LMFDB - Embedded newform 1296.2.i.e.433.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1296,2,Mod(433,1296)] 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("1296.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1296, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1296.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3486121020$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1296.433
Dual form			1296.2.i.e.865.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} -2.00000 q^{17} +4.00000 q^{19} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{29} +(4.00000 - 6.92820i) q^{31} +6.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(3.50000 - 6.06218i) q^{49} +2.00000 q^{53} +8.00000 q^{55} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{71} +10.0000 q^{73} +(-4.00000 - 6.92820i) q^{79} +(2.00000 + 3.46410i) q^{83} +(2.00000 - 3.46410i) q^{85} +6.00000 q^{89} +(-4.00000 + 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} - 4 q^{11} + 2 q^{13} - 4 q^{17} + 8 q^{19} + 8 q^{23} + q^{25} + 6 q^{29} + 8 q^{31} + 12 q^{37} - 6 q^{41} + 4 q^{43} + 7 q^{49} + 4 q^{53} + 16 q^{55} - 4 q^{59} + 2 q^{61} + 4 q^{65}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 - 4 * q^11 + 2 * q^13 - 4 * q^17 + 8 * q^19 + 8 * q^23 + q^25 + 6 * q^29 + 8 * q^31 + 12 * q^37 - 6 * q^41 + 4 * q^43 + 7 * q^49 + 4 * q^53 + 16 * q^55 - 4 * q^59 + 2 * q^61 + 4 * q^65 - 4 * q^67 + 16 * q^71 + 20 * q^73 - 8 * q^79 + 4 * q^83 + 4 * q^85 + 12 * q^89 - 8 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	0.954664	−	0.297686i	$-0.0962148\pi$
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	−0.735135	+	0.677920i	$0.762881\pi$
$84$		0			0
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	0.884182	−	0.467143i	$-0.154717\pi$
$114$		0			0
$115$	8.00000	+	13.8564i	0.746004	+	1.29212i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.00000			−0.668994
$144$		0			0
$145$	−12.0000			−0.996546
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$150$		0			0
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.00000	+	13.8564i	0.642575	+	1.11297i
$156$		0			0
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	−0.823359	−	0.567521i	$-0.807902\pi$
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	0.903167	+	0.429289i	$0.141236\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.142901	+	0.989737i	$0.545643\pi$
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.785687	+	0.618624i	$0.787690\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.00000	+	10.3923i	−0.441129	+	0.764057i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.00000	−	13.8564i	−0.553372	−	0.958468i
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	−0.482317	−	0.875997i	$-0.660205\pi$
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	0.999794	−	0.0202996i	$-0.00646202\pi$
$240$		0			0
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.00000	+	12.1244i	0.447214	+	0.774597i
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	0.895528	+	0.445005i	$0.146798\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$		0			0
$265$	−2.00000	+	3.46410i	−0.122859	+	0.212798i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	0.931305	+	0.364241i	$0.118672\pi$
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	−0.150210	+	0.988654i	$0.547995\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	0.934505	+	0.355951i	$0.115843\pi$
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	−0.158990	+	0.987280i	$0.550824\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		0			0
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.00000			−0.229039
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.00000			−0.445132
$324$		0			0
$325$	2.00000			0.110940
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$		0			0
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	−0.999937	−	0.0112091i	$-0.996432\pi$
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	0.509676	+	0.860366i	$0.329765\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−32.0000			−1.73290
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.00000	+	1.73205i	0.0532246	+	0.0921878i	0.891410	−	0.453197i	$-0.149717\pi$
$353$	1.00000	+	1.73205i	0.0532246	+	0.0921878i	−0.838186	+	0.545385i	$0.816383\pi$
$354$		0			0
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.0000	+	17.3205i	−0.523424	+	0.906597i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	0.839561	−	0.543266i	$-0.182813\pi$
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	−0.890263	+	0.455448i	$0.849479\pi$
$390$		0			0
$391$	−8.00000	+	13.8564i	−0.404577	+	0.700749i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.0000			0.805047
$396$		0			0
$397$	14.0000			0.702640			0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000			0.702640			0.351320	+	0.936255i	$0.385733\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$		0			0
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	−0.782274	−	0.622935i	$-0.785940\pi$
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	0.930614	+	0.366002i	$0.119274\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.00000			−0.392705
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.0000	−	27.7128i	0.765384	−	1.32568i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	−0.991977	−	0.126419i	$-0.959652\pi$
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	0.386507	−	0.922287i	$-0.373682\pi$
$462$		0			0
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	−0.757982	−	0.652275i	$-0.773815\pi$
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	0.943878	+	0.330294i	$0.107148\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000			0.181631
$486$		0			0
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.0000	+	27.7128i	0.705044	+	1.22117i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−26.0000			−1.13908			−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000			−1.13908			−0.569540	+	0.821963i	$0.692879\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.00000	+	10.3923i	0.259889	+	0.450141i
$534$		0			0
$535$	12.0000	−	20.7846i	0.518805	−	0.898597i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−28.0000			−1.20605
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.00000	−	3.46410i	0.0856706	−	0.148386i
$546$		0			0
$547$	22.0000	+	38.1051i	0.940652	+	1.62926i	0.764231	+	0.644942i	$0.223119\pi$
$547$	22.0000	+	38.1051i	0.940652	+	1.62926i	0.176421	+	0.984315i	$0.443548\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	26.0000			1.10166			0.550828	−	0.834619i	$-0.314312\pi$
$557$	26.0000			1.10166			0.550828	+	0.834619i	$0.314312\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$		0			0
$565$	18.0000	+	31.1769i	0.757266	+	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	−0.192950	−	0.981209i	$-0.561806\pi$
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	0.946227	−	0.323505i	$-0.104861\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.00000			0.333623
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.0000	+	38.1051i	0.908037	+	1.57277i	0.816788	+	0.576938i	$0.195753\pi$
$587$	22.0000	+	38.1051i	0.908037	+	1.57277i	0.0912496	+	0.995828i	$0.470914\pi$
$588$		0			0
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$		0			0
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$		0			0
$637$	−7.00000	−	12.1244i	−0.277350	−	0.480384i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	0.694025	−	0.719951i	$-0.255836\pi$
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	−0.970508	+	0.241068i	$0.922502\pi$
$642$		0			0
$643$	6.00000	−	10.3923i	0.236617	−	0.409832i	−0.723124	−	0.690718i	$-0.757295\pi$
$643$	6.00000	−	10.3923i	0.236617	−	0.409832i	0.959741	+	0.280885i	$0.0906280\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		0			0
$649$	16.0000			0.628055
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	48.0000			1.85857
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.00000	−	6.92820i	0.154418	−	0.267460i
$672$		0			0
$673$	−17.0000	−	29.4449i	−0.655302	−	1.13502i	−0.981818	−	0.189824i	$-0.939208\pi$
$673$	−17.0000	−	29.4449i	−0.655302	−	1.13502i	0.326516	−	0.945192i	$-0.394125\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.00000	−	1.73205i	−0.0384331	−	0.0665681i	0.846169	−	0.532915i	$-0.178903\pi$
$677$	−1.00000	−	1.73205i	−0.0384331	−	0.0665681i	−0.884602	+	0.466347i	$0.845570\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	0.825473	−	0.564441i	$-0.190908\pi$
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	−0.901557	+	0.432660i	$0.857575\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.0000	−	20.7846i	−0.455186	−	0.788405i
$696$		0			0
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	24.0000			0.905177
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−32.0000	−	55.4256i	−1.19841	−	2.07571i
$714$		0			0
$715$	8.00000	−	13.8564i	0.299183	−	0.518200i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−32.0000			−1.19340			−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000			−1.19340			−0.596699	+	0.802465i	$0.703521\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	24.0000	+	41.5692i	0.890111	+	1.54172i	0.839742	+	0.542986i	$0.182706\pi$
$727$	24.0000	+	41.5692i	0.890111	+	1.54172i	0.0503692	+	0.998731i	$0.483960\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.0000			0.589368
$738$		0			0
$739$	4.00000			0.147142			0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000			0.147142			0.0735712	+	0.997290i	$0.476560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	−0.783277	−	0.621673i	$-0.786453\pi$
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	0.930023	+	0.367502i	$0.119787\pi$
$744$		0			0
$745$	14.0000	+	24.2487i	0.512920	+	0.888404i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	−0.559640	−	0.828736i	$-0.689061\pi$
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	0.997526	+	0.0702946i	$0.0223939\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	32.0000			1.16460
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	−0.993572	−	0.113203i	$-0.963889\pi$
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	0.594822	+	0.803857i	$0.297222\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.00000	+	3.46410i	0.0713831	+	0.123639i
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.00000			0.142044
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	−0.602761	−	0.797922i	$-0.705933\pi$
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	0.992401	+	0.123045i	$0.0392661\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−20.0000	−	34.6410i	−0.705785	−	1.22245i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.0000			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.0000	−	20.7846i	0.420342	−	0.728053i
$816$		0			0
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$		0			0
$829$	−50.0000			−1.73657			−0.868286	−	0.496064i	$-0.834778\pi$
$829$	−50.0000			−1.73657			−0.868286	+	0.496064i	$0.834778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.00000	+	12.1244i	−0.242536	+	0.420084i
$834$		0			0
$835$	−24.0000	−	41.5692i	−0.830554	−	1.43856i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000			−0.619219
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−6.00000	+	10.3923i	−0.204717	+	0.354581i	−0.950043	−	0.312120i	$-0.898961\pi$
$859$	−6.00000	+	10.3923i	−0.204717	+	0.354581i	0.745325	+	0.666701i	$0.232294\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.0000	+	27.7128i	−0.542763	+	0.940093i
$870$		0			0
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−50.0000			−1.68454			−0.842271	−	0.539054i	$-0.818782\pi$
$881$	−50.0000			−1.68454			−0.842271	+	0.539054i	$0.818782\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	−0.925332	−	0.379157i	$-0.876214\pi$
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	0.791026	+	0.611783i	$0.209547\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−12.0000	+	20.7846i	−0.401116	+	0.694753i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	48.0000			1.60089
$900$		0			0
$901$	−4.00000			−0.133259
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.00000	+	10.3923i	−0.199447	+	0.345452i
$906$		0			0
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	0.897318	−	0.441384i	$-0.145512\pi$
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	−0.830909	+	0.556408i	$0.812179\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.00000	−	13.8564i	−0.265052	−	0.459083i	0.702525	−	0.711659i	$-0.252056\pi$
$911$	−8.00000	−	13.8564i	−0.265052	−	0.459083i	−0.967577	+	0.252575i	$0.918722\pi$
$912$		0			0
$913$	8.00000	−	13.8564i	0.264761	−	0.458580i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.00000	−	13.8564i	0.263323	−	0.456089i
$924$		0			0
$925$	3.00000	+	5.19615i	0.0986394	+	0.170848i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	0.905516	+	0.424313i	$0.139484\pi$
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	−0.0852924	+	0.996356i	$0.527182\pi$
$930$		0			0
$931$	14.0000	−	24.2487i	0.458831	−	0.794719i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.0000			−0.523256
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$		0			0
$943$	24.0000	+	41.5692i	0.781548	+	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$		0			0
$967$	−8.00000	+	13.8564i	−0.257263	+	0.445592i	−0.965508	−	0.260375i	$-0.916154\pi$
$967$	−8.00000	+	13.8564i	−0.257263	+	0.445592i	0.708245	+	0.705967i	$0.249487\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	−12.0000	−	20.7846i	−0.383522	−	0.664279i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	32.0000			1.01754
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	16.0000	−	27.7128i	0.507234	−	0.878555i
$996$		0			0
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.2.i.e.433.1		2
3.2	odd	2		1296.2.i.m.433.1		2
4.3	odd	2		648.2.i.b.433.1		2
9.2	odd	6		1296.2.i.m.865.1		2
9.4	even	3		144.2.a.b.1.1		1
9.5	odd	6		48.2.a.a.1.1		1
9.7	even	3	inner	1296.2.i.e.865.1		2
12.11	even	2		648.2.i.g.433.1		2
36.7	odd	6		648.2.i.b.217.1		2
36.11	even	6		648.2.i.g.217.1		2
36.23	even	6		24.2.a.a.1.1	✓	1
36.31	odd	6		72.2.a.a.1.1		1
45.4	even	6		3600.2.a.v.1.1		1
45.13	odd	12		3600.2.f.r.2449.1		2
45.14	odd	6		1200.2.a.d.1.1		1
45.22	odd	12		3600.2.f.r.2449.2		2
45.23	even	12		1200.2.f.b.49.2		2
45.32	even	12		1200.2.f.b.49.1		2
63.5	even	6		2352.2.q.r.1537.1		2
63.13	odd	6		7056.2.a.q.1.1		1
63.23	odd	6		2352.2.q.l.1537.1		2
63.32	odd	6		2352.2.q.l.961.1		2
63.41	even	6		2352.2.a.i.1.1		1
63.59	even	6		2352.2.q.r.961.1		2
72.5	odd	6		192.2.a.b.1.1		1
72.13	even	6		576.2.a.b.1.1		1
72.59	even	6		192.2.a.d.1.1		1
72.67	odd	6		576.2.a.d.1.1		1
99.32	even	6		5808.2.a.s.1.1		1
117.77	odd	6		8112.2.a.be.1.1		1
144.5	odd	12		768.2.d.d.385.1		2
144.13	even	12		2304.2.d.k.1153.1		2
144.59	even	12		768.2.d.e.385.2		2
144.67	odd	12		2304.2.d.i.1153.1		2
144.77	odd	12		768.2.d.d.385.2		2
144.85	even	12		2304.2.d.k.1153.2		2
144.131	even	12		768.2.d.e.385.1		2
144.139	odd	12		2304.2.d.i.1153.2		2
180.23	odd	12		600.2.f.e.49.1		2
180.59	even	6		600.2.a.h.1.1		1
180.67	even	12		1800.2.f.c.649.2		2
180.103	even	12		1800.2.f.c.649.1		2
180.139	odd	6		1800.2.a.m.1.1		1
180.167	odd	12		600.2.f.e.49.2		2
252.23	even	6		1176.2.q.i.361.1		2
252.31	even	6		3528.2.s.y.3313.1		2
252.59	odd	6		1176.2.q.a.961.1		2
252.67	odd	6		3528.2.s.j.3313.1		2
252.95	even	6		1176.2.q.i.961.1		2
252.103	even	6		3528.2.s.y.361.1		2
252.131	odd	6		1176.2.q.a.361.1		2
252.139	even	6		3528.2.a.d.1.1		1
252.167	odd	6		1176.2.a.i.1.1		1
252.247	odd	6		3528.2.s.j.361.1		2
360.59	even	6		4800.2.a.q.1.1		1
360.77	even	12		4800.2.f.bg.3649.2		2
360.149	odd	6		4800.2.a.cc.1.1		1
360.203	odd	12		4800.2.f.d.3649.2		2
360.293	even	12		4800.2.f.bg.3649.1		2
360.347	odd	12		4800.2.f.d.3649.1		2
396.131	odd	6		2904.2.a.c.1.1		1
396.175	even	6		8712.2.a.u.1.1		1
468.203	odd	12		4056.2.c.e.337.1		2
468.239	odd	12		4056.2.c.e.337.2		2
468.311	even	6		4056.2.a.i.1.1		1
504.293	even	6		9408.2.a.cc.1.1		1
504.419	odd	6		9408.2.a.h.1.1		1
612.203	even	6		6936.2.a.p.1.1		1
684.455	odd	6		8664.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.a.a.1.1	✓	1	36.23	even	6
48.2.a.a.1.1		1	9.5	odd	6
72.2.a.a.1.1		1	36.31	odd	6
144.2.a.b.1.1		1	9.4	even	3
192.2.a.b.1.1		1	72.5	odd	6
192.2.a.d.1.1		1	72.59	even	6
576.2.a.b.1.1		1	72.13	even	6
576.2.a.d.1.1		1	72.67	odd	6
600.2.a.h.1.1		1	180.59	even	6
600.2.f.e.49.1		2	180.23	odd	12
600.2.f.e.49.2		2	180.167	odd	12
648.2.i.b.217.1		2	36.7	odd	6
648.2.i.b.433.1		2	4.3	odd	2
648.2.i.g.217.1		2	36.11	even	6
648.2.i.g.433.1		2	12.11	even	2
768.2.d.d.385.1		2	144.5	odd	12
768.2.d.d.385.2		2	144.77	odd	12
768.2.d.e.385.1		2	144.131	even	12
768.2.d.e.385.2		2	144.59	even	12
1176.2.a.i.1.1		1	252.167	odd	6
1176.2.q.a.361.1		2	252.131	odd	6
1176.2.q.a.961.1		2	252.59	odd	6
1176.2.q.i.361.1		2	252.23	even	6
1176.2.q.i.961.1		2	252.95	even	6
1200.2.a.d.1.1		1	45.14	odd	6
1200.2.f.b.49.1		2	45.32	even	12
1200.2.f.b.49.2		2	45.23	even	12
1296.2.i.e.433.1		2	1.1	even	1	trivial
1296.2.i.e.865.1		2	9.7	even	3	inner
1296.2.i.m.433.1		2	3.2	odd	2
1296.2.i.m.865.1		2	9.2	odd	6
1800.2.a.m.1.1		1	180.139	odd	6
1800.2.f.c.649.1		2	180.103	even	12
1800.2.f.c.649.2		2	180.67	even	12
2304.2.d.i.1153.1		2	144.67	odd	12
2304.2.d.i.1153.2		2	144.139	odd	12
2304.2.d.k.1153.1		2	144.13	even	12
2304.2.d.k.1153.2		2	144.85	even	12
2352.2.a.i.1.1		1	63.41	even	6
2352.2.q.l.961.1		2	63.32	odd	6
2352.2.q.l.1537.1		2	63.23	odd	6
2352.2.q.r.961.1		2	63.59	even	6
2352.2.q.r.1537.1		2	63.5	even	6
2904.2.a.c.1.1		1	396.131	odd	6
3528.2.a.d.1.1		1	252.139	even	6
3528.2.s.j.361.1		2	252.247	odd	6
3528.2.s.j.3313.1		2	252.67	odd	6
3528.2.s.y.361.1		2	252.103	even	6
3528.2.s.y.3313.1		2	252.31	even	6
3600.2.a.v.1.1		1	45.4	even	6
3600.2.f.r.2449.1		2	45.13	odd	12
3600.2.f.r.2449.2		2	45.22	odd	12
4056.2.a.i.1.1		1	468.311	even	6
4056.2.c.e.337.1		2	468.203	odd	12
4056.2.c.e.337.2		2	468.239	odd	12
4800.2.a.q.1.1		1	360.59	even	6
4800.2.a.cc.1.1		1	360.149	odd	6
4800.2.f.d.3649.1		2	360.347	odd	12
4800.2.f.d.3649.2		2	360.203	odd	12
4800.2.f.bg.3649.1		2	360.293	even	12
4800.2.f.bg.3649.2		2	360.77	even	12
5808.2.a.s.1.1		1	99.32	even	6
6936.2.a.p.1.1		1	612.203	even	6
7056.2.a.q.1.1		1	63.13	odd	6
8112.2.a.be.1.1		1	117.77	odd	6
8664.2.a.j.1.1		1	684.455	odd	6
8712.2.a.u.1.1		1	396.175	even	6
9408.2.a.h.1.1		1	504.419	odd	6
9408.2.a.cc.1.1		1	504.293	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:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1296.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} -2.00000 q^{17} +4.00000 q^{19} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{29} +(4.00000 - 6.92820i) q^{31} +6.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(3.50000 - 6.06218i) q^{49} +2.00000 q^{53} +8.00000 q^{55} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{71} +10.0000 q^{73} +(-4.00000 - 6.92820i) q^{79} +(2.00000 + 3.46410i) q^{83} +(2.00000 - 3.46410i) q^{85} +6.00000 q^{89} +(-4.00000 + 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} - 4 q^{11} + 2 q^{13} - 4 q^{17} + 8 q^{19} + 8 q^{23} + q^{25} + 6 q^{29} + 8 q^{31} + 12 q^{37} - 6 q^{41} + 4 q^{43} + 7 q^{49} + 4 q^{53} + 16 q^{55} - 4 q^{59} + 2 q^{61} + 4 q^{65}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 - 4 * q^11 + 2 * q^13 - 4 * q^17 + 8 * q^19 + 8 * q^23 + q^25 + 6 * q^29 + 8 * q^31 + 12 * q^37 - 6 * q^41 + 4 * q^43 + 7 * q^49 + 4 * q^53 + 16 * q^55 - 4 * q^59 + 2 * q^61 + 4 * q^65 - 4 * q^67 + 16 * q^71 + 20 * q^73 - 8 * q^79 + 4 * q^83 + 4 * q^85 + 12 * q^89 - 8 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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