LMFDB - Embedded newform 3900.2.bw.i.2149.3

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			2149.3
Root			$-1.12824 - 0.651388i$ of defining polynomial
Character	$\chi$	$=$	3900.2149
Dual form			3900.2.bw.i.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-1.80278 - 3.12250i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +(3.46410 + 1.00000i) q^{13} +(-1.73205 + 1.00000i) q^{17} +(-6.12250 + 3.53483i) q^{19} -3.60555i q^{21} +(-4.54230 - 2.62250i) q^{23} +1.00000i q^{27} +(-3.62250 + 6.27435i) q^{29} +3.46410i q^{31} +(1.73205 + 3.00000i) q^{33} +(-3.60555 + 6.24500i) q^{37} +(2.50000 + 2.59808i) q^{39} +(6.24500 + 3.60555i) q^{41} +(7.14038 - 4.12250i) q^{43} +10.6752 q^{47} +(-3.00000 + 5.19615i) q^{49} -2.00000 q^{51} +9.24500i q^{53} -7.06965 q^{57} +(4.62250 - 2.66880i) q^{59} +(1.80278 - 3.12250i) q^{63} +(0.0707248 - 0.122499i) q^{67} +(-2.62250 - 4.54230i) q^{69} +(-6.24500 + 3.60555i) q^{71} -2.01495 q^{73} -12.4900i q^{77} +4.24500 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.2658 q^{83} +(-6.27435 + 3.62250i) q^{87} +(-4.37750 - 2.52735i) q^{89} +(-3.12250 - 12.6194i) q^{91} +(-1.73205 + 3.00000i) q^{93} +(0.141450 + 0.244998i) q^{97} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.928045\pi$
$7$	−1.80278	−	3.12250i	−0.681385	−	1.18019i	0.293173	−	0.956059i	$-0.405289\pi$
$8$		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
$19$	−6.12250	+	3.53483i	−1.40460	+	0.810945i	−0.994860	−	0.101259i	$-0.967713\pi$
$19$	−6.12250	+	3.53483i	−1.40460	+	0.810945i	−0.409737	+	0.912203i	$0.634380\pi$
$20$		0			0
$21$		−	3.60555i		−	0.786796i
$22$		0			0
$23$	−4.54230	−	2.62250i	−0.947135	−	0.546829i	−0.0549455	−	0.998489i	$-0.517498\pi$
$23$	−4.54230	−	2.62250i	−0.947135	−	0.546829i	−0.892190	+	0.451661i	$0.850832\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−3.62250	+	6.27435i	−0.672681	+	1.16512i	0.304460	+	0.952525i	$0.401524\pi$
$29$	−3.62250	+	6.27435i	−0.672681	+	1.16512i	−0.977141	+	0.212593i	$0.931809\pi$
$30$		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	$0.368624\pi$
$37$	−3.60555	+	6.24500i	−0.592749	+	1.02667i	−0.993860	+	0.110642i	$0.964709\pi$
$38$		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	$-0.142945\pi$
$41$	6.24500	+	3.60555i	0.975305	+	0.563093i	0.0744555	+	0.997224i	$0.476278\pi$
$42$		0			0
$43$	7.14038	−	4.12250i	1.08890	−	0.628675i	0.155615	−	0.987818i	$-0.450264\pi$
$43$	7.14038	−	4.12250i	1.08890	−	0.628675i	0.933283	+	0.359143i	$0.116931\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.6752			1.55714			0.778569	−	0.627559i	$-0.215946\pi$
$47$	10.6752			1.55714			0.778569	+	0.627559i	$0.215946\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$			9.24500i			1.26990i	0.772554	+	0.634949i	$0.218979\pi$
$53$			9.24500i			1.26990i	−0.772554	+	0.634949i	$0.781021\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.06965			−0.936398
$58$		0			0
$59$	4.62250	−	2.66880i	0.601798	−	0.347448i	−0.167951	−	0.985795i	$-0.553715\pi$
$59$	4.62250	−	2.66880i	0.601798	−	0.347448i	0.769749	+	0.638347i	$0.220382\pi$
$60$		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
$67$	0.0707248	−	0.122499i	0.00864041	−	0.0149656i	−0.861673	−	0.507464i	$-0.830583\pi$
$67$	0.0707248	−	0.122499i	0.00864041	−	0.0149656i	0.870313	+	0.492499i	$0.163916\pi$
$68$		0			0
$69$	−2.62250	−	4.54230i	−0.315712	−	0.546829i
$70$		0			0
$71$	−6.24500	+	3.60555i	−0.741145	+	0.427900i	−0.822485	−	0.568786i	$-0.807413\pi$
$71$	−6.24500	+	3.60555i	−0.741145	+	0.427900i	0.0813405	+	0.996686i	$0.474080\pi$
$72$		0			0
$73$	−2.01495			−0.235832			−0.117916	−	0.993024i	$-0.537621\pi$
$73$	−2.01495			−0.235832			−0.117916	+	0.993024i	$0.537621\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	12.4900i		−	1.42337i
$78$		0			0
$79$	4.24500			0.477600			0.238800	−	0.971069i	$-0.423246\pi$
$79$	4.24500			0.477600			0.238800	+	0.971069i	$0.423246\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.2658			1.34635			0.673174	−	0.739485i	$-0.264931\pi$
$83$	12.2658			1.34635			0.673174	+	0.739485i	$0.264931\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.27435	+	3.62250i	−0.672681	+	0.388373i
$88$		0			0
$89$	−4.37750	−	2.52735i	−0.464014	−	0.267899i	0.249716	−	0.968319i	$-0.419663\pi$
$89$	−4.37750	−	2.52735i	−0.464014	−	0.267899i	−0.713731	+	0.700420i	$0.752996\pi$
$90$		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
$97$	0.141450	+	0.244998i	0.0143620	+	0.0248758i	0.873117	−	0.487511i	$-0.162095\pi$
$97$	0.141450	+	0.244998i	0.0143620	+	0.0248758i	−0.858755	+	0.512386i	$0.828762\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	−5.62250	+	9.73845i	−0.559460	+	0.969012i	0.438082	+	0.898935i	$0.355658\pi$
$101$	−5.62250	+	9.73845i	−0.559460	+	0.969012i	−0.997542	+	0.0700774i	$0.977675\pi$
$102$		0			0
$103$			14.2450i			1.40360i	0.712373	+	0.701801i	$0.247620\pi$
$103$			14.2450i			1.40360i	−0.712373	+	0.701801i	$0.752380\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.81025	+	1.62250i	0.271677	+	0.156853i	0.629650	−	0.776879i	$-0.283198\pi$
$107$	2.81025	+	1.62250i	0.271677	+	0.156853i	−0.357972	+	0.933732i	$0.616532\pi$
$108$		0			0
$109$		−	10.9581i		−	1.04960i	−0.851227	−	0.524798i	$-0.824141\pi$
$109$		−	10.9581i		−	1.04960i	0.851227	−	0.524798i	$-0.175859\pi$
$110$		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
$127$	−14.0686	−	8.12250i	−1.24838	−	0.720755i	−0.277598	−	0.960697i	$-0.589538\pi$
$127$	−14.0686	−	8.12250i	−1.24838	−	0.720755i	−0.970787	+	0.239942i	$0.922871\pi$
$128$		0			0
$129$	8.24500			0.725932
$130$		0			0
$131$	11.2450			0.982480			0.491240	−	0.871024i	$-0.336544\pi$
$131$	11.2450			0.982480			0.491240	+	0.871024i	$0.336544\pi$
$132$		0			0
$133$	22.0750	+	12.7450i	1.91414	+	1.10513i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.14785	+	14.1125i	0.696118	+	1.20571i	0.969802	+	0.243892i	$0.0784243\pi$
$137$	8.14785	+	14.1125i	0.696118	+	1.20571i	−0.273684	+	0.961820i	$0.588242\pi$
$138$		0			0
$139$	−0.122499	−	0.212174i	−0.0103902	−	0.0179964i	0.860784	−	0.508971i	$-0.169974\pi$
$139$	−0.122499	−	0.212174i	−0.0103902	−	0.0179964i	−0.871174	+	0.490975i	$0.836641\pi$
$140$		0			0
$141$	9.24500	+	5.33760i	0.778569	+	0.449507i
$142$		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
$149$	−19.6225	+	11.3291i	−1.60754	+	0.928112i	−0.617619	+	0.786478i	$0.711903\pi$
$149$	−19.6225	+	11.3291i	−1.60754	+	0.928112i	−0.989919	+	0.141635i	$0.954764\pi$
$150$		0			0
$151$			21.2090i			1.72596i	0.505238	+	0.862980i	$0.331405\pi$
$151$			21.2090i			1.72596i	−0.505238	+	0.862980i	$0.668595\pi$
$152$		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
$159$	−4.62250	+	8.00640i	−0.366588	+	0.634949i
$160$		0			0
$161$			18.9111i			1.49040i
$162$		0			0
$163$	−5.47905	−	9.49000i	−0.429152	−	0.743314i	0.567646	−	0.823273i	$-0.307854\pi$
$163$	−5.47905	−	9.49000i	−0.429152	−	0.743314i	−0.996798	+	0.0799591i	$0.974521\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.25940	−	7.37750i	0.329602	−	0.570888i	−0.652831	−	0.757504i	$-0.726419\pi$
$167$	4.25940	−	7.37750i	0.329602	−	0.570888i	0.982433	+	0.186616i	$0.0597520\pi$
$168$		0			0
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−6.12250	−	3.53483i	−0.468199	−	0.270315i
$172$		0			0
$173$	21.8628	−	12.6225i	1.66220	−	0.959671i	0.690536	−	0.723298i	$-0.257375\pi$
$173$	21.8628	−	12.6225i	1.66220	−	0.959671i	0.971662	−	0.236373i	$-0.0759587\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.33760			0.401199
$178$		0			0
$179$	3.24500	−	5.62050i	0.242543	−	0.420096i	−0.718895	−	0.695118i	$-0.755352\pi$
$179$	3.24500	−	5.62050i	0.242543	−	0.420096i	0.961438	+	0.275022i	$0.0886853\pi$
$180$		0			0
$181$	13.4900			1.00270			0.501352	−	0.865244i	$-0.332836\pi$
$181$	13.4900			1.00270			0.501352	+	0.865244i	$0.332836\pi$
$182$		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	0.546630	−	0.837374i	$-0.315910\pi$
$191$	−6.24500	−	10.8167i	−0.451872	−	0.782666i	−0.998502	+	0.0547085i	$0.982577\pi$
$192$		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
$199$	12.1225	+	20.9968i	0.859341	+	1.48842i	0.872558	+	0.488510i	$0.162459\pi$
$199$	12.1225	+	20.9968i	0.859341	+	1.48842i	−0.0132172	+	0.999913i	$0.504207\pi$
$200$		0			0
$201$	0.122499	−	0.0707248i	0.00864041	−	0.00498854i
$202$		0			0
$203$	26.1222			1.83342
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	5.24500i		−	0.364553i
$208$		0			0
$209$	−24.4900			−1.69401
$210$		0			0
$211$	−9.24500	+	16.0128i	−0.636452	+	1.10237i	0.349754	+	0.936842i	$0.386265\pi$
$211$	−9.24500	+	16.0128i	−0.636452	+	1.10237i	−0.986206	+	0.165525i	$0.947068\pi$
$212$		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
$219$	−1.74500	−	1.00748i	−0.117916	−	0.0680789i
$220$		0			0
$221$	−7.00000	+	1.73205i	−0.470871	+	0.116510i
$222$		0			0
$223$	−12.3365	+	21.3675i	−0.826115	+	1.43087i	0.0749489	+	0.997187i	$0.476121\pi$
$223$	−12.3365	+	21.3675i	−0.826115	+	1.43087i	−0.901064	+	0.433686i	$0.857213\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.2026	−	22.8675i	−0.876284	−	1.51777i	−0.855388	−	0.517987i	$-0.826681\pi$
$227$	−13.2026	−	22.8675i	−0.876284	−	1.51777i	−0.0208962	−	0.999782i	$-0.506652\pi$
$228$		0			0
$229$			19.9013i			1.31511i	0.753406	+	0.657556i	$0.228410\pi$
$229$			19.9013i			1.31511i	−0.753406	+	0.657556i	$0.771590\pi$
$230$		0			0
$231$	6.24500	−	10.8167i	0.410891	−	0.711684i
$232$		0			0
$233$		−	2.75500i		−	0.180486i	−0.995920	−	0.0902431i	$-0.971236\pi$
$233$		−	2.75500i		−	0.180486i	0.995920	−	0.0902431i	$-0.0287644\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.67628	+	2.12250i	0.238800	+	0.137871i
$238$		0			0
$239$			16.0128i			1.03578i	0.855447	+	0.517891i	$0.173283\pi$
$239$			16.0128i			1.03578i	−0.855447	+	0.517891i	$0.826717\pi$
$240$		0			0
$241$	−22.7450	+	13.1318i	−1.46513	+	0.845896i	−0.999241	−	0.0389456i	$-0.987600\pi$
$241$	−22.7450	+	13.1318i	−1.46513	+	0.845896i	−0.465893	+	0.884841i	$0.654267\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−24.7438	+	6.12250i	−1.57441	+	0.389565i
$248$		0			0
$249$	10.6225	+	6.13290i	0.673174	+	0.388657i
$250$		0			0
$251$	0.377501	+	0.653851i	0.0238277	+	0.0412707i	0.877693	−	0.479223i	$-0.159081\pi$
$251$	0.377501	+	0.653851i	0.0238277	+	0.0412707i	−0.853866	+	0.520493i	$0.825748\pi$
$252$		0			0
$253$	−9.08460	−	15.7350i	−0.571144	−	0.989251i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.1692	−	10.4900i	−1.13336	−	0.654348i	−0.188585	−	0.982057i	$-0.560390\pi$
$257$	−18.1692	−	10.4900i	−1.13336	−	0.654348i	−0.944779	+	0.327709i	$0.893723\pi$
$258$		0			0
$259$	26.0000			1.61556
$260$		0			0
$261$	−7.24500			−0.448454
$262$		0			0
$263$	−16.4372	−	9.49000i	−1.01356	−	0.585178i	−0.101327	−	0.994853i	$-0.532309\pi$
$263$	−16.4372	−	9.49000i	−1.01356	−	0.585178i	−0.912232	+	0.409675i	$0.865642\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.52735	−	4.37750i	−0.154671	−	0.267899i
$268$		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
$271$	−12.1225	−	6.99893i	−0.736389	−	0.425155i	0.0843657	−	0.996435i	$-0.473114\pi$
$271$	−12.1225	−	6.99893i	−0.736389	−	0.425155i	−0.820755	+	0.571280i	$0.806447\pi$
$272$		0			0
$273$	3.60555	−	12.4900i	0.218218	−	0.755929i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.17373	−	1.25500i	0.130607	−	0.0754058i	−0.433273	−	0.901263i	$-0.642641\pi$
$277$	2.17373	−	1.25500i	0.130607	−	0.0754058i	0.563880	+	0.825857i	$0.309308\pi$
$278$		0			0
$279$	−3.00000	+	1.73205i	−0.179605	+	0.103695i
$280$		0			0
$281$			22.6581i			1.35167i	0.737053	+	0.675835i	$0.236217\pi$
$281$			22.6581i			1.35167i	−0.737053	+	0.675835i	$0.763783\pi$
$282$		0			0
$283$	21.6333	+	12.4900i	1.28597	+	0.742453i	0.977932	−	0.208922i	$-0.0669955\pi$
$283$	21.6333	+	12.4900i	1.28597	+	0.742453i	0.308034	+	0.951375i	$0.400329\pi$
$284$		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
$291$			0.282899i			0.0165839i
$292$		0			0
$293$	1.07820	+	1.86750i	0.0629891	+	0.109100i	0.895800	−	0.444457i	$-0.146603\pi$
$293$	1.07820	+	1.86750i	0.0629891	+	0.109100i	−0.832811	+	0.553557i	$0.813270\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.73205	+	3.00000i	−0.100504	+	0.174078i
$298$		0			0
$299$	−13.1125	−	13.6269i	−0.758315	−	0.788064i
$300$		0			0
$301$	−25.7450	−	14.8639i	−1.48392	−	0.856740i
$302$		0			0
$303$	−9.73845	+	5.62250i	−0.559460	+	0.323004i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	7.49400			0.427705			0.213853	−	0.976866i	$-0.431399\pi$
$307$	7.49400			0.427705			0.213853	+	0.976866i	$0.431399\pi$
$308$		0			0
$309$	−7.12250	+	12.3365i	−0.405185	+	0.701801i
$310$		0			0
$311$	9.73499			0.552021			0.276010	−	0.961155i	$-0.410988\pi$
$311$	9.73499			0.552021			0.276010	+	0.961155i	$0.410988\pi$
$312$		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
$317$	−9.08460			−0.510242			−0.255121	−	0.966909i	$-0.582115\pi$
$317$	−9.08460			−0.510242			−0.255121	+	0.966909i	$0.582115\pi$
$318$		0			0
$319$	−21.7350	+	12.5487i	−1.21693	+	0.702593i
$320$		0			0
$321$	1.62250	+	2.81025i	0.0905591	+	0.156853i
$322$		0			0
$323$	7.06965	−	12.2450i	0.393366	−	0.681330i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.47905	−	9.49000i	0.302992	−	0.524798i
$328$		0			0
$329$	−19.2450	−	33.3333i	−1.06101	−	1.83773i
$330$		0			0
$331$	12.1225	−	6.99893i	0.666313	−	0.384696i	−0.128365	−	0.991727i	$-0.540973\pi$
$331$	12.1225	−	6.99893i	0.666313	−	0.384696i	0.794678	+	0.607031i	$0.207640\pi$
$332$		0			0
$333$	−7.21110			−0.395166
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	19.9800i		−	1.08838i	−0.838962	−	0.544190i	$-0.816837\pi$
$337$		−	19.9800i		−	1.08838i	0.838962	−	0.544190i	$-0.183163\pi$
$338$		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
$353$	4.40085	−	7.62250i	0.234234	−	0.405705i	−0.724816	−	0.688943i	$-0.758075\pi$
$353$	4.40085	−	7.62250i	0.234234	−	0.405705i	0.959050	+	0.283238i	$0.0914086\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.60555	+	6.24500i	0.190826	+	0.330520i
$358$		0			0
$359$		−	8.23591i		−	0.434674i	−0.976097	−	0.217337i	$-0.930263\pi$
$359$		−	8.23591i		−	0.434674i	0.976097	−	0.217337i	$-0.0697371\pi$
$360$		0			0
$361$	15.4900	−	26.8295i	0.815263	−	1.41208i
$362$		0			0
$363$			1.00000i			0.0524864i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.36857	+	1.36750i	0.123639	+	0.0713828i	0.560544	−	0.828125i	$-0.310592\pi$
$367$	2.36857	+	1.36750i	0.123639	+	0.0713828i	−0.436905	+	0.899508i	$0.643925\pi$
$368$		0			0
$369$			7.21110i			0.375395i
$370$		0			0
$371$	28.8675	−	16.6667i	1.49873	−	0.865290i
$372$		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
$377$	−18.8231	+	18.1125i	−0.969437	+	0.932841i
$378$		0			0
$379$	9.12250	+	5.26688i	0.468591	+	0.270541i	0.715650	−	0.698459i	$-0.246131\pi$
$379$	9.12250	+	5.26688i	0.468591	+	0.270541i	−0.247059	+	0.969001i	$0.579464\pi$
$380$		0			0
$381$	−8.12250	−	14.0686i	−0.416128	−	0.720755i
$382$		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
$387$	7.14038	+	4.12250i	0.362966	+	0.209558i
$388$		0			0
$389$	16.9800			0.860920			0.430460	−	0.902610i	$-0.358351\pi$
$389$	16.9800			0.860920			0.430460	+	0.902610i	$0.358351\pi$
$390$		0			0
$391$	10.4900			0.530502
$392$		0			0
$393$	9.73845	+	5.62250i	0.491240	+	0.283618i
$394$		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
$399$	12.7450	+	22.0750i	0.638048	+	1.10513i
$400$		0			0
$401$	−24.9800	−	14.4222i	−1.24744	−	0.720211i	−0.276843	−	0.960915i	$-0.589288\pi$
$401$	−24.9800	−	14.4222i	−1.24744	−	0.720211i	−0.970598	+	0.240705i	$0.922621\pi$
$402$		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
$409$	−11.7550	+	6.78675i	−0.581247	+	0.335583i	−0.761629	−	0.648013i	$-0.775600\pi$
$409$	−11.7550	+	6.78675i	−0.581247	+	0.335583i	0.180382	+	0.983597i	$0.442267\pi$
$410$		0			0
$411$			16.2957i			0.803808i
$412$		0			0
$413$	−16.6667	−	9.62250i	−0.820113	−	0.473492i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	0.244998i		−	0.0119976i
$418$		0			0
$419$	16.8675	−	29.2154i	0.824031	−	1.42726i	−0.0786263	−	0.996904i	$-0.525053\pi$
$419$	16.8675	−	29.2154i	0.824031	−	1.42726i	0.902657	−	0.430360i	$-0.141613\pi$
$420$		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
$423$	5.33760	+	9.24500i	0.259523	+	0.449507i
$424$		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
$431$	22.8675	+	13.2026i	1.10149	+	0.635945i	0.936612	−	0.350369i	$-0.113944\pi$
$431$	22.8675	+	13.2026i	1.10149	+	0.635945i	0.164877	+	0.986314i	$0.447277\pi$
$432$		0			0
$433$	−9.08460	+	5.24500i	−0.436578	+	0.252059i	−0.702145	−	0.712034i	$-0.747774\pi$
$433$	−9.08460	+	5.24500i	−0.436578	+	0.252059i	0.265567	+	0.964092i	$0.414441\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	37.0803			1.77379
$438$		0			0
$439$	13.1225	−	22.7288i	0.626303	−	1.08479i	−0.361985	−	0.932184i	$-0.617901\pi$
$439$	13.1225	−	22.7288i	0.626303	−	1.08479i	0.988287	−	0.152604i	$-0.0487659\pi$
$440$		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
$447$	−22.6581			−1.07169
$448$		0			0
$449$	−7.86750	+	4.54230i	−0.371290	+	0.214364i	−0.674022	−	0.738711i	$-0.735435\pi$
$449$	−7.86750	+	4.54230i	−0.371290	+	0.214364i	0.302732	+	0.953076i	$0.402101\pi$
$450$		0			0
$451$	12.4900	+	21.6333i	0.588131	+	1.01867i
$452$		0			0
$453$	−10.6045	+	18.3675i	−0.498242	+	0.862980i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.31518	+	4.01000i	−0.108299	+	0.187580i	−0.915081	−	0.403269i	$-0.867874\pi$
$457$	−2.31518	+	4.01000i	−0.108299	+	0.187580i	0.806782	+	0.590849i	$0.201207\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	−24.7350	+	14.2808i	−1.15202	+	0.665121i	−0.949380	−	0.314131i	$-0.898287\pi$
$461$	−24.7350	+	14.2808i	−1.15202	+	0.665121i	−0.202644	+	0.979252i	$0.564953\pi$
$462$		0			0
$463$	10.5338			0.489545			0.244773	−	0.969581i	$-0.421287\pi$
$463$	10.5338			0.489545			0.244773	+	0.969581i	$0.421287\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			20.4900i			0.948164i	0.880481	+	0.474082i	$0.157220\pi$
$467$			20.4900i			0.948164i	−0.880481	+	0.474082i	$0.842780\pi$
$468$		0			0
$469$	−0.510004			−0.0235498
$470$		0			0
$471$	−8.50000	+	14.7224i	−0.391659	+	0.678374i
$472$		0			0
$473$	28.5615			1.31326
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.00640	+	4.62250i	−0.366588	+	0.211650i
$478$		0			0
$479$	−32.1125	−	18.5402i	−1.46726	−	0.847121i	−0.467929	−	0.883766i	$-0.655000\pi$
$479$	−32.1125	−	18.5402i	−1.46726	−	0.847121i	−0.999328	+	0.0366446i	$0.988333\pi$
$480$		0			0
$481$	−18.7350	+	18.0278i	−0.854242	+	0.821995i
$482$		0			0
$483$	−9.45555	+	16.3775i	−0.430243	+	0.745202i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	3.81773	+	6.61249i	0.172998	+	0.299641i	0.939467	−	0.342641i	$-0.111321\pi$
$487$	3.81773	+	6.61249i	0.172998	+	0.299641i	−0.766469	+	0.642281i	$0.777988\pi$
$488$		0			0
$489$		−	10.9581i		−	0.495543i
$490$		0			0
$491$	5.75500	−	9.96796i	0.259720	−	0.449848i	−0.706447	−	0.707766i	$-0.749703\pi$
$491$	5.75500	−	9.96796i	0.259720	−	0.449848i	0.966167	+	0.257918i	$0.0830365\pi$
$492$		0			0
$493$		−	14.4900i		−	0.652597i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.5167	+	13.0000i	1.01001	+	0.583130i
$498$		0			0
$499$			20.6432i			0.924115i	0.886850	+	0.462057i	$0.152889\pi$
$499$			20.6432i			0.924115i	−0.886850	+	0.462057i	$0.847111\pi$
$500$		0			0
$501$	7.37750	−	4.25940i	0.329602	−	0.190296i
$502$		0			0
$503$	3.23460	−	1.86750i	0.144224	−	0.0832676i	−0.426152	−	0.904652i	$-0.640131\pi$
$503$	3.23460	−	1.86750i	0.144224	−	0.0832676i	0.570375	+	0.821384i	$0.306798\pi$
$504$		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
$511$	3.63250	+	6.29168i	0.160692	+	0.278328i
$512$		0			0
$513$	−3.53483	−	6.12250i	−0.156066	−	0.270315i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	32.0256	+	18.4900i	1.40848	+	0.813189i
$518$		0			0
$519$	25.2450			1.10813
$520$		0			0
$521$	8.75500			0.383564			0.191782	−	0.981438i	$-0.438573\pi$
$521$	8.75500			0.383564			0.191782	+	0.981438i	$0.438573\pi$
$522$		0			0
$523$	−16.2250	−	9.36750i	−0.709469	−	0.409612i	0.101395	−	0.994846i	$-0.467669\pi$
$523$	−16.2250	−	9.36750i	−0.709469	−	0.409612i	−0.810864	+	0.585234i	$0.801003\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46410	−	6.00000i	−0.150899	−	0.261364i
$528$		0			0
$529$	2.25500	+	3.90578i	0.0980436	+	0.169816i
$530$		0			0
$531$	4.62250	+	2.66880i	0.200599	+	0.115816i
$532$		0			0
$533$	18.0278	+	18.7350i	0.780869	+	0.811503i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.62050	−	3.24500i	0.242543	−	0.140032i
$538$		0			0
$539$	−18.0000	+	10.3923i	−0.775315	+	0.447628i
$540$		0			0
$541$		−	6.64530i		−	0.285704i	−0.989744	−	0.142852i	$-0.954373\pi$
$541$		−	6.64530i		−	0.285704i	0.989744	−	0.142852i	$-0.0456273\pi$
$542$		0			0
$543$	11.6827	+	6.74500i	0.501352	+	0.289456i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	22.2450i		−	0.951127i	−0.879681	−	0.475564i	$-0.842244\pi$
$547$		−	22.2450i		−	0.951127i	0.879681	−	0.475564i	$-0.157756\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	51.2196i		−	2.18203i
$552$		0			0
$553$	−7.65278	−	13.2550i	−0.325429	−	0.563660i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.6902	−	21.9800i	0.537699	−	0.931322i	−0.461328	−	0.887229i	$-0.652627\pi$
$557$	12.6902	−	21.9800i	0.537699	−	0.931322i	0.999027	−	0.0440927i	$-0.0140397\pi$
$558$		0			0
$559$	28.8575	−	7.14038i	1.22054	−	0.302006i
$560$		0			0
$561$	−6.00000	−	3.46410i	−0.253320	−	0.146254i
$562$		0			0
$563$	11.7000	−	6.75500i	0.493096	−	0.284689i	−0.232762	−	0.972534i	$-0.574776\pi$
$563$	11.7000	−	6.75500i	0.493096	−	0.284689i	0.725858	+	0.687844i	$0.241443\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.60555			0.151419
$568$		0			0
$569$	19.6225	−	33.9872i	0.822618	−	1.42482i	−0.0811083	−	0.996705i	$-0.525846\pi$
$569$	19.6225	−	33.9872i	0.822618	−	1.42482i	0.903726	−	0.428111i	$-0.140821\pi$
$570$		0			0
$571$	−10.7350			−0.449246			−0.224623	−	0.974446i	$-0.572115\pi$
$571$	−10.7350			−0.449246			−0.224623	+	0.974446i	$0.572115\pi$
$572$		0			0
$573$		−	12.4900i		−	0.521777i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.6184			−0.816723			−0.408361	−	0.912820i	$-0.633900\pi$
$577$	−19.6184			−0.816723			−0.408361	+	0.912820i	$0.633900\pi$
$578$		0			0
$579$	7.50000	−	4.33013i	0.311689	−	0.179954i
$580$		0			0
$581$	−22.1125	−	38.3000i	−0.917381	−	1.58895i
$582$		0			0
$583$	−16.0128	+	27.7350i	−0.663183	+	1.14867i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.1940	−	33.2450i	0.792222	−	1.37217i	−0.132367	−	0.991201i	$-0.542258\pi$
$587$	19.1940	−	33.2450i	0.792222	−	1.37217i	0.924589	−	0.380967i	$-0.124409\pi$
$588$		0			0
$589$	−12.2450	−	21.2090i	−0.504546	−	0.873900i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.33760			−0.219189			−0.109595	−	0.993976i	$-0.534955\pi$
$593$	−5.33760			−0.219189			−0.109595	+	0.993976i	$0.534955\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			24.2450i			0.992282i
$598$		0			0
$599$	21.7350			0.888068			0.444034	−	0.896010i	$-0.353547\pi$
$599$	21.7350			0.888068			0.444034	+	0.896010i	$0.353547\pi$
$600$		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
$603$	0.141450			0.00576028
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−37.6461	+	21.7350i	−1.52801	+	0.882196i	−0.528563	+	0.848894i	$0.677269\pi$
$607$	−37.6461	+	21.7350i	−1.52801	+	0.882196i	−0.999445	+	0.0333023i	$0.989398\pi$
$608$		0			0
$609$	22.6225	+	13.0611i	0.916710	+	0.529263i
$610$		0			0
$611$	36.9800	+	10.6752i	1.49605	+	0.431873i
$612$		0			0
$613$	−12.8489	+	22.2550i	−0.518963	+	0.898871i	0.480794	+	0.876834i	$0.340349\pi$
$613$	−12.8489	+	22.2550i	−0.518963	+	0.898871i	−0.999757	+	0.0220373i	$0.992985\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.55725	+	11.3575i	0.263985	+	0.457235i	0.967297	−	0.253646i	$-0.0816297\pi$
$617$	6.55725	+	11.3575i	0.263985	+	0.457235i	−0.703312	+	0.710881i	$0.748296\pi$
$618$		0			0
$619$		−	38.5295i		−	1.54863i	−0.632800	−	0.774315i	$-0.718095\pi$
$619$		−	38.5295i		−	1.54863i	0.632800	−	0.774315i	$-0.281905\pi$
$620$		0			0
$621$	2.62250	−	4.54230i	0.105237	−	0.182276i
$622$		0			0
$623$			18.2250i			0.730169i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−21.2090	−	12.2450i	−0.847004	−	0.489018i
$628$		0			0
$629$		−	14.4222i		−	0.575051i
$630$		0			0
$631$	24.1225	−	13.9271i	0.960302	−	0.554430i	0.0640357	−	0.997948i	$-0.479603\pi$
$631$	24.1225	−	13.9271i	0.960302	−	0.554430i	0.896266	+	0.443517i	$0.146270\pi$
$632$		0			0
$633$	−16.0128	+	9.24500i	−0.636452	+	0.367456i
$634$		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
$641$	22.1125	+	38.3000i	0.873391	+	1.51276i	0.858467	+	0.512869i	$0.171417\pi$
$641$	22.1125	+	38.3000i	0.873391	+	1.51276i	0.0149242	+	0.999889i	$0.495249\pi$
$642$		0			0
$643$	12.7609	+	22.1025i	0.503240	+	0.871637i	0.999993	+	0.00374522i	$0.00119214\pi$
$643$	12.7609	+	22.1025i	0.503240	+	0.871637i	−0.496753	+	0.867892i	$0.665475\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.4385	+	12.3775i	0.842833	+	0.486610i	0.858226	−	0.513272i	$-0.171567\pi$
$647$	21.4385	+	12.3775i	0.842833	+	0.486610i	−0.0153933	+	0.999882i	$0.504900\pi$
$648$		0			0
$649$	18.4900			0.725796
$650$		0			0
$651$	12.4900			0.489522
$652$		0			0
$653$	−29.8692	−	17.2450i	−1.16887	−	0.674849i	−0.215458	−	0.976513i	$-0.569125\pi$
$653$	−29.8692	−	17.2450i	−1.16887	−	0.674849i	−0.953414	+	0.301664i	$0.902458\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.00748	−	1.74500i	−0.0393053	−	0.0680789i
$658$		0			0
$659$	5.49000	+	9.50895i	0.213860	+	0.370416i	0.952919	−	0.303224i	$-0.0980631\pi$
$659$	5.49000	+	9.50895i	0.213860	+	0.370416i	−0.739059	+	0.673640i	$0.764730\pi$
$660$		0			0
$661$	−4.01000	−	2.31518i	−0.155971	−	0.0900499i	0.419983	−	0.907532i	$-0.362036\pi$
$661$	−4.01000	−	2.31518i	−0.155971	−	0.0900499i	−0.575954	+	0.817482i	$0.695369\pi$
$662$		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
$669$	−21.3675	+	12.3365i	−0.826115	+	0.476958i
$670$		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
$677$		−	31.7350i		−	1.21967i	−0.792527	−	0.609837i	$-0.791235\pi$
$677$		−	31.7350i		−	1.21967i	0.792527	−	0.609837i	$-0.208765\pi$
$678$		0			0
$679$	0.510004	−	0.883353i	0.0195722	−	0.0339000i
$680$		0			0
$681$		−	26.4051i		−	1.01185i
$682$		0			0
$683$	−11.6120	−	20.1125i	−0.444319	−	0.769583i	0.553685	−	0.832726i	$-0.313221\pi$
$683$	−11.6120	−	20.1125i	−0.444319	−	0.769583i	−0.998005	+	0.0631427i	$0.979888\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.95063	+	17.2350i	−0.379640	+	0.657556i
$688$		0			0
$689$	−9.24500	+	32.0256i	−0.352206	+	1.22008i
$690$		0			0
$691$	−5.87750	−	3.39338i	−0.223591	−	0.129090i	0.384021	−	0.923324i	$-0.374539\pi$
$691$	−5.87750	−	3.39338i	−0.223591	−	0.129090i	−0.607612	+	0.794234i	$0.707872\pi$
$692$		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
$699$	1.37750	−	2.38590i	0.0521019	−	0.0902431i
$700$		0			0
$701$	22.9800			0.867942			0.433971	−	0.900927i	$-0.357112\pi$
$701$	22.9800			0.867942			0.433971	+	0.900927i	$0.357112\pi$
$702$		0			0
$703$		−	50.9800i		−	1.92275i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	40.5444			1.52483
$708$		0			0
$709$	−13.7450	+	7.93568i	−0.516204	+	0.298031i	−0.735380	−	0.677655i	$-0.762996\pi$
$709$	−13.7450	+	7.93568i	−0.516204	+	0.298031i	0.219176	+	0.975685i	$0.429663\pi$
$710$		0			0
$711$	2.12250	+	3.67628i	0.0795999	+	0.137871i
$712$		0			0
$713$	9.08460	−	15.7350i	0.340221	−	0.589280i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.00640	+	13.8675i	−0.299005	+	0.517891i
$718$		0			0
$719$	−19.3775	−	33.5628i	−0.722659	−	1.25168i	−0.959930	−	0.280238i	$-0.909586\pi$
$719$	−19.3775	−	33.5628i	−0.722659	−	1.25168i	0.237272	−	0.971443i	$-0.423747\pi$
$720$		0			0
$721$	44.4800	−	25.6805i	1.65652	−	0.956393i
$722$		0			0
$723$	−26.2637			−0.976756
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	51.2250i		−	1.89983i	−0.312509	−	0.949915i	$-0.601169\pi$
$727$		−	51.2250i		−	1.89983i	0.312509	−	0.949915i	$-0.398831\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.24500	+	14.2808i	−0.304952	+	0.528193i
$732$		0			0
$733$	−22.2338			−0.821223			−0.410611	−	0.911810i	$-0.634685\pi$
$733$	−22.2338			−0.821223			−0.410611	+	0.911810i	$0.634685\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.424349	−	0.244998i	0.0156311	−	0.00902462i
$738$		0			0
$739$	2.51000	+	1.44915i	0.0923320	+	0.0533079i	0.545455	−	0.838140i	$-0.316357\pi$
$739$	2.51000	+	1.44915i	0.0923320	+	0.0533079i	−0.453123	+	0.891448i	$0.649690\pi$
$740$		0			0
$741$	−24.4900	−	7.06965i	−0.899662	−	0.259710i
$742$		0			0
$743$	−17.4620	+	30.2450i	−0.640617	+	1.10958i	0.344678	+	0.938721i	$0.387988\pi$
$743$	−17.4620	+	30.2450i	−0.640617	+	1.10958i	−0.985295	+	0.170860i	$0.945345\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.13290	+	10.6225i	0.224391	+	0.388657i
$748$		0			0
$749$		−	11.7000i		−	0.427509i
$750$		0			0
$751$	5.75500	−	9.96796i	0.210003	−	0.363736i	−0.741712	−	0.670718i	$-0.765986\pi$
$751$	5.75500	−	9.96796i	0.210003	−	0.363736i	0.951715	+	0.306982i	$0.0993193\pi$
$752$		0			0
$753$			0.755002i			0.0275138i
$754$		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
$759$		−	18.1692i		−	0.659500i
$760$		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
$763$	−34.2167	+	19.7550i	−1.23873	+	0.715179i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.6816	−	4.62250i	0.674554	−	0.166909i
$768$		0			0
$769$	1.74500	+	1.00748i	0.0629262	+	0.0363305i	0.531133	−	0.847288i	$-0.321766\pi$
$769$	1.74500	+	1.00748i	0.0629262	+	0.0363305i	−0.468207	+	0.883619i	$0.655100\pi$
$770$		0			0
$771$	−10.4900	−	18.1692i	−0.377788	−	0.654348i
$772$		0			0
$773$	−22.9410	−	39.7350i	−0.825131	−	1.42917i	−0.901819	−	0.432113i	$-0.857768\pi$
$773$	−22.9410	−	39.7350i	−0.825131	−	1.42917i	0.0766886	−	0.997055i	$-0.475565\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	22.5167	+	13.0000i	0.807781	+	0.466372i
$778$		0			0
$779$	−50.9800			−1.82655
$780$		0			0
$781$	−24.9800			−0.893854
$782$		0			0
$783$	−6.27435	−	3.62250i	−0.224227	−	0.129458i
$784$		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
$789$	−9.49000	−	16.4372i	−0.337853	−	0.585178i
$790$		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
$797$	13.2026	−	7.62250i	0.467659	−	0.270003i	−0.247601	−	0.968862i	$-0.579642\pi$
$797$	13.2026	−	7.62250i	0.467659	−	0.270003i	0.715259	+	0.698859i	$0.246309\pi$
$798$		0			0
$799$	−18.4900	+	10.6752i	−0.654129	+	0.377662i
$800$		0			0
$801$		−	5.05470i		−	0.178599i
$802$		0			0
$803$	−6.04485	−	3.49000i	−0.213318	−	0.123159i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	24.0000i		−	0.844840i
$808$		0			0
$809$	2.13250	−	3.69360i	0.0749748	−	0.129860i	−0.826101	−	0.563523i	$-0.809446\pi$
$809$	2.13250	−	3.69360i	0.0749748	−	0.129860i	0.901075	+	0.433663i	$0.142779\pi$
$810$		0			0
$811$		−	34.7825i		−	1.22138i	−0.791871	−	0.610689i	$-0.790893\pi$
$811$		−	34.7825i		−	1.22138i	0.791871	−	0.610689i	$-0.209107\pi$
$812$		0			0
$813$	−6.99893	−	12.1225i	−0.245463	−	0.425155i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−29.1446	+	50.4800i	−1.01964	+	1.76607i
$818$		0			0
$819$	9.36750	−	9.01388i	0.327327	−	0.314970i
$820$		0			0
$821$	36.0925	+	20.8380i	1.25964	+	0.727251i	0.973004	−	0.230789i	$-0.0741307\pi$
$821$	36.0925	+	20.8380i	1.25964	+	0.727251i	0.286633	+	0.958041i	$0.407464\pi$
$822$		0			0
$823$	7.56473	−	4.36750i	0.263690	−	0.152241i	−0.362327	−	0.932051i	$-0.618018\pi$
$823$	7.56473	−	4.36750i	0.263690	−	0.152241i	0.626017	+	0.779810i	$0.284684\pi$
$824$		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
$829$	14.2550	−	24.6904i	0.495097	−	0.857533i	−0.504887	−	0.863185i	$-0.668466\pi$
$829$	14.2550	−	24.6904i	0.495097	−	0.857533i	0.999984	+	0.00565264i	$0.00179930\pi$
$830$		0			0
$831$	2.51000			0.0870711
$832$		0			0
$833$		−	12.0000i		−	0.415775i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.46410			−0.119737
$838$		0			0
$839$	−7.62250	+	4.40085i	−0.263158	+	0.151934i	−0.625774	−	0.780004i	$-0.715217\pi$
$839$	−7.62250	+	4.40085i	−0.263158	+	0.151934i	0.362616	+	0.931939i	$0.381884\pi$
$840$		0			0
$841$	−11.7450	−	20.3429i	−0.405000	−	0.701480i
$842$		0			0
$843$	−11.3291	+	19.6225i	−0.390193	+	0.675835i
$844$		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
$851$	32.7550	−	18.9111i	1.12283	−	0.648264i
$852$		0			0
$853$	−38.6709			−1.32407			−0.662033	−	0.749474i	$-0.730306\pi$
$853$	−38.6709			−1.32407			−0.662033	+	0.749474i	$0.730306\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			40.4900i			1.38311i	0.722323	+	0.691556i	$0.243074\pi$
$857$			40.4900i			1.38311i	−0.722323	+	0.691556i	$0.756926\pi$
$858$		0			0
$859$	−14.7350			−0.502752			−0.251376	−	0.967890i	$-0.580883\pi$
$859$	−14.7350			−0.502752			−0.251376	+	0.967890i	$0.580883\pi$
$860$		0			0
$861$	13.0000	−	22.5167i	0.443039	−	0.767366i
$862$		0			0
$863$	−38.9538			−1.32600			−0.663002	−	0.748618i	$-0.730718\pi$
$863$	−38.9538			−1.32600			−0.663002	+	0.748618i	$0.730718\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.2583	+	6.50000i	−0.382353	+	0.220752i
$868$		0			0
$869$	12.7350	+	7.35255i	0.432005	+	0.249418i
$870$		0			0
$871$	0.367497	−	0.353624i	0.0124522	−	0.0119821i
$872$		0			0
$873$	−0.141450	+	0.244998i	−0.00478735	+	0.00829193i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.2882	−	26.4800i	−0.516247	−	0.894166i	−0.999822	−	0.0188630i	$-0.993995\pi$
$877$	−15.2882	−	26.4800i	−0.516247	−	0.894166i	0.483575	−	0.875303i	$-0.339338\pi$
$878$		0			0
$879$			2.15640i			0.0727336i
$880$		0			0
$881$	−23.7350	+	41.1102i	−0.799652	+	1.38504i	0.120190	+	0.992751i	$0.461649\pi$
$881$	−23.7350	+	41.1102i	−0.799652	+	1.38504i	−0.919843	+	0.392287i	$0.871684\pi$
$882$		0			0
$883$		−	4.49000i		−	0.151100i	−0.997142	−	0.0755502i	$-0.975929\pi$
$883$		−	4.49000i		−	0.151100i	0.997142	−	0.0755502i	$-0.0240713\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.1308	+	11.6225i	0.675925	+	0.390245i	0.798318	−	0.602236i	$-0.205724\pi$
$887$	20.1308	+	11.6225i	0.675925	+	0.390245i	−0.122393	+	0.992482i	$0.539057\pi$
$888$		0			0
$889$			58.5722i			1.96445i
$890$		0			0
$891$	−3.00000	+	1.73205i	−0.100504	+	0.0580259i
$892$		0			0
$893$	−65.3589	+	37.7350i	−2.18715	+	1.26275i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.54230	−	18.3575i	−0.151663	−	0.612939i
$898$		0			0
$899$	−21.7350	−	12.5487i	−0.724903	−	0.418523i
$900$		0			0
$901$	−9.24500	−	16.0128i	−0.307996	−	0.533464i
$902$		0			0
$903$	−14.8639	−	25.7450i	−0.494639	−	0.856740i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.88845	−	2.24500i	−0.129114	−	0.0745439i	0.434052	−	0.900888i	$-0.357083\pi$
$907$	−3.88845	−	2.24500i	−0.129114	−	0.0745439i	−0.563166	+	0.826344i	$0.690417\pi$
$908$		0			0
$909$	−11.2450			−0.372973
$910$		0			0
$911$	14.7550			0.488855			0.244428	−	0.969668i	$-0.421400\pi$
$911$	14.7550			0.488855			0.244428	+	0.969668i	$0.421400\pi$
$912$		0			0
$913$	36.7974	+	21.2450i	1.21782	+	0.703107i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.2722	−	35.1125i	−0.669447	−	1.15952i
$918$		0			0
$919$	7.87750	+	13.6442i	0.259855	+	0.450082i	0.966203	−	0.257783i	$-0.0829920\pi$
$919$	7.87750	+	13.6442i	0.259855	+	0.450082i	−0.706348	+	0.707865i	$0.749659\pi$
$920$		0			0
$921$	6.49000	+	3.74700i	0.213853	+	0.123468i
$922$		0			0
$923$	−25.2389	+	6.24500i	−0.830747	+	0.205557i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−12.3365	+	7.12250i	−0.405185	+	0.233934i
$928$		0			0
$929$	3.97999	−	2.29785i	0.130579	−	0.0753900i	−0.433287	−	0.901256i	$-0.642646\pi$
$929$	3.97999	−	2.29785i	0.130579	−	0.0753900i	0.563867	+	0.825866i	$0.309313\pi$
$930$		0			0
$931$		−	42.4179i		−	1.39019i
$932$		0			0
$933$	8.43075	+	4.86750i	0.276010	+	0.159355i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			59.4900i			1.94345i	0.236108	+	0.971727i	$0.424128\pi$
$937$			59.4900i			1.94345i	−0.236108	+	0.971727i	$0.575872\pi$
$938$		0			0
$939$	3.50000	−	6.06218i	0.114218	−	0.197832i
$940$		0			0
$941$			36.7974i			1.19956i	0.800164	+	0.599781i	$0.204746\pi$
$941$			36.7974i			1.19956i	−0.800164	+	0.599781i	$0.795254\pi$
$942$		0			0
$943$	−18.9111	−	32.7550i	−0.615830	−	1.06665i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.35255	−	12.7350i	0.238926	−	0.413832i	−0.721480	−	0.692435i	$-0.756538\pi$
$947$	7.35255	−	12.7350i	0.238926	−	0.413832i	0.960406	+	0.278603i	$0.0898714\pi$
$948$		0			0
$949$	−6.97999	−	2.01495i	−0.226580	−	0.0654080i
$950$		0			0
$951$	−7.86750	−	4.54230i	−0.255121	−	0.147294i
$952$		0			0
$953$	23.8244	−	13.7550i	0.771747	−	0.445568i	−0.0617506	−	0.998092i	$-0.519668\pi$
$953$	23.8244	−	13.7550i	0.771747	−	0.445568i	0.833497	+	0.552523i	$0.186335\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−25.0974			−0.811284
$958$		0			0
$959$	29.3775	−	50.8833i	0.948649	−	1.64311i
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$			3.24500i			0.104569i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.565799			0.0181949			0.00909743	−	0.999959i	$-0.497104\pi$
$967$	0.565799			0.0181949			0.00909743	+	0.999959i	$0.497104\pi$
$968$		0			0
$969$	12.2450	−	7.06965i	0.393366	−	0.227110i
$970$		0			0
$971$	4.11249	+	7.12305i	0.131976	+	0.228590i	0.924438	−	0.381332i	$-0.124534\pi$
$971$	4.11249	+	7.12305i	0.131976	+	0.228590i	−0.792462	+	0.609921i	$0.791201\pi$
$972$		0			0
$973$	−0.441676	+	0.765006i	−0.0141595	+	0.0245250i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.8316	+	22.2250i	−0.410519	+	0.711040i	−0.994947	−	0.100406i	$-0.967986\pi$
$977$	−12.8316	+	22.2250i	−0.410519	+	0.711040i	0.584427	+	0.811446i	$0.301319\pi$
$978$		0			0
$979$	−8.75500	−	15.1641i	−0.279811	−	0.484647i
$980$		0			0
$981$	9.49000	−	5.47905i	0.302992	−	0.174933i
$982$		0			0
$983$	44.8572			1.43072			0.715362	−	0.698755i	$-0.246262\pi$
$983$	44.8572			1.43072			0.715362	+	0.698755i	$0.246262\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	38.4900i		−	1.22515i
$988$		0			0
$989$	−43.2450			−1.37511
$990$		0			0
$991$	15.6125	−	27.0416i	0.495947	−	0.859006i	−0.504042	−	0.863679i	$-0.668154\pi$
$991$	15.6125	−	27.0416i	0.495947	−	0.859006i	0.999989	+	0.00467341i	$0.00148760\pi$
$992$		0			0
$993$	13.9979			0.444209
$994$		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.2149.3		8
5.2	odd	4		3900.2.cd.h.901.2	yes	4
5.3	odd	4		3900.2.cd.f.901.1	✓	4
5.4	even	2	inner	3900.2.bw.i.2149.2		8
13.10	even	6	inner	3900.2.bw.i.49.2		8
65.23	odd	12		3900.2.cd.f.2701.1	yes	4
65.49	even	6	inner	3900.2.bw.i.49.3		8
65.62	odd	12		3900.2.cd.h.2701.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3900.2.bw.i.49.2		8	13.10	even	6	inner
3900.2.bw.i.49.3		8	65.49	even	6	inner
3900.2.bw.i.2149.2		8	5.4	even	2	inner
3900.2.bw.i.2149.3		8	1.1	even	1	trivial
3900.2.cd.f.901.1	✓	4	5.3	odd	4
3900.2.cd.f.2701.1	yes	4	65.23	odd	12
3900.2.cd.h.901.2	yes	4	5.2	odd	4
3900.2.cd.h.2701.2	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.80278 - 3.12250i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +(3.46410 + 1.00000i) q^{13} +(-1.73205 + 1.00000i) q^{17} +(-6.12250 + 3.53483i) q^{19} -3.60555i q^{21} +(-4.54230 - 2.62250i) q^{23} +1.00000i q^{27} +(-3.62250 + 6.27435i) q^{29} +3.46410i q^{31} +(1.73205 + 3.00000i) q^{33} +(-3.60555 + 6.24500i) q^{37} +(2.50000 + 2.59808i) q^{39} +(6.24500 + 3.60555i) q^{41} +(7.14038 - 4.12250i) q^{43} +10.6752 q^{47} +(-3.00000 + 5.19615i) q^{49} -2.00000 q^{51} +9.24500i q^{53} -7.06965 q^{57} +(4.62250 - 2.66880i) q^{59} +(1.80278 - 3.12250i) q^{63} +(0.0707248 - 0.122499i) q^{67} +(-2.62250 - 4.54230i) q^{69} +(-6.24500 + 3.60555i) q^{71} -2.01495 q^{73} -12.4900i q^{77} +4.24500 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.2658 q^{83} +(-6.27435 + 3.62250i) q^{87} +(-4.37750 - 2.52735i) q^{89} +(-3.12250 - 12.6194i) q^{91} +(-1.73205 + 3.00000i) q^{93} +(0.141450 + 0.244998i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} + 24 q^{11} - 24 q^{19} - 4 q^{29} + 20 q^{39} - 24 q^{49} - 16 q^{51} + 12 q^{59} + 4 q^{69} - 16 q^{79} - 4 q^{81} - 60 q^{89}+O(q^{100}) \) 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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