LMFDB - Embedded newform 1512.2.bs.a.1097.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(521,1512)] 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, 1, 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("1512.521"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.bs (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			1097.14
Character	$\chi$	$=$	1512.1097
Dual form			1512.2.bs.a.521.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.311798 + 0.540051i) q^{5} +(2.62086 + 0.362103i) q^{7} +(4.50253 + 2.59954i) q^{11} +(2.74023 + 1.58207i) q^{13} +(0.437594 + 0.757935i) q^{17} +(-1.41874 - 0.819107i) q^{19} +(-7.14886 + 4.12740i) q^{23} +(2.30556 - 3.99335i) q^{25} +(-4.96435 + 2.86617i) q^{29} -4.64486i q^{31} +(0.621624 + 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(-3.52382 + 6.10344i) q^{41} +(-1.56398 - 2.70890i) q^{43} +9.46768 q^{47} +(6.73776 + 1.89804i) q^{49} +(-1.15189 + 0.665044i) q^{53} +3.24212i q^{55} +6.36667 q^{59} +11.1541i q^{61} +1.97315i q^{65} +12.0990 q^{67} -10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(10.8592 + 8.44339i) q^{77} +9.69679 q^{79} +(-0.192030 - 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(0.0198983 - 0.0344648i) q^{89} +(6.60888 + 5.13864i) q^{91} -1.02159i q^{95} +(-5.94681 + 3.43339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 - 6 * q^43 - 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 - 12 * q^79 - 18 * q^89 + 6 * q^91

Character values

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

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

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
$5$	0.311798	+	0.540051i	0.139440	+	0.241518i	0.927285	−	0.374356i	$-0.122136\pi$
$5$	0.311798	+	0.540051i	0.139440	+	0.241518i	−0.787845	+	0.615874i	$0.788803\pi$
$6$		0			0
$7$	2.62086	+	0.362103i	0.990590	+	0.136862i
$7$	2.62086	+	0.362103i	0.990590	+	0.136862i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.50253	+	2.59954i	1.35756	+	0.783790i	0.989295	−	0.145930i	$-0.0466173\pi$
$11$	4.50253	+	2.59954i	1.35756	+	0.783790i	0.368269	+	0.929719i	$0.379951\pi$
$12$		0			0
$13$	2.74023	+	1.58207i	0.760004	+	0.438788i	0.829297	−	0.558808i	$-0.188741\pi$
$13$	2.74023	+	1.58207i	0.760004	+	0.438788i	−0.0692932	+	0.997596i	$0.522074\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.437594	+	0.757935i	0.106132	+	0.183826i	0.914200	−	0.405263i	$-0.132820\pi$
$17$	0.437594	+	0.757935i	0.106132	+	0.183826i	−0.808068	+	0.589089i	$0.799487\pi$
$18$		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
$23$	−7.14886	+	4.12740i	−1.49064	+	0.860622i	−0.999943	−	0.0107077i	$-0.996592\pi$
$23$	−7.14886	+	4.12740i	−1.49064	+	0.860622i	−0.490698	+	0.871330i	$0.663258\pi$
$24$		0			0
$25$	2.30556	−	3.99335i	0.461113	−	0.798671i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.96435	+	2.86617i	−0.921856	+	0.532234i	−0.884227	−	0.467058i	$-0.845314\pi$
$29$	−4.96435	+	2.86617i	−0.921856	+	0.532234i	−0.0376295	+	0.999292i	$0.511981\pi$
$30$		0			0
$31$		−	4.64486i		−	0.834241i	−0.908851	−	0.417120i	$-0.863039\pi$
$31$		−	4.64486i		−	0.834241i	0.908851	−	0.417120i	$-0.136961\pi$
$32$		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	0.447922	+	0.894073i	$0.352164\pi$
$41$	−3.52382	+	6.10344i	−0.550329	+	0.953198i	−0.998251	+	0.0591249i	$0.981169\pi$
$42$		0			0
$43$	−1.56398	−	2.70890i	−0.238505	−	0.413103i	0.721780	−	0.692122i	$-0.243324\pi$
$43$	−1.56398	−	2.70890i	−0.238505	−	0.413103i	−0.960286	+	0.279019i	$0.909991\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.46768			1.38100			0.690502	−	0.723331i	$-0.257390\pi$
$47$	9.46768			1.38100			0.690502	+	0.723331i	$0.257390\pi$
$48$		0			0
$49$	6.73776	+	1.89804i	0.962537	+	0.271149i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.15189	+	0.665044i	−0.158224	+	0.0913508i	−0.577021	−	0.816729i	$-0.695785\pi$
$53$	−1.15189	+	0.665044i	−0.158224	+	0.0913508i	0.418797	+	0.908080i	$0.362452\pi$
$54$		0			0
$55$			3.24212i			0.437168i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.36667			0.828870			0.414435	−	0.910079i	$-0.363979\pi$
$59$	6.36667			0.828870			0.414435	+	0.910079i	$0.363979\pi$
$60$		0			0
$61$			11.1541i			1.42814i	0.700075	+	0.714069i	$0.253150\pi$
$61$			11.1541i			1.42814i	−0.700075	+	0.714069i	$0.746850\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			1.97315i			0.244739i
$66$		0			0
$67$	12.0990			1.47813			0.739065	−	0.673634i	$-0.235267\pi$
$67$	12.0990			1.47813			0.739065	+	0.673634i	$0.235267\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.5861i		−	1.25634i	−0.778076	−	0.628171i	$-0.783804\pi$
$71$		−	10.5861i		−	1.25634i	0.778076	−	0.628171i	$-0.216196\pi$
$72$		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
$77$	10.8592	+	8.44339i	1.23752	+	0.962214i
$78$		0			0
$79$	9.69679			1.09097			0.545487	−	0.838119i	$-0.316345\pi$
$79$	9.69679			1.09097			0.545487	+	0.838119i	$0.316345\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.192030	−	0.332606i	−0.0210781	−	0.0365083i	0.855294	−	0.518143i	$-0.173377\pi$
$83$	−0.192030	−	0.332606i	−0.0210781	−	0.0365083i	−0.876372	+	0.481635i	$0.840043\pi$
$84$		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	−0.864969	−	0.501826i	$-0.832662\pi$
$89$	0.0198983	−	0.0344648i	0.00210921	−	0.00365326i	0.867078	+	0.498172i	$0.165995\pi$
$90$		0			0
$91$	6.60888	+	5.13864i	0.692799	+	0.538675i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	1.02159i		−	0.104812i
$96$		0			0
$97$	−5.94681	+	3.43339i	−0.603807	+	0.348608i	−0.770538	−	0.637394i	$-0.780012\pi$
$97$	−5.94681	+	3.43339i	−0.603807	+	0.348608i	0.166731	+	0.986002i	$0.446679\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.46299	+	7.73012i	−0.444084	+	0.769176i	−0.997988	−	0.0634046i	$-0.979804\pi$
$101$	−4.46299	+	7.73012i	−0.444084	+	0.769176i	0.553904	+	0.832581i	$0.313137\pi$
$102$		0			0
$103$	7.68060	−	4.43439i	0.756792	−	0.436934i	−0.0713510	−	0.997451i	$-0.522731\pi$
$103$	7.68060	−	4.43439i	0.756792	−	0.436934i	0.828143	+	0.560517i	$0.189398\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.64326	−	1.52609i	−0.255534	−	0.147532i	0.366762	−	0.930315i	$-0.380466\pi$
$107$	−2.64326	−	1.52609i	−0.255534	−	0.147532i	−0.622295	+	0.782782i	$0.713800\pi$
$108$		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	0.640299	−	0.768126i	$-0.278810\pi$
$113$	3.13836	+	1.81193i	0.295232	+	0.170452i	−0.345067	+	0.938578i	$0.612144\pi$
$114$		0			0
$115$	−4.45801	−	2.57383i	−0.415711	−	0.240011i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.872420	+	2.14489i	0.0799746	+	0.196622i
$120$		0			0
$121$	8.01518	+	13.8827i	0.728653	+	1.26206i
$122$		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
$131$	−10.8788	−	18.8426i	−0.950484	−	1.64629i	−0.744380	−	0.667756i	$-0.767255\pi$
$131$	−10.8788	−	18.8426i	−0.950484	−	1.64629i	−0.206103	−	0.978530i	$-0.566078\pi$
$132$		0			0
$133$	−3.42170	−	2.66049i	−0.296699	−	0.230694i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.340450	+	0.196559i	0.0290866	+	0.0167932i	0.514473	−	0.857507i	$-0.327988\pi$
$137$	0.340450	+	0.196559i	0.0290866	+	0.0167932i	−0.485386	+	0.874300i	$0.661321\pi$
$138$		0			0
$139$	15.6647	+	9.04400i	1.32866	+	0.767102i	0.985092	−	0.172026i	$-0.0550312\pi$
$139$	15.6647	+	9.04400i	1.32866	+	0.767102i	0.343568	+	0.939128i	$0.388365\pi$
$140$		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
$149$	8.87748	−	5.12542i	0.727272	−	0.419891i	−0.0901515	−	0.995928i	$-0.528735\pi$
$149$	8.87748	−	5.12542i	0.727272	−	0.419891i	0.817423	+	0.576038i	$0.195402\pi$
$150$		0			0
$151$	−11.9006	+	20.6124i	−0.968457	+	1.67742i	−0.268432	+	0.963299i	$0.586505\pi$
$151$	−11.9006	+	20.6124i	−0.968457	+	1.67742i	−0.700025	+	0.714118i	$0.746828\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.50846	−	1.44826i	0.201484	−	0.116327i
$156$		0			0
$157$		−	11.5080i		−	0.918442i	−0.888322	−	0.459221i	$-0.848129\pi$
$157$		−	11.5080i		−	0.918442i	0.888322	−	0.459221i	$-0.151871\pi$
$158$		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	0.481817	+	0.876272i	$0.339977\pi$
$167$	−6.69358	+	11.5936i	−0.517965	+	0.897141i	−0.999782	+	0.0208697i	$0.993357\pi$
$168$		0			0
$169$	−1.49408	−	2.58782i	−0.114929	−	0.199063i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.88865			0.447706			0.223853	−	0.974623i	$-0.428136\pi$
$173$	5.88865			0.447706			0.223853	+	0.974623i	$0.428136\pi$
$174$		0			0
$175$	7.48856	−	9.63115i	0.566082	−	0.728046i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.4333	−	8.33310i	1.07880	−	0.622845i	0.148227	−	0.988953i	$-0.452643\pi$
$179$	14.4333	−	8.33310i	1.07880	−	0.622845i	0.930572	+	0.366109i	$0.119310\pi$
$180$		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
$185$	1.55015			0.113969
$186$		0			0
$187$			4.55017i			0.332741i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	13.6385i		−	0.986850i	−0.869788	−	0.493425i	$-0.835745\pi$
$191$		−	13.6385i		−	0.986850i	0.869788	−	0.493425i	$-0.164255\pi$
$192$		0			0
$193$	−11.4787			−0.826251			−0.413126	−	0.910674i	$-0.635563\pi$
$193$	−11.4787			−0.826251			−0.413126	+	0.910674i	$0.635563\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	4.78184i		−	0.340692i	−0.985384	−	0.170346i	$-0.945511\pi$
$197$		−	4.78184i		−	0.340692i	0.985384	−	0.170346i	$-0.0544885\pi$
$198$		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
$203$	−14.0487	+	5.71420i	−0.986024	+	0.401058i
$204$		0			0
$205$	−4.39489			−0.306952
$206$		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	−0.810787	−	0.585341i	$-0.800960\pi$
$211$	1.47477	−	2.55437i	0.101527	−	0.175850i	0.912314	+	0.409491i	$0.134294\pi$
$212$		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
$221$			2.76923i			0.186278i
$222$		0			0
$223$	−20.4564	+	11.8105i	−1.36986	+	0.790891i	−0.990910	−	0.134524i	$-0.957049\pi$
$223$	−20.4564	+	11.8105i	−1.36986	+	0.790891i	−0.378954	+	0.925416i	$0.623716\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.02534	−	15.6323i	0.599033	−	1.03755i	−0.393932	−	0.919140i	$-0.628885\pi$
$227$	9.02534	−	15.6323i	0.599033	−	1.03755i	0.992964	−	0.118415i	$-0.0377814\pi$
$228$		0			0
$229$	−10.5212	+	6.07439i	−0.695258	+	0.401407i	−0.805579	−	0.592489i	$-0.798145\pi$
$229$	−10.5212	+	6.07439i	−0.695258	+	0.401407i	0.110321	+	0.993896i	$0.464812\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.39111	+	1.95786i	0.222159	+	0.128264i	0.606950	−	0.794740i	$-0.292393\pi$
$233$	3.39111	+	1.95786i	0.222159	+	0.128264i	−0.384791	+	0.923004i	$0.625726\pi$
$234$		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	0.124401	−	0.992232i	$-0.460299\pi$
$239$	−10.3996	−	6.00423i	−0.672696	−	0.388381i	−0.797097	+	0.603851i	$0.793632\pi$
$240$		0			0
$241$	24.4958	+	14.1427i	1.57792	+	0.911010i	0.995150	+	0.0983690i	$0.0313626\pi$
$241$	24.4958	+	14.1427i	1.57792	+	0.911010i	0.582765	+	0.812641i	$0.301971\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.07578	+	4.23054i	0.0687294	+	0.270279i
$246$		0			0
$247$	−2.59178	−	4.48909i	−0.164911	−	0.285634i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0425			−0.760117			−0.380059	−	0.924962i	$-0.624096\pi$
$251$	−12.0425			−0.760117			−0.380059	+	0.924962i	$0.624096\pi$
$252$		0			0
$253$	−42.9173			−2.69819
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.32521	−	12.6876i	−0.456934	−	0.791433i	0.541863	−	0.840467i	$-0.317719\pi$
$257$	−7.32521	−	12.6876i	−0.456934	−	0.791433i	−0.998797	+	0.0490340i	$0.984386\pi$
$258$		0			0
$259$	4.03702	−	5.19207i	0.250848	−	0.322620i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.96349	−	2.86567i	−0.306062	−	0.176705i	0.339101	−	0.940750i	$-0.389877\pi$
$263$	−4.96349	−	2.86567i	−0.306062	−	0.176705i	−0.645163	+	0.764045i	$0.723210\pi$
$264$		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	0.911107	−	0.412169i	$-0.135229\pi$
$269$	1.61724	+	2.80114i	0.0986047	+	0.170788i	−0.812503	+	0.582957i	$0.801895\pi$
$270$		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
$275$	20.7617	−	11.9868i	1.25198	−	0.722831i
$276$		0			0
$277$	3.83423	−	6.64107i	0.230376	−	0.399023i	−0.727543	−	0.686063i	$-0.759338\pi$
$277$	3.83423	−	6.64107i	0.230376	−	0.399023i	0.957919	+	0.287039i	$0.0926710\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.78880	+	5.07422i	−0.524296	+	0.302702i	−0.738690	−	0.674045i	$-0.764555\pi$
$281$	−8.78880	+	5.07422i	−0.524296	+	0.302702i	0.214395	+	0.976747i	$0.431222\pi$
$282$		0			0
$283$		−	13.6685i		−	0.812510i	−0.913760	−	0.406255i	$-0.866834\pi$
$283$		−	13.6685i		−	0.812510i	0.913760	−	0.406255i	$-0.133166\pi$
$284$		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	$-0.883923\pi$
$293$	−2.70903	+	4.69218i	−0.158263	+	0.274120i	0.775979	+	0.630758i	$0.217256\pi$
$294$		0			0
$295$	1.98512	+	3.43833i	0.115578	+	0.200187i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−26.1194			−1.51052
$300$		0			0
$301$	−3.11807	−	7.66595i	−0.179723	−	0.441858i
$302$		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
$311$	−11.2647			−0.638762			−0.319381	−	0.947626i	$-0.603475\pi$
$311$	−11.2647			−0.638762			−0.319381	+	0.947626i	$0.603475\pi$
$312$		0			0
$313$			11.4280i			0.645950i	0.946407	+	0.322975i	$0.104683\pi$
$313$			11.4280i			0.645950i	−0.946407	+	0.322975i	$0.895317\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			19.4687i			1.09347i	0.837305	+	0.546736i	$0.184130\pi$
$317$			19.4687i			1.09347i	−0.837305	+	0.546736i	$0.815870\pi$
$318$		0			0
$319$	−29.8028			−1.66864
$320$		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
$329$	24.8134	+	3.42828i	1.36801	+	0.189007i
$330$		0			0
$331$	26.9675			1.48227			0.741135	−	0.671356i	$-0.234288\pi$
$331$	26.9675			1.48227			0.741135	+	0.671356i	$0.234288\pi$
$332$		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	−0.837703	−	0.546127i	$-0.816102\pi$
$337$	0.993296	−	1.72044i	0.0541083	−	0.0937183i	0.891811	+	0.452408i	$0.149435\pi$
$338$		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
$347$		−	34.3724i		−	1.84521i	−0.385752	−	0.922603i	$-0.626058\pi$
$347$		−	34.3724i		−	1.84521i	0.385752	−	0.922603i	$-0.373942\pi$
$348$		0			0
$349$	−25.3935	+	14.6609i	−1.35928	+	0.784781i	−0.989527	−	0.144348i	$-0.953891\pi$
$349$	−25.3935	+	14.6609i	−1.35928	+	0.784781i	−0.369754	+	0.929130i	$0.620558\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.586526	+	1.01589i	−0.0312177	+	0.0540706i	−0.881212	−	0.472721i	$-0.843272\pi$
$353$	−0.586526	+	1.01589i	−0.0312177	+	0.0540706i	0.849994	+	0.526792i	$0.176605\pi$
$354$		0			0
$355$	5.71704	−	3.30074i	0.303429	−	0.175185i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.69591	+	3.28854i	0.300619	+	0.173562i	0.642721	−	0.766101i	$-0.277806\pi$
$359$	5.69591	+	3.28854i	0.300619	+	0.173562i	−0.342102	+	0.939663i	$0.611139\pi$
$360$		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
$367$	−8.24124	−	4.75808i	−0.430189	−	0.248370i	0.269238	−	0.963074i	$-0.413228\pi$
$367$	−8.24124	−	4.75808i	−0.430189	−	0.248370i	−0.699427	+	0.714704i	$0.746562\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.25975	+	1.32588i	−0.169238	+	0.0688362i
$372$		0			0
$373$	−10.3152	−	17.8664i	−0.534098	−	0.925085i	−0.999206	−	0.0398315i	$-0.987318\pi$
$373$	−10.3152	−	17.8664i	−0.534098	−	0.925085i	0.465108	−	0.885254i	$-0.346015\pi$
$374$		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
$383$	14.0484	+	24.3326i	0.717840	+	1.24334i	0.961854	+	0.273564i	$0.0882026\pi$
$383$	14.0484	+	24.3326i	0.717840	+	1.24334i	−0.244013	+	0.969772i	$0.578464\pi$
$384$		0			0
$385$	−1.17398	+	8.49714i	−0.0598318	+	0.433054i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−28.4400	−	16.4198i	−1.44196	−	0.832519i	−0.443984	−	0.896035i	$-0.646435\pi$
$389$	−28.4400	−	16.4198i	−1.44196	−	0.832519i	−0.997981	+	0.0635162i	$0.979769\pi$
$390$		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
$401$	12.3658	−	7.13943i	0.617521	−	0.356526i	−0.158382	−	0.987378i	$-0.550628\pi$
$401$	12.3658	−	7.13943i	0.617521	−	0.356526i	0.775903	+	0.630852i	$0.217294\pi$
$402$		0			0
$403$	7.34851	−	12.7280i	0.366055	−	0.634026i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.1925	−	6.46198i	0.554791	−	0.320309i
$408$		0			0
$409$		−	8.13148i		−	0.402076i	−0.979583	−	0.201038i	$-0.935569\pi$
$409$		−	8.13148i		−	0.402076i	0.979583	−	0.201038i	$-0.0644314\pi$
$410$		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	$-0.809454\pi$
$419$	1.53415	−	2.65723i	0.0749481	−	0.129814i	0.901064	+	0.433687i	$0.142788\pi$
$420$		0			0
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	0.950926	−	0.309418i	$-0.100134\pi$
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	−0.743427	+	0.668817i	$0.766801\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.03560			0.195756
$426$		0			0
$427$	−4.03894	+	29.2333i	−0.195458	+	1.41470i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	19.8414	−	11.4554i	0.955727	−	0.551789i	0.0608716	−	0.998146i	$-0.480612\pi$
$431$	19.8414	−	11.4554i	0.955727	−	0.551789i	0.894855	+	0.446356i	$0.147279\pi$
$432$		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
$437$	13.5231			0.646899
$438$		0			0
$439$			6.43498i			0.307125i	0.988139	+	0.153562i	$0.0490746\pi$
$439$			6.43498i			0.307125i	−0.988139	+	0.153562i	$0.950925\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	25.5373i		−	1.21331i	−0.794964	−	0.606656i	$-0.792510\pi$
$443$		−	25.5373i		−	1.21331i	0.794964	−	0.606656i	$-0.207490\pi$
$444$		0			0
$445$	0.0248170			0.00117644
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	40.1008i		−	1.89247i	−0.323474	−	0.946237i	$-0.604851\pi$
$449$		−	40.1008i		−	1.89247i	0.323474	−	0.946237i	$-0.395149\pi$
$450$		0			0
$451$	−31.7322	+	18.3206i	−1.49421	+	0.862684i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.714485	+	5.17135i	−0.0334956	+	0.242436i
$456$		0			0
$457$	−38.4715			−1.79962			−0.899810	−	0.436283i	$-0.856295\pi$
$457$	−38.4715			−1.79962			−0.899810	+	0.436283i	$0.856295\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.0830	−	20.9283i	−0.562759	−	0.974728i	−0.997254	−	0.0740533i	$-0.976407\pi$
$461$	−12.0830	−	20.9283i	−0.562759	−	0.974728i	0.434495	−	0.900674i	$-0.356927\pi$
$462$		0			0
$463$	−8.65455	+	14.9901i	−0.402211	+	0.696650i	−0.993992	−	0.109449i	$-0.965091\pi$
$463$	−8.65455	+	14.9901i	−0.402211	+	0.696650i	0.591781	+	0.806098i	$0.298425\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.46858	+	9.47185i	−0.253056	+	0.438305i	−0.964366	−	0.264573i	$-0.914769\pi$
$467$	−5.46858	+	9.47185i	−0.253056	+	0.438305i	0.711310	+	0.702878i	$0.248102\pi$
$468$		0			0
$469$	31.7098	+	4.38110i	1.46422	+	0.202300i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	16.2625i		−	0.747751i
$474$		0			0
$475$	−6.54197	+	3.77701i	−0.300166	+	0.173301i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.756744	+	1.31072i	−0.0345765	+	0.0598883i	−0.882796	−	0.469757i	$-0.844342\pi$
$479$	−0.756744	+	1.31072i	−0.0345765	+	0.0598883i	0.848219	+	0.529645i	$0.177675\pi$
$480$		0			0
$481$	6.81173	−	3.93275i	0.310588	−	0.179318i
$482$		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	−0.135412	−	0.990789i	$-0.543236\pi$
$491$	−23.5139	−	13.5757i	−1.06117	−	0.612665i	−0.925755	+	0.378125i	$0.876569\pi$
$492$		0			0
$493$	−4.34474	−	2.50844i	−0.195677	−	0.112974i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.83327	−	27.7447i	0.171946	−	1.24452i
$498$		0			0
$499$	−11.1327	−	19.2824i	−0.498369	−	0.863200i	0.501629	−	0.865083i	$-0.332734\pi$
$499$	−11.1327	−	19.2824i	−0.498369	−	0.863200i	−0.999998	+	0.00188245i	$0.999401\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−32.2005			−1.43575			−0.717876	−	0.696171i	$-0.754885\pi$
$503$	−32.2005			−1.43575			−0.717876	+	0.696171i	$0.754885\pi$
$504$		0			0
$505$	−5.56621			−0.247693
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.60909	+	7.98317i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$509$	4.60909	+	7.98317i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$510$		0			0
$511$	−33.0305	+	13.4349i	−1.46118	+	0.594326i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.78959	+	2.76527i	0.211055	+	0.121853i
$516$		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	0.655549	−	0.755153i	$-0.272437\pi$
$521$	−7.44581	−	12.8965i	−0.326207	−	0.565007i	−0.981756	+	0.190146i	$0.939104\pi$
$522$		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
$527$	3.52050	−	2.03256i	0.153355	−	0.0885398i
$528$		0			0
$529$	22.5708	−	39.0938i	0.981340	−	1.69973i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.3122	+	11.1499i	−0.836504	+	0.482956i
$534$		0			0
$535$		−	1.90333i		−	0.0822880i
$536$		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	0.763873	−	0.645367i	$-0.223295\pi$
$547$	−4.13892	−	7.16882i	−0.176967	−	0.306517i	−0.940840	+	0.338850i	$0.889962\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.39080			0.400061
$552$		0			0
$553$	25.4139	+	3.51124i	1.08071	+	0.149313i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.96801	+	4.02299i	−0.295244	+	0.170459i	−0.640304	−	0.768121i	$-0.721192\pi$
$557$	−6.96801	+	4.02299i	−0.295244	+	0.170459i	0.345060	+	0.938581i	$0.387858\pi$
$558$		0			0
$559$		−	9.89735i		−	0.418613i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	29.9156			1.26079			0.630396	−	0.776274i	$-0.282892\pi$
$563$	29.9156			1.26079			0.630396	+	0.776274i	$0.282892\pi$
$564$		0			0
$565$			2.25983i			0.0950718i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			30.8238i			1.29220i	0.763252	+	0.646101i	$0.223601\pi$
$569$			30.8238i			1.29220i	−0.763252	+	0.646101i	$0.776399\pi$
$570$		0			0
$571$	−5.34693			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$571$	−5.34693			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$572$		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
$581$	−0.382846	−	0.941248i	−0.0158831	−	0.0390495i
$582$		0			0
$583$	−6.91522			−0.286399
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.3955	+	21.4697i	0.511619	+	0.886150i	0.999909	+	0.0134687i	$0.00428734\pi$
$587$	12.3955	+	21.4697i	0.511619	+	0.886150i	−0.488290	+	0.872681i	$0.662379\pi$
$588$		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	−0.824967	−	0.565180i	$-0.808807\pi$
$593$	1.87451	−	3.24675i	0.0769770	−	0.133328i	0.901944	+	0.431852i	$0.142140\pi$
$594$		0			0
$595$	−0.886331	+	1.13992i	−0.0363360	+	0.0467323i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			32.0673i			1.31024i	0.755527	+	0.655118i	$0.227381\pi$
$599$			32.0673i			1.31024i	−0.755527	+	0.655118i	$0.772619\pi$
$600$		0			0
$601$	5.98069	−	3.45296i	0.243958	−	0.140849i	−0.373037	−	0.927817i	$-0.621683\pi$
$601$	5.98069	−	3.45296i	0.243958	−	0.140849i	0.616994	+	0.786968i	$0.288350\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.99824	+	8.65721i	−0.203207	+	0.351966i
$606$		0			0
$607$	−18.7892	+	10.8479i	−0.762629	+	0.440304i	−0.830239	−	0.557408i	$-0.811796\pi$
$607$	−18.7892	+	10.8479i	−0.762629	+	0.440304i	0.0676102	+	0.997712i	$0.478463\pi$
$608$		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	−0.340557	−	0.940224i	$-0.610616\pi$
$617$	−32.9146	−	19.0033i	−1.32509	−	0.765043i	−0.984536	+	0.175181i	$0.943949\pi$
$618$		0			0
$619$	37.5659	+	21.6887i	1.50990	+	0.871743i	0.999933	+	0.0115498i	$0.00367650\pi$
$619$	37.5659	+	21.6887i	1.50990	+	0.871743i	0.509969	+	0.860193i	$0.329657\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0646303	−	0.0831220i	0.00258936	−	0.00333021i
$624$		0			0
$625$	−9.65906	−	16.7300i	−0.386363	−	0.669200i
$626$		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
$635$	−3.16189	−	5.47655i	−0.125476	−	0.217330i
$636$		0			0
$637$	15.4602	+	15.8607i	0.612555	+	0.628425i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	25.7688	+	14.8776i	1.01781	+	0.587631i	0.913468	−	0.406911i	$-0.133394\pi$
$641$	25.7688	+	14.8776i	1.01781	+	0.587631i	0.104339	+	0.994542i	$0.466727\pi$
$642$		0			0
$643$	37.4271	+	21.6085i	1.47598	+	0.852158i	0.999633	−	0.0270991i	$-0.00862696\pi$
$643$	37.4271	+	21.6085i	1.47598	+	0.852158i	0.476348	+	0.879257i	$0.341960\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.42940	−	16.3322i	−0.370708	−	0.642085i	0.618967	−	0.785417i	$-0.287552\pi$
$647$	−9.42940	−	16.3322i	−0.370708	−	0.642085i	−0.989675	+	0.143332i	$0.954218\pi$
$648$		0			0
$649$	28.6661	+	16.5504i	1.12524	+	0.649660i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.41584	+	4.85889i	−0.329337	+	0.190143i	−0.655547	−	0.755155i	$-0.727562\pi$
$653$	−8.41584	+	4.85889i	−0.329337	+	0.190143i	0.326210	+	0.945297i	$0.394228\pi$
$654$		0			0
$655$	6.78397	−	11.7502i	0.265072	−	0.459118i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.172266	−	0.985050i	$-0.444891\pi$
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.939212	+	0.343338i	$0.111558\pi$
$660$		0			0
$661$			1.25812i			0.0489353i	0.999701	+	0.0244677i	$0.00778907\pi$
$661$			1.25812i			0.0489353i	−0.999701	+	0.0244677i	$0.992211\pi$
$662$		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	0.526715	−	0.850042i	$-0.323423\pi$
$673$	−12.2655	−	21.2445i	−0.472800	−	0.818914i	−0.999515	+	0.0311279i	$0.990090\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.1233			0.888699			0.444350	−	0.895853i	$-0.353435\pi$
$677$	23.1233			0.888699			0.444350	+	0.895853i	$0.353435\pi$
$678$		0			0
$679$	−16.8290	+	6.84506i	−0.645836	+	0.262689i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.4945	+	7.21370i	−0.478089	+	0.276025i	−0.719620	−	0.694368i	$-0.755684\pi$
$683$	−12.4945	+	7.21370i	−0.478089	+	0.276025i	0.241531	+	0.970393i	$0.422350\pi$
$684$		0			0
$685$			0.245147i			0.00936659i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.20859			−0.160335
$690$		0			0
$691$		−	37.4114i		−	1.42320i	−0.702586	−	0.711599i	$-0.747971\pi$
$691$		−	37.4114i		−	1.42320i	0.702586	−	0.711599i	$-0.252029\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			11.2796i			0.427860i
$696$		0			0
$697$	−6.16802			−0.233630
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	41.0429i		−	1.55017i	−0.631859	−	0.775084i	$-0.717708\pi$
$701$		−	41.0429i		−	1.55017i	0.631859	−	0.775084i	$-0.282292\pi$
$702$		0			0
$703$	−3.52672	+	2.03615i	−0.133013	+	0.0767950i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.4959	+	18.6435i	−0.545176	+	0.701160i
$708$		0			0
$709$	23.3246			0.875974			0.437987	−	0.898981i	$-0.355692\pi$
$709$	23.3246			0.875974			0.437987	+	0.898981i	$0.355692\pi$
$710$		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	$0.467795\pi$
$719$	−21.7489	+	37.6701i	−0.811096	+	1.40486i	−0.912098	+	0.409973i	$0.865538\pi$
$720$		0			0
$721$	21.7354	−	8.84073i	0.809470	−	0.329246i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			26.4325i			0.981679i
$726$		0			0
$727$	11.3715	−	6.56536i	0.421747	−	0.243496i	−0.274078	−	0.961708i	$-0.588373\pi$
$727$	11.3715	−	6.56536i	0.421747	−	0.243496i	0.695824	+	0.718212i	$0.255039\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.36878	−	2.37079i	0.0506261	−	0.0876870i
$732$		0			0
$733$	34.7965	−	20.0898i	1.28524	−	0.742032i	0.307436	−	0.951569i	$-0.400529\pi$
$733$	34.7965	−	20.0898i	1.28524	−	0.742032i	0.977801	+	0.209537i	$0.0671955\pi$
$734$		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	−0.165572	−	0.986198i	$-0.552947\pi$
$743$	−30.0501	−	17.3494i	−1.10243	−	0.636488i	−0.936858	+	0.349709i	$0.886280\pi$
$744$		0			0
$745$	5.53597	+	3.19619i	0.202822	+	0.117099i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.37500	−	4.95679i	−0.232938	−	0.181117i
$750$		0			0
$751$	14.5070	+	25.1268i	0.529367	+	0.916891i	0.999413	+	0.0342492i	$0.0109040\pi$
$751$	14.5070	+	25.1268i	0.529367	+	0.916891i	−0.470046	+	0.882642i	$0.655763\pi$
$752$		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
$761$	11.4107	+	19.7638i	0.413636	+	0.716439i	0.995284	−	0.0970019i	$-0.0309253\pi$
$761$	11.4107	+	19.7638i	0.413636	+	0.716439i	−0.581648	+	0.813440i	$0.697592\pi$
$762$		0			0
$763$	−11.0663	−	27.2070i	−0.400626	−	0.984961i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17.4462	+	10.0725i	0.629945	+	0.363699i
$768$		0			0
$769$	−27.6397	−	15.9578i	−0.996714	−	0.575453i	−0.0894399	−	0.995992i	$-0.528508\pi$
$769$	−27.6397	−	15.9578i	−0.996714	−	0.575453i	−0.907275	+	0.420539i	$0.861841\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.8503	−	30.9176i	−0.642030	−	1.11203i	−0.984979	−	0.172675i	$-0.944759\pi$
$773$	−17.8503	−	30.9176i	−0.642030	−	1.11203i	0.342949	−	0.939354i	$-0.388574\pi$
$774$		0			0
$775$	−18.5486	−	10.7090i	−0.666284	−	0.384679i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.99875	−	5.77278i	0.358242	−	0.206831i
$780$		0			0
$781$	27.5190	−	47.6643i	0.984708	−	1.70556i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.21492	−	3.58819i	0.221820	−	0.128068i
$786$		0			0
$787$			13.8834i			0.494888i	0.968902	+	0.247444i	$0.0795907\pi$
$787$			13.8834i			0.494888i	−0.968902	+	0.247444i	$0.920409\pi$
$788$		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	0.496488	+	0.868044i	$0.334623\pi$
$797$	−14.2145	+	24.6203i	−0.503504	+	0.872094i	−0.999992	+	0.00405063i	$0.998711\pi$
$798$		0			0
$799$	4.14300	+	7.17589i	0.146569	+	0.253865i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−70.0708			−2.47274
$804$		0			0
$805$	−10.7518	−	8.35990i	−0.378951	−	0.294648i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21.1074	−	12.1864i	0.742096	−	0.428449i	−0.0807348	−	0.996736i	$-0.525727\pi$
$809$	21.1074	−	12.1864i	0.742096	−	0.428449i	0.822831	+	0.568286i	$0.192393\pi$
$810$		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
$815$	13.0474			0.457030
$816$		0			0
$817$			5.12428i			0.179276i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	19.5144i		−	0.681056i	−0.940234	−	0.340528i	$-0.889394\pi$
$821$		−	19.5144i		−	0.681056i	0.940234	−	0.340528i	$-0.110606\pi$
$822$		0			0
$823$	−31.6570			−1.10349			−0.551747	−	0.834012i	$-0.686038\pi$
$823$	−31.6570			−1.10349			−0.551747	+	0.834012i	$0.686038\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	24.4749i		−	0.851075i	−0.904941	−	0.425537i	$-0.860085\pi$
$827$		−	24.4749i		−	0.851075i	0.904941	−	0.425537i	$-0.139915\pi$
$828$		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
$833$	1.50981	+	5.93736i	0.0523119	+	0.205717i
$834$		0			0
$835$	−8.34819			−0.288901
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.6920	+	34.1075i	0.679843	+	1.17752i	0.975028	+	0.222083i	$0.0712856\pi$
$839$	19.6920	+	34.1075i	0.679843	+	1.17752i	−0.295184	+	0.955440i	$0.595381\pi$
$840$		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
$851$			20.5199i			0.703415i
$852$		0			0
$853$	21.3507	−	12.3268i	0.731033	−	0.422062i	−0.0877672	−	0.996141i	$-0.527973\pi$
$853$	21.3507	−	12.3268i	0.731033	−	0.422062i	0.818800	+	0.574079i	$0.194640\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.4145	+	19.7705i	−0.389911	+	0.675346i	−0.992437	−	0.122753i	$-0.960828\pi$
$857$	−11.4145	+	19.7705i	−0.389911	+	0.675346i	0.602526	+	0.798099i	$0.294161\pi$
$858$		0			0
$859$	41.3224	−	23.8575i	1.40990	−	0.814007i	0.414523	−	0.910039i	$-0.363948\pi$
$859$	41.3224	−	23.8575i	1.40990	−	0.814007i	0.995378	+	0.0960315i	$0.0306150\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−18.0645	−	10.4296i	−0.614923	−	0.355026i	0.159967	−	0.987122i	$-0.448861\pi$
$863$	−18.0645	−	10.4296i	−0.614923	−	0.355026i	−0.774890	+	0.632096i	$0.782195\pi$
$864$		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
$871$	33.1541	+	19.1416i	1.12339	+	0.648587i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.7080	+	2.17026i	0.531028	+	0.0733680i
$876$		0			0
$877$	11.7718	+	20.3894i	0.397506	+	0.688500i	0.993417	−	0.114550i	$-0.0365426\pi$
$877$	11.7718	+	20.3894i	0.397506	+	0.688500i	−0.595912	+	0.803050i	$0.703209\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−52.5975			−1.77205			−0.886027	−	0.463633i	$-0.846546\pi$
$881$	−52.5975			−1.77205			−0.886027	+	0.463633i	$0.846546\pi$
$882$		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
$887$	−7.51139	−	13.0101i	−0.252208	−	0.436837i	0.711926	−	0.702255i	$-0.247823\pi$
$887$	−7.51139	−	13.0101i	−0.252208	−	0.436837i	−0.964133	+	0.265418i	$0.914490\pi$
$888$		0			0
$889$	−26.5776	−	3.67203i	−0.891385	−	0.123156i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.4321	−	7.75505i	−0.449489	−	0.259513i
$894$		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
$905$	0.249884	−	0.144271i	0.00830643	−	0.00479572i
$906$		0			0
$907$	5.84747	−	10.1281i	0.194162	−	0.336299i	−0.752463	−	0.658634i	$-0.771135\pi$
$907$	5.84747	−	10.1281i	0.194162	−	0.336299i	0.946626	+	0.322335i	$0.104468\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	−0.251689	−	0.967808i	$-0.580986\pi$
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	0.712302	+	0.701873i	$0.247653\pi$
$912$		0			0
$913$		−	1.99676i		−	0.0660831i
$914$		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
$929$	53.6714			1.76090			0.880451	−	0.474138i	$-0.157240\pi$
$929$	53.6714			1.76090			0.880451	+	0.474138i	$0.157240\pi$
$930$		0			0
$931$	−8.00440	−	8.21177i	−0.262334	−	0.269130i
$932$		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
$941$	−37.0686			−1.20840			−0.604200	−	0.796833i	$-0.706507\pi$
$941$	−37.0686			−1.20840			−0.604200	+	0.796833i	$0.706507\pi$
$942$		0			0
$943$		−	58.1769i		−	1.89450i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			3.16082i			0.102713i	0.998680	+	0.0513565i	$0.0163545\pi$
$947$			3.16082i			0.102713i	−0.998680	+	0.0513565i	$0.983646\pi$
$948$		0			0
$949$	−42.6450			−1.38431
$950$		0			0
$951$		0			0
$952$		0			0
$953$			38.9680i			1.26230i	0.775662	+	0.631149i	$0.217416\pi$
$953$			38.9680i			1.26230i	−0.775662	+	0.631149i	$0.782584\pi$
$954$		0			0
$955$	7.36550	−	4.25247i	0.238342	−	0.137607i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.821096	+	0.638431i	0.0265146	+	0.0206160i
$960$		0			0
$961$	9.42531			0.304042
$962$		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	−0.959159	−	0.282866i	$-0.908715\pi$
$967$	−7.29560	+	12.6363i	−0.234611	+	0.406357i	0.724549	+	0.689223i	$0.242048\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.3537	−	19.6652i	0.364358	−	0.631086i	−0.624315	−	0.781172i	$-0.714622\pi$
$971$	11.3537	−	19.6652i	0.364358	−	0.631086i	0.988673	+	0.150087i	$0.0479553\pi$
$972$		0			0
$973$	37.7800	+	29.3752i	1.21117	+	0.941727i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	41.0411i		−	1.31302i	−0.754317	−	0.656511i	$-0.772032\pi$
$977$		−	41.0411i		−	1.31302i	0.754317	−	0.656511i	$-0.227968\pi$
$978$		0			0
$979$	0.179185	−	0.103453i	0.00572678	−	0.00330636i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.4653	+	18.1263i	−0.333790	+	0.578141i	−0.983252	−	0.182253i	$-0.941661\pi$
$983$	−10.4653	+	18.1263i	−0.333790	+	0.578141i	0.649462	+	0.760394i	$0.274994\pi$
$984$		0			0
$985$	2.58243	−	1.49097i	0.0822832	−	0.0475062i
$986$		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
$997$	2.78561	+	1.60827i	0.0882211	+	0.0509345i	0.543462	−	0.839434i	$-0.317113\pi$
$997$	2.78561	+	1.60827i	0.0882211	+	0.0509345i	−0.455240	+	0.890369i	$0.650447\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.bs.a.1097.14		48
3.2	odd	2		504.2.bs.a.257.3	✓	48
4.3	odd	2		3024.2.ca.e.2609.14		48
7.3	odd	6		1512.2.cx.a.17.14		48
9.2	odd	6		1512.2.cx.a.89.14		48
9.7	even	3		504.2.cx.a.425.11	yes	48
12.11	even	2		1008.2.ca.e.257.22		48
21.17	even	6		504.2.cx.a.185.11	yes	48
28.3	even	6		3024.2.df.e.17.14		48
36.7	odd	6		1008.2.df.e.929.14		48
36.11	even	6		3024.2.df.e.1601.14		48
63.38	even	6	inner	1512.2.bs.a.521.14		48
63.52	odd	6		504.2.bs.a.353.3	yes	48
84.59	odd	6		1008.2.df.e.689.14		48
252.115	even	6		1008.2.ca.e.353.22		48
252.227	odd	6		3024.2.ca.e.2033.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.3	✓	48	3.2	odd	2
504.2.bs.a.353.3	yes	48	63.52	odd	6
504.2.cx.a.185.11	yes	48	21.17	even	6
504.2.cx.a.425.11	yes	48	9.7	even	3
1008.2.ca.e.257.22		48	12.11	even	2
1008.2.ca.e.353.22		48	252.115	even	6
1008.2.df.e.689.14		48	84.59	odd	6
1008.2.df.e.929.14		48	36.7	odd	6
1512.2.bs.a.521.14		48	63.38	even	6	inner
1512.2.bs.a.1097.14		48	1.1	even	1	trivial
1512.2.cx.a.17.14		48	7.3	odd	6
1512.2.cx.a.89.14		48	9.2	odd	6
3024.2.ca.e.2033.14		48	252.227	odd	6
3024.2.ca.e.2609.14		48	4.3	odd	2
3024.2.df.e.17.14		48	28.3	even	6
3024.2.df.e.1601.14		48	36.11	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.311798 + 0.540051i) q^{5} +(2.62086 + 0.362103i) q^{7} +(4.50253 + 2.59954i) q^{11} +(2.74023 + 1.58207i) q^{13} +(0.437594 + 0.757935i) q^{17} +(-1.41874 - 0.819107i) q^{19} +(-7.14886 + 4.12740i) q^{23} +(2.30556 - 3.99335i) q^{25} +(-4.96435 + 2.86617i) q^{29} -4.64486i q^{31} +(0.621624 + 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(-3.52382 + 6.10344i) q^{41} +(-1.56398 - 2.70890i) q^{43} +9.46768 q^{47} +(6.73776 + 1.89804i) q^{49} +(-1.15189 + 0.665044i) q^{53} +3.24212i q^{55} +6.36667 q^{59} +11.1541i q^{61} +1.97315i q^{65} +12.0990 q^{67} -10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(10.8592 + 8.44339i) q^{77} +9.69679 q^{79} +(-0.192030 - 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(0.0198983 - 0.0344648i) q^{89} +(6.60888 + 5.13864i) q^{91} -1.02159i q^{95} +(-5.94681 + 3.43339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 - 6 * q^43 - 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 - 12 * q^79 - 18 * q^89 + 6 * q^91

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