LMFDB - Embedded newform 3330.2.d.b.1999.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(1999,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("3330.1999");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.b.1999.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(1.00000 - 2.00000i) q^{10} -4.00000 q^{11} -6.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000i q^{17} -2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -4.00000i q^{22} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +6.00000 q^{26} +2.00000i q^{28} -8.00000 q^{29} +1.00000i q^{32} +6.00000 q^{34} +(-2.00000 + 4.00000i) q^{35} +1.00000i q^{37} -2.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} +2.00000 q^{41} -12.0000i q^{43} +4.00000 q^{44} -4.00000 q^{46} +6.00000i q^{47} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000i q^{52} +14.0000i q^{53} +(8.00000 + 4.00000i) q^{55} -2.00000 q^{56} -8.00000i q^{58} +14.0000 q^{59} -12.0000 q^{61} -1.00000 q^{64} +(-6.00000 + 12.0000i) q^{65} +4.00000i q^{67} +6.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} +16.0000i q^{73} -1.00000 q^{74} +2.00000 q^{76} +8.00000i q^{77} +8.00000 q^{79} +(-2.00000 - 1.00000i) q^{80} +2.00000i q^{82} -16.0000i q^{83} +(-6.00000 + 12.0000i) q^{85} +12.0000 q^{86} +4.00000i q^{88} -10.0000 q^{89} -12.0000 q^{91} -4.00000i q^{92} -6.00000 q^{94} +(4.00000 + 2.00000i) q^{95} +6.00000i q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 - 4 * q^5	$ 2 q - 2 q^{4} - 4 q^{5} + 2 q^{10} - 8 q^{11} + 4 q^{14} + 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} + 12 q^{26} - 16 q^{29} + 12 q^{34} - 4 q^{35} - 2 q^{40} + 4 q^{41} + 8 q^{44} - 8 q^{46} + 6 q^{49} - 8 q^{50} + 16 q^{55} - 4 q^{56} + 28 q^{59} - 24 q^{61} - 2 q^{64} - 12 q^{65} - 8 q^{70} - 2 q^{74} + 4 q^{76} + 16 q^{79} - 4 q^{80} - 12 q^{85} + 24 q^{86} - 20 q^{89} - 24 q^{91} - 12 q^{94} + 8 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^10 - 8 * q^11 + 4 * q^14 + 2 * q^16 - 4 * q^19 + 4 * q^20 + 6 * q^25 + 12 * q^26 - 16 * q^29 + 12 * q^34 - 4 * q^35 - 2 * q^40 + 4 * q^41 + 8 * q^44 - 8 * q^46 + 6 * q^49 - 8 * q^50 + 16 * q^55 - 4 * q^56 + 28 * q^59 - 24 * q^61 - 2 * q^64 - 12 * q^65 - 8 * q^70 - 2 * q^74 + 4 * q^76 + 16 * q^79 - 4 * q^80 - 12 * q^85 + 24 * q^86 - 20 * q^89 - 24 * q^91 - 12 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$		−	4.00000i		−	0.852803i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	6.00000			1.17670
$27$		0			0
$28$			2.00000i			0.377964i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	6.00000			1.02899
$35$	−2.00000	+	4.00000i	−0.338062	+	0.676123i
$36$		0			0
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$		−	2.00000i		−	0.324443i
$39$		0			0
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	−4.00000			−0.589768
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$			6.00000i			0.832050i
$53$			14.0000i			1.92305i	0.274721	+	0.961524i	$0.411414\pi$
$53$			14.0000i			1.92305i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	8.00000	+	4.00000i	1.07872	+	0.539360i
$56$	−2.00000			−0.267261
$57$		0			0
$58$		−	8.00000i		−	1.05045i
$59$	14.0000			1.82264			0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000			1.82264			0.911322	+	0.411693i	$0.135063\pi$
$60$		0			0
$61$	−12.0000			−1.53644			−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000			−1.53644			−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.00000	+	12.0000i	−0.744208	+	1.48842i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			6.00000i			0.727607i
$69$		0			0
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$			16.0000i			1.87266i	0.351123	+	0.936329i	$0.385800\pi$
$73$			16.0000i			1.87266i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	2.00000			0.229416
$77$			8.00000i			0.911685i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$		0			0
$82$			2.00000i			0.220863i
$83$		−	16.0000i		−	1.75623i	−0.478451	−	0.878114i	$-0.658802\pi$
$83$		−	16.0000i		−	1.75623i	0.478451	−	0.878114i	$-0.341198\pi$
$84$		0			0
$85$	−6.00000	+	12.0000i	−0.650791	+	1.30158i
$86$	12.0000			1.29399
$87$		0			0
$88$			4.00000i			0.426401i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$		−	4.00000i		−	0.417029i
$93$		0			0
$94$	−6.00000			−0.618853
$95$	4.00000	+	2.00000i	0.410391	+	0.205196i
$96$		0			0
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$		−	4.00000i		−	0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$		−	4.00000i		−	0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	−14.0000			−1.35980
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$	−4.00000	+	8.00000i	−0.381385	+	0.762770i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	4.00000	−	8.00000i	0.373002	−	0.746004i
$116$	8.00000			0.742781
$117$		0			0
$118$			14.0000i			1.28880i
$119$	−12.0000			−1.10004
$120$		0			0
$121$	5.00000			0.454545
$122$		−	12.0000i		−	1.08643i
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		−	10.0000i		−	0.887357i	−0.896186	−	0.443678i	$-0.853673\pi$
$127$		−	10.0000i		−	0.887357i	0.896186	−	0.443678i	$-0.146327\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−12.0000	−	6.00000i	−1.05247	−	0.526235i
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$			4.00000i			0.346844i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−6.00000			−0.514496
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	2.00000	−	4.00000i	0.169031	−	0.338062i
$141$		0			0
$142$		0			0
$143$			24.0000i			2.00698i
$144$		0			0
$145$	16.0000	+	8.00000i	1.32873	+	0.664364i
$146$	−16.0000			−1.32417
$147$		0			0
$148$		−	1.00000i		−	0.0821995i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$			2.00000i			0.162221i
$153$		0			0
$154$	−8.00000			−0.644658
$155$		0			0
$156$		0			0
$157$			10.0000i			0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$			10.0000i			0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$			8.00000i			0.636446i
$159$		0			0
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	8.00000			0.630488
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	16.0000			1.24184
$167$			8.00000i			0.619059i	0.950890	+	0.309529i	$0.100171\pi$
$167$			8.00000i			0.619059i	−0.950890	+	0.309529i	$0.899829\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$	−12.0000	−	6.00000i	−0.920358	−	0.460179i
$171$		0			0
$172$			12.0000i			0.914991i
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		0			0
$175$	8.00000	−	6.00000i	0.604743	−	0.453557i
$176$	−4.00000			−0.301511
$177$		0			0
$178$		−	10.0000i		−	0.749532i
$179$	−18.0000			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		−	12.0000i		−	0.889499i
$183$		0			0
$184$	4.00000			0.294884
$185$	1.00000	−	2.00000i	0.0735215	−	0.147043i
$186$		0			0
$187$			24.0000i			1.75505i
$188$		−	6.00000i		−	0.437595i
$189$		0			0
$190$	−2.00000	+	4.00000i	−0.145095	+	0.290191i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−3.00000			−0.214286
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$			6.00000i			0.422159i
$203$			16.0000i			1.12298i
$204$		0			0
$205$	−4.00000	−	2.00000i	−0.279372	−	0.139686i
$206$	4.00000			0.278693
$207$		0			0
$208$		−	6.00000i		−	0.416025i
$209$	8.00000			0.553372
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$		−	14.0000i		−	0.961524i
$213$		0			0
$214$	−4.00000			−0.273434
$215$	−12.0000	+	24.0000i	−0.818393	+	1.63679i
$216$		0			0
$217$		0			0
$218$		−	8.00000i		−	0.541828i
$219$		0			0
$220$	−8.00000	−	4.00000i	−0.539360	−	0.269680i
$221$	−36.0000			−2.42162
$222$		0			0
$223$			26.0000i			1.74109i	0.492090	+	0.870544i	$0.336233\pi$
$223$			26.0000i			1.74109i	−0.492090	+	0.870544i	$0.663767\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	8.00000	+	4.00000i	0.527504	+	0.263752i
$231$		0			0
$232$			8.00000i			0.525226i
$233$			12.0000i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$233$			12.0000i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$234$		0			0
$235$	6.00000	−	12.0000i	0.391397	−	0.782794i
$236$	−14.0000			−0.911322
$237$		0			0
$238$		−	12.0000i		−	0.777844i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$			5.00000i			0.321412i
$243$		0			0
$244$	12.0000			0.768221
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		0			0
$247$			12.0000i			0.763542i
$248$		0			0
$249$		0			0
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$		0			0
$253$		−	16.0000i		−	1.00591i
$254$	10.0000			0.627456
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	22.0000i		−	1.37232i	−0.727450	−	0.686161i	$-0.759294\pi$
$257$		−	22.0000i		−	1.37232i	0.727450	−	0.686161i	$-0.240706\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	6.00000	−	12.0000i	0.372104	−	0.744208i
$261$		0			0
$262$		−	18.0000i		−	1.11204i
$263$			2.00000i			0.123325i	0.998097	+	0.0616626i	$0.0196403\pi$
$263$			2.00000i			0.123325i	−0.998097	+	0.0616626i	$0.980360\pi$
$264$		0			0
$265$	14.0000	−	28.0000i	0.860013	−	1.72003i
$266$	−4.00000			−0.245256
$267$		0			0
$268$		−	4.00000i		−	0.244339i
$269$	26.0000			1.58525			0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000			1.58525			0.792624	+	0.609711i	$0.208714\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	12.0000			0.724947
$275$	−12.0000	−	16.0000i	−0.723627	−	0.964836i
$276$		0			0
$277$			26.0000i			1.56219i	0.624413	+	0.781094i	$0.285338\pi$
$277$			26.0000i			1.56219i	−0.624413	+	0.781094i	$0.714662\pi$
$278$			4.00000i			0.239904i
$279$		0			0
$280$	4.00000	+	2.00000i	0.239046	+	0.119523i
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		0			0
$285$		0			0
$286$	−24.0000			−1.41915
$287$		−	4.00000i		−	0.236113i
$288$		0			0
$289$	−19.0000			−1.11765
$290$	−8.00000	+	16.0000i	−0.469776	+	0.939552i
$291$		0			0
$292$		−	16.0000i		−	0.936329i
$293$			2.00000i			0.116841i	0.998292	+	0.0584206i	$0.0186065\pi$
$293$			2.00000i			0.116841i	−0.998292	+	0.0584206i	$0.981394\pi$
$294$		0			0
$295$	−28.0000	−	14.0000i	−1.63022	−	0.815112i
$296$	1.00000			0.0581238
$297$		0			0
$298$			10.0000i			0.579284i
$299$	24.0000			1.38796
$300$		0			0
$301$	−24.0000			−1.38334
$302$			8.00000i			0.460348i
$303$		0			0
$304$	−2.00000			−0.114708
$305$	24.0000	+	12.0000i	1.37424	+	0.687118i
$306$		0			0
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$		−	8.00000i		−	0.455842i
$309$		0			0
$310$		0			0
$311$	28.0000			1.58773			0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000			1.58773			0.793867	+	0.608091i	$0.208065\pi$
$312$		0			0
$313$			22.0000i			1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$313$			22.0000i			1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−8.00000			−0.450035
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	32.0000			1.79166
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$		0			0
$322$			8.00000i			0.445823i
$323$			12.0000i			0.667698i
$324$		0			0
$325$	24.0000	−	18.0000i	1.33128	−	0.998460i
$326$	−4.00000			−0.221540
$327$		0			0
$328$		−	2.00000i		−	0.110432i
$329$	12.0000			0.661581
$330$		0			0
$331$	−26.0000			−1.42909			−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000			−1.42909			−0.714545	+	0.699590i	$0.753366\pi$
$332$			16.0000i			0.878114i
$333$		0			0
$334$	−8.00000			−0.437741
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$		0			0
$337$			16.0000i			0.871576i	0.900049	+	0.435788i	$0.143530\pi$
$337$			16.0000i			0.871576i	−0.900049	+	0.435788i	$0.856470\pi$
$338$		−	23.0000i		−	1.25104i
$339$		0			0
$340$	6.00000	−	12.0000i	0.325396	−	0.650791i
$341$		0			0
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	−12.0000			−0.646997
$345$		0			0
$346$	−6.00000			−0.322562
$347$		−	20.0000i		−	1.07366i	−0.843692	−	0.536828i	$-0.819622\pi$
$347$		−	20.0000i		−	1.07366i	0.843692	−	0.536828i	$-0.180378\pi$
$348$		0			0
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$	6.00000	+	8.00000i	0.320713	+	0.427618i
$351$		0			0
$352$		−	4.00000i		−	0.213201i
$353$			2.00000i			0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$			2.00000i			0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$		0			0
$355$		0			0
$356$	10.0000			0.529999
$357$		0			0
$358$		−	18.0000i		−	0.951330i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		−	6.00000i		−	0.315353i
$363$		0			0
$364$	12.0000			0.628971
$365$	16.0000	−	32.0000i	0.837478	−	1.67496i
$366$		0			0
$367$			22.0000i			1.14839i	0.818718	+	0.574195i	$0.194685\pi$
$367$			22.0000i			1.14839i	−0.818718	+	0.574195i	$0.805315\pi$
$368$			4.00000i			0.208514i
$369$		0			0
$370$	2.00000	+	1.00000i	0.103975	+	0.0519875i
$371$	28.0000			1.45369
$372$		0			0
$373$		−	26.0000i		−	1.34623i	−0.739538	−	0.673114i	$-0.764956\pi$
$373$		−	26.0000i		−	1.34623i	0.739538	−	0.673114i	$-0.235044\pi$
$374$	−24.0000			−1.24101
$375$		0			0
$376$	6.00000			0.309426
$377$			48.0000i			2.47213i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−4.00000	−	2.00000i	−0.205196	−	0.102598i
$381$		0			0
$382$		0			0
$383$		−	36.0000i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$		−	36.0000i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$		0			0
$385$	8.00000	−	16.0000i	0.407718	−	0.815436i
$386$	−14.0000			−0.712581
$387$		0			0
$388$		−	6.00000i		−	0.304604i
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$	18.0000			0.906827
$395$	−16.0000	−	8.00000i	−0.805047	−	0.402524i
$396$		0			0
$397$			6.00000i			0.301131i	0.988600	+	0.150566i	$0.0481095\pi$
$397$			6.00000i			0.301131i	−0.988600	+	0.150566i	$0.951890\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$		0			0
$403$		0			0
$404$	−6.00000			−0.298511
$405$		0			0
$406$	−16.0000			−0.794067
$407$		−	4.00000i		−	0.198273i
$408$		0			0
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	2.00000	−	4.00000i	0.0987730	−	0.197546i
$411$		0			0
$412$			4.00000i			0.197066i
$413$		−	28.0000i		−	1.37779i
$414$		0			0
$415$	−16.0000	+	32.0000i	−0.785409	+	1.57082i
$416$	6.00000			0.294174
$417$		0			0
$418$			8.00000i			0.391293i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−8.00000			−0.389896			−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000			−0.389896			−0.194948	+	0.980814i	$0.562454\pi$
$422$		0			0
$423$		0			0
$424$	14.0000			0.679900
$425$	24.0000	−	18.0000i	1.16417	−	0.873128i
$426$		0			0
$427$			24.0000i			1.16144i
$428$		−	4.00000i		−	0.193347i
$429$		0			0
$430$	−24.0000	−	12.0000i	−1.15738	−	0.578691i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$		−	8.00000i		−	0.384455i	−0.981350	−	0.192228i	$-0.938429\pi$
$433$		−	8.00000i		−	0.384455i	0.981350	−	0.192228i	$-0.0615712\pi$
$434$		0			0
$435$		0			0
$436$	8.00000			0.383131
$437$		−	8.00000i		−	0.382692i
$438$		0			0
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$	4.00000	−	8.00000i	0.190693	−	0.381385i
$441$		0			0
$442$		−	36.0000i		−	1.71235i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$	20.0000	+	10.0000i	0.948091	+	0.474045i
$446$	−26.0000			−1.23114
$447$		0			0
$448$			2.00000i			0.0944911i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	−8.00000			−0.376705
$452$		−	6.00000i		−	0.282216i
$453$		0			0
$454$	12.0000			0.563188
$455$	24.0000	+	12.0000i	1.12514	+	0.562569i
$456$		0			0
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$			22.0000i			1.02799i
$459$		0			0
$460$	−4.00000	+	8.00000i	−0.186501	+	0.373002i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−8.00000			−0.371391
$465$		0			0
$466$	−12.0000			−0.555889
$467$			20.0000i			0.925490i	0.886492	+	0.462745i	$0.153135\pi$
$467$			20.0000i			0.925490i	−0.886492	+	0.462745i	$0.846865\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$	12.0000	+	6.00000i	0.553519	+	0.276759i
$471$		0			0
$472$		−	14.0000i		−	0.644402i
$473$			48.0000i			2.20704i
$474$		0			0
$475$	−6.00000	−	8.00000i	−0.275299	−	0.367065i
$476$	12.0000			0.550019
$477$		0			0
$478$		−	16.0000i		−	0.731823i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$	6.00000			0.273576
$482$			2.00000i			0.0910975i
$483$		0			0
$484$	−5.00000			−0.227273
$485$	6.00000	−	12.0000i	0.272446	−	0.544892i
$486$		0			0
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$			12.0000i			0.543214i
$489$		0			0
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$		0			0
$493$			48.0000i			2.16181i
$494$	−12.0000			−0.539906
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$		0			0
$502$		−	30.0000i		−	1.33897i
$503$		−	40.0000i		−	1.78351i	−0.452517	−	0.891756i	$-0.649474\pi$
$503$		−	40.0000i		−	1.78351i	0.452517	−	0.891756i	$-0.350526\pi$
$504$		0			0
$505$	−12.0000	−	6.00000i	−0.533993	−	0.266996i
$506$	16.0000			0.711287
$507$		0			0
$508$			10.0000i			0.443678i
$509$	42.0000			1.86162			0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000			1.86162			0.930809	+	0.365507i	$0.119104\pi$
$510$		0			0
$511$	32.0000			1.41560
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	22.0000			0.970378
$515$	−4.00000	+	8.00000i	−0.176261	+	0.352522i
$516$		0			0
$517$		−	24.0000i		−	1.05552i
$518$			2.00000i			0.0878750i
$519$		0			0
$520$	12.0000	+	6.00000i	0.526235	+	0.263117i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$	−2.00000			−0.0872041
$527$		0			0
$528$		0			0
$529$	7.00000			0.304348
$530$	28.0000	+	14.0000i	1.21624	+	0.608121i
$531$		0			0
$532$		−	4.00000i		−	0.173422i
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$	4.00000			0.172774
$537$		0			0
$538$			26.0000i			1.12094i
$539$	−12.0000			−0.516877
$540$		0			0
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$		−	8.00000i		−	0.343629i
$543$		0			0
$544$	6.00000			0.257248
$545$	16.0000	+	8.00000i	0.685365	+	0.342682i
$546$		0			0
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$			12.0000i			0.512615i
$549$		0			0
$550$	16.0000	−	12.0000i	0.682242	−	0.511682i
$551$	16.0000			0.681623
$552$		0			0
$553$		−	16.0000i		−	0.680389i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	−4.00000			−0.169638
$557$		−	14.0000i		−	0.593199i	−0.955002	−	0.296600i	$-0.904147\pi$
$557$		−	14.0000i		−	0.593199i	0.955002	−	0.296600i	$-0.0958526\pi$
$558$		0			0
$559$	−72.0000			−3.04528
$560$	−2.00000	+	4.00000i	−0.0845154	+	0.169031i
$561$		0			0
$562$		−	30.0000i		−	1.26547i
$563$			28.0000i			1.18006i	0.807382	+	0.590030i	$0.200884\pi$
$563$			28.0000i			1.18006i	−0.807382	+	0.590030i	$0.799116\pi$
$564$		0			0
$565$	6.00000	−	12.0000i	0.252422	−	0.504844i
$566$	4.00000			0.168133
$567$		0			0
$568$		0			0
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		−	24.0000i		−	1.00349i
$573$		0			0
$574$	4.00000			0.166957
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$		0			0
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$		−	19.0000i		−	0.790296i
$579$		0			0
$580$	−16.0000	−	8.00000i	−0.664364	−	0.332182i
$581$	−32.0000			−1.32758
$582$		0			0
$583$		−	56.0000i		−	2.31928i
$584$	16.0000			0.662085
$585$		0			0
$586$	−2.00000			−0.0826192
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$		0			0
$590$	14.0000	−	28.0000i	0.576371	−	1.15274i
$591$		0			0
$592$			1.00000i			0.0410997i
$593$		−	12.0000i		−	0.492781i	−0.969171	−	0.246390i	$-0.920755\pi$
$593$		−	12.0000i		−	0.492781i	0.969171	−	0.246390i	$-0.0792446\pi$
$594$		0			0
$595$	24.0000	+	12.0000i	0.983904	+	0.491952i
$596$	−10.0000			−0.409616
$597$		0			0
$598$			24.0000i			0.981433i
$599$	8.00000			0.326871			0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000			0.326871			0.163436	+	0.986554i	$0.447742\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		−	24.0000i		−	0.978167i
$603$		0			0
$604$	−8.00000			−0.325515
$605$	−10.0000	−	5.00000i	−0.406558	−	0.203279i
$606$		0			0
$607$		−	16.0000i		−	0.649420i	−0.945814	−	0.324710i	$-0.894733\pi$
$607$		−	16.0000i		−	0.649420i	0.945814	−	0.324710i	$-0.105267\pi$
$608$		−	2.00000i		−	0.0811107i
$609$		0			0
$610$	−12.0000	+	24.0000i	−0.485866	+	0.971732i
$611$	36.0000			1.45640
$612$		0			0
$613$			42.0000i			1.69636i	0.529705	+	0.848182i	$0.322303\pi$
$613$			42.0000i			1.69636i	−0.529705	+	0.848182i	$0.677697\pi$
$614$	8.00000			0.322854
$615$		0			0
$616$	8.00000			0.322329
$617$			16.0000i			0.644136i	0.946717	+	0.322068i	$0.104378\pi$
$617$			16.0000i			0.644136i	−0.946717	+	0.322068i	$0.895622\pi$
$618$		0			0
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$		0			0
$622$			28.0000i			1.12270i
$623$			20.0000i			0.801283i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−22.0000			−0.879297
$627$		0			0
$628$		−	10.0000i		−	0.399043i
$629$	6.00000			0.239236
$630$		0			0
$631$	−12.0000			−0.477712			−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000			−0.477712			−0.238856	+	0.971055i	$0.576772\pi$
$632$		−	8.00000i		−	0.318223i
$633$		0			0
$634$	−2.00000			−0.0794301
$635$	−10.0000	+	20.0000i	−0.396838	+	0.793676i
$636$		0			0
$637$		−	18.0000i		−	0.713186i
$638$			32.0000i			1.26689i
$639$		0			0
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$	−22.0000			−0.868948			−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000			−0.868948			−0.434474	+	0.900684i	$0.643066\pi$
$642$		0			0
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$	−8.00000			−0.315244
$645$		0			0
$646$	−12.0000			−0.472134
$647$			48.0000i			1.88707i	0.331266	+	0.943537i	$0.392524\pi$
$647$			48.0000i			1.88707i	−0.331266	+	0.943537i	$0.607476\pi$
$648$		0			0
$649$	−56.0000			−2.19819
$650$	18.0000	+	24.0000i	0.706018	+	0.941357i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$			18.0000i			0.704394i	0.935926	+	0.352197i	$0.114565\pi$
$653$			18.0000i			0.704394i	−0.935926	+	0.352197i	$0.885435\pi$
$654$		0			0
$655$	36.0000	+	18.0000i	1.40664	+	0.703318i
$656$	2.00000			0.0780869
$657$		0			0
$658$			12.0000i			0.467809i
$659$	16.0000			0.623272			0.311636	−	0.950202i	$-0.399123\pi$
$659$	16.0000			0.623272			0.311636	+	0.950202i	$0.399123\pi$
$660$		0			0
$661$	16.0000			0.622328			0.311164	−	0.950356i	$-0.399281\pi$
$661$	16.0000			0.622328			0.311164	+	0.950356i	$0.399281\pi$
$662$		−	26.0000i		−	1.01052i
$663$		0			0
$664$	−16.0000			−0.620920
$665$	4.00000	−	8.00000i	0.155113	−	0.310227i
$666$		0			0
$667$		−	32.0000i		−	1.23904i
$668$		−	8.00000i		−	0.309529i
$669$		0			0
$670$	8.00000	+	4.00000i	0.309067	+	0.154533i
$671$	48.0000			1.85302
$672$		0			0
$673$			28.0000i			1.07932i	0.841883	+	0.539660i	$0.181447\pi$
$673$			28.0000i			1.07932i	−0.841883	+	0.539660i	$0.818553\pi$
$674$	−16.0000			−0.616297
$675$		0			0
$676$	23.0000			0.884615
$677$			30.0000i			1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$			30.0000i			1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$		0			0
$679$	12.0000			0.460518
$680$	12.0000	+	6.00000i	0.460179	+	0.230089i
$681$		0			0
$682$		0			0
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	−12.0000	+	24.0000i	−0.458496	+	0.916993i
$686$	20.0000			0.763604
$687$		0			0
$688$		−	12.0000i		−	0.457496i
$689$	84.0000			3.20015
$690$		0			0
$691$	−36.0000			−1.36950			−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000			−1.36950			−0.684752	+	0.728776i	$0.740090\pi$
$692$		−	6.00000i		−	0.228086i
$693$		0			0
$694$	20.0000			0.759190
$695$	−8.00000	−	4.00000i	−0.303457	−	0.151729i
$696$		0			0
$697$		−	12.0000i		−	0.454532i
$698$			34.0000i			1.28692i
$699$		0			0
$700$	−8.00000	+	6.00000i	−0.302372	+	0.226779i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$		−	2.00000i		−	0.0754314i
$704$	4.00000			0.150756
$705$		0			0
$706$	−2.00000			−0.0752710
$707$		−	12.0000i		−	0.451306i
$708$		0			0
$709$	−36.0000			−1.35201			−0.676004	−	0.736898i	$-0.736290\pi$
$709$	−36.0000			−1.35201			−0.676004	+	0.736898i	$0.736290\pi$
$710$		0			0
$711$		0			0
$712$			10.0000i			0.374766i
$713$		0			0
$714$		0			0
$715$	24.0000	−	48.0000i	0.897549	−	1.79510i
$716$	18.0000			0.672692
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		−	15.0000i		−	0.558242i
$723$		0			0
$724$	6.00000			0.222988
$725$	−24.0000	−	32.0000i	−0.891338	−	1.18845i
$726$		0			0
$727$			16.0000i			0.593407i	0.954970	+	0.296704i	$0.0958873\pi$
$727$			16.0000i			0.593407i	−0.954970	+	0.296704i	$0.904113\pi$
$728$			12.0000i			0.444750i
$729$		0			0
$730$	32.0000	+	16.0000i	1.18437	+	0.592187i
$731$	−72.0000			−2.66302
$732$		0			0
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	−22.0000			−0.812035
$735$		0			0
$736$	−4.00000			−0.147442
$737$		−	16.0000i		−	0.589368i
$738$		0			0
$739$	28.0000			1.03000			0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000			1.03000			0.514998	+	0.857191i	$0.327793\pi$
$740$	−1.00000	+	2.00000i	−0.0367607	+	0.0735215i
$741$		0			0
$742$			28.0000i			1.02791i
$743$			38.0000i			1.39408i	0.717030	+	0.697042i	$0.245501\pi$
$743$			38.0000i			1.39408i	−0.717030	+	0.697042i	$0.754499\pi$
$744$		0			0
$745$	−20.0000	−	10.0000i	−0.732743	−	0.366372i
$746$	26.0000			0.951928
$747$		0			0
$748$		−	24.0000i		−	0.877527i
$749$	8.00000			0.292314
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$			6.00000i			0.218797i
$753$		0			0
$754$	−48.0000			−1.74806
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$		−	28.0000i		−	1.01701i
$759$		0			0
$760$	2.00000	−	4.00000i	0.0725476	−	0.145095i
$761$	−26.0000			−0.942499			−0.471250	−	0.882000i	$-0.656197\pi$
$761$	−26.0000			−0.942499			−0.471250	+	0.882000i	$0.656197\pi$
$762$		0			0
$763$			16.0000i			0.579239i
$764$		0			0
$765$		0			0
$766$	36.0000			1.30073
$767$		−	84.0000i		−	3.03306i
$768$		0			0
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	16.0000	+	8.00000i	0.576600	+	0.288300i
$771$		0			0
$772$		−	14.0000i		−	0.503871i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$		0			0
$775$		0			0
$776$	6.00000			0.215387
$777$		0			0
$778$		0			0
$779$	−4.00000			−0.143315
$780$		0			0
$781$		0			0
$782$			24.0000i			0.858238i
$783$		0			0
$784$	3.00000			0.107143
$785$	10.0000	−	20.0000i	0.356915	−	0.713831i
$786$		0			0
$787$		−	4.00000i		−	0.142585i	−0.997455	−	0.0712923i	$-0.977288\pi$
$787$		−	4.00000i		−	0.142585i	0.997455	−	0.0712923i	$-0.0227123\pi$
$788$			18.0000i			0.641223i
$789$		0			0
$790$	8.00000	−	16.0000i	0.284627	−	0.569254i
$791$	12.0000			0.426671
$792$		0			0
$793$			72.0000i			2.55679i
$794$	−6.00000			−0.212932
$795$		0			0
$796$	−8.00000			−0.283552
$797$			6.00000i			0.212531i	0.994338	+	0.106265i	$0.0338893\pi$
$797$			6.00000i			0.212531i	−0.994338	+	0.106265i	$0.966111\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$		0			0
$802$			10.0000i			0.353112i
$803$		−	64.0000i		−	2.25851i
$804$		0			0
$805$	−16.0000	−	8.00000i	−0.563926	−	0.281963i
$806$		0			0
$807$		0			0
$808$		−	6.00000i		−	0.211079i
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$		−	16.0000i		−	0.561490i
$813$		0			0
$814$	4.00000			0.140200
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$		0			0
$817$			24.0000i			0.839654i
$818$		−	14.0000i		−	0.489499i
$819$		0			0
$820$	4.00000	+	2.00000i	0.139686	+	0.0698430i
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$		0			0
$823$		−	54.0000i		−	1.88232i	−0.337959	−	0.941161i	$-0.609737\pi$
$823$		−	54.0000i		−	1.88232i	0.337959	−	0.941161i	$-0.390263\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$	28.0000			0.974245
$827$			4.00000i			0.139094i	0.997579	+	0.0695468i	$0.0221553\pi$
$827$			4.00000i			0.139094i	−0.997579	+	0.0695468i	$0.977845\pi$
$828$		0			0
$829$	40.0000			1.38926			0.694629	−	0.719368i	$-0.255569\pi$
$829$	40.0000			1.38926			0.694629	+	0.719368i	$0.255569\pi$
$830$	−32.0000	−	16.0000i	−1.11074	−	0.555368i
$831$		0			0
$832$			6.00000i			0.208013i
$833$		−	18.0000i		−	0.623663i
$834$		0			0
$835$	8.00000	−	16.0000i	0.276851	−	0.553703i
$836$	−8.00000			−0.276686
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$		−	8.00000i		−	0.275698i
$843$		0			0
$844$		0			0
$845$	46.0000	+	23.0000i	1.58245	+	0.791224i
$846$		0			0
$847$		−	10.0000i		−	0.343604i
$848$			14.0000i			0.480762i
$849$		0			0
$850$	18.0000	+	24.0000i	0.617395	+	0.823193i
$851$	−4.00000			−0.137118
$852$		0			0
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	−24.0000			−0.821263
$855$		0			0
$856$	4.00000			0.136717
$857$			30.0000i			1.02478i	0.858753	+	0.512390i	$0.171240\pi$
$857$			30.0000i			1.02478i	−0.858753	+	0.512390i	$0.828760\pi$
$858$		0			0
$859$	6.00000			0.204717			0.102359	−	0.994748i	$-0.467361\pi$
$859$	6.00000			0.204717			0.102359	+	0.994748i	$0.467361\pi$
$860$	12.0000	−	24.0000i	0.409197	−	0.818393i
$861$		0			0
$862$		−	24.0000i		−	0.817443i
$863$		−	58.0000i		−	1.97434i	−0.159664	−	0.987171i	$-0.551041\pi$
$863$		−	58.0000i		−	1.97434i	0.159664	−	0.987171i	$-0.448959\pi$
$864$		0			0
$865$	6.00000	−	12.0000i	0.204006	−	0.408012i
$866$	8.00000			0.271851
$867$		0			0
$868$		0			0
$869$	−32.0000			−1.08553
$870$		0			0
$871$	24.0000			0.813209
$872$			8.00000i			0.270914i
$873$		0			0
$874$	8.00000			0.270604
$875$	−22.0000	+	4.00000i	−0.743736	+	0.135225i
$876$		0			0
$877$		−	22.0000i		−	0.742887i	−0.928456	−	0.371444i	$-0.878863\pi$
$877$		−	22.0000i		−	0.742887i	0.928456	−	0.371444i	$-0.121137\pi$
$878$			32.0000i			1.07995i
$879$		0			0
$880$	8.00000	+	4.00000i	0.269680	+	0.134840i
$881$	22.0000			0.741199			0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000			0.741199			0.370599	+	0.928793i	$0.379152\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	36.0000			1.21081
$885$		0			0
$886$	−4.00000			−0.134383
$887$			6.00000i			0.201460i	0.994914	+	0.100730i	$0.0321179\pi$
$887$			6.00000i			0.201460i	−0.994914	+	0.100730i	$0.967882\pi$
$888$		0			0
$889$	−20.0000			−0.670778
$890$	−10.0000	+	20.0000i	−0.335201	+	0.670402i
$891$		0			0
$892$		−	26.0000i		−	0.870544i
$893$		−	12.0000i		−	0.401565i
$894$		0			0
$895$	36.0000	+	18.0000i	1.20335	+	0.601674i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$			30.0000i			1.00111i
$899$		0			0
$900$		0			0
$901$	84.0000			2.79845
$902$		−	8.00000i		−	0.266371i
$903$		0			0
$904$	6.00000			0.199557
$905$	12.0000	+	6.00000i	0.398893	+	0.199447i
$906$		0			0
$907$			4.00000i			0.132818i	0.997792	+	0.0664089i	$0.0211542\pi$
$907$			4.00000i			0.132818i	−0.997792	+	0.0664089i	$0.978846\pi$
$908$			12.0000i			0.398234i
$909$		0			0
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$			64.0000i			2.11809i
$914$	10.0000			0.330771
$915$		0			0
$916$	−22.0000			−0.726900
$917$			36.0000i			1.18882i
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	−8.00000	−	4.00000i	−0.263752	−	0.131876i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000	+	3.00000i	−0.131519	+	0.0986394i
$926$	−16.0000			−0.525793
$927$		0			0
$928$		−	8.00000i		−	0.262613i
$929$	−2.00000			−0.0656179			−0.0328089	−	0.999462i	$-0.510445\pi$
$929$	−2.00000			−0.0656179			−0.0328089	+	0.999462i	$0.510445\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$		−	12.0000i		−	0.393073i
$933$		0			0
$934$	−20.0000			−0.654420
$935$	24.0000	−	48.0000i	0.784884	−	1.56977i
$936$		0			0
$937$			36.0000i			1.17607i	0.808836	+	0.588034i	$0.200098\pi$
$937$			36.0000i			1.17607i	−0.808836	+	0.588034i	$0.799902\pi$
$938$			8.00000i			0.261209i
$939$		0			0
$940$	−6.00000	+	12.0000i	−0.195698	+	0.391397i
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$		0			0
$943$			8.00000i			0.260516i
$944$	14.0000			0.455661
$945$		0			0
$946$	−48.0000			−1.56061
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$		0			0
$949$	96.0000			3.11629
$950$	8.00000	−	6.00000i	0.259554	−	0.194666i
$951$		0			0
$952$			12.0000i			0.388922i
$953$		−	44.0000i		−	1.42530i	−0.701520	−	0.712650i	$-0.747495\pi$
$953$		−	44.0000i		−	1.42530i	0.701520	−	0.712650i	$-0.252505\pi$
$954$		0			0
$955$		0			0
$956$	16.0000			0.517477
$957$		0			0
$958$		0			0
$959$	−24.0000			−0.775000
$960$		0			0
$961$	−31.0000			−1.00000
$962$			6.00000i			0.193448i
$963$		0			0
$964$	−2.00000			−0.0644157
$965$	14.0000	−	28.0000i	0.450676	−	0.901352i
$966$		0			0
$967$			16.0000i			0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$967$			16.0000i			0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$968$		−	5.00000i		−	0.160706i
$969$		0			0
$970$	12.0000	+	6.00000i	0.385297	+	0.192648i
$971$	−28.0000			−0.898563			−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000			−0.898563			−0.449281	+	0.893390i	$0.648320\pi$
$972$		0			0
$973$		−	8.00000i		−	0.256468i
$974$	−4.00000			−0.128168
$975$		0			0
$976$	−12.0000			−0.384111
$977$		−	22.0000i		−	0.703842i	−0.936030	−	0.351921i	$-0.885529\pi$
$977$		−	22.0000i		−	0.703842i	0.936030	−	0.351921i	$-0.114471\pi$
$978$		0			0
$979$	40.0000			1.27841
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$		0			0
$982$			28.0000i			0.893516i
$983$			6.00000i			0.191370i	0.995412	+	0.0956851i	$0.0305042\pi$
$983$			6.00000i			0.191370i	−0.995412	+	0.0956851i	$0.969496\pi$
$984$		0			0
$985$	−18.0000	+	36.0000i	−0.573528	+	1.14706i
$986$	−48.0000			−1.52863
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$	48.0000			1.52631
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.0000	−	8.00000i	−0.507234	−	0.253617i
$996$		0			0
$997$		−	6.00000i		−	0.190022i	−0.995476	−	0.0950110i	$-0.969711\pi$
$997$		−	6.00000i		−	0.190022i	0.995476	−	0.0950110i	$-0.0302886\pi$
$998$		−	6.00000i		−	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.b.1999.2		2
3.2	odd	2		1110.2.d.d.889.1	✓	2
5.4	even	2	inner	3330.2.d.b.1999.1		2
15.2	even	4		5550.2.a.bc.1.1		1
15.8	even	4		5550.2.a.p.1.1		1
15.14	odd	2		1110.2.d.d.889.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.d.889.1	✓	2	3.2	odd	2
1110.2.d.d.889.2	yes	2	15.14	odd	2
3330.2.d.b.1999.1		2	5.4	even	2	inner
3330.2.d.b.1999.2		2	1.1	even	1	trivial
5550.2.a.p.1.1		1	15.8	even	4
5550.2.a.bc.1.1		1	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(1.00000 - 2.00000i) q^{10} -4.00000 q^{11} -6.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000i q^{17} -2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -4.00000i q^{22} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +6.00000 q^{26} +2.00000i q^{28} -8.00000 q^{29} +1.00000i q^{32} +6.00000 q^{34} +(-2.00000 + 4.00000i) q^{35} +1.00000i q^{37} -2.00000i q^{38} +(-1.00000 + 2.00000i) q^{40} +2.00000 q^{41} -12.0000i q^{43} +4.00000 q^{44} -4.00000 q^{46} +6.00000i q^{47} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000i q^{52} +14.0000i q^{53} +(8.00000 + 4.00000i) q^{55} -2.00000 q^{56} -8.00000i q^{58} +14.0000 q^{59} -12.0000 q^{61} -1.00000 q^{64} +(-6.00000 + 12.0000i) q^{65} +4.00000i q^{67} +6.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} +16.0000i q^{73} -1.00000 q^{74} +2.00000 q^{76} +8.00000i q^{77} +8.00000 q^{79} +(-2.00000 - 1.00000i) q^{80} +2.00000i q^{82} -16.0000i q^{83} +(-6.00000 + 12.0000i) q^{85} +12.0000 q^{86} +4.00000i q^{88} -10.0000 q^{89} -12.0000 q^{91} -4.00000i q^{92} -6.00000 q^{94} +(4.00000 + 2.00000i) q^{95} +6.00000i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 - 4 * q^5	\( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{10} - 8 q^{11} + 4 q^{14} + 2 q^{16} - 4 q^{19} + 4 q^{20} + 6 q^{25} + 12 q^{26} - 16 q^{29} + 12 q^{34} - 4 q^{35} - 2 q^{40} + 4 q^{41} + 8 q^{44} - 8 q^{46} + 6 q^{49} - 8 q^{50} + 16 q^{55} - 4 q^{56} + 28 q^{59} - 24 q^{61} - 2 q^{64} - 12 q^{65} - 8 q^{70} - 2 q^{74} + 4 q^{76} + 16 q^{79} - 4 q^{80} - 12 q^{85} + 24 q^{86} - 20 q^{89} - 24 q^{91} - 12 q^{94} + 8 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^10 - 8 * q^11 + 4 * q^14 + 2 * q^16 - 4 * q^19 + 4 * q^20 + 6 * q^25 + 12 * q^26 - 16 * q^29 + 12 * q^34 - 4 * q^35 - 2 * q^40 + 4 * q^41 + 8 * q^44 - 8 * q^46 + 6 * q^49 - 8 * q^50 + 16 * q^55 - 4 * q^56 + 28 * q^59 - 24 * q^61 - 2 * q^64 - 12 * q^65 - 8 * q^70 - 2 * q^74 + 4 * q^76 + 16 * q^79 - 4 * q^80 - 12 * q^85 + 24 * q^86 - 20 * q^89 - 24 * q^91 - 12 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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