LMFDB - Embedded newform 1512.2.cx.a.89.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(17,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.14
Character	$\chi$	$=$	1512.89
Dual form			1512.2.cx.a.17.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.623597 q^{5} +(-0.996837 - 2.45078i) q^{7} +5.19907i q^{11} +(-2.74023 + 1.58207i) q^{13} +(-0.437594 - 0.757935i) q^{17} +(-1.41874 - 0.819107i) q^{19} +8.25480i q^{23} -4.61113 q^{25} +(-4.96435 - 2.86617i) q^{29} +(4.02256 + 2.32243i) q^{31} +(-0.621624 - 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(3.52382 + 6.10344i) q^{41} +(-1.56398 + 2.70890i) q^{43} +(4.73384 + 8.19925i) q^{47} +(-5.01263 + 4.88605i) q^{49} +(1.15189 - 0.665044i) q^{53} +3.24212i q^{55} +(3.18334 - 5.51370i) q^{59} +(9.65975 - 5.57706i) q^{61} +(-1.70880 + 0.986576i) q^{65} +(-6.04951 + 10.4781i) q^{67} +10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(12.7418 - 5.18263i) q^{77} +(-4.84840 - 8.39767i) q^{79} +(0.192030 - 0.332606i) q^{83} +(-0.272882 - 0.472646i) q^{85} +(-0.0198983 + 0.0344648i) q^{89} +(6.60888 + 5.13864i) q^{91} +(-0.884719 - 0.510793i) q^{95} +(5.94681 + 3.43339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$5$	0.623597			0.278881			0.139440	−	0.990230i	$-0.455470\pi$
$5$	0.623597			0.278881			0.139440	+	0.990230i	$0.455470\pi$
$6$		0			0
$7$	−0.996837	−	2.45078i	−0.376769	−	0.926307i
$7$	−0.996837	−	2.45078i	−0.376769	−	0.926307i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			5.19907i			1.56758i	0.621026	+	0.783790i	$0.286716\pi$
$11$			5.19907i			1.56758i	−0.621026	+	0.783790i	$0.713284\pi$
$12$		0			0
$13$	−2.74023	+	1.58207i	−0.760004	+	0.438788i	−0.829297	−	0.558808i	$-0.811259\pi$
$13$	−2.74023	+	1.58207i	−0.760004	+	0.438788i	0.0692932	+	0.997596i	$0.477926\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.437594	−	0.757935i	−0.106132	−	0.183826i	0.808068	−	0.589089i	$-0.200513\pi$
$17$	−0.437594	−	0.757935i	−0.106132	−	0.183826i	−0.914200	+	0.405263i	$0.867180\pi$
$18$		0			0
$19$	−1.41874	−	0.819107i	−0.325480	−	0.187916i	0.328352	−	0.944555i	$-0.393507\pi$
$19$	−1.41874	−	0.819107i	−0.325480	−	0.187916i	−0.653833	+	0.756639i	$0.726840\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			8.25480i			1.72124i	0.509245	+	0.860622i	$0.329925\pi$
$23$			8.25480i			1.72124i	−0.509245	+	0.860622i	$0.670075\pi$
$24$		0			0
$25$	−4.61113			−0.922225
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.96435	−	2.86617i	−0.921856	−	0.532234i	−0.0376295	−	0.999292i	$-0.511981\pi$
$29$	−4.96435	−	2.86617i	−0.921856	−	0.532234i	−0.884227	+	0.467058i	$0.845314\pi$
$30$		0			0
$31$	4.02256	+	2.32243i	0.722474	+	0.417120i	0.815662	−	0.578528i	$-0.196373\pi$
$31$	4.02256	+	2.32243i	0.722474	+	0.417120i	−0.0931888	+	0.995648i	$0.529706\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.621624	−	1.52830i	−0.105074	−	0.258329i
$36$		0			0
$37$	1.24291	−	2.15278i	0.204333	−	0.353916i	−0.745587	−	0.666408i	$-0.767831\pi$
$37$	1.24291	−	2.15278i	0.204333	−	0.353916i	0.949920	+	0.312493i	$0.101164\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.52382	+	6.10344i	0.550329	+	0.953198i	0.998251	+	0.0591249i	$0.0188310\pi$
$41$	3.52382	+	6.10344i	0.550329	+	0.953198i	−0.447922	+	0.894073i	$0.647836\pi$
$42$		0			0
$43$	−1.56398	+	2.70890i	−0.238505	+	0.413103i	−0.960286	−	0.279019i	$-0.909991\pi$
$43$	−1.56398	+	2.70890i	−0.238505	+	0.413103i	0.721780	+	0.692122i	$0.243324\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.73384	+	8.19925i	0.690502	+	1.19598i	0.971674	+	0.236327i	$0.0759435\pi$
$47$	4.73384	+	8.19925i	0.690502	+	1.19598i	−0.281172	+	0.959657i	$0.590723\pi$
$48$		0			0
$49$	−5.01263	+	4.88605i	−0.716090	+	0.698007i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.15189	−	0.665044i	0.158224	−	0.0913508i	−0.418797	−	0.908080i	$-0.637548\pi$
$53$	1.15189	−	0.665044i	0.158224	−	0.0913508i	0.577021	+	0.816729i	$0.304215\pi$
$54$		0			0
$55$			3.24212i			0.437168i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.18334	−	5.51370i	0.414435	−	0.717823i	−0.580934	−	0.813951i	$-0.697313\pi$
$59$	3.18334	−	5.51370i	0.414435	−	0.717823i	0.995369	+	0.0961281i	$0.0306459\pi$
$60$		0			0
$61$	9.65975	−	5.57706i	1.23680	−	0.714069i	0.268365	−	0.963317i	$-0.413517\pi$
$61$	9.65975	−	5.57706i	1.23680	−	0.714069i	0.968440	+	0.249248i	$0.0801835\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.70880	+	0.986576i	−0.211951	+	0.122370i
$66$		0			0
$67$	−6.04951	+	10.4781i	−0.739065	+	1.28010i	0.213851	+	0.976866i	$0.431399\pi$
$67$	−6.04951	+	10.4781i	−0.739065	+	1.28010i	−0.952917	+	0.303232i	$0.901934\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.5861i			1.25634i	0.778076	+	0.628171i	$0.216196\pi$
$71$			10.5861i			1.25634i	−0.778076	+	0.628171i	$0.783804\pi$
$72$		0			0
$73$	−11.6719	+	6.73878i	−1.36609	+	0.788714i	−0.990427	−	0.138041i	$-0.955920\pi$
$73$	−11.6719	+	6.73878i	−1.36609	+	0.788714i	−0.375666	+	0.926755i	$0.622586\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.7418	−	5.18263i	1.45206	−	0.590615i
$78$		0			0
$79$	−4.84840	−	8.39767i	−0.545487	−	0.944811i	−0.998576	−	0.0533461i	$-0.983011\pi$
$79$	−4.84840	−	8.39767i	−0.545487	−	0.944811i	0.453089	−	0.891465i	$-0.350322\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.192030	−	0.332606i	0.0210781	−	0.0365083i	−0.855294	−	0.518143i	$-0.826623\pi$
$83$	0.192030	−	0.332606i	0.0210781	−	0.0365083i	0.876372	+	0.481635i	$0.159957\pi$
$84$		0			0
$85$	−0.272882	−	0.472646i	−0.0295982	−	0.0512656i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.0198983	+	0.0344648i	−0.00210921	+	0.00365326i	−0.867078	−	0.498172i	$-0.834005\pi$
$89$	−0.0198983	+	0.0344648i	−0.00210921	+	0.00365326i	0.864969	+	0.501826i	$0.167338\pi$
$90$		0			0
$91$	6.60888	+	5.13864i	0.692799	+	0.538675i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.884719	−	0.510793i	−0.0907702	−	0.0524062i
$96$		0			0
$97$	5.94681	+	3.43339i	0.603807	+	0.348608i	0.770538	−	0.637394i	$-0.219988\pi$
$97$	5.94681	+	3.43339i	0.603807	+	0.348608i	−0.166731	+	0.986002i	$0.553321\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.92598			−0.888168			−0.444084	−	0.895985i	$-0.646471\pi$
$101$	−8.92598			−0.888168			−0.444084	+	0.895985i	$0.646471\pi$
$102$		0			0
$103$			8.86879i			0.873868i	0.899494	+	0.436934i	$0.143936\pi$
$103$			8.86879i			0.873868i	−0.899494	+	0.436934i	$0.856064\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.64326	+	1.52609i	0.255534	+	0.147532i	0.622295	−	0.782782i	$-0.286200\pi$
$107$	2.64326	+	1.52609i	0.255534	+	0.147532i	−0.366762	+	0.930315i	$0.619534\pi$
$108$		0			0
$109$	−5.55069	−	9.61408i	−0.531660	−	0.920862i	−0.999317	−	0.0369519i	$-0.988235\pi$
$109$	−5.55069	−	9.61408i	−0.531660	−	0.920862i	0.467657	−	0.883910i	$-0.345098\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.13836	−	1.81193i	0.295232	−	0.170452i	−0.345067	−	0.938578i	$-0.612144\pi$
$113$	3.13836	−	1.81193i	0.295232	−	0.170452i	0.640299	+	0.768126i	$0.278810\pi$
$114$		0			0
$115$			5.14766i			0.480022i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.42132	+	1.82798i	−0.130292	+	0.167571i
$120$		0			0
$121$	−16.0304			−1.45731
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.99347			−0.536072
$126$		0			0
$127$	−10.1408			−0.899852			−0.449926	−	0.893066i	$-0.648550\pi$
$127$	−10.1408			−0.899852			−0.449926	+	0.893066i	$0.648550\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−21.7576			−1.90097			−0.950484	−	0.310774i	$-0.899412\pi$
$131$	−21.7576			−1.90097			−0.950484	+	0.310774i	$0.899412\pi$
$132$		0			0
$133$	−0.593203	+	4.29352i	−0.0514372	+	0.372296i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			0.393118i			0.0335863i	0.999859	+	0.0167932i	$0.00534568\pi$
$137$			0.393118i			0.0335863i	−0.999859	+	0.0167932i	$0.994654\pi$
$138$		0			0
$139$	−15.6647	+	9.04400i	−1.32866	+	0.767102i	−0.985092	−	0.172026i	$-0.944969\pi$
$139$	−15.6647	+	9.04400i	−1.32866	+	0.767102i	−0.343568	+	0.939128i	$0.611635\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.22532	−	14.2467i	−0.687836	−	1.19137i
$144$		0			0
$145$	−3.09575	−	1.78733i	−0.257088	−	0.148430i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	10.2508i		−	0.839781i	−0.907575	−	0.419891i	$-0.862068\pi$
$149$		−	10.2508i		−	0.839781i	0.907575	−	0.419891i	$-0.137932\pi$
$150$		0			0
$151$	23.8012			1.93691			0.968457	−	0.249181i	$-0.0801614\pi$
$151$	23.8012			1.93691			0.968457	+	0.249181i	$0.0801614\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.50846	+	1.44826i	0.201484	+	0.116327i
$156$		0			0
$157$	9.96626	+	5.75402i	0.795394	+	0.459221i	0.841858	−	0.539699i	$-0.181462\pi$
$157$	9.96626	+	5.75402i	0.795394	+	0.459221i	−0.0464641	+	0.998920i	$0.514795\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	20.2307	−	8.22868i	1.59440	−	0.648511i
$162$		0			0
$163$	10.4614	−	18.1197i	0.819399	−	1.41924i	−0.0867261	−	0.996232i	$-0.527640\pi$
$163$	10.4614	−	18.1197i	0.819399	−	1.41924i	0.906125	−	0.423009i	$-0.139026\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.69358	+	11.5936i	0.517965	+	0.897141i	0.999782	+	0.0208697i	$0.00664350\pi$
$167$	6.69358	+	11.5936i	0.517965	+	0.897141i	−0.481817	+	0.876272i	$0.660023\pi$
$168$		0			0
$169$	−1.49408	+	2.58782i	−0.114929	+	0.199063i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.94433	+	5.09972i	0.223853	+	0.387725i	0.955975	−	0.293449i	$-0.0948031\pi$
$173$	2.94433	+	5.09972i	0.223853	+	0.387725i	−0.732122	+	0.681174i	$0.761470\pi$
$174$		0			0
$175$	4.59654	+	11.3009i	0.347466	+	0.854264i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.4333	+	8.33310i	−1.07880	+	0.622845i	−0.930572	−	0.366109i	$-0.880690\pi$
$179$	−14.4333	+	8.33310i	−1.07880	+	0.622845i	−0.148227	+	0.988953i	$0.547357\pi$
$180$		0			0
$181$		−	0.462705i		−	0.0343926i	−0.999852	−	0.0171963i	$-0.994526\pi$
$181$		−	0.462705i		−	0.0343926i	0.999852	−	0.0171963i	$-0.00547402\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.775075	−	1.34247i	0.0569846	−	0.0987003i
$186$		0			0
$187$	3.94056	−	2.27508i	0.288162	−	0.166371i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.8113	−	6.81927i	0.854637	−	0.493425i	−0.00757544	−	0.999971i	$-0.502411\pi$
$191$	11.8113	−	6.81927i	0.854637	−	0.493425i	0.862213	+	0.506546i	$0.169078\pi$
$192$		0			0
$193$	5.73933	−	9.94080i	0.413126	−	0.715555i	−0.582104	−	0.813114i	$-0.697770\pi$
$193$	5.73933	−	9.94080i	0.413126	−	0.715555i	0.995230	+	0.0975597i	$0.0311037\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			4.78184i			0.340692i	0.985384	+	0.170346i	$0.0544885\pi$
$197$			4.78184i			0.340692i	−0.985384	+	0.170346i	$0.945511\pi$
$198$		0			0
$199$	7.87833	−	4.54856i	0.558480	−	0.322439i	−0.194055	−	0.980991i	$-0.562164\pi$
$199$	7.87833	−	4.54856i	0.558480	−	0.322439i	0.752535	+	0.658552i	$0.228831\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.07570	+	15.0236i	−0.145685	+	1.05445i
$204$		0			0
$205$	2.19745	+	3.80609i	0.153476	+	0.265829i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.25860	−	7.37611i	0.294573	−	0.510216i
$210$		0			0
$211$	1.47477	+	2.55437i	0.101527	+	0.175850i	0.912314	−	0.409491i	$-0.134294\pi$
$211$	1.47477	+	2.55437i	0.101527	+	0.175850i	−0.810787	+	0.585341i	$0.800960\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.975294	+	1.68926i	−0.0665145	+	0.115207i
$216$		0			0
$217$	1.68192	−	12.1735i	0.114176	−	0.826391i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.39822	+	1.38461i	0.161322	+	0.0931391i
$222$		0			0
$223$	20.4564	+	11.8105i	1.36986	+	0.790891i	0.990910	−	0.134524i	$-0.0429506\pi$
$223$	20.4564	+	11.8105i	1.36986	+	0.790891i	0.378954	+	0.925416i	$0.376284\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.0507			1.19807			0.599033	−	0.800725i	$-0.295552\pi$
$227$	18.0507			1.19807			0.599033	+	0.800725i	$0.295552\pi$
$228$		0			0
$229$		−	12.1488i		−	0.802815i	−0.915900	−	0.401407i	$-0.868521\pi$
$229$		−	12.1488i		−	0.802815i	0.915900	−	0.401407i	$-0.131479\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.39111	−	1.95786i	−0.222159	−	0.128264i	0.384791	−	0.923004i	$-0.374274\pi$
$233$	−3.39111	−	1.95786i	−0.222159	−	0.128264i	−0.606950	+	0.794740i	$0.707607\pi$
$234$		0			0
$235$	2.95201	+	5.11303i	0.192568	+	0.333537i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.3996	+	6.00423i	−0.672696	+	0.388381i	−0.797097	−	0.603851i	$-0.793632\pi$
$239$	−10.3996	+	6.00423i	−0.672696	+	0.388381i	0.124401	+	0.992232i	$0.460299\pi$
$240$		0			0
$241$		−	28.2853i		−	1.82202i	−0.412385	−	0.911010i	$-0.635304\pi$
$241$		−	28.2853i		−	1.82202i	0.412385	−	0.911010i	$-0.364696\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.12586	+	3.04693i	−0.199704	+	0.194661i
$246$		0			0
$247$	5.18355			0.329822
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0425			0.760117			0.380059	−	0.924962i	$-0.375904\pi$
$251$	12.0425			0.760117			0.380059	+	0.924962i	$0.375904\pi$
$252$		0			0
$253$	−42.9173			−2.69819
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.6504			−0.913868			−0.456934	−	0.889501i	$-0.651052\pi$
$257$	−14.6504			−0.913868			−0.456934	+	0.889501i	$0.651052\pi$
$258$		0			0
$259$	−6.51498	−	0.900125i	−0.404821	−	0.0559310i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	5.73134i		−	0.353410i	−0.984264	−	0.176705i	$-0.943456\pi$
$263$		−	5.73134i		−	0.353410i	0.984264	−	0.176705i	$-0.0565438\pi$
$264$		0			0
$265$	0.718314	−	0.414719i	0.0441257	−	0.0254760i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.61724	−	2.80114i	−0.0986047	−	0.170788i	0.812503	−	0.582957i	$-0.198105\pi$
$269$	−1.61724	−	2.80114i	−0.0986047	−	0.170788i	−0.911107	+	0.412169i	$0.864771\pi$
$270$		0			0
$271$	−20.6677	−	11.9325i	−1.25548	−	0.724849i	−0.283284	−	0.959036i	$-0.591424\pi$
$271$	−20.6677	−	11.9325i	−1.25548	−	0.724849i	−0.972192	+	0.234187i	$0.924757\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	23.9736i		−	1.44566i
$276$		0			0
$277$	−7.66845			−0.460753			−0.230376	−	0.973102i	$-0.573996\pi$
$277$	−7.66845			−0.460753			−0.230376	+	0.973102i	$0.573996\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.78880	−	5.07422i	−0.524296	−	0.302702i	0.214395	−	0.976747i	$-0.431222\pi$
$281$	−8.78880	−	5.07422i	−0.524296	−	0.302702i	−0.738690	+	0.674045i	$0.764555\pi$
$282$		0			0
$283$	11.8373	+	6.83427i	0.703654	+	0.406255i	0.808707	−	0.588212i	$-0.200168\pi$
$283$	11.8373	+	6.83427i	0.703654	+	0.406255i	−0.105053	+	0.994467i	$0.533501\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.4455	−	14.7203i	0.675607	−	0.868909i
$288$		0			0
$289$	8.11702	−	14.0591i	0.477472	−	0.827006i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.70903	+	4.69218i	0.158263	+	0.274120i	0.934242	−	0.356639i	$-0.116077\pi$
$293$	2.70903	+	4.69218i	0.158263	+	0.274120i	−0.775979	+	0.630758i	$0.782744\pi$
$294$		0			0
$295$	1.98512	−	3.43833i	0.115578	−	0.200187i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.0597	−	22.6201i	−0.755262	−	1.30815i
$300$		0			0
$301$	8.19794	+	1.13265i	0.472522	+	0.0652847i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.02379	−	3.47784i	0.344921	−	0.199140i
$306$		0			0
$307$		−	3.56336i		−	0.203372i	−0.994817	−	0.101686i	$-0.967576\pi$
$307$		−	3.56336i		−	0.203372i	0.994817	−	0.101686i	$-0.0324236\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.63234	+	9.75550i	−0.319381	+	0.553184i	−0.980359	−	0.197221i	$-0.936808\pi$
$311$	−5.63234	+	9.75550i	−0.319381	+	0.553184i	0.660978	+	0.750405i	$0.270142\pi$
$312$		0			0
$313$	9.89696	−	5.71401i	0.559409	−	0.322975i	−0.193499	−	0.981100i	$-0.561984\pi$
$313$	9.89696	−	5.71401i	0.559409	−	0.322975i	0.752908	+	0.658125i	$0.228650\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.8604	+	9.73436i	−0.946975	+	0.546736i	−0.892140	−	0.451759i	$-0.850797\pi$
$317$	−16.8604	+	9.73436i	−0.946975	+	0.546736i	−0.0548352	+	0.998495i	$0.517463\pi$
$318$		0			0
$319$	14.9014	−	25.8100i	0.834319	−	1.44508i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.43375i			0.0797758i
$324$		0			0
$325$	12.6356	−	7.29515i	0.700895	−	0.404662i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	15.3757	−	19.7749i	0.847689	−	1.09023i
$330$		0			0
$331$	−13.4838	−	23.3546i	−0.741135	−	1.28368i	−0.951979	−	0.306164i	$-0.900955\pi$
$331$	−13.4838	−	23.3546i	−0.741135	−	1.28368i	0.210844	−	0.977520i	$-0.432379\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.77245	+	6.53408i	−0.206111	+	0.356995i
$336$		0			0
$337$	0.993296	+	1.72044i	0.0541083	+	0.0937183i	0.891811	−	0.452408i	$-0.149435\pi$
$337$	0.993296	+	1.72044i	0.0541083	+	0.0937183i	−0.837703	+	0.546127i	$0.816102\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0745	+	20.9136i	−0.653869	+	1.13254i
$342$		0			0
$343$	16.9714	+	7.41426i	0.916370	+	0.400332i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−29.7673	−	17.1862i	−1.59799	−	0.922603i	−0.991873	−	0.127231i	$-0.959391\pi$
$347$	−29.7673	−	17.1862i	−1.59799	−	0.922603i	−0.606122	−	0.795372i	$-0.707276\pi$
$348$		0			0
$349$	25.3935	+	14.6609i	1.35928	+	0.784781i	0.989527	−	0.144348i	$-0.0461085\pi$
$349$	25.3935	+	14.6609i	1.35928	+	0.784781i	0.369754	+	0.929130i	$0.379442\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.17305			−0.0624353			−0.0312177	−	0.999513i	$-0.509939\pi$
$353$	−1.17305			−0.0624353			−0.0312177	+	0.999513i	$0.509939\pi$
$354$		0			0
$355$			6.60147i			0.350370i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.69591	−	3.28854i	−0.300619	−	0.173562i	0.342102	−	0.939663i	$-0.388861\pi$
$359$	−5.69591	−	3.28854i	−0.300619	−	0.173562i	−0.642721	+	0.766101i	$0.722194\pi$
$360$		0			0
$361$	−8.15813	−	14.1303i	−0.429375	−	0.743699i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.27856	+	4.20228i	−0.380977	+	0.219957i
$366$		0			0
$367$			9.51617i			0.496740i	0.968665	+	0.248370i	$0.0798948\pi$
$367$			9.51617i			0.496740i	−0.968665	+	0.248370i	$0.920105\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.77812	−	2.16009i	−0.144233	−	0.112146i
$372$		0			0
$373$	20.6303			1.06820			0.534098	−	0.845422i	$-0.320651\pi$
$373$	20.6303			1.06820			0.534098	+	0.845422i	$0.320651\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.1380			0.934153
$378$		0			0
$379$	−7.98265			−0.410041			−0.205020	−	0.978758i	$-0.565726\pi$
$379$	−7.98265			−0.410041			−0.205020	+	0.978758i	$0.565726\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	28.0968			1.43568			0.717840	−	0.696208i	$-0.245131\pi$
$383$	28.0968			1.43568			0.717840	+	0.696208i	$0.245131\pi$
$384$		0			0
$385$	7.94573	−	3.23187i	0.404952	−	0.164711i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	32.8397i		−	1.66504i	−0.553997	−	0.832519i	$-0.686898\pi$
$389$		−	32.8397i		−	1.66504i	0.553997	−	0.832519i	$-0.313102\pi$
$390$		0			0
$391$	6.25660	−	3.61225i	0.316410	−	0.182679i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.02344	−	5.23676i	−0.152126	−	0.263490i
$396$		0			0
$397$	9.24672	+	5.33859i	0.464079	+	0.267936i	0.713758	−	0.700392i	$-0.246992\pi$
$397$	9.24672	+	5.33859i	0.464079	+	0.267936i	−0.249679	+	0.968329i	$0.580325\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	14.2789i		−	0.713052i	−0.934285	−	0.356526i	$-0.883961\pi$
$401$		−	14.2789i		−	0.713052i	0.934285	−	0.356526i	$-0.116039\pi$
$402$		0			0
$403$	−14.6970			−0.732111
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.1925	+	6.46198i	0.554791	+	0.320309i
$408$		0			0
$409$	7.04206	+	4.06574i	0.348208	+	0.201038i	0.663896	−	0.747825i	$-0.268902\pi$
$409$	7.04206	+	4.06574i	0.348208	+	0.201038i	−0.315688	+	0.948863i	$0.602235\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.6861	−	2.30539i	−0.821071	−	0.113441i
$414$		0			0
$415$	0.119750	−	0.207412i	0.00587827	−	0.0101815i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.53415	−	2.65723i	−0.0749481	−	0.129814i	0.826116	−	0.563501i	$-0.190546\pi$
$419$	−1.53415	−	2.65723i	−0.0749481	−	0.129814i	−0.901064	+	0.433687i	$0.857212\pi$
$420$		0			0
$421$	4.25752	−	7.37424i	0.207499	−	0.359398i	−0.743427	−	0.668817i	$-0.766801\pi$
$421$	4.25752	−	7.37424i	0.207499	−	0.359398i	0.950926	+	0.309418i	$0.100134\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.01780	+	3.49494i	0.0978778	+	0.169529i
$426$		0			0
$427$	−23.2973	−	18.1145i	−1.12744	−	0.876622i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−19.8414	+	11.4554i	−0.955727	+	0.551789i	−0.894855	−	0.446356i	$-0.852721\pi$
$431$	−19.8414	+	11.4554i	−0.955727	+	0.551789i	−0.0608716	+	0.998146i	$0.519388\pi$
$432$		0			0
$433$			32.7273i			1.57278i	0.617733	+	0.786388i	$0.288051\pi$
$433$			32.7273i			1.57278i	−0.617733	+	0.786388i	$0.711949\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.76156	−	11.7114i	0.323449	−	0.560231i
$438$		0			0
$439$	5.57285	−	3.21749i	0.265978	−	0.153562i	−0.361081	−	0.932535i	$-0.617592\pi$
$439$	5.57285	−	3.21749i	0.265978	−	0.153562i	0.627058	+	0.778972i	$0.284259\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	22.1159	−	12.7686i	1.05076	−	0.606656i	0.127898	−	0.991787i	$-0.459177\pi$
$443$	22.1159	−	12.7686i	1.05076	−	0.606656i	0.922862	+	0.385131i	$0.125844\pi$
$444$		0			0
$445$	−0.0124085	+	0.0214921i	−0.000588219	+	0.00101882i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			40.1008i			1.89247i	0.323474	+	0.946237i	$0.395149\pi$
$449$			40.1008i			1.89247i	−0.323474	+	0.946237i	$0.604851\pi$
$450$		0			0
$451$	−31.7322	+	18.3206i	−1.49421	+	0.862684i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.12128	+	3.20444i	0.193208	+	0.150226i
$456$		0			0
$457$	19.2357	+	33.3173i	0.899810	+	1.55852i	0.827737	+	0.561116i	$0.189628\pi$
$457$	19.2357	+	33.3173i	0.899810	+	1.55852i	0.0720726	+	0.997399i	$0.477039\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.0830	−	20.9283i	0.562759	−	0.974728i	−0.434495	−	0.900674i	$-0.643073\pi$
$461$	12.0830	−	20.9283i	0.562759	−	0.974728i	0.997254	−	0.0740533i	$-0.0235935\pi$
$462$		0			0
$463$	−8.65455	−	14.9901i	−0.402211	−	0.696650i	0.591781	−	0.806098i	$-0.298425\pi$
$463$	−8.65455	−	14.9901i	−0.402211	−	0.696650i	−0.993992	+	0.109449i	$0.965091\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.46858	−	9.47185i	0.253056	−	0.438305i	−0.711310	−	0.702878i	$-0.751898\pi$
$467$	5.46858	−	9.47185i	0.253056	−	0.438305i	0.964366	+	0.264573i	$0.0852311\pi$
$468$		0			0
$469$	31.7098	+	4.38110i	1.46422	+	0.202300i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−14.0838	−	8.13126i	−0.647572	−	0.373876i
$474$		0			0
$475$	6.54197	+	3.77701i	0.300166	+	0.173301i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.51349			−0.0691531			−0.0345765	−	0.999402i	$-0.511008\pi$
$479$	−1.51349			−0.0691531			−0.0345765	+	0.999402i	$0.511008\pi$
$480$		0			0
$481$			7.86551i			0.358636i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.70841	+	2.14105i	0.168390	+	0.0972201i
$486$		0			0
$487$	−0.0853077	−	0.147757i	−0.00386566	−	0.00669552i	0.864086	−	0.503344i	$-0.167897\pi$
$487$	−0.0853077	−	0.147757i	−0.00386566	−	0.00669552i	−0.867952	+	0.496649i	$0.834564\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−23.5139	+	13.5757i	−1.06117	+	0.612665i	−0.925755	−	0.378125i	$-0.876569\pi$
$491$	−23.5139	+	13.5757i	−1.06117	+	0.612665i	−0.135412	+	0.990789i	$0.543236\pi$
$492$		0			0
$493$			5.01687i			0.225949i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.9442	−	10.5526i	1.16376	−	0.473350i
$498$		0			0
$499$	22.2654			0.996738			0.498369	−	0.866965i	$-0.333933\pi$
$499$	22.2654			0.996738			0.498369	+	0.866965i	$0.333933\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	32.2005			1.43575			0.717876	−	0.696171i	$-0.245115\pi$
$503$	32.2005			1.43575			0.717876	+	0.696171i	$0.245115\pi$
$504$		0			0
$505$	−5.56621			−0.247693
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.21817			0.408588			0.204294	−	0.978910i	$-0.434510\pi$
$509$	9.21817			0.408588			0.204294	+	0.978910i	$0.434510\pi$
$510$		0			0
$511$	28.1502	+	21.8878i	1.24529	+	0.968259i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			5.53055i			0.243705i
$516$		0			0
$517$	−42.6285	+	24.6116i	−1.87480	+	1.08242i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.44581	+	12.8965i	0.326207	+	0.565007i	0.981756	−	0.190146i	$-0.0608961\pi$
$521$	7.44581	+	12.8965i	0.326207	+	0.565007i	−0.655549	+	0.755153i	$0.727563\pi$
$522$		0			0
$523$	−29.3725	−	16.9582i	−1.28437	−	0.741532i	−0.306727	−	0.951798i	$-0.599234\pi$
$523$	−29.3725	−	16.9582i	−1.28437	−	0.741532i	−0.977644	+	0.210266i	$0.932567\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	4.06512i		−	0.177080i
$528$		0			0
$529$	−45.1416			−1.96268
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.3122	−	11.1499i	−0.836504	−	0.482956i
$534$		0			0
$535$	1.64833	+	0.951663i	0.0712635	+	0.0411440i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−25.4029	−	26.0610i	−1.09418	−	1.12253i
$540$		0			0
$541$	−2.65164	+	4.59278i	−0.114003	+	0.197459i	−0.917381	−	0.398011i	$-0.869701\pi$
$541$	−2.65164	+	4.59278i	−0.114003	+	0.197459i	0.803378	+	0.595470i	$0.203034\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.46139	−	5.99531i	−0.148270	−	0.256811i
$546$		0			0
$547$	−4.13892	+	7.16882i	−0.176967	+	0.306517i	−0.940840	−	0.338850i	$-0.889962\pi$
$547$	−4.13892	+	7.16882i	−0.176967	+	0.306517i	0.763873	+	0.645367i	$0.223295\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.69540	+	8.13267i	0.200031	+	0.346463i
$552$		0			0
$553$	−15.7478	+	20.2534i	−0.669663	+	0.861264i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.96801	−	4.02299i	0.295244	−	0.170459i	−0.345060	−	0.938581i	$-0.612142\pi$
$557$	6.96801	−	4.02299i	0.295244	−	0.170459i	0.640304	+	0.768121i	$0.278808\pi$
$558$		0			0
$559$		−	9.89735i		−	0.418613i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.9578	−	25.9077i	0.630396	−	1.09188i	−0.357074	−	0.934076i	$-0.616226\pi$
$563$	14.9578	−	25.9077i	0.630396	−	1.09188i	0.987471	−	0.157802i	$-0.0504409\pi$
$564$		0			0
$565$	1.95707	−	1.12992i	0.0823346	−	0.0475359i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−26.6942	+	15.4119i	−1.11908	+	0.646101i	−0.941166	−	0.337946i	$-0.890268\pi$
$569$	−26.6942	+	15.4119i	−1.11908	+	0.646101i	−0.177913	+	0.984046i	$0.556935\pi$
$570$		0			0
$571$	2.67347	−	4.63058i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$571$	2.67347	−	4.63058i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	38.0639i		−	1.58737i
$576$		0			0
$577$	16.3235	−	9.42437i	0.679556	−	0.392342i	−0.120132	−	0.992758i	$-0.538332\pi$
$577$	16.3235	−	9.42437i	0.679556	−	0.392342i	0.799688	+	0.600416i	$0.204998\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.00657	−	0.139070i	−0.0417595	−	0.00576959i
$582$		0			0
$583$	3.45761	+	5.98876i	0.143200	+	0.248029i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.3955	+	21.4697i	−0.511619	+	0.886150i	0.488290	+	0.872681i	$0.337621\pi$
$587$	−12.3955	+	21.4697i	−0.511619	+	0.886150i	−0.999909	+	0.0134687i	$0.995713\pi$
$588$		0			0
$589$	−3.80464	−	6.58982i	−0.156767	−	0.271529i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.87451	+	3.24675i	−0.0769770	+	0.133328i	−0.901944	−	0.431852i	$-0.857860\pi$
$593$	−1.87451	+	3.24675i	−0.0769770	+	0.133328i	0.824967	+	0.565180i	$0.191193\pi$
$594$		0			0
$595$	−0.886331	+	1.13992i	−0.0363360	+	0.0467323i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	27.7711	+	16.0337i	1.13470	+	0.655118i	0.945112	−	0.326746i	$-0.105952\pi$
$599$	27.7711	+	16.0337i	1.13470	+	0.655118i	0.189586	+	0.981864i	$0.439286\pi$
$600$		0			0
$601$	−5.98069	−	3.45296i	−0.243958	−	0.140849i	0.373037	−	0.927817i	$-0.378317\pi$
$601$	−5.98069	−	3.45296i	−0.243958	−	0.140849i	−0.616994	+	0.786968i	$0.711650\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.99648			−0.406415
$606$		0			0
$607$		−	21.6959i		−	0.880608i	−0.897849	−	0.440304i	$-0.854871\pi$
$607$		−	21.6959i		−	0.880608i	0.897849	−	0.440304i	$-0.145129\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−25.9437	−	14.9786i	−1.04957	−	0.605968i
$612$		0			0
$613$	8.96928	+	15.5352i	0.362266	+	0.627463i	0.988333	−	0.152306i	$-0.0486699\pi$
$613$	8.96928	+	15.5352i	0.362266	+	0.627463i	−0.626068	+	0.779769i	$0.715337\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−32.9146	+	19.0033i	−1.32509	+	0.765043i	−0.984536	−	0.175181i	$-0.943949\pi$
$617$	−32.9146	+	19.0033i	−1.32509	+	0.765043i	−0.340557	+	0.940224i	$0.610616\pi$
$618$		0			0
$619$		−	43.3774i		−	1.74349i	−0.489964	−	0.871743i	$-0.662990\pi$
$619$		−	43.3774i		−	1.74349i	0.489964	−	0.871743i	$-0.337010\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.104301	+	0.0144105i	0.00417873	+	0.000577343i
$624$		0			0
$625$	19.3181			0.772725
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.17556			−0.0867453
$630$		0			0
$631$	11.2735			0.448793			0.224396	−	0.974498i	$-0.427959\pi$
$631$	11.2735			0.448793			0.224396	+	0.974498i	$0.427959\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.32378			−0.250952
$636$		0			0
$637$	6.00569	−	21.3193i	0.237954	−	0.844701i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			29.7553i			1.17526i	0.809129	+	0.587631i	$0.199939\pi$
$641$			29.7553i			1.17526i	−0.809129	+	0.587631i	$0.800061\pi$
$642$		0			0
$643$	−37.4271	+	21.6085i	−1.47598	+	0.852158i	−0.999633	−	0.0270991i	$-0.991373\pi$
$643$	−37.4271	+	21.6085i	−1.47598	+	0.852158i	−0.476348	+	0.879257i	$0.658040\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.42940	+	16.3322i	0.370708	+	0.642085i	0.989675	−	0.143332i	$-0.0457817\pi$
$647$	9.42940	+	16.3322i	0.370708	+	0.642085i	−0.618967	+	0.785417i	$0.712448\pi$
$648$		0			0
$649$	28.6661	+	16.5504i	1.12524	+	0.649660i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			9.71777i			0.380286i	0.981756	+	0.190143i	$0.0608951\pi$
$653$			9.71777i			0.380286i	−0.981756	+	0.190143i	$0.939105\pi$
$654$		0			0
$655$	−13.5679			−0.530144
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.5327	+	16.4734i	1.11148	+	0.641712i	0.939212	−	0.343338i	$-0.111558\pi$
$659$	28.5327	+	16.4734i	1.11148	+	0.641712i	0.172266	+	0.985050i	$0.444891\pi$
$660$		0			0
$661$	−1.08957	−	0.629061i	−0.0423792	−	0.0244677i	0.478661	−	0.878000i	$-0.341122\pi$
$661$	−1.08957	−	0.629061i	−0.0423792	−	0.0244677i	−0.521040	+	0.853532i	$0.674456\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.369920	+	2.67743i	−0.0143449	+	0.103826i
$666$		0			0
$667$	23.6596	−	40.9797i	0.916104	−	1.58674i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.9955	+	50.2217i	1.11936	+	1.93879i
$672$		0			0
$673$	−12.2655	+	21.2445i	−0.472800	+	0.818914i	−0.999515	−	0.0311279i	$-0.990090\pi$
$673$	−12.2655	+	21.2445i	−0.472800	+	0.818914i	0.526715	+	0.850042i	$0.323423\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.5616	+	20.0253i	0.444350	+	0.769636i	0.998007	−	0.0631088i	$-0.0201015\pi$
$677$	11.5616	+	20.0253i	0.444350	+	0.769636i	−0.553657	+	0.832745i	$0.686768\pi$
$678$		0			0
$679$	2.48649	−	17.9968i	0.0954226	−	0.690655i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.4945	−	7.21370i	0.478089	−	0.276025i	−0.241531	−	0.970393i	$-0.577650\pi$
$683$	12.4945	−	7.21370i	0.478089	−	0.276025i	0.719620	+	0.694368i	$0.244316\pi$
$684$		0			0
$685$			0.245147i			0.00936659i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.10430	+	3.64475i	−0.0801673	+	0.138854i
$690$		0			0
$691$	−32.3993	+	18.7057i	−1.23253	+	0.711599i	−0.967556	−	0.252657i	$-0.918695\pi$
$691$	−32.3993	+	18.7057i	−1.23253	+	0.711599i	−0.264970	+	0.964257i	$0.585362\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.76844	+	5.63981i	−0.370538	+	0.213930i
$696$		0			0
$697$	3.08401	−	5.34166i	0.116815	−	0.202330i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			41.0429i			1.55017i	0.631859	+	0.775084i	$0.282292\pi$
$701$			41.0429i			1.55017i	−0.631859	+	0.775084i	$0.717708\pi$
$702$		0			0
$703$	−3.52672	+	2.03615i	−0.133013	+	0.0767950i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.89774	+	21.8756i	0.334634	+	0.822716i
$708$		0			0
$709$	−11.6623	−	20.1997i	−0.437987	−	0.758616i	0.559547	−	0.828798i	$-0.310975\pi$
$709$	−11.6623	−	20.1997i	−0.437987	−	0.758616i	−0.997534	+	0.0701829i	$0.977642\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−19.1712	+	33.2054i	−0.717966	+	1.24355i
$714$		0			0
$715$	−5.12928	−	8.88418i	−0.191824	−	0.332249i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.7489	−	37.6701i	0.811096	−	1.40486i	−0.101002	−	0.994886i	$-0.532205\pi$
$719$	21.7489	−	37.6701i	0.811096	−	1.40486i	0.912098	−	0.409973i	$-0.134462\pi$
$720$		0			0
$721$	21.7354	−	8.84073i	0.809470	−	0.329246i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.8912	+	13.2163i	0.850159	+	0.490840i
$726$		0			0
$727$	−11.3715	−	6.56536i	−0.421747	−	0.243496i	0.274078	−	0.961708i	$-0.411627\pi$
$727$	−11.3715	−	6.56536i	−0.421747	−	0.243496i	−0.695824	+	0.718212i	$0.744961\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.73756			0.101252
$732$		0			0
$733$			40.1795i			1.48406i	0.670364	+	0.742032i	$0.266138\pi$
$733$			40.1795i			1.48406i	−0.670364	+	0.742032i	$0.733862\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−54.4762	−	31.4518i	−2.00666	−	1.15854i
$738$		0			0
$739$	18.7073	+	32.4020i	0.688158	+	1.19193i	0.972433	+	0.233182i	$0.0749139\pi$
$739$	18.7073	+	32.4020i	0.688158	+	1.19193i	−0.284275	+	0.958743i	$0.591753\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.0501	+	17.3494i	−1.10243	+	0.636488i	−0.936858	−	0.349709i	$-0.886280\pi$
$743$	−30.0501	+	17.3494i	−1.10243	+	0.636488i	−0.165572	+	0.986198i	$0.552947\pi$
$744$		0			0
$745$		−	6.39239i		−	0.234199i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.10520	−	7.99931i	0.0403833	−	0.292288i
$750$		0			0
$751$	−29.0140			−1.05873			−0.529367	−	0.848393i	$-0.677571\pi$
$751$	−29.0140			−1.05873			−0.529367	+	0.848393i	$0.677571\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	14.8423			0.540168
$756$		0			0
$757$	−8.62406			−0.313447			−0.156723	−	0.987643i	$-0.550093\pi$
$757$	−8.62406			−0.313447			−0.156723	+	0.987643i	$0.550093\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.8213			0.827272			0.413636	−	0.910442i	$-0.364259\pi$
$761$	22.8213			0.827272			0.413636	+	0.910442i	$0.364259\pi$
$762$		0			0
$763$	−18.0288	+	23.1872i	−0.652688	+	0.839432i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			20.1451i			0.727397i
$768$		0			0
$769$	27.6397	−	15.9578i	0.996714	−	0.575453i	0.0894399	−	0.995992i	$-0.471492\pi$
$769$	27.6397	−	15.9578i	0.996714	−	0.575453i	0.907275	+	0.420539i	$0.138159\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.8503	+	30.9176i	0.642030	+	1.11203i	0.984979	+	0.172675i	$0.0552410\pi$
$773$	17.8503	+	30.9176i	0.642030	+	1.11203i	−0.342949	+	0.939354i	$0.611426\pi$
$774$		0			0
$775$	−18.5486	−	10.7090i	−0.666284	−	0.384679i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	11.5456i		−	0.413663i
$780$		0			0
$781$	−55.0380			−1.96942
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.21492	+	3.58819i	0.221820	+	0.128068i
$786$		0			0
$787$	−12.0233	−	6.94168i	−0.428586	−	0.247444i	0.270158	−	0.962816i	$-0.412924\pi$
$787$	−12.0233	−	6.94168i	−0.428586	−	0.247444i	−0.698744	+	0.715372i	$0.746257\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.56908	−	5.88522i	−0.269125	−	0.209254i
$792$		0			0
$793$	−17.6466	+	30.5649i	−0.626651	+	1.08539i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.2145	+	24.6203i	0.503504	+	0.872094i	0.999992	+	0.00405063i	$0.00128936\pi$
$797$	14.2145	+	24.6203i	0.503504	+	0.872094i	−0.496488	+	0.868044i	$0.665377\pi$
$798$		0			0
$799$	4.14300	−	7.17589i	0.146569	−	0.253865i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−35.0354	−	60.6831i	−1.23637	−	2.14146i
$804$		0			0
$805$	12.6158	−	5.13138i	0.444648	−	0.180857i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−21.1074	+	12.1864i	−0.742096	+	0.428449i	−0.822831	−	0.568286i	$-0.807607\pi$
$809$	−21.1074	+	12.1864i	−0.742096	+	0.428449i	0.0807348	+	0.996736i	$0.474273\pi$
$810$		0			0
$811$			35.2739i			1.23863i	0.785141	+	0.619317i	$0.212591\pi$
$811$			35.2739i			1.23863i	−0.785141	+	0.619317i	$0.787409\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.52369	−	11.2994i	0.228515	−	0.395799i
$816$		0			0
$817$	4.43776	−	2.56214i	0.155257	−	0.0896379i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.8999	−	9.75719i	0.589812	−	0.340528i	−0.175211	−	0.984531i	$-0.556061\pi$
$821$	16.8999	−	9.75719i	0.589812	−	0.340528i	0.765023	+	0.644003i	$0.222727\pi$
$822$		0			0
$823$	15.8285	−	27.4158i	0.551747	−	0.955653i	−0.446402	−	0.894833i	$-0.647295\pi$
$823$	15.8285	−	27.4158i	0.551747	−	0.955653i	0.998149	−	0.0608208i	$-0.0193718\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			24.4749i			0.851075i	0.904941	+	0.425537i	$0.139915\pi$
$827$			24.4749i			0.851075i	−0.904941	+	0.425537i	$0.860085\pi$
$828$		0			0
$829$	0.846010	−	0.488444i	0.0293831	−	0.0169644i	−0.485236	−	0.874383i	$-0.661266\pi$
$829$	0.846010	−	0.488444i	0.0293831	−	0.0169644i	0.514620	+	0.857419i	$0.327933\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.89681	+	1.66114i	0.204312	+	0.0575552i
$834$		0			0
$835$	4.17409	+	7.22974i	0.144450	+	0.250196i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.6920	+	34.1075i	−0.679843	+	1.17752i	0.295184	+	0.955440i	$0.404619\pi$
$839$	−19.6920	+	34.1075i	−0.679843	+	1.17752i	−0.975028	+	0.222083i	$0.928714\pi$
$840$		0			0
$841$	1.92983	+	3.34257i	0.0665459	+	0.115261i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.931704	+	1.61376i	−0.0320516	+	0.0555150i
$846$		0			0
$847$	15.9797	+	39.2869i	0.549067	+	1.34991i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.7708	+	10.2600i	0.609175	+	0.351707i
$852$		0			0
$853$	−21.3507	−	12.3268i	−0.731033	−	0.422062i	0.0877672	−	0.996141i	$-0.472027\pi$
$853$	−21.3507	−	12.3268i	−0.731033	−	0.422062i	−0.818800	+	0.574079i	$0.805360\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.8290			−0.779823			−0.389911	−	0.920852i	$-0.627494\pi$
$857$	−22.8290			−0.779823			−0.389911	+	0.920852i	$0.627494\pi$
$858$		0			0
$859$			47.7150i			1.62801i	0.580855	+	0.814007i	$0.302718\pi$
$859$			47.7150i			1.62801i	−0.580855	+	0.814007i	$0.697282\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	18.0645	+	10.4296i	0.614923	+	0.355026i	0.774890	−	0.632096i	$-0.217805\pi$
$863$	18.0645	+	10.4296i	0.614923	+	0.355026i	−0.159967	+	0.987122i	$0.551139\pi$
$864$		0			0
$865$	1.83607	+	3.18017i	0.0624283	+	0.108129i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	43.6601	−	25.2072i	1.48107	−	0.855094i
$870$		0			0
$871$		−	38.2831i		−	1.29717i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.97451	+	14.6887i	0.201975	+	0.496567i
$876$		0			0
$877$	−23.5436			−0.795011			−0.397506	−	0.917600i	$-0.630124\pi$
$877$	−23.5436			−0.795011			−0.397506	+	0.917600i	$0.630124\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	52.5975			1.77205			0.886027	−	0.463633i	$-0.153454\pi$
$881$	52.5975			1.77205			0.886027	+	0.463633i	$0.153454\pi$
$882$		0			0
$883$	−33.6815			−1.13347			−0.566737	−	0.823899i	$-0.691794\pi$
$883$	−33.6815			−1.13347			−0.566737	+	0.823899i	$0.691794\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.0228			−0.504415			−0.252208	−	0.967673i	$-0.581157\pi$
$887$	−15.0228			−0.504415			−0.252208	+	0.967673i	$0.581157\pi$
$888$		0			0
$889$	10.1087	+	24.8529i	0.339036	+	0.833540i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	15.5101i		−	0.519026i
$894$		0			0
$895$	−9.00059	+	5.19649i	−0.300856	+	0.173700i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.3129	−	23.0587i	−0.444011	−	0.769050i
$900$		0			0
$901$	−1.00812	−	0.582038i	−0.0335853	−	0.0193905i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	0.288542i		−	0.00959144i
$906$		0			0
$907$	−11.6949			−0.388324			−0.194162	−	0.980969i	$-0.562199\pi$
$907$	−11.6949			−0.388324			−0.194162	+	0.980969i	$0.562199\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.9026	+	8.02666i	0.460613	+	0.265935i	0.712302	−	0.701873i	$-0.247653\pi$
$911$	13.9026	+	8.02666i	0.460613	+	0.265935i	−0.251689	+	0.967808i	$0.580986\pi$
$912$		0			0
$913$	1.72925	+	0.998380i	0.0572297	+	0.0330416i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	21.6887	+	53.3230i	0.716225	+	1.76088i
$918$		0			0
$919$	9.26860	−	16.0537i	0.305743	−	0.529562i	−0.671683	−	0.740838i	$-0.734428\pi$
$919$	9.26860	−	16.0537i	0.305743	−	0.529562i	0.977426	+	0.211276i	$0.0677618\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.7480	−	29.0084i	−0.551268	−	0.954824i
$924$		0			0
$925$	−5.73122	+	9.92676i	−0.188441	+	0.326390i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.8357	+	46.4808i	0.880451	+	1.52499i	0.850841	+	0.525424i	$0.176093\pi$
$929$	26.8357	+	46.4808i	0.880451	+	1.52499i	0.0296102	+	0.999562i	$0.490573\pi$
$930$		0			0
$931$	11.1138	−	2.82613i	0.364240	−	0.0926227i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.45732	−	1.41873i	0.0803630	−	0.0463976i
$936$		0			0
$937$		−	16.7752i		−	0.548023i	−0.961726	−	0.274012i	$-0.911649\pi$
$937$		−	16.7752i		−	0.548023i	0.961726	−	0.274012i	$-0.0883506\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.5343	+	32.1023i	−0.604200	+	1.04651i	0.387977	+	0.921669i	$0.373174\pi$
$941$	−18.5343	+	32.1023i	−0.604200	+	1.04651i	−0.992177	+	0.124837i	$0.960159\pi$
$942$		0			0
$943$	−50.3827	+	29.0885i	−1.64069	+	0.947250i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.73735	+	1.58041i	−0.0889520	+	0.0513565i	−0.543816	−	0.839204i	$-0.683021\pi$
$947$	−2.73735	+	1.58041i	−0.0889520	+	0.0513565i	0.454864	+	0.890561i	$0.349688\pi$
$948$		0			0
$949$	21.3225	−	36.9316i	0.692157	−	1.19885i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	38.9680i		−	1.26230i	−0.775662	−	0.631149i	$-0.782584\pi$
$953$		−	38.9680i		−	1.26230i	0.775662	−	0.631149i	$-0.217416\pi$
$954$		0			0
$955$	7.36550	−	4.25247i	0.238342	−	0.137607i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.963445	−	0.391874i	0.0311113	−	0.0126543i
$960$		0			0
$961$	−4.71266	−	8.16256i	−0.152021	−	0.263308i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.57902	−	6.19905i	0.115213	−	0.199555i
$966$		0			0
$967$	−7.29560	−	12.6363i	−0.234611	−	0.406357i	0.724549	−	0.689223i	$-0.242048\pi$
$967$	−7.29560	−	12.6363i	−0.234611	−	0.406357i	−0.959159	+	0.282866i	$0.908715\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.3537	+	19.6652i	−0.364358	+	0.631086i	−0.988673	−	0.150087i	$-0.952045\pi$
$971$	−11.3537	+	19.6652i	−0.364358	+	0.631086i	0.624315	+	0.781172i	$0.285378\pi$
$972$		0			0
$973$	37.7800	+	29.3752i	1.21117	+	0.941727i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.5426	−	20.5206i	−1.13711	−	0.656511i	−0.191397	−	0.981513i	$-0.561302\pi$
$977$	−35.5426	−	20.5206i	−1.13711	−	0.656511i	−0.945713	+	0.325002i	$0.894635\pi$
$978$		0			0
$979$	−0.179185	−	0.103453i	−0.00572678	−	0.00330636i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.9305			−0.667579			−0.333790	−	0.942648i	$-0.608328\pi$
$983$	−20.9305			−0.667579			−0.333790	+	0.942648i	$0.608328\pi$
$984$		0			0
$985$			2.98194i			0.0950125i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.3614	−	12.9104i	−0.711051	−	0.410525i
$990$		0			0
$991$	26.9709	+	46.7149i	0.856758	+	1.48395i	0.875004	+	0.484116i	$0.160859\pi$
$991$	26.9709	+	46.7149i	0.856758	+	1.48395i	−0.0182456	+	0.999834i	$0.505808\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.91290	−	2.83647i	0.155749	−	0.0899220i
$996$		0			0
$997$		−	3.21654i		−	0.101869i	−0.998702	−	0.0509345i	$-0.983780\pi$
$997$		−	3.21654i		−	0.101869i	0.998702	−	0.0509345i	$-0.0162200\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.89.14		48
3.2	odd	2		504.2.cx.a.425.11	yes	48
4.3	odd	2		3024.2.df.e.1601.14		48
7.3	odd	6		1512.2.bs.a.521.14		48
9.4	even	3		504.2.bs.a.257.3	✓	48
9.5	odd	6		1512.2.bs.a.1097.14		48
12.11	even	2		1008.2.df.e.929.14		48
21.17	even	6		504.2.bs.a.353.3	yes	48
28.3	even	6		3024.2.ca.e.2033.14		48
36.23	even	6		3024.2.ca.e.2609.14		48
36.31	odd	6		1008.2.ca.e.257.22		48
63.31	odd	6		504.2.cx.a.185.11	yes	48
63.59	even	6	inner	1512.2.cx.a.17.14		48
84.59	odd	6		1008.2.ca.e.353.22		48
252.31	even	6		1008.2.df.e.689.14		48
252.59	odd	6		3024.2.df.e.17.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.3	✓	48	9.4	even	3
504.2.bs.a.353.3	yes	48	21.17	even	6
504.2.cx.a.185.11	yes	48	63.31	odd	6
504.2.cx.a.425.11	yes	48	3.2	odd	2
1008.2.ca.e.257.22		48	36.31	odd	6
1008.2.ca.e.353.22		48	84.59	odd	6
1008.2.df.e.689.14		48	252.31	even	6
1008.2.df.e.929.14		48	12.11	even	2
1512.2.bs.a.521.14		48	7.3	odd	6
1512.2.bs.a.1097.14		48	9.5	odd	6
1512.2.cx.a.17.14		48	63.59	even	6	inner
1512.2.cx.a.89.14		48	1.1	even	1	trivial
3024.2.ca.e.2033.14		48	28.3	even	6
3024.2.ca.e.2609.14		48	36.23	even	6
3024.2.df.e.17.14		48	252.59	odd	6
3024.2.df.e.1601.14		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.623597 q^{5} +(-0.996837 - 2.45078i) q^{7} +5.19907i q^{11} +(-2.74023 + 1.58207i) q^{13} +(-0.437594 - 0.757935i) q^{17} +(-1.41874 - 0.819107i) q^{19} +8.25480i q^{23} -4.61113 q^{25} +(-4.96435 - 2.86617i) q^{29} +(4.02256 + 2.32243i) q^{31} +(-0.621624 - 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(3.52382 + 6.10344i) q^{41} +(-1.56398 + 2.70890i) q^{43} +(4.73384 + 8.19925i) q^{47} +(-5.01263 + 4.88605i) q^{49} +(1.15189 - 0.665044i) q^{53} +3.24212i q^{55} +(3.18334 - 5.51370i) q^{59} +(9.65975 - 5.57706i) q^{61} +(-1.70880 + 0.986576i) q^{65} +(-6.04951 + 10.4781i) q^{67} +10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(12.7418 - 5.18263i) q^{77} +(-4.84840 - 8.39767i) q^{79} +(0.192030 - 0.332606i) q^{83} +(-0.272882 - 0.472646i) q^{85} +(-0.0198983 + 0.0344648i) q^{89} +(6.60888 + 5.13864i) q^{91} +(-0.884719 - 0.510793i) q^{95} +(5.94681 + 3.43339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

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