LMFDB - Embedded newform 2916.2.e.d.1945.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2916,2,Mod(973,2916)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2916, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2916.973");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2916 = 2^{2} \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2916.e (of order $3$, degree $2$, not 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:	$23.2843772294$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1945.9
Root			$0.472963 + 1.66622i$ of defining polynomial
Character	$\chi$	$=$	2916.1945
Dual form			2916.2.e.d.973.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10020 + 3.63766i) q^{5} +(-1.75732 + 3.04377i) q^{7} +O(q^{10})$	$q+(2.10020 + 3.63766i) q^{5} +(-1.75732 + 3.04377i) q^{7} +(-0.923950 + 1.60033i) q^{11} +(1.16509 + 2.01799i) q^{13} -1.59986 q^{17} -4.62093 q^{19} +(-0.887762 - 1.53765i) q^{23} +(-6.32172 + 10.9495i) q^{25} +(0.575890 - 0.997470i) q^{29} +(-0.929466 - 1.60988i) q^{31} -14.7630 q^{35} +8.76728 q^{37} +(1.94793 + 3.37391i) q^{41} +(-1.28685 + 2.22888i) q^{43} +(3.73527 - 6.46968i) q^{47} +(-2.67637 - 4.63562i) q^{49} -8.02417 q^{53} -7.76194 q^{55} +(0.611936 + 1.05991i) q^{59} +(2.17370 - 3.76497i) q^{61} +(-4.89385 + 8.47640i) q^{65} +(3.17446 + 5.49833i) q^{67} +1.74266 q^{71} +2.75816 q^{73} +(-3.24736 - 5.62459i) q^{77} +(4.98492 - 8.63414i) q^{79} +(5.64715 - 9.78116i) q^{83} +(-3.36002 - 5.81973i) q^{85} -5.42334 q^{89} -8.18975 q^{91} +(-9.70489 - 16.8094i) q^{95} +(6.04681 - 10.4734i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{5}+O(q^{10}) $ 18 * q + 6 * q^5	$ 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) $ 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

$n$	$1459$	$2189$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.10020	+	3.63766i	0.939240	+	1.62681i	0.766893	+	0.641775i	$0.221802\pi$
$5$	2.10020	+	3.63766i	0.939240	+	1.62681i	0.172347	+	0.985036i	$0.444865\pi$
$6$		0			0
$7$	−1.75732	+	3.04377i	−0.664206	+	1.15044i	0.315294	+	0.948994i	$0.397897\pi$
$7$	−1.75732	+	3.04377i	−0.664206	+	1.15044i	−0.979500	+	0.201445i	$0.935436\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.923950	+	1.60033i	−0.278581	+	0.482517i	−0.971032	−	0.238948i	$-0.923198\pi$
$11$	−0.923950	+	1.60033i	−0.278581	+	0.482517i	0.692451	+	0.721465i	$0.256531\pi$
$12$		0			0
$13$	1.16509	+	2.01799i	0.323138	+	0.559691i	0.981134	−	0.193331i	$-0.0619290\pi$
$13$	1.16509	+	2.01799i	0.323138	+	0.559691i	−0.657996	+	0.753021i	$0.728596\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.59986			−0.388022			−0.194011	−	0.980999i	$-0.562150\pi$
$17$	−1.59986			−0.388022			−0.194011	+	0.980999i	$0.562150\pi$
$18$		0			0
$19$	−4.62093			−1.06011			−0.530056	−	0.847962i	$-0.677829\pi$
$19$	−4.62093			−1.06011			−0.530056	+	0.847962i	$0.677829\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.887762	−	1.53765i	−0.185111	−	0.320622i	0.758503	−	0.651670i	$-0.225931\pi$
$23$	−0.887762	−	1.53765i	−0.185111	−	0.320622i	−0.943614	+	0.331048i	$0.892598\pi$
$24$		0			0
$25$	−6.32172	+	10.9495i	−1.26434	+	2.18991i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.575890	−	0.997470i	0.106940	−	0.185226i	−0.807589	−	0.589746i	$-0.799228\pi$
$29$	0.575890	−	0.997470i	0.106940	−	0.185226i	0.914529	+	0.404520i	$0.132561\pi$
$30$		0			0
$31$	−0.929466	−	1.60988i	−0.166937	−	0.289143i	0.770404	−	0.637555i	$-0.220054\pi$
$31$	−0.929466	−	1.60988i	−0.166937	−	0.289143i	−0.937341	+	0.348412i	$0.886721\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−14.7630			−2.49540
$36$		0			0
$37$	8.76728			1.44133			0.720666	−	0.693283i	$-0.243836\pi$
$37$	8.76728			1.44133			0.720666	+	0.693283i	$0.243836\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.94793	+	3.37391i	0.304215	+	0.526916i	0.977086	−	0.212844i	$-0.0682725\pi$
$41$	1.94793	+	3.37391i	0.304215	+	0.526916i	−0.672871	+	0.739760i	$0.734939\pi$
$42$		0			0
$43$	−1.28685	+	2.22888i	−0.196242	+	0.339902i	−0.947307	−	0.320327i	$-0.896207\pi$
$43$	−1.28685	+	2.22888i	−0.196242	+	0.339902i	0.751065	+	0.660229i	$0.229541\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.73527	−	6.46968i	0.544846	−	0.943700i	−0.453771	−	0.891118i	$-0.649922\pi$
$47$	3.73527	−	6.46968i	0.544846	−	0.943700i	0.998617	−	0.0525819i	$-0.0167450\pi$
$48$		0			0
$49$	−2.67637	−	4.63562i	−0.382339	−	0.662231i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.02417			−1.10220			−0.551102	−	0.834438i	$-0.685793\pi$
$53$	−8.02417			−1.10220			−0.551102	+	0.834438i	$0.685793\pi$
$54$		0			0
$55$	−7.76194			−1.04662
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.611936	+	1.05991i	0.0796673	+	0.137988i	0.903106	−	0.429417i	$-0.141281\pi$
$59$	0.611936	+	1.05991i	0.0796673	+	0.137988i	−0.823439	+	0.567405i	$0.807948\pi$
$60$		0			0
$61$	2.17370	−	3.76497i	0.278314	−	0.482055i	−0.692652	−	0.721272i	$-0.743558\pi$
$61$	2.17370	−	3.76497i	0.278314	−	0.482055i	0.970966	+	0.239218i	$0.0768910\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.89385	+	8.47640i	−0.607007	+	1.05137i
$66$		0			0
$67$	3.17446	+	5.49833i	0.387822	+	0.671728i	0.992156	−	0.125003i	$-0.0398942\pi$
$67$	3.17446	+	5.49833i	0.387822	+	0.671728i	−0.604334	+	0.796731i	$0.706561\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.74266			0.206815			0.103408	−	0.994639i	$-0.467025\pi$
$71$	1.74266			0.206815			0.103408	+	0.994639i	$0.467025\pi$
$72$		0			0
$73$	2.75816			0.322819			0.161409	−	0.986888i	$-0.448396\pi$
$73$	2.75816			0.322819			0.161409	+	0.986888i	$0.448396\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.24736	−	5.62459i	−0.370071	−	0.640982i
$78$		0			0
$79$	4.98492	−	8.63414i	0.560848	−	0.971417i	−0.436575	−	0.899668i	$-0.643809\pi$
$79$	4.98492	−	8.63414i	0.560848	−	0.971417i	0.997423	−	0.0717488i	$-0.0228580\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.64715	−	9.78116i	0.619856	−	1.07362i	−0.369656	−	0.929169i	$-0.620524\pi$
$83$	5.64715	−	9.78116i	0.619856	−	1.07362i	0.989512	−	0.144453i	$-0.0461422\pi$
$84$		0			0
$85$	−3.36002	−	5.81973i	−0.364446	−	0.631238i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.42334			−0.574872			−0.287436	−	0.957800i	$-0.592803\pi$
$89$	−5.42334			−0.574872			−0.287436	+	0.957800i	$0.592803\pi$
$90$		0			0
$91$	−8.18975			−0.858520
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.70489	−	16.8094i	−0.995701	−	1.72460i
$96$		0			0
$97$	6.04681	−	10.4734i	0.613961	−	1.06341i	−0.376605	−	0.926374i	$-0.622909\pi$
$97$	6.04681	−	10.4734i	0.613961	−	1.06341i	0.990566	−	0.137037i	$-0.0437581\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.08189	+	12.2662i	−0.704674	+	1.22053i	0.262135	+	0.965031i	$0.415574\pi$
$101$	−7.08189	+	12.2662i	−0.704674	+	1.22053i	−0.966809	+	0.255500i	$0.917760\pi$
$102$		0			0
$103$	−0.754653	−	1.30710i	−0.0743582	−	0.128792i	0.826449	−	0.563012i	$-0.190357\pi$
$103$	−0.754653	−	1.30710i	−0.0743582	−	0.128792i	−0.900807	+	0.434220i	$0.857024\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.4114			−1.87658			−0.938288	−	0.345856i	$-0.887589\pi$
$107$	−19.4114			−1.87658			−0.938288	+	0.345856i	$0.887589\pi$
$108$		0			0
$109$	15.2590			1.46155			0.730775	−	0.682619i	$-0.239159\pi$
$109$	15.2590			1.46155			0.730775	+	0.682619i	$0.239159\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.69280	−	9.86022i	−0.535534	−	0.927572i	−0.999137	−	0.0415291i	$-0.986777\pi$
$113$	−5.69280	−	9.86022i	−0.535534	−	0.927572i	0.463603	−	0.886043i	$-0.346556\pi$
$114$		0			0
$115$	3.72896	−	6.45876i	0.347728	−	0.602282i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.81146	−	4.86960i	0.257726	−	0.446395i
$120$		0			0
$121$	3.79263	+	6.56903i	0.344785	+	0.597185i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−32.1056			−2.87161
$126$		0			0
$127$	−1.61000			−0.142864			−0.0714321	−	0.997445i	$-0.522757\pi$
$127$	−1.61000			−0.142864			−0.0714321	+	0.997445i	$0.522757\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.63344	−	4.56124i	−0.230084	−	0.398518i	0.727748	−	0.685844i	$-0.240567\pi$
$131$	−2.63344	−	4.56124i	−0.230084	−	0.398518i	−0.957833	+	0.287326i	$0.907234\pi$
$132$		0			0
$133$	8.12046	−	14.0651i	0.704133	−	1.21959i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.81752	+	13.5403i	−0.667895	+	1.15683i	0.310596	+	0.950542i	$0.399471\pi$
$137$	−7.81752	+	13.5403i	−0.667895	+	1.15683i	−0.978492	+	0.206287i	$0.933862\pi$
$138$		0			0
$139$	6.12704	+	10.6123i	0.519689	+	0.900128i	0.999738	+	0.0228861i	$0.00728550\pi$
$139$	6.12704	+	10.6123i	0.519689	+	0.900128i	−0.480049	+	0.877242i	$0.659381\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.30594			−0.360080
$144$		0			0
$145$	4.83795			0.401769
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.4701	+	18.1347i	0.857743	+	1.48565i	0.874077	+	0.485788i	$0.161467\pi$
$149$	10.4701	+	18.1347i	0.857743	+	1.48565i	−0.0163334	+	0.999867i	$0.505199\pi$
$150$		0			0
$151$	4.82183	−	8.35166i	0.392395	−	0.679648i	−0.600370	−	0.799723i	$-0.704980\pi$
$151$	4.82183	−	8.35166i	0.392395	−	0.679648i	0.992765	+	0.120074i	$0.0383132\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.90414	−	6.76216i	0.313588	−	0.543150i
$156$		0			0
$157$	5.88040	+	10.1851i	0.469307	+	0.812863i	0.999384	−	0.0350862i	$-0.0111706\pi$
$157$	5.88040	+	10.1851i	0.469307	+	0.812863i	−0.530078	+	0.847949i	$0.677837\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.24034			0.491808
$162$		0			0
$163$	−14.3539			−1.12429			−0.562143	−	0.827040i	$-0.690023\pi$
$163$	−14.3539			−1.12429			−0.562143	+	0.827040i	$0.690023\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.23014	+	7.32681i	0.327338	+	0.566966i	0.981983	−	0.188971i	$-0.0605151\pi$
$167$	4.23014	+	7.32681i	0.327338	+	0.566966i	−0.654645	+	0.755937i	$0.727182\pi$
$168$		0			0
$169$	3.78514	−	6.55605i	0.291164	−	0.504311i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.5286	−	21.7002i	0.952533	−	1.64984i	0.212618	−	0.977135i	$-0.431801\pi$
$173$	12.5286	−	21.7002i	0.952533	−	1.64984i	0.739915	−	0.672700i	$-0.234866\pi$
$174$		0			0
$175$	−22.2186	−	38.4838i	−1.67957	−	2.90910i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.68320			−0.723757			−0.361878	−	0.932225i	$-0.617864\pi$
$179$	−9.68320			−0.723757			−0.361878	+	0.932225i	$0.617864\pi$
$180$		0			0
$181$	−0.604163			−0.0449071			−0.0224535	−	0.999748i	$-0.507148\pi$
$181$	−0.604163			−0.0449071			−0.0224535	+	0.999748i	$0.507148\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.4131	+	31.8924i	1.35376	+	2.34477i
$186$		0			0
$187$	1.47819	−	2.56029i	0.108096	−	0.187227i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.3540	+	17.9336i	−0.749188	+	1.29763i	0.199024	+	0.979995i	$0.436223\pi$
$191$	−10.3540	+	17.9336i	−0.749188	+	1.29763i	−0.948212	+	0.317638i	$0.897110\pi$
$192$		0			0
$193$	5.56759	+	9.64334i	0.400764	+	0.694143i	0.993818	−	0.111019i	$-0.0354116\pi$
$193$	5.56759	+	9.64334i	0.400764	+	0.694143i	−0.593055	+	0.805162i	$0.702078\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.6239			−0.899417			−0.449709	−	0.893175i	$-0.648472\pi$
$197$	−12.6239			−0.899417			−0.449709	+	0.893175i	$0.648472\pi$
$198$		0			0
$199$	−21.0486			−1.49210			−0.746049	−	0.665891i	$-0.768052\pi$
$199$	−21.0486			−1.49210			−0.746049	+	0.665891i	$0.768052\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.02405	+	3.50576i	0.142060	+	0.246056i
$204$		0			0
$205$	−8.18209	+	14.1718i	−0.571462	+	0.989802i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.26950	−	7.39500i	0.295328	−	0.511523i
$210$		0			0
$211$	11.0843	+	19.1986i	0.763076	+	1.32169i	0.941258	+	0.337689i	$0.109645\pi$
$211$	11.0843	+	19.1986i	0.763076	+	1.32169i	−0.178182	+	0.983998i	$0.557021\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.8106			−0.737275
$216$		0			0
$217$	6.53349			0.443522
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.86397	−	3.22850i	−0.125384	−	0.217172i
$222$		0			0
$223$	−6.89410	+	11.9409i	−0.461663	+	0.799624i	−0.999044	−	0.0437155i	$-0.986080\pi$
$223$	−6.89410	+	11.9409i	−0.461663	+	0.799624i	0.537381	+	0.843340i	$0.319414\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.64850	+	8.05143i	−0.308532	+	0.534392i	−0.978041	−	0.208411i	$-0.933171\pi$
$227$	−4.64850	+	8.05143i	−0.308532	+	0.534392i	0.669510	+	0.742803i	$0.266504\pi$
$228$		0			0
$229$	0.0740456	+	0.128251i	0.00489307	+	0.00847505i	0.868462	−	0.495756i	$-0.165109\pi$
$229$	0.0740456	+	0.128251i	0.00489307	+	0.00847505i	−0.863568	+	0.504232i	$0.831776\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.64881			0.108017			0.0540084	−	0.998540i	$-0.482800\pi$
$233$	1.64881			0.108017			0.0540084	+	0.998540i	$0.482800\pi$
$234$		0			0
$235$	31.3794			2.04696
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.08134	−	10.5332i	−0.393369	−	0.681336i	0.599522	−	0.800358i	$-0.295357\pi$
$239$	−6.08134	−	10.5332i	−0.393369	−	0.681336i	−0.992892	+	0.119022i	$0.962024\pi$
$240$		0			0
$241$	−0.485375	+	0.840694i	−0.0312657	+	0.0541539i	−0.881235	−	0.472679i	$-0.843287\pi$
$241$	−0.485375	+	0.840694i	−0.0312657	+	0.0541539i	0.849969	+	0.526832i	$0.176620\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.2419	−	19.4715i	0.718217	−	1.24399i
$246$		0			0
$247$	−5.38379	−	9.32500i	−0.342562	−	0.593335i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	24.3628			1.53777			0.768884	−	0.639388i	$-0.220812\pi$
$251$	24.3628			1.53777			0.768884	+	0.639388i	$0.220812\pi$
$252$		0			0
$253$	3.28099			0.206274
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.458813	−	0.794688i	−0.0286200	−	0.0495713i	0.851361	−	0.524581i	$-0.175778\pi$
$257$	−0.458813	−	0.794688i	−0.0286200	−	0.0495713i	−0.879981	+	0.475010i	$0.842445\pi$
$258$		0			0
$259$	−15.4069	+	26.6856i	−0.957341	+	1.65816i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.7252	+	20.3086i	−0.723006	+	1.25228i	0.236783	+	0.971563i	$0.423907\pi$
$263$	−11.7252	+	20.3086i	−0.723006	+	1.25228i	−0.959789	+	0.280721i	$0.909426\pi$
$264$		0			0
$265$	−16.8524	−	29.1892i	−1.03523	−	1.79308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.5865			−1.01130			−0.505649	−	0.862739i	$-0.668747\pi$
$269$	−16.5865			−1.01130			−0.505649	+	0.862739i	$0.668747\pi$
$270$		0			0
$271$	17.5443			1.06574			0.532869	−	0.846198i	$-0.321114\pi$
$271$	17.5443			1.06574			0.532869	+	0.846198i	$0.321114\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.6819	−	20.2337i	−0.704445	−	1.22014i
$276$		0			0
$277$	−12.1165	+	20.9864i	−0.728010	+	1.26095i	0.229713	+	0.973258i	$0.426221\pi$
$277$	−12.1165	+	20.9864i	−0.728010	+	1.26095i	−0.957723	+	0.287692i	$0.907112\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.5607	−	18.2917i	0.630001	−	1.09119i	−0.357550	−	0.933894i	$-0.616388\pi$
$281$	10.5607	−	18.2917i	0.630001	−	1.09119i	0.987551	−	0.157300i	$-0.0502790\pi$
$282$		0			0
$283$	12.8660	+	22.2846i	0.764805	+	1.32468i	0.940350	+	0.340210i	$0.110498\pi$
$283$	12.8660	+	22.2846i	0.764805	+	1.32468i	−0.175545	+	0.984471i	$0.556169\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.6926			−0.808246
$288$		0			0
$289$	−14.4405			−0.849439
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.15020	+	15.8486i	0.534560	+	0.925886i	0.999184	+	0.0403777i	$0.0128561\pi$
$293$	9.15020	+	15.8486i	0.534560	+	0.925886i	−0.464624	+	0.885508i	$0.653811\pi$
$294$		0			0
$295$	−2.57038	+	4.45204i	−0.149654	+	0.259208i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.06864	−	3.58300i	0.119633	−	0.207210i
$300$		0			0
$301$	−4.52281	−	7.83375i	−0.260691	−	0.451530i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	18.2609			1.04562
$306$		0			0
$307$	−12.5267			−0.714936			−0.357468	−	0.933925i	$-0.616360\pi$
$307$	−12.5267			−0.714936			−0.357468	+	0.933925i	$0.616360\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.92129	−	6.79187i	−0.222356	−	0.385132i	0.733167	−	0.680049i	$-0.238041\pi$
$311$	−3.92129	−	6.79187i	−0.222356	−	0.385132i	−0.955523	+	0.294917i	$0.904708\pi$
$312$		0			0
$313$	−3.21460	+	5.56785i	−0.181700	+	0.314714i	−0.942460	−	0.334320i	$-0.891493\pi$
$313$	−3.21460	+	5.56785i	−0.181700	+	0.314714i	0.760760	+	0.649034i	$0.224827\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.53333	+	16.5122i	−0.535445	+	0.927418i	0.463696	+	0.885994i	$0.346523\pi$
$317$	−9.53333	+	16.5122i	−0.535445	+	0.927418i	−0.999142	+	0.0414242i	$0.986810\pi$
$318$		0			0
$319$	1.06419	+	1.84323i	0.0595830	+	0.103201i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.39281			0.411347
$324$		0			0
$325$	−29.4615			−1.63423
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.1282	+	22.7387i	0.723779	+	1.25362i
$330$		0			0
$331$	−7.54178	+	13.0628i	−0.414534	+	0.717994i	−0.995379	−	0.0960200i	$-0.969389\pi$
$331$	−7.54178	+	13.0628i	−0.414534	+	0.717994i	0.580845	+	0.814014i	$0.302722\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.3340	+	23.0952i	−0.728516	+	1.26183i
$336$		0			0
$337$	1.81913	+	3.15083i	0.0990943	+	0.171636i	0.911310	−	0.411721i	$-0.135072\pi$
$337$	1.81913	+	3.15083i	0.0990943	+	0.171636i	−0.812216	+	0.583357i	$0.801739\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.43512			0.186022
$342$		0			0
$343$	−5.78950			−0.312604
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.64799	−	9.78260i	−0.303200	−	0.525158i	0.673659	−	0.739042i	$-0.264722\pi$
$347$	−5.64799	−	9.78260i	−0.303200	−	0.525158i	−0.976859	+	0.213885i	$0.931388\pi$
$348$		0			0
$349$	−13.3265	+	23.0821i	−0.713350	+	1.23556i	0.250242	+	0.968183i	$0.419490\pi$
$349$	−13.3265	+	23.0821i	−0.713350	+	1.23556i	−0.963592	+	0.267375i	$0.913844\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.956012	−	1.65586i	0.0508834	−	0.0881326i	−0.839462	−	0.543419i	$-0.817130\pi$
$353$	0.956012	−	1.65586i	0.0508834	−	0.0881326i	0.890345	+	0.455286i	$0.150463\pi$
$354$		0			0
$355$	3.65993	+	6.33919i	0.194249	+	0.336449i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.4743			−1.39726			−0.698631	−	0.715482i	$-0.746207\pi$
$359$	−26.4743			−1.39726			−0.698631	+	0.715482i	$0.746207\pi$
$360$		0			0
$361$	2.35295			0.123839
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.79271	+	10.0333i	0.303204	+	0.525165i
$366$		0			0
$367$	−6.24978	+	10.8249i	−0.326236	+	0.565057i	−0.981762	−	0.190116i	$-0.939114\pi$
$367$	−6.24978	+	10.8249i	−0.326236	+	0.565057i	0.655526	+	0.755173i	$0.272447\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.1011	−	24.4238i	0.732091	−	1.26802i
$372$		0			0
$373$	1.60167	+	2.77417i	0.0829313	+	0.143641i	0.904508	−	0.426457i	$-0.140238\pi$
$373$	1.60167	+	2.77417i	0.0829313	+	0.143641i	−0.821577	+	0.570098i	$0.806905\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.68385			0.138225
$378$		0			0
$379$	10.7650			0.552963			0.276481	−	0.961019i	$-0.410832\pi$
$379$	10.7650			0.552963			0.276481	+	0.961019i	$0.410832\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.0772	−	26.1145i	−0.770409	−	1.33439i	−0.937339	−	0.348418i	$-0.886719\pi$
$383$	−15.0772	−	26.1145i	−0.770409	−	1.33439i	0.166931	−	0.985969i	$-0.446614\pi$
$384$		0			0
$385$	13.6402	−	23.6256i	0.695171	−	1.20407i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.13974	+	15.8305i	−0.463403	+	0.802638i	−0.999128	−	0.0417550i	$-0.986705\pi$
$389$	−9.13974	+	15.8305i	−0.463403	+	0.802638i	0.535725	+	0.844393i	$0.320038\pi$
$390$		0			0
$391$	1.42029	+	2.46002i	0.0718272	+	0.124408i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	41.8774			2.10708
$396$		0			0
$397$	9.81738			0.492720			0.246360	−	0.969178i	$-0.420765\pi$
$397$	9.81738			0.492720			0.246360	+	0.969178i	$0.420765\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.5346	−	19.9785i	−0.576011	−	0.997681i	−0.995931	−	0.0901195i	$-0.971275\pi$
$401$	−11.5346	−	19.9785i	−0.576011	−	0.997681i	0.419920	−	0.907561i	$-0.362058\pi$
$402$		0			0
$403$	2.16582	−	3.75131i	0.107887	−	0.186866i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.10053	+	14.0305i	−0.401528	+	0.695467i
$408$		0			0
$409$	9.39122	+	16.2661i	0.464366	+	0.804306i	0.999173	−	0.0406689i	$-0.0129489\pi$
$409$	9.39122	+	16.2661i	0.464366	+	0.804306i	−0.534807	+	0.844974i	$0.679616\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.30148			−0.211662
$414$		0			0
$415$	47.4407			2.32877
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.6913	−	27.1781i	−0.766570	−	1.32774i	−0.939413	−	0.342788i	$-0.888629\pi$
$419$	−15.6913	−	27.1781i	−0.766570	−	1.32774i	0.172843	−	0.984949i	$-0.444705\pi$
$420$		0			0
$421$	10.4088	−	18.0285i	0.507292	−	0.878656i	−0.492672	−	0.870215i	$-0.663980\pi$
$421$	10.4088	−	18.0285i	0.507292	−	0.878656i	0.999964	−	0.00844095i	$-0.00268687\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.1138	−	17.5177i	0.490593	−	0.849732i
$426$		0			0
$427$	7.63980	+	13.2325i	0.369716	+	0.640367i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.8928			1.48806			0.744028	−	0.668149i	$-0.232913\pi$
$431$	30.8928			1.48806			0.744028	+	0.668149i	$0.232913\pi$
$432$		0			0
$433$	−15.5840			−0.748917			−0.374459	−	0.927244i	$-0.622171\pi$
$433$	−15.5840			−0.748917			−0.374459	+	0.927244i	$0.622171\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.10228	+	7.10536i	0.196239	+	0.339896i
$438$		0			0
$439$	5.58046	−	9.66564i	0.266341	−	0.461316i	−0.701573	−	0.712597i	$-0.747519\pi$
$439$	5.58046	−	9.66564i	0.266341	−	0.461316i	0.967914	+	0.251282i	$0.0808520\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.23819	−	12.5369i	0.343897	−	0.595647i	−0.641256	−	0.767327i	$-0.721586\pi$
$443$	7.23819	−	12.5369i	0.343897	−	0.595647i	0.985153	+	0.171680i	$0.0549196\pi$
$444$		0			0
$445$	−11.3901	−	19.7283i	−0.539943	−	0.935209i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	37.3873			1.76441			0.882207	−	0.470862i	$-0.156057\pi$
$449$	37.3873			1.76441			0.882207	+	0.470862i	$0.156057\pi$
$450$		0			0
$451$	−7.19915			−0.338995
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−17.2002	−	29.7916i	−0.806356	−	1.39665i
$456$		0			0
$457$	−6.85663	+	11.8760i	−0.320740	+	0.555538i	−0.980641	−	0.195815i	$-0.937265\pi$
$457$	−6.85663	+	11.8760i	−0.320740	+	0.555538i	0.659901	+	0.751353i	$0.270598\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.67268	−	4.62922i	0.124479	−	0.215604i	−0.797050	−	0.603913i	$-0.793607\pi$
$461$	2.67268	−	4.62922i	0.124479	−	0.215604i	0.921529	+	0.388309i	$0.126941\pi$
$462$		0			0
$463$	−18.1892	−	31.5046i	−0.845324	−	1.46414i	−0.885339	−	0.464946i	$-0.846074\pi$
$463$	−18.1892	−	31.5046i	−0.845324	−	1.46414i	0.0400149	−	0.999199i	$-0.487259\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.23618			−0.242302			−0.121151	−	0.992634i	$-0.538658\pi$
$467$	−5.23618			−0.242302			−0.121151	+	0.992634i	$0.538658\pi$
$468$		0			0
$469$	−22.3142			−1.03038
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.37796	−	4.11876i	−0.109339	−	0.189381i
$474$		0			0
$475$	29.2122	−	50.5970i	1.34035	−	2.32155i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.84828	−	10.1295i	0.267215	−	0.462829i	−0.700927	−	0.713233i	$-0.747230\pi$
$479$	5.84828	−	10.1295i	0.267215	−	0.462829i	0.968141	+	0.250404i	$0.0805634\pi$
$480$		0			0
$481$	10.2147	+	17.6923i	0.465748	+	0.806700i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	50.7982			2.30663
$486$		0			0
$487$	20.7362			0.939645			0.469823	−	0.882761i	$-0.344318\pi$
$487$	20.7362			0.939645			0.469823	+	0.882761i	$0.344318\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.94163	+	8.55915i	0.223013	+	0.386269i	0.955721	−	0.294273i	$-0.0950776\pi$
$491$	4.94163	+	8.55915i	0.223013	+	0.386269i	−0.732709	+	0.680542i	$0.761744\pi$
$492$		0			0
$493$	−0.921340	+	1.59581i	−0.0414951	+	0.0718716i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.06241	+	5.30425i	−0.137368	+	0.237928i
$498$		0			0
$499$	10.1339	+	17.5525i	0.453657	+	0.785756i	0.998610	−	0.0527102i	$-0.0167859\pi$
$499$	10.1339	+	17.5525i	0.453657	+	0.785756i	−0.544953	+	0.838466i	$0.683453\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.69407			−0.120123			−0.0600614	−	0.998195i	$-0.519130\pi$
$503$	−2.69407			−0.120123			−0.0600614	+	0.998195i	$0.519130\pi$
$504$		0			0
$505$	−59.4937			−2.64743
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.17929	−	2.04259i	−0.0522710	−	0.0905360i	0.838706	−	0.544584i	$-0.183313\pi$
$509$	−1.17929	−	2.04259i	−0.0522710	−	0.0905360i	−0.890977	+	0.454048i	$0.849979\pi$
$510$		0			0
$511$	−4.84699	+	8.39523i	−0.214418	+	0.371383i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.16985	−	5.49035i	0.139680	−	0.241934i
$516$		0			0
$517$	6.90241	+	11.9553i	0.303568	+	0.525795i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	35.1178			1.53854			0.769270	−	0.638924i	$-0.220620\pi$
$521$	35.1178			1.53854			0.769270	+	0.638924i	$0.220620\pi$
$522$		0			0
$523$	29.7198			1.29955			0.649777	−	0.760125i	$-0.274862\pi$
$523$	29.7198			1.29955			0.649777	+	0.760125i	$0.274862\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.48701	+	2.57558i	0.0647752	+	0.112194i
$528$		0			0
$529$	9.92376	−	17.1885i	0.431468	−	0.747324i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.53902	+	7.86181i	−0.196607	+	0.340533i
$534$		0			0
$535$	−40.7680	−	70.6123i	−1.76255	−	3.05283i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.89135			0.426050
$540$		0			0
$541$	−4.06242			−0.174657			−0.0873286	−	0.996180i	$-0.527833\pi$
$541$	−4.06242			−0.174657			−0.0873286	+	0.996180i	$0.527833\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	32.0471	+	55.5072i	1.37275	+	2.37767i
$546$		0			0
$547$	18.6355	−	32.2776i	0.796795	−	1.38009i	−0.124898	−	0.992170i	$-0.539860\pi$
$547$	18.6355	−	32.2776i	0.796795	−	1.38009i	0.921693	−	0.387920i	$-0.126806\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.66114	+	4.60924i	−0.113369	+	0.196360i
$552$		0			0
$553$	17.5202	+	30.3460i	0.745037	+	1.29044i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.63521			−0.408257			−0.204128	−	0.978944i	$-0.565436\pi$
$557$	−9.63521			−0.408257			−0.204128	+	0.978944i	$0.565436\pi$
$558$		0			0
$559$	−5.99717			−0.253653
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.00407	+	13.8635i	0.337331	+	0.584275i	0.983930	−	0.178555i	$-0.0571424\pi$
$563$	8.00407	+	13.8635i	0.337331	+	0.584275i	−0.646598	+	0.762831i	$0.723809\pi$
$564$		0			0
$565$	23.9121	−	41.4170i	1.00599	−	1.74243i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.65633	−	16.7253i	0.404814	−	0.701159i	−0.589485	−	0.807779i	$-0.700669\pi$
$569$	9.65633	−	16.7253i	0.404814	−	0.701159i	0.994300	+	0.106620i	$0.0340028\pi$
$570$		0			0
$571$	4.65104	+	8.05585i	0.194640	+	0.337127i	0.946783	−	0.321874i	$-0.104313\pi$
$571$	4.65104	+	8.05585i	0.194640	+	0.337127i	−0.752142	+	0.659001i	$0.770979\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	22.4487			0.936177
$576$		0			0
$577$	6.10165			0.254015			0.127007	−	0.991902i	$-0.459463\pi$
$577$	6.10165			0.254015			0.127007	+	0.991902i	$0.459463\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	19.8478	+	34.3773i	0.823424	+	1.42621i
$582$		0			0
$583$	7.41393	−	12.8413i	0.307054	−	0.531833i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.3783	+	19.7079i	−0.469635	+	0.813431i	−0.999397	−	0.0347148i	$-0.988948\pi$
$587$	−11.3783	+	19.7079i	−0.469635	+	0.813431i	0.529763	+	0.848146i	$0.322281\pi$
$588$		0			0
$589$	4.29499	+	7.43914i	0.176972	+	0.306525i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.4186			−0.674233			−0.337117	−	0.941463i	$-0.609452\pi$
$593$	−16.4186			−0.674233			−0.337117	+	0.941463i	$0.609452\pi$
$594$		0			0
$595$	23.6186			0.968268
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.5528	+	28.6702i	0.676327	+	1.17143i	0.976079	+	0.217416i	$0.0697628\pi$
$599$	16.5528	+	28.6702i	0.676327	+	1.17143i	−0.299752	+	0.954017i	$0.596904\pi$
$600$		0			0
$601$	−11.3603	+	19.6767i	−0.463398	+	0.802629i	−0.999128	−	0.0417604i	$-0.986703\pi$
$601$	−11.3603	+	19.6767i	−0.463398	+	0.802629i	0.535729	+	0.844390i	$0.320037\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−15.9306	+	27.5926i	−0.647671	+	1.12180i
$606$		0			0
$607$	8.56163	+	14.8292i	0.347506	+	0.601898i	0.985806	−	0.167890i	$-0.0536953\pi$
$607$	8.56163	+	14.8292i	0.347506	+	0.601898i	−0.638300	+	0.769788i	$0.720362\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.4077			0.704240
$612$		0			0
$613$	41.6723			1.68313			0.841564	−	0.540157i	$-0.181635\pi$
$613$	41.6723			1.68313			0.841564	+	0.540157i	$0.181635\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.07050	+	15.7106i	0.365164	+	0.632483i	0.988803	−	0.149230i	$-0.0476794\pi$
$617$	9.07050	+	15.7106i	0.365164	+	0.632483i	−0.623638	+	0.781713i	$0.714346\pi$
$618$		0			0
$619$	3.98944	−	6.90991i	0.160349	−	0.277733i	−0.774645	−	0.632396i	$-0.782071\pi$
$619$	3.98944	−	6.90991i	0.160349	−	0.277733i	0.934994	+	0.354664i	$0.115405\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.53056	−	16.5074i	0.381834	−	0.661355i
$624$		0			0
$625$	−35.8197	−	62.0415i	−1.43279	−	2.48166i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.0264			−0.559268
$630$		0			0
$631$	−0.237256			−0.00944501			−0.00472251	−	0.999989i	$-0.501503\pi$
$631$	−0.237256			−0.00944501			−0.00472251	+	0.999989i	$0.501503\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.38133	−	5.85663i	−0.134184	−	0.232413i
$636$		0			0
$637$	6.23643	−	10.8018i	0.247096	−	0.427983i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.9589	−	20.7134i	0.472349	−	0.818132i	−0.527151	−	0.849772i	$-0.676740\pi$
$641$	11.9589	−	20.7134i	0.472349	−	0.818132i	0.999499	+	0.0316401i	$0.0100730\pi$
$642$		0			0
$643$	12.9031	+	22.3488i	0.508848	+	0.881351i	0.999947	+	0.0102471i	$0.00326181\pi$
$643$	12.9031	+	22.3488i	0.508848	+	0.881351i	−0.491099	+	0.871103i	$0.663405\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.60899			−0.259826			−0.129913	−	0.991525i	$-0.541470\pi$
$647$	−6.60899			−0.259826			−0.129913	+	0.991525i	$0.541470\pi$
$648$		0			0
$649$	−2.26159			−0.0887753
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.4658	−	21.5913i	−0.487823	−	0.844933i	0.512079	−	0.858938i	$-0.328875\pi$
$653$	−12.4658	−	21.5913i	−0.487823	−	0.844933i	−0.999902	+	0.0140047i	$0.995542\pi$
$654$		0			0
$655$	11.0615	−	19.1591i	0.432209	−	0.748608i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.85991	−	6.68556i	0.150361	−	0.260433i	−0.780999	−	0.624532i	$-0.785290\pi$
$659$	3.85991	−	6.68556i	0.150361	−	0.260433i	0.931360	+	0.364099i	$0.118623\pi$
$660$		0			0
$661$	−8.93095	−	15.4689i	−0.347374	−	0.601669i	0.638408	−	0.769698i	$-0.279593\pi$
$661$	−8.93095	−	15.4689i	−0.347374	−	0.601669i	−0.985782	+	0.168029i	$0.946260\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	68.2185			2.64540
$666$		0			0
$667$	−2.04501			−0.0791832
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.01679	+	6.95728i	0.155066	+	0.268583i
$672$		0			0
$673$	−2.44604	+	4.23667i	−0.0942880	+	0.163312i	−0.909311	−	0.416117i	$-0.863391\pi$
$673$	−2.44604	+	4.23667i	−0.0942880	+	0.163312i	0.815023	+	0.579428i	$0.196724\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.44663	+	14.6300i	−0.324630	+	0.562276i	−0.981437	−	0.191782i	$-0.938573\pi$
$677$	−8.44663	+	14.6300i	−0.324630	+	0.562276i	0.656807	+	0.754059i	$0.271907\pi$
$678$		0			0
$679$	21.2524	+	36.8103i	0.815593	+	1.41265i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.6557			1.28780			0.643900	−	0.765109i	$-0.277315\pi$
$683$	33.6557			1.28780			0.643900	+	0.765109i	$0.277315\pi$
$684$		0			0
$685$	−65.6735			−2.50926
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.34887	−	16.1927i	−0.356164	−	0.616894i
$690$		0			0
$691$	−8.19883	+	14.2008i	−0.311898	+	0.540223i	−0.978773	−	0.204946i	$-0.934298\pi$
$691$	−8.19883	+	14.2008i	−0.311898	+	0.540223i	0.666875	+	0.745169i	$0.267631\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−25.7361	+	44.5762i	−0.976225	+	1.69087i
$696$		0			0
$697$	−3.11640	−	5.39777i	−0.118042	−	0.204455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	34.9743			1.32096			0.660481	−	0.750843i	$-0.270352\pi$
$701$	34.9743			1.32096			0.660481	+	0.750843i	$0.270352\pi$
$702$		0			0
$703$	−40.5129			−1.52797
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.8903	−	43.1113i	−0.936098	−	1.62137i
$708$		0			0
$709$	13.3652	−	23.1492i	0.501940	−	0.869385i	−0.498058	−	0.867144i	$-0.665953\pi$
$709$	13.3652	−	23.1492i	0.501940	−	0.869385i	0.999997	−	0.00224143i	$-0.000713470\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.65029	+	2.85838i	−0.0618038	+	0.107047i
$714$		0			0
$715$	−9.04335	−	15.6635i	−0.338202	−	0.585783i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	26.1125			0.973833			0.486916	−	0.873449i	$-0.338122\pi$
$719$	26.1125			0.973833			0.486916	+	0.873449i	$0.338122\pi$
$720$		0			0
$721$	5.30468			0.197557
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.28123	+	12.6115i	0.270418	+	0.468378i
$726$		0			0
$727$	−6.83482	+	11.8383i	−0.253489	+	0.439056i	−0.964484	−	0.264141i	$-0.914912\pi$
$727$	−6.83482	+	11.8383i	−0.253489	+	0.439056i	0.710995	+	0.703197i	$0.248245\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.05877	−	3.56589i	0.0761463	−	0.131889i
$732$		0			0
$733$	5.77754	+	10.0070i	0.213398	+	0.369617i	0.952776	−	0.303674i	$-0.0982134\pi$
$733$	5.77754	+	10.0070i	0.213398	+	0.369617i	−0.739378	+	0.673291i	$0.764880\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.7322			−0.432160
$738$		0			0
$739$	50.4853			1.85713			0.928566	−	0.371168i	$-0.121043\pi$
$739$	50.4853			1.85713			0.928566	+	0.371168i	$0.121043\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.5010	+	18.1883i	0.385244	+	0.667263i	0.991803	−	0.127776i	$-0.0407839\pi$
$743$	10.5010	+	18.1883i	0.385244	+	0.667263i	−0.606559	+	0.795039i	$0.707451\pi$
$744$		0			0
$745$	−43.9787	+	76.1733i	−1.61125	+	2.79077i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	34.1122	−	59.0841i	1.24643	−	2.15888i
$750$		0			0
$751$	5.59471	+	9.69032i	0.204154	+	0.353605i	0.949863	−	0.312667i	$-0.101222\pi$
$751$	5.59471	+	9.69032i	0.204154	+	0.353605i	−0.745709	+	0.666272i	$0.767889\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	40.5073			1.47421
$756$		0			0
$757$	−22.2619			−0.809123			−0.404561	−	0.914511i	$-0.632576\pi$
$757$	−22.2619			−0.809123			−0.404561	+	0.914511i	$0.632576\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.96263	−	5.13142i	−0.107395	−	0.186014i	0.807319	−	0.590115i	$-0.200918\pi$
$761$	−2.96263	−	5.13142i	−0.107395	−	0.186014i	−0.914714	+	0.404101i	$0.867584\pi$
$762$		0			0
$763$	−26.8150	+	46.4450i	−0.970770	+	1.68142i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.42592	+	2.46977i	−0.0514870	+	0.0891781i
$768$		0			0
$769$	−1.13387	−	1.96392i	−0.0408884	−	0.0708208i	0.844857	−	0.534992i	$-0.179685\pi$
$769$	−1.13387	−	1.96392i	−0.0408884	−	0.0708208i	−0.885745	+	0.464171i	$0.846352\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.27902			0.333743			0.166872	−	0.985979i	$-0.446633\pi$
$773$	9.27902			0.333743			0.166872	+	0.985979i	$0.446633\pi$
$774$		0			0
$775$	23.5033			0.844263
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.00123	−	15.5906i	−0.322502	−	0.558591i
$780$		0			0
$781$	−1.61013	+	2.78882i	−0.0576149	+	0.0997919i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−24.7001	+	42.7818i	−0.881583	+	1.52695i
$786$		0			0
$787$	11.5351	+	19.9793i	0.411181	+	0.712186i	0.995019	−	0.0996838i	$-0.0317831\pi$
$787$	11.5351	+	19.9793i	0.411181	+	0.712186i	−0.583838	+	0.811870i	$0.698450\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	40.0164			1.42282
$792$		0			0
$793$	10.1302			0.359735
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.1513	+	17.5826i	0.359579	+	0.622808i	0.987890	−	0.155153i	$-0.0495871\pi$
$797$	10.1513	+	17.5826i	0.359579	+	0.622808i	−0.628312	+	0.777962i	$0.716254\pi$
$798$		0			0
$799$	−5.97590	+	10.3506i	−0.211412	+	0.366176i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.54841	+	4.41397i	−0.0899313	+	0.155766i
$804$		0			0
$805$	13.1060	+	22.7003i	0.461926	+	0.800079i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−35.2976			−1.24100			−0.620499	−	0.784207i	$-0.713070\pi$
$809$	−35.2976			−1.24100			−0.620499	+	0.784207i	$0.713070\pi$
$810$		0			0
$811$	−40.1846			−1.41107			−0.705536	−	0.708675i	$-0.749293\pi$
$811$	−40.1846			−1.41107			−0.705536	+	0.708675i	$0.749293\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−30.1462	−	52.2147i	−1.05598	−	1.82900i
$816$		0			0
$817$	5.94642	−	10.2995i	0.208039	−	0.360334i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.78148	−	11.7459i	0.236675	−	0.409934i	−0.723083	−	0.690761i	$-0.757276\pi$
$821$	6.78148	−	11.7459i	0.236675	−	0.409934i	0.959758	+	0.280828i	$0.0906089\pi$
$822$		0			0
$823$	−10.6519	−	18.4497i	−0.371303	−	0.643116i	0.618463	−	0.785814i	$-0.287756\pi$
$823$	−10.6519	−	18.4497i	−0.371303	−	0.643116i	−0.989766	+	0.142698i	$0.954422\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−52.5438			−1.82713			−0.913564	−	0.406695i	$-0.866681\pi$
$827$	−52.5438			−1.82713			−0.913564	+	0.406695i	$0.866681\pi$
$828$		0			0
$829$	13.7833			0.478712			0.239356	−	0.970932i	$-0.423064\pi$
$829$	13.7833			0.478712			0.239356	+	0.970932i	$0.423064\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.28181	+	7.41632i	0.148356	+	0.256960i
$834$		0			0
$835$	−17.7683	+	30.7756i	−0.614898	+	1.06503i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.4656	−	21.5910i	0.430360	−	0.745405i	−0.566545	−	0.824031i	$-0.691720\pi$
$839$	12.4656	−	21.5910i	0.430360	−	0.745405i	0.996904	+	0.0786265i	$0.0250534\pi$
$840$		0			0
$841$	13.8367	+	23.9659i	0.477128	+	0.826409i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	31.7982			1.09389
$846$		0			0
$847$	−26.6595			−0.916033
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.78326	−	13.4810i	−0.266807	−	0.462123i
$852$		0			0
$853$	2.32034	−	4.01894i	0.0794468	−	0.137606i	−0.823565	−	0.567223i	$-0.808018\pi$
$853$	2.32034	−	4.01894i	0.0794468	−	0.137606i	0.903011	+	0.429617i	$0.141351\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.1228	+	31.3896i	−0.619062	+	1.07225i	0.370595	+	0.928795i	$0.379154\pi$
$857$	−18.1228	+	31.3896i	−0.619062	+	1.07225i	−0.989657	+	0.143453i	$0.954180\pi$
$858$		0			0
$859$	−13.6898	−	23.7114i	−0.467090	−	0.809024i	0.532203	−	0.846617i	$-0.321364\pi$
$859$	−13.6898	−	23.7114i	−0.467090	−	0.809024i	−0.999293	+	0.0375931i	$0.988031\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	20.9476			0.713065			0.356532	−	0.934283i	$-0.383959\pi$
$863$	20.9476			0.713065			0.356532	+	0.934283i	$0.383959\pi$
$864$		0			0
$865$	105.251			3.57863
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.21164	+	15.9550i	0.312483	+	0.541237i
$870$		0			0
$871$	−7.39706	+	12.8121i	−0.250640	+	0.434121i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	56.4199	−	97.7221i	1.90734	−	3.30361i
$876$		0			0
$877$	−9.10478	−	15.7699i	−0.307447	−	0.532513i	0.670356	−	0.742039i	$-0.266141\pi$
$877$	−9.10478	−	15.7699i	−0.307447	−	0.532513i	−0.977803	+	0.209526i	$0.932808\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−46.1164			−1.55370			−0.776851	−	0.629684i	$-0.783184\pi$
$881$	−46.1164			−1.55370			−0.776851	+	0.629684i	$0.783184\pi$
$882$		0			0
$883$	−18.0699			−0.608100			−0.304050	−	0.952656i	$-0.598339\pi$
$883$	−18.0699			−0.608100			−0.304050	+	0.952656i	$0.598339\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.2119	+	22.8838i	0.443614	+	0.768361i	0.997954	−	0.0639285i	$-0.0203629\pi$
$887$	13.2119	+	22.8838i	0.443614	+	0.768361i	−0.554341	+	0.832290i	$0.687030\pi$
$888$		0			0
$889$	2.82929	−	4.90047i	0.0948913	−	0.164357i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−17.2604	+	29.8959i	−0.577598	+	1.00043i
$894$		0			0
$895$	−20.3367	−	35.2242i	−0.679781	−	1.17742i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.14108			−0.0714090
$900$		0			0
$901$	12.8375			0.427680
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.26887	−	2.19774i	−0.0421785	−	0.0730554i
$906$		0			0
$907$	−18.7694	+	32.5095i	−0.623226	+	1.07946i	0.365655	+	0.930751i	$0.380845\pi$
$907$	−18.7694	+	32.5095i	−0.623226	+	1.07946i	−0.988881	+	0.148709i	$0.952488\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.00448	+	13.8642i	−0.265200	+	0.459340i	−0.967616	−	0.252426i	$-0.918771\pi$
$911$	−8.00448	+	13.8642i	−0.265200	+	0.459340i	0.702416	+	0.711767i	$0.252105\pi$
$912$		0			0
$913$	10.4354	+	18.0746i	0.345360	+	0.598182i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.5112			0.611294
$918$		0			0
$919$	36.8859			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$919$	36.8859			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.03035	+	3.51667i	0.0668298	+	0.115753i
$924$		0			0
$925$	−55.4243	+	95.9977i	−1.82234	+	3.15638i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.9993	+	29.4437i	−0.557730	+	0.966017i	0.439955	+	0.898020i	$0.354994\pi$
$929$	−16.9993	+	29.4437i	−0.557730	+	0.966017i	−0.997685	+	0.0679975i	$0.978339\pi$
$930$		0			0
$931$	12.3673	+	21.4208i	0.405323	+	0.702040i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.4180			0.406111
$936$		0			0
$937$	12.1842			0.398039			0.199020	−	0.979995i	$-0.436224\pi$
$937$	12.1842			0.398039			0.199020	+	0.979995i	$0.436224\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.37770	+	9.31446i	0.175308	+	0.303643i	0.940268	−	0.340435i	$-0.110574\pi$
$941$	5.37770	+	9.31446i	0.175308	+	0.303643i	−0.764960	+	0.644078i	$0.777241\pi$
$942$		0			0
$943$	3.45859	−	5.99046i	0.112627	−	0.195076i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.1842	−	33.2281i	0.623404	−	1.07977i	−0.365443	−	0.930834i	$-0.619083\pi$
$947$	19.1842	−	33.2281i	0.623404	−	1.07977i	0.988847	−	0.148934i	$-0.0475841\pi$
$948$		0			0
$949$	3.21351	+	5.56596i	0.104315	+	0.180679i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.5466			0.730355			0.365177	−	0.930938i	$-0.381008\pi$
$953$	22.5466			0.730355			0.365177	+	0.930938i	$0.381008\pi$
$954$		0			0
$955$	−86.9820			−2.81467
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−27.4758	−	47.5895i	−0.887240	−	1.53675i
$960$		0			0
$961$	13.7722	−	23.8541i	0.444264	−	0.769488i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−23.3861	+	40.5060i	−0.752826	+	1.30393i
$966$		0			0
$967$	14.6411	+	25.3592i	0.470827	+	0.815496i	0.999443	−	0.0333646i	$-0.0106222\pi$
$967$	14.6411	+	25.3592i	0.470827	+	0.815496i	−0.528616	+	0.848861i	$0.677289\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.2319			−1.06646			−0.533232	−	0.845969i	$-0.679023\pi$
$971$	−33.2319			−1.06646			−0.533232	+	0.845969i	$0.679023\pi$
$972$		0			0
$973$	−43.0688			−1.38072
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.14083	+	5.44008i	0.100484	+	0.174044i	0.911884	−	0.410447i	$-0.134627\pi$
$977$	3.14083	+	5.44008i	0.100484	+	0.174044i	−0.811400	+	0.584491i	$0.801294\pi$
$978$		0			0
$979$	5.01089	−	8.67912i	0.160149	−	0.277386i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.713165	−	1.23524i	0.0227464	−	0.0393980i	−0.854428	−	0.519570i	$-0.826092\pi$
$983$	0.713165	−	1.23524i	0.0227464	−	0.0393980i	0.877175	+	0.480172i	$0.159426\pi$
$984$		0			0
$985$	−26.5128	−	45.9216i	−0.844769	−	1.46318i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.56966			0.145307
$990$		0			0
$991$	−11.1777			−0.355072			−0.177536	−	0.984114i	$-0.556813\pi$
$991$	−11.1777			−0.355072			−0.177536	+	0.984114i	$0.556813\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−44.2064	−	76.5678i	−1.40144	−	2.42736i
$996$		0			0
$997$	20.1576	−	34.9140i	0.638398	−	1.10574i	−0.347387	−	0.937722i	$-0.612931\pi$
$997$	20.1576	−	34.9140i	0.638398	−	1.10574i	0.985784	−	0.168015i	$-0.0537358\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.2.e.d.1945.9		18
3.2	odd	2		2916.2.e.c.1945.1		18
9.2	odd	6		2916.2.a.d.1.9		9
9.4	even	3	inner	2916.2.e.d.973.9		18
9.5	odd	6		2916.2.e.c.973.1		18
9.7	even	3		2916.2.a.c.1.1		9
27.2	odd	18		108.2.i.a.49.2	✓	18
27.4	even	9		972.2.i.d.541.1		18
27.5	odd	18		108.2.i.a.97.2	yes	18
27.7	even	9		972.2.i.b.757.1		18
27.11	odd	18		972.2.i.a.433.3		18
27.13	even	9		972.2.i.b.217.1		18
27.14	odd	18		972.2.i.c.217.3		18
27.16	even	9		972.2.i.d.433.1		18
27.20	odd	18		972.2.i.c.757.3		18
27.22	even	9		324.2.i.a.289.3		18
27.23	odd	18		972.2.i.a.541.3		18
27.25	even	9		324.2.i.a.37.3		18
108.59	even	18		432.2.u.d.97.2		18
108.83	even	18		432.2.u.d.49.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.49.2	✓	18	27.2	odd	18
108.2.i.a.97.2	yes	18	27.5	odd	18
324.2.i.a.37.3		18	27.25	even	9
324.2.i.a.289.3		18	27.22	even	9
432.2.u.d.49.2		18	108.83	even	18
432.2.u.d.97.2		18	108.59	even	18
972.2.i.a.433.3		18	27.11	odd	18
972.2.i.a.541.3		18	27.23	odd	18
972.2.i.b.217.1		18	27.13	even	9
972.2.i.b.757.1		18	27.7	even	9
972.2.i.c.217.3		18	27.14	odd	18
972.2.i.c.757.3		18	27.20	odd	18
972.2.i.d.433.1		18	27.16	even	9
972.2.i.d.541.1		18	27.4	even	9
2916.2.a.c.1.1		9	9.7	even	3
2916.2.a.d.1.9		9	9.2	odd	6
2916.2.e.c.973.1		18	9.5	odd	6
2916.2.e.c.1945.1		18	3.2	odd	2
2916.2.e.d.973.9		18	9.4	even	3	inner
2916.2.e.d.1945.9		18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2916.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10020 + 3.63766i) q^{5} +(-1.75732 + 3.04377i) q^{7} +O(q^{10})\)	\(q+(2.10020 + 3.63766i) q^{5} +(-1.75732 + 3.04377i) q^{7} +(-0.923950 + 1.60033i) q^{11} +(1.16509 + 2.01799i) q^{13} -1.59986 q^{17} -4.62093 q^{19} +(-0.887762 - 1.53765i) q^{23} +(-6.32172 + 10.9495i) q^{25} +(0.575890 - 0.997470i) q^{29} +(-0.929466 - 1.60988i) q^{31} -14.7630 q^{35} +8.76728 q^{37} +(1.94793 + 3.37391i) q^{41} +(-1.28685 + 2.22888i) q^{43} +(3.73527 - 6.46968i) q^{47} +(-2.67637 - 4.63562i) q^{49} -8.02417 q^{53} -7.76194 q^{55} +(0.611936 + 1.05991i) q^{59} +(2.17370 - 3.76497i) q^{61} +(-4.89385 + 8.47640i) q^{65} +(3.17446 + 5.49833i) q^{67} +1.74266 q^{71} +2.75816 q^{73} +(-3.24736 - 5.62459i) q^{77} +(4.98492 - 8.63414i) q^{79} +(5.64715 - 9.78116i) q^{83} +(-3.36002 - 5.81973i) q^{85} -5.42334 q^{89} -8.18975 q^{91} +(-9.70489 - 16.8094i) q^{95} +(6.04681 - 10.4734i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{5}+O(q^{10}) \) 18 * q + 6 * q^5	\( 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) \) 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more