LMFDB - Embedded newform 3900.2.cd.h.2701.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3900,2,Mod(901,3900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3900.901"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.cd (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,0,0,0,0,-2,0,12,0,4,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-13})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 13x^{2} + 169 $ x^4 - 13*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2701.1
Root			$-3.12250 - 1.80278i$ of defining polynomial
Character	$\chi$	$=$	3900.2701
Dual form			3900.2.cd.h.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-3.12250 - 1.80278i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{17} +(-0.122499 - 0.0707248i) q^{19} -3.60555i q^{21} +(3.62250 + 6.27435i) q^{23} -1.00000 q^{27} +(-2.62250 - 4.54230i) q^{29} -3.46410i q^{31} +(3.00000 + 1.73205i) q^{33} +(6.24500 - 3.60555i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(-6.24500 + 3.60555i) q^{41} +(2.12250 - 3.67628i) q^{43} +3.74700i q^{47} +(3.00000 + 5.19615i) q^{49} -2.00000 q^{51} -3.24500 q^{53} -0.141450i q^{57} +(1.62250 + 0.936750i) q^{59} +(3.12250 - 1.80278i) q^{63} +(-6.12250 + 3.53483i) q^{67} +(-3.62250 + 6.27435i) q^{69} +(6.24500 + 3.60555i) q^{71} +12.4073i q^{73} -12.4900 q^{77} +8.24500 q^{79} +(-0.500000 - 0.866025i) q^{81} +5.05470i q^{83} +(2.62250 - 4.54230i) q^{87} +(10.6225 - 6.13290i) q^{89} +(3.12250 - 12.6194i) q^{91} +(3.00000 - 1.73205i) q^{93} +(12.2450 + 7.06965i) q^{97} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{9} + 12 q^{11} + 4 q^{13} - 4 q^{17} + 12 q^{19} + 2 q^{23} - 4 q^{27} + 2 q^{29} + 12 q^{33} - 10 q^{39} - 4 q^{43} + 12 q^{49} - 8 q^{51} + 12 q^{53} - 6 q^{59} - 12 q^{67} - 2 q^{69}+ \cdots + 24 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^9 + 12 * q^11 + 4 * q^13 - 4 * q^17 + 12 * q^19 + 2 * q^23 - 4 * q^27 + 2 * q^29 + 12 * q^33 - 10 * q^39 - 4 * q^43 + 12 * q^49 - 8 * q^51 + 12 * q^53 - 6 * q^59 - 12 * q^67 - 2 * q^69 + 8 * q^79 - 2 * q^81 - 2 * q^87 + 30 * q^89 + 12 * q^93 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.12250	−	1.80278i	−1.18019	−	0.681385i	−0.224134	−	0.974558i	$-0.571955\pi$
$7$	−3.12250	−	1.80278i	−1.18019	−	0.681385i	−0.956059	+	0.293173i	$0.905289\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−0.122499	−	0.0707248i	−0.0281032	−	0.0162254i	0.485883	−	0.874024i	$-0.338498\pi$
$19$	−0.122499	−	0.0707248i	−0.0281032	−	0.0162254i	−0.513986	+	0.857799i	$0.671832\pi$
$20$		0			0
$21$		−	3.60555i		−	0.786796i
$22$		0			0
$23$	3.62250	+	6.27435i	0.755343	+	1.30829i	0.945203	+	0.326482i	$0.105863\pi$
$23$	3.62250	+	6.27435i	0.755343	+	1.30829i	−0.189860	+	0.981811i	$0.560803\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.62250	−	4.54230i	−0.486986	−	0.843484i	0.512902	−	0.858447i	$-0.328570\pi$
$29$	−2.62250	−	4.54230i	−0.486986	−	0.843484i	−0.999888	+	0.0149628i	$0.995237\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$		0			0
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.24500	−	3.60555i	1.02667	−	0.592749i	0.110642	−	0.993860i	$-0.464709\pi$
$37$	6.24500	−	3.60555i	1.02667	−	0.592749i	0.916029	+	0.401111i	$0.131376\pi$
$38$		0			0
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	−6.24500	+	3.60555i	−0.975305	+	0.563093i	−0.900849	−	0.434132i	$-0.857055\pi$
$41$	−6.24500	+	3.60555i	−0.975305	+	0.563093i	−0.0744555	+	0.997224i	$0.523722\pi$
$42$		0			0
$43$	2.12250	−	3.67628i	0.323678	−	0.560627i	−0.657566	−	0.753397i	$-0.728414\pi$
$43$	2.12250	−	3.67628i	0.323678	−	0.560627i	0.981244	+	0.192770i	$0.0617472\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.74700i			0.546556i	0.961935	+	0.273278i	$0.0881079\pi$
$47$			3.74700i			0.546556i	−0.961935	+	0.273278i	$0.911892\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−3.24500			−0.445735			−0.222867	−	0.974849i	$-0.571542\pi$
$53$	−3.24500			−0.445735			−0.222867	+	0.974849i	$0.571542\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	0.141450i		−	0.0187355i
$58$		0			0
$59$	1.62250	+	0.936750i	0.211231	+	0.121954i	0.601884	−	0.798584i	$-0.294417\pi$
$59$	1.62250	+	0.936750i	0.211231	+	0.121954i	−0.390652	+	0.920538i	$0.627750\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$	3.12250	−	1.80278i	0.393398	−	0.227128i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.12250	+	3.53483i	−0.747982	+	0.431848i	−0.824964	−	0.565185i	$-0.808805\pi$
$67$	−6.12250	+	3.53483i	−0.747982	+	0.431848i	0.0769821	+	0.997032i	$0.475472\pi$
$68$		0			0
$69$	−3.62250	+	6.27435i	−0.436098	+	0.755343i
$70$		0			0
$71$	6.24500	+	3.60555i	0.741145	+	0.427900i	0.822485	−	0.568786i	$-0.192587\pi$
$71$	6.24500	+	3.60555i	0.741145	+	0.427900i	−0.0813405	+	0.996686i	$0.525920\pi$
$72$		0			0
$73$			12.4073i			1.45216i	0.687611	+	0.726080i	$0.258660\pi$
$73$			12.4073i			1.45216i	−0.687611	+	0.726080i	$0.741340\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.4900			−1.42337
$78$		0			0
$79$	8.24500			0.927635			0.463817	−	0.885931i	$-0.346479\pi$
$79$	8.24500			0.927635			0.463817	+	0.885931i	$0.346479\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			5.05470i			0.554826i	0.960751	+	0.277413i	$0.0894770\pi$
$83$			5.05470i			0.554826i	−0.960751	+	0.277413i	$0.910523\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.62250	−	4.54230i	0.281161	−	0.486986i
$88$		0			0
$89$	10.6225	−	6.13290i	1.12598	−	0.650086i	0.183061	−	0.983102i	$-0.441399\pi$
$89$	10.6225	−	6.13290i	1.12598	−	0.650086i	0.942921	+	0.333015i	$0.108066\pi$
$90$		0			0
$91$	3.12250	−	12.6194i	0.327327	−	1.32288i
$92$		0			0
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.2450	+	7.06965i	1.24329	+	0.717814i	0.969763	−	0.244049i	$-0.0784759\pi$
$97$	12.2450	+	7.06965i	1.24329	+	0.717814i	0.273528	+	0.961864i	$0.411809\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	0.622499	+	1.07820i	0.0619410	+	0.107285i	0.895333	−	0.445397i	$-0.146938\pi$
$101$	0.622499	+	1.07820i	0.0619410	+	0.107285i	−0.833392	+	0.552682i	$0.813604\pi$
$102$		0			0
$103$	1.75500			0.172925			0.0864627	−	0.996255i	$-0.472444\pi$
$103$	1.75500			0.172925			0.0864627	+	0.996255i	$0.472444\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.62250	+	8.00640i	0.446874	+	0.774008i	0.998181	−	0.0602944i	$-0.0192039\pi$
$107$	4.62250	+	8.00640i	0.446874	+	0.774008i	−0.551307	+	0.834303i	$0.685871\pi$
$108$		0			0
$109$			17.8863i			1.71320i	0.515983	+	0.856599i	$0.327427\pi$
$109$			17.8863i			1.71320i	−0.515983	+	0.856599i	$0.672573\pi$
$110$		0			0
$111$	6.24500	+	3.60555i	0.592749	+	0.342224i
$112$		0			0
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$		0			0
$119$	6.24500	−	3.60555i	0.572478	−	0.330520i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−6.24500	−	3.60555i	−0.563093	−	0.325102i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.87750	+	3.25193i	0.166601	+	0.288562i	0.937223	−	0.348731i	$-0.113387\pi$
$127$	1.87750	+	3.25193i	0.166601	+	0.288562i	−0.770621	+	0.637293i	$0.780054\pi$
$128$		0			0
$129$	4.24500			0.373751
$130$		0			0
$131$	−1.24500			−0.108776			−0.0543880	−	0.998520i	$-0.517321\pi$
$131$	−1.24500			−0.108776			−0.0543880	+	0.998520i	$0.517321\pi$
$132$		0			0
$133$	0.255002	+	0.441676i	0.0221115	+	0.0382982i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.1125	+	9.87990i	1.46202	+	0.844097i	0.999105	−	0.0423059i	$-0.0134704\pi$
$137$	17.1125	+	9.87990i	1.46202	+	0.844097i	0.462914	+	0.886403i	$0.346804\pi$
$138$		0			0
$139$	−6.12250	+	10.6045i	−0.519304	+	0.899460i	0.480445	+	0.877025i	$0.340475\pi$
$139$	−6.12250	+	10.6045i	−0.519304	+	0.899460i	−0.999748	+	0.0224352i	$0.992858\pi$
$140$		0			0
$141$	−3.24500	+	1.87350i	−0.273278	+	0.157777i
$142$		0			0
$143$	9.00000	+	8.66025i	0.752618	+	0.724207i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$		0			0
$149$	13.3775	+	7.72350i	1.09593	+	0.632734i	0.935148	−	0.354256i	$-0.115266\pi$
$149$	13.3775	+	7.72350i	1.09593	+	0.632734i	0.160779	+	0.986990i	$0.448599\pi$
$150$		0			0
$151$			0.424349i			0.0345330i	0.999851	+	0.0172665i	$0.00549638\pi$
$151$			0.424349i			0.0345330i	−0.999851	+	0.0172665i	$0.994504\pi$
$152$		0			0
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−17.0000			−1.35675			−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000			−1.35675			−0.678374	+	0.734717i	$0.737315\pi$
$158$		0			0
$159$	−1.62250	−	2.81025i	−0.128673	−	0.222867i
$160$		0			0
$161$		−	26.1222i		−	2.05872i
$162$		0			0
$163$	15.4900	+	8.94315i	1.21327	+	0.700482i	0.963470	−	0.267816i	$-0.0863018\pi$
$163$	15.4900	+	8.94315i	1.21327	+	0.700482i	0.249800	+	0.968297i	$0.419635\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.6225	−	7.86495i	1.05414	−	0.608608i	0.130335	−	0.991470i	$-0.458395\pi$
$167$	13.6225	−	7.86495i	1.05414	−	0.608608i	0.923806	+	0.382862i	$0.125061\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	0.122499	−	0.0707248i	0.00936773	−	0.00540846i
$172$		0			0
$173$	−6.37750	+	11.0462i	−0.484872	+	0.839824i	−0.999849	−	0.0173806i	$-0.994467\pi$
$173$	−6.37750	+	11.0462i	−0.484872	+	0.839824i	0.514977	+	0.857204i	$0.327801\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			1.87350i			0.140821i
$178$		0			0
$179$	9.24500	+	16.0128i	0.691004	+	1.19685i	0.971509	+	0.237001i	$0.0761645\pi$
$179$	9.24500	+	16.0128i	0.691004	+	1.19685i	−0.280506	+	0.959852i	$0.590502\pi$
$180$		0			0
$181$	−11.4900			−0.854045			−0.427022	−	0.904241i	$-0.640437\pi$
$181$	−11.4900			−0.854045			−0.427022	+	0.904241i	$0.640437\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$			6.92820i			0.506640i
$188$		0			0
$189$	3.12250	+	1.80278i	0.227128	+	0.131133i
$190$		0			0
$191$	6.24500	−	10.8167i	0.451872	−	0.782666i	−0.546630	−	0.837374i	$-0.684090\pi$
$191$	6.24500	−	10.8167i	0.451872	−	0.782666i	0.998502	+	0.0547085i	$0.0174230\pi$
$192$		0			0
$193$	−7.50000	+	4.33013i	−0.539862	+	0.311689i	−0.745023	−	0.667039i	$-0.767561\pi$
$193$	−7.50000	+	4.33013i	−0.539862	+	0.311689i	0.205161	+	0.978728i	$0.434228\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$		0			0
$199$	−5.87750	+	10.1801i	−0.416645	+	0.721650i	−0.995600	−	0.0937095i	$-0.970128\pi$
$199$	−5.87750	+	10.1801i	−0.416645	+	0.721650i	0.578955	+	0.815360i	$0.303461\pi$
$200$		0			0
$201$	−6.12250	−	3.53483i	−0.431848	−	0.249327i
$202$		0			0
$203$			18.9111i			1.32730i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.24500			−0.503562
$208$		0			0
$209$	−0.489996			−0.0338937
$210$		0			0
$211$	3.24500	+	5.62050i	0.223395	+	0.386931i	0.955837	−	0.293898i	$-0.0949527\pi$
$211$	3.24500	+	5.62050i	0.223395	+	0.386931i	−0.732442	+	0.680830i	$0.761619\pi$
$212$		0			0
$213$			7.21110i			0.494097i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.24500	+	10.8167i	−0.423938	+	0.734282i
$218$		0			0
$219$	−10.7450	+	6.20363i	−0.726080	+	0.419202i
$220$		0			0
$221$	−7.00000	−	1.73205i	−0.470871	−	0.116510i
$222$		0			0
$223$	2.63250	−	1.51988i	0.176285	−	0.101778i	−0.409261	−	0.912417i	$-0.634213\pi$
$223$	2.63250	−	1.51988i	0.176285	−	0.101778i	0.585546	+	0.810639i	$0.300880\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.13250	+	2.38590i	0.274284	+	0.158358i	0.630833	−	0.775919i	$-0.282713\pi$
$227$	4.13250	+	2.38590i	0.274284	+	0.158358i	−0.356549	+	0.934277i	$0.616047\pi$
$228$		0			0
$229$		−	23.3654i		−	1.54403i	−0.635607	−	0.772013i	$-0.719250\pi$
$229$		−	23.3654i		−	1.54403i	0.635607	−	0.772013i	$-0.280750\pi$
$230$		0			0
$231$	−6.24500	−	10.8167i	−0.410891	−	0.711684i
$232$		0			0
$233$	−15.2450			−0.998733			−0.499367	−	0.866391i	$-0.666434\pi$
$233$	−15.2450			−0.998733			−0.499367	+	0.866391i	$0.666434\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.12250	+	7.14038i	0.267785	+	0.463817i
$238$		0			0
$239$		−	5.62050i		−	0.363560i	−0.983339	−	0.181780i	$-0.941814\pi$
$239$		−	5.62050i		−	0.363560i	0.983339	−	0.181780i	$-0.0581859\pi$
$240$		0			0
$241$	−10.2550	−	5.92073i	−0.660583	−	0.381388i	0.131916	−	0.991261i	$-0.457887\pi$
$241$	−10.2550	−	5.92073i	−0.660583	−	0.381388i	−0.792499	+	0.609873i	$0.791220\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.122499	−	0.495074i	0.00779442	−	0.0315008i
$248$		0			0
$249$	−4.37750	+	2.52735i	−0.277413	+	0.160164i
$250$		0			0
$251$	6.62250	−	11.4705i	0.418008	−	0.724012i	−0.577731	−	0.816227i	$-0.696062\pi$
$251$	6.62250	−	11.4705i	0.418008	−	0.724012i	0.995739	+	0.0922157i	$0.0293949\pi$
$252$		0			0
$253$	21.7350	+	12.5487i	1.36647	+	0.788930i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.4900	−	25.0974i	−0.903861	−	1.56553i	−0.822439	−	0.568854i	$-0.807387\pi$
$257$	−14.4900	−	25.0974i	−0.903861	−	1.56553i	−0.0814224	−	0.996680i	$-0.525946\pi$
$258$		0			0
$259$	−26.0000			−1.61556
$260$		0			0
$261$	5.24500			0.324657
$262$		0			0
$263$	15.4900	+	26.8295i	0.955154	+	1.65438i	0.734015	+	0.679133i	$0.237644\pi$
$263$	15.4900	+	26.8295i	0.955154	+	1.65438i	0.221139	+	0.975242i	$0.429023\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	10.6225	+	6.13290i	0.650086	+	0.375328i
$268$		0			0
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	−5.87750	+	3.39338i	−0.357033	+	0.206133i	−0.667778	−	0.744360i	$-0.732755\pi$
$271$	−5.87750	+	3.39338i	−0.357033	+	0.206133i	0.310746	+	0.950493i	$0.399421\pi$
$272$		0			0
$273$	12.4900	−	3.60555i	0.755929	−	0.218218i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.7450	−	23.8070i	0.825857	−	1.43043i	−0.0754058	−	0.997153i	$-0.524025\pi$
$277$	13.7450	−	23.8070i	0.825857	−	1.43043i	0.901263	−	0.433273i	$-0.142641\pi$
$278$		0			0
$279$	3.00000	+	1.73205i	0.179605	+	0.103695i
$280$		0			0
$281$		−	15.4470i		−	0.921491i	−0.887532	−	0.460746i	$-0.847582\pi$
$281$		−	15.4470i		−	0.921491i	0.887532	−	0.460746i	$-0.152418\pi$
$282$		0			0
$283$	−12.4900	−	21.6333i	−0.742453	−	1.28597i	−0.951375	−	0.308034i	$-0.900329\pi$
$283$	−12.4900	−	21.6333i	−0.742453	−	1.28597i	0.208922	−	0.977932i	$-0.433005\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	26.0000			1.53473
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$			14.1393i			0.828861i
$292$		0			0
$293$	−16.8675	−	9.73845i	−0.985410	−	0.568927i	−0.0815107	−	0.996672i	$-0.525974\pi$
$293$	−16.8675	−	9.73845i	−0.985410	−	0.568927i	−0.903899	+	0.427746i	$0.859308\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.00000	+	1.73205i	−0.174078	+	0.100504i
$298$		0			0
$299$	−18.1125	+	18.8231i	−1.04747	+	1.08857i
$300$		0			0
$301$	−13.2550	+	7.65278i	−0.764006	+	0.441099i
$302$		0			0
$303$	−0.622499	+	1.07820i	−0.0357616	+	0.0619410i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			21.3504i			1.21853i	0.792966	+	0.609266i	$0.208536\pi$
$307$			21.3504i			1.21853i	−0.792966	+	0.609266i	$0.791464\pi$
$308$		0			0
$309$	0.877501	+	1.51988i	0.0499193	+	0.0864627i
$310$		0			0
$311$	−27.7350			−1.57271			−0.786354	−	0.617777i	$-0.788034\pi$
$311$	−27.7350			−1.57271			−0.786354	+	0.617777i	$0.788034\pi$
$312$		0			0
$313$	−7.00000			−0.395663			−0.197832	−	0.980236i	$-0.563390\pi$
$313$	−7.00000			−0.395663			−0.197832	+	0.980236i	$0.563390\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	12.5487i		−	0.704805i	−0.935848	−	0.352403i	$-0.885365\pi$
$317$		−	12.5487i		−	0.704805i	0.935848	−	0.352403i	$-0.114635\pi$
$318$		0			0
$319$	−15.7350	−	9.08460i	−0.880991	−	0.508640i
$320$		0			0
$321$	−4.62250	+	8.00640i	−0.258003	+	0.446874i
$322$		0			0
$323$	0.244998	−	0.141450i	0.0136321	−	0.00787047i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−15.4900	+	8.94315i	−0.856599	+	0.494558i
$328$		0			0
$329$	6.75500	−	11.7000i	0.372415	−	0.645042i
$330$		0			0
$331$	5.87750	+	3.39338i	0.323057	+	0.186517i	0.652754	−	0.757570i	$-0.273613\pi$
$331$	5.87750	+	3.39338i	0.323057	+	0.186517i	−0.329698	+	0.944087i	$0.606947\pi$
$332$		0			0
$333$			7.21110i			0.395166i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−29.9800			−1.63311			−0.816557	−	0.577265i	$-0.804120\pi$
$337$	−29.9800			−1.63311			−0.816557	+	0.577265i	$0.804120\pi$
$338$		0			0
$339$	−12.0000			−0.651751
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$			3.60555i			0.194681i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−1.50000	+	0.866025i	−0.0802932	+	0.0463573i	−0.539609	−	0.841916i	$-0.681428\pi$
$349$	−1.50000	+	0.866025i	−0.0802932	+	0.0463573i	0.459316	+	0.888273i	$0.348095\pi$
$350$		0			0
$351$	−1.00000	−	3.46410i	−0.0533761	−	0.184900i
$352$		0			0
$353$	−1.37750	+	0.795301i	−0.0733170	+	0.0423296i	−0.536210	−	0.844084i	$-0.680145\pi$
$353$	−1.37750	+	0.795301i	−0.0733170	+	0.0423296i	0.462893	+	0.886414i	$0.346811\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.24500	+	3.60555i	0.330520	+	0.190826i
$358$		0			0
$359$		−	29.8692i		−	1.57644i	−0.615396	−	0.788218i	$-0.711004\pi$
$359$		−	29.8692i		−	1.57644i	0.615396	−	0.788218i	$-0.288996\pi$
$360$		0			0
$361$	−9.49000	−	16.4372i	−0.499473	−	0.865113i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.3675	+	30.0814i	0.906576	+	1.57024i	0.818788	+	0.574096i	$0.194647\pi$
$367$	17.3675	+	30.0814i	0.906576	+	1.57024i	0.0877883	+	0.996139i	$0.472020\pi$
$368$		0			0
$369$		−	7.21110i		−	0.375395i
$370$		0			0
$371$	10.1325	+	5.85000i	0.526053	+	0.303717i
$372$		0			0
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.1125	−	13.6269i	0.675328	−	0.701821i
$378$		0			0
$379$	−2.87750	+	1.66133i	−0.147807	+	0.0853366i	−0.572080	−	0.820198i	$-0.693863\pi$
$379$	−2.87750	+	1.66133i	−0.147807	+	0.0853366i	0.424272	+	0.905535i	$0.360530\pi$
$380$		0			0
$381$	−1.87750	+	3.25193i	−0.0961873	+	0.166601i
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.12250	+	3.67628i	0.107893	+	0.186876i
$388$		0			0
$389$	32.9800			1.67215			0.836076	−	0.548614i	$-0.184844\pi$
$389$	32.9800			1.67215			0.836076	+	0.548614i	$0.184844\pi$
$390$		0			0
$391$	−14.4900			−0.732791
$392$		0			0
$393$	−0.622499	−	1.07820i	−0.0314009	−	0.0543880i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	0.0250943	−	0.999685i	$-0.492011\pi$
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$	−0.255002	+	0.441676i	−0.0127661	+	0.0221115i
$400$		0			0
$401$	24.9800	−	14.4222i	1.24744	−	0.720211i	0.276843	−	0.960915i	$-0.410712\pi$
$401$	24.9800	−	14.4222i	1.24744	−	0.720211i	0.970598	+	0.240705i	$0.0773785\pi$
$402$		0			0
$403$	12.0000	−	3.46410i	0.597763	−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.4900	−	21.6333i	0.619106	−	1.07232i
$408$		0			0
$409$	24.2450	+	13.9979i	1.19884	+	0.692149i	0.960296	−	0.278983i	$-0.0899972\pi$
$409$	24.2450	+	13.9979i	1.19884	+	0.692149i	0.238542	+	0.971132i	$0.423331\pi$
$410$		0			0
$411$			19.7598i			0.974679i
$412$		0			0
$413$	−3.37750	−	5.85000i	−0.166196	−	0.287860i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.2450			−0.599640
$418$		0			0
$419$	1.86750	+	3.23460i	0.0912332	+	0.158021i	0.908030	−	0.418905i	$-0.137586\pi$
$419$	1.86750	+	3.23460i	0.0912332	+	0.158021i	−0.816797	+	0.576925i	$0.804252\pi$
$420$		0			0
$421$		−	5.19615i		−	0.253245i	−0.991951	−	0.126622i	$-0.959586\pi$
$421$		−	5.19615i		−	0.253245i	0.991951	−	0.126622i	$-0.0404137\pi$
$422$		0			0
$423$	−3.24500	−	1.87350i	−0.157777	−	0.0910927i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.00000	+	12.1244i	−0.144841	+	0.585369i
$430$		0			0
$431$	4.13250	−	2.38590i	0.199056	−	0.114925i	−0.397159	−	0.917750i	$-0.630004\pi$
$431$	4.13250	−	2.38590i	0.199056	−	0.114925i	0.596215	+	0.802825i	$0.296671\pi$
$432$		0			0
$433$	−7.24500	+	12.5487i	−0.348172	+	0.603052i	−0.985925	−	0.167189i	$-0.946531\pi$
$433$	−7.24500	+	12.5487i	−0.348172	+	0.603052i	0.637752	+	0.770241i	$0.279864\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	1.02480i		−	0.0490230i
$438$		0			0
$439$	−6.87750	−	11.9122i	−0.328245	−	0.568537i	0.653919	−	0.756565i	$-0.273124\pi$
$439$	−6.87750	−	11.9122i	−0.328245	−	0.568537i	−0.982164	+	0.188028i	$0.939791\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			15.4470i			0.730618i
$448$		0			0
$449$	−10.8675	−	6.27435i	−0.512869	−	0.296105i	0.221143	−	0.975241i	$-0.429021\pi$
$449$	−10.8675	−	6.27435i	−0.512869	−	0.296105i	−0.734012	+	0.679136i	$0.762354\pi$
$450$		0			0
$451$	−12.4900	+	21.6333i	−0.588131	+	1.01867i
$452$		0			0
$453$	−0.367497	+	0.212174i	−0.0172665	+	0.00996883i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−28.9900	+	16.7374i	−1.35609	+	0.782942i	−0.989095	−	0.147279i	$-0.952948\pi$
$457$	−28.9900	+	16.7374i	−1.35609	+	0.782942i	−0.367000	+	0.930221i	$0.619615\pi$
$458$		0			0
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$		0			0
$461$	12.7350	+	7.35255i	0.593128	+	0.342442i	0.766333	−	0.642443i	$-0.222079\pi$
$461$	12.7350	+	7.35255i	0.593128	+	0.342442i	−0.173205	+	0.984886i	$0.555412\pi$
$462$		0			0
$463$			3.32265i			0.154417i	0.997015	+	0.0772084i	$0.0246007\pi$
$463$			3.32265i			0.154417i	−0.997015	+	0.0772084i	$0.975399\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.49000			0.207772			0.103886	−	0.994589i	$-0.466872\pi$
$467$	4.49000			0.207772			0.103886	+	0.994589i	$0.466872\pi$
$468$		0			0
$469$	25.4900			1.17702
$470$		0			0
$471$	−8.50000	−	14.7224i	−0.391659	−	0.678374i
$472$		0			0
$473$		−	14.7051i		−	0.676141i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.62250	−	2.81025i	0.0742891	−	0.128673i
$478$		0			0
$479$	0.887505	−	0.512401i	0.0405511	−	0.0234122i	−0.479587	−	0.877494i	$-0.659214\pi$
$479$	0.887505	−	0.512401i	0.0405511	−	0.0234122i	0.520139	+	0.854082i	$0.325880\pi$
$480$		0			0
$481$	18.7350	+	18.0278i	0.854242	+	0.821995i
$482$		0			0
$483$	22.6225	−	13.0611i	1.02936	−	0.594301i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	24.6125	+	14.2100i	1.11530	+	0.643918i	0.940197	−	0.340632i	$-0.110641\pi$
$487$	24.6125	+	14.2100i	1.11530	+	0.643918i	0.175102	+	0.984550i	$0.443974\pi$
$488$		0			0
$489$			17.8863i			0.808847i
$490$		0			0
$491$	18.2450	+	31.6013i	0.823385	+	1.42615i	0.903147	+	0.429331i	$0.141251\pi$
$491$	18.2450	+	31.6013i	0.823385	+	1.42615i	−0.0797619	+	0.996814i	$0.525416\pi$
$492$		0			0
$493$	10.4900			0.472446
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.0000	−	22.5167i	−0.583130	−	1.01001i
$498$		0			0
$499$			27.8543i			1.24693i	0.781852	+	0.623464i	$0.214275\pi$
$499$			27.8543i			1.24693i	−0.781852	+	0.623464i	$0.785725\pi$
$500$		0			0
$501$	13.6225	+	7.86495i	0.608608	+	0.351380i
$502$		0			0
$503$	16.8675	−	29.2154i	0.752085	−	1.30265i	−0.194726	−	0.980858i	$-0.562382\pi$
$503$	16.8675	−	29.2154i	0.752085	−	1.30265i	0.946811	−	0.321791i	$-0.104285\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$		0			0
$509$	9.00000	−	5.19615i	0.398918	−	0.230315i	−0.287099	−	0.957901i	$-0.592691\pi$
$509$	9.00000	−	5.19615i	0.398918	−	0.230315i	0.686017	+	0.727586i	$0.259358\pi$
$510$		0			0
$511$	22.3675	−	38.7416i	0.989480	−	1.71383i
$512$		0			0
$513$	0.122499	+	0.0707248i	0.00540846	+	0.00312258i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.49000	+	11.2410i	0.285430	+	0.494379i
$518$		0			0
$519$	−12.7550			−0.559882
$520$		0			0
$521$	21.2450			0.930760			0.465380	−	0.885111i	$-0.345918\pi$
$521$	21.2450			0.930760			0.465380	+	0.885111i	$0.345918\pi$
$522$		0			0
$523$	9.36750	+	16.2250i	0.409612	+	0.709469i	0.994846	−	0.101395i	$-0.0323307\pi$
$523$	9.36750	+	16.2250i	0.409612	+	0.709469i	−0.585234	+	0.810864i	$0.698997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	+	3.46410i	0.261364	+	0.150899i
$528$		0			0
$529$	−14.7450	+	25.5391i	−0.641087	+	1.11040i
$530$		0			0
$531$	−1.62250	+	0.936750i	−0.0704105	+	0.0406515i
$532$		0			0
$533$	−18.7350	−	18.0278i	−0.811503	−	0.780869i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.24500	+	16.0128i	−0.398951	+	0.691004i
$538$		0			0
$539$	18.0000	+	10.3923i	0.775315	+	0.447628i
$540$		0			0
$541$			21.0675i			0.905763i	0.891571	+	0.452881i	$0.149604\pi$
$541$			21.0675i			0.905763i	−0.891571	+	0.452881i	$0.850396\pi$
$542$		0			0
$543$	−5.74500	−	9.95063i	−0.246541	−	0.427022i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.75500			0.417094			0.208547	−	0.978012i	$-0.433127\pi$
$547$	9.75500			0.417094			0.208547	+	0.978012i	$0.433127\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			0.741903i			0.0316061i
$552$		0			0
$553$	−25.7450	−	14.8639i	−1.09479	−	0.632077i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.9800	+	16.1543i	−1.18555	+	0.684478i	−0.957292	−	0.289123i	$-0.906636\pi$
$557$	−27.9800	+	16.1543i	−1.18555	+	0.684478i	−0.228258	+	0.973601i	$0.573303\pi$
$558$		0			0
$559$	14.8575	+	3.67628i	0.628405	+	0.155490i
$560$		0			0
$561$	−6.00000	+	3.46410i	−0.253320	+	0.146254i
$562$		0			0
$563$	−19.2450	+	33.3333i	−0.811080	+	1.40483i	0.101029	+	0.994883i	$0.467787\pi$
$563$	−19.2450	+	33.3333i	−0.811080	+	1.40483i	−0.912109	+	0.409948i	$0.865547\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			3.60555i			0.151419i
$568$		0			0
$569$	−13.3775	−	23.1705i	−0.560814	−	0.971358i	−0.997426	−	0.0717083i	$-0.977155\pi$
$569$	−13.3775	−	23.1705i	−0.560814	−	0.971358i	0.436612	−	0.899650i	$-0.356178\pi$
$570$		0			0
$571$	26.7350			1.11882			0.559412	−	0.828890i	$-0.311027\pi$
$571$	26.7350			1.11882			0.559412	+	0.828890i	$0.311027\pi$
$572$		0			0
$573$	12.4900			0.521777
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	9.22605i		−	0.384086i	−0.981387	−	0.192043i	$-0.938489\pi$
$577$		−	9.22605i		−	0.384086i	0.981387	−	0.192043i	$-0.0615112\pi$
$578$		0			0
$579$	−7.50000	−	4.33013i	−0.311689	−	0.179954i
$580$		0			0
$581$	9.11249	−	15.7833i	0.378050	−	0.654802i
$582$		0			0
$583$	−9.73499	+	5.62050i	−0.403182	+	0.232777i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.7550	−	11.9829i	0.856651	−	0.494587i	−0.00623863	−	0.999981i	$-0.501986\pi$
$587$	20.7550	−	11.9829i	0.856651	−	0.494587i	0.862889	+	0.505393i	$0.168652\pi$
$588$		0			0
$589$	−0.244998	+	0.424349i	−0.0100950	+	0.0174850i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.87350i			0.0769354i	0.999260	+	0.0384677i	$0.0122477\pi$
$593$			1.87350i			0.0769354i	−0.999260	+	0.0384677i	$0.987752\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.7550			−0.481100
$598$		0			0
$599$	15.7350			0.642914			0.321457	−	0.946924i	$-0.395827\pi$
$599$	15.7350			0.642914			0.321457	+	0.946924i	$0.395827\pi$
$600$		0			0
$601$	5.50000	+	9.52628i	0.224350	+	0.388585i	0.956124	−	0.292962i	$-0.0946409\pi$
$601$	5.50000	+	9.52628i	0.224350	+	0.388585i	−0.731774	+	0.681547i	$0.761308\pi$
$602$		0			0
$603$		−	7.06965i		−	0.287899i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	15.7350	−	27.2538i	0.638664	−	1.10620i	−0.347063	−	0.937842i	$-0.612821\pi$
$607$	15.7350	−	27.2538i	0.638664	−	1.10620i	0.985726	−	0.168356i	$-0.0538458\pi$
$608$		0			0
$609$	−16.3775	+	9.45555i	−0.663650	+	0.383158i
$610$		0			0
$611$	−12.9800	+	3.74700i	−0.525114	+	0.151587i
$612$		0			0
$613$	34.7450	−	20.0600i	1.40334	−	0.810217i	0.408604	−	0.912712i	$-0.366016\pi$
$613$	34.7450	−	20.0600i	1.40334	−	0.810217i	0.994734	+	0.102495i	$0.0326825\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.3575	+	18.6816i	1.30266	+	0.752093i	0.980860	−	0.194713i	$-0.0623776\pi$
$617$	32.3575	+	18.6816i	1.30266	+	0.752093i	0.321803	+	0.946807i	$0.395711\pi$
$618$		0			0
$619$		−	16.8962i		−	0.679114i	−0.940585	−	0.339557i	$-0.889723\pi$
$619$		−	16.8962i		−	0.679114i	0.940585	−	0.339557i	$-0.110277\pi$
$620$		0			0
$621$	−3.62250	−	6.27435i	−0.145366	−	0.251781i
$622$		0			0
$623$	−44.2250			−1.77184
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.244998	−	0.424349i	−0.00978428	−	0.0169469i
$628$		0			0
$629$			14.4222i			0.575051i
$630$		0			0
$631$	17.8775	+	10.3216i	0.711692	+	0.410896i	0.811687	−	0.584092i	$-0.198549\pi$
$631$	17.8775	+	10.3216i	0.711692	+	0.410896i	−0.0999952	+	0.994988i	$0.531883\pi$
$632$		0			0
$633$	−3.24500	+	5.62050i	−0.128977	+	0.223395i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.0000	+	15.5885i	−0.594322	+	0.617637i
$638$		0			0
$639$	−6.24500	+	3.60555i	−0.247048	+	0.142633i
$640$		0			0
$641$	−9.11249	+	15.7833i	−0.359922	+	0.623403i	−0.987947	−	0.154790i	$-0.950530\pi$
$641$	−9.11249	+	15.7833i	−0.359922	+	0.623403i	0.628026	+	0.778193i	$0.283863\pi$
$642$		0			0
$643$	−34.1025	−	19.6891i	−1.34487	−	0.776462i	−0.357353	−	0.933969i	$-0.616321\pi$
$643$	−34.1025	−	19.6891i	−1.34487	−	0.776462i	−0.987518	+	0.157508i	$0.949654\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.6225	−	32.2551i	−0.732126	−	1.26808i	−0.955973	−	0.293455i	$-0.905195\pi$
$647$	−18.6225	−	32.2551i	−0.732126	−	1.26808i	0.223847	−	0.974624i	$-0.428138\pi$
$648$		0			0
$649$	6.49000			0.254755
$650$		0			0
$651$	−12.4900			−0.489522
$652$		0			0
$653$	−4.75500	−	8.23591i	−0.186078	−	0.322296i	0.757862	−	0.652415i	$-0.226244\pi$
$653$	−4.75500	−	8.23591i	−0.186078	−	0.322296i	−0.943939	+	0.330120i	$0.892911\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.7450	−	6.20363i	−0.419202	−	0.242027i
$658$		0			0
$659$	19.4900	−	33.7577i	0.759222	−	1.31501i	−0.184025	−	0.982922i	$-0.558913\pi$
$659$	19.4900	−	33.7577i	0.759222	−	1.31501i	0.943248	−	0.332090i	$-0.107754\pi$
$660$		0			0
$661$	−28.9900	+	16.7374i	−1.12758	+	0.651009i	−0.943325	−	0.331870i	$-0.892321\pi$
$661$	−28.9900	+	16.7374i	−1.12758	+	0.651009i	−0.184255	+	0.982878i	$0.558987\pi$
$662$		0			0
$663$	−2.00000	−	6.92820i	−0.0776736	−	0.269069i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	19.0000	−	32.9090i	0.735683	−	1.27424i
$668$		0			0
$669$	2.63250	+	1.51988i	0.101778	+	0.0587618i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	0.654394	−	0.756153i	$-0.272924\pi$
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	−0.982045	+	0.188645i	$0.939590\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.73499			−0.220414			−0.110207	−	0.993909i	$-0.535151\pi$
$677$	−5.73499			−0.220414			−0.110207	+	0.993909i	$0.535151\pi$
$678$		0			0
$679$	−25.4900	−	44.1500i	−0.978216	−	1.69432i
$680$		0			0
$681$			4.77180i			0.182856i
$682$		0			0
$683$	11.1125	+	6.41580i	0.425208	+	0.245494i	0.697303	−	0.716777i	$-0.254383\pi$
$683$	11.1125	+	6.41580i	0.425208	+	0.245494i	−0.272095	+	0.962270i	$0.587717\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	20.2350	−	11.6827i	0.772013	−	0.445722i
$688$		0			0
$689$	−3.24500	−	11.2410i	−0.123625	−	0.428248i
$690$		0			0
$691$	−12.1225	+	6.99893i	−0.461162	+	0.266252i	−0.712533	−	0.701639i	$-0.752452\pi$
$691$	−12.1225	+	6.99893i	−0.461162	+	0.266252i	0.251371	+	0.967891i	$0.419119\pi$
$692$		0			0
$693$	6.24500	−	10.8167i	0.237228	−	0.410891i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	14.4222i		−	0.546280i
$698$		0			0
$699$	−7.62250	−	13.2026i	−0.288309	−	0.499367i
$700$		0			0
$701$	−26.9800			−1.01902			−0.509510	−	0.860465i	$-0.670173\pi$
$701$	−26.9800			−1.01902			−0.509510	+	0.860465i	$0.670173\pi$
$702$		0			0
$703$	−1.02001			−0.0384703
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	4.48890i		−	0.168823i
$708$		0			0
$709$	1.25500	+	0.724576i	0.0471326	+	0.0272120i	0.523381	−	0.852099i	$-0.324670\pi$
$709$	1.25500	+	0.724576i	0.0471326	+	0.0272120i	−0.476249	+	0.879311i	$0.658004\pi$
$710$		0			0
$711$	−4.12250	+	7.14038i	−0.154606	+	0.267785i
$712$		0			0
$713$	21.7350	−	12.5487i	0.813982	−	0.469953i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.86750	−	2.81025i	0.181780	−	0.104951i
$718$		0			0
$719$	25.6225	−	44.3795i	0.955558	−	1.65507i	0.222472	−	0.974939i	$-0.428587\pi$
$719$	25.6225	−	44.3795i	0.955558	−	1.65507i	0.733086	−	0.680136i	$-0.238079\pi$
$720$		0			0
$721$	−5.47999	−	3.16387i	−0.204086	−	0.117829i
$722$		0			0
$723$		−	11.8415i		−	0.440388i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−11.2250			−0.416312			−0.208156	−	0.978096i	$-0.566746\pi$
$727$	−11.2250			−0.416312			−0.208156	+	0.978096i	$0.566746\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.24500	+	7.35255i	0.157007	+	0.271944i
$732$		0			0
$733$		−	36.6560i		−	1.35392i	−0.736020	−	0.676960i	$-0.763297\pi$
$733$		−	36.6560i		−	1.35392i	0.736020	−	0.676960i	$-0.236703\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.2450	+	21.2090i	−0.451050	+	0.781242i
$738$		0			0
$739$	−27.4900	+	15.8714i	−1.01124	+	0.583837i	−0.911553	−	0.411182i	$-0.865116\pi$
$739$	−27.4900	+	15.8714i	−1.01124	+	0.583837i	−0.0996826	+	0.995019i	$0.531783\pi$
$740$		0			0
$741$	0.489996	−	0.141450i	0.0180005	−	0.00519628i
$742$		0			0
$743$	17.7550	−	10.2509i	0.651368	−	0.376067i	−0.137612	−	0.990486i	$-0.543943\pi$
$743$	17.7550	−	10.2509i	0.651368	−	0.376067i	0.788980	+	0.614419i	$0.210609\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.37750	−	2.52735i	−0.160164	−	0.0924710i
$748$		0			0
$749$		−	33.3333i		−	1.21797i
$750$		0			0
$751$	18.2450	+	31.6013i	0.665769	+	1.15315i	0.979076	+	0.203494i	$0.0652299\pi$
$751$	18.2450	+	31.6013i	0.665769	+	1.15315i	−0.313307	+	0.949652i	$0.601437\pi$
$752$		0			0
$753$	13.2450			0.482675
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−13.5000	−	23.3827i	−0.490666	−	0.849858i	0.509276	−	0.860603i	$-0.329913\pi$
$757$	−13.5000	−	23.3827i	−0.490666	−	0.849858i	−0.999942	+	0.0107448i	$0.996580\pi$
$758$		0			0
$759$			25.0974i			0.910978i
$760$		0			0
$761$	3.00000	+	1.73205i	0.108750	+	0.0627868i	0.553388	−	0.832923i	$-0.313335\pi$
$761$	3.00000	+	1.73205i	0.108750	+	0.0627868i	−0.444639	+	0.895710i	$0.646668\pi$
$762$		0			0
$763$	32.2450	−	55.8500i	1.16735	−	2.02190i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.62250	+	6.55725i	−0.0585850	+	0.236769i
$768$		0			0
$769$	10.7450	−	6.20363i	0.387475	−	0.223709i	−0.293591	−	0.955931i	$-0.594850\pi$
$769$	10.7450	−	6.20363i	0.387475	−	0.223709i	0.681065	+	0.732223i	$0.261517\pi$
$770$		0			0
$771$	14.4900	−	25.0974i	0.521844	−	0.903861i
$772$		0			0
$773$	−2.26501	−	1.30770i	−0.0814666	−	0.0470348i	0.458713	−	0.888584i	$-0.348310\pi$
$773$	−2.26501	−	1.30770i	−0.0814666	−	0.0470348i	−0.540180	+	0.841550i	$0.681644\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−13.0000	−	22.5167i	−0.466372	−	0.807781i
$778$		0			0
$779$	1.02001			0.0365456
$780$		0			0
$781$	24.9800			0.893854
$782$		0			0
$783$	2.62250	+	4.54230i	0.0937205	+	0.162329i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	0.0766075	−	0.997061i	$-0.475591\pi$
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	−0.825177	+	0.564875i	$0.808924\pi$
$788$		0			0
$789$	−15.4900	+	26.8295i	−0.551458	+	0.955154i
$790$		0			0
$791$	37.4700	−	21.6333i	1.33228	−	0.769192i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.37750	−	2.38590i	0.0487936	−	0.0845130i	−0.840597	−	0.541661i	$-0.817796\pi$
$797$	1.37750	−	2.38590i	0.0487936	−	0.0845130i	0.889391	+	0.457148i	$0.151129\pi$
$798$		0			0
$799$	−6.49000	−	3.74700i	−0.229600	−	0.132559i
$800$		0			0
$801$			12.2658i			0.433391i
$802$		0			0
$803$	21.4900	+	37.2218i	0.758365	+	1.31353i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	24.0000			0.844840
$808$		0			0
$809$	−20.8675	−	36.1436i	−0.733662	−	1.27074i	−0.955308	−	0.295613i	$-0.904476\pi$
$809$	−20.8675	−	36.1436i	−0.733662	−	1.27074i	0.221646	−	0.975127i	$-0.428857\pi$
$810$		0			0
$811$			27.5714i			0.968162i	0.875023	+	0.484081i	$0.160846\pi$
$811$			27.5714i			0.968162i	−0.875023	+	0.484081i	$0.839154\pi$
$812$		0			0
$813$	−5.87750	−	3.39338i	−0.206133	−	0.119011i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.520008	+	0.300227i	−0.0181928	+	0.0105036i
$818$		0			0
$819$	9.36750	+	9.01388i	0.327327	+	0.314970i
$820$		0			0
$821$	−45.0925	+	26.0342i	−1.57374	+	0.908598i	−0.578034	+	0.816013i	$0.696180\pi$
$821$	−45.0925	+	26.0342i	−1.57374	+	0.908598i	−0.995705	+	0.0925857i	$0.970487\pi$
$822$		0			0
$823$	14.3675	−	24.8852i	0.500819	−	0.867445i	−0.499180	−	0.866498i	$-0.666365\pi$
$823$	14.3675	−	24.8852i	0.500819	−	0.867445i	1.00000		0.000946492i	$-0.000301278\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	6.92820i		−	0.240917i	−0.992718	−	0.120459i	$-0.961563\pi$
$827$		−	6.92820i		−	0.240917i	0.992718	−	0.120459i	$-0.0384365\pi$
$828$		0			0
$829$	−26.7450	−	46.3237i	−0.928892	−	1.60889i	−0.785179	−	0.619269i	$-0.787429\pi$
$829$	−26.7450	−	46.3237i	−0.928892	−	1.60889i	−0.143713	−	0.989619i	$-0.545904\pi$
$830$		0			0
$831$	27.4900			0.953617
$832$		0			0
$833$	−12.0000			−0.415775
$834$		0			0
$835$		0			0
$836$		0			0
$837$			3.46410i			0.119737i
$838$		0			0
$839$	1.37750	+	0.795301i	0.0475566	+	0.0274568i	0.523590	−	0.851970i	$-0.324592\pi$
$839$	1.37750	+	0.795301i	0.0475566	+	0.0274568i	−0.476033	+	0.879427i	$0.657926\pi$
$840$		0			0
$841$	0.744998	−	1.29037i	0.0256896	−	0.0444957i
$842$		0			0
$843$	13.3775	−	7.72350i	0.460746	−	0.266012i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.12250	+	1.80278i	−0.107290	+	0.0619441i
$848$		0			0
$849$	12.4900	−	21.6333i	0.428656	−	0.742453i
$850$		0			0
$851$	45.2450	+	26.1222i	1.55098	+	0.895458i
$852$		0			0
$853$		−	9.82651i		−	0.336453i	−0.985748	−	0.168227i	$-0.946196\pi$
$853$		−	9.82651i		−	0.336453i	0.985748	−	0.168227i	$-0.0538040\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.5100			−0.529812			−0.264906	−	0.964274i	$-0.585341\pi$
$857$	−15.5100			−0.529812			−0.264906	+	0.964274i	$0.585341\pi$
$858$		0			0
$859$	−22.7350			−0.775708			−0.387854	−	0.921721i	$-0.626784\pi$
$859$	−22.7350			−0.775708			−0.387854	+	0.921721i	$0.626784\pi$
$860$		0			0
$861$	13.0000	+	22.5167i	0.443039	+	0.767366i
$862$		0			0
$863$			4.31280i			0.146809i	0.997302	+	0.0734047i	$0.0233865\pi$
$863$			4.31280i			0.146809i	−0.997302	+	0.0734047i	$0.976614\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$		0			0
$869$	24.7350	−	14.2808i	0.839077	−	0.484441i
$870$		0			0
$871$	−18.3675	−	17.6741i	−0.622359	−	0.598865i
$872$		0			0
$873$	−12.2450	+	7.06965i	−0.414430	+	0.239271i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.4800	−	13.5562i	−0.792863	−	0.457760i	0.0481065	−	0.998842i	$-0.484681\pi$
$877$	−23.4800	−	13.5562i	−0.792863	−	0.457760i	−0.840969	+	0.541083i	$0.818015\pi$
$878$		0			0
$879$		−	19.4769i		−	0.656940i
$880$		0			0
$881$	13.7350	+	23.7897i	0.462744	+	0.801496i	0.999097	−	0.0424983i	$-0.0135317\pi$
$881$	13.7350	+	23.7897i	0.462744	+	0.801496i	−0.536353	+	0.843994i	$0.680198\pi$
$882$		0			0
$883$	20.4900			0.689543			0.344772	−	0.938687i	$-0.387956\pi$
$883$	20.4900			0.689543			0.344772	+	0.938687i	$0.387956\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.37750	−	9.31410i	−0.180559	−	0.312737i	0.761512	−	0.648151i	$-0.224457\pi$
$887$	−5.37750	−	9.31410i	−0.180559	−	0.312737i	−0.942071	+	0.335414i	$0.891124\pi$
$888$		0			0
$889$		−	13.5389i		−	0.454079i
$890$		0			0
$891$	−3.00000	−	1.73205i	−0.100504	−	0.0580259i
$892$		0			0
$893$	0.265006	−	0.459004i	0.00886809	−	0.0153600i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−25.3575	−	6.27435i	−0.846662	−	0.209495i
$898$		0			0
$899$	−15.7350	+	9.08460i	−0.524791	+	0.302988i
$900$		0			0
$901$	3.24500	−	5.62050i	0.108107	−	0.187246i
$902$		0			0
$903$	−13.2550	−	7.65278i	−0.441099	−	0.254669i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−10.2450	−	17.7449i	−0.340180	−	0.589208i	0.644286	−	0.764784i	$-0.277155\pi$
$907$	−10.2450	−	17.7449i	−0.340180	−	0.589208i	−0.984466	+	0.175576i	$0.943821\pi$
$908$		0			0
$909$	−1.24500			−0.0412940
$910$		0			0
$911$	27.2450			0.902667			0.451334	−	0.892355i	$-0.350948\pi$
$911$	27.2450			0.902667			0.451334	+	0.892355i	$0.350948\pi$
$912$		0			0
$913$	8.75500	+	15.1641i	0.289748	+	0.501859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.88751	+	2.24445i	0.128377	+	0.0741183i
$918$		0			0
$919$	−14.1225	+	24.4609i	−0.465858	+	0.806890i	−0.999240	−	0.0389846i	$-0.987588\pi$
$919$	−14.1225	+	24.4609i	−0.465858	+	0.806890i	0.533382	+	0.845875i	$0.320921\pi$
$920$		0			0
$921$	−18.4900	+	10.6752i	−0.609266	+	0.351760i
$922$		0			0
$923$	−6.24500	+	25.2389i	−0.205557	+	0.830747i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.877501	+	1.51988i	−0.0288209	+	0.0499193i
$928$		0			0
$929$	45.9800	+	26.5466i	1.50855	+	0.870964i	0.999950	+	0.00996399i	$0.00317169\pi$
$929$	45.9800	+	26.5466i	1.50855	+	0.870964i	0.508604	+	0.861000i	$0.330162\pi$
$930$		0			0
$931$		−	0.848698i		−	0.0278150i
$932$		0			0
$933$	−13.8675	−	24.0192i	−0.454001	−	0.786354i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−34.5100			−1.12739			−0.563696	−	0.825982i	$-0.690621\pi$
$937$	−34.5100			−1.12739			−0.563696	+	0.825982i	$0.690621\pi$
$938$		0			0
$939$	−3.50000	−	6.06218i	−0.114218	−	0.197832i
$940$		0			0
$941$		−	15.1641i		−	0.494336i	−0.968973	−	0.247168i	$-0.920500\pi$
$941$		−	15.1641i		−	0.494336i	0.968973	−	0.247168i	$-0.0794999\pi$
$942$		0			0
$943$	−45.2450	−	26.1222i	−1.47338	−	0.850656i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.7350	+	14.2808i	−0.803779	+	0.464062i	−0.844791	−	0.535096i	$-0.820275\pi$
$947$	−24.7350	+	14.2808i	−0.803779	+	0.464062i	0.0410117	+	0.999159i	$0.486942\pi$
$948$		0			0
$949$	−42.9800	+	12.4073i	−1.39519	+	0.402757i
$950$		0			0
$951$	10.8675	−	6.27435i	0.352403	−	0.203460i
$952$		0			0
$953$	−26.2450	+	45.4577i	−0.850159	+	1.47252i	0.0309057	+	0.999522i	$0.490161\pi$
$953$	−26.2450	+	45.4577i	−0.850159	+	1.47252i	−0.881065	+	0.472996i	$0.843172\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	18.1692i		−	0.587327i
$958$		0			0
$959$	−35.6225	−	61.7000i	−1.15031	−	1.99240i
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$	−9.24500			−0.297916
$964$		0			0
$965$		0			0
$966$		0			0
$967$			28.2786i			0.909379i	0.890650	+	0.454689i	$0.150250\pi$
$967$			28.2786i			0.909379i	−0.890650	+	0.454689i	$0.849750\pi$
$968$		0			0
$969$	0.244998	+	0.141450i	0.00787047	+	0.00454402i
$970$		0			0
$971$	−27.1125	+	46.9602i	−0.870081	+	1.50703i	−0.00816974	+	0.999967i	$0.502601\pi$
$971$	−27.1125	+	46.9602i	−0.870081	+	1.50703i	−0.861912	+	0.507059i	$0.830733\pi$
$972$		0			0
$973$	38.2350	−	22.0750i	1.22576	−	0.707691i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	40.2250	−	23.2239i	1.28691	−	0.742999i	0.308809	−	0.951124i	$-0.400070\pi$
$977$	40.2250	−	23.2239i	1.28691	−	0.742999i	0.978102	+	0.208125i	$0.0667362\pi$
$978$		0			0
$979$	21.2450	−	36.7974i	0.678993	−	1.17605i
$980$		0			0
$981$	−15.4900	−	8.94315i	−0.494558	−	0.285533i
$982$		0			0
$983$		−	34.4649i		−	1.09926i	−0.835408	−	0.549630i	$-0.814769\pi$
$983$		−	34.4649i		−	1.09926i	0.835408	−	0.549630i	$-0.185231\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	13.5100			0.430028
$988$		0			0
$989$	30.7550			0.977952
$990$		0			0
$991$	−15.6125	−	27.0416i	−0.495947	−	0.859006i	0.504042	−	0.863679i	$-0.331846\pi$
$991$	−15.6125	−	27.0416i	−0.495947	−	0.859006i	−0.999989	+	0.00467341i	$0.998512\pi$
$992$		0			0
$993$			6.78675i			0.215371i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	−0.888800	−	0.458295i	$-0.848460\pi$
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	0.841295	+	0.540576i	$0.181794\pi$
$998$		0			0
$999$	−6.24500	+	3.60555i	−0.197583	+	0.114075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.cd.h.2701.1	yes	4
5.2	odd	4		3900.2.bw.i.49.4		8
5.3	odd	4		3900.2.bw.i.49.1		8
5.4	even	2		3900.2.cd.f.2701.2	yes	4
13.4	even	6	inner	3900.2.cd.h.901.1	yes	4
65.4	even	6		3900.2.cd.f.901.2	✓	4
65.17	odd	12		3900.2.bw.i.2149.1		8
65.43	odd	12		3900.2.bw.i.2149.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3900.2.bw.i.49.1		8	5.3	odd	4
3900.2.bw.i.49.4		8	5.2	odd	4
3900.2.bw.i.2149.1		8	65.17	odd	12
3900.2.bw.i.2149.4		8	65.43	odd	12
3900.2.cd.f.901.2	✓	4	65.4	even	6
3900.2.cd.f.2701.2	yes	4	5.4	even	2
3900.2.cd.h.901.1	yes	4	13.4	even	6	inner
3900.2.cd.h.2701.1	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.cd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-3.12250 - 1.80278i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{17} +(-0.122499 - 0.0707248i) q^{19} -3.60555i q^{21} +(3.62250 + 6.27435i) q^{23} -1.00000 q^{27} +(-2.62250 - 4.54230i) q^{29} -3.46410i q^{31} +(3.00000 + 1.73205i) q^{33} +(6.24500 - 3.60555i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(-6.24500 + 3.60555i) q^{41} +(2.12250 - 3.67628i) q^{43} +3.74700i q^{47} +(3.00000 + 5.19615i) q^{49} -2.00000 q^{51} -3.24500 q^{53} -0.141450i q^{57} +(1.62250 + 0.936750i) q^{59} +(3.12250 - 1.80278i) q^{63} +(-6.12250 + 3.53483i) q^{67} +(-3.62250 + 6.27435i) q^{69} +(6.24500 + 3.60555i) q^{71} +12.4073i q^{73} -12.4900 q^{77} +8.24500 q^{79} +(-0.500000 - 0.866025i) q^{81} +5.05470i q^{83} +(2.62250 - 4.54230i) q^{87} +(10.6225 - 6.13290i) q^{89} +(3.12250 - 12.6194i) q^{91} +(3.00000 - 1.73205i) q^{93} +(12.2450 + 7.06965i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{9} + 12 q^{11} + 4 q^{13} - 4 q^{17} + 12 q^{19} + 2 q^{23} - 4 q^{27} + 2 q^{29} + 12 q^{33} - 10 q^{39} - 4 q^{43} + 12 q^{49} - 8 q^{51} + 12 q^{53} - 6 q^{59} - 12 q^{67} - 2 q^{69}+ \cdots + 24 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^9 + 12 * q^11 + 4 * q^13 - 4 * q^17 + 12 * q^19 + 2 * q^23 - 4 * q^27 + 2 * q^29 + 12 * q^33 - 10 * q^39 - 4 * q^43 + 12 * q^49 - 8 * q^51 + 12 * q^53 - 6 * q^59 - 12 * q^67 - 2 * q^69 + 8 * q^79 - 2 * q^81 - 2 * q^87 + 30 * q^89 + 12 * q^93 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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