LMFDB - Embedded newform 1638.2.bj.h.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
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} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$-2.02798 + 2.02798i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.h.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.19147i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.19147i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-1.09573 - 1.89787i) q^{10} +(-3.54195 + 2.04495i) q^{11} +(3.53557 - 0.706919i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.85204 - 4.93987i) q^{17} +(6.69612 + 3.86601i) q^{19} +(1.89787 + 1.09573i) q^{20} +(2.04495 - 3.54195i) q^{22} +(-1.23791 - 2.14412i) q^{23} +0.197462 q^{25} +(-2.70844 + 2.38000i) q^{26} +(0.866025 - 0.500000i) q^{28} +(4.90888 + 8.50243i) q^{29} -7.19507i q^{31} +(0.866025 + 0.500000i) q^{32} +5.70407i q^{34} +(-1.09573 + 1.89787i) q^{35} +(-8.79425 + 5.07736i) q^{37} -7.73201 q^{38} -2.19147 q^{40} +(-3.14093 + 1.81341i) q^{41} +(-1.37769 + 2.38624i) q^{43} +4.08989i q^{44} +(2.14412 + 1.23791i) q^{46} +7.70008i q^{47} +(0.500000 + 0.866025i) q^{49} +(-0.171007 + 0.0987308i) q^{50} +(1.15558 - 3.41535i) q^{52} +6.31111 q^{53} +(-4.48144 - 7.76207i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-8.50243 - 4.90888i) q^{58} +(4.20781 + 2.42938i) q^{59} +(5.63434 - 9.75896i) q^{61} +(3.59754 + 6.23112i) q^{62} -1.00000 q^{64} +(1.54919 + 7.74810i) q^{65} +(-5.49094 + 3.17020i) q^{67} +(-2.85204 - 4.93987i) q^{68} -2.19147i q^{70} +(-7.21341 - 4.16466i) q^{71} +7.37805i q^{73} +(5.07736 - 8.79425i) q^{74} +(6.69612 - 3.86601i) q^{76} -4.08989 q^{77} +3.45834 q^{79} +(1.89787 - 1.09573i) q^{80} +(1.81341 - 3.14093i) q^{82} -0.332783i q^{83} +(10.8256 + 6.25015i) q^{85} -2.75539i q^{86} +(-2.04495 - 3.54195i) q^{88} +(-11.7151 + 6.76374i) q^{89} +(3.41535 + 1.15558i) q^{91} -2.47582 q^{92} +(-3.85004 - 6.66847i) q^{94} +(-8.47223 + 14.6743i) q^{95} +(10.0600 + 5.80816i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.19147i			0.980055i	0.871707	+	0.490027i	$0.163013\pi$
$5$			2.19147i			0.980055i	−0.871707	+	0.490027i	$0.836987\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.09573	−	1.89787i	−0.346502	−	0.600159i
$11$	−3.54195	+	2.04495i	−1.06794	+	0.616574i	−0.927617	−	0.373532i	$-0.878147\pi$
$11$	−3.54195	+	2.04495i	−1.06794	+	0.616574i	−0.140321	+	0.990106i	$0.544813\pi$
$12$		0			0
$13$	3.53557	−	0.706919i	0.980591	−	0.196064i
$13$	3.53557	−	0.706919i	0.980591	−	0.196064i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.85204	−	4.93987i	0.691720	−	1.19809i	−0.279553	−	0.960130i	$-0.590186\pi$
$17$	2.85204	−	4.93987i	0.691720	−	1.19809i	0.971274	−	0.237965i	$-0.0764803\pi$
$18$		0			0
$19$	6.69612	+	3.86601i	1.53620	+	0.886923i	0.999057	+	0.0434286i	$0.0138281\pi$
$19$	6.69612	+	3.86601i	1.53620	+	0.886923i	0.537139	+	0.843494i	$0.319505\pi$
$20$	1.89787	+	1.09573i	0.424376	+	0.245014i
$21$		0			0
$22$	2.04495	−	3.54195i	0.435984	−	0.755146i
$23$	−1.23791	−	2.14412i	−0.258122	−	0.447080i	0.707617	−	0.706596i	$-0.249770\pi$
$23$	−1.23791	−	2.14412i	−0.258122	−	0.447080i	−0.965739	+	0.259516i	$0.916437\pi$
$24$		0			0
$25$	0.197462			0.0394923
$26$	−2.70844	+	2.38000i	−0.531168	+	0.466755i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	4.90888	+	8.50243i	0.911556	+	1.57886i	0.811866	+	0.583844i	$0.198452\pi$
$29$	4.90888	+	8.50243i	0.911556	+	1.57886i	0.0996903	+	0.995019i	$0.468215\pi$
$30$		0			0
$31$		−	7.19507i		−	1.29227i	−0.763222	−	0.646137i	$-0.776384\pi$
$31$		−	7.19507i		−	1.29227i	0.763222	−	0.646137i	$-0.223616\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			5.70407i			0.978240i
$35$	−1.09573	+	1.89787i	−0.185213	+	0.320798i
$36$		0			0
$37$	−8.79425	+	5.07736i	−1.44577	+	0.834713i	−0.998225	−	0.0595505i	$-0.981033\pi$
$37$	−8.79425	+	5.07736i	−1.44577	+	0.834713i	−0.447540	+	0.894264i	$0.647700\pi$
$38$	−7.73201			−1.25430
$39$		0			0
$40$	−2.19147			−0.346502
$41$	−3.14093	+	1.81341i	−0.490530	+	0.283208i	−0.724794	−	0.688965i	$-0.758065\pi$
$41$	−3.14093	+	1.81341i	−0.490530	+	0.283208i	0.234264	+	0.972173i	$0.424732\pi$
$42$		0			0
$43$	−1.37769	+	2.38624i	−0.210096	+	0.363897i	−0.951744	−	0.306892i	$-0.900711\pi$
$43$	−1.37769	+	2.38624i	−0.210096	+	0.363897i	0.741648	+	0.670789i	$0.234044\pi$
$44$			4.08989i			0.616574i
$45$		0			0
$46$	2.14412	+	1.23791i	0.316133	+	0.182520i
$47$			7.70008i			1.12317i	0.827418	+	0.561586i	$0.189809\pi$
$47$			7.70008i			1.12317i	−0.827418	+	0.561586i	$0.810191\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−0.171007	+	0.0987308i	−0.0241840	+	0.0139626i
$51$		0			0
$52$	1.15558	−	3.41535i	0.160250	−	0.473624i
$53$	6.31111			0.866898			0.433449	−	0.901178i	$-0.357296\pi$
$53$	6.31111			0.866898			0.433449	+	0.901178i	$0.357296\pi$
$54$		0			0
$55$	−4.48144	−	7.76207i	−0.604277	−	1.04664i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−8.50243	−	4.90888i	−1.11642	−	0.644568i
$59$	4.20781	+	2.42938i	0.547810	+	0.316278i	0.748238	−	0.663430i	$-0.230900\pi$
$59$	4.20781	+	2.42938i	0.547810	+	0.316278i	−0.200428	+	0.979708i	$0.564233\pi$
$60$		0			0
$61$	5.63434	−	9.75896i	0.721403	−	1.24951i	−0.239035	−	0.971011i	$-0.576831\pi$
$61$	5.63434	−	9.75896i	0.721403	−	1.24951i	0.960438	−	0.278496i	$-0.0898357\pi$
$62$	3.59754	+	6.23112i	0.456888	+	0.791353i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.54919	+	7.74810i	0.192153	+	0.961033i
$66$		0			0
$67$	−5.49094	+	3.17020i	−0.670825	+	0.387301i	−0.796389	−	0.604784i	$-0.793259\pi$
$67$	−5.49094	+	3.17020i	−0.670825	+	0.387301i	0.125564	+	0.992086i	$0.459926\pi$
$68$	−2.85204	−	4.93987i	−0.345860	−	0.599047i
$69$		0			0
$70$		−	2.19147i		−	0.261931i
$71$	−7.21341	−	4.16466i	−0.856074	−	0.494255i	0.00662155	−	0.999978i	$-0.497892\pi$
$71$	−7.21341	−	4.16466i	−0.856074	−	0.494255i	−0.862696	+	0.505723i	$0.831226\pi$
$72$		0			0
$73$			7.37805i			0.863536i	0.901985	+	0.431768i	$0.142110\pi$
$73$			7.37805i			0.863536i	−0.901985	+	0.431768i	$0.857890\pi$
$74$	5.07736	−	8.79425i	0.590231	−	1.02231i
$75$		0			0
$76$	6.69612	−	3.86601i	0.768098	−	0.443461i
$77$	−4.08989			−0.466086
$78$		0			0
$79$	3.45834			0.389094			0.194547	−	0.980893i	$-0.437676\pi$
$79$	3.45834			0.389094			0.194547	+	0.980893i	$0.437676\pi$
$80$	1.89787	−	1.09573i	0.212188	−	0.122507i
$81$		0			0
$82$	1.81341	−	3.14093i	0.200258	−	0.346857i
$83$		−	0.332783i		−	0.0365277i	−0.999833	−	0.0182638i	$-0.994186\pi$
$83$		−	0.332783i		−	0.0365277i	0.999833	−	0.0182638i	$-0.00581389\pi$
$84$		0			0
$85$	10.8256	+	6.25015i	1.17420	+	0.677924i
$86$		−	2.75539i		−	0.297121i
$87$		0			0
$88$	−2.04495	−	3.54195i	−0.217992	−	0.377573i
$89$	−11.7151	+	6.76374i	−1.24180	+	0.716956i	−0.969461	−	0.245245i	$-0.921132\pi$
$89$	−11.7151	+	6.76374i	−1.24180	+	0.716956i	−0.272342	+	0.962200i	$0.587798\pi$
$90$		0			0
$91$	3.41535	+	1.15558i	0.358026	+	0.121137i
$92$	−2.47582			−0.258122
$93$		0			0
$94$	−3.85004	−	6.66847i	−0.397101	−	0.687800i
$95$	−8.47223	+	14.6743i	−0.869233	+	1.50556i
$96$		0			0
$97$	10.0600	+	5.80816i	1.02144	+	0.589729i	0.914521	−	0.404539i	$-0.132568\pi$
$97$	10.0600	+	5.80816i	1.02144	+	0.589729i	0.106920	+	0.994268i	$0.465901\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	0.0987308	−	0.171007i	0.00987308	−	0.0171007i
$101$	1.12692	+	1.95189i	0.112133	+	0.194220i	0.916630	−	0.399737i	$-0.130898\pi$
$101$	1.12692	+	1.95189i	0.112133	+	0.194220i	−0.804497	+	0.593957i	$0.797565\pi$
$102$		0			0
$103$	−16.0325			−1.57973			−0.789867	−	0.613278i	$-0.789850\pi$
$103$	−16.0325			−1.57973			−0.789867	+	0.613278i	$0.789850\pi$
$104$	0.706919	+	3.53557i	0.0693191	+	0.346691i
$105$		0			0
$106$	−5.46559	+	3.15556i	−0.530865	+	0.306495i
$107$	4.30793	+	7.46156i	0.416464	+	0.721336i	0.995581	−	0.0939082i	$-0.0299360\pi$
$107$	4.30793	+	7.46156i	0.416464	+	0.721336i	−0.579117	+	0.815244i	$0.696603\pi$
$108$		0			0
$109$			10.0318i			0.960870i	0.877030	+	0.480435i	$0.159521\pi$
$109$			10.0318i			0.960870i	−0.877030	+	0.480435i	$0.840479\pi$
$110$	7.76207	+	4.48144i	0.740085	+	0.427288i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	9.27760	−	16.0693i	0.872763	−	1.51167i	0.0136363	−	0.999907i	$-0.495659\pi$
$113$	9.27760	−	16.0693i	0.872763	−	1.51167i	0.859127	−	0.511763i	$-0.171007\pi$
$114$		0			0
$115$	4.69878	−	2.71284i	0.438163	−	0.252974i
$116$	9.81776			0.911556
$117$		0			0
$118$	−4.85876			−0.447285
$119$	4.93987	−	2.85204i	0.452837	−	0.261446i
$120$		0			0
$121$	2.86360	−	4.95991i	0.260328	−	0.450901i
$122$			11.2687i			1.02022i
$123$		0			0
$124$	−6.23112	−	3.59754i	−0.559571	−	0.323068i
$125$			11.3901i			1.01876i
$126$		0			0
$127$	−0.132439	−	0.229390i	−0.0117520	−	0.0203551i	0.860090	−	0.510143i	$-0.170408\pi$
$127$	−0.132439	−	0.229390i	−0.0117520	−	0.0203551i	−0.871842	+	0.489788i	$0.837074\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−5.21569	−	5.93545i	−0.457446	−	0.520574i
$131$	5.10237			0.445796			0.222898	−	0.974842i	$-0.428448\pi$
$131$	5.10237			0.445796			0.222898	+	0.974842i	$0.428448\pi$
$132$		0			0
$133$	3.86601	+	6.69612i	0.335225	+	0.580627i
$134$	3.17020	−	5.49094i	0.273863	−	0.474345i
$135$		0			0
$136$	4.93987	+	2.85204i	0.423591	+	0.244560i
$137$	−18.8812	−	10.9011i	−1.61313	−	0.931342i	−0.988639	−	0.150312i	$-0.951972\pi$
$137$	−18.8812	−	10.9011i	−1.61313	−	0.931342i	−0.624493	−	0.781030i	$-0.714694\pi$
$138$		0			0
$139$	−8.22455	+	14.2453i	−0.697597	+	1.20827i	0.271700	+	0.962382i	$0.412414\pi$
$139$	−8.22455	+	14.2453i	−0.697597	+	1.20827i	−0.969297	+	0.245892i	$0.920919\pi$
$140$	1.09573	+	1.89787i	0.0926065	+	0.160399i
$141$		0			0
$142$	8.32933			0.698982
$143$	−11.0772	+	9.73392i	−0.926322	+	0.813991i
$144$		0			0
$145$	−18.6328	+	10.7577i	−1.54737	+	0.893375i
$146$	−3.68903	−	6.38958i	−0.305306	−	0.528806i
$147$		0			0
$148$			10.1547i			0.834713i
$149$	12.8023	+	7.39139i	1.04880	+	0.605526i	0.922314	−	0.386442i	$-0.126296\pi$
$149$	12.8023	+	7.39139i	1.04880	+	0.605526i	0.126489	+	0.991968i	$0.459629\pi$
$150$		0			0
$151$			18.9896i			1.54535i	0.634803	+	0.772674i	$0.281081\pi$
$151$			18.9896i			1.54535i	−0.634803	+	0.772674i	$0.718919\pi$
$152$	−3.86601	+	6.69612i	−0.313575	+	0.543127i
$153$		0			0
$154$	3.54195	−	2.04495i	0.285418	−	0.164786i
$155$	15.7678			1.26650
$156$		0			0
$157$	−13.5474			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$157$	−13.5474			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$158$	−2.99501	+	1.72917i	−0.238270	+	0.137565i
$159$		0			0
$160$	−1.09573	+	1.89787i	−0.0866254	+	0.150040i
$161$		−	2.47582i		−	0.195122i
$162$		0			0
$163$	−3.86502	−	2.23147i	−0.302732	−	0.174782i	0.340938	−	0.940086i	$-0.389256\pi$
$163$	−3.86502	−	2.23147i	−0.302732	−	0.174782i	−0.643670	+	0.765304i	$0.722589\pi$
$164$			3.62683i			0.283208i
$165$		0			0
$166$	0.166392	+	0.288199i	0.0129145	+	0.0223685i
$167$	2.86448	−	1.65381i	0.221660	−	0.127976i	−0.385059	−	0.922892i	$-0.625819\pi$
$167$	2.86448	−	1.65381i	0.221660	−	0.127976i	0.606719	+	0.794917i	$0.292485\pi$
$168$		0			0
$169$	12.0005	−	4.99872i	0.923118	−	0.384517i
$170$	−12.5003			−0.958729
$171$		0			0
$172$	1.37769	+	2.38624i	0.105048	+	0.181949i
$173$	−5.06107	+	8.76603i	−0.384786	+	0.666469i	−0.991740	−	0.128268i	$-0.959058\pi$
$173$	−5.06107	+	8.76603i	−0.384786	+	0.666469i	0.606953	+	0.794737i	$0.292391\pi$
$174$		0			0
$175$	0.171007	+	0.0987308i	0.0129269	+	0.00746335i
$176$	3.54195	+	2.04495i	0.266984	+	0.154144i
$177$		0			0
$178$	6.76374	−	11.7151i	0.506964	−	0.878088i
$179$	−4.62579	−	8.01210i	−0.345748	−	0.598853i	0.639742	−	0.768590i	$-0.279041\pi$
$179$	−4.62579	−	8.01210i	−0.345748	−	0.598853i	−0.985489	+	0.169737i	$0.945708\pi$
$180$		0			0
$181$	23.2645			1.72923			0.864617	−	0.502431i	$-0.167561\pi$
$181$	23.2645			1.72923			0.864617	+	0.502431i	$0.167561\pi$
$182$	−3.53557	+	0.706919i	−0.262074	+	0.0524003i
$183$		0			0
$184$	2.14412	−	1.23791i	0.158067	−	0.0912598i
$185$	−11.1269	−	19.2723i	−0.818065	−	1.41693i
$186$		0			0
$187$			23.3290i			1.70599i
$188$	6.66847	+	3.85004i	0.486348	+	0.280793i
$189$		0			0
$190$		−	16.9445i		−	1.22928i
$191$	−4.45096	+	7.70929i	−0.322060	+	0.557825i	−0.980913	−	0.194447i	$-0.937709\pi$
$191$	−4.45096	+	7.70929i	−0.322060	+	0.557825i	0.658853	+	0.752272i	$0.271042\pi$
$192$		0			0
$193$	7.69754	−	4.44417i	0.554081	−	0.319899i	−0.196685	−	0.980467i	$-0.563018\pi$
$193$	7.69754	−	4.44417i	0.554081	−	0.319899i	0.750766	+	0.660568i	$0.229684\pi$
$194$	−11.6163			−0.834003
$195$		0			0
$196$	1.00000			0.0714286
$197$	20.2586	−	11.6963i	1.44336	−	0.833326i	0.445291	−	0.895386i	$-0.353100\pi$
$197$	20.2586	−	11.6963i	1.44336	−	0.833326i	0.998072	+	0.0620596i	$0.0197669\pi$
$198$		0			0
$199$	−1.96804	+	3.40875i	−0.139511	+	0.241640i	−0.927312	−	0.374290i	$-0.877886\pi$
$199$	−1.96804	+	3.40875i	−0.139511	+	0.241640i	0.787801	+	0.615930i	$0.211220\pi$
$200$			0.197462i			0.0139626i
$201$		0			0
$202$	−1.95189	−	1.12692i	−0.137334	−	0.0792900i
$203$			9.81776i			0.689072i
$204$		0			0
$205$	−3.97404	−	6.88324i	−0.277559	−	0.480747i
$206$	13.8846	−	8.01627i	0.967385	−	0.558520i
$207$		0			0
$208$	−2.38000	−	2.70844i	−0.165023	−	0.187796i
$209$	−31.6231			−2.18741
$210$		0			0
$211$	−6.40104	−	11.0869i	−0.440666	−	0.763256i	0.557073	−	0.830464i	$-0.311924\pi$
$211$	−6.40104	−	11.0869i	−0.440666	−	0.763256i	−0.997739	+	0.0672076i	$0.978591\pi$
$212$	3.15556	−	5.46559i	0.216725	−	0.375378i
$213$		0			0
$214$	−7.46156	−	4.30793i	−0.510062	−	0.294484i
$215$	−5.22936	−	3.01917i	−0.356639	−	0.205906i
$216$		0			0
$217$	3.59754	−	6.23112i	0.244217	−	0.422996i
$218$	−5.01589	−	8.68777i	−0.339719	−	0.588410i
$219$		0			0
$220$	−8.96287			−0.604277
$221$	6.59149	−	19.4814i	0.443392	−	1.31046i
$222$		0			0
$223$	16.3236	−	9.42444i	1.09311	−	0.631107i	0.158707	−	0.987326i	$-0.449267\pi$
$223$	16.3236	−	9.42444i	1.09311	−	0.631107i	0.934403	+	0.356218i	$0.115934\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$			18.5552i			1.23427i
$227$	1.14246	+	0.659599i	0.0758276	+	0.0437791i	0.537434	−	0.843306i	$-0.319394\pi$
$227$	1.14246	+	0.659599i	0.0758276	+	0.0437791i	−0.461607	+	0.887085i	$0.652727\pi$
$228$		0			0
$229$		−	4.34109i		−	0.286867i	−0.989660	−	0.143434i	$-0.954186\pi$
$229$		−	4.34109i		−	0.286867i	0.989660	−	0.143434i	$-0.0458143\pi$
$230$	−2.71284	+	4.69878i	−0.178879	+	0.309828i
$231$		0			0
$232$	−8.50243	+	4.90888i	−0.558212	+	0.322284i
$233$	5.76422			0.377627			0.188813	−	0.982013i	$-0.439536\pi$
$233$	5.76422			0.377627			0.188813	+	0.982013i	$0.439536\pi$
$234$		0			0
$235$	−16.8745			−1.10077
$236$	4.20781	−	2.42938i	0.273905	−	0.158139i
$237$		0			0
$238$	−2.85204	+	4.93987i	−0.184870	+	0.320204i
$239$		−	13.0951i		−	0.847049i	−0.905885	−	0.423525i	$-0.860793\pi$
$239$		−	13.0951i		−	0.847049i	0.905885	−	0.423525i	$-0.139207\pi$
$240$		0			0
$241$	−0.389769	−	0.225033i	−0.0251072	−	0.0144957i	0.487394	−	0.873182i	$-0.337948\pi$
$241$	−0.389769	−	0.225033i	−0.0251072	−	0.0144957i	−0.512501	+	0.858687i	$0.671281\pi$
$242$			5.72721i			0.368159i
$243$		0			0
$244$	−5.63434	−	9.75896i	−0.360701	−	0.624753i
$245$	−1.89787	+	1.09573i	−0.121250	+	0.0700039i
$246$		0			0
$247$	26.4076	+	8.93493i	1.68027	+	0.568516i
$248$	7.19507			0.456888
$249$		0			0
$250$	−5.69504	−	9.86410i	−0.360186	−	0.623860i
$251$	−9.35111	+	16.1966i	−0.590237	+	1.02232i	0.403963	+	0.914775i	$0.367632\pi$
$251$	−9.35111	+	16.1966i	−0.590237	+	1.02232i	−0.994200	+	0.107545i	$0.965701\pi$
$252$		0			0
$253$	8.76922	+	5.06291i	0.551316	+	0.318303i
$254$	0.229390	+	0.132439i	0.0143932	+	0.00830994i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.88929	−	17.1287i	−0.616877	−	1.06846i	−0.990052	−	0.140701i	$-0.955064\pi$
$257$	−9.88929	−	17.1287i	−0.616877	−	1.06846i	0.373175	−	0.927761i	$-0.378269\pi$
$258$		0			0
$259$	−10.1547			−0.630984
$260$	7.48464	+	2.53241i	0.464178	+	0.157053i
$261$		0			0
$262$	−4.41878	+	2.55119i	−0.272993	+	0.157613i
$263$	11.7723	+	20.3903i	0.725914	+	1.25732i	0.958597	+	0.284767i	$0.0919162\pi$
$263$	11.7723	+	20.3903i	0.725914	+	1.25732i	−0.232683	+	0.972553i	$0.574750\pi$
$264$		0			0
$265$			13.8306i			0.849608i
$266$	−6.69612	−	3.86601i	−0.410565	−	0.237040i
$267$		0			0
$268$			6.34039i			0.387301i
$269$	11.4216	−	19.7827i	0.696384	−	1.20617i	−0.273327	−	0.961921i	$-0.588124\pi$
$269$	11.4216	−	19.7827i	0.696384	−	1.20617i	0.969712	−	0.244252i	$-0.0785424\pi$
$270$		0			0
$271$	−11.2562	+	6.49877i	−0.683766	+	0.394772i	−0.801272	−	0.598300i	$-0.795843\pi$
$271$	−11.2562	+	6.49877i	−0.683766	+	0.394772i	0.117507	+	0.993072i	$0.462510\pi$
$272$	−5.70407			−0.345860
$273$		0			0
$274$	21.8022			1.31712
$275$	−0.699399	+	0.403798i	−0.0421753	+	0.0243499i
$276$		0			0
$277$	−13.4753	+	23.3399i	−0.809652	+	1.40236i	0.103453	+	0.994634i	$0.467011\pi$
$277$	−13.4753	+	23.3399i	−0.809652	+	1.40236i	−0.913105	+	0.407724i	$0.866323\pi$
$278$		−	16.4491i		−	0.986551i
$279$		0			0
$280$	−1.89787	−	1.09573i	−0.113419	−	0.0654827i
$281$		−	0.0773961i		−	0.00461706i	−0.999997	−	0.00230853i	$-0.999265\pi$
$281$		−	0.0773961i		−	0.00461706i	0.999997	−	0.00230853i	$-0.000734829\pi$
$282$		0			0
$283$	11.1534	+	19.3183i	0.663002	+	1.14835i	0.979823	+	0.199867i	$0.0640511\pi$
$283$	11.1534	+	19.3183i	0.663002	+	1.14835i	−0.316821	+	0.948485i	$0.602616\pi$
$284$	−7.21341	+	4.16466i	−0.428037	+	0.247127i
$285$		0			0
$286$	4.72618	−	13.9684i	0.279465	−	0.825970i
$287$	−3.62683			−0.214085
$288$		0			0
$289$	−7.76822	−	13.4550i	−0.456954	−	0.791468i
$290$	10.7577	−	18.6328i	0.631712	−	1.09416i
$291$		0			0
$292$	6.38958	+	3.68903i	0.373922	+	0.215884i
$293$	−5.16126	−	2.97986i	−0.301524	−	0.174085i	0.341603	−	0.939844i	$-0.389030\pi$
$293$	−5.16126	−	2.97986i	−0.301524	−	0.174085i	−0.643127	+	0.765759i	$0.722363\pi$
$294$		0			0
$295$	−5.32391	+	9.22128i	−0.309970	+	0.536884i
$296$	−5.07736	−	8.79425i	−0.295116	−	0.511155i
$297$		0			0
$298$	−14.7828			−0.856344
$299$	−5.89243	−	6.70559i	−0.340768	−	0.387794i
$300$		0			0
$301$	−2.38624	+	1.37769i	−0.137540	+	0.0794089i
$302$	−9.49478	−	16.4454i	−0.546363	−	0.946329i
$303$		0			0
$304$		−	7.73201i		−	0.443461i
$305$	21.3865	+	12.3475i	1.22459	+	0.707015i
$306$		0			0
$307$		−	31.1089i		−	1.77548i	−0.460349	−	0.887738i	$-0.652276\pi$
$307$		−	31.1089i		−	1.77548i	0.460349	−	0.887738i	$-0.347724\pi$
$308$	−2.04495	+	3.54195i	−0.116522	+	0.201821i
$309$		0			0
$310$	−13.6553	+	7.88389i	−0.775569	+	0.447775i
$311$	−3.48435			−0.197579			−0.0987896	−	0.995108i	$-0.531497\pi$
$311$	−3.48435			−0.197579			−0.0987896	+	0.995108i	$0.531497\pi$
$312$		0			0
$313$	10.2750			0.580779			0.290389	−	0.956909i	$-0.406215\pi$
$313$	10.2750			0.580779			0.290389	+	0.956909i	$0.406215\pi$
$314$	11.7324	−	6.77371i	0.662098	−	0.382262i
$315$		0			0
$316$	1.72917	−	2.99501i	0.0972734	−	0.168483i
$317$		−	26.5282i		−	1.48997i	−0.667080	−	0.744986i	$-0.732456\pi$
$317$		−	26.5282i		−	1.48997i	0.667080	−	0.744986i	$-0.267544\pi$
$318$		0			0
$319$	−34.7740	−	20.0768i	−1.94697	−	1.12408i
$320$		−	2.19147i		−	0.122507i
$321$		0			0
$322$	1.23791	+	2.14412i	0.0689860	+	0.119487i
$323$	38.1951	−	22.0520i	2.12523	−	1.22700i
$324$		0			0
$325$	0.698140	−	0.139589i	0.0387258	−	0.00774302i
$326$	4.46294			0.247180
$327$		0			0
$328$	−1.81341	−	3.14093i	−0.100129	−	0.173429i
$329$	−3.85004	+	6.66847i	−0.212260	+	0.367645i
$330$		0			0
$331$	−24.8329	−	14.3373i	−1.36494	−	0.788048i	−0.374663	−	0.927161i	$-0.622242\pi$
$331$	−24.8329	−	14.3373i	−1.36494	−	0.788048i	−0.990277	+	0.139113i	$0.955575\pi$
$332$	−0.288199	−	0.166392i	−0.0158170	−	0.00913192i
$333$		0			0
$334$	−1.65381	+	2.86448i	−0.0904924	+	0.156737i
$335$	−6.94739	−	12.0332i	−0.379576	−	0.657445i
$336$		0			0
$337$	4.82923			0.263065			0.131532	−	0.991312i	$-0.458010\pi$
$337$	4.82923			0.263065			0.131532	+	0.991312i	$0.458010\pi$
$338$	−7.89340	+	10.3293i	−0.429345	+	0.561839i
$339$		0			0
$340$	10.8256	−	6.25015i	0.587099	−	0.338962i
$341$	14.7135	+	25.4846i	0.796783	+	1.38007i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.38624	−	1.37769i	−0.128657	−	0.0742803i
$345$		0			0
$346$		−	10.1221i		−	0.544170i
$347$	15.2594	−	26.4300i	0.819167	−	1.41884i	−0.0871296	−	0.996197i	$-0.527769\pi$
$347$	15.2594	−	26.4300i	0.819167	−	1.41884i	0.906297	−	0.422642i	$-0.138897\pi$
$348$		0			0
$349$	−4.60570	+	2.65910i	−0.246537	+	0.142338i	−0.618178	−	0.786038i	$-0.712129\pi$
$349$	−4.60570	+	2.65910i	−0.246537	+	0.142338i	0.371640	+	0.928377i	$0.378795\pi$
$350$	−0.197462			−0.0105548
$351$		0			0
$352$	−4.08989			−0.217992
$353$	24.4457	−	14.1137i	1.30111	−	0.751199i	0.320519	−	0.947242i	$-0.396143\pi$
$353$	24.4457	−	14.1137i	1.30111	−	0.751199i	0.980595	+	0.196043i	$0.0628094\pi$
$354$		0			0
$355$	9.12673	−	15.8080i	0.484397	−	0.839000i
$356$			13.5275i			0.716956i
$357$		0			0
$358$	8.01210	+	4.62579i	0.423453	+	0.244481i
$359$		−	7.58573i		−	0.400359i	−0.979759	−	0.200180i	$-0.935847\pi$
$359$		−	7.58573i		−	0.400359i	0.979759	−	0.200180i	$-0.0641526\pi$
$360$		0			0
$361$	20.3920	+	35.3200i	1.07326	+	1.85895i
$362$	−20.1476	+	11.6322i	−1.05894	+	0.611377i
$363$		0			0
$364$	2.70844	−	2.38000i	0.141961	−	0.124746i
$365$	−16.1688			−0.846313
$366$		0			0
$367$	5.92558	+	10.2634i	0.309313	+	0.535746i	0.978212	−	0.207607i	$-0.0665676\pi$
$367$	5.92558	+	10.2634i	0.309313	+	0.535746i	−0.668899	+	0.743353i	$0.733234\pi$
$368$	−1.23791	+	2.14412i	−0.0645305	+	0.111770i
$369$		0			0
$370$	19.2723	+	11.1269i	1.00192	+	0.578459i
$371$	5.46559	+	3.15556i	0.283759	+	0.163828i
$372$		0			0
$373$	14.9133	−	25.8306i	0.772182	−	1.33746i	−0.164183	−	0.986430i	$-0.552499\pi$
$373$	14.9133	−	25.8306i	0.772182	−	1.33746i	0.936365	−	0.351028i	$-0.114168\pi$
$374$	−11.6645	−	20.2035i	−0.603158	−	1.04470i
$375$		0			0
$376$	−7.70008			−0.397101
$377$	23.3662	+	26.5908i	1.20342	+	1.36949i
$378$		0			0
$379$	−1.55298	+	0.896611i	−0.0797711	+	0.0460558i	−0.539355	−	0.842079i	$-0.681332\pi$
$379$	−1.55298	+	0.896611i	−0.0797711	+	0.0460558i	0.459584	+	0.888134i	$0.347999\pi$
$380$	8.47223	+	14.6743i	0.434616	+	0.752778i
$381$		0			0
$382$		−	8.90192i		−	0.455462i
$383$	−14.4611	−	8.34912i	−0.738927	−	0.426620i	0.0827518	−	0.996570i	$-0.473629\pi$
$383$	−14.4611	−	8.34912i	−0.738927	−	0.426620i	−0.821679	+	0.569950i	$0.806962\pi$
$384$		0			0
$385$		−	8.96287i		−	0.456790i
$386$	−4.44417	+	7.69754i	−0.226203	+	0.391794i
$387$		0			0
$388$	10.0600	−	5.80816i	0.510720	−	0.294864i
$389$	−15.6288			−0.792413			−0.396207	−	0.918161i	$-0.629674\pi$
$389$	−15.6288			−0.792413			−0.396207	+	0.918161i	$0.629674\pi$
$390$		0			0
$391$	−14.1222			−0.714192
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−11.6963	+	20.2586i	−0.589251	+	1.02061i
$395$			7.57885i			0.381333i
$396$		0			0
$397$	4.86182	+	2.80697i	0.244008	+	0.140878i	0.617017	−	0.786950i	$-0.288341\pi$
$397$	4.86182	+	2.80697i	0.244008	+	0.140878i	−0.373010	+	0.927827i	$0.621674\pi$
$398$		−	3.93608i		−	0.197298i
$399$		0			0
$400$	−0.0987308	−	0.171007i	−0.00493654	−	0.00855034i
$401$	−21.8559	+	12.6185i	−1.09143	+	0.630139i	−0.933957	−	0.357384i	$-0.883669\pi$
$401$	−21.8559	+	12.6185i	−1.09143	+	0.630139i	−0.157475	+	0.987523i	$0.550335\pi$
$402$		0			0
$403$	−5.08633	−	25.4387i	−0.253368	−	1.26719i
$404$	2.25385			0.112133
$405$		0			0
$406$	−4.90888	−	8.50243i	−0.243624	−	0.421969i
$407$	20.7659	−	35.9675i	1.02933	−	1.78284i
$408$		0			0
$409$	25.0467	+	14.4607i	1.23848	+	0.715037i	0.968784	−	0.247908i	$-0.0797430\pi$
$409$	25.0467	+	14.4607i	1.23848	+	0.715037i	0.269697	+	0.962945i	$0.413076\pi$
$410$	6.88324	+	3.97404i	0.339939	+	0.196264i
$411$		0			0
$412$	−8.01627	+	13.8846i	−0.394933	+	0.684045i
$413$	2.42938	+	4.20781i	0.119542	+	0.207053i
$414$		0			0
$415$	0.729284			0.0357991
$416$	3.41535	+	1.15558i	0.167452	+	0.0566568i
$417$		0			0
$418$	27.3864	−	15.8115i	1.33951	−	0.773368i
$419$	−16.0468	−	27.7939i	−0.783938	−	1.35782i	−0.929631	−	0.368491i	$-0.879875\pi$
$419$	−16.0468	−	27.7939i	−0.783938	−	1.35782i	0.145693	−	0.989330i	$-0.453459\pi$
$420$		0			0
$421$		−	1.02963i		−	0.0501810i	−0.999685	−	0.0250905i	$-0.992013\pi$
$421$		−	1.02963i		−	0.0501810i	0.999685	−	0.0250905i	$-0.00798740\pi$
$422$	11.0869	+	6.40104i	0.539703	+	0.311598i
$423$		0			0
$424$			6.31111i			0.306495i
$425$	0.563168	−	0.975435i	0.0273176	−	0.0473155i
$426$		0			0
$427$	9.75896	−	5.63434i	0.472269	−	0.272665i
$428$	8.61586			0.416464
$429$		0			0
$430$	6.03835			0.291195
$431$	30.5908	−	17.6616i	1.47350	−	0.850728i	0.473950	−	0.880552i	$-0.342828\pi$
$431$	30.5908	−	17.6616i	1.47350	−	0.850728i	0.999555	+	0.0298236i	$0.00949455\pi$
$432$		0			0
$433$	10.0469	−	17.4018i	0.482824	−	0.836276i	−0.516981	−	0.855997i	$-0.672944\pi$
$433$	10.0469	−	17.4018i	0.482824	−	0.836276i	0.999806	+	0.0197204i	$0.00627760\pi$
$434$			7.19507i			0.345375i
$435$		0			0
$436$	8.68777	+	5.01589i	0.416069	+	0.240217i
$437$		−	19.1431i		−	0.915736i
$438$		0			0
$439$	6.52940	+	11.3093i	0.311631	+	0.539761i	0.978716	−	0.205221i	$-0.0657913\pi$
$439$	6.52940	+	11.3093i	0.311631	+	0.539761i	−0.667084	+	0.744982i	$0.732458\pi$
$440$	7.76207	−	4.48144i	0.370042	−	0.213644i
$441$		0			0
$442$	4.03232	+	20.1672i	0.191798	+	0.959254i
$443$	−7.46148			−0.354506			−0.177253	−	0.984165i	$-0.556721\pi$
$443$	−7.46148			−0.354506			−0.177253	+	0.984165i	$0.556721\pi$
$444$		0			0
$445$	−14.8225	−	25.6734i	−0.702656	−	1.21704i
$446$	−9.42444	+	16.3236i	−0.446260	+	0.772945i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	8.28796	+	4.78506i	0.391133	+	0.225821i	0.682651	−	0.730745i	$-0.260827\pi$
$449$	8.28796	+	4.78506i	0.391133	+	0.225821i	−0.291518	+	0.956565i	$0.594160\pi$
$450$		0			0
$451$	7.41667	−	12.8460i	0.349237	−	0.604897i
$452$	−9.27760	−	16.0693i	−0.436382	−	0.755835i
$453$		0			0
$454$	−1.31920			−0.0619130
$455$	−2.53241	+	7.48464i	−0.118721	+	0.350886i
$456$		0			0
$457$	22.3679	−	12.9141i	1.04633	−	0.604097i	0.124708	−	0.992194i	$-0.460201\pi$
$457$	22.3679	−	12.9141i	1.04633	−	0.604097i	0.921619	+	0.388097i	$0.126867\pi$
$458$	2.17054	+	3.75949i	0.101423	+	0.175670i
$459$		0			0
$460$		−	5.42568i		−	0.252974i
$461$	1.35535	+	0.782512i	0.0631250	+	0.0364452i	0.531230	−	0.847227i	$-0.321730\pi$
$461$	1.35535	+	0.782512i	0.0631250	+	0.0364452i	−0.468105	+	0.883673i	$0.655063\pi$
$462$		0			0
$463$		−	20.4863i		−	0.952080i	−0.879424	−	0.476040i	$-0.842072\pi$
$463$		−	20.4863i		−	0.952080i	0.879424	−	0.476040i	$-0.157928\pi$
$464$	4.90888	−	8.50243i	0.227889	−	0.394716i
$465$		0			0
$466$	−4.99196	+	2.88211i	−0.231248	+	0.133511i
$467$	3.80822			0.176224			0.0881118	−	0.996111i	$-0.471917\pi$
$467$	3.80822			0.176224			0.0881118	+	0.996111i	$0.471917\pi$
$468$		0			0
$469$	−6.34039			−0.292772
$470$	14.6137	−	8.43725i	0.674082	−	0.389181i
$471$		0			0
$472$	−2.42938	+	4.20781i	−0.111821	+	0.193680i
$473$		−	11.2692i		−	0.518160i
$474$		0			0
$475$	1.32223	+	0.763388i	0.0606679	+	0.0350266i
$476$		−	5.70407i		−	0.261446i
$477$		0			0
$478$	6.54753	+	11.3407i	0.299477	+	0.518710i
$479$	20.8886	−	12.0600i	0.954425	−	0.551037i	0.0599720	−	0.998200i	$-0.480899\pi$
$479$	20.8886	−	12.0600i	0.954425	−	0.551037i	0.894453	+	0.447163i	$0.147566\pi$
$480$		0			0
$481$	−27.5034	+	24.1682i	−1.25405	+	1.10197i
$482$	0.450067			0.0205000
$483$		0			0
$484$	−2.86360	−	4.95991i	−0.130164	−	0.225450i
$485$	−12.7284	+	22.0462i	−0.577967	+	1.00107i
$486$		0			0
$487$	−6.65422	−	3.84182i	−0.301532	−	0.174089i	0.341599	−	0.939846i	$-0.389031\pi$
$487$	−6.65422	−	3.84182i	−0.301532	−	0.174089i	−0.643131	+	0.765756i	$0.722365\pi$
$488$	9.75896	+	5.63434i	0.441767	+	0.255054i
$489$		0			0
$490$	1.09573	−	1.89787i	0.0495002	−	0.0857369i
$491$	−16.2767	−	28.1921i	−0.734557	−	1.27229i	−0.954917	−	0.296872i	$-0.904056\pi$
$491$	−16.2767	−	28.1921i	−0.734557	−	1.27229i	0.220360	−	0.975419i	$-0.429277\pi$
$492$		0			0
$493$	56.0012			2.52217
$494$	−27.3371	+	5.46590i	−1.22995	+	0.245923i
$495$		0			0
$496$	−6.23112	+	3.59754i	−0.279785	+	0.161534i
$497$	−4.16466	−	7.21341i	−0.186811	−	0.323566i
$498$		0			0
$499$		−	5.87524i		−	0.263012i	−0.991315	−	0.131506i	$-0.958019\pi$
$499$		−	5.87524i		−	0.263012i	0.991315	−	0.131506i	$-0.0419813\pi$
$500$	9.86410	+	5.69504i	0.441136	+	0.254690i
$501$		0			0
$502$		−	18.7022i		−	0.834721i
$503$	11.0238	−	19.0939i	0.491529	−	0.851353i	−0.508424	−	0.861107i	$-0.669772\pi$
$503$	11.0238	−	19.0939i	0.491529	−	0.851353i	0.999952	+	0.00975426i	$0.00310493\pi$
$504$		0			0
$505$	−4.27750	+	2.46962i	−0.190346	+	0.109897i
$506$	−10.1258			−0.450148
$507$		0			0
$508$	−0.264877			−0.0117520
$509$	5.86940	−	3.38870i	0.260156	−	0.150201i	−0.364249	−	0.931301i	$-0.618674\pi$
$509$	5.86940	−	3.38870i	0.260156	−	0.150201i	0.624406	+	0.781100i	$0.285341\pi$
$510$		0			0
$511$	−3.68903	+	6.38958i	−0.163193	+	0.282658i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	17.1287	+	9.88929i	0.755517	+	0.436198i
$515$		−	35.1348i		−	1.54823i
$516$		0			0
$517$	−15.7463	−	27.2733i	−0.692519	−	1.19948i
$518$	8.79425	−	5.07736i	0.386397	−	0.223086i
$519$		0			0
$520$	−7.74810	+	1.54919i	−0.339777	+	0.0679365i
$521$	2.61232			0.114448			0.0572240	−	0.998361i	$-0.481775\pi$
$521$	2.61232			0.114448			0.0572240	+	0.998361i	$0.481775\pi$
$522$		0			0
$523$	−4.02060	−	6.96388i	−0.175809	−	0.304509i	0.764632	−	0.644467i	$-0.222921\pi$
$523$	−4.02060	−	6.96388i	−0.175809	−	0.304509i	−0.940441	+	0.339957i	$0.889587\pi$
$524$	2.55119	−	4.41878i	0.111449	−	0.193035i
$525$		0			0
$526$	−20.3903	−	11.7723i	−0.889059	−	0.513299i
$527$	−35.5427	−	20.5206i	−1.54827	−	0.893892i
$528$		0			0
$529$	8.43516	−	14.6101i	0.366746	−	0.635223i
$530$	−6.91531	−	11.9777i	−0.300382	−	0.520276i
$531$		0			0
$532$	7.73201			0.335225
$533$	−9.82303	+	8.63184i	−0.425483	+	0.373886i
$534$		0			0
$535$	−16.3518	+	9.44070i	−0.706949	+	0.408157i
$536$	−3.17020	−	5.49094i	−0.136932	−	0.237172i
$537$		0			0
$538$			22.8431i			0.984836i
$539$	−3.54195	−	2.04495i	−0.152563	−	0.0880820i
$540$		0			0
$541$			21.6552i			0.931029i	0.885040	+	0.465514i	$0.154131\pi$
$541$			21.6552i			0.931029i	−0.885040	+	0.465514i	$0.845869\pi$
$542$	6.49877	−	11.2562i	0.279146	−	0.483495i
$543$		0			0
$544$	4.93987	−	2.85204i	0.211795	−	0.122280i
$545$	−21.9843			−0.941705
$546$		0			0
$547$	−32.9495			−1.40882			−0.704409	−	0.709795i	$-0.748788\pi$
$547$	−32.9495			−1.40882			−0.704409	+	0.709795i	$0.748788\pi$
$548$	−18.8812	+	10.9011i	−0.806566	+	0.465671i
$549$		0			0
$550$	0.403798	−	0.699399i	0.0172180	−	0.0298225i
$551$			75.9111i			3.23392i
$552$		0			0
$553$	2.99501	+	1.72917i	0.127361	+	0.0735318i
$554$		−	26.9506i		−	1.14502i
$555$		0			0
$556$	8.22455	+	14.2453i	0.348799	+	0.604137i
$557$	0.280535	−	0.161967i	0.0118866	−	0.00686276i	−0.494045	−	0.869436i	$-0.664482\pi$
$557$	0.280535	−	0.161967i	0.0118866	−	0.00686276i	0.505932	+	0.862574i	$0.331149\pi$
$558$		0			0
$559$	−3.18406	+	9.41062i	−0.134671	+	0.398027i
$560$	2.19147			0.0926065
$561$		0			0
$562$	0.0386980	+	0.0670270i	0.00163238	+	0.00282736i
$563$	−18.3668	+	31.8123i	−0.774070	+	1.34073i	0.161245	+	0.986914i	$0.448449\pi$
$563$	−18.3668	+	31.8123i	−0.774070	+	1.34073i	−0.935316	+	0.353815i	$0.884884\pi$
$564$		0			0
$565$	35.2153	+	20.3316i	1.48152	+	0.855356i
$566$	−19.3183	−	11.1534i	−0.812008	−	0.468813i
$567$		0			0
$568$	4.16466	−	7.21341i	0.174745	−	0.302668i
$569$	1.32995	+	2.30354i	0.0557544	+	0.0965695i	0.892556	−	0.450937i	$-0.148910\pi$
$569$	1.32995	+	2.30354i	0.0557544	+	0.0965695i	−0.836801	+	0.547507i	$0.815577\pi$
$570$		0			0
$571$	4.29994			0.179947			0.0899735	−	0.995944i	$-0.471322\pi$
$571$	4.29994			0.179947			0.0899735	+	0.995944i	$0.471322\pi$
$572$	2.89122	+	14.4601i	0.120888	+	0.604607i
$573$		0			0
$574$	3.14093	−	1.81341i	0.131100	−	0.0756905i
$575$	−0.244439	−	0.423381i	−0.0101938	−	0.0176562i
$576$		0			0
$577$			2.08429i			0.0867702i	0.999058	+	0.0433851i	$0.0138142\pi$
$577$			2.08429i			0.0867702i	−0.999058	+	0.0433851i	$0.986186\pi$
$578$	13.4550	+	7.76822i	0.559652	+	0.323115i
$579$		0			0
$580$			21.5153i			0.893375i
$581$	0.166392	−	0.288199i	0.00690308	−	0.0119565i
$582$		0			0
$583$	−22.3536	+	12.9059i	−0.925793	+	0.534507i
$584$	−7.37805			−0.305306
$585$		0			0
$586$	5.95971			0.246193
$587$	−12.9028	+	7.44945i	−0.532556	+	0.307472i	−0.742057	−	0.670337i	$-0.766150\pi$
$587$	−12.9028	+	7.44945i	−0.532556	+	0.307472i	0.209500	+	0.977809i	$0.432816\pi$
$588$		0			0
$589$	27.8162	−	48.1791i	1.14615	−	1.98518i
$590$		−	10.6478i		−	0.438364i
$591$		0			0
$592$	8.79425	+	5.07736i	0.361441	+	0.208678i
$593$			1.36361i			0.0559968i	0.999608	+	0.0279984i	$0.00891334\pi$
$593$			1.36361i			0.0559968i	−0.999608	+	0.0279984i	$0.991087\pi$
$594$		0			0
$595$	6.25015	+	10.8256i	0.256231	+	0.443805i
$596$	12.8023	−	7.39139i	0.524401	−	0.302763i
$597$		0			0
$598$	8.45579	+	2.86100i	0.345783	+	0.116995i
$599$	−18.0030			−0.735581			−0.367790	−	0.929909i	$-0.619886\pi$
$599$	−18.0030			−0.735581			−0.367790	+	0.929909i	$0.619886\pi$
$600$		0			0
$601$	6.76892	+	11.7241i	0.276110	+	0.478237i	0.970415	−	0.241445i	$-0.0776213\pi$
$601$	6.76892	+	11.7241i	0.276110	+	0.478237i	−0.694305	+	0.719681i	$0.744288\pi$
$602$	1.37769	−	2.38624i	0.0561506	−	0.0972557i
$603$		0			0
$604$	16.4454	+	9.49478i	0.669155	+	0.386337i
$605$	10.8695	+	6.27550i	0.441907	+	0.255135i
$606$		0			0
$607$	1.10556	−	1.91489i	0.0448733	−	0.0777228i	−0.842716	−	0.538358i	$-0.819045\pi$
$607$	1.10556	−	1.91489i	0.0448733	−	0.0777228i	0.887590	+	0.460635i	$0.152378\pi$
$608$	3.86601	+	6.69612i	0.156787	+	0.271563i
$609$		0			0
$610$	−24.6950			−0.999870
$611$	5.44333	+	27.2242i	0.220214	+	1.10137i
$612$		0			0
$613$	22.5849	−	13.0394i	0.912195	−	0.526656i	0.0310579	−	0.999518i	$-0.490112\pi$
$613$	22.5849	−	13.0394i	0.912195	−	0.526656i	0.881137	+	0.472862i	$0.156779\pi$
$614$	15.5544	+	26.9411i	0.627726	+	1.08725i
$615$		0			0
$616$		−	4.08989i		−	0.164786i
$617$	24.5921	+	14.1983i	0.990042	+	0.571601i	0.905287	−	0.424801i	$-0.139656\pi$
$617$	24.5921	+	14.1983i	0.990042	+	0.571601i	0.0847549	+	0.996402i	$0.472989\pi$
$618$		0			0
$619$		−	14.7197i		−	0.591633i	−0.955245	−	0.295817i	$-0.904408\pi$
$619$		−	14.7197i		−	0.591633i	0.955245	−	0.295817i	$-0.0955918\pi$
$620$	7.88389	−	13.6553i	0.316625	−	0.548410i
$621$		0			0
$622$	3.01753	−	1.74217i	0.120992	−	0.0698548i
$623$	−13.5275			−0.541967
$624$		0			0
$625$	−23.9737			−0.958948
$626$	−8.89843	+	5.13751i	−0.355653	+	0.205336i
$627$		0			0
$628$	−6.77371	+	11.7324i	−0.270300	+	0.468174i
$629$			57.9233i			2.30955i
$630$		0			0
$631$	−24.3684	−	14.0691i	−0.970090	−	0.560082i	−0.0708262	−	0.997489i	$-0.522564\pi$
$631$	−24.3684	−	14.0691i	−0.970090	−	0.560082i	−0.899264	+	0.437407i	$0.855897\pi$
$632$			3.45834i			0.137565i
$633$		0			0
$634$	13.2641	+	22.9741i	0.526785	+	0.912418i
$635$	0.502702	−	0.290235i	0.0199491	−	0.0115176i
$636$		0			0
$637$	2.38000	+	2.70844i	0.0942988	+	0.107312i
$638$	40.1536			1.58970
$639$		0			0
$640$	1.09573	+	1.89787i	0.0433127	+	0.0750198i
$641$	−3.89572	+	6.74758i	−0.153872	+	0.266513i	−0.932648	−	0.360789i	$-0.882508\pi$
$641$	−3.89572	+	6.74758i	−0.153872	+	0.266513i	0.778776	+	0.627302i	$0.215841\pi$
$642$		0			0
$643$	−29.3656	−	16.9542i	−1.15807	−	0.668610i	−0.207227	−	0.978293i	$-0.566444\pi$
$643$	−29.3656	−	16.9542i	−1.15807	−	0.668610i	−0.950840	+	0.309683i	$0.899777\pi$
$644$	−2.14412	−	1.23791i	−0.0844902	−	0.0487804i
$645$		0			0
$646$	−22.0520	+	38.1951i	−0.867624	+	1.50277i
$647$	−2.20290	−	3.81554i	−0.0866050	−	0.150004i	0.819469	−	0.573123i	$-0.194268\pi$
$647$	−2.20290	−	3.81554i	−0.0866050	−	0.150004i	−0.906074	+	0.423119i	$0.860935\pi$
$648$		0			0
$649$	−19.8718			−0.780036
$650$	−0.534812	+	0.469958i	−0.0209771	+	0.0184333i
$651$		0			0
$652$	−3.86502	+	2.23147i	−0.151366	+	0.0873912i
$653$	13.8081	+	23.9163i	0.540352	+	0.935916i	0.998884	+	0.0472385i	$0.0150421\pi$
$653$	13.8081	+	23.9163i	0.540352	+	0.935916i	−0.458532	+	0.888678i	$0.651625\pi$
$654$		0			0
$655$			11.1817i			0.436905i
$656$	3.14093	+	1.81341i	0.122633	+	0.0708019i
$657$		0			0
$658$		−	7.70008i		−	0.300181i
$659$	3.72022	−	6.44362i	0.144919	−	0.251008i	−0.784423	−	0.620226i	$-0.787041\pi$
$659$	3.72022	−	6.44362i	0.144919	−	0.251008i	0.929343	+	0.369218i	$0.120374\pi$
$660$		0			0
$661$	1.02781	−	0.593407i	0.0399772	−	0.0230809i	−0.479878	−	0.877335i	$-0.659319\pi$
$661$	1.02781	−	0.593407i	0.0399772	−	0.0230809i	0.519855	+	0.854254i	$0.325986\pi$
$662$	28.6746			1.11447
$663$		0			0
$664$	0.332783			0.0129145
$665$	−14.6743	+	8.47223i	−0.569047	+	0.328539i
$666$		0			0
$667$	12.1535	−	21.0505i	0.470585	−	0.815077i
$668$		−	3.30762i		−	0.127976i
$669$		0			0
$670$	12.0332	+	6.94739i	0.464884	+	0.268401i
$671$			46.0876i			1.77919i
$672$		0			0
$673$	−1.14981	−	1.99153i	−0.0443219	−	0.0767678i	0.843013	−	0.537893i	$-0.180779\pi$
$673$	−1.14981	−	1.99153i	−0.0443219	−	0.0767678i	−0.887335	+	0.461125i	$0.847446\pi$
$674$	−4.18223	+	2.41461i	−0.161094	+	0.0930074i
$675$		0			0
$676$	1.67124	−	12.8921i	0.0642786	−	0.495851i
$677$	−6.12752			−0.235500			−0.117750	−	0.993043i	$-0.537568\pi$
$677$	−6.12752			−0.235500			−0.117750	+	0.993043i	$0.537568\pi$
$678$		0			0
$679$	5.80816	+	10.0600i	0.222897	+	0.386068i
$680$	−6.25015	+	10.8256i	−0.239682	+	0.415142i
$681$		0			0
$682$	−25.4846	−	14.7135i	−0.975855	−	0.563410i
$683$	8.69462	+	5.01984i	0.332691	+	0.192079i	0.657035	−	0.753860i	$-0.271810\pi$
$683$	8.69462	+	5.01984i	0.332691	+	0.192079i	−0.324344	+	0.945939i	$0.605144\pi$
$684$		0			0
$685$	23.8894	−	41.3776i	0.912766	−	1.58096i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	2.75539			0.105048
$689$	22.3134	−	4.46144i	0.850073	−	0.169967i
$690$		0			0
$691$	−19.2007	+	11.0855i	−0.730428	+	0.421713i	−0.818579	−	0.574394i	$-0.805238\pi$
$691$	−19.2007	+	11.0855i	−0.730428	+	0.421713i	0.0881509	+	0.996107i	$0.471904\pi$
$692$	5.06107	+	8.76603i	0.192393	+	0.333235i
$693$		0			0
$694$			30.5188i			1.15848i
$695$	−31.2182	−	18.0238i	−1.18417	−	0.683684i
$696$		0			0
$697$			20.6877i			0.783602i
$698$	2.65910	−	4.60570i	0.100648	−	0.174328i
$699$		0			0
$700$	0.171007	−	0.0987308i	0.00646345	−	0.00373167i
$701$	−21.3510			−0.806416			−0.403208	−	0.915108i	$-0.632105\pi$
$701$	−21.3510			−0.806416			−0.403208	+	0.915108i	$0.632105\pi$
$702$		0			0
$703$	−78.5165			−2.96130
$704$	3.54195	−	2.04495i	0.133492	−	0.0770718i
$705$		0			0
$706$	−14.1137	+	24.4457i	−0.531178	+	0.920027i
$707$			2.25385i			0.0847646i
$708$		0			0
$709$	21.5442	+	12.4385i	0.809109	+	0.467139i	0.846646	−	0.532156i	$-0.178618\pi$
$709$	21.5442	+	12.4385i	0.809109	+	0.467139i	−0.0375376	+	0.999295i	$0.511951\pi$
$710$			18.2535i			0.685040i
$711$		0			0
$712$	−6.76374	−	11.7151i	−0.253482	−	0.439044i
$713$	−15.4271	+	8.90685i	−0.577750	+	0.333564i
$714$		0			0
$715$	−21.3316	−	24.2754i	−0.797756	−	0.907847i
$716$	−9.25158			−0.345748
$717$		0			0
$718$	3.79286	+	6.56943i	0.141548	+	0.245169i
$719$	−11.5010	+	19.9203i	−0.428914	+	0.742901i	−0.996777	−	0.0802222i	$-0.974437\pi$
$719$	−11.5010	+	19.9203i	−0.428914	+	0.742901i	0.567863	+	0.823123i	$0.307770\pi$
$720$		0			0
$721$	−13.8846	−	8.01627i	−0.517089	−	0.298542i
$722$	−35.3200	−	20.3920i	−1.31447	−	0.758912i
$723$		0			0
$724$	11.6322	−	20.1476i	0.432309	−	0.748781i
$725$	0.969316	+	1.67890i	0.0359995	+	0.0623529i
$726$		0			0
$727$	−3.42508			−0.127029			−0.0635146	−	0.997981i	$-0.520231\pi$
$727$	−3.42508			−0.127029			−0.0635146	+	0.997981i	$0.520231\pi$
$728$	−1.15558	+	3.41535i	−0.0428285	+	0.126581i
$729$		0			0
$730$	14.0026	−	8.08439i	0.518258	−	0.299217i
$731$	7.85846	+	13.6113i	0.290656	+	0.503431i
$732$		0			0
$733$		−	21.6929i		−	0.801247i	−0.916243	−	0.400624i	$-0.868794\pi$
$733$		−	21.6929i		−	0.801247i	0.916243	−	0.400624i	$-0.131206\pi$
$734$	−10.2634	−	5.92558i	−0.378829	−	0.218717i
$735$		0			0
$736$		−	2.47582i		−	0.0912598i
$737$	12.9658	−	22.4573i	0.477600	−	0.827227i
$738$		0			0
$739$	−44.6284	+	25.7662i	−1.64168	+	0.947826i	−0.661447	+	0.749992i	$0.730057\pi$
$739$	−44.6284	+	25.7662i	−1.64168	+	0.947826i	−0.980236	+	0.197833i	$0.936610\pi$
$740$	−22.2538			−0.818065
$741$		0			0
$742$	−6.31111			−0.231688
$743$	41.6540	−	24.0489i	1.52814	−	0.882270i	0.528697	−	0.848811i	$-0.322681\pi$
$743$	41.6540	−	24.0489i	1.52814	−	0.882270i	0.999440	−	0.0334593i	$-0.0106524\pi$
$744$		0			0
$745$	−16.1980	+	28.0558i	−0.593449	+	1.02788i
$746$			29.8266i			1.09203i
$747$		0			0
$748$	20.2035	+	11.6645i	0.738714	+	0.426497i
$749$			8.61586i			0.314817i
$750$		0			0
$751$	−14.7133	−	25.4842i	−0.536896	−	0.929931i	−0.999069	−	0.0431415i	$-0.986263\pi$
$751$	−14.7133	−	25.4842i	−0.536896	−	0.929931i	0.462173	−	0.886790i	$-0.347070\pi$
$752$	6.66847	−	3.85004i	0.243174	−	0.140397i
$753$		0			0
$754$	−33.5311	−	11.3452i	−1.22113	−	0.413167i
$755$	−41.6150			−1.51453
$756$		0			0
$757$	10.0541	+	17.4142i	0.365423	+	0.632931i	0.988844	−	0.148955i	$-0.0475911\pi$
$757$	10.0541	+	17.4142i	0.365423	+	0.632931i	−0.623421	+	0.781886i	$0.714258\pi$
$758$	0.896611	−	1.55298i	0.0325664	−	0.0564067i
$759$		0			0
$760$	−14.6743	−	8.47223i	−0.532294	−	0.307320i
$761$	−28.0939	−	16.2200i	−1.01840	−	0.587976i	−0.104763	−	0.994497i	$-0.533409\pi$
$761$	−28.0939	−	16.2200i	−1.01840	−	0.587976i	−0.913642	+	0.406521i	$0.866742\pi$
$762$		0			0
$763$	−5.01589	+	8.68777i	−0.181587	+	0.314518i
$764$	4.45096	+	7.70929i	0.161030	+	0.278912i
$765$		0			0
$766$	16.6982			0.603332
$767$	16.5944	+	5.61466i	0.599188	+	0.202734i
$768$		0			0
$769$	−37.1542	+	21.4510i	−1.33982	+	0.773543i	−0.986780	−	0.162067i	$-0.948184\pi$
$769$	−37.1542	+	21.4510i	−1.33982	+	0.773543i	−0.353036	+	0.935610i	$0.614851\pi$
$770$	4.48144	+	7.76207i	0.161500	+	0.279726i
$771$		0			0
$772$		−	8.88835i		−	0.319899i
$773$	−12.8157	−	7.39912i	−0.460947	−	0.266128i	0.251495	−	0.967858i	$-0.419078\pi$
$773$	−12.8157	−	7.39912i	−0.460947	−	0.266128i	−0.712442	+	0.701731i	$0.752411\pi$
$774$		0			0
$775$		−	1.42075i		−	0.0510349i
$776$	−5.80816	+	10.0600i	−0.208501	+	0.361134i
$777$		0			0
$778$	13.5350	−	7.81441i	0.485252	−	0.280160i
$779$	−28.0427			−1.00473
$780$		0			0
$781$	34.0660			1.21898
$782$	12.2302	−	7.06112i	0.437352	−	0.252505i
$783$

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.19147i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.19147i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-1.09573 - 1.89787i) q^{10} +(-3.54195 + 2.04495i) q^{11} +(3.53557 - 0.706919i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.85204 - 4.93987i) q^{17} +(6.69612 + 3.86601i) q^{19} +(1.89787 + 1.09573i) q^{20} +(2.04495 - 3.54195i) q^{22} +(-1.23791 - 2.14412i) q^{23} +0.197462 q^{25} +(-2.70844 + 2.38000i) q^{26} +(0.866025 - 0.500000i) q^{28} +(4.90888 + 8.50243i) q^{29} -7.19507i q^{31} +(0.866025 + 0.500000i) q^{32} +5.70407i q^{34} +(-1.09573 + 1.89787i) q^{35} +(-8.79425 + 5.07736i) q^{37} -7.73201 q^{38} -2.19147 q^{40} +(-3.14093 + 1.81341i) q^{41} +(-1.37769 + 2.38624i) q^{43} +4.08989i q^{44} +(2.14412 + 1.23791i) q^{46} +7.70008i q^{47} +(0.500000 + 0.866025i) q^{49} +(-0.171007 + 0.0987308i) q^{50} +(1.15558 - 3.41535i) q^{52} +6.31111 q^{53} +(-4.48144 - 7.76207i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-8.50243 - 4.90888i) q^{58} +(4.20781 + 2.42938i) q^{59} +(5.63434 - 9.75896i) q^{61} +(3.59754 + 6.23112i) q^{62} -1.00000 q^{64} +(1.54919 + 7.74810i) q^{65} +(-5.49094 + 3.17020i) q^{67} +(-2.85204 - 4.93987i) q^{68} -2.19147i q^{70} +(-7.21341 - 4.16466i) q^{71} +7.37805i q^{73} +(5.07736 - 8.79425i) q^{74} +(6.69612 - 3.86601i) q^{76} -4.08989 q^{77} +3.45834 q^{79} +(1.89787 - 1.09573i) q^{80} +(1.81341 - 3.14093i) q^{82} -0.332783i q^{83} +(10.8256 + 6.25015i) q^{85} -2.75539i q^{86} +(-2.04495 - 3.54195i) q^{88} +(-11.7151 + 6.76374i) q^{89} +(3.41535 + 1.15558i) q^{91} -2.47582 q^{92} +(-3.85004 - 6.66847i) q^{94} +(-8.47223 + 14.6743i) q^{95} +(10.0600 + 5.80816i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} - 24 q^{50} - 4 q^{52} - 40 q^{53} + 20 q^{55} - 8 q^{56} + 6 q^{58} + 6 q^{59} - 2 q^{61} - 14 q^{62} - 16 q^{64} - 52 q^{65} - 30 q^{67} + 6 q^{68} + 12 q^{71} + 24 q^{74} + 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} + 30 q^{89} + 4 q^{91} - 24 q^{92} - 8 q^{94} - 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

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