LMFDB - Embedded newform 81.9.b.b.80.11

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			80.11
Root			$-5.78233i$ of defining polynomial
Character	$\chi$	$=$	81.80
Dual form			81.9.b.b.80.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+10.0153i q^{2} +155.694 q^{4} -594.387i q^{5} +4409.51 q^{7} +4123.23i q^{8} +5952.96 q^{10} -3479.38i q^{11} -18263.0 q^{13} +44162.5i q^{14} -1437.76 q^{16} -86637.8i q^{17} +76109.5 q^{19} -92542.4i q^{20} +34847.0 q^{22} -524101. i q^{23} +37329.5 q^{25} -182909. i q^{26} +686534. q^{28} +775418. i q^{29} -925425. q^{31} +1.04115e6i q^{32} +867703. q^{34} -2.62095e6i q^{35} +237767. q^{37} +762259. i q^{38} +2.45080e6 q^{40} -515887. i q^{41} +3.95836e6 q^{43} -541718. i q^{44} +5.24903e6 q^{46} +5.32614e6i q^{47} +1.36790e7 q^{49} +373866. i q^{50} -2.84343e6 q^{52} -1.30260e7i q^{53} -2.06810e6 q^{55} +1.81814e7i q^{56} -7.76604e6 q^{58} +1.25431e7i q^{59} +1.18844e7 q^{61} -9.26840e6i q^{62} -1.07955e7 q^{64} +1.08553e7i q^{65} +1.35316e7 q^{67} -1.34890e7i q^{68} +2.62496e7 q^{70} +133345. i q^{71} +5.24749e7 q^{73} +2.38130e6i q^{74} +1.18498e7 q^{76} -1.53424e7i q^{77} -4.78499e7 q^{79} +854585. i q^{80} +5.16676e6 q^{82} -5.85268e7i q^{83} -5.14963e7 q^{85} +3.96441e7i q^{86} +1.43463e7 q^{88} -4.62606e7i q^{89} -8.05307e7 q^{91} -8.15994e7i q^{92} -5.33428e7 q^{94} -4.52385e7i q^{95} -8.82391e7 q^{97} +1.36999e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.0153i	0.625956i	0.949760	+	0.312978i	$0.101327\pi$
$2$	10.0153i	0.625956i	−0.949760	+	0.312978i	$0.898673\pi$
$3$	0	0
$3$	0	0
$4$	155.694	0.608179
$5$	− 594.387i	− 0.951019i	−0.879711	−	0.475509i	$-0.842264\pi$
$5$	− 594.387i	− 0.951019i	0.879711	−	0.475509i	$-0.157736\pi$
$6$	0	0
$7$	4409.51	1.83653	0.918265	−	0.395965i	$-0.129590\pi$
$7$	4409.51	1.83653	0.918265	+	0.395965i	$0.129590\pi$
$8$	4123.23i	1.00665i
$9$	0	0
$10$	5952.96	0.595296
$11$	− 3479.38i	− 0.237646i	−0.992915	−	0.118823i	$-0.962088\pi$
$11$	− 3479.38i	− 0.237646i	0.992915	−	0.118823i	$-0.0379121\pi$
$12$	0	0
$13$	−18263.0	−0.639437	−0.319718	−	0.947513i	$-0.603588\pi$
$13$	−18263.0	−0.639437	−0.319718	+	0.947513i	$0.603588\pi$
$14$	44162.5i	1.14959i
$15$	0	0
$16$	−1437.76	−0.0219385
$17$	− 86637.8i	− 1.03732i	−0.854981	−	0.518659i	$-0.826432\pi$
$17$	− 86637.8i	− 1.03732i	0.854981	−	0.518659i	$-0.173568\pi$
$18$	0	0
$19$	76109.5	0.584016	0.292008	−	0.956416i	$-0.405677\pi$
$19$	76109.5	0.584016	0.292008	+	0.956416i	$0.405677\pi$
$20$	− 92542.4i	− 0.578390i
$21$	0	0
$22$	34847.0	0.148756
$23$	− 524101.i	− 1.87285i	−0.350863	−	0.936427i	$-0.614112\pi$
$23$	− 524101.i	− 1.87285i	0.350863	−	0.936427i	$-0.385888\pi$
$24$	0	0
$25$	37329.5	0.0955636
$26$	− 182909.i	− 0.400259i
$27$	0	0
$28$	686534.	1.11694
$29$	775418.i	1.09634i	0.836368	+	0.548168i	$0.184675\pi$
$29$	775418.i	1.09634i	−0.836368	+	0.548168i	$0.815325\pi$
$30$	0	0
$31$	−925425.	−1.00206	−0.501031	−	0.865430i	$-0.667046\pi$
$31$	−925425.	−1.00206	−0.501031	+	0.865430i	$0.667046\pi$
$32$	1.04115e6i	0.992917i
$33$	0	0
$34$	867703.	0.649315
$35$	− 2.62095e6i	− 1.74658i
$36$	0	0
$37$	237767.	0.126866	0.0634329	−	0.997986i	$-0.479795\pi$
$37$	237767.	0.126866	0.0634329	+	0.997986i	$0.479795\pi$
$38$	762259.i	0.365568i
$39$	0	0
$40$	2.45080e6	0.957342
$41$	− 515887.i	− 0.182566i	−0.995825	−	0.0912829i	$-0.970903\pi$
$41$	− 515887.i	− 0.182566i	0.995825	−	0.0912829i	$-0.0290968\pi$
$42$	0	0
$43$	3.95836e6	1.15782	0.578910	−	0.815392i	$-0.303478\pi$
$43$	3.95836e6	1.15782	0.578910	+	0.815392i	$0.303478\pi$
$44$	− 541718.i	− 0.144532i
$45$	0	0
$46$	5.24903e6	1.17232
$47$	5.32614e6i	1.09149i	0.837950	+	0.545746i	$0.183754\pi$
$47$	5.32614e6i	1.09149i	−0.837950	+	0.545746i	$0.816246\pi$
$48$	0	0
$49$	1.36790e7	2.37285
$50$	373866.i	0.0598186i
$51$	0	0
$52$	−2.84343e6	−0.388892
$53$	− 1.30260e7i	− 1.65085i	−0.564514	−	0.825424i	$-0.690936\pi$
$53$	− 1.30260e7i	− 1.65085i	0.564514	−	0.825424i	$-0.309064\pi$
$54$	0	0
$55$	−2.06810e6	−0.226006
$56$	1.81814e7i	1.84874i
$57$	0	0
$58$	−7.76604e6	−0.686258
$59$	1.25431e7i	1.03513i	0.855644	+	0.517566i	$0.173162\pi$
$59$	1.25431e7i	1.03513i	−0.855644	+	0.517566i	$0.826838\pi$
$60$	0	0
$61$	1.18844e7	0.858335	0.429167	−	0.903225i	$-0.358807\pi$
$61$	1.18844e7	0.858335	0.429167	+	0.903225i	$0.358807\pi$
$62$	− 9.26840e6i	− 0.627246i
$63$	0	0
$64$	−1.07955e7	−0.643460
$65$	1.08553e7i	0.608116i
$66$	0	0
$67$	1.35316e7	0.671504	0.335752	−	0.941950i	$-0.391010\pi$
$67$	1.35316e7	0.671504	0.335752	+	0.941950i	$0.391010\pi$
$68$	− 1.34890e7i	− 0.630875i
$69$	0	0
$70$	2.62496e7	1.09328
$71$	133345.i	0.00524738i	0.999997	+	0.00262369i	$0.000835147\pi$
$71$	133345.i	0.00524738i	−0.999997	+	0.00262369i	$0.999165\pi$
$72$	0	0
$73$	5.24749e7	1.84782	0.923910	−	0.382609i	$-0.124974\pi$
$73$	5.24749e7	1.84782	0.923910	+	0.382609i	$0.124974\pi$
$74$	2.38130e6i	0.0794123i
$75$	0	0
$76$	1.18498e7	0.355186
$77$	− 1.53424e7i	− 0.436445i
$78$	0	0
$79$	−4.78499e7	−1.22849	−0.614246	−	0.789115i	$-0.710540\pi$
$79$	−4.78499e7	−1.22849	−0.614246	+	0.789115i	$0.710540\pi$
$80$	854585.i	0.0208639i
$81$	0	0
$82$	5.16676e6	0.114278
$83$	− 5.85268e7i	− 1.23322i	−0.787267	−	0.616612i	$-0.788505\pi$
$83$	− 5.85268e7i	− 1.23322i	0.787267	−	0.616612i	$-0.211495\pi$
$84$	0	0
$85$	−5.14963e7	−0.986508
$86$	3.96441e7i	0.724744i
$87$	0	0
$88$	1.43463e7	0.239226
$89$	− 4.62606e7i	− 0.737312i	−0.929566	−	0.368656i	$-0.879818\pi$
$89$	− 4.62606e7i	− 0.737312i	0.929566	−	0.368656i	$-0.120182\pi$
$90$	0	0
$91$	−8.05307e7	−1.17435
$92$	− 8.15994e7i	− 1.13903i
$93$	0	0
$94$	−5.33428e7	−0.683226
$95$	− 4.52385e7i	− 0.555410i
$96$	0	0
$97$	−8.82391e7	−0.996722	−0.498361	−	0.866969i	$-0.666065\pi$
$97$	−8.82391e7	−0.996722	−0.498361	+	0.866969i	$0.666065\pi$
$98$	1.36999e8i	1.48530i
$99$	0	0
$100$	5.81198e6	0.0581198
$101$	5.74015e7i	0.551617i	0.961213	+	0.275809i	$0.0889456\pi$
$101$	5.74015e7i	0.551617i	−0.961213	+	0.275809i	$0.911054\pi$
$102$	0	0
$103$	−7.89124e7	−0.701126	−0.350563	−	0.936539i	$-0.614010\pi$
$103$	−7.89124e7	−0.701126	−0.350563	+	0.936539i	$0.614010\pi$
$104$	− 7.53024e7i	− 0.643688i
$105$	0	0
$106$	1.30459e8	1.03336
$107$	2.50821e8i	1.91350i	0.290907	+	0.956751i	$0.406043\pi$
$107$	2.50821e8i	1.91350i	−0.290907	+	0.956751i	$0.593957\pi$
$108$	0	0
$109$	−7.76440e7	−0.550050	−0.275025	−	0.961437i	$-0.588686\pi$
$109$	−7.76440e7	−0.550050	−0.275025	+	0.961437i	$0.588686\pi$
$110$	− 2.07126e7i	− 0.141470i
$111$	0	0
$112$	−6.33981e6	−0.0402907
$113$	6.15863e7i	0.377720i	0.982004	+	0.188860i	$0.0604793\pi$
$113$	6.15863e7i	0.377720i	−0.982004	+	0.188860i	$0.939521\pi$
$114$	0	0
$115$	−3.11519e8	−1.78112
$116$	1.20728e8i	0.666769i
$117$	0	0
$118$	−1.25622e8	−0.647946
$119$	− 3.82030e8i	− 1.90507i
$120$	0	0
$121$	2.02253e8	0.943524
$122$	1.19025e8i	0.537280i
$123$	0	0
$124$	−1.44083e8	−0.609433
$125$	− 2.54370e8i	− 1.04190i
$126$	0	0
$127$	−3.58325e8	−1.37741	−0.688703	−	0.725044i	$-0.741819\pi$
$127$	−3.58325e8	−1.37741	−0.688703	+	0.725044i	$0.741819\pi$
$128$	1.58414e8i	0.590139i
$129$	0	0
$130$	−1.08719e8	−0.380654
$131$	1.87148e8i	0.635477i	0.948178	+	0.317738i	$0.102923\pi$
$131$	1.87148e8i	0.635477i	−0.948178	+	0.317738i	$0.897077\pi$
$132$	0	0
$133$	3.35606e8	1.07256
$134$	1.35523e8i	0.420332i
$135$	0	0
$136$	3.57228e8	1.04421
$137$	− 1.50180e8i	− 0.426314i	−0.977018	−	0.213157i	$-0.931625\pi$
$137$	− 1.50180e8i	− 0.426314i	0.977018	−	0.213157i	$-0.0683746\pi$
$138$	0	0
$139$	1.29964e8	0.348148	0.174074	−	0.984733i	$-0.444307\pi$
$139$	1.29964e8	0.348148	0.174074	+	0.984733i	$0.444307\pi$
$140$	− 4.08067e8i	− 1.06223i
$141$	0	0
$142$	−1.33549e6	−0.00328462
$143$	6.35437e7i	0.151960i
$144$	0	0
$145$	4.60898e8	1.04264
$146$	5.25551e8i	1.15665i
$147$	0	0
$148$	3.70189e7	0.0771571
$149$	1.50916e8i	0.306188i	0.988212	+	0.153094i	$0.0489238\pi$
$149$	1.50916e8i	0.306188i	−0.988212	+	0.153094i	$0.951076\pi$
$150$	0	0
$151$	1.71244e8	0.329388	0.164694	−	0.986345i	$-0.447336\pi$
$151$	1.71244e8	0.329388	0.164694	+	0.986345i	$0.447336\pi$
$152$	3.13817e8i	0.587899i
$153$	0	0
$154$	1.53658e8	0.273195
$155$	5.50060e8i	0.952979i
$156$	0	0
$157$	−7.21868e8	−1.18812	−0.594059	−	0.804422i	$-0.702475\pi$
$157$	−7.21868e8	−1.18812	−0.594059	+	0.804422i	$0.702475\pi$
$158$	− 4.79230e8i	− 0.768982i
$159$	0	0
$160$	6.18845e8	0.944282
$161$	− 2.31103e9i	− 3.43955i
$162$	0	0
$163$	−1.90963e8	−0.270520	−0.135260	−	0.990810i	$-0.543187\pi$
$163$	−1.90963e8	−0.270520	−0.135260	+	0.990810i	$0.543187\pi$
$164$	− 8.03205e7i	− 0.111033i
$165$	0	0
$166$	5.86163e8	0.771944
$167$	5.59370e8i	0.719173i	0.933112	+	0.359586i	$0.117082\pi$
$167$	5.59370e8i	0.719173i	−0.933112	+	0.359586i	$0.882918\pi$
$168$	0	0
$169$	−4.82195e8	−0.591121
$170$	− 5.15751e8i	− 0.617510i
$171$	0	0
$172$	6.16292e8	0.704162
$173$	6.07138e8i	0.677802i	0.940822	+	0.338901i	$0.110055\pi$
$173$	6.07138e8i	0.677802i	−0.940822	+	0.338901i	$0.889945\pi$
$174$	0	0
$175$	1.64605e8	0.175505
$176$	5.00251e6i	0.00521359i
$177$	0	0
$178$	4.63314e8	0.461525
$179$	− 4.18834e8i	− 0.407971i	−0.978974	−	0.203986i	$-0.934610\pi$
$179$	− 4.18834e8i	− 0.407971i	0.978974	−	0.203986i	$-0.0653896\pi$
$180$	0	0
$181$	1.10216e9	1.02690	0.513451	−	0.858119i	$-0.328367\pi$
$181$	1.10216e9	1.02690	0.513451	+	0.858119i	$0.328367\pi$
$182$	− 8.06538e8i	− 0.735088i
$183$	0	0
$184$	2.16099e9	1.88531
$185$	− 1.41325e8i	− 0.120652i
$186$	0	0
$187$	−3.01446e8	−0.246515
$188$	8.29247e8i	0.663823i
$189$	0	0
$190$	4.53077e8	0.347662
$191$	1.78725e9i	1.34293i	0.741038	+	0.671463i	$0.234334\pi$
$191$	1.78725e9i	1.34293i	−0.741038	+	0.671463i	$0.765666\pi$
$192$	0	0
$193$	−7.17286e8	−0.516968	−0.258484	−	0.966016i	$-0.583223\pi$
$193$	−7.17286e8	−0.516968	−0.258484	+	0.966016i	$0.583223\pi$
$194$	− 8.83741e8i	− 0.623904i
$195$	0	0
$196$	2.12973e9	1.44312
$197$	1.81939e9i	1.20798i	0.796992	+	0.603990i	$0.206423\pi$
$197$	1.81939e9i	1.20798i	−0.796992	+	0.603990i	$0.793577\pi$
$198$	0	0
$199$	−1.90300e9	−1.21346	−0.606730	−	0.794908i	$-0.707519\pi$
$199$	−1.90300e9	−1.21346	−0.606730	+	0.794908i	$0.707519\pi$
$200$	1.53918e8i	0.0961990i
$201$	0	0
$202$	−5.74893e8	−0.345288
$203$	3.41921e9i	2.01346i
$204$	0	0
$205$	−3.06637e8	−0.173624
$206$	− 7.90331e8i	− 0.438874i
$207$	0	0
$208$	2.62577e7	0.0140283
$209$	− 2.64814e8i	− 0.138789i
$210$	0	0
$211$	1.59903e8	0.0806726	0.0403363	−	0.999186i	$-0.487157\pi$
$211$	1.59903e8	0.0806726	0.0403363	+	0.999186i	$0.487157\pi$
$212$	− 2.02807e9i	− 1.00401i
$213$	0	0
$214$	−2.51205e9	−1.19777
$215$	− 2.35279e9i	− 1.10111i
$216$	0	0
$217$	−4.08067e9	−1.84032
$218$	− 7.77628e8i	− 0.344307i
$219$	0	0
$220$	−3.21990e8	−0.137452
$221$	1.58226e9i	0.663299i
$222$	0	0
$223$	−6.13186e8	−0.247955	−0.123977	−	0.992285i	$-0.539565\pi$
$223$	−6.13186e8	−0.247955	−0.123977	+	0.992285i	$0.539565\pi$
$224$	4.59096e9i	1.82352i
$225$	0	0
$226$	−6.16805e8	−0.236436
$227$	− 2.96458e9i	− 1.11650i	−0.829672	−	0.558251i	$-0.811473\pi$
$227$	− 2.96458e9i	− 1.11650i	0.829672	−	0.558251i	$-0.188527\pi$
$228$	0	0
$229$	−3.78965e9	−1.37803	−0.689013	−	0.724749i	$-0.741956\pi$
$229$	−3.78965e9	−1.37803	−0.689013	+	0.724749i	$0.741956\pi$
$230$	− 3.11995e9i	− 1.11490i
$231$	0	0
$232$	−3.19723e9	−1.10363
$233$	3.76374e9i	1.27701i	0.769616	+	0.638507i	$0.220448\pi$
$233$	3.76374e9i	1.27701i	−0.769616	+	0.638507i	$0.779552\pi$
$234$	0	0
$235$	3.16578e9	1.03803
$236$	1.95288e9i	0.629545i
$237$	0	0
$238$	3.82614e9	1.19249
$239$	− 5.29760e8i	− 0.162363i	−0.996699	−	0.0811816i	$-0.974131\pi$
$239$	− 5.29760e8i	− 0.162363i	0.996699	−	0.0811816i	$-0.0258694\pi$
$240$	0	0
$241$	−8.38906e8	−0.248682	−0.124341	−	0.992240i	$-0.539682\pi$
$241$	−8.38906e8	−0.248682	−0.124341	+	0.992240i	$0.539682\pi$
$242$	2.02562e9i	0.590604i
$243$	0	0
$244$	1.85032e9	0.522021
$245$	− 8.13060e9i	− 2.25662i
$246$	0	0
$247$	−1.38998e9	−0.373441
$248$	− 3.81574e9i	− 1.00872i
$249$	0	0
$250$	2.54759e9	0.652184
$251$	− 2.40283e9i	− 0.605380i	−0.953089	−	0.302690i	$-0.902115\pi$
$251$	− 2.40283e9i	− 0.605380i	0.953089	−	0.302690i	$-0.0978847\pi$
$252$	0	0
$253$	−1.82355e9	−0.445076
$254$	− 3.58873e9i	− 0.862195i
$255$	0	0
$256$	−4.35021e9	−1.01286
$257$	4.79378e9i	1.09887i	0.835537	+	0.549434i	$0.185157\pi$
$257$	4.79378e9i	1.09887i	−0.835537	+	0.549434i	$0.814843\pi$
$258$	0	0
$259$	1.04844e9	0.232993
$260$	1.69010e9i	0.369844i
$261$	0	0
$262$	−1.87434e9	−0.397780
$263$	2.24924e9i	0.470124i	0.971980	+	0.235062i	$0.0755292\pi$
$263$	2.24924e9i	0.470124i	−0.971980	+	0.235062i	$0.924471\pi$
$264$	0	0
$265$	−7.74247e9	−1.56999
$266$	3.36119e9i	0.671377i
$267$	0	0
$268$	2.10678e9	0.408395
$269$	− 2.01512e9i	− 0.384851i	−0.981312	−	0.192425i	$-0.938365\pi$
$269$	− 2.01512e9i	− 0.384851i	0.981312	−	0.192425i	$-0.0616353\pi$
$270$	0	0
$271$	−5.85840e9	−1.08618	−0.543090	−	0.839675i	$-0.682746\pi$
$271$	−5.85840e9	−1.08618	−0.543090	+	0.839675i	$0.682746\pi$
$272$	1.24564e8i	0.0227571i
$273$	0	0
$274$	1.50410e9	0.266854
$275$	− 1.29883e8i	− 0.0227103i
$276$	0	0
$277$	−6.81588e9	−1.15772	−0.578859	−	0.815427i	$-0.696502\pi$
$277$	−6.81588e9	−1.15772	−0.578859	+	0.815427i	$0.696502\pi$
$278$	1.30163e9i	0.217925i
$279$	0	0
$280$	1.08068e10	1.75819
$281$	2.07175e9i	0.332286i	0.986102	+	0.166143i	$0.0531314\pi$
$281$	2.07175e9i	0.332286i	−0.986102	+	0.166143i	$0.946869\pi$
$282$	0	0
$283$	9.61757e8	0.149941	0.0749704	−	0.997186i	$-0.476114\pi$
$283$	9.61757e8	0.149941	0.0749704	+	0.997186i	$0.476114\pi$
$284$	2.07609e7i	0.00319135i
$285$	0	0
$286$	−6.36409e8	−0.0951200
$287$	− 2.27481e9i	− 0.335288i
$288$	0	0
$289$	−5.30347e8	−0.0760272
$290$	4.61603e9i	0.652644i
$291$	0	0
$292$	8.17002e9	1.12381
$293$	− 1.21580e10i	− 1.64965i	−0.565391	−	0.824823i	$-0.691275\pi$
$293$	− 1.21580e10i	− 1.64965i	0.565391	−	0.824823i	$-0.308725\pi$
$294$	0	0
$295$	7.45543e9	0.984429
$296$	9.80369e8i	0.127709i
$297$	0	0
$298$	−1.51146e9	−0.191660
$299$	9.57163e9i	1.19757i
$300$	0	0
$301$	1.74544e10	2.12637
$302$	1.71506e9i	0.206182i
$303$	0	0
$304$	−1.09427e8	−0.0128124
$305$	− 7.06391e9i	− 0.816292i
$306$	0	0
$307$	4.91035e9	0.552788	0.276394	−	0.961044i	$-0.410860\pi$
$307$	4.91035e9	0.552788	0.276394	+	0.961044i	$0.410860\pi$
$308$	− 2.38871e9i	− 0.265437i
$309$	0	0
$310$	−5.50901e9	−0.596523
$311$	2.68957e9i	0.287502i	0.989614	+	0.143751i	$0.0459165\pi$
$311$	2.68957e9i	0.287502i	−0.989614	+	0.143751i	$0.954083\pi$
$312$	0	0
$313$	−5.13306e9	−0.534809	−0.267405	−	0.963584i	$-0.586166\pi$
$313$	−5.13306e9	−0.534809	−0.267405	+	0.963584i	$0.586166\pi$
$314$	− 7.22972e9i	− 0.743709i
$315$	0	0
$316$	−7.44993e9	−0.747144
$317$	1.53801e10i	1.52308i	0.648117	+	0.761540i	$0.275557\pi$
$317$	1.53801e10i	1.52308i	−0.648117	+	0.761540i	$0.724443\pi$
$318$	0	0
$319$	2.69797e9	0.260540
$320$	6.41669e9i	0.611943i
$321$	0	0
$322$	2.31456e10	2.15301
$323$	− 6.59396e9i	− 0.605810i
$324$	0	0
$325$	−6.81747e8	−0.0611068
$326$	− 1.91256e9i	− 0.169334i
$327$	0	0
$328$	2.12713e9	0.183780
$329$	2.34857e10i	2.00456i
$330$	0	0
$331$	−7.40976e9	−0.617294	−0.308647	−	0.951177i	$-0.599876\pi$
$331$	−7.40976e9	−0.617294	−0.308647	+	0.951177i	$0.599876\pi$
$332$	− 9.11226e9i	− 0.750022i
$333$	0	0
$334$	−5.60225e9	−0.450170
$335$	− 8.04298e9i	− 0.638613i
$336$	0	0
$337$	4.70501e9	0.364788	0.182394	−	0.983226i	$-0.441615\pi$
$337$	4.70501e9	0.364788	0.182394	+	0.983226i	$0.441615\pi$
$338$	− 4.82933e9i	− 0.370015i
$339$	0	0
$340$	−8.01767e9	−0.599974
$341$	3.21990e9i	0.238136i
$342$	0	0
$343$	3.48977e10	2.52127
$344$	1.63212e10i	1.16552i
$345$	0	0
$346$	−6.08066e9	−0.424274
$347$	− 4.87208e9i	− 0.336044i	−0.985783	−	0.168022i	$-0.946262\pi$
$347$	− 4.87208e9i	− 0.336044i	0.985783	−	0.168022i	$-0.0537380\pi$
$348$	0	0
$349$	2.37996e10	1.60423	0.802117	−	0.597168i	$-0.203707\pi$
$349$	2.37996e10	1.60423	0.802117	+	0.597168i	$0.203707\pi$
$350$	1.64857e9i	0.109859i
$351$	0	0
$352$	3.62255e9	0.235963
$353$	7.90818e9i	0.509305i	0.967033	+	0.254652i	$0.0819611\pi$
$353$	7.90818e9i	0.509305i	−0.967033	+	0.254652i	$0.918039\pi$
$354$	0	0
$355$	7.92583e7	0.00499035
$356$	− 7.20250e9i	− 0.448418i
$357$	0	0
$358$	4.19474e9	0.255372
$359$	7.90247e9i	0.475757i	0.971295	+	0.237879i	$0.0764520\pi$
$359$	7.90247e9i	0.475757i	−0.971295	+	0.237879i	$0.923548\pi$
$360$	0	0
$361$	−1.11909e10	−0.658926
$362$	1.10384e10i	0.642795i
$363$	0	0
$364$	−1.25381e10	−0.714213
$365$	− 3.11904e10i	− 1.75731i
$366$	0	0
$367$	−1.38911e10	−0.765725	−0.382863	−	0.923805i	$-0.625062\pi$
$367$	−1.38911e10	−0.765725	−0.382863	+	0.923805i	$0.625062\pi$
$368$	7.53531e8i	0.0410875i
$369$	0	0
$370$	1.41542e9	0.0755226
$371$	− 5.74382e10i	− 3.03183i
$372$	0	0
$373$	2.17709e10	1.12471	0.562356	−	0.826895i	$-0.309895\pi$
$373$	2.17709e10	1.12471	0.562356	+	0.826895i	$0.309895\pi$
$374$	− 3.01907e9i	− 0.154307i
$375$	0	0
$376$	−2.19609e10	−1.09875
$377$	− 1.41614e10i	− 0.701038i
$378$	0	0
$379$	−1.86928e10	−0.905975	−0.452988	−	0.891517i	$-0.649642\pi$
$379$	−1.86928e10	−0.905975	−0.452988	+	0.891517i	$0.649642\pi$
$380$	− 7.04336e9i	− 0.337789i
$381$	0	0
$382$	−1.78998e10	−0.840612
$383$	− 1.48977e10i	− 0.692347i	−0.938170	−	0.346174i	$-0.887481\pi$
$383$	− 1.48977e10i	− 0.692347i	0.938170	−	0.346174i	$-0.112519\pi$
$384$	0	0
$385$	−9.11929e9	−0.415067
$386$	− 7.18383e9i	− 0.323599i
$387$	0	0
$388$	−1.37383e10	−0.606186
$389$	1.67875e10i	0.733140i	0.930390	+	0.366570i	$0.119468\pi$
$389$	1.67875e10i	0.733140i	−0.930390	+	0.366570i	$0.880532\pi$
$390$	0	0
$391$	−4.54070e10	−1.94274
$392$	5.64017e10i	2.38862i
$393$	0	0
$394$	−1.82217e10	−0.756142
$395$	2.84413e10i	1.16832i
$396$	0	0
$397$	3.63950e10	1.46514	0.732570	−	0.680692i	$-0.238321\pi$
$397$	3.63950e10	1.46514	0.732570	+	0.680692i	$0.238321\pi$
$398$	− 1.90591e10i	− 0.759573i
$399$	0	0
$400$	−5.36709e7	−0.00209652
$401$	− 3.09381e9i	− 0.119651i	−0.998209	−	0.0598255i	$-0.980946\pi$
$401$	− 3.09381e9i	− 0.119651i	0.998209	−	0.0598255i	$-0.0190544\pi$
$402$	0	0
$403$	1.69010e10	0.640755
$404$	8.93706e9i	0.335482i
$405$	0	0
$406$	−3.42444e10	−1.26033
$407$	− 8.27281e8i	− 0.0301492i
$408$	0	0
$409$	−5.78841e9	−0.206855	−0.103427	−	0.994637i	$-0.532981\pi$
$409$	−5.78841e9	−0.206855	−0.103427	+	0.994637i	$0.532981\pi$
$410$	− 3.07106e9i	− 0.108681i
$411$	0	0
$412$	−1.22862e10	−0.426411
$413$	5.53087e10i	1.90105i
$414$	0	0
$415$	−3.47875e10	−1.17282
$416$	− 1.90144e10i	− 0.634907i
$417$	0	0
$418$	2.65219e9	0.0868759
$419$	− 2.41615e10i	− 0.783914i	−0.919984	−	0.391957i	$-0.871798\pi$
$419$	− 2.41615e10i	− 0.783914i	0.919984	−	0.391957i	$-0.128202\pi$
$420$	0	0
$421$	1.16694e10	0.371468	0.185734	−	0.982600i	$-0.440534\pi$
$421$	1.16694e10	0.371468	0.185734	+	0.982600i	$0.440534\pi$
$422$	1.60147e9i	0.0504975i
$423$	0	0
$424$	5.37092e10	1.66182
$425$	− 3.23415e9i	− 0.0991297i
$426$	0	0
$427$	5.24042e10	1.57636
$428$	3.90513e10i	1.16375i
$429$	0	0
$430$	2.35639e10	0.689245
$431$	6.44251e10i	1.86701i	0.358568	+	0.933504i	$0.383265\pi$
$431$	6.44251e10i	1.86701i	−0.358568	+	0.933504i	$0.616735\pi$
$432$	0	0
$433$	−5.35776e10	−1.52416	−0.762082	−	0.647480i	$-0.775823\pi$
$433$	−5.35776e10	−1.52416	−0.762082	+	0.647480i	$0.775823\pi$
$434$	− 4.08691e10i	− 1.15196i
$435$	0	0
$436$	−1.20887e10	−0.334529
$437$	− 3.98891e10i	− 1.09378i
$438$	0	0
$439$	−4.27951e9	−0.115222	−0.0576111	−	0.998339i	$-0.518348\pi$
$439$	−4.27951e9	−0.115222	−0.0576111	+	0.998339i	$0.518348\pi$
$440$	− 8.52725e9i	− 0.227509i
$441$	0	0
$442$	−1.58468e10	−0.415196
$443$	1.20749e10i	0.313522i	0.987637	+	0.156761i	$0.0501052\pi$
$443$	1.20749e10i	0.313522i	−0.987637	+	0.156761i	$0.949895\pi$
$444$	0	0
$445$	−2.74967e10	−0.701198
$446$	− 6.14124e9i	− 0.155209i
$447$	0	0
$448$	−4.76028e10	−1.18173
$449$	− 3.17911e10i	− 0.782205i	−0.920347	−	0.391103i	$-0.872094\pi$
$449$	− 3.17911e10i	− 0.782205i	0.920347	−	0.391103i	$-0.127906\pi$
$450$	0	0
$451$	−1.79497e9	−0.0433861
$452$	9.58861e9i	0.229722i
$453$	0	0
$454$	2.96911e10	0.698881
$455$	4.78664e10i	1.11682i
$456$	0	0
$457$	−8.30400e9	−0.190381	−0.0951903	−	0.995459i	$-0.530346\pi$
$457$	−8.30400e9	−0.190381	−0.0951903	+	0.995459i	$0.530346\pi$
$458$	− 3.79544e10i	− 0.862583i
$459$	0	0
$460$	−4.85016e10	−1.08324
$461$	3.19035e10i	0.706374i	0.935553	+	0.353187i	$0.114902\pi$
$461$	3.19035e10i	0.706374i	−0.935553	+	0.353187i	$0.885098\pi$
$462$	0	0
$463$	2.75541e10	0.599601	0.299800	−	0.954002i	$-0.403080\pi$
$463$	2.75541e10	0.599601	0.299800	+	0.954002i	$0.403080\pi$
$464$	− 1.11486e9i	− 0.0240519i
$465$	0	0
$466$	−3.76949e10	−0.799354
$467$	− 2.60699e10i	− 0.548114i	−0.961713	−	0.274057i	$-0.911634\pi$
$467$	− 2.60699e10i	− 0.548114i	0.961713	−	0.274057i	$-0.0883658\pi$
$468$	0	0
$469$	5.96675e10	1.23324
$470$	3.17063e10i	0.649761i
$471$	0	0
$472$	−5.17180e10	−1.04201
$473$	− 1.37726e10i	− 0.275151i
$474$	0	0
$475$	2.84113e9	0.0558106
$476$	− 5.94798e10i	− 1.15862i
$477$	0	0
$478$	5.30570e9	0.101632
$479$	− 2.22131e9i	− 0.0421956i	−0.999777	−	0.0210978i	$-0.993284\pi$
$479$	− 2.22131e9i	− 0.0421956i	0.999777	−	0.0210978i	$-0.00671614\pi$
$480$	0	0
$481$	−4.34232e9	−0.0811226
$482$	− 8.40188e9i	− 0.155664i
$483$	0	0
$484$	3.14895e10	0.573832
$485$	5.24482e10i	0.947902i
$486$	0	0
$487$	8.62519e10	1.53339	0.766696	−	0.642011i	$-0.221900\pi$
$487$	8.62519e10	1.53339	0.766696	+	0.642011i	$0.221900\pi$
$488$	4.90020e10i	0.864042i
$489$	0	0
$490$	8.14304e10	1.41254
$491$	4.40442e9i	0.0757814i	0.999282	+	0.0378907i	$0.0120639\pi$
$491$	4.40442e9i	0.0757814i	−0.999282	+	0.0378907i	$0.987936\pi$
$492$	0	0
$493$	6.71805e10	1.13725
$494$	− 1.39211e10i	− 0.233758i
$495$	0	0
$496$	1.33054e9	0.0219837
$497$	5.87985e8i	0.00963697i
$498$	0	0
$499$	−2.77040e10	−0.446829	−0.223414	−	0.974724i	$-0.571720\pi$
$499$	−2.77040e10	−0.446829	−0.223414	+	0.974724i	$0.571720\pi$
$500$	− 3.96039e10i	− 0.633663i
$501$	0	0
$502$	2.40650e10	0.378941
$503$	− 2.37306e10i	− 0.370712i	−0.982671	−	0.185356i	$-0.940656\pi$
$503$	− 2.37306e10i	− 0.370712i	0.982671	−	0.185356i	$-0.0593438\pi$
$504$	0	0
$505$	3.41187e10	0.524598
$506$	− 1.82633e10i	− 0.278598i
$507$	0	0
$508$	−5.57890e10	−0.837709
$509$	− 3.83002e10i	− 0.570597i	−0.958439	−	0.285299i	$-0.907907\pi$
$509$	− 3.83002e10i	− 0.570597i	0.958439	−	0.285299i	$-0.0920928\pi$
$510$	0	0
$511$	2.31388e11	3.39358
$512$	− 3.01455e9i	− 0.0438674i
$513$	0	0
$514$	−4.80111e10	−0.687843
$515$	4.69045e10i	0.666784i
$516$	0	0
$517$	1.85316e10	0.259389
$518$	1.05004e10i	0.145843i
$519$	0	0
$520$	−4.47588e10	−0.612160
$521$	− 1.29094e11i	− 1.75208i	−0.482238	−	0.876040i	$-0.660176\pi$
$521$	− 1.29094e11i	− 1.75208i	0.482238	−	0.876040i	$-0.339824\pi$
$522$	0	0
$523$	1.37220e11	1.83405	0.917024	−	0.398831i	$-0.130584\pi$
$523$	1.37220e11	1.83405	0.917024	+	0.398831i	$0.130584\pi$
$524$	2.91378e10i	0.386484i
$525$	0	0
$526$	−2.25268e10	−0.294277
$527$	8.01767e10i	1.03946i
$528$	0	0
$529$	−1.96371e11	−2.50758
$530$	− 7.75431e10i	− 0.982742i
$531$	0	0
$532$	5.22518e10	0.652311
$533$	9.42163e9i	0.116739i
$534$	0	0
$535$	1.49085e11	1.81978
$536$	5.57938e10i	0.675969i
$537$	0	0
$538$	2.01820e10	0.240900
$539$	− 4.75944e10i	− 0.563898i
$540$	0	0
$541$	−7.71547e10	−0.900686	−0.450343	−	0.892856i	$-0.648698\pi$
$541$	−7.71547e10	−0.900686	−0.450343	+	0.892856i	$0.648698\pi$
$542$	− 5.86735e10i	− 0.679900i
$543$	0	0
$544$	9.02028e10	1.02997
$545$	4.61506e10i	0.523108i
$546$	0	0
$547$	−5.33068e10	−0.595434	−0.297717	−	0.954654i	$-0.596225\pi$
$547$	−5.33068e10	−0.595434	−0.297717	+	0.954654i	$0.596225\pi$
$548$	− 2.33821e10i	− 0.259276i
$549$	0	0
$550$	1.30082e9	0.0142157
$551$	5.90167e10i	0.640278i
$552$	0	0
$553$	−2.10995e11	−2.25616
$554$	− 6.82631e10i	− 0.724681i
$555$	0	0
$556$	2.02346e10	0.211736
$557$	1.56229e11i	1.62309i	0.584291	+	0.811544i	$0.301373\pi$
$557$	1.56229e11i	1.62309i	−0.584291	+	0.811544i	$0.698627\pi$
$558$	0	0
$559$	−7.22912e10	−0.740352
$560$	3.76830e9i	0.0383172i
$561$	0	0
$562$	−2.07492e10	−0.207996
$563$	− 4.85065e10i	− 0.482799i	−0.970426	−	0.241399i	$-0.922394\pi$
$563$	− 4.85065e10i	− 0.482799i	0.970426	−	0.241399i	$-0.0776064\pi$
$564$	0	0
$565$	3.66061e10	0.359219
$566$	9.63228e9i	0.0938563i
$567$	0	0
$568$	−5.49811e8	−0.00528227
$569$	4.85523e10i	0.463192i	0.972812	+	0.231596i	$0.0743947\pi$
$569$	4.85523e10i	0.463192i	−0.972812	+	0.231596i	$0.925605\pi$
$570$	0	0
$571$	1.65482e11	1.55670	0.778351	−	0.627830i	$-0.216057\pi$
$571$	1.65482e11	1.55670	0.778351	+	0.627830i	$0.216057\pi$
$572$	9.89337e9i	0.0924188i
$573$	0	0
$574$	2.27829e10	0.209875
$575$	− 1.95644e10i	− 0.178977i
$576$	0	0
$577$	−1.25738e11	−1.13439	−0.567194	−	0.823584i	$-0.691971\pi$
$577$	−1.25738e11	−1.13439	−0.567194	+	0.823584i	$0.691971\pi$
$578$	− 5.31158e9i	− 0.0475897i
$579$	0	0
$580$	7.17590e10	0.634110
$581$	− 2.58074e11i	− 2.26486i
$582$	0	0
$583$	−4.53223e10	−0.392318
$584$	2.16366e11i	1.86011i
$585$	0	0
$586$	1.21766e11	1.03261
$587$	− 6.82411e10i	− 0.574769i	−0.957815	−	0.287385i	$-0.907214\pi$
$587$	− 6.82411e10i	− 0.574769i	0.957815	−	0.287385i	$-0.0927858\pi$
$588$	0	0
$589$	−7.04336e10	−0.585220
$590$	7.46683e10i	0.616209i
$591$	0	0
$592$	−3.41851e8	−0.00278324
$593$	2.22279e10i	0.179755i	0.995953	+	0.0898774i	$0.0286475\pi$
$593$	2.22279e10i	0.179755i	−0.995953	+	0.0898774i	$0.971352\pi$
$594$	0	0
$595$	−2.27074e11	−1.81175
$596$	2.34966e10i	0.186218i
$597$	0	0
$598$	−9.58627e10	−0.749627
$599$	2.13320e11i	1.65701i	0.559984	+	0.828503i	$0.310807\pi$
$599$	2.13320e11i	1.65701i	−0.559984	+	0.828503i	$0.689193\pi$
$600$	0	0
$601$	3.49960e10	0.268238	0.134119	−	0.990965i	$-0.457180\pi$
$601$	3.49960e10	0.268238	0.134119	+	0.990965i	$0.457180\pi$
$602$	1.74811e11i	1.33101i
$603$	0	0
$604$	2.66617e10	0.200327
$605$	− 1.20216e11i	− 0.897309i
$606$	0	0
$607$	−1.10769e11	−0.815951	−0.407975	−	0.912993i	$-0.633765\pi$
$607$	−1.10769e11	−0.815951	−0.407975	+	0.912993i	$0.633765\pi$
$608$	7.92413e10i	0.579879i
$609$	0	0
$610$	7.07471e10	0.510963
$611$	− 9.72710e10i	− 0.697940i
$612$	0	0
$613$	−4.84434e10	−0.343078	−0.171539	−	0.985177i	$-0.554874\pi$
$613$	−4.84434e10	−0.343078	−0.171539	+	0.985177i	$0.554874\pi$
$614$	4.91786e10i	0.346021i
$615$	0	0
$616$	6.32601e10	0.439347
$617$	7.67452e10i	0.529554i	0.964310	+	0.264777i	$0.0852984\pi$
$617$	7.67452e10i	0.529554i	−0.964310	+	0.264777i	$0.914702\pi$
$618$	0	0
$619$	−2.11915e11	−1.44344	−0.721721	−	0.692184i	$-0.756648\pi$
$619$	−2.11915e11	−1.44344	−0.721721	+	0.692184i	$0.756648\pi$
$620$	8.56410e10i	0.579582i
$621$	0	0
$622$	−2.69368e10	−0.179964
$623$	− 2.03987e11i	− 1.35410i
$624$	0	0
$625$	−1.36613e11	−0.895304
$626$	− 5.14091e10i	− 0.334767i
$627$	0	0
$628$	−1.12391e11	−0.722589
$629$	− 2.05996e10i	− 0.131600i
$630$	0	0
$631$	−1.44761e10	−0.0913130	−0.0456565	−	0.998957i	$-0.514538\pi$
$631$	−1.44761e10	−0.0913130	−0.0456565	+	0.998957i	$0.514538\pi$
$632$	− 1.97296e11i	− 1.23666i
$633$	0	0
$634$	−1.54036e11	−0.953381
$635$	2.12983e11i	1.30994i
$636$	0	0
$637$	−2.49819e11	−1.51728
$638$	2.70210e10i	0.163087i
$639$	0	0
$640$	9.41593e10	0.561233
$641$	− 2.38883e10i	− 0.141499i	−0.997494	−	0.0707494i	$-0.977461\pi$
$641$	− 2.38883e10i	− 0.141499i	0.997494	−	0.0707494i	$-0.0225390\pi$
$642$	0	0
$643$	1.51535e11	0.886480	0.443240	−	0.896403i	$-0.353829\pi$
$643$	1.51535e11	0.886480	0.443240	+	0.896403i	$0.353829\pi$
$644$	− 3.59813e11i	− 2.09187i
$645$	0	0
$646$	6.60404e10	0.379210
$647$	1.51614e11i	0.865208i	0.901584	+	0.432604i	$0.142405\pi$
$647$	1.51614e11i	0.865208i	−0.901584	+	0.432604i	$0.857595\pi$
$648$	0	0
$649$	4.36420e10	0.245995
$650$	− 6.82790e9i	− 0.0382502i
$651$	0	0
$652$	−2.97319e10	−0.164525
$653$	− 1.82933e11i	− 1.00610i	−0.864258	−	0.503048i	$-0.832212\pi$
$653$	− 1.82933e11i	− 1.00610i	0.864258	−	0.503048i	$-0.167788\pi$
$654$	0	0
$655$	1.11238e11	0.604350
$656$	7.41722e8i	0.00400521i
$657$	0	0
$658$	−2.35216e11	−1.25477
$659$	− 2.97761e11i	− 1.57880i	−0.613881	−	0.789398i	$-0.710393\pi$
$659$	− 2.97761e11i	− 1.57880i	0.613881	−	0.789398i	$-0.289607\pi$
$660$	0	0
$661$	1.11919e11	0.586270	0.293135	−	0.956071i	$-0.405301\pi$
$661$	1.11919e11	0.586270	0.293135	+	0.956071i	$0.405301\pi$
$662$	− 7.42109e10i	− 0.386399i
$663$	0	0
$664$	2.41320e11	1.24142
$665$	− 1.99480e11i	− 1.02003i
$666$	0	0
$667$	4.06397e11	2.05328
$668$	8.70905e10i	0.437386i
$669$	0	0
$670$	8.05528e10	0.399743
$671$	− 4.13502e10i	− 0.203980i
$672$	0	0
$673$	−4.67096e10	−0.227691	−0.113845	−	0.993498i	$-0.536317\pi$
$673$	−4.67096e10	−0.227691	−0.113845	+	0.993498i	$0.536317\pi$
$674$	4.71220e10i	0.228341i
$675$	0	0
$676$	−7.50749e10	−0.359507
$677$	1.71821e11i	0.817941i	0.912548	+	0.408970i	$0.134112\pi$
$677$	1.71821e11i	0.817941i	−0.912548	+	0.408970i	$0.865888\pi$
$678$	0	0
$679$	−3.89091e11	−1.83051
$680$	− 2.12332e11i	− 0.993068i
$681$	0	0
$682$	−3.22483e10	−0.149063
$683$	6.74141e10i	0.309790i	0.987931	+	0.154895i	$0.0495040\pi$
$683$	6.74141e10i	0.309790i	−0.987931	+	0.154895i	$0.950496\pi$
$684$	0	0
$685$	−8.92650e10	−0.405433
$686$	3.49510e11i	1.57821i
$687$	0	0
$688$	−5.69116e9	−0.0254008
$689$	2.37893e11i	1.05561i
$690$	0	0
$691$	6.86155e10	0.300961	0.150481	−	0.988613i	$-0.451918\pi$
$691$	6.86155e10	0.300961	0.150481	+	0.988613i	$0.451918\pi$
$692$	9.45277e10i	0.412225i
$693$	0	0
$694$	4.87953e10	0.210349
$695$	− 7.72488e10i	− 0.331095i
$696$	0	0
$697$	−4.46953e10	−0.189379
$698$	2.38360e11i	1.00418i
$699$	0	0
$700$	2.56280e10	0.106739
$701$	− 3.47803e11i	− 1.44033i	−0.693804	−	0.720164i	$-0.744066\pi$
$701$	− 3.47803e11i	− 1.44033i	0.693804	−	0.720164i	$-0.255934\pi$
$702$	0	0
$703$	1.80963e10	0.0740916
$704$	3.75615e10i	0.152916i
$705$	0	0
$706$	−7.92027e10	−0.318802
$707$	2.53113e11i	1.01306i
$708$	0	0
$709$	−2.64810e11	−1.04797	−0.523986	−	0.851727i	$-0.675555\pi$
$709$	−2.64810e11	−1.04797	−0.523986	+	0.851727i	$0.675555\pi$
$710$	7.93795e8i	0.00312374i
$711$	0	0
$712$	1.90743e11	0.742215
$713$	4.85016e11i	1.87671i
$714$	0	0
$715$	3.77695e10	0.144517
$716$	− 6.52098e10i	− 0.248120i
$717$	0	0
$718$	−7.91456e10	−0.297803
$719$	− 2.48269e11i	− 0.928981i	−0.885578	−	0.464491i	$-0.846237\pi$
$719$	− 2.48269e11i	− 0.928981i	0.885578	−	0.464491i	$-0.153763\pi$
$720$	0	0
$721$	−3.47965e11	−1.28764
$722$	− 1.12080e11i	− 0.412458i
$723$	0	0
$724$	1.71599e11	0.624540
$725$	2.89460e10i	0.104770i
$726$	0	0
$727$	2.95500e11	1.05784	0.528921	−	0.848671i	$-0.322597\pi$
$727$	2.95500e11	1.05784	0.528921	+	0.848671i	$0.322597\pi$
$728$	− 3.32047e11i	− 1.18215i
$729$	0	0
$730$	3.12380e11	1.10000
$731$	− 3.42943e11i	− 1.20103i
$732$	0	0
$733$	4.27907e11	1.48229	0.741146	−	0.671344i	$-0.234283\pi$
$733$	4.27907e11	1.48229	0.741146	+	0.671344i	$0.234283\pi$
$734$	− 1.39124e11i	− 0.479310i
$735$	0	0
$736$	5.45667e11	1.85959
$737$	− 4.70814e10i	− 0.159580i
$738$	0	0
$739$	−1.19830e10	−0.0401781	−0.0200890	−	0.999798i	$-0.506395\pi$
$739$	−1.19830e10	−0.0401781	−0.0200890	+	0.999798i	$0.506395\pi$
$740$	− 2.20035e10i	− 0.0733779i
$741$	0	0
$742$	5.75260e11	1.89779
$743$	2.77564e11i	0.910769i	0.890295	+	0.455384i	$0.150498\pi$
$743$	2.77564e11i	0.910769i	−0.890295	+	0.455384i	$0.849502\pi$
$744$	0	0
$745$	8.97022e10	0.291191
$746$	2.18042e11i	0.704020i
$747$	0	0
$748$	−4.69332e10	−0.149925
$749$	1.10600e12i	3.51421i
$750$	0	0
$751$	1.44914e10	0.0455566	0.0227783	−	0.999741i	$-0.492749\pi$
$751$	1.44914e10	0.0455566	0.0227783	+	0.999741i	$0.492749\pi$
$752$	− 7.65770e9i	− 0.0239457i
$753$	0	0
$754$	1.41831e11	0.438819
$755$	− 1.01785e11i	− 0.313254i
$756$	0	0
$757$	1.94269e11	0.591590	0.295795	−	0.955251i	$-0.404415\pi$
$757$	1.94269e11	0.591590	0.295795	+	0.955251i	$0.404415\pi$
$758$	− 1.87213e11i	− 0.567100i
$759$	0	0
$760$	1.86529e11	0.559103
$761$	− 4.48052e11i	− 1.33595i	−0.744185	−	0.667974i	$-0.767162\pi$
$761$	− 4.48052e11i	− 1.33595i	0.744185	−	0.667974i	$-0.232838\pi$
$762$	0	0
$763$	−3.42372e11	−1.01018
$764$	2.78264e11i	0.816740i
$765$	0	0
$766$	1.49205e11	0.433379
$767$	− 2.29073e11i	− 0.661901i
$768$	0	0
$769$	2.27389e11	0.650225	0.325113	−	0.945675i	$-0.394598\pi$
$769$	2.27389e11	0.650225	0.325113	+	0.945675i	$0.394598\pi$
$770$	− 9.13324e10i	− 0.259814i
$771$	0	0
$772$	−1.11677e11	−0.314409
$773$	− 3.48003e11i	− 0.974686i	−0.873211	−	0.487343i	$-0.837966\pi$
$773$	− 3.48003e11i	− 0.974686i	0.873211	−	0.487343i	$-0.162034\pi$
$774$	0	0
$775$	−3.45457e10	−0.0957605
$776$	− 3.63831e11i	− 1.00335i
$777$	0	0
$778$	−1.68131e11	−0.458913
$779$	− 3.92639e10i	− 0.106621i
$780$	0	0
$781$	4.63956e8	0.00124702
$782$	− 4.54764e11i	− 1.21607i
$783$	0	0
$784$	−1.96671e10	−0.0520566
$785$	4.29069e11i	1.12992i
$786$	0	0
$787$	2.54239e11	0.662741	0.331370	−	0.943501i	$-0.392489\pi$
$787$	2.54239e11	0.662741	0.331370	+	0.943501i	$0.392489\pi$
$788$	2.83267e11i	0.734669i
$789$	0	0
$790$	−2.84848e11	−0.731316
$791$	2.71565e11i	0.693695i
$792$	0	0
$793$	−2.17044e11	−0.548851
$794$	3.64506e11i	0.917113i
$795$	0	0
$796$	−2.96285e11	−0.738002
$797$	5.53726e11i	1.37234i	0.727442	+	0.686169i	$0.240709\pi$
$797$	5.53726e11i	1.37234i	−0.727442	+	0.686169i	$0.759291\pi$
$798$	0	0
$799$	4.61445e11	1.13222
$800$	3.88656e10i	0.0948866i
$801$	0	0
$802$	3.09854e10	0.0748962
$803$	− 1.82580e11i	− 0.439128i
$804$	0	0
$805$	−1.37365e12	−3.27108
$806$	1.69268e11i	0.401084i
$807$	0	0
$808$	−2.36680e11	−0.555285
$809$	1.00027e11i	0.233519i	0.993160	+	0.116759i	$0.0372506\pi$
$809$	1.00027e11i	0.233519i	−0.993160	+	0.116759i	$0.962749\pi$
$810$	0	0
$811$	9.06002e10	0.209433	0.104717	−	0.994502i	$-0.466606\pi$
$811$	9.06002e10	0.209433	0.104717	+	0.994502i	$0.466606\pi$
$812$	5.32351e11i	1.22454i
$813$	0	0
$814$	8.28546e9	0.0188720
$815$	1.13506e11i	0.257270i
$816$	0	0
$817$	3.01269e11	0.676185
$818$	− 5.79726e10i	− 0.129482i
$819$	0	0
$820$	−4.77415e10	−0.105594
$821$	− 6.19591e11i	− 1.36374i	−0.731472	−	0.681871i	$-0.761166\pi$
$821$	− 6.19591e11i	− 1.36374i	0.731472	−	0.681871i	$-0.238834\pi$
$822$	0	0
$823$	3.63723e10	0.0792813	0.0396407	−	0.999214i	$-0.487379\pi$
$823$	3.63723e10	0.0792813	0.0396407	+	0.999214i	$0.487379\pi$
$824$	− 3.25374e11i	− 0.705788i
$825$	0	0
$826$	−5.53933e11	−1.18997
$827$	6.85214e10i	0.146489i	0.997314	+	0.0732444i	$0.0233353\pi$
$827$	6.85214e10i	0.146489i	−0.997314	+	0.0732444i	$0.976665\pi$
$828$	0	0
$829$	−6.13133e11	−1.29819	−0.649093	−	0.760709i	$-0.724851\pi$
$829$	−6.13133e11	−1.29819	−0.649093	+	0.760709i	$0.724851\pi$
$830$	− 3.48407e11i	− 0.734133i
$831$	0	0
$832$	1.97157e11	0.411452
$833$	− 1.18512e12i	− 2.46139i
$834$	0	0
$835$	3.32482e11	0.683947
$836$	− 4.12299e10i	− 0.0844087i
$837$	0	0
$838$	2.41985e11	0.490695
$839$	− 3.69496e11i	− 0.745697i	−0.927892	−	0.372848i	$-0.878381\pi$
$839$	− 3.69496e11i	− 0.745697i	0.927892	−	0.372848i	$-0.121619\pi$
$840$	0	0
$841$	−1.01027e11	−0.201954
$842$	1.16873e11i	0.232522i
$843$	0	0
$844$	2.48959e10	0.0490634
$845$	2.86610e11i	0.562167i
$846$	0	0
$847$	8.91836e11	1.73281
$848$	1.87282e10i	0.0362171i
$849$	0	0
$850$	3.23909e10	0.0620508
$851$	− 1.24614e11i	− 0.237601i
$852$	0	0
$853$	2.05380e11	0.387937	0.193969	−	0.981008i	$-0.437864\pi$
$853$	2.05380e11	0.387937	0.193969	+	0.981008i	$0.437864\pi$
$854$	5.24844e11i	0.986730i
$855$	0	0
$856$	−1.03419e12	−1.92623
$857$	− 5.65349e11i	− 1.04808i	−0.851694	−	0.524039i	$-0.824425\pi$
$857$	− 5.65349e11i	− 1.04808i	0.851694	−	0.524039i	$-0.175575\pi$
$858$	0	0
$859$	6.34065e10	0.116456	0.0582279	−	0.998303i	$-0.481455\pi$
$859$	6.34065e10	0.116456	0.0582279	+	0.998303i	$0.481455\pi$
$860$	− 3.66316e11i	− 0.669671i
$861$	0	0
$862$	−6.45236e11	−1.16866
$863$	7.20037e11i	1.29811i	0.760742	+	0.649055i	$0.224835\pi$
$863$	7.20037e11i	1.29811i	−0.760742	+	0.649055i	$0.775165\pi$
$864$	0	0
$865$	3.60875e11	0.644602
$866$	− 5.36596e11i	− 0.954060i
$867$	0	0
$868$	−6.35336e11	−1.11924
$869$	1.66488e11i	0.291947i
$870$	0	0
$871$	−2.47126e11	−0.429384
$872$	− 3.20145e11i	− 0.553707i
$873$	0	0
$874$	3.99501e11	0.684655
$875$	− 1.12165e12i	− 1.91348i
$876$	0	0
$877$	4.86955e11	0.823171	0.411586	−	0.911371i	$-0.364975\pi$
$877$	4.86955e11	0.823171	0.411586	+	0.911371i	$0.364975\pi$
$878$	− 4.28606e10i	− 0.0721240i
$879$	0	0
$880$	2.97342e9	0.00495822
$881$	1.10625e12i	1.83633i	0.396196	+	0.918166i	$0.370330\pi$
$881$	1.10625e12i	1.83633i	−0.396196	+	0.918166i	$0.629670\pi$
$882$	0	0
$883$	7.45262e10	0.122593	0.0612966	−	0.998120i	$-0.480476\pi$
$883$	7.45262e10	0.122593	0.0612966	+	0.998120i	$0.480476\pi$
$884$	2.46348e11i	0.403405i
$885$	0	0
$886$	−1.20933e11	−0.196251
$887$	1.15964e12i	1.87338i	0.350153	+	0.936692i	$0.386130\pi$
$887$	1.15964e12i	1.87338i	−0.350153	+	0.936692i	$0.613870\pi$
$888$	0	0
$889$	−1.58004e12	−2.52965
$890$	− 2.75387e11i	− 0.438919i
$891$	0	0
$892$	−9.54693e10	−0.150801
$893$	4.05370e11i	0.637449i
$894$	0	0
$895$	−2.48949e11	−0.387988
$896$	6.98529e11i	1.08381i
$897$	0	0
$898$	3.18397e11	0.489626
$899$	− 7.17591e11i	− 1.09860i
$900$	0	0
$901$	−1.12854e12	−1.71245
$902$	− 1.79771e10i	− 0.0271578i
$903$	0	0
$904$	−2.53935e11	−0.380232
$905$	− 6.55107e11i	− 0.976602i
$906$	0	0
$907$	1.26174e12	1.86440	0.932201	−	0.361941i	$-0.117886\pi$
$907$	1.26174e12	1.86440	0.932201	+	0.361941i	$0.117886\pi$
$908$	− 4.61567e11i	− 0.679034i
$909$	0	0
$910$	−4.79396e11	−0.699083
$911$	7.43367e11i	1.07927i	0.841899	+	0.539635i	$0.181438\pi$
$911$	7.43367e11i	1.07927i	−0.841899	+	0.539635i	$0.818562\pi$
$912$	0	0
$913$	−2.03637e11	−0.293071
$914$	− 8.31670e10i	− 0.119170i
$915$	0	0
$916$	−5.90025e11	−0.838086
$917$	8.25230e11i	1.16707i
$918$	0	0
$919$	−8.99130e10	−0.126055	−0.0630276	−	0.998012i	$-0.520076\pi$
$919$	−8.99130e10	−0.126055	−0.0630276	+	0.998012i	$0.520076\pi$
$920$	− 1.28446e12i	− 1.79296i
$921$	0	0
$922$	−3.19523e11	−0.442159
$923$	− 2.43527e9i	− 0.00335536i
$924$	0	0
$925$	8.87572e9	0.0121237
$926$	2.75962e11i	0.375323i
$927$	0	0
$928$	−8.07325e11	−1.08857
$929$	8.58727e11i	1.15290i	0.817132	+	0.576451i	$0.195563\pi$
$929$	8.58727e11i	1.15290i	−0.817132	+	0.576451i	$0.804437\pi$
$930$	0	0
$931$	1.04110e12	1.38578
$932$	5.85991e11i	0.776653i
$933$	0	0
$934$	2.61097e11	0.343095
$935$	1.79175e11i	0.234440i
$936$	0	0
$937$	1.25416e11	0.162702	0.0813512	−	0.996685i	$-0.474076\pi$
$937$	1.25416e11	0.162702	0.0813512	+	0.996685i	$0.474076\pi$
$938$	5.97588e11i	0.771952i
$939$	0	0
$940$	4.92893e11	0.631308
$941$	− 1.01295e12i	− 1.29191i	−0.763377	−	0.645954i	$-0.776460\pi$
$941$	− 1.01295e12i	− 1.29191i	0.763377	−	0.645954i	$-0.223540\pi$
$942$	0	0
$943$	−2.70377e11	−0.341919
$944$	− 1.80339e10i	− 0.0227092i
$945$	0	0
$946$	1.37937e11	0.172233
$947$	2.99006e11i	0.371774i	0.982571	+	0.185887i	$0.0595159\pi$
$947$	2.99006e11i	0.371774i	−0.982571	+	0.185887i	$0.940484\pi$
$948$	0	0
$949$	−9.58346e11	−1.18156
$950$	2.84548e10i	0.0349350i
$951$	0	0
$952$	1.57520e12	1.91773
$953$	9.57954e11i	1.16138i	0.814126	+	0.580688i	$0.197217\pi$
$953$	9.57954e11i	1.16138i	−0.814126	+	0.580688i	$0.802783\pi$
$954$	0	0
$955$	1.06232e12	1.27715
$956$	− 8.24804e10i	− 0.0987460i
$957$	0	0
$958$	2.22471e10	0.0264126
$959$	− 6.62220e11i	− 0.782939i
$960$	0	0
$961$	3.51989e9	0.00412701
$962$	− 4.34896e10i	− 0.0507792i
$963$	0	0
$964$	−1.30612e11	−0.151243
$965$	4.26345e11i	0.491646i
$966$	0	0
$967$	1.18590e12	1.35626	0.678131	−	0.734941i	$-0.262790\pi$
$967$	1.18590e12	1.35626	0.678131	+	0.734941i	$0.262790\pi$
$968$	8.33936e11i	0.949798i
$969$	0	0
$970$	−5.25284e11	−0.593345
$971$	5.47759e10i	0.0616187i	0.999525	+	0.0308093i	$0.00980847\pi$
$971$	5.47759e10i	0.0616187i	−0.999525	+	0.0308093i	$0.990192\pi$
$972$	0	0
$973$	5.73077e11	0.639384
$974$	8.63838e11i	0.959835i
$975$	0	0
$976$	−1.70869e10	−0.0188305
$977$	− 9.25105e11i	− 1.01534i	−0.861551	−	0.507672i	$-0.830506\pi$
$977$	− 9.25105e11i	− 1.01534i	0.861551	−	0.507672i	$-0.169494\pi$
$978$	0	0
$979$	−1.60958e11	−0.175219
$980$	− 1.26589e12i	− 1.37243i
$981$	0	0
$982$	−4.41116e10	−0.0474358
$983$	5.78240e11i	0.619290i	0.950852	+	0.309645i	$0.100210\pi$
$983$	5.78240e11i	0.619290i	−0.950852	+	0.309645i	$0.899790\pi$
$984$	0	0
$985$	1.08142e12	1.14881
$986$	6.72832e11i	0.711867i
$987$	0	0
$988$	−2.16412e11	−0.227119
$989$	− 2.07458e12i	− 2.16843i
$990$	0	0
$991$	−1.41284e11	−0.146487	−0.0732435	−	0.997314i	$-0.523335\pi$
$991$	−1.41284e11	−0.146487	−0.0732435	+	0.997314i	$0.523335\pi$
$992$	− 9.63505e11i	− 0.994963i
$993$	0	0
$994$	−5.88884e9	−0.00603231
$995$	1.13112e12i	1.15402i
$996$	0	0
$997$	−1.24199e12	−1.25700	−0.628502	−	0.777808i	$-0.716332\pi$
$997$	−1.24199e12	−1.25700	−0.628502	+	0.777808i	$0.716332\pi$
$998$	− 2.77464e11i	− 0.279695i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.b.b.80.11	yes	16
3.2	odd	2	inner	81.9.b.b.80.6	✓	16
9.2	odd	6		81.9.d.g.53.6		32
9.4	even	3		81.9.d.g.26.6		32
9.5	odd	6		81.9.d.g.26.11		32
9.7	even	3		81.9.d.g.53.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.9.b.b.80.6	✓	16	3.2	odd	2	inner
81.9.b.b.80.11	yes	16	1.1	even	1	trivial
81.9.d.g.26.6		32	9.4	even	3
81.9.d.g.26.11		32	9.5	odd	6
81.9.d.g.53.6		32	9.2	odd	6
81.9.d.g.53.11		32	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+10.0153i q^{2} +155.694 q^{4} -594.387i q^{5} +4409.51 q^{7} +4123.23i q^{8} +5952.96 q^{10} -3479.38i q^{11} -18263.0 q^{13} +44162.5i q^{14} -1437.76 q^{16} -86637.8i q^{17} +76109.5 q^{19} -92542.4i q^{20} +34847.0 q^{22} -524101. i q^{23} +37329.5 q^{25} -182909. i q^{26} +686534. q^{28} +775418. i q^{29} -925425. q^{31} +1.04115e6i q^{32} +867703. q^{34} -2.62095e6i q^{35} +237767. q^{37} +762259. i q^{38} +2.45080e6 q^{40} -515887. i q^{41} +3.95836e6 q^{43} -541718. i q^{44} +5.24903e6 q^{46} +5.32614e6i q^{47} +1.36790e7 q^{49} +373866. i q^{50} -2.84343e6 q^{52} -1.30260e7i q^{53} -2.06810e6 q^{55} +1.81814e7i q^{56} -7.76604e6 q^{58} +1.25431e7i q^{59} +1.18844e7 q^{61} -9.26840e6i q^{62} -1.07955e7 q^{64} +1.08553e7i q^{65} +1.35316e7 q^{67} -1.34890e7i q^{68} +2.62496e7 q^{70} +133345. i q^{71} +5.24749e7 q^{73} +2.38130e6i q^{74} +1.18498e7 q^{76} -1.53424e7i q^{77} -4.78499e7 q^{79} +854585. i q^{80} +5.16676e6 q^{82} -5.85268e7i q^{83} -5.14963e7 q^{85} +3.96441e7i q^{86} +1.43463e7 q^{88} -4.62606e7i q^{89} -8.05307e7 q^{91} -8.15994e7i q^{92} -5.33428e7 q^{94} -4.52385e7i q^{95} -8.82391e7 q^{97} +1.36999e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) \) 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

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Groups

Database

Properties

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