LMFDB - Embedded newform 1638.2.j.n.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

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

Embedding invariants

Embedding label			235.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.n.1171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.707107 + 1.22474i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.707107 + 1.22474i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(-0.707107 + 1.22474i) q^{10} +(-1.20711 + 2.09077i) q^{11} +1.00000 q^{13} +(-2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.62132 + 2.80821i) q^{17} +(-1.50000 - 2.59808i) q^{19} -1.41421 q^{20} -2.41421 q^{22} +(2.53553 + 4.39167i) q^{23} +(1.50000 - 2.59808i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-1.00000 - 2.44949i) q^{28} -5.00000 q^{29} +(-0.585786 + 1.01461i) q^{31} +(0.500000 - 0.866025i) q^{32} -3.24264 q^{34} +(-3.70711 - 0.507306i) q^{35} +(-4.53553 - 7.85578i) q^{37} +(1.50000 - 2.59808i) q^{38} +(-0.707107 - 1.22474i) q^{40} -7.41421 q^{41} -0.828427 q^{43} +(-1.20711 - 2.09077i) q^{44} +(-2.53553 + 4.39167i) q^{46} +(4.50000 + 7.79423i) q^{47} +(-1.74264 - 6.77962i) q^{49} +3.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-5.15685 + 8.93193i) q^{53} -3.41421 q^{55} +(1.62132 - 2.09077i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(5.20711 - 9.01897i) q^{59} +(-1.62132 - 2.80821i) q^{61} -1.17157 q^{62} +1.00000 q^{64} +(0.707107 + 1.22474i) q^{65} +(1.67157 - 2.89525i) q^{67} +(-1.62132 - 2.80821i) q^{68} +(-1.41421 - 3.46410i) q^{70} +1.00000 q^{71} +(-6.53553 + 11.3199i) q^{73} +(4.53553 - 7.85578i) q^{74} +3.00000 q^{76} +(-2.41421 - 5.91359i) q^{77} +(4.65685 + 8.06591i) q^{79} +(0.707107 - 1.22474i) q^{80} +(-3.70711 - 6.42090i) q^{82} -3.65685 q^{83} -4.58579 q^{85} +(-0.414214 - 0.717439i) q^{86} +(1.20711 - 2.09077i) q^{88} +(1.12132 + 1.94218i) q^{89} +(-1.62132 + 2.09077i) q^{91} -5.07107 q^{92} +(-4.50000 + 7.79423i) q^{94} +(2.12132 - 3.67423i) q^{95} -11.8995 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} - 2 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} - 6 q^{19} - 4 q^{22} - 4 q^{23} + 6 q^{25} + 2 q^{26} - 4 q^{28} - 20 q^{29} - 8 q^{31} + 2 q^{32} + 4 q^{34} - 12 q^{35} - 4 q^{37} + 6 q^{38} - 24 q^{41} + 8 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 2 q^{52} + 2 q^{53} - 8 q^{55} - 2 q^{56} - 10 q^{58} + 18 q^{59} + 2 q^{61} - 16 q^{62} + 4 q^{64} + 18 q^{67} + 2 q^{68} + 4 q^{71} - 12 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 4 q^{79} - 12 q^{82} + 8 q^{83} - 24 q^{85} + 4 q^{86} + 2 q^{88} - 4 q^{89} + 2 q^{91} + 8 q^{92} - 18 q^{94} - 8 q^{97} + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8 - 2 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 - 6 * q^19 - 4 * q^22 - 4 * q^23 + 6 * q^25 + 2 * q^26 - 4 * q^28 - 20 * q^29 - 8 * q^31 + 2 * q^32 + 4 * q^34 - 12 * q^35 - 4 * q^37 + 6 * q^38 - 24 * q^41 + 8 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 2 * q^52 + 2 * q^53 - 8 * q^55 - 2 * q^56 - 10 * q^58 + 18 * q^59 + 2 * q^61 - 16 * q^62 + 4 * q^64 + 18 * q^67 + 2 * q^68 + 4 * q^71 - 12 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 4 * q^79 - 12 * q^82 + 8 * q^83 - 24 * q^85 + 4 * q^86 + 2 * q^88 - 4 * q^89 + 2 * q^91 + 8 * q^92 - 18 * q^94 - 8 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.707107	+	1.22474i	0.316228	+	0.547723i	0.979698	−	0.200480i	$-0.0642503\pi$
$5$	0.707107	+	1.22474i	0.316228	+	0.547723i	−0.663470	+	0.748203i	$0.730917\pi$
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	−0.988608	−	0.150513i	$-0.951908\pi$
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	0.624652	+	0.780903i	$0.285241\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−2.62132	−	0.358719i	−0.700577	−	0.0958718i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.62132	+	2.80821i	−0.393228	+	0.681091i	−0.992873	−	0.119175i	$-0.961975\pi$
$17$	−1.62132	+	2.80821i	−0.393228	+	0.681091i	0.599645	+	0.800266i	$0.295308\pi$
$18$		0			0
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	−1.41421			−0.316228
$21$		0			0
$22$	−2.41421			−0.514712
$23$	2.53553	+	4.39167i	0.528695	+	0.915727i	0.999440	+	0.0334578i	$0.0106519\pi$
$23$	2.53553	+	4.39167i	0.528695	+	0.915727i	−0.470745	+	0.882269i	$0.656015\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$	−1.00000	−	2.44949i	−0.188982	−	0.462910i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	−0.913824	−	0.406110i	$-0.866885\pi$
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	0.808614	+	0.588340i	$0.200218\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−3.24264			−0.556108
$35$	−3.70711	−	0.507306i	−0.626615	−	0.0857504i
$36$		0			0
$37$	−4.53553	−	7.85578i	−0.745637	−	1.29148i	−0.949896	−	0.312565i	$-0.898812\pi$
$37$	−4.53553	−	7.85578i	−0.745637	−	1.29148i	0.204259	−	0.978917i	$-0.434521\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	−0.707107	−	1.22474i	−0.111803	−	0.193649i
$41$	−7.41421			−1.15791			−0.578953	−	0.815361i	$-0.696538\pi$
$41$	−7.41421			−1.15791			−0.578953	+	0.815361i	$0.696538\pi$
$42$		0			0
$43$	−0.828427			−0.126334			−0.0631670	−	0.998003i	$-0.520120\pi$
$43$	−0.828427			−0.126334			−0.0631670	+	0.998003i	$0.520120\pi$
$44$	−1.20711	−	2.09077i	−0.181978	−	0.315195i
$45$		0			0
$46$	−2.53553	+	4.39167i	−0.373844	+	0.647517i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	3.00000			0.424264
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−5.15685	+	8.93193i	−0.708348	+	1.22690i	0.257121	+	0.966379i	$0.417226\pi$
$53$	−5.15685	+	8.93193i	−0.708348	+	1.22690i	−0.965469	+	0.260516i	$0.916107\pi$
$54$		0			0
$55$	−3.41421			−0.460372
$56$	1.62132	−	2.09077i	0.216658	−	0.279391i
$57$		0			0
$58$	−2.50000	−	4.33013i	−0.328266	−	0.568574i
$59$	5.20711	−	9.01897i	0.677908	−	1.17417i	−0.297702	−	0.954659i	$-0.596220\pi$
$59$	5.20711	−	9.01897i	0.677908	−	1.17417i	0.975610	−	0.219512i	$-0.0704464\pi$
$60$		0			0
$61$	−1.62132	−	2.80821i	−0.207589	−	0.359554i	0.743366	−	0.668885i	$-0.233228\pi$
$61$	−1.62132	−	2.80821i	−0.207589	−	0.359554i	−0.950954	+	0.309331i	$0.899895\pi$
$62$	−1.17157			−0.148790
$63$		0			0
$64$	1.00000			0.125000
$65$	0.707107	+	1.22474i	0.0877058	+	0.151911i
$66$		0			0
$67$	1.67157	−	2.89525i	0.204215	−	0.353711i	−0.745667	−	0.666319i	$-0.767869\pi$
$67$	1.67157	−	2.89525i	0.204215	−	0.353711i	0.949882	+	0.312608i	$0.101202\pi$
$68$	−1.62132	−	2.80821i	−0.196614	−	0.340545i
$69$		0			0
$70$	−1.41421	−	3.46410i	−0.169031	−	0.414039i
$71$	1.00000			0.118678			0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000			0.118678			0.0593391	+	0.998238i	$0.481101\pi$
$72$		0			0
$73$	−6.53553	+	11.3199i	−0.764926	+	1.32489i	0.175359	+	0.984505i	$0.443891\pi$
$73$	−6.53553	+	11.3199i	−0.764926	+	1.32489i	−0.940285	+	0.340387i	$0.889442\pi$
$74$	4.53553	−	7.85578i	0.527245	−	0.913215i
$75$		0			0
$76$	3.00000			0.344124
$77$	−2.41421	−	5.91359i	−0.275125	−	0.673916i
$78$		0			0
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	0.999612	+	0.0278643i	$0.00887063\pi$
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	−0.475675	+	0.879621i	$0.657796\pi$
$80$	0.707107	−	1.22474i	0.0790569	−	0.136931i
$81$		0			0
$82$	−3.70711	−	6.42090i	−0.409381	−	0.709069i
$83$	−3.65685			−0.401392			−0.200696	−	0.979654i	$-0.564320\pi$
$83$	−3.65685			−0.401392			−0.200696	+	0.979654i	$0.564320\pi$
$84$		0			0
$85$	−4.58579			−0.497398
$86$	−0.414214	−	0.717439i	−0.0446658	−	0.0773634i
$87$		0			0
$88$	1.20711	−	2.09077i	0.128678	−	0.222877i
$89$	1.12132	+	1.94218i	0.118860	+	0.205871i	0.919316	−	0.393520i	$-0.128743\pi$
$89$	1.12132	+	1.94218i	0.118860	+	0.205871i	−0.800456	+	0.599391i	$0.795409\pi$
$90$		0			0
$91$	−1.62132	+	2.09077i	−0.169961	+	0.219172i
$92$	−5.07107			−0.528695
$93$		0			0
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	2.12132	−	3.67423i	0.217643	−	0.376969i
$96$		0			0
$97$	−11.8995			−1.20821			−0.604105	−	0.796904i	$-0.706469\pi$
$97$	−11.8995			−1.20821			−0.604105	+	0.796904i	$0.706469\pi$
$98$	5.00000	−	4.89898i	0.505076	−	0.494872i
$99$		0			0
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	−3.41421	+	5.91359i	−0.339727	+	0.588424i	−0.984381	−	0.176050i	$-0.943668\pi$
$101$	−3.41421	+	5.91359i	−0.339727	+	0.588424i	0.644654	+	0.764474i	$0.277001\pi$
$102$		0			0
$103$	5.24264	+	9.08052i	0.516573	+	0.894730i	0.999815	+	0.0192435i	$0.00612576\pi$
$103$	5.24264	+	9.08052i	0.516573	+	0.894730i	−0.483242	+	0.875487i	$0.660541\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−10.3137			−1.00176
$107$	1.17157	+	2.02922i	0.113260	+	0.196172i	0.917083	−	0.398696i	$-0.130537\pi$
$107$	1.17157	+	2.02922i	0.113260	+	0.196172i	−0.803823	+	0.594869i	$0.797204\pi$
$108$		0			0
$109$	4.82843	−	8.36308i	0.462479	−	0.801038i	−0.536604	−	0.843834i	$-0.680293\pi$
$109$	4.82843	−	8.36308i	0.462479	−	0.801038i	0.999084	+	0.0427961i	$0.0136266\pi$
$110$	−1.70711	−	2.95680i	−0.162766	−	0.281919i
$111$		0			0
$112$	2.62132	+	0.358719i	0.247691	+	0.0338958i
$113$	−8.07107			−0.759262			−0.379631	−	0.925138i	$-0.623949\pi$
$113$	−8.07107			−0.759262			−0.379631	+	0.925138i	$0.623949\pi$
$114$		0			0
$115$	−3.58579	+	6.21076i	−0.334376	+	0.579157i
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$		0			0
$118$	10.4142			0.958706
$119$	−3.24264	−	7.94282i	−0.297252	−	0.728117i
$120$		0			0
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$	1.62132	−	2.80821i	0.146787	−	0.254243i
$123$		0			0
$124$	−0.585786	−	1.01461i	−0.0526052	−	0.0911148i
$125$	11.3137			1.01193
$126$		0			0
$127$	−9.89949			−0.878438			−0.439219	−	0.898380i	$-0.644745\pi$
$127$	−9.89949			−0.878438			−0.439219	+	0.898380i	$0.644745\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.707107	+	1.22474i	−0.0620174	+	0.107417i
$131$	−4.94975	−	8.57321i	−0.432461	−	0.749045i	0.564623	−	0.825349i	$-0.309022\pi$
$131$	−4.94975	−	8.57321i	−0.432461	−	0.749045i	−0.997085	+	0.0763036i	$0.975688\pi$
$132$		0			0
$133$	7.86396	+	1.07616i	0.681892	+	0.0933148i
$134$	3.34315			0.288804
$135$		0			0
$136$	1.62132	−	2.80821i	0.139027	−	0.240802i
$137$	0.535534	−	0.927572i	0.0457537	−	0.0792478i	−0.842242	−	0.539100i	$-0.818764\pi$
$137$	0.535534	−	0.927572i	0.0457537	−	0.0792478i	0.887995	+	0.459852i	$0.152098\pi$
$138$		0			0
$139$	21.2132			1.79928			0.899640	−	0.436632i	$-0.143829\pi$
$139$	21.2132			1.79928			0.899640	+	0.436632i	$0.143829\pi$
$140$	2.29289	−	2.95680i	0.193785	−	0.249895i
$141$		0			0
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	−1.20711	+	2.09077i	−0.100943	+	0.174839i
$144$		0			0
$145$	−3.53553	−	6.12372i	−0.293610	−	0.508548i
$146$	−13.0711			−1.08177
$147$		0			0
$148$	9.07107			0.745637
$149$	−1.94975	−	3.37706i	−0.159730	−	0.276660i	0.775042	−	0.631910i	$-0.217729\pi$
$149$	−1.94975	−	3.37706i	−0.159730	−	0.276660i	−0.934771	+	0.355251i	$0.884396\pi$
$150$		0			0
$151$	5.20711	−	9.01897i	0.423748	−	0.733954i	−0.572554	−	0.819867i	$-0.694047\pi$
$151$	5.20711	−	9.01897i	0.423748	−	0.733954i	0.996303	+	0.0859132i	$0.0273808\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$		0			0
$154$	3.91421	−	5.04757i	0.315416	−	0.406744i
$155$	−1.65685			−0.133082
$156$		0			0
$157$	−11.0355	+	19.1141i	−0.880731	+	1.52547i	−0.0302023	+	0.999544i	$0.509615\pi$
$157$	−11.0355	+	19.1141i	−0.880731	+	1.52547i	−0.850529	+	0.525928i	$0.823718\pi$
$158$	−4.65685	+	8.06591i	−0.370479	+	0.641689i
$159$		0			0
$160$	1.41421			0.111803
$161$	−13.2929	−	1.81909i	−1.04763	−	0.143364i
$162$		0			0
$163$	5.57107	+	9.64937i	0.436360	+	0.755797i	0.997406	−	0.0719876i	$-0.0229342\pi$
$163$	5.57107	+	9.64937i	0.436360	+	0.755797i	−0.561046	+	0.827785i	$0.689601\pi$
$164$	3.70711	−	6.42090i	0.289476	−	0.501388i
$165$		0			0
$166$	−1.82843	−	3.16693i	−0.141913	−	0.245801i
$167$	10.3137			0.798099			0.399049	−	0.916929i	$-0.369340\pi$
$167$	10.3137			0.798099			0.399049	+	0.916929i	$0.369340\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−2.29289	−	3.97141i	−0.175857	−	0.304593i
$171$		0			0
$172$	0.414214	−	0.717439i	0.0315835	−	0.0547042i
$173$	−1.15685	−	2.00373i	−0.0879540	−	0.152341i	0.818692	−	0.574233i	$-0.194700\pi$
$173$	−1.15685	−	2.00373i	−0.0879540	−	0.152341i	−0.906646	+	0.421892i	$0.861366\pi$
$174$		0			0
$175$	3.00000	+	7.34847i	0.226779	+	0.555492i
$176$	2.41421			0.181978
$177$		0			0
$178$	−1.12132	+	1.94218i	−0.0840465	+	0.145573i
$179$	−11.8284	+	20.4874i	−0.884098	+	1.53130i	−0.0373543	+	0.999302i	$0.511893\pi$
$179$	−11.8284	+	20.4874i	−0.884098	+	1.53130i	−0.846744	+	0.532001i	$0.821440\pi$
$180$		0			0
$181$	−14.4142			−1.07140			−0.535700	−	0.844408i	$-0.679952\pi$
$181$	−14.4142			−1.07140			−0.535700	+	0.844408i	$0.679952\pi$
$182$	−2.62132	−	0.358719i	−0.194305	−	0.0265901i
$183$		0			0
$184$	−2.53553	−	4.39167i	−0.186922	−	0.323758i
$185$	6.41421	−	11.1097i	0.471582	−	0.816805i
$186$		0			0
$187$	−3.91421	−	6.77962i	−0.286236	−	0.495775i
$188$	−9.00000			−0.656392
$189$		0			0
$190$	4.24264			0.307794
$191$	6.82843	+	11.8272i	0.494088	+	0.855785i	0.999977	−	0.00681360i	$-0.00216885\pi$
$191$	6.82843	+	11.8272i	0.494088	+	0.855785i	−0.505889	+	0.862599i	$0.668836\pi$
$192$		0			0
$193$	12.1213	−	20.9947i	0.872512	−	1.51123i	0.0131218	−	0.999914i	$-0.495823\pi$
$193$	12.1213	−	20.9947i	0.872512	−	1.51123i	0.859390	−	0.511321i	$-0.170844\pi$
$194$	−5.94975	−	10.3053i	−0.427167	−	0.739875i
$195$		0			0
$196$	6.74264	+	1.88064i	0.481617	+	0.134331i
$197$	21.5563			1.53583			0.767913	−	0.640554i	$-0.221295\pi$
$197$	21.5563			1.53583			0.767913	+	0.640554i	$0.221295\pi$
$198$		0			0
$199$	−6.70711	+	11.6170i	−0.475454	+	0.823511i	−0.999605	−	0.0281148i	$-0.991050\pi$
$199$	−6.70711	+	11.6170i	−0.475454	+	0.823511i	0.524151	+	0.851626i	$0.324383\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	−6.82843			−0.480446
$203$	8.10660	−	10.4539i	0.568972	−	0.733717i
$204$		0			0
$205$	−5.24264	−	9.08052i	−0.366162	−	0.634211i
$206$	−5.24264	+	9.08052i	−0.365272	+	0.632670i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	7.24264			0.500984
$210$		0			0
$211$	8.38478			0.577232			0.288616	−	0.957445i	$-0.406805\pi$
$211$	8.38478			0.577232			0.288616	+	0.957445i	$0.406805\pi$
$212$	−5.15685	−	8.93193i	−0.354174	−	0.613448i
$213$		0			0
$214$	−1.17157	+	2.02922i	−0.0800871	+	0.138715i
$215$	−0.585786	−	1.01461i	−0.0399503	−	0.0691960i
$216$		0			0
$217$	−1.17157	−	2.86976i	−0.0795315	−	0.194812i
$218$	9.65685			0.654045
$219$		0			0
$220$	1.70711	−	2.95680i	0.115093	−	0.199347i
$221$	−1.62132	+	2.80821i	−0.109062	+	0.188901i
$222$		0			0
$223$	−15.3848			−1.03024			−0.515120	−	0.857118i	$-0.672253\pi$
$223$	−15.3848			−1.03024			−0.515120	+	0.857118i	$0.672253\pi$
$224$	1.00000	+	2.44949i	0.0668153	+	0.163663i
$225$		0			0
$226$	−4.03553	−	6.98975i	−0.268440	−	0.464951i
$227$	1.07107	−	1.85514i	0.0710893	−	0.123130i	−0.828290	−	0.560300i	$-0.810686\pi$
$227$	1.07107	−	1.85514i	0.0710893	−	0.123130i	0.899379	+	0.437170i	$0.144019\pi$
$228$		0			0
$229$	6.41421	+	11.1097i	0.423863	+	0.734153i	0.996314	−	0.0857869i	$-0.0273404\pi$
$229$	6.41421	+	11.1097i	0.423863	+	0.734153i	−0.572450	+	0.819939i	$0.694007\pi$
$230$	−7.17157			−0.472880
$231$		0			0
$232$	5.00000			0.328266
$233$	10.8640	+	18.8169i	0.711722	+	1.23274i	0.964210	+	0.265138i	$0.0854176\pi$
$233$	10.8640	+	18.8169i	0.711722	+	1.23274i	−0.252489	+	0.967600i	$0.581249\pi$
$234$		0			0
$235$	−6.36396	+	11.0227i	−0.415139	+	0.719042i
$236$	5.20711	+	9.01897i	0.338954	+	0.587085i
$237$		0			0
$238$	5.25736	−	6.77962i	0.340784	−	0.439457i
$239$	19.4853			1.26040			0.630199	−	0.776434i	$-0.282973\pi$
$239$	19.4853			1.26040			0.630199	+	0.776434i	$0.282973\pi$
$240$		0			0
$241$	−0.242641	+	0.420266i	−0.0156299	+	0.0270717i	−0.873735	−	0.486403i	$-0.838309\pi$
$241$	−0.242641	+	0.420266i	−0.0156299	+	0.0270717i	0.858105	+	0.513475i	$0.171642\pi$
$242$	−2.58579	+	4.47871i	−0.166221	+	0.287903i
$243$		0			0
$244$	3.24264			0.207589
$245$	7.07107	−	6.92820i	0.451754	−	0.442627i
$246$		0			0
$247$	−1.50000	−	2.59808i	−0.0954427	−	0.165312i
$248$	0.585786	−	1.01461i	0.0371975	−	0.0644279i
$249$		0			0
$250$	5.65685	+	9.79796i	0.357771	+	0.619677i
$251$	−7.17157			−0.452666			−0.226333	−	0.974050i	$-0.572674\pi$
$251$	−7.17157			−0.452666			−0.226333	+	0.974050i	$0.572674\pi$
$252$		0			0
$253$	−12.2426			−0.769688
$254$	−4.94975	−	8.57321i	−0.310575	−	0.537931i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.89949	+	15.4144i	0.555135	+	0.961522i	0.997893	+	0.0648812i	$0.0206668\pi$
$257$	8.89949	+	15.4144i	0.555135	+	0.961522i	−0.442758	+	0.896641i	$0.646000\pi$
$258$		0			0
$259$	23.7782	+	3.25397i	1.47750	+	0.202192i
$260$	−1.41421			−0.0877058
$261$		0			0
$262$	4.94975	−	8.57321i	0.305796	−	0.529655i
$263$	11.7782	−	20.4004i	0.726273	−	1.25794i	−0.232174	−	0.972674i	$-0.574584\pi$
$263$	11.7782	−	20.4004i	0.726273	−	1.25794i	0.958448	−	0.285268i	$-0.0920827\pi$
$264$		0			0
$265$	−14.5858			−0.895998
$266$	3.00000	+	7.34847i	0.183942	+	0.450564i
$267$		0			0
$268$	1.67157	+	2.89525i	0.102108	+	0.176855i
$269$	−13.1569	+	22.7883i	−0.802188	+	1.38943i	0.115986	+	0.993251i	$0.462997\pi$
$269$	−13.1569	+	22.7883i	−0.802188	+	1.38943i	−0.918173	+	0.396179i	$0.870336\pi$
$270$		0			0
$271$	−10.6924	−	18.5198i	−0.649516	−	1.12500i	−0.983239	−	0.182324i	$-0.941638\pi$
$271$	−10.6924	−	18.5198i	−0.649516	−	1.12500i	0.333722	−	0.942671i	$-0.391695\pi$
$272$	3.24264			0.196614
$273$		0			0
$274$	1.07107			0.0647056
$275$	3.62132	+	6.27231i	0.218374	+	0.378235i
$276$		0			0
$277$	6.79289	−	11.7656i	0.408145	−	0.706929i	−0.586537	−	0.809923i	$-0.699509\pi$
$277$	6.79289	−	11.7656i	0.408145	−	0.706929i	0.994682	+	0.102994i	$0.0328423\pi$
$278$	10.6066	+	18.3712i	0.636142	+	1.10183i
$279$		0			0
$280$	3.70711	+	0.507306i	0.221542	+	0.0303173i
$281$	15.3137			0.913539			0.456770	−	0.889585i	$-0.349006\pi$
$281$	15.3137			0.913539			0.456770	+	0.889585i	$0.349006\pi$
$282$		0			0
$283$	−1.46447	+	2.53653i	−0.0870535	+	0.150781i	−0.906264	−	0.422711i	$-0.861078\pi$
$283$	−1.46447	+	2.53653i	−0.0870535	+	0.150781i	0.819211	+	0.573492i	$0.194412\pi$
$284$	−0.500000	+	0.866025i	−0.0296695	+	0.0513892i
$285$		0			0
$286$	−2.41421			−0.142755
$287$	12.0208	−	15.5014i	0.709566	−	0.915020i
$288$		0			0
$289$	3.24264	+	5.61642i	0.190744	+	0.330378i
$290$	3.53553	−	6.12372i	0.207614	−	0.359597i
$291$		0			0
$292$	−6.53553	−	11.3199i	−0.382463	−	0.662446i
$293$	−6.72792			−0.393049			−0.196525	−	0.980499i	$-0.562966\pi$
$293$	−6.72792			−0.393049			−0.196525	+	0.980499i	$0.562966\pi$
$294$		0			0
$295$	14.7279			0.857493
$296$	4.53553	+	7.85578i	0.263623	+	0.456608i
$297$		0			0
$298$	1.94975	−	3.37706i	0.112946	−	0.195628i
$299$	2.53553	+	4.39167i	0.146634	+	0.253977i
$300$		0			0
$301$	1.34315	−	1.73205i	0.0774176	−	0.0998337i
$302$	10.4142			0.599271
$303$		0			0
$304$	−1.50000	+	2.59808i	−0.0860309	+	0.149010i
$305$	2.29289	−	3.97141i	0.131291	−	0.227402i
$306$		0			0
$307$	25.6274			1.46263			0.731317	−	0.682038i	$-0.238906\pi$
$307$	25.6274			1.46263			0.731317	+	0.682038i	$0.238906\pi$
$308$	6.32843	+	0.866025i	0.360596	+	0.0493464i
$309$		0			0
$310$	−0.828427	−	1.43488i	−0.0470515	−	0.0814956i
$311$	−4.70711	+	8.15295i	−0.266916	+	0.462311i	−0.968064	−	0.250704i	$-0.919338\pi$
$311$	−4.70711	+	8.15295i	−0.266916	+	0.462311i	0.701148	+	0.713016i	$0.252671\pi$
$312$		0			0
$313$	5.07107	+	8.78335i	0.286634	+	0.496464i	0.973004	−	0.230788i	$-0.0741304\pi$
$313$	5.07107	+	8.78335i	0.286634	+	0.496464i	−0.686370	+	0.727252i	$0.740797\pi$
$314$	−22.0711			−1.24554
$315$		0			0
$316$	−9.31371			−0.523937
$317$	−2.41421	−	4.18154i	−0.135596	−	0.234859i	0.790229	−	0.612811i	$-0.209962\pi$
$317$	−2.41421	−	4.18154i	−0.135596	−	0.234859i	−0.925825	+	0.377953i	$0.876628\pi$
$318$		0			0
$319$	6.03553	−	10.4539i	0.337925	−	0.585303i
$320$	0.707107	+	1.22474i	0.0395285	+	0.0684653i
$321$		0			0
$322$	−5.07107	−	12.4215i	−0.282600	−	0.692225i
$323$	9.72792			0.541276
$324$		0			0
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$	−5.57107	+	9.64937i	−0.308553	+	0.534429i
$327$		0			0
$328$	7.41421			0.409381
$329$	−23.5919	−	3.22848i	−1.30066	−	0.177992i
$330$		0			0
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	0.931800	−	0.362971i	$-0.118238\pi$
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	−0.780242	+	0.625477i	$0.784904\pi$
$332$	1.82843	−	3.16693i	0.100348	−	0.173808i
$333$		0			0
$334$	5.15685	+	8.93193i	0.282171	+	0.488734i
$335$	4.72792			0.258314
$336$		0			0
$337$	17.3431			0.944741			0.472371	−	0.881400i	$-0.343398\pi$
$337$	17.3431			0.944741			0.472371	+	0.881400i	$0.343398\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	2.29289	−	3.97141i	0.124350	−	0.215380i
$341$	−1.41421	−	2.44949i	−0.0765840	−	0.132647i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	0.828427			0.0446658
$345$		0			0
$346$	1.15685	−	2.00373i	0.0621929	−	0.107721i
$347$	7.12132	−	12.3345i	0.382293	−	0.662150i	−0.609097	−	0.793096i	$-0.708468\pi$
$347$	7.12132	−	12.3345i	0.382293	−	0.662150i	0.991390	+	0.130946i	$0.0418013\pi$
$348$		0			0
$349$	2.58579			0.138414			0.0692070	−	0.997602i	$-0.477953\pi$
$349$	2.58579			0.138414			0.0692070	+	0.997602i	$0.477953\pi$
$350$	−4.86396	+	6.27231i	−0.259990	+	0.335269i
$351$		0			0
$352$	1.20711	+	2.09077i	0.0643390	+	0.111438i
$353$	−16.3137	+	28.2562i	−0.868291	+	1.50392i	−0.00454930	+	0.999990i	$0.501448\pi$
$353$	−16.3137	+	28.2562i	−0.868291	+	1.50392i	−0.863742	+	0.503935i	$0.831885\pi$
$354$		0			0
$355$	0.707107	+	1.22474i	0.0375293	+	0.0650027i
$356$	−2.24264			−0.118860
$357$		0			0
$358$	−23.6569			−1.25030
$359$	17.7279	+	30.7057i	0.935644	+	1.62058i	0.773482	+	0.633819i	$0.218513\pi$
$359$	17.7279	+	30.7057i	0.935644	+	1.62058i	0.162162	+	0.986764i	$0.448153\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	−7.20711	−	12.4831i	−0.378797	−	0.656096i
$363$		0			0
$364$	−1.00000	−	2.44949i	−0.0524142	−	0.128388i
$365$	−18.4853			−0.967564
$366$		0			0
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	−0.988840	−	0.148983i	$-0.952400\pi$
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	0.623443	+	0.781869i	$0.285733\pi$
$368$	2.53553	−	4.39167i	0.132174	−	0.228932i
$369$		0			0
$370$	12.8284			0.666918
$371$	−10.3137	−	25.2633i	−0.535461	−	1.31161i
$372$		0			0
$373$	15.4497	+	26.7597i	0.799958	+	1.38557i	0.919643	+	0.392755i	$0.128478\pi$
$373$	15.4497	+	26.7597i	0.799958	+	1.38557i	−0.119685	+	0.992812i	$0.538189\pi$
$374$	3.91421	−	6.77962i	0.202399	−	0.350566i
$375$		0			0
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−22.3431			−1.14769			−0.573845	−	0.818964i	$-0.694549\pi$
$379$	−22.3431			−1.14769			−0.573845	+	0.818964i	$0.694549\pi$
$380$	2.12132	+	3.67423i	0.108821	+	0.188484i
$381$		0			0
$382$	−6.82843	+	11.8272i	−0.349373	+	0.605131i
$383$	−5.24264	−	9.08052i	−0.267886	−	0.463993i	0.700429	−	0.713722i	$-0.252992\pi$
$383$	−5.24264	−	9.08052i	−0.267886	−	0.463993i	−0.968316	+	0.249729i	$0.919659\pi$
$384$		0			0
$385$	5.53553	−	7.13834i	0.282117	−	0.363803i
$386$	24.2426			1.23392
$387$		0			0
$388$	5.94975	−	10.3053i	0.302053	−	0.523171i
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	−0.412039	−	0.911166i	$-0.635183\pi$
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	0.995113	−	0.0987463i	$-0.0314832\pi$
$390$		0			0
$391$	−16.4437			−0.831591
$392$	1.74264	+	6.77962i	0.0880166	+	0.342422i
$393$		0			0
$394$	10.7782	+	18.6683i	0.542997	+	0.940498i
$395$	−6.58579	+	11.4069i	−0.331367	+	0.573944i
$396$		0			0
$397$	14.1213	+	24.4588i	0.708729	+	1.22755i	0.965329	+	0.261037i	$0.0840643\pi$
$397$	14.1213	+	24.4588i	0.708729	+	1.22755i	−0.256600	+	0.966518i	$0.582602\pi$
$398$	−13.4142			−0.672394
$399$		0			0
$400$	−3.00000			−0.150000
$401$	2.46447	+	4.26858i	0.123070	+	0.213163i	0.920977	−	0.389618i	$-0.127393\pi$
$401$	2.46447	+	4.26858i	0.123070	+	0.213163i	−0.797907	+	0.602780i	$0.794060\pi$
$402$		0			0
$403$	−0.585786	+	1.01461i	−0.0291801	+	0.0505414i
$404$	−3.41421	−	5.91359i	−0.169863	−	0.294212i
$405$		0			0
$406$	13.1066	+	1.79360i	0.650470	+	0.0890147i
$407$	21.8995			1.08552
$408$		0			0
$409$	2.70711	−	4.68885i	0.133858	−	0.231849i	−0.791303	−	0.611425i	$-0.790597\pi$
$409$	2.70711	−	4.68885i	0.133858	−	0.231849i	0.925161	+	0.379576i	$0.123930\pi$
$410$	5.24264	−	9.08052i	0.258916	−	0.448455i
$411$		0			0
$412$	−10.4853			−0.516573
$413$	10.4142	+	25.5095i	0.512450	+	1.25524i
$414$		0			0
$415$	−2.58579	−	4.47871i	−0.126931	−	0.219851i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	3.62132	+	6.27231i	0.177125	+	0.306789i
$419$	−23.4558			−1.14589			−0.572946	−	0.819593i	$-0.694200\pi$
$419$	−23.4558			−1.14589			−0.572946	+	0.819593i	$0.694200\pi$
$420$		0			0
$421$	13.4142			0.653769			0.326884	−	0.945064i	$-0.394001\pi$
$421$	13.4142			0.653769			0.326884	+	0.945064i	$0.394001\pi$
$422$	4.19239	+	7.26143i	0.204082	+	0.353481i
$423$		0			0
$424$	5.15685	−	8.93193i	0.250439	−	0.433773i
$425$	4.86396	+	8.42463i	0.235937	+	0.408654i
$426$		0			0
$427$	8.50000	+	1.16320i	0.411344	+	0.0562911i
$428$	−2.34315			−0.113260
$429$		0			0
$430$	0.585786	−	1.01461i	0.0282491	−	0.0489289i
$431$	−1.24264	+	2.15232i	−0.0598559	+	0.103673i	−0.894401	−	0.447267i	$-0.852397\pi$
$431$	−1.24264	+	2.15232i	−0.0598559	+	0.103673i	0.834545	+	0.550940i	$0.185731\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	1.89949	−	2.44949i	0.0911787	−	0.117579i
$435$		0			0
$436$	4.82843	+	8.36308i	0.231240	+	0.400519i
$437$	7.60660	−	13.1750i	0.363873	−	0.630247i
$438$		0			0
$439$	6.70711	+	11.6170i	0.320113	+	0.554452i	0.980511	−	0.196464i	$-0.0629459\pi$
$439$	6.70711	+	11.6170i	0.320113	+	0.554452i	−0.660398	+	0.750915i	$0.729613\pi$
$440$	3.41421			0.162766
$441$		0			0
$442$	−3.24264			−0.154237
$443$	−1.36396	−	2.36245i	−0.0648037	−	0.112243i	0.831803	−	0.555071i	$-0.187309\pi$
$443$	−1.36396	−	2.36245i	−0.0648037	−	0.112243i	−0.896607	+	0.442827i	$0.853975\pi$
$444$		0			0
$445$	−1.58579	+	2.74666i	−0.0751735	+	0.130204i
$446$	−7.69239	−	13.3236i	−0.364245	−	0.630891i
$447$		0			0
$448$	−1.62132	+	2.09077i	−0.0766002	+	0.0987796i
$449$	−33.9411			−1.60178			−0.800890	−	0.598811i	$-0.795640\pi$
$449$	−33.9411			−1.60178			−0.800890	+	0.598811i	$0.795640\pi$
$450$		0			0
$451$	8.94975	−	15.5014i	0.421427	−	0.729933i
$452$	4.03553	−	6.98975i	0.189816	−	0.328770i
$453$		0			0
$454$	2.14214			0.100535
$455$	−3.70711	−	0.507306i	−0.173792	−	0.0237829i
$456$		0			0
$457$	−13.6066	−	23.5673i	−0.636490	−	1.10243i	−0.986197	−	0.165574i	$-0.947052\pi$
$457$	−13.6066	−	23.5673i	−0.636490	−	1.10243i	0.349707	−	0.936859i	$-0.386281\pi$
$458$	−6.41421	+	11.1097i	−0.299717	+	0.519124i
$459$		0			0
$460$	−3.58579	−	6.21076i	−0.167188	−	0.289578i
$461$	−17.4558			−0.813000			−0.406500	−	0.913651i	$-0.633251\pi$
$461$	−17.4558			−0.813000			−0.406500	+	0.913651i	$0.633251\pi$
$462$		0			0
$463$	29.9411			1.39148			0.695741	−	0.718293i	$-0.255076\pi$
$463$	29.9411			1.39148			0.695741	+	0.718293i	$0.255076\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$		0			0
$466$	−10.8640	+	18.8169i	−0.503263	+	0.871678i
$467$	4.12132	+	7.13834i	0.190712	+	0.330323i	0.945486	−	0.325662i	$-0.105587\pi$
$467$	4.12132	+	7.13834i	0.190712	+	0.330323i	−0.754774	+	0.655984i	$0.772254\pi$
$468$		0			0
$469$	3.34315	+	8.18900i	0.154372	+	0.378133i
$470$	−12.7279			−0.587095
$471$		0			0
$472$	−5.20711	+	9.01897i	−0.239677	+	0.415132i
$473$	1.00000	−	1.73205i	0.0459800	−	0.0796398i
$474$		0			0
$475$	−9.00000			−0.412948
$476$	8.50000	+	1.16320i	0.389597	+	0.0533151i
$477$		0			0
$478$	9.74264	+	16.8747i	0.445618	+	0.771833i
$479$	−1.42893	+	2.47498i	−0.0652896	+	0.113085i	−0.896822	−	0.442391i	$-0.854130\pi$
$479$	−1.42893	+	2.47498i	−0.0652896	+	0.113085i	0.831533	+	0.555476i	$0.187464\pi$
$480$		0			0
$481$	−4.53553	−	7.85578i	−0.206803	−	0.358193i
$482$	−0.485281			−0.0221040
$483$		0			0
$484$	−5.17157			−0.235071
$485$	−8.41421	−	14.5738i	−0.382070	−	0.661764i
$486$		0			0
$487$	−0.863961	+	1.49642i	−0.0391498	+	0.0678095i	−0.884936	−	0.465712i	$-0.845798\pi$
$487$	−0.863961	+	1.49642i	−0.0391498	+	0.0678095i	0.845787	+	0.533521i	$0.179132\pi$
$488$	1.62132	+	2.80821i	0.0733937	+	0.127122i
$489$		0			0
$490$	9.53553	+	2.65962i	0.430772	+	0.120150i
$491$	−30.2843			−1.36671			−0.683355	−	0.730086i	$-0.739480\pi$
$491$	−30.2843			−1.36671			−0.683355	+	0.730086i	$0.739480\pi$
$492$		0			0
$493$	8.10660	−	14.0410i	0.365103	−	0.632377i
$494$	1.50000	−	2.59808i	0.0674882	−	0.116893i
$495$		0			0
$496$	1.17157			0.0526052
$497$	−1.62132	+	2.09077i	−0.0727262	+	0.0937839i
$498$		0			0
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	0.977481	+	0.211024i	$0.0676797\pi$
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	−0.305989	+	0.952035i	$0.598987\pi$
$500$	−5.65685	+	9.79796i	−0.252982	+	0.438178i
$501$		0			0
$502$	−3.58579	−	6.21076i	−0.160041	−	0.277200i
$503$	3.79899			0.169389			0.0846943	−	0.996407i	$-0.473009\pi$
$503$	3.79899			0.169389			0.0846943	+	0.996407i	$0.473009\pi$
$504$		0			0
$505$	−9.65685			−0.429724
$506$	−6.12132	−	10.6024i	−0.272126	−	0.471336i
$507$		0			0
$508$	4.94975	−	8.57321i	0.219610	−	0.380375i
$509$	−10.4853	−	18.1610i	−0.464752	−	0.804974i	0.534438	−	0.845207i	$-0.320523\pi$
$509$	−10.4853	−	18.1610i	−0.464752	−	0.804974i	−0.999190	+	0.0402335i	$0.987190\pi$
$510$		0			0
$511$	−13.0711	−	32.0174i	−0.578230	−	1.41637i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.89949	+	15.4144i	−0.392540	+	0.679899i
$515$	−7.41421	+	12.8418i	−0.326709	+	0.565877i
$516$		0			0
$517$	−21.7279			−0.955593
$518$	9.07107	+	22.2195i	0.398560	+	0.976268i
$519$		0			0
$520$	−0.707107	−	1.22474i	−0.0310087	−	0.0537086i
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$		0			0
$523$	16.0711	+	27.8359i	0.702739	+	1.21718i	0.967501	+	0.252866i	$0.0813730\pi$
$523$	16.0711	+	27.8359i	0.702739	+	1.21718i	−0.264763	+	0.964314i	$0.585294\pi$
$524$	9.89949			0.432461
$525$		0			0
$526$	23.5563			1.02711
$527$	−1.89949	−	3.29002i	−0.0827433	−	0.143316i
$528$		0			0
$529$	−1.35786	+	2.35189i	−0.0590376	+	0.102256i
$530$	−7.29289	−	12.6317i	−0.316783	−	0.548684i
$531$		0			0
$532$	−4.86396	+	6.27231i	−0.210879	+	0.271939i
$533$	−7.41421			−0.321145
$534$		0			0
$535$	−1.65685	+	2.86976i	−0.0716321	+	0.124070i
$536$	−1.67157	+	2.89525i	−0.0722010	+	0.125056i
$537$		0			0
$538$	−26.3137			−1.13446
$539$	16.2782	+	4.54026i	0.701151	+	0.195563i
$540$		0			0
$541$	20.4350	+	35.3945i	0.878571	+	1.52173i	0.852910	+	0.522058i	$0.174836\pi$
$541$	20.4350	+	35.3945i	0.878571	+	1.52173i	0.0256606	+	0.999671i	$0.491831\pi$
$542$	10.6924	−	18.5198i	0.459277	−	0.795492i
$543$		0			0
$544$	1.62132	+	2.80821i	0.0695135	+	0.120401i
$545$	13.6569			0.584995
$546$		0			0
$547$	−14.2426			−0.608971			−0.304486	−	0.952517i	$-0.598485\pi$
$547$	−14.2426			−0.608971			−0.304486	+	0.952517i	$0.598485\pi$
$548$	0.535534	+	0.927572i	0.0228769	+	0.0396239i
$549$		0			0
$550$	−3.62132	+	6.27231i	−0.154414	+	0.267452i
$551$	7.50000	+	12.9904i	0.319511	+	0.553409i
$552$		0			0
$553$	−24.4142	−	3.34101i	−1.03820	−	0.142074i
$554$	13.5858			0.577205
$555$		0			0
$556$	−10.6066	+	18.3712i	−0.449820	+	0.779111i
$557$	11.4853	−	19.8931i	0.486647	−	0.842897i	−0.513235	−	0.858248i	$-0.671553\pi$
$557$	11.4853	−	19.8931i	0.486647	−	0.842897i	0.999882	+	0.0153507i	$0.00488647\pi$
$558$		0			0
$559$	−0.828427			−0.0350387
$560$	1.41421	+	3.46410i	0.0597614	+	0.146385i
$561$		0			0
$562$	7.65685	+	13.2621i	0.322985	+	0.559426i
$563$	8.24264	−	14.2767i	0.347386	−	0.601690i	−0.638398	−	0.769706i	$-0.720403\pi$
$563$	8.24264	−	14.2767i	0.347386	−	0.601690i	0.985784	+	0.168016i	$0.0537361\pi$
$564$		0			0
$565$	−5.70711	−	9.88500i	−0.240100	−	0.415865i
$566$	−2.92893			−0.123112
$567$		0			0
$568$	−1.00000			−0.0419591
$569$	−14.2071	−	24.6074i	−0.595593	−	1.03160i	−0.993463	−	0.114155i	$-0.963584\pi$
$569$	−14.2071	−	24.6074i	−0.595593	−	1.03160i	0.397870	−	0.917442i	$-0.369750\pi$
$570$		0			0
$571$	−4.82843	+	8.36308i	−0.202063	+	0.349984i	−0.949193	−	0.314694i	$-0.898098\pi$
$571$	−4.82843	+	8.36308i	−0.202063	+	0.349984i	0.747130	+	0.664678i	$0.231431\pi$
$572$	−1.20711	−	2.09077i	−0.0504717	−	0.0874195i
$573$		0			0
$574$	19.4350	+	2.65962i	0.811202	+	0.111011i
$575$	15.2132			0.634434
$576$		0			0
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	−3.24264	+	5.61642i	−0.134876	+	0.233612i
$579$		0			0
$580$	7.07107			0.293610
$581$	5.92893	−	7.64564i	0.245974	−	0.317195i
$582$		0			0
$583$	−12.4497	−	21.5636i	−0.515616	−	0.893073i
$584$	6.53553	−	11.3199i	0.270442	−	0.468420i
$585$		0			0
$586$	−3.36396	−	5.82655i	−0.138964	−	0.240693i
$587$	−2.75736			−0.113808			−0.0569042	−	0.998380i	$-0.518123\pi$
$587$	−2.75736			−0.113808			−0.0569042	+	0.998380i	$0.518123\pi$
$588$		0			0
$589$	3.51472			0.144821
$590$	7.36396	+	12.7548i	0.303169	+	0.525105i
$591$		0			0
$592$	−4.53553	+	7.85578i	−0.186409	+	0.322870i
$593$	−15.7071	−	27.2055i	−0.645014	−	1.11720i	−0.984298	−	0.176513i	$-0.943518\pi$
$593$	−15.7071	−	27.2055i	−0.645014	−	1.11720i	0.339285	−	0.940684i	$-0.389815\pi$
$594$		0			0
$595$	7.43503	−	9.58783i	0.304806	−	0.393063i
$596$	3.89949			0.159730
$597$		0			0
$598$	−2.53553	+	4.39167i	−0.103686	+	0.179589i
$599$	19.4350	−	33.6625i	0.794094	−	1.37541i	−0.129319	−	0.991603i	$-0.541279\pi$
$599$	19.4350	−	33.6625i	0.794094	−	1.37541i	0.923413	−	0.383808i	$-0.125387\pi$
$600$		0			0
$601$	−12.1716			−0.496489			−0.248244	−	0.968697i	$-0.579854\pi$
$601$	−12.1716			−0.496489			−0.248244	+	0.968697i	$0.579854\pi$
$602$	2.17157	+	0.297173i	0.0885067	+	0.0121119i
$603$		0			0
$604$	5.20711	+	9.01897i	0.211874	+	0.366977i
$605$	−3.65685	+	6.33386i	−0.148672	+	0.257508i
$606$		0			0
$607$	−6.46447	−	11.1968i	−0.262385	−	0.454463i	0.704491	−	0.709713i	$-0.251176\pi$
$607$	−6.46447	−	11.1968i	−0.262385	−	0.454463i	−0.966875	+	0.255250i	$0.917842\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$	4.58579			0.185673
$611$	4.50000	+	7.79423i	0.182051	+	0.315321i
$612$		0			0
$613$	−1.89949	+	3.29002i	−0.0767199	+	0.132883i	−0.901833	−	0.432085i	$-0.857778\pi$
$613$	−1.89949	+	3.29002i	−0.0767199	+	0.132883i	0.825113	+	0.564968i	$0.191111\pi$
$614$	12.8137	+	22.1940i	0.517119	+	0.895677i
$615$		0			0
$616$	2.41421	+	5.91359i	0.0972714	+	0.238265i
$617$	−10.4853			−0.422122			−0.211061	−	0.977473i	$-0.567692\pi$
$617$	−10.4853			−0.422122			−0.211061	+	0.977473i	$0.567692\pi$
$618$		0			0
$619$	3.72792	−	6.45695i	0.149838	−	0.259527i	−0.781330	−	0.624119i	$-0.785458\pi$
$619$	3.72792	−	6.45695i	0.149838	−	0.259527i	0.931167	+	0.364592i	$0.118792\pi$
$620$	0.828427	−	1.43488i	0.0332704	−	0.0576261i
$621$		0			0
$622$	−9.41421			−0.377476
$623$	−5.87868	−	0.804479i	−0.235524	−	0.0322308i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−5.07107	+	8.78335i	−0.202681	+	0.351053i
$627$		0			0
$628$	−11.0355	−	19.1141i	−0.440366	−	0.762736i
$629$	29.4142			1.17282
$630$		0			0
$631$	−8.62742			−0.343452			−0.171726	−	0.985145i	$-0.554934\pi$
$631$	−8.62742			−0.343452			−0.171726	+	0.985145i	$0.554934\pi$
$632$	−4.65685	−	8.06591i	−0.185240	−	0.320845i
$633$		0			0
$634$	2.41421	−	4.18154i	0.0958807	−	0.166070i
$635$	−7.00000	−	12.1244i	−0.277787	−	0.481140i
$636$		0			0
$637$	−1.74264	−	6.77962i	−0.0690459	−	0.268618i
$638$	12.0711			0.477898
$639$		0			0
$640$	−0.707107	+	1.22474i	−0.0279508	+	0.0484123i
$641$	19.4142	−	33.6264i	0.766815	−	1.32816i	−0.172466	−	0.985015i	$-0.555174\pi$
$641$	19.4142	−	33.6264i	0.766815	−	1.32816i	0.939281	−	0.343148i	$-0.111493\pi$
$642$		0			0
$643$	13.6863			0.539735			0.269867	−	0.962898i	$-0.413020\pi$
$643$	13.6863			0.539735			0.269867	+	0.962898i	$0.413020\pi$
$644$	8.22183	−	10.6024i	0.323985	−	0.417795i
$645$		0			0
$646$	4.86396	+	8.42463i	0.191370	+	0.331463i
$647$	−8.31371	+	14.3998i	−0.326846	+	0.566113i	−0.981884	−	0.189482i	$-0.939319\pi$
$647$	−8.31371	+	14.3998i	−0.326846	+	0.566113i	0.655039	+	0.755595i	$0.272652\pi$
$648$		0			0
$649$	12.5711	+	21.7737i	0.493458	+	0.854694i
$650$	3.00000			0.117670
$651$		0			0
$652$	−11.1421			−0.436360
$653$	−23.5563	−	40.8008i	−0.921831	−	1.59666i	−0.796580	−	0.604533i	$-0.793360\pi$
$653$	−23.5563	−	40.8008i	−0.921831	−	1.59666i	−0.125251	−	0.992125i	$-0.539974\pi$
$654$		0			0
$655$	7.00000	−	12.1244i	0.273513	−	0.473738i
$656$	3.70711	+	6.42090i	0.144738	+	0.250694i
$657$		0			0
$658$	−9.00000	−	22.0454i	−0.350857	−	0.859419i
$659$	−5.27208			−0.205371			−0.102685	−	0.994714i	$-0.532744\pi$
$659$	−5.27208			−0.205371			−0.102685	+	0.994714i	$0.532744\pi$
$660$		0			0
$661$	−8.77817	+	15.2042i	−0.341431	+	0.591377i	−0.984699	−	0.174265i	$-0.944245\pi$
$661$	−8.77817	+	15.2042i	−0.341431	+	0.591377i	0.643267	+	0.765642i	$0.277578\pi$
$662$	−2.75736	+	4.77589i	−0.107168	+	0.185620i
$663$		0			0
$664$	3.65685			0.141913
$665$	4.24264	+	10.3923i	0.164523	+	0.402996i
$666$		0			0
$667$	−12.6777	−	21.9584i	−0.490881	−	0.850231i
$668$	−5.15685	+	8.93193i	−0.199525	+	0.345587i
$669$		0			0
$670$	2.36396	+	4.09450i	0.0913278	+	0.158184i
$671$	7.82843			0.302213
$672$		0			0
$673$	−6.82843			−0.263217			−0.131608	−	0.991302i	$-0.542014\pi$
$673$	−6.82843			−0.263217			−0.131608	+	0.991302i	$0.542014\pi$
$674$	8.67157	+	15.0196i	0.334017	+	0.578534i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	16.9142	+	29.2963i	0.650066	+	1.12595i	0.983106	+	0.183035i	$0.0585921\pi$
$677$	16.9142	+	29.2963i	0.650066	+	1.12595i	−0.333040	+	0.942913i	$0.608075\pi$
$678$		0			0
$679$	19.2929	−	24.8791i	0.740393	−	0.954773i
$680$	4.58579			0.175857
$681$		0			0
$682$	1.41421	−	2.44949i	0.0541530	−	0.0937958i
$683$	−22.7279	+	39.3659i	−0.869660	+	1.50629i	−0.00731507	+	0.999973i	$0.502328\pi$
$683$	−22.7279	+	39.3659i	−0.869660	+	1.50629i	−0.862345	+	0.506322i	$0.831005\pi$
$684$		0			0
$685$	1.51472			0.0578744
$686$	2.13604	+	18.3967i	0.0815543	+	0.702388i
$687$		0			0
$688$	0.414214	+	0.717439i	0.0157917	+	0.0273521i
$689$	−5.15685	+	8.93193i	−0.196461	+	0.340280i
$690$		0			0
$691$	8.57107	+	14.8455i	0.326059	+	0.564750i	0.981726	−	0.190300i	$-0.0609459\pi$
$691$	8.57107	+	14.8455i	0.326059	+	0.564750i	−0.655667	+	0.755050i	$0.727613\pi$
$692$	2.31371			0.0879540
$693$		0			0
$694$	14.2426			0.540643
$695$	15.0000	+	25.9808i	0.568982	+	0.985506i
$696$		0			0
$697$	12.0208	−	20.8207i	0.455321	−	0.788639i
$698$	1.29289	+	2.23936i	0.0489367	+	0.0847609i
$699$		0			0
$700$	−7.86396	−	1.07616i	−0.297230	−	0.0406750i
$701$	−31.5147			−1.19029			−0.595147	−	0.803617i	$-0.702906\pi$
$701$	−31.5147			−1.19029			−0.595147	+	0.803617i	$0.702906\pi$
$702$		0			0
$703$	−13.6066	+	23.5673i	−0.513183	+	0.888859i
$704$	−1.20711	+	2.09077i	−0.0454945	+	0.0787989i
$705$		0			0
$706$	−32.6274			−1.22795
$707$	−6.82843	−	16.7262i	−0.256809	−	0.629052i
$708$		0			0
$709$	−8.02082	−	13.8925i	−0.301228	−	0.521742i	0.675186	−	0.737647i	$-0.264063\pi$
$709$	−8.02082	−	13.8925i	−0.301228	−	0.521742i	−0.976414	+	0.215905i	$0.930730\pi$
$710$	−0.707107	+	1.22474i	−0.0265372	+	0.0459639i
$711$		0			0
$712$	−1.12132	−	1.94218i	−0.0420233	−	0.0727864i
$713$	−5.94113			−0.222497
$714$		0			0
$715$	−3.41421			−0.127684
$716$	−11.8284	−	20.4874i	−0.442049	−	0.765651i
$717$		0			0
$718$	−17.7279	+	30.7057i	−0.661600	+	1.14593i
$719$	17.1421	+	29.6910i	0.639294	+	1.10729i	0.985588	+	0.169163i	$0.0541065\pi$
$719$	17.1421	+	29.6910i	0.639294	+	1.10729i	−0.346294	+	0.938126i	$0.612560\pi$
$720$		0			0
$721$	−27.4853	−	3.76127i	−1.02361	−	0.140077i
$722$	10.0000			0.372161
$723$		0			0
$724$	7.20711	−	12.4831i	0.267850	−	0.463930i
$725$	−7.50000	+	12.9904i	−0.278543	+	0.482451i
$726$		0			0
$727$	−33.1716			−1.23027			−0.615133	−	0.788424i	$-0.710898\pi$
$727$	−33.1716			−1.23027			−0.615133	+	0.788424i	$0.710898\pi$
$728$	1.62132	−	2.09077i	0.0600901	−	0.0774891i
$729$		0			0
$730$	−9.24264	−	16.0087i	−0.342085	−	0.592509i
$731$	1.34315	−	2.32640i	0.0496780	−	0.0860449i
$732$		0			0
$733$	−26.5061	−	45.9099i	−0.979025	−	1.69572i	−0.665957	−	0.745991i	$-0.731976\pi$
$733$	−26.5061	−	45.9099i	−0.979025	−	1.69572i	−0.313068	−	0.949731i	$-0.601357\pi$
$734$	−14.0000			−0.516749
$735$		0			0
$736$	5.07107			0.186922
$737$	4.03553	+	6.98975i	0.148651	+	0.257471i
$738$		0			0
$739$	13.4853	−	23.3572i	0.496064	−	0.859208i	−0.503926	−	0.863747i	$-0.668111\pi$
$739$	13.4853	−	23.3572i	0.496064	−	0.859208i	0.999990	+	0.00453885i	$0.00144476\pi$
$740$	6.41421	+	11.1097i	0.235791	+	0.408402i
$741$		0			0
$742$	16.7218	−	21.5636i	0.613878	−	0.791624i
$743$	5.48528			0.201235			0.100618	−	0.994925i	$-0.467918\pi$
$743$	5.48528			0.201235			0.100618	+	0.994925i	$0.467918\pi$
$744$		0			0
$745$	2.75736	−	4.77589i	0.101022	−	0.174975i
$746$	−15.4497	+	26.7597i	−0.565655	+	0.979744i
$747$		0			0
$748$	7.82843			0.286236
$749$	−6.14214	−	0.840532i	−0.224429	−	0.0307124i
$750$		0			0
$751$	22.8284	+	39.5400i	0.833021	+	1.44283i	0.895631	+	0.444797i	$0.146724\pi$
$751$	22.8284	+	39.5400i	0.833021	+	1.44283i	−0.0626103	+	0.998038i	$0.519943\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$		0			0
$754$	−2.50000	−	4.33013i	−0.0910446	−	0.157694i
$755$	14.7279			0.536004
$756$		0			0
$757$	54.5563			1.98288			0.991442	−	0.130547i	$-0.0416734\pi$
$757$	54.5563			1.98288			0.991442	+	0.130547i	$0.0416734\pi$
$758$	−11.1716	−	19.3497i	−0.405770	−	0.702814i
$759$		0			0
$760$	−2.12132	+	3.67423i	−0.0769484	+	0.133278i
$761$	−23.0711	−	39.9603i	−0.836326	−	1.44856i	−0.892947	−	0.450163i	$-0.851366\pi$
$761$	−23.0711	−	39.9603i	−0.836326	−	1.44856i	0.0566210	−	0.998396i	$-0.481967\pi$
$762$		0			0
$763$	9.65685	+	23.6544i	0.349602	+	0.856346i
$764$	−13.6569			−0.494088
$765$		0			0
$766$	5.24264	−	9.08052i	0.189424	−	0.328093i
$767$	5.20711	−	9.01897i	0.188018	−	0.325656i
$768$		0			0
$769$	−21.0711			−0.759842			−0.379921	−	0.925019i	$-0.624049\pi$
$769$	−21.0711			−0.759842			−0.379921	+	0.925019i	$0.624049\pi$
$770$	8.94975	+	1.22474i	0.322527	+	0.0441367i
$771$		0			0
$772$	12.1213	+	20.9947i	0.436256	+	0.755617i
$773$	24.7990	−	42.9531i	0.891958	−	1.54492i	0.0544324	−	0.998517i	$-0.482665\pi$
$773$	24.7990	−	42.9531i	0.891958	−	1.54492i	0.837525	−	0.546399i	$-0.184002\pi$
$774$		0			0
$775$	1.75736	+	3.04384i	0.0631262	+	0.109338i
$776$	11.8995			0.427167
$777$		0			0
$778$	23.0000			0.824590
$779$	11.1213	+	19.2627i	0.398463	+	0.690158i
$780$		0			0
$781$	−1.20711	+	2.09077i	−0.0431937	+	0.0748136i
$782$	−8.22183	−	14.2406i	−0.294012	−	0.509244i
$783$		0			0
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$	−31.2132			−1.11405

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.707107 + 1.22474i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.707107 + 1.22474i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(-0.707107 + 1.22474i) q^{10} +(-1.20711 + 2.09077i) q^{11} +1.00000 q^{13} +(-2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.62132 + 2.80821i) q^{17} +(-1.50000 - 2.59808i) q^{19} -1.41421 q^{20} -2.41421 q^{22} +(2.53553 + 4.39167i) q^{23} +(1.50000 - 2.59808i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-1.00000 - 2.44949i) q^{28} -5.00000 q^{29} +(-0.585786 + 1.01461i) q^{31} +(0.500000 - 0.866025i) q^{32} -3.24264 q^{34} +(-3.70711 - 0.507306i) q^{35} +(-4.53553 - 7.85578i) q^{37} +(1.50000 - 2.59808i) q^{38} +(-0.707107 - 1.22474i) q^{40} -7.41421 q^{41} -0.828427 q^{43} +(-1.20711 - 2.09077i) q^{44} +(-2.53553 + 4.39167i) q^{46} +(4.50000 + 7.79423i) q^{47} +(-1.74264 - 6.77962i) q^{49} +3.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-5.15685 + 8.93193i) q^{53} -3.41421 q^{55} +(1.62132 - 2.09077i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(5.20711 - 9.01897i) q^{59} +(-1.62132 - 2.80821i) q^{61} -1.17157 q^{62} +1.00000 q^{64} +(0.707107 + 1.22474i) q^{65} +(1.67157 - 2.89525i) q^{67} +(-1.62132 - 2.80821i) q^{68} +(-1.41421 - 3.46410i) q^{70} +1.00000 q^{71} +(-6.53553 + 11.3199i) q^{73} +(4.53553 - 7.85578i) q^{74} +3.00000 q^{76} +(-2.41421 - 5.91359i) q^{77} +(4.65685 + 8.06591i) q^{79} +(0.707107 - 1.22474i) q^{80} +(-3.70711 - 6.42090i) q^{82} -3.65685 q^{83} -4.58579 q^{85} +(-0.414214 - 0.717439i) q^{86} +(1.20711 - 2.09077i) q^{88} +(1.12132 + 1.94218i) q^{89} +(-1.62132 + 2.09077i) q^{91} -5.07107 q^{92} +(-4.50000 + 7.79423i) q^{94} +(2.12132 - 3.67423i) q^{95} -11.8995 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} - 2 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} - 6 q^{19} - 4 q^{22} - 4 q^{23} + 6 q^{25} + 2 q^{26} - 4 q^{28} - 20 q^{29} - 8 q^{31} + 2 q^{32} + 4 q^{34} - 12 q^{35} - 4 q^{37} + 6 q^{38} - 24 q^{41} + 8 q^{43} - 2 q^{44} + 4 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 2 q^{52} + 2 q^{53} - 8 q^{55} - 2 q^{56} - 10 q^{58} + 18 q^{59} + 2 q^{61} - 16 q^{62} + 4 q^{64} + 18 q^{67} + 2 q^{68} + 4 q^{71} - 12 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 4 q^{79} - 12 q^{82} + 8 q^{83} - 24 q^{85} + 4 q^{86} + 2 q^{88} - 4 q^{89} + 2 q^{91} + 8 q^{92} - 18 q^{94} - 8 q^{97} + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 - 4 * q^8 - 2 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 - 6 * q^19 - 4 * q^22 - 4 * q^23 + 6 * q^25 + 2 * q^26 - 4 * q^28 - 20 * q^29 - 8 * q^31 + 2 * q^32 + 4 * q^34 - 12 * q^35 - 4 * q^37 + 6 * q^38 - 24 * q^41 + 8 * q^43 - 2 * q^44 + 4 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 2 * q^52 + 2 * q^53 - 8 * q^55 - 2 * q^56 - 10 * q^58 + 18 * q^59 + 2 * q^61 - 16 * q^62 + 4 * q^64 + 18 * q^67 + 2 * q^68 + 4 * q^71 - 12 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 4 * q^79 - 12 * q^82 + 8 * q^83 - 24 * q^85 + 4 * q^86 + 2 * q^88 - 4 * q^89 + 2 * q^91 + 8 * q^92 - 18 * q^94 - 8 * q^97 + 20 * q^98

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