LMFDB - Embedded newform 441.2.bb.f.100.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.6
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.f.172.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.49548 + 0.769754i) q^{2} +(3.98243 + 2.71518i) q^{4} +(1.69843 - 0.255997i) q^{5} +(-2.62887 - 0.298395i) q^{7} +(4.59158 + 5.75765i) q^{8} +O(q^{10})$	\(q+(2.49548 + 0.769754i) q^{2} +(3.98243 + 2.71518i) q^{4} +(1.69843 - 0.255997i) q^{5} +(-2.62887 - 0.298395i) q^{7} +(4.59158 + 5.75765i) q^{8} +(4.43546 + 0.668538i) q^{10} +(-2.79059 + 2.58929i) q^{11} +(-0.351587 - 1.54041i) q^{13} +(-6.33061 - 2.76822i) q^{14} +(3.50436 + 8.92897i) q^{16} +(-0.385913 - 5.14966i) q^{17} +(1.59925 - 2.76998i) q^{19} +(7.45897 + 3.59205i) q^{20} +(-8.95699 + 4.31346i) q^{22} +(0.388520 - 5.18444i) q^{23} +(-1.95873 + 0.604187i) q^{25} +(0.308353 - 4.11469i) q^{26} +(-9.65910 - 8.32618i) q^{28} +(3.72828 + 1.79544i) q^{29} +(5.21402 + 9.03095i) q^{31} +(0.771289 + 10.2921i) q^{32} +(3.00093 - 13.1479i) q^{34} +(-4.54135 + 0.166180i) q^{35} +(-1.68787 + 1.15077i) q^{37} +(6.12310 - 5.68141i) q^{38} +(9.27242 + 8.60355i) q^{40} +(-4.23617 - 5.31199i) q^{41} +(-7.22334 + 9.05779i) q^{43} +(-18.1437 + 2.73473i) q^{44} +(4.96028 - 12.6386i) q^{46} +(-11.8376 - 3.65142i) q^{47} +(6.82192 + 1.56889i) q^{49} -5.35304 q^{50} +(2.78230 - 7.08918i) q^{52} +(-1.50059 - 1.02308i) q^{53} +(-4.07678 + 5.11212i) q^{55} +(-10.3526 - 16.5062i) q^{56} +(7.92180 + 7.35036i) q^{58} +(1.27898 + 0.192775i) q^{59} +(7.03671 - 4.79755i) q^{61} +(6.05989 + 26.5501i) q^{62} +(-1.72882 + 7.57447i) q^{64} +(-0.991487 - 2.52627i) q^{65} +(3.93580 + 6.81700i) q^{67} +(12.4453 - 21.5560i) q^{68} +(-11.4608 - 3.08102i) q^{70} +(10.8760 - 5.23762i) q^{71} +(2.74013 - 0.845219i) q^{73} +(-5.09786 + 1.57248i) q^{74} +(13.8899 - 6.68902i) q^{76} +(8.10874 - 5.97421i) q^{77} +(-0.483737 + 0.837858i) q^{79} +(8.23772 + 14.2681i) q^{80} +(-6.48236 - 16.5168i) q^{82} +(-2.28170 + 9.99677i) q^{83} +(-1.97375 - 8.64755i) q^{85} +(-24.9980 + 17.0433i) q^{86} +(-27.7215 - 4.17834i) q^{88} +(0.289929 + 0.269015i) q^{89} +(0.464628 + 4.15444i) q^{91} +(15.6239 - 19.5918i) q^{92} +(-26.7298 - 18.2241i) q^{94} +(2.00711 - 5.11403i) q^{95} +7.55821 q^{97} +(15.8163 + 9.16633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	2.49548	+	0.769754i	1.76457	+	0.544298i	0.995491	−	0.0948530i	$-0.0302381\pi$
$2$	2.49548	+	0.769754i	1.76457	+	0.544298i	0.769081	+	0.639151i	$0.220714\pi$
$3$		0			0
$3$		0			0
$4$	3.98243	+	2.71518i	1.99122	+	1.35759i
$5$	1.69843	−	0.255997i	0.759562	−	0.114486i	0.242170	−	0.970234i	$-0.422141\pi$
$5$	1.69843	−	0.255997i	0.759562	−	0.114486i	0.517392	+	0.855748i	$0.326903\pi$
$6$		0			0
$7$	−2.62887	−	0.298395i	−0.993620	−	0.112783i
$7$	−2.62887	−	0.298395i	−0.993620	−	0.112783i
$8$	4.59158	+	5.75765i	1.62337	+	2.03564i
$9$		0			0
$10$	4.43546	+	0.668538i	1.40262	+	0.211410i
$11$	−2.79059	+	2.58929i	−0.841395	+	0.780701i	−0.977709	−	0.209965i	$-0.932665\pi$
$11$	−2.79059	+	2.58929i	−0.841395	+	0.780701i	0.136314	+	0.990666i	$0.456475\pi$
$12$		0			0
$13$	−0.351587	−	1.54041i	−0.0975128	−	0.427231i	0.902481	−	0.430729i	$-0.141744\pi$
$13$	−0.351587	−	1.54041i	−0.0975128	−	0.427231i	−0.999994	+	0.00349800i	$0.998887\pi$
$14$	−6.33061	−	2.76822i	−1.69193	−	0.739839i
$15$		0			0
$16$	3.50436	+	8.92897i	0.876091	+	2.23224i
$17$	−0.385913	−	5.14966i	−0.0935977	−	1.24898i	−0.824250	−	0.566226i	$-0.808403\pi$
$17$	−0.385913	−	5.14966i	−0.0935977	−	1.24898i	0.730653	−	0.682749i	$-0.239216\pi$
$18$		0			0
$19$	1.59925	−	2.76998i	0.366893	−	0.635477i	−0.622185	−	0.782870i	$-0.713755\pi$
$19$	1.59925	−	2.76998i	0.366893	−	0.635477i	0.989078	+	0.147393i	$0.0470882\pi$
$20$	7.45897	+	3.59205i	1.66788	+	0.803207i
$21$		0			0
$22$	−8.95699	+	4.31346i	−1.90964	+	0.919633i
$23$	0.388520	−	5.18444i	0.0810120	−	1.08103i	−0.797503	−	0.603315i	$-0.793846\pi$
$23$	0.388520	−	5.18444i	0.0810120	−	1.08103i	0.878515	−	0.477715i	$-0.158535\pi$
$24$		0			0
$25$	−1.95873	+	0.604187i	−0.391745	+	0.120837i
$26$	0.308353	−	4.11469i	0.0604731	−	0.806957i
$27$		0			0
$28$	−9.65910	−	8.32618i	−1.82540	−	1.57350i
$29$	3.72828	+	1.79544i	0.692324	+	0.333406i	0.746743	−	0.665113i	$-0.231616\pi$
$29$	3.72828	+	1.79544i	0.692324	+	0.333406i	−0.0544193	+	0.998518i	$0.517331\pi$
$30$		0			0
$31$	5.21402	+	9.03095i	0.936466	+	1.62201i	0.771999	+	0.635624i	$0.219257\pi$
$31$	5.21402	+	9.03095i	0.936466	+	1.62201i	0.164467	+	0.986383i	$0.447409\pi$
$32$	0.771289	+	10.2921i	0.136346	+	1.81941i
$33$		0			0
$34$	3.00093	−	13.1479i	0.514655	−	2.25485i
$35$	−4.54135	+	0.166180i	−0.767628	+	0.0280895i
$36$		0			0
$37$	−1.68787	+	1.15077i	−0.277484	+	0.189185i	−0.694063	−	0.719914i	$-0.744181\pi$
$37$	−1.68787	+	1.15077i	−0.277484	+	0.189185i	0.416579	+	0.909099i	$0.363229\pi$
$38$	6.12310	−	5.68141i	0.993299	−	0.921646i
$39$		0			0
$40$	9.27242	+	8.60355i	1.46610	+	1.36034i
$41$	−4.23617	−	5.31199i	−0.661578	−	0.829593i	0.331936	−	0.943302i	$-0.392298\pi$
$41$	−4.23617	−	5.31199i	−0.661578	−	0.829593i	−0.993514	+	0.113709i	$0.963727\pi$
$42$		0			0
$43$	−7.22334	+	9.05779i	−1.10155	+	1.38130i	−0.184355	+	0.982860i	$0.559020\pi$
$43$	−7.22334	+	9.05779i	−1.10155	+	1.38130i	−0.917195	+	0.398440i	$0.869552\pi$
$44$	−18.1437	+	2.73473i	−2.73527	+	0.412276i
$45$		0			0
$46$	4.96028	−	12.6386i	0.731354	−	1.86346i
$47$	−11.8376	−	3.65142i	−1.72669	−	0.532614i	−0.737009	−	0.675883i	$-0.763762\pi$
$47$	−11.8376	−	3.65142i	−1.72669	−	0.532614i	−0.989684	+	0.143269i	$0.954238\pi$
$48$		0			0
$49$	6.82192	+	1.56889i	0.974560	+	0.224127i
$50$	−5.35304			−0.757034
$51$		0			0
$52$	2.78230	−	7.08918i	0.385835	−	0.983092i
$53$	−1.50059	−	1.02308i	−0.206121	−	0.140531i	0.455860	−	0.890052i	$-0.349332\pi$
$53$	−1.50059	−	1.02308i	−0.206121	−	0.140531i	−0.661981	+	0.749520i	$0.730284\pi$
$54$		0			0
$55$	−4.07678	+	5.11212i	−0.549713	+	0.689318i
$56$	−10.3526	−	16.5062i	−1.38342	−	2.20574i
$57$		0			0
$58$	7.92180	+	7.35036i	1.04018	+	0.965149i
$59$	1.27898	+	0.192775i	0.166509	+	0.0250972i	0.231768	−	0.972771i	$-0.425549\pi$
$59$	1.27898	+	0.192775i	0.166509	+	0.0250972i	−0.0652585	+	0.997868i	$0.520787\pi$
$60$		0			0
$61$	7.03671	−	4.79755i	0.900958	−	0.614263i	−0.0217495	−	0.999763i	$-0.506924\pi$
$61$	7.03671	−	4.79755i	0.900958	−	0.614263i	0.922708	+	0.385501i	$0.125971\pi$
$62$	6.05989	+	26.5501i	0.769606	+	3.37186i
$63$		0			0
$64$	−1.72882	+	7.57447i	−0.216103	+	0.946808i
$65$	−0.991487	−	2.52627i	−0.122979	−	0.313345i
$66$		0			0
$67$	3.93580	+	6.81700i	0.480834	+	0.832829i	0.999758	−	0.0219914i	$-0.00700065\pi$
$67$	3.93580	+	6.81700i	0.480834	+	0.832829i	−0.518924	+	0.854820i	$0.673667\pi$
$68$	12.4453	−	21.5560i	1.50922	−	2.61405i
$69$		0			0
$70$	−11.4608	−	3.08102i	−1.36982	−	0.368253i
$71$	10.8760	−	5.23762i	1.29075	−	0.621591i	0.342618	−	0.939475i	$-0.388686\pi$
$71$	10.8760	−	5.23762i	1.29075	−	0.621591i	0.948130	+	0.317883i	$0.102972\pi$
$72$		0			0
$73$	2.74013	−	0.845219i	0.320708	−	0.0989254i	−0.130221	−	0.991485i	$-0.541569\pi$
$73$	2.74013	−	0.845219i	0.320708	−	0.0989254i	0.450929	+	0.892560i	$0.351093\pi$
$74$	−5.09786	+	1.57248i	−0.592614	+	0.182797i
$75$		0			0
$76$	13.8899	−	6.68902i	1.59328	−	0.767283i
$77$	8.10874	−	5.97421i	0.924077	−	0.680825i
$78$		0			0
$79$	−0.483737	+	0.837858i	−0.0544247	+	0.0942664i	−0.891954	−	0.452126i	$-0.850666\pi$
$79$	−0.483737	+	0.837858i	−0.0544247	+	0.0942664i	0.837529	+	0.546392i	$0.183999\pi$
$80$	8.23772	+	14.2681i	0.921005	+	1.59523i
$81$		0			0
$82$	−6.48236	−	16.5168i	−0.715857	−	1.82397i
$83$	−2.28170	+	9.99677i	−0.250449	+	1.09729i	0.680675	+	0.732585i	$0.261687\pi$
$83$	−2.28170	+	9.99677i	−0.250449	+	1.09729i	−0.931124	+	0.364703i	$0.881171\pi$
$84$		0			0
$85$	−1.97375	−	8.64755i	−0.214083	−	0.937959i
$86$	−24.9980	+	17.0433i	−2.69560	+	1.83783i
$87$		0			0
$88$	−27.7215	−	4.17834i	−2.95512	−	0.445412i
$89$	0.289929	+	0.269015i	0.0307325	+	0.0285155i	0.695390	−	0.718633i	$-0.255232\pi$
$89$	0.289929	+	0.269015i	0.0307325	+	0.0285155i	−0.664657	+	0.747149i	$0.731422\pi$
$90$		0			0
$91$	0.464628	+	4.15444i	0.0487062	+	0.435503i
$92$	15.6239	−	19.5918i	1.62890	−	2.04258i
$93$		0			0
$94$	−26.7298	−	18.2241i	−2.75697	−	1.87967i
$95$	2.00711	−	5.11403i	0.205925	−	0.524688i
$96$		0			0
$97$	7.55821			0.767420			0.383710	−	0.923454i	$-0.374646\pi$
$97$	7.55821			0.767420			0.383710	+	0.923454i	$0.374646\pi$
$98$	15.8163	+	9.16633i	1.59769	+	0.925939i
$99$		0			0
$100$	−9.44097	−	2.91215i	−0.944097	−	0.291215i
$101$	2.24733	−	5.72611i	0.223618	−	0.569769i	−0.774400	−	0.632696i	$-0.781948\pi$
$101$	2.24733	−	5.72611i	0.223618	−	0.569769i	0.998018	+	0.0629268i	$0.0200435\pi$
$102$		0			0
$103$	−18.8434	+	2.84019i	−1.85670	+	0.279852i	−0.979675	−	0.200594i	$-0.935713\pi$
$103$	−18.8434	+	2.84019i	−1.85670	+	0.279852i	−0.877024	+	0.480446i	$0.840475\pi$
$104$	7.25478	−	9.09720i	0.711389	−	0.892054i
$105$		0			0
$106$	−2.95716	−	3.70817i	−0.287225	−	0.360169i
$107$	6.36556	+	5.90638i	0.615382	+	0.570991i	0.925046	−	0.379855i	$-0.124026\pi$
$107$	6.36556	+	5.90638i	0.615382	+	0.570991i	−0.309664	+	0.950846i	$0.600217\pi$
$108$		0			0
$109$	−8.12935	+	7.54293i	−0.778650	+	0.722482i	−0.965641	−	0.259880i	$-0.916317\pi$
$109$	−8.12935	+	7.54293i	−0.778650	+	0.722482i	0.186991	+	0.982362i	$0.440127\pi$
$110$	−14.1086	+	9.61909i	−1.34520	+	0.917144i
$111$		0			0
$112$	−6.54815	−	24.5188i	−0.618742	−	2.31681i
$113$	−0.649444	+	2.84540i	−0.0610945	+	0.267673i	−0.996245	−	0.0865779i	$-0.972407\pi$
$113$	−0.649444	+	2.84540i	−0.0610945	+	0.267673i	0.935151	+	0.354251i	$0.115264\pi$
$114$		0			0
$115$	−0.667328	−	8.90487i	−0.0622286	−	0.830384i
$116$	9.97266	+	17.2732i	0.925939	+	1.60377i
$117$		0			0
$118$	3.04328	+	1.46557i	0.280157	+	0.134917i
$119$	−0.522118	+	13.6529i	−0.0478625	+	1.25156i
$120$		0			0
$121$	0.260945	−	3.48208i	0.0237223	−	0.316552i
$122$	21.2529	−	6.55565i	1.92415	−	0.593521i
$123$		0			0
$124$	−3.75613	+	50.1221i	−0.337311	+	4.50110i
$125$	−10.9097	+	5.25383i	−0.975792	+	0.469917i
$126$		0			0
$127$	13.0092	+	6.26488i	1.15438	+	0.555919i	0.910346	−	0.413849i	$-0.135816\pi$
$127$	13.0092	+	6.26488i	1.15438	+	0.555919i	0.244031	+	0.969767i	$0.421530\pi$
$128$	0.176272	−	0.305312i	0.0155804	−	0.0269860i
$129$		0			0
$130$	−0.529633	−	7.06746i	−0.0464519	−	0.619857i
$131$	−5.93545	−	15.1233i	−0.518583	−	1.32133i	−0.915073	−	0.403289i	$-0.867867\pi$
$131$	−5.93545	−	15.1233i	−0.518583	−	1.32133i	0.396490	−	0.918039i	$-0.370228\pi$
$132$		0			0
$133$	−5.03077	+	6.80471i	−0.436223	+	0.590044i
$134$	4.57429	+	20.0413i	0.395159	+	1.73130i
$135$		0			0
$136$	27.8780	−	25.8670i	2.39052	−	2.21808i
$137$	−15.0611	−	2.27009i	−1.28676	−	0.193947i	−0.530198	−	0.847874i	$-0.677882\pi$
$137$	−15.0611	−	2.27009i	−1.28676	−	0.193947i	−0.756558	+	0.653927i	$0.773120\pi$
$138$		0			0
$139$	2.45552	+	3.07913i	0.208275	+	0.261168i	0.874986	−	0.484148i	$-0.160870\pi$
$139$	2.45552	+	3.07913i	0.208275	+	0.261168i	−0.666712	+	0.745316i	$0.732299\pi$
$140$	−18.5368	−	11.6688i	−1.56665	−	0.986190i
$141$		0			0
$142$	31.1726	−	4.69852i	2.61595	−	0.394291i
$143$	4.96970	+	3.38828i	0.415587	+	0.283342i
$144$		0			0
$145$	6.79186	+	2.09501i	0.564033	+	0.173981i
$146$	7.48856			0.619758
$147$		0			0
$148$	−9.84637			−0.809367
$149$	13.8941	+	4.28577i	1.13825	+	0.351104i	0.805900	−	0.592051i	$-0.201682\pi$
$149$	13.8941	+	4.28577i	1.13825	+	0.351104i	0.332352	+	0.943156i	$0.392158\pi$
$150$		0			0
$151$	1.01797	+	0.694042i	0.0828415	+	0.0564804i	0.604032	−	0.796960i	$-0.293560\pi$
$151$	1.01797	+	0.694042i	0.0828415	+	0.0564804i	−0.521191	+	0.853440i	$0.674512\pi$
$152$	23.2917	−	3.51065i	1.88920	−	0.284752i
$153$		0			0
$154$	24.8339	−	8.66680i	2.00117	−	0.698391i
$155$	11.1676	+	14.0037i	0.897000	+	1.12480i
$156$		0			0
$157$	−3.10689	−	0.468288i	−0.247957	−	0.0373735i	0.0238878	−	0.999715i	$-0.492396\pi$
$157$	−3.10689	−	0.468288i	−0.247957	−	0.0373735i	−0.271845	+	0.962341i	$0.587634\pi$
$158$	−1.85210	+	1.71850i	−0.147345	+	0.136717i
$159$		0			0
$160$	3.94474	+	17.2831i	0.311859	+	1.36635i
$161$	−2.56838	+	13.5133i	−0.202417	+	1.06500i
$162$		0			0
$163$	−2.66250	−	6.78395i	−0.208543	−	0.531360i	0.787883	−	0.615825i	$-0.211177\pi$
$163$	−2.66250	−	6.78395i	−0.208543	−	0.531360i	−0.996426	+	0.0844649i	$0.973082\pi$
$164$	−2.44727	−	32.6566i	−0.191100	−	2.55005i
$165$		0			0
$166$	−13.3890	+	23.1904i	−1.03919	+	1.79993i
$167$	11.8835	+	5.72280i	0.919574	+	0.442843i	0.832919	−	0.553395i	$-0.186668\pi$
$167$	11.8835	+	5.72280i	0.919574	+	0.442843i	0.0866547	+	0.996238i	$0.472382\pi$
$168$		0			0
$169$	9.46336	−	4.55731i	0.727951	−	0.350563i
$170$	1.73104	−	23.0991i	0.132765	−	1.77162i
$171$		0			0
$172$	−53.3599	+	16.4594i	−4.06866	+	1.25501i
$173$	−1.44410	+	19.2702i	−0.109793	+	1.46508i	0.621711	+	0.783247i	$0.286438\pi$
$173$	−1.44410	+	19.2702i	−0.109793	+	1.46508i	−0.731503	+	0.681838i	$0.761181\pi$
$174$		0			0
$175$	5.32952	−	1.00385i	0.402874	−	0.0758843i
$176$	−32.8990	−	15.8433i	−2.47985	−	1.19423i
$177$		0			0
$178$	0.516438	+	0.894497i	0.0387087	+	0.0670454i
$179$	0.108159	+	1.44328i	0.00808418	+	0.107876i	0.999786	−	0.0206827i	$-0.00658399\pi$
$179$	0.108159	+	1.44328i	0.00808418	+	0.107876i	−0.991702	+	0.128559i	$0.958965\pi$
$180$		0			0
$181$	−3.38463	+	14.8290i	−0.251578	+	1.10223i	0.678422	+	0.734672i	$0.262664\pi$
$181$	−3.38463	+	14.8290i	−0.251578	+	1.10223i	−0.930000	+	0.367561i	$0.880193\pi$
$182$	−2.03843	+	10.7250i	−0.151098	+	0.794988i
$183$		0			0
$184$	31.6341	−	21.5678i	2.33210	−	1.59000i
$185$	−2.57214	+	2.38660i	−0.189107	+	0.175466i
$186$		0			0
$187$	14.4109	+	13.3714i	1.05383	+	0.977810i
$188$	−37.2282	−	46.6827i	−2.71515	−	3.40469i
$189$		0			0
$190$	8.94525	−	11.2170i	0.648957	−	0.813766i
$191$	8.47349	−	1.27717i	0.613120	−	0.0924130i	0.164861	−	0.986317i	$-0.447282\pi$
$191$	8.47349	−	1.27717i	0.613120	−	0.0924130i	0.448259	+	0.893904i	$0.352044\pi$
$192$		0			0
$193$	8.33106	−	21.2272i	0.599683	−	1.52797i	−0.231999	−	0.972716i	$-0.574527\pi$
$193$	8.33106	−	21.2272i	0.599683	−	1.52797i	0.831682	−	0.555252i	$-0.187378\pi$
$194$	18.8614	+	5.81796i	1.35417	+	0.417705i
$195$		0			0
$196$	22.9080	+	24.7707i	1.63629	+	1.76934i
$197$	3.97035			0.282876			0.141438	−	0.989947i	$-0.454827\pi$
$197$	3.97035			0.282876			0.141438	+	0.989947i	$0.454827\pi$
$198$		0			0
$199$	−5.82262	+	14.8358i	−0.412755	+	1.05168i	0.561748	+	0.827308i	$0.310129\pi$
$199$	−5.82262	+	14.8358i	−0.412755	+	1.05168i	−0.974503	+	0.224374i	$0.927966\pi$
$200$	−12.4723	−	8.50350i	−0.881928	−	0.601288i
$201$		0			0
$202$	10.0159	−	12.5595i	0.704715	−	0.883684i
$203$	−9.26541	−	5.83249i	−0.650304	−	0.409361i
$204$		0			0
$205$	−8.55470	−	7.93760i	−0.597486	−	0.554386i
$206$	−49.2097	−	7.41717i	−3.42860	−	0.516779i
$207$		0			0
$208$	12.5221	−	8.53745i	0.868254	−	0.591966i
$209$	2.70944	+	11.8708i	0.187416	+	0.821121i
$210$		0			0
$211$	0.450809	−	1.97512i	0.0310350	−	0.135973i	−0.957037	−	0.289966i	$-0.906356\pi$
$211$	0.450809	−	1.97512i	0.0310350	−	0.135973i	0.988072	+	0.153993i	$0.0492132\pi$
$212$	−3.19813	−	8.14871i	−0.219649	−	0.559656i
$213$		0			0
$214$	11.3387	+	19.6392i	0.775096	+	1.34251i
$215$	−9.94959	+	17.2332i	−0.678556	+	1.17529i
$216$		0			0
$217$	−11.0122	−	25.2970i	−0.747556	−	1.71728i
$218$	−26.0928	+	12.5657i	−1.76723	+	0.851053i
$219$		0			0
$220$	−30.1158	+	9.28950i	−2.03041	+	0.626298i
$221$	−7.79687	+	2.40502i	−0.524475	+	0.161779i
$222$		0			0
$223$	−20.1422	+	9.69996i	−1.34882	+	0.649557i	−0.962114	−	0.272646i	$-0.912101\pi$
$223$	−20.1422	+	9.69996i	−1.34882	+	0.649557i	−0.386705	+	0.922203i	$0.626387\pi$
$224$	1.04351	−	27.2868i	0.0697223	−	1.82318i
$225$		0			0
$226$	−3.81093	+	6.60073i	−0.253500	+	0.439074i
$227$	−5.82472	−	10.0887i	−0.386600	−	0.669611i	0.605390	−	0.795929i	$-0.293017\pi$
$227$	−5.82472	−	10.0887i	−0.386600	−	0.669611i	−0.991990	+	0.126318i	$0.959684\pi$
$228$		0			0
$229$	−1.52259	−	3.87949i	−0.100616	−	0.256364i	0.871698	−	0.490043i	$-0.163019\pi$
$229$	−1.52259	−	3.87949i	−0.100616	−	0.256364i	−0.972314	+	0.233679i	$0.924924\pi$
$230$	5.18926	−	22.7356i	0.342170	−	1.49914i
$231$		0			0
$232$	6.78112	+	29.7100i	0.445203	+	1.95056i
$233$	13.3178	−	9.07991i	0.872477	−	0.594844i	−0.0421648	−	0.999111i	$-0.513425\pi$
$233$	13.3178	−	9.07991i	0.872477	−	0.594844i	0.914641	+	0.404266i	$0.132473\pi$
$234$		0			0
$235$	−21.0401	−	3.17129i	−1.37251	−	0.206872i
$236$	4.57003	+	4.24037i	0.297484	+	0.276025i
$237$		0			0
$238$	−11.8123	+	33.6687i	−0.765680	+	2.18242i
$239$	7.73805	−	9.70321i	0.500533	−	0.627648i	−0.465817	−	0.884881i	$-0.654239\pi$
$239$	7.73805	−	9.70321i	0.500533	−	0.627648i	0.966349	+	0.257233i	$0.0828108\pi$
$240$		0			0
$241$	3.48357	+	2.37506i	0.224397	+	0.152991i	0.670300	−	0.742090i	$-0.266165\pi$
$241$	3.48357	+	2.37506i	0.224397	+	0.152991i	−0.445904	+	0.895081i	$0.647118\pi$
$242$	3.33153	−	8.48859i	0.214159	−	0.545667i
$243$		0			0
$244$	41.0494			2.62792
$245$	11.9882	+	0.918253i	0.765898	+	0.0586650i
$246$		0			0
$247$	−4.82917	−	1.48960i	−0.307273	−	0.0947811i
$248$	−28.0565	+	71.4868i	−1.78159	+	4.53942i
$249$		0			0
$250$	−31.2691	+	4.71306i	−1.97763	+	0.298080i
$251$	−5.32606	+	6.67867i	−0.336178	+	0.421554i	−0.920972	−	0.389628i	$-0.872604\pi$
$251$	−5.32606	+	6.67867i	−0.336178	+	0.421554i	0.584795	+	0.811181i	$0.301175\pi$
$252$		0			0
$253$	12.3398	+	15.4736i	0.775797	+	0.972819i
$254$	27.6417	+	25.6478i	1.73440	+	1.60928i
$255$		0			0
$256$	12.0654	−	11.1951i	0.754090	−	0.699693i
$257$	−1.35475	+	0.923655i	−0.0845072	+	0.0576160i	−0.604837	−	0.796350i	$-0.706762\pi$
$257$	−1.35475	+	0.923655i	−0.0845072	+	0.0576160i	0.520329	+	0.853966i	$0.325809\pi$
$258$		0			0
$259$	4.78058	−	2.52157i	0.297051	−	0.156683i
$260$	2.91073	−	12.7528i	0.180516	−	0.790892i
$261$		0			0
$262$	−3.17060	−	42.3087i	−0.195880	−	2.61384i
$263$	−11.1172	−	19.2555i	−0.685513	−	1.18734i	−0.973275	−	0.229642i	$-0.926245\pi$
$263$	−11.1172	−	19.2555i	−0.685513	−	1.18734i	0.287762	−	0.957702i	$-0.407089\pi$
$264$		0			0
$265$	−2.81055	−	1.35349i	−0.172651	−	0.0831442i
$266$	−17.7922	+	13.1086i	−1.09091	+	0.803739i
$267$		0			0
$268$	−2.83531	+	37.8346i	−0.173194	+	2.31112i
$269$	18.9224	−	5.83678i	1.15372	−	0.355875i	0.341872	−	0.939747i	$-0.388939\pi$
$269$	18.9224	−	5.83678i	1.15372	−	0.355875i	0.811846	+	0.583872i	$0.198463\pi$
$270$		0			0
$271$	0.803367	−	10.7202i	0.0488011	−	0.651205i	−0.918148	−	0.396237i	$-0.870316\pi$
$271$	0.803367	−	10.7202i	0.0488011	−	0.651205i	0.966949	−	0.254968i	$-0.0820650\pi$
$272$	44.6287	−	21.4921i	2.70602	−	1.30315i
$273$		0			0
$274$	−35.8373	−	17.2583i	−2.16501	−	1.04261i
$275$	3.90159	−	6.75775i	0.235275	−	0.407508i
$276$		0			0
$277$	0.102015	+	1.36129i	0.00612948	+	0.0817922i	0.999430	−	0.0337711i	$-0.0107517\pi$
$277$	0.102015	+	1.36129i	0.00612948	+	0.0817922i	−0.993300	+	0.115563i	$0.963133\pi$
$278$	3.75754	+	9.57406i	0.225362	+	0.574214i
$279$		0			0
$280$	−21.8087	−	25.3845i	−1.30332	−	1.51701i
$281$	3.34721	+	14.6651i	0.199678	+	0.874847i	0.971128	+	0.238557i	$0.0766744\pi$
$281$	3.34721	+	14.6651i	0.199678	+	0.874847i	−0.771450	+	0.636289i	$0.780468\pi$
$282$		0			0
$283$	17.4476	−	16.1890i	1.03715	−	0.962339i	0.0378373	−	0.999284i	$-0.487953\pi$
$283$	17.4476	−	16.1890i	1.03715	−	0.962339i	0.999317	+	0.0369450i	$0.0117626\pi$
$284$	57.5341	+	8.67187i	3.41402	+	0.514581i
$285$		0			0
$286$	9.79364	+	12.2808i	0.579110	+	0.726181i
$287$	9.55126	+	15.2286i	0.563793	+	0.898915i
$288$		0			0
$289$	−9.55991	+	1.44092i	−0.562348	+	0.0847602i
$290$	15.3363	+	10.4561i	0.900579	+	0.614005i
$291$		0			0
$292$	13.2073	+	4.07391i	0.772899	+	0.238408i
$293$	−31.1663			−1.82075			−0.910377	−	0.413780i	$-0.864208\pi$
$293$	−31.1663			−1.82075			−0.910377	+	0.413780i	$0.864208\pi$
$294$		0			0
$295$	2.22161			0.129347
$296$	−14.3757	−	4.43432i	−0.835572	−	0.257740i
$297$		0			0
$298$	31.3736	+	21.3901i	1.81742	+	1.23910i
$299$	−8.12273	+	1.22430i	−0.469750	+	0.0708033i
$300$		0			0
$301$	21.6920	−	21.6563i	1.25031	−	1.24825i
$302$	2.00609	+	2.51556i	0.115438	+	0.144754i
$303$		0			0
$304$	30.3374	+	4.57263i	1.73997	+	0.262258i
$305$	10.7232	−	9.94969i	0.614009	−	0.569717i
$306$		0			0
$307$	0.121847	+	0.533847i	0.00695418	+	0.0304682i	0.978286	−	0.207260i	$-0.0664545\pi$
$307$	0.121847	+	0.533847i	0.00695418	+	0.0304682i	−0.971332	+	0.237728i	$0.923597\pi$
$308$	48.5135	−	1.77524i	2.76432	−	0.101153i
$309$		0			0
$310$	17.0891	+	43.5422i	0.970593	+	2.47303i
$311$	−1.56398	−	20.8699i	−0.0886853	−	1.18342i	−0.847021	−	0.531559i	$-0.821606\pi$
$311$	−1.56398	−	20.8699i	−0.0886853	−	1.18342i	0.758336	−	0.651864i	$-0.226013\pi$
$312$		0			0
$313$	11.6552	−	20.1873i	0.658789	−	1.14106i	−0.322141	−	0.946692i	$-0.604402\pi$
$313$	11.6552	−	20.1873i	0.658789	−	1.14106i	0.980929	−	0.194364i	$-0.0622643\pi$
$314$	−7.39272	−	3.56015i	−0.417195	−	0.200911i
$315$		0			0
$316$	−4.20138	+	2.02328i	−0.236346	+	0.113818i
$317$	−0.397685	+	5.30674i	−0.0223362	+	0.298056i	0.974837	+	0.222919i	$0.0715586\pi$
$317$	−0.397685	+	5.30674i	−0.0223362	+	0.298056i	−0.997173	+	0.0751373i	$0.976060\pi$
$318$		0			0
$319$	−15.0530	+	4.64325i	−0.842808	+	0.259972i
$320$	−0.997244	+	13.3073i	−0.0557476	+	0.743900i
$321$		0			0
$322$	−16.8112	+	31.7451i	−0.936854	+	1.76909i
$323$	−14.8816	−	7.16661i	−0.828036	−	0.398761i
$324$		0			0
$325$	1.61936	+	2.80481i	0.0898257	+	0.155583i
$326$	−1.42226	−	18.9787i	−0.0787715	−	1.05113i
$327$		0			0
$328$	11.1339	−	48.7808i	0.614766	−	2.69347i
$329$	30.0300	+	13.1314i	1.65561	+	0.723957i
$330$		0			0
$331$	−10.3887	+	7.08286i	−0.571012	+	0.389309i	−0.814126	−	0.580688i	$-0.802783\pi$
$331$	−10.3887	+	7.08286i	−0.571012	+	0.389309i	0.243114	+	0.969998i	$0.421831\pi$
$332$	−36.2297	+	33.6162i	−1.98836	+	1.84493i
$333$		0			0
$334$	25.2499	+	23.4285i	1.38162	+	1.28195i
$335$	8.42982	+	10.5707i	0.460570	+	0.577537i
$336$		0			0
$337$	−7.44269	+	9.33284i	−0.405429	+	0.508392i	−0.942069	−	0.335419i	$-0.891122\pi$
$337$	−7.44269	+	9.33284i	−0.405429	+	0.508392i	0.536640	+	0.843812i	$0.319693\pi$
$338$	27.1237	−	4.08823i	1.47533	−	0.222371i
$339$		0			0
$340$	15.6193	−	39.7973i	0.847076	−	2.15831i
$341$	−37.9340	−	11.7011i	−2.05424	−	0.633649i
$342$		0			0
$343$	−17.4658	−	6.16003i	−0.943064	−	0.332610i
$344$	−85.3181			−4.60004
$345$		0			0
$346$	−18.4370	+	46.9768i	−0.991181	+	2.52549i
$347$	3.29079	+	2.24362i	0.176659	+	0.120444i	0.648421	−	0.761282i	$-0.275430\pi$
$347$	3.29079	+	2.24362i	0.176659	+	0.120444i	−0.471762	+	0.881726i	$0.656382\pi$
$348$		0			0
$349$	7.55174	−	9.46958i	0.404235	−	0.506895i	−0.537494	−	0.843268i	$-0.680629\pi$
$349$	7.55174	−	9.46958i	0.404235	−	0.506895i	0.941729	+	0.336373i	$0.109200\pi$
$350$	14.0725	+	1.59732i	0.752204	+	0.0853805i
$351$		0			0
$352$	−28.8017	−	26.7241i	−1.53514	−	1.42440i
$353$	−4.39316	−	0.662162i	−0.233824	−	0.0352433i	0.0310848	−	0.999517i	$-0.490104\pi$
$353$	−4.39316	−	0.662162i	−0.233824	−	0.0352433i	−0.264909	+	0.964273i	$0.585342\pi$
$354$		0			0
$355$	17.1314	−	11.6800i	0.909240	−	0.619909i
$356$	0.424200	+	1.85854i	0.0224826	+	0.0985026i
$357$		0			0
$358$	−0.841063	+	3.68494i	−0.0444516	+	0.194755i
$359$	0.213363	+	0.543640i	0.0112609	+	0.0286922i	0.936394	−	0.350952i	$-0.114142\pi$
$359$	0.213363	+	0.543640i	0.0112609	+	0.0286922i	−0.925133	+	0.379644i	$0.876047\pi$
$360$		0			0
$361$	4.38480	+	7.59470i	0.230779	+	0.399721i
$362$	−19.8610	+	34.4002i	−1.04387	+	1.80804i
$363$		0			0
$364$	−9.42968	+	17.8063i	−0.494249	+	0.933304i
$365$	4.43756	−	2.13701i	0.232272	−	0.111856i
$366$		0			0
$367$	−1.72093	+	0.530838i	−0.0898320	+	0.0277095i	−0.339345	−	0.940662i	$-0.610206\pi$
$367$	−1.72093	+	0.530838i	−0.0898320	+	0.0277095i	0.249513	+	0.968371i	$0.419729\pi$
$368$	47.6532	−	14.6991i	2.48409	−	0.766241i
$369$		0			0
$370$	−8.25582	+	3.97579i	−0.429200	+	0.206692i
$371$	3.63956	+	3.13732i	0.188957	+	0.162881i
$372$		0			0
$373$	10.2267	−	17.7131i	0.529516	−	0.917149i	−0.469891	−	0.882724i	$-0.655707\pi$
$373$	10.2267	−	17.7131i	0.529516	−	0.917149i	0.999407	−	0.0344248i	$-0.0109599\pi$
$374$	25.6695	+	44.4608i	1.32734	+	2.29901i
$375$		0			0
$376$	−33.3297	−	84.9226i	−1.71885	−	4.37955i
$377$	1.45490	−	6.37431i	0.0749309	−	0.328294i
$378$		0			0
$379$	4.46660	+	19.5694i	0.229434	+	1.00521i	0.950103	+	0.311936i	$0.100977\pi$
$379$	4.46660	+	19.5694i	0.229434	+	1.00521i	−0.720670	+	0.693279i	$0.756165\pi$
$380$	21.8787	−	14.9166i	1.12235	−	0.765206i
$381$		0			0
$382$	22.1285	+	3.33534i	1.13219	+	0.170651i
$383$	10.1445	+	9.41270i	0.518359	+	0.480967i	0.895420	−	0.445221i	$-0.146875\pi$
$383$	10.1445	+	9.41270i	0.518359	+	0.480967i	−0.377062	+	0.926188i	$0.623066\pi$
$384$		0			0
$385$	12.2428	−	12.2226i	0.623949	−	0.622922i
$386$	37.1297	−	46.5592i	1.88985	−	2.36980i
$387$		0			0
$388$	30.1000	+	20.5219i	1.52810	+	1.04184i
$389$	8.90724	−	22.6953i	0.451615	−	1.15070i	−0.505971	−	0.862550i	$-0.668866\pi$
$389$	8.90724	−	22.6953i	0.451615	−	1.15070i	0.957586	−	0.288146i	$-0.0930389\pi$
$390$		0			0
$391$	−26.8480			−1.35776
$392$	22.2903	+	46.4819i	1.12583	+	2.34769i
$393$		0			0
$394$	9.90794	+	3.05620i	0.499155	+	0.153969i
$395$	−0.607106	+	1.54688i	−0.0305468	+	0.0778320i
$396$		0			0
$397$	6.72395	−	1.01347i	0.337465	−	0.0508647i	0.0218763	−	0.999761i	$-0.493036\pi$
$397$	6.72395	−	1.01347i	0.337465	−	0.0508647i	0.315589	+	0.948896i	$0.397798\pi$
$398$	−25.9502	+	32.5405i	−1.30076	+	1.63111i
$399$		0			0
$400$	−12.2589	−	15.3721i	−0.612943	−	0.768606i
$401$	−23.6232	−	21.9191i	−1.17969	−	1.09459i	−0.993704	−	0.112035i	$-0.964263\pi$
$401$	−23.6232	−	21.9191i	−1.17969	−	1.09459i	−0.185981	−	0.982553i	$-0.559546\pi$
$402$		0			0
$403$	12.0781	−	11.2069i	0.601655	−	0.558254i
$404$	24.4972	−	16.7019i	1.21878	−	0.830952i
$405$		0			0
$406$	−18.6321	−	21.6870i	−0.924694	−	1.07631i
$407$	1.73048	−	7.58172i	0.0857766	−	0.375812i
$408$		0			0
$409$	0.451630	+	6.02658i	0.0223316	+	0.297995i	0.997176	+	0.0751063i	$0.0239296\pi$
$409$	0.451630	+	6.02658i	0.0223316	+	0.297995i	−0.974844	+	0.222889i	$0.928451\pi$
$410$	−15.2381	−	26.3932i	−0.752556	−	1.30347i
$411$		0			0
$412$	−82.7543	−	39.8524i	−4.07701	−	1.96339i
$413$	−3.30475	−	0.888424i	−0.162616	−	0.0437165i
$414$		0			0
$415$	−1.31616	+	17.5629i	−0.0646078	+	0.862131i
$416$	15.5829	−	4.80668i	0.764014	−	0.235667i
$417$		0			0
$418$	−2.37626	+	31.7090i	−0.116227	+	1.55094i
$419$	9.19292	−	4.42708i	0.449103	−	0.216277i	−0.195640	−	0.980676i	$-0.562678\pi$
$419$	9.19292	−	4.42708i	0.449103	−	0.216277i	0.644744	+	0.764399i	$0.276964\pi$
$420$		0			0
$421$	−23.1814	−	11.1636i	−1.12979	−	0.544080i	−0.226889	−	0.973921i	$-0.572855\pi$
$421$	−23.1814	−	11.1636i	−1.12979	−	0.544080i	−0.902905	+	0.429841i	$0.858570\pi$
$422$	2.64534	−	4.58187i	0.128773	−	0.223042i
$423$		0			0
$424$	−0.999501	−	13.3374i	−0.0485401	−	0.647722i
$425$	3.86725	+	9.85360i	0.187589	+	0.477970i
$426$		0			0
$427$	−19.9302	+	10.5124i	−0.964488	+	0.508731i
$428$	9.31355	+	40.8053i	0.450188	+	1.97240i
$429$		0			0
$430$	−38.0943	+	35.3464i	−1.83707	+	1.70455i
$431$	−6.66968	−	1.00529i	−0.321267	−	0.0484232i	−0.0135710	−	0.999908i	$-0.504320\pi$
$431$	−6.66968	−	1.00529i	−0.321267	−	0.0484232i	−0.307696	+	0.951485i	$0.599558\pi$
$432$		0			0
$433$	−10.2693	−	12.8773i	−0.493511	−	0.618843i	0.471241	−	0.882005i	$-0.343806\pi$
$433$	−10.2693	−	12.8773i	−0.493511	−	0.618843i	−0.964752	+	0.263161i	$0.915235\pi$
$434$	−8.00823	−	71.6050i	−0.384407	−	3.43715i
$435$		0			0
$436$	−52.8550	+	7.96660i	−2.53129	+	0.381531i
$437$	−13.7394	−	9.36740i	−0.657247	−	0.448103i
$438$		0			0
$439$	−8.65409	−	2.66943i	−0.413037	−	0.127405i	0.0812706	−	0.996692i	$-0.474102\pi$
$439$	−8.65409	−	2.66943i	−0.413037	−	0.127405i	−0.494308	+	0.869287i	$0.664578\pi$
$440$	−48.1527			−2.29559
$441$		0			0
$442$	−21.3082			−1.01353
$443$	−4.52712	−	1.39643i	−0.215090	−	0.0663464i	0.185338	−	0.982675i	$-0.440662\pi$
$443$	−4.52712	−	1.39643i	−0.215090	−	0.0663464i	−0.400427	+	0.916328i	$0.631138\pi$
$444$		0			0
$445$	0.561293	+	0.382683i	0.0266078	+	0.0181409i
$446$	−57.7310	+	8.70155i	−2.73364	+	0.412030i
$447$		0			0
$448$	6.80504	−	19.3964i	0.321508	−	0.916395i
$449$	6.74742	+	8.46100i	0.318430	+	0.399299i	0.915126	−	0.403169i	$-0.132091\pi$
$449$	6.74742	+	8.46100i	0.318430	+	0.399299i	−0.596695	+	0.802468i	$0.703520\pi$
$450$		0			0
$451$	25.5757	+	3.85492i	1.20431	+	0.181521i
$452$	−10.3121	+	9.56825i	−0.485042	+	0.450053i
$453$		0			0
$454$	−6.76966	−	29.6598i	−0.317716	−	1.39200i
$455$	1.85266	+	6.93709i	0.0868543	+	0.325216i
$456$		0			0
$457$	−7.51500	−	19.1479i	−0.351537	−	0.895701i	−0.991830	−	0.127570i	$-0.959282\pi$
$457$	−7.51500	−	19.1479i	−0.351537	−	0.895701i	0.640293	−	0.768131i	$-0.278813\pi$
$458$	−0.813337	−	10.8532i	−0.0380047	−	0.507138i
$459$		0			0
$460$	21.5207	−	37.2750i	1.00341	−	1.73795i
$461$	−6.28012	−	3.02435i	−0.292495	−	0.140858i	0.281882	−	0.959449i	$-0.409041\pi$
$461$	−6.28012	−	3.02435i	−0.292495	−	0.140858i	−0.574377	+	0.818591i	$0.694756\pi$
$462$		0			0
$463$	−5.06099	+	2.43725i	−0.235204	+	0.113268i	−0.547774	−	0.836626i	$-0.684525\pi$
$463$	−5.06099	+	2.43725i	−0.235204	+	0.113268i	0.312570	+	0.949895i	$0.398810\pi$
$464$	−2.96623	+	39.5816i	−0.137704	+	1.83753i
$465$		0			0
$466$	40.2236	−	12.4073i	1.86332	−	0.574758i
$467$	2.93227	−	39.1284i	0.135689	−	1.81065i	−0.350253	−	0.936655i	$-0.613904\pi$
$467$	2.93227	−	39.1284i	0.135689	−	1.81065i	0.485942	−	0.873991i	$-0.338477\pi$
$468$		0			0
$469$	−8.31254	−	19.0954i	−0.383837	−	0.881745i
$470$	−50.0641	−	24.1096i	−2.30929	−	1.11209i
$471$		0			0
$472$	4.76260	+	8.24907i	0.219217	+	0.379694i
$473$	−3.29584	−	43.9799i	−0.151543	−	2.02220i
$474$		0			0
$475$	−1.45891	+	6.39188i	−0.0669392	+	0.293280i
$476$	−39.1494	+	52.9542i	−1.79441	+	2.42715i
$477$		0			0
$478$	26.7793	−	18.2578i	1.22485	−	0.835092i
$479$	−3.80819	+	3.53348i	−0.174001	+	0.161449i	−0.762366	−	0.647146i	$-0.775962\pi$
$479$	−3.80819	+	3.53348i	−0.174001	+	0.161449i	0.588365	+	0.808595i	$0.299772\pi$
$480$		0			0
$481$	2.36609	+	2.19541i	0.107884	+	0.100102i
$482$	6.86498	+	8.60841i	0.312691	+	0.392102i
$483$		0			0
$484$	10.4936	−	13.1586i	0.476984	−	0.598119i
$485$	12.8371	−	1.93488i	0.582903	−	0.0878585i
$486$		0			0
$487$	−8.32620	+	21.2148i	−0.377296	+	0.961335i	0.608525	+	0.793535i	$0.291762\pi$
$487$	−8.32620	+	21.2148i	−0.377296	+	0.961335i	−0.985821	+	0.167800i	$0.946334\pi$
$488$	59.9322	+	18.4866i	2.71300	+	0.836850i
$489$		0			0
$490$	29.2095	+	11.5195i	1.31955	+	0.520396i
$491$	−13.6563			−0.616302			−0.308151	−	0.951337i	$-0.599710\pi$
$491$	−13.6563			−0.616302			−0.308151	+	0.951337i	$0.599710\pi$
$492$		0			0
$493$	7.80713	−	19.8922i	0.351615	−	0.895901i
$494$	−10.9045	−	7.43455i	−0.490616	−	0.334496i
$495$		0			0
$496$	−62.3653	+	78.2036i	−2.80028	+	3.51144i
$497$	−30.1546	+	10.5237i	−1.35262	+	0.472051i
$498$		0			0
$499$	16.4777	+	15.2890i	0.737642	+	0.684432i	0.956633	−	0.291295i	$-0.0940862\pi$
$499$	16.4777	+	15.2890i	0.737642	+	0.684432i	−0.218991	+	0.975727i	$0.570277\pi$
$500$	−57.7122	−	8.69871i	−2.58097	−	0.389018i
$501$		0			0
$502$	−18.4320	+	12.5667i	−0.822661	+	0.560881i
$503$	−6.22443	−	27.2710i	−0.277534	−	1.21595i	−0.900901	−	0.434025i	$-0.857093\pi$
$503$	−6.22443	−	27.2710i	−0.277534	−	1.21595i	0.623367	−	0.781929i	$-0.285764\pi$
$504$		0			0
$505$	2.35107	−	10.3007i	0.104621	−	0.458376i
$506$	18.8829	+	48.1128i	0.839447	+	2.13888i
$507$		0			0
$508$	34.7978	+	60.2716i	1.54390	+	2.67412i
$509$	−4.45457	+	7.71554i	−0.197445	+	0.341985i	−0.947699	−	0.319164i	$-0.896598\pi$
$509$	−4.45457	+	7.71554i	−0.197445	+	0.341985i	0.750254	+	0.661150i	$0.229931\pi$
$510$		0			0
$511$	−7.45566	+	1.40433i	−0.329819	+	0.0621238i
$512$	38.0913	−	18.3438i	1.68341	−	0.810689i
$513$		0			0
$514$	−4.09175	+	1.26214i	−0.180479	+	0.0556705i
$515$	−31.2772	+	9.64774i	−1.37824	+	0.425130i
$516$		0			0
$517$	42.4885	−	20.4614i	1.86864	−	0.899891i
$518$	13.8708	−	2.61267i	0.609449	−	0.114794i
$519$		0			0
$520$	9.99289	−	17.3082i	0.438217	−	0.759014i
$521$	−12.8583	−	22.2713i	−0.563333	−	0.975721i	−0.997203	−	0.0747457i	$-0.976186\pi$
$521$	−12.8583	−	22.2713i	−0.563333	−	0.975721i	0.433870	−	0.900976i	$-0.357148\pi$
$522$		0			0
$523$	−6.34565	−	16.1684i	−0.277476	−	0.706997i	−0.999879	−	0.0155252i	$-0.995058\pi$
$523$	−6.34565	−	16.1684i	−0.277476	−	0.706997i	0.722404	−	0.691472i	$-0.243037\pi$
$524$	17.4248	−	76.3432i	0.761208	−	3.33507i
$525$		0			0
$526$	−12.9207	−	56.6092i	−0.563368	−	2.46828i
$527$	44.4941	−	30.3356i	1.93819	−	1.32144i
$528$		0			0
$529$	−3.98431	−	0.600538i	−0.173231	−	0.0261104i
$530$	−5.97182	−	5.54104i	−0.259399	−	0.240688i
$531$		0			0
$532$	−38.5107	+	13.4399i	−1.66965	+	0.582693i
$533$	−6.69323	+	8.39304i	−0.289916	+	0.363543i
$534$		0			0
$535$	12.3235	+	8.40201i	0.532791	+	0.363251i
$536$	−21.1784	+	53.9617i	−0.914768	+	2.33079i
$537$		0			0
$538$	51.7133			2.22952
$539$	−23.0995	+	13.2858i	−0.994966	+	0.572261i
$540$		0			0
$541$	−26.1194	−	8.05678i	−1.12296	−	0.346388i	−0.322976	−	0.946407i	$-0.604683\pi$
$541$	−26.1194	−	8.05678i	−1.12296	−	0.346388i	−0.799986	+	0.600019i	$0.795160\pi$
$542$	10.2567	−	26.1336i	0.440563	−	1.12254i
$543$		0			0
$544$	52.7033	−	7.94375i	2.25964	−	0.340585i
$545$	−11.8762	+	14.8923i	−0.508720	+	0.637914i
$546$		0			0
$547$	1.44712	+	1.81463i	0.0618742	+	0.0775878i	0.811806	−	0.583928i	$-0.198485\pi$
$547$	1.44712	+	1.81463i	0.0618742	+	0.0775878i	−0.749931	+	0.661516i	$0.769913\pi$
$548$	−53.8160	−	49.9340i	−2.29891	−	2.13307i
$549$		0			0
$550$	14.9382	−	13.8606i	0.636965	−	0.591017i
$551$	10.9358	−	7.45590i	0.465880	−	0.317632i
$552$		0			0
$553$	1.52170	−	2.05827i	0.0647091	−	0.0875267i
$554$	−0.793285	+	3.47561i	−0.0337035	+	0.147665i
$555$		0			0
$556$	1.41858	+	18.9296i	0.0601610	+	0.802793i
$557$	21.0582	+	36.4738i	0.892264	+	1.54545i	0.837155	+	0.546966i	$0.184217\pi$
$557$	21.0582	+	36.4738i	0.892264	+	1.54545i	0.0551086	+	0.998480i	$0.482450\pi$
$558$		0			0
$559$	16.4923	+	7.94227i	0.697550	+	0.335922i
$560$	−17.3983	−	39.9672i	−0.735214	−	1.68892i
$561$		0			0
$562$	−2.93561	+	39.1730i	−0.123831	+	1.65241i
$563$	27.5244	−	8.49015i	1.16002	−	0.357817i	0.345759	−	0.938323i	$-0.387621\pi$
$563$	27.5244	−	8.49015i	1.16002	−	0.357817i	0.814256	+	0.580506i	$0.197145\pi$
$564$		0			0
$565$	−0.374621	+	4.99898i	−0.0157604	+	0.210308i
$566$	56.0019	−	26.9691i	2.35393	−	1.13359i
$567$		0			0
$568$	80.0945	+	38.5715i	3.36069	+	1.61842i
$569$	−11.2218	+	19.4367i	−0.470442	+	0.814830i	−0.999429	−	0.0338006i	$-0.989239\pi$
$569$	−11.2218	+	19.4367i	−0.470442	+	0.814830i	0.528986	+	0.848630i	$0.322572\pi$
$570$		0			0
$571$	−1.51796	−	20.2558i	−0.0635248	−	0.847679i	−0.934412	−	0.356195i	$-0.884074\pi$
$571$	−1.51796	−	20.2558i	−0.0635248	−	0.847679i	0.870887	−	0.491484i	$-0.163545\pi$
$572$	10.5917	+	26.9872i	0.442861	+	1.12839i
$573$		0			0
$574$	12.1127	+	45.3548i	0.505576	+	1.89307i
$575$	2.37136	+	10.3896i	0.0988927	+	0.433277i
$576$		0			0
$577$	0.425690	−	0.394982i	0.0177217	−	0.0164433i	−0.671262	−	0.741220i	$-0.734248\pi$
$577$	0.425690	−	0.394982i	0.0177217	−	0.0164433i	0.688984	+	0.724777i	$0.258057\pi$
$578$	−24.9657	−	3.76298i	−1.03844	−	0.156519i
$579$		0			0
$580$	21.3598	+	26.7843i	0.886917	+	1.11216i
$581$	8.98128	−	25.5994i	0.372606	−	1.06204i
$582$		0			0
$583$	6.83658	−	1.03045i	0.283142	−	0.0426768i
$584$	17.4480	+	11.8958i	0.722003	+	0.492254i
$585$		0			0
$586$	−77.7749	−	23.9904i	−3.21285	−	0.991034i
$587$	−4.76773			−0.196785			−0.0983926	−	0.995148i	$-0.531370\pi$
$587$	−4.76773			−0.196785			−0.0983926	+	0.995148i	$0.531370\pi$
$588$		0			0
$589$	33.3541			1.37433
$590$	5.54399	+	1.71010i	0.228243	+	0.0704035i
$591$		0			0
$592$	−16.1901	−	11.0382i	−0.665409	−	0.453668i
$593$	7.56007	−	1.13950i	0.310455	−	0.0467935i	0.00803305	−	0.999968i	$-0.497443\pi$
$593$	7.56007	−	1.13950i	0.310455	−	0.0467935i	0.302422	+	0.953174i	$0.402205\pi$
$594$		0			0
$595$	2.60834	+	23.3222i	0.106931	+	0.956119i
$596$	43.6958	+	54.7928i	1.78985	+	2.24440i
$597$		0			0
$598$	−21.2125	−	3.19728i	−0.867445	−	0.130746i
$599$	−25.0128	+	23.2085i	−1.02199	+	0.948272i	−0.998675	−	0.0514564i	$-0.983614\pi$
$599$	−25.0128	+	23.2085i	−1.02199	+	0.948272i	−0.0233186	+	0.999728i	$0.507423\pi$
$600$		0			0
$601$	9.93938	+	43.5473i	0.405436	+	1.77633i	0.604772	+	0.796399i	$0.293264\pi$
$601$	9.93938	+	43.5473i	0.405436	+	1.77633i	−0.199336	+	0.979931i	$0.563878\pi$
$602$	70.8021	−	37.3454i	2.88568	−	1.52209i
$603$		0			0
$604$	2.16956	+	5.52795i	0.0882782	+	0.224929i
$605$	−0.448204	−	5.98087i	−0.0182221	−	0.243157i
$606$		0			0
$607$	−3.40654	+	5.90030i	−0.138267	+	0.239486i	−0.926841	−	0.375455i	$-0.877487\pi$
$607$	−3.40654	+	5.90030i	−0.138267	+	0.239486i	0.788574	+	0.614940i	$0.210820\pi$
$608$	29.7425	+	14.3232i	1.20622	+	0.580884i
$609$		0			0
$610$	34.4184	−	16.5750i	1.39356	−	0.671103i
$611$	−1.46271	+	19.5185i	−0.0591749	+	0.789634i
$612$		0			0
$613$	−26.6691	+	8.22633i	−1.07716	+	0.332258i	−0.782056	−	0.623208i	$-0.785829\pi$
$613$	−26.6691	+	8.22633i	−1.07716	+	0.332258i	−0.295099	+	0.955467i	$0.595353\pi$
$614$	−0.106864	+	1.42600i	−0.00431267	+	0.0575486i
$615$		0			0
$616$	71.6293	+	19.2563i	2.88603	+	0.775857i
$617$	35.3753	+	17.0358i	1.42416	+	0.685837i	0.977901	−	0.209069i	$-0.0670432\pi$
$617$	35.3753	+	17.0358i	1.42416	+	0.685837i	0.446255	+	0.894906i	$0.352757\pi$
$618$		0			0
$619$	−3.51094	−	6.08112i	−0.141116	−	0.244421i	0.786801	−	0.617207i	$-0.211736\pi$
$619$	−3.51094	−	6.08112i	−0.141116	−	0.244421i	−0.927917	+	0.372786i	$0.878403\pi$
$620$	6.45160	+	86.0906i	0.259102	+	3.45748i
$621$		0			0
$622$	12.1618	−	53.2843i	0.487644	−	2.13651i
$623$	−0.681914	−	0.793720i	−0.0273203	−	0.0317997i
$624$		0			0
$625$	−8.71631	+	5.94268i	−0.348652	+	0.237707i
$626$	44.6245	−	41.4055i	1.78356	−	1.65490i
$627$		0			0
$628$	−11.1015	−	10.3007i	−0.442998	−	0.411042i
$629$	6.57744	+	8.24785i	0.262260	+	0.328863i
$630$		0			0
$631$	−15.0954	+	18.9290i	−0.600937	+	0.753551i	−0.985524	−	0.169538i	$-0.945772\pi$
$631$	−15.0954	+	18.9290i	−0.600937	+	0.753551i	0.384587	+	0.923089i	$0.374344\pi$
$632$	−7.04521	+	1.06189i	−0.280243	+	0.0422399i
$633$		0			0
$634$	−5.07730	+	12.9368i	−0.201646	+	0.513784i
$635$	23.6990	+	7.31017i	0.940465	+	0.290095i
$636$		0			0
$637$	0.0182190	−	11.0601i	0.000721862	−	0.438218i
$638$	−41.1387			−1.62870
$639$		0			0
$640$	0.221227	−	0.563677i	0.00874477	−	0.0222813i
$641$	30.0872	+	20.5131i	1.18837	+	0.810218i	0.985614	−	0.169011i	$-0.0540573\pi$
$641$	30.0872	+	20.5131i	1.18837	+	0.810218i	0.202757	+	0.979229i	$0.435010\pi$
$642$		0			0
$643$	−18.6589	+	23.3976i	−0.735837	+	0.922710i	−0.999117	−	0.0420095i	$-0.986624\pi$
$643$	−18.6589	+	23.3976i	−0.735837	+	0.922710i	0.263281	+	0.964719i	$0.415195\pi$
$644$	−46.9193	+	46.8421i	−1.84888	+	1.84584i
$645$		0			0
$646$	−31.6203	−	29.3393i	−1.24408	−	1.15434i
$647$	−43.1638	−	6.50590i	−1.69695	−	0.255773i	−0.771931	−	0.635706i	$-0.780709\pi$
$647$	−43.1638	−	6.50590i	−1.69695	−	0.255773i	−0.925014	+	0.379933i	$0.875947\pi$
$648$		0			0
$649$	−4.06827	+	2.77370i	−0.159693	+	0.108877i
$650$	1.88206	+	8.24585i	0.0738205	+	0.323429i
$651$		0			0
$652$	7.81638	−	34.2458i	0.306113	−	1.34117i
$653$	−8.97306	−	22.8630i	−0.351143	−	0.894697i	−0.991908	−	0.126960i	$-0.959478\pi$
$653$	−8.97306	−	22.8630i	−0.351143	−	0.894697i	0.640765	−	0.767737i	$-0.278617\pi$
$654$		0			0
$655$	−13.9525	−	24.1664i	−0.545169	−	0.944260i
$656$	32.5855	−	56.4398i	1.27225	−	2.20360i
$657$		0			0
$658$	64.8313	+	55.8848i	2.52739	+	2.17862i
$659$	−5.89632	+	2.83952i	−0.229688	+	0.110612i	−0.545189	−	0.838313i	$-0.683542\pi$
$659$	−5.89632	+	2.83952i	−0.229688	+	0.110612i	0.315500	+	0.948925i	$0.397828\pi$
$660$		0			0
$661$	−14.3186	+	4.41672i	−0.556931	+	0.171790i	−0.560427	−	0.828204i	$-0.689363\pi$
$661$	−14.3186	+	4.41672i	−0.556931	+	0.171790i	0.00349685	+	0.999994i	$0.498887\pi$
$662$	−31.3768	+	9.67845i	−1.21949	+	0.376164i
$663$		0			0
$664$	−68.0345	+	32.7637i	−2.64025	+	1.27148i
$665$	−6.80243	+	12.8452i	−0.263787	+	0.498116i
$666$		0			0
$667$	10.7569	−	18.6314i	0.416508	−	0.721413i
$668$	31.7869	+	55.0565i	1.22987	+	2.13020i
$669$		0			0
$670$	12.8996	+	32.8678i	0.498357	+	1.26979i
$671$	−7.21434	+	31.6081i	−0.278506	+	1.22022i
$672$		0			0
$673$	−4.09355	−	17.9350i	−0.157795	−	0.691344i	−0.990487	−	0.137607i	$-0.956059\pi$
$673$	−4.09355	−	17.9350i	−0.157795	−	0.691344i	0.832692	−	0.553736i	$-0.186798\pi$
$674$	−25.7571	+	17.5609i	−0.992126	+	0.676420i
$675$		0			0
$676$	50.0611	+	7.54550i	1.92543	+	0.290211i
$677$	8.98052	+	8.33270i	0.345149	+	0.320252i	0.833630	−	0.552323i	$-0.186258\pi$
$677$	8.98052	+	8.33270i	0.345149	+	0.320252i	−0.488481	+	0.872574i	$0.662449\pi$
$678$		0			0
$679$	−19.8695	−	2.25533i	−0.762523	−	0.0865518i
$680$	40.7270	−	51.0700i	1.56181	−	1.95845i
$681$		0			0
$682$	−85.6566	−	58.3997i	−3.27996	−	2.23624i
$683$	12.5728	−	32.0349i	0.481083	−	1.22578i	−0.460095	−	0.887870i	$-0.652185\pi$
$683$	12.5728	−	32.0349i	0.481083	−	1.22578i	0.941178	−	0.337911i	$-0.109720\pi$
$684$		0			0
$685$	−26.1614			−0.999575
$686$	−38.8439	−	28.8166i	−1.48307	−	1.10022i
$687$		0			0
$688$	−106.190	−	32.7552i	−4.04845	−	1.24878i
$689$	−1.04837	+	2.67121i	−0.0399399	+	0.101765i
$690$		0			0
$691$	7.81770	−	1.17833i	0.297399	−	0.0448257i	0.00135224	−	0.999999i	$-0.499570\pi$
$691$	7.81770	−	1.17833i	0.297399	−	0.0448257i	0.296047	+	0.955173i	$0.404331\pi$
$692$	−58.0730	+	72.8212i	−2.20760	+	2.76825i
$693$		0			0
$694$	6.48507	+	8.13202i	0.246170	+	0.308687i
$695$	4.95879	+	4.60108i	0.188098	+	0.174529i
$696$		0			0
$697$	−25.7201	+	23.8648i	−0.974219	+	0.903943i
$698$	26.1345	−	17.8182i	0.989204	−	0.674428i
$699$		0			0
$700$	23.9501	+	10.4728i	0.905229	+	0.395835i
$701$	4.10883	−	18.0020i	0.155188	−	0.679925i	−0.836140	−	0.548516i	$-0.815193\pi$
$701$	4.10883	−	18.0020i	0.155188	−	0.679925i	0.991328	−	0.131409i	$-0.0419500\pi$
$702$		0			0
$703$	0.488287	+	6.51574i	0.0184161	+	0.245746i
$704$	−14.7881	−	25.6137i	−0.557346	−	0.965352i
$705$		0			0
$706$	−10.4533	−	5.03406i	−0.393417	−	0.189459i
$707$	−7.61659	+	14.3826i	−0.286451	+	0.540914i
$708$		0			0
$709$	2.78550	−	37.1700i	0.104612	−	1.39595i	−0.659908	−	0.751346i	$-0.729405\pi$
$709$	2.78550	−	37.1700i	0.104612	−	1.39595i	0.764520	−	0.644600i	$-0.222976\pi$
$710$	51.7418	−	15.9602i	1.94183	−	0.598977i
$711$		0			0
$712$	−0.217663	+	2.90452i	−0.00815728	+	0.108851i
$713$	48.8461	−	23.5231i	1.82930	−	0.880945i
$714$		0			0
$715$	9.30808	+	4.48254i	0.348103	+	0.167637i
$716$	−3.48803	+	6.04144i	−0.130354	+	0.225779i
$717$		0			0
$718$	0.113974	+	1.52088i	0.00425348	+	0.0567588i
$719$	1.39031	+	3.54246i	0.0518499	+	0.132111i	0.954452	−	0.298364i	$-0.0964411\pi$
$719$	1.39031	+	3.54246i	0.0518499	+	0.132111i	−0.902602	+	0.430476i	$0.858346\pi$
$720$		0			0
$721$	50.3845	−	1.84370i	1.87642	−	0.0686629i
$722$	5.09614	+	22.3277i	0.189659	+	0.830949i
$723$		0			0
$724$	−53.7425	+	49.8657i	−1.99732	+	1.85325i
$725$	−8.38746	−	1.26421i	−0.311502	−	0.0469514i
$726$		0			0
$727$	3.48721	+	4.37282i	0.129333	+	0.162179i	0.842282	−	0.539038i	$-0.181212\pi$
$727$	3.48721	+	4.37282i	0.129333	+	0.162179i	−0.712948	+	0.701217i	$0.752641\pi$
$728$	−21.7864	+	21.7506i	−0.807459	+	0.806130i
$729$		0			0
$730$	12.7188	−	1.91705i	0.470744	−	0.0709533i
$731$	49.4321	+	33.7022i	1.82831	+	1.24652i
$732$		0			0
$733$	36.9583	+	11.4001i	1.36509	+	0.421074i	0.888832	−	0.458233i	$-0.151518\pi$
$733$	36.9583	+	11.4001i	1.36509	+	0.421074i	0.476255	+	0.879307i	$0.341994\pi$
$734$	−4.70317			−0.173597
$735$		0			0
$736$	53.6586			1.97788
$737$	−28.6344	−	8.83254i	−1.05476	−	0.325351i
$738$		0			0
$739$	−3.27473	−	2.23267i	−0.120463	−	0.0821301i	0.501590	−	0.865106i	$-0.332749\pi$
$739$	−3.27473	−	2.23267i	−0.120463	−	0.0821301i	−0.622053	+	0.782975i	$0.713701\pi$
$740$	−16.7234	+	2.52065i	−0.614764	+	0.0926608i
$741$		0			0
$742$	6.66750	+	10.6307i	0.244772	+	0.390265i
$743$	1.00788	+	1.26384i	0.0369754	+	0.0463657i	0.799975	−	0.600033i	$-0.204846\pi$
$743$	1.00788	+	1.26384i	0.0369754	+	0.0463657i	−0.763000	+	0.646398i	$0.776274\pi$
$744$		0			0
$745$	24.6954	+	3.72223i	0.904769	+	0.136372i
$746$	39.1552	−	36.3307i	1.43357	−	1.33016i
$747$		0			0
$748$	21.0848	+	92.3786i	0.770937	+	3.37770i
$749$	−14.9718	−	17.4265i	−0.547057	−	0.636752i
$750$		0			0
$751$	−9.34928	−	23.8216i	−0.341160	−	0.869262i	−0.993758	−	0.111557i	$-0.964416\pi$
$751$	−9.34928	−	23.8216i	−0.341160	−	0.869262i	0.652598	−	0.757705i	$-0.273679\pi$
$752$	−8.87986	−	118.494i	−0.323815	−	4.32101i
$753$		0			0
$754$	8.53732	−	14.7871i	0.310911	−	0.538513i
$755$	1.90663	+	0.918185i	0.0693894	+	0.0334162i
$756$		0			0
$757$	−10.0801	+	4.85434i	−0.366369	+	0.176434i	−0.608005	−	0.793933i	$-0.708030\pi$
$757$	−10.0801	+	4.85434i	−0.366369	+	0.176434i	0.241637	+	0.970367i	$0.422316\pi$
$758$	−3.91735	+	52.2734i	−0.142284	+	1.89865i
$759$		0			0
$760$	38.6606	−	11.9252i	1.40237	−	0.432573i
$761$	1.23188	−	16.4383i	0.0446555	−	0.595886i	−0.929326	−	0.369260i	$-0.879611\pi$
$761$	1.23188	−	16.4383i	0.0446555	−	0.595886i	0.973982	−	0.226626i	$-0.0727697\pi$
$762$		0			0
$763$	23.6218	−	17.4036i	0.855166	−	0.630054i
$764$	37.2128	+	17.9207i	1.34631	+	0.648350i
$765$		0			0
$766$	18.0699	+	31.2980i	0.652892	+	1.13084i
$767$	−0.152721	−	2.03793i	−0.00551445	−	0.0735852i
$768$		0			0
$769$	1.08770	−	4.76553i	0.0392235	−	0.171849i	−0.951522	−	0.307580i	$-0.900481\pi$
$769$	1.08770	−	4.76553i	0.0392235	−	0.171849i	0.990746	+	0.135730i	$0.0433381\pi$
$770$	39.9600	−	21.0774i	1.44006	−	0.759576i
$771$		0			0
$772$	90.8135	−	61.9156i	3.26845	−	2.22839i
$773$	−23.4654	+	21.7727i	−0.843990	+	0.783108i	−0.978161	−	0.207850i	$-0.933353\pi$
$773$	−23.4654	+	21.7727i	−0.843990	+	0.783108i	0.134171	+	0.990958i	$0.457163\pi$
$774$		0			0
$775$	−15.6692	−	14.5389i	−0.562855	−	0.522253i
$776$	34.7041	+	43.5175i	1.24580	+	1.56219i
$777$		0			0
$778$	39.6976	−	49.7793i	1.42323	−	1.78467i
$779$	−21.4888	+	3.23892i	−0.769916	+	0.116046i
$780$		0			0
$781$	−16.7889	+	42.7773i	−0.600752	+	1.53069i
$782$	−66.9987	−	20.6664i	−2.39587	−	0.739027i
$783$		0			0
$784$	9.89794	+	66.4107i	0.353498	+	2.37181i
$785$	−5.39672			−0.192617
$786$		0			0
$787$	1.41670	−	3.60970i	0.0505000	−	0.128672i	−0.903398	−	0.428803i	$-0.858935\pi$
$787$	1.41670	−	3.60970i	0.0505000	−	0.128672i	0.953898	+	0.300131i	$0.0970305\pi$
$788$	15.8117	+	10.7802i	0.563267	+	0.384029i
$789$		0			0
$790$	−2.70574	+	3.39289i	−0.0962659	+	0.120714i
$791$	2.55636	−	7.28640i	0.0908936	−	0.259074i
$792$		0			0
$793$	−9.86418	−	9.15262i	−0.350287	−	0.325019i
$794$	17.5596	+	2.64669i	0.623168	+	0.0939274i
$795$		0			0
$796$	−63.4700	+	43.2731i	−2.24963	+	1.53377i
$797$	9.11843	+	39.9504i	0.322991	+	1.41512i	0.832201	+	0.554475i	$0.187081\pi$
$797$	9.11843	+	39.9504i	0.322991	+	1.41512i	−0.509209	+	0.860643i	$0.670062\pi$
$798$		0			0
$799$	−14.2353	+	62.3687i	−0.503607	+	2.20645i
$800$	−7.72912	−	19.6935i	−0.273266	−	0.696270i
$801$		0			0
$802$	−42.0789	−	72.8828i	−1.48586	−	2.57358i
$803$	−5.45807	+	9.45366i	−0.192611	+	0.333613i
$804$		0			0
$805$	−0.902855	+	23.6089i	−0.0318215	+	0.832104i
$806$	38.7673	−	18.6694i	1.36552	−	0.657600i
$807$		0			0
$808$	43.2878	−	13.3525i	1.52286	−	0.469739i
$809$	16.4538	−	5.07532i	0.578485	−	0.178439i	0.00831439	−	0.999965i	$-0.497353\pi$
$809$	16.4538	−	5.07532i	0.578485	−	0.178439i	0.570170	+	0.821527i	$0.306877\pi$
$810$		0			0
$811$	−2.68918	+	1.29504i	−0.0944298	+	0.0454750i	−0.480502	−	0.876993i	$-0.659546\pi$
$811$	−2.68918	+	1.29504i	−0.0944298	+	0.0454750i	0.386073	+	0.922468i	$0.373831\pi$
$812$	−21.0626	−	48.3847i	−0.739153	−	1.69797i
$813$		0			0
$814$	10.1544	−	17.5880i	0.355913	−	0.616459i
$815$	−6.25876	−	10.8405i	−0.219235	−	0.379726i
$816$		0			0
$817$	13.5380	+	34.4942i	0.473634	+	1.20680i
$818$	−3.51195	+	15.3869i	−0.122792	+	0.537989i
$819$		0			0
$820$	−12.5165	−	54.8385i	−0.437096	−	1.91504i
$821$	−18.7449	+	12.7801i	−0.654203	+	0.446028i	−0.844396	−	0.535719i	$-0.820041\pi$
$821$	−18.7449	+	12.7801i	−0.654203	+	0.446028i	0.190194	+	0.981747i	$0.439088\pi$
$822$		0			0
$823$	−12.7230	−	1.91768i	−0.443495	−	0.0668461i	−0.0765011	−	0.997069i	$-0.524375\pi$
$823$	−12.7230	−	1.91768i	−0.443495	−	0.0668461i	−0.366994	+	0.930223i	$0.619613\pi$
$824$	−102.874	−	95.4530i	−3.58378	−	3.32526i
$825$		0			0
$826$	−7.56308	−	4.76089i	−0.263153	−	0.165653i
$827$	14.3930	−	18.0482i	0.500492	−	0.627598i	−0.465848	−	0.884865i	$-0.654251\pi$
$827$	14.3930	−	18.0482i	0.500492	−	0.627598i	0.966340	+	0.257267i	$0.0828221\pi$
$828$		0			0
$829$	14.7871	+	10.0817i	0.513576	+	0.350151i	0.792212	−	0.610247i	$-0.208930\pi$
$829$	14.7871	+	10.0817i	0.513576	+	0.350151i	−0.278635	+	0.960397i	$0.589882\pi$
$830$	−16.8036	+	42.8149i	−0.583262	+	1.48613i
$831$		0			0
$832$	12.2756			0.425579
$833$	5.44655	−	35.7360i	0.188712	−	1.23818i
$834$		0			0
$835$	21.6484	+	6.67763i	0.749172	+	0.231089i
$836$	−21.4412	+	54.6313i	−0.741560	+	1.88946i
$837$		0			0
$838$	26.3485	−	3.97140i	0.910195	−	0.137190i
$839$	−15.0875	+	18.9191i	−0.520878	+	0.653160i	−0.970795	−	0.239910i	$-0.922882\pi$
$839$	−15.0875	+	18.9191i	−0.520878	+	0.653160i	0.449917	+	0.893070i	$0.351453\pi$
$840$		0			0
$841$	−7.40477	−	9.28529i	−0.255337	−	0.320182i
$842$	−49.2556	−	45.7025i	−1.69746	−	1.57501i
$843$		0			0
$844$	7.15812	−	6.64177i	0.246393	−	0.228619i
$845$	14.9062	−	10.1629i	0.512789	−	0.349614i
$846$		0			0
$847$	−1.72503	+	9.07606i	−0.0592726	+	0.311857i
$848$	3.87647	−	16.9839i	0.133119	−	0.583231i
$849$		0			0
$850$	2.06581	+	27.5663i	0.0708567	+	0.945517i
$851$	5.31032	+	9.19775i	0.182036	+	0.315295i
$852$		0			0
$853$	21.8247	+	10.5102i	0.747263	+	0.359863i	0.768448	−	0.639913i	$-0.221029\pi$
$853$	21.8247	+	10.5102i	0.747263	+	0.359863i	−0.0211846	+	0.999776i	$0.506744\pi$
$854$	−57.8273	+	10.8922i	−1.97881	+	0.372723i
$855$		0			0
$856$	−4.77892	+	63.7702i	−0.163340	+	2.17962i
$857$	26.4497	−	8.15867i	0.903506	−	0.278695i	0.192017	−	0.981392i	$-0.438497\pi$
$857$	26.4497	−	8.15867i	0.903506	−	0.278695i	0.711489	+	0.702697i	$0.248021\pi$
$858$		0			0
$859$	3.79189	−	50.5993i	0.129378	−	1.72643i	−0.434589	−	0.900629i	$-0.643106\pi$
$859$	3.79189	−	50.5993i	0.129378	−	1.72643i	0.563967	−	0.825797i	$-0.309275\pi$
$860$	−86.4147	+	41.6151i	−2.94672	+	1.41906i
$861$		0			0
$862$	−15.8702	−	7.64270i	−0.540542	−	0.260311i
$863$	−12.0287	+	20.8344i	−0.409463	+	0.709211i	−0.994830	−	0.101558i	$-0.967617\pi$
$863$	−12.0287	+	20.8344i	−0.409463	+	0.709211i	0.585367	+	0.810769i	$0.300951\pi$
$864$		0			0
$865$	2.48041	+	33.0988i	0.0843365	+	1.12539i
$866$	−15.7145	−	40.0399i	−0.534000	−	1.36061i
$867$		0			0
$868$	24.8306	−	130.644i	0.842806	−	4.43434i
$869$	−0.819544	−	3.59066i	−0.0278011	−	0.121805i
$870$		0			0
$871$	9.11716	−	8.45949i	0.308923	−	0.286639i
$872$	−80.7561	−	12.1720i	−2.73475	−	0.412197i
$873$		0			0
$874$	−27.0760	−	33.9522i	−0.915858	−	1.14845i
$875$	30.2479	−	10.5562i	1.02256	−	0.356866i
$876$		0			0
$877$	4.04456	−	0.609620i	0.136575	−	0.0205854i	−0.0803989	−	0.996763i	$-0.525619\pi$
$877$	4.04456	−	0.609620i	0.136575	−	0.0205854i	0.216974	+	0.976177i	$0.430381\pi$
$878$	−19.5413	−	13.3230i	−0.659487	−	0.449631i
$879$		0			0
$880$	−59.9325	−	18.4867i	−2.02032	−	0.623187i
$881$	16.5619			0.557983			0.278992	−	0.960294i	$-0.410000\pi$
$881$	16.5619			0.557983			0.278992	+	0.960294i	$0.410000\pi$
$882$		0			0
$883$	30.5572			1.02833			0.514166	−	0.857690i	$-0.328101\pi$
$883$	30.5572			1.02833			0.514166	+	0.857690i	$0.328101\pi$
$884$	−37.5806	−	11.5921i	−1.26397	−	0.389883i
$885$		0			0
$886$	−10.2224	−	6.96953i	−0.343429	−	0.234146i
$887$	−9.01759	+	1.35918i	−0.302781	+	0.0456369i	−0.298676	−	0.954355i	$-0.596545\pi$
$887$	−9.01759	+	1.35918i	−0.302781	+	0.0456369i	−0.00410539	+	0.999992i	$0.501307\pi$
$888$		0			0
$889$	−32.3300	−	20.3514i	−1.08431	−	0.682566i
$890$	1.10612	+	1.38704i	0.0370774	+	0.0464935i
$891$		0			0
$892$	−106.552	−	16.0601i	−3.56762	−	0.537732i
$893$	−29.0456	+	26.9504i	−0.971975	+	0.901861i
$894$		0			0
$895$	0.553177	+	2.42363i	0.0184907	+	0.0810129i
$896$	−0.554500	+	0.750027i	−0.0185246	+	0.0250567i
$897$		0			0
$898$	10.3252	+	26.3081i	0.344556	+	0.877913i
$899$	3.22476	+	43.0314i	0.107552	+	1.43518i
$900$		0			0
$901$	−4.68943	+	8.12232i	−0.156227	+	0.270594i
$902$	60.8564	+	29.3069i	2.02630	+	0.975812i
$903$		0			0
$904$	−19.3648	+	9.32559i	−0.644064	+	0.310165i
$905$	−1.95237	+	26.0526i	−0.0648990	+	0.866017i
$906$		0			0
$907$	20.6163	−	6.35929i	0.684553	−	0.211157i	0.0670789	−	0.997748i	$-0.478632\pi$
$907$	20.6163	−	6.35929i	0.684553	−	0.211157i	0.617474	+	0.786591i	$0.288156\pi$
$908$	4.19608	−	55.9927i	0.139252	−	1.85818i
$909$		0			0
$910$	−0.716562	+	18.7375i	−0.0237538	+	0.621141i
$911$	−43.1242	−	20.7675i	−1.42877	−	0.688059i	−0.450001	−	0.893028i	$-0.648576\pi$
$911$	−43.1242	−	20.7675i	−1.42877	−	0.688059i	−0.978768	+	0.204969i	$0.934290\pi$
$912$		0			0
$913$	−19.5173	−	33.8049i	−0.645927	−	1.11878i
$914$	−4.01436	−	53.5680i	−0.132783	−	1.77187i
$915$		0			0
$916$	4.46990	−	19.5839i	0.147690	−	0.647071i
$917$	11.0908	+	41.5283i	0.366251	+	1.37138i
$918$		0			0
$919$	−8.42115	+	5.74144i	−0.277788	+	0.189393i	−0.694198	−	0.719784i	$-0.744241\pi$
$919$	−8.42115	+	5.74144i	−0.277788	+	0.189393i	0.416410	+	0.909177i	$0.363288\pi$
$920$	48.2071	−	44.7296i	1.58934	−	1.47469i
$921$		0			0
$922$	−13.3439	−	12.3814i	−0.439459	−	0.407758i
$923$	−11.8919	−	14.9120i	−0.391428	−	0.490835i
$924$		0			0
$925$	2.61080	−	3.27383i	0.0858424	−	0.107643i
$926$	−14.5057	+	2.18638i	−0.476687	+	0.0718490i
$927$		0			0
$928$	−15.6034	+	39.7568i	−0.512206	+	1.30508i
$929$	−8.54408	−	2.63550i	−0.280322	−	0.0864679i	0.151406	−	0.988472i	$-0.451620\pi$
$929$	−8.54408	−	2.63550i	−0.280322	−	0.0864679i	−0.431728	+	0.902004i	$0.642096\pi$
$930$		0			0
$931$	15.2557	−	16.3876i	0.499987	−	0.537080i
$932$	77.6907			2.54484
$933$		0			0
$934$	37.4367	−	95.3871i	1.22497	−	3.12116i
$935$	27.8990	+	19.0212i	0.912393	+	0.622059i
$936$		0			0
$937$	−12.2362	+	15.3438i	−0.399741	+	0.501259i	−0.940441	−	0.339956i	$-0.889588\pi$
$937$	−12.2362	+	15.3438i	−0.399741	+	0.501259i	0.540701	+	0.841215i	$0.318159\pi$
$938$	−6.04500	−	54.0509i	−0.197376	−	1.76482i
$939$		0			0
$940$	−75.1802	−	69.7571i	−2.45211	−	2.27522i
$941$	15.9280	+	2.40076i	0.519239	+	0.0782627i	0.403433	−	0.915009i	$-0.367817\pi$
$941$	15.9280	+	2.40076i	0.519239	+	0.0782627i	0.115806	+	0.993272i	$0.463055\pi$
$942$		0			0
$943$	−29.1855	+	19.8983i	−0.950410	+	0.647979i
$944$	2.76073	+	12.0955i	0.0898540	+	0.393676i
$945$		0			0
$946$	25.6290	−	112.288i	0.833272	−	3.65080i
$947$	−0.772015	−	1.96706i	−0.0250871	−	0.0639209i	0.917781	−	0.397086i	$-0.129979\pi$
$947$	−0.772015	−	1.96706i	−0.0250871	−	0.0639209i	−0.942868	+	0.333165i	$0.891883\pi$
$948$		0			0
$949$	−2.26538	−	3.92375i	−0.0735372	−	0.127370i
$950$	−8.56085	+	14.8278i	−0.277751	+	0.481078i
$951$		0			0
$952$	−81.0062	+	59.6823i	−2.62543	+	1.93431i
$953$	−14.3178	+	6.89510i	−0.463799	+	0.223354i	−0.651165	−	0.758936i	$-0.725719\pi$
$953$	−14.3178	+	6.89510i	−0.463799	+	0.223354i	0.187366	+	0.982290i	$0.440005\pi$
$954$		0			0
$955$	14.0647	−	4.33838i	0.455123	−	0.140387i
$956$	57.1622	−	17.6322i	1.84876	−	0.570266i
$957$		0			0
$958$	−12.2232	+	5.88638i	−0.394913	+	0.190180i
$959$	38.9163	+	10.4619i	1.25667	+	0.337834i
$960$		0			0
$961$	−38.8721	+	67.3284i	−1.25394	+	2.17188i
$962$	4.21460	+	7.29990i	0.135884	+	0.235358i
$963$		0			0
$964$	7.42438	+	18.9170i	0.239123	+	0.609276i
$965$	8.71564	−	38.1857i	0.280566	−	1.22924i
$966$		0			0
$967$	9.70518	+	42.5212i	0.312098	+	1.36739i	0.851064	+	0.525062i	$0.175958\pi$
$967$	9.70518	+	42.5212i	0.312098	+	1.36739i	−0.538967	+	0.842327i	$0.681185\pi$
$968$	21.2467	−	14.4858i	0.682896	−	0.465591i
$969$		0			0
$970$	33.5241	+	5.05295i	1.07640	+	0.162240i
$971$	34.1207	+	31.6594i	1.09499	+	1.01600i	0.999789	+	0.0205407i	$0.00653875\pi$
$971$	34.1207	+	31.6594i	1.09499	+	1.01600i	0.0951976	+	0.995458i	$0.469652\pi$
$972$		0			0
$973$	−5.53645	−	8.82734i	−0.177491	−	0.282992i
$974$	−37.1081	+	46.5321i	−1.18902	+	1.49098i
$975$		0			0
$976$	67.4963	+	46.0182i	2.16050	+	1.47301i
$977$	−3.83768	+	9.77825i	−0.122778	+	0.312834i	−0.979027	−	0.203729i	$-0.934694\pi$
$977$	−3.83768	+	9.77825i	−0.122778	+	0.312834i	0.856249	+	0.516563i	$0.172789\pi$
$978$		0			0
$979$	−1.50563			−0.0481203
$980$	45.2490	+	36.2069i	1.44543	+	1.15659i
$981$		0			0
$982$	−34.0791	−	10.5120i	−1.08751	−	0.335452i
$983$	1.40490	−	3.57963i	0.0448094	−	0.114173i	−0.906717	−	0.421740i	$-0.861420\pi$
$983$	1.40490	−	3.57963i	0.0448094	−	0.114173i	0.951526	+	0.307567i	$0.0995149\pi$
$984$		0			0
$985$	6.74337	−	1.01640i	0.214862	−	0.0323852i
$986$	34.7947	−	43.6311i	1.10809	−	1.38950i
$987$		0			0
$988$	−15.1873	−	19.0443i	−0.483173	−	0.605879i
$989$	44.1531	+	40.9681i	1.40399	+	1.30271i
$990$		0			0
$991$	7.60080	−	7.05251i	0.241447	−	0.224030i	−0.550162	−	0.835058i	$-0.685434\pi$
$991$	7.60080	−	7.05251i	0.241447	−	0.224030i	0.791609	+	0.611028i	$0.209244\pi$
$992$	−88.9263	+	60.6289i	−2.82341	+	1.92497i
$993$		0			0
$994$	−83.3508	+	3.05002i	−2.64373	+	0.0967409i
$995$	−6.09140	+	26.6882i	−0.193110	+	0.846072i
$996$		0			0
$997$	4.54087	+	60.5937i	0.143811	+	1.91902i	0.343484	+	0.939158i	$0.388393\pi$
$997$	4.54087	+	60.5937i	0.143811	+	1.91902i	−0.199674	+	0.979862i	$0.563988\pi$
$998$	29.3509	+	50.8373i	0.929087	+	1.60923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.100.6	yes	72
3.2	odd	2	inner	441.2.bb.f.100.1	✓	72
49.25	even	21	inner	441.2.bb.f.172.6	yes	72
147.74	odd	42	inner	441.2.bb.f.172.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.100.1	✓	72	3.2	odd	2	inner
441.2.bb.f.100.6	yes	72	1.1	even	1	trivial
441.2.bb.f.172.1	yes	72	147.74	odd	42	inner
441.2.bb.f.172.6	yes	72	49.25	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.49548 + 0.769754i) q^{2} +(3.98243 + 2.71518i) q^{4} +(1.69843 - 0.255997i) q^{5} +(-2.62887 - 0.298395i) q^{7} +(4.59158 + 5.75765i) q^{8} +O(q^{10})\)	\(q+(2.49548 + 0.769754i) q^{2} +(3.98243 + 2.71518i) q^{4} +(1.69843 - 0.255997i) q^{5} +(-2.62887 - 0.298395i) q^{7} +(4.59158 + 5.75765i) q^{8} +(4.43546 + 0.668538i) q^{10} +(-2.79059 + 2.58929i) q^{11} +(-0.351587 - 1.54041i) q^{13} +(-6.33061 - 2.76822i) q^{14} +(3.50436 + 8.92897i) q^{16} +(-0.385913 - 5.14966i) q^{17} +(1.59925 - 2.76998i) q^{19} +(7.45897 + 3.59205i) q^{20} +(-8.95699 + 4.31346i) q^{22} +(0.388520 - 5.18444i) q^{23} +(-1.95873 + 0.604187i) q^{25} +(0.308353 - 4.11469i) q^{26} +(-9.65910 - 8.32618i) q^{28} +(3.72828 + 1.79544i) q^{29} +(5.21402 + 9.03095i) q^{31} +(0.771289 + 10.2921i) q^{32} +(3.00093 - 13.1479i) q^{34} +(-4.54135 + 0.166180i) q^{35} +(-1.68787 + 1.15077i) q^{37} +(6.12310 - 5.68141i) q^{38} +(9.27242 + 8.60355i) q^{40} +(-4.23617 - 5.31199i) q^{41} +(-7.22334 + 9.05779i) q^{43} +(-18.1437 + 2.73473i) q^{44} +(4.96028 - 12.6386i) q^{46} +(-11.8376 - 3.65142i) q^{47} +(6.82192 + 1.56889i) q^{49} -5.35304 q^{50} +(2.78230 - 7.08918i) q^{52} +(-1.50059 - 1.02308i) q^{53} +(-4.07678 + 5.11212i) q^{55} +(-10.3526 - 16.5062i) q^{56} +(7.92180 + 7.35036i) q^{58} +(1.27898 + 0.192775i) q^{59} +(7.03671 - 4.79755i) q^{61} +(6.05989 + 26.5501i) q^{62} +(-1.72882 + 7.57447i) q^{64} +(-0.991487 - 2.52627i) q^{65} +(3.93580 + 6.81700i) q^{67} +(12.4453 - 21.5560i) q^{68} +(-11.4608 - 3.08102i) q^{70} +(10.8760 - 5.23762i) q^{71} +(2.74013 - 0.845219i) q^{73} +(-5.09786 + 1.57248i) q^{74} +(13.8899 - 6.68902i) q^{76} +(8.10874 - 5.97421i) q^{77} +(-0.483737 + 0.837858i) q^{79} +(8.23772 + 14.2681i) q^{80} +(-6.48236 - 16.5168i) q^{82} +(-2.28170 + 9.99677i) q^{83} +(-1.97375 - 8.64755i) q^{85} +(-24.9980 + 17.0433i) q^{86} +(-27.7215 - 4.17834i) q^{88} +(0.289929 + 0.269015i) q^{89} +(0.464628 + 4.15444i) q^{91} +(15.6239 - 19.5918i) q^{92} +(-26.7298 - 18.2241i) q^{94} +(2.00711 - 5.11403i) q^{95} +7.55821 q^{97} +(15.8163 + 9.16633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

L-functions

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