LMFDB - Embedded newform 5292.2.bm.a.4625.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(2285,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("5292.2285");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.bm (of order $6$, 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:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4625.7
Root			$-0.811340 + 1.53027i$ of defining polynomial
Character	$\chi$	$=$	5292.4625
Dual form			5292.2.bm.a.2285.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74332 q^{5} +O(q^{10})$	$q+2.74332 q^{5} +0.418355i q^{11} +(1.32512 - 0.765056i) q^{13} +(1.95291 + 3.38253i) q^{17} +(5.11994 + 2.95600i) q^{19} +8.92450i q^{23} +2.52579 q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 + 1.76453i) q^{31} +(-4.54861 + 7.87842i) q^{37} +(-1.06236 - 1.84006i) q^{41} +(-5.77846 + 10.0086i) q^{43} +(-0.885373 - 1.53351i) q^{47} +(-3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(1.61459 - 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} -8.51021i q^{71} +(-1.65059 + 0.952971i) q^{73} +(0.433633 + 0.751074i) q^{79} +(-3.45880 + 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +(4.88864 - 8.46738i) q^{89} +(14.0456 + 8.10924i) q^{95} +(0.200411 + 0.115707i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) $ 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.74332			1.22685			0.613425	−	0.789753i	$-0.289791\pi$
$5$	2.74332			1.22685			0.613425	+	0.789753i	$0.289791\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$			0.418355i			0.126139i	0.998009	+	0.0630695i	$0.0200890\pi$
$11$			0.418355i			0.126139i	−0.998009	+	0.0630695i	$0.979911\pi$
$12$		0			0
$13$	1.32512	−	0.765056i	0.367521	−	0.212188i	−0.304854	−	0.952399i	$-0.598608\pi$
$13$	1.32512	−	0.765056i	0.367521	−	0.212188i	0.672375	+	0.740211i	$0.265274\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.95291	+	3.38253i	0.473649	+	0.820385i	0.999545	−	0.0301645i	$-0.00960312\pi$
$17$	1.95291	+	3.38253i	0.473649	+	0.820385i	−0.525896	+	0.850549i	$0.676270\pi$
$18$		0			0
$19$	5.11994	+	2.95600i	1.17459	+	0.678152i	0.954758	−	0.297385i	$-0.0961144\pi$
$19$	5.11994	+	2.95600i	1.17459	+	0.678152i	0.219836	+	0.975537i	$0.429448\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			8.92450i			1.86089i	0.366436	+	0.930443i	$0.380578\pi$
$23$			8.92450i			1.86089i	−0.366436	+	0.930443i	$0.619422\pi$
$24$		0			0
$25$	2.52579			0.505159
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.00378	−	3.46629i	−1.11487	−	0.643673i	−0.174787	−	0.984606i	$-0.555924\pi$
$29$	−6.00378	−	3.46629i	−1.11487	−	0.643673i	−0.940088	+	0.340933i	$0.889257\pi$
$30$		0			0
$31$	3.05626	+	1.76453i	0.548921	+	0.316920i	0.748687	−	0.662924i	$-0.230685\pi$
$31$	3.05626	+	1.76453i	0.548921	+	0.316920i	−0.199766	+	0.979844i	$0.564018\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.54861	+	7.87842i	−0.747787	+	1.29520i	0.201095	+	0.979572i	$0.435550\pi$
$37$	−4.54861	+	7.87842i	−0.747787	+	1.29520i	−0.948881	+	0.315633i	$0.897783\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.06236	−	1.84006i	−0.165913	−	0.287370i	0.771066	−	0.636755i	$-0.219724\pi$
$41$	−1.06236	−	1.84006i	−0.165913	−	0.287370i	−0.936979	+	0.349385i	$0.886390\pi$
$42$		0			0
$43$	−5.77846	+	10.0086i	−0.881208	+	1.52630i	−0.0312079	+	0.999513i	$0.509935\pi$
$43$	−5.77846	+	10.0086i	−0.881208	+	1.52630i	−0.850000	+	0.526783i	$0.823398\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.885373	−	1.53351i	−0.129145	−	0.223686i	0.794201	−	0.607656i	$-0.207890\pi$
$47$	−0.885373	−	1.53351i	−0.129145	−	0.223686i	−0.923346	+	0.383970i	$0.874557\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	−0.714721	−	0.699410i	$-0.753446\pi$
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	0.248346	+	0.968671i	$0.420113\pi$
$54$		0			0
$55$			1.14768i			0.154753i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.02728	+	3.51135i	−0.263929	+	0.457139i	−0.967283	−	0.253702i	$-0.918352\pi$
$59$	−2.02728	+	3.51135i	−0.263929	+	0.457139i	0.703353	+	0.710840i	$0.251685\pi$
$60$		0			0
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	−0.393062	−	0.919512i	$-0.628584\pi$
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	0.599789	+	0.800158i	$0.295251\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.63521	−	2.09879i	0.450893	−	0.260323i
$66$		0			0
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	−0.151974	−	0.988385i	$-0.548563\pi$
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	0.931953	−	0.362579i	$-0.118104\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.51021i		−	1.00998i	−0.863126	−	0.504988i	$-0.831497\pi$
$71$		−	8.51021i		−	1.00998i	0.863126	−	0.504988i	$-0.168503\pi$
$72$		0			0
$73$	−1.65059	+	0.952971i	−0.193187	+	0.111537i	−0.593474	−	0.804853i	$-0.702244\pi$
$73$	−1.65059	+	0.952971i	−0.193187	+	0.111537i	0.400286	+	0.916390i	$0.368911\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	0.889388	−	0.457153i	$-0.151131\pi$
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	−0.840600	+	0.541656i	$0.817798\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.45880	+	5.99082i	−0.379653	+	0.657578i	−0.991012	−	0.133775i	$-0.957290\pi$
$83$	−3.45880	+	5.99082i	−0.379653	+	0.657578i	0.611359	+	0.791354i	$0.290623\pi$
$84$		0			0
$85$	5.35744	+	9.27936i	0.581096	+	1.00649i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.88864	−	8.46738i	0.518195	−	0.897540i	−0.481581	−	0.876401i	$-0.659937\pi$
$89$	4.88864	−	8.46738i	0.518195	−	0.897540i	0.999777	−	0.0211389i	$-0.00672921\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.0456	+	8.10924i	1.44105	+	0.831990i
$96$		0			0
$97$	0.200411	+	0.115707i	0.0203486	+	0.0117483i	0.510140	−	0.860091i	$-0.329594\pi$
$97$	0.200411	+	0.115707i	0.0203486	+	0.0117483i	−0.489791	+	0.871840i	$0.662927\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−14.2806			−1.42097			−0.710487	−	0.703710i	$-0.751525\pi$
$101$	−14.2806			−1.42097			−0.710487	+	0.703710i	$0.751525\pi$
$102$		0			0
$103$			10.7458i			1.05882i	0.848366	+	0.529410i	$0.177587\pi$
$103$			10.7458i			1.05882i	−0.848366	+	0.529410i	$0.822413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.50534	−	3.17851i	−0.532221	−	0.307278i	0.209699	−	0.977766i	$-0.432751\pi$
$107$	−5.50534	−	3.17851i	−0.532221	−	0.307278i	−0.741920	+	0.670488i	$0.766085\pi$
$108$		0			0
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	0.962735	−	0.270447i	$-0.0871714\pi$
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	−0.715581	+	0.698530i	$0.753838\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.19186	+	5.30692i	−0.864697	+	0.499233i	−0.865582	−	0.500766i	$-0.833052\pi$
$113$	−9.19186	+	5.30692i	−0.864697	+	0.499233i	0.000885276		1.00000i	$0.499718\pi$
$114$		0			0
$115$			24.4827i			2.28303i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.8250			0.984089
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.78753			−0.607096
$126$		0			0
$127$	10.2909			0.913169			0.456584	−	0.889680i	$-0.349073\pi$
$127$	10.2909			0.913169			0.456584	+	0.889680i	$0.349073\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	19.6610			1.71779			0.858893	−	0.512155i	$-0.171153\pi$
$131$	19.6610			1.71779			0.858893	+	0.512155i	$0.171153\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$			5.38565i			0.460127i	0.973176	+	0.230063i	$0.0738933\pi$
$137$			5.38565i			0.460127i	−0.973176	+	0.230063i	$0.926107\pi$
$138$		0			0
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.282062	−	0.959396i	$-0.408982\pi$
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.971892	+	0.235425i	$0.0756484\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.320065	+	0.554369i	0.0267652	+	0.0463587i
$144$		0			0
$145$	−16.4703	−	9.50912i	−1.36778	−	0.789690i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			10.7521i			0.880849i	0.897790	+	0.440425i	$0.145172\pi$
$149$			10.7521i			0.880849i	−0.897790	+	0.440425i	$0.854828\pi$
$150$		0			0
$151$	7.56447			0.615588			0.307794	−	0.951453i	$-0.400409\pi$
$151$	7.56447			0.615588			0.307794	+	0.951453i	$0.400409\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.38430	+	4.84068i	0.673443	+	0.388812i
$156$		0			0
$157$	10.6317	+	6.13820i	0.848500	+	0.489882i	0.860144	−	0.510051i	$-0.170373\pi$
$157$	10.6317	+	6.13820i	0.848500	+	0.489882i	−0.0116445	+	0.999932i	$0.503707\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.91745	−	10.2493i	0.463490	−	0.802789i	−0.535642	−	0.844445i	$-0.679930\pi$
$163$	5.91745	−	10.2493i	0.463490	−	0.802789i	0.999132	+	0.0416566i	$0.0132635\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.78854	−	11.7581i	−0.525313	−	0.909869i	−0.999565	−	0.0294798i	$-0.990615\pi$
$167$	−6.78854	−	11.7581i	−0.525313	−	0.909869i	0.474252	−	0.880389i	$-0.342718\pi$
$168$		0			0
$169$	−5.32938	+	9.23075i	−0.409952	+	0.710058i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.31085	−	14.3948i	−0.631862	−	1.09442i	−0.987171	−	0.159668i	$-0.948957\pi$
$173$	−8.31085	−	14.3948i	−0.631862	−	1.09442i	0.355308	−	0.934749i	$-0.384376\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.8080	−	8.54942i	1.10680	−	0.639014i	0.168805	−	0.985650i	$-0.446009\pi$
$179$	14.8080	−	8.54942i	1.10680	−	0.639014i	0.938000	+	0.346636i	$0.112676\pi$
$180$		0			0
$181$			18.2171i			1.35407i	0.735952	+	0.677034i	$0.236735\pi$
$181$			18.2171i			1.35407i	−0.735952	+	0.677034i	$0.763265\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.4783	+	21.6130i	−0.917422	+	1.58902i
$186$		0			0
$187$	−1.41510	+	0.817009i	−0.103482	+	0.0597456i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.332826	−	0.942988i	$-0.391998\pi$
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.983065	+	0.183258i	$0.0586644\pi$
$192$		0			0
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	−0.712780	−	0.701388i	$-0.752564\pi$
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	0.963810	+	0.266592i	$0.0858975\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			16.0756i			1.14534i	0.819786	+	0.572670i	$0.194092\pi$
$197$			16.0756i			1.14534i	−0.819786	+	0.572670i	$0.805908\pi$
$198$		0			0
$199$	5.44956	−	3.14630i	0.386309	−	0.223036i	−0.294251	−	0.955728i	$-0.595070\pi$
$199$	5.44956	−	3.14630i	0.386309	−	0.223036i	0.680560	+	0.732693i	$0.261737\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.91440	−	5.04788i	−0.203550	−	0.352559i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.23666	+	2.14195i	−0.0855414	+	0.148162i
$210$		0			0
$211$	−1.29814	−	2.24844i	−0.0893674	−	0.154789i	0.817876	−	0.575394i	$-0.195151\pi$
$211$	−1.29814	−	2.24844i	−0.0893674	−	0.154789i	−0.907244	+	0.420605i	$0.861818\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.8522	+	27.4568i	−1.08111	+	1.87254i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.17565	+	2.98816i	0.348152	+	0.201006i
$222$		0			0
$223$	−20.7215	−	11.9636i	−1.38762	−	0.801141i	−0.394571	−	0.918866i	$-0.629107\pi$
$223$	−20.7215	−	11.9636i	−1.38762	−	0.801141i	−0.993046	+	0.117725i	$0.962440\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.73218			−0.247713			−0.123857	−	0.992300i	$-0.539526\pi$
$227$	−3.73218			−0.247713			−0.123857	+	0.992300i	$0.539526\pi$
$228$		0			0
$229$		−	21.0681i		−	1.39222i	−0.717935	−	0.696111i	$-0.754912\pi$
$229$		−	21.0681i		−	1.39222i	0.717935	−	0.696111i	$-0.245088\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	0.0921057	−	0.995749i	$-0.470640\pi$
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	−0.816291	+	0.577640i	$0.803974\pi$
$234$		0			0
$235$	−2.42886	−	4.20691i	−0.158441	−	0.274429i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.0521	+	6.38091i	−0.714899	+	0.412747i	−0.812872	−	0.582442i	$-0.802097\pi$
$239$	−11.0521	+	6.38091i	−0.714899	+	0.412747i	0.0979736	+	0.995189i	$0.468764\pi$
$240$		0			0
$241$		−	3.04192i		−	0.195947i	−0.995189	−	0.0979737i	$-0.968764\pi$
$241$		−	3.04192i		−	0.195947i	0.995189	−	0.0979737i	$-0.0312361\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.04601			0.575584
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.32067			0.398957			0.199478	−	0.979902i	$-0.436075\pi$
$251$	6.32067			0.398957			0.199478	+	0.979902i	$0.436075\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.5076			−1.52874			−0.764372	−	0.644776i	$-0.776951\pi$
$257$	−24.5076			−1.52874			−0.764372	+	0.644776i	$0.776951\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$			24.3830i			1.50352i	0.659438	+	0.751759i	$0.270794\pi$
$263$			24.3830i			1.50352i	−0.659438	+	0.751759i	$0.729206\pi$
$264$		0			0
$265$	−9.31427	+	5.37760i	−0.572171	+	0.330343i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.94525	−	8.56542i	−0.301517	−	0.522243i	0.674963	−	0.737852i	$-0.264160\pi$
$269$	−4.94525	−	8.56542i	−0.301517	−	0.522243i	−0.976480	+	0.215609i	$0.930826\pi$
$270$		0			0
$271$	5.10505	+	2.94740i	0.310110	+	0.179042i	0.646976	−	0.762511i	$-0.276034\pi$
$271$	5.10505	+	2.94740i	0.310110	+	0.179042i	−0.336866	+	0.941553i	$0.609367\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			1.05668i			0.0637202i
$276$		0			0
$277$	23.2939			1.39959			0.699796	−	0.714343i	$-0.253274\pi$
$277$	23.2939			1.39959			0.699796	+	0.714343i	$0.253274\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.7962	−	12.5840i	−1.30025	−	0.750700i	−0.319803	−	0.947484i	$-0.603617\pi$
$281$	−21.7962	−	12.5840i	−1.30025	−	0.750700i	−0.980447	+	0.196784i	$0.936950\pi$
$282$		0			0
$283$	8.62942	+	4.98220i	0.512966	+	0.296161i	0.734052	−	0.679093i	$-0.237627\pi$
$283$	8.62942	+	4.98220i	0.512966	+	0.296161i	−0.221086	+	0.975254i	$0.570960\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.872317	−	1.51090i	0.0513128	−	0.0888764i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.79065	+	11.7618i	0.396714	+	0.687129i	0.993318	−	0.115406i	$-0.0368171\pi$
$293$	6.79065	+	11.7618i	0.396714	+	0.687129i	−0.596604	+	0.802536i	$0.703484\pi$
$294$		0			0
$295$	−5.56147	+	9.63275i	−0.323801	+	0.560841i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.82774	+	11.8260i	0.394858	+	0.683915i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.42933	−	2.55728i	0.253623	−	0.146429i
$306$		0			0
$307$		−	16.9849i		−	0.969381i	−0.874686	−	0.484691i	$-0.838932\pi$
$307$		−	16.9849i		−	0.969381i	0.874686	−	0.484691i	$-0.161068\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	−0.865983	−	0.500073i	$-0.833306\pi$
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	0.866068	+	0.499927i	$0.166640\pi$
$312$		0			0
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	−0.169032	−	0.985611i	$-0.554064\pi$
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	0.769048	+	0.639191i	$0.220731\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.942256	−	0.334894i	$-0.891300\pi$
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.181102	+	0.983464i	$0.557966\pi$
$318$		0			0
$319$	1.45014	−	2.51172i	0.0811922	−	0.140629i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			23.0911i			1.28482i
$324$		0			0
$325$	3.34697	−	1.93237i	0.185656	−	0.107189i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	0.909670	−	0.415331i	$-0.136334\pi$
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	−0.814522	+	0.580132i	$0.803001\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.5145	−	30.3359i	0.956917	−	1.65743i
$336$		0			0
$337$	−9.13018	−	15.8139i	−0.497352	−	0.861440i	0.502643	−	0.864494i	$-0.332361\pi$
$337$	−9.13018	−	15.8139i	−0.497352	−	0.861440i	−0.999995	+	0.00305455i	$0.999028\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.738202	+	1.27860i	−0.0399759	+	0.0692403i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	0.618950	−	0.785431i	$-0.287558\pi$
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	−0.370728	+	0.928741i	$0.620892\pi$
$348$		0			0
$349$	−0.0136817	−	0.00789914i	−0.000732365	−	0.000422831i	0.499634	−	0.866237i	$-0.333468\pi$
$349$	−0.0136817	−	0.00789914i	−0.000732365	−	0.000422831i	−0.500366	+	0.865814i	$0.666801\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	34.3085			1.82606			0.913029	−	0.407894i	$-0.133737\pi$
$353$	34.3085			1.82606			0.913029	+	0.407894i	$0.133737\pi$
$354$		0			0
$355$		−	23.3462i		−	1.23909i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.42754	−	3.13359i	−0.286454	−	0.165385i	0.349887	−	0.936792i	$-0.386220\pi$
$359$	−5.42754	−	3.13359i	−0.286454	−	0.165385i	−0.636342	+	0.771407i	$0.719553\pi$
$360$		0			0
$361$	7.97583	+	13.8145i	0.419781	+	0.727081i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.52811	+	2.61430i	−0.237012	+	0.136839i
$366$		0			0
$367$			19.0397i			0.993863i	0.867790	+	0.496931i	$0.165540\pi$
$367$			19.0397i			0.993863i	−0.867790	+	0.496931i	$0.834460\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.8380			0.561172			0.280586	−	0.959829i	$-0.409471\pi$
$373$	10.8380			0.561172			0.280586	+	0.959829i	$0.409471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.6076			−0.546320
$378$		0			0
$379$	0.700312			0.0359726			0.0179863	−	0.999838i	$-0.494274\pi$
$379$	0.700312			0.0359726			0.0179863	+	0.999838i	$0.494274\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	38.0470			1.94411			0.972056	−	0.234749i	$-0.0754269\pi$
$383$	38.0470			1.94411			0.972056	+	0.234749i	$0.0754269\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	19.2787i		−	0.977468i	−0.872433	−	0.488734i	$-0.837459\pi$
$389$		−	19.2787i		−	0.977468i	0.872433	−	0.488734i	$-0.162541\pi$
$390$		0			0
$391$	−30.1874	+	17.4287i	−1.52664	+	0.881407i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.18959	+	2.06044i	0.0598549	+	0.103672i
$396$		0			0
$397$	17.3610	+	10.0234i	0.871325	+	0.503059i	0.867788	−	0.496934i	$-0.165541\pi$
$397$	17.3610	+	10.0234i	0.871325	+	0.503059i	0.00353639	+	0.999994i	$0.498874\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			30.5109i			1.52364i	0.647789	+	0.761820i	$0.275694\pi$
$401$			30.5109i			1.52364i	−0.647789	+	0.761820i	$0.724306\pi$
$402$		0			0
$403$	5.39987			0.268987
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.29598	−	1.90294i	−0.163376	−	0.0943250i
$408$		0			0
$409$	0.150631	+	0.0869667i	0.00744821	+	0.00430023i	0.503719	−	0.863867i	$-0.331965\pi$
$409$	0.150631	+	0.0869667i	0.00744821	+	0.00430023i	−0.496271	+	0.868168i	$0.665298\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.48860	+	16.4347i	−0.465777	+	0.806749i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	14.0690	+	24.3682i	0.687316	+	1.19047i	0.972703	+	0.232054i	$0.0745445\pi$
$419$	14.0690	+	24.3682i	0.687316	+	1.19047i	−0.285387	+	0.958412i	$0.592122\pi$
$420$		0			0
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	−0.901561	−	0.432652i	$-0.857578\pi$
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	0.825468	+	0.564449i	$0.190911\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.93264	+	8.54358i	0.239268	+	0.414424i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.58876	−	4.95872i	0.413706	−	0.238853i	−0.278675	−	0.960385i	$-0.589895\pi$
$431$	8.58876	−	4.95872i	0.413706	−	0.238853i	0.692381	+	0.721532i	$0.256562\pi$
$432$		0			0
$433$		−	17.1274i		−	0.823092i	−0.911389	−	0.411546i	$-0.864989\pi$
$433$		−	17.1274i		−	0.823092i	0.911389	−	0.411546i	$-0.135011\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−26.3808	+	45.6929i	−1.26196	+	2.18579i
$438$		0			0
$439$	18.5795	−	10.7269i	0.886750	−	0.511965i	0.0138721	−	0.999904i	$-0.495584\pi$
$439$	18.5795	−	10.7269i	0.886750	−	0.511965i	0.872878	+	0.487938i	$0.162251\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	−0.354721	−	0.934972i	$-0.615424\pi$
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	0.632349	+	0.774683i	$0.282091\pi$
$444$		0			0
$445$	13.4111	−	23.2287i	0.635747	−	1.10115i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			5.81624i			0.274485i	0.990537	+	0.137243i	$0.0438240\pi$
$449$			5.81624i			0.274485i	−0.990537	+	0.137243i	$0.956176\pi$
$450$		0			0
$451$	0.769801	−	0.444445i	0.0362485	−	0.0209281i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	0.931386	+	0.364032i	$0.118600\pi$
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	−0.150432	+	0.988620i	$0.548066\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.5154	−	32.0696i	0.862347	−	1.49363i	−0.00730959	−	0.999973i	$-0.502327\pi$
$461$	18.5154	−	32.0696i	0.862347	−	1.49363i	0.869657	−	0.493656i	$-0.164340\pi$
$462$		0			0
$463$	10.5618	+	18.2935i	0.490848	+	0.850173i	0.999944	−	0.0105362i	$-0.00335383\pi$
$463$	10.5618	+	18.2935i	0.490848	+	0.850173i	−0.509097	+	0.860709i	$0.670020\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.30470	+	16.1162i	−0.430570	+	0.745770i	−0.996922	−	0.0783937i	$-0.975021\pi$
$467$	−9.30470	+	16.1162i	−0.430570	+	0.745770i	0.566352	+	0.824163i	$0.308354\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.18715	−	2.41745i	−0.192525	−	0.111155i
$474$		0			0
$475$	12.9319	+	7.46624i	0.593356	+	0.342574i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.3341			0.654940			0.327470	−	0.944862i	$-0.393804\pi$
$479$	14.3341			0.654940			0.327470	+	0.944862i	$0.393804\pi$
$480$		0			0
$481$			13.9198i			0.634687i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.549791	+	0.317422i	0.0249647	+	0.0144134i
$486$		0			0
$487$	−5.64829	−	9.78313i	−0.255949	−	0.443316i	0.709204	−	0.705003i	$-0.249054\pi$
$487$	−5.64829	−	9.78313i	−0.255949	−	0.443316i	−0.965153	+	0.261687i	$0.915721\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.84097	−	5.10434i	0.398988	−	0.230356i	−0.287059	−	0.957913i	$-0.592678\pi$
$491$	8.84097	−	5.10434i	0.398988	−	0.230356i	0.686047	+	0.727557i	$0.259344\pi$
$492$		0			0
$493$		−	27.0773i		−	1.21950i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.1334			−0.856531			−0.428265	−	0.903653i	$-0.640875\pi$
$499$	−19.1334			−0.856531			−0.428265	+	0.903653i	$0.640875\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−0.268917			−0.0119904			−0.00599520	−	0.999982i	$-0.501908\pi$
$503$	−0.268917			−0.0119904			−0.00599520	+	0.999982i	$0.501908\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.8877			0.970157			0.485079	−	0.874471i	$-0.338791\pi$
$509$	21.8877			0.970157			0.485079	+	0.874471i	$0.338791\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$			29.4793i			1.29901i
$516$		0			0
$517$	0.641553	−	0.370401i	0.0282155	−	0.0162902i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.856074	−	1.48276i	−0.0375053	−	0.0649610i	0.846663	−	0.532129i	$-0.178608\pi$
$521$	−0.856074	−	1.48276i	−0.0375053	−	0.0649610i	−0.884169	+	0.467168i	$0.845274\pi$
$522$		0			0
$523$	−7.16320	−	4.13568i	−0.313225	−	0.180841i	0.335144	−	0.942167i	$-0.391215\pi$
$523$	−7.16320	−	4.13568i	−0.313225	−	0.180841i	−0.648369	+	0.761326i	$0.724548\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			13.7839i			0.600435i
$528$		0			0
$529$	−56.6466			−2.46290
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.81550	−	1.62553i	−0.121953	−	0.0704096i
$534$		0			0
$535$	−15.1029	−	8.71966i	−0.652955	−	0.376984i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.1997	+	17.6664i	−0.438518	+	0.759536i	−0.997575	−	0.0695932i	$-0.977830\pi$
$541$	−10.1997	+	17.6664i	−0.438518	+	0.759536i	0.559057	+	0.829129i	$0.311163\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.07875	+	12.2608i	0.303220	+	0.525193i
$546$		0			0
$547$	18.9630	−	32.8449i	0.810801	−	1.40435i	−0.101503	−	0.994835i	$-0.532365\pi$
$547$	18.9630	−	32.8449i	0.810801	−	1.40435i	0.912304	−	0.409513i	$-0.134301\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.4927	−	35.4943i	−0.873017	−	1.51211i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	−0.157920	−	0.987452i	$-0.550479\pi$
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	0.776198	+	0.630489i	$0.217146\pi$
$558$		0			0
$559$			17.6834i			0.747928i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.28035	+	14.3420i	−0.348975	+	0.604443i	−0.986068	−	0.166345i	$-0.946804\pi$
$563$	−8.28035	+	14.3420i	−0.348975	+	0.604443i	0.637093	+	0.770787i	$0.280137\pi$
$564$		0			0
$565$	−25.2162	+	14.5586i	−1.06085	+	0.612484i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	−0.380296	−	0.924865i	$-0.624178\pi$
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	0.610808	+	0.791779i	$0.290845\pi$
$570$		0			0
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.227585	+	0.973758i	$0.573083\pi$
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.729507	+	0.683973i	$0.760250\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			22.5414i			0.940043i
$576$		0			0
$577$	−15.3719	+	8.87497i	−0.639940	+	0.369470i	−0.784592	−	0.620013i	$-0.787127\pi$
$577$	−15.3719	+	8.87497i	−0.639940	+	0.369470i	0.144651	+	0.989483i	$0.453794\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.820082	−	1.42042i	−0.0339643	−	0.0588280i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.41148	+	7.64091i	−0.182081	+	0.315374i	−0.942589	−	0.333955i	$-0.891617\pi$
$587$	−4.41148	+	7.64091i	−0.182081	+	0.315374i	0.760508	+	0.649329i	$0.224950\pi$
$588$		0			0
$589$	10.4319	+	18.0686i	0.429839	+	0.744503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.24849	+	7.35860i	−0.174465	+	0.302181i	−0.939976	−	0.341241i	$-0.889153\pi$
$593$	−4.24849	+	7.35860i	−0.174465	+	0.302181i	0.765511	+	0.643422i	$0.222486\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	0.564174	−	0.825656i	$-0.309195\pi$
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	−0.432952	+	0.901417i	$0.642528\pi$
$600$		0			0
$601$	6.14043	+	3.54518i	0.250473	+	0.144611i	0.619981	−	0.784617i	$-0.287140\pi$
$601$	6.14043	+	3.54518i	0.250473	+	0.144611i	−0.369508	+	0.929228i	$0.620474\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	29.6964			1.20733
$606$		0			0
$607$			33.9940i			1.37977i	0.723918	+	0.689886i	$0.242339\pi$
$607$			33.9940i			1.37977i	−0.723918	+	0.689886i	$0.757661\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.34644	−	1.35472i	−0.0949270	−	0.0548061i
$612$		0			0
$613$	−11.6761	−	20.2237i	−0.471595	−	0.816827i	0.527877	−	0.849321i	$-0.322988\pi$
$613$	−11.6761	−	20.2237i	−0.471595	−	0.816827i	−0.999472	+	0.0324944i	$0.989655\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.0817	−	22.5638i	1.57337	−	0.908386i	0.577618	−	0.816307i	$-0.303982\pi$
$617$	39.0817	−	22.5638i	1.57337	−	0.908386i	0.995752	−	0.0920787i	$-0.0293511\pi$
$618$		0			0
$619$		−	9.21352i		−	0.370323i	−0.982708	−	0.185161i	$-0.940719\pi$
$619$		−	9.21352i		−	0.370323i	0.982708	−	0.185161i	$-0.0592808\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−31.2493			−1.24997
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−35.5320			−1.41675
$630$		0			0
$631$	17.6136			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$631$	17.6136			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	28.2312			1.12032
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	19.1402i		−	0.755991i	−0.925807	−	0.377996i	$-0.876613\pi$
$641$		−	19.1402i		−	0.755991i	0.925807	−	0.377996i	$-0.123387\pi$
$642$		0			0
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	−0.539134	−	0.842220i	$-0.681248\pi$
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	0.459817	+	0.888014i	$0.347915\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.9310	−	22.3971i	−0.508370	−	0.880522i	−0.999953	−	0.00969167i	$-0.996915\pi$
$647$	−12.9310	−	22.3971i	−0.508370	−	0.880522i	0.491583	−	0.870831i	$-0.336418\pi$
$648$		0			0
$649$	−1.46899	−	0.848123i	−0.0576630	−	0.0332918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	23.2257i		−	0.908891i	−0.890774	−	0.454446i	$-0.849837\pi$
$653$		−	23.2257i		−	0.908891i	0.890774	−	0.454446i	$-0.150163\pi$
$654$		0			0
$655$	53.9363			2.10746
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.7002	−	7.90981i	−0.533684	−	0.308122i	0.208832	−	0.977952i	$-0.433034\pi$
$659$	−13.7002	−	7.90981i	−0.533684	−	0.308122i	−0.742515	+	0.669829i	$0.766367\pi$
$660$		0			0
$661$	15.8006	+	9.12248i	0.614572	+	0.354823i	0.774753	−	0.632264i	$-0.217874\pi$
$661$	15.8006	+	9.12248i	0.614572	+	0.354823i	−0.160181	+	0.987088i	$0.551208\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	30.9349	−	53.5807i	1.19780	−	2.07465i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.389984	+	0.675472i	0.0150552	+	0.0260763i
$672$		0			0
$673$	14.4184	−	24.9733i	0.555787	−	0.962651i	−0.442055	−	0.896988i	$-0.645750\pi$
$673$	14.4184	−	24.9733i	0.555787	−	0.962651i	0.997842	−	0.0656633i	$-0.0209163\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.7668	−	29.0409i	−0.644400	−	1.11613i	−0.984440	−	0.175722i	$-0.943774\pi$
$677$	−16.7668	−	29.0409i	−0.644400	−	1.11613i	0.340040	−	0.940411i	$-0.389559\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.0943	+	11.0241i	−0.730621	+	0.421824i	−0.818649	−	0.574294i	$-0.805277\pi$
$683$	−19.0943	+	11.0241i	−0.730621	+	0.421824i	0.0880282	+	0.996118i	$0.471943\pi$
$684$		0			0
$685$			14.7745i			0.564506i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.99941	+	5.19512i	−0.114268	+	0.197918i
$690$		0			0
$691$	22.8662	−	13.2018i	0.869869	−	0.502219i	0.00256453	−	0.999997i	$-0.499184\pi$
$691$	22.8662	−	13.2018i	0.869869	−	0.502219i	0.867305	+	0.497777i	$0.165850\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	40.5569	−	23.4156i	1.53841	−	0.888203i
$696$		0			0
$697$	4.14938	−	7.18694i	0.157169	−	0.272225i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	20.5140i		−	0.774804i	−0.921911	−	0.387402i	$-0.873373\pi$
$701$		−	20.5140i		−	0.774804i	0.921911	−	0.387402i	$-0.126627\pi$
$702$		0			0
$703$	−46.5772	+	26.8913i	−1.75669	+	1.01423i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	0.918804	−	0.394714i	$-0.129156\pi$
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	−0.801234	+	0.598351i	$0.795823\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−15.7476	+	27.2756i	−0.589751	+	1.02148i
$714$		0			0
$715$	0.878041	+	1.52081i	0.0328369	+	0.0568751i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.6111	−	20.1111i	0.433023	−	0.750017i	−0.564109	−	0.825700i	$-0.690780\pi$
$719$	11.6111	−	20.1111i	0.433023	−	0.750017i	0.997132	+	0.0756828i	$0.0241136\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.1643	−	8.75512i	−0.563189	−	0.325157i
$726$		0			0
$727$	2.50999	+	1.44914i	0.0930903	+	0.0537457i	0.545822	−	0.837901i	$-0.316217\pi$
$727$	2.50999	+	1.44914i	0.0930903	+	0.0537457i	−0.452732	+	0.891647i	$0.649551\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−45.1392			−1.66953
$732$		0			0
$733$		−	11.8891i		−	0.439135i	−0.975597	−	0.219568i	$-0.929535\pi$
$733$		−	11.8891i		−	0.439135i	0.975597	−	0.219568i	$-0.0704647\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.62622	+	2.67095i	0.170409	+	0.0983858i
$738$		0			0
$739$	17.2254	+	29.8354i	0.633648	+	1.09751i	0.986800	+	0.161945i	$0.0517767\pi$
$739$	17.2254	+	29.8354i	0.633648	+	1.09751i	−0.353151	+	0.935566i	$0.614890\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.44069	−	1.40913i	0.0895401	−	0.0516960i	−0.454561	−	0.890715i	$-0.650204\pi$
$743$	2.44069	−	1.40913i	0.0895401	−	0.0516960i	0.544101	+	0.839019i	$0.316871\pi$
$744$		0			0
$745$			29.4965i			1.08067i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.72089			0.281739			0.140870	−	0.990028i	$-0.455010\pi$
$751$	7.72089			0.281739			0.140870	+	0.990028i	$0.455010\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.7517			0.755233
$756$		0			0
$757$	1.17924			0.0428603			0.0214302	−	0.999770i	$-0.493178\pi$
$757$	1.17924			0.0428603			0.0214302	+	0.999770i	$0.493178\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.13289			−0.113567			−0.0567835	−	0.998387i	$-0.518084\pi$
$761$	−3.13289			−0.113567			−0.0567835	+	0.998387i	$0.518084\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$			6.20393i			0.224011i
$768$		0			0
$769$	5.53497	−	3.19562i	0.199596	−	0.115237i	−0.396871	−	0.917874i	$-0.629904\pi$
$769$	5.53497	−	3.19562i	0.199596	−	0.115237i	0.596467	+	0.802637i	$0.296571\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.9779	−	41.5309i	−0.862425	−	1.49376i	−0.869581	−	0.493790i	$-0.835611\pi$
$773$	−23.9779	−	41.5309i	−0.862425	−	1.49376i	0.00715621	−	0.999974i	$-0.497722\pi$
$774$		0			0
$775$	7.71948	+	4.45685i	0.277292	+	0.160095i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	12.5613i		−	0.450057i
$780$		0			0
$781$	3.56029			0.127397
$782$		0			0
$783$		0			0
$784$		0			0
$785$	29.1661	+	16.8390i	1.04098	+	0.601011i
$786$		0			0
$787$	−5.23136	−	3.02033i	−0.186478	−	0.107663i	0.403855	−	0.914823i	$-0.367670\pi$
$787$	−5.23136	−	3.02033i	−0.186478	−	0.107663i	−0.590333	+	0.807160i	$0.701003\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.42635	−	2.47050i	0.0506510	−	0.0877301i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.782501	−	1.35533i	−0.0277176	−	0.0480083i	0.851834	−	0.523812i	$-0.175491\pi$
$797$	−0.782501	−	1.35533i	−0.0277176	−	0.0480083i	−0.879551	+	0.475804i	$0.842157\pi$
$798$		0			0
$799$	3.45810	−	5.98961i	0.122339	−	0.211897i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.398681	−	0.690535i	−0.0140691	−	0.0243685i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	−0.744870	−	0.667209i	$-0.767489\pi$
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	0.205385	+	0.978681i	$0.434155\pi$
$810$		0			0
$811$		−	27.5261i		−	0.966571i	−0.875463	−	0.483285i	$-0.839443\pi$
$811$		−	27.5261i		−	0.966571i	0.875463	−	0.483285i	$-0.160557\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.2334	−	28.1171i	0.568633	−	0.984901i
$816$		0			0
$817$	−59.1707	+	34.1622i	−2.07012	+	1.19519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	−0.844834	−	0.535028i	$-0.820301\pi$
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	0.0409311	+	0.999162i	$0.486968\pi$
$822$		0			0
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	−0.996045	−	0.0888537i	$-0.971680\pi$
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	0.574972	+	0.818173i	$0.305013\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	9.64923i		−	0.335537i	−0.985826	−	0.167768i	$-0.946344\pi$
$827$		−	9.64923i		−	0.335537i	0.985826	−	0.167768i	$-0.0536561\pi$
$828$		0			0
$829$	25.1481	−	14.5193i	0.873430	−	0.504275i	0.00494329	−	0.999988i	$-0.498426\pi$
$829$	25.1481	−	14.5193i	0.873430	−	0.504275i	0.868486	+	0.495713i	$0.165093\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.6231	−	32.2562i	−0.644480	−	1.11627i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.84383	+	11.8539i	−0.236275	+	0.409241i	−0.959642	−	0.281223i	$-0.909260\pi$
$839$	−6.84383	+	11.8539i	−0.236275	+	0.409241i	0.723367	+	0.690463i	$0.242593\pi$
$840$		0			0
$841$	9.53027	+	16.5069i	0.328630	+	0.569204i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.6202	+	25.3229i	−0.502949	+	0.871134i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−70.3110	−	40.5941i	−2.41023	−	1.39155i
$852$		0			0
$853$	40.5184	+	23.3933i	1.38732	+	0.800972i	0.993013	−	0.118006i	$-0.0376501\pi$
$853$	40.5184	+	23.3933i	1.38732	+	0.800972i	0.394310	+	0.918977i	$0.370983\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	31.7960			1.08613			0.543065	−	0.839691i	$-0.317264\pi$
$857$	31.7960			1.08613			0.543065	+	0.839691i	$0.317264\pi$
$858$		0			0
$859$		−	25.2885i		−	0.862832i	−0.902153	−	0.431416i	$-0.858014\pi$
$859$		−	25.2885i		−	0.862832i	0.902153	−	0.431416i	$-0.141986\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.9513	+	9.20946i	0.542987	+	0.313494i	0.746289	−	0.665622i	$-0.231834\pi$
$863$	15.9513	+	9.20946i	0.542987	+	0.313494i	−0.203302	+	0.979116i	$0.565167\pi$
$864$		0			0
$865$	−22.7993	−	39.4896i	−0.775200	−	1.34269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.314216	+	0.181413i	−0.0106590	+	0.00615400i
$870$		0			0
$871$		−	19.5377i		−	0.662010i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.89389			−0.300325			−0.150163	−	0.988661i	$-0.547980\pi$
$877$	−8.89389			−0.300325			−0.150163	+	0.988661i	$0.547980\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−13.1721			−0.443780			−0.221890	−	0.975072i	$-0.571223\pi$
$881$	−13.1721			−0.443780			−0.221890	+	0.975072i	$0.571223\pi$
$882$		0			0
$883$	12.6729			0.426477			0.213239	−	0.977000i	$-0.431599\pi$
$883$	12.6729			0.426477			0.213239	+	0.977000i	$0.431599\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.3983			−1.12141			−0.560703	−	0.828017i	$-0.689469\pi$
$887$	−33.3983			−1.12141			−0.560703	+	0.828017i	$0.689469\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	10.4686i		−	0.350320i
$894$		0			0
$895$	40.6231	−	23.4538i	1.35788	−	0.783974i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.2328	−	21.1877i	−0.407985	−	0.706651i
$900$		0			0
$901$	−13.2612	−	7.65638i	−0.441796	−	0.255071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			49.9753i			1.66124i
$906$		0			0
$907$	−29.3127			−0.973311			−0.486655	−	0.873594i	$-0.661783\pi$
$907$	−29.3127			−0.973311			−0.486655	+	0.873594i	$0.661783\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.72555	−	0.996246i	−0.0571700	−	0.0330071i	0.471143	−	0.882057i	$-0.343842\pi$
$911$	−1.72555	−	0.996246i	−0.0571700	−	0.0330071i	−0.528313	+	0.849050i	$0.677175\pi$
$912$		0			0
$913$	−2.50629	−	1.44701i	−0.0829462	−	0.0478890i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.897678	+	1.55482i	−0.0296117	+	0.0512889i	−0.880451	−	0.474136i	$-0.842760\pi$
$919$	−0.897678	+	1.55482i	−0.0296117	+	0.0512889i	0.850840	+	0.525425i	$0.176094\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.51079	−	11.2770i	−0.214305	−	0.371188i
$924$		0			0
$925$	−11.4889	+	19.8993i	−0.377751	+	0.654284i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.4178	−	21.5083i	−0.407415	−	0.705664i	0.587184	−	0.809453i	$-0.300237\pi$
$929$	−12.4178	−	21.5083i	−0.407415	−	0.705664i	−0.994599	+	0.103789i	$0.966903\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.88207	+	2.24132i	−0.126957	+	0.0732988i
$936$		0			0
$937$		−	27.9046i		−	0.911605i	−0.890081	−	0.455802i	$-0.849352\pi$
$937$		−	27.9046i		−	0.911605i	0.890081	−	0.455802i	$-0.150648\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.2537	−	45.4728i	0.855847	−	1.48237i	−0.0200094	−	0.999800i	$-0.506370\pi$
$941$	26.2537	−	45.4728i	0.855847	−	1.48237i	0.875857	−	0.482571i	$-0.160297\pi$
$942$		0			0
$943$	16.4216	−	9.48104i	0.534762	−	0.308745i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.250377	−	0.968148i	$-0.419445\pi$
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.963630	+	0.267241i	$0.0861121\pi$
$948$		0			0
$949$	−1.45815	+	2.52559i	−0.0473336	+	0.0819843i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	59.9829i		−	1.94304i	−0.236965	−	0.971518i	$-0.576153\pi$
$953$		−	59.9829i		−	1.94304i	0.236965	−	0.971518i	$-0.423847\pi$
$954$		0			0
$955$	49.8899	−	28.8040i	1.61440	−	0.932074i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.27285	−	16.0610i	−0.299124	−	0.518098i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.56709	−	16.5707i	0.307975	−	0.533429i
$966$		0			0
$967$	−26.6398	−	46.1414i	−0.856677	−	1.48381i	−0.875080	−	0.483978i	$-0.839191\pi$
$967$	−26.6398	−	46.1414i	−0.856677	−	1.48381i	0.0184029	−	0.999831i	$-0.494142\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.1556	+	48.7669i	−0.903555	+	1.56500i	−0.0807100	+	0.996738i	$0.525719\pi$
$971$	−28.1556	+	48.7669i	−0.903555	+	1.56500i	−0.822845	+	0.568266i	$0.807615\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	0.815582	−	0.578642i	$-0.196417\pi$
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	−0.0933275	+	0.995635i	$0.529750\pi$
$978$		0			0
$979$	3.54237	+	2.04519i	0.113215	+	0.0653646i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	38.0505			1.21362			0.606811	−	0.794846i	$-0.292449\pi$
$983$	38.0505			1.21362			0.606811	+	0.794846i	$0.292449\pi$
$984$		0			0
$985$			44.1005i			1.40516i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−89.3217	−	51.5699i	−2.84026	−	1.63983i
$990$		0			0
$991$	−5.68758	−	9.85118i	−0.180672	−	0.312933i	0.761438	−	0.648238i	$-0.224494\pi$
$991$	−5.68758	−	9.85118i	−0.180672	−	0.312933i	−0.942110	+	0.335305i	$0.891161\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.9499	−	8.63131i	0.473943	−	0.273631i
$996$		0			0
$997$		−	50.9904i		−	1.61488i	−0.589948	−	0.807441i	$-0.700852\pi$
$997$		−	50.9904i		−	1.61488i	0.589948	−	0.807441i	$-0.299148\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.a.4625.7		16
3.2	odd	2		1764.2.bm.a.1685.4		16
7.2	even	3		5292.2.x.a.4409.2		16
7.3	odd	6		5292.2.w.b.521.7		16
7.4	even	3		756.2.w.a.521.2		16
7.5	odd	6		5292.2.x.b.4409.7		16
7.6	odd	2		756.2.bm.a.89.2		16
9.4	even	3		1764.2.w.b.509.2		16
9.5	odd	6		5292.2.w.b.1097.7		16
21.2	odd	6		1764.2.x.a.1469.2		16
21.5	even	6		1764.2.x.b.1469.7		16
21.11	odd	6		252.2.w.a.101.7	yes	16
21.17	even	6		1764.2.w.b.1109.2		16
21.20	even	2		252.2.bm.a.173.5	yes	16
28.11	odd	6		3024.2.ca.d.2033.2		16
28.27	even	2		3024.2.df.d.1601.2		16
63.4	even	3		252.2.bm.a.185.5	yes	16
63.5	even	6		5292.2.x.a.881.2		16
63.11	odd	6		2268.2.t.b.1781.7		16
63.13	odd	6		252.2.w.a.5.7	✓	16
63.20	even	6		2268.2.t.a.2105.2		16
63.23	odd	6		5292.2.x.b.881.7		16
63.25	even	3		2268.2.t.a.1781.2		16
63.31	odd	6		1764.2.bm.a.1697.4		16
63.32	odd	6		756.2.bm.a.17.2		16
63.34	odd	6		2268.2.t.b.2105.7		16
63.40	odd	6		1764.2.x.a.293.2		16
63.41	even	6		756.2.w.a.341.2		16
63.58	even	3		1764.2.x.b.293.7		16
63.59	even	6	inner	5292.2.bm.a.2285.7		16
84.11	even	6		1008.2.ca.d.353.2		16
84.83	odd	2		1008.2.df.d.929.4		16
252.67	odd	6		1008.2.df.d.689.4		16
252.95	even	6		3024.2.df.d.17.2		16
252.139	even	6		1008.2.ca.d.257.2		16
252.167	odd	6		3024.2.ca.d.2609.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	63.13	odd	6
252.2.w.a.101.7	yes	16	21.11	odd	6
252.2.bm.a.173.5	yes	16	21.20	even	2
252.2.bm.a.185.5	yes	16	63.4	even	3
756.2.w.a.341.2		16	63.41	even	6
756.2.w.a.521.2		16	7.4	even	3
756.2.bm.a.17.2		16	63.32	odd	6
756.2.bm.a.89.2		16	7.6	odd	2
1008.2.ca.d.257.2		16	252.139	even	6
1008.2.ca.d.353.2		16	84.11	even	6
1008.2.df.d.689.4		16	252.67	odd	6
1008.2.df.d.929.4		16	84.83	odd	2
1764.2.w.b.509.2		16	9.4	even	3
1764.2.w.b.1109.2		16	21.17	even	6
1764.2.x.a.293.2		16	63.40	odd	6
1764.2.x.a.1469.2		16	21.2	odd	6
1764.2.x.b.293.7		16	63.58	even	3
1764.2.x.b.1469.7		16	21.5	even	6
1764.2.bm.a.1685.4		16	3.2	odd	2
1764.2.bm.a.1697.4		16	63.31	odd	6
2268.2.t.a.1781.2		16	63.25	even	3
2268.2.t.a.2105.2		16	63.20	even	6
2268.2.t.b.1781.7		16	63.11	odd	6
2268.2.t.b.2105.7		16	63.34	odd	6
3024.2.ca.d.2033.2		16	28.11	odd	6
3024.2.ca.d.2609.2		16	252.167	odd	6
3024.2.df.d.17.2		16	252.95	even	6
3024.2.df.d.1601.2		16	28.27	even	2
5292.2.w.b.521.7		16	7.3	odd	6
5292.2.w.b.1097.7		16	9.5	odd	6
5292.2.x.a.881.2		16	63.5	even	6
5292.2.x.a.4409.2		16	7.2	even	3
5292.2.x.b.881.7		16	63.23	odd	6
5292.2.x.b.4409.7		16	7.5	odd	6
5292.2.bm.a.2285.7		16	63.59	even	6	inner
5292.2.bm.a.4625.7		16	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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.74332 q^{5} +O(q^{10})\)	\(q+2.74332 q^{5} +0.418355i q^{11} +(1.32512 - 0.765056i) q^{13} +(1.95291 + 3.38253i) q^{17} +(5.11994 + 2.95600i) q^{19} +8.92450i q^{23} +2.52579 q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 + 1.76453i) q^{31} +(-4.54861 + 7.87842i) q^{37} +(-1.06236 - 1.84006i) q^{41} +(-5.77846 + 10.0086i) q^{43} +(-0.885373 - 1.53351i) q^{47} +(-3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(1.61459 - 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} -8.51021i q^{71} +(-1.65059 + 0.952971i) q^{73} +(0.433633 + 0.751074i) q^{79} +(-3.45880 + 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +(4.88864 - 8.46738i) q^{89} +(14.0456 + 8.10924i) q^{95} +(0.200411 + 0.115707i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) \) 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

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