LMFDB - Embedded newform 81.9.b.b.80.10

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			80.10
Root			$5.26228i$ of defining polynomial
Character	$\chi$	$=$	81.80
Dual form			81.9.b.b.80.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+9.11454i q^{2} +172.925 q^{4} +181.837i q^{5} -873.072 q^{7} +3909.46i q^{8} -1657.36 q^{10} -2607.53i q^{11} -25473.3 q^{13} -7957.65i q^{14} +8635.93 q^{16} +43929.5i q^{17} -107202. q^{19} +31444.1i q^{20} +23766.4 q^{22} +331625. i q^{23} +357560. q^{25} -232177. i q^{26} -150976. q^{28} -14672.0i q^{29} -979646. q^{31} +1.07953e6i q^{32} -400398. q^{34} -158757. i q^{35} -1.63930e6 q^{37} -977094. i q^{38} -710883. q^{40} +3.48515e6i q^{41} -4.63519e6 q^{43} -450907. i q^{44} -3.02261e6 q^{46} -8.23369e6i q^{47} -5.00255e6 q^{49} +3.25900e6i q^{50} -4.40497e6 q^{52} -1.20746e7i q^{53} +474145. q^{55} -3.41324e6i q^{56} +133728. q^{58} +2.11207e7i q^{59} -1.57894e7 q^{61} -8.92903e6i q^{62} -7.62865e6 q^{64} -4.63198e6i q^{65} -5.16949e6 q^{67} +7.59652e6i q^{68} +1.44699e6 q^{70} +1.07917e7i q^{71} -1.53154e6 q^{73} -1.49415e7i q^{74} -1.85379e7 q^{76} +2.27656e6i q^{77} +2.99414e7 q^{79} +1.57033e6i q^{80} -3.17656e7 q^{82} +2.23404e7i q^{83} -7.98801e6 q^{85} -4.22477e7i q^{86} +1.01940e7 q^{88} +7.39067e7i q^{89} +2.22400e7 q^{91} +5.73463e7i q^{92} +7.50463e7 q^{94} -1.94932e7i q^{95} +5.45203e7 q^{97} -4.55959e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.11454i	0.569659i	0.958578	+	0.284829i	$0.0919370\pi$
$2$	9.11454i	0.569659i	−0.958578	+	0.284829i	$0.908063\pi$
$3$	0	0
$3$	0	0
$4$	172.925	0.675489
$5$	181.837i	0.290939i	0.989363	+	0.145469i	$0.0464692\pi$
$5$	181.837i	0.290939i	−0.989363	+	0.145469i	$0.953531\pi$
$6$	0	0
$7$	−873.072	−0.363628	−0.181814	−	0.983333i	$-0.558197\pi$
$7$	−873.072	−0.363628	−0.181814	+	0.983333i	$0.558197\pi$
$8$	3909.46i	0.954457i
$9$	0	0
$10$	−1657.36	−0.165736
$11$	− 2607.53i	− 0.178098i	−0.996027	−	0.0890489i	$-0.971617\pi$
$11$	− 2607.53i	− 0.178098i	0.996027	−	0.0890489i	$-0.0283827\pi$
$12$	0	0
$13$	−25473.3	−0.891891	−0.445945	−	0.895060i	$-0.647132\pi$
$13$	−25473.3	−0.891891	−0.445945	+	0.895060i	$0.647132\pi$
$14$	− 7957.65i	− 0.207144i
$15$	0	0
$16$	8635.93	0.131774
$17$	43929.5i	0.525970i	0.964800	+	0.262985i	$0.0847070\pi$
$17$	43929.5i	0.525970i	−0.964800	+	0.262985i	$0.915293\pi$
$18$	0	0
$19$	−107202.	−0.822597	−0.411299	−	0.911501i	$-0.634925\pi$
$19$	−107202.	−0.822597	−0.411299	+	0.911501i	$0.634925\pi$
$20$	31444.1i	0.196526i
$21$	0	0
$22$	23766.4	0.101455
$23$	331625.i	1.18505i	0.805553	+	0.592524i	$0.201869\pi$
$23$	331625.i	1.18505i	−0.805553	+	0.592524i	$0.798131\pi$
$24$	0	0
$25$	357560.	0.915355
$26$	− 232177.i	− 0.508073i
$27$	0	0
$28$	−150976.	−0.245627
$29$	− 14672.0i	− 0.0207442i	−0.999946	−	0.0103721i	$-0.996698\pi$
$29$	− 14672.0i	− 0.0207442i	0.999946	−	0.0103721i	$-0.00330160\pi$
$30$	0	0
$31$	−979646.	−1.06077	−0.530387	−	0.847756i	$-0.677953\pi$
$31$	−979646.	−1.06077	−0.530387	+	0.847756i	$0.677953\pi$
$32$	1.07953e6i	1.02952i
$33$	0	0
$34$	−400398.	−0.299624
$35$	− 158757.i	− 0.105794i
$36$	0	0
$37$	−1.63930e6	−0.874687	−0.437344	−	0.899294i	$-0.644081\pi$
$37$	−1.63930e6	−0.874687	−0.437344	+	0.899294i	$0.644081\pi$
$38$	− 977094.i	− 0.468600i
$39$	0	0
$40$	−710883.	−0.277689
$41$	3.48515e6i	1.23335i	0.787218	+	0.616675i	$0.211521\pi$
$41$	3.48515e6i	1.23335i	−0.787218	+	0.616675i	$0.788479\pi$
$42$	0	0
$43$	−4.63519e6	−1.35579	−0.677897	−	0.735156i	$-0.737109\pi$
$43$	−4.63519e6	−1.35579	−0.677897	+	0.735156i	$0.737109\pi$
$44$	− 450907.i	− 0.120303i
$45$	0	0
$46$	−3.02261e6	−0.675073
$47$	− 8.23369e6i	− 1.68734i	−0.536860	−	0.843671i	$-0.680390\pi$
$47$	− 8.23369e6i	− 1.68734i	0.536860	−	0.843671i	$-0.319610\pi$
$48$	0	0
$49$	−5.00255e6	−0.867774
$50$	3.25900e6i	0.521440i
$51$	0	0
$52$	−4.40497e6	−0.602462
$53$	− 1.20746e7i	− 1.53027i	−0.643870	−	0.765135i	$-0.722672\pi$
$53$	− 1.20746e7i	− 1.53027i	0.643870	−	0.765135i	$-0.277328\pi$
$54$	0	0
$55$	474145.	0.0518156
$56$	− 3.41324e6i	− 0.347068i
$57$	0	0
$58$	133728.	0.0118171
$59$	2.11207e7i	1.74301i	0.490386	+	0.871505i	$0.336856\pi$
$59$	2.11207e7i	1.74301i	−0.490386	+	0.871505i	$0.663144\pi$
$60$	0	0
$61$	−1.57894e7	−1.14037	−0.570186	−	0.821516i	$-0.693129\pi$
$61$	−1.57894e7	−1.14037	−0.570186	+	0.821516i	$0.693129\pi$
$62$	− 8.92903e6i	− 0.604279i
$63$	0	0
$64$	−7.62865e6	−0.454703
$65$	− 4.63198e6i	− 0.259486i
$66$	0	0
$67$	−5.16949e6	−0.256536	−0.128268	−	0.991740i	$-0.540942\pi$
$67$	−5.16949e6	−0.256536	−0.128268	+	0.991740i	$0.540942\pi$
$68$	7.59652e6i	0.355287i
$69$	0	0
$70$	1.44699e6	0.0602663
$71$	1.07917e7i	0.424673i	0.977197	+	0.212337i	$0.0681074\pi$
$71$	1.07917e7i	0.424673i	−0.977197	+	0.212337i	$0.931893\pi$
$72$	0	0
$73$	−1.53154e6	−0.0539308	−0.0269654	−	0.999636i	$-0.508584\pi$
$73$	−1.53154e6	−0.0539308	−0.0269654	+	0.999636i	$0.508584\pi$
$74$	− 1.49415e7i	− 0.498273i
$75$	0	0
$76$	−1.85379e7	−0.555655
$77$	2.27656e6i	0.0647614i
$78$	0	0
$79$	2.99414e7	0.768711	0.384356	−	0.923185i	$-0.374424\pi$
$79$	2.99414e7	0.768711	0.384356	+	0.923185i	$0.374424\pi$
$80$	1.57033e6i	0.0383381i
$81$	0	0
$82$	−3.17656e7	−0.702589
$83$	2.23404e7i	0.470738i	0.971906	+	0.235369i	$0.0756299\pi$
$83$	2.23404e7i	0.470738i	−0.971906	+	0.235369i	$0.924370\pi$
$84$	0	0
$85$	−7.98801e6	−0.153025
$86$	− 4.22477e7i	− 0.772341i
$87$	0	0
$88$	1.01940e7	0.169987
$89$	7.39067e7i	1.17794i	0.808154	+	0.588971i	$0.200467\pi$
$89$	7.39067e7i	1.17794i	−0.808154	+	0.588971i	$0.799533\pi$
$90$	0	0
$91$	2.22400e7	0.324317
$92$	5.73463e7i	0.800487i
$93$	0	0
$94$	7.50463e7	0.961210
$95$	− 1.94932e7i	− 0.239326i
$96$	0	0
$97$	5.45203e7	0.615845	0.307922	−	0.951411i	$-0.400366\pi$
$97$	5.45203e7	0.615845	0.307922	+	0.951411i	$0.400366\pi$
$98$	− 4.55959e7i	− 0.494335i
$99$	0	0
$100$	6.18312e7	0.618312
$101$	8.22803e7i	0.790698i	0.918531	+	0.395349i	$0.129376\pi$
$101$	8.22803e7i	0.790698i	−0.918531	+	0.395349i	$0.870624\pi$
$102$	0	0
$103$	6.46516e7	0.574421	0.287210	−	0.957868i	$-0.407272\pi$
$103$	6.46516e7	0.574421	0.287210	+	0.957868i	$0.407272\pi$
$104$	− 9.95867e7i	− 0.851271i
$105$	0	0
$106$	1.10054e8	0.871732
$107$	4.66645e7i	0.356001i	0.984030	+	0.178001i	$0.0569629\pi$
$107$	4.66645e7i	0.356001i	−0.984030	+	0.178001i	$0.943037\pi$
$108$	0	0
$109$	2.53493e8	1.79581	0.897904	−	0.440192i	$-0.145089\pi$
$109$	2.53493e8	1.79581	0.897904	+	0.440192i	$0.145089\pi$
$110$	4.32161e6i	0.0295172i
$111$	0	0
$112$	−7.53979e6	−0.0479167
$113$	− 2.29100e8i	− 1.40511i	−0.711627	−	0.702557i	$-0.752041\pi$
$113$	− 2.29100e8i	− 1.40511i	0.711627	−	0.702557i	$-0.247959\pi$
$114$	0	0
$115$	−6.03016e7	−0.344777
$116$	− 2.53715e6i	− 0.0140125i
$117$	0	0
$118$	−1.92505e8	−0.992921
$119$	− 3.83537e7i	− 0.191258i
$120$	0	0
$121$	2.07560e8	0.968281
$122$	− 1.43913e8i	− 0.649623i
$123$	0	0
$124$	−1.69405e8	−0.716540
$125$	1.36048e8i	0.557251i
$126$	0	0
$127$	1.98537e8	0.763181	0.381591	−	0.924331i	$-0.375376\pi$
$127$	1.98537e8	0.763181	0.381591	+	0.924331i	$0.375376\pi$
$128$	2.06829e8i	0.770497i
$129$	0	0
$130$	4.22184e7	0.147818
$131$	− 3.10300e7i	− 0.105365i	−0.998611	−	0.0526825i	$-0.983223\pi$
$131$	− 3.10300e7i	− 0.105365i	0.998611	−	0.0526825i	$-0.0167771\pi$
$132$	0	0
$133$	9.35948e7	0.299120
$134$	− 4.71175e7i	− 0.146138i
$135$	0	0
$136$	−1.71741e8	−0.502016
$137$	− 3.10592e8i	− 0.881675i	−0.897587	−	0.440838i	$-0.854681\pi$
$137$	− 3.10592e8i	− 0.881675i	0.897587	−	0.440838i	$-0.145319\pi$
$138$	0	0
$139$	−2.37384e8	−0.635905	−0.317953	−	0.948107i	$-0.602995\pi$
$139$	−2.37384e8	−0.635905	−0.317953	+	0.948107i	$0.602995\pi$
$140$	− 2.74530e7i	− 0.0714624i
$141$	0	0
$142$	−9.83611e7	−0.241919
$143$	6.64224e7i	0.158844i
$144$	0	0
$145$	2.66791e6	0.00603529
$146$	− 1.39593e7i	− 0.0307222i
$147$	0	0
$148$	−2.83477e8	−0.590841
$149$	8.90891e8i	1.80750i	0.428056	+	0.903752i	$0.359198\pi$
$149$	8.90891e8i	1.80750i	−0.428056	+	0.903752i	$0.640802\pi$
$150$	0	0
$151$	3.03017e8	0.582853	0.291427	−	0.956593i	$-0.405870\pi$
$151$	3.03017e8	0.582853	0.291427	+	0.956593i	$0.405870\pi$
$152$	− 4.19100e8i	− 0.785134i
$153$	0	0
$154$	−2.07498e7	−0.0368919
$155$	− 1.78136e8i	− 0.308620i
$156$	0	0
$157$	−5.99222e7	−0.0986255	−0.0493128	−	0.998783i	$-0.515703\pi$
$157$	−5.99222e7	−0.0986255	−0.0493128	+	0.998783i	$0.515703\pi$
$158$	2.72902e8i	0.437903i
$159$	0	0
$160$	−1.96299e8	−0.299528
$161$	− 2.89533e8i	− 0.430917i
$162$	0	0
$163$	−7.08582e8	−1.00378	−0.501891	−	0.864931i	$-0.667362\pi$
$163$	−7.08582e8	−1.00378	−0.501891	+	0.864931i	$0.667362\pi$
$164$	6.02671e8i	0.833115i
$165$	0	0
$166$	−2.03623e8	−0.268160
$167$	1.33552e9i	1.71705i	0.512770	+	0.858526i	$0.328619\pi$
$167$	1.33552e9i	1.71705i	−0.512770	+	0.858526i	$0.671381\pi$
$168$	0	0
$169$	−1.66842e8	−0.204531
$170$	− 7.28070e7i	− 0.0871721i
$171$	0	0
$172$	−8.01541e8	−0.915824
$173$	− 1.38680e9i	− 1.54820i	−0.633061	−	0.774102i	$-0.718202\pi$
$173$	− 1.38680e9i	− 1.54820i	0.633061	−	0.774102i	$-0.281798\pi$
$174$	0	0
$175$	−3.12176e8	−0.332849
$176$	− 2.25184e7i	− 0.0234686i
$177$	0	0
$178$	−6.73626e8	−0.671025
$179$	7.03513e8i	0.685268i	0.939469	+	0.342634i	$0.111319\pi$
$179$	7.03513e8i	0.685268i	−0.939469	+	0.342634i	$0.888681\pi$
$180$	0	0
$181$	−1.61661e8	−0.150623	−0.0753114	−	0.997160i	$-0.523995\pi$
$181$	−1.61661e8	−0.150623	−0.0753114	+	0.997160i	$0.523995\pi$
$182$	2.02708e8i	0.184750i
$183$	0	0
$184$	−1.29647e9	−1.13108
$185$	− 2.98086e8i	− 0.254481i
$186$	0	0
$187$	1.14548e8	0.0936741
$188$	− 1.42381e9i	− 1.13978i
$189$	0	0
$190$	1.77672e8	0.136334
$191$	− 1.96614e9i	− 1.47734i	−0.674068	−	0.738669i	$-0.735454\pi$
$191$	− 1.96614e9i	− 1.47734i	0.674068	−	0.738669i	$-0.264546\pi$
$192$	0	0
$193$	9.74772e8	0.702545	0.351272	−	0.936273i	$-0.385749\pi$
$193$	9.74772e8	0.702545	0.351272	+	0.936273i	$0.385749\pi$
$194$	4.96928e8i	0.350821i
$195$	0	0
$196$	−8.65066e8	−0.586172
$197$	5.21456e8i	0.346220i	0.984902	+	0.173110i	$0.0553817\pi$
$197$	5.21456e8i	0.346220i	−0.984902	+	0.173110i	$0.944618\pi$
$198$	0	0
$199$	1.16358e9	0.741968	0.370984	−	0.928639i	$-0.379020\pi$
$199$	1.16358e9	0.741968	0.370984	+	0.928639i	$0.379020\pi$
$200$	1.39787e9i	0.873667i
$201$	0	0
$202$	−7.49948e8	−0.450428
$203$	1.28097e7i	0.00754318i
$204$	0	0
$205$	−6.33729e8	−0.358830
$206$	5.89269e8i	0.327224i
$207$	0	0
$208$	−2.19985e8	−0.117528
$209$	2.79532e8i	0.146503i
$210$	0	0
$211$	3.16340e9	1.59597	0.797985	−	0.602677i	$-0.205899\pi$
$211$	3.16340e9	1.59597	0.797985	+	0.602677i	$0.205899\pi$
$212$	− 2.08800e9i	− 1.03368i
$213$	0	0
$214$	−4.25326e8	−0.202799
$215$	− 8.42849e8i	− 0.394453i
$216$	0	0
$217$	8.55302e8	0.385727
$218$	2.31047e9i	1.02300i
$219$	0	0
$220$	8.19916e7	0.0350008
$221$	− 1.11903e9i	− 0.469108i
$222$	0	0
$223$	3.02468e9	1.22310	0.611548	−	0.791208i	$-0.290547\pi$
$223$	3.02468e9	1.22310	0.611548	+	0.791208i	$0.290547\pi$
$224$	− 9.42510e8i	− 0.374364i
$225$	0	0
$226$	2.08814e9	0.800436
$227$	− 1.80522e9i	− 0.679870i	−0.940449	−	0.339935i	$-0.889595\pi$
$227$	− 1.80522e9i	− 0.679870i	0.940449	−	0.339935i	$-0.110405\pi$
$228$	0	0
$229$	1.90665e8	0.0693311	0.0346656	−	0.999399i	$-0.488963\pi$
$229$	1.90665e8	0.0693311	0.0346656	+	0.999399i	$0.488963\pi$
$230$	− 5.49622e8i	− 0.196405i
$231$	0	0
$232$	5.73595e7	0.0197994
$233$	1.24700e9i	0.423099i	0.977367	+	0.211550i	$0.0678510\pi$
$233$	1.24700e9i	0.423099i	−0.977367	+	0.211550i	$0.932149\pi$
$234$	0	0
$235$	1.49719e9	0.490913
$236$	3.65230e9i	1.17738i
$237$	0	0
$238$	3.49576e8	0.108952
$239$	− 3.88186e9i	− 1.18973i	−0.803825	−	0.594865i	$-0.797205\pi$
$239$	− 3.88186e9i	− 1.18973i	0.803825	−	0.594865i	$-0.202795\pi$
$240$	0	0
$241$	5.01748e9	1.48737	0.743683	−	0.668533i	$-0.233077\pi$
$241$	5.01748e9	1.48737	0.743683	+	0.668533i	$0.233077\pi$
$242$	1.89181e9i	0.551590i
$243$	0	0
$244$	−2.73038e9	−0.770308
$245$	− 9.09647e8i	− 0.252469i
$246$	0	0
$247$	2.73078e9	0.733667
$248$	− 3.82988e9i	− 1.01246i
$249$	0	0
$250$	−1.24001e9	−0.317443
$251$	7.11370e9i	1.79226i	0.443793	+	0.896129i	$0.353633\pi$
$251$	7.11370e9i	1.79226i	−0.443793	+	0.896129i	$0.646367\pi$
$252$	0	0
$253$	8.64723e8	0.211055
$254$	1.80958e9i	0.434753i
$255$	0	0
$256$	−3.83809e9	−0.893624
$257$	1.89939e9i	0.435393i	0.976017	+	0.217696i	$0.0698543\pi$
$257$	1.89939e9i	0.435393i	−0.976017	+	0.217696i	$0.930146\pi$
$258$	0	0
$259$	1.43123e9	0.318061
$260$	− 8.00986e8i	− 0.175280i
$261$	0	0
$262$	2.82824e8	0.0600221
$263$	4.95165e9i	1.03497i	0.855693	+	0.517484i	$0.173131\pi$
$263$	4.95165e9i	1.03497i	−0.855693	+	0.517484i	$0.826869\pi$
$264$	0	0
$265$	2.19560e9	0.445215
$266$	8.53074e8i	0.170396i
$267$	0	0
$268$	−8.93934e8	−0.173287
$269$	− 4.96899e8i	− 0.0948985i	−0.998874	−	0.0474492i	$-0.984891\pi$
$269$	− 4.96899e8i	− 0.0948985i	0.998874	−	0.0474492i	$-0.0151092\pi$
$270$	0	0
$271$	−1.12765e9	−0.209072	−0.104536	−	0.994521i	$-0.533336\pi$
$271$	−1.12765e9	−0.209072	−0.104536	+	0.994521i	$0.533336\pi$
$272$	3.79372e8i	0.0693091i
$273$	0	0
$274$	2.83091e9	0.502254
$275$	− 9.32350e8i	− 0.163023i
$276$	0	0
$277$	2.48144e9	0.421488	0.210744	−	0.977541i	$-0.432411\pi$
$277$	2.48144e9	0.421488	0.210744	+	0.977541i	$0.432411\pi$
$278$	− 2.16365e9i	− 0.362249i
$279$	0	0
$280$	6.20652e8	0.100976
$281$	− 5.60122e9i	− 0.898374i	−0.893438	−	0.449187i	$-0.851714\pi$
$281$	− 5.60122e9i	− 0.898374i	0.893438	−	0.449187i	$-0.148286\pi$
$282$	0	0
$283$	−7.50388e9	−1.16988	−0.584938	−	0.811078i	$-0.698881\pi$
$283$	−7.50388e9	−1.16988	−0.584938	+	0.811078i	$0.698881\pi$
$284$	1.86615e9i	0.286862i
$285$	0	0
$286$	−6.05410e8	−0.0904868
$287$	− 3.04279e9i	− 0.448481i
$288$	0	0
$289$	5.04595e9	0.723356
$290$	2.43167e7i	0.00343806i
$291$	0	0
$292$	−2.64842e8	−0.0364296
$293$	4.54136e9i	0.616192i	0.951355	+	0.308096i	$0.0996918\pi$
$293$	4.54136e9i	0.616192i	−0.951355	+	0.308096i	$0.900308\pi$
$294$	0	0
$295$	−3.84052e9	−0.507109
$296$	− 6.40879e9i	− 0.834851i
$297$	0	0
$298$	−8.12006e9	−1.02966
$299$	− 8.44758e9i	− 1.05693i
$300$	0	0
$301$	4.04686e9	0.493006
$302$	2.76186e9i	0.332028i
$303$	0	0
$304$	−9.25786e8	−0.108397
$305$	− 2.87109e9i	− 0.331778i
$306$	0	0
$307$	−2.23711e9	−0.251845	−0.125923	−	0.992040i	$-0.540189\pi$
$307$	−2.23711e9	−0.251845	−0.125923	+	0.992040i	$0.540189\pi$
$308$	3.93675e8i	0.0437456i
$309$	0	0
$310$	1.62363e9	0.175808
$311$	1.18006e10i	1.26143i	0.776016	+	0.630713i	$0.217237\pi$
$311$	1.18006e10i	1.26143i	−0.776016	+	0.630713i	$0.782763\pi$
$312$	0	0
$313$	−1.78305e10	−1.85774	−0.928870	−	0.370405i	$-0.879219\pi$
$313$	−1.78305e10	−1.85774	−0.928870	+	0.370405i	$0.879219\pi$
$314$	− 5.46164e8i	− 0.0561829i
$315$	0	0
$316$	5.17761e9	0.519256
$317$	− 4.28295e9i	− 0.424137i	−0.977255	−	0.212068i	$-0.931980\pi$
$317$	− 4.28295e9i	− 0.424137i	0.977255	−	0.212068i	$-0.0680199\pi$
$318$	0	0
$319$	−3.82576e7	−0.00369450
$320$	− 1.38717e9i	− 0.132291i
$321$	0	0
$322$	2.63896e9	0.245476
$323$	− 4.70932e9i	− 0.432662i
$324$	0	0
$325$	−9.10824e9	−0.816396
$326$	− 6.45840e9i	− 0.571814i
$327$	0	0
$328$	−1.36251e10	−1.17718
$329$	7.18861e9i	0.613566i
$330$	0	0
$331$	−1.55202e10	−1.29296	−0.646481	−	0.762930i	$-0.723760\pi$
$331$	−1.55202e10	−1.29296	−0.646481	+	0.762930i	$0.723760\pi$
$332$	3.86322e9i	0.317978i
$333$	0	0
$334$	−1.21726e10	−0.978134
$335$	− 9.40003e8i	− 0.0746363i
$336$	0	0
$337$	−1.86578e10	−1.44657	−0.723287	−	0.690547i	$-0.757370\pi$
$337$	−1.86578e10	−1.44657	−0.723287	+	0.690547i	$0.757370\pi$
$338$	− 1.52069e9i	− 0.116513i
$339$	0	0
$340$	−1.38133e9	−0.103367
$341$	2.55446e9i	0.188921i
$342$	0	0
$343$	9.40067e9	0.679176
$344$	− 1.81211e10i	− 1.29405i
$345$	0	0
$346$	1.26400e10	0.881948
$347$	7.90715e8i	0.0545384i	0.999628	+	0.0272692i	$0.00868112\pi$
$347$	7.90715e8i	0.0545384i	−0.999628	+	0.0272692i	$0.991319\pi$
$348$	0	0
$349$	2.50802e10	1.69056	0.845278	−	0.534326i	$-0.179435\pi$
$349$	2.50802e10	1.69056	0.845278	+	0.534326i	$0.179435\pi$
$350$	− 2.84534e9i	− 0.189610i
$351$	0	0
$352$	2.81492e9	0.183356
$353$	2.21719e10i	1.42792i	0.700185	+	0.713961i	$0.253101\pi$
$353$	2.21719e10i	1.42792i	−0.700185	+	0.713961i	$0.746899\pi$
$354$	0	0
$355$	−1.96232e9	−0.123554
$356$	1.27803e10i	0.795687i
$357$	0	0
$358$	−6.41220e9	−0.390369
$359$	− 1.72279e9i	− 0.103718i	−0.998654	−	0.0518589i	$-0.983485\pi$
$359$	− 1.72279e9i	− 0.103718i	0.998654	−	0.0518589i	$-0.0165146\pi$
$360$	0	0
$361$	−5.49136e9	−0.323334
$362$	− 1.47346e9i	− 0.0858036i
$363$	0	0
$364$	3.84586e9	0.219072
$365$	− 2.78490e8i	− 0.0156906i
$366$	0	0
$367$	−2.29525e9	−0.126522	−0.0632611	−	0.997997i	$-0.520150\pi$
$367$	−2.29525e9	−0.126522	−0.0632611	+	0.997997i	$0.520150\pi$
$368$	2.86389e9i	0.156158i
$369$	0	0
$370$	2.71692e9	0.144967
$371$	1.05420e10i	0.556450i
$372$	0	0
$373$	9.21146e9	0.475875	0.237938	−	0.971280i	$-0.423529\pi$
$373$	9.21146e9	0.475875	0.237938	+	0.971280i	$0.423529\pi$
$374$	1.04405e9i	0.0533623i
$375$	0	0
$376$	3.21893e10	1.61050
$377$	3.73744e8i	0.0185016i
$378$	0	0
$379$	−1.60658e10	−0.778656	−0.389328	−	0.921099i	$-0.627293\pi$
$379$	−1.60658e10	−0.778656	−0.389328	+	0.921099i	$0.627293\pi$
$380$	− 3.37087e9i	− 0.161662i
$381$	0	0
$382$	1.79204e10	0.841579
$383$	− 1.51904e10i	− 0.705951i	−0.935633	−	0.352976i	$-0.885170\pi$
$383$	− 1.51904e10i	− 0.705951i	0.935633	−	0.352976i	$-0.114830\pi$
$384$	0	0
$385$	−4.13963e8	−0.0188416
$386$	8.88460e9i	0.400211i
$387$	0	0
$388$	9.42793e9	0.415996
$389$	2.81033e10i	1.22732i	0.789569	+	0.613662i	$0.210304\pi$
$389$	2.81033e10i	1.22732i	−0.789569	+	0.613662i	$0.789696\pi$
$390$	0	0
$391$	−1.45681e10	−0.623300
$392$	− 1.95572e10i	− 0.828253i
$393$	0	0
$394$	−4.75283e9	−0.197228
$395$	5.44444e9i	0.223648i
$396$	0	0
$397$	3.42573e10	1.37909	0.689543	−	0.724244i	$-0.257811\pi$
$397$	3.42573e10	1.37909	0.689543	+	0.724244i	$0.257811\pi$
$398$	1.06055e10i	0.422669i
$399$	0	0
$400$	3.08786e9	0.120620
$401$	− 2.12611e10i	− 0.822258i	−0.911577	−	0.411129i	$-0.865135\pi$
$401$	− 2.12611e10i	− 0.822258i	0.911577	−	0.411129i	$-0.134865\pi$
$402$	0	0
$403$	2.49548e10	0.946094
$404$	1.42283e10i	0.534107i
$405$	0	0
$406$	−1.16754e8	−0.00429704
$407$	4.27454e9i	0.155780i
$408$	0	0
$409$	8.96413e9	0.320343	0.160171	−	0.987089i	$-0.448795\pi$
$409$	8.96413e9	0.320343	0.160171	+	0.987089i	$0.448795\pi$
$410$	− 5.77615e9i	− 0.204411i
$411$	0	0
$412$	1.11799e10	0.388015
$413$	− 1.84399e10i	− 0.633808i
$414$	0	0
$415$	−4.06231e9	−0.136956
$416$	− 2.74993e10i	− 0.918222i
$417$	0	0
$418$	−2.54780e9	−0.0834566
$419$	− 5.17120e10i	− 1.67778i	−0.544300	−	0.838891i	$-0.683205\pi$
$419$	− 5.17120e10i	− 1.67778i	0.544300	−	0.838891i	$-0.316795\pi$
$420$	0	0
$421$	−3.51595e10	−1.11922	−0.559609	−	0.828757i	$-0.689049\pi$
$421$	−3.51595e10	−1.11922	−0.559609	+	0.828757i	$0.689049\pi$
$422$	2.88330e10i	0.909159i
$423$	0	0
$424$	4.72050e10	1.46058
$425$	1.57075e10i	0.481449i
$426$	0	0
$427$	1.37853e10	0.414672
$428$	8.06947e9i	0.240475i
$429$	0	0
$430$	7.68218e9	0.224704
$431$	4.11665e10i	1.19298i	0.802619	+	0.596492i	$0.203439\pi$
$431$	4.11665e10i	1.19298i	−0.802619	+	0.596492i	$0.796561\pi$
$432$	0	0
$433$	−2.99706e10	−0.852598	−0.426299	−	0.904582i	$-0.640183\pi$
$433$	−2.99706e10	−0.852598	−0.426299	+	0.904582i	$0.640183\pi$
$434$	7.79569e9i	0.219733i
$435$	0	0
$436$	4.38353e10	1.21305
$437$	− 3.55508e10i	− 0.974818i
$438$	0	0
$439$	−3.84956e10	−1.03646	−0.518231	−	0.855241i	$-0.673409\pi$
$439$	−3.84956e10	−1.03646	−0.518231	+	0.855241i	$0.673409\pi$
$440$	1.85365e9i	0.0494557i
$441$	0	0
$442$	1.01994e10	0.267231
$443$	1.63124e10i	0.423548i	0.977319	+	0.211774i	$0.0679241\pi$
$443$	1.63124e10i	0.423548i	−0.977319	+	0.211774i	$0.932076\pi$
$444$	0	0
$445$	−1.34390e10	−0.342709
$446$	2.75686e10i	0.696747i
$447$	0	0
$448$	6.66037e9	0.165343
$449$	− 6.80379e10i	− 1.67404i	−0.547174	−	0.837019i	$-0.684296\pi$
$449$	− 6.80379e10i	− 1.67404i	0.547174	−	0.837019i	$-0.315704\pi$
$450$	0	0
$451$	9.08765e9	0.219657
$452$	− 3.96172e10i	− 0.949139i
$453$	0	0
$454$	1.64537e10	0.387294
$455$	4.04405e9i	0.0943564i
$456$	0	0
$457$	4.67693e10	1.07225	0.536125	−	0.844138i	$-0.319887\pi$
$457$	4.67693e10	1.07225	0.536125	+	0.844138i	$0.319887\pi$
$458$	1.73782e9i	0.0394951i
$459$	0	0
$460$	−1.04277e10	−0.232893
$461$	1.57255e10i	0.348178i	0.984730	+	0.174089i	$0.0556980\pi$
$461$	1.57255e10i	0.348178i	−0.984730	+	0.174089i	$0.944302\pi$
$462$	0	0
$463$	−2.47842e9	−0.0539326	−0.0269663	−	0.999636i	$-0.508585\pi$
$463$	−2.47842e9	−0.0539326	−0.0269663	+	0.999636i	$0.508585\pi$
$464$	− 1.26706e8i	− 0.00273354i
$465$	0	0
$466$	−1.13658e10	−0.241022
$467$	− 4.52500e10i	− 0.951373i	−0.879615	−	0.475687i	$-0.842200\pi$
$467$	− 4.52500e10i	− 0.951373i	0.879615	−	0.475687i	$-0.157800\pi$
$468$	0	0
$469$	4.51333e9	0.0932838
$470$	1.36462e10i	0.279653i
$471$	0	0
$472$	−8.25704e10	−1.66363
$473$	1.20864e10i	0.241464i
$474$	0	0
$475$	−3.83311e10	−0.752968
$476$	− 6.63231e9i	− 0.129192i
$477$	0	0
$478$	3.53814e10	0.677741
$479$	− 8.22196e9i	− 0.156183i	−0.996946	−	0.0780914i	$-0.975117\pi$
$479$	− 8.22196e9i	− 0.156183i	0.996946	−	0.0780914i	$-0.0248826\pi$
$480$	0	0
$481$	4.17585e10	0.780125
$482$	4.57320e10i	0.847291i
$483$	0	0
$484$	3.58923e10	0.654063
$485$	9.91379e9i	0.179173i
$486$	0	0
$487$	−1.03191e11	−1.83453	−0.917266	−	0.398276i	$-0.869609\pi$
$487$	−1.03191e11	−1.83453	−0.917266	+	0.398276i	$0.869609\pi$
$488$	− 6.17280e10i	− 1.08844i
$489$	0	0
$490$	8.29102e9	0.143821
$491$	5.64706e10i	0.971620i	0.874064	+	0.485810i	$0.161475\pi$
$491$	5.64706e10i	0.971620i	−0.874064	+	0.485810i	$0.838525\pi$
$492$	0	0
$493$	6.44533e8	0.0109108
$494$	2.48898e10i	0.417940i
$495$	0	0
$496$	−8.46015e9	−0.139782
$497$	− 9.42190e9i	− 0.154423i
$498$	0	0
$499$	−1.13472e11	−1.83016	−0.915078	−	0.403277i	$-0.867871\pi$
$499$	−1.13472e11	−1.83016	−0.915078	+	0.403277i	$0.867871\pi$
$500$	2.35261e10i	0.376417i
$501$	0	0
$502$	−6.48381e10	−1.02098
$503$	1.07680e10i	0.168214i	0.996457	+	0.0841071i	$0.0268038\pi$
$503$	1.07680e10i	0.168214i	−0.996457	+	0.0841071i	$0.973196\pi$
$504$	0	0
$505$	−1.49616e10	−0.230045
$506$	7.88155e9i	0.120229i
$507$	0	0
$508$	3.43321e10	0.515520
$509$	1.26178e11i	1.87981i	0.341435	+	0.939905i	$0.389087\pi$
$509$	1.26178e11i	1.87981i	−0.341435	+	0.939905i	$0.610913\pi$
$510$	0	0
$511$	1.33714e9	0.0196108
$512$	1.79658e10i	0.261437i
$513$	0	0
$514$	−1.73121e10	−0.248025
$515$	1.17560e10i	0.167121i
$516$	0	0
$517$	−2.14696e10	−0.300512
$518$	1.30450e10i	0.181186i
$519$	0	0
$520$	1.81085e10	0.247668
$521$	− 4.35596e10i	− 0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$521$	− 4.35596e10i	− 0.591198i	0.955312	−	0.295599i	$-0.0955192\pi$
$522$	0	0
$523$	−7.05635e10	−0.943133	−0.471567	−	0.881830i	$-0.656311\pi$
$523$	−7.05635e10	−0.943133	−0.471567	+	0.881830i	$0.656311\pi$
$524$	− 5.36586e9i	− 0.0711728i
$525$	0	0
$526$	−4.51320e10	−0.589579
$527$	− 4.30354e10i	− 0.557935i
$528$	0	0
$529$	−3.16642e10	−0.404340
$530$	2.00119e10i	0.253621i
$531$	0	0
$532$	1.61849e10	0.202052
$533$	− 8.87784e10i	− 1.10001i
$534$	0	0
$535$	−8.48533e9	−0.103575
$536$	− 2.02099e10i	− 0.244853i
$537$	0	0
$538$	4.52901e9	0.0540597
$539$	1.30443e10i	0.154549i
$540$	0	0
$541$	−6.48118e10	−0.756598	−0.378299	−	0.925684i	$-0.623491\pi$
$541$	−6.48118e10	−0.756598	−0.378299	+	0.925684i	$0.623491\pi$
$542$	− 1.02780e10i	− 0.119100i
$543$	0	0
$544$	−4.74234e10	−0.541498
$545$	4.60943e10i	0.522470i
$546$	0	0
$547$	−1.16187e10	−0.129780	−0.0648901	−	0.997892i	$-0.520670\pi$
$547$	−1.16187e10	−0.129780	−0.0648901	+	0.997892i	$0.520670\pi$
$548$	− 5.37092e10i	− 0.595562i
$549$	0	0
$550$	8.49794e9	0.0928673
$551$	1.57286e9i	0.0170641i
$552$	0	0
$553$	−2.61410e10	−0.279525
$554$	2.26172e10i	0.240104i
$555$	0	0
$556$	−4.10497e10	−0.429547
$557$	− 7.67569e10i	− 0.797437i	−0.917073	−	0.398719i	$-0.869455\pi$
$557$	− 7.67569e10i	− 0.797437i	0.917073	−	0.398719i	$-0.130545\pi$
$558$	0	0
$559$	1.18074e11	1.20922
$560$	− 1.37101e9i	− 0.0139408i
$561$	0	0
$562$	5.10526e10	0.511767
$563$	− 6.25521e10i	− 0.622599i	−0.950312	−	0.311299i	$-0.899236\pi$
$563$	− 6.25521e10i	− 0.622599i	0.950312	−	0.311299i	$-0.100764\pi$
$564$	0	0
$565$	4.16589e10	0.408803
$566$	− 6.83944e10i	− 0.666430i
$567$	0	0
$568$	−4.21895e10	−0.405333
$569$	6.16316e10i	0.587969i	0.955810	+	0.293985i	$0.0949814\pi$
$569$	6.16316e10i	0.587969i	−0.955810	+	0.293985i	$0.905019\pi$
$570$	0	0
$571$	1.73991e11	1.63675	0.818374	−	0.574686i	$-0.194876\pi$
$571$	1.73991e11	1.63675	0.818374	+	0.574686i	$0.194876\pi$
$572$	1.14861e10i	0.107297i
$573$	0	0
$574$	2.77336e10	0.255481
$575$	1.18576e11i	1.08474i
$576$	0	0
$577$	1.61116e11	1.45357	0.726786	−	0.686864i	$-0.241013\pi$
$577$	1.61116e11	1.45357	0.726786	+	0.686864i	$0.241013\pi$
$578$	4.59915e10i	0.412066i
$579$	0	0
$580$	4.61348e8	0.00407677
$581$	− 1.95048e10i	− 0.171174i
$582$	0	0
$583$	−3.14848e10	−0.272538
$584$	− 5.98749e9i	− 0.0514746i
$585$	0	0
$586$	−4.13925e10	−0.351019
$587$	− 1.04941e11i	− 0.883880i	−0.897045	−	0.441940i	$-0.854290\pi$
$587$	− 1.04941e11i	− 0.883880i	0.897045	−	0.441940i	$-0.145710\pi$
$588$	0	0
$589$	1.05020e11	0.872589
$590$	− 3.50046e10i	− 0.288879i
$591$	0	0
$592$	−1.41569e10	−0.115261
$593$	− 2.84415e10i	− 0.230003i	−0.993365	−	0.115002i	$-0.963313\pi$
$593$	− 2.84415e10i	− 0.230003i	0.993365	−	0.115002i	$-0.0366873\pi$
$594$	0	0
$595$	6.97411e9	0.0556443
$596$	1.54057e11i	1.22095i
$597$	0	0
$598$	7.69959e10	0.602092
$599$	− 1.42403e11i	− 1.10614i	−0.833133	−	0.553072i	$-0.813455\pi$
$599$	− 1.42403e11i	− 1.10614i	0.833133	−	0.553072i	$-0.186545\pi$
$600$	0	0
$601$	−4.44715e10	−0.340866	−0.170433	−	0.985369i	$-0.554517\pi$
$601$	−4.44715e10	−0.340866	−0.170433	+	0.985369i	$0.554517\pi$
$602$	3.68853e10i	0.280845i
$603$	0	0
$604$	5.23992e10	0.393711
$605$	3.77420e10i	0.281711i
$606$	0	0
$607$	−2.18843e11	−1.61205	−0.806024	−	0.591883i	$-0.798385\pi$
$607$	−2.18843e11	−1.61205	−0.806024	+	0.591883i	$0.798385\pi$
$608$	− 1.15728e11i	− 0.846883i
$609$	0	0
$610$	2.61687e10	0.189001
$611$	2.09739e11i	1.50493i
$612$	0	0
$613$	2.20837e11	1.56397	0.781987	−	0.623295i	$-0.214206\pi$
$613$	2.20837e11	1.56397	0.781987	+	0.623295i	$0.214206\pi$
$614$	− 2.03902e10i	− 0.143466i
$615$	0	0
$616$	−8.90012e9	−0.0618120
$617$	− 1.36342e11i	− 0.940781i	−0.882458	−	0.470390i	$-0.844113\pi$
$617$	− 1.36342e11i	− 0.940781i	0.882458	−	0.470390i	$-0.155887\pi$
$618$	0	0
$619$	1.55549e11	1.05951	0.529755	−	0.848151i	$-0.322284\pi$
$619$	1.55549e11	1.05951	0.529755	+	0.848151i	$0.322284\pi$
$620$	− 3.08041e10i	− 0.208469i
$621$	0	0
$622$	−1.07557e11	−0.718582
$623$	− 6.45259e10i	− 0.428333i
$624$	0	0
$625$	1.14934e11	0.753229
$626$	− 1.62516e11i	− 1.05828i
$627$	0	0
$628$	−1.03621e10	−0.0666204
$629$	− 7.20139e10i	− 0.460059i
$630$	0	0
$631$	−5.86878e10	−0.370195	−0.185097	−	0.982720i	$-0.559260\pi$
$631$	−5.86878e10	−0.370195	−0.185097	+	0.982720i	$0.559260\pi$
$632$	1.17054e11i	0.733702i
$633$	0	0
$634$	3.90371e10	0.241613
$635$	3.61014e10i	0.222039i
$636$	0	0
$637$	1.27431e11	0.773960
$638$	− 3.48701e8i	− 0.00210460i
$639$	0	0
$640$	−3.76091e10	−0.224168
$641$	2.36986e11i	1.40375i	0.712300	+	0.701875i	$0.247654\pi$
$641$	2.36986e11i	1.40375i	−0.712300	+	0.701875i	$0.752346\pi$
$642$	0	0
$643$	4.28799e10	0.250848	0.125424	−	0.992103i	$-0.459971\pi$
$643$	4.28799e10	0.250848	0.125424	+	0.992103i	$0.459971\pi$
$644$	− 5.00675e10i	− 0.291080i
$645$	0	0
$646$	4.29233e10	0.246469
$647$	2.79793e11i	1.59668i	0.602204	+	0.798342i	$0.294289\pi$
$647$	2.79793e11i	1.59668i	−0.602204	+	0.798342i	$0.705711\pi$
$648$	0	0
$649$	5.50728e10	0.310426
$650$	− 8.30174e10i	− 0.465067i
$651$	0	0
$652$	−1.22532e11	−0.678044
$653$	1.86068e11i	1.02334i	0.859183	+	0.511669i	$0.170972\pi$
$653$	1.86068e11i	1.02334i	−0.859183	+	0.511669i	$0.829028\pi$
$654$	0	0
$655$	5.64239e9	0.0306547
$656$	3.00975e10i	0.162523i
$657$	0	0
$658$	−6.55209e10	−0.349523
$659$	− 1.52675e11i	− 0.809517i	−0.914424	−	0.404758i	$-0.867356\pi$
$659$	− 1.52675e11i	− 0.809517i	0.914424	−	0.404758i	$-0.132644\pi$
$660$	0	0
$661$	2.24390e11	1.17543	0.587717	−	0.809066i	$-0.300027\pi$
$661$	2.24390e11	1.17543	0.587717	+	0.809066i	$0.300027\pi$
$662$	− 1.41460e11i	− 0.736548i
$663$	0	0
$664$	−8.73390e10	−0.449299
$665$	1.70190e10i	0.0870256i
$666$	0	0
$667$	4.86560e9	0.0245829
$668$	2.30944e11i	1.15985i
$669$	0	0
$670$	8.56769e9	0.0425172
$671$	4.11714e10i	0.203098i
$672$	0	0
$673$	3.64364e11	1.77613	0.888066	−	0.459716i	$-0.152049\pi$
$673$	3.64364e11	1.77613	0.888066	+	0.459716i	$0.152049\pi$
$674$	− 1.70057e11i	− 0.824054i
$675$	0	0
$676$	−2.88512e10	−0.138158
$677$	− 6.27441e10i	− 0.298688i	−0.988785	−	0.149344i	$-0.952284\pi$
$677$	− 6.27441e10i	− 0.298688i	0.988785	−	0.149344i	$-0.0477162\pi$
$678$	0	0
$679$	−4.76001e10	−0.223939
$680$	− 3.12288e10i	− 0.146056i
$681$	0	0
$682$	−2.32827e10	−0.107621
$683$	1.33372e11i	0.612888i	0.951889	+	0.306444i	$0.0991392\pi$
$683$	1.33372e11i	0.612888i	−0.951889	+	0.306444i	$0.900861\pi$
$684$	0	0
$685$	5.64771e10	0.256514
$686$	8.56828e10i	0.386899i
$687$	0	0
$688$	−4.00292e10	−0.178658
$689$	3.07579e11i	1.36483i
$690$	0	0
$691$	−2.10513e11	−0.923353	−0.461676	−	0.887048i	$-0.652752\pi$
$691$	−2.10513e11	−0.923353	−0.461676	+	0.887048i	$0.652752\pi$
$692$	− 2.39812e11i	− 1.04579i
$693$	0	0
$694$	−7.20700e9	−0.0310683
$695$	− 4.31652e10i	− 0.185010i
$696$	0	0
$697$	−1.53101e11	−0.648706
$698$	2.28595e11i	0.963041i
$699$	0	0
$700$	−5.39831e10	−0.224836
$701$	− 1.97734e11i	− 0.818859i	−0.912342	−	0.409429i	$-0.865728\pi$
$701$	− 1.97734e11i	− 0.818859i	0.912342	−	0.409429i	$-0.134272\pi$
$702$	0	0
$703$	1.75736e11	0.719515
$704$	1.98919e10i	0.0809817i
$705$	0	0
$706$	−2.02087e11	−0.813429
$707$	− 7.18367e10i	− 0.287520i
$708$	0	0
$709$	8.72608e10	0.345330	0.172665	−	0.984981i	$-0.444762\pi$
$709$	8.72608e10	0.345330	0.172665	+	0.984981i	$0.444762\pi$
$710$	− 1.78857e10i	− 0.0703836i
$711$	0	0
$712$	−2.88935e11	−1.12430
$713$	− 3.24875e11i	− 1.25707i
$714$	0	0
$715$	−1.20780e10	−0.0462138
$716$	1.21655e11i	0.462890i
$717$	0	0
$718$	1.57024e10	0.0590838
$719$	− 7.40213e10i	− 0.276975i	−0.990364	−	0.138488i	$-0.955776\pi$
$719$	− 7.40213e10i	− 0.276975i	0.990364	−	0.138488i	$-0.0442241\pi$
$720$	0	0
$721$	−5.64455e10	−0.208876
$722$	− 5.00512e10i	− 0.184190i
$723$	0	0
$724$	−2.79552e10	−0.101744
$725$	− 5.24612e9i	− 0.0189883i
$726$	0	0
$727$	−4.22377e11	−1.51204	−0.756019	−	0.654550i	$-0.772858\pi$
$727$	−4.22377e11	−1.51204	−0.756019	+	0.654550i	$0.772858\pi$
$728$	8.69464e10i	0.309547i
$729$	0	0
$730$	2.53831e9	0.00893827
$731$	− 2.03622e11i	− 0.713108i
$732$	0	0
$733$	4.80823e10	0.166560	0.0832798	−	0.996526i	$-0.473460\pi$
$733$	4.80823e10	0.166560	0.0832798	+	0.996526i	$0.473460\pi$
$734$	− 2.09202e10i	− 0.0720745i
$735$	0	0
$736$	−3.58000e11	−1.22003
$737$	1.34796e10i	0.0456885i
$738$	0	0
$739$	−3.18346e11	−1.06739	−0.533693	−	0.845678i	$-0.679196\pi$
$739$	−3.18346e11	−1.06739	−0.533693	+	0.845678i	$0.679196\pi$
$740$	− 5.15465e10i	− 0.171899i
$741$	0	0
$742$	−9.60852e10	−0.316987
$743$	2.47368e11i	0.811686i	0.913943	+	0.405843i	$0.133022\pi$
$743$	2.47368e11i	0.811686i	−0.913943	+	0.405843i	$0.866978\pi$
$744$	0	0
$745$	−1.61997e11	−0.525873
$746$	8.39582e10i	0.271087i
$747$	0	0
$748$	1.98082e10	0.0632758
$749$	− 4.07415e10i	− 0.129452i
$750$	0	0
$751$	−3.11386e10	−0.0978903	−0.0489452	−	0.998801i	$-0.515586\pi$
$751$	−3.11386e10	−0.0978903	−0.0489452	+	0.998801i	$0.515586\pi$
$752$	− 7.11056e10i	− 0.222347i
$753$	0	0
$754$	−3.40650e9	−0.0105396
$755$	5.50996e10i	0.169575i
$756$	0	0
$757$	2.81381e10	0.0856862	0.0428431	−	0.999082i	$-0.486358\pi$
$757$	2.81381e10	0.0856862	0.0428431	+	0.999082i	$0.486358\pi$
$758$	− 1.46433e11i	− 0.443569i
$759$	0	0
$760$	7.62079e10	0.228426
$761$	5.60784e11i	1.67208i	0.548670	+	0.836039i	$0.315134\pi$
$761$	5.60784e11i	1.67208i	−0.548670	+	0.836039i	$0.684866\pi$
$762$	0	0
$763$	−2.21318e11	−0.653007
$764$	− 3.39994e11i	− 0.997926i
$765$	0	0
$766$	1.38454e11	0.402151
$767$	− 5.38013e11i	− 1.55457i
$768$	0	0
$769$	2.88371e11	0.824607	0.412303	−	0.911047i	$-0.364724\pi$
$769$	2.88371e11	0.824607	0.412303	+	0.911047i	$0.364724\pi$
$770$	− 3.77308e9i	− 0.0107333i
$771$	0	0
$772$	1.68563e11	0.474561
$773$	− 2.78651e11i	− 0.780445i	−0.920721	−	0.390222i	$-0.872398\pi$
$773$	− 2.78651e11i	− 0.780445i	0.920721	−	0.390222i	$-0.127602\pi$
$774$	0	0
$775$	−3.50283e11	−0.970984
$776$	2.13145e11i	0.587797i
$777$	0	0
$778$	−2.56149e11	−0.699156
$779$	− 3.73614e11i	− 1.01455i
$780$	0	0
$781$	2.81396e10	0.0756334
$782$	− 1.32782e11i	− 0.355068i
$783$	0	0
$784$	−4.32016e10	−0.114350
$785$	− 1.08961e10i	− 0.0286940i
$786$	0	0
$787$	−6.16668e11	−1.60751	−0.803753	−	0.594963i	$-0.797167\pi$
$787$	−6.16668e11	−1.60751	−0.803753	+	0.594963i	$0.797167\pi$
$788$	9.01728e10i	0.233868i
$789$	0	0
$790$	−4.96236e10	−0.127403
$791$	2.00021e11i	0.510940i
$792$	0	0
$793$	4.02208e11	1.01709
$794$	3.12240e11i	0.785609i
$795$	0	0
$796$	2.01213e11	0.501191
$797$	− 3.10128e10i	− 0.0768614i	−0.999261	−	0.0384307i	$-0.987764\pi$
$797$	− 3.10128e10i	− 0.0768614i	0.999261	−	0.0384307i	$-0.0122359\pi$
$798$	0	0
$799$	3.61702e11	0.887492
$800$	3.85998e11i	0.942379i
$801$	0	0
$802$	1.93785e11	0.468406
$803$	3.99354e9i	0.00960496i
$804$	0	0
$805$	5.26477e10	0.125371
$806$	2.27452e11i	0.538951i
$807$	0	0
$808$	−3.21671e11	−0.754687
$809$	− 7.09731e11i	− 1.65691i	−0.560053	−	0.828457i	$-0.689219\pi$
$809$	− 7.09731e11i	− 1.65691i	0.560053	−	0.828457i	$-0.310781\pi$
$810$	0	0
$811$	−1.66915e11	−0.385845	−0.192922	−	0.981214i	$-0.561797\pi$
$811$	−1.66915e11	−0.385845	−0.192922	+	0.981214i	$0.561797\pi$
$812$	2.21512e9i	0.00509533i
$813$	0	0
$814$	−3.89604e10	−0.0887414
$815$	− 1.28846e11i	− 0.292039i
$816$	0	0
$817$	4.96901e11	1.11527
$818$	8.17040e10i	0.182486i
$819$	0	0
$820$	−1.09588e11	−0.242385
$821$	5.28938e11i	1.16421i	0.813113	+	0.582106i	$0.197771\pi$
$821$	5.28938e11i	1.16421i	−0.813113	+	0.582106i	$0.802229\pi$
$822$	0	0
$823$	3.82958e11	0.834740	0.417370	−	0.908737i	$-0.362952\pi$
$823$	3.82958e11	0.834740	0.417370	+	0.908737i	$0.362952\pi$
$824$	2.52752e11i	0.548260i
$825$	0	0
$826$	1.68071e11	0.361055
$827$	7.05611e11i	1.50849i	0.656591	+	0.754247i	$0.271998\pi$
$827$	7.05611e11i	1.50849i	−0.656591	+	0.754247i	$0.728002\pi$
$828$	0	0
$829$	−2.63063e10	−0.0556982	−0.0278491	−	0.999612i	$-0.508866\pi$
$829$	−2.63063e10	−0.0556982	−0.0278491	+	0.999612i	$0.508866\pi$
$830$	− 3.70261e10i	− 0.0780182i
$831$	0	0
$832$	1.94327e11	0.405546
$833$	− 2.19760e11i	− 0.456423i
$834$	0	0
$835$	−2.42846e11	−0.499557
$836$	4.83380e10i	0.0989610i
$837$	0	0
$838$	4.71331e11	0.955763
$839$	5.22454e11i	1.05439i	0.849745	+	0.527194i	$0.176756\pi$
$839$	5.22454e11i	1.05439i	−0.849745	+	0.527194i	$0.823244\pi$
$840$	0	0
$841$	5.00031e11	0.999570
$842$	− 3.20463e11i	− 0.637572i
$843$	0	0
$844$	5.47032e11	1.07806
$845$	− 3.03381e10i	− 0.0595060i
$846$	0	0
$847$	−1.81215e11	−0.352095
$848$	− 1.04275e11i	− 0.201649i
$849$	0	0
$850$	−1.43166e11	−0.274262
$851$	− 5.43635e11i	− 1.03655i
$852$	0	0
$853$	8.00236e11	1.51155	0.755774	−	0.654833i	$-0.227261\pi$
$853$	8.00236e11	1.51155	0.755774	+	0.654833i	$0.227261\pi$
$854$	1.25647e11i	0.236221i
$855$	0	0
$856$	−1.82433e11	−0.339788
$857$	2.96033e11i	0.548803i	0.961615	+	0.274401i	$0.0884797\pi$
$857$	2.96033e11i	0.548803i	−0.961615	+	0.274401i	$0.911520\pi$
$858$	0	0
$859$	−3.75039e11	−0.688818	−0.344409	−	0.938820i	$-0.611921\pi$
$859$	−3.75039e11	−0.688818	−0.344409	+	0.938820i	$0.611921\pi$
$860$	− 1.45750e11i	− 0.266449i
$861$	0	0
$862$	−3.75214e11	−0.679594
$863$	4.47076e11i	0.806005i	0.915199	+	0.403002i	$0.132033\pi$
$863$	4.47076e11i	0.806005i	−0.915199	+	0.403002i	$0.867967\pi$
$864$	0	0
$865$	2.52171e11	0.450433
$866$	− 2.73169e11i	− 0.485690i
$867$	0	0
$868$	1.47903e11	0.260555
$869$	− 7.80730e10i	− 0.136906i
$870$	0	0
$871$	1.31684e11	0.228802
$872$	9.91019e11i	1.71402i
$873$	0	0
$874$	3.24029e11	0.555313
$875$	− 1.18779e11i	− 0.202632i
$876$	0	0
$877$	3.50046e10	0.0591735	0.0295867	−	0.999562i	$-0.490581\pi$
$877$	3.50046e10	0.0591735	0.0295867	+	0.999562i	$0.490581\pi$
$878$	− 3.50870e11i	− 0.590430i
$879$	0	0
$880$	4.09468e9	0.00682793
$881$	− 5.09104e11i	− 0.845090i	−0.906342	−	0.422545i	$-0.861137\pi$
$881$	− 5.09104e11i	− 0.845090i	0.906342	−	0.422545i	$-0.138863\pi$
$882$	0	0
$883$	−8.34773e11	−1.37317	−0.686587	−	0.727048i	$-0.740892\pi$
$883$	−8.34773e11	−1.37317	−0.686587	+	0.727048i	$0.740892\pi$
$884$	− 1.93508e11i	− 0.316877i
$885$	0	0
$886$	−1.48680e11	−0.241278
$887$	− 1.15850e12i	− 1.87155i	−0.352603	−	0.935773i	$-0.614704\pi$
$887$	− 1.15850e12i	− 1.87155i	0.352603	−	0.935773i	$-0.385296\pi$
$888$	0	0
$889$	−1.73338e11	−0.277514
$890$	− 1.22490e11i	− 0.195227i
$891$	0	0
$892$	5.23044e11	0.826187
$893$	8.82666e11i	1.38800i
$894$	0	0
$895$	−1.27925e11	−0.199371
$896$	− 1.80576e11i	− 0.280175i
$897$	0	0
$898$	6.20134e11	0.953631
$899$	1.43734e10i	0.0220049i
$900$	0	0
$901$	5.30430e11	0.804876
$902$	8.28297e10i	0.125130i
$903$	0	0
$904$	8.95657e11	1.34112
$905$	− 2.93959e10i	− 0.0438220i
$906$	0	0
$907$	−4.11434e11	−0.607954	−0.303977	−	0.952679i	$-0.598315\pi$
$907$	−4.11434e11	−0.607954	−0.303977	+	0.952679i	$0.598315\pi$
$908$	− 3.12167e11i	− 0.459245i
$909$	0	0
$910$	−3.68597e10	−0.0537510
$911$	− 4.57566e10i	− 0.0664324i	−0.999448	−	0.0332162i	$-0.989425\pi$
$911$	− 4.57566e10i	− 0.0664324i	0.999448	−	0.0332162i	$-0.0105750\pi$
$912$	0	0
$913$	5.82534e10	0.0838374
$914$	4.26281e11i	0.610817i
$915$	0	0
$916$	3.29707e10	0.0468324
$917$	2.70914e10i	0.0383137i
$918$	0	0
$919$	1.14471e12	1.60485	0.802425	−	0.596753i	$-0.203543\pi$
$919$	1.14471e12	1.60485	0.802425	+	0.596753i	$0.203543\pi$
$920$	− 2.35747e11i	− 0.329074i
$921$	0	0
$922$	−1.43331e11	−0.198342
$923$	− 2.74899e11i	− 0.378762i
$924$	0	0
$925$	−5.86150e11	−0.800649
$926$	− 2.25897e10i	− 0.0307232i
$927$	0	0
$928$	1.58389e10	0.0213566
$929$	4.85565e11i	0.651906i	0.945386	+	0.325953i	$0.105685\pi$
$929$	4.85565e11i	0.651906i	−0.945386	+	0.325953i	$0.894315\pi$
$930$	0	0
$931$	5.36281e11	0.713829
$932$	2.15637e11i	0.285799i
$933$	0	0
$934$	4.12433e11	0.541958
$935$	2.08290e10i	0.0272534i
$936$	0	0
$937$	−1.18902e12	−1.54252	−0.771258	−	0.636523i	$-0.780372\pi$
$937$	−1.18902e12	−1.54252	−0.771258	+	0.636523i	$0.780372\pi$
$938$	4.11370e10i	0.0531399i
$939$	0	0
$940$	2.58901e11	0.331607
$941$	7.54055e11i	0.961711i	0.876800	+	0.480856i	$0.159674\pi$
$941$	7.54055e11i	0.961711i	−0.876800	+	0.480856i	$0.840326\pi$
$942$	0	0
$943$	−1.15576e12	−1.46158
$944$	1.82397e11i	0.229683i
$945$	0	0
$946$	−1.10162e11	−0.137552
$947$	− 4.73039e11i	− 0.588162i	−0.955781	−	0.294081i	$-0.904986\pi$
$947$	− 4.73039e11i	− 0.588162i	0.955781	−	0.294081i	$-0.0950135\pi$
$948$	0	0
$949$	3.90134e10	0.0481004
$950$	− 3.49370e11i	− 0.428935i
$951$	0	0
$952$	1.49942e11	0.182547
$953$	− 1.57467e12i	− 1.90906i	−0.298118	−	0.954529i	$-0.596359\pi$
$953$	− 1.57467e12i	− 1.90906i	0.298118	−	0.954529i	$-0.403641\pi$
$954$	0	0
$955$	3.57516e11	0.429815
$956$	− 6.71272e11i	− 0.803650i
$957$	0	0
$958$	7.49394e10	0.0889710
$959$	2.71170e11i	0.320602i
$960$	0	0
$961$	1.06816e11	0.125240
$962$	3.80609e11i	0.444405i
$963$	0	0
$964$	8.67649e11	1.00470
$965$	1.77249e11i	0.204398i
$966$	0	0
$967$	−1.36908e12	−1.56575	−0.782875	−	0.622179i	$-0.786248\pi$
$967$	−1.36908e12	−1.56575	−0.782875	+	0.622179i	$0.786248\pi$
$968$	8.11445e11i	0.924183i
$969$	0	0
$970$	−9.03597e10	−0.102068
$971$	6.81686e11i	0.766845i	0.923573	+	0.383422i	$0.125255\pi$
$971$	6.81686e11i	0.766845i	−0.923573	+	0.383422i	$0.874745\pi$
$972$	0	0
$973$	2.07253e11	0.231233
$974$	− 9.40537e11i	− 1.04506i
$975$	0	0
$976$	−1.36356e11	−0.150271
$977$	− 1.69136e11i	− 0.185634i	−0.995683	−	0.0928170i	$-0.970413\pi$
$977$	− 1.69136e11i	− 0.185634i	0.995683	−	0.0928170i	$-0.0295872\pi$
$978$	0	0
$979$	1.92714e11	0.209789
$980$	− 1.57301e11i	− 0.170540i
$981$	0	0
$982$	−5.14704e11	−0.553492
$983$	5.53061e11i	0.592323i	0.955138	+	0.296161i	$0.0957067\pi$
$983$	5.53061e11i	0.592323i	−0.955138	+	0.296161i	$0.904293\pi$
$984$	0	0
$985$	−9.48199e10	−0.100729
$986$	5.87463e9i	0.00621545i
$987$	0	0
$988$	4.72220e11	0.495584
$989$	− 1.53715e12i	− 1.60668i
$990$	0	0
$991$	−1.81811e12	−1.88506	−0.942529	−	0.334125i	$-0.891559\pi$
$991$	−1.81811e12	−1.88506	−0.942529	+	0.334125i	$0.891559\pi$
$992$	− 1.05756e12i	− 1.09209i
$993$	0	0
$994$	8.58763e10	0.0879686
$995$	2.11582e11i	0.215867i
$996$	0	0
$997$	−1.18104e12	−1.19532	−0.597660	−	0.801750i	$-0.703903\pi$
$997$	−1.18104e12	−1.19532	−0.597660	+	0.801750i	$0.703903\pi$
$998$	− 1.03425e12i	− 1.04256i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.b.b.80.10	yes	16
3.2	odd	2	inner	81.9.b.b.80.7	✓	16
9.2	odd	6		81.9.d.g.53.7		32
9.4	even	3		81.9.d.g.26.7		32
9.5	odd	6		81.9.d.g.26.10		32
9.7	even	3		81.9.d.g.53.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.9.b.b.80.7	✓	16	3.2	odd	2	inner
81.9.b.b.80.10	yes	16	1.1	even	1	trivial
81.9.d.g.26.7		32	9.4	even	3
81.9.d.g.26.10		32	9.5	odd	6
81.9.d.g.53.7		32	9.2	odd	6
81.9.d.g.53.10		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)

\(f(q)\)	\(=\)	\(q+9.11454i q^{2} +172.925 q^{4} +181.837i q^{5} -873.072 q^{7} +3909.46i q^{8} -1657.36 q^{10} -2607.53i q^{11} -25473.3 q^{13} -7957.65i q^{14} +8635.93 q^{16} +43929.5i q^{17} -107202. q^{19} +31444.1i q^{20} +23766.4 q^{22} +331625. i q^{23} +357560. q^{25} -232177. i q^{26} -150976. q^{28} -14672.0i q^{29} -979646. q^{31} +1.07953e6i q^{32} -400398. q^{34} -158757. i q^{35} -1.63930e6 q^{37} -977094. i q^{38} -710883. q^{40} +3.48515e6i q^{41} -4.63519e6 q^{43} -450907. i q^{44} -3.02261e6 q^{46} -8.23369e6i q^{47} -5.00255e6 q^{49} +3.25900e6i q^{50} -4.40497e6 q^{52} -1.20746e7i q^{53} +474145. q^{55} -3.41324e6i q^{56} +133728. q^{58} +2.11207e7i q^{59} -1.57894e7 q^{61} -8.92903e6i q^{62} -7.62865e6 q^{64} -4.63198e6i q^{65} -5.16949e6 q^{67} +7.59652e6i q^{68} +1.44699e6 q^{70} +1.07917e7i q^{71} -1.53154e6 q^{73} -1.49415e7i q^{74} -1.85379e7 q^{76} +2.27656e6i q^{77} +2.99414e7 q^{79} +1.57033e6i q^{80} -3.17656e7 q^{82} +2.23404e7i q^{83} -7.98801e6 q^{85} -4.22477e7i q^{86} +1.01940e7 q^{88} +7.39067e7i q^{89} +2.22400e7 q^{91} +5.73463e7i q^{92} +7.50463e7 q^{94} -1.94932e7i q^{95} +5.45203e7 q^{97} -4.55959e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2048 q^{4} + 3692 q^{7} + 10752 q^{10} + 63860 q^{13} + 95116 q^{16} + 185108 q^{19} - 691980 q^{22} - 541712 q^{25} - 997132 q^{28} + 571136 q^{31} + 1027656 q^{34} + 4354268 q^{37} - 2973768 q^{40}+ \cdots - 133878688 q^{97}+O(q^{100}) \) 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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