LMFDB - Embedded newform 5292.2.x.b.4409.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(881,5292)]

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, 3]))

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

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

chi := DirichletCharacter("5292.881");

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.x (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			4409.7
Root			$-0.811340 - 1.53027i$ of defining polynomial
Character	$\chi$	$=$	5292.4409
Dual form			5292.2.x.b.881.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37166 + 2.37578i) q^{5} +O(q^{10})$	$q+(1.37166 + 2.37578i) q^{5} +(-0.362306 - 0.209178i) q^{11} +(-1.32512 + 0.765056i) q^{13} +3.90581 q^{17} +5.91199i q^{19} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 - 1.76453i) q^{31} +9.09722 q^{37} +(1.06236 + 1.84006i) q^{41} +(-5.77846 + 10.0086i) q^{43} +(0.885373 - 1.53351i) q^{47} -3.92050i q^{53} -1.14768i q^{55} +(2.02728 + 3.51135i) q^{59} +(1.61459 + 0.932184i) q^{61} +(-3.63521 - 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} -8.51021i q^{71} +1.90594i q^{73} +(0.433633 - 0.751074i) q^{79} +(3.45880 - 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +9.77729 q^{89} +(-14.0456 + 8.10924i) q^{95} +(-0.200411 - 0.115707i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 6 q^{11} + 3 q^{13} - 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} - 6 q^{31} - 2 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} - 42 q^{89} + 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q - 6 * q^11 + 3 * q^13 - 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 - 6 * q^31 - 2 * 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 - 42 * q^89 + 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.37166	+	2.37578i	0.613425	+	1.06248i	0.990659	+	0.136365i	$0.0435419\pi$
$5$	1.37166	+	2.37578i	0.613425	+	1.06248i	−0.377234	+	0.926118i	$0.623125\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	0.444385	−	0.895836i	$-0.353422\pi$
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	−0.553624	+	0.832767i	$0.686756\pi$
$12$		0			0
$13$	−1.32512	+	0.765056i	−0.367521	+	0.212188i	−0.672375	−	0.740211i	$-0.734726\pi$
$13$	−1.32512	+	0.765056i	−0.367521	+	0.212188i	0.304854	+	0.952399i	$0.401392\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.90581			0.947298			0.473649	−	0.880714i	$-0.342936\pi$
$17$	3.90581			0.947298			0.473649	+	0.880714i	$0.342936\pi$
$18$		0			0
$19$			5.91199i			1.35630i	0.734922	+	0.678152i	$0.237219\pi$
$19$			5.91199i			1.35630i	−0.734922	+	0.678152i	$0.762781\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.622569	−	0.782565i	$-0.286089\pi$
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.989006	−	0.147878i	$-0.0472444\pi$
$24$		0			0
$25$	−1.26290	+	2.18740i	−0.252579	+	0.437480i
$26$		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	−0.199766	−	0.979844i	$-0.564018\pi$
$31$	3.05626	−	1.76453i	0.548921	−	0.316920i	0.748687	+	0.662924i	$0.230685\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.09722			1.49557			0.747787	−	0.663939i	$-0.231116\pi$
$37$	9.09722			1.49557			0.747787	+	0.663939i	$0.231116\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	0.936979	−	0.349385i	$-0.113610\pi$
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	−0.771066	+	0.636755i	$0.780276\pi$
$42$		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	$-0.792110\pi$
$47$	0.885373	−	1.53351i	0.129145	−	0.223686i	0.923346	+	0.383970i	$0.125443\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	3.92050i		−	0.538523i	−0.963067	−	0.269261i	$-0.913220\pi$
$53$		−	3.92050i		−	0.538523i	0.963067	−	0.269261i	$-0.0867795\pi$
$54$		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	$-0.0816481\pi$
$59$	2.02728	+	3.51135i	0.263929	+	0.457139i	−0.703353	+	0.710840i	$0.748315\pi$
$60$		0			0
$61$	1.61459	+	0.932184i	0.206727	+	0.119354i	0.599789	−	0.800158i	$-0.295251\pi$
$61$	1.61459	+	0.932184i	0.206727	+	0.119354i	−0.393062	+	0.919512i	$0.628584\pi$
$62$		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	0.931953	+	0.362579i	$0.118104\pi$
$67$	6.38441	+	11.0581i	0.779979	+	1.35096i	−0.151974	+	0.988385i	$0.548563\pi$
$68$		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
$73$			1.90594i			0.223074i	0.993760	+	0.111537i	$0.0355773\pi$
$73$			1.90594i			0.223074i	−0.993760	+	0.111537i	$0.964423\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	−0.840600	−	0.541656i	$-0.817798\pi$
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	0.889388	+	0.457153i	$0.151131\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.45880	−	5.99082i	0.379653	−	0.657578i	−0.611359	−	0.791354i	$-0.709377\pi$
$83$	3.45880	−	5.99082i	0.379653	−	0.657578i	0.991012	+	0.133775i	$0.0427100\pi$
$84$		0			0
$85$	5.35744	+	9.27936i	0.581096	+	1.00649i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.77729			1.03639			0.518195	−	0.855262i	$-0.326604\pi$
$89$	9.77729			1.03639			0.518195	+	0.855262i	$0.326604\pi$
$90$		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	0.489791	−	0.871840i	$-0.337073\pi$
$97$	−0.200411	−	0.115707i	−0.0203486	−	0.0117483i	−0.510140	+	0.860091i	$0.670406\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.14031	+	12.3674i	−0.710487	+	1.23060i	0.254187	+	0.967155i	$0.418192\pi$
$101$	−7.14031	+	12.3674i	−0.710487	+	1.23060i	−0.964674	+	0.263445i	$0.915141\pi$
$102$		0			0
$103$	−9.30617	+	5.37292i	−0.916964	+	0.529410i	−0.882665	−	0.470002i	$-0.844253\pi$
$103$	−9.30617	+	5.37292i	−0.916964	+	0.529410i	−0.0342991	+	0.999412i	$0.510920\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			6.35702i			0.614556i	0.951620	+	0.307278i	$0.0994181\pi$
$107$			6.35702i			0.614556i	−0.951620	+	0.307278i	$0.900582\pi$
$108$		0			0
$109$	−5.16072			−0.494308			−0.247154	−	0.968976i	$-0.579495\pi$
$109$	−5.16072			−0.494308			−0.247154	+	0.968976i	$0.579495\pi$
$110$		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
$115$	21.2027	+	12.2414i	1.97716	+	1.14151i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.41249	−	9.37471i	−0.492044	−	0.852246i
$122$		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
$131$	9.83048	+	17.0269i	0.858893	+	1.48765i	0.872986	+	0.487746i	$0.162181\pi$
$131$	9.83048	+	17.0269i	0.858893	+	1.48765i	−0.0140928	+	0.999901i	$0.504486\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	0.287347	−	0.957827i	$-0.407227\pi$
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	−0.685829	+	0.727763i	$0.740560\pi$
$138$		0			0
$139$	−14.7839	+	8.53549i	−1.25395	+	0.723971i	−0.971892	−	0.235425i	$-0.924352\pi$
$139$	−14.7839	+	8.53549i	−1.25395	+	0.723971i	−0.282062	+	0.959396i	$0.591018\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.640131			0.0535304
$144$		0			0
$145$		−	19.0182i		−	1.57938i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	−0.0674758	−	0.997721i	$-0.521495\pi$
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	0.830314	+	0.557296i	$0.188161\pi$
$150$		0			0
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	−0.977879	−	0.209169i	$-0.932924\pi$
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	0.670086	+	0.742284i	$0.266257\pi$
$152$		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	−0.0116445	−	0.999932i	$-0.503707\pi$
$157$	10.6317	−	6.13820i	0.848500	−	0.489882i	0.860144	+	0.510051i	$0.170373\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−11.8349			−0.926981			−0.463490	−	0.886102i	$-0.653403\pi$
$163$	−11.8349			−0.926981			−0.463490	+	0.886102i	$0.653403\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.78854	+	11.7581i	0.525313	+	0.909869i	0.999565	+	0.0294798i	$0.00938508\pi$
$167$	6.78854	+	11.7581i	0.525313	+	0.909869i	−0.474252	+	0.880389i	$0.657282\pi$
$168$		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	−0.355308	−	0.934749i	$-0.615624\pi$
$173$	8.31085	−	14.3948i	0.631862	−	1.09442i	0.987171	−	0.159668i	$-0.0510425\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$			17.0988i			1.27803i	0.769195	+	0.639014i	$0.220657\pi$
$179$			17.0988i			1.27803i	−0.769195	+	0.639014i	$0.779343\pi$
$180$		0			0
$181$		−	18.2171i		−	1.35407i	−0.735952	−	0.677034i	$-0.763265\pi$
$181$		−	18.2171i		−	1.35407i	0.735952	−	0.677034i	$-0.236735\pi$
$182$		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	$-0.608002\pi$
$191$	−18.1860	−	10.4997i	−1.31589	−	0.759730i	−0.983065	+	0.183258i	$0.941336\pi$
$192$		0			0
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	0.963810	−	0.266592i	$-0.0858975\pi$
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	−0.712780	+	0.701388i	$0.752564\pi$
$194$		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
$199$		−	6.29261i		−	0.446071i	−0.974810	−	0.223036i	$-0.928403\pi$
$199$		−	6.29261i		−	0.446071i	0.974810	−	0.223036i	$-0.0715966\pi$
$200$		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
$215$	−31.7043			−2.16222
$216$		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	0.993046	−	0.117725i	$-0.0375600\pi$
$223$	20.7215	+	11.9636i	1.38762	+	0.801141i	0.394571	+	0.918866i	$0.370893\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.86609	+	3.23216i	−0.123857	+	0.214526i	−0.921285	−	0.388887i	$-0.872860\pi$
$227$	−1.86609	+	3.23216i	−0.123857	+	0.214526i	0.797429	+	0.603413i	$0.206193\pi$
$228$		0			0
$229$	18.2455	−	10.5341i	1.20570	−	0.696111i	0.243882	−	0.969805i	$-0.421579\pi$
$229$	18.2455	−	10.5341i	1.20570	−	0.696111i	0.961817	+	0.273694i	$0.0882457\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			12.7643i			0.836217i	0.908397	+	0.418109i	$0.137307\pi$
$233$			12.7643i			0.836217i	−0.908397	+	0.418109i	$0.862693\pi$
$234$		0			0
$235$	4.85772			0.316883
$236$		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
$241$	−2.63438	−	1.52096i	−0.169695	−	0.0979737i	0.412747	−	0.910846i	$-0.364569\pi$
$241$	−2.63438	−	1.52096i	−0.169695	−	0.0979737i	−0.582442	+	0.812872i	$0.697903\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.52301	−	7.83408i	−0.287792	−	0.498470i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.32067			−0.398957			−0.199478	−	0.979902i	$-0.563925\pi$
$251$	−6.32067			−0.398957			−0.199478	+	0.979902i	$0.563925\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.2538	−	21.2242i	−0.764372	−	1.32393i	−0.940578	−	0.339577i	$-0.889716\pi$
$257$	−12.2538	−	21.2242i	−0.764372	−	1.32393i	0.176206	−	0.984353i	$-0.443617\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.321323	−	0.946970i	$-0.604128\pi$
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.980761	+	0.195211i	$0.937461\pi$
$264$		0			0
$265$	9.31427	−	5.37760i	0.572171	−	0.330343i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.89049			−0.603034			−0.301517	−	0.953461i	$-0.597493\pi$
$269$	−9.89049			−0.603034			−0.301517	+	0.953461i	$0.597493\pi$
$270$		0			0
$271$			5.89481i			0.358084i	0.983841	+	0.179042i	$0.0572998\pi$
$271$			5.89481i			0.358084i	−0.983841	+	0.179042i	$0.942700\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.915111	−	0.528340i	0.0551833	−	0.0318601i
$276$		0			0
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	0.268741	+	0.963213i	$0.413392\pi$
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	−0.968537	+	0.248870i	$0.919941\pi$
$278$		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	−0.221086	−	0.975254i	$-0.570960\pi$
$283$	8.62942	−	4.98220i	0.512966	−	0.296161i	0.734052	+	0.679093i	$0.237627\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.74463			−0.102626
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.79065	−	11.7618i	−0.396714	−	0.687129i	0.596604	−	0.802536i	$-0.296516\pi$
$293$	−6.79065	−	11.7618i	−0.396714	−	0.687129i	−0.993318	+	0.115406i	$0.963183\pi$
$294$		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
$305$			5.11455i			0.292858i
$306$		0			0
$307$			16.9849i			0.969381i	0.874686	+	0.484691i	$0.161068\pi$
$307$			16.9849i			0.969381i	−0.874686	+	0.484691i	$0.838932\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	0.865983	−	0.500073i	$-0.166694\pi$
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	−0.866068	+	0.499927i	$0.833360\pi$
$312$		0			0
$313$	10.6154	+	6.12878i	0.600015	+	0.346419i	0.769048	−	0.639191i	$-0.220731\pi$
$313$	10.6154	+	6.12878i	0.600015	+	0.346419i	−0.169032	+	0.985611i	$0.554064\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.0008	+	11.5475i	1.12336	+	0.648571i	0.942256	−	0.334894i	$-0.108700\pi$
$317$	20.0008	+	11.5475i	1.12336	+	0.648571i	0.181102	+	0.983464i	$0.442034\pi$
$318$		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
$325$		−	3.86475i		−	0.214378i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	−0.814522	−	0.580132i	$-0.803001\pi$
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	0.909670	+	0.415331i	$0.136334\pi$
$332$		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
$341$	−1.47640			−0.0799518
$342$		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	$-0.712442\pi$
$347$	−4.62386	+	2.66959i	−0.248222	+	0.143311i	0.370728	+	0.928741i	$0.379108\pi$
$348$		0			0
$349$	0.0136817	+	0.00789914i	0.000732365	+	0.000422831i	0.500366	−	0.865814i	$-0.333199\pi$
$349$	0.0136817	+	0.00789914i	0.000732365	+	0.000422831i	−0.499634	+	0.866237i	$0.666532\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.1543	−	29.7121i	0.913029	−	1.58141i	0.103268	−	0.994654i	$-0.467070\pi$
$353$	17.1543	−	29.7121i	0.913029	−	1.58141i	0.809761	−	0.586760i	$-0.199597\pi$
$354$		0			0
$355$	20.2184	−	11.6731i	1.07308	−	0.619544i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			6.26718i			0.330769i	0.986229	+	0.165385i	$0.0528865\pi$
$359$			6.26718i			0.330769i	−0.986229	+	0.165385i	$0.947113\pi$
$360$		0			0
$361$	−15.9517			−0.839561
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.52811	+	2.61430i	−0.237012	+	0.136839i
$366$		0			0
$367$	16.4888	+	9.51984i	0.860711	+	0.496931i	0.864250	−	0.503062i	$-0.167793\pi$
$367$	16.4888	+	9.51984i	0.860711	+	0.496931i	−0.00353959	+	0.999994i	$0.501127\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	0.690943	−	0.722909i	$-0.257195\pi$
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	−0.971529	+	0.236920i	$0.923862\pi$
$374$		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
$383$	19.0235	+	32.9497i	0.972056	+	1.68365i	0.689327	+	0.724451i	$0.257906\pi$
$383$	19.0235	+	32.9497i	0.972056	+	1.68365i	0.282729	+	0.959200i	$0.408760\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	0.859473	−	0.511182i	$-0.170792\pi$
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	−0.0129603	+	0.999916i	$0.504125\pi$
$390$		0			0
$391$	30.1874	−	17.4287i	1.52664	−	0.881407i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.37919			0.119710
$396$		0			0
$397$			20.0468i			1.00612i	0.864252	+	0.503059i	$0.167792\pi$
$397$			20.0468i			1.00612i	−0.864252	+	0.503059i	$0.832208\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.335861	−	0.941912i	$-0.390973\pi$
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.983650	+	0.180092i	$0.0576395\pi$
$402$		0			0
$403$	−2.69993	+	4.67642i	−0.134493	+	0.232949i
$404$		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	−0.496271	−	0.868168i	$-0.665298\pi$
$409$	0.150631	−	0.0869667i	0.00744821	−	0.00430023i	0.503719	+	0.863867i	$0.331965\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	18.9772			0.931554
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.0690	−	24.3682i	−0.687316	−	1.19047i	−0.972703	−	0.232054i	$-0.925455\pi$
$419$	−14.0690	−	24.3682i	−0.687316	−	1.19047i	0.285387	−	0.958412i	$-0.407878\pi$
$420$		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
$431$			9.91744i			0.477706i	0.971056	+	0.238853i	$0.0767715\pi$
$431$			9.91744i			0.477706i	−0.971056	+	0.238853i	$0.923229\pi$
$432$		0			0
$433$			17.1274i			0.823092i	0.911389	+	0.411546i	$0.135011\pi$
$433$			17.1274i			0.823092i	−0.911389	+	0.411546i	$0.864989\pi$
$434$		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	0.872878	−	0.487938i	$-0.162251\pi$
$439$	18.5795	+	10.7269i	0.886750	+	0.511965i	0.0138721	+	0.999904i	$0.495584\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.84340	−	3.37369i	−0.277628	−	0.160289i	0.354721	−	0.934972i	$-0.384576\pi$
$443$	−5.84340	−	3.37369i	−0.277628	−	0.160289i	−0.632349	+	0.774683i	$0.717909\pi$
$444$		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
$451$		−	0.888889i		−	0.0418562i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	−0.150432	−	0.988620i	$-0.548066\pi$
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	0.931386	−	0.364032i	$-0.118600\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.5154	+	32.0696i	−0.862347	+	1.49363i	0.00730959	+	0.999973i	$0.497673\pi$
$461$	−18.5154	+	32.0696i	−0.862347	+	1.49363i	−0.869657	+	0.493656i	$0.835660\pi$
$462$		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
$467$	−18.6094			−0.861141			−0.430570	−	0.902557i	$-0.641688\pi$
$467$	−18.6094			−0.861141			−0.430570	+	0.902557i	$0.641688\pi$
$468$		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
$479$	7.16703	−	12.4137i	0.327470	−	0.567194i	−0.654539	−	0.756028i	$-0.727137\pi$
$479$	7.16703	−	12.4137i	0.327470	−	0.567194i	0.982009	+	0.188834i	$0.0604707\pi$
$480$		0			0
$481$	−12.0549	+	6.95988i	−0.549655	+	0.317343i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	0.634844i		−	0.0288268i
$486$		0			0
$487$	11.2966			0.511897			0.255949	−	0.966690i	$-0.417612\pi$
$487$	11.2966			0.511897			0.255949	+	0.966690i	$0.417612\pi$
$488$		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
$493$	−23.4496	−	13.5387i	−1.05612	−	0.609751i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	0.996719	−	0.0809379i	$-0.0257915\pi$
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	−0.568454	+	0.822715i	$0.692458\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.268917			0.0119904			0.00599520	−	0.999982i	$-0.498092\pi$
$503$	0.268917			0.0119904			0.00599520	+	0.999982i	$0.498092\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.9439	+	18.9553i	0.485079	+	0.840181i	0.999853	−	0.0171449i	$-0.00545767\pi$
$509$	10.9439	+	18.9553i	0.485079	+	0.840181i	−0.514774	+	0.857326i	$0.672124\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.5298	−	14.7396i	−1.12498	−	0.649506i
$516$		0			0
$517$	−0.641553	+	0.370401i	−0.0282155	+	0.0162902i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.71215			−0.0750105			−0.0375053	−	0.999296i	$-0.511941\pi$
$521$	−1.71215			−0.0750105			−0.0375053	+	0.999296i	$0.511941\pi$
$522$		0			0
$523$		−	8.27136i		−	0.361681i	−0.983512	−	0.180841i	$-0.942118\pi$
$523$		−	8.27136i		−	0.361681i	0.983512	−	0.180841i	$-0.0578818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.9372	−	6.89193i	0.519992	−	0.300217i
$528$		0			0
$529$	28.3233	−	49.0574i	1.23145	−	2.13293i
$530$		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
$541$	20.3993			0.877036			0.438518	−	0.898722i	$-0.355503\pi$
$541$	20.3993			0.877036			0.438518	+	0.898722i	$0.355503\pi$
$542$		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
$557$			16.8493i			0.713926i	0.934119	+	0.356963i	$0.116188\pi$
$557$			16.8493i			0.713926i	−0.934119	+	0.356963i	$0.883812\pi$
$558$		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	$-0.0531965\pi$
$563$	8.28035	+	14.3420i	0.348975	+	0.604443i	−0.637093	+	0.770787i	$0.719863\pi$
$564$		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	$-0.375822\pi$
$569$	−5.49856	−	3.17460i	−0.230512	−	0.133086i	−0.610808	+	0.791779i	$0.709155\pi$
$570$		0			0
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.729507	−	0.683973i	$-0.760250\pi$
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.227585	−	0.973758i	$-0.573083\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			22.5414i			0.940043i
$576$		0			0
$577$			17.7499i			0.738939i	0.929243	+	0.369470i	$0.120461\pi$
$577$			17.7499i			0.738939i	−0.929243	+	0.369470i	$0.879539\pi$
$578$		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	−0.760508	−	0.649329i	$-0.775050\pi$
$587$	4.41148	−	7.64091i	0.182081	−	0.315374i	0.942589	+	0.333955i	$0.108383\pi$
$588$		0			0
$589$	10.4319	+	18.0686i	0.429839	+	0.744503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.49698			−0.348929			−0.174465	−	0.984663i	$-0.555819\pi$
$593$	−8.49698			−0.348929			−0.174465	+	0.984663i	$0.555819\pi$
$594$		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	$-0.690805\pi$
$599$	−3.21158	+	1.85421i	−0.131222	+	0.0757609i	0.432952	+	0.901417i	$0.357472\pi$
$600$		0			0
$601$	−6.14043	−	3.54518i	−0.250473	−	0.144611i	0.369508	−	0.929228i	$-0.379526\pi$
$601$	−6.14043	−	3.54518i	−0.250473	−	0.144611i	−0.619981	+	0.784617i	$0.712860\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.8482	−	25.7178i	0.603664	−	1.04558i
$606$		0			0
$607$	−29.4396	+	16.9970i	−1.19492	+	0.689886i	−0.959418	−	0.281988i	$-0.909006\pi$
$607$	−29.4396	+	16.9970i	−1.19492	+	0.689886i	−0.235500	+	0.971874i	$0.575673\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			2.70944i			0.109612i
$612$		0			0
$613$	23.3523			0.943190			0.471595	−	0.881815i	$-0.343678\pi$
$613$	23.3523			0.943190			0.471595	+	0.881815i	$0.343678\pi$
$614$		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
$619$	−7.97914	−	4.60676i	−0.320709	−	0.185161i	0.331000	−	0.943631i	$-0.392614\pi$
$619$	−7.97914	−	4.60676i	−0.320709	−	0.185161i	−0.651708	+	0.758470i	$0.725947\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.6247	+	27.0627i	0.624987	+	1.08251i
$626$		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
$635$	14.1156	+	24.4489i	0.560160	+	0.970226i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	0.790258	−	0.612775i	$-0.209947\pi$
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	−0.135550	+	0.990771i	$0.543280\pi$
$642$		0			0
$643$	2.01129	−	1.16122i	0.0793177	−	0.0457941i	−0.459817	−	0.888014i	$-0.652085\pi$
$643$	2.01129	−	1.16122i	0.0793177	−	0.0457941i	0.539134	+	0.842220i	$0.318752\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−25.8620			−1.01674			−0.508370	−	0.861139i	$-0.669752\pi$
$647$	−25.8620			−1.01674			−0.508370	+	0.861139i	$0.669752\pi$
$648$		0			0
$649$		−	1.69625i		−	0.0665835i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	−0.838949	−	0.544211i	$-0.816829\pi$
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	0.0518258	+	0.998656i	$0.483496\pi$
$654$		0			0
$655$	−26.9681	+	46.7102i	−1.05373	+	1.82512i
$656$		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	−0.160181	−	0.987088i	$-0.551208\pi$
$661$	15.8006	−	9.12248i	0.614572	−	0.354823i	0.774753	+	0.632264i	$0.217874\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−61.8697			−2.39560
$668$		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	−0.340040	−	0.940411i	$-0.610441\pi$
$677$	16.7668	−	29.0409i	0.644400	−	1.11613i	0.984440	−	0.175722i	$-0.0562261\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	22.0481i		−	0.843649i	−0.906678	−	0.421824i	$-0.861390\pi$
$683$		−	22.0481i		−	0.843649i	0.906678	−	0.421824i	$-0.138610\pi$
$684$		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	0.867305	−	0.497777i	$-0.165850\pi$
$691$	22.8662	+	13.2018i	0.869869	+	0.502219i	0.00256453	+	0.999997i	$0.499184\pi$
$692$		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
$703$			53.7827i			2.02845i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	−0.801234	−	0.598351i	$-0.795823\pi$
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	0.918804	+	0.394714i	$0.129156\pi$
$710$		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
$719$	23.2223			0.866045			0.433023	−	0.901383i	$-0.357447\pi$
$719$	23.2223			0.866045			0.433023	+	0.901383i	$0.357447\pi$
$720$		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	0.452732	−	0.891647i	$-0.350449\pi$
$727$	−2.50999	−	1.44914i	−0.0930903	−	0.0537457i	−0.545822	+	0.837901i	$0.683783\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−22.5696	+	39.0917i	−0.834767	+	1.44586i
$732$		0			0
$733$	10.2963	−	5.94457i	0.380302	−	0.219568i	−0.297647	−	0.954676i	$-0.596202\pi$
$733$	10.2963	−	5.94457i	0.380302	−	0.219568i	0.677950	+	0.735108i	$0.262869\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.34190i		−	0.196772i
$738$		0			0
$739$	−34.4509			−1.26730			−0.633648	−	0.773621i	$-0.718443\pi$
$739$	−34.4509			−1.26730			−0.633648	+	0.773621i	$0.718443\pi$
$740$		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
$745$	25.5447	+	14.7483i	0.935887	+	0.540335i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	0.786955	−	0.617011i	$-0.211657\pi$
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	−0.927824	+	0.373017i	$0.878323\pi$
$752$		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
$761$	−1.56644	−	2.71316i	−0.0567835	−	0.0983520i	0.836236	−	0.548369i	$-0.184751\pi$
$761$	−1.56644	−	2.71316i	−0.0567835	−	0.0983520i	−0.893020	+	0.450017i	$0.851418\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.37276	−	3.10196i	−0.193999	−	0.112005i
$768$		0			0
$769$	−5.53497	+	3.19562i	−0.199596	+	0.115237i	−0.596467	−	0.802637i	$-0.703429\pi$
$769$	−5.53497	+	3.19562i	−0.199596	+	0.115237i	0.396871	+	0.917874i	$0.370096\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−47.9558			−1.72485			−0.862425	−	0.506185i	$-0.831055\pi$
$773$	−47.9558			−1.72485			−0.862425	+	0.506185i	$0.831055\pi$
$774$		0			0
$775$			8.91369i			0.320189i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.8784	+	6.28067i	−0.389761	+	0.225028i
$780$		0			0
$781$	−1.78015	+	3.08331i	−0.0636987	+	0.110329i
$782$		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	−0.590333	−	0.807160i	$-0.701003\pi$
$787$	−5.23136	+	3.02033i	−0.186478	+	0.107663i	0.403855	+	0.914823i	$0.367670\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.85269			−0.101302
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.782501	+	1.35533i	0.0277176	+	0.0480083i	0.879551	−	0.475804i	$-0.157843\pi$
$797$	0.782501	+	1.35533i	0.0277176	+	0.0480083i	−0.851834	+	0.523812i	$0.824509\pi$
$798$		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
$809$		−	17.7184i		−	0.622944i	−0.950255	−	0.311472i	$-0.899178\pi$
$809$		−	17.7184i		−	0.622944i	0.950255	−	0.311472i	$-0.100822\pi$
$810$		0			0
$811$			27.5261i			0.966571i	0.875463	+	0.483285i	$0.160557\pi$
$811$			27.5261i			0.966571i	−0.875463	+	0.483285i	$0.839443\pi$
$812$		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	$-0.179699\pi$
$821$	23.0343	+	13.2989i	0.803903	+	0.464134i	−0.0409311	+	0.999162i	$0.513032\pi$
$822$		0			0
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	0.574972	−	0.818173i	$-0.305013\pi$
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	−0.996045	+	0.0888537i	$0.971680\pi$
$824$		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
$829$		−	29.0385i		−	1.00855i	−0.863543	−	0.504275i	$-0.831760\pi$
$829$		−	29.0385i		−	1.00855i	0.863543	−	0.504275i	$-0.168240\pi$
$830$		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	−0.723367	−	0.690463i	$-0.757407\pi$
$839$	6.84383	−	11.8539i	0.236275	−	0.409241i	0.959642	+	0.281223i	$0.0907400\pi$
$840$		0			0
$841$	9.53027	+	16.5069i	0.328630	+	0.569204i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−29.2404			−1.00590
$846$		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	−0.394310	−	0.918977i	$-0.629017\pi$
$853$	−40.5184	−	23.3933i	−1.38732	−	0.800972i	−0.993013	+	0.118006i	$0.962350\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.8980	−	27.5361i	0.543065	−	0.940616i	−0.455661	−	0.890153i	$-0.650597\pi$
$857$	15.8980	−	27.5361i	0.543065	−	0.940616i	0.998726	−	0.0504623i	$-0.0160695\pi$
$858$		0			0
$859$	21.9005	−	12.6442i	0.747235	−	0.431416i	−0.0774592	−	0.996996i	$-0.524681\pi$
$859$	21.9005	−	12.6442i	0.747235	−	0.431416i	0.824694	+	0.565579i	$0.191347\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	18.4189i		−	0.626987i	−0.949590	−	0.313494i	$-0.898501\pi$
$863$		−	18.4189i		−	0.626987i	0.949590	−	0.313494i	$-0.101499\pi$
$864$		0			0
$865$	45.5986			1.55040
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.314216	+	0.181413i	−0.0106590	+	0.00615400i
$870$		0			0
$871$	−16.9202	−	9.76886i	−0.573318	−	0.331005i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	0.931287	−	0.364286i	$-0.118687\pi$
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	−0.781124	+	0.624375i	$0.785354\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.1721			0.443780			0.221890	−	0.975072i	$-0.428777\pi$
$881$	13.1721			0.443780			0.221890	+	0.975072i	$0.428777\pi$
$882$		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
$887$	−16.6991	−	28.9238i	−0.560703	−	0.971165i	−0.997435	−	0.0715740i	$-0.977198\pi$
$887$	−16.6991	−	28.9238i	−0.560703	−	0.971165i	0.436733	−	0.899591i	$-0.356136\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.06611	+	5.23432i	0.303386	+	0.175160i
$894$		0			0
$895$	−40.6231	+	23.4538i	−1.35788	+	0.783974i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−24.4655			−0.815970
$900$		0			0
$901$		−	15.3128i		−	0.510142i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	43.2799	−	24.9877i	1.43867	−	0.830618i
$906$		0			0
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	−0.513227	−	0.858253i	$-0.671550\pi$
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	0.999882	+	0.0153411i	$0.00488340\pi$
$908$		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
$919$	1.79536			0.0592233			0.0296117	−	0.999561i	$-0.490573\pi$
$919$	1.79536			0.0592233			0.0296117	+	0.999561i	$0.490573\pi$
$920$		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	$-0.699763\pi$
$929$	12.4178	−	21.5083i	0.407415	−	0.705664i	0.994599	+	0.103789i	$0.0330968\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	4.48263i		−	0.146598i
$936$		0			0
$937$			27.9046i			0.911605i	0.890081	+	0.455802i	$0.150648\pi$
$937$			27.9046i			0.911605i	−0.890081	+	0.455802i	$0.849352\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	−0.875857	−	0.482571i	$-0.839703\pi$
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	0.0200094	−	0.999800i	$-0.493630\pi$
$942$		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	$-0.580555\pi$
$947$	−37.3591	−	21.5693i	−1.21401	−	0.700907i	−0.963630	+	0.267241i	$0.913888\pi$
$948$		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
$955$		−	57.6079i		−	1.86415i
$956$		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
$971$	−56.3111			−1.80711			−0.903555	−	0.428472i	$-0.859052\pi$
$971$	−56.3111			−1.80711			−0.903555	+	0.428472i	$0.859052\pi$
$972$		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	$-0.803583\pi$
$977$	−22.5755	+	13.0340i	−0.722254	+	0.416994i	0.0933275	+	0.995635i	$0.470250\pi$
$978$		0			0
$979$	−3.54237	−	2.04519i	−0.113215	−	0.0653646i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.0252	−	32.9527i	0.606811	−	1.05103i	−0.384952	−	0.922937i	$-0.625782\pi$
$983$	19.0252	−	32.9527i	0.606811	−	1.05103i	0.991763	−	0.128090i	$-0.0408848\pi$
$984$		0			0
$985$	−38.1922	+	22.0503i	−1.21690	+	0.702580i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			103.140i			3.27965i
$990$		0			0
$991$	11.3752			0.361344			0.180672	−	0.983543i	$-0.442173\pi$
$991$	11.3752			0.361344			0.180672	+	0.983543i	$0.442173\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.9499	−	8.63131i	0.473943	−	0.273631i
$996$		0			0
$997$	−44.1590	−	25.4952i	−1.39853	−	0.807441i	−0.404290	−	0.914631i	$-0.632482\pi$
$997$	−44.1590	−	25.4952i	−1.39853	−	0.807441i	−0.994239	+	0.107189i	$0.965815\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	63.4	even	3
252.2.w.a.101.7	yes	16	21.5	even	6
252.2.bm.a.173.5	yes	16	21.11	odd	6
252.2.bm.a.185.5	yes	16	63.40	odd	6
756.2.w.a.341.2		16	63.32	odd	6
756.2.w.a.521.2		16	7.5	odd	6
756.2.bm.a.17.2		16	63.5	even	6
756.2.bm.a.89.2		16	7.4	even	3
1008.2.ca.d.257.2		16	252.67	odd	6
1008.2.ca.d.353.2		16	84.47	odd	6
1008.2.df.d.689.4		16	252.103	even	6
1008.2.df.d.929.4		16	84.11	even	6
1764.2.w.b.509.2		16	63.31	odd	6
1764.2.w.b.1109.2		16	21.2	odd	6
1764.2.x.a.293.2		16	9.4	even	3
1764.2.x.a.1469.2		16	21.20	even	2
1764.2.x.b.293.7		16	63.13	odd	6
1764.2.x.b.1469.7		16	3.2	odd	2
1764.2.bm.a.1685.4		16	21.17	even	6
1764.2.bm.a.1697.4		16	63.58	even	3
2268.2.t.a.1781.2		16	63.61	odd	6
2268.2.t.a.2105.2		16	63.11	odd	6
2268.2.t.b.1781.7		16	63.47	even	6
2268.2.t.b.2105.7		16	63.25	even	3
3024.2.ca.d.2033.2		16	28.19	even	6
3024.2.ca.d.2609.2		16	252.95	even	6
3024.2.df.d.17.2		16	252.131	odd	6
3024.2.df.d.1601.2		16	28.11	odd	6
5292.2.w.b.521.7		16	7.2	even	3
5292.2.w.b.1097.7		16	63.59	even	6
5292.2.x.a.881.2		16	9.5	odd	6
5292.2.x.a.4409.2		16	7.6	odd	2
5292.2.x.b.881.7		16	63.41	even	6	inner
5292.2.x.b.4409.7		16	1.1	even	1	trivial
5292.2.bm.a.2285.7		16	63.23	odd	6
5292.2.bm.a.4625.7		16	7.3	odd	6

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.x (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37166 + 2.37578i) q^{5} +O(q^{10})\)	\(q+(1.37166 + 2.37578i) q^{5} +(-0.362306 - 0.209178i) q^{11} +(-1.32512 + 0.765056i) q^{13} +3.90581 q^{17} +5.91199i q^{19} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 - 1.76453i) q^{31} +9.09722 q^{37} +(1.06236 + 1.84006i) q^{41} +(-5.77846 + 10.0086i) q^{43} +(0.885373 - 1.53351i) q^{47} -3.92050i q^{53} -1.14768i q^{55} +(2.02728 + 3.51135i) q^{59} +(1.61459 + 0.932184i) q^{61} +(-3.63521 - 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} -8.51021i q^{71} +1.90594i q^{73} +(0.433633 - 0.751074i) q^{79} +(3.45880 - 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +9.77729 q^{89} +(-14.0456 + 8.10924i) q^{95} +(-0.200411 - 0.115707i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 6 q^{11} + 3 q^{13} - 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} - 6 q^{31} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 42 q^{89} + 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q - 6 * q^11 + 3 * q^13 - 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 - 6 * q^31 - 2 * 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 - 42 * q^89 + 6 * q^95 + 3 * q^97

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