LMFDB - Embedded newform 864.2.p.b.143.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(143,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("864.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.p (of order $6$, degree $2$, not 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:	$6.89907473464$
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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.5
Root			$-0.409484 + 1.35363i$ of defining polynomial
Character	$\chi$	$=$	864.143
Dual form			864.2.p.b.719.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.565188 + 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +O(q^{10})$	$q+(0.565188 + 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(1.00953 + 0.582853i) q^{11} +(2.64466 - 1.52689i) q^{13} -1.49654i q^{17} +3.42378 q^{19} +(-3.85938 - 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(0.709580 - 1.22903i) q^{29} +(4.66408 - 2.69281i) q^{31} -4.84897i q^{35} -2.97201i q^{37} +(4.23339 - 2.44415i) q^{41} +(1.74292 - 3.01882i) q^{43} +(-1.77991 + 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} -11.2786 q^{53} +1.31769i q^{55} +(7.50935 - 4.33553i) q^{59} +(-3.16057 - 1.82476i) q^{61} +(2.98946 + 1.72596i) q^{65} +(5.58255 + 9.66925i) q^{67} +2.54954 q^{71} -7.06491 q^{73} +(-2.50026 - 4.33059i) q^{77} +(2.24998 + 1.29902i) q^{79} +(-3.98482 - 2.30064i) q^{83} +(1.46501 - 0.845824i) q^{85} -8.63803i q^{89} -13.0998 q^{91} +(1.93508 + 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) $ 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	0.964285	−	0.264868i	$-0.0853285\pi$
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	−0.711525	+	0.702661i	$0.751995\pi$
$6$		0			0
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.409320	−	0.912391i	$-0.634234\pi$
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.994814	+	0.101714i	$0.967567\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00953	+	0.582853i	0.304385	+	0.175737i	0.644411	−	0.764679i	$-0.277103\pi$
$11$	1.00953	+	0.582853i	0.304385	+	0.175737i	−0.340026	+	0.940416i	$0.610436\pi$
$12$		0			0
$13$	2.64466	−	1.52689i	0.733496	−	0.423484i	−0.0862038	−	0.996278i	$-0.527474\pi$
$13$	2.64466	−	1.52689i	0.733496	−	0.423484i	0.819700	+	0.572793i	$0.194140\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	1.49654i		−	0.362963i	−0.983394	−	0.181482i	$-0.941911\pi$
$17$		−	1.49654i		−	0.362963i	0.983394	−	0.181482i	$-0.0580893\pi$
$18$		0			0
$19$	3.42378			0.785468			0.392734	−	0.919652i	$-0.371529\pi$
$19$	3.42378			0.785468			0.392734	+	0.919652i	$0.371529\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.85938	−	6.68464i	−0.804736	−	1.39384i	−0.916469	−	0.400106i	$-0.868973\pi$
$23$	−3.85938	−	6.68464i	−0.804736	−	1.39384i	0.111733	−	0.993738i	$-0.464360\pi$
$24$		0			0
$25$	1.86113	−	3.22356i	0.372225	−	0.644713i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	−0.792592	−	0.609753i	$-0.791269\pi$
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	0.924357	+	0.381528i	$0.124602\pi$
$30$		0			0
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	−0.0187859	−	0.999824i	$-0.505980\pi$
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	0.856480	+	0.516181i	$0.172647\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	4.84897i		−	0.819625i
$36$		0			0
$37$		−	2.97201i		−	0.488596i	−0.969700	−	0.244298i	$-0.921443\pi$
$37$		−	2.97201i		−	0.488596i	0.969700	−	0.244298i	$-0.0785575\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	−0.131569	−	0.991307i	$-0.542001\pi$
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	0.792713	+	0.609595i	$0.208668\pi$
$42$		0			0
$43$	1.74292	−	3.01882i	0.265793	−	0.460366i	−0.701978	−	0.712198i	$-0.747700\pi$
$43$	1.74292	−	3.01882i	0.265793	−	0.460366i	0.967771	+	0.251832i	$0.0810330\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.77991	+	3.08289i	−0.259627	+	0.449686i	−0.966142	−	0.258011i	$-0.916933\pi$
$47$	−1.77991	+	3.08289i	−0.259627	+	0.449686i	0.706515	+	0.707698i	$0.250266\pi$
$48$		0			0
$49$	5.70075	+	9.87399i	0.814393	+	1.41057i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.2786			−1.54923			−0.774616	−	0.632432i	$-0.782057\pi$
$53$	−11.2786			−1.54923			−0.774616	+	0.632432i	$0.782057\pi$
$54$		0			0
$55$			1.31769i			0.177677i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.50935	−	4.33553i	0.977634	−	0.564437i	0.0760791	−	0.997102i	$-0.475760\pi$
$59$	7.50935	−	4.33553i	0.977634	−	0.564437i	0.901555	+	0.432664i	$0.142427\pi$
$60$		0			0
$61$	−3.16057	−	1.82476i	−0.404670	−	0.233636i	0.283827	−	0.958875i	$-0.408396\pi$
$61$	−3.16057	−	1.82476i	−0.404670	−	0.233636i	−0.688497	+	0.725239i	$0.741729\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.98946	+	1.72596i	0.370796	+	0.214079i
$66$		0			0
$67$	5.58255	+	9.66925i	0.682017	+	1.18129i	0.974364	+	0.224975i	$0.0722301\pi$
$67$	5.58255	+	9.66925i	0.682017	+	1.18129i	−0.292348	+	0.956312i	$0.594437\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.54954			0.302574			0.151287	−	0.988490i	$-0.451658\pi$
$71$	2.54954			0.302574			0.151287	+	0.988490i	$0.451658\pi$
$72$		0			0
$73$	−7.06491			−0.826885			−0.413442	−	0.910530i	$-0.635674\pi$
$73$	−7.06491			−0.826885			−0.413442	+	0.910530i	$0.635674\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.50026	−	4.33059i	−0.284932	−	0.493516i
$78$		0			0
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	0.621202	−	0.783650i	$-0.286645\pi$
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	−0.368060	+	0.929802i	$0.619978\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.98482	−	2.30064i	−0.437391	−	0.252528i	0.265099	−	0.964221i	$-0.414595\pi$
$83$	−3.98482	−	2.30064i	−0.437391	−	0.252528i	−0.702490	+	0.711693i	$0.747929\pi$
$84$		0			0
$85$	1.46501	−	0.845824i	0.158903	−	0.0917425i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	8.63803i		−	0.915630i	−0.889048	−	0.457815i	$-0.848632\pi$
$89$		−	8.63803i		−	0.915630i	0.889048	−	0.457815i	$-0.151368\pi$
$90$		0			0
$91$	−13.0998			−1.37323
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.93508	+	3.35165i	0.198535	+	0.343872i
$96$		0			0
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	−0.643600	−	0.765362i	$-0.722560\pi$
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	0.984623	+	0.174693i	$0.0558931\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	−0.290967	−	0.956733i	$-0.593977\pi$
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	0.974039	−	0.226382i	$-0.0726897\pi$
$102$		0			0
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	−0.205022	−	0.978757i	$-0.565727\pi$
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	0.745118	+	0.666933i	$0.232393\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			10.4483i			1.01007i	0.863097	+	0.505037i	$0.168521\pi$
$107$			10.4483i			1.01007i	−0.863097	+	0.505037i	$0.831479\pi$
$108$		0			0
$109$			9.67531i			0.926727i	0.886168	+	0.463364i	$0.153358\pi$
$109$			9.67531i			0.926727i	−0.886168	+	0.463364i	$0.846642\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	−0.797120	−	0.603821i	$-0.793644\pi$
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	0.124364	+	0.992237i	$0.460311\pi$
$114$		0			0
$115$	4.36255	−	7.55615i	0.406810	−	0.704615i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.20984	+	5.55961i	−0.294246	+	0.509649i
$120$		0			0
$121$	−4.82056	−	8.34946i	−0.438233	−	0.759042i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.85942			0.881853
$126$		0			0
$127$			2.78757i			0.247357i	0.992322	+	0.123678i	$0.0394691\pi$
$127$			2.78757i			0.247357i	−0.992322	+	0.123678i	$0.960531\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.0529	+	7.53612i	−1.14044	+	0.658434i	−0.946540	−	0.322587i	$-0.895447\pi$
$131$	−13.0529	+	7.53612i	−1.14044	+	0.658434i	−0.193901	+	0.981021i	$0.562114\pi$
$132$		0			0
$133$	−12.7193	−	7.34348i	−1.10290	−	0.636761i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	0.141402	−	0.989952i	$-0.454839\pi$
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	−0.786623	+	0.617434i	$0.788172\pi$
$138$		0			0
$139$	−1.18897	−	2.05935i	−0.100847	−	0.174672i	0.811187	−	0.584787i	$-0.198822\pi$
$139$	−1.18897	−	2.05935i	−0.100847	−	0.174672i	−0.912034	+	0.410115i	$0.865489\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.55982			0.297687
$144$		0			0
$145$	1.60418			0.133220
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	0.955707	+	0.294320i	$0.0950931\pi$
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	−0.222965	+	0.974826i	$0.571574\pi$
$150$		0			0
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	0.399520	−	0.916725i	$-0.369177\pi$
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	−0.594147	+	0.804357i	$0.702510\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.27216	+	3.04388i	0.423470	+	0.244491i
$156$		0			0
$157$	2.21148	−	1.27680i	0.176495	−	0.101900i	−0.409150	−	0.912467i	$-0.634175\pi$
$157$	2.21148	−	1.27680i	0.176495	−	0.101900i	0.585645	+	0.810568i	$0.300841\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			33.1111i			2.60952i
$162$		0			0
$163$	−6.93355			−0.543077			−0.271539	−	0.962428i	$-0.587532\pi$
$163$	−6.93355			−0.543077			−0.271539	+	0.962428i	$0.587532\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.36829	+	14.4943i	0.647558	+	1.12160i	0.983704	+	0.179794i	$0.0575430\pi$
$167$	8.36829	+	14.4943i	0.647558	+	1.12160i	−0.336146	+	0.941810i	$0.609124\pi$
$168$		0			0
$169$	−1.83719	+	3.18211i	−0.141322	+	0.244778i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	0.156761	+	0.987637i	$0.449895\pi$
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	−0.933699	+	0.358059i	$0.883438\pi$
$174$		0			0
$175$	−13.8281	+	7.98367i	−1.04531	+	0.603508i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	4.07982i		−	0.304940i	−0.988308	−	0.152470i	$-0.951277\pi$
$179$		−	4.07982i		−	0.304940i	0.988308	−	0.152470i	$-0.0487227\pi$
$180$		0			0
$181$			22.3226i			1.65923i	0.558337	+	0.829614i	$0.311440\pi$
$181$			22.3226i			1.65923i	−0.558337	+	0.829614i	$0.688560\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.90940	−	1.67974i	0.213904	−	0.123497i
$186$		0			0
$187$	0.872261	−	1.51080i	0.0637861	−	0.110481i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.27481	−	12.6003i	0.526387	−	0.911728i	−0.473141	−	0.880987i	$-0.656880\pi$
$191$	7.27481	−	12.6003i	0.526387	−	0.911728i	0.999527	−	0.0307415i	$-0.00978686\pi$
$192$		0			0
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	0.934154	−	0.356870i	$-0.116156\pi$
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	−0.776136	+	0.630566i	$0.782823\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.69721			0.548404			0.274202	−	0.961672i	$-0.411586\pi$
$197$	7.69721			0.548404			0.274202	+	0.961672i	$0.411586\pi$
$198$		0			0
$199$			20.9790i			1.48716i	0.668646	+	0.743580i	$0.266874\pi$
$199$			20.9790i			1.48716i	−0.668646	+	0.743580i	$0.733126\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.27216	+	3.04388i	−0.370033	+	0.213639i
$204$		0			0
$205$	4.78532	+	2.76280i	0.334221	+	0.192963i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.45641	+	1.99556i	0.239085	+	0.138036i
$210$		0			0
$211$	−2.38482	−	4.13063i	−0.164178	−	0.284364i	0.772185	−	0.635397i	$-0.219164\pi$
$211$	−2.38482	−	4.13063i	−0.164178	−	0.284364i	−0.936363	+	0.351033i	$0.885830\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.94031			0.268727
$216$		0			0
$217$	−23.1027			−1.56831
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.28505	−	3.95783i	−0.153709	−	0.266232i
$222$		0			0
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	0.0179997	−	0.999838i	$-0.494270\pi$
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	−0.856885	+	0.515507i	$0.827604\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.561821	+	0.324367i	0.0372894	+	0.0215290i	0.518529	−	0.855060i	$-0.326480\pi$
$227$	0.561821	+	0.324367i	0.0372894	+	0.0215290i	−0.481239	+	0.876589i	$0.659813\pi$
$228$		0			0
$229$	12.0007	−	6.92863i	0.793032	−	0.457857i	−0.0479971	−	0.998847i	$-0.515284\pi$
$229$	12.0007	−	6.92863i	0.793032	−	0.457857i	0.841029	+	0.540990i	$0.181950\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	23.1276i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$233$		−	23.1276i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$234$		0			0
$235$	−4.02393			−0.262492
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.44075	−	12.8878i	−0.481302	−	0.833640i	0.518468	−	0.855097i	$-0.326503\pi$
$239$	−7.44075	−	12.8878i	−0.481302	−	0.833640i	−0.999770	+	0.0214576i	$0.993169\pi$
$240$		0			0
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	−0.990879	−	0.134755i	$-0.956975\pi$
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	0.612141	+	0.790749i	$0.290309\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.44399	+	11.1613i	−0.411691	+	0.713071i
$246$		0			0
$247$	9.05472	−	5.22774i	0.576138	−	0.332633i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			5.51619i			0.348179i	0.984730	+	0.174089i	$0.0556981\pi$
$251$			5.51619i			0.348179i	−0.984730	+	0.174089i	$0.944302\pi$
$252$		0			0
$253$		−	8.99781i		−	0.565687i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.924157	−	0.382013i	$-0.875231\pi$
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.131245	+	0.991350i	$0.541898\pi$
$258$		0			0
$259$	−6.37451	+	11.0410i	−0.396093	+	0.686053i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.62576	−	9.74411i	0.346899	−	0.600847i	−0.638798	−	0.769375i	$-0.720568\pi$
$263$	5.62576	−	9.74411i	0.346899	−	0.600847i	0.985697	+	0.168527i	$0.0539012\pi$
$264$		0			0
$265$	−6.37451	−	11.0410i	−0.391583	−	0.678242i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.1600			0.863350			0.431675	−	0.902029i	$-0.357923\pi$
$269$	14.1600			0.863350			0.431675	+	0.902029i	$0.357923\pi$
$270$		0			0
$271$		−	3.91574i		−	0.237864i	−0.992902	−	0.118932i	$-0.962053\pi$
$271$		−	3.91574i		−	0.237864i	0.992902	−	0.118932i	$-0.0379471\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.75773	−	2.16953i	0.226600	−	0.130827i
$276$		0			0
$277$	22.9537	+	13.2523i	1.37915	+	0.796253i	0.992057	−	0.125787i	$-0.0401455\pi$
$277$	22.9537	+	13.2523i	1.37915	+	0.796253i	0.387094	+	0.922040i	$0.373479\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	0.527289	−	0.849686i	$-0.323209\pi$
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	−0.472205	+	0.881489i	$0.656542\pi$
$282$		0			0
$283$	−1.77840	−	3.08028i	−0.105715	−	0.183103i	0.808315	−	0.588750i	$-0.200380\pi$
$283$	−1.77840	−	3.08028i	−0.105715	−	0.183103i	−0.914030	+	0.405647i	$0.867046\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.9693			−1.23778
$288$		0			0
$289$	14.7604			0.868258
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	0.543620	−	0.839331i	$-0.317053\pi$
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	−0.998692	+	0.0511233i	$0.983720\pi$
$294$		0			0
$295$	8.48839	+	4.90077i	0.494213	+	0.285334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.4135	−	11.7857i	−1.18054	−	0.681586i
$300$		0			0
$301$	−12.9498	+	7.47659i	−0.746416	+	0.430944i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	4.12532i		−	0.236215i
$306$		0			0
$307$	0.960690			0.0548295			0.0274147	−	0.999624i	$-0.491273\pi$
$307$	0.960690			0.0548295			0.0274147	+	0.999624i	$0.491273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.49539	+	7.78624i	0.254910	+	0.441517i	0.964871	−	0.262724i	$-0.0846208\pi$
$311$	4.49539	+	7.78624i	0.254910	+	0.441517i	−0.709961	+	0.704241i	$0.751287\pi$
$312$		0			0
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	−0.516051	−	0.856558i	$-0.672599\pi$
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	0.999826	+	0.0186349i	$0.00593201\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	−0.732919	−	0.680316i	$-0.761842\pi$
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	0.955631	+	0.294568i	$0.0951757\pi$
$318$		0			0
$319$	1.43269	−	0.827162i	0.0802151	−	0.0463122i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	5.12381i		−	0.285096i
$324$		0			0
$325$		−	11.3670i		−	0.630526i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.2247	−	7.63528i	0.729101	−	0.420946i
$330$		0			0
$331$	−4.78348	+	8.28523i	−0.262924	+	0.455397i	−0.967018	−	0.254710i	$-0.918020\pi$
$331$	−4.78348	+	8.28523i	−0.262924	+	0.455397i	0.704094	+	0.710107i	$0.251353\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.31037	+	10.9299i	−0.344773	+	0.597164i
$336$		0			0
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.783305	+	0.621638i	$0.213532\pi$
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.146702	+	0.989181i	$0.453134\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.27805			0.339975
$342$		0			0
$343$		−	18.8811i		−	1.01949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	20.9431	−	12.0915i	1.12428	−	0.649105i	0.181792	−	0.983337i	$-0.441810\pi$
$347$	20.9431	−	12.0915i	1.12428	−	0.649105i	0.942491	+	0.334232i	$0.108477\pi$
$348$		0			0
$349$	−9.71845	−	5.61095i	−0.520217	−	0.300347i	0.216807	−	0.976215i	$-0.430436\pi$
$349$	−9.71845	−	5.61095i	−0.520217	−	0.300347i	−0.737023	+	0.675867i	$0.763769\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	0.647579	−	0.761999i	$-0.275782\pi$
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	−0.336121	+	0.941819i	$0.609115\pi$
$354$		0			0
$355$	1.44097	+	2.49583i	0.0764786	+	0.132465i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.3395			−1.07348			−0.536739	−	0.843748i	$-0.680344\pi$
$359$	−20.3395			−1.07348			−0.536739	+	0.843748i	$0.680344\pi$
$360$		0			0
$361$	−7.27775			−0.383039
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.99300	−	6.91608i	−0.209003	−	0.362004i
$366$		0			0
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	0.773657	−	0.633605i	$-0.218425\pi$
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	−0.161889	+	0.986809i	$0.551759\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	41.8998	+	24.1908i	2.17533	+	1.25593i
$372$		0			0
$373$	−23.0364	+	13.3001i	−1.19278	+	0.688651i	−0.958936	−	0.283623i	$-0.908464\pi$
$373$	−23.0364	+	13.3001i	−1.19278	+	0.688651i	−0.233843	+	0.972274i	$0.575130\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	4.33381i		−	0.223203i
$378$		0			0
$379$	28.5030			1.46410			0.732050	−	0.681251i	$-0.238564\pi$
$379$	28.5030			1.46410			0.732050	+	0.681251i	$0.238564\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.0515	+	17.4097i	0.513606	+	0.889592i	0.999875	+	0.0157832i	$0.00502416\pi$
$383$	10.0515	+	17.4097i	0.513606	+	0.889592i	−0.486269	+	0.873809i	$0.661643\pi$
$384$		0			0
$385$	2.82624	−	4.89519i	0.144038	−	0.249482i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	−0.892130	−	0.451778i	$-0.850790\pi$
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	0.837316	+	0.546719i	$0.184123\pi$
$390$		0			0
$391$	−10.0038	+	5.77570i	−0.505914	+	0.292090i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			2.93677i			0.147765i
$396$		0			0
$397$		−	18.8504i		−	0.946076i	−0.881042	−	0.473038i	$-0.843157\pi$
$397$		−	18.8504i		−	0.946076i	0.881042	−	0.473038i	$-0.156843\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	−0.0741601	−	0.997246i	$-0.523628\pi$
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	0.826561	+	0.562848i	$0.190294\pi$
$402$		0			0
$403$	8.22326	−	14.2431i	0.409630	−	0.709500i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.73225	−	3.00034i	0.0858643	−	0.148721i
$408$		0			0
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	−0.999950	−	0.0100370i	$-0.996805\pi$
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	0.491282	−	0.871000i	$-0.336528\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−37.1962			−1.83030
$414$		0			0
$415$		−	5.20117i		−	0.255316i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−24.1959	+	13.9695i	−1.18205	+	0.682455i	−0.956487	−	0.291774i	$-0.905755\pi$
$419$	−24.1959	+	13.9695i	−1.18205	+	0.682455i	−0.225560	+	0.974229i	$0.572421\pi$
$420$		0			0
$421$	−6.27826	−	3.62475i	−0.305983	−	0.176660i	0.339144	−	0.940734i	$-0.389863\pi$
$421$	−6.27826	−	3.62475i	−0.305983	−	0.176660i	−0.645128	+	0.764075i	$0.723196\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.82418	−	2.78524i	−0.234007	−	0.135104i
$426$		0			0
$427$	7.82766	+	13.5579i	0.378807	+	0.656113i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	37.7004			1.81596			0.907982	−	0.419009i	$-0.137623\pi$
$431$	37.7004			1.81596			0.907982	+	0.419009i	$0.137623\pi$
$432$		0			0
$433$	36.1185			1.73575			0.867873	−	0.496787i	$-0.165487\pi$
$433$	36.1185			1.73575			0.867873	+	0.496787i	$0.165487\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.2137	−	22.8867i	−0.632095	−	1.09482i
$438$		0			0
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	0.268993	−	0.963142i	$-0.413309\pi$
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	−0.699609	+	0.714526i	$0.746642\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.7905	−	17.7769i	−1.46290	−	0.844606i	−0.463756	−	0.885963i	$-0.653498\pi$
$443$	−30.7905	−	17.7769i	−1.46290	−	0.844606i	−0.999144	+	0.0413574i	$0.986832\pi$
$444$		0			0
$445$	8.45606	−	4.88211i	0.400856	−	0.231434i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			16.7750i			0.791662i	0.918323	+	0.395831i	$0.129543\pi$
$449$			16.7750i			0.791662i	−0.918323	+	0.395831i	$0.870457\pi$
$450$		0			0
$451$	5.69832			0.268323
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.40386	−	12.8239i	−0.347098	−	0.601192i
$456$		0			0
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	−0.881479	−	0.472223i	$-0.843452\pi$
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	0.849697	+	0.527272i	$0.176785\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	−0.723332	−	0.690500i	$-0.757391\pi$
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	0.959657	+	0.281174i	$0.0907238\pi$
$462$		0			0
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.150012	−	0.988684i	$-0.452069\pi$
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.931232	+	0.364428i	$0.118735\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	31.4118i		−	1.45356i	−0.686868	−	0.726782i	$-0.741015\pi$
$467$		−	31.4118i		−	1.45356i	0.686868	−	0.726782i	$-0.258985\pi$
$468$		0			0
$469$		−	47.8949i		−	2.21158i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.51906	−	2.03173i	0.161807	−	0.0934191i
$474$		0			0
$475$	6.37208	−	11.0368i	0.292371	−	0.506402i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.42488	−	4.20001i	0.110796	−	0.191904i	−0.805296	−	0.592873i	$-0.797993\pi$
$479$	2.42488	−	4.20001i	0.110796	−	0.191904i	0.916091	+	0.400970i	$0.131327\pi$
$480$		0			0
$481$	−4.53794	−	7.85995i	−0.206912	−	0.358383i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.59316			0.344788
$486$		0			0
$487$		−	23.2664i		−	1.05430i	−0.849772	−	0.527150i	$-0.823261\pi$
$487$		−	23.2664i		−	1.05430i	0.849772	−	0.527150i	$-0.176739\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.48139	−	5.47408i	0.427889	−	0.247042i	−0.270558	−	0.962704i	$-0.587208\pi$
$491$	9.48139	−	5.47408i	0.427889	−	0.247042i	0.698447	+	0.715662i	$0.253875\pi$
$492$		0			0
$493$	−1.83929	−	1.06191i	−0.0828373	−	0.0478262i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.47149	−	5.46837i	−0.424855	−	0.245290i
$498$		0			0
$499$	−19.4409	−	33.6726i	−0.870293	−	1.50739i	−0.861694	−	0.507429i	$-0.830596\pi$
$499$	−19.4409	−	33.6726i	−0.870293	−	1.50739i	−0.00859924	−	0.999963i	$-0.502737\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.97588			−0.444803			−0.222401	−	0.974955i	$-0.571390\pi$
$503$	−9.97588			−0.444803			−0.222401	+	0.974955i	$0.571390\pi$
$504$		0			0
$505$	15.5196			0.690612
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	0.985719	−	0.168396i	$-0.0538589\pi$
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	−0.638695	+	0.769460i	$0.720526\pi$
$510$		0			0
$511$	26.2460	+	15.1532i	1.16106	+	0.670336i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.19601	+	3.57727i	0.273029	+	0.157633i
$516$		0			0
$517$	−3.59375	+	2.07485i	−0.158053	+	0.0912519i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	9.78813i		−	0.428826i	−0.976743	−	0.214413i	$-0.931216\pi$
$521$		−	9.78813i		−	0.428826i	0.976743	−	0.214413i	$-0.0687838\pi$
$522$		0			0
$523$	32.9015			1.43868			0.719342	−	0.694656i	$-0.244443\pi$
$523$	32.9015			1.43868			0.719342	+	0.694656i	$0.244443\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.02989	−	6.97997i	−0.175545	−	0.304052i
$528$		0			0
$529$	−18.2896	+	31.6786i	−0.795201	+	1.37733i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.46391	−	12.9279i	0.323298	−	0.559968i
$534$		0			0
$535$	−10.2282	+	5.90525i	−0.442203	+	0.255306i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			13.2908i			0.572476i
$540$		0			0
$541$			26.4228i			1.13601i	0.823027	+	0.568003i	$0.192284\pi$
$541$			26.4228i			1.13601i	−0.823027	+	0.568003i	$0.807716\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.47149	+	5.46837i	−0.405714	+	0.234239i
$546$		0			0
$547$	−17.7776	+	30.7917i	−0.760116	+	1.31656i	0.182674	+	0.983174i	$0.441525\pi$
$547$	−17.7776	+	30.7917i	−0.760116	+	1.31656i	−0.942790	+	0.333387i	$0.891809\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.42944	−	4.20792i	0.103498	−	0.179263i
$552$		0			0
$553$	−5.57242	−	9.65172i	−0.236964	−	0.410433i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.4413			−0.781384			−0.390692	−	0.920522i	$-0.627764\pi$
$557$	−18.4413			−0.781384			−0.390692	+	0.920522i	$0.627764\pi$
$558$		0			0
$559$		−	10.6450i		−	0.450236i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	35.4943	−	20.4926i	1.49591	−	0.863661i	0.495917	−	0.868370i	$-0.334832\pi$
$563$	35.4943	−	20.4926i	1.49591	−	0.863661i	0.999989	+	0.00470871i	$0.00149884\pi$
$564$		0			0
$565$	−8.08387	−	4.66722i	−0.340091	−	0.196352i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	0.576012	−	0.817441i	$-0.304608\pi$
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	−0.419919	+	0.907562i	$0.637941\pi$
$570$		0			0
$571$	2.17462	+	3.76656i	0.0910052	+	0.157626i	0.907934	−	0.419112i	$-0.137659\pi$
$571$	2.17462	+	3.76656i	0.0910052	+	0.157626i	−0.816929	+	0.576738i	$0.804325\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−28.7312			−1.19817
$576$		0			0
$577$	12.5475			0.522361			0.261180	−	0.965290i	$-0.415888\pi$
$577$	12.5475			0.522361			0.261180	+	0.965290i	$0.415888\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.86905	+	17.0937i	0.409437	+	0.709166i
$582$		0			0
$583$	−11.3861	−	6.57376i	−0.471563	−	0.272257i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.02388	−	4.63259i	−0.331181	−	0.191207i	0.325184	−	0.945651i	$-0.394574\pi$
$587$	−8.02388	−	4.63259i	−0.331181	−	0.191207i	−0.656365	+	0.754443i	$0.727907\pi$
$588$		0			0
$589$	15.9688	−	9.21958i	0.657982	−	0.379886i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	11.1342i		−	0.457228i	−0.973517	−	0.228614i	$-0.926581\pi$
$593$		−	11.1342i		−	0.457228i	0.973517	−	0.228614i	$-0.0734193\pi$
$594$		0			0
$595$	−7.25666			−0.297494
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−22.8693	−	39.6108i	−0.934415	−	1.61845i	−0.775675	−	0.631133i	$-0.782590\pi$
$599$	−22.8693	−	39.6108i	−0.934415	−	1.61845i	−0.158740	−	0.987320i	$-0.550743\pi$
$600$		0			0
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	−0.998907	−	0.0467325i	$-0.985119\pi$
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	0.539925	+	0.841713i	$0.318453\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.44905	−	9.43803i	0.221535	−	0.383710i
$606$		0			0
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.909366	−	0.415997i	$-0.863433\pi$
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.0944185	+	0.995533i	$0.530099\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			10.8709i			0.439791i
$612$		0			0
$613$			40.4574i			1.63406i	0.576596	+	0.817030i	$0.304381\pi$
$613$			40.4574i			1.63406i	−0.576596	+	0.817030i	$0.695619\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.299112	−	0.954218i	$-0.403309\pi$
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.975933	+	0.218070i	$0.0699761\pi$
$618$		0			0
$619$	−20.3697	+	35.2814i	−0.818727	+	1.41808i	0.0878927	+	0.996130i	$0.471987\pi$
$619$	−20.3697	+	35.2814i	−0.818727	+	1.41808i	−0.906620	+	0.421948i	$0.861347\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.5273	+	32.0902i	−0.742279	+	1.28567i
$624$		0			0
$625$	−3.73321	−	6.46610i	−0.149328	−	0.258644i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.44772			−0.177342
$630$		0			0
$631$			15.0916i			0.600788i	0.953815	+	0.300394i	$0.0971182\pi$
$631$			15.0916i			0.600788i	−0.953815	+	0.300394i	$0.902882\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.72884	+	1.57550i	−0.108291	+	0.0625218i
$636$		0			0
$637$	30.1531	+	17.4089i	1.19471	+	0.689765i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.926529	−	0.376222i	$-0.122777\pi$
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.137447	+	0.990509i	$0.456110\pi$
$642$		0			0
$643$	1.93125	+	3.34503i	0.0761612	+	0.131915i	0.901591	−	0.432590i	$-0.142400\pi$
$643$	1.93125	+	3.34503i	0.0761612	+	0.131915i	−0.825429	+	0.564505i	$0.809067\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.1359			0.948879			0.474440	−	0.880288i	$-0.342651\pi$
$647$	24.1359			0.948879			0.474440	+	0.880288i	$0.342651\pi$
$648$		0			0
$649$	10.1079			0.396770
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	0.986667	+	0.162750i	$0.0520364\pi$
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	−0.352388	+	0.935854i	$0.614630\pi$
$654$		0			0
$655$	−14.7547	−	8.51864i	−0.576515	−	0.332851i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.7202	+	11.3855i	0.768191	+	0.443515i	0.832229	−	0.554432i	$-0.187064\pi$
$659$	19.7202	+	11.3855i	0.768191	+	0.443515i	−0.0640377	+	0.997947i	$0.520398\pi$
$660$		0			0
$661$	25.6004	−	14.7804i	0.995740	−	0.574891i	0.0887549	−	0.996053i	$-0.471711\pi$
$661$	25.6004	−	14.7804i	0.995740	−	0.574891i	0.906985	+	0.421163i	$0.138378\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	16.6018i		−	0.643790i
$666$		0			0
$667$	−10.9542			−0.424147
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.12713	−	3.68430i	−0.0821171	−	0.142231i
$672$		0			0
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	−0.641961	−	0.766738i	$-0.721879\pi$
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	0.984995	+	0.172585i	$0.0552121\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.0320192	+	0.999487i	$0.510194\pi$
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.849572	+	0.527473i	$0.823140\pi$
$678$		0			0
$679$	−24.9550	+	14.4078i	−0.957684	+	0.552919i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			2.20513i			0.0843769i	0.999110	+	0.0421884i	$0.0134330\pi$
$683$			2.20513i			0.0843769i	−0.999110	+	0.0421884i	$0.986567\pi$
$684$		0			0
$685$		−	9.85735i		−	0.376630i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−29.8280	+	17.2212i	−1.13636	+	0.656075i
$690$		0			0
$691$	10.2512	−	17.7556i	0.389975	−	0.675457i	−0.602471	−	0.798141i	$-0.705817\pi$
$691$	10.2512	−	17.7556i	0.389975	−	0.675457i	0.992446	+	0.122684i	$0.0391503\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.34398	−	2.32784i	0.0509801	−	0.0883001i
$696$		0			0
$697$	−3.65776	−	6.33542i	−0.138547	−	0.239971i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.6854			1.00789			0.503947	−	0.863734i	$-0.331881\pi$
$701$	26.6854			1.00789			0.503947	+	0.863734i	$0.331881\pi$
$702$		0			0
$703$		−	10.1755i		−	0.383776i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−51.0052	+	29.4479i	−1.91825	+	1.10750i
$708$		0			0
$709$	37.8684	+	21.8633i	1.42218	+	0.821095i	0.996485	−	0.0837727i	$-0.0266970\pi$
$709$	37.8684	+	21.8633i	1.42218	+	0.821095i	0.425693	+	0.904868i	$0.360030\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−36.0009	−	20.7851i	−1.34825	−	0.778410i
$714$		0			0
$715$	2.01197	+	3.48483i	0.0752433	+	0.130325i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.9253			0.519327			0.259663	−	0.965699i	$-0.416388\pi$
$719$	13.9253			0.519327			0.259663	+	0.965699i	$0.416388\pi$
$720$		0			0
$721$	−27.1510			−1.01115
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.64124	−	4.57475i	−0.0980930	−	0.169902i
$726$		0			0
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.948259	−	0.317497i	$-0.102842\pi$
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.199169	+	0.979965i	$0.436176\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.51778	−	2.60834i	−0.167096	−	0.0964730i
$732$		0			0
$733$	−30.2141	+	17.4441i	−1.11598	+	0.644312i	−0.940372	−	0.340148i	$-0.889523\pi$
$733$	−30.2141	+	17.4441i	−1.11598	+	0.644312i	−0.175610	+	0.984460i	$0.556190\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			13.0152i			0.479422i
$738$		0			0
$739$	−13.1128			−0.482361			−0.241181	−	0.970480i	$-0.577535\pi$
$739$	−13.1128			−0.482361			−0.241181	+	0.970480i	$0.577535\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.1665	+	19.3410i	0.409660	+	0.709551i	0.994851	−	0.101344i	$-0.0323142\pi$
$743$	11.1665	+	19.3410i	0.409660	+	0.709551i	−0.585192	+	0.810895i	$0.698981\pi$
$744$		0			0
$745$	−10.1104	+	17.5117i	−0.370415	+	0.641578i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	22.4100	−	38.8153i	0.818844	−	1.41828i
$750$		0			0
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	−0.622174	−	0.782879i	$-0.713750\pi$
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	0.366906	+	0.930258i	$0.380417\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	3.12165i		−	0.113608i
$756$		0			0
$757$		−	12.7751i		−	0.464319i	−0.972678	−	0.232160i	$-0.925421\pi$
$757$		−	12.7751i		−	0.464319i	0.972678	−	0.232160i	$-0.0745792\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.570679	+	0.821173i	$0.693320\pi$
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.996496	+	0.0836361i	$0.973347\pi$
$762$		0			0
$763$	20.7521	−	35.9437i	0.751276	−	1.30125i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.2398	−	22.9320i	0.478060	−	0.828025i
$768$		0			0
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	−0.999869	−	0.0161588i	$-0.994856\pi$
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	0.485941	−	0.873992i	$-0.338477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.8254			−0.749037			−0.374518	−	0.927220i	$-0.622192\pi$
$773$	−20.8254			−0.749037			−0.374518	+	0.927220i	$0.622192\pi$
$774$		0			0
$775$		−	20.0466i		−	0.720096i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.4942	−	8.36822i	0.519308	−	0.299822i
$780$		0			0
$781$	2.57384	+	1.48601i	0.0920991	+	0.0531735i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.49980	+	1.44326i	0.0892218	+	0.0515122i
$786$		0			0
$787$	−10.4386	−	18.0802i	−0.372096	−	0.644488i	0.617792	−	0.786341i	$-0.288027\pi$
$787$	−10.4386	−	18.0802i	−0.372096	−	0.644488i	−0.989888	+	0.141853i	$0.954694\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	35.4236			1.25952
$792$		0			0
$793$	−11.1448			−0.395765
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	0.999920	+	0.0126529i	$0.00402764\pi$
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	−0.489002	+	0.872283i	$0.662639\pi$
$798$		0			0
$799$	4.61367	+	2.66370i	0.163220	+	0.0942350i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.13225	−	4.11780i	−0.251691	−	0.145314i
$804$		0			0
$805$	−32.4136	+	18.7140i	−1.14243	+	0.659582i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			43.6746i			1.53552i	0.640739	+	0.767759i	$0.278628\pi$
$809$			43.6746i			1.53552i	−0.640739	+	0.767759i	$0.721372\pi$
$810$		0			0
$811$	−42.3445			−1.48692			−0.743458	−	0.668782i	$-0.766816\pi$
$811$	−42.3445			−1.48692			−0.743458	+	0.668782i	$0.766816\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.91876	−	6.78749i	−0.137268	−	0.237755i
$816$		0			0
$817$	5.96737	−	10.3358i	0.208772	−	0.361603i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	−0.840380	−	0.541997i	$-0.817668\pi$
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	0.889573	+	0.456792i	$0.151002\pi$
$822$		0			0
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	−0.575841	−	0.817562i	$-0.695325\pi$
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	0.420109	+	0.907474i	$0.361992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.8630i			0.760251i	0.924935	+	0.380125i	$0.124119\pi$
$827$			21.8630i			0.760251i	−0.924935	+	0.380125i	$0.875881\pi$
$828$		0			0
$829$		−	22.0815i		−	0.766924i	−0.923557	−	0.383462i	$-0.874732\pi$
$829$		−	22.0815i		−	0.766924i	0.923557	−	0.383462i	$-0.125268\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.7768	−	8.53139i	0.511986	−	0.295595i
$834$		0			0
$835$	−9.45931	+	16.3840i	−0.327353	+	0.566992i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.4035	+	44.0002i	−0.877026	+	1.51905i	−0.0224378	+	0.999748i	$0.507143\pi$
$839$	−25.4035	+	44.0002i	−0.877026	+	1.51905i	−0.854588	+	0.519306i	$0.826191\pi$
$840$		0			0
$841$	13.4930	+	23.3705i	0.465276	+	0.805881i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.15343			−0.142882
$846$		0			0
$847$			41.3575i			1.42106i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−19.8668	+	11.4701i	−0.681026	+	0.393191i
$852$		0			0
$853$	−45.4891	−	26.2631i	−1.55752	−	0.899233i	−0.997494	−	0.0707558i	$-0.977459\pi$
$853$	−45.4891	−	26.2631i	−1.55752	−	0.899233i	−0.560023	−	0.828477i	$-0.689208\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.974867	+	0.222786i	$0.0715151\pi$
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.680372	+	0.732867i	$0.261818\pi$
$858$		0			0
$859$	−15.4078	−	26.6871i	−0.525708	−	0.910554i	−0.999552	−	0.0299443i	$-0.990467\pi$
$859$	−15.4078	−	26.6871i	−0.525708	−	0.910554i	0.473843	−	0.880609i	$-0.342866\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.1750			0.856966			0.428483	−	0.903550i	$-0.359048\pi$
$863$	25.1750			0.856966			0.428483	+	0.903550i	$0.359048\pi$
$864$		0			0
$865$	−23.1027			−0.785514
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.51428	+	2.62281i	0.0513685	+	0.0889728i
$870$		0			0
$871$	29.5278	+	17.0479i	1.00051	+	0.577646i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−36.6276	−	21.1470i	−1.23824	−	0.714898i
$876$		0			0
$877$	−31.8486	+	18.3878i	−1.07545	+	0.620913i	−0.929666	−	0.368404i	$-0.879904\pi$
$877$	−31.8486	+	18.3878i	−1.07545	+	0.620913i	−0.145786	+	0.989316i	$0.546571\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			8.15439i			0.274728i	0.990521	+	0.137364i	$0.0438631\pi$
$881$			8.15439i			0.274728i	−0.990521	+	0.137364i	$0.956137\pi$
$882$		0			0
$883$	20.3792			0.685814			0.342907	−	0.939369i	$-0.388588\pi$
$883$	20.3792			0.685814			0.342907	+	0.939369i	$0.388588\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.3561	+	38.7220i	0.750646	+	1.30016i	0.947510	+	0.319726i	$0.103591\pi$
$887$	22.3561	+	38.7220i	0.750646	+	1.30016i	−0.196864	+	0.980431i	$0.563076\pi$
$888$		0			0
$889$	5.97891	−	10.3558i	0.200526	−	0.347322i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.09402	+	10.5551i	−0.203928	+	0.353214i
$894$		0			0
$895$	3.99387	−	2.30586i	0.133500	−	0.0770765i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	7.64305i		−	0.254910i
$900$		0			0
$901$			16.8788i			0.562315i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.8524	+	12.6165i	−0.726398	+	0.419386i
$906$		0			0
$907$	−7.99519	+	13.8481i	−0.265476	+	0.459818i	−0.967688	−	0.252150i	$-0.918862\pi$
$907$	−7.99519	+	13.8481i	−0.265476	+	0.459818i	0.702212	+	0.711968i	$0.252196\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14.1609	−	24.5275i	0.469173	−	0.812631i	−0.530206	−	0.847869i	$-0.677885\pi$
$911$	14.1609	−	24.5275i	0.469173	−	0.812631i	0.999379	+	0.0352377i	$0.0112188\pi$
$912$		0			0
$913$	−2.68187	−	4.64514i	−0.0887570	−	0.153732i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	64.6553			2.13511
$918$		0			0
$919$			17.1474i			0.565642i	0.959173	+	0.282821i	$0.0912702\pi$
$919$			17.1474i			0.565642i	−0.959173	+	0.282821i	$0.908730\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.74265	−	3.89287i	0.221937	−	0.128135i
$924$		0			0
$925$	−9.58047	−	5.53129i	−0.315004	−	0.181868i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.278040	−	0.960569i	$-0.589685\pi$
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.970898	+	0.239495i	$0.923018\pi$
$930$		0			0
$931$	19.5181	+	33.8064i	0.639680	+	1.10796i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.97197			0.0644902
$936$		0			0
$937$	−13.5845			−0.443786			−0.221893	−	0.975071i	$-0.571223\pi$
$937$	−13.5845			−0.443786			−0.221893	+	0.975071i	$0.571223\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	0.557258	−	0.830339i	$-0.311853\pi$
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	−0.997724	+	0.0674301i	$0.978520\pi$
$942$		0			0
$943$	−32.6765	−	18.8658i	−1.06409	−	0.614354i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	34.5376	+	19.9403i	1.12232	+	0.647972i	0.941992	−	0.335634i	$-0.108951\pi$
$947$	34.5376	+	19.9403i	1.12232	+	0.647972i	0.180328	+	0.983607i	$0.442284\pi$
$948$		0			0
$949$	−18.6843	+	10.7874i	−0.606516	+	0.350172i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	14.0999i		−	0.456741i	−0.973574	−	0.228371i	$-0.926660\pi$
$953$		−	14.0999i		−	0.456741i	0.973574	−	0.228371i	$-0.0733398\pi$
$954$		0			0
$955$	16.4465			0.532197
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.7040	+	32.3963i	0.603983	+	1.04613i
$960$		0			0
$961$	−0.997565	+	1.72783i	−0.0321795	+	0.0557366i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.48147	+	4.29803i	−0.0798813	+	0.138358i
$966$		0			0
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.463063	−	0.886326i	$-0.346750\pi$
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.999112	+	0.0421387i	$0.0134171\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			61.3864i			1.96998i	0.172599	+	0.984992i	$0.444784\pi$
$971$			61.3864i			1.96998i	−0.172599	+	0.984992i	$0.555216\pi$
$972$		0			0
$973$			10.2006i			0.327017i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	−0.0235691	−	0.999722i	$-0.507503\pi$
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	0.854000	+	0.520273i	$0.174170\pi$
$978$		0			0
$979$	5.03471	−	8.72037i	0.160910	−	0.278704i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.1703	+	36.6681i	−0.675228	+	1.16953i	0.301174	+	0.953569i	$0.402622\pi$
$983$	−21.1703	+	36.6681i	−0.675228	+	1.16953i	−0.976402	+	0.215961i	$0.930712\pi$
$984$		0			0
$985$	4.35037	+	7.53506i	0.138614	+	0.240087i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−26.9063			−0.855572
$990$		0			0
$991$			12.3787i			0.393222i	0.980482	+	0.196611i	$0.0629937\pi$
$991$			12.3787i			0.393222i	−0.980482	+	0.196611i	$0.937006\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.5370	+	11.8571i	−0.651068	+	0.375894i
$996$		0			0
$997$	−6.20535	−	3.58266i	−0.196525	−	0.113464i	0.398508	−	0.917165i	$-0.369528\pi$
$997$	−6.20535	−	3.58266i	−0.196525	−	0.113464i	−0.595034	+	0.803701i	$0.702861\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.p.b.143.5		16
3.2	odd	2		288.2.p.b.47.5		16
4.3	odd	2		216.2.l.b.35.3		16
8.3	odd	2	inner	864.2.p.b.143.4		16
8.5	even	2		216.2.l.b.35.1		16
9.2	odd	6		2592.2.f.b.1295.10		16
9.4	even	3		288.2.p.b.239.6		16
9.5	odd	6	inner	864.2.p.b.719.4		16
9.7	even	3		2592.2.f.b.1295.8		16
12.11	even	2		72.2.l.b.11.6	✓	16
24.5	odd	2		72.2.l.b.11.8	yes	16
24.11	even	2		288.2.p.b.47.6		16
36.7	odd	6		648.2.f.b.323.6		16
36.11	even	6		648.2.f.b.323.11		16
36.23	even	6		216.2.l.b.179.1		16
36.31	odd	6		72.2.l.b.59.8	yes	16
72.5	odd	6		216.2.l.b.179.3		16
72.11	even	6		2592.2.f.b.1295.7		16
72.13	even	6		72.2.l.b.59.6	yes	16
72.29	odd	6		648.2.f.b.323.5		16
72.43	odd	6		2592.2.f.b.1295.9		16
72.59	even	6	inner	864.2.p.b.719.5		16
72.61	even	6		648.2.f.b.323.12		16
72.67	odd	6		288.2.p.b.239.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.6	✓	16	12.11	even	2
72.2.l.b.11.8	yes	16	24.5	odd	2
72.2.l.b.59.6	yes	16	72.13	even	6
72.2.l.b.59.8	yes	16	36.31	odd	6
216.2.l.b.35.1		16	8.5	even	2
216.2.l.b.35.3		16	4.3	odd	2
216.2.l.b.179.1		16	36.23	even	6
216.2.l.b.179.3		16	72.5	odd	6
288.2.p.b.47.5		16	3.2	odd	2
288.2.p.b.47.6		16	24.11	even	2
288.2.p.b.239.5		16	72.67	odd	6
288.2.p.b.239.6		16	9.4	even	3
648.2.f.b.323.5		16	72.29	odd	6
648.2.f.b.323.6		16	36.7	odd	6
648.2.f.b.323.11		16	36.11	even	6
648.2.f.b.323.12		16	72.61	even	6
864.2.p.b.143.4		16	8.3	odd	2	inner
864.2.p.b.143.5		16	1.1	even	1	trivial
864.2.p.b.719.4		16	9.5	odd	6	inner
864.2.p.b.719.5		16	72.59	even	6	inner
2592.2.f.b.1295.7		16	72.11	even	6
2592.2.f.b.1295.8		16	9.7	even	3
2592.2.f.b.1295.9		16	72.43	odd	6
2592.2.f.b.1295.10		16	9.2	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.565188 + 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +O(q^{10})\)	\(q+(0.565188 + 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(1.00953 + 0.582853i) q^{11} +(2.64466 - 1.52689i) q^{13} -1.49654i q^{17} +3.42378 q^{19} +(-3.85938 - 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(0.709580 - 1.22903i) q^{29} +(4.66408 - 2.69281i) q^{31} -4.84897i q^{35} -2.97201i q^{37} +(4.23339 - 2.44415i) q^{41} +(1.74292 - 3.01882i) q^{43} +(-1.77991 + 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} -11.2786 q^{53} +1.31769i q^{55} +(7.50935 - 4.33553i) q^{59} +(-3.16057 - 1.82476i) q^{61} +(2.98946 + 1.72596i) q^{65} +(5.58255 + 9.66925i) q^{67} +2.54954 q^{71} -7.06491 q^{73} +(-2.50026 - 4.33059i) q^{77} +(2.24998 + 1.29902i) q^{79} +(-3.98482 - 2.30064i) q^{83} +(1.46501 - 0.845824i) q^{85} -8.63803i q^{89} -13.0998 q^{91} +(1.93508 + 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) \) 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

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