LMFDB - Embedded newform 3900.2.bw.i.2149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3900,2,Mod(49,3900)] 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, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3900.49"); 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.bw (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,4,0,24,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2149.4
Root			$1.99426 + 1.15139i$ of defining polynomial
Character	$\chi$	$=$	3900.2149
Dual form			3900.2.bw.i.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(1.80278 + 3.12250i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +(3.46410 + 1.00000i) q^{13} +(-1.73205 + 1.00000i) q^{17} +(0.122499 - 0.0707248i) q^{19} +3.60555i q^{21} +(6.27435 + 3.62250i) q^{23} +1.00000i q^{27} +(2.62250 - 4.54230i) q^{29} +3.46410i q^{31} +(1.73205 + 3.00000i) q^{33} +(3.60555 - 6.24500i) q^{37} +(2.50000 + 2.59808i) q^{39} +(-6.24500 - 3.60555i) q^{41} +(-3.67628 + 2.12250i) q^{43} -3.74700 q^{47} +(-3.00000 + 5.19615i) q^{49} -2.00000 q^{51} -3.24500i q^{53} +0.141450 q^{57} +(-1.62250 + 0.936750i) q^{59} +(-1.80278 + 3.12250i) q^{63} +(-3.53483 + 6.12250i) q^{67} +(3.62250 + 6.27435i) q^{69} +(6.24500 - 3.60555i) q^{71} +12.4073 q^{73} +12.4900i q^{77} -8.24500 q^{79} +(-0.500000 + 0.866025i) q^{81} +5.05470 q^{83} +(4.54230 - 2.62250i) q^{87} +(-10.6225 - 6.13290i) q^{89} +(3.12250 + 12.6194i) q^{91} +(-1.73205 + 3.00000i) q^{93} +(-7.06965 - 12.2450i) q^{97} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9} + 24 q^{11} - 24 q^{19} - 4 q^{29} + 20 q^{39} - 24 q^{49} - 16 q^{51} + 12 q^{59} + 4 q^{69} - 16 q^{79} - 4 q^{81} - 60 q^{89}+O(q^{100}) $ 8 * q + 4 * q^9 + 24 * q^11 - 24 * q^19 - 4 * q^29 + 20 * q^39 - 24 * q^49 - 16 * q^51 + 12 * q^59 + 4 * q^69 - 16 * q^79 - 4 * q^81 - 60 * q^89

Character values

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

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

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.80278	+	3.12250i	0.681385	+	1.18019i	0.974558	+	0.224134i	$0.0719554\pi$
$7$	1.80278	+	3.12250i	0.681385	+	1.18019i	−0.293173	+	0.956059i	$0.594711\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$		0			0
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	0.122499	−	0.0707248i	0.0281032	−	0.0162254i	−0.485883	−	0.874024i	$-0.661502\pi$
$19$	0.122499	−	0.0707248i	0.0281032	−	0.0162254i	0.513986	+	0.857799i	$0.328168\pi$
$20$		0			0
$21$			3.60555i			0.786796i
$22$		0			0
$23$	6.27435	+	3.62250i	1.30829	+	0.755343i	0.981811	−	0.189860i	$-0.0608035\pi$
$23$	6.27435	+	3.62250i	1.30829	+	0.755343i	0.326482	+	0.945203i	$0.394137\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	2.62250	−	4.54230i	0.486986	−	0.843484i	−0.512902	−	0.858447i	$-0.671430\pi$
$29$	2.62250	−	4.54230i	0.486986	−	0.843484i	0.999888	+	0.0149628i	$0.00476299\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		0			0
$33$	1.73205	+	3.00000i	0.301511	+	0.522233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.60555	−	6.24500i	0.592749	−	1.02667i	−0.401111	−	0.916029i	$-0.631376\pi$
$37$	3.60555	−	6.24500i	0.592749	−	1.02667i	0.993860	−	0.110642i	$-0.0352907\pi$
$38$		0			0
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	−6.24500	−	3.60555i	−0.975305	−	0.563093i	−0.0744555	−	0.997224i	$-0.523722\pi$
$41$	−6.24500	−	3.60555i	−0.975305	−	0.563093i	−0.900849	+	0.434132i	$0.857055\pi$
$42$		0			0
$43$	−3.67628	+	2.12250i	−0.560627	+	0.323678i	−0.753397	−	0.657566i	$-0.771586\pi$
$43$	−3.67628	+	2.12250i	−0.560627	+	0.323678i	0.192770	+	0.981244i	$0.438253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.74700			−0.546556			−0.273278	−	0.961935i	$-0.588108\pi$
$47$	−3.74700			−0.546556			−0.273278	+	0.961935i	$0.588108\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$		−	3.24500i		−	0.445735i	−0.974849	−	0.222867i	$-0.928458\pi$
$53$		−	3.24500i		−	0.445735i	0.974849	−	0.222867i	$-0.0715417\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.141450			0.0187355
$58$		0			0
$59$	−1.62250	+	0.936750i	−0.211231	+	0.121954i	−0.601884	−	0.798584i	$-0.705583\pi$
$59$	−1.62250	+	0.936750i	−0.211231	+	0.121954i	0.390652	+	0.920538i	$0.372250\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$	−1.80278	+	3.12250i	−0.227128	+	0.393398i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.53483	+	6.12250i	−0.431848	+	0.747982i	−0.997032	−	0.0769821i	$-0.975472\pi$
$67$	−3.53483	+	6.12250i	−0.431848	+	0.747982i	0.565185	+	0.824964i	$0.308805\pi$
$68$		0			0
$69$	3.62250	+	6.27435i	0.436098	+	0.755343i
$70$		0			0
$71$	6.24500	−	3.60555i	0.741145	−	0.427900i	−0.0813405	−	0.996686i	$-0.525920\pi$
$71$	6.24500	−	3.60555i	0.741145	−	0.427900i	0.822485	+	0.568786i	$0.192587\pi$
$72$		0			0
$73$	12.4073			1.45216			0.726080	−	0.687611i	$-0.241340\pi$
$73$	12.4073			1.45216			0.726080	+	0.687611i	$0.241340\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			12.4900i			1.42337i
$78$		0			0
$79$	−8.24500			−0.927635			−0.463817	−	0.885931i	$-0.653521\pi$
$79$	−8.24500			−0.927635			−0.463817	+	0.885931i	$0.653521\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	5.05470			0.554826			0.277413	−	0.960751i	$-0.410523\pi$
$83$	5.05470			0.554826			0.277413	+	0.960751i	$0.410523\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.54230	−	2.62250i	0.486986	−	0.281161i
$88$		0			0
$89$	−10.6225	−	6.13290i	−1.12598	−	0.650086i	−0.183061	−	0.983102i	$-0.558601\pi$
$89$	−10.6225	−	6.13290i	−1.12598	−	0.650086i	−0.942921	+	0.333015i	$0.891934\pi$
$90$		0			0
$91$	3.12250	+	12.6194i	0.327327	+	1.32288i
$92$		0			0
$93$	−1.73205	+	3.00000i	−0.179605	+	0.311086i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.06965	−	12.2450i	−0.717814	−	1.24329i	−0.961864	−	0.273528i	$-0.911809\pi$
$97$	−7.06965	−	12.2450i	−0.717814	−	1.24329i	0.244049	−	0.969763i	$-0.421524\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	0.622499	−	1.07820i	0.0619410	−	0.107285i	−0.833392	−	0.552682i	$-0.813604\pi$
$101$	0.622499	−	1.07820i	0.0619410	−	0.107285i	0.895333	+	0.445397i	$0.146938\pi$
$102$		0			0
$103$			1.75500i			0.172925i	0.996255	+	0.0864627i	$0.0275564\pi$
$103$			1.75500i			0.172925i	−0.996255	+	0.0864627i	$0.972444\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.00640	−	4.62250i	−0.774008	−	0.446874i	0.0602944	−	0.998181i	$-0.480796\pi$
$107$	−8.00640	−	4.62250i	−0.774008	−	0.446874i	−0.834303	+	0.551307i	$0.814129\pi$
$108$		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
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.0760733	−	0.997102i	$-0.475762\pi$
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.901553	+	0.432670i	$0.142428\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.866025	+	3.50000i	0.0800641	+	0.323575i
$118$		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
$123$	−3.60555	−	6.24500i	−0.325102	−	0.563093i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.25193	−	1.87750i	−0.288562	−	0.166601i	0.348731	−	0.937223i	$-0.386613\pi$
$127$	−3.25193	−	1.87750i	−0.288562	−	0.166601i	−0.637293	+	0.770621i	$0.719946\pi$
$128$		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
$133$	0.441676	+	0.255002i	0.0382982	+	0.0221115i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.87990	−	17.1125i	−0.844097	−	1.46202i	−0.886403	−	0.462914i	$-0.846804\pi$
$137$	−9.87990	−	17.1125i	−0.844097	−	1.46202i	0.0423059	−	0.999105i	$-0.486530\pi$
$138$		0			0
$139$	6.12250	+	10.6045i	0.519304	+	0.899460i	0.999748	+	0.0224352i	$0.00714194\pi$
$139$	6.12250	+	10.6045i	0.519304	+	0.899460i	−0.480445	+	0.877025i	$0.659525\pi$
$140$		0			0
$141$	−3.24500	−	1.87350i	−0.273278	−	0.157777i
$142$		0			0
$143$	8.66025	+	9.00000i	0.724207	+	0.752618i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.19615	+	3.00000i	−0.428571	+	0.247436i
$148$		0			0
$149$	−13.3775	+	7.72350i	−1.09593	+	0.632734i	−0.935148	−	0.354256i	$-0.884734\pi$
$149$	−13.3775	+	7.72350i	−1.09593	+	0.632734i	−0.160779	+	0.986990i	$0.551401\pi$
$150$		0			0
$151$		−	0.424349i		−	0.0345330i	−0.999851	−	0.0172665i	$-0.994504\pi$
$151$		−	0.424349i		−	0.0345330i	0.999851	−	0.0172665i	$-0.00549638\pi$
$152$		0			0
$153$	−1.73205	−	1.00000i	−0.140028	−	0.0808452i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			17.0000i			1.35675i	0.734717	+	0.678374i	$0.237315\pi$
$157$			17.0000i			1.35675i	−0.734717	+	0.678374i	$0.762685\pi$
$158$		0			0
$159$	1.62250	−	2.81025i	0.128673	−	0.222867i
$160$		0			0
$161$			26.1222i			2.05872i
$162$		0			0
$163$	8.94315	+	15.4900i	0.700482	+	1.21327i	0.968297	+	0.249800i	$0.0803649\pi$
$163$	8.94315	+	15.4900i	0.700482	+	1.21327i	−0.267816	+	0.963470i	$0.586302\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.86495	−	13.6225i	0.608608	−	1.05414i	−0.382862	−	0.923806i	$-0.625061\pi$
$167$	7.86495	−	13.6225i	0.608608	−	1.05414i	0.991470	−	0.130335i	$-0.0416053\pi$
$168$		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
$173$	11.0462	−	6.37750i	0.839824	−	0.484872i	−0.0173806	−	0.999849i	$-0.505533\pi$
$173$	11.0462	−	6.37750i	0.839824	−	0.484872i	0.857204	+	0.514977i	$0.172199\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.87350			−0.140821
$178$		0			0
$179$	−9.24500	+	16.0128i	−0.691004	+	1.19685i	0.280506	+	0.959852i	$0.409498\pi$
$179$	−9.24500	+	16.0128i	−0.691004	+	1.19685i	−0.971509	+	0.237001i	$0.923836\pi$
$180$		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
$187$	−6.92820			−0.506640
$188$		0			0
$189$	−3.12250	+	1.80278i	−0.227128	+	0.131133i
$190$		0			0
$191$	6.24500	+	10.8167i	0.451872	+	0.782666i	0.998502	−	0.0547085i	$-0.0174230\pi$
$191$	6.24500	+	10.8167i	0.451872	+	0.782666i	−0.546630	+	0.837374i	$0.684090\pi$
$192$		0			0
$193$	4.33013	−	7.50000i	0.311689	−	0.539862i	−0.667039	−	0.745023i	$-0.732439\pi$
$193$	4.33013	−	7.50000i	0.311689	−	0.539862i	0.978728	+	0.205161i	$0.0657718\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$		0			0
$199$	5.87750	+	10.1801i	0.416645	+	0.721650i	0.995600	−	0.0937095i	$-0.0298725\pi$
$199$	5.87750	+	10.1801i	0.416645	+	0.721650i	−0.578955	+	0.815360i	$0.696539\pi$
$200$		0			0
$201$	−6.12250	+	3.53483i	−0.431848	+	0.249327i
$202$		0			0
$203$	18.9111			1.32730
$204$		0			0
$205$		0			0
$206$		0			0
$207$			7.24500i			0.503562i
$208$		0			0
$209$	0.489996			0.0338937
$210$		0			0
$211$	3.24500	−	5.62050i	0.223395	−	0.386931i	−0.732442	−	0.680830i	$-0.761619\pi$
$211$	3.24500	−	5.62050i	0.223395	−	0.386931i	0.955837	+	0.293898i	$0.0949527\pi$
$212$		0			0
$213$	7.21110			0.494097
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.8167	+	6.24500i	−0.734282	+	0.423938i
$218$		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
$223$	−1.51988	+	2.63250i	−0.101778	+	0.176285i	−0.912417	−	0.409261i	$-0.865787\pi$
$223$	−1.51988	+	2.63250i	−0.101778	+	0.176285i	0.810639	+	0.585546i	$0.199120\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.38590	−	4.13250i	−0.158358	−	0.274284i	0.775919	−	0.630833i	$-0.217287\pi$
$227$	−2.38590	−	4.13250i	−0.158358	−	0.274284i	−0.934277	+	0.356549i	$0.883953\pi$
$228$		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
$233$		−	15.2450i		−	0.998733i	−0.866391	−	0.499367i	$-0.833566\pi$
$233$		−	15.2450i		−	0.998733i	0.866391	−	0.499367i	$-0.166434\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.14038	−	4.12250i	−0.463817	−	0.267785i
$238$		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	−0.792499	−	0.609873i	$-0.791220\pi$
$241$	−10.2550	+	5.92073i	−0.660583	+	0.381388i	0.131916	+	0.991261i	$0.457887\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.495074	−	0.122499i	0.0315008	−	0.00779442i
$248$		0			0
$249$	4.37750	+	2.52735i	0.277413	+	0.160164i
$250$		0			0
$251$	6.62250	+	11.4705i	0.418008	+	0.724012i	0.995739	−	0.0922157i	$-0.0293949\pi$
$251$	6.62250	+	11.4705i	0.418008	+	0.724012i	−0.577731	+	0.816227i	$0.696062\pi$
$252$		0			0
$253$	12.5487	+	21.7350i	0.788930	+	1.36647i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	25.0974	+	14.4900i	1.56553	+	0.903861i	0.996680	+	0.0814224i	$0.0259463\pi$
$257$	25.0974	+	14.4900i	1.56553	+	0.903861i	0.568854	+	0.822439i	$0.307387\pi$
$258$		0			0
$259$	26.0000			1.61556
$260$		0			0
$261$	5.24500			0.324657
$262$		0			0
$263$	26.8295	+	15.4900i	1.65438	+	0.955154i	0.975242	+	0.221139i	$0.0709774\pi$
$263$	26.8295	+	15.4900i	1.65438	+	0.955154i	0.679133	+	0.734015i	$0.262356\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.13290	−	10.6225i	−0.375328	−	0.650086i
$268$		0			0
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	−5.87750	−	3.39338i	−0.357033	−	0.206133i	0.310746	−	0.950493i	$-0.399421\pi$
$271$	−5.87750	−	3.39338i	−0.357033	−	0.206133i	−0.667778	+	0.744360i	$0.732755\pi$
$272$		0			0
$273$	−3.60555	+	12.4900i	−0.218218	+	0.755929i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	23.8070	−	13.7450i	1.43043	−	0.825857i	0.433273	−	0.901263i	$-0.357359\pi$
$277$	23.8070	−	13.7450i	1.43043	−	0.825857i	0.997153	+	0.0754058i	$0.0240252\pi$
$278$		0			0
$279$	−3.00000	+	1.73205i	−0.179605	+	0.103695i
$280$		0			0
$281$			15.4470i			0.921491i	0.887532	+	0.460746i	$0.152418\pi$
$281$			15.4470i			0.921491i	−0.887532	+	0.460746i	$0.847582\pi$
$282$		0			0
$283$	−21.6333	−	12.4900i	−1.28597	−	0.742453i	−0.308034	−	0.951375i	$-0.599671\pi$
$283$	−21.6333	−	12.4900i	−1.28597	−	0.742453i	−0.977932	+	0.208922i	$0.933005\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	26.0000i		−	1.53473i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$		−	14.1393i		−	0.828861i
$292$		0			0
$293$	−9.73845	−	16.8675i	−0.568927	−	0.985410i	−0.996672	−	0.0815107i	$-0.974026\pi$
$293$	−9.73845	−	16.8675i	−0.568927	−	0.985410i	0.427746	−	0.903899i	$-0.359308\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.73205	+	3.00000i	−0.100504	+	0.174078i
$298$		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
$303$	1.07820	−	0.622499i	0.0619410	−	0.0357616i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−21.3504			−1.21853			−0.609266	−	0.792966i	$-0.708536\pi$
$307$	−21.3504			−1.21853			−0.609266	+	0.792966i	$0.708536\pi$
$308$		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
$313$		−	7.00000i		−	0.395663i	−0.980236	−	0.197832i	$-0.936610\pi$
$313$		−	7.00000i		−	0.395663i	0.980236	−	0.197832i	$-0.0633900\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.5487			0.704805			0.352403	−	0.935848i	$-0.385365\pi$
$317$	12.5487			0.704805			0.352403	+	0.935848i	$0.385365\pi$
$318$		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
$323$	−0.141450	+	0.244998i	−0.00787047	+	0.0136321i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.94315	+	15.4900i	−0.494558	+	0.856599i
$328$		0			0
$329$	−6.75500	−	11.7000i	−0.372415	−	0.645042i
$330$		0			0
$331$	5.87750	−	3.39338i	0.323057	−	0.186517i	−0.329698	−	0.944087i	$-0.606947\pi$
$331$	5.87750	−	3.39338i	0.323057	−	0.186517i	0.652754	+	0.757570i	$0.273613\pi$
$332$		0			0
$333$	7.21110			0.395166
$334$		0			0
$335$		0			0
$336$		0			0
$337$			29.9800i			1.63311i	0.577265	+	0.816557i	$0.304120\pi$
$337$			29.9800i			1.63311i	−0.577265	+	0.816557i	$0.695880\pi$
$338$		0			0
$339$	12.0000			0.651751
$340$		0			0
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$	3.60555			0.194681
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	1.50000	+	0.866025i	0.0802932	+	0.0463573i	0.539609	−	0.841916i	$-0.318572\pi$
$349$	1.50000	+	0.866025i	0.0802932	+	0.0463573i	−0.459316	+	0.888273i	$0.651905\pi$
$350$		0			0
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$		0			0
$353$	0.795301	−	1.37750i	0.0423296	−	0.0733170i	−0.844084	−	0.536210i	$-0.819855\pi$
$353$	0.795301	−	1.37750i	0.0423296	−	0.0733170i	0.886414	+	0.462893i	$0.153189\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.60555	−	6.24500i	−0.190826	−	0.330520i
$358$		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
$363$			1.00000i			0.0524864i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−30.0814	−	17.3675i	−1.57024	−	0.906576i	−0.996139	−	0.0877883i	$-0.972020\pi$
$367$	−30.0814	−	17.3675i	−1.57024	−	0.906576i	−0.574096	−	0.818788i	$-0.694647\pi$
$368$		0			0
$369$		−	7.21110i		−	0.375395i
$370$		0			0
$371$	10.1325	−	5.85000i	0.526053	−	0.303717i
$372$		0			0
$373$	−6.06218	+	3.50000i	−0.313888	+	0.181223i	−0.648665	−	0.761074i	$-0.724672\pi$
$373$	−6.06218	+	3.50000i	−0.313888	+	0.181223i	0.334777	+	0.942297i	$0.391339\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.6269	−	13.1125i	0.701821	−	0.675328i
$378$		0			0
$379$	2.87750	+	1.66133i	0.147807	+	0.0853366i	0.572080	−	0.820198i	$-0.306137\pi$
$379$	2.87750	+	1.66133i	0.147807	+	0.0853366i	−0.424272	+	0.905535i	$0.639470\pi$
$380$		0			0
$381$	−1.87750	−	3.25193i	−0.0961873	−	0.166601i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.67628	−	2.12250i	−0.186876	−	0.107893i
$388$		0			0
$389$	−32.9800			−1.67215			−0.836076	−	0.548614i	$-0.815156\pi$
$389$	−32.9800			−1.67215			−0.836076	+	0.548614i	$0.815156\pi$
$390$		0			0
$391$	−14.4900			−0.732791
$392$		0			0
$393$	−1.07820	−	0.622499i	−0.0543880	−	0.0314009i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.52628	+	16.5000i	0.478110	+	0.828111i	0.999685	−	0.0250943i	$-0.00798860\pi$
$397$	9.52628	+	16.5000i	0.478110	+	0.828111i	−0.521575	+	0.853206i	$0.674655\pi$
$398$		0			0
$399$	0.255002	+	0.441676i	0.0127661	+	0.0221115i
$400$		0			0
$401$	24.9800	+	14.4222i	1.24744	+	0.720211i	0.970598	−	0.240705i	$-0.0773785\pi$
$401$	24.9800	+	14.4222i	1.24744	+	0.720211i	0.276843	+	0.960915i	$0.410712\pi$
$402$		0			0
$403$	−3.46410	+	12.0000i	−0.172559	+	0.597763i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6333	−	12.4900i	1.07232	−	0.619106i
$408$		0			0
$409$	−24.2450	+	13.9979i	−1.19884	+	0.692149i	−0.960296	−	0.278983i	$-0.910003\pi$
$409$	−24.2450	+	13.9979i	−1.19884	+	0.692149i	−0.238542	+	0.971132i	$0.576669\pi$
$410$		0			0
$411$		−	19.7598i		−	0.974679i
$412$		0			0
$413$	−5.85000	−	3.37750i	−0.287860	−	0.166196i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			12.2450i			0.599640i
$418$		0			0
$419$	−1.86750	+	3.23460i	−0.0912332	+	0.158021i	−0.908030	−	0.418905i	$-0.862414\pi$
$419$	−1.86750	+	3.23460i	−0.0912332	+	0.158021i	0.816797	+	0.576925i	$0.195748\pi$
$420$		0			0
$421$			5.19615i			0.253245i	0.991951	+	0.126622i	$0.0404137\pi$
$421$			5.19615i			0.253245i	−0.991951	+	0.126622i	$0.959586\pi$
$422$		0			0
$423$	−1.87350	−	3.24500i	−0.0910927	−	0.157777i
$424$		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	0.596215	−	0.802825i	$-0.296671\pi$
$431$	4.13250	+	2.38590i	0.199056	+	0.114925i	−0.397159	+	0.917750i	$0.630004\pi$
$432$		0			0
$433$	12.5487	−	7.24500i	0.603052	−	0.348172i	−0.167189	−	0.985925i	$-0.553469\pi$
$433$	12.5487	−	7.24500i	0.603052	−	0.348172i	0.770241	+	0.637752i	$0.220136\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.02480			0.0490230
$438$		0			0
$439$	6.87750	−	11.9122i	0.328245	−	0.568537i	−0.653919	−	0.756565i	$-0.726876\pi$
$439$	6.87750	−	11.9122i	0.328245	−	0.568537i	0.982164	+	0.188028i	$0.0602094\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$		−	18.0000i		−	0.855206i	−0.903967	−	0.427603i	$-0.859358\pi$
$443$		−	18.0000i		−	0.855206i	0.903967	−	0.427603i	$-0.140642\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−15.4470			−0.730618
$448$		0			0
$449$	10.8675	−	6.27435i	0.512869	−	0.296105i	−0.221143	−	0.975241i	$-0.570979\pi$
$449$	10.8675	−	6.27435i	0.512869	−	0.296105i	0.734012	+	0.679136i	$0.237646\pi$
$450$		0			0
$451$	−12.4900	−	21.6333i	−0.588131	−	1.01867i
$452$		0			0
$453$	0.212174	−	0.367497i	0.00996883	−	0.0172665i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.7374	+	28.9900i	−0.782942	+	1.35609i	0.147279	+	0.989095i	$0.452948\pi$
$457$	−16.7374	+	28.9900i	−0.782942	+	1.35609i	−0.930221	+	0.367000i	$0.880385\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	12.7350	−	7.35255i	0.593128	−	0.342442i	−0.173205	−	0.984886i	$-0.555412\pi$
$461$	12.7350	−	7.35255i	0.593128	−	0.342442i	0.766333	+	0.642443i	$0.222079\pi$
$462$		0			0
$463$	3.32265			0.154417			0.0772084	−	0.997015i	$-0.475399\pi$
$463$	3.32265			0.154417			0.0772084	+	0.997015i	$0.475399\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	4.49000i		−	0.207772i	−0.994589	−	0.103886i	$-0.966872\pi$
$467$		−	4.49000i		−	0.207772i	0.994589	−	0.103886i	$-0.0331277\pi$
$468$		0			0
$469$	−25.4900			−1.17702
$470$		0			0
$471$	−8.50000	+	14.7224i	−0.391659	+	0.678374i
$472$		0			0
$473$	−14.7051			−0.676141
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.81025	−	1.62250i	0.128673	−	0.0742891i
$478$		0			0
$479$	−0.887505	−	0.512401i	−0.0405511	−	0.0234122i	0.479587	−	0.877494i	$-0.340786\pi$
$479$	−0.887505	−	0.512401i	−0.0405511	−	0.0234122i	−0.520139	+	0.854082i	$0.674120\pi$
$480$		0			0
$481$	18.7350	−	18.0278i	0.854242	−	0.821995i
$482$		0			0
$483$	−13.0611	+	22.6225i	−0.594301	+	1.02936i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−14.2100	−	24.6125i	−0.643918	−	1.11530i	−0.984550	−	0.175102i	$-0.943974\pi$
$487$	−14.2100	−	24.6125i	−0.643918	−	1.11530i	0.340632	−	0.940197i	$-0.389359\pi$
$488$		0			0
$489$			17.8863i			0.808847i
$490$		0			0
$491$	18.2450	−	31.6013i	0.823385	−	1.42615i	−0.0797619	−	0.996814i	$-0.525416\pi$
$491$	18.2450	−	31.6013i	0.823385	−	1.42615i	0.903147	−	0.429331i	$-0.141251\pi$
$492$		0			0
$493$			10.4900i			0.472446i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.5167	+	13.0000i	1.01001	+	0.583130i
$498$		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
$503$	−29.2154	+	16.8675i	−1.30265	+	0.752085i	−0.980858	−	0.194726i	$-0.937618\pi$
$503$	−29.2154	+	16.8675i	−1.30265	+	0.752085i	−0.321791	+	0.946811i	$0.604285\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.06218	+	11.5000i	0.269231	+	0.510733i
$508$		0			0
$509$	−9.00000	−	5.19615i	−0.398918	−	0.230315i	0.287099	−	0.957901i	$-0.407309\pi$
$509$	−9.00000	−	5.19615i	−0.398918	−	0.230315i	−0.686017	+	0.727586i	$0.740642\pi$
$510$		0			0
$511$	22.3675	+	38.7416i	0.989480	+	1.71383i
$512$		0			0
$513$	0.0707248	+	0.122499i	0.00312258	+	0.00540846i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−11.2410	−	6.49000i	−0.494379	−	0.285430i
$518$		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
$523$	16.2250	+	9.36750i	0.709469	+	0.409612i	0.810864	−	0.585234i	$-0.198997\pi$
$523$	16.2250	+	9.36750i	0.709469	+	0.409612i	−0.101395	+	0.994846i	$0.532331\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46410	−	6.00000i	−0.150899	−	0.261364i
$528$		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
$533$	−18.0278	−	18.7350i	−0.780869	−	0.811503i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−16.0128	+	9.24500i	−0.691004	+	0.398951i
$538$		0			0
$539$	−18.0000	+	10.3923i	−0.775315	+	0.447628i
$540$		0			0
$541$		−	21.0675i		−	0.905763i	−0.891571	−	0.452881i	$-0.850396\pi$
$541$		−	21.0675i		−	0.905763i	0.891571	−	0.452881i	$-0.149604\pi$
$542$		0			0
$543$	−9.95063	−	5.74500i	−0.427022	−	0.246541i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	9.75500i		−	0.417094i	−0.978012	−	0.208547i	$-0.933127\pi$
$547$		−	9.75500i		−	0.417094i	0.978012	−	0.208547i	$-0.0668734\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	0.741903i		−	0.0316061i
$552$		0			0
$553$	−14.8639	−	25.7450i	−0.632077	−	1.09479i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.1543	+	27.9800i	−0.684478	+	1.18555i	0.289123	+	0.957292i	$0.406636\pi$
$557$	−16.1543	+	27.9800i	−0.684478	+	1.18555i	−0.973601	+	0.228258i	$0.926697\pi$
$558$		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
$563$	33.3333	−	19.2450i	1.40483	−	0.811080i	0.409948	−	0.912109i	$-0.365547\pi$
$563$	33.3333	−	19.2450i	1.40483	−	0.811080i	0.994883	+	0.101029i	$0.0322134\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−3.60555			−0.151419
$568$		0			0
$569$	13.3775	−	23.1705i	0.560814	−	0.971358i	−0.436612	−	0.899650i	$-0.643822\pi$
$569$	13.3775	−	23.1705i	0.560814	−	0.971358i	0.997426	−	0.0717083i	$-0.0228451\pi$
$570$		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
$573$			12.4900i			0.521777i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.22605			0.384086			0.192043	−	0.981387i	$-0.438489\pi$
$577$	9.22605			0.384086			0.192043	+	0.981387i	$0.438489\pi$
$578$		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
$583$	5.62050	−	9.73499i	0.232777	−	0.403182i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.9829	−	20.7550i	0.494587	−	0.856651i	−0.505393	−	0.862889i	$-0.668652\pi$
$587$	11.9829	−	20.7550i	0.494587	−	0.856651i	0.999981	+	0.00623863i	$0.00198583\pi$
$588$		0			0
$589$	0.244998	+	0.424349i	0.0100950	+	0.0174850i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.87350			0.0769354			0.0384677	−	0.999260i	$-0.487752\pi$
$593$	1.87350			0.0769354			0.0384677	+	0.999260i	$0.487752\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			11.7550i			0.481100i
$598$		0			0
$599$	−15.7350			−0.642914			−0.321457	−	0.946924i	$-0.604173\pi$
$599$	−15.7350			−0.642914			−0.321457	+	0.946924i	$0.604173\pi$
$600$		0			0
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	−0.731774	−	0.681547i	$-0.761308\pi$
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	0.956124	+	0.292962i	$0.0946409\pi$
$602$		0			0
$603$	−7.06965			−0.287899
$604$		0			0
$605$		0			0
$606$		0			0
$607$	27.2538	−	15.7350i	1.10620	−	0.638664i	0.168356	−	0.985726i	$-0.446154\pi$
$607$	27.2538	−	15.7350i	1.10620	−	0.638664i	0.937842	+	0.347063i	$0.112821\pi$
$608$		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
$613$	−20.0600	+	34.7450i	−0.810217	+	1.40334i	0.102495	+	0.994734i	$0.467318\pi$
$613$	−20.0600	+	34.7450i	−0.810217	+	1.40334i	−0.912712	+	0.408604i	$0.866016\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.6816	−	32.3575i	−0.752093	−	1.30266i	−0.946807	−	0.321803i	$-0.895711\pi$
$617$	−18.6816	−	32.3575i	−0.752093	−	1.30266i	0.194713	−	0.980860i	$-0.437622\pi$
$618$		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
$623$		−	44.2250i		−	1.77184i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.424349	+	0.244998i	0.0169469	+	0.00978428i
$628$		0			0
$629$			14.4222i			0.575051i
$630$		0			0
$631$	17.8775	−	10.3216i	0.711692	−	0.410896i	−0.0999952	−	0.994988i	$-0.531883\pi$
$631$	17.8775	−	10.3216i	0.711692	−	0.410896i	0.811687	+	0.584092i	$0.198549\pi$
$632$		0			0
$633$	5.62050	−	3.24500i	0.223395	−	0.128977i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.5885	+	15.0000i	−0.617637	+	0.594322i
$638$		0			0
$639$	6.24500	+	3.60555i	0.247048	+	0.142633i
$640$		0			0
$641$	−9.11249	−	15.7833i	−0.359922	−	0.623403i	0.628026	−	0.778193i	$-0.283863\pi$
$641$	−9.11249	−	15.7833i	−0.359922	−	0.623403i	−0.987947	+	0.154790i	$0.950530\pi$
$642$		0			0
$643$	−19.6891	−	34.1025i	−0.776462	−	1.34487i	−0.933969	−	0.357353i	$-0.883679\pi$
$643$	−19.6891	−	34.1025i	−0.776462	−	1.34487i	0.157508	−	0.987518i	$-0.449654\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	32.2551	+	18.6225i	1.26808	+	0.732126i	0.974624	−	0.223847i	$-0.0718616\pi$
$647$	32.2551	+	18.6225i	1.26808	+	0.732126i	0.293455	+	0.955973i	$0.405195\pi$
$648$		0			0
$649$	−6.49000			−0.254755
$650$		0			0
$651$	−12.4900			−0.489522
$652$		0			0
$653$	−8.23591	−	4.75500i	−0.322296	−	0.186078i	0.330120	−	0.943939i	$-0.392911\pi$
$653$	−8.23591	−	4.75500i	−0.322296	−	0.186078i	−0.652415	+	0.757862i	$0.726244\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.20363	+	10.7450i	0.242027	+	0.419202i
$658$		0			0
$659$	−19.4900	−	33.7577i	−0.759222	−	1.31501i	−0.943248	−	0.332090i	$-0.892246\pi$
$659$	−19.4900	−	33.7577i	−0.759222	−	1.31501i	0.184025	−	0.982922i	$-0.441087\pi$
$660$		0			0
$661$	−28.9900	−	16.7374i	−1.12758	−	0.651009i	−0.184255	−	0.982878i	$-0.558987\pi$
$661$	−28.9900	−	16.7374i	−1.12758	−	0.651009i	−0.943325	+	0.331870i	$0.892321\pi$
$662$		0			0
$663$	−6.92820	−	2.00000i	−0.269069	−	0.0776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	32.9090	−	19.0000i	1.27424	−	0.735683i
$668$		0			0
$669$	−2.63250	+	1.51988i	−0.101778	+	0.0587618i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.7224	−	8.50000i	−0.567508	−	0.327651i	0.188645	−	0.982045i	$-0.439590\pi$
$673$	−14.7224	−	8.50000i	−0.567508	−	0.327651i	−0.756153	+	0.654394i	$0.772924\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			5.73499i			0.220414i	0.993909	+	0.110207i	$0.0351513\pi$
$677$			5.73499i			0.220414i	−0.993909	+	0.110207i	$0.964849\pi$
$678$		0			0
$679$	25.4900	−	44.1500i	0.978216	−	1.69432i
$680$		0			0
$681$		−	4.77180i		−	0.182856i
$682$		0			0
$683$	6.41580	+	11.1125i	0.245494	+	0.425208i	0.962270	−	0.272095i	$-0.0877166\pi$
$683$	6.41580	+	11.1125i	0.245494	+	0.425208i	−0.716777	+	0.697303i	$0.754383\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	11.6827	−	20.2350i	0.445722	−	0.772013i
$688$		0			0
$689$	3.24500	−	11.2410i	0.123625	−	0.428248i
$690$		0			0
$691$	−12.1225	−	6.99893i	−0.461162	−	0.266252i	0.251371	−	0.967891i	$-0.419119\pi$
$691$	−12.1225	−	6.99893i	−0.461162	−	0.266252i	−0.712533	+	0.701639i	$0.752452\pi$
$692$		0			0
$693$	−10.8167	+	6.24500i	−0.410891	+	0.237228i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	14.4222			0.546280
$698$		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
$703$		−	1.02001i		−	0.0384703i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.48890			0.168823
$708$		0			0
$709$	−1.25500	+	0.724576i	−0.0471326	+	0.0272120i	−0.523381	−	0.852099i	$-0.675330\pi$
$709$	−1.25500	+	0.724576i	−0.0471326	+	0.0272120i	0.476249	+	0.879311i	$0.341996\pi$
$710$		0			0
$711$	−4.12250	−	7.14038i	−0.154606	−	0.267785i
$712$		0			0
$713$	−12.5487	+	21.7350i	−0.469953	+	0.813982i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.81025	−	4.86750i	0.104951	−	0.181780i
$718$		0			0
$719$	−25.6225	−	44.3795i	−0.955558	−	1.65507i	−0.733086	−	0.680136i	$-0.761921\pi$
$719$	−25.6225	−	44.3795i	−0.955558	−	1.65507i	−0.222472	−	0.974939i	$-0.571413\pi$
$720$		0			0
$721$	−5.47999	+	3.16387i	−0.204086	+	0.117829i
$722$		0			0
$723$	−11.8415			−0.440388
$724$		0			0
$725$		0			0
$726$		0			0
$727$			11.2250i			0.416312i	0.978096	+	0.208156i	$0.0667461\pi$
$727$			11.2250i			0.416312i	−0.978096	+	0.208156i	$0.933254\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.24500	−	7.35255i	0.157007	−	0.271944i
$732$		0			0
$733$	−36.6560			−1.35392			−0.676960	−	0.736020i	$-0.736703\pi$
$733$	−36.6560			−1.35392			−0.676960	+	0.736020i	$0.736703\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.2090	+	12.2450i	−0.781242	+	0.451050i
$738$		0			0
$739$	27.4900	+	15.8714i	1.01124	+	0.583837i	0.911553	−	0.411182i	$-0.134884\pi$
$739$	27.4900	+	15.8714i	1.01124	+	0.583837i	0.0996826	+	0.995019i	$0.468217\pi$
$740$		0			0
$741$	0.489996	+	0.141450i	0.0180005	+	0.00519628i
$742$		0			0
$743$	−10.2509	+	17.7550i	−0.376067	+	0.651368i	−0.990486	−	0.137612i	$-0.956057\pi$
$743$	−10.2509	+	17.7550i	−0.376067	+	0.651368i	0.614419	+	0.788980i	$0.289391\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.52735	+	4.37750i	0.0924710	+	0.160164i
$748$		0			0
$749$		−	33.3333i		−	1.21797i
$750$		0			0
$751$	18.2450	−	31.6013i	0.665769	−	1.15315i	−0.313307	−	0.949652i	$-0.601437\pi$
$751$	18.2450	−	31.6013i	0.665769	−	1.15315i	0.979076	−	0.203494i	$-0.0652299\pi$
$752$		0			0
$753$			13.2450i			0.482675i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	23.3827	+	13.5000i	0.849858	+	0.490666i	0.860603	−	0.509276i	$-0.170087\pi$
$757$	23.3827	+	13.5000i	0.849858	+	0.490666i	−0.0107448	+	0.999942i	$0.503420\pi$
$758$		0			0
$759$			25.0974i			0.910978i
$760$		0			0
$761$	3.00000	−	1.73205i	0.108750	−	0.0627868i	−0.444639	−	0.895710i	$-0.646668\pi$
$761$	3.00000	−	1.73205i	0.108750	−	0.0627868i	0.553388	+	0.832923i	$0.313335\pi$
$762$		0			0
$763$	−55.8500	+	32.2450i	−2.02190	+	1.16735i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.55725	+	1.62250i	−0.236769	+	0.0585850i
$768$		0			0
$769$	−10.7450	−	6.20363i	−0.387475	−	0.223709i	0.293591	−	0.955931i	$-0.405150\pi$
$769$	−10.7450	−	6.20363i	−0.387475	−	0.223709i	−0.681065	+	0.732223i	$0.738483\pi$
$770$		0			0
$771$	14.4900	+	25.0974i	0.521844	+	0.903861i
$772$		0			0
$773$	−1.30770	−	2.26501i	−0.0470348	−	0.0814666i	0.841550	−	0.540180i	$-0.181644\pi$
$773$	−1.30770	−	2.26501i	−0.0470348	−	0.0814666i	−0.888584	+	0.458713i	$0.848310\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	22.5167	+	13.0000i	0.807781	+	0.466372i
$778$		0			0
$779$	−1.02001			−0.0365456
$780$		0			0
$781$	24.9800			0.893854
$782$		0			0
$783$	4.54230	+	2.62250i	0.162329	+	0.0937205i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	12.1244	+	21.0000i	0.432187	+	0.748569i	0.997061	−	0.0766075i	$-0.0244088\pi$
$787$	12.1244	+	21.0000i	0.432187	+	0.748569i	−0.564875	+	0.825177i	$0.691076\pi$
$788$		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
$797$	2.38590	−	1.37750i	0.0845130	−	0.0487936i	−0.457148	−	0.889391i	$-0.651129\pi$
$797$	2.38590	−	1.37750i	0.0845130	−	0.0487936i	0.541661	+	0.840597i	$0.317796\pi$
$798$		0			0
$799$	6.49000	−	3.74700i	0.229600	−	0.132559i
$800$		0			0
$801$		−	12.2658i		−	0.433391i
$802$		0			0
$803$	37.2218	+	21.4900i	1.31353	+	0.758365i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	24.0000i		−	0.844840i
$808$		0			0
$809$	20.8675	−	36.1436i	0.733662	−	1.27074i	−0.221646	−	0.975127i	$-0.571143\pi$
$809$	20.8675	−	36.1436i	0.733662	−	1.27074i	0.955308	−	0.295613i	$-0.0955238\pi$
$810$		0			0
$811$		−	27.5714i		−	0.968162i	−0.875023	−	0.484081i	$-0.839154\pi$
$811$		−	27.5714i		−	0.968162i	0.875023	−	0.484081i	$-0.160846\pi$
$812$		0			0
$813$	−3.39338	−	5.87750i	−0.119011	−	0.206133i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.300227	+	0.520008i	−0.0105036	+	0.0181928i
$818$		0			0
$819$	−9.36750	+	9.01388i	−0.327327	+	0.314970i
$820$		0			0
$821$	−45.0925	−	26.0342i	−1.57374	−	0.908598i	−0.995705	−	0.0925857i	$-0.970487\pi$
$821$	−45.0925	−	26.0342i	−1.57374	−	0.908598i	−0.578034	−	0.816013i	$-0.696180\pi$
$822$		0			0
$823$	−24.8852	+	14.3675i	−0.867445	+	0.500819i	−0.866498	−	0.499180i	$-0.833635\pi$
$823$	−24.8852	+	14.3675i	−0.867445	+	0.500819i	−0.000946492		1.00000i	$0.500301\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.92820			0.240917			0.120459	−	0.992718i	$-0.461563\pi$
$827$	6.92820			0.240917			0.120459	+	0.992718i	$0.461563\pi$
$828$		0			0
$829$	26.7450	−	46.3237i	0.928892	−	1.60889i	0.143713	−	0.989619i	$-0.454096\pi$
$829$	26.7450	−	46.3237i	0.928892	−	1.60889i	0.785179	−	0.619269i	$-0.212571\pi$
$830$		0			0
$831$	27.4900			0.953617
$832$		0			0
$833$		−	12.0000i		−	0.415775i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.46410			−0.119737
$838$		0			0
$839$	−1.37750	+	0.795301i	−0.0475566	+	0.0274568i	−0.523590	−	0.851970i	$-0.675408\pi$
$839$	−1.37750	+	0.795301i	−0.0475566	+	0.0274568i	0.476033	+	0.879427i	$0.342074\pi$
$840$		0			0
$841$	0.744998	+	1.29037i	0.0256896	+	0.0444957i
$842$		0			0
$843$	−7.72350	+	13.3775i	−0.266012	+	0.460746i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.80278	+	3.12250i	−0.0619441	+	0.107290i
$848$		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
$853$	−9.82651			−0.336453			−0.168227	−	0.985748i	$-0.553804\pi$
$853$	−9.82651			−0.336453			−0.168227	+	0.985748i	$0.553804\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			15.5100i			0.529812i	0.964274	+	0.264906i	$0.0853409\pi$
$857$			15.5100i			0.529812i	−0.964274	+	0.264906i	$0.914659\pi$
$858$		0			0
$859$	22.7350			0.775708			0.387854	−	0.921721i	$-0.373216\pi$
$859$	22.7350			0.775708			0.387854	+	0.921721i	$0.373216\pi$
$860$		0			0
$861$	13.0000	−	22.5167i	0.443039	−	0.767366i
$862$		0			0
$863$	4.31280			0.146809			0.0734047	−	0.997302i	$-0.476614\pi$
$863$	4.31280			0.146809			0.0734047	+	0.997302i	$0.476614\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.2583	+	6.50000i	−0.382353	+	0.220752i
$868$		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
$873$	7.06965	−	12.2450i	0.239271	−	0.414430i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	13.5562	+	23.4800i	0.457760	+	0.792863i	0.998842	−	0.0481065i	$-0.0153187\pi$
$877$	13.5562	+	23.4800i	0.457760	+	0.792863i	−0.541083	+	0.840969i	$0.681985\pi$
$878$		0			0
$879$		−	19.4769i		−	0.656940i
$880$		0			0
$881$	13.7350	−	23.7897i	0.462744	−	0.801496i	−0.536353	−	0.843994i	$-0.680198\pi$
$881$	13.7350	−	23.7897i	0.462744	−	0.801496i	0.999097	+	0.0424983i	$0.0135317\pi$
$882$		0			0
$883$			20.4900i			0.689543i	0.938687	+	0.344772i	$0.112044\pi$
$883$			20.4900i			0.689543i	−0.938687	+	0.344772i	$0.887956\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.31410	+	5.37750i	0.312737	+	0.180559i	0.648151	−	0.761512i	$-0.275543\pi$
$887$	9.31410	+	5.37750i	0.312737	+	0.180559i	−0.335414	+	0.942071i	$0.608876\pi$
$888$		0			0
$889$		−	13.5389i		−	0.454079i
$890$		0			0
$891$	−3.00000	+	1.73205i	−0.100504	+	0.0580259i
$892$		0			0
$893$	−0.459004	+	0.265006i	−0.0153600	+	0.00886809i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.27435	+	25.3575i	0.209495	+	0.846662i
$898$		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
$903$	−7.65278	−	13.2550i	−0.254669	−	0.441099i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	17.7449	+	10.2450i	0.589208	+	0.340180i	0.764784	−	0.644286i	$-0.222845\pi$
$907$	17.7449	+	10.2450i	0.589208	+	0.340180i	−0.175576	+	0.984466i	$0.556179\pi$
$908$		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
$913$	15.1641	+	8.75500i	0.501859	+	0.289748i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.24445	−	3.88751i	−0.0741183	−	0.128377i
$918$		0			0
$919$	14.1225	+	24.4609i	0.465858	+	0.806890i	0.999240	−	0.0389846i	$-0.0124123\pi$
$919$	14.1225	+	24.4609i	0.465858	+	0.806890i	−0.533382	+	0.845875i	$0.679079\pi$
$920$		0			0
$921$	−18.4900	−	10.6752i	−0.609266	−	0.351760i
$922$		0			0
$923$	25.2389	−	6.24500i	0.830747	−	0.205557i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.51988	+	0.877501i	−0.0499193	+	0.0288209i
$928$		0			0
$929$	−45.9800	+	26.5466i	−1.50855	+	0.870964i	−0.508604	+	0.861000i	$0.669838\pi$
$929$	−45.9800	+	26.5466i	−1.50855	+	0.870964i	−0.999950	+	0.00996399i	$0.996828\pi$
$930$		0			0
$931$			0.848698i			0.0278150i
$932$		0			0
$933$	−24.0192	−	13.8675i	−0.786354	−	0.454001i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			34.5100i			1.12739i	0.825982	+	0.563696i	$0.190621\pi$
$937$			34.5100i			1.12739i	−0.825982	+	0.563696i	$0.809379\pi$
$938$		0			0
$939$	3.50000	−	6.06218i	0.114218	−	0.197832i
$940$		0			0
$941$			15.1641i			0.494336i	0.968973	+	0.247168i	$0.0794999\pi$
$941$			15.1641i			0.494336i	−0.968973	+	0.247168i	$0.920500\pi$
$942$		0			0
$943$	−26.1222	−	45.2450i	−0.850656	−	1.47338i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.2808	+	24.7350i	−0.464062	+	0.803779i	−0.999159	−	0.0410117i	$-0.986942\pi$
$947$	−14.2808	+	24.7350i	−0.464062	+	0.803779i	0.535096	+	0.844791i	$0.320275\pi$
$948$		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
$953$	45.4577	−	26.2450i	1.47252	−	0.850159i	0.472996	−	0.881065i	$-0.343172\pi$
$953$	45.4577	−	26.2450i	1.47252	−	0.850159i	0.999522	+	0.0309057i	$0.00983915\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	18.1692			0.587327
$958$		0			0
$959$	35.6225	−	61.7000i	1.15031	−	1.99240i
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$		−	9.24500i		−	0.297916i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−28.2786			−0.909379			−0.454689	−	0.890650i	$-0.650250\pi$
$967$	−28.2786			−0.909379			−0.454689	+	0.890650i	$0.650250\pi$
$968$		0			0
$969$	−0.244998	+	0.141450i	−0.00787047	+	0.00454402i
$970$		0			0
$971$	−27.1125	−	46.9602i	−0.870081	−	1.50703i	−0.861912	−	0.507059i	$-0.830733\pi$
$971$	−27.1125	−	46.9602i	−0.870081	−	1.50703i	−0.00816974	−	0.999967i	$-0.502601\pi$
$972$		0			0
$973$	−22.0750	+	38.2350i	−0.707691	+	1.22576i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.2239	−	40.2250i	0.742999	−	1.28691i	−0.208125	−	0.978102i	$-0.566736\pi$
$977$	23.2239	−	40.2250i	0.742999	−	1.28691i	0.951124	−	0.308809i	$-0.0999305\pi$
$978$		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
$983$	−34.4649			−1.09926			−0.549630	−	0.835408i	$-0.685231\pi$
$983$	−34.4649			−1.09926			−0.549630	+	0.835408i	$0.685231\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	13.5100i		−	0.430028i
$988$		0			0
$989$	−30.7550			−0.977952
$990$		0			0
$991$	−15.6125	+	27.0416i	−0.495947	+	0.859006i	−0.999989	−	0.00467341i	$-0.998512\pi$
$991$	−15.6125	+	27.0416i	−0.495947	+	0.859006i	0.504042	+	0.863679i	$0.331846\pi$
$992$		0			0
$993$	6.78675			0.215371
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.59808	+	1.50000i	−0.0822819	+	0.0475055i	−0.540576	−	0.841295i	$-0.681794\pi$
$997$	−2.59808	+	1.50000i	−0.0822819	+	0.0475055i	0.458295	+	0.888800i	$0.348460\pi$
$998$		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.bw.i.2149.4		8
5.2	odd	4		3900.2.cd.h.901.1	yes	4
5.3	odd	4		3900.2.cd.f.901.2	✓	4
5.4	even	2	inner	3900.2.bw.i.2149.1		8
13.10	even	6	inner	3900.2.bw.i.49.1		8
65.23	odd	12		3900.2.cd.f.2701.2	yes	4
65.49	even	6	inner	3900.2.bw.i.49.4		8
65.62	odd	12		3900.2.cd.h.2701.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3900.2.bw.i.49.1		8	13.10	even	6	inner
3900.2.bw.i.49.4		8	65.49	even	6	inner
3900.2.bw.i.2149.1		8	5.4	even	2	inner
3900.2.bw.i.2149.4		8	1.1	even	1	trivial
3900.2.cd.f.901.2	✓	4	5.3	odd	4
3900.2.cd.f.2701.2	yes	4	65.23	odd	12
3900.2.cd.h.901.1	yes	4	5.2	odd	4
3900.2.cd.h.2701.1	yes	4	65.62	odd	12

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.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(1.80278 + 3.12250i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +(3.46410 + 1.00000i) q^{13} +(-1.73205 + 1.00000i) q^{17} +(0.122499 - 0.0707248i) q^{19} +3.60555i q^{21} +(6.27435 + 3.62250i) q^{23} +1.00000i q^{27} +(2.62250 - 4.54230i) q^{29} +3.46410i q^{31} +(1.73205 + 3.00000i) q^{33} +(3.60555 - 6.24500i) q^{37} +(2.50000 + 2.59808i) q^{39} +(-6.24500 - 3.60555i) q^{41} +(-3.67628 + 2.12250i) q^{43} -3.74700 q^{47} +(-3.00000 + 5.19615i) q^{49} -2.00000 q^{51} -3.24500i q^{53} +0.141450 q^{57} +(-1.62250 + 0.936750i) q^{59} +(-1.80278 + 3.12250i) q^{63} +(-3.53483 + 6.12250i) q^{67} +(3.62250 + 6.27435i) q^{69} +(6.24500 - 3.60555i) q^{71} +12.4073 q^{73} +12.4900i q^{77} -8.24500 q^{79} +(-0.500000 + 0.866025i) q^{81} +5.05470 q^{83} +(4.54230 - 2.62250i) q^{87} +(-10.6225 - 6.13290i) q^{89} +(3.12250 + 12.6194i) q^{91} +(-1.73205 + 3.00000i) q^{93} +(-7.06965 - 12.2450i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} + 24 q^{11} - 24 q^{19} - 4 q^{29} + 20 q^{39} - 24 q^{49} - 16 q^{51} + 12 q^{59} + 4 q^{69} - 16 q^{79} - 4 q^{81} - 60 q^{89}+O(q^{100}) \) 8 * q + 4 * q^9 + 24 * q^11 - 24 * q^19 - 4 * q^29 + 20 * q^39 - 24 * q^49 - 16 * q^51 + 12 * q^59 + 4 * q^69 - 16 * q^79 - 4 * q^81 - 60 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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