LMFDB - Embedded newform 2160.2.q.f.721.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2160,2,Mod(721,2160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2160.721"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-2,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			721.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	2160.721
Dual form			2160.2.q.f.1441.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-0.686141 + 1.18843i) q^{11} +(-2.37228 - 4.10891i) q^{13} +7.37228 q^{17} -3.37228 q^{19} +(2.18614 + 3.78651i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.18614 + 3.78651i) q^{29} +(-3.37228 - 5.84096i) q^{31} +2.37228 q^{35} -4.00000 q^{37} +(-1.50000 - 2.59808i) q^{41} +(-5.68614 + 9.84868i) q^{43} +(0.813859 - 1.40965i) q^{47} +(0.686141 + 1.18843i) q^{49} -11.4891 q^{53} +1.37228 q^{55} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} +(-2.37228 + 4.10891i) q^{65} +(-3.50000 - 6.06218i) q^{67} -6.00000 q^{71} -14.1168 q^{73} +(-1.62772 - 2.81929i) q^{77} +(1.00000 - 1.73205i) q^{79} +(-0.813859 + 1.40965i) q^{83} +(-3.68614 - 6.38458i) q^{85} +1.11684 q^{89} +11.2554 q^{91} +(1.68614 + 2.92048i) q^{95} +(1.31386 - 2.27567i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + q^{7} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 2 q^{19} + 3 q^{23} - 2 q^{25} - 3 q^{29} - 2 q^{31} - 2 q^{35} - 16 q^{37} - 6 q^{41} - 17 q^{43} + 9 q^{47} - 3 q^{49} - 6 q^{55} - 3 q^{59}+ \cdots + 11 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 + q^7 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 2 * q^19 + 3 * q^23 - 2 * q^25 - 3 * q^29 - 2 * q^31 - 2 * q^35 - 16 * q^37 - 6 * q^41 - 17 * q^43 + 9 * q^47 - 3 * q^49 - 6 * q^55 - 3 * q^59 - q^61 + 2 * q^65 - 14 * q^67 - 24 * q^71 - 22 * q^73 - 18 * q^77 + 4 * q^79 - 9 * q^83 - 9 * q^85 - 30 * q^89 + 68 * q^91 + q^95 + 11 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	−0.998277	−	0.0586811i	$-0.981310\pi$
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	0.549958	+	0.835192i	$0.314644\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	−0.950730	−	0.310021i	$-0.899664\pi$
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	0.743851	+	0.668346i	$0.232997\pi$
$12$		0			0
$13$	−2.37228	−	4.10891i	−0.657952	−	1.13961i	−0.981145	−	0.193274i	$-0.938089\pi$
$13$	−2.37228	−	4.10891i	−0.657952	−	1.13961i	0.323192	−	0.946333i	$-0.395244\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.37228			1.78804			0.894020	−	0.448026i	$-0.147873\pi$
$17$	7.37228			1.78804			0.894020	+	0.448026i	$0.147873\pi$
$18$		0			0
$19$	−3.37228			−0.773654			−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228			−0.773654			−0.386827	+	0.922152i	$0.626429\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.18614	+	3.78651i	0.455842	+	0.789541i	0.998736	−	0.0502598i	$-0.0160049\pi$
$23$	2.18614	+	3.78651i	0.455842	+	0.789541i	−0.542894	+	0.839801i	$0.682672\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.18614	+	3.78651i	−0.405956	+	0.703137i	−0.994432	−	0.105378i	$-0.966395\pi$
$29$	−2.18614	+	3.78651i	−0.405956	+	0.703137i	0.588476	+	0.808515i	$0.299728\pi$
$30$		0			0
$31$	−3.37228	−	5.84096i	−0.605680	−	1.04907i	−0.991944	−	0.126680i	$-0.959568\pi$
$31$	−3.37228	−	5.84096i	−0.605680	−	1.04907i	0.386264	−	0.922388i	$-0.373765\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.37228			0.400989
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.00221007	+	0.999998i	$0.500703\pi$
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.864918	+	0.501913i	$0.832630\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.813859	−	1.40965i	0.118714	−	0.205618i	−0.800545	−	0.599273i	$-0.795456\pi$
$47$	0.813859	−	1.40965i	0.118714	−	0.205618i	0.919258	+	0.393655i	$0.128790\pi$
$48$		0			0
$49$	0.686141	+	1.18843i	0.0980201	+	0.169776i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.4891			−1.57815			−0.789076	−	0.614295i	$-0.789440\pi$
$53$	−11.4891			−1.57815			−0.789076	+	0.614295i	$0.789440\pi$
$54$		0			0
$55$	1.37228			0.185038
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	0.907227	−	0.420641i	$-0.138195\pi$
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	−0.817899	+	0.575361i	$0.804861\pi$
$60$		0			0
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	0.411397	+	0.911456i	$0.365041\pi$
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	−0.995043	+	0.0994483i	$0.968292\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.37228	+	4.10891i	−0.294245	+	0.509648i
$66$		0			0
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−14.1168			−1.65225			−0.826126	−	0.563486i	$-0.809460\pi$
$73$	−14.1168			−1.65225			−0.826126	+	0.563486i	$0.809460\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.62772	−	2.81929i	−0.185496	−	0.321288i
$78$		0			0
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.813859	+	1.40965i	−0.0893327	+	0.154729i	−0.907229	−	0.420637i	$-0.861807\pi$
$83$	−0.813859	+	1.40965i	−0.0893327	+	0.154729i	0.817897	+	0.575365i	$0.195140\pi$
$84$		0			0
$85$	−3.68614	−	6.38458i	−0.399818	−	0.692505i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.11684			0.118385			0.0591926	−	0.998247i	$-0.481147\pi$
$89$	1.11684			0.118385			0.0591926	+	0.998247i	$0.481147\pi$
$90$		0			0
$91$	11.2554			1.17989
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.68614	+	2.92048i	0.172994	+	0.299635i
$96$		0			0
$97$	1.31386	−	2.27567i	0.133402	−	0.231059i	−0.791584	−	0.611061i	$-0.790743\pi$
$97$	1.31386	−	2.27567i	0.133402	−	0.231059i	0.924986	+	0.380001i	$0.124076\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.37228	+	7.57301i	−0.435058	+	0.753543i	−0.997300	−	0.0734297i	$-0.976606\pi$
$101$	−4.37228	+	7.57301i	−0.435058	+	0.753543i	0.562242	+	0.826973i	$0.309939\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.4891			−1.40072			−0.700358	−	0.713791i	$-0.746976\pi$
$107$	−14.4891			−1.40072			−0.700358	+	0.713791i	$0.746976\pi$
$108$		0			0
$109$	9.62772			0.922168			0.461084	−	0.887356i	$-0.347461\pi$
$109$	9.62772			0.922168			0.461084	+	0.887356i	$0.347461\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.37228	+	12.7692i	0.693526	+	1.20122i	0.970675	+	0.240395i	$0.0772770\pi$
$113$	7.37228	+	12.7692i	0.693526	+	1.20122i	−0.277149	+	0.960827i	$0.589390\pi$
$114$		0			0
$115$	2.18614	−	3.78651i	0.203859	−	0.353094i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.74456	+	15.1460i	−0.801613	+	1.38843i
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.11684			−0.808989			−0.404495	−	0.914540i	$-0.632553\pi$
$127$	−9.11684			−0.808989			−0.404495	+	0.914540i	$0.632553\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.37228	−	7.57301i	−0.382008	−	0.661657i	0.609341	−	0.792908i	$-0.291434\pi$
$131$	−4.37228	−	7.57301i	−0.382008	−	0.661657i	−0.991349	+	0.131251i	$0.958101\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.941578	+	1.63086i	−0.0804444	+	0.139334i	−0.903441	−	0.428713i	$-0.858967\pi$
$137$	−0.941578	+	1.63086i	−0.0804444	+	0.139334i	0.822996	+	0.568046i	$0.192301\pi$
$138$		0			0
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	0.938470	+	0.345359i	$0.112243\pi$
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	−0.170145	+	0.985419i	$0.554424\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.51087			0.544467
$144$		0			0
$145$	4.37228			0.363098
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.55842	+	16.5557i	0.783056	+	1.35629i	0.930153	+	0.367171i	$0.119674\pi$
$149$	9.55842	+	16.5557i	0.783056	+	1.35629i	−0.147097	+	0.989122i	$0.546993\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.37228	+	5.84096i	−0.270868	+	0.469157i
$156$		0			0
$157$	−2.37228	−	4.10891i	−0.189329	−	0.327927i	0.755698	−	0.654920i	$-0.227298\pi$
$157$	−2.37228	−	4.10891i	−0.189329	−	0.327927i	−0.945027	+	0.326993i	$0.893964\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.3723			−0.817450
$162$		0			0
$163$	−1.48913			−0.116637			−0.0583186	−	0.998298i	$-0.518574\pi$
$163$	−1.48913			−0.116637			−0.0583186	+	0.998298i	$0.518574\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.81386	−	6.60580i	−0.295125	−	0.511172i	0.679889	−	0.733315i	$-0.262028\pi$
$167$	−3.81386	−	6.60580i	−0.295125	−	0.511172i	−0.975014	+	0.222143i	$0.928695\pi$
$168$		0			0
$169$	−4.75544	+	8.23666i	−0.365803	+	0.633589i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.62772	−	8.01544i	0.351839	−	0.609403i	−0.634733	−	0.772732i	$-0.718890\pi$
$173$	4.62772	−	8.01544i	0.351839	−	0.609403i	0.986572	+	0.163329i	$0.0522231\pi$
$174$		0			0
$175$	−1.18614	−	2.05446i	−0.0896638	−	0.155302i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.25544			−0.243323			−0.121661	−	0.992572i	$-0.538822\pi$
$179$	−3.25544			−0.243323			−0.121661	+	0.992572i	$0.538822\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$		0			0
$187$	−5.05842	+	8.76144i	−0.369908	+	0.640700i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	−0.749482	−	0.662025i	$-0.769697\pi$
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	0.948071	+	0.318058i	$0.103031\pi$
$192$		0			0
$193$	−1.94158	−	3.36291i	−0.139758	−	0.242068i	0.787647	−	0.616127i	$-0.211299\pi$
$193$	−1.94158	−	3.36291i	−0.139758	−	0.242068i	−0.927405	+	0.374059i	$0.877966\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.4891			−1.24605			−0.623024	−	0.782202i	$-0.714096\pi$
$197$	−17.4891			−1.24605			−0.623024	+	0.782202i	$0.714096\pi$
$198$		0			0
$199$	9.48913			0.672666			0.336333	−	0.941743i	$-0.390813\pi$
$199$	9.48913			0.672666			0.336333	+	0.941743i	$0.390813\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.18614	−	8.98266i	−0.363996	−	0.630459i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.31386	−	4.00772i	0.160053	−	0.277220i
$210$		0			0
$211$	−3.62772	−	6.28339i	−0.249742	−	0.432567i	0.713712	−	0.700439i	$-0.247013\pi$
$211$	−3.62772	−	6.28339i	−0.249742	−	0.432567i	−0.963454	+	0.267873i	$0.913679\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.3723			0.775583
$216$		0			0
$217$	16.0000			1.08615
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.4891	−	30.2921i	−1.17645	−	2.03766i
$222$		0			0
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	−0.581095	−	0.813836i	$-0.697376\pi$
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	0.995350	+	0.0963255i	$0.0307090\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.941578	+	1.63086i	−0.0624947	+	0.108244i	−0.895580	−	0.444901i	$-0.853239\pi$
$227$	−0.941578	+	1.63086i	−0.0624947	+	0.108244i	0.833085	+	0.553145i	$0.186572\pi$
$228$		0			0
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	−0.991726	−	0.128373i	$-0.959025\pi$
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	0.384689	−	0.923046i	$-0.374309\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.1168			0.662776			0.331388	−	0.943494i	$-0.392483\pi$
$233$	10.1168			0.662776			0.331388	+	0.943494i	$0.392483\pi$
$234$		0			0
$235$	−1.62772			−0.106181
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	0.999649	−	0.0265017i	$-0.00843674\pi$
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	−0.522776	+	0.852470i	$0.675103\pi$
$240$		0			0
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	−0.984025	−	0.178032i	$-0.943027\pi$
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	0.646193	+	0.763174i	$0.276360\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.686141	−	1.18843i	0.0438359	−	0.0759260i
$246$		0			0
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.6060			0.985040			0.492520	−	0.870301i	$-0.336076\pi$
$251$	15.6060			0.985040			0.492520	+	0.870301i	$0.336076\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.686141	−	1.18843i	−0.0428003	−	0.0741323i	0.843832	−	0.536608i	$-0.180295\pi$
$257$	−0.686141	−	1.18843i	−0.0428003	−	0.0741323i	−0.886632	+	0.462476i	$0.846961\pi$
$258$		0			0
$259$	4.74456	−	8.21782i	0.294813	−	0.510631i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.74456	+	4.75372i	−0.169237	+	0.293127i	−0.938152	−	0.346224i	$-0.887464\pi$
$263$	−2.74456	+	4.75372i	−0.169237	+	0.293127i	0.768915	+	0.639351i	$0.220797\pi$
$264$		0			0
$265$	5.74456	+	9.94987i	0.352886	+	0.611216i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.37228			−0.266583			−0.133291	−	0.991077i	$-0.542555\pi$
$269$	−4.37228			−0.266583			−0.133291	+	0.991077i	$0.542555\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.686141	−	1.18843i	−0.0413758	−	0.0716651i
$276$		0			0
$277$	−2.62772	+	4.55134i	−0.157884	+	0.273464i	−0.934106	−	0.356997i	$-0.883801\pi$
$277$	−2.62772	+	4.55134i	−0.157884	+	0.273464i	0.776221	+	0.630461i	$0.217134\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.18614	−	3.78651i	0.130414	−	0.225884i	−0.793422	−	0.608672i	$-0.791703\pi$
$281$	2.18614	−	3.78651i	0.130414	−	0.225884i	0.923836	+	0.382788i	$0.125036\pi$
$282$		0			0
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.751733	−	0.659467i	$-0.770782\pi$
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.195249	−	0.980754i	$-0.562551\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.11684			0.420094
$288$		0			0
$289$	37.3505			2.19709
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.11684	−	7.13058i	−0.240509	−	0.416573i	0.720351	−	0.693610i	$-0.243981\pi$
$293$	−4.11684	−	7.13058i	−0.240509	−	0.416573i	−0.960859	+	0.277037i	$0.910648\pi$
$294$		0			0
$295$	0.686141	−	1.18843i	0.0399487	−	0.0691931i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.3723	−	17.9653i	0.599845	−	1.03896i
$300$		0			0
$301$	−13.4891	−	23.3639i	−0.777500	−	1.34667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.11684			0.522029
$306$		0			0
$307$	33.2337			1.89675			0.948373	−	0.317156i	$-0.102728\pi$
$307$	33.2337			1.89675			0.948373	+	0.317156i	$0.102728\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.62772	+	8.01544i	0.262414	+	0.454514i	0.966883	−	0.255221i	$-0.0821481\pi$
$311$	4.62772	+	8.01544i	0.262414	+	0.454514i	−0.704469	+	0.709735i	$0.748815\pi$
$312$		0			0
$313$	−4.68614	+	8.11663i	−0.264876	+	0.458779i	−0.967531	−	0.252752i	$-0.918664\pi$
$313$	−4.68614	+	8.11663i	−0.264876	+	0.458779i	0.702655	+	0.711531i	$0.251998\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.37228	+	7.57301i	−0.245572	+	0.425343i	−0.962292	−	0.272018i	$-0.912309\pi$
$317$	−4.37228	+	7.57301i	−0.245572	+	0.425343i	0.716720	+	0.697361i	$0.245642\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.8614			−1.38333
$324$		0			0
$325$	4.74456			0.263181
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.93070	+	3.34408i	0.106443	+	0.184365i
$330$		0			0
$331$	−9.11684	+	15.7908i	−0.501107	+	0.867943i	0.498892	+	0.866664i	$0.333740\pi$
$331$	−9.11684	+	15.7908i	−0.501107	+	0.867943i	−0.999999	+	0.00127880i	$0.999593\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.50000	+	6.06218i	−0.191225	+	0.331212i
$336$		0			0
$337$	−1.68614	−	2.92048i	−0.0918499	−	0.159089i	0.816440	−	0.577431i	$-0.195945\pi$
$337$	−1.68614	−	2.92048i	−0.0918499	−	0.159089i	−0.908290	+	0.418342i	$0.862611\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.25544			0.501210
$342$		0			0
$343$	−19.8614			−1.07242
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.0584	+	19.1537i	0.593647	+	1.02823i	0.993736	+	0.111751i	$0.0356459\pi$
$347$	11.0584	+	19.1537i	0.593647	+	1.02823i	−0.400089	+	0.916476i	$0.631021\pi$
$348$		0			0
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	−0.877602	−	0.479390i	$-0.840858\pi$
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	0.853965	+	0.520331i	$0.174191\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.1753	−	26.2843i	0.807698	−	1.39897i	−0.106757	−	0.994285i	$-0.534047\pi$
$353$	15.1753	−	26.2843i	0.807698	−	1.39897i	0.914455	−	0.404689i	$-0.132620\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.48913			0.289705			0.144852	−	0.989453i	$-0.453729\pi$
$359$	5.48913			0.289705			0.144852	+	0.989453i	$0.453729\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.05842	+	12.2255i	0.369455	+	0.639914i
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.6277	−	23.6039i	0.707516	−	1.22545i
$372$		0			0
$373$	−3.74456	−	6.48577i	−0.193886	−	0.335821i	0.752649	−	0.658422i	$-0.228776\pi$
$373$	−3.74456	−	6.48577i	−0.193886	−	0.335821i	−0.946535	+	0.322602i	$0.895443\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.7446			1.06840
$378$		0			0
$379$	10.8614			0.557913			0.278956	−	0.960304i	$-0.410011\pi$
$379$	10.8614			0.557913			0.278956	+	0.960304i	$0.410011\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.4891	−	19.8997i	−0.587067	−	1.01683i	−0.994614	−	0.103646i	$-0.966949\pi$
$383$	−11.4891	−	19.8997i	−0.587067	−	1.01683i	0.407547	−	0.913184i	$-0.366384\pi$
$384$		0			0
$385$	−1.62772	+	2.81929i	−0.0829562	+	0.143684i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.18614	+	8.98266i	−0.262948	+	0.455439i	−0.967024	−	0.254686i	$-0.918028\pi$
$389$	−5.18614	+	8.98266i	−0.262948	+	0.455439i	0.704076	+	0.710124i	$0.251361\pi$
$390$		0			0
$391$	16.1168	+	27.9152i	0.815064	+	1.41173i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.00000			−0.100631
$396$		0			0
$397$	11.2554			0.564894			0.282447	−	0.959283i	$-0.408854\pi$
$397$	11.2554			0.564894			0.282447	+	0.959283i	$0.408854\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.05842	+	13.9576i	0.402418	+	0.697009i	0.994017	−	0.109223i	$-0.0348364\pi$
$401$	8.05842	+	13.9576i	0.402418	+	0.697009i	−0.591599	+	0.806232i	$0.701503\pi$
$402$		0			0
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.74456	−	4.75372i	0.136043	−	0.235633i
$408$		0			0
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	0.968483	−	0.249081i	$-0.0801285\pi$
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	−0.699952	+	0.714190i	$0.746795\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.25544			−0.160190
$414$		0			0
$415$	1.62772			0.0799016
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	0.934862	+	0.355012i	$0.115523\pi$
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	−0.159981	+	0.987120i	$0.551143\pi$
$420$		0			0
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.167082	−	0.985943i	$-0.446566\pi$
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.770311	−	0.637669i	$-0.220101\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.68614	+	6.38458i	−0.178804	+	0.309698i
$426$		0			0
$427$	−10.8139	−	18.7302i	−0.523319	−	0.906416i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.2337			−1.26363			−0.631816	−	0.775118i	$-0.717690\pi$
$431$	−26.2337			−1.26363			−0.631816	+	0.775118i	$0.717690\pi$
$432$		0			0
$433$	0.627719			0.0301662			0.0150831	−	0.999886i	$-0.495199\pi$
$433$	0.627719			0.0301662			0.0150831	+	0.999886i	$0.495199\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.37228	−	12.7692i	−0.352664	−	0.610832i
$438$		0			0
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	−0.604703	−	0.796451i	$-0.706708\pi$
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	0.992098	+	0.125462i	$0.0400414\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.2446	−	22.9403i	0.629268	−	1.08992i	−0.358431	−	0.933556i	$-0.616688\pi$
$443$	13.2446	−	22.9403i	0.629268	−	1.08992i	0.987699	−	0.156368i	$-0.0499786\pi$
$444$		0			0
$445$	−0.558422	−	0.967215i	−0.0264717	−	0.0458504i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.8614			0.890125			0.445062	−	0.895500i	$-0.353181\pi$
$449$	18.8614			0.890125			0.445062	+	0.895500i	$0.353181\pi$
$450$		0			0
$451$	4.11684			0.193855
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.62772	−	9.74749i	−0.263832	−	0.456970i
$456$		0			0
$457$	−15.0584	+	26.0820i	−0.704403	+	1.22006i	0.262503	+	0.964931i	$0.415452\pi$
$457$	−15.0584	+	26.0820i	−0.704403	+	1.22006i	−0.966906	+	0.255131i	$0.917881\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.55842	−	16.5557i	0.445180	−	0.771075i	−0.552885	−	0.833258i	$-0.686473\pi$
$461$	9.55842	−	16.5557i	0.445180	−	0.771075i	0.998065	+	0.0621833i	$0.0198063\pi$
$462$		0			0
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.8832			1.19773			0.598865	−	0.800850i	$-0.295619\pi$
$467$	25.8832			1.19773			0.598865	+	0.800850i	$0.295619\pi$
$468$		0			0
$469$	16.6060			0.766792
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.80298	−	13.5152i	−0.358782	−	0.621428i
$474$		0			0
$475$	1.68614	−	2.92048i	0.0773654	−	0.134001i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	−0.462460	−	0.886640i	$-0.653033\pi$
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	0.999083	−	0.0428178i	$-0.0136335\pi$
$480$		0			0
$481$	9.48913	+	16.4356i	0.432667	+	0.749401i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.62772			−0.119319
$486$		0			0
$487$	1.25544			0.0568893			0.0284446	−	0.999595i	$-0.490945\pi$
$487$	1.25544			0.0568893			0.0284446	+	0.999595i	$0.490945\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.80298	−	3.12286i	−0.0813676	−	0.140933i	0.822470	−	0.568808i	$-0.192595\pi$
$491$	−1.80298	−	3.12286i	−0.0813676	−	0.140933i	−0.903838	+	0.427876i	$0.859262\pi$
$492$		0			0
$493$	−16.1168	+	27.9152i	−0.725866	+	1.25724i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.11684	−	12.3267i	0.319234	−	0.552930i
$498$		0			0
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	0.841362	−	0.540472i	$-0.181754\pi$
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	−0.888743	+	0.458405i	$0.848421\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.8614			0.974752			0.487376	−	0.873192i	$-0.337954\pi$
$503$	21.8614			0.974752			0.487376	+	0.873192i	$0.337954\pi$
$504$		0			0
$505$	8.74456			0.389128
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.67527	+	8.09780i	0.207228	+	0.358929i	0.950840	−	0.309682i	$-0.100223\pi$
$509$	4.67527	+	8.09780i	0.207228	+	0.358929i	−0.743613	+	0.668611i	$0.766889\pi$
$510$		0			0
$511$	16.7446	−	29.0024i	0.740736	−	1.28299i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$	1.11684	+	1.93443i	0.0491187	+	0.0850762i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	41.2337			1.80648			0.903240	−	0.429135i	$-0.141182\pi$
$521$	41.2337			1.80648			0.903240	+	0.429135i	$0.141182\pi$
$522$		0			0
$523$	11.1168			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$523$	11.1168			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.8614	−	43.0612i	−1.08298	−	1.87578i
$528$		0			0
$529$	1.94158	−	3.36291i	0.0844164	−	0.146214i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.11684	+	12.3267i	−0.308265	+	0.533930i
$534$		0			0
$535$	7.24456	+	12.5480i	0.313210	+	0.542495i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.88316			−0.0811133
$540$		0			0
$541$	21.6277			0.929848			0.464924	−	0.885351i	$-0.346082\pi$
$541$	21.6277			0.929848			0.464924	+	0.885351i	$0.346082\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.81386	−	8.33785i	−0.206203	−	0.357154i
$546$		0			0
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	−0.0429494	−	0.999077i	$-0.513675\pi$
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	0.886701	−	0.462343i	$-0.152991\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.37228	−	12.7692i	0.314070	−	0.543985i
$552$		0			0
$553$	2.37228	+	4.10891i	0.100880	+	0.174729i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.76631			0.413812			0.206906	−	0.978361i	$-0.433661\pi$
$557$	9.76631			0.413812			0.206906	+	0.978361i	$0.433661\pi$
$558$		0			0
$559$	53.9565			2.28212
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.36141	−	14.4824i	−0.352391	−	0.610360i	0.634277	−	0.773106i	$-0.281298\pi$
$563$	−8.36141	−	14.4824i	−0.352391	−	0.610360i	−0.986668	+	0.162747i	$0.947965\pi$
$564$		0			0
$565$	7.37228	−	12.7692i	0.310154	−	0.537203i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.80298	−	8.31901i	0.201352	−	0.348751i	−0.747613	−	0.664135i	$-0.768800\pi$
$569$	4.80298	−	8.31901i	0.201352	−	0.348751i	0.948964	+	0.315384i	$0.102133\pi$
$570$		0			0
$571$	−15.8030	−	27.3716i	−0.661334	−	1.14546i	−0.980265	−	0.197687i	$-0.936657\pi$
$571$	−15.8030	−	27.3716i	−0.661334	−	1.14546i	0.318931	−	0.947778i	$-0.396676\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.37228			−0.182337
$576$		0			0
$577$	−23.8832			−0.994269			−0.497134	−	0.867674i	$-0.665614\pi$
$577$	−23.8832			−0.994269			−0.497134	+	0.867674i	$0.665614\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.93070	−	3.34408i	−0.0800991	−	0.138736i
$582$		0			0
$583$	7.88316	−	13.6540i	0.326487	−	0.565492i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	0.440524	+	0.897741i	$0.354793\pi$
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	−0.997728	+	0.0673658i	$0.978541\pi$
$588$		0			0
$589$	11.3723	+	19.6974i	0.468587	+	0.811616i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−37.7228			−1.54909			−0.774545	−	0.632519i	$-0.782021\pi$
$593$	−37.7228			−1.54909			−0.774545	+	0.632519i	$0.782021\pi$
$594$		0			0
$595$	17.4891			0.716984
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	0.931305	+	0.364239i	$0.118671\pi$
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	−0.150212	+	0.988654i	$0.547996\pi$
$600$		0			0
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	0.450572	+	0.892740i	$0.351220\pi$
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	−0.998422	+	0.0561635i	$0.982113\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.55842	−	7.89542i	0.185326	−	0.320994i
$606$		0			0
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	0.874848	−	0.484398i	$-0.160961\pi$
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	−0.856925	+	0.515442i	$0.827628\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.72281			−0.312432
$612$		0			0
$613$	−0.233688			−0.00943857			−0.00471928	−	0.999989i	$-0.501502\pi$
$613$	−0.233688			−0.00943857			−0.00471928	+	0.999989i	$0.501502\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.0584	−	19.1537i	−0.445195	−	0.771101i	0.552870	−	0.833267i	$-0.313532\pi$
$617$	−11.0584	−	19.1537i	−0.445195	−	0.771101i	−0.998066	+	0.0621663i	$0.980199\pi$
$618$		0			0
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	0.173682	+	0.984802i	$0.444434\pi$
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	−0.939704	+	0.341988i	$0.888900\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.32473	+	2.29451i	−0.0530743	+	0.0919275i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.4891			−1.17581
$630$		0			0
$631$	−33.7228			−1.34248			−0.671242	−	0.741238i	$-0.734239\pi$
$631$	−33.7228			−1.34248			−0.671242	+	0.741238i	$0.734239\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.55842	+	7.89542i	0.180895	+	0.313320i
$636$		0			0
$637$	3.25544	−	5.63858i	0.128985	−	0.223409i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−19.5000	+	33.7750i	−0.770204	+	1.33403i	0.167247	+	0.985915i	$0.446512\pi$
$641$	−19.5000	+	33.7750i	−0.770204	+	1.33403i	−0.937451	+	0.348117i	$0.886821\pi$
$642$		0			0
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.0951			0.947276			0.473638	−	0.880720i	$-0.342941\pi$
$647$	24.0951			0.947276			0.473638	+	0.880720i	$0.342941\pi$
$648$		0			0
$649$	−1.88316			−0.0739203
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.8614	−	32.6689i	−0.738104	−	1.27843i	−0.953348	−	0.301873i	$-0.902388\pi$
$653$	−18.8614	−	32.6689i	−0.738104	−	1.27843i	0.215244	−	0.976560i	$-0.430945\pi$
$654$		0			0
$655$	−4.37228	+	7.57301i	−0.170839	+	0.295902i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	−0.807605	−	0.589724i	$-0.799237\pi$
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	0.914518	+	0.404545i	$0.132570\pi$
$660$		0			0
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	0.564684	−	0.825307i	$-0.308998\pi$
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	−0.997079	+	0.0763770i	$0.975665\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.00000			−0.310227
$666$		0			0
$667$	−19.1168			−0.740207
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.25544	−	10.8347i	−0.241488	−	0.418270i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.8614	+	37.8651i	−0.840202	+	1.45527i	0.0495215	+	0.998773i	$0.484230\pi$
$677$	−21.8614	+	37.8651i	−0.840202	+	1.45527i	−0.889724	+	0.456500i	$0.849103\pi$
$678$		0			0
$679$	3.11684	+	5.39853i	0.119613	+	0.207177i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.0951			1.26635			0.633174	−	0.774009i	$-0.281752\pi$
$683$	33.0951			1.26635			0.633174	+	0.774009i	$0.281752\pi$
$684$		0			0
$685$	1.88316			0.0719517
$686$		0			0
$687$		0			0
$688$		0			0
$689$	27.2554	+	47.2078i	1.03835	+	1.79847i
$690$		0			0
$691$	−0.883156	+	1.52967i	−0.0335968	+	0.0581914i	−0.882335	−	0.470622i	$-0.844030\pi$
$691$	−0.883156	+	1.52967i	−0.0335968	+	0.0581914i	0.848738	+	0.528813i	$0.177363\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.05842	−	15.6896i	0.343606	−	0.595142i
$696$		0			0
$697$	−11.0584	−	19.1537i	−0.418868	−	0.725500i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.1386			−0.534007			−0.267004	−	0.963696i	$-0.586034\pi$
$701$	−14.1386			−0.534007			−0.267004	+	0.963696i	$0.586034\pi$
$702$		0			0
$703$	13.4891			0.508752
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.3723	−	17.9653i	−0.390090	−	0.675655i
$708$		0			0
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	−0.514241	−	0.857646i	$-0.671926\pi$
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	0.999863	+	0.0165226i	$0.00525955\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.7446	−	25.5383i	0.552188	−	0.956418i
$714$		0			0
$715$	−3.25544	−	5.63858i	−0.121746	−	0.210871i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−38.2337			−1.42588			−0.712938	−	0.701227i	$-0.752636\pi$
$719$	−38.2337			−1.42588			−0.712938	+	0.701227i	$0.752636\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.18614	−	3.78651i	−0.0811912	−	0.140627i
$726$		0			0
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	−0.857721	−	0.514116i	$-0.828120\pi$
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	0.874098	+	0.485750i	$0.161453\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−41.9198	+	72.6073i	−1.55046	+	2.68548i
$732$		0			0
$733$	−17.1168	−	29.6472i	−0.632225	−	1.09505i	−0.987096	−	0.160131i	$-0.948808\pi$
$733$	−17.1168	−	29.6472i	−0.632225	−	1.09505i	0.354871	−	0.934915i	$-0.384525\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.60597			0.353840
$738$		0			0
$739$	23.8832			0.878556			0.439278	−	0.898351i	$-0.355234\pi$
$739$	23.8832			0.878556			0.439278	+	0.898351i	$0.355234\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.5584	−	21.7518i	−0.460724	−	0.797997i	0.538273	−	0.842770i	$-0.319077\pi$
$743$	−12.5584	−	21.7518i	−0.460724	−	0.797997i	−0.998997	+	0.0447732i	$0.985743\pi$
$744$		0			0
$745$	9.55842	−	16.5557i	0.350193	−	0.606553i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.1861	−	29.7673i	0.627968	−	1.08767i
$750$		0			0
$751$	−9.11684	−	15.7908i	−0.332678	−	0.576216i	0.650358	−	0.759628i	$-0.274619\pi$
$751$	−9.11684	−	15.7908i	−0.332678	−	0.576216i	−0.983036	+	0.183412i	$0.941286\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.0000			0.363937
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.04755	+	10.4747i	0.219223	+	0.379706i	0.954571	−	0.297984i	$-0.0963143\pi$
$761$	6.04755	+	10.4747i	0.219223	+	0.379706i	−0.735347	+	0.677690i	$0.762981\pi$
$762$		0			0
$763$	−11.4198	+	19.7797i	−0.413426	+	0.716074i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.25544	−	5.63858i	0.117547	−	0.203597i
$768$		0			0
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	0.981925	−	0.189273i	$-0.0606131\pi$
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	−0.654877	+	0.755735i	$0.727280\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.7446			−0.530325			−0.265163	−	0.964204i	$-0.585426\pi$
$773$	−14.7446			−0.530325			−0.265163	+	0.964204i	$0.585426\pi$
$774$		0			0
$775$	6.74456			0.242272
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.05842	+	8.76144i	0.181237	+	0.313911i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.37228	+	4.10891i	−0.0846704	+	0.146653i
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−34.9783			−1.24368
$792$		0			0
$793$	43.2554			1.53605
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.62772	+	2.81929i	0.0576568	+	0.0998644i	0.893413	−	0.449236i	$-0.148304\pi$
$797$	1.62772	+	2.81929i	0.0576568	+	0.0998644i	−0.835756	+	0.549100i	$0.814970\pi$
$798$		0			0
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.68614	−	16.7769i	0.341816	−	0.592044i
$804$		0			0
$805$	5.18614	+	8.98266i	0.182787	+	0.316597i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.3505			0.434222			0.217111	−	0.976147i	$-0.430337\pi$
$809$	12.3505			0.434222			0.217111	+	0.976147i	$0.430337\pi$
$810$		0			0
$811$	−9.37228			−0.329105			−0.164553	−	0.986368i	$-0.552618\pi$
$811$	−9.37228			−0.329105			−0.164553	+	0.986368i	$0.552618\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.744563	+	1.28962i	0.0260809	+	0.0451734i
$816$		0			0
$817$	19.1753	−	33.2125i	0.670858	−	1.16196i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.4198	−	44.0284i	0.887158	−	1.53660i	0.0439382	−	0.999034i	$-0.486010\pi$
$821$	25.4198	−	44.0284i	0.887158	−	1.53660i	0.843220	−	0.537569i	$-0.180657\pi$
$822$		0			0
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	0.979567	+	0.201117i	$0.0644570\pi$
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	−0.315612	+	0.948888i	$0.602210\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8.13859			0.283007			0.141503	−	0.989938i	$-0.454806\pi$
$827$	8.13859			0.283007			0.141503	+	0.989938i	$0.454806\pi$
$828$		0			0
$829$	−32.8832			−1.14208			−0.571040	−	0.820923i	$-0.693460\pi$
$829$	−32.8832			−1.14208			−0.571040	+	0.820923i	$0.693460\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.05842	+	8.76144i	0.175264	+	0.303566i
$834$		0			0
$835$	−3.81386	+	6.60580i	−0.131984	+	0.228603i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	0.177447	+	0.984130i	$0.443216\pi$
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	−0.941005	+	0.338391i	$0.890117\pi$
$840$		0			0
$841$	4.94158	+	8.55906i	0.170399	+	0.295140i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.51087			0.327184
$846$		0			0
$847$	−21.6277			−0.743137
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−8.74456	−	15.1460i	−0.299760	−	0.519199i
$852$		0			0
$853$	0.883156	−	1.52967i	0.0302387	−	0.0523749i	−0.850510	−	0.525959i	$-0.823707\pi$
$853$	0.883156	−	1.52967i	0.0302387	−	0.0523749i	0.880749	+	0.473584i	$0.157040\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.7446	−	20.3422i	0.401187	−	0.694876i	−0.592683	−	0.805436i	$-0.701931\pi$
$857$	11.7446	−	20.3422i	0.401187	−	0.694876i	0.993869	+	0.110560i	$0.0352646\pi$
$858$		0			0
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	0.867020	−	0.498273i	$-0.166032\pi$
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	−0.865027	+	0.501725i	$0.832699\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−42.6060			−1.45032			−0.725162	−	0.688578i	$-0.758235\pi$
$863$	−42.6060			−1.45032			−0.725162	+	0.688578i	$0.758235\pi$
$864$		0			0
$865$	−9.25544			−0.314694
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.37228	+	2.37686i	0.0465515	+	0.0806295i
$870$		0			0
$871$	−16.6060	+	28.7624i	−0.562672	+	0.974576i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.18614	+	2.05446i	−0.0400989	+	0.0694533i
$876$		0			0
$877$	27.9783	+	48.4598i	0.944758	+	1.63637i	0.756234	+	0.654301i	$0.227037\pi$
$877$	27.9783	+	48.4598i	0.944758	+	1.63637i	0.188524	+	0.982069i	$0.439630\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.3505			−0.921463			−0.460731	−	0.887540i	$-0.652413\pi$
$881$	−27.3505			−0.921463			−0.460731	+	0.887540i	$0.652413\pi$
$882$		0			0
$883$	−12.7228			−0.428157			−0.214078	−	0.976816i	$-0.568675\pi$
$883$	−12.7228			−0.428157			−0.214078	+	0.976816i	$0.568675\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.8614	+	32.6689i	0.633304	+	1.09691i	0.986872	+	0.161506i	$0.0516351\pi$
$887$	18.8614	+	32.6689i	0.633304	+	1.09691i	−0.353568	+	0.935409i	$0.615032\pi$
$888$		0			0
$889$	10.8139	−	18.7302i	0.362685	−	0.628189i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.74456	+	4.75372i	−0.0918433	+	0.159077i
$894$		0			0
$895$	1.62772	+	2.81929i	0.0544086	+	0.0942385i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	29.4891			0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.93070	+	6.80818i	0.130661	+	0.226311i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	−0.274162	−	0.961683i	$-0.588401\pi$
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	0.969923	−	0.243410i	$-0.0782661\pi$
$912$		0			0
$913$	−1.11684	−	1.93443i	−0.0369621	−	0.0640203i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.7446			0.685046
$918$		0			0
$919$	−42.4674			−1.40087			−0.700435	−	0.713716i	$-0.747011\pi$
$919$	−42.4674			−1.40087			−0.700435	+	0.713716i	$0.747011\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	14.2337	+	24.6535i	0.468508	+	0.811479i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.9783	+	34.6033i	−0.655465	+	1.13530i	0.326312	+	0.945262i	$0.394194\pi$
$929$	−19.9783	+	34.6033i	−0.655465	+	1.13530i	−0.981777	+	0.190037i	$0.939139\pi$
$930$		0			0
$931$	−2.31386	−	4.00772i	−0.0758337	−	0.131348i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.1168			0.330856
$936$		0			0
$937$	−17.7228			−0.578979			−0.289490	−	0.957181i	$-0.593486\pi$
$937$	−17.7228			−0.578979			−0.289490	+	0.957181i	$0.593486\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.8139	+	32.5866i	0.613314	+	1.06229i	0.990678	+	0.136226i	$0.0434974\pi$
$941$	18.8139	+	32.5866i	0.613314	+	1.06229i	−0.377363	+	0.926065i	$0.623169\pi$
$942$		0			0
$943$	6.55842	−	11.3595i	0.213572	−	0.369917i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.3614	+	19.6785i	−0.369196	+	0.639466i	−0.989440	−	0.144943i	$-0.953700\pi$
$947$	−11.3614	+	19.6785i	−0.369196	+	0.639466i	0.620244	+	0.784409i	$0.287034\pi$
$948$		0			0
$949$	33.4891	+	58.0049i	1.08710	+	1.88292i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−30.8614			−0.999699			−0.499850	−	0.866112i	$-0.666611\pi$
$953$	−30.8614			−0.999699			−0.499850	+	0.866112i	$0.666611\pi$
$954$		0			0
$955$	−5.48913			−0.177624
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.23369	−	3.86886i	−0.0721295	−	0.124932i
$960$		0			0
$961$	−7.24456	+	12.5480i	−0.233696	+	0.404773i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.94158	+	3.36291i	−0.0625016	+	0.108256i
$966$		0			0
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	0.976953	−	0.213453i	$-0.0684711\pi$
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	−0.673333	+	0.739340i	$0.735138\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.9783			0.737407			0.368704	−	0.929547i	$-0.379802\pi$
$971$	22.9783			0.737407			0.368704	+	0.929547i	$0.379802\pi$
$972$		0			0
$973$	−42.9783			−1.37782
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	−0.985047	−	0.172284i	$-0.944885\pi$
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	0.343322	−	0.939218i	$-0.388448\pi$
$978$		0			0
$979$	−0.766312	+	1.32729i	−0.0244914	+	0.0424204i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.93070	+	13.7364i	−0.252950	+	0.438123i	−0.964337	−	0.264678i	$-0.914734\pi$
$983$	−7.93070	+	13.7364i	−0.252950	+	0.438123i	0.711387	+	0.702801i	$0.248068\pi$
$984$		0			0
$985$	8.74456	+	15.1460i	0.278625	+	0.482593i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−49.7228			−1.58109
$990$		0			0
$991$	18.2337			0.579212			0.289606	−	0.957146i	$-0.406476\pi$
$991$	18.2337			0.579212			0.289606	+	0.957146i	$0.406476\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.74456	−	8.21782i	−0.150413	−	0.260523i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.q.f.721.1		4
3.2	odd	2		720.2.q.f.241.1		4
4.3	odd	2		270.2.e.c.181.2		4
9.2	odd	6		6480.2.a.be.1.2		2
9.4	even	3	inner	2160.2.q.f.1441.1		4
9.5	odd	6		720.2.q.f.481.2		4
9.7	even	3		6480.2.a.bn.1.2		2
12.11	even	2		90.2.e.c.61.2	yes	4
20.3	even	4		1350.2.j.f.1099.3		8
20.7	even	4		1350.2.j.f.1099.2		8
20.19	odd	2		1350.2.e.l.451.1		4
36.7	odd	6		810.2.a.k.1.1		2
36.11	even	6		810.2.a.i.1.1		2
36.23	even	6		90.2.e.c.31.1	✓	4
36.31	odd	6		270.2.e.c.91.2		4
60.23	odd	4		450.2.j.g.349.1		8
60.47	odd	4		450.2.j.g.349.4		8
60.59	even	2		450.2.e.j.151.1		4
180.7	even	12		4050.2.c.ba.649.3		4
180.23	odd	12		450.2.j.g.49.4		8
180.43	even	12		4050.2.c.ba.649.2		4
180.47	odd	12		4050.2.c.v.649.1		4
180.59	even	6		450.2.e.j.301.2		4
180.67	even	12		1350.2.j.f.199.3		8
180.79	odd	6		4050.2.a.bo.1.2		2
180.83	odd	12		4050.2.c.v.649.4		4
180.103	even	12		1350.2.j.f.199.2		8
180.119	even	6		4050.2.a.bw.1.2		2
180.139	odd	6		1350.2.e.l.901.1		4
180.167	odd	12		450.2.j.g.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	36.23	even	6
90.2.e.c.61.2	yes	4	12.11	even	2
270.2.e.c.91.2		4	36.31	odd	6
270.2.e.c.181.2		4	4.3	odd	2
450.2.e.j.151.1		4	60.59	even	2
450.2.e.j.301.2		4	180.59	even	6
450.2.j.g.49.1		8	180.167	odd	12
450.2.j.g.49.4		8	180.23	odd	12
450.2.j.g.349.1		8	60.23	odd	4
450.2.j.g.349.4		8	60.47	odd	4
720.2.q.f.241.1		4	3.2	odd	2
720.2.q.f.481.2		4	9.5	odd	6
810.2.a.i.1.1		2	36.11	even	6
810.2.a.k.1.1		2	36.7	odd	6
1350.2.e.l.451.1		4	20.19	odd	2
1350.2.e.l.901.1		4	180.139	odd	6
1350.2.j.f.199.2		8	180.103	even	12
1350.2.j.f.199.3		8	180.67	even	12
1350.2.j.f.1099.2		8	20.7	even	4
1350.2.j.f.1099.3		8	20.3	even	4
2160.2.q.f.721.1		4	1.1	even	1	trivial
2160.2.q.f.1441.1		4	9.4	even	3	inner
4050.2.a.bo.1.2		2	180.79	odd	6
4050.2.a.bw.1.2		2	180.119	even	6
4050.2.c.v.649.1		4	180.47	odd	12
4050.2.c.v.649.4		4	180.83	odd	12
4050.2.c.ba.649.2		4	180.43	even	12
4050.2.c.ba.649.3		4	180.7	even	12
6480.2.a.be.1.2		2	9.2	odd	6
6480.2.a.bn.1.2		2	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-0.686141 + 1.18843i) q^{11} +(-2.37228 - 4.10891i) q^{13} +7.37228 q^{17} -3.37228 q^{19} +(2.18614 + 3.78651i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.18614 + 3.78651i) q^{29} +(-3.37228 - 5.84096i) q^{31} +2.37228 q^{35} -4.00000 q^{37} +(-1.50000 - 2.59808i) q^{41} +(-5.68614 + 9.84868i) q^{43} +(0.813859 - 1.40965i) q^{47} +(0.686141 + 1.18843i) q^{49} -11.4891 q^{53} +1.37228 q^{55} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} +(-2.37228 + 4.10891i) q^{65} +(-3.50000 - 6.06218i) q^{67} -6.00000 q^{71} -14.1168 q^{73} +(-1.62772 - 2.81929i) q^{77} +(1.00000 - 1.73205i) q^{79} +(-0.813859 + 1.40965i) q^{83} +(-3.68614 - 6.38458i) q^{85} +1.11684 q^{89} +11.2554 q^{91} +(1.68614 + 2.92048i) q^{95} +(1.31386 - 2.27567i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + q^{7} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 2 q^{19} + 3 q^{23} - 2 q^{25} - 3 q^{29} - 2 q^{31} - 2 q^{35} - 16 q^{37} - 6 q^{41} - 17 q^{43} + 9 q^{47} - 3 q^{49} - 6 q^{55} - 3 q^{59}+ \cdots + 11 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 + q^7 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 2 * q^19 + 3 * q^23 - 2 * q^25 - 3 * q^29 - 2 * q^31 - 2 * q^35 - 16 * q^37 - 6 * q^41 - 17 * q^43 + 9 * q^47 - 3 * q^49 - 6 * q^55 - 3 * q^59 - q^61 + 2 * q^65 - 14 * q^67 - 24 * q^71 - 22 * q^73 - 18 * q^77 + 4 * q^79 - 9 * q^83 - 9 * q^85 - 30 * q^89 + 68 * q^91 + q^95 + 11 * q^97

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