LMFDB - Embedded newform 1638.2.bj.h.127.3

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			127.3
Root			$2.24849 - 2.24849i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.h.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.623842 - 1.08053i) q^{10} +(1.41441 - 0.816612i) q^{11} +(3.60364 + 0.117447i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78174 + 4.81811i) q^{17} +(-4.23947 - 2.44766i) q^{19} +(1.08053 + 0.623842i) q^{20} +(-0.816612 + 1.41441i) q^{22} +(2.83571 + 4.91159i) q^{23} +3.44329 q^{25} +(-3.17957 + 1.70011i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.59985 - 2.77102i) q^{29} +3.53063i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56348i q^{34} +(-0.623842 + 1.08053i) q^{35} +(6.12562 - 3.53663i) q^{37} +4.89532 q^{38} -1.24768 q^{40} +(3.46229 - 1.99895i) q^{41} +(2.69078 - 4.66057i) q^{43} -1.63322i q^{44} +(-4.91159 - 2.83571i) q^{46} +11.4980i q^{47} +(0.500000 + 0.866025i) q^{49} +(-2.98197 + 1.72164i) q^{50} +(1.90353 - 3.06212i) q^{52} -4.82030 q^{53} +(1.01887 + 1.76474i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(2.77102 + 1.59985i) q^{58} +(-4.48259 - 2.58803i) q^{59} +(-2.97263 + 5.14874i) q^{61} +(-1.76532 - 3.05762i) q^{62} -1.00000 q^{64} +(-0.146537 + 4.49620i) q^{65} +(-5.48962 + 3.16943i) q^{67} +(2.78174 + 4.81811i) q^{68} -1.24768i q^{70} +(11.3538 + 6.55514i) q^{71} -6.62310i q^{73} +(-3.53663 + 6.12562i) q^{74} +(-4.23947 + 2.44766i) q^{76} +1.63322 q^{77} -8.21115 q^{79} +(1.08053 - 0.623842i) q^{80} +(-1.99895 + 3.46229i) q^{82} +11.1721i q^{83} +(-6.01148 - 3.47073i) q^{85} +5.38157i q^{86} +(0.816612 + 1.41441i) q^{88} +(2.16375 - 1.24924i) q^{89} +(3.06212 + 1.90353i) q^{91} +5.67142 q^{92} +(-5.74902 - 9.95759i) q^{94} +(3.05390 - 5.28951i) q^{95} +(9.02271 + 5.20926i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$			1.24768i			0.557981i	0.960294	+	0.278991i	$0.0899998\pi$
$5$			1.24768i			0.557981i	−0.960294	+	0.278991i	$0.910000\pi$
$6$		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
$10$	−0.623842	−	1.08053i	−0.197276	−	0.341692i
$11$	1.41441	−	0.816612i	0.426461	−	0.246218i	−0.271377	−	0.962473i	$-0.587479\pi$
$11$	1.41441	−	0.816612i	0.426461	−	0.246218i	0.697838	+	0.716256i	$0.254146\pi$
$12$		0			0
$13$	3.60364	+	0.117447i	0.999469	+	0.0325741i
$13$	3.60364	+	0.117447i	0.999469	+	0.0325741i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.78174	+	4.81811i	−0.674671	+	1.16856i	0.301894	+	0.953341i	$0.402381\pi$
$17$	−2.78174	+	4.81811i	−0.674671	+	1.16856i	−0.976565	+	0.215223i	$0.930952\pi$
$18$		0			0
$19$	−4.23947	−	2.44766i	−0.972601	−	0.561531i	−0.0725725	−	0.997363i	$-0.523121\pi$
$19$	−4.23947	−	2.44766i	−0.972601	−	0.561531i	−0.900028	+	0.435832i	$0.856454\pi$
$20$	1.08053	+	0.623842i	0.241613	+	0.139495i
$21$		0			0
$22$	−0.816612	+	1.41441i	−0.174102	+	0.301554i
$23$	2.83571	+	4.91159i	0.591286	+	1.02414i	0.994059	+	0.108838i	$0.0347131\pi$
$23$	2.83571	+	4.91159i	0.591286	+	1.02414i	−0.402773	+	0.915300i	$0.631954\pi$
$24$		0			0
$25$	3.44329			0.688657
$26$	−3.17957	+	1.70011i	−0.623564	+	0.333418i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−1.59985	−	2.77102i	−0.297085	−	0.514566i	0.678383	−	0.734708i	$-0.262681\pi$
$29$	−1.59985	−	2.77102i	−0.297085	−	0.514566i	−0.975468	+	0.220143i	$0.929348\pi$
$30$		0			0
$31$			3.53063i			0.634121i	0.948405	+	0.317060i	$0.102696\pi$
$31$			3.53063i			0.634121i	−0.948405	+	0.317060i	$0.897304\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	5.56348i		−	0.954129i
$35$	−0.623842	+	1.08053i	−0.105449	+	0.182642i
$36$		0			0
$37$	6.12562	−	3.53663i	1.00705	−	0.581418i	0.0967201	−	0.995312i	$-0.469165\pi$
$37$	6.12562	−	3.53663i	1.00705	−	0.581418i	0.910325	+	0.413894i	$0.135832\pi$
$38$	4.89532			0.794125
$39$		0			0
$40$	−1.24768			−0.197276
$41$	3.46229	−	1.99895i	0.540718	−	0.312184i	−0.204652	−	0.978835i	$-0.565606\pi$
$41$	3.46229	−	1.99895i	0.540718	−	0.312184i	0.745370	+	0.666651i	$0.232273\pi$
$42$		0			0
$43$	2.69078	−	4.66057i	0.410341	−	0.710731i	−0.584586	−	0.811332i	$-0.698743\pi$
$43$	2.69078	−	4.66057i	0.410341	−	0.710731i	0.994927	+	0.100601i	$0.0320765\pi$
$44$		−	1.63322i		−	0.246218i
$45$		0			0
$46$	−4.91159	−	2.83571i	−0.724175	−	0.418103i
$47$			11.4980i			1.67716i	0.544778	+	0.838580i	$0.316614\pi$
$47$			11.4980i			1.67716i	−0.544778	+	0.838580i	$0.683386\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−2.98197	+	1.72164i	−0.421715	+	0.243477i
$51$		0			0
$52$	1.90353	−	3.06212i	0.263972	−	0.424639i
$53$	−4.82030			−0.662120			−0.331060	−	0.943610i	$-0.607406\pi$
$53$	−4.82030			−0.662120			−0.331060	+	0.943610i	$0.607406\pi$
$54$		0			0
$55$	1.01887	+	1.76474i	0.137385	+	0.237957i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	2.77102	+	1.59985i	0.363853	+	0.210071i
$59$	−4.48259	−	2.58803i	−0.583584	−	0.336932i	0.178972	−	0.983854i	$-0.442723\pi$
$59$	−4.48259	−	2.58803i	−0.583584	−	0.336932i	−0.762556	+	0.646922i	$0.776056\pi$
$60$		0			0
$61$	−2.97263	+	5.14874i	−0.380606	+	0.659229i	−0.991149	−	0.132754i	$-0.957618\pi$
$61$	−2.97263	+	5.14874i	−0.380606	+	0.659229i	0.610543	+	0.791983i	$0.290951\pi$
$62$	−1.76532	−	3.05762i	−0.224196	−	0.388318i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.146537	+	4.49620i	−0.0181757	+	0.557685i
$66$		0			0
$67$	−5.48962	+	3.16943i	−0.670664	+	0.387208i	−0.796328	−	0.604865i	$-0.793227\pi$
$67$	−5.48962	+	3.16943i	−0.670664	+	0.387208i	0.125664	+	0.992073i	$0.459894\pi$
$68$	2.78174	+	4.81811i	0.337335	+	0.584282i
$69$		0			0
$70$		−	1.24768i		−	0.149127i
$71$	11.3538	+	6.55514i	1.34745	+	0.777952i	0.987888	−	0.155168i	$-0.0495919\pi$
$71$	11.3538	+	6.55514i	1.34745	+	0.777952i	0.359565	+	0.933120i	$0.382925\pi$
$72$		0			0
$73$		−	6.62310i		−	0.775175i	−0.921833	−	0.387588i	$-0.873308\pi$
$73$		−	6.62310i		−	0.775175i	0.921833	−	0.387588i	$-0.126692\pi$
$74$	−3.53663	+	6.12562i	−0.411125	+	0.712089i
$75$		0			0
$76$	−4.23947	+	2.44766i	−0.486300	+	0.280766i
$77$	1.63322			0.186123
$78$		0			0
$79$	−8.21115			−0.923827			−0.461914	−	0.886925i	$-0.652837\pi$
$79$	−8.21115			−0.923827			−0.461914	+	0.886925i	$0.652837\pi$
$80$	1.08053	−	0.623842i	0.120806	−	0.0697476i
$81$		0			0
$82$	−1.99895	+	3.46229i	−0.220747	+	0.382346i
$83$			11.1721i			1.22630i	0.789968	+	0.613148i	$0.210097\pi$
$83$			11.1721i			1.22630i	−0.789968	+	0.613148i	$0.789903\pi$
$84$		0			0
$85$	−6.01148	−	3.47073i	−0.652037	−	0.376453i
$86$			5.38157i			0.580309i
$87$		0			0
$88$	0.816612	+	1.41441i	0.0870511	+	0.150777i
$89$	2.16375	−	1.24924i	0.229357	−	0.132419i	−0.380918	−	0.924609i	$-0.624392\pi$
$89$	2.16375	−	1.24924i	0.229357	−	0.132419i	0.610275	+	0.792189i	$0.291059\pi$
$90$		0			0
$91$	3.06212	+	1.90353i	0.320997	+	0.199544i
$92$	5.67142			0.591286
$93$		0			0
$94$	−5.74902	−	9.95759i	−0.592966	−	1.02705i
$95$	3.05390	−	5.28951i	0.313324	−	0.542693i
$96$		0			0
$97$	9.02271	+	5.20926i	0.916117	+	0.528920i	0.882394	−	0.470511i	$-0.155930\pi$
$97$	9.02271	+	5.20926i	0.916117	+	0.528920i	0.0337228	+	0.999431i	$0.489264\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	1.72164	−	2.98197i	0.172164	−	0.298197i
$101$	−1.78522	−	3.09210i	−0.177636	−	0.307675i	0.763434	−	0.645886i	$-0.223512\pi$
$101$	−1.78522	−	3.09210i	−0.177636	−	0.307675i	−0.941071	+	0.338210i	$0.890178\pi$
$102$		0			0
$103$	9.63810			0.949670			0.474835	−	0.880075i	$-0.342508\pi$
$103$	9.63810			0.949670			0.474835	+	0.880075i	$0.342508\pi$
$104$	−0.117447	+	3.60364i	−0.0115167	+	0.353366i
$105$		0			0
$106$	4.17451	−	2.41015i	0.405464	−	0.234095i
$107$	2.18140	+	3.77830i	0.210884	+	0.365262i	0.951991	−	0.306125i	$-0.0990324\pi$
$107$	2.18140	+	3.77830i	0.210884	+	0.365262i	−0.741107	+	0.671387i	$0.765699\pi$
$108$		0			0
$109$			19.3037i			1.84896i	0.381230	+	0.924480i	$0.375501\pi$
$109$			19.3037i			1.84896i	−0.381230	+	0.924480i	$0.624499\pi$
$110$	−1.76474	−	1.01887i	−0.168261	−	0.0971457i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	4.73647	−	8.20380i	0.445569	−	0.771748i	−0.552522	−	0.833498i	$-0.686335\pi$
$113$	4.73647	−	8.20380i	0.445569	−	0.771748i	0.998092	+	0.0617495i	$0.0196680\pi$
$114$		0			0
$115$	−6.12812	+	3.53807i	−0.571450	+	0.329927i
$116$	−3.19970			−0.297085
$117$		0			0
$118$	5.17605			0.476494
$119$	−4.81811	+	2.78174i	−0.441676	+	0.255002i
$120$		0			0
$121$	−4.16629	+	7.21623i	−0.378754	+	0.656021i
$122$		−	5.94526i		−	0.538258i
$123$		0			0
$124$	3.05762	+	1.76532i	0.274582	+	0.158530i
$125$			10.5345i			0.942239i
$126$		0			0
$127$	7.47672	+	12.9501i	0.663452	+	1.14913i	0.979703	+	0.200457i	$0.0642425\pi$
$127$	7.47672	+	12.9501i	0.663452	+	1.14913i	−0.316251	+	0.948676i	$0.602424\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.12119	−	3.96709i	−0.186041	−	0.347937i
$131$	−13.3546			−1.16680			−0.583398	−	0.812187i	$-0.698277\pi$
$131$	−13.3546			−1.16680			−0.583398	+	0.812187i	$0.698277\pi$
$132$		0			0
$133$	−2.44766	−	4.23947i	−0.212239	−	0.367608i
$134$	3.16943	−	5.48962i	0.273797	−	0.474231i
$135$		0			0
$136$	−4.81811	−	2.78174i	−0.413150	−	0.238532i
$137$	6.27707	+	3.62407i	0.536286	+	0.309625i	0.743573	−	0.668655i	$-0.233130\pi$
$137$	6.27707	+	3.62407i	0.536286	+	0.309625i	−0.207286	+	0.978280i	$0.566463\pi$
$138$		0			0
$139$	7.86534	−	13.6232i	0.667129	−	1.15550i	−0.311574	−	0.950222i	$-0.600856\pi$
$139$	7.86534	−	13.6232i	0.667129	−	1.15550i	0.978703	−	0.205280i	$-0.0658104\pi$
$140$	0.623842	+	1.08053i	0.0527243	+	0.0913211i
$141$		0			0
$142$	−13.1103			−1.10019
$143$	5.19294	−	2.77665i	0.434255	−	0.232195i
$144$		0			0
$145$	3.45736	−	1.99611i	0.287118	−	0.165768i
$146$	3.31155	+	5.73577i	0.274066	+	0.474696i
$147$		0			0
$148$		−	7.07325i		−	0.581418i
$149$	−2.20523	−	1.27319i	−0.180659	−	0.104304i	0.406943	−	0.913454i	$-0.366595\pi$
$149$	−2.20523	−	1.27319i	−0.180659	−	0.104304i	−0.587602	+	0.809150i	$0.699928\pi$
$150$		0			0
$151$			9.89437i			0.805192i	0.915378	+	0.402596i	$0.131892\pi$
$151$			9.89437i			0.805192i	−0.915378	+	0.402596i	$0.868108\pi$
$152$	2.44766	−	4.23947i	0.198531	−	0.343866i
$153$		0			0
$154$	−1.41441	+	0.816612i	−0.113977	+	0.0658044i
$155$	−4.40511			−0.353827
$156$		0			0
$157$	8.96414			0.715416			0.357708	−	0.933833i	$-0.383558\pi$
$157$	8.96414			0.715416			0.357708	+	0.933833i	$0.383558\pi$
$158$	7.11107	−	4.10558i	0.565726	−	0.326622i
$159$		0			0
$160$	−0.623842	+	1.08053i	−0.0493190	+	0.0854231i
$161$			5.67142i			0.446971i
$162$		0			0
$163$	0.371849	+	0.214687i	0.0291254	+	0.0168156i	0.514492	−	0.857495i	$-0.327981\pi$
$163$	0.371849	+	0.214687i	0.0291254	+	0.0168156i	−0.485367	+	0.874311i	$0.661314\pi$
$164$		−	3.99790i		−	0.312184i
$165$		0			0
$166$	−5.58604	−	9.67531i	−0.433561	−	0.750949i
$167$	−19.5072	+	11.2625i	−1.50951	+	0.871516i	−0.509572	+	0.860428i	$0.670196\pi$
$167$	−19.5072	+	11.2625i	−1.50951	+	0.871516i	−0.999939	+	0.0110885i	$0.996470\pi$
$168$		0			0
$169$	12.9724	+	0.846476i	0.997878	+	0.0651136i
$170$	6.94146			0.532386
$171$		0			0
$172$	−2.69078	−	4.66057i	−0.205170	−	0.355365i
$173$	−5.50562	+	9.53601i	−0.418584	+	0.725010i	−0.995797	−	0.0915841i	$-0.970807\pi$
$173$	−5.50562	+	9.53601i	−0.418584	+	0.725010i	0.577213	+	0.816594i	$0.304140\pi$
$174$		0			0
$175$	2.98197	+	1.72164i	0.225416	+	0.130144i
$176$	−1.41441	−	0.816612i	−0.106615	−	0.0615544i
$177$		0			0
$178$	−1.24924	+	2.16375i	−0.0936347	+	0.162180i
$179$	1.09732	+	1.90062i	0.0820179	+	0.142059i	0.904117	−	0.427286i	$-0.140530\pi$
$179$	1.09732	+	1.90062i	0.0820179	+	0.142059i	−0.822099	+	0.569345i	$0.807197\pi$
$180$		0			0
$181$	−4.81625			−0.357989			−0.178995	−	0.983850i	$-0.557284\pi$
$181$	−4.81625			−0.357989			−0.178995	+	0.983850i	$0.557284\pi$
$182$	−3.60364	−	0.117447i	−0.267119	−	0.00870579i
$183$		0			0
$184$	−4.91159	+	2.83571i	−0.362088	+	0.209051i
$185$	4.41259	+	7.64283i	0.324420	+	0.561912i
$186$		0			0
$187$			9.08640i			0.664463i
$188$	9.95759	+	5.74902i	0.726232	+	0.419290i
$189$		0			0
$190$			6.10780i			0.443107i
$191$	6.13215	−	10.6212i	0.443707	−	0.768523i	−0.554254	−	0.832347i	$-0.686996\pi$
$191$	6.13215	−	10.6212i	0.443707	−	0.768523i	0.997961	+	0.0638244i	$0.0203298\pi$
$192$		0			0
$193$	−16.2180	+	9.36349i	−1.16740	+	0.673999i	−0.953066	−	0.302762i	$-0.902091\pi$
$193$	−16.2180	+	9.36349i	−1.16740	+	0.673999i	−0.214334	+	0.976760i	$0.568758\pi$
$194$	−10.4185			−0.748006
$195$		0			0
$196$	1.00000			0.0714286
$197$	15.7761	−	9.10832i	1.12400	−	0.648941i	0.181580	−	0.983376i	$-0.441879\pi$
$197$	15.7761	−	9.10832i	1.12400	−	0.648941i	0.942419	+	0.334435i	$0.108546\pi$
$198$		0			0
$199$	−4.60392	+	7.97423i	−0.326364	+	0.565278i	−0.981787	−	0.189983i	$-0.939157\pi$
$199$	−4.60392	+	7.97423i	−0.326364	+	0.565278i	0.655424	+	0.755261i	$0.272490\pi$
$200$			3.44329i			0.243477i
$201$		0			0
$202$	3.09210	+	1.78522i	0.217559	+	0.125608i
$203$		−	3.19970i		−	0.224575i
$204$		0			0
$205$	2.49406	+	4.31984i	0.174193	+	0.301711i
$206$	−8.34684	+	4.81905i	−0.581552	+	0.335759i
$207$		0			0
$208$	−1.70011	−	3.17957i	−0.117881	−	0.220463i
$209$	−7.99514			−0.553036
$210$		0			0
$211$	−2.17384	−	3.76520i	−0.149653	−	0.259207i	0.781446	−	0.623973i	$-0.214482\pi$
$211$	−2.17384	−	3.76520i	−0.149653	−	0.259207i	−0.931099	+	0.364766i	$0.881149\pi$
$212$	−2.41015	+	4.17451i	−0.165530	+	0.286706i
$213$		0			0
$214$	−3.77830	−	2.18140i	−0.258279	−	0.149118i
$215$	5.81492	+	3.35725i	0.396574	+	0.228962i
$216$		0			0
$217$	−1.76532	+	3.05762i	−0.119838	+	0.207565i
$218$	−9.65186	−	16.7175i	−0.653706	−	1.13225i
$219$		0			0
$220$	2.03775			0.137385
$221$	−10.5903	+	17.0360i	−0.712378	+	1.14597i
$222$		0			0
$223$	−4.15095	+	2.39655i	−0.277968	+	0.160485i	−0.632503	−	0.774558i	$-0.717973\pi$
$223$	−4.15095	+	2.39655i	−0.277968	+	0.160485i	0.354535	+	0.935043i	$0.384639\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$			9.47293i			0.630130i
$227$	−4.71526	−	2.72236i	−0.312963	−	0.180689i	0.335289	−	0.942115i	$-0.391166\pi$
$227$	−4.71526	−	2.72236i	−0.312963	−	0.180689i	−0.648252	+	0.761426i	$0.724500\pi$
$228$		0			0
$229$			15.0809i			0.996573i	0.867012	+	0.498287i	$0.166037\pi$
$229$			15.0809i			0.996573i	−0.867012	+	0.498287i	$0.833963\pi$
$230$	3.53807	−	6.12812i	0.233293	−	0.404076i
$231$		0			0
$232$	2.77102	−	1.59985i	0.181927	−	0.105035i
$233$	5.27514			0.345586			0.172793	−	0.984958i	$-0.444721\pi$
$233$	5.27514			0.345586			0.172793	+	0.984958i	$0.444721\pi$
$234$		0			0
$235$	−14.3459			−0.935824
$236$	−4.48259	+	2.58803i	−0.291792	+	0.168466i
$237$		0			0
$238$	2.78174	−	4.81811i	0.180313	−	0.312312i
$239$		−	29.0721i		−	1.88052i	−0.340461	−	0.940259i	$-0.610583\pi$
$239$		−	29.0721i		−	1.88052i	0.340461	−	0.940259i	$-0.389417\pi$
$240$		0			0
$241$	25.5375	+	14.7441i	1.64502	+	0.949751i	0.979012	+	0.203805i	$0.0653307\pi$
$241$	25.5375	+	14.7441i	1.64502	+	0.949751i	0.666006	+	0.745947i	$0.268003\pi$
$242$		−	8.33258i		−	0.535639i
$243$		0			0
$244$	2.97263	+	5.14874i	0.190303	+	0.329615i
$245$	−1.08053	+	0.623842i	−0.0690323	+	0.0398558i
$246$		0			0
$247$	−14.9900	−	9.31839i	−0.953793	−	0.592915i
$248$	−3.53063			−0.224196
$249$		0			0
$250$	−5.26727	−	9.12319i	−0.333132	−	0.577001i
$251$	1.04396	−	1.80819i	0.0658941	−	0.114132i	−0.831196	−	0.555979i	$-0.812343\pi$
$251$	1.04396	−	1.80819i	0.0658941	−	0.114132i	0.897090	+	0.441847i	$0.145677\pi$
$252$		0			0
$253$	8.02173	+	4.63135i	0.504322	+	0.291170i
$254$	−12.9501	−	7.47672i	−0.812559	−	0.469131i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.1891	−	24.5763i	−0.885094	−	1.53303i	−0.845606	−	0.533808i	$-0.820760\pi$
$257$	−14.1891	−	24.5763i	−0.885094	−	1.53303i	−0.0394885	−	0.999220i	$-0.512573\pi$
$258$		0			0
$259$	7.07325			0.439511
$260$	3.82055	+	2.37500i	0.236941	+	0.147292i
$261$		0			0
$262$	11.5654	−	6.67729i	0.714513	−	0.412524i
$263$	−12.2799	−	21.2695i	−0.757214	−	1.31153i	−0.944266	−	0.329183i	$-0.893227\pi$
$263$	−12.2799	−	21.2695i	−0.757214	−	1.31153i	0.187053	−	0.982350i	$-0.440106\pi$
$264$		0			0
$265$		−	6.01421i		−	0.369450i
$266$	4.23947	+	2.44766i	0.259938	+	0.150076i
$267$		0			0
$268$			6.33887i			0.387208i
$269$	13.3076	−	23.0494i	0.811379	−	1.40535i	−0.100521	−	0.994935i	$-0.532051\pi$
$269$	13.3076	−	23.0494i	0.811379	−	1.40535i	0.911899	−	0.410414i	$-0.134616\pi$
$270$		0			0
$271$	−16.9931	+	9.81095i	−1.03225	+	0.595973i	−0.917630	−	0.397436i	$-0.869900\pi$
$271$	−16.9931	+	9.81095i	−1.03225	+	0.595973i	−0.114625	+	0.993409i	$0.536567\pi$
$272$	5.56348			0.337335
$273$		0			0
$274$	−7.24814			−0.437876
$275$	4.87023	−	2.81183i	0.293686	−	0.169560i
$276$		0			0
$277$	11.6675	−	20.2087i	0.701034	−	1.21423i	−0.267070	−	0.963677i	$-0.586056\pi$
$277$	11.6675	−	20.2087i	0.701034	−	1.21423i	0.968104	−	0.250549i	$-0.0806110\pi$
$278$			15.7307i			0.943463i
$279$		0			0
$280$	−1.08053	−	0.623842i	−0.0645738	−	0.0372817i
$281$		−	21.2604i		−	1.26829i	−0.773215	−	0.634143i	$-0.781353\pi$
$281$		−	21.2604i		−	1.26829i	0.773215	−	0.634143i	$-0.218647\pi$
$282$		0			0
$283$	−9.32039	−	16.1434i	−0.554039	−	0.959625i	−0.997978	−	0.0635671i	$-0.979752\pi$
$283$	−9.32039	−	16.1434i	−0.554039	−	0.959625i	0.443938	−	0.896057i	$-0.353581\pi$
$284$	11.3538	−	6.55514i	0.673726	−	0.388976i
$285$		0			0
$286$	−3.10889	+	5.00112i	−0.183833	+	0.295723i
$287$	3.99790			0.235989
$288$		0			0
$289$	−6.97614	−	12.0830i	−0.410361	−	0.710767i
$290$	−1.99611	+	3.45736i	−0.117215	+	0.203023i
$291$		0			0
$292$	−5.73577	−	3.31155i	−0.335661	−	0.193794i
$293$	−10.0804	−	5.81994i	−0.588905	−	0.340004i	0.175760	−	0.984433i	$-0.443762\pi$
$293$	−10.0804	−	5.81994i	−0.588905	−	0.340004i	−0.764664	+	0.644429i	$0.777095\pi$
$294$		0			0
$295$	3.22904	−	5.59286i	0.188002	−	0.325629i
$296$	3.53663	+	6.12562i	0.205562	+	0.356044i
$297$		0			0
$298$	2.54638			0.147508
$299$	9.64202	+	18.0327i	0.557612	+	1.04286i
$300$		0			0
$301$	4.66057	−	2.69078i	0.268631	−	0.155094i
$302$	−4.94718	−	8.56877i	−0.284678	−	0.493077i
$303$		0			0
$304$			4.89532i			0.280766i
$305$	−6.42400	−	3.70890i	−0.367837	−	0.212371i
$306$		0			0
$307$		−	0.802209i		−	0.0457845i	−0.999738	−	0.0228922i	$-0.992713\pi$
$307$		−	0.802209i		−	0.0457845i	0.999738	−	0.0228922i	$-0.00728747\pi$
$308$	0.816612	−	1.41441i	0.0465308	−	0.0805936i
$309$		0			0
$310$	3.81494	−	2.20256i	0.216674	−	0.125097i
$311$	−10.2961			−0.583838			−0.291919	−	0.956443i	$-0.594294\pi$
$311$	−10.2961			−0.583838			−0.291919	+	0.956443i	$0.594294\pi$
$312$		0			0
$313$	−12.2030			−0.689752			−0.344876	−	0.938648i	$-0.612079\pi$
$313$	−12.2030			−0.689752			−0.344876	+	0.938648i	$0.612079\pi$
$314$	−7.76317	+	4.48207i	−0.438101	+	0.252938i
$315$		0			0
$316$	−4.10558	+	7.11107i	−0.230957	+	0.400029i
$317$			8.53952i			0.479627i	0.970819	+	0.239814i	$0.0770863\pi$
$317$			8.53952i			0.479627i	−0.970819	+	0.239814i	$0.922914\pi$
$318$		0			0
$319$	−4.52570	−	2.61291i	−0.253390	−	0.146295i
$320$		−	1.24768i		−	0.0697476i
$321$		0			0
$322$	−2.83571	−	4.91159i	−0.158028	−	0.273712i
$323$	23.5862	−	13.6175i	1.31237	−	0.757697i
$324$		0			0
$325$	12.4084	+	0.404405i	0.688292	+	0.0224324i
$326$	−0.429374			−0.0237808
$327$		0			0
$328$	1.99895	+	3.46229i	0.110374	+	0.191173i
$329$	−5.74902	+	9.95759i	−0.316954	+	0.548980i
$330$		0			0
$331$	23.3998	+	13.5099i	1.28617	+	0.742571i	0.977969	−	0.208750i	$-0.0669396\pi$
$331$	23.3998	+	13.5099i	1.28617	+	0.742571i	0.308202	+	0.951321i	$0.400273\pi$
$332$	9.67531	+	5.58604i	0.531001	+	0.306574i
$333$		0			0
$334$	11.2625	−	19.5072i	0.616255	−	1.06739i
$335$	−3.95445	−	6.84931i	−0.216055	−	0.374218i
$336$		0			0
$337$	3.48883			0.190048			0.0950242	−	0.995475i	$-0.469707\pi$
$337$	3.48883			0.190048			0.0950242	+	0.995475i	$0.469707\pi$
$338$	−11.6577	+	5.75314i	−0.634094	+	0.312929i
$339$		0			0
$340$	−6.01148	+	3.47073i	−0.326018	+	0.188227i
$341$	2.88316	+	4.99377i	0.156132	+	0.270428i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	4.66057	+	2.69078i	0.251281	+	0.145077i
$345$		0			0
$346$		−	11.0112i		−	0.591968i
$347$	10.8293	−	18.7569i	0.581347	−	1.00692i	−0.413973	−	0.910289i	$-0.635859\pi$
$347$	10.8293	−	18.7569i	0.581347	−	1.00692i	0.995320	−	0.0966337i	$-0.0308075\pi$
$348$		0			0
$349$	26.8664	−	15.5113i	1.43813	−	0.830303i	0.440407	−	0.897798i	$-0.354834\pi$
$349$	26.8664	−	15.5113i	1.43813	−	0.830303i	0.997720	+	0.0674949i	$0.0215007\pi$
$350$	−3.44329			−0.184051
$351$		0			0
$352$	1.63322			0.0870511
$353$	25.8321	−	14.9142i	1.37491	−	0.793802i	0.383365	−	0.923597i	$-0.374765\pi$
$353$	25.8321	−	14.9142i	1.37491	−	0.793802i	0.991541	+	0.129795i	$0.0414318\pi$
$354$		0			0
$355$	−8.17874	+	14.1660i	−0.434083	+	0.751853i
$356$		−	2.49848i		−	0.132419i
$357$		0			0
$358$	−1.90062	−	1.09732i	−0.100451	−	0.0579954i
$359$			21.5254i			1.13607i	0.823006	+	0.568033i	$0.192295\pi$
$359$			21.5254i			1.13607i	−0.823006	+	0.568033i	$0.807705\pi$
$360$		0			0
$361$	2.48206	+	4.29905i	0.130635	+	0.226266i
$362$	4.17100	−	2.40813i	0.219223	−	0.126568i
$363$		0			0
$364$	3.17957	−	1.70011i	0.166655	−	0.0891098i
$365$	8.26353			0.432533
$366$		0			0
$367$	−2.21213	−	3.83153i	−0.115472	−	0.200004i	0.802496	−	0.596657i	$-0.203505\pi$
$367$	−2.21213	−	3.83153i	−0.115472	−	0.200004i	−0.917969	+	0.396653i	$0.870172\pi$
$368$	2.83571	−	4.91159i	0.147822	−	0.256035i
$369$		0			0
$370$	−7.64283	−	4.41259i	−0.397332	−	0.229400i
$371$	−4.17451	−	2.41015i	−0.216730	−	0.125129i
$372$		0			0
$373$	13.3688	−	23.1554i	0.692209	−	1.19894i	−0.278903	−	0.960319i	$-0.589971\pi$
$373$	13.3688	−	23.1554i	0.692209	−	1.19894i	0.971112	−	0.238622i	$-0.0766958\pi$
$374$	−4.54320	−	7.86905i	−0.234923	−	0.406899i
$375$		0			0
$376$	−11.4980			−0.592966
$377$	−5.43983	−	10.1737i	−0.280166	−	0.523970i
$378$		0			0
$379$	−14.0198	+	8.09436i	−0.720151	+	0.415780i	−0.814808	−	0.579730i	$-0.803158\pi$
$379$	−14.0198	+	8.09436i	−0.720151	+	0.415780i	0.0946571	+	0.995510i	$0.469825\pi$
$380$	−3.05390	−	5.28951i	−0.156662	−	0.271346i
$381$		0			0
$382$			12.2643i			0.627496i
$383$	0.351106	+	0.202711i	0.0179407	+	0.0103580i	0.508944	−	0.860800i	$-0.330036\pi$
$383$	0.351106	+	0.202711i	0.0179407	+	0.0103580i	−0.491003	+	0.871158i	$0.663370\pi$
$384$		0			0
$385$			2.03775i			0.103853i
$386$	9.36349	−	16.2180i	0.476589	−	0.825477i
$387$		0			0
$388$	9.02271	−	5.20926i	0.458058	−	0.264460i
$389$	2.18998			0.111037			0.0555183	−	0.998458i	$-0.482319\pi$
$389$	2.18998			0.111037			0.0555183	+	0.998458i	$0.482319\pi$
$390$		0			0
$391$	−31.5528			−1.59569
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−9.10832	+	15.7761i	−0.458871	+	0.794787i
$395$		−	10.2449i		−	0.515478i
$396$		0			0
$397$	−6.24673	−	3.60655i	−0.313515	−	0.181008i	0.334984	−	0.942224i	$-0.391269\pi$
$397$	−6.24673	−	3.60655i	−0.313515	−	0.181008i	−0.648498	+	0.761216i	$0.724603\pi$
$398$		−	9.20785i		−	0.461548i
$399$		0			0
$400$	−1.72164	−	2.98197i	−0.0860821	−	0.149099i
$401$	2.39085	−	1.38036i	0.119393	−	0.0689318i	−0.439114	−	0.898431i	$-0.644708\pi$
$401$	2.39085	−	1.38036i	0.119393	−	0.0689318i	0.558507	+	0.829500i	$0.311374\pi$
$402$		0			0
$403$	−0.414664	+	12.7231i	−0.0206559	+	0.633784i
$404$	−3.57045			−0.177636
$405$		0			0
$406$	1.59985	+	2.77102i	0.0793992	+	0.137524i
$407$	5.77610	−	10.0045i	0.286311	−	0.495905i
$408$		0			0
$409$	8.60545	+	4.96836i	0.425512	+	0.245670i	0.697433	−	0.716650i	$-0.254325\pi$
$409$	8.60545	+	4.96836i	0.425512	+	0.245670i	−0.271921	+	0.962320i	$0.587659\pi$
$410$	−4.31984	−	2.49406i	−0.213342	−	0.123173i
$411$		0			0
$412$	4.81905	−	8.34684i	0.237418	−	0.411219i
$413$	−2.58803	−	4.48259i	−0.127348	−	0.220574i
$414$		0			0
$415$	−13.9392			−0.684249
$416$	3.06212	+	1.90353i	0.150133	+	0.0933283i
$417$		0			0
$418$	6.92400	−	3.99757i	0.338664	−	0.195528i
$419$	9.01445	+	15.6135i	0.440385	+	0.762769i	0.997718	−	0.0675201i	$-0.0215087\pi$
$419$	9.01445	+	15.6135i	0.440385	+	0.762769i	−0.557333	+	0.830289i	$0.688175\pi$
$420$		0			0
$421$		−	3.61265i		−	0.176070i	−0.996117	−	0.0880348i	$-0.971941\pi$
$421$		−	3.61265i		−	0.176070i	0.996117	−	0.0880348i	$-0.0280587\pi$
$422$	3.76520	+	2.17384i	0.183287	+	0.105821i
$423$		0			0
$424$		−	4.82030i		−	0.234095i
$425$	−9.57832	+	16.5901i	−0.464617	+	0.804740i
$426$		0			0
$427$	−5.14874	+	2.97263i	−0.249165	+	0.143856i
$428$	4.36280			0.210884
$429$		0			0
$430$	−6.71449			−0.323802
$431$	24.7893	−	14.3121i	1.19406	−	0.689389i	0.234833	−	0.972036i	$-0.424546\pi$
$431$	24.7893	−	14.3121i	1.19406	−	0.689389i	0.959224	+	0.282646i	$0.0912122\pi$
$432$		0			0
$433$	12.3338	−	21.3627i	0.592723	−	1.02663i	−0.401141	−	0.916016i	$-0.631386\pi$
$433$	12.3338	−	21.3627i	0.592723	−	1.02663i	0.993864	−	0.110610i	$-0.0352804\pi$
$434$		−	3.53063i		−	0.169476i
$435$		0			0
$436$	16.7175	+	9.65186i	0.800623	+	0.462240i
$437$		−	27.7634i		−	1.32810i
$438$		0			0
$439$	7.13469	+	12.3576i	0.340520	+	0.589798i	0.984529	−	0.175219i	$-0.0560635\pi$
$439$	7.13469	+	12.3576i	0.340520	+	0.589798i	−0.644009	+	0.765018i	$0.722730\pi$
$440$	−1.76474	+	1.01887i	−0.0841306	+	0.0485729i
$441$		0			0
$442$	0.653416	−	20.0488i	0.0310799	−	0.953622i
$443$	−32.2838			−1.53385			−0.766925	−	0.641736i	$-0.778214\pi$
$443$	−32.2838			−1.53385			−0.766925	+	0.641736i	$0.778214\pi$
$444$		0			0
$445$	1.55866	+	2.69968i	0.0738875	+	0.127977i
$446$	2.39655	−	4.15095i	0.113480	−	0.196553i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−18.8020	−	10.8554i	−0.887323	−	0.512296i	−0.0142572	−	0.999898i	$-0.504538\pi$
$449$	−18.8020	−	10.8554i	−0.887323	−	0.512296i	−0.873066	+	0.487602i	$0.837872\pi$
$450$		0			0
$451$	3.26473	−	5.65469i	0.153730	−	0.266269i
$452$	−4.73647	−	8.20380i	−0.222785	−	0.385874i
$453$		0			0
$454$	5.44472			0.255533
$455$	−2.37500	+	3.82055i	−0.111342	+	0.179110i
$456$		0			0
$457$	2.41901	−	1.39662i	0.113156	−	0.0653309i	−0.442354	−	0.896841i	$-0.645856\pi$
$457$	2.41901	−	1.39662i	0.113156	−	0.0653309i	0.555510	+	0.831510i	$0.312523\pi$
$458$	−7.54045	−	13.0604i	−0.352342	−	0.610274i
$459$		0			0
$460$			7.07614i			0.329927i
$461$	12.4200	+	7.17070i	0.578458	+	0.333973i	0.760520	−	0.649314i	$-0.224944\pi$
$461$	12.4200	+	7.17070i	0.578458	+	0.333973i	−0.182062	+	0.983287i	$0.558277\pi$
$462$		0			0
$463$		−	38.1760i		−	1.77419i	−0.461588	−	0.887095i	$-0.652720\pi$
$463$		−	38.1760i		−	1.77419i	0.461588	−	0.887095i	$-0.347280\pi$
$464$	−1.59985	+	2.77102i	−0.0742712	+	0.128641i
$465$		0			0
$466$	−4.56841	+	2.63757i	−0.211627	+	0.122183i
$467$	−13.0228			−0.602622			−0.301311	−	0.953526i	$-0.597424\pi$
$467$	−13.0228			−0.602622			−0.301311	+	0.953526i	$0.597424\pi$
$468$		0			0
$469$	−6.33887			−0.292702
$470$	12.4239	−	7.17295i	0.573073	−	0.330864i
$471$		0			0
$472$	2.58803	−	4.48259i	0.119124	−	0.206328i
$473$		−	8.78930i		−	0.404132i
$474$		0			0
$475$	−14.5977	−	8.42799i	−0.669788	−	0.386702i
$476$			5.56348i			0.255002i
$477$		0			0
$478$	14.5360	+	25.1772i	0.664863	+	1.15158i
$479$	17.5949	−	10.1584i	0.803932	−	0.464150i	−0.0409123	−	0.999163i	$-0.513026\pi$
$479$	17.5949	−	10.1584i	0.803932	−	0.464150i	0.844844	+	0.535012i	$0.179693\pi$
$480$		0			0
$481$	22.4899	−	12.0253i	1.02545	−	0.548306i
$482$	−29.4882			−1.34315
$483$		0			0
$484$	4.16629	+	7.21623i	0.189377	+	0.328010i
$485$	−6.49951	+	11.2575i	−0.295128	+	0.511176i
$486$		0			0
$487$	−4.36922	−	2.52257i	−0.197988	−	0.114309i	0.397728	−	0.917503i	$-0.369799\pi$
$487$	−4.36922	−	2.52257i	−0.197988	−	0.114309i	−0.595717	+	0.803195i	$0.703132\pi$
$488$	−5.14874	−	2.97263i	−0.233073	−	0.134565i
$489$		0			0
$490$	0.623842	−	1.08053i	0.0281823	−	0.0488132i
$491$	−17.9099	−	31.0208i	−0.808261	−	1.39995i	−0.914067	−	0.405562i	$-0.867076\pi$
$491$	−17.9099	−	31.0208i	−0.808261	−	1.39995i	0.105807	−	0.994387i	$-0.466258\pi$
$492$		0			0
$493$	17.8015			0.801738
$494$	17.6409	+	0.574942i	0.793704	+	0.0258679i
$495$		0			0
$496$	3.05762	−	1.76532i	0.137291	−	0.0792651i
$497$	6.55514	+	11.3538i	0.294038	+	0.509289i
$498$		0			0
$499$		−	33.0174i		−	1.47806i	−0.673670	−	0.739032i	$-0.735283\pi$
$499$		−	33.0174i		−	1.47806i	0.673670	−	0.739032i	$-0.264717\pi$
$500$	9.12319	+	5.26727i	0.408001	+	0.235560i
$501$		0			0
$502$			2.08792i			0.0931883i
$503$	−3.46368	+	5.99927i	−0.154438	+	0.267494i	−0.932854	−	0.360254i	$-0.882690\pi$
$503$	−3.46368	+	5.99927i	−0.154438	+	0.267494i	0.778416	+	0.627748i	$0.216023\pi$
$504$		0			0
$505$	3.85796	−	2.22740i	0.171677	−	0.0991178i
$506$	−9.26269			−0.411777
$507$		0			0
$508$	14.9534			0.663452
$509$	4.11620	−	2.37649i	0.182447	−	0.105336i	−0.405995	−	0.913875i	$-0.633075\pi$
$509$	4.11620	−	2.37649i	0.182447	−	0.105336i	0.588442	+	0.808539i	$0.299742\pi$
$510$		0			0
$511$	3.31155	−	5.73577i	0.146494	−	0.253736i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	24.5763	+	14.1891i	1.08401	+	0.625856i
$515$			12.0253i			0.529898i
$516$		0			0
$517$	9.38943	+	16.2630i	0.412946	+	0.715244i
$518$	−6.12562	+	3.53663i	−0.269144	+	0.155390i
$519$		0			0
$520$	−4.49620	−	0.146537i	−0.197171	−	0.00642609i
$521$	−0.0344780			−0.00151051			−0.000755255	−	1.00000i	$-0.500240\pi$
$521$	−0.0344780			−0.00151051			−0.000755255		1.00000i	$0.500240\pi$
$522$		0			0
$523$	−1.60834	−	2.78573i	−0.0703278	−	0.121811i	0.828717	−	0.559668i	$-0.189071\pi$
$523$	−1.60834	−	2.78573i	−0.0703278	−	0.121811i	−0.899045	+	0.437856i	$0.855738\pi$
$524$	−6.67729	+	11.5654i	−0.291699	+	0.505237i
$525$		0			0
$526$	21.2695	+	12.2799i	0.927393	+	0.535431i
$527$	−17.0110	−	9.82130i	−0.741011	−	0.427823i
$528$		0			0
$529$	−4.58250	+	7.93713i	−0.199239	+	0.345093i
$530$	3.00711	+	5.20846i	0.130620	+	0.226241i
$531$		0			0
$532$	−4.89532			−0.212239
$533$	12.7116	−	6.79686i	0.550600	−	0.294405i
$534$		0			0
$535$	−4.71412	+	2.72170i	−0.203809	+	0.117669i
$536$	−3.16943	−	5.48962i	−0.136899	−	0.237115i
$537$		0			0
$538$			26.6152i			1.14746i
$539$	1.41441	+	0.816612i	0.0609231	+	0.0351739i
$540$		0			0
$541$		−	41.4438i		−	1.78181i	−0.454190	−	0.890905i	$-0.650071\pi$
$541$		−	41.4438i		−	1.78181i	0.454190	−	0.890905i	$-0.349929\pi$
$542$	9.81095	−	16.9931i	0.421416	−	0.729915i
$543$		0			0
$544$	−4.81811	+	2.78174i	−0.206575	+	0.119266i
$545$	−24.0849			−1.03168
$546$		0			0
$547$	−28.9393			−1.23736			−0.618678	−	0.785645i	$-0.712331\pi$
$547$	−28.9393			−1.23736			−0.618678	+	0.785645i	$0.712331\pi$
$548$	6.27707	−	3.62407i	0.268143	−	0.154813i
$549$		0			0
$550$	−2.81183	+	4.87023i	−0.119897	+	0.207667i
$551$			15.6635i			0.667289i
$552$		0			0
$553$	−7.11107	−	4.10558i	−0.302393	−	0.174587i
$554$			23.3350i			0.991411i
$555$		0			0
$556$	−7.86534	−	13.6232i	−0.333565	−	0.577751i
$557$	27.8019	−	16.0514i	1.17800	−	0.680121i	0.222453	−	0.974944i	$-0.428594\pi$
$557$	27.8019	−	16.0514i	1.17800	−	0.680121i	0.955552	+	0.294822i	$0.0952604\pi$
$558$		0			0
$559$	10.2440	−	16.4790i	0.433274	−	0.696987i
$560$	1.24768			0.0527243
$561$		0			0
$562$	10.6302	+	18.4120i	0.448407	+	0.776664i
$563$	−1.79857	+	3.11521i	−0.0758006	+	0.131291i	−0.901434	−	0.432916i	$-0.857485\pi$
$563$	−1.79857	+	3.11521i	−0.0758006	+	0.131291i	0.825634	+	0.564207i	$0.190818\pi$
$564$		0			0
$565$	10.2357	+	5.90961i	0.430621	+	0.248619i
$566$	16.1434	+	9.32039i	0.678557	+	0.391765i
$567$		0			0
$568$	−6.55514	+	11.3538i	−0.275048	+	0.476396i
$569$	−18.3294	−	31.7474i	−0.768407	−	1.33092i	−0.938426	−	0.345480i	$-0.887716\pi$
$569$	−18.3294	−	31.7474i	−0.768407	−	1.33092i	0.170019	−	0.985441i	$-0.445617\pi$
$570$		0			0
$571$	−47.5969			−1.99187			−0.995934	−	0.0900902i	$-0.971284\pi$
$571$	−47.5969			−1.99187			−0.995934	+	0.0900902i	$0.971284\pi$
$572$	0.191818	−	5.88554i	0.00802031	−	0.246087i
$573$		0			0
$574$	−3.46229	+	1.99895i	−0.144513	+	0.0834346i
$575$	9.76416	+	16.9120i	0.407194	+	0.705280i
$576$		0			0
$577$			25.7012i			1.06996i	0.844866	+	0.534978i	$0.179680\pi$
$577$			25.7012i			1.06996i	−0.844866	+	0.534978i	$0.820320\pi$
$578$	12.0830	+	6.97614i	0.502588	+	0.290169i
$579$		0			0
$580$		−	3.99221i		−	0.165768i
$581$	−5.58604	+	9.67531i	−0.231748	+	0.401399i
$582$		0			0
$583$	−6.81790	+	3.93632i	−0.282368	+	0.163026i
$584$	6.62310			0.274066
$585$		0			0
$586$	11.6399			0.480839
$587$	25.7531	−	14.8686i	1.06294	−	0.613691i	0.136699	−	0.990613i	$-0.456351\pi$
$587$	25.7531	−	14.8686i	1.06294	−	0.613691i	0.926245	+	0.376921i	$0.123017\pi$
$588$		0			0
$589$	8.64179	−	14.9680i	0.356079	−	0.616746i
$590$			6.45808i			0.265875i
$591$		0			0
$592$	−6.12562	−	3.53663i	−0.251761	−	0.145354i
$593$			38.5870i			1.58458i	0.610146	+	0.792289i	$0.291111\pi$
$593$			38.5870i			1.58458i	−0.610146	+	0.792289i	$0.708889\pi$
$594$		0			0
$595$	−3.47073	−	6.01148i	−0.142286	−	0.246447i
$596$	−2.20523	+	1.27319i	−0.0903297	+	0.0521519i
$597$		0			0
$598$	−17.3666	−	10.7957i	−0.710171	−	0.441470i
$599$	−24.8717			−1.01623			−0.508114	−	0.861290i	$-0.669657\pi$
$599$	−24.8717			−1.01623			−0.508114	+	0.861290i	$0.669657\pi$
$600$		0			0
$601$	−1.82588	−	3.16252i	−0.0744792	−	0.129002i	0.826380	−	0.563112i	$-0.190396\pi$
$601$	−1.82588	−	3.16252i	−0.0744792	−	0.129002i	−0.900860	+	0.434110i	$0.857063\pi$
$602$	−2.69078	+	4.66057i	−0.109668	+	0.189951i
$603$		0			0
$604$	8.56877	+	4.94718i	0.348658	+	0.201298i
$605$	−9.00357	−	5.19821i	−0.366047	−	0.211337i
$606$		0			0
$607$	−8.01855	+	13.8885i	−0.325463	+	0.563718i	−0.981606	−	0.190918i	$-0.938853\pi$
$607$	−8.01855	+	13.8885i	−0.325463	+	0.563718i	0.656143	+	0.754636i	$0.272187\pi$
$608$	−2.44766	−	4.23947i	−0.0992656	−	0.171933i
$609$		0			0
$610$	7.41780			0.300338
$611$	−1.35041	+	41.4347i	−0.0546319	+	1.67627i
$612$		0			0
$613$	16.1663	−	9.33363i	0.652952	−	0.376982i	−0.136635	−	0.990622i	$-0.543629\pi$
$613$	16.1663	−	9.33363i	0.652952	−	0.376982i	0.789586	+	0.613640i	$0.210295\pi$
$614$	0.401105	+	0.694734i	0.0161873	+	0.0280372i
$615$		0			0
$616$			1.63322i			0.0658044i
$617$	−15.3613	−	8.86883i	−0.618422	−	0.357046i	0.157833	−	0.987466i	$-0.449549\pi$
$617$	−15.3613	−	8.86883i	−0.618422	−	0.357046i	−0.776254	+	0.630420i	$0.782883\pi$
$618$		0			0
$619$			25.3244i			1.01787i	0.860804	+	0.508937i	$0.169961\pi$
$619$			25.3244i			1.01787i	−0.860804	+	0.508937i	$0.830039\pi$
$620$	−2.20256	+	3.81494i	−0.0884568	+	0.153212i
$621$		0			0
$622$	8.91668	−	5.14805i	0.357526	−	0.206418i
$623$	2.49848			0.100100
$624$		0			0
$625$	4.07265			0.162906
$626$	10.5681	−	6.10148i	0.422385	−	0.243864i
$627$		0			0
$628$	4.48207	−	7.76317i	0.178854	−	0.309784i
$629$			39.3519i			1.56906i
$630$		0			0
$631$	−3.68116	−	2.12532i	−0.146545	−	0.0846075i	0.424935	−	0.905224i	$-0.360297\pi$
$631$	−3.68116	−	2.12532i	−0.146545	−	0.0846075i	−0.571479	+	0.820616i	$0.693630\pi$
$632$		−	8.21115i		−	0.326622i
$633$		0			0
$634$	−4.26976	−	7.39544i	−0.169574	−	0.293710i
$635$	−16.1576	+	9.32858i	−0.641194	+	0.370194i
$636$		0			0
$637$	1.70011	+	3.17957i	0.0673607	+	0.125979i
$638$	5.22582			0.206892
$639$		0			0
$640$	0.623842	+	1.08053i	0.0246595	+	0.0427115i
$641$	−17.2678	+	29.9086i	−0.682036	+	1.18132i	0.292323	+	0.956320i	$0.405572\pi$
$641$	−17.2678	+	29.9086i	−0.682036	+	1.18132i	−0.974359	+	0.225001i	$0.927762\pi$
$642$		0			0
$643$	−8.67586	−	5.00901i	−0.342143	−	0.197536i	0.319077	−	0.947729i	$-0.396627\pi$
$643$	−8.67586	−	5.00901i	−0.342143	−	0.197536i	−0.661219	+	0.750193i	$0.729961\pi$
$644$	4.91159	+	2.83571i	0.193544	+	0.111743i
$645$		0			0
$646$	−13.6175	+	23.5862i	−0.535773	+	0.927986i
$647$	−7.91081	−	13.7019i	−0.311006	−	0.538678i	0.667574	−	0.744543i	$-0.267333\pi$
$647$	−7.91081	−	13.7019i	−0.311006	−	0.538678i	−0.978580	+	0.205865i	$0.933999\pi$
$648$		0			0
$649$	−8.45365			−0.331835
$650$	−10.9482	+	5.85395i	−0.429422	+	0.229611i
$651$		0			0
$652$	0.371849	−	0.214687i	0.0145627	−	0.00840779i
$653$	5.37123	+	9.30325i	0.210193	+	0.364064i	0.951775	−	0.306798i	$-0.0992576\pi$
$653$	5.37123	+	9.30325i	0.210193	+	0.364064i	−0.741582	+	0.670862i	$0.765924\pi$
$654$		0			0
$655$		−	16.6623i		−	0.651050i
$656$	−3.46229	−	1.99895i	−0.135180	−	0.0780460i
$657$		0			0
$658$		−	11.4980i		−	0.448240i
$659$	8.19715	−	14.1979i	0.319315	−	0.553071i	−0.661030	−	0.750360i	$-0.729880\pi$
$659$	8.19715	−	14.1979i	0.319315	−	0.553071i	0.980345	+	0.197289i	$0.0632137\pi$
$660$		0			0
$661$	−16.7580	+	9.67522i	−0.651809	+	0.376322i	−0.789149	−	0.614202i	$-0.789478\pi$
$661$	−16.7580	+	9.67522i	−0.651809	+	0.376322i	0.137340	+	0.990524i	$0.456145\pi$
$662$	−27.0198			−1.05015
$663$		0			0
$664$	−11.1721			−0.433561
$665$	5.28951	−	3.05390i	0.205119	−	0.118425i
$666$		0			0
$667$	9.07342	−	15.7156i	0.351324	−	0.608512i
$668$			22.5249i			0.871516i
$669$		0			0
$670$	6.84931	+	3.95445i	0.264612	+	0.152774i
$671$			9.70993i			0.374848i
$672$		0			0
$673$	11.4635	+	19.8553i	0.441884	+	0.765366i	0.997829	−	0.0658530i	$-0.0209768\pi$
$673$	11.4635	+	19.8553i	0.441884	+	0.765366i	−0.555945	+	0.831219i	$0.687643\pi$
$674$	−3.02141	+	1.74441i	−0.116380	+	0.0671923i
$675$		0			0
$676$	7.21928	−	10.8112i	0.277664	−	0.415815i
$677$	22.8391			0.877776			0.438888	−	0.898542i	$-0.355372\pi$
$677$	22.8391			0.877776			0.438888	+	0.898542i	$0.355372\pi$
$678$		0			0
$679$	5.20926	+	9.02271i	0.199913	+	0.346260i
$680$	3.47073	−	6.01148i	0.133096	−	0.230530i
$681$		0			0
$682$	−4.99377	−	2.88316i	−0.191222	−	0.110402i
$683$	6.52984	+	3.77001i	0.249857	+	0.144255i	0.619699	−	0.784840i	$-0.287255\pi$
$683$	6.52984	+	3.77001i	0.249857	+	0.144255i	−0.369842	+	0.929095i	$0.620588\pi$
$684$		0			0
$685$	−4.52169	+	7.83180i	−0.172765	+	0.299238i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−5.38157			−0.205170
$689$	−17.3706	−	0.566133i	−0.661768	−	0.0215679i
$690$		0			0
$691$	22.6929	−	13.1017i	0.863278	−	0.498414i	−0.00183036	−	0.999998i	$-0.500583\pi$
$691$	22.6929	−	13.1017i	0.863278	−	0.498414i	0.865109	+	0.501584i	$0.167249\pi$
$692$	5.50562	+	9.53601i	0.209292	+	0.362505i
$693$		0			0
$694$			21.6586i			0.822149i
$695$	16.9974	+	9.81345i	0.644748	+	0.372245i
$696$		0			0
$697$			22.2422i			0.842485i
$698$	−15.5113	+	26.8664i	−0.587113	+	1.01691i
$699$		0			0
$700$	2.98197	−	1.72164i	0.112708	−	0.0650720i
$701$	37.4467			1.41434			0.707171	−	0.707043i	$-0.249971\pi$
$701$	37.4467			1.41434			0.707171	+	0.707043i	$0.249971\pi$
$702$		0			0
$703$	−34.6258			−1.30594
$704$	−1.41441	+	0.816612i	−0.0533077	+	0.0307772i
$705$		0			0
$706$	−14.9142	+	25.8321i	−0.561303	+	0.972205i
$707$		−	3.57045i		−	0.134281i
$708$		0			0
$709$	−29.1468	−	16.8279i	−1.09463	−	0.631986i	−0.159826	−	0.987145i	$-0.551093\pi$
$709$	−29.1468	−	16.8279i	−1.09463	−	0.631986i	−0.934806	+	0.355159i	$0.884427\pi$
$710$		−	16.3575i		−	0.613885i
$711$		0			0
$712$	1.24924	+	2.16375i	0.0468173	+	0.0810900i
$713$	−17.3410	+	10.0119i	−0.649427	+	0.374947i
$714$		0			0
$715$	3.46438	+	6.47915i	0.129561	+	0.242306i
$716$	2.19465			0.0820179
$717$		0			0
$718$	−10.7627	−	18.6415i	−0.401660	−	0.695695i
$719$	−10.7899	+	18.6887i	−0.402396	+	0.696971i	−0.994015	−	0.109247i	$-0.965156\pi$
$719$	−10.7899	+	18.6887i	−0.402396	+	0.696971i	0.591618	+	0.806218i	$0.298489\pi$
$720$		0			0
$721$	8.34684	+	4.81905i	0.310853	+	0.179471i
$722$	−4.29905	−	2.48206i	−0.159994	−	0.0923726i
$723$		0			0
$724$	−2.40813	+	4.17100i	−0.0894973	+	0.155014i
$725$	−5.50874	−	9.54142i	−0.204590	−	0.354359i
$726$		0			0
$727$	26.5309			0.983978			0.491989	−	0.870601i	$-0.336270\pi$
$727$	26.5309			0.983978			0.491989	+	0.870601i	$0.336270\pi$
$728$	−1.90353	+	3.06212i	−0.0705496	+	0.113490i
$729$		0			0
$730$	−7.15643	+	4.13177i	−0.264871	+	0.152924i
$731$	14.9701	+	25.9290i	0.553690	+	0.959019i
$732$		0			0
$733$		−	15.0423i		−	0.555599i	−0.960639	−	0.277799i	$-0.910395\pi$
$733$		−	15.0423i		−	0.555599i	0.960639	−	0.277799i	$-0.0896050\pi$
$734$	3.83153	+	2.21213i	0.141424	+	0.0816514i
$735$		0			0
$736$			5.67142i			0.209051i
$737$	−5.17639	+	8.96577i	−0.190675	+	0.330258i
$738$		0			0
$739$	−13.1481	+	7.59105i	−0.483660	+	0.279241i	−0.721941	−	0.691955i	$-0.756750\pi$
$739$	−13.1481	+	7.59105i	−0.483660	+	0.279241i	0.238280	+	0.971196i	$0.423416\pi$
$740$	8.82518			0.324420
$741$		0			0
$742$	4.82030			0.176959
$743$	31.1626	−	17.9917i	1.14324	−	0.660052i	0.196012	−	0.980602i	$-0.437201\pi$
$743$	31.1626	−	17.9917i	1.14324	−	0.660052i	0.947232	+	0.320550i	$0.103868\pi$
$744$		0			0
$745$	1.58854	−	2.75143i	0.0581995	−	0.100804i
$746$			26.7376i			0.978932i
$747$		0			0
$748$	7.86905	+	4.54320i	0.287721	+	0.166116i
$749$			4.36280i			0.159413i
$750$		0			0
$751$	8.91824	+	15.4468i	0.325431	+	0.563663i	0.981599	−	0.190951i	$-0.0611573\pi$
$751$	8.91824	+	15.4468i	0.325431	+	0.563663i	−0.656168	+	0.754614i	$0.727824\pi$
$752$	9.95759	−	5.74902i	0.363116	−	0.209645i
$753$		0			0
$754$	9.79786	+	6.09073i	0.356817	+	0.221811i
$755$	−12.3450			−0.449282
$756$		0			0
$757$	0.850916	+	1.47383i	0.0309271	+	0.0535673i	0.881075	−	0.472977i	$-0.156821\pi$
$757$	0.850916	+	1.47383i	0.0309271	+	0.0535673i	−0.850148	+	0.526544i	$0.823487\pi$
$758$	8.09436	−	14.0198i	0.294001	−	0.509224i
$759$		0			0
$760$	5.28951	+	3.05390i	0.191871	+	0.110777i
$761$	13.2906	+	7.67330i	0.481782	+	0.278157i	0.721159	−	0.692770i	$-0.243610\pi$
$761$	13.2906	+	7.67330i	0.481782	+	0.278157i	−0.239377	+	0.970927i	$0.576943\pi$
$762$		0			0
$763$	−9.65186	+	16.7175i	−0.349421	+	0.605214i
$764$	−6.13215	−	10.6212i	−0.221854	−	0.384262i
$765$		0			0
$766$	−0.405422			−0.0146485
$767$	−15.8497	−	9.85278i	−0.572299	−	0.355763i
$768$		0			0
$769$	−19.5852	+	11.3075i	−0.706259	+	0.407759i	−0.809674	−	0.586880i	$-0.800356\pi$
$769$	−19.5852	+	11.3075i	−0.706259	+	0.407759i	0.103415	+	0.994638i	$0.467023\pi$
$770$	−1.01887	−	1.76474i	−0.0367176	−	0.0635968i
$771$		0			0
$772$			18.7270i			0.673999i
$773$	37.9606	+	21.9166i	1.36535	+	0.788285i	0.990330	−	0.138732i	$-0.0443028\pi$
$773$	37.9606	+	21.9166i	1.36535	+	0.788285i	0.375019	+	0.927017i	$0.377636\pi$
$774$		0			0
$775$			12.1570i			0.436692i
$776$	−5.20926	+	9.02271i	−0.187002	+	0.323896i
$777$		0			0
$778$	−1.89658	+	1.09499i	−0.0679957	+	0.0392573i
$779$	−19.5710			−0.701204
$780$		0			0
$781$	21.4120			0.766182
$782$	27.3255	−	15.7764i	0.977159	−	0.564163i
$783$

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.24768i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.623842 - 1.08053i) q^{10} +(1.41441 - 0.816612i) q^{11} +(3.60364 + 0.117447i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78174 + 4.81811i) q^{17} +(-4.23947 - 2.44766i) q^{19} +(1.08053 + 0.623842i) q^{20} +(-0.816612 + 1.41441i) q^{22} +(2.83571 + 4.91159i) q^{23} +3.44329 q^{25} +(-3.17957 + 1.70011i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.59985 - 2.77102i) q^{29} +3.53063i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56348i q^{34} +(-0.623842 + 1.08053i) q^{35} +(6.12562 - 3.53663i) q^{37} +4.89532 q^{38} -1.24768 q^{40} +(3.46229 - 1.99895i) q^{41} +(2.69078 - 4.66057i) q^{43} -1.63322i q^{44} +(-4.91159 - 2.83571i) q^{46} +11.4980i q^{47} +(0.500000 + 0.866025i) q^{49} +(-2.98197 + 1.72164i) q^{50} +(1.90353 - 3.06212i) q^{52} -4.82030 q^{53} +(1.01887 + 1.76474i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(2.77102 + 1.59985i) q^{58} +(-4.48259 - 2.58803i) q^{59} +(-2.97263 + 5.14874i) q^{61} +(-1.76532 - 3.05762i) q^{62} -1.00000 q^{64} +(-0.146537 + 4.49620i) q^{65} +(-5.48962 + 3.16943i) q^{67} +(2.78174 + 4.81811i) q^{68} -1.24768i q^{70} +(11.3538 + 6.55514i) q^{71} -6.62310i q^{73} +(-3.53663 + 6.12562i) q^{74} +(-4.23947 + 2.44766i) q^{76} +1.63322 q^{77} -8.21115 q^{79} +(1.08053 - 0.623842i) q^{80} +(-1.99895 + 3.46229i) q^{82} +11.1721i q^{83} +(-6.01148 - 3.47073i) q^{85} +5.38157i q^{86} +(0.816612 + 1.41441i) q^{88} +(2.16375 - 1.24924i) q^{89} +(3.06212 + 1.90353i) q^{91} +5.67142 q^{92} +(-5.74902 - 9.95759i) q^{94} +(3.05390 - 5.28951i) q^{95} +(9.02271 + 5.20926i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 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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