LMFDB - Embedded newform 504.2.bl.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(17,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Root			$0.144868 - 1.25092i$ of defining polynomial
Character	$\chi$	$=$	504.89
Dual form			504.2.bl.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.144868 + 0.250919i) q^{5} +(-2.26907 + 1.36064i) q^{7} +O(q^{10})$	$q+(-0.144868 + 0.250919i) q^{5} +(-2.26907 + 1.36064i) q^{7} +(5.23077 - 3.01999i) q^{11} +5.46050i q^{13} +(2.22666 + 3.85669i) q^{17} +(3.51739 + 2.03076i) q^{19} +(-1.11743 - 0.645146i) q^{23} +(2.45803 + 4.25743i) q^{25} +0.377918i q^{29} +(-3.09749 + 1.78834i) q^{31} +(-0.0126942 - 0.766467i) q^{35} +(1.01555 - 1.75898i) q^{37} +5.50384 q^{41} -6.45419 q^{43} +(5.38833 - 9.33287i) q^{47} +(3.29733 - 6.17475i) q^{49} +(-9.77422 + 5.64315i) q^{53} +1.75000i q^{55} +(0.790140 + 1.36856i) q^{59} +(9.54984 + 5.51360i) q^{61} +(-1.37015 - 0.791054i) q^{65} +(-2.04381 - 3.53999i) q^{67} +0.410536i q^{71} +(-11.1149 + 6.41718i) q^{73} +(-7.75986 + 13.9697i) q^{77} +(6.01355 - 10.4158i) q^{79} -0.155917 q^{83} -1.29029 q^{85} +(3.34409 - 5.79213i) q^{89} +(-7.42976 - 12.3902i) q^{91} +(-1.01912 + 0.588387i) q^{95} -16.5090i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) $ 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.144868	+	0.250919i	−0.0647871	+	0.112215i	−0.896600	−	0.442842i	$-0.853970\pi$
$5$	−0.144868	+	0.250919i	−0.0647871	+	0.112215i	0.831812	+	0.555057i	$0.187304\pi$
$6$		0			0
$7$	−2.26907	+	1.36064i	−0.857627	+	0.514273i
$7$	−2.26907	+	1.36064i	−0.857627	+	0.514273i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.23077	−	3.01999i	1.57714	−	0.910560i	0.581880	−	0.813275i	$-0.302317\pi$
$11$	5.23077	−	3.01999i	1.57714	−	0.910560i	0.995256	−	0.0972858i	$-0.0310161\pi$
$12$		0			0
$13$			5.46050i			1.51447i	0.653142	+	0.757235i	$0.273450\pi$
$13$			5.46050i			1.51447i	−0.653142	+	0.757235i	$0.726550\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.22666	+	3.85669i	0.540045	+	0.935385i	0.998901	+	0.0468746i	$0.0149261\pi$
$17$	2.22666	+	3.85669i	0.540045	+	0.935385i	−0.458856	+	0.888511i	$0.651741\pi$
$18$		0			0
$19$	3.51739	+	2.03076i	0.806944	+	0.465889i	0.845893	−	0.533352i	$-0.179068\pi$
$19$	3.51739	+	2.03076i	0.806944	+	0.465889i	−0.0389497	+	0.999241i	$0.512401\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.11743	−	0.645146i	−0.232999	−	0.134522i	0.378956	−	0.925415i	$-0.376283\pi$
$23$	−1.11743	−	0.645146i	−0.232999	−	0.134522i	−0.611955	+	0.790893i	$0.709617\pi$
$24$		0			0
$25$	2.45803	+	4.25743i	0.491605	+	0.851485i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			0.377918i			0.0701776i	0.999384	+	0.0350888i	$0.0111714\pi$
$29$			0.377918i			0.0701776i	−0.999384	+	0.0350888i	$0.988829\pi$
$30$		0			0
$31$	−3.09749	+	1.78834i	−0.556326	+	0.321195i	−0.751670	−	0.659540i	$-0.770751\pi$
$31$	−3.09749	+	1.78834i	−0.556326	+	0.321195i	0.195343	+	0.980735i	$0.437418\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0126942	−	0.766467i	−0.00214570	−	0.129557i
$36$		0			0
$37$	1.01555	−	1.75898i	0.166955	−	0.289174i	−0.770393	−	0.637569i	$-0.779940\pi$
$37$	1.01555	−	1.75898i	0.166955	−	0.289174i	0.937348	+	0.348395i	$0.113273\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.50384			0.859556			0.429778	−	0.902935i	$-0.358592\pi$
$41$	5.50384			0.859556			0.429778	+	0.902935i	$0.358592\pi$
$42$		0			0
$43$	−6.45419			−0.984254			−0.492127	−	0.870523i	$-0.663780\pi$
$43$	−6.45419			−0.984254			−0.492127	+	0.870523i	$0.663780\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.38833	−	9.33287i	0.785969	−	1.36134i	−0.142449	−	0.989802i	$-0.545498\pi$
$47$	5.38833	−	9.33287i	0.785969	−	1.36134i	0.928418	−	0.371536i	$-0.121169\pi$
$48$		0			0
$49$	3.29733	−	6.17475i	0.471048	−	0.882108i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.77422	+	5.64315i	−1.34259	+	0.775146i	−0.987187	−	0.159567i	$-0.948990\pi$
$53$	−9.77422	+	5.64315i	−1.34259	+	0.775146i	−0.355405	+	0.934713i	$0.615657\pi$
$54$		0			0
$55$			1.75000i			0.235970i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.790140	+	1.36856i	0.102867	+	0.178172i	0.912865	−	0.408262i	$-0.133865\pi$
$59$	0.790140	+	1.36856i	0.102867	+	0.178172i	−0.809998	+	0.586433i	$0.800532\pi$
$60$		0			0
$61$	9.54984	+	5.51360i	1.22273	+	0.705945i	0.965500	−	0.260405i	$-0.0838560\pi$
$61$	9.54984	+	5.51360i	1.22273	+	0.705945i	0.257233	+	0.966350i	$0.417189\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.37015	−	0.791054i	−0.169946	−	0.0981182i
$66$		0			0
$67$	−2.04381	−	3.53999i	−0.249691	−	0.432478i	0.713749	−	0.700402i	$-0.246996\pi$
$67$	−2.04381	−	3.53999i	−0.249691	−	0.432478i	−0.963440	+	0.267924i	$0.913663\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.410536i			0.0487216i	0.999703	+	0.0243608i	$0.00775505\pi$
$71$			0.410536i			0.0487216i	−0.999703	+	0.0243608i	$0.992245\pi$
$72$		0			0
$73$	−11.1149	+	6.41718i	−1.30090	+	0.751074i	−0.980558	−	0.196229i	$-0.937131\pi$
$73$	−11.1149	+	6.41718i	−1.30090	+	0.751074i	−0.320340	+	0.947303i	$0.603797\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.75986	+	13.9697i	−0.884319	+	1.59200i
$78$		0			0
$79$	6.01355	−	10.4158i	0.676577	−	1.17187i	−0.299428	−	0.954119i	$-0.596796\pi$
$79$	6.01355	−	10.4158i	0.676577	−	1.17187i	0.976005	−	0.217747i	$-0.0698707\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.155917			−0.0171142			−0.00855708	−	0.999963i	$-0.502724\pi$
$83$	−0.155917			−0.0171142			−0.00855708	+	0.999963i	$0.502724\pi$
$84$		0			0
$85$	−1.29029			−0.139952
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.34409	−	5.79213i	0.354473	−	0.613965i	−0.632555	−	0.774516i	$-0.717994\pi$
$89$	3.34409	−	5.79213i	0.354473	−	0.613965i	0.987028	+	0.160551i	$0.0513271\pi$
$90$		0			0
$91$	−7.42976	−	12.3902i	−0.778851	−	1.29885i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.01912	+	0.588387i	−0.104559	+	0.0603672i
$96$		0			0
$97$		−	16.5090i		−	1.67623i	−0.545494	−	0.838115i	$-0.683658\pi$
$97$		−	16.5090i		−	1.67623i	0.545494	−	0.838115i	$-0.316342\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.99552	−	10.3845i	−0.596577	−	1.03330i	−0.993322	−	0.115373i	$-0.963194\pi$
$101$	−5.99552	−	10.3845i	−0.596577	−	1.03330i	0.396746	−	0.917929i	$-0.370140\pi$
$102$		0			0
$103$	−0.100344	−	0.0579336i	−0.00988718	−	0.00570837i	0.495048	−	0.868865i	$-0.335150\pi$
$103$	−0.100344	−	0.0579336i	−0.00988718	−	0.00570837i	−0.504935	+	0.863157i	$0.668484\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.1501	−	8.16957i	−1.36794	−	0.789782i	−0.377278	−	0.926100i	$-0.623140\pi$
$107$	−14.1501	−	8.16957i	−1.36794	−	0.789782i	−0.990665	+	0.136318i	$0.956473\pi$
$108$		0			0
$109$	0.454348	+	0.786954i	0.0435187	+	0.0753766i	0.886964	−	0.461838i	$-0.152810\pi$
$109$	0.454348	+	0.786954i	0.0435187	+	0.0753766i	−0.843446	+	0.537215i	$0.819477\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.37176i			0.787549i	0.919207	+	0.393775i	$0.128831\pi$
$113$			8.37176i			0.787549i	−0.919207	+	0.393775i	$0.871169\pi$
$114$		0			0
$115$	0.323760	−	0.186923i	0.0301907	−	0.0174306i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.3000	−	5.72142i	−0.944200	−	0.524481i
$120$		0			0
$121$	12.7406	−	22.0674i	1.15824	−	2.00613i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.87305			−0.256973
$126$		0			0
$127$	6.13280			0.544198			0.272099	−	0.962269i	$-0.412282\pi$
$127$	6.13280			0.544198			0.272099	+	0.962269i	$0.412282\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.36514	+	12.7568i	−0.643495	+	1.11457i	0.341152	+	0.940008i	$0.389183\pi$
$131$	−7.36514	+	12.7568i	−0.643495	+	1.11457i	−0.984647	+	0.174558i	$0.944150\pi$
$132$		0			0
$133$	−10.7443	+	0.177947i	−0.931651	+	0.0154299i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.7797	−	6.80101i	1.00641	−	0.581050i	0.0962696	−	0.995355i	$-0.469309\pi$
$137$	11.7797	−	6.80101i	1.00641	−	0.581050i	0.910138	+	0.414306i	$0.135976\pi$
$138$		0			0
$139$			17.3580i			1.47229i	0.676827	+	0.736143i	$0.263355\pi$
$139$			17.3580i			1.47229i	−0.676827	+	0.736143i	$0.736645\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	16.4906	+	28.5626i	1.37902	+	2.38853i
$144$		0			0
$145$	−0.0948270	−	0.0547484i	−0.00787495	−	0.00454661i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−13.3600	−	7.71339i	−1.09449	−	0.631905i	−0.159723	−	0.987162i	$-0.551060\pi$
$149$	−13.3600	−	7.71339i	−1.09449	−	0.631905i	−0.934769	+	0.355257i	$0.884393\pi$
$150$		0			0
$151$	−2.68712	−	4.65423i	−0.218675	−	0.378756i	0.735728	−	0.677277i	$-0.236840\pi$
$151$	−2.68712	−	4.65423i	−0.218675	−	0.378756i	−0.954403	+	0.298521i	$0.903507\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	1.03630i		−	0.0832373i
$156$		0			0
$157$	−6.03109	+	3.48205i	−0.481334	+	0.277898i	−0.720972	−	0.692964i	$-0.756304\pi$
$157$	−6.03109	+	3.48205i	−0.481334	+	0.277898i	0.239638	+	0.970862i	$0.422971\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.41332	−	0.0565312i	0.269008	−	0.00445528i
$162$		0			0
$163$	5.00803	−	8.67416i	0.392259	−	0.679413i	−0.600488	−	0.799634i	$-0.705027\pi$
$163$	5.00803	−	8.67416i	0.392259	−	0.679413i	0.992747	+	0.120221i	$0.0383603\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.03254			−0.466812			−0.233406	−	0.972379i	$-0.574987\pi$
$167$	−6.03254			−0.466812			−0.233406	+	0.972379i	$0.574987\pi$
$168$		0			0
$169$	−16.8171			−1.29362
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.18258	−	15.9047i	0.698139	−	1.20921i	−0.270972	−	0.962587i	$-0.587345\pi$
$173$	9.18258	−	15.9047i	0.698139	−	1.20921i	0.969111	−	0.246625i	$-0.0793214\pi$
$174$		0			0
$175$	−11.3702	−	6.31591i	−0.859509	−	0.477438i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.83604	−	5.67884i	0.735180	−	0.424457i	−0.0851340	−	0.996370i	$-0.527132\pi$
$179$	9.83604	−	5.67884i	0.735180	−	0.424457i	0.820314	+	0.571913i	$0.193799\pi$
$180$		0			0
$181$			11.8647i			0.881893i	0.897533	+	0.440947i	$0.145357\pi$
$181$			11.8647i			0.881893i	−0.897533	+	0.440947i	$0.854643\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.294241	+	0.509641i	0.0216331	+	0.0374696i
$186$		0			0
$187$	23.2943	+	13.4490i	1.70345	+	0.983487i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.6310	−	6.71514i	−0.841587	−	0.485890i	0.0162166	−	0.999869i	$-0.494838\pi$
$191$	−11.6310	−	6.71514i	−0.841587	−	0.485890i	−0.857803	+	0.513978i	$0.828171\pi$
$192$		0			0
$193$	2.87792	+	4.98470i	0.207157	+	0.358807i	0.950818	−	0.309751i	$-0.100246\pi$
$193$	2.87792	+	4.98470i	0.207157	+	0.358807i	−0.743661	+	0.668557i	$0.766912\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.66053i		−	0.189555i	−0.995498	−	0.0947775i	$-0.969786\pi$
$197$		−	2.66053i		−	0.189555i	0.995498	−	0.0947775i	$-0.0302140\pi$
$198$		0			0
$199$	7.25552	−	4.18898i	0.514330	−	0.296949i	−0.220282	−	0.975436i	$-0.570698\pi$
$199$	7.25552	−	4.18898i	0.514330	−	0.296949i	0.734612	+	0.678488i	$0.237364\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.514209	−	0.857521i	−0.0360904	−	0.0601862i
$204$		0			0
$205$	−0.797333	+	1.38102i	−0.0556881	+	0.0964547i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	24.5315			1.69688
$210$		0			0
$211$	7.12240			0.490326			0.245163	−	0.969482i	$-0.421159\pi$
$211$	7.12240			0.490326			0.245163	+	0.969482i	$0.421159\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.935008	−	1.61948i	0.0637670	−	0.110448i
$216$		0			0
$217$	4.59514	−	8.27243i	0.311939	−	0.561569i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−21.0595	+	12.1587i	−1.41661	+	0.817882i
$222$		0			0
$223$			13.6407i			0.913449i	0.889608	+	0.456725i	$0.150977\pi$
$223$			13.6407i			0.913449i	−0.889608	+	0.456725i	$0.849023\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.59561	+	9.69188i	0.371393	+	0.643272i	0.989780	−	0.142602i	$-0.0455468\pi$
$227$	5.59561	+	9.69188i	0.371393	+	0.643272i	−0.618387	+	0.785874i	$0.712213\pi$
$228$		0			0
$229$	7.40517	+	4.27538i	0.489348	+	0.282525i	0.724304	−	0.689481i	$-0.242161\pi$
$229$	7.40517	+	4.27538i	0.489348	+	0.282525i	−0.234956	+	0.972006i	$0.575495\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.8863	+	6.28522i	0.713186	+	0.411758i	0.812240	−	0.583324i	$-0.198248\pi$
$233$	10.8863	+	6.28522i	0.713186	+	0.411758i	−0.0990536	+	0.995082i	$0.531582\pi$
$234$		0			0
$235$	1.56120	+	2.70408i	0.101841	+	0.176394i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			21.3263i			1.37948i	0.724056	+	0.689741i	$0.242275\pi$
$239$			21.3263i			1.37948i	−0.724056	+	0.689741i	$0.757725\pi$
$240$		0			0
$241$	−17.7751	+	10.2625i	−1.14499	+	0.661063i	−0.947663	−	0.319274i	$-0.896561\pi$
$241$	−17.7751	+	10.2625i	−1.14499	+	0.661063i	−0.197332	+	0.980337i	$0.563228\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.07169	+	1.72189i	0.0684676	+	0.110008i
$246$		0			0
$247$	−11.0890	+	19.2067i	−0.705575	+	1.22209i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.9577			−0.754764			−0.377382	−	0.926058i	$-0.623176\pi$
$251$	−11.9577			−0.754764			−0.377382	+	0.926058i	$0.623176\pi$
$252$		0			0
$253$	−7.79333			−0.489963
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.8581	−	27.4670i	0.989199	−	1.71334i	0.367658	−	0.929961i	$-0.380160\pi$
$257$	15.8581	−	27.4670i	0.989199	−	1.71334i	0.621541	−	0.783381i	$-0.286507\pi$
$258$		0			0
$259$	0.0889877	+	5.37303i	0.00552943	+	0.333864i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.8678	−	12.0480i	1.28676	−	0.742912i	0.308686	−	0.951164i	$-0.400111\pi$
$263$	20.8678	−	12.0480i	1.28676	−	0.742912i	0.978075	+	0.208252i	$0.0667775\pi$
$264$		0			0
$265$		−	3.27006i		−	0.200878i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.31897	−	7.48068i	−0.263332	−	0.456105i	0.703793	−	0.710405i	$-0.251488\pi$
$269$	−4.31897	−	7.48068i	−0.263332	−	0.456105i	−0.967125	+	0.254300i	$0.918155\pi$
$270$		0			0
$271$	21.1099	+	12.1878i	1.28233	+	0.740356i	0.977275	−	0.211977i	$-0.0679902\pi$
$271$	21.1099	+	12.1878i	1.28233	+	0.740356i	0.305060	+	0.952333i	$0.401324\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	25.7147	+	14.8464i	1.55066	+	0.895272i
$276$		0			0
$277$	12.9122	+	22.3646i	0.775820	+	1.34376i	0.934333	+	0.356402i	$0.115997\pi$
$277$	12.9122	+	22.3646i	0.775820	+	1.34376i	−0.158513	+	0.987357i	$0.550670\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	29.9846i		−	1.78873i	−0.447334	−	0.894367i	$-0.647626\pi$
$281$		−	29.9846i		−	1.78873i	0.447334	−	0.894367i	$-0.352374\pi$
$282$		0			0
$283$	−19.8489	+	11.4597i	−1.17989	+	0.681211i	−0.955990	−	0.293401i	$-0.905213\pi$
$283$	−19.8489	+	11.4597i	−1.17989	+	0.681211i	−0.223902	+	0.974612i	$0.571880\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.4886	+	7.48873i	−0.737178	+	0.442046i
$288$		0			0
$289$	−1.41605	+	2.45267i	−0.0832972	+	0.144275i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	28.4782			1.66372			0.831858	−	0.554988i	$-0.187277\pi$
$293$	28.4782			1.66372			0.831858	+	0.554988i	$0.187277\pi$
$294$		0			0
$295$	−0.457865			−0.0266579
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.52282	−	6.10171i	0.203730	−	0.352871i
$300$		0			0
$301$	14.6450	−	8.78181i	0.844123	−	0.506175i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.76694	+	1.59749i	−0.158435	+	0.0914723i
$306$		0			0
$307$		−	5.73643i		−	0.327395i	−0.986511	−	0.163698i	$-0.947658\pi$
$307$		−	5.73643i		−	0.327395i	0.986511	−	0.163698i	$-0.0523422\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.71985	−	8.17502i	−0.267638	−	0.463563i	0.700613	−	0.713541i	$-0.252910\pi$
$311$	−4.71985	−	8.17502i	−0.267638	−	0.463563i	−0.968251	+	0.249978i	$0.919577\pi$
$312$		0			0
$313$	−10.0870	−	5.82373i	−0.570150	−	0.329176i	0.187059	−	0.982349i	$-0.440104\pi$
$313$	−10.0870	−	5.82373i	−0.570150	−	0.329176i	−0.757209	+	0.653172i	$0.773438\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.90757	−	1.10133i	−0.107140	−	0.0618571i	0.445473	−	0.895296i	$-0.353036\pi$
$317$	−1.90757	−	1.10133i	−0.107140	−	0.0618571i	−0.552612	+	0.833438i	$0.686369\pi$
$318$		0			0
$319$	1.14131	+	1.97680i	0.0639009	+	0.110680i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			18.0873i			1.00640i
$324$		0			0
$325$	−23.2477	+	13.4221i	−1.28955	+	0.744522i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.472155	+	28.5085i	0.0260307	+	1.57172i
$330$		0			0
$331$	12.5017	−	21.6535i	0.687154	−	1.19019i	−0.285600	−	0.958349i	$-0.592193\pi$
$331$	12.5017	−	21.6535i	0.687154	−	1.19019i	0.972755	−	0.231837i	$-0.0744737\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.18434			0.0647072
$336$		0			0
$337$	11.8462			0.645303			0.322651	−	0.946518i	$-0.395426\pi$
$337$	11.8462			0.645303			0.322651	+	0.946518i	$0.395426\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.8015	+	18.7088i	−0.584935	+	1.01314i
$342$		0			0
$343$	0.919731	+	18.4974i	0.0496608	+	0.998766i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.2907	+	7.67341i	−0.713484	+	0.411930i	−0.812350	−	0.583170i	$-0.801812\pi$
$347$	−13.2907	+	7.67341i	−0.713484	+	0.411930i	0.0988655	+	0.995101i	$0.468479\pi$
$348$		0			0
$349$		−	0.666155i		−	0.0356585i	−0.999841	−	0.0178292i	$-0.994324\pi$
$349$		−	0.666155i		−	0.0356585i	0.999841	−	0.0178292i	$-0.00567552\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.18680	−	7.25175i	−0.222841	−	0.385972i	0.732829	−	0.680413i	$-0.238200\pi$
$353$	−4.18680	−	7.25175i	−0.222841	−	0.385972i	−0.955669	+	0.294442i	$0.904866\pi$
$354$		0			0
$355$	−0.103011	−	0.0594736i	−0.00546728	−	0.00315653i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−24.9438	−	14.4013i	−1.31649	−	0.760073i	−0.333324	−	0.942812i	$-0.608170\pi$
$359$	−24.9438	−	14.4013i	−1.31649	−	0.760073i	−0.983161	+	0.182739i	$0.941504\pi$
$360$		0			0
$361$	−1.25200	−	2.16852i	−0.0658946	−	0.114133i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	3.71859i		−	0.194640i
$366$		0			0
$367$	24.5554	−	14.1770i	1.28178	−	0.740036i	0.304606	−	0.952478i	$-0.401475\pi$
$367$	24.5554	−	14.1770i	1.28178	−	0.740036i	0.977173	+	0.212443i	$0.0681419\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	14.5001	−	26.1038i	0.752807	−	1.35524i
$372$		0			0
$373$	3.87744	−	6.71593i	0.200766	−	0.347737i	−0.748009	−	0.663688i	$-0.768990\pi$
$373$	3.87744	−	6.71593i	0.200766	−	0.347737i	0.948776	+	0.315951i	$0.102323\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.06362			−0.106282
$378$		0			0
$379$	−17.3391			−0.890652			−0.445326	−	0.895368i	$-0.646912\pi$
$379$	−17.3391			−0.890652			−0.445326	+	0.895368i	$0.646912\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.930503	−	1.61168i	0.0475465	−	0.0823530i	−0.841273	−	0.540611i	$-0.818193\pi$
$383$	0.930503	−	1.61168i	0.0475465	−	0.0823530i	0.888819	+	0.458258i	$0.151526\pi$
$384$		0			0
$385$	−2.38112	−	3.97087i	−0.121353	−	0.202375i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.34272	+	2.50727i	−0.220184	+	0.127124i	−0.606036	−	0.795437i	$-0.707241\pi$
$389$	−4.34272	+	2.50727i	−0.220184	+	0.127124i	0.385851	+	0.922561i	$0.373908\pi$
$390$		0			0
$391$		−	5.74609i		−	0.290592i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.74235	+	3.01783i	0.0876670	+	0.151844i
$396$		0			0
$397$	−20.0838	−	11.5954i	−1.00798	−	0.581955i	−0.0973778	−	0.995247i	$-0.531046\pi$
$397$	−20.0838	−	11.5954i	−1.00798	−	0.581955i	−0.910599	+	0.413292i	$0.864379\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.51104	+	0.872401i	0.0754579	+	0.0435656i	0.537254	−	0.843420i	$-0.319462\pi$
$401$	1.51104	+	0.872401i	0.0754579	+	0.0435656i	−0.461796	+	0.886986i	$0.652795\pi$
$402$		0			0
$403$	−9.76523	−	16.9139i	−0.486441	−	0.842540i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	12.2678i		−	0.608090i
$408$		0			0
$409$	27.7362	−	16.0135i	1.37147	−	0.791816i	0.380352	−	0.924842i	$-0.375803\pi$
$409$	27.7362	−	16.0135i	1.37147	−	0.791816i	0.991113	+	0.133026i	$0.0424694\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.65500	−	2.03027i	−0.179851	−	0.0999028i
$414$		0			0
$415$	0.0225875	−	0.0391227i	0.00110878	−	0.00192046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.5506			−0.808549			−0.404274	−	0.914638i	$-0.632476\pi$
$419$	−16.5506			−0.808549			−0.404274	+	0.914638i	$0.632476\pi$
$420$		0			0
$421$	19.2673			0.939029			0.469514	−	0.882925i	$-0.344429\pi$
$421$	19.2673			0.939029			0.469514	+	0.882925i	$0.344429\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−10.9464	+	18.9597i	−0.530978	+	0.919681i
$426$		0			0
$427$	−29.1713	+	0.483132i	−1.41170	+	0.0233804i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.7026	−	17.7262i	1.47889	−	0.853840i	0.479179	−	0.877717i	$-0.340935\pi$
$431$	30.7026	−	17.7262i	1.47889	−	0.853840i	0.999715	+	0.0238778i	$0.00760125\pi$
$432$		0			0
$433$			10.7841i			0.518251i	0.965844	+	0.259125i	$0.0834343\pi$
$433$			10.7841i			0.518251i	−0.965844	+	0.259125i	$0.916566\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.62028	−	4.53846i	−0.125345	−	0.217104i
$438$		0			0
$439$	−35.4313	−	20.4563i	−1.69104	−	0.976324i	−0.953678	−	0.300829i	$-0.902737\pi$
$439$	−35.4313	−	20.4563i	−1.69104	−	0.976324i	−0.737364	−	0.675495i	$-0.763930\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.84672	−	2.22090i	−0.182763	−	0.105518i	0.405827	−	0.913950i	$-0.366983\pi$
$443$	−3.84672	−	2.22090i	−0.182763	−	0.105518i	−0.588590	+	0.808432i	$0.700317\pi$
$444$		0			0
$445$	0.968906	+	1.67819i	0.0459305	+	0.0795540i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.3226i			0.959082i	0.877519	+	0.479541i	$0.159197\pi$
$449$			20.3226i			0.959082i	−0.877519	+	0.479541i	$0.840803\pi$
$450$		0			0
$451$	28.7893	−	16.6215i	1.35564	−	0.782677i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.18529	−	0.0693165i	0.196209	−	0.00324961i
$456$		0			0
$457$	−0.324749	+	0.562482i	−0.0151911	+	0.0263118i	−0.873521	−	0.486786i	$-0.838169\pi$
$457$	−0.324749	+	0.562482i	−0.0151911	+	0.0263118i	0.858330	+	0.513098i	$0.171502\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−35.7882			−1.66682			−0.833412	−	0.552652i	$-0.813616\pi$
$461$	−35.7882			−1.66682			−0.833412	+	0.552652i	$0.813616\pi$
$462$		0			0
$463$	−16.8281			−0.782068			−0.391034	−	0.920376i	$-0.627883\pi$
$463$	−16.8281			−0.782068			−0.391034	+	0.920376i	$0.627883\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.6807	+	20.2315i	−0.540517	+	0.936203i	0.458357	+	0.888768i	$0.348438\pi$
$467$	−11.6807	+	20.2315i	−0.540517	+	0.936203i	−0.998874	+	0.0474348i	$0.984895\pi$
$468$		0			0
$469$	9.45419	+	5.25158i	0.436554	+	0.242496i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−33.7604	+	19.4916i	−1.55230	+	0.896223i
$474$		0			0
$475$			19.9667i			0.916134i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.9020	+	32.7393i	0.863657	+	1.49590i	0.868375	+	0.495908i	$0.165165\pi$
$479$	18.9020	+	32.7393i	0.863657	+	1.49590i	−0.00471828	+	0.999989i	$0.501502\pi$
$480$		0			0
$481$	9.60491	+	5.54540i	0.437946	+	0.252848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.14242	+	2.39163i	0.188098	+	0.108598i
$486$		0			0
$487$	−15.1049	−	26.1624i	−0.684466	−	1.18553i	−0.973604	−	0.228243i	$-0.926702\pi$
$487$	−15.1049	−	26.1624i	−0.684466	−	1.18553i	0.289138	−	0.957287i	$-0.406631\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	38.8318i		−	1.75245i	−0.481899	−	0.876227i	$-0.660053\pi$
$491$		−	38.8318i		−	1.75245i	0.481899	−	0.876227i	$-0.339947\pi$
$492$		0			0
$493$	−1.45751	+	0.841496i	−0.0656431	+	0.0378991i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.558590	−	0.931533i	−0.0250562	−	0.0417850i
$498$		0			0
$499$	−3.52542	+	6.10620i	−0.157819	+	0.273351i	−0.934082	−	0.357058i	$-0.883780\pi$
$499$	−3.52542	+	6.10620i	−0.157819	+	0.273351i	0.776263	+	0.630410i	$0.217113\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.9561			−0.577683			−0.288842	−	0.957377i	$-0.593270\pi$
$503$	−12.9561			−0.577683			−0.288842	+	0.957377i	$0.593270\pi$
$504$		0			0
$505$	3.47425			0.154602
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.964368	+	1.67033i	−0.0427449	+	0.0740363i	−0.886606	−	0.462525i	$-0.846944\pi$
$509$	−0.964368	+	1.67033i	−0.0427449	+	0.0740363i	0.843861	+	0.536561i	$0.180277\pi$
$510$		0			0
$511$	16.4890	−	29.6843i	0.729429	−	1.31316i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0290733	−	0.0167855i	0.00128112	−	0.000739657i
$516$		0			0
$517$		−	65.0908i		−	2.86269i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.43874	−	16.3484i	−0.413519	−	0.716235i	0.581753	−	0.813366i	$-0.302367\pi$
$521$	−9.43874	−	16.3484i	−0.413519	−	0.716235i	−0.995272	+	0.0971301i	$0.969034\pi$
$522$		0			0
$523$	−3.87627	−	2.23797i	−0.169497	−	0.0978594i	0.412851	−	0.910798i	$-0.364533\pi$
$523$	−3.87627	−	2.23797i	−0.169497	−	0.0978594i	−0.582349	+	0.812939i	$0.697866\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.7941	−	7.96406i	−0.600883	−	0.346920i
$528$		0			0
$529$	−10.6676	−	18.4768i	−0.463808	−	0.803338i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			30.0537i			1.30177i
$534$		0			0
$535$	4.09981	−	2.36703i	0.177250	−	0.102335i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.40009	−	42.2566i	−0.0603060	−	1.82012i
$540$		0			0
$541$	−0.637629	+	1.10441i	−0.0274138	+	0.0474821i	−0.879407	−	0.476071i	$-0.842061\pi$
$541$	−0.637629	+	1.10441i	−0.0274138	+	0.0474821i	0.851993	+	0.523553i	$0.175394\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.263283			−0.0112778
$546$		0			0
$547$	30.8770			1.32020			0.660102	−	0.751176i	$-0.270513\pi$
$547$	30.8770			1.32020			0.660102	+	0.751176i	$0.270513\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.767462	+	1.32928i	−0.0326950	+	0.0566294i
$552$		0			0
$553$	0.526940	+	31.8163i	0.0224078	+	1.35297i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	29.0859	−	16.7927i	1.23241	−	0.711531i	0.264876	−	0.964282i	$-0.414669\pi$
$557$	29.0859	−	16.7927i	1.23241	−	0.711531i	0.967531	+	0.252751i	$0.0813355\pi$
$558$		0			0
$559$		−	35.2431i		−	1.49062i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−13.4046	−	23.2175i	−0.564937	−	0.978499i	−0.997056	−	0.0766823i	$-0.975567\pi$
$563$	−13.4046	−	23.2175i	−0.564937	−	0.978499i	0.432119	−	0.901817i	$-0.357766\pi$
$564$		0			0
$565$	−2.10064	−	1.21280i	−0.0883745	−	0.0510231i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.7065	+	7.91345i	0.574606	+	0.331749i	0.758987	−	0.651106i	$-0.225695\pi$
$569$	13.7065	+	7.91345i	0.574606	+	0.331749i	−0.184381	+	0.982855i	$0.559028\pi$
$570$		0			0
$571$	−3.77658	−	6.54124i	−0.158045	−	0.273742i	0.776119	−	0.630587i	$-0.217186\pi$
$571$	−3.77658	−	6.54124i	−0.158045	−	0.273742i	−0.934164	+	0.356845i	$0.883852\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	6.34315i		−	0.264527i
$576$		0			0
$577$	11.7609	−	6.79013i	0.489611	−	0.282677i	−0.234802	−	0.972043i	$-0.575444\pi$
$577$	11.7609	−	6.79013i	0.489611	−	0.282677i	0.724413	+	0.689366i	$0.242111\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.353787	−	0.212147i	0.0146776	−	0.00880134i
$582$		0			0
$583$	−34.0845	+	59.0360i	−1.41163	+	2.44502i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.7243			−1.06176			−0.530878	−	0.847449i	$-0.678138\pi$
$587$	−25.7243			−1.06176			−0.530878	+	0.847449i	$0.678138\pi$
$588$		0			0
$589$	−14.5268			−0.598565
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.59806	+	11.4282i	−0.270950	+	0.469299i	−0.969105	−	0.246647i	$-0.920671\pi$
$593$	−6.59806	+	11.4282i	−0.270950	+	0.469299i	0.698156	+	0.715946i	$0.254004\pi$
$594$		0			0
$595$	2.92776	−	1.75562i	0.120026	−	0.0719734i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.8018	+	8.54581i	−0.604784	+	0.349172i	−0.770921	−	0.636930i	$-0.780204\pi$
$599$	−14.8018	+	8.54581i	−0.604784	+	0.349172i	0.166137	+	0.986103i	$0.446871\pi$
$600$		0			0
$601$			10.7137i			0.437019i	0.975835	+	0.218510i	$0.0701195\pi$
$601$			10.7137i			0.437019i	−0.975835	+	0.218510i	$0.929881\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.69143	+	6.39375i	0.150078	+	0.259943i
$606$		0			0
$607$	−14.0938	−	8.13707i	−0.572050	−	0.330273i	0.185917	−	0.982565i	$-0.440474\pi$
$607$	−14.0938	−	8.13707i	−0.572050	−	0.330273i	−0.757968	+	0.652292i	$0.773808\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	50.9621	+	29.4230i	2.06171	+	1.19033i
$612$		0			0
$613$	7.76754	+	13.4538i	0.313728	+	0.543393i	0.979166	−	0.203060i	$-0.0650886\pi$
$613$	7.76754	+	13.4538i	0.313728	+	0.543393i	−0.665438	+	0.746453i	$0.731755\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			3.18413i			0.128188i	0.997944	+	0.0640941i	$0.0204158\pi$
$617$			3.18413i			0.128188i	−0.997944	+	0.0640941i	$0.979584\pi$
$618$		0			0
$619$	−23.3325	+	13.4710i	−0.937811	+	0.541446i	−0.889274	−	0.457376i	$-0.848789\pi$
$619$	−23.3325	+	13.4710i	−0.937811	+	0.541446i	−0.0485379	+	0.998821i	$0.515456\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.293027	+	17.6928i	0.0117399	+	0.708848i
$624$		0			0
$625$	−11.8739	+	20.5662i	−0.474957	+	0.822649i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.04512			0.360653
$630$		0			0
$631$	19.7789			0.787387			0.393693	−	0.919242i	$-0.371197\pi$
$631$	19.7789			0.787387			0.393693	+	0.919242i	$0.371197\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.888449	+	1.53884i	−0.0352570	+	0.0610670i
$636$		0			0
$637$	33.7173	+	18.0051i	1.33593	+	0.713388i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−39.5884	+	22.8564i	−1.56365	+	0.902772i	−0.566764	+	0.823880i	$0.691805\pi$
$641$	−39.5884	+	22.8564i	−1.56365	+	0.902772i	−0.996883	+	0.0788925i	$0.974862\pi$
$642$		0			0
$643$			11.1743i			0.440672i	0.975424	+	0.220336i	$0.0707155\pi$
$643$			11.1743i			0.440672i	−0.975424	+	0.220336i	$0.929285\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.35600	−	14.4730i	−0.328508	−	0.568993i	0.653708	−	0.756747i	$-0.273213\pi$
$647$	−8.35600	−	14.4730i	−0.328508	−	0.568993i	−0.982216	+	0.187754i	$0.939879\pi$
$648$		0			0
$649$	8.26608	+	4.77242i	0.324472	+	0.187334i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	37.0979	+	21.4185i	1.45175	+	0.838170i	0.998581	−	0.0532524i	$-0.0169588\pi$
$653$	37.0979	+	21.4185i	1.45175	+	0.838170i	0.453173	+	0.891423i	$0.350292\pi$
$654$		0			0
$655$	−2.13395	−	3.69611i	−0.0833804	−	0.144419i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			3.00672i			0.117125i	0.998284	+	0.0585627i	$0.0186518\pi$
$659$			3.00672i			0.117125i	−0.998284	+	0.0585627i	$0.981348\pi$
$660$		0			0
$661$	13.0503	−	7.53461i	0.507599	−	0.293062i	−0.224247	−	0.974532i	$-0.571992\pi$
$661$	13.0503	−	7.53461i	0.507599	−	0.293062i	0.731846	+	0.681470i	$0.238659\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.51186	−	2.72174i	0.0586275	−	0.105544i
$666$		0			0
$667$	0.243812	−	0.422295i	0.00944045	−	0.0163513i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	66.6040			2.57122
$672$		0			0
$673$	−6.01408			−0.231826			−0.115913	−	0.993259i	$-0.536979\pi$
$673$	−6.01408			−0.231826			−0.115913	+	0.993259i	$0.536979\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.93572	−	6.81687i	0.151262	−	0.261994i	−0.780430	−	0.625244i	$-0.785000\pi$
$677$	3.93572	−	6.81687i	0.151262	−	0.261994i	0.931692	+	0.363250i	$0.118333\pi$
$678$		0			0
$679$	22.4627	+	37.4599i	0.862039	+	1.43758i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.4955	−	7.79165i	0.516393	−	0.298139i	−0.219065	−	0.975710i	$-0.570301\pi$
$683$	13.4955	−	7.79165i	0.516393	−	0.298139i	0.735457	+	0.677571i	$0.236967\pi$
$684$		0			0
$685$			3.94101i			0.150578i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−30.8144	−	53.3721i	−1.17394	−	2.03332i
$690$		0			0
$691$	−24.4535	−	14.1183i	−0.930256	−	0.537084i	−0.0433635	−	0.999059i	$-0.513807\pi$
$691$	−24.4535	−	14.1183i	−0.930256	−	0.537084i	−0.886893	+	0.461976i	$0.847141\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.35546	−	2.51462i	−0.165212	−	0.0953851i
$696$		0			0
$697$	12.2552	+	21.2266i	0.464199	+	0.804016i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	16.7937i		−	0.634288i	−0.948377	−	0.317144i	$-0.897276\pi$
$701$		−	16.7937i		−	0.634288i	0.948377	−	0.317144i	$-0.102724\pi$
$702$		0			0
$703$	7.14414	−	4.12467i	0.269446	−	0.155565i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.7338	+	15.4055i	1.04304	+	0.579384i
$708$		0			0
$709$	−3.57291	+	6.18846i	−0.134183	+	0.232412i	−0.925285	−	0.379272i	$-0.876174\pi$
$709$	−3.57291	+	6.18846i	−0.134183	+	0.232412i	0.791102	+	0.611684i	$0.209508\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.61496			0.172832
$714$		0			0
$715$	−9.55589			−0.357370
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.03223	−	12.1802i	0.262258	−	0.454244i	−0.704584	−	0.709621i	$-0.748866\pi$
$719$	7.03223	−	12.1802i	0.262258	−	0.454244i	0.966842	+	0.255377i	$0.0821995\pi$
$720$		0			0
$721$	0.306514	−	0.00507646i	0.0114152	−	0.000189057i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.60896	+	0.928932i	−0.0597552	+	0.0344997i
$726$		0			0
$727$			12.0721i			0.447728i	0.974620	+	0.223864i	$0.0718672\pi$
$727$			12.0721i			0.447728i	−0.974620	+	0.223864i	$0.928133\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−14.3713	−	24.8918i	−0.531542	−	0.920657i
$732$		0			0
$733$	−21.2754	−	12.2834i	−0.785827	−	0.453697i	0.0526646	−	0.998612i	$-0.483229\pi$
$733$	−21.2754	−	12.2834i	−0.785827	−	0.453697i	−0.838491	+	0.544915i	$0.816562\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.3814	−	12.3446i	−0.787595	−	0.454718i
$738$		0			0
$739$	19.0963	+	33.0758i	0.702470	+	1.21671i	0.967597	+	0.252501i	$0.0812530\pi$
$739$	19.0963	+	33.0758i	0.702470	+	1.21671i	−0.265126	+	0.964214i	$0.585414\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	9.94867i		−	0.364981i	−0.983208	−	0.182491i	$-0.941584\pi$
$743$		−	9.94867i		−	0.364981i	0.983208	−	0.182491i	$-0.0584159\pi$
$744$		0			0
$745$	3.87088	−	2.23485i	0.141818	−	0.0818786i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	43.2234	−	0.715862i	1.57935	−	0.0261570i
$750$		0			0
$751$	−1.96469	+	3.40295i	−0.0716927	+	0.124175i	−0.899643	−	0.436626i	$-0.856173\pi$
$751$	−1.96469	+	3.40295i	−0.0716927	+	0.124175i	0.827951	+	0.560801i	$0.189507\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.55712			0.0566692
$756$		0			0
$757$	−10.7492			−0.390686			−0.195343	−	0.980735i	$-0.562582\pi$
$757$	−10.7492			−0.390686			−0.195343	+	0.980735i	$0.562582\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.24304	+	3.88506i	−0.0813102	+	0.140833i	−0.903813	−	0.427928i	$-0.859244\pi$
$761$	−2.24304	+	3.88506i	−0.0813102	+	0.140833i	0.822503	+	0.568761i	$0.192577\pi$
$762$		0			0
$763$	−2.10171	−	1.16745i	−0.0760869	−	0.0422645i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.47303	+	4.31456i	−0.269836	+	0.155790i
$768$		0			0
$769$			9.74739i			0.351500i	0.984435	+	0.175750i	$0.0562350\pi$
$769$			9.74739i			0.351500i	−0.984435	+	0.175750i	$0.943765\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.4609	+	31.9752i	0.663992	+	1.15007i	0.979557	+	0.201165i	$0.0644726\pi$
$773$	18.4609	+	31.9752i	0.663992	+	1.15007i	−0.315565	+	0.948904i	$0.602194\pi$
$774$		0			0
$775$	−15.2274	−	8.79157i	−0.546986	−	0.315803i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	19.3591	+	11.1770i	0.693613	+	0.400458i
$780$		0			0
$781$	1.23981	+	2.14742i	0.0443640	+	0.0768406i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	2.01776i		−	0.0720169i
$786$		0			0
$787$	16.7796	−	9.68771i	0.598128	−	0.345330i	−0.170177	−	0.985414i	$-0.554434\pi$
$787$	16.7796	−	9.68771i	0.598128	−	0.345330i	0.768305	+	0.640084i	$0.221100\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−11.3909	−	18.9961i	−0.405015	−	0.675423i
$792$		0			0
$793$	−30.1070	+	52.1469i	−1.06913	+	1.85179i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.8237			0.843880			0.421940	−	0.906624i	$-0.361349\pi$
$797$	23.8237			0.843880			0.421940	+	0.906624i	$0.361349\pi$
$798$		0			0
$799$	47.9920			1.69783
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−38.7596	+	67.1336i	−1.36780	+	2.36909i
$804$		0			0
$805$	−0.480298	+	0.864659i	−0.0169283	+	0.0304752i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.6571	−	10.7717i	0.655948	−	0.378712i	−0.134783	−	0.990875i	$-0.543034\pi$
$809$	18.6571	−	10.7717i	0.655948	−	0.378712i	0.790731	+	0.612163i	$0.209701\pi$
$810$		0			0
$811$		−	6.36360i		−	0.223456i	−0.993739	−	0.111728i	$-0.964361\pi$
$811$		−	6.36360i		−	0.223456i	0.993739	−	0.111728i	$-0.0356386\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.45101	+	2.51322i	0.0508267	+	0.0880344i
$816$		0			0
$817$	−22.7019	−	13.1069i	−0.794238	−	0.458553i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.0269	+	5.78905i	0.349942	+	0.202039i	0.664660	−	0.747146i	$-0.268576\pi$
$821$	10.0269	+	5.78905i	0.349942	+	0.202039i	−0.314717	+	0.949185i	$0.601910\pi$
$822$		0			0
$823$	7.91237	+	13.7046i	0.275808	+	0.477714i	0.970339	−	0.241750i	$-0.0777213\pi$
$823$	7.91237	+	13.7046i	0.275808	+	0.477714i	−0.694531	+	0.719463i	$0.744388\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			12.6537i			0.440011i	0.975499	+	0.220006i	$0.0706076\pi$
$827$			12.6537i			0.440011i	−0.975499	+	0.220006i	$0.929392\pi$
$828$		0			0
$829$	7.47709	−	4.31690i	0.259690	−	0.149932i	−0.364503	−	0.931202i	$-0.618761\pi$
$829$	7.47709	−	4.31690i	0.259690	−	0.149932i	0.624193	+	0.781270i	$0.285428\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.1562	−	1.03230i	1.07950	−	0.0357669i
$834$		0			0
$835$	0.873924	−	1.51368i	0.0302434	−	0.0523831i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−33.7820			−1.16628			−0.583142	−	0.812371i	$-0.698177\pi$
$839$	−33.7820			−1.16628			−0.583142	+	0.812371i	$0.698177\pi$
$840$		0			0
$841$	28.8572			0.995075
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.43626	−	4.21973i	0.0838100	−	0.145163i
$846$		0			0
$847$	1.11640	+	67.4079i	0.0383601	+	2.31616i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.26960	+	1.31035i	−0.0778008	+	0.0449183i
$852$		0			0
$853$		−	1.23446i		−	0.0422671i	−0.999777	−	0.0211336i	$-0.993272\pi$
$853$		−	1.23446i		−	0.0422671i	0.999777	−	0.0211336i	$-0.00672752\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.5237	+	30.3519i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376082\pi$
$857$	17.5237	+	30.3519i	0.598597	+	1.03680i	−0.394431	+	0.918925i	$0.629058\pi$
$858$		0			0
$859$	18.5187	+	10.6918i	0.631852	+	0.364800i	0.781469	−	0.623944i	$-0.214471\pi$
$859$	18.5187	+	10.6918i	0.631852	+	0.364800i	−0.149617	+	0.988744i	$0.547804\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.61471	+	2.66430i	0.157087	+	0.0906940i	0.576483	−	0.817109i	$-0.304425\pi$
$863$	4.61471	+	2.66430i	0.157087	+	0.0906940i	−0.419396	+	0.907803i	$0.637758\pi$
$864$		0			0
$865$	2.66053	+	4.60818i	0.0904608	+	0.156683i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	72.6433i		−	2.46426i
$870$		0			0
$871$	19.3301	−	11.1602i	0.654976	−	0.378150i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.51913	−	3.90917i	0.220387	−	0.132154i
$876$		0			0
$877$	−1.76822	+	3.06264i	−0.0597085	+	0.103418i	−0.894335	−	0.447399i	$-0.852350\pi$
$877$	−1.76822	+	3.06264i	−0.0597085	+	0.103418i	0.834626	+	0.550817i	$0.185684\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−49.3358			−1.66217			−0.831083	−	0.556148i	$-0.812279\pi$
$881$	−49.3358			−1.66217			−0.831083	+	0.556148i	$0.812279\pi$
$882$		0			0
$883$	−33.9893			−1.14383			−0.571915	−	0.820313i	$-0.693799\pi$
$883$	−33.9893			−1.14383			−0.571915	+	0.820313i	$0.693799\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.8153	−	32.5891i	0.631757	−	1.09423i	−0.355436	−	0.934701i	$-0.615668\pi$
$887$	18.8153	−	32.5891i	0.631757	−	1.09423i	0.987192	−	0.159534i	$-0.0509991\pi$
$888$		0			0
$889$	−13.9157	+	8.34452i	−0.466719	+	0.279866i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	37.9057	−	21.8849i	1.26847	−	0.732349i
$894$		0			0
$895$			3.29074i			0.109997i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.675845	−	1.17060i	−0.0225407	−	0.0390417i
$900$		0			0
$901$	−43.5278	−	25.1308i	−1.45012	−	0.837227i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.97707	−	1.71881i	−0.0989613	−	0.0571353i
$906$		0			0
$907$	5.75787	+	9.97293i	0.191187	+	0.331146i	0.945644	−	0.325204i	$-0.105433\pi$
$907$	5.75787	+	9.97293i	0.191187	+	0.331146i	−0.754457	+	0.656350i	$0.772100\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			51.3469i			1.70120i	0.525815	+	0.850599i	$0.323760\pi$
$911$			51.3469i			1.70120i	−0.525815	+	0.850599i	$0.676240\pi$
$912$		0			0
$913$	−0.815568	+	0.470869i	−0.0269914	+	0.0155835i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.645373	−	38.9673i	−0.0213121	−	1.28681i
$918$		0			0
$919$	−1.49832	+	2.59517i	−0.0494251	+	0.0856068i	−0.889680	−	0.456586i	$-0.849072\pi$
$919$	−1.49832	+	2.59517i	−0.0494251	+	0.0856068i	0.840254	+	0.542192i	$0.182406\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.24173			−0.0737874
$924$		0			0
$925$	9.98497			0.328304
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18.7345	+	32.4491i	−0.614659	+	1.06462i	0.375785	+	0.926707i	$0.377373\pi$
$929$	−18.7345	+	32.4491i	−0.614659	+	1.06462i	−0.990444	+	0.137914i	$0.955960\pi$
$930$		0			0
$931$	24.1375	−	15.0229i	0.791073	−	0.492355i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.74922	+	3.89667i	−0.220723	+	0.127435i
$936$		0			0
$937$		−	4.97716i		−	0.162597i	−0.996690	−	0.0812983i	$-0.974093\pi$
$937$		−	4.97716i		−	0.162597i	0.996690	−	0.0812983i	$-0.0259067\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.0429	−	29.5192i	−0.555584	−	0.962299i	−0.997858	−	0.0654193i	$-0.979162\pi$
$941$	−17.0429	−	29.5192i	−0.555584	−	0.962299i	0.442274	−	0.896880i	$-0.354172\pi$
$942$		0			0
$943$	−6.15014	−	3.55078i	−0.200276	−	0.115629i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.1735	+	15.1113i	0.850524	+	0.491050i	0.860828	−	0.508897i	$-0.169946\pi$
$947$	26.1735	+	15.1113i	0.850524	+	0.491050i	−0.0103036	+	0.999947i	$0.503280\pi$
$948$		0			0
$949$	−35.0410	−	60.6928i	−1.13748	−	1.97017i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	20.5265i		−	0.664917i	−0.943118	−	0.332459i	$-0.892122\pi$
$953$		−	20.5265i		−	0.664917i	0.943118	−	0.332459i	$-0.107878\pi$
$954$		0			0
$955$	3.36992	−	1.94562i	0.109048	−	0.0629589i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.4752	+	31.4598i	−0.564304	+	1.01589i
$960$		0			0
$961$	−9.10369	+	15.7680i	−0.293667	+	0.508647i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.66768			−0.0536845
$966$		0			0
$967$	−21.8044			−0.701181			−0.350591	−	0.936529i	$-0.614019\pi$
$967$	−21.8044			−0.701181			−0.350591	+	0.936529i	$0.614019\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−17.7817	+	30.7988i	−0.570642	+	0.988382i	0.425858	+	0.904790i	$0.359972\pi$
$971$	−17.7817	+	30.7988i	−0.570642	+	0.988382i	−0.996500	+	0.0835915i	$0.973361\pi$
$972$		0			0
$973$	−23.6179	−	39.3864i	−0.757156	−	1.26267i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.92632	−	5.15362i	0.285578	−	0.164879i	−0.350368	−	0.936612i	$-0.613943\pi$
$977$	8.92632	−	5.15362i	0.285578	−	0.164879i	0.635946	+	0.771733i	$0.280610\pi$
$978$		0			0
$979$		−	40.3964i		−	1.29108i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	14.1069	+	24.4340i	0.449942	+	0.779322i	0.998382	−	0.0568679i	$-0.0181114\pi$
$983$	14.1069	+	24.4340i	0.449942	+	0.779322i	−0.548440	+	0.836190i	$0.684778\pi$
$984$		0			0
$985$	0.667579	+	0.385427i	0.0212708	+	0.0122807i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.21208	+	4.16389i	0.229331	+	0.132404i
$990$		0			0
$991$	−17.2085	−	29.8061i	−0.546647	−	0.946821i	−0.998501	−	0.0547288i	$-0.982571\pi$
$991$	−17.2085	−	29.8061i	−0.546647	−	0.946821i	0.451854	−	0.892092i	$-0.350763\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			2.42740i			0.0769538i
$996$		0			0
$997$	41.0269	−	23.6869i	1.29934	−	0.750172i	0.319047	−	0.947739i	$-0.396637\pi$
$997$	41.0269	−	23.6869i	1.29934	−	0.750172i	0.980289	+	0.197567i	$0.0633040\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bl.a.89.4	yes	16
3.2	odd	2	inner	504.2.bl.a.89.5	yes	16
4.3	odd	2		1008.2.bt.d.593.4		16
7.2	even	3		3528.2.k.b.881.10		16
7.3	odd	6	inner	504.2.bl.a.17.5	yes	16
7.4	even	3		3528.2.bl.a.521.4		16
7.5	odd	6		3528.2.k.b.881.8		16
7.6	odd	2		3528.2.bl.a.1097.5		16
12.11	even	2		1008.2.bt.d.593.5		16
21.2	odd	6		3528.2.k.b.881.7		16
21.5	even	6		3528.2.k.b.881.9		16
21.11	odd	6		3528.2.bl.a.521.5		16
21.17	even	6	inner	504.2.bl.a.17.4	✓	16
21.20	even	2		3528.2.bl.a.1097.4		16
28.3	even	6		1008.2.bt.d.17.5		16
28.19	even	6		7056.2.k.h.881.7		16
28.23	odd	6		7056.2.k.h.881.9		16
84.23	even	6		7056.2.k.h.881.8		16
84.47	odd	6		7056.2.k.h.881.10		16
84.59	odd	6		1008.2.bt.d.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bl.a.17.4	✓	16	21.17	even	6	inner
504.2.bl.a.17.5	yes	16	7.3	odd	6	inner
504.2.bl.a.89.4	yes	16	1.1	even	1	trivial
504.2.bl.a.89.5	yes	16	3.2	odd	2	inner
1008.2.bt.d.17.4		16	84.59	odd	6
1008.2.bt.d.17.5		16	28.3	even	6
1008.2.bt.d.593.4		16	4.3	odd	2
1008.2.bt.d.593.5		16	12.11	even	2
3528.2.k.b.881.7		16	21.2	odd	6
3528.2.k.b.881.8		16	7.5	odd	6
3528.2.k.b.881.9		16	21.5	even	6
3528.2.k.b.881.10		16	7.2	even	3
3528.2.bl.a.521.4		16	7.4	even	3
3528.2.bl.a.521.5		16	21.11	odd	6
3528.2.bl.a.1097.4		16	21.20	even	2
3528.2.bl.a.1097.5		16	7.6	odd	2
7056.2.k.h.881.7		16	28.19	even	6
7056.2.k.h.881.8		16	84.23	even	6
7056.2.k.h.881.9		16	28.23	odd	6
7056.2.k.h.881.10		16	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.144868 + 0.250919i) q^{5} +(-2.26907 + 1.36064i) q^{7} +O(q^{10})\)	\(q+(-0.144868 + 0.250919i) q^{5} +(-2.26907 + 1.36064i) q^{7} +(5.23077 - 3.01999i) q^{11} +5.46050i q^{13} +(2.22666 + 3.85669i) q^{17} +(3.51739 + 2.03076i) q^{19} +(-1.11743 - 0.645146i) q^{23} +(2.45803 + 4.25743i) q^{25} +0.377918i q^{29} +(-3.09749 + 1.78834i) q^{31} +(-0.0126942 - 0.766467i) q^{35} +(1.01555 - 1.75898i) q^{37} +5.50384 q^{41} -6.45419 q^{43} +(5.38833 - 9.33287i) q^{47} +(3.29733 - 6.17475i) q^{49} +(-9.77422 + 5.64315i) q^{53} +1.75000i q^{55} +(0.790140 + 1.36856i) q^{59} +(9.54984 + 5.51360i) q^{61} +(-1.37015 - 0.791054i) q^{65} +(-2.04381 - 3.53999i) q^{67} +0.410536i q^{71} +(-11.1149 + 6.41718i) q^{73} +(-7.75986 + 13.9697i) q^{77} +(6.01355 - 10.4158i) q^{79} -0.155917 q^{83} -1.29029 q^{85} +(3.34409 - 5.79213i) q^{89} +(-7.42976 - 12.3902i) q^{91} +(-1.01912 + 0.588387i) q^{95} -16.5090i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) \) 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

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