LMFDB - Embedded newform 1512.2.cx.a.17.9

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			17.9
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36828 q^{5} +(2.64451 + 0.0810554i) q^{7} +1.20384i q^{11} +(0.639364 + 0.369137i) q^{13} +(0.693066 - 1.20043i) q^{17} +(2.81671 - 1.62623i) q^{19} +3.81129i q^{23} -3.12781 q^{25} +(3.50030 - 2.02090i) q^{29} +(1.02924 - 0.594230i) q^{31} +(-3.61843 - 0.110906i) q^{35} +(5.10537 + 8.84276i) q^{37} +(0.670586 - 1.16149i) q^{41} +(-0.490044 - 0.848782i) q^{43} +(1.63634 - 2.83422i) q^{47} +(6.98686 + 0.428704i) q^{49} +(5.77421 + 3.33374i) q^{53} -1.64718i q^{55} +(6.73912 + 11.6725i) q^{59} +(-4.36067 - 2.51764i) q^{61} +(-0.874829 - 0.505083i) q^{65} +(-2.19665 - 3.80471i) q^{67} -8.84538i q^{71} +(10.2939 + 5.94320i) q^{73} +(-0.0975775 + 3.18356i) q^{77} +(6.34799 - 10.9950i) q^{79} +(3.14219 + 5.44243i) q^{83} +(-0.948308 + 1.64252i) q^{85} +(6.05868 + 10.4939i) q^{89} +(1.66088 + 1.02801i) q^{91} +(-3.85404 + 2.22513i) q^{95} +(10.9781 - 6.33821i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

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

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
$5$	−1.36828			−0.611913			−0.305956	−	0.952046i	$-0.598976\pi$
$5$	−1.36828			−0.611913			−0.305956	+	0.952046i	$0.598976\pi$
$6$		0			0
$7$	2.64451	+	0.0810554i	0.999531	+	0.0306361i
$7$	2.64451	+	0.0810554i	0.999531	+	0.0306361i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			1.20384i			0.362971i	0.983394	+	0.181485i	$0.0580905\pi$
$11$			1.20384i			0.362971i	−0.983394	+	0.181485i	$0.941910\pi$
$12$		0			0
$13$	0.639364	+	0.369137i	0.177328	+	0.102380i	0.586037	−	0.810285i	$-0.300687\pi$
$13$	0.639364	+	0.369137i	0.177328	+	0.102380i	−0.408709	+	0.912665i	$0.634021\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.693066	−	1.20043i	0.168093	−	0.291146i	−0.769656	−	0.638459i	$-0.779572\pi$
$17$	0.693066	−	1.20043i	0.168093	−	0.291146i	0.937749	+	0.347313i	$0.112906\pi$
$18$		0			0
$19$	2.81671	−	1.62623i	0.646197	−	0.373082i	−0.140801	−	0.990038i	$-0.544968\pi$
$19$	2.81671	−	1.62623i	0.646197	−	0.373082i	0.786998	+	0.616956i	$0.211634\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			3.81129i			0.794709i	0.917665	+	0.397355i	$0.130072\pi$
$23$			3.81129i			0.794709i	−0.917665	+	0.397355i	$0.869928\pi$
$24$		0			0
$25$	−3.12781			−0.625563
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.50030	−	2.02090i	0.649989	−	0.375271i	−0.138463	−	0.990368i	$-0.544216\pi$
$29$	3.50030	−	2.02090i	0.649989	−	0.375271i	0.788452	+	0.615096i	$0.210883\pi$
$30$		0			0
$31$	1.02924	−	0.594230i	0.184856	−	0.106727i	−0.404716	−	0.914442i	$-0.632630\pi$
$31$	1.02924	−	0.594230i	0.184856	−	0.106727i	0.589572	+	0.807716i	$0.299296\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.61843	−	0.110906i	−0.611626	−	0.0187466i
$36$		0			0
$37$	5.10537	+	8.84276i	0.839317	+	1.45374i	0.890466	+	0.455049i	$0.150378\pi$
$37$	5.10537	+	8.84276i	0.839317	+	1.45374i	−0.0511491	+	0.998691i	$0.516288\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.670586	−	1.16149i	0.104728	−	0.181394i	−0.808899	−	0.587948i	$-0.799936\pi$
$41$	0.670586	−	1.16149i	0.104728	−	0.181394i	0.913627	+	0.406553i	$0.133269\pi$
$42$		0			0
$43$	−0.490044	−	0.848782i	−0.0747311	−	0.129438i	0.826238	−	0.563321i	$-0.190476\pi$
$43$	−0.490044	−	0.848782i	−0.0747311	−	0.129438i	−0.900969	+	0.433883i	$0.857143\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.63634	−	2.83422i	0.238684	−	0.413413i	−0.721653	−	0.692255i	$-0.756617\pi$
$47$	1.63634	−	2.83422i	0.238684	−	0.413413i	0.960337	+	0.278842i	$0.0899506\pi$
$48$		0			0
$49$	6.98686	+	0.428704i	0.998123	+	0.0612434i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.77421	+	3.33374i	0.793148	+	0.457924i	0.841070	−	0.540927i	$-0.181926\pi$
$53$	5.77421	+	3.33374i	0.793148	+	0.457924i	−0.0479213	+	0.998851i	$0.515260\pi$
$54$		0			0
$55$		−	1.64718i		−	0.222106i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.73912	+	11.6725i	0.877359	+	1.51963i	0.854228	+	0.519898i	$0.174030\pi$
$59$	6.73912	+	11.6725i	0.877359	+	1.51963i	0.0231309	+	0.999732i	$0.492637\pi$
$60$		0			0
$61$	−4.36067	−	2.51764i	−0.558327	−	0.322350i	0.194147	−	0.980972i	$-0.437806\pi$
$61$	−4.36067	−	2.51764i	−0.558327	−	0.322350i	−0.752474	+	0.658622i	$0.771140\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.874829	−	0.505083i	−0.108509	−	0.0626478i
$66$		0			0
$67$	−2.19665	−	3.80471i	−0.268364	−	0.464819i	0.700076	−	0.714069i	$-0.253150\pi$
$67$	−2.19665	−	3.80471i	−0.268364	−	0.464819i	−0.968439	+	0.249249i	$0.919816\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.84538i		−	1.04975i	−0.851178	−	0.524877i	$-0.824111\pi$
$71$		−	8.84538i		−	1.04975i	0.851178	−	0.524877i	$-0.175889\pi$
$72$		0			0
$73$	10.2939	+	5.94320i	1.20481	+	0.695599i	0.961621	−	0.274380i	$-0.0884726\pi$
$73$	10.2939	+	5.94320i	1.20481	+	0.695599i	0.243191	+	0.969978i	$0.421806\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0975775	+	3.18356i	−0.0111200	+	0.362800i
$78$		0			0
$79$	6.34799	−	10.9950i	0.714205	−	1.23704i	−0.249060	−	0.968488i	$-0.580122\pi$
$79$	6.34799	−	10.9950i	0.714205	−	1.23704i	0.963265	−	0.268551i	$-0.0865449\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.14219	+	5.44243i	0.344900	+	0.597384i	0.985336	−	0.170628i	$-0.0545795\pi$
$83$	3.14219	+	5.44243i	0.344900	+	0.597384i	−0.640436	+	0.768012i	$0.721246\pi$
$84$		0			0
$85$	−0.948308	+	1.64252i	−0.102858	+	0.178156i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.05868	+	10.4939i	0.642219	+	1.11236i	0.984936	+	0.172917i	$0.0553193\pi$
$89$	6.05868	+	10.4939i	0.642219	+	1.11236i	−0.342718	+	0.939438i	$0.611347\pi$
$90$		0			0
$91$	1.66088	+	1.02801i	0.174108	+	0.107765i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.85404	+	2.22513i	−0.395416	+	0.228294i
$96$		0			0
$97$	10.9781	−	6.33821i	1.11466	−	0.643548i	0.174626	−	0.984635i	$-0.444128\pi$
$97$	10.9781	−	6.33821i	1.11466	−	0.643548i	0.940032	+	0.341087i	$0.110795\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	13.2437			1.31779			0.658897	−	0.752233i	$-0.271023\pi$
$101$	13.2437			1.31779			0.658897	+	0.752233i	$0.271023\pi$
$102$		0			0
$103$		−	13.1827i		−	1.29893i	−0.760391	−	0.649465i	$-0.774993\pi$
$103$		−	13.1827i		−	1.29893i	0.760391	−	0.649465i	$-0.225007\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.8800	+	9.16833i	−1.53518	+	0.886336i	−0.536069	+	0.844174i	$0.680091\pi$
$107$	−15.8800	+	9.16833i	−1.53518	+	0.886336i	−0.999111	+	0.0421621i	$0.986575\pi$
$108$		0			0
$109$	−8.74665	+	15.1496i	−0.837777	+	1.45107i	0.0539715	+	0.998542i	$0.482812\pi$
$109$	−8.74665	+	15.1496i	−0.837777	+	1.45107i	−0.891749	+	0.452531i	$0.850521\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.13627	+	2.38808i	0.389108	+	0.224652i	0.681774	−	0.731563i	$-0.261209\pi$
$113$	4.13627	+	2.38808i	0.389108	+	0.224652i	−0.292666	+	0.956215i	$0.594542\pi$
$114$		0			0
$115$		−	5.21491i		−	0.486293i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.93012	−	3.11836i	0.176934	−	0.285860i
$120$		0			0
$121$	9.55078			0.868252
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1211			0.994703
$126$		0			0
$127$	−4.81674			−0.427416			−0.213708	−	0.976898i	$-0.568554\pi$
$127$	−4.81674			−0.427416			−0.213708	+	0.976898i	$0.568554\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.14127			0.536566			0.268283	−	0.963340i	$-0.413544\pi$
$131$	6.14127			0.536566			0.268283	+	0.963340i	$0.413544\pi$
$132$		0			0
$133$	7.58063	−	4.07226i	0.657324	−	0.353110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			3.51935i			0.300678i	0.988634	+	0.150339i	$0.0480366\pi$
$137$			3.51935i			0.300678i	−0.988634	+	0.150339i	$0.951963\pi$
$138$		0			0
$139$	−12.6807	−	7.32119i	−1.07556	−	0.620975i	−0.145865	−	0.989304i	$-0.546597\pi$
$139$	−12.6807	−	7.32119i	−1.07556	−	0.620975i	−0.929695	+	0.368329i	$0.879930\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.444381	+	0.769691i	−0.0371610	+	0.0643648i
$144$		0			0
$145$	−4.78939	+	2.76515i	−0.397737	+	0.229633i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			14.8374i			1.21553i	0.794118	+	0.607763i	$0.207933\pi$
$149$			14.8374i			1.21553i	−0.794118	+	0.607763i	$0.792067\pi$
$150$		0			0
$151$	2.92894			0.238354			0.119177	−	0.992873i	$-0.461974\pi$
$151$	2.92894			0.238354			0.119177	+	0.992873i	$0.461974\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.40828	+	0.813072i	−0.113116	+	0.0653075i
$156$		0			0
$157$	−16.8177	+	9.70973i	−1.34220	+	0.774920i	−0.987130	−	0.159919i	$-0.948877\pi$
$157$	−16.8177	+	9.70973i	−1.34220	+	0.774920i	−0.355071	+	0.934839i	$0.615543\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.308926	+	10.0790i	−0.0243468	+	0.794336i
$162$		0			0
$163$	4.94115	+	8.55832i	0.387021	+	0.670340i	0.992047	−	0.125866i	$-0.0401709\pi$
$163$	4.94115	+	8.55832i	0.387021	+	0.670340i	−0.605027	+	0.796205i	$0.706838\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.58375	−	16.5995i	0.741613	−	1.28451i	−0.210148	−	0.977670i	$-0.567395\pi$
$167$	9.58375	−	16.5995i	0.741613	−	1.28451i	0.951761	−	0.306841i	$-0.0992721\pi$
$168$		0			0
$169$	−6.22748	−	10.7863i	−0.479037	−	0.829716i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.88299	+	3.26143i	−0.143161	+	0.247962i	−0.928685	−	0.370869i	$-0.879060\pi$
$173$	−1.88299	+	3.26143i	−0.143161	+	0.247962i	0.785524	+	0.618831i	$0.212393\pi$
$174$		0			0
$175$	−8.27153	−	0.253526i	−0.625269	−	0.0191648i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−22.7425	−	13.1304i	−1.69986	−	0.981412i	−0.945884	−	0.324504i	$-0.894802\pi$
$179$	−22.7425	−	13.1304i	−1.69986	−	0.981412i	−0.753971	−	0.656908i	$-0.771864\pi$
$180$		0			0
$181$		−	7.60186i		−	0.565042i	−0.959261	−	0.282521i	$-0.908829\pi$
$181$		−	7.60186i		−	0.565042i	0.959261	−	0.282521i	$-0.0911706\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.98557	−	12.0994i	−0.513589	−	0.889562i
$186$		0			0
$187$	1.44512	+	0.834339i	0.105677	+	0.0610129i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.2060	−	9.35655i	−1.17263	−	0.677016i	−0.218329	−	0.975875i	$-0.570061\pi$
$191$	−16.2060	−	9.35655i	−1.17263	−	0.677016i	−0.954297	+	0.298859i	$0.903394\pi$
$192$		0			0
$193$	−6.82526	−	11.8217i	−0.491293	−	0.850945i	0.508657	−	0.860969i	$-0.330142\pi$
$193$	−6.82526	−	11.8217i	−0.491293	−	0.850945i	−0.999950	+	0.0100249i	$0.996809\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	16.3308i		−	1.16352i	−0.813361	−	0.581760i	$-0.802364\pi$
$197$		−	16.3308i		−	1.16352i	0.813361	−	0.581760i	$-0.197636\pi$
$198$		0			0
$199$	10.3429	+	5.97146i	0.733186	+	0.423305i	0.819587	−	0.572955i	$-0.194203\pi$
$199$	10.3429	+	5.97146i	0.733186	+	0.423305i	−0.0864004	+	0.996260i	$0.527536\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.42038	−	5.06057i	0.661181	−	0.355182i
$204$		0			0
$205$	−0.917549	+	1.58924i	−0.0640844	+	0.110997i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.95771	+	3.39086i	0.135418	+	0.234551i
$210$		0			0
$211$	−8.33236	+	14.4321i	−0.573623	+	0.993544i	0.422567	+	0.906332i	$0.361129\pi$
$211$	−8.33236	+	14.4321i	−0.573623	+	0.993544i	−0.996190	+	0.0872125i	$0.972204\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.670517	+	1.16137i	0.0457289	+	0.0792048i
$216$		0			0
$217$	2.76999	−	1.48802i	0.188039	−	0.101014i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.886244	−	0.511673i	0.0596152	−	0.0344188i
$222$		0			0
$223$	2.30524	−	1.33093i	0.154370	−	0.0891258i	−0.420825	−	0.907142i	$-0.638259\pi$
$223$	2.30524	−	1.33093i	0.154370	−	0.0891258i	0.575195	+	0.818016i	$0.304926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.68069			−0.310669			−0.155334	−	0.987862i	$-0.549645\pi$
$227$	−4.68069			−0.310669			−0.155334	+	0.987862i	$0.549645\pi$
$228$		0			0
$229$			4.29143i			0.283586i	0.989896	+	0.141793i	$0.0452867\pi$
$229$			4.29143i			0.283586i	−0.989896	+	0.141793i	$0.954713\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00156	+	1.73295i	−0.196639	+	0.113530i	−0.595087	−	0.803661i	$-0.702882\pi$
$233$	−3.00156	+	1.73295i	−0.196639	+	0.113530i	0.398448	+	0.917191i	$0.369549\pi$
$234$		0			0
$235$	−2.23896	+	3.87800i	−0.146054	+	0.252973i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−22.5074	−	12.9946i	−1.45588	−	0.840554i	−0.457077	−	0.889427i	$-0.651104\pi$
$239$	−22.5074	−	12.9946i	−1.45588	−	0.840554i	−0.998805	+	0.0488730i	$0.984437\pi$
$240$		0			0
$241$			14.7470i			0.949939i	0.880002	+	0.474970i	$0.157541\pi$
$241$			14.7470i			0.949939i	−0.880002	+	0.474970i	$0.842459\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.55997	−	0.586586i	−0.610764	−	0.0374756i
$246$		0			0
$247$	2.40120			0.152785
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.2564			0.836734			0.418367	−	0.908278i	$-0.362603\pi$
$251$	13.2564			0.836734			0.418367	+	0.908278i	$0.362603\pi$
$252$		0			0
$253$	−4.58818			−0.288456
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.9917			−1.55894			−0.779471	−	0.626438i	$-0.784512\pi$
$257$	−24.9917			−1.55894			−0.779471	+	0.626438i	$0.784512\pi$
$258$		0			0
$259$	12.7844	+	23.7986i	0.794386	+	1.47877i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			14.5621i			0.897940i	0.893547	+	0.448970i	$0.148209\pi$
$263$			14.5621i			0.897940i	−0.893547	+	0.448970i	$0.851791\pi$
$264$		0			0
$265$	−7.90073	−	4.56149i	−0.485338	−	0.280210i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.64288	−	14.9699i	0.526966	−	0.912731i	−0.472540	−	0.881309i	$-0.656663\pi$
$269$	8.64288	−	14.9699i	0.526966	−	0.912731i	0.999506	−	0.0314225i	$-0.0100037\pi$
$270$		0			0
$271$	3.37299	−	1.94740i	0.204895	−	0.118296i	−0.394042	−	0.919092i	$-0.628924\pi$
$271$	3.37299	−	1.94740i	0.204895	−	0.118296i	0.598936	+	0.800797i	$0.295590\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	3.76538i		−	0.227061i
$276$		0			0
$277$	19.7457			1.18641			0.593203	−	0.805053i	$-0.297863\pi$
$277$	19.7457			1.18641			0.593203	+	0.805053i	$0.297863\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.41396	−	0.816352i	0.0843499	−	0.0486994i	−0.457232	−	0.889348i	$-0.651159\pi$
$281$	1.41396	−	0.816352i	0.0843499	−	0.0486994i	0.541582	+	0.840648i	$0.317826\pi$
$282$		0			0
$283$	−23.1548	+	13.3684i	−1.37641	+	0.794671i	−0.991726	−	0.128376i	$-0.959023\pi$
$283$	−23.1548	+	13.3684i	−1.37641	+	0.794671i	−0.384686	+	0.923048i	$0.625690\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.86752	−	3.01722i	0.110236	−	0.178101i
$288$		0			0
$289$	7.53932	+	13.0585i	0.443489	+	0.768146i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.68847	−	9.85271i	0.332324	−	0.575602i	−0.650643	−	0.759383i	$-0.725501\pi$
$293$	5.68847	−	9.85271i	0.332324	−	0.575602i	0.982967	+	0.183782i	$0.0588340\pi$
$294$		0			0
$295$	−9.22100	−	15.9712i	−0.536867	−	0.929882i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.40689	+	2.43681i	−0.0813626	+	0.140924i
$300$		0			0
$301$	−1.22713	−	2.28433i	−0.0707305	−	0.131667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.96662	+	3.44483i	0.341647	+	0.197250i
$306$		0			0
$307$		−	19.4683i		−	1.11111i	−0.831479	−	0.555556i	$-0.812505\pi$
$307$		−	19.4683i		−	1.11111i	0.831479	−	0.555556i	$-0.187495\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.0992	−	19.2243i	−0.629375	−	1.09011i	−0.987677	−	0.156504i	$-0.949978\pi$
$311$	−11.0992	−	19.2243i	−0.629375	−	1.09011i	0.358302	−	0.933606i	$-0.383356\pi$
$312$		0			0
$313$	−12.1557	−	7.01812i	−0.687083	−	0.396688i	0.115435	−	0.993315i	$-0.463174\pi$
$313$	−12.1557	−	7.01812i	−0.687083	−	0.396688i	−0.802518	+	0.596627i	$0.796507\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.2557	−	6.49848i	−0.632183	−	0.364991i	0.149414	−	0.988775i	$-0.452261\pi$
$317$	−11.2557	−	6.49848i	−0.632183	−	0.364991i	−0.781597	+	0.623784i	$0.785595\pi$
$318$		0			0
$319$	2.43283	+	4.21379i	0.136212	+	0.235927i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	4.50833i		−	0.250850i
$324$		0			0
$325$	−1.99981	−	1.15459i	−0.110930	−	0.0640453i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.55703	−	7.36248i	0.251237	−	0.405906i
$330$		0			0
$331$	−6.26139	+	10.8451i	−0.344157	+	0.596098i	−0.985200	−	0.171407i	$-0.945169\pi$
$331$	−6.26139	+	10.8451i	−0.344157	+	0.596098i	0.641043	+	0.767505i	$0.278502\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.00563	+	5.20590i	0.164215	+	0.284429i
$336$		0			0
$337$	−10.9647	+	18.9915i	−0.597287	+	1.03453i	0.395933	+	0.918279i	$0.370421\pi$
$337$	−10.9647	+	18.9915i	−0.597287	+	1.03453i	−0.993220	+	0.116251i	$0.962912\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.715356	+	1.23903i	0.0387387	+	0.0670974i
$342$		0			0
$343$	18.4421	+	1.70003i	0.995778	+	0.0917932i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.33668	−	0.771734i	0.0717569	−	0.0414288i	−0.463692	−	0.885996i	$-0.653476\pi$
$347$	1.33668	−	0.771734i	0.0717569	−	0.0414288i	0.535449	+	0.844567i	$0.320142\pi$
$348$		0			0
$349$	5.10876	−	2.94954i	0.273465	−	0.157885i	−0.356996	−	0.934106i	$-0.616199\pi$
$349$	5.10876	−	2.94954i	0.273465	−	0.157885i	0.630461	+	0.776221i	$0.282866\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.3268			−0.656091			−0.328046	−	0.944662i	$-0.606390\pi$
$353$	−12.3268			−0.656091			−0.328046	+	0.944662i	$0.606390\pi$
$354$		0			0
$355$			12.1030i			0.642358i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.03896	−	2.33189i	0.213168	−	0.123073i	−0.389615	−	0.920978i	$-0.627392\pi$
$359$	4.03896	−	2.33189i	0.213168	−	0.123073i	0.602783	+	0.797905i	$0.294059\pi$
$360$		0			0
$361$	−4.21077	+	7.29327i	−0.221619	+	0.383856i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.0850	−	8.13195i	−0.737240	−	0.425646i
$366$		0			0
$367$		−	23.4243i		−	1.22274i	−0.791345	−	0.611370i	$-0.790619\pi$
$367$		−	23.4243i		−	1.22274i	0.791345	−	0.611370i	$-0.209381\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.9997	+	9.28414i	0.778747	+	0.482008i
$372$		0			0
$373$	−12.0306			−0.622923			−0.311461	−	0.950259i	$-0.600818\pi$
$373$	−12.0306			−0.622923			−0.311461	+	0.950259i	$0.600818\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.98396			0.153682
$378$		0			0
$379$	−31.6065			−1.62352			−0.811758	−	0.583994i	$-0.801489\pi$
$379$	−31.6065			−1.62352			−0.811758	+	0.583994i	$0.801489\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	22.2570			1.13728			0.568641	−	0.822586i	$-0.307470\pi$
$383$	22.2570			1.13728			0.568641	+	0.822586i	$0.307470\pi$
$384$		0			0
$385$	0.133513	−	4.35600i	0.00680447	−	0.222002i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	35.5575i		−	1.80283i	−0.432951	−	0.901417i	$-0.642528\pi$
$389$		−	35.5575i		−	1.80283i	0.432951	−	0.901417i	$-0.357472\pi$
$390$		0			0
$391$	4.57517	+	2.64148i	0.231376	+	0.133585i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.68582	+	15.0443i	−0.437031	+	0.756960i
$396$		0			0
$397$	−5.16204	+	2.98030i	−0.259075	+	0.149577i	−0.623913	−	0.781494i	$-0.714458\pi$
$397$	−5.16204	+	2.98030i	−0.259075	+	0.149577i	0.364837	+	0.931071i	$0.381125\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			19.1472i			0.956165i	0.878315	+	0.478083i	$0.158668\pi$
$401$			19.1472i			0.956165i	−0.878315	+	0.478083i	$0.841332\pi$
$402$		0			0
$403$	0.877410			0.0437069
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.6452	+	6.14603i	−0.527665	+	0.304647i
$408$		0			0
$409$	−8.83357	+	5.10006i	−0.436792	+	0.252182i	−0.702236	−	0.711944i	$-0.747815\pi$
$409$	−8.83357	+	5.10006i	−0.436792	+	0.252182i	0.265444	+	0.964126i	$0.414481\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.8756	+	31.4143i	0.830392	+	1.54580i
$414$		0			0
$415$	−4.29939	−	7.44676i	−0.211049	−	0.365547i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.14385	+	5.44530i	−0.153587	+	0.266021i	−0.932544	−	0.361057i	$-0.882416\pi$
$419$	−3.14385	+	5.44530i	−0.153587	+	0.266021i	0.778957	+	0.627078i	$0.215749\pi$
$420$		0			0
$421$	−1.14723	−	1.98705i	−0.0559123	−	0.0968430i	0.836714	−	0.547639i	$-0.184473\pi$
$421$	−1.14723	−	1.98705i	−0.0559123	−	0.0968430i	−0.892627	+	0.450796i	$0.851140\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.16778	+	3.75471i	−0.105153	+	0.182130i
$426$		0			0
$427$	−11.3278	−	7.01137i	−0.548189	−	0.339304i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−19.3251	−	11.1574i	−0.930859	−	0.537432i	−0.0437761	−	0.999041i	$-0.513939\pi$
$431$	−19.3251	−	11.1574i	−0.930859	−	0.537432i	−0.887083	+	0.461610i	$0.847272\pi$
$432$		0			0
$433$		−	36.2306i		−	1.74113i	−0.492053	−	0.870565i	$-0.663753\pi$
$433$		−	36.2306i		−	1.74113i	0.492053	−	0.870565i	$-0.336247\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.19803	+	10.7353i	0.296492	+	0.513539i
$438$		0			0
$439$	−15.6320	−	9.02511i	−0.746072	−	0.430745i	0.0782007	−	0.996938i	$-0.475083\pi$
$439$	−15.6320	−	9.02511i	−0.746072	−	0.430745i	−0.824273	+	0.566193i	$0.808416\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.7590	−	6.21170i	−0.511174	−	0.295127i	0.222142	−	0.975014i	$-0.428695\pi$
$443$	−10.7590	−	6.21170i	−0.511174	−	0.295127i	−0.733316	+	0.679888i	$0.762029\pi$
$444$		0			0
$445$	−8.28996	−	14.3586i	−0.392982	−	0.680665i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.5762i		−	0.923858i	−0.886917	−	0.461929i	$-0.847158\pi$
$449$		−	19.5762i		−	0.923858i	0.886917	−	0.461929i	$-0.152842\pi$
$450$		0			0
$451$	1.39824	+	0.807277i	0.0658407	+	0.0380132i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.27255	−	1.40661i	−0.106539	−	0.0659427i
$456$		0			0
$457$	−11.8799	+	20.5765i	−0.555717	+	0.962530i	0.442131	+	0.896951i	$0.354223\pi$
$457$	−11.8799	+	20.5765i	−0.555717	+	0.962530i	−0.997847	+	0.0655789i	$0.979111\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.6541	−	18.4535i	−0.496213	−	0.859466i	0.503778	−	0.863833i	$-0.331943\pi$
$461$	−10.6541	−	18.4535i	−0.496213	−	0.859466i	−0.999990	+	0.00436764i	$0.998610\pi$
$462$		0			0
$463$	8.72943	−	15.1198i	0.405691	−	0.702677i	−0.588711	−	0.808344i	$-0.700364\pi$
$463$	8.72943	−	15.1198i	0.405691	−	0.702677i	0.994402	+	0.105667i	$0.0336977\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.11806	−	8.86473i	−0.236835	−	0.410211i	0.722969	−	0.690880i	$-0.242777\pi$
$467$	−5.11806	−	8.86473i	−0.236835	−	0.410211i	−0.959804	+	0.280669i	$0.909444\pi$
$468$		0			0
$469$	−5.50067	−	10.2396i	−0.253997	−	0.472823i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.02179	−	0.589933i	0.0469822	−	0.0271252i
$474$		0			0
$475$	−8.81014	+	5.08654i	−0.404237	+	0.233386i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.1247			−0.691063			−0.345531	−	0.938407i	$-0.612301\pi$
$479$	−15.1247			−0.691063			−0.345531	+	0.938407i	$0.612301\pi$
$480$		0			0
$481$			7.53832i			0.343718i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.0211	+	8.67244i	−0.682074	+	0.393795i
$486$		0			0
$487$	−17.3450	+	30.0425i	−0.785979	+	1.36136i	0.142433	+	0.989804i	$0.454507\pi$
$487$	−17.3450	+	30.0425i	−0.785979	+	1.36136i	−0.928412	+	0.371551i	$0.878826\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.2050	+	6.46922i	0.505676	+	0.291952i	0.731054	−	0.682319i	$-0.239029\pi$
$491$	11.2050	+	6.46922i	0.505676	+	0.291952i	−0.225379	+	0.974271i	$0.572362\pi$
$492$		0			0
$493$		−	5.60247i		−	0.252322i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.716966	−	23.3917i	0.0321603	−	1.04926i
$498$		0			0
$499$	−7.04669			−0.315453			−0.157727	−	0.987483i	$-0.550416\pi$
$499$	−7.04669			−0.315453			−0.157727	+	0.987483i	$0.550416\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	36.3853			1.62234			0.811170	−	0.584810i	$-0.198831\pi$
$503$	36.3853			1.62234			0.811170	+	0.584810i	$0.198831\pi$
$504$		0			0
$505$	−18.1210			−0.806376
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−36.7611			−1.62941			−0.814704	−	0.579877i	$-0.803101\pi$
$509$	−36.7611			−1.62941			−0.814704	+	0.579877i	$0.803101\pi$
$510$		0			0
$511$	26.7406	+	16.5512i	1.18294	+	0.732183i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			18.0376i			0.794832i
$516$		0			0
$517$	3.41193	+	1.96988i	0.150057	+	0.0866353i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.9686	+	24.1943i	−0.611976	+	1.05997i	0.378931	+	0.925425i	$0.376292\pi$
$521$	−13.9686	+	24.1943i	−0.611976	+	1.05997i	−0.990907	+	0.134548i	$0.957042\pi$
$522$		0			0
$523$	15.0082	−	8.66497i	0.656261	−	0.378893i	−0.134590	−	0.990901i	$-0.542972\pi$
$523$	15.0082	−	8.66497i	0.656261	−	0.378893i	0.790851	+	0.612009i	$0.209638\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	1.64736i		−	0.0717603i
$528$		0			0
$529$	8.47405			0.368437
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.857498	−	0.495077i	0.0371424	−	0.0214442i
$534$		0			0
$535$	21.7283	−	12.5448i	0.939396	−	0.542361i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.516089	+	8.41104i	−0.0222295	+	0.362289i
$540$		0			0
$541$	5.30043	+	9.18061i	0.227883	+	0.394705i	0.957181	−	0.289491i	$-0.0934862\pi$
$541$	5.30043	+	9.18061i	0.227883	+	0.394705i	−0.729297	+	0.684197i	$0.760153\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.9679	−	20.7289i	0.512647	−	0.887930i
$546$		0			0
$547$	−8.55403	−	14.8160i	−0.365744	−	0.633487i	0.623151	−	0.782101i	$-0.285852\pi$
$547$	−8.55403	−	14.8160i	−0.365744	−	0.633487i	−0.988895	+	0.148614i	$0.952519\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.57288	−	11.3846i	0.280014	−	0.484999i
$552$		0			0
$553$	17.6785	−	28.5620i	0.751768	−	1.21458i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.02890	−	1.17139i	−0.0859673	−	0.0496333i	0.456400	−	0.889775i	$-0.349139\pi$
$557$	−2.02890	−	1.17139i	−0.0859673	−	0.0496333i	−0.542367	+	0.840141i	$0.682472\pi$
$558$		0			0
$559$		−	0.723574i		−	0.0306039i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	21.0507	+	36.4608i	0.887180	+	1.53664i	0.843194	+	0.537609i	$0.180672\pi$
$563$	21.0507	+	36.4608i	0.887180	+	1.53664i	0.0439857	+	0.999032i	$0.485994\pi$
$564$		0			0
$565$	−5.65958	−	3.26756i	−0.238100	−	0.137467i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	35.0375	+	20.2289i	1.46885	+	0.848040i	0.999390	−	0.0349152i	$-0.0111161\pi$
$569$	35.0375	+	20.2289i	1.46885	+	0.848040i	0.469458	+	0.882955i	$0.344449\pi$
$570$		0			0
$571$	−0.160538	−	0.278060i	−0.00671832	−	0.0116365i	0.862647	−	0.505807i	$-0.168805\pi$
$571$	−0.160538	−	0.278060i	−0.00671832	−	0.0116365i	−0.869365	+	0.494170i	$0.835472\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	11.9210i		−	0.497141i
$576$		0			0
$577$	20.9395	+	12.0894i	0.871721	+	0.503288i	0.867920	−	0.496704i	$-0.165457\pi$
$577$	20.9395	+	12.0894i	0.871721	+	0.503288i	0.00380123	+	0.999993i	$0.498790\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.86841	+	14.6472i	0.326436	+	0.607670i
$582$		0			0
$583$	−4.01328	+	6.95120i	−0.166213	+	0.287889i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.4257	+	24.9860i	0.595411	+	1.03128i	0.993489	+	0.113931i	$0.0363442\pi$
$587$	14.4257	+	24.9860i	0.595411	+	1.03128i	−0.398077	+	0.917352i	$0.630322\pi$
$588$		0			0
$589$	1.93271	−	3.34755i	0.0796358	−	0.137933i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.07472	−	1.86147i	−0.0441335	−	0.0764414i	0.843115	−	0.537734i	$-0.180719\pi$
$593$	−1.07472	−	1.86147i	−0.0441335	−	0.0764414i	−0.887248	+	0.461292i	$0.847386\pi$
$594$		0			0
$595$	−2.64094	+	4.26679i	−0.108268	+	0.174921i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.58798	−	3.22622i	0.228319	−	0.131820i	−0.381477	−	0.924378i	$-0.624585\pi$
$599$	5.58798	−	3.22622i	0.228319	−	0.131820i	0.609796	+	0.792558i	$0.291251\pi$
$600$		0			0
$601$	10.6341	−	6.13960i	0.433774	−	0.250439i	−0.267179	−	0.963647i	$-0.586092\pi$
$601$	10.6341	−	6.13960i	0.433774	−	0.250439i	0.700953	+	0.713207i	$0.252758\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.0681			−0.531295
$606$		0			0
$607$			38.3682i			1.55732i	0.627448	+	0.778658i	$0.284099\pi$
$607$			38.3682i			1.55732i	−0.627448	+	0.778658i	$0.715901\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.09243	−	1.20806i	0.0846506	−	0.0488731i
$612$		0			0
$613$	6.96098	−	12.0568i	0.281151	−	0.486969i	−0.690517	−	0.723316i	$-0.742617\pi$
$613$	6.96098	−	12.0568i	0.281151	−	0.486969i	0.971669	+	0.236347i	$0.0759503\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.0193	−	8.67142i	−0.604656	−	0.349098i	0.166215	−	0.986090i	$-0.446845\pi$
$617$	−15.0193	−	8.67142i	−0.604656	−	0.349098i	−0.770871	+	0.636991i	$0.780179\pi$
$618$		0			0
$619$		−	29.6508i		−	1.19177i	−0.803071	−	0.595884i	$-0.796802\pi$
$619$		−	29.6508i		−	1.19177i	0.803071	−	0.595884i	$-0.203198\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.1716	+	28.2424i	0.607839	+	1.13151i
$624$		0			0
$625$	0.422282			0.0168913
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.1534			0.564334
$630$		0			0
$631$	−16.6402			−0.662437			−0.331218	−	0.943554i	$-0.607460\pi$
$631$	−16.6402			−0.662437			−0.331218	+	0.943554i	$0.607460\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.59064			0.261541
$636$		0			0
$637$	4.30890	+	2.85321i	0.170725	+	0.113048i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	15.5930i		−	0.615888i	−0.951404	−	0.307944i	$-0.900359\pi$
$641$		−	15.5930i		−	0.615888i	0.951404	−	0.307944i	$-0.0996410\pi$
$642$		0			0
$643$	13.7474	+	7.93708i	0.542146	+	0.313008i	0.745948	−	0.666004i	$-0.231997\pi$
$643$	13.7474	+	7.93708i	0.542146	+	0.313008i	−0.203802	+	0.979012i	$0.565330\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.18164	+	2.04666i	−0.0464549	+	0.0804623i	−0.888318	−	0.459229i	$-0.848126\pi$
$647$	−1.18164	+	2.04666i	−0.0464549	+	0.0804623i	0.841863	+	0.539691i	$0.181459\pi$
$648$		0			0
$649$	−14.0518	+	8.11281i	−0.551581	+	0.318455i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			18.6821i			0.731088i	0.930794	+	0.365544i	$0.119117\pi$
$653$			18.6821i			0.731088i	−0.930794	+	0.365544i	$0.880883\pi$
$654$		0			0
$655$	−8.40297			−0.328331
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.5543	−	10.1350i	0.683819	−	0.394803i	−0.117473	−	0.993076i	$-0.537479\pi$
$659$	17.5543	−	10.1350i	0.683819	−	0.394803i	0.801293	+	0.598273i	$0.204146\pi$
$660$		0			0
$661$	27.1506	−	15.6754i	1.05604	−	0.609703i	0.131704	−	0.991289i	$-0.457955\pi$
$661$	27.1506	−	15.6754i	1.05604	−	0.609703i	0.924333	+	0.381586i	$0.124622\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.3724	+	5.57199i	−0.402225	+	0.216073i
$666$		0			0
$667$	7.70224	+	13.3407i	0.298232	+	0.516553i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.03082	−	5.24954i	0.117004	−	0.202656i
$672$		0			0
$673$	9.49210	+	16.4408i	0.365893	+	0.633746i	0.988919	−	0.148455i	$-0.0474301\pi$
$673$	9.49210	+	16.4408i	0.365893	+	0.633746i	−0.623026	+	0.782201i	$0.714097\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.8417	−	22.2424i	0.493545	−	0.854845i	−0.506427	−	0.862283i	$-0.669034\pi$
$677$	12.8417	−	22.2424i	0.493545	−	0.854845i	0.999972	+	0.00743750i	$0.00236745\pi$
$678$		0			0
$679$	29.5455	−	15.8716i	1.13385	−	0.609097i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	32.2147	+	18.5992i	1.23266	+	0.711677i	0.967584	−	0.252550i	$-0.0812691\pi$
$683$	32.2147	+	18.5992i	1.23266	+	0.711677i	0.265078	+	0.964227i	$0.414602\pi$
$684$		0			0
$685$		−	4.81545i		−	0.183989i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.46122	+	4.26295i	0.0937648	+	0.162405i
$690$		0			0
$691$	38.8499	+	22.4300i	1.47792	+	0.853277i	0.999689	−	0.0249572i	$-0.00794496\pi$
$691$	38.8499	+	22.4300i	1.47792	+	0.853277i	0.478231	+	0.878234i	$0.341278\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.3507	+	10.0174i	0.658150	+	0.379983i
$696$		0			0
$697$	−0.929521	−	1.60998i	−0.0352081	−	0.0609823i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	26.0630i		−	0.984387i	−0.870486	−	0.492194i	$-0.836195\pi$
$701$		−	26.0630i		−	0.984387i	0.870486	−	0.492194i	$-0.163805\pi$
$702$		0			0
$703$	28.7607	+	16.6050i	1.08473	+	0.626269i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	35.0230	+	1.07347i	1.31718	+	0.0403721i
$708$		0			0
$709$	−16.6461	+	28.8319i	−0.625158	+	1.08281i	0.363352	+	0.931652i	$0.381632\pi$
$709$	−16.6461	+	28.8319i	−0.625158	+	1.08281i	−0.988510	+	0.151154i	$0.951701\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.26478	+	3.92272i	0.0848169	+	0.146907i
$714$		0			0
$715$	0.608037	−	1.05315i	0.0227393	−	0.0393856i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.3474	−	42.1709i	−0.908003	−	1.57271i	−0.816834	−	0.576872i	$-0.804273\pi$
$719$	−24.3474	−	42.1709i	−0.908003	−	1.57271i	−0.0911690	−	0.995835i	$-0.529060\pi$
$720$		0			0
$721$	1.06853	−	34.8618i	0.0397941	−	1.29832i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.9483	+	6.32099i	−0.406609	+	0.234756i
$726$		0			0
$727$	−8.76540	+	5.06071i	−0.325091	+	0.187691i	−0.653659	−	0.756789i	$-0.726767\pi$
$727$	−8.76540	+	5.06071i	−0.325091	+	0.187691i	0.328569	+	0.944480i	$0.393434\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.35853			−0.0502471
$732$		0			0
$733$		−	18.6611i		−	0.689262i	−0.938738	−	0.344631i	$-0.888004\pi$
$733$		−	18.6611i		−	0.689262i	0.938738	−	0.344631i	$-0.111996\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.58025	−	2.64441i	0.168716	−	0.0974081i
$738$		0			0
$739$	−13.5646	+	23.4946i	−0.498983	+	0.864264i	−0.999999	−	0.00117395i	$-0.999626\pi$
$739$	−13.5646	+	23.4946i	−0.498983	+	0.864264i	0.501016	+	0.865438i	$0.332960\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.9378	−	8.04698i	−0.511328	−	0.295215i	0.222052	−	0.975035i	$-0.428725\pi$
$743$	−13.9378	−	8.04698i	−0.511328	−	0.295215i	−0.733379	+	0.679820i	$0.762058\pi$
$744$		0			0
$745$		−	20.3017i		−	0.743796i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−42.7380	+	22.9586i	−1.56161	+	0.838888i
$750$		0			0
$751$	47.6328			1.73815			0.869073	−	0.494683i	$-0.164716\pi$
$751$	47.6328			1.73815			0.869073	+	0.494683i	$0.164716\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.00761			−0.145852
$756$		0			0
$757$	50.4788			1.83468			0.917341	−	0.398102i	$-0.130331\pi$
$757$	50.4788			1.83468			0.917341	+	0.398102i	$0.130331\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.39506			−0.231821			−0.115910	−	0.993260i	$-0.536979\pi$
$761$	−6.39506			−0.231821			−0.115910	+	0.993260i	$0.536979\pi$
$762$		0			0
$763$	−24.3586	+	39.3544i	−0.881839	+	1.42473i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			9.95065i			0.359297i
$768$		0			0
$769$	21.1676	+	12.2211i	0.763322	+	0.440704i	0.830487	−	0.557038i	$-0.188062\pi$
$769$	21.1676	+	12.2211i	0.763322	+	0.440704i	−0.0671654	+	0.997742i	$0.521396\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.32573	+	14.4206i	−0.299456	+	0.518672i	−0.976011	−	0.217719i	$-0.930138\pi$
$773$	−8.32573	+	14.4206i	−0.299456	+	0.518672i	0.676556	+	0.736391i	$0.263472\pi$
$774$		0			0
$775$	−3.21926	+	1.85864i	−0.115639	+	0.0667643i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	4.36210i		−	0.156289i
$780$		0			0
$781$	10.6484			0.381030
$782$		0			0
$783$		0			0
$784$		0			0
$785$	23.0114	−	13.2856i	0.821310	−	0.474184i
$786$		0			0
$787$	1.21582	−	0.701955i	0.0433394	−	0.0250220i	−0.478174	−	0.878265i	$-0.658701\pi$
$787$	1.21582	−	0.701955i	0.0433394	−	0.0250220i	0.521513	+	0.853243i	$0.325368\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.7448	+	6.65056i	0.382043	+	0.236467i
$792$		0			0
$793$	−1.85871	−	3.21937i	−0.0660046	−	0.114323i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.7211	+	25.4977i	−0.521448	+	0.903174i	0.478241	+	0.878229i	$0.341274\pi$
$797$	−14.7211	+	25.4977i	−0.521448	+	0.903174i	−0.999689	+	0.0249452i	$0.992059\pi$
$798$		0			0
$799$	−2.26818	−	3.92860i	−0.0802423	−	0.138984i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.15464	+	12.3922i	−0.252482	+	0.437311i
$804$		0			0
$805$	0.422697	−	13.7909i	0.0148981	−	0.486065i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−41.2228	−	23.8000i	−1.44932	−	0.836764i	−0.450877	−	0.892586i	$-0.648889\pi$
$809$	−41.2228	−	23.8000i	−1.44932	−	0.836764i	−0.998441	+	0.0558222i	$0.982222\pi$
$810$		0			0
$811$		−	24.9460i		−	0.875973i	−0.898981	−	0.437987i	$-0.855692\pi$
$811$		−	24.9460i		−	0.875973i	0.898981	−	0.437987i	$-0.144308\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.76087	−	11.7102i	−0.236823	−	0.410189i
$816$		0			0
$817$	−2.76062	−	1.59385i	−0.0965820	−	0.0557616i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.91506	+	3.41506i	0.206437	+	0.119186i	0.599654	−	0.800259i	$-0.295305\pi$
$821$	5.91506	+	3.41506i	0.206437	+	0.119186i	−0.393218	+	0.919445i	$0.628638\pi$
$822$		0			0
$823$	−3.68905	−	6.38962i	−0.128592	−	0.222728i	0.794539	−	0.607213i	$-0.207712\pi$
$823$	−3.68905	−	6.38962i	−0.128592	−	0.222728i	−0.923131	+	0.384485i	$0.874379\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.1804i			0.736516i	0.929724	+	0.368258i	$0.120046\pi$
$827$			21.1804i			0.736516i	−0.929724	+	0.368258i	$0.879954\pi$
$828$		0			0
$829$	−1.60383	−	0.925970i	−0.0557032	−	0.0321603i	0.471890	−	0.881658i	$-0.343572\pi$
$829$	−1.60383	−	0.925970i	−0.0557032	−	0.0321603i	−0.527593	+	0.849497i	$0.676905\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.35698	−	8.09009i	0.185608	−	0.280305i
$834$		0			0
$835$	−13.1132	+	22.7128i	−0.453802	+	0.786009i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.90568	−	13.6930i	−0.272934	−	0.472736i	0.696678	−	0.717384i	$-0.254661\pi$
$839$	−7.90568	−	13.6930i	−0.272934	−	0.472736i	−0.969612	+	0.244648i	$0.921328\pi$
$840$		0			0
$841$	−6.33194	+	10.9672i	−0.218343	+	0.378181i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.52092	+	14.7587i	0.293129	+	0.507714i
$846$		0			0
$847$	25.2571	+	0.774142i	0.867845	+	0.0265998i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−33.7023	+	19.4581i	−1.15530	+	0.667013i
$852$		0			0
$853$	−8.16324	+	4.71305i	−0.279504	+	0.161372i	−0.633199	−	0.773989i	$-0.718258\pi$
$853$	−8.16324	+	4.71305i	−0.279504	+	0.161372i	0.353695	+	0.935361i	$0.384925\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.8222			1.05287			0.526433	−	0.850217i	$-0.323529\pi$
$857$	30.8222			1.05287			0.526433	+	0.850217i	$0.323529\pi$
$858$		0			0
$859$		−	1.53925i		−	0.0525185i	−0.999655	−	0.0262592i	$-0.991640\pi$
$859$		−	1.53925i		−	0.0525185i	0.999655	−	0.0262592i	$-0.00835953\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.645937	−	0.372932i	0.0219879	−	0.0126947i	−0.488966	−	0.872303i	$-0.662626\pi$
$863$	0.645937	−	0.372932i	0.0219879	−	0.0126947i	0.510954	+	0.859608i	$0.329292\pi$
$864$		0			0
$865$	2.57645	−	4.46255i	0.0876020	−	0.151731i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.2362	+	7.64195i	0.449009	+	0.259235i
$870$		0			0
$871$		−	3.24346i		−	0.109901i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	29.4099	+	0.901427i	0.994236	+	0.0304738i
$876$		0			0
$877$	3.47691			0.117407			0.0587034	−	0.998275i	$-0.481303\pi$
$877$	3.47691			0.117407			0.0587034	+	0.998275i	$0.481303\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−49.4437			−1.66580			−0.832900	−	0.553424i	$-0.813321\pi$
$881$	−49.4437			−1.66580			−0.832900	+	0.553424i	$0.813321\pi$
$882$		0			0
$883$	3.02160			0.101685			0.0508424	−	0.998707i	$-0.483809\pi$
$883$	3.02160			0.101685			0.0508424	+	0.998707i	$0.483809\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	35.5134			1.19242			0.596212	−	0.802827i	$-0.296672\pi$
$887$	35.5134			1.19242			0.596212	+	0.802827i	$0.296672\pi$
$888$		0			0
$889$	−12.7379	−	0.390423i	−0.427216	−	0.0130944i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	10.6442i		−	0.356195i
$894$		0			0
$895$	31.1181	+	17.9660i	1.04016	+	0.600539i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.40176	−	4.15997i	0.0801031	−	0.138743i
$900$		0			0
$901$	8.00381	−	4.62100i	0.266646	−	0.153948i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			10.4015i			0.345756i
$906$		0			0
$907$	−16.1292			−0.535561			−0.267781	−	0.963480i	$-0.586290\pi$
$907$	−16.1292			−0.535561			−0.267781	+	0.963480i	$0.586290\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.7485	+	9.66977i	−0.554903	+	0.320374i	−0.751097	−	0.660191i	$-0.770475\pi$
$911$	−16.7485	+	9.66977i	−0.554903	+	0.320374i	0.196194	+	0.980565i	$0.437142\pi$
$912$		0			0
$913$	−6.55180	+	3.78268i	−0.216833	+	0.125188i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.2407	+	0.497784i	0.536314	+	0.0164383i
$918$		0			0
$919$	−18.3378	−	31.7620i	−0.604908	−	1.04773i	−0.992066	−	0.125718i	$-0.959876\pi$
$919$	−18.3378	−	31.7620i	−0.604908	−	1.04773i	0.387158	−	0.922014i	$-0.373457\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.26516	−	5.65542i	0.107474	−	0.186151i
$924$		0			0
$925$	−15.9686	−	27.6585i	−0.525046	−	0.909405i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.4172	−	21.5073i	0.407397	−	0.705632i	−0.587200	−	0.809442i	$-0.699770\pi$
$929$	12.4172	−	21.5073i	0.407397	−	0.705632i	0.994597	+	0.103810i	$0.0331033\pi$
$930$		0			0
$931$	20.3771	−	10.1547i	0.667833	−	0.332807i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.97732	−	1.14161i	−0.0646654	−	0.0373346i
$936$		0			0
$937$		−	53.1227i		−	1.73544i	−0.497050	−	0.867722i	$-0.665584\pi$
$937$		−	53.1227i		−	1.73544i	0.497050	−	0.867722i	$-0.334416\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.2471	+	29.8729i	0.562240	+	0.973829i	0.997301	+	0.0734277i	$0.0233938\pi$
$941$	17.2471	+	29.8729i	0.562240	+	0.973829i	−0.435060	+	0.900401i	$0.643273\pi$
$942$		0			0
$943$	4.42678	+	2.55580i	0.144156	+	0.0832283i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.2611	−	9.96572i	−0.560912	−	0.323842i	0.192600	−	0.981277i	$-0.438308\pi$
$947$	−17.2611	−	9.96572i	−0.560912	−	0.323842i	−0.753511	+	0.657435i	$0.771641\pi$
$948$		0			0
$949$	4.38771	+	7.59974i	0.142431	+	0.246698i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			37.0472i			1.20008i	0.799971	+	0.600039i	$0.204848\pi$
$953$			37.0472i			1.20008i	−0.799971	+	0.600039i	$0.795152\pi$
$954$		0			0
$955$	22.1744	+	12.8024i	0.717545	+	0.414275i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.285263	+	9.30696i	−0.00921161	+	0.300537i
$960$		0			0
$961$	−14.7938	+	25.6236i	−0.477219	+	0.826567i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.33886	+	16.1754i	0.300629	+	0.520704i
$966$		0			0
$967$	16.5292	−	28.6294i	0.531543	−	0.920659i	−0.467780	−	0.883845i	$-0.654946\pi$
$967$	16.5292	−	28.6294i	0.531543	−	0.920659i	0.999322	−	0.0368136i	$-0.0117208\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.1441	−	22.7662i	−0.421813	−	0.730602i	0.574304	−	0.818642i	$-0.305273\pi$
$971$	−13.1441	−	22.7662i	−0.421813	−	0.730602i	−0.996117	+	0.0880404i	$0.971940\pi$
$972$		0			0
$973$	−32.9407	−	20.3888i	−1.05603	−	0.653635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.7246	−	14.2748i	0.791011	−	0.456690i	−0.0493073	−	0.998784i	$-0.515701\pi$
$977$	24.7246	−	14.2748i	0.791011	−	0.456690i	0.840318	+	0.542093i	$0.182368\pi$
$978$		0			0
$979$	−12.6330	+	7.29366i	−0.403752	+	0.233106i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.12317			−0.0996138			−0.0498069	−	0.998759i	$-0.515861\pi$
$983$	−3.12317			−0.0996138			−0.0498069	+	0.998759i	$0.515861\pi$
$984$		0			0
$985$			22.3451i			0.711973i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.23496	−	1.86770i	0.102866	−	0.0593895i
$990$		0			0
$991$	−9.31103	+	16.1272i	−0.295775	+	0.512297i	−0.975165	−	0.221481i	$-0.928911\pi$
$991$	−9.31103	+	16.1272i	−0.295775	+	0.512297i	0.679390	+	0.733777i	$0.262244\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−14.1519	−	8.17062i	−0.448646	−	0.259026i
$996$		0			0
$997$		−	0.0372304i		−	0.00117910i	−1.00000		0.000589549i	$-0.999812\pi$
$997$		−	0.0372304i		−	0.00117910i	1.00000		0.000589549i	$-0.000187659\pi$
$998$		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.17.9		48
3.2	odd	2		504.2.cx.a.185.16	yes	48
4.3	odd	2		3024.2.df.e.17.9		48
7.5	odd	6		1512.2.bs.a.1097.9		48
9.2	odd	6		1512.2.bs.a.521.9		48
9.7	even	3		504.2.bs.a.353.24	yes	48
12.11	even	2		1008.2.df.e.689.9		48
21.5	even	6		504.2.bs.a.257.24	✓	48
28.19	even	6		3024.2.ca.e.2609.9		48
36.7	odd	6		1008.2.ca.e.353.1		48
36.11	even	6		3024.2.ca.e.2033.9		48
63.47	even	6	inner	1512.2.cx.a.89.9		48
63.61	odd	6		504.2.cx.a.425.16	yes	48
84.47	odd	6		1008.2.ca.e.257.1		48
252.47	odd	6		3024.2.df.e.1601.9		48
252.187	even	6		1008.2.df.e.929.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.24	✓	48	21.5	even	6
504.2.bs.a.353.24	yes	48	9.7	even	3
504.2.cx.a.185.16	yes	48	3.2	odd	2
504.2.cx.a.425.16	yes	48	63.61	odd	6
1008.2.ca.e.257.1		48	84.47	odd	6
1008.2.ca.e.353.1		48	36.7	odd	6
1008.2.df.e.689.9		48	12.11	even	2
1008.2.df.e.929.9		48	252.187	even	6
1512.2.bs.a.521.9		48	9.2	odd	6
1512.2.bs.a.1097.9		48	7.5	odd	6
1512.2.cx.a.17.9		48	1.1	even	1	trivial
1512.2.cx.a.89.9		48	63.47	even	6	inner
3024.2.ca.e.2033.9		48	36.11	even	6
3024.2.ca.e.2609.9		48	28.19	even	6
3024.2.df.e.17.9		48	4.3	odd	2
3024.2.df.e.1601.9		48	252.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q-1.36828 q^{5} +(2.64451 + 0.0810554i) q^{7} +1.20384i q^{11} +(0.639364 + 0.369137i) q^{13} +(0.693066 - 1.20043i) q^{17} +(2.81671 - 1.62623i) q^{19} +3.81129i q^{23} -3.12781 q^{25} +(3.50030 - 2.02090i) q^{29} +(1.02924 - 0.594230i) q^{31} +(-3.61843 - 0.110906i) q^{35} +(5.10537 + 8.84276i) q^{37} +(0.670586 - 1.16149i) q^{41} +(-0.490044 - 0.848782i) q^{43} +(1.63634 - 2.83422i) q^{47} +(6.98686 + 0.428704i) q^{49} +(5.77421 + 3.33374i) q^{53} -1.64718i q^{55} +(6.73912 + 11.6725i) q^{59} +(-4.36067 - 2.51764i) q^{61} +(-0.874829 - 0.505083i) q^{65} +(-2.19665 - 3.80471i) q^{67} -8.84538i q^{71} +(10.2939 + 5.94320i) q^{73} +(-0.0975775 + 3.18356i) q^{77} +(6.34799 - 10.9950i) q^{79} +(3.14219 + 5.44243i) q^{83} +(-0.948308 + 1.64252i) q^{85} +(6.05868 + 10.4939i) q^{89} +(1.66088 + 1.02801i) q^{91} +(-3.85404 + 2.22513i) q^{95} +(10.9781 - 6.33821i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 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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