LMFDB - Embedded newform 81.9.b.b.80.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(80,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.80");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.b (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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1024 x^{14} + 419701 x^{12} + 88203292 x^{10} + 10121979748 x^{8} + 629108384896 x^{6} + \cdots + 16\!\cdots\!24 $ x^16 + 1024x^14 + 419701x^12 + 88203292x^10 + 10121979748x^8 + 629108384896x^6 + 20221245756928x^4 + 305638522445824*x^2 + 1623834669236224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{84} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			80.2
Root			$14.8268i$ of defining polynomial
Character	$\chi$	$=$	81.80
Dual form			81.9.b.b.80.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-25.6809i q^{2} -403.506 q^{4} -204.369i q^{5} -3702.42 q^{7} +3788.08i q^{8} -5248.38 q^{10} -16110.0i q^{11} -36927.6 q^{13} +95081.3i q^{14} -6016.39 q^{16} +47526.9i q^{17} +213962. q^{19} +82464.3i q^{20} -413718. q^{22} -166164. i q^{23} +348858. q^{25} +948331. i q^{26} +1.49395e6 q^{28} +1.36079e6i q^{29} -218596. q^{31} +1.12426e6i q^{32} +1.22053e6 q^{34} +756662. i q^{35} +1.15091e6 q^{37} -5.49473e6i q^{38} +774168. q^{40} +743082. i q^{41} -2.93033e6 q^{43} +6.50048e6i q^{44} -4.26723e6 q^{46} -7.29432e6i q^{47} +7.94312e6 q^{49} -8.95897e6i q^{50} +1.49005e7 q^{52} -2.55324e6i q^{53} -3.29239e6 q^{55} -1.40251e7i q^{56} +3.49462e7 q^{58} -5.13009e6i q^{59} -2.69536e6 q^{61} +5.61372e6i q^{62} +2.73316e7 q^{64} +7.54686e6i q^{65} +638615. q^{67} -1.91774e7i q^{68} +1.94317e7 q^{70} +3.72932e7i q^{71} -2.13898e7 q^{73} -2.95563e7i q^{74} -8.63350e7 q^{76} +5.96459e7i q^{77} -5.00618e7 q^{79} +1.22957e6i q^{80} +1.90830e7 q^{82} +3.27763e7i q^{83} +9.71304e6 q^{85} +7.52535e7i q^{86} +6.10259e7 q^{88} +6.85873e6i q^{89} +1.36721e8 q^{91} +6.70482e7i q^{92} -1.87324e8 q^{94} -4.37273e7i q^{95} -8.28116e7 q^{97} -2.03986e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) $ 16 * q - 2048 * q^4 + 3692 * q^7 + 10752 * q^10 + 63860 * q^13 + 95116 * q^16 + 185108 * q^19 - 691980 * q^22 - 541712 * q^25 - 997132 * q^28 + 571136 * q^31 + 1027656 * q^34 + 4354268 * q^37 - 2973768 * q^40 + 5453084 * q^43 - 4234044 * q^46 + 14602560 * q^49 - 25384960 * q^52 - 14452572 * q^55 + 1213068 * q^58 + 31037996 * q^61 + 24253000 * q^64 - 62356828 * q^67 + 11075124 * q^70 - 21273664 * q^73 + 69593876 * q^76 - 151045036 * q^79 - 40201140 * q^82 + 160995564 * q^85 + 366976068 * q^88 + 373680796 * q^91 - 544741584 * q^94 - 133878688 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 25.6809i	− 1.60505i	−0.596616	−	0.802527i	$-0.703489\pi$
$2$	− 25.6809i	− 1.60505i	0.596616	−	0.802527i	$-0.296511\pi$
$3$	0	0
$3$	0	0
$4$	−403.506	−1.57620
$5$	− 204.369i	− 0.326991i	−0.986544	−	0.163496i	$-0.947723\pi$
$5$	− 204.369i	− 0.326991i	0.986544	−	0.163496i	$-0.0522769\pi$
$6$	0	0
$7$	−3702.42	−1.54203	−0.771017	−	0.636815i	$-0.780251\pi$
$7$	−3702.42	−1.54203	−0.771017	+	0.636815i	$0.780251\pi$
$8$	3788.08i	0.924825i
$9$	0	0
$10$	−5248.38	−0.524838
$11$	− 16110.0i	− 1.10033i	−0.835055	−	0.550167i	$-0.814564\pi$
$11$	− 16110.0i	− 1.10033i	0.835055	−	0.550167i	$-0.185436\pi$
$12$	0	0
$13$	−36927.6	−1.29294	−0.646468	−	0.762941i	$-0.723755\pi$
$13$	−36927.6	−1.29294	−0.646468	+	0.762941i	$0.723755\pi$
$14$	95081.3i	2.47505i
$15$	0	0
$16$	−6016.39	−0.0918028
$17$	47526.9i	0.569041i	0.958670	+	0.284520i	$0.0918344\pi$
$17$	47526.9i	0.569041i	−0.958670	+	0.284520i	$0.908166\pi$
$18$	0	0
$19$	213962.	1.64181	0.820904	−	0.571066i	$-0.193470\pi$
$19$	213962.	1.64181	0.820904	+	0.571066i	$0.193470\pi$
$20$	82464.3i	0.515402i
$21$	0	0
$22$	−413718.	−1.76609
$23$	− 166164.i	− 0.593780i	−0.954912	−	0.296890i	$-0.904051\pi$
$23$	− 166164.i	− 0.593780i	0.954912	−	0.296890i	$-0.0959495\pi$
$24$	0	0
$25$	348858.	0.893077
$26$	948331.i	2.07523i
$27$	0	0
$28$	1.49395e6	2.43055
$29$	1.36079e6i	1.92397i	0.273105	+	0.961984i	$0.411949\pi$
$29$	1.36079e6i	1.92397i	−0.273105	+	0.961984i	$0.588051\pi$
$30$	0	0
$31$	−218596.	−0.236698	−0.118349	−	0.992972i	$-0.537760\pi$
$31$	−218596.	−0.236698	−0.118349	+	0.992972i	$0.537760\pi$
$32$	1.12426e6i	1.07217i
$33$	0	0
$34$	1.22053e6	0.913341
$35$	756662.i	0.504231i
$36$	0	0
$37$	1.15091e6	0.614093	0.307046	−	0.951695i	$-0.400659\pi$
$37$	1.15091e6	0.614093	0.307046	+	0.951695i	$0.400659\pi$
$38$	− 5.49473e6i	− 2.63519i
$39$	0	0
$40$	774168.	0.302409
$41$	743082.i	0.262967i	0.991318	+	0.131484i	$0.0419740\pi$
$41$	743082.i	0.262967i	−0.991318	+	0.131484i	$0.958026\pi$
$42$	0	0
$43$	−2.93033e6	−0.857123	−0.428562	−	0.903513i	$-0.640980\pi$
$43$	−2.93033e6	−0.857123	−0.428562	+	0.903513i	$0.640980\pi$
$44$	6.50048e6i	1.73434i
$45$	0	0
$46$	−4.26723e6	−0.953048
$47$	− 7.29432e6i	− 1.49483i	−0.664355	−	0.747417i	$-0.731294\pi$
$47$	− 7.29432e6i	− 1.49483i	0.664355	−	0.747417i	$-0.268706\pi$
$48$	0	0
$49$	7.94312e6	1.37787
$50$	− 8.95897e6i	− 1.43344i
$51$	0	0
$52$	1.49005e7	2.03792
$53$	− 2.55324e6i	− 0.323585i	−0.986825	−	0.161792i	$-0.948273\pi$
$53$	− 2.55324e6i	− 0.323585i	0.986825	−	0.161792i	$-0.0517275\pi$
$54$	0	0
$55$	−3.29239e6	−0.359799
$56$	− 1.40251e7i	− 1.42611i
$57$	0	0
$58$	3.49462e7	3.08807
$59$	− 5.13009e6i	− 0.423367i	−0.977338	−	0.211684i	$-0.932105\pi$
$59$	− 5.13009e6i	− 0.423367i	0.977338	−	0.211684i	$-0.0678946\pi$
$60$	0	0
$61$	−2.69536e6	−0.194669	−0.0973346	−	0.995252i	$-0.531032\pi$
$61$	−2.69536e6	−0.194669	−0.0973346	+	0.995252i	$0.531032\pi$
$62$	5.61372e6i	0.379913i
$63$	0	0
$64$	2.73316e7	1.62909
$65$	7.54686e6i	0.422779i
$66$	0	0
$67$	638615.	0.0316913	0.0158456	−	0.999874i	$-0.494956\pi$
$67$	638615.	0.0316913	0.0158456	+	0.999874i	$0.494956\pi$
$68$	− 1.91774e7i	− 0.896920i
$69$	0	0
$70$	1.94317e7	0.809318
$71$	3.72932e7i	1.46756i	0.679387	+	0.733780i	$0.262246\pi$
$71$	3.72932e7i	1.46756i	−0.679387	+	0.733780i	$0.737754\pi$
$72$	0	0
$73$	−2.13898e7	−0.753209	−0.376604	−	0.926374i	$-0.622908\pi$
$73$	−2.13898e7	−0.753209	−0.376604	+	0.926374i	$0.622908\pi$
$74$	− 2.95563e7i	− 0.985652i
$75$	0	0
$76$	−8.63350e7	−2.58781
$77$	5.96459e7i	1.69675i
$78$	0	0
$79$	−5.00618e7	−1.28528	−0.642641	−	0.766167i	$-0.722161\pi$
$79$	−5.00618e7	−1.28528	−0.642641	+	0.766167i	$0.722161\pi$
$80$	1.22957e6i	0.0300187i
$81$	0	0
$82$	1.90830e7	0.422076
$83$	3.27763e7i	0.690634i	0.938486	+	0.345317i	$0.112229\pi$
$83$	3.27763e7i	0.690634i	−0.938486	+	0.345317i	$0.887771\pi$
$84$	0	0
$85$	9.71304e6	0.186071
$86$	7.52535e7i	1.37573i
$87$	0	0
$88$	6.10259e7	1.01762
$89$	6.85873e6i	0.109316i	0.998505	+	0.0546580i	$0.0174069\pi$
$89$	6.85873e6i	0.109316i	−0.998505	+	0.0546580i	$0.982593\pi$
$90$	0	0
$91$	1.36721e8	1.99375
$92$	6.70482e7i	0.935913i
$93$	0	0
$94$	−1.87324e8	−2.39929
$95$	− 4.37273e7i	− 0.536856i
$96$	0	0
$97$	−8.28116e7	−0.935415	−0.467708	−	0.883883i	$-0.654920\pi$
$97$	−8.28116e7	−0.935415	−0.467708	+	0.883883i	$0.654920\pi$
$98$	− 2.03986e8i	− 2.21155i
$99$	0	0
$100$	−1.40766e8	−1.40766
$101$	1.98231e8i	1.90496i	0.304601	+	0.952480i	$0.401477\pi$
$101$	1.98231e8i	1.90496i	−0.304601	+	0.952480i	$0.598523\pi$
$102$	0	0
$103$	2.11965e8	1.88328	0.941641	−	0.336617i	$-0.109283\pi$
$103$	2.11965e8	1.88328	0.941641	+	0.336617i	$0.109283\pi$
$104$	− 1.39885e8i	− 1.19574i
$105$	0	0
$106$	−6.55693e7	−0.519370
$107$	1.63763e8i	1.24934i	0.780887	+	0.624672i	$0.214767\pi$
$107$	1.63763e8i	1.24934i	−0.780887	+	0.624672i	$0.785233\pi$
$108$	0	0
$109$	−2.21458e8	−1.56887	−0.784434	−	0.620213i	$-0.787046\pi$
$109$	−2.21458e8	−1.56887	−0.784434	+	0.620213i	$0.787046\pi$
$110$	8.45513e7i	0.577497i
$111$	0	0
$112$	2.22752e7	0.141563
$113$	− 7.09376e7i	− 0.435074i	−0.976052	−	0.217537i	$-0.930198\pi$
$113$	− 7.09376e7i	− 0.435074i	0.976052	−	0.217537i	$-0.0698022\pi$
$114$	0	0
$115$	−3.39588e7	−0.194161
$116$	− 5.49086e8i	− 3.03255i
$117$	0	0
$118$	−1.31745e8	−0.679527
$119$	− 1.75964e8i	− 0.877480i
$120$	0	0
$121$	−4.51727e7	−0.210734
$122$	6.92191e7i	0.312454i
$123$	0	0
$124$	8.82047e7	0.373082
$125$	− 1.51128e8i	− 0.619019i
$126$	0	0
$127$	−2.24298e8	−0.862205	−0.431102	−	0.902303i	$-0.641875\pi$
$127$	−2.24298e8	−0.862205	−0.431102	+	0.902303i	$0.641875\pi$
$128$	− 4.14090e8i	− 1.54261i
$129$	0	0
$130$	1.93810e8	0.678582
$131$	3.54929e8i	1.20519i	0.798046	+	0.602596i	$0.205867\pi$
$131$	3.54929e8i	1.20519i	−0.798046	+	0.602596i	$0.794133\pi$
$132$	0	0
$133$	−7.92178e8	−2.53172
$134$	− 1.64002e7i	− 0.0508662i
$135$	0	0
$136$	−1.80036e8	−0.526263
$137$	7.45724e7i	0.211688i	0.994383	+	0.105844i	$0.0337544\pi$
$137$	7.45724e7i	0.211688i	−0.994383	+	0.105844i	$0.966246\pi$
$138$	0	0
$139$	8.33165e6	0.0223189	0.0111594	−	0.999938i	$-0.496448\pi$
$139$	8.33165e6	0.0223189	0.0111594	+	0.999938i	$0.496448\pi$
$140$	− 3.05318e8i	− 0.794767i
$141$	0	0
$142$	9.57720e8	2.35551
$143$	5.94902e8i	1.42266i
$144$	0	0
$145$	2.78103e8	0.629121
$146$	5.49308e8i	1.20894i
$147$	0	0
$148$	−4.64399e8	−0.967931
$149$	− 6.82669e8i	− 1.38505i	−0.721395	−	0.692524i	$-0.756499\pi$
$149$	− 6.82669e8i	− 1.38505i	0.721395	−	0.692524i	$-0.243501\pi$
$150$	0	0
$151$	1.21678e8	0.234048	0.117024	−	0.993129i	$-0.462665\pi$
$151$	1.21678e8	0.234048	0.117024	+	0.993129i	$0.462665\pi$
$152$	8.10506e8i	1.51838i
$153$	0	0
$154$	1.53176e9	2.72338
$155$	4.46743e7i	0.0773981i
$156$	0	0
$157$	−7.46851e7	−0.122924	−0.0614618	−	0.998109i	$-0.519576\pi$
$157$	−7.46851e7	−0.122924	−0.0614618	+	0.998109i	$0.519576\pi$
$158$	1.28563e9i	2.06295i
$159$	0	0
$160$	2.29763e8	0.350591
$161$	6.15209e8i	0.915628i
$162$	0	0
$163$	5.65546e8	0.801157	0.400578	−	0.916262i	$-0.368809\pi$
$163$	5.65546e8	0.801157	0.400578	+	0.916262i	$0.368809\pi$
$164$	− 2.99838e8i	− 0.414487i
$165$	0	0
$166$	8.41724e8	1.10850
$167$	− 2.52056e8i	− 0.324064i	−0.986786	−	0.162032i	$-0.948195\pi$
$167$	− 2.52056e8i	− 0.324064i	0.986786	−	0.162032i	$-0.0518048\pi$
$168$	0	0
$169$	5.47914e8	0.671684
$170$	− 2.49439e8i	− 0.298654i
$171$	0	0
$172$	1.18241e9	1.35099
$173$	2.80329e8i	0.312956i	0.987681	+	0.156478i	$0.0500140\pi$
$173$	2.80329e8i	0.312956i	−0.987681	+	0.156478i	$0.949986\pi$
$174$	0	0
$175$	−1.29162e9	−1.37715
$176$	9.69239e7i	0.101014i
$177$	0	0
$178$	1.76138e8	0.175458
$179$	4.01384e8i	0.390974i	0.980706	+	0.195487i	$0.0626287\pi$
$179$	4.01384e8i	0.390974i	−0.980706	+	0.195487i	$0.937371\pi$
$180$	0	0
$181$	−1.39158e9	−1.29657	−0.648284	−	0.761399i	$-0.724513\pi$
$181$	−1.39158e9	−1.29657	−0.648284	+	0.761399i	$0.724513\pi$
$182$	− 3.51112e9i	− 3.20008i
$183$	0	0
$184$	6.29443e8	0.549142
$185$	− 2.35211e8i	− 0.200803i
$186$	0	0
$187$	7.65657e8	0.626135
$188$	2.94330e9i	2.35615i
$189$	0	0
$190$	−1.12295e9	−0.861683
$191$	1.70072e8i	0.127791i	0.997957	+	0.0638953i	$0.0203524\pi$
$191$	1.70072e8i	0.127791i	−0.997957	+	0.0638953i	$0.979648\pi$
$192$	0	0
$193$	−5.81891e8	−0.419384	−0.209692	−	0.977767i	$-0.567246\pi$
$193$	−5.81891e8	−0.419384	−0.209692	+	0.977767i	$0.567246\pi$
$194$	2.12667e9i	1.50139i
$195$	0	0
$196$	−3.20510e9	−2.17179
$197$	− 1.19043e9i	− 0.790385i	−0.918598	−	0.395193i	$-0.870678\pi$
$197$	− 1.19043e9i	− 0.790385i	0.918598	−	0.395193i	$-0.129322\pi$
$198$	0	0
$199$	−1.88525e9	−1.20214	−0.601071	−	0.799196i	$-0.705259\pi$
$199$	−1.88525e9	−1.20214	−0.601071	+	0.799196i	$0.705259\pi$
$200$	1.32150e9i	0.825940i
$201$	0	0
$202$	5.09074e9	3.05756
$203$	− 5.03820e9i	− 2.96682i
$204$	0	0
$205$	1.51863e8	0.0859879
$206$	− 5.44345e9i	− 3.02277i
$207$	0	0
$208$	2.22171e8	0.118695
$209$	− 3.44692e9i	− 1.80654i
$210$	0	0
$211$	−3.97153e8	−0.200368	−0.100184	−	0.994969i	$-0.531943\pi$
$211$	−3.97153e8	−0.200368	−0.100184	+	0.994969i	$0.531943\pi$
$212$	1.03025e9i	0.510033i
$213$	0	0
$214$	4.20558e9	2.00526
$215$	5.98871e8i	0.280272i
$216$	0	0
$217$	8.09333e8	0.364996
$218$	5.68724e9i	2.51812i
$219$	0	0
$220$	1.32850e9	0.567114
$221$	− 1.75505e9i	− 0.735734i
$222$	0	0
$223$	−1.86106e9	−0.752559	−0.376279	−	0.926506i	$-0.622797\pi$
$223$	−1.86106e9	−0.752559	−0.376279	+	0.926506i	$0.622797\pi$
$224$	− 4.16247e9i	− 1.65333i
$225$	0	0
$226$	−1.82174e9	−0.698316
$227$	2.18925e9i	0.824504i	0.911070	+	0.412252i	$0.135258\pi$
$227$	2.18925e9i	0.824504i	−0.911070	+	0.412252i	$0.864742\pi$
$228$	0	0
$229$	−2.15049e9	−0.781981	−0.390990	−	0.920395i	$-0.627867\pi$
$229$	−2.15049e9	−0.781981	−0.390990	+	0.920395i	$0.627867\pi$
$230$	8.72092e8i	0.311638i
$231$	0	0
$232$	−5.15477e9	−1.77933
$233$	3.41313e9i	1.15805i	0.815308	+	0.579027i	$0.196567\pi$
$233$	3.41313e9i	1.15805i	−0.815308	+	0.579027i	$0.803433\pi$
$234$	0	0
$235$	−1.49074e9	−0.488798
$236$	2.07002e9i	0.667310i
$237$	0	0
$238$	−4.51892e9	−1.40840
$239$	3.28566e9i	1.00700i	0.863994	+	0.503502i	$0.167955\pi$
$239$	3.28566e9i	1.00700i	−0.863994	+	0.503502i	$0.832045\pi$
$240$	0	0
$241$	4.03482e9	1.19607	0.598035	−	0.801470i	$-0.295949\pi$
$241$	4.03482e9	1.19607	0.598035	+	0.801470i	$0.295949\pi$
$242$	1.16007e9i	0.338239i
$243$	0	0
$244$	1.08759e9	0.306837
$245$	− 1.62333e9i	− 0.450550i
$246$	0	0
$247$	−7.90109e9	−2.12275
$248$	− 8.28058e8i	− 0.218904i
$249$	0	0
$250$	−3.88109e9	−0.993559
$251$	− 4.69477e9i	− 1.18282i	−0.806371	−	0.591411i	$-0.798571\pi$
$251$	− 4.69477e9i	− 1.18282i	0.806371	−	0.591411i	$-0.201429\pi$
$252$	0	0
$253$	−2.67690e9	−0.653356
$254$	5.76016e9i	1.38388i
$255$	0	0
$256$	−3.63729e9	−0.846873
$257$	1.27509e8i	0.0292287i	0.999893	+	0.0146143i	$0.00465206\pi$
$257$	1.27509e8i	0.0292287i	−0.999893	+	0.0146143i	$0.995348\pi$
$258$	0	0
$259$	−4.26115e9	−0.946952
$260$	− 3.04521e9i	− 0.666382i
$261$	0	0
$262$	9.11488e9	1.93440
$263$	− 2.32140e9i	− 0.485206i	−0.970126	−	0.242603i	$-0.921999\pi$
$263$	− 2.32140e9i	− 0.485206i	0.970126	−	0.242603i	$-0.0780013\pi$
$264$	0	0
$265$	−5.21804e8	−0.105809
$266$	2.03438e10i	4.06355i
$267$	0	0
$268$	−2.57685e8	−0.0499517
$269$	7.86019e9i	1.50115i	0.660785	+	0.750575i	$0.270223\pi$
$269$	7.86019e9i	1.50115i	−0.660785	+	0.750575i	$0.729777\pi$
$270$	0	0
$271$	2.14381e9	0.397474	0.198737	−	0.980053i	$-0.436316\pi$
$271$	2.14381e9	0.397474	0.198737	+	0.980053i	$0.436316\pi$
$272$	− 2.85940e8i	− 0.0522396i
$273$	0	0
$274$	1.91508e9	0.339770
$275$	− 5.62010e9i	− 0.982682i
$276$	0	0
$277$	7.75038e8	0.131645	0.0658224	−	0.997831i	$-0.479033\pi$
$277$	7.75038e8	0.131645	0.0658224	+	0.997831i	$0.479033\pi$
$278$	− 2.13964e8i	− 0.0358229i
$279$	0	0
$280$	−2.86630e9	−0.466325
$281$	7.95756e9i	1.27631i	0.769910	+	0.638153i	$0.220301\pi$
$281$	7.95756e9i	1.27631i	−0.769910	+	0.638153i	$0.779699\pi$
$282$	0	0
$283$	1.95801e9	0.305259	0.152630	−	0.988283i	$-0.451226\pi$
$283$	1.95801e9	0.305259	0.152630	+	0.988283i	$0.451226\pi$
$284$	− 1.50480e10i	− 2.31316i
$285$	0	0
$286$	1.52776e10	2.28345
$287$	− 2.75120e9i	− 0.405504i
$288$	0	0
$289$	4.71695e9	0.676192
$290$	− 7.14193e9i	− 1.00977i
$291$	0	0
$292$	8.63091e9	1.18720
$293$	− 1.23905e10i	− 1.68119i	−0.541665	−	0.840595i	$-0.682206\pi$
$293$	− 1.23905e10i	− 1.68119i	0.541665	−	0.840595i	$-0.317794\pi$
$294$	0	0
$295$	−1.04843e9	−0.138437
$296$	4.35974e9i	0.567928i
$297$	0	0
$298$	−1.75315e10	−2.22308
$299$	6.13603e9i	0.767720i
$300$	0	0
$301$	1.08493e10	1.32171
$302$	− 3.12479e9i	− 0.375659i
$303$	0	0
$304$	−1.28728e9	−0.150723
$305$	5.50849e8i	0.0636551i
$306$	0	0
$307$	−3.61263e8	−0.0406696	−0.0203348	−	0.999793i	$-0.506473\pi$
$307$	−3.61263e8	−0.0406696	−0.0203348	+	0.999793i	$0.506473\pi$
$308$	− 2.40675e10i	− 2.67441i
$309$	0	0
$310$	1.14727e9	0.124228
$311$	5.21355e9i	0.557304i	0.960392	+	0.278652i	$0.0898876\pi$
$311$	5.21355e9i	0.557304i	−0.960392	+	0.278652i	$0.910112\pi$
$312$	0	0
$313$	−1.45147e10	−1.51227	−0.756136	−	0.654415i	$-0.772915\pi$
$313$	−1.45147e10	−1.51227	−0.756136	+	0.654415i	$0.772915\pi$
$314$	1.91798e9i	0.197299i
$315$	0	0
$316$	2.02003e10	2.02586
$317$	− 1.14468e10i	− 1.13356i	−0.823868	−	0.566781i	$-0.808189\pi$
$317$	− 1.14468e10i	− 1.13356i	0.823868	−	0.566781i	$-0.191811\pi$
$318$	0	0
$319$	2.19222e10	2.11701
$320$	− 5.58575e9i	− 0.532699i
$321$	0	0
$322$	1.57991e10	1.46963
$323$	1.01689e10i	0.934256i
$324$	0	0
$325$	−1.28825e10	−1.15469
$326$	− 1.45237e10i	− 1.28590i
$327$	0	0
$328$	−2.81486e9	−0.243198
$329$	2.70066e10i	2.30508i
$330$	0	0
$331$	1.32060e10	1.10017	0.550083	−	0.835110i	$-0.314596\pi$
$331$	1.32060e10	1.10017	0.550083	+	0.835110i	$0.314596\pi$
$332$	− 1.32254e10i	− 1.08857i
$333$	0	0
$334$	−6.47301e9	−0.520140
$335$	− 1.30513e8i	− 0.0103628i
$336$	0	0
$337$	−1.19351e10	−0.925348	−0.462674	−	0.886529i	$-0.653110\pi$
$337$	−1.19351e10	−0.925348	−0.462674	+	0.886529i	$0.653110\pi$
$338$	− 1.40709e10i	− 1.07809i
$339$	0	0
$340$	−3.91927e9	−0.293285
$341$	3.52157e9i	0.260447i
$342$	0	0
$343$	−8.06507e9	−0.582682
$344$	− 1.11003e10i	− 0.792689i
$345$	0	0
$346$	7.19908e9	0.502311
$347$	9.18444e9i	0.633483i	0.948512	+	0.316741i	$0.102589\pi$
$347$	9.18444e9i	0.633483i	−0.948512	+	0.316741i	$0.897411\pi$
$348$	0	0
$349$	−2.08869e10	−1.40790	−0.703950	−	0.710249i	$-0.748582\pi$
$349$	−2.08869e10	−1.40790	−0.703950	+	0.710249i	$0.748582\pi$
$350$	3.31699e10i	2.21041i
$351$	0	0
$352$	1.81117e10	1.17975
$353$	1.09743e10i	0.706770i	0.935478	+	0.353385i	$0.114970\pi$
$353$	1.09743e10i	0.706770i	−0.935478	+	0.353385i	$0.885030\pi$
$354$	0	0
$355$	7.62158e9	0.479879
$356$	− 2.76754e9i	− 0.172303i
$357$	0	0
$358$	1.03079e10	0.627533
$359$	1.19761e10i	0.721001i	0.932759	+	0.360501i	$0.117394\pi$
$359$	1.19761e10i	0.721001i	−0.932759	+	0.360501i	$0.882606\pi$
$360$	0	0
$361$	2.87962e10	1.69553
$362$	3.57371e10i	2.08106i
$363$	0	0
$364$	−5.51679e10	−3.14254
$365$	4.37142e9i	0.246292i
$366$	0	0
$367$	−6.22148e9	−0.342949	−0.171474	−	0.985189i	$-0.554853\pi$
$367$	−6.22148e9	−0.342949	−0.171474	+	0.985189i	$0.554853\pi$
$368$	9.99707e8i	0.0545107i
$369$	0	0
$370$	−6.04041e9	−0.322299
$371$	9.45316e9i	0.498978i
$372$	0	0
$373$	−1.23028e10	−0.635578	−0.317789	−	0.948161i	$-0.602940\pi$
$373$	−1.23028e10	−0.635578	−0.317789	+	0.948161i	$0.602940\pi$
$374$	− 1.96627e10i	− 1.00498i
$375$	0	0
$376$	2.76315e10	1.38246
$377$	− 5.02505e10i	− 2.48757i
$378$	0	0
$379$	2.26268e10	1.09665	0.548324	−	0.836266i	$-0.315266\pi$
$379$	2.26268e10	1.09665	0.548324	+	0.836266i	$0.315266\pi$
$380$	1.76442e10i	0.846191i
$381$	0	0
$382$	4.36759e9	0.205111
$383$	− 1.14841e10i	− 0.533707i	−0.963737	−	0.266854i	$-0.914016\pi$
$383$	− 1.14841e10i	− 0.533707i	0.963737	−	0.266854i	$-0.0859840\pi$
$384$	0	0
$385$	1.21898e10	0.554822
$386$	1.49435e10i	0.673134i
$387$	0	0
$388$	3.34150e10	1.47440
$389$	7.52786e8i	0.0328755i	0.999865	+	0.0164378i	$0.00523254\pi$
$389$	7.52786e8i	0.0328755i	−0.999865	+	0.0164378i	$0.994767\pi$
$390$	0	0
$391$	7.89725e9	0.337885
$392$	3.00892e10i	1.27428i
$393$	0	0
$394$	−3.05712e10	−1.26861
$395$	1.02311e10i	0.420276i
$396$	0	0
$397$	−5.67666e9	−0.228524	−0.114262	−	0.993451i	$-0.536450\pi$
$397$	−5.67666e9	−0.228524	−0.114262	+	0.993451i	$0.536450\pi$
$398$	4.84147e10i	1.92950i
$399$	0	0
$400$	−2.09887e9	−0.0819870
$401$	4.19263e10i	1.62147i	0.585413	+	0.810735i	$0.300932\pi$
$401$	4.19263e10i	1.62147i	−0.585413	+	0.810735i	$0.699068\pi$
$402$	0	0
$403$	8.07220e9	0.306035
$404$	− 7.99874e10i	− 3.00259i
$405$	0	0
$406$	−1.29385e11	−4.76191
$407$	− 1.85411e10i	− 0.675707i
$408$	0	0
$409$	2.50137e10	0.893891	0.446946	−	0.894561i	$-0.352512\pi$
$409$	2.50137e10	0.893891	0.446946	+	0.894561i	$0.352512\pi$
$410$	− 3.89998e9i	− 0.138015i
$411$	0	0
$412$	−8.55292e10	−2.96842
$413$	1.89938e10i	0.652846i
$414$	0	0
$415$	6.69848e9	0.225831
$416$	− 4.15160e10i	− 1.38625i
$417$	0	0
$418$	−8.85200e10	−2.89959
$419$	5.05040e9i	0.163859i	0.996638	+	0.0819294i	$0.0261082\pi$
$419$	5.05040e9i	0.163859i	−0.996638	+	0.0819294i	$0.973892\pi$
$420$	0	0
$421$	1.42319e10	0.453037	0.226519	−	0.974007i	$-0.427266\pi$
$421$	1.42319e10	0.453037	0.226519	+	0.974007i	$0.427266\pi$
$422$	1.01992e10i	0.321601i
$423$	0	0
$424$	9.67187e9	0.299259
$425$	1.65801e10i	0.508197i
$426$	0	0
$427$	9.97935e9	0.300186
$428$	− 6.60796e10i	− 1.96921i
$429$	0	0
$430$	1.53795e10	0.449851
$431$	− 3.72124e10i	− 1.07840i	−0.842179	−	0.539199i	$-0.818727\pi$
$431$	− 3.72124e10i	− 1.07840i	0.842179	−	0.539199i	$-0.181273\pi$
$432$	0	0
$433$	−3.76284e10	−1.07044	−0.535222	−	0.844711i	$-0.679772\pi$
$433$	−3.76284e10	−1.07044	−0.535222	+	0.844711i	$0.679772\pi$
$434$	− 2.07844e10i	− 0.585838i
$435$	0	0
$436$	8.93598e10	2.47284
$437$	− 3.55528e10i	− 0.974873i
$438$	0	0
$439$	5.36553e9	0.144462	0.0722312	−	0.997388i	$-0.476988\pi$
$439$	5.36553e9	0.144462	0.0722312	+	0.997388i	$0.476988\pi$
$440$	− 1.24718e10i	− 0.332751i
$441$	0	0
$442$	−4.50712e10	−1.18089
$443$	− 2.40303e10i	− 0.623942i	−0.950092	−	0.311971i	$-0.899011\pi$
$443$	− 2.40303e10i	− 0.623942i	0.950092	−	0.311971i	$-0.100989\pi$
$444$	0	0
$445$	1.40171e9	0.0357454
$446$	4.77936e10i	1.20790i
$447$	0	0
$448$	−1.01193e11	−2.51211
$449$	− 7.28050e10i	− 1.79133i	−0.444729	−	0.895665i	$-0.646700\pi$
$449$	− 7.28050e10i	− 1.79133i	0.444729	−	0.895665i	$-0.353300\pi$
$450$	0	0
$451$	1.19710e10	0.289351
$452$	2.86238e10i	0.685761i
$453$	0	0
$454$	5.62219e10	1.32337
$455$	− 2.79417e10i	− 0.651939i
$456$	0	0
$457$	6.19755e10	1.42087	0.710436	−	0.703762i	$-0.248498\pi$
$457$	6.19755e10	1.42087	0.710436	+	0.703762i	$0.248498\pi$
$458$	5.52265e10i	1.25512i
$459$	0	0
$460$	1.37026e10	0.306035
$461$	− 1.20417e10i	− 0.266615i	−0.991075	−	0.133308i	$-0.957440\pi$
$461$	− 1.20417e10i	− 0.266615i	0.991075	−	0.133308i	$-0.0425598\pi$
$462$	0	0
$463$	−5.92621e9	−0.128959	−0.0644797	−	0.997919i	$-0.520539\pi$
$463$	−5.92621e9	−0.128959	−0.0644797	+	0.997919i	$0.520539\pi$
$464$	− 8.18702e9i	− 0.176626i
$465$	0	0
$466$	8.76520e10	1.85874
$467$	− 5.80782e10i	− 1.22109i	−0.791983	−	0.610543i	$-0.790951\pi$
$467$	− 5.80782e10i	− 1.22109i	0.791983	−	0.610543i	$-0.209049\pi$
$468$	0	0
$469$	−2.36442e9	−0.0488690
$470$	3.82833e10i	0.784546i
$471$	0	0
$472$	1.94332e10	0.391541
$473$	4.72076e10i	0.943121i
$474$	0	0
$475$	7.46424e10	1.46626
$476$	7.10027e10i	1.38308i
$477$	0	0
$478$	8.43786e10	1.61629
$479$	4.61362e10i	0.876394i	0.898879	+	0.438197i	$0.144383\pi$
$479$	4.61362e10i	0.876394i	−0.898879	+	0.438197i	$0.855617\pi$
$480$	0	0
$481$	−4.25003e10	−0.793983
$482$	− 1.03618e11i	− 1.91975i
$483$	0	0
$484$	1.82274e10	0.332158
$485$	1.69242e10i	0.305872i
$486$	0	0
$487$	8.55813e10	1.52147	0.760735	−	0.649063i	$-0.224839\pi$
$487$	8.55813e10	1.52147	0.760735	+	0.649063i	$0.224839\pi$
$488$	− 1.02102e10i	− 0.180035i
$489$	0	0
$490$	−4.16885e10	−0.723157
$491$	2.98026e10i	0.512776i	0.966574	+	0.256388i	$0.0825325\pi$
$491$	2.98026e10i	0.512776i	−0.966574	+	0.256388i	$0.917467\pi$
$492$	0	0
$493$	−6.46739e10	−1.09482
$494$	2.02907e11i	3.40713i
$495$	0	0
$496$	1.31516e9	0.0217295
$497$	− 1.38075e11i	− 2.26303i
$498$	0	0
$499$	−5.14533e10	−0.829871	−0.414936	−	0.909851i	$-0.636196\pi$
$499$	−5.14533e10	−0.829871	−0.414936	+	0.909851i	$0.636196\pi$
$500$	6.09810e10i	0.975695i
$501$	0	0
$502$	−1.20566e11	−1.89849
$503$	1.97425e10i	0.308412i	0.988039	+	0.154206i	$0.0492819\pi$
$503$	1.97425e10i	0.308412i	−0.988039	+	0.154206i	$0.950718\pi$
$504$	0	0
$505$	4.05123e10	0.622905
$506$	6.87450e10i	1.04867i
$507$	0	0
$508$	9.05056e10	1.35900
$509$	2.84904e10i	0.424451i	0.977221	+	0.212226i	$0.0680712\pi$
$509$	2.84904e10i	0.424451i	−0.977221	+	0.212226i	$0.931929\pi$
$510$	0	0
$511$	7.91941e10	1.16147
$512$	− 1.25983e10i	− 0.183330i
$513$	0	0
$514$	3.27455e9	0.0469136
$515$	− 4.33192e10i	− 0.615817i
$516$	0	0
$517$	−1.17511e11	−1.64482
$518$	1.09430e11i	1.51991i
$519$	0	0
$520$	−2.85881e10	−0.390996
$521$	1.19310e11i	1.61929i	0.586919	+	0.809646i	$0.300341\pi$
$521$	1.19310e11i	1.61929i	−0.586919	+	0.809646i	$0.699659\pi$
$522$	0	0
$523$	−8.33461e10	−1.11398	−0.556992	−	0.830518i	$-0.688044\pi$
$523$	−8.33461e10	−1.11398	−0.556992	+	0.830518i	$0.688044\pi$
$524$	− 1.43216e11i	− 1.89962i
$525$	0	0
$526$	−5.96155e10	−0.778782
$527$	− 1.03892e10i	− 0.134691i
$528$	0	0
$529$	5.07005e10	0.647425
$530$	1.34004e10i	0.169829i
$531$	0	0
$532$	3.19648e11	3.99049
$533$	− 2.74402e10i	− 0.340000i
$534$	0	0
$535$	3.34682e10	0.408524
$536$	2.41913e9i	0.0293089i
$537$	0	0
$538$	2.01856e11	2.40943
$539$	− 1.27964e11i	− 1.51611i
$540$	0	0
$541$	−1.38210e11	−1.61343	−0.806717	−	0.590937i	$-0.798758\pi$
$541$	−1.38210e11	−1.61343	−0.806717	+	0.590937i	$0.798758\pi$
$542$	− 5.50548e10i	− 0.637967i
$543$	0	0
$544$	−5.34323e10	−0.610110
$545$	4.52593e10i	0.513006i
$546$	0	0
$547$	−7.91364e10	−0.883949	−0.441974	−	0.897028i	$-0.645722\pi$
$547$	−7.91364e10	−0.883949	−0.441974	+	0.897028i	$0.645722\pi$
$548$	− 3.00904e10i	− 0.333661i
$549$	0	0
$550$	−1.44329e11	−1.57726
$551$	2.91157e11i	3.15879i
$552$	0	0
$553$	1.85350e11	1.98195
$554$	− 1.99036e10i	− 0.211297i
$555$	0	0
$556$	−3.36187e9	−0.0351789
$557$	1.12395e11i	1.16769i	0.811865	+	0.583846i	$0.198453\pi$
$557$	1.12395e11i	1.16769i	−0.811865	+	0.583846i	$0.801547\pi$
$558$	0	0
$559$	1.08210e11	1.10821
$560$	− 4.55237e9i	− 0.0462898i
$561$	0	0
$562$	2.04357e11	2.04854
$563$	− 1.20023e11i	− 1.19462i	−0.802010	−	0.597310i	$-0.796236\pi$
$563$	− 1.20023e11i	− 1.19462i	0.802010	−	0.597310i	$-0.203764\pi$
$564$	0	0
$565$	−1.44975e10	−0.142265
$566$	− 5.02833e10i	− 0.489957i
$567$	0	0
$568$	−1.41270e11	−1.35724
$569$	− 1.53448e11i	− 1.46390i	−0.681357	−	0.731951i	$-0.738610\pi$
$569$	− 1.53448e11i	− 1.46390i	0.681357	−	0.731951i	$-0.261390\pi$
$570$	0	0
$571$	4.66781e10	0.439106	0.219553	−	0.975601i	$-0.429540\pi$
$571$	4.66781e10	0.439106	0.219553	+	0.975601i	$0.429540\pi$
$572$	− 2.40047e11i	− 2.24239i
$573$	0	0
$574$	−7.06532e10	−0.650855
$575$	− 5.79677e10i	− 0.530291i
$576$	0	0
$577$	9.25710e10	0.835164	0.417582	−	0.908639i	$-0.362878\pi$
$577$	9.25710e10	0.835164	0.417582	+	0.908639i	$0.362878\pi$
$578$	− 1.21135e11i	− 1.08532i
$579$	0	0
$580$	−1.12216e11	−0.991617
$581$	− 1.21352e11i	− 1.06498i
$582$	0	0
$583$	−4.11326e10	−0.356051
$584$	− 8.10263e10i	− 0.696586i
$585$	0	0
$586$	−3.18197e11	−2.69840
$587$	7.76202e10i	0.653766i	0.945065	+	0.326883i	$0.105998\pi$
$587$	7.76202e10i	0.653766i	−0.945065	+	0.326883i	$0.894002\pi$
$588$	0	0
$589$	−4.67712e10	−0.388613
$590$	2.69247e10i	0.222199i
$591$	0	0
$592$	−6.92432e9	−0.0563754
$593$	− 2.09190e11i	− 1.69169i	−0.533427	−	0.845846i	$-0.679096\pi$
$593$	− 2.09190e11i	− 1.69169i	0.533427	−	0.845846i	$-0.320904\pi$
$594$	0	0
$595$	−3.59618e10	−0.286928
$596$	2.75461e11i	2.18311i
$597$	0	0
$598$	1.57578e11	1.23223
$599$	− 9.32838e10i	− 0.724601i	−0.932061	−	0.362300i	$-0.881991\pi$
$599$	− 9.32838e10i	− 0.724601i	0.932061	−	0.362300i	$-0.118009\pi$
$600$	0	0
$601$	−8.12537e10	−0.622795	−0.311398	−	0.950280i	$-0.600797\pi$
$601$	−8.12537e10	−0.622795	−0.311398	+	0.950280i	$0.600797\pi$
$602$	− 2.78620e11i	− 2.12142i
$603$	0	0
$604$	−4.90978e10	−0.368905
$605$	9.23191e9i	0.0689081i
$606$	0	0
$607$	4.12325e10	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$607$	4.12325e10	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$608$	2.40548e11i	1.76030i
$609$	0	0
$610$	1.41463e10	0.102170
$611$	2.69361e11i	1.93273i
$612$	0	0
$613$	2.01264e10	0.142536	0.0712681	−	0.997457i	$-0.477295\pi$
$613$	2.01264e10	0.142536	0.0712681	+	0.997457i	$0.477295\pi$
$614$	9.27755e9i	0.0652769i
$615$	0	0
$616$	−2.25944e11	−1.56920
$617$	1.37297e11i	0.947370i	0.880694	+	0.473685i	$0.157076\pi$
$617$	1.37297e11i	0.947370i	−0.880694	+	0.473685i	$0.842924\pi$
$618$	0	0
$619$	−9.70400e10	−0.660980	−0.330490	−	0.943810i	$-0.607214\pi$
$619$	−9.70400e10	−0.660980	−0.330490	+	0.943810i	$0.607214\pi$
$620$	− 1.80263e10i	− 0.121995i
$621$	0	0
$622$	1.33888e11	0.894502
$623$	− 2.53939e10i	− 0.168569i
$624$	0	0
$625$	1.05387e11	0.690663
$626$	3.72749e11i	2.42728i
$627$	0	0
$628$	3.01359e10	0.193752
$629$	5.46991e10i	0.349444i
$630$	0	0
$631$	−2.86142e11	−1.80495	−0.902473	−	0.430747i	$-0.858250\pi$
$631$	−2.86142e11	−1.80495	−0.902473	+	0.430747i	$0.858250\pi$
$632$	− 1.89638e11i	− 1.18866i
$633$	0	0
$634$	−2.93962e11	−1.81943
$635$	4.58396e10i	0.281933i
$636$	0	0
$637$	−2.93320e11	−1.78149
$638$	− 5.62982e11i	− 3.39791i
$639$	0	0
$640$	−8.46274e10	−0.504418
$641$	− 5.72835e10i	− 0.339311i	−0.985503	−	0.169655i	$-0.945735\pi$
$641$	− 5.72835e10i	− 0.339311i	0.985503	−	0.169655i	$-0.0542654\pi$
$642$	0	0
$643$	−1.34466e11	−0.786624	−0.393312	−	0.919405i	$-0.628671\pi$
$643$	−1.34466e11	−0.786624	−0.393312	+	0.919405i	$0.628671\pi$
$644$	− 2.48241e11i	− 1.44321i
$645$	0	0
$646$	2.61147e11	1.49953
$647$	2.98401e11i	1.70288i	0.524454	+	0.851439i	$0.324269\pi$
$647$	2.98401e11i	1.70288i	−0.524454	+	0.851439i	$0.675731\pi$
$648$	0	0
$649$	−8.26457e10	−0.465845
$650$	3.30833e11i	1.85334i
$651$	0	0
$652$	−2.28201e11	−1.26278
$653$	1.01831e11i	0.560049i	0.959993	+	0.280025i	$0.0903427\pi$
$653$	1.01831e11i	0.560049i	−0.959993	+	0.280025i	$0.909657\pi$
$654$	0	0
$655$	7.25367e10	0.394087
$656$	− 4.47067e9i	− 0.0241411i
$657$	0	0
$658$	6.93553e11	3.69978
$659$	2.42067e11i	1.28349i	0.766917	+	0.641746i	$0.221790\pi$
$659$	2.42067e11i	1.28349i	−0.766917	+	0.641746i	$0.778210\pi$
$660$	0	0
$661$	−3.06803e11	−1.60714	−0.803570	−	0.595210i	$-0.797069\pi$
$661$	−3.06803e11	−1.60714	−0.803570	+	0.595210i	$0.797069\pi$
$662$	− 3.39140e11i	− 1.76582i
$663$	0	0
$664$	−1.24159e11	−0.638715
$665$	1.61897e11i	0.827850i
$666$	0	0
$667$	2.26114e11	1.14241
$668$	1.01706e11i	0.510788i
$669$	0	0
$670$	−3.35170e9	−0.0166328
$671$	4.34222e10i	0.214201i
$672$	0	0
$673$	−1.79425e11	−0.874627	−0.437314	−	0.899309i	$-0.644070\pi$
$673$	−1.79425e11	−0.874627	−0.437314	+	0.899309i	$0.644070\pi$
$674$	3.06502e11i	1.48523i
$675$	0	0
$676$	−2.21086e11	−1.05871
$677$	1.46877e11i	0.699195i	0.936900	+	0.349597i	$0.113682\pi$
$677$	1.46877e11i	0.699195i	−0.936900	+	0.349597i	$0.886318\pi$
$678$	0	0
$679$	3.06604e11	1.44244
$680$	3.67938e10i	0.172083i
$681$	0	0
$682$	9.04369e10	0.418031
$683$	5.39354e10i	0.247851i	0.992291	+	0.123926i	$0.0395485\pi$
$683$	5.39354e10i	0.247851i	−0.992291	+	0.123926i	$0.960452\pi$
$684$	0	0
$685$	1.52403e10	0.0692200
$686$	2.07118e11i	0.935236i
$687$	0	0
$688$	1.76300e10	0.0786863
$689$	9.42848e10i	0.418374i
$690$	0	0
$691$	1.03857e11	0.455539	0.227769	−	0.973715i	$-0.426857\pi$
$691$	1.03857e11	0.455539	0.227769	+	0.973715i	$0.426857\pi$
$692$	− 1.13114e11i	− 0.493279i
$693$	0	0
$694$	2.35864e11	1.01677
$695$	− 1.70273e9i	− 0.00729807i
$696$	0	0
$697$	−3.53164e10	−0.149639
$698$	5.36393e11i	2.25975i
$699$	0	0
$700$	5.21177e11	2.17066
$701$	1.65918e11i	0.687103i	0.939134	+	0.343552i	$0.111630\pi$
$701$	1.65918e11i	0.687103i	−0.939134	+	0.343552i	$0.888370\pi$
$702$	0	0
$703$	2.46251e11	1.00822
$704$	− 4.40312e11i	− 1.79254i
$705$	0	0
$706$	2.81830e11	1.13440
$707$	− 7.33934e11i	− 2.93751i
$708$	0	0
$709$	−1.52689e11	−0.604258	−0.302129	−	0.953267i	$-0.597697\pi$
$709$	−1.52689e11	−0.604258	−0.302129	+	0.953267i	$0.597697\pi$
$710$	− 1.95729e11i	− 0.770232i
$711$	0	0
$712$	−2.59814e10	−0.101098
$713$	3.63227e10i	0.140547i
$714$	0	0
$715$	1.21580e11	0.465198
$716$	− 1.61961e11i	− 0.616251i
$717$	0	0
$718$	3.07555e11	1.15725
$719$	− 2.64075e11i	− 0.988125i	−0.869427	−	0.494062i	$-0.835511\pi$
$719$	− 2.64075e11i	− 0.988125i	0.869427	−	0.494062i	$-0.164489\pi$
$720$	0	0
$721$	−7.84784e11	−2.90408
$722$	− 7.39511e11i	− 2.72142i
$723$	0	0
$724$	5.61513e11	2.04364
$725$	4.74721e11i	1.71825i
$726$	0	0
$727$	−2.56660e11	−0.918799	−0.459399	−	0.888230i	$-0.651935\pi$
$727$	−2.56660e11	−0.918799	−0.459399	+	0.888230i	$0.651935\pi$
$728$	5.17912e11i	1.84387i
$729$	0	0
$730$	1.12262e11	0.395313
$731$	− 1.39270e11i	− 0.487738i
$732$	0	0
$733$	−2.76412e11	−0.957504	−0.478752	−	0.877950i	$-0.658911\pi$
$733$	−2.76412e11	−0.957504	−0.478752	+	0.877950i	$0.658911\pi$
$734$	1.59773e11i	0.550451i
$735$	0	0
$736$	1.86811e11	0.636635
$737$	− 1.02881e10i	− 0.0348710i
$738$	0	0
$739$	3.69193e11	1.23787	0.618935	−	0.785442i	$-0.287564\pi$
$739$	3.69193e11	1.23787	0.618935	+	0.785442i	$0.287564\pi$
$740$	9.49089e10i	0.316505i
$741$	0	0
$742$	2.42765e11	0.800886
$743$	− 5.22453e11i	− 1.71432i	−0.515051	−	0.857160i	$-0.672227\pi$
$743$	− 5.22453e11i	− 1.71432i	0.515051	−	0.857160i	$-0.327773\pi$
$744$	0	0
$745$	−1.39517e11	−0.452899
$746$	3.15947e11i	1.02014i
$747$	0	0
$748$	−3.08947e11	−0.986911
$749$	− 6.06321e11i	− 1.92653i
$750$	0	0
$751$	2.23495e11	0.702599	0.351300	−	0.936263i	$-0.385740\pi$
$751$	2.23495e11	0.702599	0.351300	+	0.936263i	$0.385740\pi$
$752$	4.38854e10i	0.137230i
$753$	0	0
$754$	−1.29048e12	−3.99268
$755$	− 2.48673e10i	− 0.0765315i
$756$	0	0
$757$	−2.44183e11	−0.743588	−0.371794	−	0.928315i	$-0.621257\pi$
$757$	−2.44183e11	−0.743588	−0.371794	+	0.928315i	$0.621257\pi$
$758$	− 5.81077e11i	− 1.76018i
$759$	0	0
$760$	1.65643e11	0.496498
$761$	− 2.25029e11i	− 0.670965i	−0.942046	−	0.335483i	$-0.891101\pi$
$761$	− 2.25029e11i	− 0.670965i	0.942046	−	0.335483i	$-0.108899\pi$
$762$	0	0
$763$	8.19933e11	2.41925
$764$	− 6.86251e10i	− 0.201423i
$765$	0	0
$766$	−2.94922e11	−0.856628
$767$	1.89442e11i	0.547387i
$768$	0	0
$769$	−4.83053e11	−1.38130	−0.690652	−	0.723188i	$-0.742676\pi$
$769$	−4.83053e11	−1.38130	−0.690652	+	0.723188i	$0.742676\pi$
$770$	− 3.13045e11i	− 0.890519i
$771$	0	0
$772$	2.34797e11	0.661032
$773$	1.32482e10i	0.0371056i	0.999828	+	0.0185528i	$0.00590588\pi$
$773$	1.32482e10i	0.0371056i	−0.999828	+	0.0185528i	$0.994094\pi$
$774$	0	0
$775$	−7.62588e10	−0.211390
$776$	− 3.13697e11i	− 0.865095i
$777$	0	0
$778$	1.93322e10	0.0527670
$779$	1.58991e11i	0.431741i
$780$	0	0
$781$	6.00792e11	1.61481
$782$	− 2.02808e11i	− 0.542324i
$783$	0	0
$784$	−4.77889e10	−0.126492
$785$	1.52633e10i	0.0401949i
$786$	0	0
$787$	4.74600e11	1.23717	0.618584	−	0.785719i	$-0.287707\pi$
$787$	4.74600e11	1.23717	0.618584	+	0.785719i	$0.287707\pi$
$788$	4.80346e11i	1.24580i
$789$	0	0
$790$	2.62744e11	0.674565
$791$	2.62641e11i	0.670898i
$792$	0	0
$793$	9.95330e10	0.251695
$794$	1.45781e11i	0.366792i
$795$	0	0
$796$	7.60708e11	1.89481
$797$	− 2.98199e11i	− 0.739049i	−0.929221	−	0.369524i	$-0.879521\pi$
$797$	− 2.98199e11i	− 0.739049i	0.929221	−	0.369524i	$-0.120479\pi$
$798$	0	0
$799$	3.46676e11	0.850622
$800$	3.92206e11i	0.957533i
$801$	0	0
$802$	1.07670e12	2.60255
$803$	3.44589e11i	0.828781i
$804$	0	0
$805$	1.25730e11	0.299402
$806$	− 2.07301e11i	− 0.491203i
$807$	0	0
$808$	−7.50915e11	−1.76175
$809$	− 3.19136e11i	− 0.745044i	−0.928023	−	0.372522i	$-0.878493\pi$
$809$	− 3.19136e11i	− 0.745044i	0.928023	−	0.372522i	$-0.121507\pi$
$810$	0	0
$811$	2.94415e11	0.680575	0.340288	−	0.940321i	$-0.389476\pi$
$811$	2.94415e11	0.680575	0.340288	+	0.940321i	$0.389476\pi$
$812$	2.03295e12i	4.67629i
$813$	0	0
$814$	−4.76152e11	−1.08455
$815$	− 1.15580e11i	− 0.261971i
$816$	0	0
$817$	−6.26980e11	−1.40723
$818$	− 6.42373e11i	− 1.43474i
$819$	0	0
$820$	−6.12777e10	−0.135534
$821$	− 6.16033e10i	− 0.135591i	−0.997699	−	0.0677956i	$-0.978403\pi$
$821$	− 6.16033e10i	− 0.135591i	0.997699	−	0.0677956i	$-0.0215966\pi$
$822$	0	0
$823$	−4.71053e11	−1.02676	−0.513381	−	0.858160i	$-0.671607\pi$
$823$	−4.71053e11	−1.02676	−0.513381	+	0.858160i	$0.671607\pi$
$824$	8.02941e11i	1.74171i
$825$	0	0
$826$	4.87776e11	1.04785
$827$	− 4.35038e11i	− 0.930048i	−0.885298	−	0.465024i	$-0.846046\pi$
$827$	− 4.35038e11i	− 0.930048i	0.885298	−	0.465024i	$-0.153954\pi$
$828$	0	0
$829$	2.07438e11	0.439208	0.219604	−	0.975589i	$-0.429524\pi$
$829$	2.07438e11	0.439208	0.219604	+	0.975589i	$0.429524\pi$
$830$	− 1.72023e11i	− 0.362471i
$831$	0	0
$832$	−1.00929e12	−2.10631
$833$	3.77512e11i	0.784062i
$834$	0	0
$835$	−5.15125e10	−0.105966
$836$	1.39086e12i	2.84745i
$837$	0	0
$838$	1.29699e11	0.263002
$839$	− 2.38837e11i	− 0.482008i	−0.970524	−	0.241004i	$-0.922523\pi$
$839$	− 2.38837e11i	− 0.482008i	0.970524	−	0.241004i	$-0.0774767\pi$
$840$	0	0
$841$	−1.35149e12	−2.70166
$842$	− 3.65487e11i	− 0.727149i
$843$	0	0
$844$	1.60254e11	0.315819
$845$	− 1.11977e11i	− 0.219635i
$846$	0	0
$847$	1.67248e11	0.324959
$848$	1.53613e10i	0.0297060i
$849$	0	0
$850$	4.25792e11	0.815684
$851$	− 1.91240e11i	− 0.364636i
$852$	0	0
$853$	−3.15684e11	−0.596289	−0.298144	−	0.954521i	$-0.596368\pi$
$853$	−3.15684e11	−0.596289	−0.298144	+	0.954521i	$0.596368\pi$
$854$	− 2.56278e11i	− 0.481815i
$855$	0	0
$856$	−6.20349e11	−1.15542
$857$	− 4.83714e11i	− 0.896737i	−0.893849	−	0.448369i	$-0.852005\pi$
$857$	− 4.83714e11i	− 0.896737i	0.893849	−	0.448369i	$-0.147995\pi$
$858$	0	0
$859$	−5.69187e11	−1.04540	−0.522700	−	0.852517i	$-0.675075\pi$
$859$	−5.69187e11	−1.04540	−0.522700	+	0.852517i	$0.675075\pi$
$860$	− 2.41648e11i	− 0.441763i
$861$	0	0
$862$	−9.55647e11	−1.73089
$863$	− 1.70442e11i	− 0.307279i	−0.988127	−	0.153639i	$-0.950901\pi$
$863$	− 1.70442e11i	− 0.307279i	0.988127	−	0.153639i	$-0.0490994\pi$
$864$	0	0
$865$	5.72906e10	0.102334
$866$	9.66329e11i	1.71812i
$867$	0	0
$868$	−3.26571e11	−0.575305
$869$	8.06495e11i	1.41424i
$870$	0	0
$871$	−2.35825e10	−0.0409748
$872$	− 8.38903e11i	− 1.45093i
$873$	0	0
$874$	−9.13026e11	−1.56472
$875$	5.59539e11i	0.954548i
$876$	0	0
$877$	6.98793e11	1.18127	0.590636	−	0.806938i	$-0.298877\pi$
$877$	6.98793e11	1.18127	0.590636	+	0.806938i	$0.298877\pi$
$878$	− 1.37791e11i	− 0.231870i
$879$	0	0
$880$	1.98083e10	0.0330306
$881$	2.05065e11i	0.340399i	0.985410	+	0.170199i	$0.0544412\pi$
$881$	2.05065e11i	0.340399i	−0.985410	+	0.170199i	$0.945559\pi$
$882$	0	0
$883$	−7.79882e11	−1.28288	−0.641440	−	0.767173i	$-0.721663\pi$
$883$	−7.79882e11	−1.28288	−0.641440	+	0.767173i	$0.721663\pi$
$884$	7.08174e11i	1.15966i
$885$	0	0
$886$	−6.17119e11	−1.00146
$887$	4.85342e11i	0.784068i	0.919951	+	0.392034i	$0.128228\pi$
$887$	4.85342e11i	0.784068i	−0.919951	+	0.392034i	$0.871772\pi$
$888$	0	0
$889$	8.30445e11	1.32955
$890$	− 3.59972e10i	− 0.0573732i
$891$	0	0
$892$	7.50948e11	1.18618
$893$	− 1.56071e12i	− 2.45423i
$894$	0	0
$895$	8.20305e10	0.127845
$896$	1.53314e12i	2.37875i
$897$	0	0
$898$	−1.86969e12	−2.87518
$899$	− 2.97462e11i	− 0.455400i
$900$	0	0
$901$	1.21347e11	0.184133
$902$	− 3.07426e11i	− 0.464424i
$903$	0	0
$904$	2.68717e11	0.402367
$905$	2.84397e11i	0.423966i
$906$	0	0
$907$	7.37444e11	1.08968	0.544841	−	0.838539i	$-0.316590\pi$
$907$	7.37444e11	1.08968	0.544841	+	0.838539i	$0.316590\pi$
$908$	− 8.83377e11i	− 1.29958i
$909$	0	0
$910$	−7.17566e11	−1.04640
$911$	6.28854e11i	0.913012i	0.889720	+	0.456506i	$0.150899\pi$
$911$	6.28854e11i	0.913012i	−0.889720	+	0.456506i	$0.849101\pi$
$912$	0	0
$913$	5.28026e11	0.759927
$914$	− 1.59158e12i	− 2.28058i
$915$	0	0
$916$	8.67737e11	1.23255
$917$	− 1.31410e12i	− 1.85845i
$918$	0	0
$919$	3.48346e11	0.488370	0.244185	−	0.969729i	$-0.421480\pi$
$919$	3.48346e11	0.488370	0.244185	+	0.969729i	$0.421480\pi$
$920$	− 1.28639e11i	− 0.179565i
$921$	0	0
$922$	−3.09242e11	−0.427932
$923$	− 1.37715e12i	− 1.89746i
$924$	0	0
$925$	4.01504e11	0.548432
$926$	1.52190e11i	0.206987i
$927$	0	0
$928$	−1.52987e12	−2.06283
$929$	6.08637e8i	0 0.000817138i	1.00000		0.000408569i	$0.000130052\pi$
$929$	6.08637e8i	0 0.000817138i	−1.00000		0.000408569i	$0.999870\pi$
$930$	0	0
$931$	1.69953e12	2.26219
$932$	− 1.37722e12i	− 1.82532i
$933$	0	0
$934$	−1.49150e12	−1.95991
$935$	− 1.56477e11i	− 0.204740i
$936$	0	0
$937$	5.98470e10	0.0776398	0.0388199	−	0.999246i	$-0.487640\pi$
$937$	5.98470e10	0.0776398	0.0388199	+	0.999246i	$0.487640\pi$
$938$	6.07204e10i	0.0784374i
$939$	0	0
$940$	6.01521e11	0.770441
$941$	1.29938e12i	1.65721i	0.559836	+	0.828603i	$0.310864\pi$
$941$	1.29938e12i	1.65721i	−0.559836	+	0.828603i	$0.689136\pi$
$942$	0	0
$943$	1.23473e11	0.156145
$944$	3.08646e10i	0.0388663i
$945$	0	0
$946$	1.21233e12	1.51376
$947$	1.31300e12i	1.63255i	0.577664	+	0.816275i	$0.303964\pi$
$947$	1.31300e12i	1.63255i	−0.577664	+	0.816275i	$0.696036\pi$
$948$	0	0
$949$	7.89873e11	0.973851
$950$	− 1.91688e12i	− 2.35343i
$951$	0	0
$952$	6.66568e11	0.811515
$953$	1.49915e12i	1.81750i	0.417341	+	0.908750i	$0.362962\pi$
$953$	1.49915e12i	1.81750i	−0.417341	+	0.908750i	$0.637038\pi$
$954$	0	0
$955$	3.47575e10	0.0417864
$956$	− 1.32578e12i	− 1.58724i
$957$	0	0
$958$	1.18482e12	1.40666
$959$	− 2.76098e11i	− 0.326429i
$960$	0	0
$961$	−8.05107e11	−0.943974
$962$	1.09144e12i	1.27438i
$963$	0	0
$964$	−1.62808e12	−1.88524
$965$	1.18921e11i	0.137135i
$966$	0	0
$967$	−2.59401e11	−0.296665	−0.148332	−	0.988938i	$-0.547391\pi$
$967$	−2.59401e11	−0.296665	−0.148332	+	0.988938i	$0.547391\pi$
$968$	− 1.71118e11i	− 0.194892i
$969$	0	0
$970$	4.34627e11	0.490941
$971$	− 1.15804e12i	− 1.30271i	−0.758772	−	0.651356i	$-0.774200\pi$
$971$	− 1.15804e12i	− 1.30271i	0.758772	−	0.651356i	$-0.225800\pi$
$972$	0	0
$973$	−3.08473e10	−0.0344164
$974$	− 2.19780e12i	− 2.44204i
$975$	0	0
$976$	1.62163e10	0.0178712
$977$	− 8.99908e10i	− 0.0987688i	−0.998780	−	0.0493844i	$-0.984274\pi$
$977$	− 8.99908e10i	− 0.0987688i	0.998780	−	0.0493844i	$-0.0157259\pi$
$978$	0	0
$979$	1.10494e11	0.120284
$980$	6.55024e11i	0.710155i
$981$	0	0
$982$	7.65356e11	0.823033
$983$	1.64561e12i	1.76243i	0.472712	+	0.881217i	$0.343275\pi$
$983$	1.64561e12i	1.76243i	−0.472712	+	0.881217i	$0.656725\pi$
$984$	0	0
$985$	−2.43287e11	−0.258449
$986$	1.66088e12i	1.75724i
$987$	0	0
$988$	3.18814e12	3.34587
$989$	4.86916e11i	0.508943i
$990$	0	0
$991$	6.39028e11	0.662560	0.331280	−	0.943533i	$-0.392520\pi$
$991$	6.39028e11	0.662560	0.331280	+	0.943533i	$0.392520\pi$
$992$	− 2.45757e11i	− 0.253781i
$993$	0	0
$994$	−3.54588e12	−3.63228
$995$	3.85287e11i	0.393090i
$996$	0	0
$997$	−8.92347e11	−0.903136	−0.451568	−	0.892237i	$-0.649135\pi$
$997$	−8.92347e11	−0.903136	−0.451568	+	0.892237i	$0.649135\pi$
$998$	1.32136e12i	1.33199i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.b.b.80.2	✓	16
3.2	odd	2	inner	81.9.b.b.80.15	yes	16
9.2	odd	6		81.9.d.g.53.15		32
9.4	even	3		81.9.d.g.26.15		32
9.5	odd	6		81.9.d.g.26.2		32
9.7	even	3		81.9.d.g.53.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.9.b.b.80.2	✓	16	1.1	even	1	trivial
81.9.b.b.80.15	yes	16	3.2	odd	2	inner
81.9.d.g.26.2		32	9.5	odd	6
81.9.d.g.26.15		32	9.4	even	3
81.9.d.g.53.2		32	9.7	even	3
81.9.d.g.53.15		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-25.6809i q^{2} -403.506 q^{4} -204.369i q^{5} -3702.42 q^{7} +3788.08i q^{8} -5248.38 q^{10} -16110.0i q^{11} -36927.6 q^{13} +95081.3i q^{14} -6016.39 q^{16} +47526.9i q^{17} +213962. q^{19} +82464.3i q^{20} -413718. q^{22} -166164. i q^{23} +348858. q^{25} +948331. i q^{26} +1.49395e6 q^{28} +1.36079e6i q^{29} -218596. q^{31} +1.12426e6i q^{32} +1.22053e6 q^{34} +756662. i q^{35} +1.15091e6 q^{37} -5.49473e6i q^{38} +774168. q^{40} +743082. i q^{41} -2.93033e6 q^{43} +6.50048e6i q^{44} -4.26723e6 q^{46} -7.29432e6i q^{47} +7.94312e6 q^{49} -8.95897e6i q^{50} +1.49005e7 q^{52} -2.55324e6i q^{53} -3.29239e6 q^{55} -1.40251e7i q^{56} +3.49462e7 q^{58} -5.13009e6i q^{59} -2.69536e6 q^{61} +5.61372e6i q^{62} +2.73316e7 q^{64} +7.54686e6i q^{65} +638615. q^{67} -1.91774e7i q^{68} +1.94317e7 q^{70} +3.72932e7i q^{71} -2.13898e7 q^{73} -2.95563e7i q^{74} -8.63350e7 q^{76} +5.96459e7i q^{77} -5.00618e7 q^{79} +1.22957e6i q^{80} +1.90830e7 q^{82} +3.27763e7i q^{83} +9.71304e6 q^{85} +7.52535e7i q^{86} +6.10259e7 q^{88} +6.85873e6i q^{89} +1.36721e8 q^{91} +6.70482e7i q^{92} -1.87324e8 q^{94} -4.37273e7i q^{95} -8.28116e7 q^{97} -2.03986e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) \) 16 * q - 2048 * q^4 + 3692 * q^7 + 10752 * q^10 + 63860 * q^13 + 95116 * q^16 + 185108 * q^19 - 691980 * q^22 - 541712 * q^25 - 997132 * q^28 + 571136 * q^31 + 1027656 * q^34 + 4354268 * q^37 - 2973768 * q^40 + 5453084 * q^43 - 4234044 * q^46 + 14602560 * q^49 - 25384960 * q^52 - 14452572 * q^55 + 1213068 * q^58 + 31037996 * q^61 + 24253000 * q^64 - 62356828 * q^67 + 11075124 * q^70 - 21273664 * q^73 + 69593876 * q^76 - 151045036 * q^79 - 40201140 * q^82 + 160995564 * q^85 + 366976068 * q^88 + 373680796 * q^91 - 544741584 * q^94 - 133878688 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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