LMFDB - Embedded newform 1512.2.bs.a.1097.13

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			1097.13
Character	$\chi$	$=$	1512.1097
Dual form			1512.2.bs.a.521.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.271038 + 0.469451i) q^{5} +(1.60655 - 2.10214i) q^{7} +(0.666300 + 0.384688i) q^{11} +(-2.96386 - 1.71119i) q^{13} +(3.23477 + 5.60278i) q^{17} +(5.60413 + 3.23554i) q^{19} +(-0.100353 + 0.0579388i) q^{23} +(2.35308 - 4.07565i) q^{25} +(-4.40174 + 2.54135i) q^{29} -4.63530i q^{31} +(1.42229 + 0.184434i) q^{35} +(5.47518 - 9.48329i) q^{37} +(4.04575 - 7.00745i) q^{41} +(3.32569 + 5.76026i) q^{43} -1.54617 q^{47} +(-1.83802 - 6.75438i) q^{49} +(0.221011 - 0.127601i) q^{53} +0.417060i q^{55} +10.2411 q^{59} +5.57913i q^{61} -1.85518i q^{65} -3.28349 q^{67} +5.67917i q^{71} +(-5.35354 + 3.09087i) q^{73} +(1.87911 - 0.782639i) q^{77} +4.02459 q^{79} +(5.80057 + 10.0469i) q^{83} +(-1.75349 + 3.03713i) q^{85} +(2.00832 - 3.47851i) q^{89} +(-8.35874 + 3.48136i) q^{91} +3.50781i q^{95} +(15.0653 - 8.69795i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.271038	+	0.469451i	0.121212	+	0.209945i	0.920246	−	0.391341i	$-0.127989\pi$
$5$	0.271038	+	0.469451i	0.121212	+	0.209945i	−0.799034	+	0.601286i	$0.794655\pi$
$6$		0			0
$7$	1.60655	−	2.10214i	0.607217	−	0.794536i
$7$	1.60655	−	2.10214i	0.607217	−	0.794536i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.666300	+	0.384688i	0.200897	+	0.115988i	0.597074	−	0.802186i	$-0.296330\pi$
$11$	0.666300	+	0.384688i	0.200897	+	0.115988i	−0.396177	+	0.918174i	$0.629663\pi$
$12$		0			0
$13$	−2.96386	−	1.71119i	−0.822027	−	0.474598i	0.0290877	−	0.999577i	$-0.490740\pi$
$13$	−2.96386	−	1.71119i	−0.822027	−	0.474598i	−0.851115	+	0.524979i	$0.824073\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.23477	+	5.60278i	0.784547	+	1.35887i	0.929269	+	0.369403i	$0.120438\pi$
$17$	3.23477	+	5.60278i	0.784547	+	1.35887i	−0.144723	+	0.989472i	$0.546229\pi$
$18$		0			0
$19$	5.60413	+	3.23554i	1.28567	+	0.742285i	0.977880	−	0.209168i	$-0.0670756\pi$
$19$	5.60413	+	3.23554i	1.28567	+	0.742285i	0.307795	+	0.951453i	$0.400409\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.100353	+	0.0579388i	−0.0209250	+	0.0120811i	−0.510426	−	0.859922i	$-0.670512\pi$
$23$	−0.100353	+	0.0579388i	−0.0209250	+	0.0120811i	0.489501	+	0.872003i	$0.337179\pi$
$24$		0			0
$25$	2.35308	−	4.07565i	0.470615	−	0.815130i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.40174	+	2.54135i	−0.817383	+	0.471916i	−0.849513	−	0.527568i	$-0.823104\pi$
$29$	−4.40174	+	2.54135i	−0.817383	+	0.471916i	0.0321304	+	0.999484i	$0.489771\pi$
$30$		0			0
$31$		−	4.63530i		−	0.832524i	−0.909245	−	0.416262i	$-0.863340\pi$
$31$		−	4.63530i		−	0.832524i	0.909245	−	0.416262i	$-0.136660\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.42229	+	0.184434i	0.240410	+	0.0311751i
$36$		0			0
$37$	5.47518	−	9.48329i	0.900114	−	1.55904i	0.0727692	−	0.997349i	$-0.476816\pi$
$37$	5.47518	−	9.48329i	0.900114	−	1.55904i	0.827345	−	0.561694i	$-0.189850\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.04575	−	7.00745i	0.631841	−	1.09438i	−0.355334	−	0.934739i	$-0.615633\pi$
$41$	4.04575	−	7.00745i	0.631841	−	1.09438i	0.987175	−	0.159641i	$-0.0510337\pi$
$42$		0			0
$43$	3.32569	+	5.76026i	0.507162	+	0.878431i	0.999966	+	0.00829006i	$0.00263884\pi$
$43$	3.32569	+	5.76026i	0.507162	+	0.878431i	−0.492803	+	0.870141i	$0.664028\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.54617			−0.225532			−0.112766	−	0.993622i	$-0.535971\pi$
$47$	−1.54617			−0.225532			−0.112766	+	0.993622i	$0.535971\pi$
$48$		0			0
$49$	−1.83802	−	6.75438i	−0.262574	−	0.964912i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.221011	−	0.127601i	0.0303582	−	0.0175273i	−0.484744	−	0.874656i	$-0.661087\pi$
$53$	0.221011	−	0.127601i	0.0303582	−	0.0175273i	0.515102	+	0.857129i	$0.327754\pi$
$54$		0			0
$55$			0.417060i			0.0562364i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	10.2411			1.33328			0.666640	−	0.745380i	$-0.267732\pi$
$59$	10.2411			1.33328			0.666640	+	0.745380i	$0.267732\pi$
$60$		0			0
$61$			5.57913i			0.714335i	0.934040	+	0.357167i	$0.116257\pi$
$61$			5.57913i			0.714335i	−0.934040	+	0.357167i	$0.883743\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	1.85518i		−	0.230107i
$66$		0			0
$67$	−3.28349			−0.401143			−0.200571	−	0.979679i	$-0.564280\pi$
$67$	−3.28349			−0.401143			−0.200571	+	0.979679i	$0.564280\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.67917i			0.673994i	0.941506	+	0.336997i	$0.109411\pi$
$71$			5.67917i			0.673994i	−0.941506	+	0.336997i	$0.890589\pi$
$72$		0			0
$73$	−5.35354	+	3.09087i	−0.626585	+	0.361759i	−0.779428	−	0.626492i	$-0.784490\pi$
$73$	−5.35354	+	3.09087i	−0.626585	+	0.361759i	0.152844	+	0.988250i	$0.451157\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.87911	−	0.782639i	0.214145	−	0.0891900i
$78$		0			0
$79$	4.02459			0.452802			0.226401	−	0.974034i	$-0.427304\pi$
$79$	4.02459			0.452802			0.226401	+	0.974034i	$0.427304\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.80057	+	10.0469i	0.636695	+	1.10279i	0.986153	+	0.165836i	$0.0530323\pi$
$83$	5.80057	+	10.0469i	0.636695	+	1.10279i	−0.349458	+	0.936952i	$0.613634\pi$
$84$		0			0
$85$	−1.75349	+	3.03713i	−0.190192	+	0.329423i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.00832	−	3.47851i	0.212881	−	0.368721i	−0.739734	−	0.672900i	$-0.765049\pi$
$89$	2.00832	−	3.47851i	0.212881	−	0.368721i	0.952615	+	0.304178i	$0.0983819\pi$
$90$		0			0
$91$	−8.35874	+	3.48136i	−0.876234	+	0.364946i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			3.50781i			0.359894i
$96$		0			0
$97$	15.0653	−	8.69795i	1.52965	−	0.883143i	0.530272	−	0.847828i	$-0.322090\pi$
$97$	15.0653	−	8.69795i	1.52965	−	0.883143i	0.999376	−	0.0353150i	$-0.0112435\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.25113	−	14.2914i	0.821019	−	1.42205i	−0.0839060	−	0.996474i	$-0.526740\pi$
$101$	8.25113	−	14.2914i	0.821019	−	1.42205i	0.904925	−	0.425572i	$-0.139927\pi$
$102$		0			0
$103$	0.254604	−	0.146996i	0.0250869	−	0.0144839i	−0.487404	−	0.873177i	$-0.662056\pi$
$103$	0.254604	−	0.146996i	0.0250869	−	0.0144839i	0.512491	+	0.858693i	$0.328723\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.17327	+	1.83209i	0.306772	+	0.177115i	0.645481	−	0.763776i	$-0.276657\pi$
$107$	3.17327	+	1.83209i	0.306772	+	0.177115i	−0.338709	+	0.940891i	$0.609990\pi$
$108$		0			0
$109$	1.26497	+	2.19099i	0.121162	+	0.209858i	0.920226	−	0.391387i	$-0.128005\pi$
$109$	1.26497	+	2.19099i	0.121162	+	0.209858i	−0.799064	+	0.601246i	$0.794671\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.9275	+	6.88637i	1.12205	+	0.647815i	0.941923	−	0.335828i	$-0.109016\pi$
$113$	11.9275	+	6.88637i	1.12205	+	0.647815i	0.180126	+	0.983644i	$0.442350\pi$
$114$		0			0
$115$	−0.0543988	−	0.0314072i	−0.00507271	−	0.00292873i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	16.9747	+	2.20118i	1.55607	+	0.201782i
$120$		0			0
$121$	−5.20403	−	9.01364i	−0.473094	−	0.819422i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.26146			0.470600
$126$		0			0
$127$	9.44974			0.838529			0.419265	−	0.907864i	$-0.362288\pi$
$127$	9.44974			0.838529			0.419265	+	0.907864i	$0.362288\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.25067	−	10.8265i	−0.546123	−	0.945913i	−0.998535	−	0.0541043i	$-0.982770\pi$
$131$	−6.25067	−	10.8265i	−0.546123	−	0.945913i	0.452412	−	0.891809i	$-0.350564\pi$
$132$		0			0
$133$	15.8049	−	6.58263i	1.37046	−	0.570786i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.7171	−	9.65163i	−1.42824	−	0.824594i	−0.431257	−	0.902229i	$-0.641930\pi$
$137$	−16.7171	−	9.65163i	−1.42824	−	0.824594i	−0.996982	+	0.0776349i	$0.975263\pi$
$138$		0			0
$139$	−0.863952	−	0.498803i	−0.0732794	−	0.0423079i	0.462913	−	0.886404i	$-0.346804\pi$
$139$	−0.863952	−	0.498803i	−0.0732794	−	0.0423079i	−0.536192	+	0.844096i	$0.680138\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.31655	−	2.28033i	−0.110095	−	0.190690i
$144$		0			0
$145$	−2.38607	−	1.37760i	−0.198153	−	0.114403i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.0179	+	9.82530i	−1.39416	+	0.804920i	−0.993773	−	0.111425i	$-0.964459\pi$
$149$	−17.0179	+	9.82530i	−1.39416	+	0.804920i	−0.400390	+	0.916345i	$0.631125\pi$
$150$		0			0
$151$	−8.51708	+	14.7520i	−0.693111	+	1.20050i	0.277703	+	0.960667i	$0.410427\pi$
$151$	−8.51708	+	14.7520i	−0.693111	+	1.20050i	−0.970813	+	0.239836i	$0.922906\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.17604	−	1.25634i	0.174784	−	0.100912i
$156$		0			0
$157$			1.12908i			0.0901107i	0.998984	+	0.0450553i	$0.0143464\pi$
$157$			1.12908i			0.0901107i	−0.998984	+	0.0450553i	$0.985654\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.0394259	+	0.304037i	−0.00310720	+	0.0239615i
$162$		0			0
$163$	−8.60142	+	14.8981i	−0.673715	+	1.16691i	0.303127	+	0.952950i	$0.401969\pi$
$163$	−8.60142	+	14.8981i	−0.673715	+	1.16691i	−0.976843	+	0.213959i	$0.931364\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.22256	−	3.84959i	0.171987	−	0.297890i	−0.767128	−	0.641495i	$-0.778315\pi$
$167$	2.22256	−	3.84959i	0.171987	−	0.297890i	0.939114	+	0.343605i	$0.111648\pi$
$168$		0			0
$169$	−0.643682	−	1.11489i	−0.0495140	−	0.0857607i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−19.8858			−1.51189			−0.755946	−	0.654634i	$-0.772823\pi$
$173$	−19.8858			−1.51189			−0.755946	+	0.654634i	$0.772823\pi$
$174$		0			0
$175$	−4.78728	−	11.4942i	−0.361884	−	0.868882i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.71472	+	0.989994i	−0.128164	+	0.0739956i	−0.562711	−	0.826653i	$-0.690242\pi$
$179$	−1.71472	+	0.989994i	−0.128164	+	0.0739956i	0.434547	+	0.900649i	$0.356908\pi$
$180$		0			0
$181$			5.68137i			0.422293i	0.977454	+	0.211146i	$0.0677197\pi$
$181$			5.68137i			0.422293i	−0.977454	+	0.211146i	$0.932280\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.93592			0.436417
$186$		0			0
$187$			4.97751i			0.363992i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	4.15021i		−	0.300299i	−0.988663	−	0.150149i	$-0.952025\pi$
$191$		−	4.15021i		−	0.300299i	0.988663	−	0.150149i	$-0.0479755\pi$
$192$		0			0
$193$	5.87065			0.422579			0.211289	−	0.977424i	$-0.432234\pi$
$193$	5.87065			0.422579			0.211289	+	0.977424i	$0.432234\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			3.37912i			0.240753i	0.992728	+	0.120376i	$0.0384101\pi$
$197$			3.37912i			0.240753i	−0.992728	+	0.120376i	$0.961590\pi$
$198$		0			0
$199$	−4.03812	+	2.33141i	−0.286255	+	0.165269i	−0.636252	−	0.771482i	$-0.719516\pi$
$199$	−4.03812	+	2.33141i	−0.286255	+	0.165269i	0.349997	+	0.936751i	$0.386183\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.72932	+	13.3359i	−0.121375	+	0.935995i
$204$		0			0
$205$	4.38620			0.306346
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.48935	+	4.31168i	0.172192	+	0.298245i
$210$		0			0
$211$	−3.09622	+	5.36281i	−0.213153	+	0.369191i	−0.952699	−	0.303914i	$-0.901706\pi$
$211$	−3.09622	+	5.36281i	−0.213153	+	0.369191i	0.739547	+	0.673105i	$0.235040\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.80277	+	3.12249i	−0.122948	+	0.212952i
$216$		0			0
$217$	−9.74406	−	7.44682i	−0.661470	−	0.505523i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	22.1412i		−	1.48938i
$222$		0			0
$223$	8.84510	−	5.10672i	0.592312	−	0.341971i	−0.173699	−	0.984799i	$-0.555572\pi$
$223$	8.84510	−	5.10672i	0.592312	−	0.341971i	0.766011	+	0.642827i	$0.222239\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.12394	+	14.0711i	−0.539205	+	0.933930i	0.459742	+	0.888052i	$0.347942\pi$
$227$	−8.12394	+	14.0711i	−0.539205	+	0.933930i	−0.998947	+	0.0458777i	$0.985392\pi$
$228$		0			0
$229$	−7.51527	+	4.33894i	−0.496623	+	0.286726i	−0.727318	−	0.686301i	$-0.759233\pi$
$229$	−7.51527	+	4.33894i	−0.496623	+	0.286726i	0.230695	+	0.973026i	$0.425900\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−19.0308	−	10.9874i	−1.24675	−	0.719811i	−0.276290	−	0.961074i	$-0.589105\pi$
$233$	−19.0308	−	10.9874i	−1.24675	−	0.719811i	−0.970460	+	0.241263i	$0.922438\pi$
$234$		0			0
$235$	−0.419070	−	0.725851i	−0.0273371	−	0.0473493i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.3752	−	8.29955i	−0.929857	−	0.536853i	−0.0430908	−	0.999071i	$-0.513720\pi$
$239$	−14.3752	−	8.29955i	−0.929857	−	0.536853i	−0.886766	+	0.462218i	$0.847054\pi$
$240$		0			0
$241$	−9.52821	−	5.50112i	−0.613766	−	0.354358i	0.160672	−	0.987008i	$-0.448634\pi$
$241$	−9.52821	−	5.50112i	−0.613766	−	0.354358i	−0.774438	+	0.632650i	$0.781967\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.67268	−	2.69355i	0.170751	−	0.172085i
$246$		0			0
$247$	−11.0732	−	19.1794i	−0.704573	−	1.22036i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.0406			1.13871			0.569356	−	0.822091i	$-0.307192\pi$
$251$	18.0406			1.13871			0.569356	+	0.822091i	$0.307192\pi$
$252$		0			0
$253$	−0.0891535			−0.00560503
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.20321	+	12.4763i	0.449324	+	0.778252i	0.998342	−	0.0575585i	$-0.0183316\pi$
$257$	7.20321	+	12.4763i	0.449324	+	0.778252i	−0.549018	+	0.835810i	$0.684998\pi$
$258$		0			0
$259$	−11.1391	−	26.7450i	−0.692151	−	1.66185i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	21.6064	+	12.4745i	1.33231	+	0.769209i	0.985653	−	0.168783i	$-0.0539838\pi$
$263$	21.6064	+	12.4745i	1.33231	+	0.769209i	0.346656	+	0.937992i	$0.387317\pi$
$264$		0			0
$265$	0.119805	+	0.0691692i	0.00735954	+	0.00424903i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.0059	−	19.0627i	−0.671040	−	1.16228i	−0.977609	−	0.210428i	$-0.932514\pi$
$269$	−11.0059	−	19.0627i	−0.671040	−	1.16228i	0.306569	−	0.951848i	$-0.400819\pi$
$270$		0			0
$271$	22.7444	+	13.1315i	1.38162	+	0.797680i	0.992352	−	0.123443i	$-0.0393935\pi$
$271$	22.7444	+	13.1315i	1.38162	+	0.797680i	0.389271	+	0.921123i	$0.372727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.13571	−	1.81040i	0.189090	−	0.109171i
$276$		0			0
$277$	−2.38206	+	4.12584i	−0.143124	+	0.247898i	−0.928671	−	0.370903i	$-0.879048\pi$
$277$	−2.38206	+	4.12584i	−0.143124	+	0.247898i	0.785548	+	0.618801i	$0.212381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.1963	+	11.0830i	−1.14515	+	0.661155i	−0.947702	−	0.319158i	$-0.896600\pi$
$281$	−19.1963	+	11.0830i	−1.14515	+	0.661155i	−0.197452	+	0.980312i	$0.563267\pi$
$282$		0			0
$283$			2.90557i			0.172718i	0.996264	+	0.0863590i	$0.0275232\pi$
$283$			2.90557i			0.172718i	−0.996264	+	0.0863590i	$0.972477\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.23098	−	19.7626i	−0.485860	−	1.16655i
$288$		0			0
$289$	−12.4275	+	21.5250i	−0.731027	+	1.26618i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.9866	+	24.2255i	−0.817104	+	1.41527i	0.0907025	+	0.995878i	$0.471089\pi$
$293$	−13.9866	+	24.2255i	−0.817104	+	1.41527i	−0.907807	+	0.419388i	$0.862245\pi$
$294$		0			0
$295$	2.77573	+	4.80770i	0.161609	+	0.279915i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.396576			0.0229346
$300$		0			0
$301$	17.4518	+	2.26305i	1.00590	+	0.130440i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.61913	+	1.51215i	−0.149971	+	0.0865857i
$306$		0			0
$307$			30.3968i			1.73484i	0.497579	+	0.867419i	$0.334223\pi$
$307$			30.3968i			1.73484i	−0.497579	+	0.867419i	$0.665777\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−27.8260			−1.57787			−0.788934	−	0.614477i	$-0.789367\pi$
$311$	−27.8260			−1.57787			−0.788934	+	0.614477i	$0.789367\pi$
$312$		0			0
$313$			0.0465719i			0.00263240i	0.999999	+	0.00131620i	$0.000418959\pi$
$313$			0.0465719i			0.00263240i	−0.999999	+	0.00131620i	$0.999581\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	8.49402i		−	0.477072i	−0.971134	−	0.238536i	$-0.923333\pi$
$317$		−	8.49402i		−	0.477072i	0.971134	−	0.238536i	$-0.0766675\pi$
$318$		0			0
$319$	−3.91051			−0.218946
$320$		0			0
$321$		0			0
$322$		0			0
$323$			41.8649i			2.32943i
$324$		0			0
$325$	−13.9484	+	8.05311i	−0.773718	+	0.446706i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.48399	+	3.25027i	−0.136947	+	0.179193i
$330$		0			0
$331$	7.25461			0.398749			0.199375	−	0.979923i	$-0.436109\pi$
$331$	7.25461			0.398749			0.199375	+	0.979923i	$0.436109\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.889950	−	1.54144i	−0.0486232	−	0.0842178i
$336$		0			0
$337$	−4.82349	+	8.35454i	−0.262752	+	0.455101i	−0.966972	−	0.254881i	$-0.917964\pi$
$337$	−4.82349	+	8.35454i	−0.262752	+	0.455101i	0.704220	+	0.709982i	$0.251297\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.78315	−	3.08850i	0.0965627	−	0.167252i
$342$		0			0
$343$	−17.1515	−	6.98745i	−0.926097	−	0.377287i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			13.0603i			0.701113i	0.936542	+	0.350556i	$0.114008\pi$
$347$			13.0603i			0.701113i	−0.936542	+	0.350556i	$0.885992\pi$
$348$		0			0
$349$	17.4929	−	10.0995i	0.936372	−	0.540614i	0.0475506	−	0.998869i	$-0.484858\pi$
$349$	17.4929	−	10.0995i	0.936372	−	0.540614i	0.888821	+	0.458254i	$0.151525\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.05422	+	3.55801i	−0.109335	+	0.189374i	−0.915501	−	0.402316i	$-0.868205\pi$
$353$	−2.05422	+	3.55801i	−0.109335	+	0.189374i	0.806166	+	0.591689i	$0.201539\pi$
$354$		0			0
$355$	−2.66609	+	1.53927i	−0.141501	+	0.0816959i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−28.7322	−	16.5885i	−1.51643	−	0.875510i	−0.999814	−	0.0192910i	$-0.993859\pi$
$359$	−28.7322	−	16.5885i	−1.51643	−	0.875510i	−0.516613	−	0.856219i	$-0.672808\pi$
$360$		0			0
$361$	11.4375	+	19.8103i	0.601973	+	1.04265i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.90202	−	1.67548i	−0.151899	−	0.0876988i
$366$		0			0
$367$	−2.75059	−	1.58806i	−0.143580	−	0.0828958i	0.426489	−	0.904493i	$-0.359750\pi$
$367$	−2.75059	−	1.58806i	−0.143580	−	0.0828958i	−0.570069	+	0.821597i	$0.693084\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0868292	−	0.669594i	0.00450795	−	0.0347636i
$372$		0			0
$373$	−10.4803	−	18.1524i	−0.542649	−	0.939895i	−0.998751	−	0.0499677i	$-0.984088\pi$
$373$	−10.4803	−	18.1524i	−0.542649	−	0.939895i	0.456102	−	0.889927i	$-0.349245\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.3949			0.895881
$378$		0			0
$379$	−20.1198			−1.03348			−0.516742	−	0.856141i	$-0.672855\pi$
$379$	−20.1198			−1.03348			−0.516742	+	0.856141i	$0.672855\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.5838	−	21.7958i	−0.643003	−	1.11371i	−0.984759	−	0.173925i	$-0.944355\pi$
$383$	−12.5838	−	21.7958i	−0.643003	−	1.11371i	0.341756	−	0.939789i	$-0.388978\pi$
$384$		0			0
$385$	0.876720	+	0.670026i	0.0446818	+	0.0341477i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.4054	−	10.0490i	−0.882488	−	0.509505i	−0.0110101	−	0.999939i	$-0.503505\pi$
$389$	−17.4054	−	10.0490i	−0.882488	−	0.509505i	−0.871478	+	0.490435i	$0.836838\pi$
$390$		0			0
$391$	−0.649237	−	0.374837i	−0.0328333	−	0.0189563i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.09081	+	1.88935i	0.0548848	+	0.0950633i
$396$		0			0
$397$	6.64273	+	3.83518i	0.333389	+	0.192482i	0.657345	−	0.753590i	$-0.271680\pi$
$397$	6.64273	+	3.83518i	0.333389	+	0.192482i	−0.323956	+	0.946072i	$0.605013\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.07360	+	1.77454i	−0.153488	+	0.0886165i	−0.574777	−	0.818310i	$-0.694911\pi$
$401$	−3.07360	+	1.77454i	−0.153488	+	0.0886165i	0.421289	+	0.906927i	$0.361578\pi$
$402$		0			0
$403$	−7.93186	+	13.7384i	−0.395114	+	0.684357i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.29622	−	4.21248i	0.361660	−	0.208805i
$408$		0			0
$409$			3.45157i			0.170669i	0.996352	+	0.0853345i	$0.0271959\pi$
$409$			3.45157i			0.170669i	−0.996352	+	0.0853345i	$0.972804\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.4528	−	21.5283i	0.809590	−	1.05934i
$414$		0			0
$415$	−3.14434	+	5.44616i	−0.154350	+	0.267342i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.49112	−	14.7071i	0.414818	−	0.718487i	−0.580591	−	0.814195i	$-0.697178\pi$
$419$	8.49112	−	14.7071i	0.414818	−	0.718487i	0.995409	+	0.0957088i	$0.0305118\pi$
$420$		0			0
$421$	10.3437	+	17.9158i	0.504120	+	0.873162i	0.999989	+	0.00476397i	$0.00151642\pi$
$421$	10.3437	+	17.9158i	0.504120	+	0.873162i	−0.495869	+	0.868398i	$0.665150\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	30.4466			1.47688
$426$		0			0
$427$	11.7281	+	8.96313i	0.567564	+	0.433756i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−32.0588	+	18.5091i	−1.54422	+	0.891554i	−0.545651	+	0.838012i	$0.683718\pi$
$431$	−32.0588	+	18.5091i	−1.54422	+	0.891554i	−0.998566	+	0.0535418i	$0.982949\pi$
$432$		0			0
$433$		−	15.2206i		−	0.731453i	−0.930722	−	0.365727i	$-0.880821\pi$
$433$		−	15.2206i		−	0.731453i	0.930722	−	0.365727i	$-0.119179\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.749853			−0.0358704
$438$		0			0
$439$		−	32.8075i		−	1.56582i	−0.622136	−	0.782909i	$-0.713735\pi$
$439$		−	32.8075i		−	1.56582i	0.622136	−	0.782909i	$-0.286265\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	23.7626i		−	1.12900i	−0.825434	−	0.564499i	$-0.809070\pi$
$443$		−	23.7626i		−	1.12900i	0.825434	−	0.564499i	$-0.190930\pi$
$444$		0			0
$445$	2.17732			0.103215
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	21.8105i		−	1.02930i	−0.857400	−	0.514651i	$-0.827921\pi$
$449$		−	21.8105i		−	1.02930i	0.857400	−	0.514651i	$-0.172079\pi$
$450$		0			0
$451$	5.39137	−	3.11271i	0.253870	−	0.146572i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.89986	−	2.98044i	−0.182828	−	0.139725i
$456$		0			0
$457$	−39.7064			−1.85739			−0.928693	−	0.370849i	$-0.879067\pi$
$457$	−39.7064			−1.85739			−0.928693	+	0.370849i	$0.879067\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.37073	+	12.7665i	0.343289	+	0.594594i	0.985041	−	0.172318i	$-0.0551256\pi$
$461$	7.37073	+	12.7665i	0.343289	+	0.594594i	−0.641752	+	0.766912i	$0.721792\pi$
$462$		0			0
$463$	−12.4381	+	21.5434i	−0.578046	+	1.00120i	0.417658	+	0.908604i	$0.362851\pi$
$463$	−12.4381	+	21.5434i	−0.578046	+	1.00120i	−0.995703	+	0.0926000i	$0.970482\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.70092	−	11.6063i	0.310081	−	0.537077i	−0.668298	−	0.743893i	$-0.732977\pi$
$467$	6.70092	−	11.6063i	0.310081	−	0.537077i	0.978380	+	0.206817i	$0.0663103\pi$
$468$		0			0
$469$	−5.27509	+	6.90238i	−0.243581	+	0.318722i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			5.11741i			0.235299i
$474$		0			0
$475$	26.3739	−	15.2270i	1.21012	−	0.698661i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	20.5731	−	35.6336i	0.940007	−	1.62814i	0.174555	−	0.984647i	$-0.444151\pi$
$479$	20.5731	−	35.6336i	0.940007	−	1.62814i	0.765452	−	0.643493i	$-0.222515\pi$
$480$		0			0
$481$	−32.4554	+	18.7381i	−1.47984	+	0.854384i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.16651	+	4.71494i	0.370822	+	0.214094i
$486$		0			0
$487$	−14.7695	−	25.5814i	−0.669268	−	1.15921i	−0.978109	−	0.208092i	$-0.933275\pi$
$487$	−14.7695	−	25.5814i	−0.669268	−	1.15921i	0.308841	−	0.951114i	$-0.400059\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.53341	−	4.92676i	−0.385107	−	0.222342i	0.294931	−	0.955519i	$-0.404703\pi$
$491$	−8.53341	−	4.92676i	−0.385107	−	0.222342i	−0.680038	+	0.733177i	$0.738037\pi$
$492$		0			0
$493$	−28.4772	−	16.4413i	−1.28255	−	0.740480i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.9384	+	9.12385i	0.535512	+	0.409261i
$498$		0			0
$499$	20.3875	+	35.3122i	0.912671	+	1.58079i	0.810275	+	0.586050i	$0.199318\pi$
$499$	20.3875	+	35.3122i	0.912671	+	1.58079i	0.102396	+	0.994744i	$0.467349\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.6750			−1.05561			−0.527807	−	0.849364i	$-0.676986\pi$
$503$	−23.6750			−1.05561			−0.527807	+	0.849364i	$0.676986\pi$
$504$		0			0
$505$	8.94547			0.398068
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.3838	+	24.9135i	0.637551	+	1.10427i	0.985969	+	0.166931i	$0.0533857\pi$
$509$	14.3838	+	24.9135i	0.637551	+	1.10427i	−0.348418	+	0.937339i	$0.613281\pi$
$510$		0			0
$511$	−2.10326	+	16.2195i	−0.0930427	+	0.717510i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.138015	+	0.0796827i	0.00608165	+	0.00351124i
$516$		0			0
$517$	−1.03021	−	0.594794i	−0.0453087	−	0.0261590i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.64967	−	6.32142i	−0.159895	−	0.276947i	0.774936	−	0.632040i	$-0.217782\pi$
$521$	−3.64967	−	6.32142i	−0.159895	−	0.276947i	−0.934831	+	0.355094i	$0.884449\pi$
$522$		0			0
$523$	−21.2167	−	12.2495i	−0.927742	−	0.535632i	−0.0416450	−	0.999132i	$-0.513260\pi$
$523$	−21.2167	−	12.2495i	−0.927742	−	0.535632i	−0.886097	+	0.463501i	$0.846593\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	25.9706	−	14.9941i	1.13130	−	0.653154i
$528$		0			0
$529$	−11.4933	+	19.9070i	−0.499708	+	0.865520i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.9821	+	13.8461i	−1.03878	+	0.599740i
$534$		0			0
$535$			1.98626i			0.0858736i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.37366	−	5.20751i	0.0591678	−	0.224303i
$540$		0			0
$541$	−12.1854	+	21.1057i	−0.523891	+	0.907406i	0.475722	+	0.879596i	$0.342187\pi$
$541$	−12.1854	+	21.1057i	−0.523891	+	0.907406i	−0.999613	+	0.0278106i	$0.991146\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.685707	+	1.18768i	−0.0293724	+	0.0508746i
$546$		0			0
$547$	19.3409	+	33.4994i	0.826957	+	1.43233i	0.900414	+	0.435034i	$0.143264\pi$
$547$	19.3409	+	33.4994i	0.826957	+	1.43233i	−0.0734566	+	0.997298i	$0.523403\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−32.8905			−1.40118
$552$		0			0
$553$	6.46569	−	8.46027i	0.274949	−	0.359767i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.55184	−	3.20536i	0.235239	−	0.135815i	−0.377748	−	0.925909i	$-0.623301\pi$
$557$	5.55184	−	3.20536i	0.235239	−	0.135815i	0.612987	+	0.790093i	$0.289968\pi$
$558$		0			0
$559$		−	22.7635i		−	0.962792i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.9507			0.714388			0.357194	−	0.934030i	$-0.383733\pi$
$563$	16.9507			0.714388			0.357194	+	0.934030i	$0.383733\pi$
$564$		0			0
$565$			7.46586i			0.314091i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			12.5694i			0.526938i	0.964668	+	0.263469i	$0.0848666\pi$
$569$			12.5694i			0.526938i	−0.964668	+	0.263469i	$0.915133\pi$
$570$		0			0
$571$	−9.64161			−0.403489			−0.201744	−	0.979438i	$-0.564661\pi$
$571$	−9.64161			−0.403489			−0.201744	+	0.979438i	$0.564661\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.545337i			0.0227421i
$576$		0			0
$577$	20.9563	−	12.0991i	0.872421	−	0.503692i	0.00426870	−	0.999991i	$-0.498641\pi$
$577$	20.9563	−	12.0991i	0.872421	−	0.503692i	0.868152	+	0.496299i	$0.165308\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	30.4389	+	3.94714i	1.26282	+	0.163755i
$582$		0			0
$583$	0.196346			0.00813183
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.5498	+	21.7368i	0.517984	+	0.897175i	0.999782	+	0.0208923i	$0.00665069\pi$
$587$	12.5498	+	21.7368i	0.517984	+	0.897175i	−0.481798	+	0.876283i	$0.660016\pi$
$588$		0			0
$589$	14.9977	−	25.9768i	0.617970	−	1.07035i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.1605	+	33.1869i	−0.786826	+	1.36282i	0.141076	+	0.989999i	$0.454944\pi$
$593$	−19.1605	+	33.1869i	−0.786826	+	1.36282i	−0.927902	+	0.372824i	$0.878390\pi$
$594$		0			0
$595$	3.56743	+	8.56537i	0.146250	+	0.351146i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	1.27897i		−	0.0522572i	−0.999659	−	0.0261286i	$-0.991682\pi$
$599$		−	1.27897i		−	0.0522572i	0.999659	−	0.0261286i	$-0.00831794\pi$
$600$		0			0
$601$	31.2150	−	18.0220i	1.27329	−	0.735133i	0.297682	−	0.954665i	$-0.403786\pi$
$601$	31.2150	−	18.0220i	1.27329	−	0.735133i	0.975605	+	0.219532i	$0.0704531\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.82097	−	4.88607i	0.114689	−	0.198647i
$606$		0			0
$607$	39.1131	−	22.5820i	1.58755	−	0.916573i	0.593843	−	0.804581i	$-0.297610\pi$
$607$	39.1131	−	22.5820i	1.58755	−	0.916573i	0.993709	−	0.111992i	$-0.0357231\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.58264	+	2.64579i	0.185394	+	0.107037i
$612$		0			0
$613$	−9.50638	−	16.4655i	−0.383959	−	0.665037i	0.607665	−	0.794193i	$-0.292106\pi$
$613$	−9.50638	−	16.4655i	−0.383959	−	0.665037i	−0.991624	+	0.129157i	$0.958773\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.2379	−	9.95232i	−0.693973	−	0.400665i	0.111126	−	0.993806i	$-0.464554\pi$
$617$	−17.2379	−	9.95232i	−0.693973	−	0.400665i	−0.805099	+	0.593141i	$0.797888\pi$
$618$		0			0
$619$	−22.0428	−	12.7264i	−0.885977	−	0.511519i	−0.0133522	−	0.999911i	$-0.504250\pi$
$619$	−22.0428	−	12.7264i	−0.885977	−	0.511519i	−0.872624	+	0.488392i	$0.837584\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.08587	−	9.81016i	−0.163697	−	0.393036i
$624$		0			0
$625$	−10.3393	−	17.9082i	−0.413573	−	0.716330i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	70.8438			2.82473
$630$		0			0
$631$	40.8171			1.62490			0.812452	−	0.583028i	$-0.198132\pi$
$631$	40.8171			1.62490			0.812452	+	0.583028i	$0.198132\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.56124	+	4.43619i	0.101640	+	0.176045i
$636$		0			0
$637$	−6.11037	+	23.1643i	−0.242102	+	0.917801i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.64806	+	4.99296i	0.341578	+	0.197210i	0.660970	−	0.750413i	$-0.270145\pi$
$641$	8.64806	+	4.99296i	0.341578	+	0.197210i	−0.319392	+	0.947623i	$0.603479\pi$
$642$		0			0
$643$	4.32793	+	2.49873i	0.170677	+	0.0985403i	0.582905	−	0.812540i	$-0.301916\pi$
$643$	4.32793	+	2.49873i	0.170677	+	0.0985403i	−0.412228	+	0.911081i	$0.635249\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.04602	−	8.73996i	−0.198379	−	0.343603i	0.749624	−	0.661864i	$-0.230234\pi$
$647$	−5.04602	−	8.73996i	−0.198379	−	0.343603i	−0.948003	+	0.318261i	$0.896901\pi$
$648$		0			0
$649$	6.82365	+	3.93964i	0.267852	+	0.154644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−14.8236	+	8.55844i	−0.580094	+	0.334918i	−0.761171	−	0.648551i	$-0.775375\pi$
$653$	−14.8236	+	8.55844i	−0.580094	+	0.334918i	0.181077	+	0.983469i	$0.442042\pi$
$654$		0			0
$655$	3.38833	−	5.86876i	0.132393	−	0.229311i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.7790	+	7.37798i	−0.497800	+	0.287405i	−0.727805	−	0.685784i	$-0.759459\pi$
$659$	−12.7790	+	7.37798i	−0.497800	+	0.287405i	0.230004	+	0.973190i	$0.426126\pi$
$660$		0			0
$661$			30.0316i			1.16810i	0.811719	+	0.584048i	$0.198532\pi$
$661$			30.0316i			1.16810i	−0.811719	+	0.584048i	$0.801468\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.37393	+	5.63547i	0.285949	+	0.218534i
$666$		0			0
$667$	0.294485	−	0.510063i	0.0114025	−	0.0197497i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.14623	+	3.71737i	−0.0828542	+	0.143508i
$672$		0			0
$673$	18.1953	+	31.5152i	0.701378	+	1.21482i	0.967983	+	0.251016i	$0.0807648\pi$
$673$	18.1953	+	31.5152i	0.701378	+	1.21482i	−0.266605	+	0.963806i	$0.585902\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.3219			0.704168			0.352084	−	0.935968i	$-0.385473\pi$
$677$	18.3219			0.704168			0.352084	+	0.935968i	$0.385473\pi$
$678$		0			0
$679$	5.91874	−	45.6431i	0.227140	−	1.75162i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.46067	+	3.73007i	−0.247210	+	0.142727i	−0.618486	−	0.785796i	$-0.712254\pi$
$683$	−6.46067	+	3.73007i	−0.247210	+	0.142727i	0.371276	+	0.928523i	$0.378920\pi$
$684$		0			0
$685$		−	10.4638i		−	0.399802i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.873395			−0.0332737
$690$		0			0
$691$		−	17.5167i		−	0.666365i	−0.942862	−	0.333182i	$-0.891878\pi$
$691$		−	17.5167i		−	0.666365i	0.942862	−	0.333182i	$-0.108122\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	0.540777i		−	0.0205128i
$696$		0			0
$697$	52.3483			1.98283
$698$		0			0
$699$		0			0
$700$		0			0
$701$			37.8622i			1.43004i	0.699106	+	0.715018i	$0.253582\pi$
$701$			37.8622i			1.43004i	−0.699106	+	0.715018i	$0.746418\pi$
$702$		0			0
$703$	61.3672	−	35.4304i	2.31451	−	1.33628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−16.7867	−	40.3048i	−0.631330	−	1.51582i
$708$		0			0
$709$	−37.1014			−1.39337			−0.696686	−	0.717376i	$-0.745343\pi$
$709$	−37.1014			−1.39337			−0.696686	+	0.717376i	$0.745343\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.268563	+	0.465165i	0.0100578	+	0.0174206i
$714$		0			0
$715$	0.713667	−	1.23611i	0.0266896	−	0.0462278i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.73941	+	9.94096i	−0.214044	+	0.370735i	−0.952976	−	0.303044i	$-0.901997\pi$
$719$	−5.73941	+	9.94096i	−0.214044	+	0.370735i	0.738932	+	0.673780i	$0.235330\pi$
$720$		0			0
$721$	0.100027	−	0.771370i	0.00372520	−	0.0287273i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			23.9199i			0.888364i
$726$		0			0
$727$	13.1105	−	7.56936i	0.486242	−	0.280732i	−0.236772	−	0.971565i	$-0.576089\pi$
$727$	13.1105	−	7.56936i	0.486242	−	0.280732i	0.723014	+	0.690833i	$0.242756\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.5156	+	37.2662i	−0.795785	+	1.37834i
$732$		0			0
$733$	−7.96753	+	4.60005i	−0.294287	+	0.169907i	−0.639874	−	0.768480i	$-0.721013\pi$
$733$	−7.96753	+	4.60005i	−0.294287	+	0.169907i	0.345586	+	0.938387i	$0.387680\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.18779	−	1.26312i	−0.0805884	−	0.0465277i
$738$		0			0
$739$	−14.6669	−	25.4038i	−0.539529	−	0.934492i	−0.998929	−	0.0462628i	$-0.985269\pi$
$739$	−14.6669	−	25.4038i	−0.539529	−	0.934492i	0.459400	−	0.888230i	$-0.348065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	33.9829	+	19.6200i	1.24671	+	0.719789i	0.970452	−	0.241294i	$-0.0775719\pi$
$743$	33.9829	+	19.6200i	1.24671	+	0.719789i	0.276259	+	0.961083i	$0.410905\pi$
$744$		0			0
$745$	−9.22499	−	5.32605i	−0.337977	−	0.195131i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.94933	−	3.72734i	0.327001	−	0.136194i
$750$		0			0
$751$	−10.5034	−	18.1924i	−0.383274	−	0.663851i	0.608254	−	0.793743i	$-0.291870\pi$
$751$	−10.5034	−	18.1924i	−0.383274	−	0.663851i	−0.991528	+	0.129892i	$0.958537\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−9.23380			−0.336052
$756$		0			0
$757$	12.1528			0.441703			0.220851	−	0.975307i	$-0.429116\pi$
$757$	12.1528			0.441703			0.220851	+	0.975307i	$0.429116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.24026	−	12.5405i	−0.262459	−	0.454593i	0.704436	−	0.709768i	$-0.251200\pi$
$761$	−7.24026	−	12.5405i	−0.262459	−	0.454593i	−0.966895	+	0.255175i	$0.917867\pi$
$762$		0			0
$763$	6.63799	+	0.860778i	0.240312	+	0.0311623i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−30.3532	−	17.5245i	−1.09599	−	0.632771i
$768$		0			0
$769$	6.13371	+	3.54130i	0.221187	+	0.127702i	0.606500	−	0.795084i	$-0.292573\pi$
$769$	6.13371	+	3.54130i	0.221187	+	0.127702i	−0.385313	+	0.922786i	$0.625906\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.1640	+	33.1930i	0.689280	+	1.19387i	0.972071	+	0.234687i	$0.0754065\pi$
$773$	19.1640	+	33.1930i	0.689280	+	1.19387i	−0.282791	+	0.959182i	$0.591260\pi$
$774$		0			0
$775$	−18.8918	−	10.9072i	−0.678615	−	0.391799i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	45.3458	−	26.1804i	1.62468	−	0.938011i
$780$		0			0
$781$	−2.18471	+	3.78403i	−0.0781751	+	0.135403i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.530049	+	0.306024i	−0.0189183	+	0.0109225i
$786$		0			0
$787$			15.6191i			0.556760i	0.960471	+	0.278380i	$0.0897974\pi$
$787$			15.6191i			0.556760i	−0.960471	+	0.278380i	$0.910203\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	33.6383	−	14.0101i	1.19604	−	0.498143i
$792$		0			0
$793$	9.54693	−	16.5358i	0.339022	−	0.587203i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.0230	+	20.8244i	−0.425875	+	0.737637i	−0.996502	−	0.0835726i	$-0.973367\pi$
$797$	−12.0230	+	20.8244i	−0.425875	+	0.737637i	0.570627	+	0.821210i	$0.306700\pi$
$798$		0			0
$799$	−5.00151	−	8.66286i	−0.176941	−	0.306470i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.75608			−0.167839
$804$		0			0
$805$	−0.153417	+	0.0638970i	−0.00540722	+	0.00225207i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25.2846	−	14.5980i	0.888958	−	0.513240i	0.0153562	−	0.999882i	$-0.495112\pi$
$809$	25.2846	−	14.5980i	0.888958	−	0.513240i	0.873601	+	0.486642i	$0.161778\pi$
$810$		0			0
$811$		−	26.0991i		−	0.916464i	−0.888833	−	0.458232i	$-0.848483\pi$
$811$		−	26.0991i		−	0.916464i	0.888833	−	0.458232i	$-0.151517\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.32523			−0.326649
$816$		0			0
$817$			43.0416i			1.50583i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	54.9905i		−	1.91918i	−0.281402	−	0.959590i	$-0.590799\pi$
$821$		−	54.9905i		−	1.91918i	0.281402	−	0.959590i	$-0.409201\pi$
$822$		0			0
$823$	−18.1157			−0.631474			−0.315737	−	0.948847i	$-0.602252\pi$
$823$	−18.1157			−0.631474			−0.315737	+	0.948847i	$0.602252\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			38.1934i			1.32812i	0.747681	+	0.664058i	$0.231167\pi$
$827$			38.1934i			1.32812i	−0.747681	+	0.664058i	$0.768833\pi$
$828$		0			0
$829$	47.0722	−	27.1771i	1.63488	−	0.943901i	0.652327	−	0.757938i	$-0.273793\pi$
$829$	47.0722	−	27.1771i	1.63488	−	0.943901i	0.982557	−	0.185963i	$-0.0595404\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.8978	−	32.1469i	1.10519	−	1.11382i
$834$		0			0
$835$	2.40959			0.0833873
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.3919	+	23.1955i	0.462341	+	0.800798i	0.999077	−	0.0429523i	$-0.0136764\pi$
$839$	13.3919	+	23.1955i	0.462341	+	0.800798i	−0.536736	+	0.843750i	$0.680343\pi$
$840$		0			0
$841$	−1.58312	+	2.74205i	−0.0545904	+	0.0945534i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.348924	−	0.604354i	0.0120033	−	0.0207904i
$846$		0			0
$847$	−27.3085	−	3.54121i	−0.938331	−	0.121678i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			1.26890i			0.0434973i
$852$		0			0
$853$	−15.6735	+	9.04908i	−0.536649	+	0.309835i	−0.743720	−	0.668491i	$-0.766940\pi$
$853$	−15.6735	+	9.04908i	−0.536649	+	0.309835i	0.207071	+	0.978326i	$0.433607\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.6561	+	30.5812i	−0.603120	+	1.04464i	0.389225	+	0.921143i	$0.372743\pi$
$857$	−17.6561	+	30.5812i	−0.603120	+	1.04464i	−0.992346	+	0.123492i	$0.960591\pi$
$858$		0			0
$859$	−20.1598	+	11.6393i	−0.687844	+	0.397127i	−0.802804	−	0.596243i	$-0.796659\pi$
$859$	−20.1598	+	11.6393i	−0.687844	+	0.397127i	0.114960	+	0.993370i	$0.463326\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	28.3933	+	16.3929i	0.966520	+	0.558020i	0.898173	−	0.439641i	$-0.144894\pi$
$863$	28.3933	+	16.3929i	0.966520	+	0.558020i	0.0683462	+	0.997662i	$0.478228\pi$
$864$		0			0
$865$	−5.38980	−	9.33541i	−0.183259	−	0.317414i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.68158	+	1.54821i	0.0909665	+	0.0525195i
$870$		0			0
$871$	9.73182	+	5.61867i	0.329750	+	0.190381i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.45278	−	11.0604i	0.285756	−	0.373908i
$876$		0			0
$877$	−10.7688	−	18.6521i	−0.363636	−	0.629837i	0.624920	−	0.780689i	$-0.285132\pi$
$877$	−10.7688	−	18.6521i	−0.363636	−	0.629837i	−0.988556	+	0.150852i	$0.951798\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−22.9322			−0.772606			−0.386303	−	0.922372i	$-0.626248\pi$
$881$	−22.9322			−0.772606			−0.386303	+	0.922372i	$0.626248\pi$
$882$		0			0
$883$	31.8225			1.07091			0.535455	−	0.844564i	$-0.320140\pi$
$883$	31.8225			1.07091			0.535455	+	0.844564i	$0.320140\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.1135	+	19.2492i	0.373156	+	0.646325i	0.990049	−	0.140722i	$-0.0449423\pi$
$887$	11.1135	+	19.2492i	0.373156	+	0.646325i	−0.616893	+	0.787047i	$0.711609\pi$
$888$		0			0
$889$	15.1814	−	19.8647i	0.509169	−	0.666241i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.66494	−	5.00270i	−0.289961	−	0.167409i
$894$		0			0
$895$	−0.929507	−	0.536651i	−0.0310700	−	0.0179383i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.7799	+	20.4034i	0.392881	+	0.680491i
$900$		0			0
$901$	1.42984	+	0.825518i	0.0476349	+	0.0275020i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.66712	+	1.53986i	−0.0886581	+	0.0511868i
$906$		0			0
$907$	−19.9099	+	34.4849i	−0.661097	+	1.14505i	0.319231	+	0.947677i	$0.396575\pi$
$907$	−19.9099	+	34.4849i	−0.661097	+	1.14505i	−0.980328	+	0.197376i	$0.936758\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.87819	+	3.39378i	−0.194753	+	0.112441i	−0.594206	−	0.804313i	$-0.702534\pi$
$911$	−5.87819	+	3.39378i	−0.194753	+	0.112441i	0.399453	+	0.916754i	$0.369200\pi$
$912$		0			0
$913$			8.92565i			0.295396i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−32.8008	−	4.25342i	−1.08318	−	0.140460i
$918$		0			0
$919$	14.0173	−	24.2787i	0.462389	−	0.800882i	−0.536690	−	0.843779i	$-0.680326\pi$
$919$	14.0173	−	24.2787i	0.462389	−	0.800882i	0.999079	+	0.0428977i	$0.0136590\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.71812	−	16.8323i	0.319876	−	0.554041i
$924$		0			0
$925$	−25.7670	−	44.6298i	−0.847215	−	1.46742i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.7408			0.582057			0.291028	−	0.956714i	$-0.406003\pi$
$929$	17.7408			0.582057			0.291028	+	0.956714i	$0.406003\pi$
$930$		0			0
$931$	11.5536	−	43.7994i	0.378654	−	1.43547i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.33670	+	1.34909i	−0.0764182	+	0.0441200i
$936$		0			0
$937$			10.2459i			0.334719i	0.985896	+	0.167360i	$0.0535241\pi$
$937$			10.2459i			0.334719i	−0.985896	+	0.167360i	$0.946476\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.99655			−0.325878			−0.162939	−	0.986636i	$-0.552097\pi$
$941$	−9.99655			−0.325878			−0.162939	+	0.986636i	$0.552097\pi$
$942$		0			0
$943$			0.937624i			0.0305332i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	48.2494i		−	1.56790i	−0.620827	−	0.783948i	$-0.713203\pi$
$947$		−	48.2494i		−	1.56790i	0.620827	−	0.783948i	$-0.286797\pi$
$948$		0			0
$949$	21.1562			0.686760
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	40.4708i		−	1.31098i	−0.755205	−	0.655489i	$-0.772463\pi$
$953$		−	40.4708i		−	1.31098i	0.755205	−	0.655489i	$-0.227537\pi$
$954$		0			0
$955$	1.94832	−	1.12486i	0.0630462	−	0.0363997i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−47.1459	+	19.6360i	−1.52242	+	0.634079i
$960$		0			0
$961$	9.51402			0.306904
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.59117	+	2.75598i	0.0512215	+	0.0887182i
$966$		0			0
$967$	−14.6566	+	25.3860i	−0.471325	+	0.816359i	−0.999462	−	0.0328000i	$-0.989558\pi$
$967$	−14.6566	+	25.3860i	−0.471325	+	0.816359i	0.528137	+	0.849159i	$0.322891\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.02830	−	15.6375i	0.289732	−	0.501831i	−0.684014	−	0.729469i	$-0.739767\pi$
$971$	9.02830	−	15.6375i	0.289732	−	0.501831i	0.973746	+	0.227639i	$0.0731005\pi$
$972$		0			0
$973$	−2.43653	+	1.01480i	−0.0781117	+	0.0325330i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	39.2466i		−	1.25561i	−0.778371	−	0.627805i	$-0.783953\pi$
$977$		−	39.2466i		−	1.25561i	0.778371	−	0.627805i	$-0.216047\pi$
$978$		0			0
$979$	2.67628	−	1.54515i	0.0855344	−	0.0493833i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.2334	−	22.9209i	0.422079	−	0.731063i	−0.574063	−	0.818811i	$-0.694634\pi$
$983$	13.2334	−	22.9209i	0.422079	−	0.731063i	0.996143	+	0.0877479i	$0.0279670\pi$
$984$		0			0
$985$	−1.58633	+	0.915869i	−0.0505447	+	0.0291820i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.667484	−	0.385372i	−0.0212248	−	0.0122541i
$990$		0			0
$991$	7.32864	+	12.6936i	0.232802	+	0.403225i	0.958632	−	0.284650i	$-0.0918773\pi$
$991$	7.32864	+	12.6936i	0.232802	+	0.403225i	−0.725830	+	0.687875i	$0.758544\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.18896	−	1.26380i	−0.0693948	−	0.0400651i
$996$		0			0
$997$	3.41103	+	1.96936i	0.108028	+	0.0623703i	0.553041	−	0.833154i	$-0.313467\pi$
$997$	3.41103	+	1.96936i	0.108028	+	0.0623703i	−0.445012	+	0.895524i	$0.646801\pi$
$998$		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.1097.13		48
3.2	odd	2		504.2.bs.a.257.8	✓	48
4.3	odd	2		3024.2.ca.e.2609.13		48
7.3	odd	6		1512.2.cx.a.17.13		48
9.2	odd	6		1512.2.cx.a.89.13		48
9.7	even	3		504.2.cx.a.425.1	yes	48
12.11	even	2		1008.2.ca.e.257.17		48
21.17	even	6		504.2.cx.a.185.1	yes	48
28.3	even	6		3024.2.df.e.17.13		48
36.7	odd	6		1008.2.df.e.929.24		48
36.11	even	6		3024.2.df.e.1601.13		48
63.38	even	6	inner	1512.2.bs.a.521.13		48
63.52	odd	6		504.2.bs.a.353.8	yes	48
84.59	odd	6		1008.2.df.e.689.24		48
252.115	even	6		1008.2.ca.e.353.17		48
252.227	odd	6		3024.2.ca.e.2033.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.8	✓	48	3.2	odd	2
504.2.bs.a.353.8	yes	48	63.52	odd	6
504.2.cx.a.185.1	yes	48	21.17	even	6
504.2.cx.a.425.1	yes	48	9.7	even	3
1008.2.ca.e.257.17		48	12.11	even	2
1008.2.ca.e.353.17		48	252.115	even	6
1008.2.df.e.689.24		48	84.59	odd	6
1008.2.df.e.929.24		48	36.7	odd	6
1512.2.bs.a.521.13		48	63.38	even	6	inner
1512.2.bs.a.1097.13		48	1.1	even	1	trivial
1512.2.cx.a.17.13		48	7.3	odd	6
1512.2.cx.a.89.13		48	9.2	odd	6
3024.2.ca.e.2033.13		48	252.227	odd	6
3024.2.ca.e.2609.13		48	4.3	odd	2
3024.2.df.e.17.13		48	28.3	even	6
3024.2.df.e.1601.13		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)

\(f(q)\)	\(=\)	\(q+(0.271038 + 0.469451i) q^{5} +(1.60655 - 2.10214i) q^{7} +(0.666300 + 0.384688i) q^{11} +(-2.96386 - 1.71119i) q^{13} +(3.23477 + 5.60278i) q^{17} +(5.60413 + 3.23554i) q^{19} +(-0.100353 + 0.0579388i) q^{23} +(2.35308 - 4.07565i) q^{25} +(-4.40174 + 2.54135i) q^{29} -4.63530i q^{31} +(1.42229 + 0.184434i) q^{35} +(5.47518 - 9.48329i) q^{37} +(4.04575 - 7.00745i) q^{41} +(3.32569 + 5.76026i) q^{43} -1.54617 q^{47} +(-1.83802 - 6.75438i) q^{49} +(0.221011 - 0.127601i) q^{53} +0.417060i q^{55} +10.2411 q^{59} +5.57913i q^{61} -1.85518i q^{65} -3.28349 q^{67} +5.67917i q^{71} +(-5.35354 + 3.09087i) q^{73} +(1.87911 - 0.782639i) q^{77} +4.02459 q^{79} +(5.80057 + 10.0469i) q^{83} +(-1.75349 + 3.03713i) q^{85} +(2.00832 - 3.47851i) q^{89} +(-8.35874 + 3.48136i) q^{91} +3.50781i q^{95} +(15.0653 - 8.69795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) \) 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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