2.31726i	−0.420976	−	0.136783i
$288$		0			0
$289$	−4.34064	−	13.3591i	−0.255332	−	0.785830i
$290$		0			0
$291$	−0.871498	−	0.283167i	−0.0510881	−	0.0165995i
$292$		0			0
$293$	−23.5633			−1.37658			−0.688291	−	0.725434i	$-0.741639\pi$
$293$	−23.5633			−1.37658			−0.688291	+	0.725434i	$0.741639\pi$
$294$		0			0
$295$	−0.553423	−	2.82112i	−0.0322215	−	0.164252i
$296$		0			0
$297$	28.4604	+	39.1724i	1.65144	+	2.27301i
$298$		0			0
$299$			1.98327i			0.114696i
$300$		0			0
$301$			3.48167i			0.200680i
$302$		0			0
$303$	−14.4869	−	19.9396i	−0.832252	−	1.14550i
$304$		0			0
$305$	25.3728	+	23.5788i	1.45284	+	1.35012i
$306$		0			0
$307$	−29.1918			−1.66607			−0.833033	−	0.553223i	$-0.813398\pi$
$307$	−29.1918			−1.66607			−0.833033	+	0.553223i	$0.813398\pi$
$308$		0			0
$309$	−39.3617	−	12.7894i	−2.23921	−	0.727563i
$310$		0			0
$311$	−0.303724	−	0.934766i	−0.0172226	−	0.0530057i	0.942076	−	0.335400i	$-0.108871\pi$
$311$	−0.303724	−	0.934766i	−0.0172226	−	0.0530057i	−0.959298	+	0.282394i	$0.908871\pi$
$312$		0			0
$313$	−9.11237	−	2.96079i	−0.515062	−	0.167354i	0.0399413	−	0.999202i	$-0.487283\pi$
$313$	−9.11237	−	2.96079i	−0.515062	−	0.167354i	−0.555003	+	0.831848i	$0.687283\pi$
$314$		0			0
$315$	3.48163	+	17.7479i	0.196168	+	0.999983i
$316$		0			0
$317$	14.8949	+	10.8218i	0.836580	+	0.607811i	0.921413	−	0.388584i	$-0.127036\pi$
$317$	14.8949	+	10.8218i	0.836580	+	0.607811i	−0.0848334	+	0.996395i	$0.527036\pi$
$318$		0			0
$319$	−20.0003	−	14.5311i	−1.11980	−	0.813584i
$320$		0			0
$321$	−17.8171	+	12.9449i	−0.994453	+	0.722512i
$322$		0			0
$323$	7.75880	+	23.8791i	0.431711	+	1.32867i
$324$		0			0
$325$	−2.93396	−	3.47216i	−0.162747	−	0.192601i
$326$		0			0
$327$	8.07726	−	2.62446i	0.446673	−	0.145133i
$328$		0			0
$329$	5.05833	−	3.67509i	0.278875	−	0.202614i
$330$		0			0
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	−0.909705	−	0.415255i	$-0.863692\pi$
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	0.676046	+	0.736860i	$0.263692\pi$
$332$		0			0
$333$	−38.9525	−	28.3007i	−2.13458	−	1.55087i
$334$		0			0
$335$	0.815824	−	6.74046i	0.0445733	−	0.368271i
$336$		0			0
$337$	−8.66935	−	2.81684i	−0.472250	−	0.153443i	0.0632165	−	0.998000i	$-0.479864\pi$
$337$	−8.66935	−	2.81684i	−0.472250	−	0.153443i	−0.535466	+	0.844557i	$0.679864\pi$
$338$		0			0
$339$	13.6625	−	4.43923i	0.742047	−	0.241106i
$340$		0			0
$341$	−5.45277	−	1.77171i	−0.295284	−	0.0959436i
$342$		0			0
$343$		−	14.8365i		−	0.801096i
$344$		0			0
$345$	−15.2202	−	1.84216i	−0.819426	−	0.0991784i
$346$		0			0
$347$	8.27687	−	6.01350i	0.444326	−	0.322821i	−0.343026	−	0.939326i	$-0.611452\pi$
$347$	8.27687	−	6.01350i	0.444326	−	0.322821i	0.787351	+	0.616505i	$0.211452\pi$
$348$		0			0
$349$			4.76436i			0.255030i	0.991837	+	0.127515i	$0.0407001\pi$
$349$			4.76436i			0.255030i	−0.991837	+	0.127515i	$0.959300\pi$
$350$		0			0
$351$	11.0829			0.591562
$352$		0			0
$353$	−10.7305	−	14.7692i	−0.571126	−	0.786087i	0.421562	−	0.906800i	$-0.361482\pi$
$353$	−10.7305	−	14.7692i	−0.571126	−	0.786087i	−0.992687	+	0.120713i	$0.961482\pi$
$354$		0			0
$355$	−3.96608	−	1.84109i	−0.210498	−	0.0977149i
$356$		0			0
$357$	−20.5930			−1.08990
$358$		0			0
$359$	−5.64467	+	17.3725i	−0.297914	+	0.916885i	0.684313	+	0.729188i	$0.260102\pi$
$359$	−5.64467	+	17.3725i	−0.297914	+	0.916885i	−0.982227	+	0.187697i	$0.939898\pi$
$360$		0			0
$361$	−0.403370	−	1.24145i	−0.0212300	−	0.0653393i
$362$		0			0
$363$	4.63917	−	14.2779i	0.243493	−	0.749396i
$364$		0			0
$365$	−6.91695	−	6.42789i	−0.362050	−	0.336451i
$366$		0			0
$367$	−8.85005	+	12.1811i	−0.461969	+	0.635846i	−0.974916	−	0.222575i	$-0.928554\pi$
$367$	−8.85005	+	12.1811i	−0.461969	+	0.635846i	0.512947	+	0.858421i	$0.328554\pi$
$368$		0			0
$369$	−35.4880	−	25.7835i	−1.84743	−	1.34224i
$370$		0			0
$371$	−9.03100	−	12.4301i	−0.468866	−	0.645339i
$372$		0			0
$373$	−0.219092	−	0.674295i	−0.0113441	−	0.0349137i	0.945224	−	0.326422i	$-0.105843\pi$
$373$	−0.219092	−	0.674295i	−0.0113441	−	0.0349137i	−0.956568	+	0.291508i	$0.905843\pi$
$374$		0			0
$375$	29.3715	−	19.2909i	1.51674	−	0.996176i
$376$		0			0
$377$	−5.38166	+	1.74861i	−0.277170	+	0.0900579i
$378$		0			0
$379$	−10.8210	−	14.8938i	−0.555838	−	0.765045i	0.434952	−	0.900454i	$-0.356765\pi$
$379$	−10.8210	−	14.8938i	−0.555838	−	0.765045i	−0.990790	+	0.135408i	$0.956765\pi$
$380$		0			0
$381$	15.9437	−	21.9446i	0.816821	−	1.12426i
$382$		0			0
$383$	10.5490	−	14.5194i	0.539027	−	0.741907i	−0.449445	−	0.893308i	$-0.648378\pi$
$383$	10.5490	−	14.5194i	0.539027	−	0.741907i	0.988472	+	0.151401i	$0.0483783\pi$
$384$		0			0
$385$	7.10942	−	7.65034i	0.362330	−	0.389897i
$386$		0			0
$387$	−6.29365	+	19.3699i	−0.319924	+	0.984625i
$388$		0			0
$389$	22.7077	−	7.37819i	1.15133	−	0.374089i	0.329685	−	0.944091i	$-0.393058\pi$
$389$	22.7077	−	7.37819i	1.15133	−	0.374089i	0.821643	+	0.570002i	$0.193058\pi$
$390$		0			0
$391$	3.75608	−	11.5600i	0.189953	−	0.584616i
$392$		0			0
$393$		−	27.3377i		−	1.37900i
$394$		0			0
$395$	5.59558	+	2.59752i	0.281544	+	0.130695i
$396$		0			0
$397$	1.16804	−	0.848630i	0.0586222	−	0.0425915i	−0.558088	−	0.829782i	$-0.688465\pi$
$397$	1.16804	−	0.848630i	0.0586222	−	0.0425915i	0.616710	+	0.787190i	$0.288465\pi$
$398$		0			0
$399$	16.6539			0.833740
$400$		0			0
$401$	−26.0682			−1.30178			−0.650891	−	0.759171i	$-0.725605\pi$
$401$	−26.0682			−1.30178			−0.650891	+	0.759171i	$0.725605\pi$
$402$		0			0
$403$	−1.06170	+	0.771367i	−0.0528868	+	0.0384245i
$404$		0			0
$405$	−4.74996	+	39.2448i	−0.236027	+	1.95009i
$406$		0			0
$407$			27.8026i			1.37813i
$408$		0			0
$409$	0.312601	−	0.962088i	0.0154571	−	0.0475722i	−0.943030	−	0.332706i	$-0.892038\pi$
$409$	0.312601	−	0.962088i	0.0154571	−	0.0475722i	0.958488	+	0.285134i	$0.0920382\pi$
$410$		0			0
$411$	10.8918	−	3.53897i	0.537254	−	0.174564i
$412$		0			0
$413$	0.467180	−	1.43783i	0.0229884	−	0.0707512i
$414$		0			0
$415$	2.54353	−	21.0150i	0.124857	−	1.03158i
$416$		0			0
$417$	25.8025	−	35.5140i	1.26355	−	1.73913i
$418$		0			0
$419$	19.6696	−	27.0728i	0.960920	−	1.32259i	0.0144183	−	0.999896i	$-0.495410\pi$
$419$	19.6696	−	27.0728i	0.960920	−	1.32259i	0.946502	−	0.322697i	$-0.104590\pi$
$420$		0			0
$421$	−16.1696	−	22.2556i	−0.788060	−	1.08467i	−0.994347	−	0.106180i	$-0.966138\pi$
$421$	−16.1696	−	22.2556i	−0.788060	−	1.08467i	0.206287	−	0.978492i	$-0.433862\pi$
$422$		0			0
$423$	34.7847	−	11.3022i	1.69129	−	0.549533i
$424$		0			0
$425$	10.5255	+	25.7949i	0.510562	+	1.25124i
$426$		0			0
$427$	5.62868	+	17.3233i	0.272391	+	0.838333i
$428$		0			0
$429$	−6.67126	−	9.18220i	−0.322092	−	0.443321i
$430$		0			0
$431$	−21.6348	−	15.7186i	−1.04211	−	0.757138i	−0.0714143	−	0.997447i	$-0.522751\pi$
$431$	−21.6348	−	15.7186i	−1.04211	−	0.757138i	−0.970696	+	0.240309i	$0.922751\pi$
$432$		0			0
$433$	−12.1996	+	16.7912i	−0.586273	+	0.806936i	−0.994366	−	0.106005i	$-0.966194\pi$
$433$	−12.1996	+	16.7912i	−0.586273	+	0.806936i	0.408092	+	0.912941i	$0.366194\pi$
$434$		0			0
$435$	−8.42055	−	42.9245i	−0.403734	−	2.05807i
$436$		0			0
$437$	−3.03762	+	9.34882i	−0.145309	+	0.447215i
$438$		0			0
$439$	−0.0935999	−	0.288071i	−0.00446728	−	0.0137489i	0.948798	−	0.315883i	$-0.102301\pi$
$439$	−0.0935999	−	0.288071i	−0.00446728	−	0.0137489i	−0.953265	+	0.302134i	$0.902301\pi$
$440$		0			0
$441$	11.9401	−	36.7478i	0.568575	−	1.74989i
$442$		0			0
$443$	33.9046			1.61086			0.805428	−	0.592693i	$-0.201935\pi$
$443$	33.9046			1.61086			0.805428	+	0.592693i	$0.201935\pi$
$444$		0			0
$445$	3.97472	−	4.27713i	0.188420	−	0.202755i
$446$		0			0
$447$	−4.82848	−	6.64583i	−0.228379	−	0.314337i
$448$		0			0
$449$	−12.6049			−0.594860			−0.297430	−	0.954744i	$-0.596129\pi$
$449$	−12.6049			−0.594860			−0.297430	+	0.954744i	$0.596129\pi$
$450$		0			0
$451$			25.3298i			1.19273i
$452$		0			0
$453$	−26.9986	+	19.6156i	−1.26850	+	0.921621i
$454$		0			0
$455$	−0.460174	−	2.34578i	−0.0215733	−	0.109972i
$456$		0			0
$457$			2.58934i			0.121124i	0.998164	+	0.0605622i	$0.0192893\pi$
$457$			2.58934i			0.121124i	−0.998164	+	0.0605622i	$0.980711\pi$
$458$		0			0
$459$	−64.5997	−	20.9897i	−3.01526	−	0.979716i
$460$		0			0
$461$	6.49523	−	2.11043i	0.302513	−	0.0982925i	−0.153827	−	0.988098i	$-0.549160\pi$
$461$	6.49523	−	2.11043i	0.302513	−	0.0982925i	0.456340	+	0.889805i	$0.349160\pi$
$462$		0			0
$463$	−20.7530	−	6.74304i	−0.964472	−	0.313376i	−0.215889	−	0.976418i	$-0.569265\pi$
$463$	−20.7530	−	6.74304i	−0.964472	−	0.313376i	−0.748582	+	0.663042i	$0.769265\pi$
$464$		0			0
$465$	−4.93352	−	8.86421i	−0.228787	−	0.411068i
$466$		0			0
$467$	−2.43118	−	1.76636i	−0.112502	−	0.0817373i	0.530112	−	0.847928i	$-0.322150\pi$
$467$	−2.43118	−	1.76636i	−0.112502	−	0.0817373i	−0.642614	+	0.766190i	$0.722150\pi$
$468$		0			0
$469$	2.09868	−	2.88859i	0.0969081	−	0.133383i
$470$		0			0
$471$	−9.92583	+	7.21154i	−0.457358	+	0.332290i
$472$		0			0
$473$	11.1850	−	3.63421i	0.514285	−	0.167101i
$474$		0			0
$475$	−8.51217	−	20.8609i	−0.390565	−	0.957163i
$476$		0			0
$477$	−27.7736	−	85.4782i	−1.27166	−	3.91378i
$478$		0			0
$479$	−15.3717	+	11.1682i	−0.702349	+	0.510287i	−0.880697	−	0.473681i	$-0.842925\pi$
$479$	−15.3717	+	11.1682i	−0.702349	+	0.510287i	0.178347	+	0.983968i	$0.442925\pi$
$480$		0			0
$481$	5.14843	+	3.74055i	0.234748	+	0.170555i
$482$		0			0
$483$	−6.52251	−	4.73888i	−0.296785	−	0.215627i
$484$		0			0
$485$	−0.274496	+	0.591320i	−0.0124642	+	0.0268504i
$486$		0			0
$487$	1.80539	+	0.586607i	0.0818101	+	0.0265817i	0.349636	−	0.936886i	$-0.386305\pi$
$487$	1.80539	+	0.586607i	0.0818101	+	0.0265817i	−0.267826	+	0.963467i	$0.586305\pi$
$488$		0			0
$489$	19.0651	+	58.6762i	0.862151	+	2.65343i
$490$		0			0
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.441234	−	0.897392i	$-0.645459\pi$
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.884440	+	0.466654i	$0.845459\pi$
$492$		0			0
$493$	34.6801			1.56191
$494$		0			0
$495$	53.3816	−	29.7104i	2.39932	−	1.33538i
$496$		0			0
$497$	−1.35156	−	1.86027i	−0.0606258	−	0.0834443i
$498$		0			0
$499$		−	10.5948i		−	0.474289i	−0.971474	−	0.237145i	$-0.923788\pi$
$499$		−	10.5948i		−	0.474289i	0.971474	−	0.237145i	$-0.0762115\pi$
$500$		0			0
$501$			52.9371i			2.36506i
$502$		0			0
$503$	−15.5618	−	21.4189i	−0.693865	−	0.955024i	−0.999995	−	0.00303389i	$-0.999034\pi$
$503$	−15.5618	−	21.4189i	−0.693865	−	0.955024i	0.306130	−	0.951990i	$-0.400966\pi$
$504$		0			0
$505$	−15.3214	+	8.52739i	−0.681794	+	0.379464i
$506$		0			0
$507$	38.2613			1.69925
$508$		0			0
$509$	17.5095	+	5.68919i	0.776096	+	0.252169i	0.670172	−	0.742205i	$-0.266220\pi$
$509$	17.5095	+	5.68919i	0.776096	+	0.252169i	0.105923	+	0.994374i	$0.466220\pi$
$510$		0			0
$511$	−1.53445	−	4.72255i	−0.0678800	−	0.208913i
$512$		0			0
$513$	52.2431	+	16.9748i	2.30659	+	0.749456i
$514$		0			0
$515$	−12.3978	+	26.7073i	−0.546311	+	1.17686i
$516$		0			0
$517$	−17.0863	−	12.4139i	−0.751453	−	0.545963i
$518$		0			0
$519$	25.8888	+	18.8093i	1.13639	+	0.825637i
$520$		0			0
$521$	32.7039	−	23.7608i	1.43278	−	1.04098i	0.443295	−	0.896376i	$-0.353809\pi$
$521$	32.7039	−	23.7608i	1.43278	−	1.04098i	0.989490	−	0.144603i	$-0.0461906\pi$
$522$		0			0
$523$	5.37852	+	16.5534i	0.235186	+	0.723828i	0.997097	+	0.0761461i	$0.0242615\pi$
$523$	5.37852	+	16.5534i	0.235186	+	0.723828i	−0.761911	+	0.647682i	$0.775738\pi$
$524$		0			0
$525$	18.4296	−	1.35263i	0.804333	−	0.0590336i
$526$		0			0
$527$	7.64925	−	2.48539i	0.333206	−	0.108265i
$528$		0			0
$529$	−14.7575	+	10.7220i	−0.641630	+	0.466172i
$530$		0			0
$531$	5.19820	−	7.15471i	0.225583	−	0.310488i
$532$		0			0
$533$	4.69052	+	3.40786i	0.203169	+	0.147611i
$534$		0			0
$535$	7.61969	+	13.6905i	0.329428	+	0.591893i
$536$		0			0
$537$	−45.1434	−	14.6680i	−1.94808	−	0.632970i
$538$		0			0
$539$	−21.2197	+	6.89469i	−0.913996	+	0.296975i
$540$		0			0
$541$	−7.69917	−	2.50161i	−0.331013	−	0.107553i	0.138795	−	0.990321i	$-0.455677\pi$
$541$	−7.69917	−	2.50161i	−0.331013	−	0.107553i	−0.469808	+	0.882768i	$0.655677\pi$
$542$		0			0
$543$			59.4701i			2.55211i
$544$		0			0
$545$	−1.16314	−	5.92920i	−0.0498233	−	0.253979i
$546$		0			0
$547$	−20.7126	+	15.0486i	−0.885607	+	0.643431i	−0.934729	−	0.355362i	$-0.884358\pi$
$547$	−20.7126	+	15.0486i	−0.885607	+	0.643431i	0.0491221	+	0.998793i	$0.484358\pi$
$548$		0			0
$549$			106.551i			4.54747i
$550$		0			0
$551$	−28.0465			−1.19482
$552$		0			0
$553$	1.90686	+	2.62457i	0.0810881	+	0.111608i
$554$		0			0
$555$	−33.4881	+	36.0360i	−1.42149	+	1.52964i
$556$		0			0
$557$	−1.74254			−0.0738336			−0.0369168	−	0.999318i	$-0.511754\pi$
$557$	−1.74254			−0.0738336			−0.0369168	+	0.999318i	$0.511754\pi$
$558$		0			0
$559$	0.831844	−	2.56015i	0.0351832	−	0.108283i
$560$		0			0
$561$	21.4952	+	66.1555i	0.907529	+	2.79309i
$562$		0			0
$563$	7.94233	−	24.4440i	0.334729	−	1.03019i	−0.632126	−	0.774866i	$-0.717817\pi$
$563$	7.94233	−	24.4440i	0.334729	−	1.03019i	0.966855	−	0.255325i	$-0.0821826\pi$
$564$		0			0
$565$	−1.96742	−	10.0291i	−0.0827702	−	0.421929i
$566$		0			0
$567$	−12.2191	+	16.8181i	−0.513154	+	0.706296i
$568$		0			0
$569$	−11.5604	−	8.39915i	−0.484639	−	0.352111i	0.318480	−	0.947930i	$-0.396828\pi$
$569$	−11.5604	−	8.39915i	−0.484639	−	0.352111i	−0.803119	+	0.595819i	$0.796828\pi$
$570$		0			0
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	0.490174	−	0.871625i	$-0.336933\pi$
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	−0.980436	+	0.196836i	$0.936933\pi$
$572$		0			0
$573$	−2.17652	−	6.69863i	−0.0909253	−	0.279839i
$574$		0			0
$575$	−2.60218	+	10.5923i	−0.108518	+	0.441729i
$576$		0			0
$577$	14.6528	−	4.76100i	0.610006	−	0.198203i	0.0123079	−	0.999924i	$-0.496082\pi$
$577$	14.6528	−	4.76100i	0.610006	−	0.198203i	0.597698	+	0.801721i	$0.296082\pi$
$578$		0			0
$579$	41.9275	+	57.7083i	1.74245	+	2.39827i
$580$		0			0
$581$	6.54313	−	9.00585i	0.271455	−	0.373626i
$582$		0			0
$583$	−30.5054	+	41.9870i	−1.26340	+	1.73892i
$584$		0			0
$585$	1.68023	−	13.8823i	0.0694690	−	0.573963i
$586$		0			0
$587$	4.25364	−	13.0914i	0.175567	−	0.540338i	−0.824092	−	0.566455i	$-0.808314\pi$
$587$	4.25364	−	13.0914i	0.175567	−	0.540338i	0.999659	+	0.0261173i	$0.00831433\pi$
$588$		0			0
$589$	−6.18610	+	2.00998i	−0.254894	+	0.0828200i
$590$		0			0
$591$	−12.6092	+	38.8072i	−0.518675	+	1.59632i
$592$		0			0
$593$			6.37493i			0.261787i	0.991396	+	0.130894i	$0.0417846\pi$
$593$			6.37493i			0.261787i	−0.991396	+	0.130894i	$0.958215\pi$
$594$		0			0
$595$	−1.76038	+	14.5445i	−0.0721686	+	0.596267i
$596$		0			0
$597$	46.3205	−	33.6538i	1.89577	−	1.37736i
$598$		0			0
$599$	−38.8351			−1.58676			−0.793380	−	0.608727i	$-0.791681\pi$
$599$	−38.8351			−1.58676			−0.793380	+	0.608727i	$0.791681\pi$
$600$		0			0
$601$	41.0478			1.67438			0.837188	−	0.546916i	$-0.184198\pi$
$601$	41.0478			1.67438			0.837188	+	0.546916i	$0.184198\pi$
$602$		0			0
$603$	16.8973	−	12.2766i	0.688112	−	0.499942i
$604$		0			0
$605$	−9.68770	−	4.49712i	−0.393861	−	0.182834i
$606$		0			0
$607$		−	28.6948i		−	1.16469i	−0.812943	−	0.582343i	$-0.802136\pi$
$607$		−	28.6948i		−	1.16469i	0.812943	−	0.582343i	$-0.197864\pi$
$608$		0			0
$609$	7.10833	−	21.8772i	0.288044	−	0.886509i
$610$		0			0
$611$	−4.59756	+	1.49384i	−0.185997	+	0.0604342i
$612$		0			0
$613$	−2.30831	+	7.10423i	−0.0932316	+	0.286937i	−0.986789	−	0.162012i	$-0.948202\pi$
$613$	−2.30831	+	7.10423i	−0.0932316	+	0.286937i	0.893557	+	0.448949i	$0.148202\pi$
$614$		0			0
$615$	−30.5096	+	32.8309i	−1.23027	+	1.32387i
$616$		0			0
$617$	−23.8187	+	32.7837i	−0.958906	+	1.31982i	−0.0114498	+	0.999934i	$0.503645\pi$
$617$	−23.8187	+	32.7837i	−0.958906	+	1.31982i	−0.947456	+	0.319886i	$0.896355\pi$
$618$		0			0
$619$	5.89273	−	8.11065i	0.236849	−	0.325994i	−0.674003	−	0.738729i	$-0.735426\pi$
$619$	5.89273	−	8.11065i	0.236849	−	0.325994i	0.910851	+	0.412735i	$0.135426\pi$
$620$		0			0
$621$	−15.6308	−	21.5140i	−0.627242	−	0.863325i
$622$		0			0
$623$	2.92021	−	0.948834i	0.116996	−	0.0380142i
$624$		0			0
$625$	−11.1141	−	22.3937i	−0.444562	−	0.895748i
$626$		0			0
$627$	−17.3836	−	53.5012i	−0.694234	−	2.13663i
$628$		0			0
$629$	−22.9248	−	31.5533i	−0.914073	−	1.25811i
$630$		0			0
$631$	24.4964	+	17.7976i	0.975184	+	0.708513i	0.956627	−	0.291315i	$-0.0940927\pi$
$631$	24.4964	+	17.7976i	0.975184	+	0.708513i	0.0185571	+	0.999828i	$0.494093\pi$
$632$		0			0
$633$	3.24593	−	4.46765i	0.129014	−	0.177573i
$634$		0			0
$635$	−14.1362	−	13.1367i	−0.560979	−	0.521316i
$636$		0			0
$637$	−1.57814	+	4.85702i	−0.0625283	+	0.192442i
$638$		0			0
$639$	−4.15654	−	12.7925i	−0.164430	−	0.506064i
$640$		0			0
$641$	−12.1688	+	37.4516i	−0.480637	+	1.47925i	0.357564	+	0.933889i	$0.383607\pi$
$641$	−12.1688	+	37.4516i	−0.480637	+	1.47925i	−0.838201	+	0.545361i	$0.816393\pi$
$642$		0			0
$643$	15.6623			0.617660			0.308830	−	0.951117i	$-0.400063\pi$
$643$	15.6623			0.617660			0.308830	+	0.951117i	$0.400063\pi$
$644$		0			0
$645$	18.8746	+	8.76178i	0.743188	+	0.344995i
$646$		0			0
$647$	−19.5134	−	26.8579i	−0.767152	−	1.05589i	−0.996585	−	0.0825693i	$-0.973687\pi$
$647$	−19.5134	−	26.8579i	−0.767152	−	1.05589i	0.229434	−	0.973324i	$-0.426313\pi$
$648$		0			0
$649$	−5.10673			−0.200457
$650$		0			0
$651$		−	5.33479i		−	0.209087i
$652$		0			0
$653$	3.13976	−	2.28117i	0.122868	−	0.0892690i	−0.524654	−	0.851316i	$-0.675805\pi$
$653$	3.13976	−	2.28117i	0.122868	−	0.0892690i	0.647522	+	0.762047i	$0.275805\pi$
$654$		0			0
$655$	−19.3082	−	2.33695i	−0.754434	−	0.0913121i
$656$		0			0
$657$		−	29.0471i		−	1.13323i
$658$		0			0
$659$	38.7539	+	12.5919i	1.50964	+	0.490511i	0.942811	−	0.333327i	$-0.108171\pi$
$659$	38.7539	+	12.5919i	1.50964	+	0.490511i	0.566826	+	0.823838i	$0.308171\pi$
$660$		0			0
$661$	−35.9253	+	11.6728i	−1.39733	+	0.454020i	−0.908327	−	0.418261i	$-0.862640\pi$
$661$	−35.9253	+	11.6728i	−1.39733	+	0.454020i	−0.489004	+	0.872282i	$0.662640\pi$
$662$		0			0
$663$	15.1425	+	4.92009i	0.588085	+	0.191081i
$664$		0			0
$665$	1.42365	−	11.7624i	0.0552070	−	0.456128i
$666$		0			0
$667$	10.9844	+	7.98063i	0.425318	+	0.309011i
$668$		0			0
$669$	2.87936	−	3.96311i	0.111323	−	0.153223i
$670$		0			0
$671$	49.7762	−	36.1645i	1.92159	−	1.39612i
$672$		0			0
$673$	1.57662	−	0.512274i	0.0607742	−	0.0197467i	−0.278472	−	0.960444i	$-0.589828\pi$
$673$	1.57662	−	0.512274i	0.0607742	−	0.0197467i	0.339246	+	0.940698i	$0.389828\pi$
$674$		0			0
$675$	59.1919	+	14.5415i	2.27830	+	0.559702i
$676$		0			0
$677$	0.0701106	+	0.215778i	0.00269457	+	0.00829304i	0.952395	−	0.304868i	$-0.0986122\pi$
$677$	0.0701106	+	0.215778i	0.00269457	+	0.00829304i	−0.949700	+	0.313161i	$0.898612\pi$
$678$		0			0
$679$	−0.277355	+	0.201510i	−0.0106439	+	0.00773325i
$680$		0			0
$681$	23.4497	+	17.0372i	0.898596	+	0.652868i
$682$		0			0
$683$	24.0637	+	17.4833i	0.920773	+	0.668981i	0.943716	−	0.330756i	$-0.107304\pi$
$683$	24.0637	+	17.4833i	0.920773	+	0.668981i	−0.0229435	+	0.999737i	$0.507304\pi$
$684$		0			0
$685$	−1.56844	−	7.99527i	−0.0599270	−	0.305483i
$686$		0			0
$687$	33.7717	+	10.9731i	1.28847	+	0.418649i
$688$		0			0
$689$	3.67089	+	11.2978i	0.139850	+	0.430413i
$690$		0			0
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.322077	−	0.946714i	$-0.604381\pi$
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.817030	+	0.576595i	$0.804381\pi$
$692$		0			0
$693$	32.1269			1.22040
$694$		0			0
$695$	−22.8773	−	21.2598i	−0.867787	−	0.806430i
$696$		0			0
$697$	−20.8859	−	28.7469i	−0.791108	−	1.08887i
$698$		0			0
$699$			39.0712i			1.47781i
$700$		0			0
$701$		−	2.30506i		−	0.0870611i	−0.999052	−	0.0435305i	$-0.986139\pi$
$701$		−	2.30506i		−	0.0870611i	0.999052	−	0.0435305i	$-0.0138606\pi$
$702$		0			0
$703$	18.5398	+	25.5178i	0.699240	+	0.962422i
$704$		0			0
$705$	−7.19368	−	36.6704i	−0.270930	−	1.38109i
$706$		0			0
$707$	−9.22096			−0.346790
$708$		0			0
$709$	−25.4956	−	8.28402i	−0.957508	−	0.311113i	−0.211745	−	0.977325i	$-0.567915\pi$
$709$	−25.4956	−	8.28402i	−0.957508	−	0.311113i	−0.745763	+	0.666212i	$0.767915\pi$
$710$		0			0
$711$	5.86429	+	18.0484i	0.219928	+	0.676869i
$712$		0			0
$713$	2.99472	+	0.973045i	0.112153	+	0.0364408i
$714$		0			0
$715$	−7.05555	+	3.92688i	−0.263862	+	0.146857i
$716$		0			0
$717$	70.2688	+	51.0533i	2.62424	+	1.90662i
$718$		0			0
$719$	−12.3313	−	8.95922i	−0.459880	−	0.334123i	0.333604	−	0.942713i	$-0.391735\pi$
$719$	−12.3313	−	8.95922i	−0.459880	−	0.334123i	−0.793484	+	0.608591i	$0.791735\pi$
$720$		0			0
$721$	−12.5269	+	9.10133i	−0.466526	+	0.338951i
$722$		0			0
$723$	4.16038	+	12.8043i	0.154726	+	0.476198i
$724$		0			0
$725$	−31.0368	+	2.27793i	−1.15268	+	0.0846001i
$726$		0			0
$727$	2.11778	−	0.688107i	0.0785440	−	0.0255205i	−0.269481	−	0.963006i	$-0.586852\pi$
$727$	2.11778	−	0.688107i	0.0785440	−	0.0255205i	0.348025	+	0.937485i	$0.386852\pi$
$728$		0			0
$729$	−5.38937	+	3.91560i	−0.199606	+	0.145022i
$730$		0			0
$731$	−9.69724	+	13.3471i	−0.358665	+	0.493661i
$732$		0			0
$733$	40.0434	+	29.0933i	1.47904	+	1.07458i	0.977865	+	0.209237i	$0.0670979\pi$
$733$	40.0434	+	29.0933i	1.47904	+	1.07458i	0.501173	+	0.865347i	$0.332902\pi$
$734$		0			0
$735$	−35.8082	−	16.6225i	−1.32081	−	0.613131i
$736$		0			0
$737$	−11.4703	−	3.72692i	−0.422513	−	0.137283i
$738$		0			0
$739$	17.2361	−	5.60033i	0.634039	−	0.206012i	0.0256753	−	0.999670i	$-0.491826\pi$
$739$	17.2361	−	5.60033i	0.634039	−	0.206012i	0.608363	+	0.793659i	$0.291826\pi$
$740$		0			0
$741$	−12.2460	−	3.97897i	−0.449869	−	0.146171i
$742$		0			0
$743$		−	15.5632i		−	0.570959i	−0.958385	−	0.285479i	$-0.907847\pi$
$743$		−	15.5632i		−	0.570959i	0.958385	−	0.285479i	$-0.0921528\pi$
$744$		0			0
$745$	−5.10661	+	2.84217i	−0.187092	+	0.104129i
$746$		0			0
$747$	52.6813	−	38.2752i	1.92751	−	1.40042i
$748$		0			0
$749$			8.23944i			0.301062i
$750$		0			0
$751$	−41.5803			−1.51729			−0.758643	−	0.651507i	$-0.774137\pi$
$751$	−41.5803			−1.51729			−0.758643	+	0.651507i	$0.774137\pi$
$752$		0			0
$753$	24.7554	+	34.0729i	0.902137	+	1.24169i
$754$		0			0
$755$	11.5463	+	20.7455i	0.420211	+	0.755007i
$756$		0			0
$757$	−1.83755			−0.0667870			−0.0333935	−	0.999442i	$-0.510631\pi$
$757$	−1.83755			−0.0667870			−0.0333935	+	0.999442i	$0.510631\pi$
$758$		0			0
$759$	−8.41550	+	25.9003i	−0.305463	+	0.940120i
$760$		0			0
$761$	−9.18935	−	28.2819i	−0.333114	−	1.02522i	−0.967644	−	0.252320i	$-0.918806\pi$
$761$	−9.18935	−	28.2819i	−0.333114	−	1.02522i	0.634530	−	0.772898i	$-0.281194\pi$
$762$		0			0
$763$	0.981880	−	3.02192i	0.0355464	−	0.109401i
$764$		0			0
$765$	−36.0851	+	77.7345i	−1.30466	+	2.81050i
$766$		0			0
$767$	−0.687057	+	0.945653i	−0.0248082	+	0.0341455i
$768$		0			0
$769$	7.63237	+	5.54524i	0.275230	+	0.199966i	0.716834	−	0.697244i	$-0.245590\pi$
$769$	7.63237	+	5.54524i	0.275230	+	0.199966i	−0.441604	+	0.897210i	$0.645590\pi$
$770$		0			0
$771$	−14.4450	−	19.8818i	−0.520222	−	0.716025i
$772$		0			0
$773$	7.49873	+	23.0787i	0.269711	+	0.830084i	0.990571	+	0.137003i	$0.0437471\pi$
$773$	7.49873	+	23.0787i	0.269711	+	0.830084i	−0.720860	+	0.693081i	$0.756253\pi$
$774$		0			0
$775$	−6.68240	+	2.72672i	−0.240039	+	0.0979467i
$776$		0			0
$777$	−24.6036	+	7.99420i	−0.882649	+	0.286790i
$778$		0			0
$779$	16.8908	+	23.2482i	0.605176	+	0.832953i
$780$		0			0
$781$	−4.56537	+	6.28370i	−0.163362	+	0.224848i
$782$		0			0
$783$	44.5974	−	61.3830i	1.59378	−	2.19365i
$784$		0			0
$785$	4.24490	+	7.62695i	0.151507	+	0.272217i
$786$		0			0
$787$	−11.5135	+	35.4350i	−0.410413	+	1.26312i	0.505877	+	0.862606i	$0.331169\pi$
$787$	−11.5135	+	35.4350i	−0.410413	+	1.26312i	−0.916290	+	0.400515i	$0.868831\pi$
$788$		0			0
$789$	82.0264	−	26.6520i	2.92022	−	0.948837i
$790$		0			0
$791$	1.66083	−	5.11151i	0.0590524	−	0.181745i
$792$		0			0
$793$		−	14.0830i		−	0.500103i
$794$		0			0
$795$	−90.1123	+	17.6774i	−3.19595	+	0.626953i
$796$		0			0
$797$	4.03520	−	2.93174i	0.142934	−	0.103848i	−0.514020	−	0.857778i	$-0.671844\pi$
$797$	4.03520	−	2.93174i	0.142934	−	0.103848i	0.656954	+	0.753930i	$0.271844\pi$
$798$		0			0
$799$	29.6272			1.04814
$800$		0			0
$801$	17.9614			0.634635
$802$		0			0
$803$	−13.5696	+	9.85892i	−0.478862	+	0.347914i
$804$		0			0
$805$	−3.90458	+	4.20166i	−0.137618	+	0.148089i
$806$		0			0
$807$		−	67.0587i		−	2.36058i
$808$		0			0
$809$	−2.74204	+	8.43914i	−0.0964051	+	0.296704i	−0.987617	−	0.156882i	$-0.949856\pi$
$809$	−2.74204	+	8.43914i	−0.0964051	+	0.296704i	0.891212	+	0.453587i	$0.149856\pi$
$810$		0			0
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.0785467	−	0.996910i	$-0.474972\pi$
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.649515	+	0.760349i	$0.274972\pi$
$812$		0			0
$813$	−1.03769	+	3.19368i	−0.0363934	+	0.112007i
$814$		0			0
$815$	43.0719	−	8.44946i	1.50874	−	0.295972i
$816$		0			0
$817$	7.84235	−	10.7941i	0.274369	−	0.377637i
$818$		0			0
$819$	4.32233	−	5.94918i	0.151035	−	0.207881i
$820$		0			0
$821$	21.5298	+	29.6332i	0.751394	+	1.03420i	0.997881	+	0.0650589i	$0.0207235\pi$
$821$	21.5298	+	29.6332i	0.751394	+	1.03420i	−0.246488	+	0.969146i	$0.579276\pi$
$822$		0			0
$823$	5.63427	−	1.83068i	0.196398	−	0.0638136i	−0.209166	−	0.977880i	$-0.567075\pi$
$823$	5.63427	−	1.83068i	0.196398	−	0.0638136i	0.405564	+	0.914066i	$0.367075\pi$
$824$		0			0
$825$	−23.5824	−	57.7936i	−0.821033	−	2.01212i
$826$		0			0
$827$	−4.70692	−	14.4864i	−0.163676	−	0.503742i	0.835261	−	0.549854i	$-0.185317\pi$
$827$	−4.70692	−	14.4864i	−0.163676	−	0.503742i	−0.998936	+	0.0461123i	$0.985317\pi$
$828$		0			0
$829$	25.2244	+	34.7183i	0.876078	+	1.20582i	0.977492	+	0.210974i	$0.0676634\pi$
$829$	25.2244	+	34.7183i	0.876078	+	1.20582i	−0.101414	+	0.994844i	$0.532337\pi$
$830$		0			0
$831$	45.1419	+	32.7975i	1.56595	+	1.13773i
$832$		0			0
$833$	18.3972	−	25.3216i	0.637427	−	0.877343i
$834$		0			0
$835$	37.3887	+	4.52531i	1.29389	+	0.156605i
$836$		0			0
$837$	5.43757	−	16.7351i	0.187950	−	0.578450i
$838$		0			0
$839$	−14.0891	−	43.3617i	−0.486409	−	1.49701i	−0.829930	−	0.557868i	$-0.811620\pi$
$839$	−14.0891	−	43.3617i	−0.486409	−	1.49701i	0.343521	−	0.939145i	$-0.388380\pi$
$840$		0			0
$841$	−3.00946	+	9.26218i	−0.103775	+	0.319385i
$842$		0			0
$843$	−34.1050			−1.17464
$844$		0			0
$845$	3.27075	−	27.0234i	0.112517	−	0.929634i
$846$		0			0
$847$	−3.30138	−	4.54396i	−0.113437	−	0.156132i
$848$		0			0
$849$	−72.9986			−2.50531
$850$		0			0
$851$		−	15.2695i		−	0.523433i
$852$		0			0
$853$	39.8951	−	28.9855i	1.36598	−	0.992445i	0.367944	−	0.929848i	$-0.380062\pi$
$853$	39.8951	−	28.9855i	1.36598	−	0.992445i	0.998039	−	0.0625971i	$-0.0199383\pi$
$854$		0			0
$855$	29.1827	−	62.8654i	0.998028	−	2.14995i
$856$		0			0
$857$			57.0345i			1.94826i	0.225989	+	0.974130i	$0.427439\pi$
$857$			57.0345i			1.94826i	−0.225989	+	0.974130i	$0.572561\pi$
$858$		0			0
$859$	−20.6564	−	6.71166i	−0.704786	−	0.228999i	−0.0653714	−	0.997861i	$-0.520823\pi$
$859$	−20.6564	−	6.71166i	−0.704786	−	0.228999i	−0.639415	+	0.768862i	$0.720823\pi$
$860$		0			0
$861$	−22.4153	+	7.28318i	−0.763912	+	0.248210i
$862$		0			0
$863$	17.9981	+	5.84794i	0.612663	+	0.199066i	0.598880	−	0.800839i	$-0.295613\pi$
$863$	17.9981	+	5.84794i	0.612663	+	0.199066i	0.0137830	+	0.999905i	$0.495613\pi$
$864$		0			0
$865$	15.4978	−	16.6770i	0.526942	−	0.567034i
$866$		0			0
$867$	−35.7171	−	25.9500i	−1.21302	−	0.881307i
$868$		0			0
$869$	6.44110	−	8.86542i	0.218499	−	0.300739i
$870$		0			0
$871$	−2.23335	+	1.62262i	−0.0756742	+	0.0549805i
$872$		0			0
$873$	−1.90729	+	0.619716i	−0.0645520	+	0.0209742i
$874$		0			0
$875$	0.620102	−	13.1322i	0.0209633	−	0.443949i
$876$		0			0
$877$	−4.30447	−	13.2478i	−0.145352	−	0.447347i	0.851704	−	0.524023i	$-0.175569\pi$
$877$	−4.30447	−	13.2478i	−0.145352	−	0.447347i	−0.997056	+	0.0766761i	$0.975569\pi$
$878$		0			0
$879$	−59.9157	+	43.5313i	−2.02091	+	1.46827i
$880$		0			0
$881$	−32.7294	−	23.7793i	−1.10268	−	0.801145i	−0.121186	−	0.992630i	$-0.538670\pi$
$881$	−32.7294	−	23.7793i	−1.10268	−	0.801145i	−0.981496	+	0.191485i	$0.938670\pi$
$882$		0			0
$883$	−3.31224	−	2.40648i	−0.111466	−	0.0809845i	0.530656	−	0.847587i	$-0.321946\pi$
$883$	−3.31224	−	2.40648i	−0.111466	−	0.0809845i	−0.642122	+	0.766603i	$0.721946\pi$
$884$		0			0
$885$	−6.61902	−	6.15102i	−0.222496	−	0.206764i
$886$		0			0
$887$	−5.39637	−	1.75339i	−0.181192	−	0.0588730i	0.217016	−	0.976168i	$-0.430368\pi$
$887$	−5.39637	−	1.75339i	−0.181192	−	0.0588730i	−0.398208	+	0.917295i	$0.630368\pi$
$888$		0			0
$889$	−3.13597	−	9.65152i	−0.105177	−	0.323701i
$890$		0			0
$891$	66.7832	+	21.6992i	2.23732	+	0.726950i
$892$		0			0
$893$	−23.9601			−0.801795
$894$		0			0
$895$	−14.2188	+	30.6302i	−0.475284	+	1.02386i
$896$		0			0
$897$	3.66394	+	5.04297i	0.122335	+	0.168380i
$898$		0			0
$899$			8.98418i			0.299639i
$900$		0			0
$901$		−	72.8046i		−	2.42547i
$902$		0			0
$903$	6.43211	+	8.85304i	0.214047	+	0.294611i
$904$		0			0
$905$	42.0029	+	5.08377i	1.39622	+	0.168990i
$906$		0			0
$907$	49.8362			1.65478			0.827392	−	0.561625i	$-0.189824\pi$
$907$	49.8362			1.65478			0.827392	+	0.561625i	$0.189824\pi$
$908$		0			0
$909$	−51.2997	−	16.6683i	−1.70150	−	0.552852i
$910$		0			0
$911$	−1.08071	−	3.32610i	−0.0358057	−	0.110199i	0.931556	−	0.363597i	$-0.118452\pi$
$911$	−1.08071	−	3.32610i	−0.0358057	−	0.110199i	−0.967362	+	0.253399i	$0.918452\pi$
$912$		0			0
$913$	−35.7613	−	11.6196i	−1.18353	−	0.384551i
$914$		0			0
$915$	108.077	+	13.0810i	3.57291	+	0.432443i
$916$		0			0
$917$	−8.27442	−	6.01172i	−0.273246	−	0.198525i
$918$		0			0
$919$	35.2395	+	25.6030i	1.16244	+	0.844564i	0.990085	−	0.140471i	$-0.0448616\pi$
$919$	35.2395	+	25.6030i	1.16244	+	0.844564i	0.172357	+	0.985034i	$0.444862\pi$
$920$		0			0
$921$	−74.2277	+	53.9296i	−2.44589	+	1.77704i
$922$		0			0
$923$	0.549378	+	1.69081i	0.0180830	+	0.0556538i
$924$		0			0
$925$	22.5890	+	26.7327i	0.742722	+	0.878965i
$926$		0			0
$927$	−86.1439	+	27.9899i	−2.82934	+	0.919307i
$928$		0			0
$929$	−20.6493	+	15.0026i	−0.677483	+	0.492220i	−0.872522	−	0.488576i	$-0.837517\pi$
$929$	−20.6493	+	15.0026i	−0.677483	+	0.492220i	0.195039	+	0.980795i	$0.437517\pi$
$930$		0			0
$931$	−14.8782	+	20.4781i	−0.487614	+	0.671143i
$932$		0			0
$933$	−2.49920	−	1.81577i	−0.0818201	−	0.0594458i
$934$		0			0
$935$	48.5622	−	9.52649i	1.58815	−	0.311549i
$936$		0			0
$937$	3.76427	+	1.22309i	0.122973	+	0.0399565i	0.369857	−	0.929089i	$-0.379407\pi$
$937$	3.76427	+	1.22309i	0.122973	+	0.0399565i	−0.246884	+	0.969045i	$0.579407\pi$
$938$		0			0
$939$	−28.6403	+	9.30581i	−0.934642	+	0.303684i
$940$		0			0
$941$	7.54079	+	2.45015i	0.245823	+	0.0798727i	0.429337	−	0.903144i	$-0.358747\pi$
$941$	7.54079	+	2.45015i	0.245823	+	0.0798727i	−0.183514	+	0.983017i	$0.558747\pi$
$942$		0			0
$943$		−	13.9114i		−	0.453018i
$944$		0			0
$945$	23.4797	+	21.8196i	0.763794	+	0.709791i
$946$		0			0
$947$	−0.630350	+	0.457976i	−0.0204836	+	0.0148822i	−0.597980	−	0.801511i	$-0.704030\pi$
$947$	−0.630350	+	0.457976i	−0.0204836	+	0.0148822i	0.577496	+	0.816393i	$0.304030\pi$
$948$		0			0
$949$			3.83921i			0.124626i
$950$		0			0
$951$	57.8664			1.87645
$952$		0			0
$953$	6.29429	+	8.66334i	0.203892	+	0.280633i	0.898702	−	0.438560i	$-0.144511\pi$
$953$	6.29429	+	8.66334i	0.203892	+	0.280633i	−0.694810	+	0.719194i	$0.744511\pi$
$954$		0			0
$955$	−4.91720	+	0.964613i	−0.159117	+	0.0312141i
$956$		0			0
$957$	−77.7008			−2.51171
$958$		0			0
$959$	1.32402	−	4.07492i	0.0427549	−	0.131586i
$960$		0			0
$961$	−8.93566	−	27.5011i	−0.288247	−	0.887134i
$962$		0			0
$963$	−14.8940	+	45.8391i	−0.479953	+	1.47714i
$964$		0			0
$965$	44.3427	−	24.6796i	1.42744	−	0.794465i
$966$		0			0
$967$	−5.37219	+	7.39419i	−0.172758	+	0.237781i	−0.886612	−	0.462513i	$-0.846948\pi$
$967$	−5.37219	+	7.39419i	−0.172758	+	0.237781i	0.713854	+	0.700294i	$0.246948\pi$
$968$		0			0
$969$	63.8435	+	46.3850i	2.05095	+	1.49010i
$970$		0			0
$971$	15.2665	+	21.0125i	0.489924	+	0.674323i	0.980374	−	0.197147i	$-0.0631675\pi$
$971$	15.2665	+	21.0125i	0.489924	+	0.674323i	−0.490450	+	0.871469i	$0.663167\pi$
$972$		0			0
$973$	−5.07508	−	15.6195i	−0.162700	−	0.500738i
$974$		0			0
$975$	−13.8749	−	3.40859i	−0.444351	−	0.109162i
$976$		0			0
$977$	29.0332	−	9.43346i	0.928855	−	0.301803i	0.194760	−	0.980851i	$-0.437607\pi$
$977$	29.0332	−	9.43346i	0.928855	−	0.301803i	0.734094	+	0.679048i	$0.237607\pi$
$978$		0			0
$979$	−6.09631	−	8.39085i	−0.194839	−	0.268173i
$980$		0			0
$981$	10.9251	−	15.0372i	0.348813	−	0.480100i
$982$		0			0
$983$	23.5163	−	32.3674i	0.750052	−	1.03236i	−0.247924	−	0.968779i	$-0.579748\pi$
$983$	23.5163	−	32.3674i	0.750052	−	1.03236i	0.997977	−	0.0635791i	$-0.0202515\pi$
$984$		0			0
$985$	26.3311	+	12.2231i	0.838978	+	0.389462i
$986$		0			0
$987$	6.07265	−	18.6897i	0.193295	−	0.594900i
$988$		0			0
$989$	−6.14291	+	1.99595i	−0.195333	+	0.0634676i
$990$		0			0
$991$	−14.8786	+	45.7916i	−0.472634	+	1.45462i	0.376488	+	0.926422i	$0.377132\pi$
$991$	−14.8786	+	45.7916i	−0.472634	+	1.45462i	−0.849122	+	0.528197i	$0.822868\pi$
$992$		0			0
$993$			22.7314i			0.721358i
$994$		0			0
$995$	−19.8095	−	35.5923i	−0.628003	−	1.12835i
$996$		0			0
$997$	0.969621	−	0.704471i	0.0307082	−	0.0223108i	−0.572325	−	0.820027i	$-0.693959\pi$
$997$	0.969621	−	0.704471i	0.0307082	−	0.0223108i	0.603033	+	0.797716i	$0.293959\pi$
$998$		0			0
$999$	−85.3292			−2.69970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.369.27		112
4.3	odd	2		200.2.o.a.69.10	yes	112
8.3	odd	2		200.2.o.a.69.16	yes	112
8.5	even	2	inner	800.2.be.a.369.2		112
20.3	even	4		1000.2.t.b.901.10		224
20.7	even	4		1000.2.t.b.901.47		224
20.19	odd	2		1000.2.o.a.349.19		112
25.4	even	10	inner	800.2.be.a.529.2		112
40.3	even	4		1000.2.t.b.901.55		224
40.19	odd	2		1000.2.o.a.349.13		112
40.27	even	4		1000.2.t.b.901.2		224
100.3	even	20		1000.2.t.b.101.55		224
100.47	even	20		1000.2.t.b.101.2		224
100.71	odd	10		1000.2.o.a.149.13		112
100.79	odd	10		200.2.o.a.29.16	yes	112
200.3	even	20		1000.2.t.b.101.10		224
200.29	even	10	inner	800.2.be.a.529.27		112
200.147	even	20		1000.2.t.b.101.47		224
200.171	odd	10		1000.2.o.a.149.19		112
200.179	odd	10		200.2.o.a.29.10	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.10	✓	112	200.179	odd	10
200.2.o.a.29.16	yes	112	100.79	odd	10
200.2.o.a.69.10	yes	112	4.3	odd	2
200.2.o.a.69.16	yes	112	8.3	odd	2
800.2.be.a.369.2		112	8.5	even	2	inner
800.2.be.a.369.27		112	1.1	even	1	trivial
800.2.be.a.529.2		112	25.4	even	10	inner
800.2.be.a.529.27		112	200.29	even	10	inner
1000.2.o.a.149.13		112	100.71	odd	10
1000.2.o.a.149.19		112	200.171	odd	10
1000.2.o.a.349.13		112	40.19	odd	2
1000.2.o.a.349.19		112	20.19	odd	2
1000.2.t.b.101.2		224	100.47	even	20
1000.2.t.b.101.10		224	200.3	even	20
1000.2.t.b.101.47		224	200.147	even	20
1000.2.t.b.101.55		224	100.3	even	20
1000.2.t.b.901.2		224	40.27	even	4
1000.2.t.b.901.10		224	20.3	even	4
1000.2.t.b.901.47		224	20.7	even	4
1000.2.t.b.901.55		224	40.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(2.54275 - 1.84742i) q^{3} +(-1.08744 - 1.95384i) q^{5} -1.17589i q^{7} +(2.12559 - 6.54190i) q^{9} +O(q^{10})\)	\(q+(2.54275 - 1.84742i) q^{3} +(-1.08744 - 1.95384i) q^{5} -1.17589i q^{7} +(2.12559 - 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(-0.280944 + 0.864656i) q^{13} +(-6.37465 - 2.95917i) q^{15} +(3.27511 - 4.50780i) q^{17} +(-2.64864 + 3.64555i) q^{19} +(-2.17235 - 2.98999i) q^{21} +(2.07468 - 0.674105i) q^{23} +(-2.63495 + 4.24936i) q^{25} +(-3.76703 - 11.5937i) q^{27} +(3.65841 + 5.03536i) q^{29} +(1.16778 + 0.848445i) q^{31} +(-7.33789 + 10.0997i) q^{33} +(-2.29749 + 1.27870i) q^{35} +(2.16303 - 6.65712i) q^{37} +(0.883011 + 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} -2.96089 q^{43} +(-15.0933 + 2.96086i) q^{45} +(3.12538 + 4.30172i) q^{47} +5.61729 q^{49} -17.5127i q^{51} +(10.5708 - 7.68016i) q^{53} +(6.50602 + 6.04601i) q^{55} +14.1629i q^{57} +(1.22277 + 0.397301i) q^{59} +(-14.7321 + 4.78675i) q^{61} +(-7.69253 - 2.49945i) q^{63} +(1.99491 - 0.391343i) q^{65} +(2.45652 + 1.78477i) q^{67} +(4.03005 - 5.54689i) q^{69} +(1.58201 - 1.14940i) q^{71} +(4.01616 - 1.30493i) q^{73} +(1.15031 + 15.6729i) q^{75} +(1.44329 + 4.44199i) q^{77} +(-2.23200 + 1.62164i) q^{79} +(-14.3025 - 10.3914i) q^{81} +(7.65878 + 5.56443i) q^{83} +(-12.3690 - 1.49707i) q^{85} +(18.6049 + 6.04509i) q^{87} +(0.806910 + 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +4.53682 q^{93} +(10.0030 + 1.21071i) q^{95} +(-0.171369 - 0.235869i) q^{97} +27.3214i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 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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