LMFDB - Embedded newform 2160.2.by.d.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2160,2,Mod(289,2160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2160.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2160, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2160.by (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2160.289
Dual form			2160.2.by.d.1009.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81431 - 1.30701i) q^{5} +(3.85337 + 2.22474i) q^{7} +(-0.724745 + 1.25529i) q^{11} +(2.12132 - 1.22474i) q^{13} -3.89898i q^{17} -0.550510 q^{19} +(2.51059 - 1.44949i) q^{23} +(1.58346 - 4.74264i) q^{25} +(3.00000 - 5.19615i) q^{29} +(3.22474 + 5.58542i) q^{31} +(9.89898 - 1.00000i) q^{35} +8.00000i q^{37} +(-0.500000 - 0.866025i) q^{41} +(-6.45145 - 3.72474i) q^{43} +(-0.389270 - 0.224745i) q^{47} +(6.39898 + 11.0834i) q^{49} +8.44949i q^{53} +(0.325765 + 3.22474i) q^{55} +(-5.62372 - 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +(2.24799 - 4.99465i) q^{65} +(-8.18350 + 4.72474i) q^{67} +2.44949 q^{71} +4.79796i q^{73} +(-5.58542 + 3.22474i) q^{77} +(3.67423 - 6.36396i) q^{79} +(-3.46410 - 2.00000i) q^{83} +(-5.09599 - 7.07397i) q^{85} +12.8990 q^{89} +10.8990 q^{91} +(-0.998798 + 0.719521i) q^{95} +(-11.2583 - 6.50000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 4 q^{11} - 24 q^{19} + 24 q^{29} + 16 q^{31} + 40 q^{35} - 4 q^{41} + 12 q^{49} + 32 q^{55} + 4 q^{59} - 8 q^{61} + 12 q^{65} - 20 q^{85} + 64 q^{89} + 48 q^{91} - 24 q^{95}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^11 - 24 * q^19 + 24 * q^29 + 16 * q^31 + 40 * q^35 - 4 * q^41 + 12 * q^49 + 32 * q^55 + 4 * q^59 - 8 * q^61 + 12 * q^65 - 20 * q^85 + 64 * q^89 + 48 * q^91 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	1.81431	−	1.30701i	0.811386	−	0.584511i
$5$	1.81431	−	1.30701i	0.811386	−	0.584511i
$6$		0			0
$7$	3.85337	+	2.22474i	1.45644	+	0.840875i	0.998834	−	0.0482818i	$-0.0153745\pi$
$7$	3.85337	+	2.22474i	1.45644	+	0.840875i	0.457604	+	0.889156i	$0.348708\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.724745	+	1.25529i	−0.218519	+	0.378486i	−0.954355	−	0.298674i	$-0.903456\pi$
$11$	−0.724745	+	1.25529i	−0.218519	+	0.378486i	0.735837	+	0.677159i	$0.236789\pi$
$12$		0			0
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	3.89898i		−	0.945641i	−0.881159	−	0.472821i	$-0.843236\pi$
$17$		−	3.89898i		−	0.945641i	0.881159	−	0.472821i	$-0.156764\pi$
$18$		0			0
$19$	−0.550510			−0.126296			−0.0631479	−	0.998004i	$-0.520114\pi$
$19$	−0.550510			−0.126296			−0.0631479	+	0.998004i	$0.520114\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.51059	−	1.44949i	0.523494	−	0.302240i	−0.214869	−	0.976643i	$-0.568932\pi$
$23$	2.51059	−	1.44949i	0.523494	−	0.302240i	0.738363	+	0.674403i	$0.235599\pi$
$24$		0			0
$25$	1.58346	−	4.74264i	0.316693	−	0.948528i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	0.995573	+	0.0939863i	$0.0299610\pi$
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	−0.416392	+	0.909185i	$0.636706\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.89898	−	1.00000i	1.67323	−	0.169031i
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$		0			0
$43$	−6.45145	−	3.72474i	−0.983836	−	0.568018i	−0.0804103	−	0.996762i	$-0.525623\pi$
$43$	−6.45145	−	3.72474i	−0.983836	−	0.568018i	−0.903426	+	0.428744i	$0.858956\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.389270	−	0.224745i	−0.0567808	−	0.0327824i	0.471341	−	0.881951i	$-0.343770\pi$
$47$	−0.389270	−	0.224745i	−0.0567808	−	0.0327824i	−0.528122	+	0.849169i	$0.677104\pi$
$48$		0			0
$49$	6.39898	+	11.0834i	0.914140	+	1.58334i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			8.44949i			1.16063i	0.814393	+	0.580313i	$0.197070\pi$
$53$			8.44949i			1.16063i	−0.814393	+	0.580313i	$0.802930\pi$
$54$		0			0
$55$	0.325765	+	3.22474i	0.0439262	+	0.434825i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.62372	−	9.74058i	−0.732147	−	1.26812i	−0.955964	−	0.293484i	$-0.905185\pi$
$59$	−5.62372	−	9.74058i	−0.732147	−	1.26812i	0.223817	−	0.974631i	$-0.428148\pi$
$60$		0			0
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	−0.851279	−	0.524713i	$-0.824173\pi$
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	0.880055	+	0.474873i	$0.157506\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.24799	−	4.99465i	0.278829	−	0.619510i
$66$		0			0
$67$	−8.18350	+	4.72474i	−0.999773	+	0.577219i	−0.908181	−	0.418577i	$-0.862529\pi$
$67$	−8.18350	+	4.72474i	−0.999773	+	0.577219i	−0.0915922	+	0.995797i	$0.529196\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.44949			0.290701			0.145350	−	0.989380i	$-0.453569\pi$
$71$	2.44949			0.290701			0.145350	+	0.989380i	$0.453569\pi$
$72$		0			0
$73$			4.79796i			0.561559i	0.959772	+	0.280779i	$0.0905929\pi$
$73$			4.79796i			0.561559i	−0.959772	+	0.280779i	$0.909407\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.58542	+	3.22474i	−0.636518	+	0.367494i
$78$		0			0
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	−0.581874	−	0.813279i	$-0.697680\pi$
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	0.995257	+	0.0972777i	$0.0310135\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	0.297686	−	0.954664i	$-0.403785\pi$
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	−0.677920	+	0.735135i	$0.737119\pi$
$84$		0			0
$85$	−5.09599	−	7.07397i	−0.552738	−	0.767280i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.8990			1.36729			0.683645	−	0.729815i	$-0.260394\pi$
$89$	12.8990			1.36729			0.683645	+	0.729815i	$0.260394\pi$
$90$		0			0
$91$	10.8990			1.14252
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.998798	+	0.719521i	−0.102475	+	0.0738213i
$96$		0			0
$97$	−11.2583	−	6.50000i	−1.14311	−	0.659975i	−0.195911	−	0.980622i	$-0.562766\pi$
$97$	−11.2583	−	6.50000i	−1.14311	−	0.659975i	−0.947199	+	0.320647i	$0.896100\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$	8.87455	−	5.12372i	0.874435	−	0.504856i	0.00561582	−	0.999984i	$-0.498212\pi$
$103$	8.87455	−	5.12372i	0.874435	−	0.504856i	0.868820	+	0.495129i	$0.164879\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			1.65153i			0.159660i	0.996809	+	0.0798298i	$0.0254377\pi$
$107$			1.65153i			0.159660i	−0.996809	+	0.0798298i	$0.974562\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.24264	−	2.44949i	0.399114	−	0.230429i	−0.286988	−	0.957934i	$-0.592654\pi$
$113$	4.24264	−	2.44949i	0.399114	−	0.230429i	0.686102	+	0.727506i	$0.259321\pi$
$114$		0			0
$115$	2.66050	−	5.91119i	0.248093	−	0.551221i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.67423	−	15.0242i	0.795166	−	1.37727i
$120$		0			0
$121$	4.44949	+	7.70674i	0.404499	+	0.700613i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.32577	−	10.6742i	−0.297465	−	0.954733i
$126$		0			0
$127$			2.89898i			0.257243i	0.991694	+	0.128621i	$0.0410552\pi$
$127$			2.89898i			0.257243i	−0.991694	+	0.128621i	$0.958945\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.44949	+	4.24264i	0.214013	+	0.370681i	0.952967	−	0.303075i	$-0.0980132\pi$
$131$	2.44949	+	4.24264i	0.214013	+	0.370681i	−0.738954	+	0.673756i	$0.764680\pi$
$132$		0			0
$133$	−2.12132	−	1.22474i	−0.183942	−	0.106199i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	0.606861	−	0.794808i	$-0.292428\pi$
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	−0.384893	+	0.922961i	$0.625762\pi$
$138$		0			0
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	0.999653	−	0.0263597i	$-0.00839153\pi$
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	−0.522654	+	0.852545i	$0.675058\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			3.55051i			0.296909i
$144$		0			0
$145$	−1.34847	−	13.3485i	−0.111984	−	1.10853i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.12372	−	14.0707i	−0.665521	−	1.15272i	−0.979144	−	0.203169i	$-0.934876\pi$
$149$	−8.12372	−	14.0707i	−0.665521	−	1.15272i	0.313622	−	0.949548i	$-0.398457\pi$
$150$		0			0
$151$	−3.44949	+	5.97469i	−0.280715	+	0.486213i	−0.971561	−	0.236789i	$-0.923905\pi$
$151$	−3.44949	+	5.97469i	−0.280715	+	0.486213i	0.690846	+	0.723002i	$0.257238\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	13.1509	+	5.91894i	1.05630	+	0.475421i
$156$		0			0
$157$	13.8564	−	8.00000i	1.10586	−	0.638470i	0.168107	−	0.985769i	$-0.446235\pi$
$157$	13.8564	−	8.00000i	1.10586	−	0.638470i	0.937754	+	0.347299i	$0.112901\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.8990			1.01658
$162$		0			0
$163$		−	0.898979i		−	0.0704135i	−0.999380	−	0.0352068i	$-0.988791\pi$
$163$		−	0.898979i		−	0.0704135i	0.999380	−	0.0352068i	$-0.0112090\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.9989	+	12.1237i	−1.62494	+	0.938162i	−0.639374	+	0.768896i	$0.720806\pi$
$167$	−20.9989	+	12.1237i	−1.62494	+	0.938162i	−0.985570	+	0.169266i	$0.945860\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.75323	−	3.89898i	−0.513439	−	0.296434i	0.220807	−	0.975317i	$-0.429131\pi$
$173$	−6.75323	−	3.89898i	−0.513439	−	0.296434i	−0.734246	+	0.678884i	$0.762464\pi$
$174$		0			0
$175$	16.6528	−	14.7524i	1.25884	−	1.11517i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.89898			−0.665141			−0.332570	−	0.943078i	$-0.607916\pi$
$179$	−8.89898			−0.665141			−0.332570	+	0.943078i	$0.607916\pi$
$180$		0			0
$181$	10.4495			0.776704			0.388352	−	0.921511i	$-0.373044\pi$
$181$	10.4495			0.776704			0.388352	+	0.921511i	$0.373044\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.4561	+	14.5145i	0.768745	+	1.06713i
$186$		0			0
$187$	4.89437	+	2.82577i	0.357912	+	0.206640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.12372	−	5.41045i	0.226025	−	0.391486i	−0.730602	−	0.682804i	$-0.760760\pi$
$191$	3.12372	−	5.41045i	0.226025	−	0.391486i	0.956626	+	0.291318i	$0.0940936\pi$
$192$		0			0
$193$	13.5939	−	7.84847i	0.978514	−	0.564945i	0.0766927	−	0.997055i	$-0.475564\pi$
$193$	13.5939	−	7.84847i	0.978514	−	0.564945i	0.901821	+	0.432110i	$0.142231\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		0			0
$199$	20.4495			1.44963			0.724813	−	0.688946i	$-0.241926\pi$
$199$	20.4495			1.44963			0.724813	+	0.688946i	$0.241926\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	23.1202	−	13.3485i	1.62272	−	0.936879i
$204$		0			0
$205$	−2.03906	−	0.917738i	−0.142414	−	0.0640976i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.398979	−	0.691053i	0.0275980	−	0.0478011i
$210$		0			0
$211$	−7.89898	−	13.6814i	−0.543788	−	0.941869i	−0.998682	−	0.0513231i	$-0.983656\pi$
$211$	−7.89898	−	13.6814i	−0.543788	−	0.941869i	0.454894	−	0.890546i	$-0.349677\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−16.5732	+	1.67423i	−1.13028	+	0.114182i
$216$		0			0
$217$			28.6969i			1.94808i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.77526	−	8.27098i	−0.321218	−	0.556367i
$222$		0			0
$223$	−16.3670	−	9.44949i	−1.09602	−	0.632785i	−0.160844	−	0.986980i	$-0.551421\pi$
$223$	−16.3670	−	9.44949i	−1.09602	−	0.632785i	−0.935171	+	0.354195i	$0.884755\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.25529	−	0.724745i	−0.0833169	−	0.0481030i	0.457763	−	0.889074i	$-0.348651\pi$
$227$	−1.25529	−	0.724745i	−0.0833169	−	0.0481030i	−0.541080	+	0.840971i	$0.681984\pi$
$228$		0			0
$229$	−6.77526	−	11.7351i	−0.447721	−	0.775476i	0.550516	−	0.834825i	$-0.314431\pi$
$229$	−6.77526	−	11.7351i	−0.447721	−	0.775476i	−0.998237	+	0.0593484i	$0.981098\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			15.6969i			1.02834i	0.857688	+	0.514170i	$0.171900\pi$
$233$			15.6969i			1.02834i	−0.857688	+	0.514170i	$0.828100\pi$
$234$		0			0
$235$	−1.00000	+	0.101021i	−0.0652328	+	0.00658985i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.3485	+	24.8523i	0.928125	+	1.60756i	0.786456	+	0.617646i	$0.211914\pi$
$239$	14.3485	+	24.8523i	0.928125	+	1.60756i	0.141669	+	0.989914i	$0.454753\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	26.0958	+	11.7452i	1.66720	+	0.750371i
$246$		0			0
$247$	−1.16781	+	0.674235i	−0.0743059	+	0.0429005i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.4495			0.722685			0.361343	−	0.932433i	$-0.382318\pi$
$251$	11.4495			0.722685			0.361343	+	0.932433i	$0.382318\pi$
$252$		0			0
$253$			4.20204i			0.264180i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−17.2330	+	9.94949i	−1.07497	+	0.620632i	−0.929534	−	0.368736i	$-0.879791\pi$
$257$	−17.2330	+	9.94949i	−1.07497	+	0.620632i	−0.145432	+	0.989368i	$0.546457\pi$
$258$		0			0
$259$	−17.7980	+	30.8270i	−1.10591	+	1.91549i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.53893	−	3.77526i	−0.403208	−	0.232792i	0.284659	−	0.958629i	$-0.408120\pi$
$263$	−6.53893	−	3.77526i	−0.403208	−	0.232792i	−0.687867	+	0.725837i	$0.741453\pi$
$264$		0			0
$265$	11.0435	+	15.3300i	0.678400	+	0.941716i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−28.0454			−1.70996			−0.854979	−	0.518662i	$-0.826430\pi$
$269$	−28.0454			−1.70996			−0.854979	+	0.518662i	$0.826430\pi$
$270$		0			0
$271$	−23.5959			−1.43335			−0.716675	−	0.697407i	$-0.754337\pi$
$271$	−23.5959			−1.43335			−0.716675	+	0.697407i	$0.754337\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.80581	+	5.42492i	0.289801	+	0.327135i
$276$		0			0
$277$	−8.31031	−	4.79796i	−0.499318	−	0.288281i	0.229114	−	0.973400i	$-0.426417\pi$
$277$	−8.31031	−	4.79796i	−0.499318	−	0.288281i	−0.728432	+	0.685118i	$0.759751\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	0.987615	+	0.156898i	$0.0501493\pi$
$282$		0			0
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	4.44949i		−	0.262645i
$288$		0			0
$289$	1.79796			0.105762
$290$		0			0
$291$		0			0
$292$		0			0
$293$	15.5885	−	9.00000i	0.910687	−	0.525786i	0.0300351	−	0.999549i	$-0.490438\pi$
$293$	15.5885	−	9.00000i	0.910687	−	0.525786i	0.880652	+	0.473763i	$0.157105\pi$
$294$		0			0
$295$	−22.9342	−	10.3222i	−1.33528	−	0.600982i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.55051	−	6.14966i	0.205331	−	0.355644i
$300$		0			0
$301$	−16.5732	−	28.7056i	−0.955264	−	1.65457i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.101021	−	1.00000i	−0.00578442	−	0.0572598i
$306$		0			0
$307$			23.9444i			1.36658i	0.730148	+	0.683289i	$0.239451\pi$
$307$			23.9444i			1.36658i	−0.730148	+	0.683289i	$0.760549\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.4495	−	19.8311i	−0.649241	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$311$	−11.4495	−	19.8311i	−0.649241	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$312$		0			0
$313$	6.66574	+	3.84847i	0.376770	+	0.217528i	0.676412	−	0.736523i	$-0.263534\pi$
$313$	6.66574	+	3.84847i	0.376770	+	0.217528i	−0.299642	+	0.954052i	$0.596867\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−26.7986	−	15.4722i	−1.50516	−	0.869005i	−0.999982	−	0.00599020i	$-0.998093\pi$
$317$	−26.7986	−	15.4722i	−1.50516	−	0.869005i	−0.505179	−	0.863015i	$-0.668573\pi$
$318$		0			0
$319$	4.34847	+	7.53177i	0.243468	+	0.421698i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			2.14643i			0.119430i
$324$		0			0
$325$	−2.44949	−	12.0000i	−0.135873	−	0.665640i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.00000	−	1.73205i	−0.0551318	−	0.0954911i
$330$		0			0
$331$	16.6969	−	28.9199i	0.917747	−	1.58958i	0.114917	−	0.993375i	$-0.463340\pi$
$331$	16.6969	−	28.9199i	0.917747	−	1.58958i	0.802829	−	0.596209i	$-0.203327\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.67215	+	19.2681i	−0.473810	+	1.05273i
$336$		0			0
$337$	−17.8366	+	10.2980i	−0.971621	+	0.560966i	−0.899730	−	0.436447i	$-0.856237\pi$
$337$	−17.8366	+	10.2980i	−0.971621	+	0.560966i	−0.0718909	+	0.997413i	$0.522903\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.34847			−0.506248
$342$		0			0
$343$			25.7980i			1.39296i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.2047	+	7.62372i	−0.708864	+	0.409263i	−0.810640	−	0.585544i	$-0.800881\pi$
$347$	−13.2047	+	7.62372i	−0.708864	+	0.409263i	0.101776	+	0.994807i	$0.467547\pi$
$348$		0			0
$349$	5.79796	−	10.0424i	0.310358	−	0.537555i	−0.668082	−	0.744088i	$-0.732885\pi$
$349$	5.79796	−	10.0424i	0.310358	−	0.537555i	0.978440	+	0.206532i	$0.0662179\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.71223	+	3.29796i	0.304031	+	0.175533i	0.644253	−	0.764813i	$-0.277169\pi$
$353$	5.71223	+	3.29796i	0.304031	+	0.175533i	−0.340221	+	0.940345i	$0.610502\pi$
$354$		0			0
$355$	4.44414	−	3.20150i	0.235871	−	0.169918i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.44949			−0.445947			−0.222974	−	0.974825i	$-0.571576\pi$
$359$	−8.44949			−0.445947			−0.222974	+	0.974825i	$0.571576\pi$
$360$		0			0
$361$	−18.6969			−0.984049
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.27097	+	8.70500i	0.328237	+	0.455641i
$366$		0			0
$367$	−10.0424	−	5.79796i	−0.524207	−	0.302651i	0.214447	−	0.976736i	$-0.431205\pi$
$367$	−10.0424	−	5.79796i	−0.524207	−	0.302651i	−0.738654	+	0.674085i	$0.764538\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.7980	+	32.5590i	−0.975941	+	1.69038i
$372$		0			0
$373$	−22.1667	+	12.7980i	−1.14775	+	0.662653i	−0.948338	−	0.317263i	$-0.897236\pi$
$373$	−22.1667	+	12.7980i	−1.14775	+	0.662653i	−0.199411	+	0.979916i	$0.563903\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	14.6969i		−	0.756931i
$378$		0			0
$379$	−30.1464			−1.54852			−0.774259	−	0.632869i	$-0.781877\pi$
$379$	−30.1464			−1.54852			−0.774259	+	0.632869i	$0.781877\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.55708	+	0.898979i	−0.0795630	+	0.0459357i	−0.539254	−	0.842143i	$-0.681294\pi$
$383$	−1.55708	+	0.898979i	−0.0795630	+	0.0459357i	0.459691	+	0.888079i	$0.347960\pi$
$384$		0			0
$385$	−5.91894	+	13.1509i	−0.301657	+	0.670231i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.2247	+	19.4418i	−0.569117	+	0.985740i	0.427536	+	0.903998i	$0.359382\pi$
$389$	−11.2247	+	19.4418i	−0.569117	+	0.985740i	−0.996654	+	0.0817417i	$0.973952\pi$
$390$		0			0
$391$	−5.65153	−	9.78874i	−0.285810	−	0.495038i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.65153	−	16.3485i	−0.0830975	−	0.822581i
$396$		0			0
$397$			17.7980i			0.893254i	0.894720	+	0.446627i	$0.147375\pi$
$397$			17.7980i			0.893254i	−0.894720	+	0.446627i	$0.852625\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.3990	+	24.9398i	0.719051	+	1.24543i	0.961376	+	0.275237i	$0.0887565\pi$
$401$	14.3990	+	24.9398i	0.719051	+	1.24543i	−0.242326	+	0.970195i	$0.577910\pi$
$402$		0			0
$403$	13.6814	+	7.89898i	0.681521	+	0.393476i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.0424	−	5.79796i	−0.497781	−	0.287394i
$408$		0			0
$409$	3.05051	+	5.28364i	0.150838	+	0.261259i	0.931536	−	0.363650i	$-0.118469\pi$
$409$	3.05051	+	5.28364i	0.150838	+	0.261259i	−0.780698	+	0.624909i	$0.785136\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	50.0454i		−	2.46257i
$414$		0			0
$415$	−8.89898	+	0.898979i	−0.436834	+	0.0441292i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.449490	+	0.778539i	0.0219590	+	0.0380341i	0.876796	−	0.480862i	$-0.159676\pi$
$419$	0.449490	+	0.778539i	0.0219590	+	0.0380341i	−0.854837	+	0.518896i	$0.826343\pi$
$420$		0			0
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	−0.592979	−	0.805218i	$-0.702048\pi$
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	0.993829	+	0.110926i	$0.0353817\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.4915	−	6.17389i	−0.896968	−	0.299478i
$426$		0			0
$427$	1.73205	−	1.00000i	0.0838198	−	0.0483934i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.7526			0.662437			0.331219	−	0.943554i	$-0.392540\pi$
$431$	13.7526			0.662437			0.331219	+	0.943554i	$0.392540\pi$
$432$		0			0
$433$		−	23.0000i		−	1.10531i	−0.833410	−	0.552655i	$-0.813615\pi$
$433$		−	23.0000i		−	1.10531i	0.833410	−	0.552655i	$-0.186385\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.38211	+	0.797959i	−0.0661151	+	0.0381716i
$438$		0			0
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	−0.473453	−	0.880819i	$-0.656993\pi$
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	0.999538	−	0.0303869i	$-0.00967395\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.81237	−	1.62372i	−0.133620	−	0.0771455i	0.431700	−	0.902017i	$-0.357914\pi$
$443$	−2.81237	−	1.62372i	−0.133620	−	0.0771455i	−0.565320	+	0.824872i	$0.691247\pi$
$444$		0			0
$445$	23.4028	−	16.8591i	1.10940	−	0.799196i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.797959			−0.0376580			−0.0188290	−	0.999823i	$-0.505994\pi$
$449$	−0.797959			−0.0376580			−0.0188290	+	0.999823i	$0.505994\pi$
$450$		0			0
$451$	1.44949			0.0682538
$452$		0			0
$453$		0			0
$454$		0			0
$455$	19.7742	−	14.2450i	0.927027	−	0.667818i
$456$		0			0
$457$	7.01569	+	4.05051i	0.328180	+	0.189475i	0.655033	−	0.755600i	$-0.272655\pi$
$457$	7.01569	+	4.05051i	0.328180	+	0.189475i	−0.326853	+	0.945075i	$0.605988\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.22474	−	2.12132i	0.0570421	−	0.0987997i	−0.836094	−	0.548586i	$-0.815166\pi$
$461$	1.22474	−	2.12132i	0.0570421	−	0.0987997i	0.893136	+	0.449786i	$0.148500\pi$
$462$		0			0
$463$	20.7846	−	12.0000i	0.965943	−	0.557687i	0.0679458	−	0.997689i	$-0.478356\pi$
$463$	20.7846	−	12.0000i	0.965943	−	0.557687i	0.897997	+	0.440002i	$0.145022\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			4.34847i			0.201223i	0.994926	+	0.100612i	$0.0320799\pi$
$467$			4.34847i			0.201223i	−0.994926	+	0.100612i	$0.967920\pi$
$468$		0			0
$469$	−42.0454			−1.94148
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.35131	−	5.39898i	0.429974	−	0.248245i
$474$		0			0
$475$	−0.871713	+	2.61087i	−0.0399970	+	0.119795i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.34847	+	10.9959i	−0.290069	+	0.502414i	−0.973826	−	0.227296i	$-0.927012\pi$
$479$	−6.34847	+	10.9959i	−0.290069	+	0.502414i	0.683757	+	0.729710i	$0.260345\pi$
$480$		0			0
$481$	9.79796	+	16.9706i	0.446748	+	0.773791i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−28.9217	+	2.92168i	−1.31327	+	0.132667i
$486$		0			0
$487$			34.8990i			1.58142i	0.612188	+	0.790712i	$0.290289\pi$
$487$			34.8990i			1.58142i	−0.612188	+	0.790712i	$0.709711\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.7247	−	20.3079i	−0.529130	−	0.916481i	−0.999423	−	0.0339700i	$-0.989185\pi$
$491$	−11.7247	−	20.3079i	−0.529130	−	0.916481i	0.470293	−	0.882511i	$-0.344148\pi$
$492$		0			0
$493$	−20.2597	−	11.6969i	−0.912451	−	0.526804i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.43879	+	5.44949i	0.423388	+	0.244443i
$498$		0			0
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	0.827391	−	0.561627i	$-0.189824\pi$
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	−0.900078	+	0.435728i	$0.856491\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	9.55051i		−	0.425836i	−0.977070	−	0.212918i	$-0.931703\pi$
$503$		−	9.55051i		−	0.425836i	0.977070	−	0.212918i	$-0.0682968\pi$
$504$		0			0
$505$	1.79796	+	17.7980i	0.0800081	+	0.791999i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.79796	+	6.57826i	0.168342	+	0.291576i	0.937837	−	0.347076i	$-0.112826\pi$
$509$	3.79796	+	6.57826i	0.168342	+	0.291576i	−0.769495	+	0.638652i	$0.779492\pi$
$510$		0			0
$511$	−10.6742	+	18.4883i	−0.472200	+	0.817875i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.40447	−	20.8951i	0.414410	−	0.920750i
$516$		0			0
$517$	0.564242	−	0.325765i	0.0248153	−	0.0143271i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.69694			0.337209			0.168604	−	0.985684i	$-0.446074\pi$
$521$	7.69694			0.337209			0.168604	+	0.985684i	$0.446074\pi$
$522$		0			0
$523$		−	29.7980i		−	1.30297i	−0.758660	−	0.651487i	$-0.774146\pi$
$523$		−	29.7980i		−	1.30297i	0.758660	−	0.651487i	$-0.225854\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.7774	−	12.5732i	0.948640	−	0.547698i
$528$		0			0
$529$	−7.29796	+	12.6404i	−0.317303	+	0.549584i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.12132	−	1.22474i	−0.0918846	−	0.0530496i
$534$		0			0
$535$	2.15856	+	2.99639i	0.0933228	+	0.129545i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.5505			−0.799027
$540$		0			0
$541$	−39.5959			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$541$	−39.5959			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.5145	−	10.4561i	0.621733	−	0.447888i
$546$		0			0
$547$	−6.27647	−	3.62372i	−0.268363	−	0.154939i	0.359781	−	0.933037i	$-0.382852\pi$
$547$	−6.27647	−	3.62372i	−0.268363	−	0.154939i	−0.628143	+	0.778098i	$0.716185\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.65153	+	2.86054i	−0.0703576	+	0.121863i
$552$		0			0
$553$	28.3164	−	16.3485i	1.20413	−	0.695208i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			38.9444i			1.65013i	0.565040	+	0.825063i	$0.308861\pi$
$557$			38.9444i			1.65013i	−0.565040	+	0.825063i	$0.691139\pi$
$558$		0			0
$559$	−18.2474			−0.771785
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−31.3037	+	18.0732i	−1.31929	+	0.761695i	−0.983615	−	0.180281i	$-0.942299\pi$
$563$	−31.3037	+	18.0732i	−1.31929	+	0.761695i	−0.335680	+	0.941976i	$0.608966\pi$
$564$		0			0
$565$	4.49598	−	9.98930i	0.189147	−	0.420253i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.74745	+	15.1510i	−0.366712	+	0.635164i	−0.989049	−	0.147585i	$-0.952850\pi$
$569$	−8.74745	+	15.1510i	−0.366712	+	0.635164i	0.622337	+	0.782749i	$0.286183\pi$
$570$		0			0
$571$	6.37628	+	11.0440i	0.266839	+	0.462178i	0.968044	−	0.250781i	$-0.0806875\pi$
$571$	6.37628	+	11.0440i	0.266839	+	0.462178i	−0.701205	+	0.712960i	$0.747354\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.89898	−	14.2020i	−0.120896	−	0.592266i
$576$		0			0
$577$			13.6969i			0.570211i	0.958496	+	0.285106i	$0.0920286\pi$
$577$			13.6969i			0.570211i	−0.958496	+	0.285106i	$0.907971\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.89898	−	15.4135i	−0.369192	−	0.639459i
$582$		0			0
$583$	−10.6066	−	6.12372i	−0.439281	−	0.253619i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.9326	−	14.9722i	−1.07035	−	0.617969i	−0.142075	−	0.989856i	$-0.545377\pi$
$587$	−25.9326	−	14.9722i	−1.07035	−	0.617969i	−0.928278	+	0.371887i	$0.878711\pi$
$588$		0			0
$589$	−1.77526	−	3.07483i	−0.0731481	−	0.126696i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			41.3939i			1.69984i	0.526910	+	0.849921i	$0.323351\pi$
$593$			41.3939i			1.69984i	−0.526910	+	0.849921i	$0.676649\pi$
$594$		0			0
$595$	−3.89898	−	38.5959i	−0.159843	−	1.58228i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	0.973843	−	0.227224i	$-0.0729648\pi$
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	−0.683703	+	0.729761i	$0.739632\pi$
$600$		0			0
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	−0.992665	−	0.120896i	$-0.961423\pi$
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	0.601031	+	0.799225i	$0.294757\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	18.1455	+	8.16693i	0.737721	+	0.332033i
$606$		0			0
$607$	−10.0424	+	5.79796i	−0.407607	+	0.235332i	−0.689761	−	0.724037i	$-0.742284\pi$
$607$	−10.0424	+	5.79796i	−0.407607	+	0.235332i	0.282154	+	0.959369i	$0.408951\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.10102			−0.0445425
$612$		0			0
$613$		−	16.9444i		−	0.684377i	−0.939631	−	0.342189i	$-0.888832\pi$
$613$		−	16.9444i		−	0.684377i	0.939631	−	0.342189i	$-0.111168\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−32.6465	+	18.8485i	−1.31430	+	0.758811i	−0.982805	−	0.184647i	$-0.940886\pi$
$617$	−32.6465	+	18.8485i	−1.31430	+	0.758811i	−0.331494	+	0.943457i	$0.607553\pi$
$618$		0			0
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	−0.305048	−	0.952337i	$-0.598672\pi$
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	0.977272	−	0.211989i	$-0.0679943\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	49.7046	+	28.6969i	1.99137	+	1.14972i
$624$		0			0
$625$	−19.9853	−	15.0196i	−0.799411	−	0.600784i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	31.1918			1.24370
$630$		0			0
$631$	−3.34847			−0.133300			−0.0666502	−	0.997776i	$-0.521231\pi$
$631$	−3.34847			−0.133300			−0.0666502	+	0.997776i	$0.521231\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.78899	+	5.25966i	0.150361	+	0.208723i
$636$		0			0
$637$	27.1486	+	15.6742i	1.07567	+	0.621036i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$642$		0			0
$643$	−8.00853	+	4.62372i	−0.315825	+	0.182342i	−0.649530	−	0.760336i	$-0.725034\pi$
$643$	−8.00853	+	4.62372i	−0.315825	+	0.182342i	0.333705	+	0.942678i	$0.391701\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			25.1010i			0.986823i	0.869796	+	0.493411i	$0.164250\pi$
$647$			25.1010i			0.986823i	−0.869796	+	0.493411i	$0.835750\pi$
$648$		0			0
$649$	16.3031			0.639951
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−29.4449	+	17.0000i	−1.15227	+	0.665261i	−0.949439	−	0.313953i	$-0.898347\pi$
$653$	−29.4449	+	17.0000i	−1.15227	+	0.665261i	−0.202828	+	0.979214i	$0.565013\pi$
$654$		0			0
$655$	9.98930	+	4.49598i	0.390314	+	0.175672i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.10102	+	14.0314i	−0.315571	+	0.546585i	−0.979559	−	0.201159i	$-0.935529\pi$
$659$	−8.10102	+	14.0314i	−0.315571	+	0.546585i	0.663988	+	0.747743i	$0.268863\pi$
$660$		0			0
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	0.968433	−	0.249274i	$-0.0801919\pi$
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	−0.700094	+	0.714051i	$0.746859\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.44949	+	0.550510i	−0.211322	+	0.0213479i
$666$		0			0
$667$		−	17.3939i		−	0.673494i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.325765	+	0.564242i	0.0125760	+	0.0217823i
$672$		0			0
$673$	−16.5420	−	9.55051i	−0.637646	−	0.368145i	0.146061	−	0.989276i	$-0.453340\pi$
$673$	−16.5420	−	9.55051i	−0.637646	−	0.368145i	−0.783707	+	0.621130i	$0.786674\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.349945	+	0.202041i	0.0134495	+	0.00776507i	0.506710	−	0.862117i	$-0.330862\pi$
$677$	0.349945	+	0.202041i	0.0134495	+	0.00776507i	−0.493260	+	0.869882i	$0.664195\pi$
$678$		0			0
$679$	−28.9217	−	50.0938i	−1.10991	−	1.92242i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			40.5505i			1.55162i	0.630965	+	0.775811i	$0.282659\pi$
$683$			40.5505i			1.55162i	−0.630965	+	0.775811i	$0.717341\pi$
$684$		0			0
$685$	6.67423	−	0.674235i	0.255009	−	0.0257612i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.3485	+	17.9241i	0.394245	+	0.682853i
$690$		0			0
$691$	−10.7980	+	18.7026i	−0.410774	+	0.711481i	−0.994975	−	0.100128i	$-0.968075\pi$
$691$	−10.7980	+	18.7026i	−0.410774	+	0.711481i	0.584201	+	0.811609i	$0.301408\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.9342	+	10.3222i	0.869944	+	0.391544i
$696$		0			0
$697$	−3.37662	+	1.94949i	−0.127898	+	0.0738422i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.3939			−0.732497			−0.366248	−	0.930517i	$-0.619358\pi$
$701$	−19.3939			−0.732497			−0.366248	+	0.930517i	$0.619358\pi$
$702$		0			0
$703$		−	4.40408i		−	0.166103i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.8270	+	17.7980i	−1.15937	+	0.669361i
$708$		0			0
$709$	11.3258	−	19.6168i	0.425348	−	0.736724i	−0.571105	−	0.820877i	$-0.693485\pi$
$709$	11.3258	−	19.6168i	0.425348	−	0.736724i	0.996453	+	0.0841527i	$0.0268184\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.1920	+	9.34847i	0.606396	+	0.350103i
$714$		0			0
$715$	4.64054	+	6.44174i	0.173546	+	0.240907i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−22.2020			−0.827996			−0.413998	−	0.910278i	$-0.635868\pi$
$719$	−22.2020			−0.827996			−0.413998	+	0.910278i	$0.635868\pi$
$720$		0			0
$721$	45.5959			1.69808
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.8931	−	22.4558i	−0.738811	−	0.833989i
$726$		0			0
$727$	−9.22450	−	5.32577i	−0.342118	−	0.197522i	0.319090	−	0.947724i	$-0.396623\pi$
$727$	−9.22450	−	5.32577i	−0.342118	−	0.197522i	−0.661208	+	0.750203i	$0.729956\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−14.5227	+	25.1541i	−0.537142	+	0.930357i
$732$		0			0
$733$	11.3851	−	6.57321i	0.420520	−	0.242787i	−0.274780	−	0.961507i	$-0.588605\pi$
$733$	11.3851	−	6.57321i	0.420520	−	0.242787i	0.695300	+	0.718720i	$0.255272\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	13.6969i		−	0.504533i
$738$		0			0
$739$	7.24745			0.266602			0.133301	−	0.991076i	$-0.457442\pi$
$739$	7.24745			0.266602			0.133301	+	0.991076i	$0.457442\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.3458	−	6.55051i	0.416238	−	0.240315i	−0.277229	−	0.960804i	$-0.589416\pi$
$743$	11.3458	−	6.55051i	0.416238	−	0.240315i	0.693466	+	0.720489i	$0.256083\pi$
$744$		0			0
$745$	−33.1295	−	14.9109i	−1.21377	−	0.546293i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.67423	+	6.36396i	−0.134254	+	0.232534i
$750$		0			0
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	0.905050	+	0.425306i	$0.139833\pi$
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	−0.0841993	+	0.996449i	$0.526833\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.55051	+	15.3485i	0.0564288	+	0.558588i
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.2474	−	41.9978i	−0.878969	−	1.52242i	−0.852473	−	0.522771i	$-0.824898\pi$
$761$	−24.2474	−	41.9978i	−0.878969	−	1.52242i	−0.0264959	−	0.999649i	$-0.508435\pi$
$762$		0			0
$763$	30.8270	+	17.7980i	1.11601	+	0.644329i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.8594	−	13.7753i	−0.861515	−	0.497396i
$768$		0			0
$769$	−12.2474	−	21.2132i	−0.441654	−	0.764968i	0.556158	−	0.831076i	$-0.312275\pi$
$769$	−12.2474	−	21.2132i	−0.441654	−	0.764968i	−0.997812	+	0.0661088i	$0.978942\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	23.3939i		−	0.841419i	−0.907195	−	0.420710i	$-0.861781\pi$
$773$		−	23.3939i		−	0.841419i	0.907195	−	0.420710i	$-0.138219\pi$
$774$		0			0
$775$	31.5959	−	6.44949i	1.13496	−	0.231673i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.275255	+	0.476756i	0.00986204	+	0.0170816i
$780$		0			0
$781$	−1.77526	+	3.07483i	−0.0635236	+	0.110026i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.6838	−	32.6249i	0.524087	−	1.16443i
$786$		0			0
$787$	−6.40329	+	3.69694i	−0.228252	+	0.131782i	−0.609766	−	0.792582i	$-0.708736\pi$
$787$	−6.40329	+	3.69694i	−0.228252	+	0.131782i	0.381513	+	0.924363i	$0.375403\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	21.7980			0.775046
$792$		0			0
$793$		−	1.10102i		−	0.0390984i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	30.8270	−	17.7980i	1.09195	−	0.630436i	0.157853	−	0.987463i	$-0.449543\pi$
$797$	30.8270	−	17.7980i	1.09195	−	0.630436i	0.934094	+	0.357027i	$0.116209\pi$
$798$		0			0
$799$	−0.876276	+	1.51775i	−0.0310004	+	0.0536943i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.02285	−	3.47730i	−0.212542	−	0.122711i
$804$		0			0
$805$	23.4028	−	16.8591i	0.824840	−	0.594204i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	47.0908			1.65562			0.827812	−	0.561005i	$-0.189585\pi$
$809$	47.0908			1.65562			0.827812	+	0.561005i	$0.189585\pi$
$810$		0			0
$811$	17.2474			0.605640			0.302820	−	0.953048i	$-0.402072\pi$
$811$	17.2474			0.605640			0.302820	+	0.953048i	$0.402072\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.17497	−	1.63103i	−0.0411575	−	0.0571325i
$816$		0			0
$817$	3.55159	+	2.05051i	0.124254	+	0.0717383i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.0227	+	36.4124i	−0.733697	+	1.27080i	0.221595	+	0.975139i	$0.428874\pi$
$821$	−21.0227	+	36.4124i	−0.733697	+	1.27080i	−0.955292	+	0.295662i	$0.904460\pi$
$822$		0			0
$823$	6.57826	−	3.79796i	0.229304	−	0.132389i	−0.380947	−	0.924597i	$-0.624402\pi$
$823$	6.57826	−	3.79796i	0.229304	−	0.132389i	0.610251	+	0.792208i	$0.291069\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	13.7980i		−	0.479802i	−0.970797	−	0.239901i	$-0.922885\pi$
$827$		−	13.7980i		−	0.479802i	0.970797	−	0.239901i	$-0.0771150\pi$
$828$		0			0
$829$	21.5505			0.748480			0.374240	−	0.927332i	$-0.377904\pi$
$829$	21.5505			0.748480			0.374240	+	0.927332i	$0.377904\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	43.2138	−	24.9495i	1.49727	−	0.864449i
$834$		0			0
$835$	−22.2528	+	49.4420i	−0.770090	+	1.71101i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.87628	−	13.6421i	0.271919	−	0.470978i	−0.697434	−	0.716649i	$-0.745675\pi$
$839$	7.87628	−	13.6421i	0.271919	−	0.470978i	0.969353	+	0.245671i	$0.0790083\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.57321	+	15.5732i	0.0541202	+	0.535735i
$846$		0			0
$847$			39.5959i			1.36053i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.5959	+	20.0847i	0.397503	+	0.688495i
$852$		0			0
$853$	−21.7774	−	12.5732i	−0.745646	−	0.430499i	0.0784728	−	0.996916i	$-0.474996\pi$
$853$	−21.7774	−	12.5732i	−0.745646	−	0.430499i	−0.824118	+	0.566418i	$0.808329\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−46.2405	−	26.6969i	−1.57954	−	0.911950i	−0.994923	−	0.100644i	$-0.967910\pi$
$857$	−46.2405	−	26.6969i	−1.57954	−	0.911950i	−0.584621	−	0.811306i	$-0.698757\pi$
$858$		0			0
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	−0.991280	−	0.131770i	$-0.957934\pi$
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	0.381524	−	0.924359i	$-0.375399\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	21.5505i		−	0.733588i	−0.930302	−	0.366794i	$-0.880455\pi$
$863$		−	21.5505i		−	0.733588i	0.930302	−	0.366794i	$-0.119545\pi$
$864$		0			0
$865$	−17.3485	+	1.75255i	−0.589866	+	0.0595885i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.32577	+	9.22450i	0.180664	+	0.312920i
$870$		0			0
$871$	−11.5732	+	20.0454i	−0.392143	+	0.679212i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.9320	−	48.5308i	0.369570	−	1.64064i
$876$		0			0
$877$	−47.7582	+	27.5732i	−1.61268	+	0.931081i	−0.623934	+	0.781477i	$0.714467\pi$
$877$	−47.7582	+	27.5732i	−1.61268	+	0.931081i	−0.988746	+	0.149604i	$0.952200\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$		−	11.4495i		−	0.385306i	−0.981267	−	0.192653i	$-0.938291\pi$
$883$		−	11.4495i		−	0.385306i	0.981267	−	0.192653i	$-0.0617092\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.02834	−	2.32577i	0.135259	−	0.0780916i	−0.430844	−	0.902427i	$-0.641784\pi$
$887$	4.02834	−	2.32577i	0.135259	−	0.0780916i	0.566102	+	0.824335i	$0.308451\pi$
$888$		0			0
$889$	−6.44949	+	11.1708i	−0.216309	+	0.374658i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.214297	+	0.123724i	0.00717117	+	0.00414028i
$894$		0			0
$895$	−16.1455	+	11.6310i	−0.539686	+	0.388782i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	38.6969			1.29062
$900$		0			0
$901$	32.9444			1.09754
$902$		0			0
$903$		0			0
$904$		0			0
$905$	18.9586	−	13.6576i	0.630207	−	0.453993i
$906$		0			0
$907$	29.2217	+	16.8712i	0.970292	+	0.560198i	0.899325	−	0.437281i	$-0.144058\pi$
$907$	29.2217	+	16.8712i	0.970292	+	0.560198i	0.0709665	+	0.997479i	$0.477392\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.123724	−	0.214297i	0.00409917	−	0.00709997i	−0.863969	−	0.503546i	$-0.832029\pi$
$911$	0.123724	−	0.214297i	0.00409917	−	0.00709997i	0.868068	+	0.496446i	$0.165362\pi$
$912$		0			0
$913$	5.02118	−	2.89898i	0.166177	−	0.0959422i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			21.7980i			0.719832i
$918$		0			0
$919$	10.8990			0.359524			0.179762	−	0.983710i	$-0.442467\pi$
$919$	10.8990			0.359524			0.179762	+	0.983710i	$0.442467\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.19615	−	3.00000i	0.171033	−	0.0987462i
$924$		0			0
$925$	37.9411	+	12.6677i	1.24750	+	0.416512i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.7980	−	48.1475i	0.912021	−	1.57967i	0.100817	−	0.994905i	$-0.467854\pi$
$929$	27.7980	−	48.1475i	0.912021	−	1.57967i	0.811205	−	0.584762i	$-0.198812\pi$
$930$		0			0
$931$	−3.52270	−	6.10150i	−0.115452	−	0.199969i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.5732	−	1.27015i	0.411188	−	0.0415384i
$936$		0			0
$937$		−	39.5959i		−	1.29354i	−0.762684	−	0.646771i	$-0.776119\pi$
$937$		−	39.5959i		−	1.29354i	0.762684	−	0.646771i	$-0.223881\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.8990	−	43.1263i	−0.811684	−	1.40588i	−0.911685	−	0.410890i	$-0.865218\pi$
$941$	−24.8990	−	43.1263i	−0.811684	−	1.40588i	0.100001	−	0.994987i	$-0.468115\pi$
$942$		0			0
$943$	−2.51059	−	1.44949i	−0.0817561	−	0.0472019i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.4008	+	10.6237i	0.597947	+	0.345225i	0.768233	−	0.640170i	$-0.221136\pi$
$947$	18.4008	+	10.6237i	0.597947	+	0.345225i	−0.170287	+	0.985395i	$0.554469\pi$
$948$		0			0
$949$	5.87628	+	10.1780i	0.190752	+	0.330392i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	50.7980i		−	1.64551i	−0.568398	−	0.822754i	$-0.692437\pi$
$953$		−	50.7980i		−	1.64551i	0.568398	−	0.822754i	$-0.307563\pi$
$954$		0			0
$955$	−1.40408	−	13.8990i	−0.0454350	−	0.449760i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.67423	+	11.5601i	0.215522	+	0.373296i
$960$		0			0
$961$	−5.29796	+	9.17633i	−0.170902	+	0.296011i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	14.4057	−	32.0070i	0.463735	−	1.03034i
$966$		0			0
$967$	24.8523	−	14.3485i	0.799195	−	0.461416i	−0.0439944	−	0.999032i	$-0.514008\pi$
$967$	24.8523	−	14.3485i	0.799195	−	0.461416i	0.843190	+	0.537616i	$0.180675\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.3939			−0.750745			−0.375373	−	0.926874i	$-0.622485\pi$
$971$	−23.3939			−0.750745			−0.375373	+	0.926874i	$0.622485\pi$
$972$		0			0
$973$			50.0454i			1.60438i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.8215	+	18.9495i	−1.05005	+	0.606248i	−0.922664	−	0.385605i	$-0.873993\pi$
$977$	−32.8215	+	18.9495i	−1.05005	+	0.606248i	−0.127388	+	0.991853i	$0.540659\pi$
$978$		0			0
$979$	−9.34847	+	16.1920i	−0.298778	+	0.517499i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−32.3840	−	18.6969i	−1.03289	−	0.596340i	−0.115079	−	0.993356i	$-0.536712\pi$
$983$	−32.3840	−	18.6969i	−1.03289	−	0.596340i	−0.917811	+	0.397017i	$0.870046\pi$
$984$		0			0
$985$	10.4561	+	14.5145i	0.333158	+	0.462471i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.5959			−0.686710
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	37.1018	−	26.7276i	1.17621	−	0.847323i
$996$		0			0
$997$	28.5307	+	16.4722i	0.903576	+	0.521680i	0.878359	−	0.478002i	$-0.158639\pi$
$997$	28.5307	+	16.4722i	0.903576	+	0.521680i	0.0252170	+	0.999682i	$0.491972\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.by.d.289.4		8
3.2	odd	2		720.2.by.c.529.1		8
4.3	odd	2		270.2.i.b.19.2		8
5.4	even	2	inner	2160.2.by.d.289.1		8
9.4	even	3	inner	2160.2.by.d.1009.1		8
9.5	odd	6		720.2.by.c.49.4		8
12.11	even	2		90.2.i.b.79.4	yes	8
15.14	odd	2		720.2.by.c.529.4		8
20.3	even	4		1350.2.e.j.451.1		4
20.7	even	4		1350.2.e.m.451.2		4
20.19	odd	2		270.2.i.b.19.3		8
36.7	odd	6		810.2.c.e.649.4		4
36.11	even	6		810.2.c.f.649.1		4
36.23	even	6		90.2.i.b.49.1	✓	8
36.31	odd	6		270.2.i.b.199.3		8
45.4	even	6	inner	2160.2.by.d.1009.4		8
45.14	odd	6		720.2.by.c.49.1		8
60.23	odd	4		450.2.e.n.151.2		4
60.47	odd	4		450.2.e.k.151.1		4
60.59	even	2		90.2.i.b.79.1	yes	8
180.7	even	12		4050.2.a.bm.1.1		2
180.23	odd	12		450.2.e.n.301.2		4
180.43	even	12		4050.2.a.bz.1.2		2
180.47	odd	12		4050.2.a.bs.1.1		2
180.59	even	6		90.2.i.b.49.4	yes	8
180.67	even	12		1350.2.e.m.901.2		4
180.79	odd	6		810.2.c.e.649.2		4
180.83	odd	12		4050.2.a.bq.1.2		2
180.103	even	12		1350.2.e.j.901.1		4
180.119	even	6		810.2.c.f.649.3		4
180.139	odd	6		270.2.i.b.199.2		8
180.167	odd	12		450.2.e.k.301.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.1	✓	8	36.23	even	6
90.2.i.b.49.4	yes	8	180.59	even	6
90.2.i.b.79.1	yes	8	60.59	even	2
90.2.i.b.79.4	yes	8	12.11	even	2
270.2.i.b.19.2		8	4.3	odd	2
270.2.i.b.19.3		8	20.19	odd	2
270.2.i.b.199.2		8	180.139	odd	6
270.2.i.b.199.3		8	36.31	odd	6
450.2.e.k.151.1		4	60.47	odd	4
450.2.e.k.301.1		4	180.167	odd	12
450.2.e.n.151.2		4	60.23	odd	4
450.2.e.n.301.2		4	180.23	odd	12
720.2.by.c.49.1		8	45.14	odd	6
720.2.by.c.49.4		8	9.5	odd	6
720.2.by.c.529.1		8	3.2	odd	2
720.2.by.c.529.4		8	15.14	odd	2
810.2.c.e.649.2		4	180.79	odd	6
810.2.c.e.649.4		4	36.7	odd	6
810.2.c.f.649.1		4	36.11	even	6
810.2.c.f.649.3		4	180.119	even	6
1350.2.e.j.451.1		4	20.3	even	4
1350.2.e.j.901.1		4	180.103	even	12
1350.2.e.m.451.2		4	20.7	even	4
1350.2.e.m.901.2		4	180.67	even	12
2160.2.by.d.289.1		8	5.4	even	2	inner
2160.2.by.d.289.4		8	1.1	even	1	trivial
2160.2.by.d.1009.1		8	9.4	even	3	inner
2160.2.by.d.1009.4		8	45.4	even	6	inner
4050.2.a.bm.1.1		2	180.7	even	12
4050.2.a.bq.1.2		2	180.83	odd	12
4050.2.a.bs.1.1		2	180.47	odd	12
4050.2.a.bz.1.2		2	180.43	even	12

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:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.81431 - 1.30701i) q^{5} +(3.85337 + 2.22474i) q^{7} +(-0.724745 + 1.25529i) q^{11} +(2.12132 - 1.22474i) q^{13} -3.89898i q^{17} -0.550510 q^{19} +(2.51059 - 1.44949i) q^{23} +(1.58346 - 4.74264i) q^{25} +(3.00000 - 5.19615i) q^{29} +(3.22474 + 5.58542i) q^{31} +(9.89898 - 1.00000i) q^{35} +8.00000i q^{37} +(-0.500000 - 0.866025i) q^{41} +(-6.45145 - 3.72474i) q^{43} +(-0.389270 - 0.224745i) q^{47} +(6.39898 + 11.0834i) q^{49} +8.44949i q^{53} +(0.325765 + 3.22474i) q^{55} +(-5.62372 - 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +(2.24799 - 4.99465i) q^{65} +(-8.18350 + 4.72474i) q^{67} +2.44949 q^{71} +4.79796i q^{73} +(-5.58542 + 3.22474i) q^{77} +(3.67423 - 6.36396i) q^{79} +(-3.46410 - 2.00000i) q^{83} +(-5.09599 - 7.07397i) q^{85} +12.8990 q^{89} +10.8990 q^{91} +(-0.998798 + 0.719521i) q^{95} +(-11.2583 - 6.50000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 4 q^{11} - 24 q^{19} + 24 q^{29} + 16 q^{31} + 40 q^{35} - 4 q^{41} + 12 q^{49} + 32 q^{55} + 4 q^{59} - 8 q^{61} + 12 q^{65} - 20 q^{85} + 64 q^{89} + 48 q^{91} - 24 q^{95}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^11 - 24 * q^19 + 24 * q^29 + 16 * q^31 + 40 * q^35 - 4 * q^41 + 12 * q^49 + 32 * q^55 + 4 * q^59 - 8 * q^61 + 12 * q^65 - 20 * q^85 + 64 * q^89 + 48 * q^91 - 24 * q^95

Introduction

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