LMFDB - Embedded newform 9.76.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,76,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 76, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 76);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

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:	yes
Analytic conductor:	$320.605553540$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + \cdots + 45\!\cdots\!00 $ x^12 - 1169219512457442397270x^10 + 517313289742851992169322351293202914547200x^8 - 108123907718504640450742349966711894965247206710933993816064000x^6 + 10672177691229489583624559311046771533520428225563059654950107921756681152757760000x^4 - 420737875005760685790205772350190624520087925893939802179554814136523036111675964498741126443827200000*x^2 + 4544006259432754991173598121024865011324666371148581357312785512705782818361302784030047007356086785380445690265600000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{121}\cdot 3^{148}\cdot 5^{17}\cdot 7^{6}\cdot 11^{4}\cdot 13^{2}\cdot 19^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.36756e10$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46161e11 q^{2} +2.28162e22 q^{4} +2.44523e26 q^{5} +2.48041e31 q^{7} +3.68323e33 q^{8} +O(q^{10})$	\(q-2.46161e11 q^{2} +2.28162e22 q^{4} +2.44523e26 q^{5} +2.48041e31 q^{7} +3.68323e33 q^{8} -6.01919e37 q^{10} +1.71346e39 q^{11} +3.81422e41 q^{13} -6.10581e42 q^{14} -1.76864e45 q^{16} +1.76703e46 q^{17} +7.97978e47 q^{19} +5.57909e48 q^{20} -4.21788e50 q^{22} -3.65819e50 q^{23} +3.33215e52 q^{25} -9.38913e52 q^{26} +5.65938e53 q^{28} +1.31632e55 q^{29} -1.28965e56 q^{31} +2.96222e56 q^{32} -4.34974e57 q^{34} +6.06517e57 q^{35} -9.63780e58 q^{37} -1.96431e59 q^{38} +9.00632e59 q^{40} +1.59300e60 q^{41} +2.14702e61 q^{43} +3.90948e61 q^{44} +9.00503e61 q^{46} +4.13773e62 q^{47} -1.79662e63 q^{49} -8.20244e63 q^{50} +8.70263e63 q^{52} +4.05768e64 q^{53} +4.18981e65 q^{55} +9.13593e64 q^{56} -3.24026e66 q^{58} -1.28466e66 q^{59} +2.33030e66 q^{61} +3.17461e67 q^{62} -6.10084e66 q^{64} +9.32664e67 q^{65} +3.41971e68 q^{67} +4.03171e68 q^{68} -1.49301e69 q^{70} +3.60642e69 q^{71} +4.19029e69 q^{73} +2.37245e70 q^{74} +1.82069e70 q^{76} +4.25010e70 q^{77} +2.71488e70 q^{79} -4.32472e71 q^{80} -3.92134e71 q^{82} +2.01863e71 q^{83} +4.32079e72 q^{85} -5.28512e72 q^{86} +6.31108e72 q^{88} -4.77047e72 q^{89} +9.46086e72 q^{91} -8.34661e72 q^{92} -1.01855e74 q^{94} +1.95123e74 q^{95} +3.90660e74 q^{97} +4.42257e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 30\!\cdots\!44 q^{4}+ \cdots - 23\!\cdots\!60 q^{7}+O(q^{10}) $ 12 * q + 304307061716936732916144 * q^4 - 23264696115715922069186217167760 * q^7	$ 12 q + 30\!\cdots\!44 q^{4}+ \cdots + 91\!\cdots\!40 q^{97}+O(q^{100}) $ 12 * q + 304307061716936732916144 * q^4 - 23264696115715922069186217167760 * q^7 + 27638934325035006400986687037139427840 * q^10 + 1566891994715058692610510600704204863669560 * q^13 + 1054925289288995929257926590400056818650475648 * q^16 + 985377875069853565681479994616529689369356159392 * q^19 + 159085566085665366088358455484252399362269037824000 * q^22 + 55287387450371943461933903806192645052614192225444260 * q^25 + 3825429694688756764966117420913941574684905356160543680 * q^28 + 3302831127672592933100655272047800132609471485143616496 * q^31 - 2865456277005415897826369042421146930334611723465937976320 * q^34 + 192681748803326931713618210444828383889638160821949090334120 * q^37 - 1780314724794332033651772571439008995626905148286612946391040 * q^40 - 20767095120844290419389762980464184600692870397019624059942240 * q^43 + 235054227730242679255713190614178313572258446734724900485591040 * q^46 - 2200398774833185524931209968117643549966640237509759919611052116 * q^49 - 14448231238764964137515766569708046936012135467108945293436290080 * q^52 + 81306325536746630777151726268587417594554465906840413536114892800 * q^55 - 1004718700793757564164031209344099479511820176480140633172540224000 * q^58 + 13323361359468573502772030313904437139549082575557497083657618663944 * q^61 + 18469889473975432554749180704169560068135223154596132970935656877056 * q^64 - 257204799077995311988310370425723150669455151846154408147457213335360 * q^67 + 3005342015625853695505588875605919452594091965633096933257896848025600 * q^70 + 18552266347809363939749233798674669950739794719850824673010584204923080 * q^73 + 50292969204567460035372103145366232214661826641543367705647193837707904 * q^76 + 937842303842237087819497830837715967722050800328496953380955050567674608 * q^79 + 3919742272718992426068840649563282345597351553486852179684355735105920000 * q^82 + 12520323007424135125100238558304387667646006748328044453585486149043384320 * q^85 + 76483098460394896817433565470216620635024204139674266152191759167166464000 * q^88 + 216807679711985636819127226029841126565807512697835494720868255078103720800 * q^91 + 409517007122285307430588897723573953284046066392035360178770164560460656640 * q^94 + 916586077653930597838313492271046040715613339491256556458911897082224060840 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46161e11	−1.26647	−0.633234	−	0.773960i	$-0.718273\pi$
$2$	−2.46161e11	−1.26647	−0.633234	+	0.773960i	$0.718273\pi$
$3$	0	0
$3$	0	0
$4$	2.28162e22	0.603941
$5$	2.44523e26	1.50295	0.751474	−	0.659763i	$-0.229343\pi$
$5$	2.44523e26	1.50295	0.751474	+	0.659763i	$0.229343\pi$
$6$	0	0
$7$	2.48041e31	0.505066	0.252533	−	0.967588i	$-0.418736\pi$
$7$	2.48041e31	0.505066	0.252533	+	0.967588i	$0.418736\pi$
$8$	3.68323e33	0.501596
$9$	0	0
$10$	−6.01919e37	−1.90343
$11$	1.71346e39	1.51932	0.759660	−	0.650320i	$-0.225365\pi$
$11$	1.71346e39	1.51932	0.759660	+	0.650320i	$0.225365\pi$
$12$	0	0
$13$	3.81422e41	0.643473	0.321737	−	0.946829i	$-0.395733\pi$
$13$	3.81422e41	0.643473	0.321737	+	0.946829i	$0.395733\pi$
$14$	−6.10581e42	−0.639649
$15$	0	0
$16$	−1.76864e45	−1.23920
$17$	1.76703e46	1.27471	0.637353	−	0.770572i	$-0.280029\pi$
$17$	1.76703e46	1.27471	0.637353	+	0.770572i	$0.280029\pi$
$18$	0	0
$19$	7.97978e47	0.888650	0.444325	−	0.895866i	$-0.353444\pi$
$19$	7.97978e47	0.888650	0.444325	+	0.895866i	$0.353444\pi$
$20$	5.57909e48	0.907691
$21$	0	0
$22$	−4.21788e50	−1.92417
$23$	−3.65819e50	−0.315117	−0.157559	−	0.987510i	$-0.550362\pi$
$23$	−3.65819e50	−0.315117	−0.157559	+	0.987510i	$0.550362\pi$
$24$	0	0
$25$	3.33215e52	1.25885
$26$	−9.38913e52	−0.814938
$27$	0	0
$28$	5.65938e53	0.305030
$29$	1.31632e55	1.90299	0.951495	−	0.307665i	$-0.0995475\pi$
$29$	1.31632e55	1.90299	0.951495	+	0.307665i	$0.0995475\pi$
$30$	0	0
$31$	−1.28965e56	−1.52900	−0.764500	−	0.644624i	$-0.777014\pi$
$31$	−1.28965e56	−1.52900	−0.764500	+	0.644624i	$0.777014\pi$
$32$	2.96222e56	1.06781
$33$	0	0
$34$	−4.34974e57	−1.61437
$35$	6.06517e57	0.759087
$36$	0	0
$37$	−9.63780e58	−1.50111	−0.750556	−	0.660807i	$-0.770214\pi$
$37$	−9.63780e58	−1.50111	−0.750556	+	0.660807i	$0.770214\pi$
$38$	−1.96431e59	−1.12545
$39$	0	0
$40$	9.00632e59	0.753872
$41$	1.59300e60	0.528227	0.264114	−	0.964492i	$-0.414921\pi$
$41$	1.59300e60	0.528227	0.264114	+	0.964492i	$0.414921\pi$
$42$	0	0
$43$	2.14702e61	1.19335	0.596676	−	0.802482i	$-0.296488\pi$
$43$	2.14702e61	1.19335	0.596676	+	0.802482i	$0.296488\pi$
$44$	3.90948e61	0.917580
$45$	0	0
$46$	9.00503e61	0.399086
$47$	4.13773e62	0.818639	0.409320	−	0.912391i	$-0.365766\pi$
$47$	4.13773e62	0.818639	0.409320	+	0.912391i	$0.365766\pi$
$48$	0	0
$49$	−1.79662e63	−0.744909
$50$	−8.20244e63	−1.59429
$51$	0	0
$52$	8.70263e63	0.388620
$53$	4.05768e64	0.887018	0.443509	−	0.896270i	$-0.353733\pi$
$53$	4.05768e64	0.887018	0.443509	+	0.896270i	$0.353733\pi$
$54$	0	0
$55$	4.18981e65	2.28346
$56$	9.13593e64	0.253339
$57$	0	0
$58$	−3.24026e66	−2.41008
$59$	−1.28466e66	−0.503313	−0.251657	−	0.967817i	$-0.580975\pi$
$59$	−1.28466e66	−0.503313	−0.251657	+	0.967817i	$0.580975\pi$
$60$	0	0
$61$	2.33030e66	0.261543	0.130772	−	0.991413i	$-0.458255\pi$
$61$	2.33030e66	0.261543	0.130772	+	0.991413i	$0.458255\pi$
$62$	3.17461e67	1.93643
$63$	0	0
$64$	−6.10084e66	−0.113146
$65$	9.32664e67	0.967106
$66$	0	0
$67$	3.41971e68	1.13811	0.569055	−	0.822299i	$-0.307309\pi$
$67$	3.41971e68	1.13811	0.569055	+	0.822299i	$0.307309\pi$
$68$	4.03171e68	0.769847
$69$	0	0
$70$	−1.49301e69	−0.961359
$71$	3.60642e69	1.36423	0.682116	−	0.731244i	$-0.261060\pi$
$71$	3.60642e69	1.36423	0.682116	+	0.731244i	$0.261060\pi$
$72$	0	0
$73$	4.19029e69	0.559289	0.279645	−	0.960104i	$-0.409783\pi$
$73$	4.19029e69	0.559289	0.279645	+	0.960104i	$0.409783\pi$
$74$	2.37245e70	1.90111
$75$	0	0
$76$	1.82069e70	0.536692
$77$	4.25010e70	0.767357
$78$	0	0
$79$	2.71488e70	0.187385	0.0936926	−	0.995601i	$-0.470133\pi$
$79$	2.71488e70	0.187385	0.0936926	+	0.995601i	$0.470133\pi$
$80$	−4.32472e71	−1.86245
$81$	0	0
$82$	−3.92134e71	−0.668983
$83$	2.01863e71	0.218589	0.109294	−	0.994009i	$-0.465141\pi$
$83$	2.01863e71	0.218589	0.109294	+	0.994009i	$0.465141\pi$
$84$	0	0
$85$	4.32079e72	1.91582
$86$	−5.28512e72	−1.51134
$87$	0	0
$88$	6.31108e72	0.762085
$89$	−4.77047e72	−0.377082	−0.188541	−	0.982065i	$-0.560376\pi$
$89$	−4.77047e72	−0.377082	−0.188541	+	0.982065i	$0.560376\pi$
$90$	0	0
$91$	9.46086e72	0.324996
$92$	−8.34661e72	−0.190312
$93$	0	0
$94$	−1.01855e74	−1.03678
$95$	1.95123e74	1.33559
$96$	0	0
$97$	3.90660e74	1.22422	0.612110	−	0.790773i	$-0.290321\pi$
$97$	3.90660e74	1.22422	0.612110	+	0.790773i	$0.290321\pi$
$98$	4.42257e74	0.943403
$99$	0	0
$100$	7.60271e74	0.760271
$101$	−4.11096e74	−0.283069	−0.141534	−	0.989933i	$-0.545204\pi$
$101$	−4.11096e74	−0.283069	−0.141534	+	0.989933i	$0.545204\pi$
$102$	0	0
$103$	−4.26100e75	−1.40642	−0.703211	−	0.710982i	$-0.748251\pi$
$103$	−4.26100e75	−1.40642	−0.703211	+	0.710982i	$0.748251\pi$
$104$	1.40487e75	0.322764
$105$	0	0
$106$	−9.98841e75	−1.12338
$107$	−1.70829e75	−0.135104	−0.0675521	−	0.997716i	$-0.521519\pi$
$107$	−1.70829e75	−0.135104	−0.0675521	+	0.997716i	$0.521519\pi$
$108$	0	0
$109$	2.45585e76	0.969860	0.484930	−	0.874553i	$-0.338845\pi$
$109$	2.45585e76	0.969860	0.484930	+	0.874553i	$0.338845\pi$
$110$	−1.03137e77	−2.89193
$111$	0	0
$112$	−4.38696e76	−0.625875
$113$	9.70325e76	0.991917	0.495959	−	0.868346i	$-0.334817\pi$
$113$	9.70325e76	0.991917	0.495959	+	0.868346i	$0.334817\pi$
$114$	0	0
$115$	−8.94509e76	−0.473604
$116$	3.00335e77	1.14929
$117$	0	0
$118$	3.16233e77	0.637430
$119$	4.38297e77	0.643810
$120$	0	0
$121$	1.66407e78	1.30834
$122$	−5.73629e77	−0.331236
$123$	0	0
$124$	−2.94249e78	−0.923426
$125$	1.67539e78	0.389038
$126$	0	0
$127$	7.00233e78	0.896609	0.448305	−	0.893881i	$-0.352028\pi$
$127$	7.00233e78	0.896609	0.448305	+	0.893881i	$0.352028\pi$
$128$	−9.68915e78	−0.924510
$129$	0	0
$130$	−2.29585e79	−1.22481
$131$	−2.91625e78	−0.116722	−0.0583608	−	0.998296i	$-0.518587\pi$
$131$	−2.91625e78	−0.116722	−0.0583608	+	0.998296i	$0.518587\pi$
$132$	0	0
$133$	1.97932e79	0.448827
$134$	−8.41799e79	−1.44138
$135$	0	0
$136$	6.50838e79	0.639387
$137$	1.07240e80	0.800455	0.400228	−	0.916416i	$-0.368931\pi$
$137$	1.07240e80	0.800455	0.400228	+	0.916416i	$0.368931\pi$
$138$	0	0
$139$	−2.74555e80	−1.19008	−0.595039	−	0.803697i	$-0.702863\pi$
$139$	−2.74555e80	−1.19008	−0.595039	+	0.803697i	$0.702863\pi$
$140$	1.38384e80	0.458444
$141$	0	0
$142$	−8.87760e80	−1.72776
$143$	6.53554e80	0.977642
$144$	0	0
$145$	3.21870e81	2.86009
$146$	−1.03148e81	−0.708322
$147$	0	0
$148$	−2.19898e81	−0.906583
$149$	−5.97999e81	−1.91521	−0.957604	−	0.288089i	$-0.906980\pi$
$149$	−5.97999e81	−1.91521	−0.957604	+	0.288089i	$0.906980\pi$
$150$	0	0
$151$	7.62808e81	1.48177	0.740883	−	0.671634i	$-0.234407\pi$
$151$	7.62808e81	1.48177	0.740883	+	0.671634i	$0.234407\pi$
$152$	2.93913e81	0.445743
$153$	0	0
$154$	−1.04621e82	−0.971833
$155$	−3.15348e82	−2.29801
$156$	0	0
$157$	−2.42876e82	−1.09433	−0.547163	−	0.837026i	$-0.684292\pi$
$157$	−2.42876e82	−1.09433	−0.547163	+	0.837026i	$0.684292\pi$
$158$	−6.68298e81	−0.237317
$159$	0	0
$160$	7.24328e82	1.60486
$161$	−9.07382e81	−0.159155
$162$	0	0
$163$	−8.21476e82	−0.906901	−0.453450	−	0.891281i	$-0.649807\pi$
$163$	−8.21476e82	−0.906901	−0.453450	+	0.891281i	$0.649807\pi$
$164$	3.63463e82	0.319018
$165$	0	0
$166$	−4.96907e82	−0.276836
$167$	−2.65351e83	−1.18019	−0.590097	−	0.807333i	$-0.700910\pi$
$167$	−2.65351e83	−1.18019	−0.590097	+	0.807333i	$0.700910\pi$
$168$	0	0
$169$	−2.05876e83	−0.585942
$170$	−1.06361e84	−2.42632
$171$	0	0
$172$	4.89869e83	0.720715
$173$	−1.35698e84	−1.60636	−0.803182	−	0.595734i	$-0.796861\pi$
$173$	−1.35698e84	−1.60636	−0.803182	+	0.595734i	$0.796861\pi$
$174$	0	0
$175$	8.26511e83	0.635802
$176$	−3.03050e84	−1.88274
$177$	0	0
$178$	1.17430e84	0.477563
$179$	−1.18380e84	−0.390204	−0.195102	−	0.980783i	$-0.562504\pi$
$179$	−1.18380e84	−0.390204	−0.195102	+	0.980783i	$0.562504\pi$
$180$	0	0
$181$	−5.35554e84	−1.16374	−0.581871	−	0.813281i	$-0.697679\pi$
$181$	−5.35554e84	−1.16374	−0.581871	+	0.813281i	$0.697679\pi$
$182$	−2.32889e84	−0.411597
$183$	0	0
$184$	−1.34739e84	−0.158061
$185$	−2.35666e85	−2.25609
$186$	0	0
$187$	3.02775e85	1.93669
$188$	9.44075e84	0.494410
$189$	0	0
$190$	−4.80318e85	−1.69149
$191$	2.50784e85	0.725353	0.362677	−	0.931915i	$-0.381863\pi$
$191$	2.50784e85	0.725353	0.362677	+	0.931915i	$0.381863\pi$
$192$	0	0
$193$	−2.86873e85	−0.561423	−0.280711	−	0.959792i	$-0.590570\pi$
$193$	−2.86873e85	−0.561423	−0.280711	+	0.959792i	$0.590570\pi$
$194$	−9.61653e85	−1.55043
$195$	0	0
$196$	−4.09921e85	−0.449881
$197$	−1.93164e86	−1.75163	−0.875817	−	0.482644i	$-0.839677\pi$
$197$	−1.93164e86	−1.75163	−0.875817	+	0.482644i	$0.839677\pi$
$198$	0	0
$199$	1.83809e86	1.14124	0.570621	−	0.821214i	$-0.306703\pi$
$199$	1.83809e86	1.14124	0.570621	+	0.821214i	$0.306703\pi$
$200$	1.22731e86	0.631434
$201$	0	0
$202$	1.01196e86	0.358498
$203$	3.26502e86	0.961135
$204$	0	0
$205$	3.89524e86	0.793898
$206$	1.04889e87	1.78119
$207$	0	0
$208$	−6.74599e86	−0.797390
$209$	1.36731e87	1.35014
$210$	0	0
$211$	−6.67718e86	−0.461319	−0.230659	−	0.973035i	$-0.574088\pi$
$211$	−6.67718e86	−0.461319	−0.230659	+	0.973035i	$0.574088\pi$
$212$	9.25810e86	0.535706
$213$	0	0
$214$	4.20513e86	0.171105
$215$	5.24994e87	1.79355
$216$	0	0
$217$	−3.19886e87	−0.772245
$218$	−6.04535e87	−1.22830
$219$	0	0
$220$	9.55957e87	1.37907
$221$	6.73986e87	0.820239
$222$	0	0
$223$	−4.10287e87	−0.356168	−0.178084	−	0.984015i	$-0.556990\pi$
$223$	−4.10287e87	−0.356168	−0.178084	+	0.984015i	$0.556990\pi$
$224$	7.34752e87	0.539312
$225$	0	0
$226$	−2.38856e88	−1.25623
$227$	−6.86055e87	−0.305766	−0.152883	−	0.988244i	$-0.548856\pi$
$227$	−6.86055e87	−0.305766	−0.152883	+	0.988244i	$0.548856\pi$
$228$	0	0
$229$	8.68087e87	0.278441	0.139220	−	0.990261i	$-0.455540\pi$
$229$	8.68087e87	0.278441	0.139220	+	0.990261i	$0.455540\pi$
$230$	2.20193e88	0.599805
$231$	0	0
$232$	4.84830e88	0.954532
$233$	2.74446e88	0.459844	0.229922	−	0.973209i	$-0.426153\pi$
$233$	2.74446e88	0.459844	0.229922	+	0.973209i	$0.426153\pi$
$234$	0	0
$235$	1.01177e89	1.23037
$236$	−2.93112e88	−0.303972
$237$	0	0
$238$	−1.07892e89	−0.815365
$239$	−2.74529e89	−1.77283	−0.886416	−	0.462889i	$-0.846813\pi$
$239$	−2.74529e89	−1.77283	−0.886416	+	0.462889i	$0.846813\pi$
$240$	0	0
$241$	−2.33457e89	−1.10298	−0.551491	−	0.834181i	$-0.685941\pi$
$241$	−2.33457e89	−1.10298	−0.551491	+	0.834181i	$0.685941\pi$
$242$	−4.09628e89	−1.65696
$243$	0	0
$244$	5.31688e88	0.157957
$245$	−4.39314e89	−1.11956
$246$	0	0
$247$	3.04367e89	0.571823
$248$	−4.75006e89	−0.766940
$249$	0	0
$250$	−4.12416e89	−0.492704
$251$	8.50965e89	0.875281	0.437640	−	0.899150i	$-0.355814\pi$
$251$	8.50965e89	0.875281	0.437640	+	0.899150i	$0.355814\pi$
$252$	0	0
$253$	−6.26817e89	−0.478764
$254$	−1.72370e90	−1.13553
$255$	0	0
$256$	2.61557e90	1.28401
$257$	1.40299e90	0.595063	0.297532	−	0.954712i	$-0.403837\pi$
$257$	1.40299e90	0.595063	0.297532	+	0.954712i	$0.403837\pi$
$258$	0	0
$259$	−2.39057e90	−0.758160
$260$	2.12799e90	0.584075
$261$	0	0
$262$	7.17867e89	0.147824
$263$	9.43704e90	1.68459	0.842297	−	0.539014i	$-0.181203\pi$
$263$	9.43704e90	1.68459	0.842297	+	0.539014i	$0.181203\pi$
$264$	0	0
$265$	9.92193e90	1.33314
$266$	−4.87230e90	−0.568424
$267$	0	0
$268$	7.80250e90	0.687351
$269$	1.09749e91	0.840798	0.420399	−	0.907339i	$-0.361890\pi$
$269$	1.09749e91	0.840798	0.420399	+	0.907339i	$0.361890\pi$
$270$	0	0
$271$	−3.28817e91	−1.90812	−0.954060	−	0.299614i	$-0.903142\pi$
$271$	−3.28817e91	−1.90812	−0.954060	+	0.299614i	$0.903142\pi$
$272$	−3.12525e91	−1.57961
$273$	0	0
$274$	−2.63984e91	−1.01375
$275$	5.70952e91	1.91260
$276$	0	0
$277$	4.47785e91	1.14309	0.571543	−	0.820572i	$-0.306345\pi$
$277$	4.47785e91	1.14309	0.571543	+	0.820572i	$0.306345\pi$
$278$	6.75848e91	1.50719
$279$	0	0
$280$	2.23394e91	0.380755
$281$	3.36542e91	0.501825	0.250912	−	0.968010i	$-0.419269\pi$
$281$	3.36542e91	0.501825	0.250912	+	0.968010i	$0.419269\pi$
$282$	0	0
$283$	1.20893e92	1.38169	0.690845	−	0.723003i	$-0.257239\pi$
$283$	1.20893e92	1.38169	0.690845	+	0.723003i	$0.257239\pi$
$284$	8.22850e91	0.823916
$285$	0	0
$286$	−1.60879e92	−1.23815
$287$	3.95130e91	0.266790
$288$	0	0
$289$	1.20078e92	0.624876
$290$	−7.92318e92	−3.62222
$291$	0	0
$292$	9.56066e91	0.337778
$293$	7.04755e91	0.219029	0.109515	−	0.993985i	$-0.465070\pi$
$293$	7.04755e91	0.219029	0.109515	+	0.993985i	$0.465070\pi$
$294$	0	0
$295$	−3.14129e92	−0.756453
$296$	−3.54982e92	−0.752952
$297$	0	0
$298$	1.47204e93	2.42555
$299$	−1.39531e92	−0.202769
$300$	0	0
$301$	5.32550e92	0.602721
$302$	−1.87773e93	−1.87661
$303$	0	0
$304$	−1.41134e93	−1.10121
$305$	5.69812e92	0.393086
$306$	0	0
$307$	−2.50898e93	−1.35459	−0.677296	−	0.735711i	$-0.736848\pi$
$307$	−2.50898e93	−1.35459	−0.677296	+	0.735711i	$0.736848\pi$
$308$	9.69714e92	0.463438
$309$	0	0
$310$	7.76263e93	2.91035
$311$	9.71396e92	0.322761	0.161381	−	0.986892i	$-0.448405\pi$
$311$	9.71396e92	0.322761	0.161381	+	0.986892i	$0.448405\pi$
$312$	0	0
$313$	−2.52357e93	−0.659330	−0.329665	−	0.944098i	$-0.606936\pi$
$313$	−2.52357e93	−0.659330	−0.329665	+	0.944098i	$0.606936\pi$
$314$	5.97865e93	1.38593
$315$	0	0
$316$	6.19434e92	0.113170
$317$	−9.61160e93	−1.55982	−0.779908	−	0.625895i	$-0.784734\pi$
$317$	−9.61160e93	−1.55982	−0.779908	+	0.625895i	$0.784734\pi$
$318$	0	0
$319$	2.25547e94	2.89125
$320$	−1.49179e93	−0.170053
$321$	0	0
$322$	2.23362e93	0.201565
$323$	1.41005e94	1.13277
$324$	0	0
$325$	1.27096e94	0.810036
$326$	2.02215e94	1.14856
$327$	0	0
$328$	5.86738e93	0.264957
$329$	1.02633e94	0.413467
$330$	0	0
$331$	−1.39070e93	−0.0446359	−0.0223179	−	0.999751i	$-0.507105\pi$
$331$	−1.39070e93	−0.0446359	−0.0223179	+	0.999751i	$0.507105\pi$
$332$	4.60575e93	0.132015
$333$	0	0
$334$	6.53190e94	1.49468
$335$	8.36196e94	1.71052
$336$	0	0
$337$	7.66690e94	1.25458	0.627290	−	0.778786i	$-0.284164\pi$
$337$	7.66690e94	1.25458	0.627290	+	0.778786i	$0.284164\pi$
$338$	5.06787e94	0.742077
$339$	0	0
$340$	9.85843e94	1.15704
$341$	−2.20976e95	−2.32304
$342$	0	0
$343$	−1.04388e95	−0.881293
$344$	7.90796e94	0.598581
$345$	0	0
$346$	3.34035e95	2.03441
$347$	−2.54283e95	−1.38983	−0.694916	−	0.719091i	$-0.744558\pi$
$347$	−2.54283e95	−1.38983	−0.694916	+	0.719091i	$0.744558\pi$
$348$	0	0
$349$	2.23198e95	0.983414	0.491707	−	0.870761i	$-0.336373\pi$
$349$	2.23198e95	0.983414	0.491707	+	0.870761i	$0.336373\pi$
$350$	−2.03455e95	−0.805223
$351$	0	0
$352$	5.07565e95	1.62234
$353$	−5.15672e95	−1.48191	−0.740956	−	0.671554i	$-0.765627\pi$
$353$	−5.15672e95	−1.48191	−0.740956	+	0.671554i	$0.765627\pi$
$354$	0	0
$355$	8.81851e95	2.05037
$356$	−1.08844e95	−0.227735
$357$	0	0
$358$	2.91406e95	0.494180
$359$	−5.65417e95	−0.863629	−0.431815	−	0.901962i	$-0.642127\pi$
$359$	−5.65417e95	−0.863629	−0.431815	+	0.901962i	$0.642127\pi$
$360$	0	0
$361$	−1.69575e95	−0.210301
$362$	1.31832e96	1.47384
$363$	0	0
$364$	2.15861e95	0.196279
$365$	1.02462e96	0.840582
$366$	0	0
$367$	1.49304e96	0.997919	0.498960	−	0.866625i	$-0.333716\pi$
$367$	1.49304e96	0.997919	0.498960	+	0.866625i	$0.333716\pi$
$368$	6.47002e95	0.390492
$369$	0	0
$370$	5.80117e96	2.85727
$371$	1.00647e96	0.448002
$372$	0	0
$373$	−2.36030e96	−0.858789	−0.429394	−	0.903117i	$-0.641273\pi$
$373$	−2.36030e96	−0.858789	−0.429394	+	0.903117i	$0.641273\pi$
$374$	−7.45313e96	−2.45275
$375$	0	0
$376$	1.52402e96	0.410626
$377$	5.02074e96	1.22452
$378$	0	0
$379$	6.71210e96	1.34242	0.671209	−	0.741268i	$-0.265775\pi$
$379$	6.71210e96	1.34242	0.671209	+	0.741268i	$0.265775\pi$
$380$	4.45199e96	0.806620
$381$	0	0
$382$	−6.17333e96	−0.918636
$383$	9.42998e96	1.27220	0.636102	−	0.771605i	$-0.280546\pi$
$383$	9.42998e96	1.27220	0.636102	+	0.771605i	$0.280546\pi$
$384$	0	0
$385$	1.03925e97	1.15330
$386$	7.06168e96	0.711024
$387$	0	0
$388$	8.91340e96	0.739356
$389$	9.60054e96	0.723079	0.361539	−	0.932357i	$-0.382251\pi$
$389$	9.60054e96	0.723079	0.361539	+	0.932357i	$0.382251\pi$
$390$	0	0
$391$	−6.46414e96	−0.401682
$392$	−6.61736e96	−0.373643
$393$	0	0
$394$	4.75495e97	2.21839
$395$	6.63850e96	0.281630
$396$	0	0
$397$	−4.39879e97	−1.54415	−0.772074	−	0.635532i	$-0.780781\pi$
$397$	−4.39879e97	−1.54415	−0.772074	+	0.635532i	$0.780781\pi$
$398$	−4.52467e97	−1.44535
$399$	0	0
$400$	−5.89337e97	−1.55996
$401$	1.08509e96	0.0261548	0.0130774	−	0.999914i	$-0.495837\pi$
$401$	1.08509e96	0.0261548	0.0130774	+	0.999914i	$0.495837\pi$
$402$	0	0
$403$	−4.91900e97	−0.983871
$404$	−9.37968e96	−0.170957
$405$	0	0
$406$	−8.03720e97	−1.21725
$407$	−1.65140e98	−2.28067
$408$	0	0
$409$	1.63608e98	1.88010	0.940051	−	0.341034i	$-0.110777\pi$
$409$	1.63608e98	1.88010	0.940051	+	0.341034i	$0.110777\pi$
$410$	−9.58856e97	−1.00545
$411$	0	0
$412$	−9.72200e97	−0.849396
$413$	−3.18649e97	−0.254206
$414$	0	0
$415$	4.93600e97	0.328527
$416$	1.12986e98	0.687105
$417$	0	0
$418$	−3.36577e98	−1.70991
$419$	4.78918e97	0.222451	0.111226	−	0.993795i	$-0.464522\pi$
$419$	4.78918e97	0.222451	0.111226	+	0.993795i	$0.464522\pi$
$420$	0	0
$421$	−4.81093e98	−1.86918	−0.934589	−	0.355728i	$-0.884233\pi$
$421$	−4.81093e98	−1.86918	−0.934589	+	0.355728i	$0.884233\pi$
$422$	1.64366e98	0.584245
$423$	0	0
$424$	1.49453e98	0.444924
$425$	5.88801e98	1.60466
$426$	0	0
$427$	5.78012e97	0.132097
$428$	−3.89767e97	−0.0815949
$429$	0	0
$430$	−1.29233e99	−2.27147
$431$	−6.24480e98	−1.00605	−0.503027	−	0.864271i	$-0.667780\pi$
$431$	−6.24480e98	−1.00605	−0.503027	+	0.864271i	$0.667780\pi$
$432$	0	0
$433$	−7.41357e98	−1.00399	−0.501997	−	0.864869i	$-0.667401\pi$
$433$	−7.41357e98	−1.00399	−0.501997	+	0.864869i	$0.667401\pi$
$434$	7.87434e98	0.978024
$435$	0	0
$436$	5.60334e98	0.585738
$437$	−2.91915e98	−0.280029
$438$	0	0
$439$	−1.52132e99	−1.22971	−0.614853	−	0.788642i	$-0.710784\pi$
$439$	−1.52132e99	−1.22971	−0.614853	+	0.788642i	$0.710784\pi$
$440$	1.54320e99	1.14537
$441$	0	0
$442$	−1.65909e99	−1.03881
$443$	6.19312e98	0.356262	0.178131	−	0.984007i	$-0.442995\pi$
$443$	6.19312e98	0.356262	0.178131	+	0.984007i	$0.442995\pi$
$444$	0	0
$445$	−1.16649e99	−0.566735
$446$	1.00997e99	0.451076
$447$	0	0
$448$	−1.51326e98	−0.0571463
$449$	−2.99075e99	−1.03882	−0.519412	−	0.854524i	$-0.673849\pi$
$449$	−2.99075e99	−1.03882	−0.519412	+	0.854524i	$0.673849\pi$
$450$	0	0
$451$	2.72955e99	0.802547
$452$	2.21392e99	0.599060
$453$	0	0
$454$	1.68880e99	0.387243
$455$	2.31339e99	0.488452
$456$	0	0
$457$	−2.95011e99	−0.528421	−0.264211	−	0.964465i	$-0.585111\pi$
$457$	−2.95011e99	−0.528421	−0.264211	+	0.964465i	$0.585111\pi$
$458$	−2.13689e99	−0.352636
$459$	0	0
$460$	−2.04093e99	−0.286029
$461$	−5.46613e99	−0.706148	−0.353074	−	0.935595i	$-0.614864\pi$
$461$	−5.46613e99	−0.706148	−0.353074	+	0.935595i	$0.614864\pi$
$462$	0	0
$463$	1.02267e100	1.12317	0.561587	−	0.827418i	$-0.310191\pi$
$463$	1.02267e100	1.12317	0.561587	+	0.827418i	$0.310191\pi$
$464$	−2.32810e100	−2.35818
$465$	0	0
$466$	−6.75580e99	−0.582378
$467$	−1.16980e100	−0.930525	−0.465263	−	0.885173i	$-0.654040\pi$
$467$	−1.16980e100	−0.930525	−0.465263	+	0.885173i	$0.654040\pi$
$468$	0	0
$469$	8.48230e99	0.574820
$470$	−2.49058e100	−1.55823
$471$	0	0
$472$	−4.73170e99	−0.252460
$473$	3.67884e100	1.81309
$474$	0	0
$475$	2.65898e100	1.11868
$476$	1.00003e100	0.388823
$477$	0	0
$478$	6.75784e100	2.24524
$479$	−1.27080e100	−0.390388	−0.195194	−	0.980765i	$-0.562534\pi$
$479$	−1.27080e100	−0.390388	−0.195194	+	0.980765i	$0.562534\pi$
$480$	0	0
$481$	−3.67607e100	−0.965925
$482$	5.74681e100	1.39689
$483$	0	0
$484$	3.79677e100	0.790157
$485$	9.55253e100	1.83994
$486$	0	0
$487$	−3.18849e100	−0.526319	−0.263159	−	0.964752i	$-0.584765\pi$
$487$	−3.18849e100	−0.526319	−0.263159	+	0.964752i	$0.584765\pi$
$488$	8.58304e99	0.131189
$489$	0	0
$490$	1.08142e101	1.41788
$491$	−2.74357e100	−0.333243	−0.166621	−	0.986021i	$-0.553286\pi$
$491$	−2.74357e100	−0.333243	−0.166621	+	0.986021i	$0.553286\pi$
$492$	0	0
$493$	2.32598e101	2.42575
$494$	−7.49232e100	−0.724195
$495$	0	0
$496$	2.28092e101	1.89473
$497$	8.94542e100	0.689027
$498$	0	0
$499$	−1.37204e101	−0.909069	−0.454534	−	0.890729i	$-0.650194\pi$
$499$	−1.37204e101	−0.909069	−0.454534	+	0.890729i	$0.650194\pi$
$500$	3.82262e100	0.234956
$501$	0	0
$502$	−2.09474e101	−1.10851
$503$	2.20150e99	0.0108123	0.00540615	−	0.999985i	$-0.498279\pi$
$503$	2.20150e99	0.0108123	0.00540615	+	0.999985i	$0.498279\pi$
$504$	0	0
$505$	−1.00522e101	−0.425438
$506$	1.54298e101	0.606339
$507$	0	0
$508$	1.59767e101	0.541499
$509$	1.33832e100	0.0421349	0.0210675	−	0.999778i	$-0.493294\pi$
$509$	1.33832e100	0.0421349	0.0210675	+	0.999778i	$0.493294\pi$
$510$	0	0
$511$	1.03937e101	0.282478
$512$	−2.77806e101	−0.701646
$513$	0	0
$514$	−3.45362e101	−0.753628
$515$	−1.04191e102	−2.11378
$516$	0	0
$517$	7.08986e101	1.24378
$518$	5.88466e101	0.960185
$519$	0	0
$520$	3.43521e101	0.485097
$521$	5.35548e101	0.703694	0.351847	−	0.936058i	$-0.385554\pi$
$521$	5.35548e101	0.703694	0.351847	+	0.936058i	$0.385554\pi$
$522$	0	0
$523$	4.62005e100	0.0525816	0.0262908	−	0.999654i	$-0.491630\pi$
$523$	4.62005e100	0.0525816	0.0262908	+	0.999654i	$0.491630\pi$
$524$	−6.65379e100	−0.0704929
$525$	0	0
$526$	−2.32303e102	−2.13348
$527$	−2.27885e102	−1.94903
$528$	0	0
$529$	−1.21386e102	−0.900701
$530$	−2.44239e102	−1.68838
$531$	0	0
$532$	4.51606e101	0.271065
$533$	6.07606e101	0.339900
$534$	0	0
$535$	−4.17714e101	−0.203054
$536$	1.25956e102	0.570871
$537$	0	0
$538$	−2.70160e102	−1.06484
$539$	−3.07844e102	−1.13176
$540$	0	0
$541$	−4.54607e102	−1.45458	−0.727292	−	0.686328i	$-0.759221\pi$
$541$	−4.54607e102	−1.45458	−0.727292	+	0.686328i	$0.759221\pi$
$542$	8.09419e102	2.41657
$543$	0	0
$544$	5.23433e102	1.36114
$545$	6.00512e102	1.45765
$546$	0	0
$547$	−5.65435e102	−1.19635	−0.598174	−	0.801366i	$-0.704107\pi$
$547$	−5.65435e102	−1.19635	−0.598174	+	0.801366i	$0.704107\pi$
$548$	2.44682e102	0.483428
$549$	0	0
$550$	−1.40546e103	−2.42224
$551$	1.05039e103	1.69109
$552$	0	0
$553$	6.73403e101	0.0946418
$554$	−1.10227e103	−1.44768
$555$	0	0
$556$	−6.26433e102	−0.718736
$557$	7.74932e102	0.831178	0.415589	−	0.909553i	$-0.363576\pi$
$557$	7.74932e102	0.831178	0.415589	+	0.909553i	$0.363576\pi$
$558$	0	0
$559$	8.18921e102	0.767891
$560$	−1.07271e103	−0.940658
$561$	0	0
$562$	−8.28434e102	−0.635545
$563$	1.78877e103	1.28378	0.641888	−	0.766798i	$-0.278151\pi$
$563$	1.78877e103	1.28378	0.641888	+	0.766798i	$0.278151\pi$
$564$	0	0
$565$	2.37266e103	1.49080
$566$	−2.97592e103	−1.74987
$567$	0	0
$568$	1.32833e103	0.684293
$569$	−2.18769e103	−1.05505	−0.527527	−	0.849538i	$-0.676881\pi$
$569$	−2.18769e103	−1.05505	−0.527527	+	0.849538i	$0.676881\pi$
$570$	0	0
$571$	−3.73120e103	−1.57759	−0.788796	−	0.614656i	$-0.789295\pi$
$571$	−3.73120e103	−1.57759	−0.788796	+	0.614656i	$0.789295\pi$
$572$	1.49116e103	0.590438
$573$	0	0
$574$	−9.72655e102	−0.337880
$575$	−1.21896e103	−0.396685
$576$	0	0
$577$	−1.02249e103	−0.292124	−0.146062	−	0.989275i	$-0.546660\pi$
$577$	−1.02249e103	−0.292124	−0.146062	+	0.989275i	$0.546660\pi$
$578$	−2.95585e103	−0.791385
$579$	0	0
$580$	7.34386e103	1.72733
$581$	5.00703e102	0.110402
$582$	0	0
$583$	6.95268e103	1.34766
$584$	1.54338e103	0.280537
$585$	0	0
$586$	−1.73483e103	−0.277394
$587$	−1.53321e103	−0.229971	−0.114985	−	0.993367i	$-0.536682\pi$
$587$	−1.53321e103	−0.229971	−0.114985	+	0.993367i	$0.536682\pi$
$588$	0	0
$589$	−1.02911e104	−1.35875
$590$	7.73262e103	0.958024
$591$	0	0
$592$	1.70458e104	1.86017
$593$	−1.64986e104	−1.69004	−0.845021	−	0.534734i	$-0.820412\pi$
$593$	−1.64986e104	−1.69004	−0.845021	+	0.534734i	$0.820412\pi$
$594$	0	0
$595$	1.07174e104	0.967613
$596$	−1.36441e104	−1.15667
$597$	0	0
$598$	3.43472e103	0.256801
$599$	9.70370e103	0.681446	0.340723	−	0.940164i	$-0.389328\pi$
$599$	9.70370e103	0.681446	0.340723	+	0.940164i	$0.389328\pi$
$600$	0	0
$601$	1.28191e104	0.794448	0.397224	−	0.917722i	$-0.369974\pi$
$601$	1.28191e104	0.794448	0.397224	+	0.917722i	$0.369974\pi$
$602$	−1.31093e104	−0.763327
$603$	0	0
$604$	1.74044e104	0.894899
$605$	4.06901e104	1.96636
$606$	0	0
$607$	2.28168e104	0.974270	0.487135	−	0.873327i	$-0.338042\pi$
$607$	2.28168e104	0.974270	0.487135	+	0.873327i	$0.338042\pi$
$608$	2.36378e104	0.948906
$609$	0	0
$610$	−1.40265e104	−0.497830
$611$	1.57822e104	0.526773
$612$	0	0
$613$	4.41391e104	1.30333	0.651667	−	0.758505i	$-0.274070\pi$
$613$	4.41391e104	1.30333	0.651667	+	0.758505i	$0.274070\pi$
$614$	6.17613e104	1.71555
$615$	0	0
$616$	1.56541e104	0.384903
$617$	3.21643e104	0.744185	0.372092	−	0.928196i	$-0.378640\pi$
$617$	3.21643e104	0.744185	0.372092	+	0.928196i	$0.378640\pi$
$618$	0	0
$619$	−6.36255e104	−1.30386	−0.651931	−	0.758278i	$-0.726041\pi$
$619$	−6.36255e104	−1.30386	−0.651931	+	0.758278i	$0.726041\pi$
$620$	−7.19505e104	−1.38786
$621$	0	0
$622$	−2.39120e104	−0.408767
$623$	−1.18328e104	−0.190451
$624$	0	0
$625$	−4.72341e104	−0.674147
$626$	6.21205e104	0.835021
$627$	0	0
$628$	−5.54151e104	−0.660909
$629$	−1.70303e105	−1.91348
$630$	0	0
$631$	5.83460e103	0.0581983	0.0290992	−	0.999577i	$-0.490736\pi$
$631$	5.83460e103	0.0581983	0.0290992	+	0.999577i	$0.490736\pi$
$632$	9.99953e103	0.0939916
$633$	0	0
$634$	2.36600e105	1.97546
$635$	1.71223e105	1.34756
$636$	0	0
$637$	−6.85271e104	−0.479329
$638$	−5.55208e105	−3.66168
$639$	0	0
$640$	−2.36921e105	−1.38949
$641$	−1.14109e105	−0.631168	−0.315584	−	0.948898i	$-0.602200\pi$
$641$	−1.14109e105	−0.631168	−0.315584	+	0.948898i	$0.602200\pi$
$642$	0	0
$643$	−4.74494e104	−0.233517	−0.116759	−	0.993160i	$-0.537250\pi$
$643$	−4.74494e104	−0.233517	−0.116759	+	0.993160i	$0.537250\pi$
$644$	−2.07031e104	−0.0961202
$645$	0	0
$646$	−3.47100e105	−1.43461
$647$	3.50841e105	1.36836	0.684179	−	0.729314i	$-0.260161\pi$
$647$	3.50841e105	1.36836	0.684179	+	0.729314i	$0.260161\pi$
$648$	0	0
$649$	−2.20122e105	−0.764694
$650$	−3.12860e105	−1.02588
$651$	0	0
$652$	−1.87430e105	−0.547715
$653$	4.21713e105	1.16352	0.581759	−	0.813361i	$-0.302365\pi$
$653$	4.21713e105	1.16352	0.581759	+	0.813361i	$0.302365\pi$
$654$	0	0
$655$	−7.13089e104	−0.175426
$656$	−2.81744e105	−0.654577
$657$	0	0
$658$	−2.52642e105	−0.523642
$659$	6.99778e105	1.37012	0.685058	−	0.728489i	$-0.259777\pi$
$659$	6.99778e105	1.37012	0.685058	+	0.728489i	$0.259777\pi$
$660$	0	0
$661$	2.47496e105	0.432528	0.216264	−	0.976335i	$-0.430613\pi$
$661$	2.47496e105	0.432528	0.216264	+	0.976335i	$0.430613\pi$
$662$	3.42336e104	0.0565299
$663$	0	0
$664$	7.43506e104	0.109643
$665$	4.83987e105	0.674563
$666$	0	0
$667$	−4.81534e105	−0.599665
$668$	−6.05431e105	−0.712767
$669$	0	0
$670$	−2.05839e106	−2.16632
$671$	3.99289e105	0.397368
$672$	0	0
$673$	−3.25575e105	−0.289792	−0.144896	−	0.989447i	$-0.546285\pi$
$673$	−3.25575e105	−0.289792	−0.144896	+	0.989447i	$0.546285\pi$
$674$	−1.88729e106	−1.58889
$675$	0	0
$676$	−4.69732e105	−0.353874
$677$	1.77793e106	1.26718	0.633591	−	0.773668i	$-0.281580\pi$
$677$	1.77793e106	1.26718	0.633591	+	0.773668i	$0.281580\pi$
$678$	0	0
$679$	9.69000e105	0.618311
$680$	1.59145e106	0.960965
$681$	0	0
$682$	5.43958e106	2.94206
$683$	1.81574e106	0.929560	0.464780	−	0.885426i	$-0.346133\pi$
$683$	1.81574e106	0.929560	0.464780	+	0.885426i	$0.346133\pi$
$684$	0	0
$685$	2.62227e106	1.20304
$686$	2.56962e106	1.11613
$687$	0	0
$688$	−3.79730e106	−1.47880
$689$	1.54769e106	0.570772
$690$	0	0
$691$	−2.23026e106	−0.737783	−0.368891	−	0.929473i	$-0.620263\pi$
$691$	−2.23026e106	−0.737783	−0.368891	+	0.929473i	$0.620263\pi$
$692$	−3.09611e106	−0.970149
$693$	0	0
$694$	6.25946e106	1.76018
$695$	−6.71350e106	−1.78862
$696$	0	0
$697$	2.81488e106	0.673335
$698$	−5.49425e106	−1.24546
$699$	0	0
$700$	1.88579e106	0.383987
$701$	1.84181e106	0.355483	0.177742	−	0.984077i	$-0.443121\pi$
$701$	1.84181e106	0.355483	0.177742	+	0.984077i	$0.443121\pi$
$702$	0	0
$703$	−7.69075e106	−1.33396
$704$	−1.04536e106	−0.171906
$705$	0	0
$706$	1.26938e107	1.87679
$707$	−1.01969e106	−0.142968
$708$	0	0
$709$	1.69695e106	0.214010	0.107005	−	0.994258i	$-0.465874\pi$
$709$	1.69695e106	0.214010	0.107005	+	0.994258i	$0.465874\pi$
$710$	−2.17077e107	−2.59673
$711$	0	0
$712$	−1.75707e106	−0.189143
$713$	4.71777e106	0.481814
$714$	0	0
$715$	1.59809e107	1.46934
$716$	−2.70100e106	−0.235660
$717$	0	0
$718$	1.39184e107	1.09376
$719$	3.82777e106	0.285504	0.142752	−	0.989758i	$-0.454405\pi$
$719$	3.82777e106	0.285504	0.142752	+	0.989758i	$0.454405\pi$
$720$	0	0
$721$	−1.05690e107	−0.710335
$722$	4.17428e106	0.266340
$723$	0	0
$724$	−1.22193e107	−0.702832
$725$	4.38617e107	2.39558
$726$	0	0
$727$	2.55464e107	1.25831	0.629157	−	0.777278i	$-0.283400\pi$
$727$	2.55464e107	1.25831	0.629157	+	0.777278i	$0.283400\pi$
$728$	3.48465e106	0.163017
$729$	0	0
$730$	−2.52221e107	−1.06457
$731$	3.79385e107	1.52117
$732$	0	0
$733$	5.43876e107	1.96834	0.984172	−	0.177214i	$-0.0567086\pi$
$733$	5.43876e107	1.96834	0.984172	+	0.177214i	$0.0567086\pi$
$734$	−3.67529e107	−1.26383
$735$	0	0
$736$	−1.08363e107	−0.336484
$737$	5.85955e107	1.72915
$738$	0	0
$739$	−2.11026e107	−0.562560	−0.281280	−	0.959626i	$-0.590759\pi$
$739$	−2.11026e107	−0.562560	−0.281280	+	0.959626i	$0.590759\pi$
$740$	−5.37701e107	−1.36255
$741$	0	0
$742$	−2.47754e107	−0.567380
$743$	−3.66092e107	−0.797093	−0.398547	−	0.917148i	$-0.630485\pi$
$743$	−3.66092e107	−0.797093	−0.398547	+	0.917148i	$0.630485\pi$
$744$	0	0
$745$	−1.46224e108	−2.87845
$746$	5.81014e107	1.08763
$747$	0	0
$748$	6.90819e107	1.16964
$749$	−4.23726e106	−0.0682365
$750$	0	0
$751$	−6.28876e107	−0.916363	−0.458182	−	0.888859i	$-0.651499\pi$
$751$	−6.28876e107	−0.916363	−0.458182	+	0.888859i	$0.651499\pi$
$752$	−7.31816e107	−1.01445
$753$	0	0
$754$	−1.23591e108	−1.55082
$755$	1.86524e108	2.22702
$756$	0	0
$757$	−1.98621e105	−0.00214748	−0.00107374	−	0.999999i	$-0.500342\pi$
$757$	−1.98621e105	−0.00214748	−0.00107374	+	0.999999i	$0.500342\pi$
$758$	−1.65226e108	−1.70013
$759$	0	0
$760$	7.18684e107	0.669928
$761$	−1.93627e106	−0.0171807	−0.00859034	−	0.999963i	$-0.502734\pi$
$761$	−1.93627e106	−0.0171807	−0.00859034	+	0.999963i	$0.502734\pi$
$762$	0	0
$763$	6.09154e107	0.489843
$764$	5.72196e107	0.438070
$765$	0	0
$766$	−2.32129e108	−1.61121
$767$	−4.89999e107	−0.323869
$768$	0	0
$769$	6.69512e107	0.401347	0.200674	−	0.979658i	$-0.435687\pi$
$769$	6.69512e107	0.401347	0.200674	+	0.979658i	$0.435687\pi$
$770$	−2.55822e108	−1.46061
$771$	0	0
$772$	−6.54536e107	−0.339066
$773$	−2.68911e108	−1.32702	−0.663510	−	0.748167i	$-0.730934\pi$
$773$	−2.68911e108	−1.32702	−0.663510	+	0.748167i	$0.730934\pi$
$774$	0	0
$775$	−4.29730e108	−1.92478
$776$	1.43889e108	0.614064
$777$	0	0
$778$	−2.36328e108	−0.915756
$779$	1.27118e108	0.469409
$780$	0	0
$781$	6.17947e108	2.07271
$782$	1.59122e108	0.508717
$783$	0	0
$784$	3.17757e108	0.923088
$785$	−5.93885e108	−1.64471
$786$	0	0
$787$	−4.19602e108	−1.05630	−0.528148	−	0.849153i	$-0.677113\pi$
$787$	−4.19602e108	−1.05630	−0.528148	+	0.849153i	$0.677113\pi$
$788$	−4.40728e108	−1.05788
$789$	0	0
$790$	−1.63414e108	−0.356675
$791$	2.40681e108	0.500983
$792$	0	0
$793$	8.88830e107	0.168296
$794$	1.08281e109	1.95561
$795$	0	0
$796$	4.19384e108	0.689243
$797$	−3.82811e108	−0.600203	−0.300101	−	0.953907i	$-0.597020\pi$
$797$	−3.82811e108	−0.600203	−0.300101	+	0.953907i	$0.597020\pi$
$798$	0	0
$799$	7.31151e108	1.04352
$800$	9.87054e108	1.34421
$801$	0	0
$802$	−2.67107e107	−0.0331243
$803$	7.17991e108	0.849740
$804$	0	0
$805$	−2.21875e108	−0.239201
$806$	1.21087e109	1.24604
$807$	0	0
$808$	−1.51416e108	−0.141986
$809$	1.69904e109	1.52102	0.760509	−	0.649327i	$-0.224950\pi$
$809$	1.69904e109	1.52102	0.760509	+	0.649327i	$0.224950\pi$
$810$	0	0
$811$	−1.82762e108	−0.149143	−0.0745717	−	0.997216i	$-0.523759\pi$
$811$	−1.82762e108	−0.149143	−0.0745717	+	0.997216i	$0.523759\pi$
$812$	7.44955e108	0.580469
$813$	0	0
$814$	4.06511e109	2.88840
$815$	−2.00869e109	−1.36302
$816$	0	0
$817$	1.71327e109	1.06047
$818$	−4.02740e109	−2.38109
$819$	0	0
$820$	8.88748e108	0.479468
$821$	3.36119e108	0.173231	0.0866153	−	0.996242i	$-0.472395\pi$
$821$	3.36119e108	0.173231	0.0866153	+	0.996242i	$0.472395\pi$
$822$	0	0
$823$	2.65551e109	1.24926	0.624631	−	0.780920i	$-0.285249\pi$
$823$	2.65551e109	1.24926	0.624631	+	0.780920i	$0.285249\pi$
$824$	−1.56942e109	−0.705455
$825$	0	0
$826$	7.84390e108	0.321944
$827$	−9.29747e105	−0.000364677 0	−0.000182338	−	1.00000i	$-0.500058\pi$
$827$	−9.29747e105	−0.000364677 0	−0.000182338		1.00000i	$0.500058\pi$
$828$	0	0
$829$	−4.36996e109	−1.56560	−0.782802	−	0.622270i	$-0.786210\pi$
$829$	−4.36996e109	−1.56560	−0.782802	+	0.622270i	$0.786210\pi$
$830$	−1.21505e109	−0.416069
$831$	0	0
$832$	−2.32700e108	−0.0728066
$833$	−3.17469e109	−0.949540
$834$	0	0
$835$	−6.48843e109	−1.77377
$836$	3.11968e109	0.815407
$837$	0	0
$838$	−1.17891e109	−0.281727
$839$	−6.12601e109	−1.39992	−0.699961	−	0.714181i	$-0.746799\pi$
$839$	−6.12601e109	−1.39992	−0.699961	+	0.714181i	$0.746799\pi$
$840$	0	0
$841$	1.25423e110	2.62137
$842$	1.18426e110	2.36726
$843$	0	0
$844$	−1.52348e109	−0.278609
$845$	−5.03414e109	−0.880640
$846$	0	0
$847$	4.12757e109	0.660795
$848$	−7.17657e109	−1.09919
$849$	0	0
$850$	−1.44940e110	−2.03225
$851$	3.52569e109	0.473026
$852$	0	0
$853$	1.20493e109	0.148038	0.0740191	−	0.997257i	$-0.476417\pi$
$853$	1.20493e109	0.148038	0.0740191	+	0.997257i	$0.476417\pi$
$854$	−1.42284e109	−0.167296
$855$	0	0
$856$	−6.29200e108	−0.0677677
$857$	−9.76590e108	−0.100677	−0.0503386	−	0.998732i	$-0.516030\pi$
$857$	−9.76590e108	−0.100677	−0.0503386	+	0.998732i	$0.516030\pi$
$858$	0	0
$859$	−1.42699e110	−1.34797	−0.673983	−	0.738747i	$-0.735418\pi$
$859$	−1.42699e110	−1.34797	−0.673983	+	0.738747i	$0.735418\pi$
$860$	1.19784e110	1.08320
$861$	0	0
$862$	1.53723e110	1.27413
$863$	−1.79341e110	−1.42323	−0.711614	−	0.702571i	$-0.752035\pi$
$863$	−1.79341e110	−1.42323	−0.711614	+	0.702571i	$0.752035\pi$
$864$	0	0
$865$	−3.31812e110	−2.41428
$866$	1.82493e110	1.27153
$867$	0	0
$868$	−7.29860e109	−0.466391
$869$	4.65185e109	0.284698
$870$	0	0
$871$	1.30435e110	0.732344
$872$	9.04547e109	0.486478
$873$	0	0
$874$	7.18581e109	0.354648
$875$	4.15567e109	0.196489
$876$	0	0
$877$	1.95013e109	0.0846405	0.0423202	−	0.999104i	$-0.486525\pi$
$877$	1.95013e109	0.0846405	0.0423202	+	0.999104i	$0.486525\pi$
$878$	3.74489e110	1.55738
$879$	0	0
$880$	−7.41026e110	−2.82965
$881$	−2.08958e110	−0.764651	−0.382325	−	0.924028i	$-0.624877\pi$
$881$	−2.08958e110	−0.764651	−0.382325	+	0.924028i	$0.624877\pi$
$882$	0	0
$883$	−1.34684e110	−0.452677	−0.226339	−	0.974049i	$-0.572676\pi$
$883$	−1.34684e110	−0.452677	−0.226339	+	0.974049i	$0.572676\pi$
$884$	1.53778e110	0.495376
$885$	0	0
$886$	−1.52450e110	−0.451195
$887$	5.33284e109	0.151294	0.0756472	−	0.997135i	$-0.475898\pi$
$887$	5.33284e109	0.151294	0.0756472	+	0.997135i	$0.475898\pi$
$888$	0	0
$889$	1.73687e110	0.452847
$890$	2.87144e110	0.717751
$891$	0	0
$892$	−9.36121e109	−0.215105
$893$	3.30182e110	0.727484
$894$	0	0
$895$	−2.89467e110	−0.586455
$896$	−2.40331e110	−0.466938
$897$	0	0
$898$	7.36205e110	1.31564
$899$	−1.69759e111	−2.90967
$900$	0	0
$901$	7.17005e110	1.13069
$902$	−6.71908e110	−1.01640
$903$	0	0
$904$	3.57393e110	0.497542
$905$	−1.30955e111	−1.74904
$906$	0	0
$907$	1.05351e109	0.0129528	0.00647640	−	0.999979i	$-0.497938\pi$
$907$	1.05351e109	0.0129528	0.00647640	+	0.999979i	$0.497938\pi$
$908$	−1.56532e110	−0.184665
$909$	0	0
$910$	−5.69467e110	−0.618609
$911$	7.96762e110	0.830596	0.415298	−	0.909686i	$-0.363677\pi$
$911$	7.96762e110	0.830596	0.415298	+	0.909686i	$0.363677\pi$
$912$	0	0
$913$	3.45885e110	0.332106
$914$	7.26201e110	0.669229
$915$	0	0
$916$	1.98065e110	0.168162
$917$	−7.23351e109	−0.0589521
$918$	0	0
$919$	2.54206e111	1.90921	0.954605	−	0.297875i	$-0.0962778\pi$
$919$	2.54206e111	1.90921	0.954605	+	0.297875i	$0.0962778\pi$
$920$	−3.29468e110	−0.237558
$921$	0	0
$922$	1.34555e111	0.894313
$923$	1.37557e111	0.877847
$924$	0	0
$925$	−3.21146e111	−1.88967
$926$	−2.51741e111	−1.42246
$927$	0	0
$928$	3.89922e111	2.03202
$929$	1.97150e111	0.986750	0.493375	−	0.869817i	$-0.335763\pi$
$929$	1.97150e111	0.986750	0.493375	+	0.869817i	$0.335763\pi$
$930$	0	0
$931$	−1.43366e111	−0.661963
$932$	6.26184e110	0.277719
$933$	0	0
$934$	2.87959e111	1.17848
$935$	7.40353e111	2.91074
$936$	0	0
$937$	1.57128e111	0.570190	0.285095	−	0.958499i	$-0.407975\pi$
$937$	1.57128e111	0.570190	0.285095	+	0.958499i	$0.407975\pi$
$938$	−2.08801e111	−0.727992
$939$	0	0
$940$	2.30848e111	0.743072
$941$	2.61102e110	0.0807606	0.0403803	−	0.999184i	$-0.487143\pi$
$941$	2.61102e110	0.0807606	0.0403803	+	0.999184i	$0.487143\pi$
$942$	0	0
$943$	−5.82749e110	−0.166454
$944$	2.27210e111	0.623704
$945$	0	0
$946$	−9.05587e111	−2.29621
$947$	7.25875e108	0.00176904	0.000884520	−	1.00000i	$-0.499718\pi$
$947$	7.25875e108	0.00176904	0.000884520		1.00000i	$0.499718\pi$
$948$	0	0
$949$	1.59827e111	0.359888
$950$	−6.54537e111	−1.41677
$951$	0	0
$952$	1.61435e111	0.322933
$953$	2.31739e111	0.445671	0.222836	−	0.974856i	$-0.428469\pi$
$953$	2.31739e111	0.445671	0.222836	+	0.974856i	$0.428469\pi$
$954$	0	0
$955$	6.13225e111	1.09017
$956$	−6.26373e111	−1.07069
$957$	0	0
$958$	3.12822e111	0.494414
$959$	2.66001e111	0.404282
$960$	0	0
$961$	9.51769e111	1.33784
$962$	9.04905e111	1.22331
$963$	0	0
$964$	−5.32662e111	−0.666136
$965$	−7.01468e111	−0.843789
$966$	0	0
$967$	−9.05520e111	−1.00787	−0.503936	−	0.863741i	$-0.668115\pi$
$967$	−9.05520e111	−1.00787	−0.503936	+	0.863741i	$0.668115\pi$
$968$	6.12913e111	0.656256
$969$	0	0
$970$	−2.35146e112	−2.33022
$971$	−7.09802e110	−0.0676731	−0.0338365	−	0.999427i	$-0.510773\pi$
$971$	−7.09802e110	−0.0676731	−0.0338365	+	0.999427i	$0.510773\pi$
$972$	0	0
$973$	−6.81012e111	−0.601067
$974$	7.84882e111	0.666566
$975$	0	0
$976$	−4.12147e111	−0.324103
$977$	−2.19960e112	−1.66455	−0.832275	−	0.554364i	$-0.812962\pi$
$977$	−2.19960e112	−1.66455	−0.832275	+	0.554364i	$0.812962\pi$
$978$	0	0
$979$	−8.17403e111	−0.572909
$980$	−1.00235e112	−0.676147
$981$	0	0
$982$	6.75361e111	0.422041
$983$	1.53865e112	0.925515	0.462758	−	0.886485i	$-0.346860\pi$
$983$	1.53865e112	0.925515	0.462758	+	0.886485i	$0.346860\pi$
$984$	0	0
$985$	−4.72330e112	−2.63261
$986$	−5.72565e112	−3.07214
$987$	0	0
$988$	6.94450e111	0.345347
$989$	−7.85420e111	−0.376046
$990$	0	0
$991$	2.43685e112	1.08160	0.540799	−	0.841152i	$-0.318122\pi$
$991$	2.43685e112	1.08160	0.540799	+	0.841152i	$0.318122\pi$
$992$	−3.82021e112	−1.63268
$993$	0	0
$994$	−2.20201e112	−0.872630
$995$	4.49456e112	1.71523
$996$	0	0
$997$	2.11906e112	0.750025	0.375012	−	0.927020i	$-0.377638\pi$
$997$	2.11906e112	0.750025	0.375012	+	0.927020i	$0.377638\pi$
$998$	3.37743e112	1.15131
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.76.a.e.1.4	✓	12
3.2	odd	2	inner	9.76.a.e.1.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.76.a.e.1.4	✓	12	1.1	even	1	trivial
9.76.a.e.1.9	yes	12	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46161e11 q^{2} +2.28162e22 q^{4} +2.44523e26 q^{5} +2.48041e31 q^{7} +3.68323e33 q^{8} +O(q^{10})\)	\(q-2.46161e11 q^{2} +2.28162e22 q^{4} +2.44523e26 q^{5} +2.48041e31 q^{7} +3.68323e33 q^{8} -6.01919e37 q^{10} +1.71346e39 q^{11} +3.81422e41 q^{13} -6.10581e42 q^{14} -1.76864e45 q^{16} +1.76703e46 q^{17} +7.97978e47 q^{19} +5.57909e48 q^{20} -4.21788e50 q^{22} -3.65819e50 q^{23} +3.33215e52 q^{25} -9.38913e52 q^{26} +5.65938e53 q^{28} +1.31632e55 q^{29} -1.28965e56 q^{31} +2.96222e56 q^{32} -4.34974e57 q^{34} +6.06517e57 q^{35} -9.63780e58 q^{37} -1.96431e59 q^{38} +9.00632e59 q^{40} +1.59300e60 q^{41} +2.14702e61 q^{43} +3.90948e61 q^{44} +9.00503e61 q^{46} +4.13773e62 q^{47} -1.79662e63 q^{49} -8.20244e63 q^{50} +8.70263e63 q^{52} +4.05768e64 q^{53} +4.18981e65 q^{55} +9.13593e64 q^{56} -3.24026e66 q^{58} -1.28466e66 q^{59} +2.33030e66 q^{61} +3.17461e67 q^{62} -6.10084e66 q^{64} +9.32664e67 q^{65} +3.41971e68 q^{67} +4.03171e68 q^{68} -1.49301e69 q^{70} +3.60642e69 q^{71} +4.19029e69 q^{73} +2.37245e70 q^{74} +1.82069e70 q^{76} +4.25010e70 q^{77} +2.71488e70 q^{79} -4.32472e71 q^{80} -3.92134e71 q^{82} +2.01863e71 q^{83} +4.32079e72 q^{85} -5.28512e72 q^{86} +6.31108e72 q^{88} -4.77047e72 q^{89} +9.46086e72 q^{91} -8.34661e72 q^{92} -1.01855e74 q^{94} +1.95123e74 q^{95} +3.90660e74 q^{97} +4.42257e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30\!\cdots\!44 q^{4}+ \cdots - 23\!\cdots\!60 q^{7}+O(q^{10}) \) 12 * q + 304307061716936732916144 * q^4 - 23264696115715922069186217167760 * q^7	\( 12 q + 30\!\cdots\!44 q^{4}+ \cdots + 91\!\cdots\!40 q^{97}+O(q^{100}) \) 12 * q + 304307061716936732916144 * q^4 - 23264696115715922069186217167760 * q^7 + 27638934325035006400986687037139427840 * q^10 + 1566891994715058692610510600704204863669560 * q^13 + 1054925289288995929257926590400056818650475648 * q^16 + 985377875069853565681479994616529689369356159392 * q^19 + 159085566085665366088358455484252399362269037824000 * q^22 + 55287387450371943461933903806192645052614192225444260 * q^25 + 3825429694688756764966117420913941574684905356160543680 * q^28 + 3302831127672592933100655272047800132609471485143616496 * q^31 - 2865456277005415897826369042421146930334611723465937976320 * q^34 + 192681748803326931713618210444828383889638160821949090334120 * q^37 - 1780314724794332033651772571439008995626905148286612946391040 * q^40 - 20767095120844290419389762980464184600692870397019624059942240 * q^43 + 235054227730242679255713190614178313572258446734724900485591040 * q^46 - 2200398774833185524931209968117643549966640237509759919611052116 * q^49 - 14448231238764964137515766569708046936012135467108945293436290080 * q^52 + 81306325536746630777151726268587417594554465906840413536114892800 * q^55 - 1004718700793757564164031209344099479511820176480140633172540224000 * q^58 + 13323361359468573502772030313904437139549082575557497083657618663944 * q^61 + 18469889473975432554749180704169560068135223154596132970935656877056 * q^64 - 257204799077995311988310370425723150669455151846154408147457213335360 * q^67 + 3005342015625853695505588875605919452594091965633096933257896848025600 * q^70 + 18552266347809363939749233798674669950739794719850824673010584204923080 * q^73 + 50292969204567460035372103145366232214661826641543367705647193837707904 * q^76 + 937842303842237087819497830837715967722050800328496953380955050567674608 * q^79 + 3919742272718992426068840649563282345597351553486852179684355735105920000 * q^82 + 12520323007424135125100238558304387667646006748328044453585486149043384320 * q^85 + 76483098460394896817433565470216620635024204139674266152191759167166464000 * q^88 + 216807679711985636819127226029841126565807512697835494720868255078103720800 * q^91 + 409517007122285307430588897723573953284046066392035360178770164560460656640 * q^94 + 916586077653930597838313492271046040715613339491256556458911897082224060840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more