LMFDB - Embedded newform 54.21.b.c.53.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,21,Mod(53,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.53"); S:= CuspForms(chi, 21); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 21, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	54.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$136.897433155$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 64181120673558 x^{10} + \cdots + 59\!\cdots\!25 $ x^12 + 64181120673558x^10 + 1147499603855864639145548799x^8 + 4865528987041184601846573424159143560500x^6 + 7351376169346404374160247268269786722486327446859375x^4 + 3743587722766332549450519467149040800968992595997641252058593750*x^2 + 591904334199598449749405348007426564811862653246069965388281744211181640625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{63}\cdot 3^{90} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.12
Root			$5.97401e6i$ of defining polynomial
Character	$\chi$	$=$	54.53
Dual form			54.21.b.c.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+724.077i q^{2} -524288. q^{4} +1.79220e7i q^{5} +3.70310e8 q^{7} -3.79625e8i q^{8} -1.29769e10 q^{10} -7.93961e9i q^{11} +8.82019e10 q^{13} +2.68133e11i q^{14} +2.74878e11 q^{16} -1.27952e12i q^{17} +6.13964e11 q^{19} -9.39630e12i q^{20} +5.74889e12 q^{22} +5.25696e13i q^{23} -2.25831e14 q^{25} +6.38650e13i q^{26} -1.94149e14 q^{28} +4.94778e14i q^{29} +4.08497e14 q^{31} +1.99033e14i q^{32} +9.26469e14 q^{34} +6.63671e15i q^{35} +8.86884e15 q^{37} +4.44558e14i q^{38} +6.80365e15 q^{40} +1.66486e16i q^{41} -5.50910e15 q^{43} +4.16264e15i q^{44} -3.80644e16 q^{46} -6.38595e16i q^{47} +5.73373e16 q^{49} -1.63519e17i q^{50} -4.62432e16 q^{52} +2.19038e17i q^{53} +1.42294e17 q^{55} -1.40579e17i q^{56} -3.58257e17 q^{58} -6.16324e17i q^{59} +4.13350e17 q^{61} +2.95784e17i q^{62} -1.44115e17 q^{64} +1.58076e18i q^{65} +7.34220e17 q^{67} +6.70835e17i q^{68} -4.80549e18 q^{70} +5.12039e18i q^{71} +5.57613e18 q^{73} +6.42173e18i q^{74} -3.21894e17 q^{76} -2.94012e18i q^{77} -9.30637e18 q^{79} +4.92637e18i q^{80} -1.20548e19 q^{82} +1.56494e19i q^{83} +2.29315e19 q^{85} -3.98902e18i q^{86} -3.01407e18 q^{88} -2.32089e19i q^{89} +3.26621e19 q^{91} -2.75616e19i q^{92} +4.62392e19 q^{94} +1.10035e19i q^{95} -1.26064e20 q^{97} +4.15167e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6291456 q^{4} + 355856172 q^{7} - 5360984064 q^{10} + 374332013160 q^{13} + 3298534883328 q^{16} + 13268452496064 q^{19} + 64109345587200 q^{22} - 10850992436544 q^{25} - 186571120705536 q^{28} + 13\!\cdots\!76 q^{31}+ \cdots - 30\!\cdots\!60 q^{97}+O(q^{100}) $ 12 * q - 6291456 * q^4 + 355856172 * q^7 - 5360984064 * q^10 + 374332013160 * q^13 + 3298534883328 * q^16 + 13268452496064 * q^19 + 64109345587200 * q^22 - 10850992436544 * q^25 - 186571120705536 * q^28 + 1341631815613476 * q^31 - 1150892216451072 * q^34 - 1840381413631248 * q^37 + 2810699612946432 * q^40 - 58876514549555304 * q^43 - 52022884060053504 * q^46 + 301701288785631840 * q^49 - 196257782515630080 * q^52 + 1198488617517746484 * q^55 - 952998745417777152 * q^58 - 611525981019002448 * q^61 - 1729382256910270464 * q^64 - 3378608356010016504 * q^67 - 10123347229078487040 * q^70 + 35504687328043033068 * q^73 - 6956490422256402432 * q^76 + 15118277214382580040 * q^79 - 16372057824399605760 * q^82 - 2077217010606501720 * q^85 - 33611760579221913600 * q^88 - 154840755366303827352 * q^91 + 150175394882225012736 * q^94 - 3033444647600404860 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$-1$

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 $

$2$	724.077i	0.707107i
$2$	724.077i	0.707107i
$3$	0	0
$3$	0	0
$4$	−524288.	−0.500000
$5$	1.79220e7i	1.83521i	0.397488	+	0.917607i	$0.369882\pi$
$5$	1.79220e7i	1.83521i	−0.397488	+	0.917607i	$0.630118\pi$
$6$	0	0
$7$	3.70310e8	1.31095	0.655474	−	0.755218i	$-0.272469\pi$
$7$	3.70310e8	1.31095	0.655474	+	0.755218i	$0.272469\pi$
$8$	− 3.79625e8i	− 0.353553i
$9$	0	0
$10$	−1.29769e10	−1.29769
$11$	− 7.93961e9i	− 0.306106i	−0.988218	−	0.153053i	$-0.951089\pi$
$11$	− 7.93961e9i	− 0.306106i	0.988218	−	0.153053i	$-0.0489106\pi$
$12$	0	0
$13$	8.82019e10	0.639800	0.319900	−	0.947451i	$-0.396351\pi$
$13$	8.82019e10	0.639800	0.319900	+	0.947451i	$0.396351\pi$
$14$	2.68133e11i	0.926980i
$15$	0	0
$16$	2.74878e11	0.250000
$17$	− 1.27952e12i	− 0.634683i	−0.948311	−	0.317341i	$-0.897210\pi$
$17$	− 1.27952e12i	− 0.634683i	0.948311	−	0.317341i	$-0.102790\pi$
$18$	0	0
$19$	6.13964e11	0.100140	0.0500699	−	0.998746i	$-0.484056\pi$
$19$	6.13964e11	0.100140	0.0500699	+	0.998746i	$0.484056\pi$
$20$	− 9.39630e12i	− 0.917607i
$21$	0	0
$22$	5.74889e12	0.216450
$23$	5.25696e13i	1.26898i	0.772930	+	0.634492i	$0.218791\pi$
$23$	5.25696e13i	1.26898i	−0.772930	+	0.634492i	$0.781209\pi$
$24$	0	0
$25$	−2.25831e14	−2.36801
$26$	6.38650e13i	0.452407i
$27$	0	0
$28$	−1.94149e14	−0.655474
$29$	4.94778e14i	1.17606i	0.808839	+	0.588031i	$0.200097\pi$
$29$	4.94778e14i	1.17606i	−0.808839	+	0.588031i	$0.799903\pi$
$30$	0	0
$31$	4.08497e14	0.498393	0.249197	−	0.968453i	$-0.419833\pi$
$31$	4.08497e14	0.498393	0.249197	+	0.968453i	$0.419833\pi$
$32$	1.99033e14i	0.176777i
$33$	0	0
$34$	9.26469e14	0.448789
$35$	6.63671e15i	2.40587i
$36$	0	0
$37$	8.86884e15	1.84438	0.922188	−	0.386741i	$-0.126399\pi$
$37$	8.86884e15	1.84438	0.922188	+	0.386741i	$0.126399\pi$
$38$	4.44558e14i	0.0708096i
$39$	0	0
$40$	6.80365e15	0.648846
$41$	1.66486e16i	1.24033i	0.784471	+	0.620166i	$0.212935\pi$
$41$	1.66486e16i	1.24033i	−0.784471	+	0.620166i	$0.787065\pi$
$42$	0	0
$43$	−5.50910e15	−0.254915	−0.127458	−	0.991844i	$-0.540682\pi$
$43$	−5.50910e15	−0.254915	−0.127458	+	0.991844i	$0.540682\pi$
$44$	4.16264e15i	0.153053i
$45$	0	0
$46$	−3.80644e16	−0.897307
$47$	− 6.38595e16i	− 1.21408i	−0.794671	−	0.607040i	$-0.792357\pi$
$47$	− 6.38595e16i	− 1.21408i	0.794671	−	0.607040i	$-0.207643\pi$
$48$	0	0
$49$	5.73373e16	0.718582
$50$	− 1.63519e17i	− 1.67444i
$51$	0	0
$52$	−4.62432e16	−0.319900
$53$	2.19038e17i	1.25245i	0.779642	+	0.626225i	$0.215401\pi$
$53$	2.19038e17i	1.25245i	−0.779642	+	0.626225i	$0.784599\pi$
$54$	0	0
$55$	1.42294e17	0.561771
$56$	− 1.40579e17i	− 0.463490i
$57$	0	0
$58$	−3.58257e17	−0.831601
$59$	− 6.16324e17i	− 1.20584i	−0.797803	−	0.602919i	$-0.794004\pi$
$59$	− 6.16324e17i	− 1.20584i	0.797803	−	0.602919i	$-0.205996\pi$
$60$	0	0
$61$	4.13350e17	0.579455	0.289728	−	0.957109i	$-0.406435\pi$
$61$	4.13350e17	0.579455	0.289728	+	0.957109i	$0.406435\pi$
$62$	2.95784e17i	0.352417i
$63$	0	0
$64$	−1.44115e17	−0.125000
$65$	1.58076e18i	1.17417i
$66$	0	0
$67$	7.34220e17	0.402789	0.201395	−	0.979510i	$-0.435453\pi$
$67$	7.34220e17	0.402789	0.201395	+	0.979510i	$0.435453\pi$
$68$	6.70835e17i	0.317341i
$69$	0	0
$70$	−4.80549e18	−1.70121
$71$	5.12039e18i	1.57297i	0.617612	+	0.786483i	$0.288100\pi$
$71$	5.12039e18i	1.57297i	−0.617612	+	0.786483i	$0.711900\pi$
$72$	0	0
$73$	5.57613e18	1.29749	0.648745	−	0.761006i	$-0.275294\pi$
$73$	5.57613e18	1.29749	0.648745	+	0.761006i	$0.275294\pi$
$74$	6.42173e18i	1.30417i
$75$	0	0
$76$	−3.21894e17	−0.0500699
$77$	− 2.94012e18i	− 0.401289i
$78$	0	0
$79$	−9.30637e18	−0.982900	−0.491450	−	0.870906i	$-0.663533\pi$
$79$	−9.30637e18	−0.982900	−0.491450	+	0.870906i	$0.663533\pi$
$80$	4.92637e18i	0.458804i
$81$	0	0
$82$	−1.20548e19	−0.877047
$83$	1.56494e19i	1.00859i	0.863531	+	0.504296i	$0.168248\pi$
$83$	1.56494e19i	1.00859i	−0.863531	+	0.504296i	$0.831752\pi$
$84$	0	0
$85$	2.29315e19	1.16478
$86$	− 3.98902e18i	− 0.180252i
$87$	0	0
$88$	−3.01407e18	−0.108225
$89$	− 2.32089e19i	− 0.744311i	−0.928170	−	0.372156i	$-0.878619\pi$
$89$	− 2.32089e19i	− 0.744311i	0.928170	−	0.372156i	$-0.121381\pi$
$90$	0	0
$91$	3.26621e19	0.838744
$92$	− 2.75616e19i	− 0.634492i
$93$	0	0
$94$	4.62392e19	0.858484
$95$	1.10035e19i	0.183778i
$96$	0	0
$97$	−1.26064e20	−1.70952	−0.854758	−	0.519027i	$-0.826295\pi$
$97$	−1.26064e20	−1.70952	−0.854758	+	0.519027i	$0.826295\pi$
$98$	4.15167e19i	0.508114i
$99$	0	0
$100$	1.18401e20	1.18401
$101$	1.27785e20i	1.15682i	0.815746	+	0.578411i	$0.196327\pi$
$101$	1.27785e20i	1.15682i	−0.815746	+	0.578411i	$0.803673\pi$
$102$	0	0
$103$	5.93903e19	0.441919	0.220960	−	0.975283i	$-0.429081\pi$
$103$	5.93903e19	0.441919	0.220960	+	0.975283i	$0.429081\pi$
$104$	− 3.34837e19i	− 0.226204i
$105$	0	0
$106$	−1.58600e20	−0.885616
$107$	2.59219e20i	1.31774i	0.752258	+	0.658868i	$0.228965\pi$
$107$	2.59219e20i	1.31774i	−0.752258	+	0.658868i	$0.771035\pi$
$108$	0	0
$109$	−4.46833e20	−1.88747	−0.943735	−	0.330704i	$-0.892714\pi$
$109$	−4.46833e20	−1.88747	−0.943735	+	0.330704i	$0.892714\pi$
$110$	1.03032e20i	0.397232i
$111$	0	0
$112$	1.01790e20	0.327737
$113$	3.89079e20i	1.14618i	0.819492	+	0.573090i	$0.194256\pi$
$113$	3.89079e20i	1.14618i	−0.819492	+	0.573090i	$0.805744\pi$
$114$	0	0
$115$	−9.42153e20	−2.32886
$116$	− 2.59406e20i	− 0.588031i
$117$	0	0
$118$	4.46266e20	0.852656
$119$	− 4.73818e20i	− 0.832036i
$120$	0	0
$121$	6.09713e20	0.906299
$122$	2.99298e20i	0.409737i
$123$	0	0
$124$	−2.14170e20	−0.249197
$125$	− 2.33818e21i	− 2.51060i
$126$	0	0
$127$	8.65544e20	0.792961	0.396481	−	0.918043i	$-0.370231\pi$
$127$	8.65544e20	0.792961	0.396481	+	0.918043i	$0.370231\pi$
$128$	− 1.04351e20i	− 0.0883883i
$129$	0	0
$130$	−1.14459e21	−0.830264
$131$	− 2.05503e21i	− 1.38072i	−0.723466	−	0.690360i	$-0.757452\pi$
$131$	− 2.05503e21i	− 1.38072i	0.723466	−	0.690360i	$-0.242548\pi$
$132$	0	0
$133$	2.27357e20	0.131278
$134$	5.31632e20i	0.284815i
$135$	0	0
$136$	−4.85737e20	−0.224394
$137$	5.57533e20i	0.239367i	0.992812	+	0.119684i	$0.0381880\pi$
$137$	5.57533e20i	0.239367i	−0.992812	+	0.119684i	$0.961812\pi$
$138$	0	0
$139$	−2.78892e21	−1.03583	−0.517914	−	0.855433i	$-0.673291\pi$
$139$	−2.78892e21	−1.03583	−0.517914	+	0.855433i	$0.673291\pi$
$140$	− 3.47954e21i	− 1.20293i
$141$	0	0
$142$	−3.70756e21	−1.11225
$143$	− 7.00289e20i	− 0.195847i
$144$	0	0
$145$	−8.86741e21	−2.15833
$146$	4.03755e21i	0.917464i
$147$	0	0
$148$	−4.64983e21	−0.922188
$149$	3.26701e21i	0.605743i	0.953031	+	0.302871i	$0.0979452\pi$
$149$	3.26701e21i	0.605743i	−0.953031	+	0.302871i	$0.902055\pi$
$150$	0	0
$151$	1.13621e22	1.84370	0.921852	−	0.387543i	$-0.126676\pi$
$151$	1.13621e22	1.84370	0.921852	+	0.387543i	$0.126676\pi$
$152$	− 2.33076e20i	− 0.0354048i
$153$	0	0
$154$	2.12887e21	0.283754
$155$	7.32109e21i	0.914659i
$156$	0	0
$157$	−8.25874e21	−0.907648	−0.453824	−	0.891091i	$-0.649940\pi$
$157$	−8.25874e21	−0.907648	−0.453824	+	0.891091i	$0.649940\pi$
$158$	− 6.73853e21i	− 0.695015i
$159$	0	0
$160$	−3.56707e21	−0.324423
$161$	1.94670e22i	1.66357i
$162$	0	0
$163$	−2.26009e22	−1.70706	−0.853531	−	0.521042i	$-0.825543\pi$
$163$	−2.26009e22	−1.70706	−0.853531	+	0.521042i	$0.825543\pi$
$164$	− 8.72864e21i	− 0.620166i
$165$	0	0
$166$	−1.13314e22	−0.713183
$167$	− 1.47582e22i	− 0.874721i	−0.899286	−	0.437360i	$-0.855913\pi$
$167$	− 1.47582e22i	− 0.874721i	0.899286	−	0.437360i	$-0.144087\pi$
$168$	0	0
$169$	−1.12254e22	−0.590655
$170$	1.66042e22i	0.823623i
$171$	0	0
$172$	2.88836e21	0.127458
$173$	− 2.17119e22i	− 0.904143i	−0.891982	−	0.452071i	$-0.850685\pi$
$173$	− 2.17119e22i	− 0.904143i	0.891982	−	0.452071i	$-0.149315\pi$
$174$	0	0
$175$	−8.36276e22	−3.10434
$176$	− 2.18242e21i	− 0.0765266i
$177$	0	0
$178$	1.68050e22	0.526308
$179$	− 6.20662e22i	− 1.83791i	−0.394359	−	0.918956i	$-0.629033\pi$
$179$	− 6.20662e22i	− 1.83791i	0.394359	−	0.918956i	$-0.370967\pi$
$180$	0	0
$181$	−5.26480e22	−1.39507	−0.697536	−	0.716550i	$-0.745720\pi$
$181$	−5.26480e22	−1.39507	−0.697536	+	0.716550i	$0.745720\pi$
$182$	2.36499e22i	0.593082i
$183$	0	0
$184$	1.99567e22	0.448653
$185$	1.58948e23i	3.38483i
$186$	0	0
$187$	−1.01589e22	−0.194280
$188$	3.34808e22i	0.607040i
$189$	0	0
$190$	−7.96737e21	−0.129951
$191$	− 2.32314e22i	− 0.359536i	−0.983709	−	0.179768i	$-0.942465\pi$
$191$	− 2.32314e22i	− 0.359536i	0.983709	−	0.179768i	$-0.0575347\pi$
$192$	0	0
$193$	−1.61258e22	−0.224878	−0.112439	−	0.993659i	$-0.535866\pi$
$193$	−1.61258e22	−0.224878	−0.112439	+	0.993659i	$0.535866\pi$
$194$	− 9.12800e22i	− 1.20881i
$195$	0	0
$196$	−3.00613e22	−0.359291
$197$	− 4.46555e22i	− 0.507239i	−0.967304	−	0.253620i	$-0.918379\pi$
$197$	− 4.46555e22i	− 0.507239i	0.967304	−	0.253620i	$-0.0816212\pi$
$198$	0	0
$199$	7.41394e22	0.761234	0.380617	−	0.924733i	$-0.375712\pi$
$199$	7.41394e22	0.761234	0.380617	+	0.924733i	$0.375712\pi$
$200$	8.57312e22i	0.837219i
$201$	0	0
$202$	−9.25263e22	−0.817997
$203$	1.83221e23i	1.54175i
$204$	0	0
$205$	−2.98376e23	−2.27628
$206$	4.30032e22i	0.312484i
$207$	0	0
$208$	2.42448e22	0.159950
$209$	− 4.87464e21i	− 0.0306534i
$210$	0	0
$211$	1.49478e23	0.854581	0.427291	−	0.904114i	$-0.359468\pi$
$211$	1.49478e23	0.854581	0.427291	+	0.904114i	$0.359468\pi$
$212$	− 1.14839e23i	− 0.626225i
$213$	0	0
$214$	−1.87694e23	−0.931780
$215$	− 9.87342e22i	− 0.467825i
$216$	0	0
$217$	1.51271e23	0.653367
$218$	− 3.23541e23i	− 1.33464i
$219$	0	0
$220$	−7.46029e22	−0.280885
$221$	− 1.12856e23i	− 0.406070i
$222$	0	0
$223$	−8.55234e22	−0.281214	−0.140607	−	0.990066i	$-0.544905\pi$
$223$	−8.55234e22	−0.281214	−0.140607	+	0.990066i	$0.544905\pi$
$224$	7.37039e22i	0.231745i
$225$	0	0
$226$	−2.81723e23	−0.810472
$227$	− 6.04428e23i	− 1.66374i	−0.554970	−	0.831870i	$-0.687270\pi$
$227$	− 6.04428e23i	− 1.66374i	0.554970	−	0.831870i	$-0.312730\pi$
$228$	0	0
$229$	−4.82857e23	−1.21749	−0.608743	−	0.793368i	$-0.708326\pi$
$229$	−4.82857e23	−1.21749	−0.608743	+	0.793368i	$0.708326\pi$
$230$	− 6.82191e23i	− 1.64675i
$231$	0	0
$232$	1.87830e23	0.415800
$233$	6.98154e22i	0.148044i	0.997257	+	0.0740222i	$0.0235836\pi$
$233$	6.98154e22i	0.148044i	−0.997257	+	0.0740222i	$0.976416\pi$
$234$	0	0
$235$	1.14449e24	2.22810
$236$	3.23131e23i	0.602919i
$237$	0	0
$238$	3.43081e23	0.588338
$239$	− 2.05591e23i	− 0.338084i	−0.985609	−	0.169042i	$-0.945933\pi$
$239$	− 2.05591e23i	− 0.338084i	0.985609	−	0.169042i	$-0.0540674\pi$
$240$	0	0
$241$	3.09008e23	0.467518	0.233759	−	0.972295i	$-0.424897\pi$
$241$	3.09008e23	0.467518	0.233759	+	0.972295i	$0.424897\pi$
$242$	4.41479e23i	0.640850i
$243$	0	0
$244$	−2.16715e23	−0.289728
$245$	1.02760e24i	1.31875i
$246$	0	0
$247$	5.41528e22	0.0640695
$248$	− 1.55076e23i	− 0.176209i
$249$	0	0
$250$	1.69302e24	1.77526
$251$	3.58739e23i	0.361445i	0.983534	+	0.180722i	$0.0578435\pi$
$251$	3.58739e23i	0.361445i	−0.983534	+	0.180722i	$0.942156\pi$
$252$	0	0
$253$	4.17382e23	0.388444
$254$	6.26721e23i	0.560708i
$255$	0	0
$256$	7.55579e22	0.0625000
$257$	1.92190e24i	1.52897i	0.644640	+	0.764486i	$0.277007\pi$
$257$	1.92190e24i	1.52897i	−0.644640	+	0.764486i	$0.722993\pi$
$258$	0	0
$259$	3.28422e24	2.41788
$260$	− 8.28772e23i	− 0.587086i
$261$	0	0
$262$	1.48800e24	0.976316
$263$	1.30638e24i	0.825112i	0.910932	+	0.412556i	$0.135364\pi$
$263$	1.30638e24i	0.825112i	−0.910932	+	0.412556i	$0.864636\pi$
$264$	0	0
$265$	−3.92560e24	−2.29851
$266$	1.64624e23i	0.0928276i
$267$	0	0
$268$	−3.84943e23	−0.201395
$269$	− 2.89981e24i	− 1.46166i	−0.682558	−	0.730832i	$-0.739132\pi$
$269$	− 2.89981e24i	− 1.46166i	0.682558	−	0.730832i	$-0.260868\pi$
$270$	0	0
$271$	2.75714e23	0.129052	0.0645262	−	0.997916i	$-0.479446\pi$
$271$	2.75714e23	0.129052	0.0645262	+	0.997916i	$0.479446\pi$
$272$	− 3.51711e23i	− 0.158671i
$273$	0	0
$274$	−4.03697e23	−0.169258
$275$	1.79301e24i	0.724864i
$276$	0	0
$277$	1.27944e24	0.481086	0.240543	−	0.970639i	$-0.422675\pi$
$277$	1.27944e24	0.481086	0.240543	+	0.970639i	$0.422675\pi$
$278$	− 2.01939e24i	− 0.732441i
$279$	0	0
$280$	2.51946e24	0.850603
$281$	1.00119e24i	0.326175i	0.986612	+	0.163088i	$0.0521454\pi$
$281$	1.00119e24i	0.326175i	−0.986612	+	0.163088i	$0.947855\pi$
$282$	0	0
$283$	3.53395e24	1.07250	0.536249	−	0.844060i	$-0.319841\pi$
$283$	3.53395e24	1.07250	0.536249	+	0.844060i	$0.319841\pi$
$284$	− 2.68456e24i	− 0.786483i
$285$	0	0
$286$	5.07063e23	0.138485
$287$	6.16513e24i	1.62601i
$288$	0	0
$289$	2.42707e24	0.597178
$290$	− 6.42069e24i	− 1.52617i
$291$	0	0
$292$	−2.92350e24	−0.648745
$293$	− 1.47544e24i	− 0.316407i	−0.987407	−	0.158203i	$-0.949430\pi$
$293$	− 1.47544e24i	− 0.316407i	0.987407	−	0.158203i	$-0.0505702\pi$
$294$	0	0
$295$	1.10458e25	2.21297
$296$	− 3.36683e24i	− 0.652086i
$297$	0	0
$298$	−2.36557e24	−0.428325
$299$	4.63674e24i	0.811896i
$300$	0	0
$301$	−2.04008e24	−0.334181
$302$	8.22707e24i	1.30369i
$303$	0	0
$304$	1.68765e23	0.0250350
$305$	7.40808e24i	1.06343i
$306$	0	0
$307$	1.00958e25	1.35755	0.678776	−	0.734345i	$-0.262511\pi$
$307$	1.00958e25	1.35755	0.678776	+	0.734345i	$0.262511\pi$
$308$	1.54147e24i	0.200645i
$309$	0	0
$310$	−5.30104e24	−0.646761
$311$	− 2.60865e24i	− 0.308185i	−0.988056	−	0.154093i	$-0.950755\pi$
$311$	− 2.60865e24i	− 0.308185i	0.988056	−	0.154093i	$-0.0492454\pi$
$312$	0	0
$313$	−1.34890e25	−1.49464	−0.747320	−	0.664464i	$-0.768660\pi$
$313$	−1.34890e25	−1.49464	−0.747320	+	0.664464i	$0.768660\pi$
$314$	− 5.97997e24i	− 0.641804i
$315$	0	0
$316$	4.87922e24	0.491450
$317$	5.50004e24i	0.536752i	0.963314	+	0.268376i	$0.0864869\pi$
$317$	5.50004e24i	0.536752i	−0.963314	+	0.268376i	$0.913513\pi$
$318$	0	0
$319$	3.92834e24	0.360000
$320$	− 2.58284e24i	− 0.229402i
$321$	0	0
$322$	−1.40956e25	−1.17632
$323$	− 7.85578e23i	− 0.0635571i
$324$	0	0
$325$	−1.99188e25	−1.51506
$326$	− 1.63648e25i	− 1.20707i
$327$	0	0
$328$	6.32021e24	0.438524
$329$	− 2.36478e25i	− 1.59159i
$330$	0	0
$331$	−1.36160e25	−0.862518	−0.431259	−	0.902228i	$-0.641930\pi$
$331$	−1.36160e25	−0.862518	−0.431259	+	0.902228i	$0.641930\pi$
$332$	− 8.20478e24i	− 0.504296i
$333$	0	0
$334$	1.06861e25	0.618521
$335$	1.31587e25i	0.739205i
$336$	0	0
$337$	2.43469e25	1.28868	0.644341	−	0.764739i	$-0.277132\pi$
$337$	2.43469e25	1.28868	0.644341	+	0.764739i	$0.277132\pi$
$338$	− 8.12805e24i	− 0.417656i
$339$	0	0
$340$	−1.20227e25	−0.582390
$341$	− 3.24331e24i	− 0.152561i
$342$	0	0
$343$	−8.31529e24	−0.368924
$344$	2.09139e24i	0.0901262i
$345$	0	0
$346$	1.57211e25	0.639325
$347$	2.22862e25i	0.880525i	0.897869	+	0.440263i	$0.145115\pi$
$347$	2.22862e25i	0.880525i	−0.897869	+	0.440263i	$0.854885\pi$
$348$	0	0
$349$	−4.54909e25	−1.69696	−0.848478	−	0.529231i	$-0.822481\pi$
$349$	−4.54909e25	−1.69696	−0.848478	+	0.529231i	$0.822481\pi$
$350$	− 6.05529e25i	− 2.19510i
$351$	0	0
$352$	1.58024e24	0.0541124
$353$	− 9.99616e24i	− 0.332726i	−0.986065	−	0.166363i	$-0.946798\pi$
$353$	− 9.99616e24i	− 0.332726i	0.986065	−	0.166363i	$-0.0532023\pi$
$354$	0	0
$355$	−9.17677e25	−2.88673
$356$	1.21682e25i	0.372156i
$357$	0	0
$358$	4.49407e25	1.29960
$359$	3.43781e25i	0.966800i	0.875399	+	0.483400i	$0.160598\pi$
$359$	3.43781e25i	0.966800i	−0.875399	+	0.483400i	$0.839402\pi$
$360$	0	0
$361$	−3.72130e25	−0.989972
$362$	− 3.81212e25i	− 0.986464i
$363$	0	0
$364$	−1.71243e25	−0.419372
$365$	9.99355e25i	2.38117i
$366$	0	0
$367$	−5.51538e24	−0.124427	−0.0622135	−	0.998063i	$-0.519816\pi$
$367$	−5.51538e24	−0.124427	−0.0622135	+	0.998063i	$0.519816\pi$
$368$	1.44502e25i	0.317246i
$369$	0	0
$370$	−1.15090e26	−2.39343
$371$	8.11119e25i	1.64190i
$372$	0	0
$373$	−9.56724e23	−0.0183526	−0.00917632	−	0.999958i	$-0.502921\pi$
$373$	−9.56724e23	−0.0183526	−0.00917632	+	0.999958i	$0.502921\pi$
$374$	− 7.35580e24i	− 0.137377i
$375$	0	0
$376$	−2.42427e25	−0.429242
$377$	4.36403e25i	0.752444i
$378$	0	0
$379$	9.44840e24	0.154513	0.0772567	−	0.997011i	$-0.475384\pi$
$379$	9.44840e24	0.154513	0.0772567	+	0.997011i	$0.475384\pi$
$380$	− 5.76899e24i	− 0.0918891i
$381$	0	0
$382$	1.68214e25	0.254230
$383$	− 1.22672e25i	− 0.180616i	−0.995914	−	0.0903080i	$-0.971215\pi$
$383$	− 1.22672e25i	− 0.180616i	0.995914	−	0.0903080i	$-0.0287851\pi$
$384$	0	0
$385$	5.26928e25	0.736452
$386$	− 1.16763e25i	− 0.159013i
$387$	0	0
$388$	6.60938e25	0.854758
$389$	1.01074e26i	1.27392i	0.770897	+	0.636960i	$0.219808\pi$
$389$	1.01074e26i	1.27392i	−0.770897	+	0.636960i	$0.780192\pi$
$390$	0	0
$391$	6.72636e25	0.805402
$392$	− 2.17667e25i	− 0.254057i
$393$	0	0
$394$	3.23341e25	0.358672
$395$	− 1.66789e26i	− 1.80383i
$396$	0	0
$397$	5.51713e25	0.567294	0.283647	−	0.958929i	$-0.408456\pi$
$397$	5.51713e25	0.567294	0.283647	+	0.958929i	$0.408456\pi$
$398$	5.36826e25i	0.538274i
$399$	0	0
$400$	−6.20760e25	−0.592003
$401$	1.22452e26i	1.13900i	0.821992	+	0.569498i	$0.192863\pi$
$401$	1.22452e26i	1.13900i	−0.821992	+	0.569498i	$0.807137\pi$
$402$	0	0
$403$	3.60302e25	0.318872
$404$	− 6.69962e25i	− 0.578411i
$405$	0	0
$406$	−1.32666e26	−1.09018
$407$	− 7.04151e25i	− 0.564575i
$408$	0	0
$409$	9.48941e25	0.724446	0.362223	−	0.932091i	$-0.382018\pi$
$409$	9.48941e25	0.724446	0.362223	+	0.932091i	$0.382018\pi$
$410$	− 2.16047e26i	− 1.60957i
$411$	0	0
$412$	−3.11376e25	−0.220960
$413$	− 2.28231e26i	− 1.58079i
$414$	0	0
$415$	−2.80468e26	−1.85098
$416$	1.75551e25i	0.113102i
$417$	0	0
$418$	3.52961e24	0.0216753
$419$	2.42017e25i	0.145113i	0.997364	+	0.0725563i	$0.0231157\pi$
$419$	2.42017e25i	0.145113i	−0.997364	+	0.0725563i	$0.976884\pi$
$420$	0	0
$421$	1.18993e26	0.680299	0.340149	−	0.940371i	$-0.389522\pi$
$421$	1.18993e26	0.680299	0.340149	+	0.940371i	$0.389522\pi$
$422$	1.08234e26i	0.604280i
$423$	0	0
$424$	8.31522e25	0.442808
$425$	2.88955e26i	1.50294i
$426$	0	0
$427$	1.53068e26	0.759636
$428$	− 1.35905e26i	− 0.658868i
$429$	0	0
$430$	7.14912e25	0.330802
$431$	− 2.57610e26i	− 1.16464i	−0.812961	−	0.582319i	$-0.802146\pi$
$431$	− 2.57610e26i	− 1.16464i	0.812961	−	0.582319i	$-0.197854\pi$
$432$	0	0
$433$	2.61817e26	1.13011	0.565054	−	0.825054i	$-0.308855\pi$
$433$	2.61817e26	1.13011	0.565054	+	0.825054i	$0.308855\pi$
$434$	1.09532e26i	0.462000i
$435$	0	0
$436$	2.34269e26	0.943735
$437$	3.22758e25i	0.127076i
$438$	0	0
$439$	−3.87193e26	−1.45640	−0.728202	−	0.685363i	$-0.759644\pi$
$439$	−3.87193e26	−1.45640	−0.728202	+	0.685363i	$0.759644\pi$
$440$	− 5.40183e25i	− 0.198616i
$441$	0	0
$442$	8.17163e25	0.287135
$443$	3.50390e26i	1.20369i	0.798613	+	0.601845i	$0.205567\pi$
$443$	3.50390e26i	1.20369i	−0.798613	+	0.601845i	$0.794433\pi$
$444$	0	0
$445$	4.15950e26	1.36597
$446$	− 6.19256e25i	− 0.198848i
$447$	0	0
$448$	−5.33673e25	−0.163868
$449$	3.06377e25i	0.0920011i	0.998941	+	0.0460005i	$0.0146476\pi$
$449$	3.06377e25i	0.0920011i	−0.998941	+	0.0460005i	$0.985352\pi$
$450$	0	0
$451$	1.32183e26	0.379673
$452$	− 2.03989e26i	− 0.573090i
$453$	0	0
$454$	4.37652e26	1.17644
$455$	5.85370e26i	1.53928i
$456$	0	0
$457$	1.33467e26	0.335900	0.167950	−	0.985795i	$-0.446285\pi$
$457$	1.33467e26	0.335900	0.167950	+	0.985795i	$0.446285\pi$
$458$	− 3.49626e26i	− 0.860892i
$459$	0	0
$460$	4.93959e26	1.16443
$461$	− 5.24477e26i	− 1.20981i	−0.796298	−	0.604905i	$-0.793211\pi$
$461$	− 5.24477e26i	− 1.20981i	0.796298	−	0.604905i	$-0.206789\pi$
$462$	0	0
$463$	5.76823e25	0.127419	0.0637093	−	0.997969i	$-0.479707\pi$
$463$	5.76823e25	0.127419	0.0637093	+	0.997969i	$0.479707\pi$
$464$	1.36003e26i	0.294015i
$465$	0	0
$466$	−5.05517e25	−0.104683
$467$	− 5.24346e26i	− 1.06279i	−0.847123	−	0.531397i	$-0.821667\pi$
$467$	− 5.24346e26i	− 1.06279i	0.847123	−	0.531397i	$-0.178333\pi$
$468$	0	0
$469$	2.71889e26	0.528036
$470$	8.28701e26i	1.57550i
$471$	0	0
$472$	−2.33972e26	−0.426328
$473$	4.37401e25i	0.0780312i
$474$	0	0
$475$	−1.38652e26	−0.237133
$476$	2.48417e26i	0.416018i
$477$	0	0
$478$	1.48864e26	0.239062
$479$	− 4.90998e26i	− 0.772191i	−0.922459	−	0.386095i	$-0.873824\pi$
$479$	− 4.90998e26i	− 0.772191i	0.922459	−	0.386095i	$-0.126176\pi$
$480$	0	0
$481$	7.82249e26	1.18003
$482$	2.23745e26i	0.330585i
$483$	0	0
$484$	−3.19665e26	−0.453149
$485$	− 2.25932e27i	− 3.13733i
$486$	0	0
$487$	3.91048e26	0.521123	0.260562	−	0.965457i	$-0.416092\pi$
$487$	3.91048e26	0.521123	0.260562	+	0.965457i	$0.416092\pi$
$488$	− 1.56918e26i	− 0.204868i
$489$	0	0
$490$	−7.44062e26	−0.932499
$491$	1.26266e26i	0.155050i	0.996990	+	0.0775252i	$0.0247018\pi$
$491$	1.26266e26i	0.155050i	−0.996990	+	0.0775252i	$0.975298\pi$
$492$	0	0
$493$	6.33076e26	0.746426
$494$	3.92108e25i	0.0453040i
$495$	0	0
$496$	1.12287e26	0.124598
$497$	1.89613e27i	2.06207i
$498$	0	0
$499$	−1.49652e27	−1.56343	−0.781714	−	0.623637i	$-0.785654\pi$
$499$	−1.49652e27	−1.56343	−0.781714	+	0.623637i	$0.785654\pi$
$500$	1.22588e27i	1.25530i
$501$	0	0
$502$	−2.59755e26	−0.255580
$503$	2.05910e26i	0.198609i	0.995057	+	0.0993044i	$0.0316617\pi$
$503$	2.05910e26i	0.198609i	−0.995057	+	0.0993044i	$0.968338\pi$
$504$	0	0
$505$	−2.29017e27	−2.12302
$506$	3.02217e26i	0.274671i
$507$	0	0
$508$	−4.53794e26	−0.396481
$509$	1.05248e27i	0.901646i	0.892613	+	0.450823i	$0.148869\pi$
$509$	1.05248e27i	0.901646i	−0.892613	+	0.450823i	$0.851131\pi$
$510$	0	0
$511$	2.06490e27	1.70094
$512$	5.47097e25i	0.0441942i
$513$	0	0
$514$	−1.39160e27	−1.08115
$515$	1.06439e27i	0.811017i
$516$	0	0
$517$	−5.07020e26	−0.371637
$518$	2.37803e27i	1.70970i
$519$	0	0
$520$	6.00095e26	0.415132
$521$	− 1.57372e27i	− 1.06795i	−0.845500	−	0.533975i	$-0.820698\pi$
$521$	− 1.57372e27i	− 1.06795i	0.845500	−	0.533975i	$-0.179302\pi$
$522$	0	0
$523$	2.77555e27	1.81273	0.906364	−	0.422497i	$-0.138846\pi$
$523$	2.77555e27	1.81273	0.906364	+	0.422497i	$0.138846\pi$
$524$	1.07743e27i	0.690360i
$525$	0	0
$526$	−9.45922e26	−0.583442
$527$	− 5.22679e26i	− 0.316322i
$528$	0	0
$529$	−1.04740e27	−0.610319
$530$	− 2.84244e27i	− 1.62530i
$531$	0	0
$532$	−1.19201e26	−0.0656391
$533$	1.46843e27i	0.793565i
$534$	0	0
$535$	−4.64572e27	−2.41833
$536$	− 2.78728e26i	− 0.142408i
$537$	0	0
$538$	2.09969e27	1.03355
$539$	− 4.55236e26i	− 0.219963i
$540$	0	0
$541$	−1.61554e27	−0.752221	−0.376111	−	0.926575i	$-0.622739\pi$
$541$	−1.61554e27	−0.752221	−0.376111	+	0.926575i	$0.622739\pi$
$542$	1.99638e26i	0.0912539i
$543$	0	0
$544$	2.54666e26	0.112197
$545$	− 8.00814e27i	− 3.46391i
$546$	0	0
$547$	−8.51258e26	−0.354967	−0.177483	−	0.984124i	$-0.556796\pi$
$547$	−8.51258e26	−0.354967	−0.177483	+	0.984124i	$0.556796\pi$
$548$	− 2.92308e26i	− 0.119684i
$549$	0	0
$550$	−1.29828e27	−0.512556
$551$	3.03776e26i	0.117771i
$552$	0	0
$553$	−3.44624e27	−1.28853
$554$	9.26414e26i	0.340179i
$555$	0	0
$556$	1.46220e27	0.517914
$557$	− 2.85564e27i	− 0.993462i	−0.867905	−	0.496731i	$-0.834534\pi$
$557$	− 2.85564e27i	− 0.993462i	0.867905	−	0.496731i	$-0.165466\pi$
$558$	0	0
$559$	−4.85913e26	−0.163095
$560$	1.82428e27i	0.601467i
$561$	0	0
$562$	−7.24936e26	−0.230641
$563$	− 1.04630e27i	− 0.327017i	−0.986542	−	0.163509i	$-0.947719\pi$
$563$	− 1.04630e27i	− 0.327017i	0.986542	−	0.163509i	$-0.0522811\pi$
$564$	0	0
$565$	−6.97308e27	−2.10349
$566$	2.55886e27i	0.758371i
$567$	0	0
$568$	1.94383e27	0.556127
$569$	− 1.50905e27i	− 0.424210i	−0.977247	−	0.212105i	$-0.931968\pi$
$569$	− 1.50905e27i	− 0.424210i	0.977247	−	0.212105i	$-0.0680319\pi$
$570$	0	0
$571$	2.32597e27	0.631311	0.315656	−	0.948874i	$-0.397776\pi$
$571$	2.32597e27	0.631311	0.315656	+	0.948874i	$0.397776\pi$
$572$	3.67153e26i	0.0979234i
$573$	0	0
$574$	−4.46403e27	−1.14976
$575$	− 1.18719e28i	− 3.00497i
$576$	0	0
$577$	1.87613e26	0.0458674	0.0229337	−	0.999737i	$-0.492699\pi$
$577$	1.87613e26	0.0458674	0.0229337	+	0.999737i	$0.492699\pi$
$578$	1.75739e27i	0.422268i
$579$	0	0
$580$	4.64908e27	1.07916
$581$	5.79512e27i	1.32221i
$582$	0	0
$583$	1.73907e27	0.383383
$584$	− 2.11684e27i	− 0.458732i
$585$	0	0
$586$	1.06833e27	0.223734
$587$	3.52653e27i	0.726049i	0.931780	+	0.363025i	$0.118256\pi$
$587$	3.52653e27i	0.726049i	−0.931780	+	0.363025i	$0.881744\pi$
$588$	0	0
$589$	2.50803e26	0.0499090
$590$	7.99799e27i	1.56481i
$591$	0	0
$592$	2.43785e27	0.461094
$593$	9.16023e26i	0.170357i	0.996366	+	0.0851784i	$0.0271460\pi$
$593$	9.16023e26i	0.170357i	−0.996366	+	0.0851784i	$0.972854\pi$
$594$	0	0
$595$	8.49177e27	1.52696
$596$	− 1.71286e27i	− 0.302871i
$597$	0	0
$598$	−3.35735e27	−0.574097
$599$	4.92879e27i	0.828843i	0.910085	+	0.414422i	$0.136016\pi$
$599$	4.92879e27i	0.828843i	−0.910085	+	0.414422i	$0.863984\pi$
$600$	0	0
$601$	−3.14905e27	−0.512195	−0.256097	−	0.966651i	$-0.582437\pi$
$601$	−3.14905e27	−0.512195	−0.256097	+	0.966651i	$0.582437\pi$
$602$	− 1.47717e27i	− 0.236301i
$603$	0	0
$604$	−5.95704e27	−0.921852
$605$	1.09273e28i	1.66325i
$606$	0	0
$607$	2.25730e27	0.332431	0.166216	−	0.986089i	$-0.446845\pi$
$607$	2.25730e27	0.332431	0.166216	+	0.986089i	$0.446845\pi$
$608$	1.22199e26i	0.0177024i
$609$	0	0
$610$	−5.36402e27	−0.751955
$611$	− 5.63253e27i	− 0.776769i
$612$	0	0
$613$	−2.54609e27	−0.339836	−0.169918	−	0.985458i	$-0.554350\pi$
$613$	−2.54609e27	−0.339836	−0.169918	+	0.985458i	$0.554350\pi$
$614$	7.31013e27i	0.959934i
$615$	0	0
$616$	−1.11614e27	−0.141877
$617$	3.58358e27i	0.448194i	0.974567	+	0.224097i	$0.0719432\pi$
$617$	3.58358e27i	0.448194i	−0.974567	+	0.224097i	$0.928057\pi$
$618$	0	0
$619$	−4.86472e27	−0.589049	−0.294525	−	0.955644i	$-0.595161\pi$
$619$	−4.86472e27	−0.589049	−0.294525	+	0.955644i	$0.595161\pi$
$620$	− 3.83836e27i	− 0.457329i
$621$	0	0
$622$	1.88886e27	0.217920
$623$	− 8.59449e27i	− 0.975753i
$624$	0	0
$625$	2.03679e28	2.23947
$626$	− 9.76709e27i	− 1.05687i
$627$	0	0
$628$	4.32996e27	0.453824
$629$	− 1.13478e28i	− 1.17059i
$630$	0	0
$631$	5.80990e27	0.580597	0.290299	−	0.956936i	$-0.406245\pi$
$631$	5.80990e27	0.580597	0.290299	+	0.956936i	$0.406245\pi$
$632$	3.53293e27i	0.347508i
$633$	0	0
$634$	−3.98246e27	−0.379541
$635$	1.55123e28i	1.45525i
$636$	0	0
$637$	5.05726e27	0.459749
$638$	2.84442e27i	0.254558i
$639$	0	0
$640$	1.87017e27	0.162212
$641$	3.97009e27i	0.339016i	0.985529	+	0.169508i	$0.0542178\pi$
$641$	3.97009e27i	0.339016i	−0.985529	+	0.169508i	$0.945782\pi$
$642$	0	0
$643$	1.29641e28	1.07308	0.536542	−	0.843873i	$-0.319730\pi$
$643$	1.29641e28	1.07308	0.536542	+	0.843873i	$0.319730\pi$
$644$	− 1.02063e28i	− 0.831785i
$645$	0	0
$646$	5.68819e26	0.0449416
$647$	1.41306e28i	1.09930i	0.835395	+	0.549651i	$0.185239\pi$
$647$	1.41306e28i	1.09930i	−0.835395	+	0.549651i	$0.814761\pi$
$648$	0	0
$649$	−4.89337e27	−0.369114
$650$	− 1.44227e28i	− 1.07131i
$651$	0	0
$652$	1.18494e28	0.853531
$653$	− 1.12247e27i	− 0.0796236i	−0.999207	−	0.0398118i	$-0.987324\pi$
$653$	− 1.12247e27i	− 0.0796236i	0.999207	−	0.0398118i	$-0.0126758\pi$
$654$	0	0
$655$	3.68303e28	2.53392
$656$	4.57632e27i	0.310083i
$657$	0	0
$658$	1.71229e28	1.12543
$659$	− 6.43837e27i	− 0.416795i	−0.978044	−	0.208397i	$-0.933175\pi$
$659$	− 6.43837e27i	− 0.416795i	0.978044	−	0.208397i	$-0.0668247\pi$
$660$	0	0
$661$	1.60160e28	1.00587	0.502933	−	0.864326i	$-0.332254\pi$
$661$	1.60160e28	1.00587	0.502933	+	0.864326i	$0.332254\pi$
$662$	− 9.85900e27i	− 0.609892i
$663$	0	0
$664$	5.94089e27	0.356591
$665$	4.07470e27i	0.240924i
$666$	0	0
$667$	−2.60102e28	−1.49240
$668$	7.73756e27i	0.437360i
$669$	0	0
$670$	−9.52792e27	−0.522697
$671$	− 3.28184e27i	− 0.177375i
$672$	0	0
$673$	2.40723e28	1.26289	0.631446	−	0.775420i	$-0.282462\pi$
$673$	2.40723e28	1.26289	0.631446	+	0.775420i	$0.282462\pi$
$674$	1.76291e28i	0.911235i
$675$	0	0
$676$	5.88534e27	0.295328
$677$	2.04502e28i	1.01114i	0.862785	+	0.505570i	$0.168718\pi$
$677$	2.04502e28i	1.01114i	−0.862785	+	0.505570i	$0.831282\pi$
$678$	0	0
$679$	−4.66827e28	−2.24109
$680$	− 8.70538e27i	− 0.411812i
$681$	0	0
$682$	2.34841e27	0.107877
$683$	1.09771e28i	0.496914i	0.968643	+	0.248457i	$0.0799234\pi$
$683$	1.09771e28i	0.496914i	−0.968643	+	0.248457i	$0.920077\pi$
$684$	0	0
$685$	−9.99211e27	−0.439290
$686$	− 6.02092e27i	− 0.260868i
$687$	0	0
$688$	−1.51433e27	−0.0637289
$689$	1.93196e28i	0.801318i
$690$	0	0
$691$	−4.38615e28	−1.76727	−0.883635	−	0.468176i	$-0.844911\pi$
$691$	−4.38615e28	−1.76727	−0.883635	+	0.468176i	$0.844911\pi$
$692$	1.13833e28i	0.452071i
$693$	0	0
$694$	−1.61370e28	−0.622625
$695$	− 4.99830e28i	− 1.90097i
$696$	0	0
$697$	2.13021e28	0.787217
$698$	− 3.29390e28i	− 1.19993i
$699$	0	0
$700$	4.38450e28	1.55217
$701$	− 6.56979e27i	− 0.229283i	−0.993407	−	0.114641i	$-0.963428\pi$
$701$	− 6.56979e27i	− 0.229283i	0.993407	−	0.114641i	$-0.0365719\pi$
$702$	0	0
$703$	5.44515e27	0.184696
$704$	1.14422e27i	0.0382633i
$705$	0	0
$706$	7.23799e27	0.235273
$707$	4.73201e28i	1.51653i
$708$	0	0
$709$	−5.35721e28	−1.66908	−0.834539	−	0.550949i	$-0.814266\pi$
$709$	−5.35721e28	−1.66908	−0.834539	+	0.550949i	$0.814266\pi$
$710$	− 6.64469e28i	− 2.04123i
$711$	0	0
$712$	−8.81068e27	−0.263154
$713$	2.14745e28i	0.632453i
$714$	0	0
$715$	1.25506e28	0.359421
$716$	3.25406e28i	0.918956i
$717$	0	0
$718$	−2.48924e28	−0.683631
$719$	− 4.01717e27i	− 0.108801i	−0.998519	−	0.0544003i	$-0.982675\pi$
$719$	− 4.01717e27i	− 0.108801i	0.998519	−	0.0544003i	$-0.0173247\pi$
$720$	0	0
$721$	2.19928e28	0.579333
$722$	− 2.69451e28i	− 0.700016i
$723$	0	0
$724$	2.76027e28	0.697536
$725$	− 1.11736e29i	− 2.78493i
$726$	0	0
$727$	2.02877e28	0.491913	0.245957	−	0.969281i	$-0.420898\pi$
$727$	2.02877e28	0.491913	0.245957	+	0.969281i	$0.420898\pi$
$728$	− 1.23993e28i	− 0.296541i
$729$	0	0
$730$	−7.23610e28	−1.68374
$731$	7.04899e27i	0.161790i
$732$	0	0
$733$	6.60151e28	1.47436	0.737179	−	0.675697i	$-0.236157\pi$
$733$	6.60151e28	1.47436	0.737179	+	0.675697i	$0.236157\pi$
$734$	− 3.99356e27i	− 0.0879832i
$735$	0	0
$736$	−1.04631e28	−0.224327
$737$	− 5.82942e27i	− 0.123296i
$738$	0	0
$739$	3.98588e28	0.820503	0.410252	−	0.911972i	$-0.365441\pi$
$739$	3.98588e28	0.820503	0.410252	+	0.911972i	$0.365441\pi$
$740$	− 8.33343e28i	− 1.69241i
$741$	0	0
$742$	−5.87313e28	−1.16100
$743$	5.81918e28i	1.13494i	0.823394	+	0.567471i	$0.192078\pi$
$743$	5.81918e28i	1.13494i	−0.823394	+	0.567471i	$0.807922\pi$
$744$	0	0
$745$	−5.85515e28	−1.11167
$746$	− 6.92743e26i	− 0.0129773i
$747$	0	0
$748$	5.32617e27	0.0971402
$749$	9.59913e28i	1.72748i
$750$	0	0
$751$	−1.06188e29	−1.86070	−0.930352	−	0.366667i	$-0.880499\pi$
$751$	−1.06188e29	−1.86070	−0.930352	+	0.366667i	$0.880499\pi$
$752$	− 1.75536e28i	− 0.303520i
$753$	0	0
$754$	−3.15990e28	−0.532059
$755$	2.03633e29i	3.38359i
$756$	0	0
$757$	2.17859e28	0.352547	0.176273	−	0.984341i	$-0.443596\pi$
$757$	2.17859e28	0.352547	0.176273	+	0.984341i	$0.443596\pi$
$758$	6.84137e27i	0.109257i
$759$	0	0
$760$	4.17720e27	0.0649754
$761$	− 4.01925e28i	− 0.617019i	−0.951221	−	0.308509i	$-0.900170\pi$
$761$	− 4.01925e28i	− 0.617019i	0.951221	−	0.308509i	$-0.0998301\pi$
$762$	0	0
$763$	−1.65467e29	−2.47437
$764$	1.21800e28i	0.179768i
$765$	0	0
$766$	8.88237e27	0.127715
$767$	− 5.43609e28i	− 0.771495i
$768$	0	0
$769$	4.34858e28	0.601290	0.300645	−	0.953736i	$-0.402798\pi$
$769$	4.34858e28	0.601290	0.300645	+	0.953736i	$0.402798\pi$
$770$	3.81537e28i	0.520750i
$771$	0	0
$772$	8.45455e27	0.112439
$773$	1.20791e29i	1.58576i	0.609377	+	0.792881i	$0.291420\pi$
$773$	1.20791e29i	1.58576i	−0.609377	+	0.792881i	$0.708580\pi$
$774$	0	0
$775$	−9.22515e28	−1.18020
$776$	4.78570e28i	0.604405i
$777$	0	0
$778$	−7.31852e28	−0.900798
$779$	1.02216e28i	0.124207i
$780$	0	0
$781$	4.06539e28	0.481495
$782$	4.87041e28i	0.569505i
$783$	0	0
$784$	1.57608e28	0.179646
$785$	− 1.48013e29i	− 1.66573i
$786$	0	0
$787$	9.03878e28	0.991660	0.495830	−	0.868420i	$-0.334864\pi$
$787$	9.03878e28	0.991660	0.495830	+	0.868420i	$0.334864\pi$
$788$	2.34124e28i	0.253620i
$789$	0	0
$790$	1.20768e29	1.27550
$791$	1.44080e29i	1.50258i
$792$	0	0
$793$	3.64583e28	0.370736
$794$	3.99483e28i	0.401138i
$795$	0	0
$796$	−3.88704e28	−0.380617
$797$	− 7.89198e28i	− 0.763138i	−0.924340	−	0.381569i	$-0.875384\pi$
$797$	− 7.89198e28i	− 0.763138i	0.924340	−	0.381569i	$-0.124616\pi$
$798$	0	0
$799$	−8.17093e28	−0.770556
$800$	− 4.49479e28i	− 0.418610i
$801$	0	0
$802$	−8.86648e28	−0.805392
$803$	− 4.42723e28i	− 0.397170i
$804$	0	0
$805$	−3.48889e29	−3.05301
$806$	2.60887e28i	0.225477i
$807$	0	0
$808$	4.85104e28	0.408998
$809$	6.67905e28i	0.556198i	0.960552	+	0.278099i	$0.0897043\pi$
$809$	6.67905e28i	0.556198i	−0.960552	+	0.278099i	$0.910296\pi$
$810$	0	0
$811$	1.08205e29	0.879103	0.439552	−	0.898217i	$-0.355137\pi$
$811$	1.08205e29	0.879103	0.439552	+	0.898217i	$0.355137\pi$
$812$	− 9.60606e28i	− 0.770877i
$813$	0	0
$814$	5.09860e28	0.399215
$815$	− 4.05053e29i	− 3.13282i
$816$	0	0
$817$	−3.38239e27	−0.0255272
$818$	6.87106e28i	0.512261i
$819$	0	0
$820$	1.56435e29	1.13814
$821$	8.56226e28i	0.615399i	0.951484	+	0.307700i	$0.0995592\pi$
$821$	8.56226e28i	0.615399i	−0.951484	+	0.307700i	$0.900441\pi$
$822$	0	0
$823$	1.37589e29	0.965131	0.482566	−	0.875860i	$-0.339705\pi$
$823$	1.37589e29	0.965131	0.482566	+	0.875860i	$0.339705\pi$
$824$	− 2.25460e28i	− 0.156242i
$825$	0	0
$826$	1.65257e29	1.11779
$827$	3.93801e28i	0.263161i	0.991306	+	0.131580i	$0.0420051\pi$
$827$	3.93801e28i	0.263161i	−0.991306	+	0.131580i	$0.957995\pi$
$828$	0	0
$829$	−1.83729e29	−1.19848	−0.599241	−	0.800568i	$-0.704531\pi$
$829$	−1.83729e29	−1.19848	−0.599241	+	0.800568i	$0.704531\pi$
$830$	− 2.03081e29i	− 1.30884i
$831$	0	0
$832$	−1.27112e28	−0.0799750
$833$	− 7.33641e28i	− 0.456072i
$834$	0	0
$835$	2.64497e29	1.60530
$836$	2.55571e27i	0.0153267i
$837$	0	0
$838$	−1.75239e28	−0.102610
$839$	− 3.01869e29i	− 1.74662i	−0.487161	−	0.873312i	$-0.661967\pi$
$839$	− 3.01869e29i	− 1.74662i	0.487161	−	0.873312i	$-0.338033\pi$
$840$	0	0
$841$	−6.78102e28	−0.383120
$842$	8.61600e28i	0.481044i
$843$	0	0
$844$	−7.83697e28	−0.427291
$845$	− 2.01182e29i	− 1.08398i
$846$	0	0
$847$	2.25783e29	1.18811
$848$	6.02086e28i	0.313112i
$849$	0	0
$850$	−2.09226e29	−1.06274
$851$	4.66231e29i	2.34048i
$852$	0	0
$853$	1.94621e29	0.954330	0.477165	−	0.878814i	$-0.341664\pi$
$853$	1.94621e29	0.954330	0.477165	+	0.878814i	$0.341664\pi$
$854$	1.10833e29i	0.537143i
$855$	0	0
$856$	9.84059e28	0.465890
$857$	2.07350e29i	0.970279i	0.874437	+	0.485140i	$0.161231\pi$
$857$	2.07350e29i	0.970279i	−0.874437	+	0.485140i	$0.838769\pi$
$858$	0	0
$859$	1.03740e29	0.474256	0.237128	−	0.971478i	$-0.423794\pi$
$859$	1.03740e29	0.474256	0.237128	+	0.971478i	$0.423794\pi$
$860$	5.17652e28i	0.233912i
$861$	0	0
$862$	1.86530e29	0.823523
$863$	2.81523e28i	0.122859i	0.998111	+	0.0614293i	$0.0195659\pi$
$863$	2.81523e28i	0.122859i	−0.998111	+	0.0614293i	$0.980434\pi$
$864$	0	0
$865$	3.89121e29	1.65930
$866$	1.89576e29i	0.799106i
$867$	0	0
$868$	−7.93094e28	−0.326684
$869$	7.38889e28i	0.300872i
$870$	0	0
$871$	6.47596e28	0.257705
$872$	1.69629e29i	0.667321i
$873$	0	0
$874$	−2.33702e28	−0.0898562
$875$	− 8.65851e29i	− 3.29126i
$876$	0	0
$877$	−7.33263e28	−0.272436	−0.136218	−	0.990679i	$-0.543495\pi$
$877$	−7.33263e28	−0.272436	−0.136218	+	0.990679i	$0.543495\pi$
$878$	− 2.80357e29i	− 1.02983i
$879$	0	0
$880$	3.91134e28	0.140443
$881$	1.56240e29i	0.554669i	0.960773	+	0.277335i	$0.0894511\pi$
$881$	1.56240e29i	0.554669i	−0.960773	+	0.277335i	$0.910549\pi$
$882$	0	0
$883$	−4.14726e29	−1.43931	−0.719654	−	0.694333i	$-0.755700\pi$
$883$	−4.14726e29	−1.43931	−0.719654	+	0.694333i	$0.755700\pi$
$884$	5.91690e28i	0.203035i
$885$	0	0
$886$	−2.53709e29	−0.851137
$887$	2.74914e29i	0.911929i	0.889998	+	0.455965i	$0.150706\pi$
$887$	2.74914e29i	0.911929i	−0.889998	+	0.455965i	$0.849294\pi$
$888$	0	0
$889$	3.20520e29	1.03953
$890$	3.01180e29i	0.965887i
$891$	0	0
$892$	4.48389e28	0.140607
$893$	− 3.92075e28i	− 0.121578i
$894$	0	0
$895$	1.11235e30	3.37297
$896$	− 3.86421e28i	− 0.115872i
$897$	0	0
$898$	−2.21841e28	−0.0650546
$899$	2.02115e29i	0.586141i
$900$	0	0
$901$	2.80262e29	0.794908
$902$	9.57107e28i	0.268470i
$903$	0	0
$904$	1.47704e29	0.405236
$905$	− 9.43559e29i	− 2.56026i
$906$	0	0
$907$	−2.38915e29	−0.634119	−0.317060	−	0.948406i	$-0.602696\pi$
$907$	−2.38915e29	−0.634119	−0.317060	+	0.948406i	$0.602696\pi$
$908$	3.16894e29i	0.831870i
$909$	0	0
$910$	−4.23853e29	−1.08843
$911$	− 6.69574e29i	− 1.70065i	−0.526258	−	0.850325i	$-0.676405\pi$
$911$	− 6.69574e29i	− 1.70065i	0.526258	−	0.850325i	$-0.323595\pi$
$912$	0	0
$913$	1.24250e29	0.308737
$914$	9.66401e28i	0.237517i
$915$	0	0
$916$	2.53156e29	0.608743
$917$	− 7.60999e29i	− 1.81005i
$918$	0	0
$919$	4.35929e29	1.01452	0.507260	−	0.861793i	$-0.330658\pi$
$919$	4.35929e29	1.01452	0.507260	+	0.861793i	$0.330658\pi$
$920$	3.57665e29i	0.823375i
$921$	0	0
$922$	3.79762e29	0.855464
$923$	4.51628e29i	1.00638i
$924$	0	0
$925$	−2.00286e30	−4.36751
$926$	4.17664e28i	0.0900985i
$927$	0	0
$928$	−9.84770e28	−0.207900
$929$	7.97362e29i	1.66532i	0.553783	+	0.832661i	$0.313184\pi$
$929$	7.97362e29i	1.66532i	−0.553783	+	0.832661i	$0.686816\pi$
$930$	0	0
$931$	3.52031e28	0.0719588
$932$	− 3.66034e28i	− 0.0740222i
$933$	0	0
$934$	3.79667e29	0.751509
$935$	− 1.82067e29i	− 0.356546i
$936$	0	0
$937$	−3.21295e28	−0.0615896	−0.0307948	−	0.999526i	$-0.509804\pi$
$937$	−3.21295e28	−0.0615896	−0.0307948	+	0.999526i	$0.509804\pi$
$938$	1.96869e29i	0.373378i
$939$	0	0
$940$	−6.00043e29	−1.11405
$941$	− 1.49046e29i	− 0.273794i	−0.990585	−	0.136897i	$-0.956287\pi$
$941$	− 1.49046e29i	− 0.273794i	0.990585	−	0.136897i	$-0.0437129\pi$
$942$	0	0
$943$	−8.75207e29	−1.57396
$944$	− 1.69414e29i	− 0.301459i
$945$	0	0
$946$	−3.16712e28	−0.0551764
$947$	1.03653e30i	1.78682i	0.449243	+	0.893410i	$0.351694\pi$
$947$	1.03653e30i	1.78682i	−0.449243	+	0.893410i	$0.648306\pi$
$948$	0	0
$949$	4.91825e29	0.830135
$950$	− 1.00395e29i	− 0.167678i
$951$	0	0
$952$	−1.79873e29	−0.294169
$953$	4.46099e29i	0.721942i	0.932577	+	0.360971i	$0.117555\pi$
$953$	4.46099e29i	0.721942i	−0.932577	+	0.360971i	$0.882445\pi$
$954$	0	0
$955$	4.16354e29	0.659826
$956$	1.07789e29i	0.169042i
$957$	0	0
$958$	3.55521e29	0.546021
$959$	2.06460e29i	0.313798i
$960$	0	0
$961$	−5.04921e29	−0.751604
$962$	5.66409e29i	0.834409i
$963$	0	0
$964$	−1.62009e29	−0.233759
$965$	− 2.89006e29i	− 0.412700i
$966$	0	0
$967$	−1.29392e29	−0.180985	−0.0904923	−	0.995897i	$-0.528844\pi$
$967$	−1.29392e29	−0.180985	−0.0904923	+	0.995897i	$0.528844\pi$
$968$	− 2.31462e29i	− 0.320425i
$969$	0	0
$970$	1.63592e30	2.21843
$971$	− 4.60306e29i	− 0.617810i	−0.951093	−	0.308905i	$-0.900038\pi$
$971$	− 4.60306e29i	− 0.617810i	0.951093	−	0.308905i	$-0.0999624\pi$
$972$	0	0
$973$	−1.03276e30	−1.35792
$974$	2.83149e29i	0.368490i
$975$	0	0
$976$	1.13621e29	0.144864
$977$	− 4.70028e29i	− 0.593169i	−0.955007	−	0.296584i	$-0.904152\pi$
$977$	− 4.70028e29i	− 0.593169i	0.955007	−	0.296584i	$-0.0958476\pi$
$978$	0	0
$979$	−1.84270e29	−0.227838
$980$	− 5.38759e29i	− 0.659377i
$981$	0	0
$982$	−9.14266e28	−0.109637
$983$	8.69352e29i	1.03195i	0.856602	+	0.515977i	$0.172571\pi$
$983$	8.69352e29i	1.03195i	−0.856602	+	0.515977i	$0.827429\pi$
$984$	0	0
$985$	8.00317e29	0.930893
$986$	4.58396e29i	0.527803i
$987$	0	0
$988$	−2.83917e28	−0.0320348
$989$	− 2.89611e29i	− 0.323484i
$990$	0	0
$991$	−1.67605e30	−1.83463	−0.917317	−	0.398158i	$-0.869650\pi$
$991$	−1.67605e30	−1.83463	−0.917317	+	0.398158i	$0.869650\pi$
$992$	8.13044e28i	0.0881043i
$993$	0	0
$994$	−1.37295e30	−1.45811
$995$	1.32873e30i	1.39703i
$996$	0	0
$997$	1.13481e30	1.16942	0.584709	−	0.811243i	$-0.301209\pi$
$997$	1.13481e30	1.16942	0.584709	+	0.811243i	$0.301209\pi$
$998$	− 1.08360e30i	− 1.10551i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.b.c.53.12	yes	12
3.2	odd	2	inner	54.21.b.c.53.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.21.b.c.53.1	✓	12	3.2	odd	2	inner
54.21.b.c.53.12	yes	12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+724.077i q^{2} -524288. q^{4} +1.79220e7i q^{5} +3.70310e8 q^{7} -3.79625e8i q^{8} -1.29769e10 q^{10} -7.93961e9i q^{11} +8.82019e10 q^{13} +2.68133e11i q^{14} +2.74878e11 q^{16} -1.27952e12i q^{17} +6.13964e11 q^{19} -9.39630e12i q^{20} +5.74889e12 q^{22} +5.25696e13i q^{23} -2.25831e14 q^{25} +6.38650e13i q^{26} -1.94149e14 q^{28} +4.94778e14i q^{29} +4.08497e14 q^{31} +1.99033e14i q^{32} +9.26469e14 q^{34} +6.63671e15i q^{35} +8.86884e15 q^{37} +4.44558e14i q^{38} +6.80365e15 q^{40} +1.66486e16i q^{41} -5.50910e15 q^{43} +4.16264e15i q^{44} -3.80644e16 q^{46} -6.38595e16i q^{47} +5.73373e16 q^{49} -1.63519e17i q^{50} -4.62432e16 q^{52} +2.19038e17i q^{53} +1.42294e17 q^{55} -1.40579e17i q^{56} -3.58257e17 q^{58} -6.16324e17i q^{59} +4.13350e17 q^{61} +2.95784e17i q^{62} -1.44115e17 q^{64} +1.58076e18i q^{65} +7.34220e17 q^{67} +6.70835e17i q^{68} -4.80549e18 q^{70} +5.12039e18i q^{71} +5.57613e18 q^{73} +6.42173e18i q^{74} -3.21894e17 q^{76} -2.94012e18i q^{77} -9.30637e18 q^{79} +4.92637e18i q^{80} -1.20548e19 q^{82} +1.56494e19i q^{83} +2.29315e19 q^{85} -3.98902e18i q^{86} -3.01407e18 q^{88} -2.32089e19i q^{89} +3.26621e19 q^{91} -2.75616e19i q^{92} +4.62392e19 q^{94} +1.10035e19i q^{95} -1.26064e20 q^{97} +4.15167e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6291456 q^{4} + 355856172 q^{7} - 5360984064 q^{10} + 374332013160 q^{13} + 3298534883328 q^{16} + 13268452496064 q^{19} + 64109345587200 q^{22} - 10850992436544 q^{25} - 186571120705536 q^{28} + 13\!\cdots\!76 q^{31}+ \cdots - 30\!\cdots\!60 q^{97}+O(q^{100}) \) 12 * q - 6291456 * q^4 + 355856172 * q^7 - 5360984064 * q^10 + 374332013160 * q^13 + 3298534883328 * q^16 + 13268452496064 * q^19 + 64109345587200 * q^22 - 10850992436544 * q^25 - 186571120705536 * q^28 + 1341631815613476 * q^31 - 1150892216451072 * q^34 - 1840381413631248 * q^37 + 2810699612946432 * q^40 - 58876514549555304 * q^43 - 52022884060053504 * q^46 + 301701288785631840 * q^49 - 196257782515630080 * q^52 + 1198488617517746484 * q^55 - 952998745417777152 * q^58 - 611525981019002448 * q^61 - 1729382256910270464 * q^64 - 3378608356010016504 * q^67 - 10123347229078487040 * q^70 + 35504687328043033068 * q^73 - 6956490422256402432 * q^76 + 15118277214382580040 * q^79 - 16372057824399605760 * q^82 - 2077217010606501720 * q^85 - 33611760579221913600 * q^88 - 154840755366303827352 * q^91 + 150175394882225012736 * q^94 - 3033444647600404860 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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