LMFDB - Embedded newform 1638.2.bj.f.1135.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.4
Root			$1.30512 - 1.13871i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.f.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.166404 - 0.288220i) q^{10} +(-2.26053 - 1.30512i) q^{11} +(3.41140 + 1.16719i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.94383 + 3.36681i) q^{17} +(4.85997 - 2.80591i) q^{19} +(0.288220 - 0.166404i) q^{20} +(-1.30512 - 2.26053i) q^{22} +(-2.10628 + 3.64819i) q^{23} +4.88924 q^{25} +(2.37076 + 2.71652i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-0.593337 + 1.02769i) q^{29} +7.07434i q^{31} +(-0.866025 + 0.500000i) q^{32} +3.88766i q^{34} +(0.166404 + 0.288220i) q^{35} +(0.499211 + 0.288220i) q^{37} +5.61181 q^{38} +0.332808 q^{40} +(-0.451251 - 0.260530i) q^{41} +(1.53717 + 2.66245i) q^{43} -2.61023i q^{44} +(-3.64819 + 2.10628i) q^{46} +12.0528i q^{47} +(0.500000 - 0.866025i) q^{49} +(4.23421 + 2.44462i) q^{50} +(0.694883 + 3.53796i) q^{52} +9.71047 q^{53} +(-0.434353 + 0.752321i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.02769 + 0.593337i) q^{58} +(-9.07175 + 5.23758i) q^{59} +(-3.71989 - 6.44304i) q^{61} +(-3.53717 + 6.12656i) q^{62} -1.00000 q^{64} +(0.388451 - 1.13534i) q^{65} +(10.3233 + 5.96015i) q^{67} +(-1.94383 + 3.36681i) q^{68} +0.332808i q^{70} +(0.818065 - 0.472310i) q^{71} -4.66562i q^{73} +(0.288220 + 0.499211i) q^{74} +(4.85997 + 2.80591i) q^{76} +2.61023 q^{77} -0.943042 q^{79} +(0.288220 + 0.166404i) q^{80} +(-0.260530 - 0.451251i) q^{82} -13.7172i q^{83} +(1.12050 - 0.646922i) q^{85} +3.07434i q^{86} +(1.30512 - 2.26053i) q^{88} +(-2.92741 - 1.69014i) q^{89} +(-3.53796 + 0.694883i) q^{91} -4.21257 q^{92} +(-6.02638 + 10.4380i) q^{94} +(-0.933827 - 1.61744i) q^{95} +(-5.03669 + 2.90793i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$		−	0.332808i		−	0.148836i	−0.997227	−	0.0744180i	$-0.976290\pi$
$5$		−	0.332808i		−	0.148836i	0.997227	−	0.0744180i	$-0.0237099\pi$
$6$		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
$10$	0.166404	−	0.288220i	0.0526215	−	0.0911431i
$11$	−2.26053	−	1.30512i	−0.681575	−	0.393508i	0.118873	−	0.992909i	$-0.462072\pi$
$11$	−2.26053	−	1.30512i	−0.681575	−	0.393508i	−0.800448	+	0.599402i	$0.795405\pi$
$12$		0			0
$13$	3.41140	+	1.16719i	0.946153	+	0.323721i
$13$	3.41140	+	1.16719i	0.946153	+	0.323721i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.94383	+	3.36681i	0.471448	+	0.816572i	0.999466	−	0.0326607i	$-0.0103981\pi$
$17$	1.94383	+	3.36681i	0.471448	+	0.816572i	−0.528018	+	0.849233i	$0.677065\pi$
$18$		0			0
$19$	4.85997	−	2.80591i	1.11495	−	0.643719i	0.174846	−	0.984596i	$-0.444057\pi$
$19$	4.85997	−	2.80591i	1.11495	−	0.643719i	0.940108	+	0.340877i	$0.110724\pi$
$20$	0.288220	−	0.166404i	0.0644479	−	0.0372090i
$21$		0			0
$22$	−1.30512	−	2.26053i	−0.278252	−	0.481947i
$23$	−2.10628	+	3.64819i	−0.439191	+	0.760701i	−0.997627	−	0.0688467i	$-0.978068\pi$
$23$	−2.10628	+	3.64819i	−0.439191	+	0.760701i	0.558437	+	0.829547i	$0.311401\pi$
$24$		0			0
$25$	4.88924			0.977848
$26$	2.37076	+	2.71652i	0.464945	+	0.532753i
$27$		0			0
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	−0.593337	+	1.02769i	−0.110180	+	0.190837i	−0.915843	−	0.401537i	$-0.868476\pi$
$29$	−0.593337	+	1.02769i	−0.110180	+	0.190837i	0.805663	+	0.592374i	$0.201809\pi$
$30$		0			0
$31$			7.07434i			1.27059i	0.772270	+	0.635294i	$0.219121\pi$
$31$			7.07434i			1.27059i	−0.772270	+	0.635294i	$0.780879\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			3.88766i			0.666729i
$35$	0.166404	+	0.288220i	0.0281274	+	0.0487180i
$36$		0			0
$37$	0.499211	+	0.288220i	0.0820699	+	0.0473831i	0.540473	−	0.841361i	$-0.318245\pi$
$37$	0.499211	+	0.288220i	0.0820699	+	0.0473831i	−0.458403	+	0.888744i	$0.651579\pi$
$38$	5.61181			0.910356
$39$		0			0
$40$	0.332808			0.0526215
$41$	−0.451251	−	0.260530i	−0.0704735	−	0.0406879i	0.464349	−	0.885652i	$-0.346288\pi$
$41$	−0.451251	−	0.260530i	−0.0704735	−	0.0406879i	−0.534823	+	0.844964i	$0.679622\pi$
$42$		0			0
$43$	1.53717	+	2.66245i	0.234416	+	0.406020i	0.959103	−	0.283058i	$-0.0913489\pi$
$43$	1.53717	+	2.66245i	0.234416	+	0.406020i	−0.724687	+	0.689078i	$0.758016\pi$
$44$		−	2.61023i		−	0.393508i
$45$		0			0
$46$	−3.64819	+	2.10628i	−0.537896	+	0.310555i
$47$			12.0528i			1.75807i	0.476753	+	0.879037i	$0.341814\pi$
$47$			12.0528i			1.75807i	−0.476753	+	0.879037i	$0.658186\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	4.23421	+	2.44462i	0.598807	+	0.345721i
$51$		0			0
$52$	0.694883	+	3.53796i	0.0963629	+	0.490626i
$53$	9.71047			1.33384			0.666918	−	0.745132i	$-0.267613\pi$
$53$	9.71047			1.33384			0.666918	+	0.745132i	$0.267613\pi$
$54$		0			0
$55$	−0.434353	+	0.752321i	−0.0585681	+	0.101443i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−1.02769	+	0.593337i	−0.134942	+	0.0779090i
$59$	−9.07175	+	5.23758i	−1.18104	+	0.681875i	−0.956255	−	0.292533i	$-0.905502\pi$
$59$	−9.07175	+	5.23758i	−1.18104	+	0.681875i	−0.224786	+	0.974408i	$0.572168\pi$
$60$		0			0
$61$	−3.71989	−	6.44304i	−0.476283	−	0.824947i	0.523347	−	0.852119i	$-0.324683\pi$
$61$	−3.71989	−	6.44304i	−0.476283	−	0.824947i	−0.999631	+	0.0271724i	$0.991350\pi$
$62$	−3.53717	+	6.12656i	−0.449221	+	0.778073i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.388451	−	1.13534i	0.0481814	−	0.140822i
$66$		0			0
$67$	10.3233	+	5.96015i	1.26119	+	0.728148i	0.973305	−	0.229517i	$-0.0737145\pi$
$67$	10.3233	+	5.96015i	1.26119	+	0.728148i	0.287885	+	0.957665i	$0.407048\pi$
$68$	−1.94383	+	3.36681i	−0.235724	+	0.408286i
$69$		0			0
$70$			0.332808i			0.0397781i
$71$	0.818065	−	0.472310i	0.0970864	−	0.0560529i	−0.450671	−	0.892690i	$-0.648815\pi$
$71$	0.818065	−	0.472310i	0.0970864	−	0.0560529i	0.547757	+	0.836637i	$0.315482\pi$
$72$		0			0
$73$		−	4.66562i		−	0.546069i	−0.962004	−	0.273034i	$-0.911973\pi$
$73$		−	4.66562i		−	0.546069i	0.962004	−	0.273034i	$-0.0880273\pi$
$74$	0.288220	+	0.499211i	0.0335049	+	0.0580321i
$75$		0			0
$76$	4.85997	+	2.80591i	0.557477	+	0.321859i
$77$	2.61023			0.297464
$78$		0			0
$79$	−0.943042			−0.106101			−0.0530503	−	0.998592i	$-0.516894\pi$
$79$	−0.943042			−0.106101			−0.0530503	+	0.998592i	$0.516894\pi$
$80$	0.288220	+	0.166404i	0.0322240	+	0.0186045i
$81$		0			0
$82$	−0.260530	−	0.451251i	−0.0287707	−	0.0498323i
$83$		−	13.7172i		−	1.50566i	−0.658215	−	0.752830i	$-0.728688\pi$
$83$		−	13.7172i		−	1.50566i	0.658215	−	0.752830i	$-0.271312\pi$
$84$		0			0
$85$	1.12050	−	0.646922i	0.121535	−	0.0701685i
$86$			3.07434i			0.331514i
$87$		0			0
$88$	1.30512	−	2.26053i	0.139126	−	0.240973i
$89$	−2.92741	−	1.69014i	−0.310305	−	0.179155i	0.336758	−	0.941591i	$-0.390670\pi$
$89$	−2.92741	−	1.69014i	−0.310305	−	0.179155i	−0.647063	+	0.762436i	$0.724003\pi$
$90$		0			0
$91$	−3.53796	+	0.694883i	−0.370879	+	0.0728435i
$92$	−4.21257			−0.439191
$93$		0			0
$94$	−6.02638	+	10.4380i	−0.621573	+	1.07660i
$95$	−0.933827	−	1.61744i	−0.0958086	−	0.165945i
$96$		0			0
$97$	−5.03669	+	2.90793i	−0.511398	+	0.295256i	−0.733408	−	0.679789i	$-0.762072\pi$
$97$	−5.03669	+	2.90793i	−0.511398	+	0.295256i	0.222010	+	0.975044i	$0.428738\pi$
$98$	0.866025	−	0.500000i	0.0874818	−	0.0505076i
$99$		0			0
$100$	2.44462	+	4.23421i	0.244462	+	0.423421i
$101$	7.98516	−	13.8307i	0.794553	−	1.37621i	−0.128569	−	0.991701i	$-0.541038\pi$
$101$	7.98516	−	13.8307i	0.794553	−	1.37621i	0.923122	−	0.384506i	$-0.125628\pi$
$102$		0			0
$103$	−7.50641			−0.739629			−0.369814	−	0.929106i	$-0.620579\pi$
$103$	−7.50641			−0.739629			−0.369814	+	0.929106i	$0.620579\pi$
$104$	−1.16719	+	3.41140i	−0.114453	+	0.334515i
$105$		0			0
$106$	8.40951	+	4.85523i	0.816804	+	0.471582i
$107$	4.32539	−	7.49179i	0.418151	−	0.724259i	−0.577602	−	0.816318i	$-0.696012\pi$
$107$	4.32539	−	7.49179i	0.418151	−	0.724259i	0.995754	+	0.0920593i	$0.0293449\pi$
$108$		0			0
$109$			18.6144i			1.78293i	0.453088	+	0.891466i	$0.350322\pi$
$109$			18.6144i			1.78293i	−0.453088	+	0.891466i	$0.649678\pi$
$110$	−0.752321	+	0.434353i	−0.0717310	+	0.0414139i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	4.57512	+	7.92435i	0.430392	+	0.745460i	0.996907	−	0.0785911i	$-0.0250422\pi$
$113$	4.57512	+	7.92435i	0.430392	+	0.745460i	−0.566515	+	0.824051i	$0.691709\pi$
$114$		0			0
$115$	1.21415	+	0.700987i	0.113220	+	0.0653674i
$116$	−1.18667			−0.110180
$117$		0			0
$118$	−10.4752			−0.964316
$119$	−3.36681	−	1.94383i	−0.308635	−	0.178191i
$120$		0			0
$121$	−2.09334	−	3.62577i	−0.190303	−	0.329615i
$122$		−	7.43978i		−	0.673566i
$123$		0			0
$124$	−6.12656	+	3.53717i	−0.550181	+	0.317647i
$125$		−	3.29121i		−	0.294375i
$126$		0			0
$127$	3.38977	−	5.87125i	0.300793	−	0.520989i	−0.675523	−	0.737339i	$-0.736082\pi$
$127$	3.38977	−	5.87125i	0.300793	−	0.520989i	0.976316	+	0.216350i	$0.0694153\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	0.904078	−	0.789008i	0.0792929	−	0.0692006i
$131$	−7.22879			−0.631583			−0.315791	−	0.948829i	$-0.602270\pi$
$131$	−7.22879			−0.631583			−0.315791	+	0.948829i	$0.602270\pi$
$132$		0			0
$133$	−2.80591	+	4.85997i	−0.243303	+	0.421413i
$134$	5.96015	+	10.3233i	0.514879	+	0.891796i
$135$		0			0
$136$	−3.36681	+	1.94383i	−0.288702	+	0.166682i
$137$	10.2964	−	5.94462i	0.879679	−	0.507883i	0.00912669	−	0.999958i	$-0.497095\pi$
$137$	10.2964	−	5.94462i	0.879679	−	0.507883i	0.870553	+	0.492075i	$0.163762\pi$
$138$		0			0
$139$	−7.16056	−	12.4025i	−0.607351	−	1.05196i	−0.991675	−	0.128764i	$-0.958899\pi$
$139$	−7.16056	−	12.4025i	−0.607351	−	1.05196i	0.384324	−	0.923198i	$-0.374434\pi$
$140$	−0.166404	+	0.288220i	−0.0140637	+	0.0243590i
$141$		0			0
$142$	0.944620			0.0792707
$143$	−6.18825	−	7.09075i	−0.517488	−	0.592959i
$144$		0			0
$145$	0.342023	+	0.197467i	0.0284035	+	0.0163988i
$146$	2.33281	−	4.04054i	0.193065	−	0.334398i
$147$		0			0
$148$			0.576440i			0.0473831i
$149$	5.24548	−	3.02848i	0.429726	−	0.248103i	−0.269504	−	0.962999i	$-0.586860\pi$
$149$	5.24548	−	3.02848i	0.429726	−	0.248103i	0.699230	+	0.714897i	$0.253526\pi$
$150$		0			0
$151$			21.4953i			1.74926i	0.484791	+	0.874630i	$0.338896\pi$
$151$			21.4953i			1.74926i	−0.484791	+	0.874630i	$0.661104\pi$
$152$	2.80591	+	4.85997i	0.227589	+	0.394196i
$153$		0			0
$154$	2.26053	+	1.30512i	0.182159	+	0.105169i
$155$	2.35439			0.189109
$156$		0			0
$157$	2.29227			0.182943			0.0914714	−	0.995808i	$-0.470843\pi$
$157$	2.29227			0.182943			0.0914714	+	0.995808i	$0.470843\pi$
$158$	−0.816699	−	0.471521i	−0.0649731	−	0.0375122i
$159$		0			0
$160$	0.166404	+	0.288220i	0.0131554	+	0.0227858i
$161$		−	4.21257i		−	0.331997i
$162$		0			0
$163$	2.89314	−	1.67035i	0.226608	−	0.130832i	−0.382398	−	0.923998i	$-0.624902\pi$
$163$	2.89314	−	1.67035i	0.226608	−	0.130832i	0.609006	+	0.793165i	$0.291568\pi$
$164$		−	0.521059i		−	0.0406879i
$165$		0			0
$166$	6.85861	−	11.8795i	0.532331	−	0.922024i
$167$	−5.57802	−	3.22047i	−0.431640	−	0.249207i	0.268405	−	0.963306i	$-0.413503\pi$
$167$	−5.57802	−	3.22047i	−0.431640	−	0.249207i	−0.700045	+	0.714099i	$0.746837\pi$
$168$		0			0
$169$	10.2753	+	7.96352i	0.790410	+	0.612579i
$170$	1.29384			0.0992333
$171$		0			0
$172$	−1.53717	+	2.66245i	−0.117208	+	0.203010i
$173$	9.30718	+	16.1205i	0.707611	+	1.22562i	0.965741	+	0.259509i	$0.0835606\pi$
$173$	9.30718	+	16.1205i	0.707611	+	1.22562i	−0.258129	+	0.966110i	$0.583106\pi$
$174$		0			0
$175$	−4.23421	+	2.44462i	−0.320076	+	0.184796i
$176$	2.26053	−	1.30512i	0.170394	−	0.0983769i
$177$		0			0
$178$	−1.69014	−	2.92741i	−0.126682	−	0.219419i
$179$	11.1081	−	19.2398i	0.830261	−	1.43805i	−0.0675707	−	0.997714i	$-0.521525\pi$
$179$	11.1081	−	19.2398i	0.830261	−	1.43805i	0.897831	−	0.440339i	$-0.145142\pi$
$180$		0			0
$181$	−4.05853			−0.301669			−0.150834	−	0.988559i	$-0.548196\pi$
$181$	−4.05853			−0.301669			−0.150834	+	0.988559i	$0.548196\pi$
$182$	−3.41140	−	1.16719i	−0.252870	−	0.0865181i
$183$		0			0
$184$	−3.64819	−	2.10628i	−0.268948	−	0.155277i
$185$	0.0959218	−	0.166141i	0.00705231	−	0.0122150i
$186$		0			0
$187$		−	10.1477i		−	0.742074i
$188$	−10.4380	+	6.02638i	−0.761269	+	0.439519i
$189$		0			0
$190$		−	1.86765i		−	0.135494i
$191$	−5.86018	−	10.1501i	−0.424028	−	0.734438i	0.572301	−	0.820044i	$-0.306051\pi$
$191$	−5.86018	−	10.1501i	−0.424028	−	0.734438i	−0.996329	+	0.0856056i	$0.972718\pi$
$192$		0			0
$193$	−20.6123	−	11.9005i	−1.48371	−	0.856618i	−0.483877	−	0.875136i	$-0.660772\pi$
$193$	−20.6123	−	11.9005i	−1.48371	−	0.856618i	−0.999829	+	0.0185185i	$0.994105\pi$
$194$	−5.81587			−0.417555
$195$		0			0
$196$	1.00000			0.0714286
$197$	−8.73184	−	5.04133i	−0.622118	−	0.359180i	0.155575	−	0.987824i	$-0.450277\pi$
$197$	−8.73184	−	5.04133i	−0.622118	−	0.359180i	−0.777693	+	0.628644i	$0.783610\pi$
$198$		0			0
$199$	6.92504	+	11.9945i	0.490903	+	0.850269i	0.999945	−	0.0104725i	$-0.00333355\pi$
$199$	6.92504	+	11.9945i	0.490903	+	0.850269i	−0.509042	+	0.860742i	$0.670000\pi$
$200$			4.88924i			0.345721i
$201$		0			0
$202$	13.8307	−	7.98516i	0.973125	−	0.561834i
$203$		−	1.18667i		−	0.0832882i
$204$		0			0
$205$	−0.0867062	+	0.150180i	−0.00605583	+	0.0104890i
$206$	−6.50074	−	3.75321i	−0.452928	−	0.261498i
$207$		0			0
$208$	−2.71652	+	2.37076i	−0.188357	+	0.164383i
$209$	−14.6481			−1.01323
$210$		0			0
$211$	−2.27743	+	3.94462i	−0.156785	+	0.271559i	−0.933707	−	0.358037i	$-0.883446\pi$
$211$	−2.27743	+	3.94462i	−0.156785	+	0.271559i	0.776923	+	0.629596i	$0.216779\pi$
$212$	4.85523	+	8.40951i	0.333459	+	0.577568i
$213$		0			0
$214$	7.49179	−	4.32539i	0.512128	−	0.295677i
$215$	0.886085	−	0.511581i	0.0604305	−	0.0348896i
$216$		0			0
$217$	−3.53717	−	6.12656i	−0.240119	−	0.415898i
$218$	−9.30718	+	16.1205i	−0.630361	+	1.09182i
$219$		0			0
$220$	−0.868706			−0.0585681
$221$	2.70147	+	13.7544i	0.181720	+	0.925220i
$222$		0			0
$223$	−7.30359	−	4.21673i	−0.489085	−	0.282373i	0.235110	−	0.971969i	$-0.424455\pi$
$223$	−7.30359	−	4.21673i	−0.489085	−	0.282373i	−0.724195	+	0.689596i	$0.757788\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$			9.15025i			0.608666i
$227$	−24.2394	+	13.9946i	−1.60883	+	0.928857i	−0.619194	+	0.785238i	$0.712541\pi$
$227$	−24.2394	+	13.9946i	−1.60883	+	0.928857i	−0.989633	+	0.143619i	$0.954126\pi$
$228$		0			0
$229$		−	28.7785i		−	1.90174i	−0.309598	−	0.950868i	$-0.600194\pi$
$229$		−	28.7785i		−	1.90174i	0.309598	−	0.950868i	$-0.399806\pi$
$230$	0.700987	+	1.21415i	0.0462217	+	0.0800584i
$231$		0			0
$232$	−1.02769	−	0.593337i	−0.0674712	−	0.0389545i
$233$	18.8877			1.23737			0.618686	−	0.785638i	$-0.287665\pi$
$233$	18.8877			1.23737			0.618686	+	0.785638i	$0.287665\pi$
$234$		0			0
$235$	4.01125			0.261665
$236$	−9.07175	−	5.23758i	−0.590521	−	0.340937i
$237$		0			0
$238$	−1.94383	−	3.36681i	−0.126000	−	0.218238i
$239$		−	11.0933i		−	0.717565i	−0.933421	−	0.358783i	$-0.883192\pi$
$239$		−	11.0933i		−	0.717565i	0.933421	−	0.358783i	$-0.116808\pi$
$240$		0			0
$241$	−7.02686	+	4.05696i	−0.452640	+	0.261332i	−0.708944	−	0.705264i	$-0.750828\pi$
$241$	−7.02686	+	4.05696i	−0.452640	+	0.261332i	0.256305	+	0.966596i	$0.417495\pi$
$242$		−	4.18667i		−	0.269130i
$243$		0			0
$244$	3.71989	−	6.44304i	0.238142	−	0.412474i
$245$	−0.288220	−	0.166404i	−0.0184137	−	0.0106311i
$246$		0			0
$247$	19.8543	−	3.89955i	1.26330	−	0.248122i
$248$	−7.07434			−0.449221
$249$		0			0
$250$	1.64561	−	2.85027i	0.104077	−	0.180267i
$251$	1.58465	+	2.74469i	0.100022	+	0.173243i	0.911694	−	0.410871i	$-0.134775\pi$
$251$	1.58465	+	2.74469i	0.100022	+	0.173243i	−0.811671	+	0.584114i	$0.801442\pi$
$252$		0			0
$253$	9.52264	−	5.49790i	0.598683	−	0.345650i
$254$	5.87125	−	3.38977i	0.368395	−	0.212693i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.0967103	−	0.167507i	0.00603263	−	0.0104488i	−0.862993	−	0.505215i	$-0.831413\pi$
$257$	0.0967103	−	0.167507i	0.00603263	−	0.0104488i	0.869026	+	0.494766i	$0.164746\pi$
$258$		0			0
$259$	−0.576440			−0.0358182
$260$	1.17746	−	0.231262i	0.0730229	−	0.0143423i
$261$		0			0
$262$	−6.26032	−	3.61440i	−0.386764	−	0.223298i
$263$	6.02185	−	10.4301i	0.371323	−	0.643150i	−0.618446	−	0.785827i	$-0.712238\pi$
$263$	6.02185	−	10.4301i	0.371323	−	0.643150i	0.989769	+	0.142677i	$0.0455709\pi$
$264$		0			0
$265$		−	3.23172i		−	0.198523i
$266$	−4.85997	+	2.80591i	−0.297984	+	0.172041i
$267$		0			0
$268$			11.9203i			0.728148i
$269$	8.60487	+	14.9041i	0.524648	+	0.908718i	0.999588	+	0.0286993i	$0.00913654\pi$
$269$	8.60487	+	14.9041i	0.524648	+	0.908718i	−0.474940	+	0.880018i	$0.657530\pi$
$270$		0			0
$271$	−14.8453	−	8.57096i	−0.901790	−	0.520649i	−0.0240098	−	0.999712i	$-0.507643\pi$
$271$	−14.8453	−	8.57096i	−0.901790	−	0.520649i	−0.877781	+	0.479063i	$0.840977\pi$
$272$	−3.88766			−0.235724
$273$		0			0
$274$	11.8892			0.718255
$275$	−11.0523	−	6.38103i	−0.666477	−	0.384791i
$276$		0			0
$277$	−7.85660	−	13.6080i	−0.472057	−	0.817627i	0.527432	−	0.849598i	$-0.323155\pi$
$277$	−7.85660	−	13.6080i	−0.472057	−	0.817627i	−0.999489	+	0.0319704i	$0.989822\pi$
$278$		−	14.3211i		−	0.858924i
$279$		0			0
$280$	−0.288220	+	0.166404i	−0.0172244	+	0.00994453i
$281$			4.07337i			0.242997i	0.992592	+	0.121499i	$0.0387700\pi$
$281$			4.07337i			0.242997i	−0.992592	+	0.121499i	$0.961230\pi$
$282$		0			0
$283$	10.7674	−	18.6497i	0.640057	−	1.10861i	−0.345363	−	0.938469i	$-0.612244\pi$
$283$	10.7674	−	18.6497i	0.640057	−	1.10861i	0.985420	−	0.170142i	$-0.0544226\pi$
$284$	0.818065	+	0.472310i	0.0485432	+	0.0280264i
$285$		0			0
$286$	−1.81381	−	9.23490i	−0.107253	−	0.546071i
$287$	0.521059			0.0307572
$288$		0			0
$289$	0.943042	−	1.63340i	0.0554731	−	0.0960822i
$290$	0.197467	+	0.342023i	0.0115957	+	0.0200843i
$291$		0			0
$292$	4.04054	−	2.33281i	0.236455	−	0.136517i
$293$	−0.152457	+	0.0880210i	−0.00890662	+	0.00514224i	−0.504447	−	0.863443i	$-0.668303\pi$
$293$	−0.152457	+	0.0880210i	−0.00890662	+	0.00514224i	0.495540	+	0.868585i	$0.334970\pi$
$294$		0			0
$295$	1.74311	+	3.01915i	0.101488	+	0.175782i
$296$	−0.288220	+	0.499211i	−0.0167524	+	0.0290161i
$297$		0			0
$298$	6.05696			0.350870
$299$	−11.4435	+	9.98701i	−0.661796	+	0.577564i
$300$		0			0
$301$	−2.66245	−	1.53717i	−0.153461	−	0.0886009i
$302$	−10.7476	+	18.6154i	−0.618457	+	1.07120i
$303$		0			0
$304$			5.61181i			0.321859i
$305$	−2.14429	+	1.23801i	−0.122782	+	0.0708882i
$306$		0			0
$307$		−	20.7405i		−	1.18372i	−0.806040	−	0.591861i	$-0.798394\pi$
$307$		−	20.7405i		−	1.18372i	0.806040	−	0.591861i	$-0.201606\pi$
$308$	1.30512	+	2.26053i	0.0743660	+	0.128806i
$309$		0			0
$310$	2.03896	+	1.17720i	0.115805	+	0.0668603i
$311$	−10.9678			−0.621926			−0.310963	−	0.950422i	$-0.600652\pi$
$311$	−10.9678			−0.621926			−0.310963	+	0.950422i	$0.600652\pi$
$312$		0			0
$313$	16.2189			0.916746			0.458373	−	0.888760i	$-0.348432\pi$
$313$	16.2189			0.916746			0.458373	+	0.888760i	$0.348432\pi$
$314$	1.98516	+	1.14613i	0.112029	+	0.0646800i
$315$		0			0
$316$	−0.471521	−	0.816699i	−0.0265251	−	0.0459429i
$317$		−	10.5358i		−	0.591750i	−0.955227	−	0.295875i	$-0.904389\pi$
$317$		−	10.5358i		−	0.591750i	0.955227	−	0.295875i	$-0.0956112\pi$
$318$		0			0
$319$	2.68251	−	1.54875i	0.150192	−	0.0867133i
$320$			0.332808i			0.0186045i
$321$		0			0
$322$	2.10628	−	3.64819i	0.117379	−	0.203306i
$323$	18.8939	+	10.9084i	1.05129	+	0.606960i
$324$		0			0
$325$	16.6792	+	5.70668i	0.925193	+	0.316550i
$326$	3.34071			0.185025
$327$		0			0
$328$	0.260530	−	0.451251i	0.0143853	−	0.0249161i
$329$	−6.02638	−	10.4380i	−0.332245	−	0.575465i
$330$		0			0
$331$	−13.9687	+	8.06486i	−0.767792	+	0.443285i	−0.832086	−	0.554646i	$-0.812854\pi$
$331$	−13.9687	+	8.06486i	−0.767792	+	0.443285i	0.0642946	+	0.997931i	$0.479520\pi$
$332$	11.8795	−	6.85861i	0.651970	−	0.376415i
$333$		0			0
$334$	−3.22047	−	5.57802i	−0.176216	−	0.305216i
$335$	1.98358	−	3.43567i	0.108375	−	0.187711i
$336$		0			0
$337$	1.78785			0.0973906			0.0486953	−	0.998814i	$-0.484494\pi$
$337$	1.78785			0.0973906			0.0486953	+	0.998814i	$0.484494\pi$
$338$	4.91693	+	12.0343i	0.267446	+	0.654578i
$339$		0			0
$340$	1.12050	+	0.646922i	0.0607677	+	0.0350843i
$341$	9.23284	−	15.9917i	0.499986	−	0.866002i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.66245	+	1.53717i	−0.143550	+	0.0828786i
$345$		0			0
$346$			18.6144i			1.00071i
$347$	12.7030	+	22.0023i	0.681935	+	1.18115i	0.974389	+	0.224867i	$0.0721947\pi$
$347$	12.7030	+	22.0023i	0.681935	+	1.18115i	−0.292454	+	0.956280i	$0.594472\pi$
$348$		0			0
$349$	−24.5419	−	14.1693i	−1.31370	−	0.758463i	−0.330990	−	0.943634i	$-0.607383\pi$
$349$	−24.5419	−	14.1693i	−1.31370	−	0.758463i	−0.982706	+	0.185172i	$0.940716\pi$
$350$	−4.88924			−0.261341
$351$		0			0
$352$	2.61023			0.139126
$353$	1.69146	+	0.976568i	0.0900276	+	0.0519774i	0.544338	−	0.838866i	$-0.316781\pi$
$353$	1.69146	+	0.976568i	0.0900276	+	0.0519774i	−0.454310	+	0.890843i	$0.650114\pi$
$354$		0			0
$355$	−0.157188	−	0.272258i	−0.00834269	−	0.0144500i
$356$		−	3.38029i		−	0.179155i
$357$		0			0
$358$	19.2398	−	11.1081i	1.01686	−	0.587083i
$359$		−	27.6565i		−	1.45965i	−0.683633	−	0.729826i	$-0.739601\pi$
$359$		−	27.6565i		−	1.45965i	0.683633	−	0.729826i	$-0.260399\pi$
$360$		0			0
$361$	6.24622	−	10.8188i	0.328748	−	0.569409i
$362$	−3.51479	−	2.02927i	−0.184733	−	0.106656i
$363$		0			0
$364$	−2.37076	−	2.71652i	−0.124262	−	0.142384i
$365$	−1.55275			−0.0812748
$366$		0			0
$367$	−2.87888	+	4.98636i	−0.150276	+	0.260286i	−0.931329	−	0.364179i	$-0.881350\pi$
$367$	−2.87888	+	4.98636i	−0.150276	+	0.260286i	0.781053	+	0.624465i	$0.214683\pi$
$368$	−2.10628	−	3.64819i	−0.109798	−	0.190175i
$369$		0			0
$370$	0.166141	−	0.0959218i	0.00863728	−	0.00498673i
$371$	−8.40951	+	4.85523i	−0.436600	+	0.252071i
$372$		0			0
$373$	−13.9243	−	24.1177i	−0.720975	−	1.24877i	−0.960609	−	0.277903i	$-0.910361\pi$
$373$	−13.9243	−	24.1177i	−0.720975	−	1.24877i	0.239634	−	0.970863i	$-0.422973\pi$
$374$	5.07386	−	8.78817i	0.262363	−	0.454426i
$375$		0			0
$376$	−12.0528			−0.621573
$377$	−3.22362	+	2.81333i	−0.166025	+	0.144894i
$378$		0			0
$379$	−10.7836	−	6.22590i	−0.553915	−	0.319803i	0.196784	−	0.980447i	$-0.436950\pi$
$379$	−10.7836	−	6.22590i	−0.553915	−	0.319803i	−0.750700	+	0.660644i	$0.770283\pi$
$380$	0.933827	−	1.61744i	0.0479043	−	0.0829727i
$381$		0			0
$382$		−	11.7204i		−	0.599666i
$383$	8.42273	−	4.86286i	0.430381	−	0.248481i	−0.269128	−	0.963104i	$-0.586735\pi$
$383$	8.42273	−	4.86286i	0.430381	−	0.248481i	0.699509	+	0.714624i	$0.253402\pi$
$384$		0			0
$385$		−	0.868706i		−	0.0442734i
$386$	−11.9005	−	20.6123i	−0.605720	−	1.04914i
$387$		0			0
$388$	−5.03669	−	2.90793i	−0.255699	−	0.147628i
$389$	13.8910			0.704302			0.352151	−	0.935943i	$-0.385450\pi$
$389$	13.8910			0.704302			0.352151	+	0.935943i	$0.385450\pi$
$390$		0			0
$391$	−16.3770			−0.828223
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$		0			0
$394$	−5.04133	−	8.73184i	−0.253979	−	0.439904i
$395$			0.313852i			0.0157916i
$396$		0			0
$397$	5.87033	−	3.38924i	0.294624	−	0.170101i	−0.345401	−	0.938455i	$-0.612257\pi$
$397$	5.87033	−	3.38924i	0.294624	−	0.170101i	0.640025	+	0.768354i	$0.278924\pi$
$398$			13.8501i			0.694242i
$399$		0			0
$400$	−2.44462	+	4.23421i	−0.122231	+	0.211710i
$401$	−12.5254	−	7.23152i	−0.625487	−	0.361125i	0.153515	−	0.988146i	$-0.450941\pi$
$401$	−12.5254	−	7.23152i	−0.625487	−	0.361125i	−0.779002	+	0.627021i	$0.784274\pi$
$402$		0			0
$403$	−8.25711	+	24.1334i	−0.411316	+	1.20217i
$404$	15.9703			0.794553
$405$		0			0
$406$	0.593337	−	1.02769i	0.0294468	−	0.0510034i
$407$	−0.752321	−	1.30306i	−0.0372912	−	0.0645902i
$408$		0			0
$409$	20.2032	−	11.6643i	0.998982	−	0.576763i	0.0910351	−	0.995848i	$-0.470982\pi$
$409$	20.2032	−	11.6643i	0.998982	−	0.576763i	0.907947	+	0.419085i	$0.137649\pi$
$410$	−0.150180	+	0.0867062i	−0.00741684	+	0.00428212i
$411$		0			0
$412$	−3.75321	−	6.50074i	−0.184907	−	0.320269i
$413$	5.23758	−	9.07175i	0.257724	−	0.446392i
$414$		0			0
$415$	−4.56519			−0.224096
$416$	−3.53796	+	0.694883i	−0.173463	+	0.0340694i
$417$		0			0
$418$	−12.6857	−	7.32407i	−0.620476	−	0.358232i
$419$	−11.2898	+	19.5544i	−0.551540	+	0.955296i	0.446623	+	0.894722i	$0.352626\pi$
$419$	−11.2898	+	19.5544i	−0.551540	+	0.955296i	−0.998164	+	0.0605740i	$0.980707\pi$
$420$		0			0
$421$			34.1708i			1.66538i	0.553738	+	0.832691i	$0.313201\pi$
$421$			34.1708i			1.66538i	−0.553738	+	0.832691i	$0.686799\pi$
$422$	−3.94462	+	2.27743i	−0.192021	+	0.110863i
$423$		0			0
$424$			9.71047i			0.471582i
$425$	9.50385	+	16.4612i	0.461005	+	0.798483i
$426$		0			0
$427$	6.44304	+	3.71989i	0.311801	+	0.180018i
$428$	8.65078			0.418151
$429$		0			0
$430$	1.02316			0.0493413
$431$	−4.53528	−	2.61844i	−0.218457	−	0.126126i	0.386779	−	0.922173i	$-0.373588\pi$
$431$	−4.53528	−	2.61844i	−0.218457	−	0.126126i	−0.605235	+	0.796047i	$0.706921\pi$
$432$		0			0
$433$	8.41030	+	14.5671i	0.404173	+	0.700048i	0.994225	−	0.107317i	$-0.0342260\pi$
$433$	8.41030	+	14.5671i	0.404173	+	0.700048i	−0.590052	+	0.807365i	$0.700893\pi$
$434$		−	7.07434i		−	0.339579i
$435$		0			0
$436$	−16.1205	+	9.30718i	−0.772032	+	0.445733i
$437$			23.6401i			1.13086i
$438$		0			0
$439$	−7.36282	+	12.7528i	−0.351408	+	0.608657i	−0.986496	−	0.163783i	$-0.947630\pi$
$439$	−7.36282	+	12.7528i	−0.351408	+	0.608657i	0.635088	+	0.772440i	$0.280964\pi$
$440$	−0.752321	−	0.434353i	−0.0358655	−	0.0207070i
$441$		0			0
$442$	−4.53765	+	13.2624i	−0.215834	+	0.630827i
$443$	−36.2393			−1.72178			−0.860891	−	0.508789i	$-0.830093\pi$
$443$	−36.2393			−1.72178			−0.860891	+	0.508789i	$0.830093\pi$
$444$		0			0
$445$	−0.562493	+	0.974266i	−0.0266647	+	0.0461846i
$446$	−4.21673	−	7.30359i	−0.199668	−	0.345835i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	21.0351	−	12.1446i	0.992708	−	0.573140i	0.0866255	−	0.996241i	$-0.472392\pi$
$449$	21.0351	−	12.1446i	0.992708	−	0.573140i	0.906083	+	0.423101i	$0.139058\pi$
$450$		0			0
$451$	0.680043	+	1.17787i	0.0320220	+	0.0554637i
$452$	−4.57512	+	7.92435i	−0.215196	+	0.372730i
$453$		0			0
$454$	−27.9893			−1.31360
$455$	0.231262	+	1.17746i	0.0108417	+	0.0552001i
$456$		0			0
$457$	−28.8744	−	16.6706i	−1.35069	−	0.779819i	−0.362340	−	0.932046i	$-0.618022\pi$
$457$	−28.8744	−	16.6706i	−1.35069	−	0.779819i	−0.988345	+	0.152227i	$0.951355\pi$
$458$	14.3892	−	24.9229i	0.672365	−	1.16457i
$459$		0			0
$460$			1.40197i			0.0653674i
$461$	25.6317	−	14.7985i	1.19379	−	0.689234i	0.234625	−	0.972086i	$-0.424614\pi$
$461$	25.6317	−	14.7985i	1.19379	−	0.689234i	0.959164	+	0.282852i	$0.0912804\pi$
$462$		0			0
$463$			36.6027i			1.70107i	0.525918	+	0.850535i	$0.323722\pi$
$463$			36.6027i			1.70107i	−0.525918	+	0.850535i	$0.676278\pi$
$464$	−0.593337	−	1.02769i	−0.0275450	−	0.0477093i
$465$		0			0
$466$	16.3572	+	9.44383i	0.757732	+	0.437477i
$467$	6.21635			0.287658			0.143829	−	0.989603i	$-0.454058\pi$
$467$	6.21635			0.287658			0.143829	+	0.989603i	$0.454058\pi$
$468$		0			0
$469$	−11.9203			−0.550428
$470$	3.47384	+	2.00562i	0.160236	+	0.0925125i
$471$		0			0
$472$	−5.23758	−	9.07175i	−0.241079	−	0.417561i
$473$		−	8.02474i		−	0.368978i
$474$		0			0
$475$	23.7616	−	13.7187i	1.09026	−	0.629459i
$476$		−	3.88766i		−	0.178191i
$477$		0			0
$478$	5.54665	−	9.60707i	0.253698	−	0.439417i
$479$	29.0757	+	16.7869i	1.32850	+	0.767011i	0.985068	−	0.172165i	$-0.0550764\pi$
$479$	29.0757	+	16.7869i	1.32850	+	0.767011i	0.343434	+	0.939177i	$0.388410\pi$
$480$		0			0
$481$	1.36660	+	1.56591i	0.0623117	+	0.0713993i
$482$	−8.11392			−0.369579
$483$		0			0
$484$	2.09334	−	3.62577i	0.0951517	−	0.164808i
$485$	0.967782	+	1.67625i	0.0439447	+	0.0761145i
$486$		0			0
$487$	17.5020	−	10.1048i	0.793089	−	0.457890i	−0.0479597	−	0.998849i	$-0.515272\pi$
$487$	17.5020	−	10.1048i	0.793089	−	0.457890i	0.841049	+	0.540959i	$0.181939\pi$
$488$	6.44304	−	3.71989i	0.291663	−	0.168392i
$489$		0			0
$490$	−0.166404	−	0.288220i	−0.00751736	−	0.0130204i
$491$	3.38977	−	5.87125i	0.152978	−	0.264966i	−0.779343	−	0.626598i	$-0.784447\pi$
$491$	3.38977	−	5.87125i	0.152978	−	0.264966i	0.932321	+	0.361632i	$0.117780\pi$
$492$		0			0
$493$	−4.61339			−0.207777
$494$	19.1441	+	6.55006i	0.861336	+	0.294701i
$495$		0			0
$496$	−6.12656	−	3.53717i	−0.275090	−	0.158824i
$497$	−0.472310	+	0.818065i	−0.0211860	+	0.0366952i
$498$		0			0
$499$		−	11.0813i		−	0.496066i	−0.968752	−	0.248033i	$-0.920216\pi$
$499$		−	11.0813i		−	0.496066i	0.968752	−	0.248033i	$-0.0797841\pi$
$500$	2.85027	−	1.64561i	0.127468	−	0.0735938i
$501$		0			0
$502$			3.16930i			0.141453i
$503$	−14.9958	−	25.9735i	−0.668629	−	1.15810i	−0.978288	−	0.207252i	$-0.933548\pi$
$503$	−14.9958	−	25.9735i	−0.668629	−	1.15810i	0.309658	−	0.950848i	$-0.399785\pi$
$504$		0			0
$505$	−4.60296	−	2.65752i	−0.204829	−	0.118258i
$506$	10.9958			0.488823
$507$		0			0
$508$	6.77953			0.300793
$509$	−27.2629	−	15.7402i	−1.20840	−	0.697673i	−0.245994	−	0.969271i	$-0.579114\pi$
$509$	−27.2629	−	15.7402i	−1.20840	−	0.697673i	−0.962411	+	0.271599i	$0.912448\pi$
$510$		0			0
$511$	2.33281	+	4.04054i	0.103197	+	0.178743i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	0.167507	−	0.0967103i	0.00738843	−	0.00426571i
$515$			2.49819i			0.110083i
$516$		0			0
$517$	15.7303	−	27.2456i	0.691816	−	1.19826i
$518$	−0.499211	−	0.288220i	−0.0219341	−	0.0126637i
$519$		0			0
$520$	1.13534	+	0.388451i	0.0497880	+	0.0170347i
$521$	−17.8010			−0.779877			−0.389939	−	0.920841i	$-0.627504\pi$
$521$	−17.8010			−0.779877			−0.389939	+	0.920841i	$0.627504\pi$
$522$		0			0
$523$	−16.4702	+	28.5272i	−0.720192	+	1.24741i	0.240731	+	0.970592i	$0.422613\pi$
$523$	−16.4702	+	28.5272i	−0.720192	+	1.24741i	−0.960923	+	0.276817i	$0.910720\pi$
$524$	−3.61440	−	6.26032i	−0.157896	−	0.273483i
$525$		0			0
$526$	10.4301	−	6.02185i	0.454776	−	0.262565i
$527$	−23.8180	+	13.7513i	−1.03753	+	0.599017i
$528$		0			0
$529$	2.62713	+	4.55033i	0.114223	+	0.197840i
$530$	1.61586	−	2.79875i	0.0701884	−	0.121570i
$531$		0			0
$532$	−5.61181			−0.243303
$533$	−1.23531	−	1.41547i	−0.0535072	−	0.0613107i
$534$		0			0
$535$	−2.49333	−	1.43952i	−0.107796	−	0.0622360i
$536$	−5.96015	+	10.3233i	−0.257439	+	0.445898i
$537$		0			0
$538$			17.2097i			0.741965i
$539$	−2.26053	+	1.30512i	−0.0973679	+	0.0562154i
$540$		0			0
$541$			15.5204i			0.667276i	0.942701	+	0.333638i	$0.108276\pi$
$541$			15.5204i			0.667276i	−0.942701	+	0.333638i	$0.891724\pi$
$542$	−8.57096	−	14.8453i	−0.368154	−	0.637662i
$543$		0			0
$544$	−3.36681	−	1.94383i	−0.144351	−	0.0833411i
$545$	6.19500			0.265365
$546$		0			0
$547$	22.9529			0.981397			0.490698	−	0.871329i	$-0.336742\pi$
$547$	22.9529			0.981397			0.490698	+	0.871329i	$0.336742\pi$
$548$	10.2964	+	5.94462i	0.439840	+	0.253942i
$549$		0			0
$550$	−6.38103	−	11.0523i	−0.272088	−	0.471270i
$551$			6.65939i			0.283700i
$552$		0			0
$553$	0.816699	−	0.471521i	0.0347296	−	0.0200511i
$554$		−	15.7132i		−	0.667590i
$555$		0			0
$556$	7.16056	−	12.4025i	0.303675	−	0.525981i
$557$	20.8161	+	12.0182i	0.882005	+	0.509226i	0.871319	−	0.490717i	$-0.163265\pi$
$557$	20.8161	+	12.0182i	0.882005	+	0.509226i	0.0106863	+	0.999943i	$0.496598\pi$
$558$		0			0
$559$	2.13630	+	10.8769i	0.0903560	+	0.460043i
$560$	−0.332808			−0.0140637
$561$		0			0
$562$	−2.03669	+	3.52765i	−0.0859125	+	0.148805i
$563$	18.9379	+	32.8015i	0.798139	+	1.38242i	0.920827	+	0.389972i	$0.127515\pi$
$563$	18.9379	+	32.8015i	0.798139	+	1.38242i	−0.122687	+	0.992445i	$0.539151\pi$
$564$		0			0
$565$	2.63728	−	1.52264i	0.110951	−	0.0640578i
$566$	18.6497	−	10.7674i	0.783906	−	0.452589i
$567$		0			0
$568$	0.472310	+	0.818065i	0.0198177	+	0.0343252i
$569$	13.6833	−	23.7001i	0.573632	−	0.993560i	−0.422557	−	0.906336i	$-0.638867\pi$
$569$	13.6833	−	23.7001i	0.573632	−	0.993560i	0.996189	−	0.0872233i	$-0.0277994\pi$
$570$		0			0
$571$	17.6639			0.739213			0.369607	−	0.929188i	$-0.379492\pi$
$571$	17.6639			0.739213			0.369607	+	0.929188i	$0.379492\pi$
$572$	3.04665	−	8.90456i	0.127387	−	0.372318i
$573$		0			0
$574$	0.451251	+	0.260530i	0.0188348	+	0.0108743i
$575$	−10.2981	+	17.8369i	−0.429462	+	0.743849i
$576$		0			0
$577$		−	11.3804i		−	0.473772i	−0.971537	−	0.236886i	$-0.923873\pi$
$577$		−	11.3804i		−	0.473772i	0.971537	−	0.236886i	$-0.0761268\pi$
$578$	1.63340	−	0.943042i	0.0679404	−	0.0392254i
$579$		0			0
$580$			0.394934i			0.0163988i
$581$	6.85861	+	11.8795i	0.284543	+	0.492843i
$582$		0			0
$583$	−21.9508	−	12.6733i	−0.909109	−	0.524874i
$584$	4.66562			0.193065
$585$		0			0
$586$	−0.176042			−0.00727222
$587$	−15.9949	−	9.23469i	−0.660182	−	0.381156i	0.132164	−	0.991228i	$-0.457807\pi$
$587$	−15.9949	−	9.23469i	−0.660182	−	0.381156i	−0.792346	+	0.610072i	$0.791141\pi$
$588$		0			0
$589$	19.8499	+	34.3811i	0.817902	+	1.41665i
$590$			3.48621i			0.143525i
$591$		0			0
$592$	−0.499211	+	0.288220i	−0.0205175	+	0.0118458i
$593$		−	19.3561i		−	0.794859i	−0.917633	−	0.397429i	$-0.869902\pi$
$593$		−	19.3561i		−	0.794859i	0.917633	−	0.397429i	$-0.130098\pi$
$594$		0			0
$595$	−0.646922	+	1.12050i	−0.0265212	+	0.0459361i
$596$	5.24548	+	3.02848i	0.214863	+	0.124051i
$597$		0			0
$598$	−14.9039	+	2.92724i	−0.609465	+	0.119704i
$599$	−21.1818			−0.865466			−0.432733	−	0.901522i	$-0.642451\pi$
$599$	−21.1818			−0.865466			−0.432733	+	0.901522i	$0.642451\pi$
$600$		0			0
$601$	−11.0721	+	19.1774i	−0.451639	+	0.782261i	−0.998488	−	0.0549699i	$-0.982494\pi$
$601$	−11.0721	+	19.1774i	−0.451639	+	0.782261i	0.546849	+	0.837231i	$0.315827\pi$
$602$	−1.53717	−	2.66245i	−0.0626503	−	0.108513i
$603$		0			0
$604$	−18.6154	+	10.7476i	−0.757452	+	0.437315i
$605$	−1.20668	+	0.696679i	−0.0490586	+	0.0283240i
$606$		0			0
$607$	−17.1439	−	29.6942i	−0.695851	−	1.20525i	−0.969893	−	0.243531i	$-0.921694\pi$
$607$	−17.1439	−	29.6942i	−0.695851	−	1.20525i	0.274042	−	0.961718i	$-0.411639\pi$
$608$	−2.80591	+	4.85997i	−0.113795	+	0.197098i
$609$		0			0
$610$	−2.47602			−0.100251
$611$	−14.0679	+	41.1168i	−0.569125	+	1.66341i
$612$		0			0
$613$	14.7308	+	8.50484i	0.594972	+	0.343507i	0.767061	−	0.641574i	$-0.221718\pi$
$613$	14.7308	+	8.50484i	0.594972	+	0.343507i	−0.172089	+	0.985081i	$0.555052\pi$
$614$	10.3702	−	17.9618i	0.418509	−	0.724878i
$615$		0			0
$616$			2.61023i			0.105169i
$617$	−15.0005	+	8.66052i	−0.603896	+	0.348659i	−0.770573	−	0.637352i	$-0.780030\pi$
$617$	−15.0005	+	8.66052i	−0.603896	+	0.348659i	0.166677	+	0.986012i	$0.446696\pi$
$618$		0			0
$619$		−	0.621482i		−	0.0249795i	−0.999922	−	0.0124897i	$-0.996024\pi$
$619$		−	0.621482i		−	0.0249795i	0.999922	−	0.0124897i	$-0.00397571\pi$
$620$	1.17720	+	2.03896i	0.0472773	+	0.0818868i
$621$		0			0
$622$	−9.49838	−	5.48389i	−0.380850	−	0.219884i
$623$	3.38029			0.135428
$624$		0			0
$625$	23.3509			0.934034
$626$	14.0460	+	8.10945i	0.561390	+	0.324119i
$627$		0			0
$628$	1.14613	+	1.98516i	0.0457357	+	0.0792165i
$629$			2.24100i			0.0893546i
$630$		0			0
$631$	11.7575	−	6.78817i	0.468057	−	0.270233i	−0.247369	−	0.968921i	$-0.579566\pi$
$631$	11.7575	−	6.78817i	0.468057	−	0.270233i	0.715426	+	0.698688i	$0.246233\pi$
$632$		−	0.943042i		−	0.0375122i
$633$		0			0
$634$	5.26790	−	9.12428i	0.209215	−	0.362371i
$635$	−1.95400	−	1.12814i	−0.0775419	−	0.0447689i
$636$		0			0
$637$	2.71652	−	2.37076i	0.107632	−	0.0939331i
$638$	3.09750			0.122631
$639$		0			0
$640$	−0.166404	+	0.288220i	−0.00657769	+	0.0113929i
$641$	10.2558	+	17.7636i	0.405081	+	0.701622i	0.994331	−	0.106330i	$-0.0339098\pi$
$641$	10.2558	+	17.7636i	0.405081	+	0.701622i	−0.589250	+	0.807951i	$0.700577\pi$
$642$		0			0
$643$	−37.0253	+	21.3766i	−1.46013	+	0.843009i	−0.999017	−	0.0443295i	$-0.985885\pi$
$643$	−37.0253	+	21.3766i	−1.46013	+	0.843009i	−0.461118	+	0.887339i	$0.652552\pi$
$644$	3.64819	−	2.10628i	0.143759	−	0.0829992i
$645$		0			0
$646$	10.9084	+	18.8939i	0.429186	+	0.743372i
$647$	13.1115	−	22.7098i	0.515466	−	0.892814i	−0.484372	−	0.874862i	$-0.660952\pi$
$647$	13.1115	−	22.7098i	0.515466	−	0.892814i	0.999839	−	0.0179521i	$-0.00571465\pi$
$648$		0			0
$649$	27.3426			1.07329
$650$	11.5912	+	13.2817i	0.454646	+	0.520952i
$651$		0			0
$652$	2.89314	+	1.67035i	0.113304	+	0.0654161i
$653$	−4.36935	+	7.56794i	−0.170986	+	0.296156i	−0.938765	−	0.344558i	$-0.888029\pi$
$653$	−4.36935	+	7.56794i	−0.170986	+	0.296156i	0.767779	+	0.640715i	$0.221362\pi$
$654$		0			0
$655$			2.40580i			0.0940023i
$656$	0.451251	−	0.260530i	0.0176184	−	0.0101720i
$657$		0			0
$658$		−	12.0528i		−	0.469865i
$659$	0.251052	+	0.434834i	0.00977958	+	0.0169387i	0.870874	−	0.491507i	$-0.163554\pi$
$659$	0.251052	+	0.434834i	0.00977958	+	0.0169387i	−0.861094	+	0.508445i	$0.830220\pi$
$660$		0			0
$661$	27.1062	+	15.6498i	1.05431	+	0.608705i	0.923853	−	0.382749i	$-0.125022\pi$
$661$	27.1062	+	15.6498i	1.05431	+	0.608705i	0.130456	+	0.991454i	$0.458356\pi$
$662$	−16.1297			−0.626899
$663$		0			0
$664$	13.7172			0.532331
$665$	1.61744	+	0.933827i	0.0627215	+	0.0362123i
$666$		0			0
$667$	−2.49947	−	4.32922i	−0.0967800	−	0.167628i
$668$		−	6.44094i		−	0.249207i
$669$		0			0
$670$	3.43567	−	1.98358i	0.132731	−	0.0766325i
$671$			19.4196i			0.749685i
$672$		0			0
$673$	−11.8585	+	20.5395i	−0.457112	+	0.791741i	−0.998807	−	0.0488340i	$-0.984449\pi$
$673$	−11.8585	+	20.5395i	−0.457112	+	0.791741i	0.541695	+	0.840575i	$0.317783\pi$
$674$	1.54833	+	0.893927i	0.0596393	+	0.0344328i
$675$		0			0
$676$	−1.75895	+	12.8805i	−0.0676520	+	0.495402i
$677$	−17.8136			−0.684631			−0.342315	−	0.939585i	$-0.611211\pi$
$677$	−17.8136			−0.684631			−0.342315	+	0.939585i	$0.611211\pi$
$678$		0			0
$679$	2.90793	−	5.03669i	0.111596	−	0.193290i
$680$	0.646922	+	1.12050i	0.0248083	+	0.0429693i
$681$		0			0
$682$	15.9917	−	9.23284i	0.612356	−	0.353544i
$683$	−10.3174	+	5.95673i	−0.394783	+	0.227928i	−0.684230	−	0.729266i	$-0.739862\pi$
$683$	−10.3174	+	5.95673i	−0.394783	+	0.227928i	0.289448	+	0.957194i	$0.406528\pi$
$684$		0			0
$685$	−1.97841	−	3.42671i	−0.0755913	−	0.130928i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	−3.07434			−0.117208
$689$	33.1263	+	11.3340i	1.26201	+	0.431790i
$690$		0			0
$691$	−17.3085	−	9.99306i	−0.658446	−	0.380154i	0.133239	−	0.991084i	$-0.457462\pi$
$691$	−17.3085	−	9.99306i	−0.658446	−	0.380154i	−0.791685	+	0.610930i	$0.790796\pi$
$692$	−9.30718	+	16.1205i	−0.353806	+	0.612810i
$693$		0			0
$694$			25.4061i			0.964402i
$695$	−4.12763	+	2.38309i	−0.156570	+	0.0903957i
$696$		0			0
$697$		−	2.02570i		−	0.0767289i
$698$	−14.1693	−	24.5419i	−0.536314	−	0.928923i
$699$		0			0
$700$	−4.23421	−	2.44462i	−0.160038	−	0.0923979i
$701$	23.9244			0.903613			0.451806	−	0.892116i	$-0.350780\pi$
$701$	23.9244			0.903613			0.451806	+	0.892116i	$0.350780\pi$
$702$		0			0
$703$	3.23487			0.122005
$704$	2.26053	+	1.30512i	0.0851969	+	0.0491885i
$705$		0			0
$706$	0.976568	+	1.69146i	0.0367536	+	0.0636591i
$707$			15.9703i			0.600626i
$708$		0			0
$709$	30.7406	−	17.7481i	1.15449	−	0.666544i	0.204512	−	0.978864i	$-0.434439\pi$
$709$	30.7406	−	17.7481i	1.15449	−	0.666544i	0.949977	+	0.312320i	$0.101106\pi$
$710$		−	0.314377i		−	0.0117983i
$711$		0			0
$712$	1.69014	−	2.92741i	0.0633408	−	0.109710i
$713$	−25.8085	−	14.9006i	−0.966537	−	0.558031i
$714$		0			0
$715$	−2.35986	+	2.05950i	−0.0882536	+	0.0770208i
$716$	22.2163			0.830261
$717$		0			0
$718$	13.8282	−	23.9512i	0.516065	−	0.893851i
$719$	3.09097	+	5.35372i	0.115274	+	0.199660i	0.917889	−	0.396837i	$-0.129892\pi$
$719$	3.09097	+	5.35372i	0.115274	+	0.199660i	−0.802615	+	0.596497i	$0.796559\pi$
$720$		0			0
$721$	6.50074	−	3.75321i	0.242100	−	0.139777i
$722$	10.8188	−	6.24622i	0.402633	−	0.232460i
$723$		0			0
$724$	−2.02927	−	3.51479i	−0.0754171	−	0.130626i
$725$	−2.90097	+	5.02462i	−0.107739	+	0.186610i
$726$		0			0
$727$	−43.2387			−1.60363			−0.801817	−	0.597569i	$-0.796133\pi$
$727$	−43.2387			−1.60363			−0.801817	+	0.597569i	$0.796133\pi$
$728$	−0.694883	−	3.53796i	−0.0257541	−	0.131125i
$729$		0			0
$730$	−1.34472	−	0.776376i	−0.0497704	−	0.0287350i
$731$	−5.97599	+	10.3507i	−0.221030	+	0.382835i
$732$		0			0
$733$			32.0306i			1.18308i	0.806277	+	0.591538i	$0.201479\pi$
$733$			32.0306i			1.18308i	−0.806277	+	0.591538i	$0.798521\pi$
$734$	−4.98636	+	2.87888i	−0.184050	+	0.106261i
$735$		0			0
$736$		−	4.21257i		−	0.155277i
$737$	−15.5574	−	26.9462i	−0.573064	−	0.992576i
$738$		0			0
$739$	−22.0558	−	12.7339i	−0.811334	−	0.468424i	0.0360848	−	0.999349i	$-0.488511\pi$
$739$	−22.0558	−	12.7339i	−0.811334	−	0.468424i	−0.847419	+	0.530925i	$0.821845\pi$
$740$	0.191844			0.00705231
$741$		0			0
$742$	−9.71047			−0.356482
$743$	12.5533	+	7.24763i	0.460535	+	0.265890i	0.712269	−	0.701906i	$-0.247668\pi$
$743$	12.5533	+	7.24763i	0.460535	+	0.265890i	−0.251734	+	0.967796i	$0.581001\pi$
$744$		0			0
$745$	−1.00790	−	1.74574i	−0.0369266	−	0.0639588i
$746$		−	27.8487i		−	1.01961i
$747$		0			0
$748$	8.78817	−	5.07386i	0.321327	−	0.185519i
$749$			8.65078i			0.316092i
$750$		0			0
$751$	14.5632	−	25.2243i	0.531420	−	0.920447i	−0.467907	−	0.883777i	$-0.654992\pi$
$751$	14.5632	−	25.2243i	0.531420	−	0.920447i	0.999327	−	0.0366690i	$-0.0116747\pi$
$752$	−10.4380	−	6.02638i	−0.380634	−	0.219759i
$753$		0			0
$754$	−4.19840	+	0.824599i	−0.152897	+	0.0300301i
$755$	7.15379			0.260353
$756$		0			0
$757$	10.0230	−	17.3603i	0.364292	−	0.630973i	−0.624370	−	0.781129i	$-0.714644\pi$
$757$	10.0230	−	17.3603i	0.364292	−	0.630973i	0.988662	+	0.150156i	$0.0479776\pi$
$758$	−6.22590	−	10.7836i	−0.226135	−	0.391677i
$759$		0			0
$760$	1.61744	−	0.933827i	0.0586706	−	0.0338735i
$761$	−16.4954	+	9.52360i	−0.597956	+	0.345230i	−0.768237	−	0.640165i	$-0.778866\pi$
$761$	−16.4954	+	9.52360i	−0.597956	+	0.345230i	0.170281	+	0.985396i	$0.445532\pi$
$762$		0			0
$763$	−9.30718	−	16.1205i	−0.336942	−	0.583601i
$764$	5.86018	−	10.1501i	0.212014	−	0.367219i
$765$		0			0
$766$	9.72573			0.351405
$767$	−37.0607	+	7.27900i	−1.33818	+	0.262830i
$768$		0			0
$769$	13.2055	+	7.62418i	0.476201	+	0.274935i	0.718832	−	0.695184i	$-0.244677\pi$
$769$	13.2055	+	7.62418i	0.476201	+	0.274935i	−0.242631	+	0.970119i	$0.578010\pi$
$770$	0.434353	−	0.752321i	0.0156530	−	0.0271118i
$771$		0			0
$772$		−	23.8010i		−	0.856618i
$773$	5.77259	−	3.33281i	0.207626	−	0.119873i	−0.392582	−	0.919717i	$-0.628418\pi$
$773$	5.77259	−	3.33281i	0.207626	−	0.119873i	0.600207	+	0.799844i	$0.295085\pi$
$774$		0			0
$775$			34.5881i			1.24244i
$776$	−2.90793	−	5.03669i	−0.104389	−	0.180807i
$777$		0			0
$778$	12.0300	+	6.94550i	0.431295	+	0.249008i
$779$	−2.92409			−0.104766
$780$		0			0
$781$	−2.46568			−0.0882289
$782$	−14.1829	−	8.18852i	−0.507181	−	0.292821i

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.166404 - 0.288220i) q^{10} +(-2.26053 - 1.30512i) q^{11} +(3.41140 + 1.16719i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.94383 + 3.36681i) q^{17} +(4.85997 - 2.80591i) q^{19} +(0.288220 - 0.166404i) q^{20} +(-1.30512 - 2.26053i) q^{22} +(-2.10628 + 3.64819i) q^{23} +4.88924 q^{25} +(2.37076 + 2.71652i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-0.593337 + 1.02769i) q^{29} +7.07434i q^{31} +(-0.866025 + 0.500000i) q^{32} +3.88766i q^{34} +(0.166404 + 0.288220i) q^{35} +(0.499211 + 0.288220i) q^{37} +5.61181 q^{38} +0.332808 q^{40} +(-0.451251 - 0.260530i) q^{41} +(1.53717 + 2.66245i) q^{43} -2.61023i q^{44} +(-3.64819 + 2.10628i) q^{46} +12.0528i q^{47} +(0.500000 - 0.866025i) q^{49} +(4.23421 + 2.44462i) q^{50} +(0.694883 + 3.53796i) q^{52} +9.71047 q^{53} +(-0.434353 + 0.752321i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.02769 + 0.593337i) q^{58} +(-9.07175 + 5.23758i) q^{59} +(-3.71989 - 6.44304i) q^{61} +(-3.53717 + 6.12656i) q^{62} -1.00000 q^{64} +(0.388451 - 1.13534i) q^{65} +(10.3233 + 5.96015i) q^{67} +(-1.94383 + 3.36681i) q^{68} +0.332808i q^{70} +(0.818065 - 0.472310i) q^{71} -4.66562i q^{73} +(0.288220 + 0.499211i) q^{74} +(4.85997 + 2.80591i) q^{76} +2.61023 q^{77} -0.943042 q^{79} +(0.288220 + 0.166404i) q^{80} +(-0.260530 - 0.451251i) q^{82} -13.7172i q^{83} +(1.12050 - 0.646922i) q^{85} +3.07434i q^{86} +(1.30512 - 2.26053i) q^{88} +(-2.92741 - 1.69014i) q^{89} +(-3.53796 + 0.694883i) q^{91} -4.21257 q^{92} +(-6.02638 + 10.4380i) q^{94} +(-0.933827 - 1.61744i) q^{95} +(-5.03669 + 2.90793i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

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