LMFDB - Embedded newform 1638.2.bj.i.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$1.15585 - 1.15585i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.i.1135.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.62374i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.62374i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(1.81187 + 3.13825i) q^{10} +(1.74589 - 1.00799i) q^{11} +(3.59505 - 0.275040i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.79054 - 6.56541i) q^{17} +(2.40547 + 1.38880i) q^{19} +(-3.13825 - 1.81187i) q^{20} +(-1.00799 + 1.74589i) q^{22} +(3.95583 + 6.85169i) q^{23} -8.13150 q^{25} +(-2.97588 + 2.03571i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-2.83454 - 4.90957i) q^{29} +5.83236i q^{31} +(0.866025 + 0.500000i) q^{32} +7.58108i q^{34} +(-1.81187 + 3.13825i) q^{35} +(-1.48866 + 0.859480i) q^{37} -2.77760 q^{38} +3.62374 q^{40} +(10.0684 - 5.81297i) q^{41} +(2.63741 - 4.56813i) q^{43} -2.01598i q^{44} +(-6.85169 - 3.95583i) q^{46} -5.63658i q^{47} +(0.500000 + 0.866025i) q^{49} +(7.04209 - 4.06575i) q^{50} +(1.55933 - 3.25092i) q^{52} -0.0731130 q^{53} +(-3.65269 - 6.32665i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.90957 + 2.83454i) q^{58} +(-1.15686 - 0.667915i) q^{59} +(0.187787 - 0.325257i) q^{61} +(-2.91618 - 5.05098i) q^{62} -1.00000 q^{64} +(-0.996674 - 13.0275i) q^{65} +(-12.3907 + 7.15378i) q^{67} +(-3.79054 - 6.56541i) q^{68} -3.62374i q^{70} +(-11.0728 - 6.39291i) q^{71} +4.80070i q^{73} +(0.859480 - 1.48866i) q^{74} +(2.40547 - 1.38880i) q^{76} -2.01598 q^{77} +10.1368 q^{79} +(-3.13825 + 1.81187i) q^{80} +(-5.81297 + 10.0684i) q^{82} +1.97093i q^{83} +(-23.7913 - 13.7359i) q^{85} +5.27482i q^{86} +(1.00799 + 1.74589i) q^{88} +(-11.8252 + 6.82727i) q^{89} +(-3.25092 - 1.55933i) q^{91} +7.91165 q^{92} +(2.81829 + 4.88142i) q^{94} +(5.03265 - 8.71681i) q^{95} +(-13.6356 - 7.87254i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.62374i		−	1.62059i	−0.586025	−	0.810293i	$-0.699308\pi$
$5$		−	3.62374i		−	1.62059i	0.586025	−	0.810293i	$-0.300692\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.81187	+	3.13825i	0.572964	+	0.992402i
$11$	1.74589	−	1.00799i	0.526406	−	0.303920i	−0.213146	−	0.977020i	$-0.568371\pi$
$11$	1.74589	−	1.00799i	0.526406	−	0.303920i	0.739551	+	0.673100i	$0.235038\pi$
$12$		0			0
$13$	3.59505	−	0.275040i	0.997086	−	0.0762824i
$13$	3.59505	−	0.275040i	0.997086	−	0.0762824i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.79054	−	6.56541i	0.919341	−	1.59235i	0.118923	−	0.992904i	$-0.462056\pi$
$17$	3.79054	−	6.56541i	0.919341	−	1.59235i	0.800418	−	0.599442i	$-0.204611\pi$
$18$		0			0
$19$	2.40547	+	1.38880i	0.551853	+	0.318613i	0.749869	−	0.661586i	$-0.230116\pi$
$19$	2.40547	+	1.38880i	0.551853	+	0.318613i	−0.198016	+	0.980199i	$0.563450\pi$
$20$	−3.13825	−	1.81187i	−0.701734	−	0.405147i
$21$		0			0
$22$	−1.00799	+	1.74589i	−0.214904	+	0.372225i
$23$	3.95583	+	6.85169i	0.824847	+	1.42868i	0.902036	+	0.431660i	$0.142072\pi$
$23$	3.95583	+	6.85169i	0.824847	+	1.42868i	−0.0771895	+	0.997016i	$0.524595\pi$
$24$		0			0
$25$	−8.13150			−1.62630
$26$	−2.97588	+	2.03571i	−0.583618	+	0.399236i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−2.83454	−	4.90957i	−0.526361	−	0.911684i	−0.999528	−	0.0307115i	$-0.990223\pi$
$29$	−2.83454	−	4.90957i	−0.526361	−	0.911684i	0.473167	−	0.880973i	$-0.343111\pi$
$30$		0			0
$31$			5.83236i			1.04752i	0.851865	+	0.523762i	$0.175472\pi$
$31$			5.83236i			1.04752i	−0.851865	+	0.523762i	$0.824528\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			7.58108i			1.30014i
$35$	−1.81187	+	3.13825i	−0.306262	+	0.530461i
$36$		0			0
$37$	−1.48866	+	0.859480i	−0.244735	+	0.141298i	−0.617351	−	0.786688i	$-0.711794\pi$
$37$	−1.48866	+	0.859480i	−0.244735	+	0.141298i	0.372616	+	0.927986i	$0.378461\pi$
$38$	−2.77760			−0.450586
$39$		0			0
$40$	3.62374			0.572964
$41$	10.0684	−	5.81297i	1.57241	−	0.907834i	0.576542	−	0.817068i	$-0.304402\pi$
$41$	10.0684	−	5.81297i	1.57241	−	0.907834i	0.995872	−	0.0907662i	$-0.0289316\pi$
$42$		0			0
$43$	2.63741	−	4.56813i	0.402201	−	0.696633i	−0.591790	−	0.806092i	$-0.701579\pi$
$43$	2.63741	−	4.56813i	0.402201	−	0.696633i	0.993991	+	0.109459i	$0.0349119\pi$
$44$		−	2.01598i		−	0.303920i
$45$		0			0
$46$	−6.85169	−	3.95583i	−1.01023	−	0.583255i
$47$		−	5.63658i		−	0.822180i	−0.911595	−	0.411090i	$-0.865148\pi$
$47$		−	5.63658i		−	0.822180i	0.911595	−	0.411090i	$-0.134852\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	7.04209	−	4.06575i	0.995901	−	0.574984i
$51$		0			0
$52$	1.55933	−	3.25092i	0.216240	−	0.450822i
$53$	−0.0731130			−0.0100428			−0.00502142	−	0.999987i	$-0.501598\pi$
$53$	−0.0731130			−0.0100428			−0.00502142	+	0.999987i	$0.501598\pi$
$54$		0			0
$55$	−3.65269	−	6.32665i	−0.492529	−	0.853086i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	4.90957	+	2.83454i	0.644658	+	0.372194i
$59$	−1.15686	−	0.667915i	−0.150611	−	0.0869551i	0.422801	−	0.906223i	$-0.361047\pi$
$59$	−1.15686	−	0.667915i	−0.150611	−	0.0869551i	−0.573411	+	0.819268i	$0.694380\pi$
$60$		0			0
$61$	0.187787	−	0.325257i	0.0240437	−	0.0416449i	−0.853753	−	0.520678i	$-0.825679\pi$
$61$	0.187787	−	0.325257i	0.0240437	−	0.0416449i	0.877797	+	0.479033i	$0.159013\pi$
$62$	−2.91618	−	5.05098i	−0.370356	−	0.641475i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.996674	−	13.0275i	−0.123622	−	1.61586i
$66$		0			0
$67$	−12.3907	+	7.15378i	−1.51377	+	0.873973i	−0.513895	+	0.857853i	$0.671798\pi$
$67$	−12.3907	+	7.15378i	−1.51377	+	0.873973i	−0.999870	+	0.0161201i	$0.994869\pi$
$68$	−3.79054	−	6.56541i	−0.459670	−	0.796173i
$69$		0			0
$70$		−	3.62374i		−	0.433120i
$71$	−11.0728	−	6.39291i	−1.31410	−	0.758698i	−0.331331	−	0.943515i	$-0.607498\pi$
$71$	−11.0728	−	6.39291i	−1.31410	−	0.758698i	−0.982773	+	0.184816i	$0.940831\pi$
$72$		0			0
$73$			4.80070i			0.561880i	0.959725	+	0.280940i	$0.0906462\pi$
$73$			4.80070i			0.561880i	−0.959725	+	0.280940i	$0.909354\pi$
$74$	0.859480	−	1.48866i	0.0999125	−	0.173053i
$75$		0			0
$76$	2.40547	−	1.38880i	0.275927	−	0.159306i
$77$	−2.01598			−0.229742
$78$		0			0
$79$	10.1368			1.14048			0.570241	−	0.821477i	$-0.306850\pi$
$79$	10.1368			1.14048			0.570241	+	0.821477i	$0.306850\pi$
$80$	−3.13825	+	1.81187i	−0.350867	+	0.202573i
$81$		0			0
$82$	−5.81297	+	10.0684i	−0.641935	+	1.11186i
$83$			1.97093i			0.216338i	0.994133	+	0.108169i	$0.0344987\pi$
$83$			1.97093i			0.216338i	−0.994133	+	0.108169i	$0.965501\pi$
$84$		0			0
$85$	−23.7913	−	13.7359i	−2.58053	−	1.48987i
$86$			5.27482i			0.568798i
$87$		0			0
$88$	1.00799	+	1.74589i	0.107452	+	0.186112i
$89$	−11.8252	+	6.82727i	−1.25347	+	0.723689i	−0.971796	−	0.235823i	$-0.924222\pi$
$89$	−11.8252	+	6.82727i	−1.25347	+	0.723689i	−0.281670	+	0.959511i	$0.590888\pi$
$90$		0			0
$91$	−3.25092	−	1.55933i	−0.340789	−	0.163462i
$92$	7.91165			0.824847
$93$		0			0
$94$	2.81829	+	4.88142i	0.290684	+	0.503480i
$95$	5.03265	−	8.71681i	0.516339	−	0.894326i
$96$		0			0
$97$	−13.6356	−	7.87254i	−1.38449	−	0.799336i	−0.391802	−	0.920049i	$-0.628148\pi$
$97$	−13.6356	−	7.87254i	−1.38449	−	0.799336i	−0.992687	+	0.120714i	$0.961482\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−4.06575	+	7.04209i	−0.406575	+	0.704209i
$101$	−0.160081	−	0.277268i	−0.0159286	−	0.0275892i	0.857951	−	0.513731i	$-0.171737\pi$
$101$	−0.160081	−	0.277268i	−0.0159286	−	0.0275892i	−0.873880	+	0.486142i	$0.838404\pi$
$102$		0			0
$103$	−0.139970			−0.0137917			−0.00689583	−	0.999976i	$-0.502195\pi$
$103$	−0.139970			−0.0137917			−0.00689583	+	0.999976i	$0.502195\pi$
$104$	0.275040	+	3.59505i	0.0269699	+	0.352523i
$105$		0			0
$106$	0.0633177	−	0.0365565i	0.00614996	−	0.00355068i
$107$	0.690440	+	1.19588i	0.0667474	+	0.115610i	0.897468	−	0.441080i	$-0.145405\pi$
$107$	0.690440	+	1.19588i	0.0667474	+	0.115610i	−0.830720	+	0.556690i	$0.812071\pi$
$108$		0			0
$109$		−	3.13642i		−	0.300415i	−0.988655	−	0.150207i	$-0.952006\pi$
$109$		−	3.13642i		−	0.300415i	0.988655	−	0.150207i	$-0.0479941\pi$
$110$	6.32665	+	3.65269i	0.603223	+	0.348271i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	6.23703	−	10.8029i	0.586731	−	1.01625i	−0.407927	−	0.913015i	$-0.633748\pi$
$113$	6.23703	−	10.8029i	0.586731	−	1.01625i	0.994657	−	0.103233i	$-0.0329186\pi$
$114$		0			0
$115$	24.8288	−	14.3349i	2.31529	−	1.33674i
$116$	−5.66908			−0.526361
$117$		0			0
$118$	1.33583			0.122973
$119$	−6.56541	+	3.79054i	−0.601850	+	0.347478i
$120$		0			0
$121$	−3.46791	+	6.00660i	−0.315265	+	0.546055i
$122$			0.375574i			0.0340029i
$123$		0			0
$124$	5.05098	+	2.91618i	0.453591	+	0.261881i
$125$			11.3477i			1.01497i
$126$		0			0
$127$	−3.04409	−	5.27252i	−0.270119	−	0.467861i	0.698773	−	0.715344i	$-0.253730\pi$
$127$	−3.04409	−	5.27252i	−0.270119	−	0.467861i	−0.968892	+	0.247483i	$0.920397\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	7.37690	+	10.7838i	0.646997	+	0.945804i
$131$	−4.04885			−0.353749			−0.176875	−	0.984233i	$-0.556599\pi$
$131$	−4.04885			−0.353749			−0.176875	+	0.984233i	$0.556599\pi$
$132$		0			0
$133$	−1.38880	−	2.40547i	−0.120424	−	0.208581i
$134$	7.15378	−	12.3907i	0.617992	−	1.07039i
$135$		0			0
$136$	6.56541	+	3.79054i	0.562979	+	0.325036i
$137$	−7.38057	−	4.26117i	−0.630565	−	0.364057i	0.150406	−	0.988624i	$-0.451942\pi$
$137$	−7.38057	−	4.26117i	−0.630565	−	0.364057i	−0.780971	+	0.624568i	$0.785275\pi$
$138$		0			0
$139$	9.60631	−	16.6386i	0.814797	−	1.41127i	−0.0946772	−	0.995508i	$-0.530182\pi$
$139$	9.60631	−	16.6386i	0.814797	−	1.41127i	0.909474	−	0.415761i	$-0.136485\pi$
$140$	1.81187	+	3.13825i	0.153131	+	0.265231i
$141$		0			0
$142$	12.7858			1.07296
$143$	5.99932	−	4.10396i	0.501688	−	0.343190i
$144$		0			0
$145$	−17.7910	+	10.2716i	−1.47746	+	0.853014i
$146$	−2.40035	−	4.15753i	−0.198655	−	0.344080i
$147$		0			0
$148$			1.71896i			0.141298i
$149$	0.132571	+	0.0765401i	0.0108607	+	0.00627041i	0.505421	−	0.862873i	$-0.331337\pi$
$149$	0.132571	+	0.0765401i	0.0108607	+	0.00627041i	−0.494560	+	0.869144i	$0.664671\pi$
$150$		0			0
$151$		−	11.7618i		−	0.957159i	−0.878044	−	0.478580i	$-0.841152\pi$
$151$		−	11.7618i		−	0.957159i	0.878044	−	0.478580i	$-0.158848\pi$
$152$	−1.38880	+	2.40547i	−0.112647	+	0.195110i
$153$		0			0
$154$	1.74589	−	1.00799i	0.140688	−	0.0812261i
$155$	21.1350			1.69760
$156$		0			0
$157$	23.5119			1.87645			0.938226	−	0.346024i	$-0.112468\pi$
$157$	23.5119			1.87645			0.938226	+	0.346024i	$0.112468\pi$
$158$	−8.77875	+	5.06841i	−0.698400	+	0.403221i
$159$		0			0
$160$	1.81187	−	3.13825i	0.143241	−	0.248101i
$161$		−	7.91165i		−	0.623526i
$162$		0			0
$163$	16.0068	+	9.24154i	1.25375	+	0.723853i	0.971852	−	0.235591i	$-0.0757026\pi$
$163$	16.0068	+	9.24154i	1.25375	+	0.723853i	0.281898	+	0.959444i	$0.409036\pi$
$164$		−	11.6259i		−	0.907834i
$165$		0			0
$166$	−0.985464	−	1.70687i	−0.0764869	−	0.132479i
$167$	−11.5477	+	6.66706i	−0.893587	+	0.515912i	−0.875114	−	0.483917i	$-0.839214\pi$
$167$	−11.5477	+	6.66706i	−0.893587	+	0.515912i	−0.0184727	+	0.999829i	$0.505880\pi$
$168$		0			0
$169$	12.8487	−	1.97756i	0.988362	−	0.152120i
$170$	27.4719			2.10700
$171$		0			0
$172$	−2.63741	−	4.56813i	−0.201101	−	0.348316i
$173$	−8.41536	+	14.5758i	−0.639808	+	1.10818i	0.345667	+	0.938357i	$0.387653\pi$
$173$	−8.41536	+	14.5758i	−0.639808	+	1.10818i	−0.985475	+	0.169823i	$0.945681\pi$
$174$		0			0
$175$	7.04209	+	4.06575i	0.532332	+	0.307342i
$176$	−1.74589	−	1.00799i	−0.131601	−	0.0759801i
$177$		0			0
$178$	6.82727	−	11.8252i	0.511725	−	0.886334i
$179$	5.44812	+	9.43642i	0.407212	+	0.705311i	0.994576	−	0.104011i	$-0.0331678\pi$
$179$	5.44812	+	9.43642i	0.407212	+	0.705311i	−0.587364	+	0.809323i	$0.699834\pi$
$180$		0			0
$181$	16.4301			1.22124			0.610619	−	0.791924i	$-0.290921\pi$
$181$	16.4301			1.22124			0.610619	+	0.791924i	$0.290921\pi$
$182$	3.59505	−	0.275040i	0.266483	−	0.0203873i
$183$		0			0
$184$	−6.85169	+	3.95583i	−0.505113	+	0.291627i
$185$	3.11453	+	5.39453i	0.228985	+	0.396613i
$186$		0			0
$187$		−	15.2833i		−	1.11763i
$188$	−4.88142	−	2.81829i	−0.356014	−	0.205545i
$189$		0			0
$190$			10.0653i			0.730214i
$191$	−3.49738	+	6.05765i	−0.253062	+	0.438316i	−0.964367	−	0.264567i	$-0.914771\pi$
$191$	−3.49738	+	6.05765i	−0.253062	+	0.438316i	0.711305	+	0.702883i	$0.248104\pi$
$192$		0			0
$193$	4.67583	−	2.69959i	0.336574	−	0.194321i	−0.322182	−	0.946678i	$-0.604416\pi$
$193$	4.67583	−	2.69959i	0.336574	−	0.194321i	0.658756	+	0.752357i	$0.271083\pi$
$194$	15.7451			1.13043
$195$		0			0
$196$	1.00000			0.0714286
$197$	3.43204	−	1.98149i	0.244523	−	0.141175i	−0.372731	−	0.927939i	$-0.621579\pi$
$197$	3.43204	−	1.98149i	0.244523	−	0.141175i	0.617254	+	0.786764i	$0.288245\pi$
$198$		0			0
$199$	−12.7019	+	22.0004i	−0.900417	+	1.55957i	−0.0734626	+	0.997298i	$0.523405\pi$
$199$	−12.7019	+	22.0004i	−0.900417	+	1.55957i	−0.826954	+	0.562270i	$0.809928\pi$
$200$		−	8.13150i		−	0.574984i
$201$		0			0
$202$	0.277268	+	0.160081i	0.0195085	+	0.0112632i
$203$			5.66908i			0.397892i
$204$		0			0
$205$	−21.0647	−	36.4851i	−1.47122	−	2.54823i
$206$	0.121218	−	0.0699850i	0.00844563	−	0.00487609i
$207$		0			0
$208$	−2.03571	−	2.97588i	−0.141151	−	0.206340i
$209$	5.59959			0.387331
$210$		0			0
$211$	−1.10268	−	1.90990i	−0.0759118	−	0.131483i	0.825571	−	0.564299i	$-0.190853\pi$
$211$	−1.10268	−	1.90990i	−0.0759118	−	0.131483i	−0.901482	+	0.432816i	$0.857520\pi$
$212$	−0.0365565	+	0.0633177i	−0.00251071	+	0.00434868i
$213$		0			0
$214$	−1.19588	−	0.690440i	−0.0817485	−	0.0471975i
$215$	−16.5537	−	9.55729i	−1.12895	−	0.651802i
$216$		0			0
$217$	2.91618	−	5.05098i	0.197963	−	0.342883i
$218$	1.56821	+	2.71622i	0.106213	+	0.183966i
$219$		0			0
$220$	−7.30539			−0.492529
$221$	11.8214	−	24.6455i	0.795194	−	1.65784i
$222$		0			0
$223$	−7.93739	+	4.58265i	−0.531527	+	0.306877i	−0.741638	−	0.670800i	$-0.765951\pi$
$223$	−7.93739	+	4.58265i	−0.531527	+	0.306877i	0.210111	+	0.977678i	$0.432617\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$			12.4741i			0.829762i
$227$	−8.63738	−	4.98679i	−0.573283	−	0.330985i	0.185176	−	0.982705i	$-0.440714\pi$
$227$	−8.63738	−	4.98679i	−0.573283	−	0.330985i	−0.758460	+	0.651720i	$0.774048\pi$
$228$		0			0
$229$			1.30526i			0.0862538i	0.999070	+	0.0431269i	$0.0137320\pi$
$229$			1.30526i			0.0862538i	−0.999070	+	0.0431269i	$0.986268\pi$
$230$	−14.3349	+	24.8288i	−0.945215	+	1.63716i
$231$		0			0
$232$	4.90957	−	2.83454i	0.322329	−	0.186097i
$233$	−27.4165			−1.79612			−0.898058	−	0.439876i	$-0.855022\pi$
$233$	−27.4165			−1.79612			−0.898058	+	0.439876i	$0.855022\pi$
$234$		0			0
$235$	−20.4255			−1.33241
$236$	−1.15686	+	0.667915i	−0.0753053	+	0.0434775i
$237$		0			0
$238$	3.79054	−	6.56541i	0.245704	−	0.425572i
$239$			0.343121i			0.0221946i	0.999938	+	0.0110973i	$0.00353246\pi$
$239$			0.343121i			0.0221946i	−0.999938	+	0.0110973i	$0.996468\pi$
$240$		0			0
$241$	9.39860	+	5.42628i	0.605417	+	0.349538i	0.771170	−	0.636630i	$-0.219672\pi$
$241$	9.39860	+	5.42628i	0.605417	+	0.349538i	−0.165753	+	0.986167i	$0.553005\pi$
$242$		−	6.93583i		−	0.445852i
$243$		0			0
$244$	−0.187787	−	0.325257i	−0.0120218	−	0.0208224i
$245$	3.13825	−	1.81187i	0.200496	−	0.115756i
$246$		0			0
$247$	9.02976	+	4.33120i	0.574550	+	0.275588i
$248$	−5.83236			−0.370356
$249$		0			0
$250$	−5.67387	−	9.82744i	−0.358847	−	0.621542i
$251$	−2.26799	+	3.92828i	−0.143154	+	0.247951i	−0.928683	−	0.370875i	$-0.879058\pi$
$251$	−2.26799	+	3.92828i	−0.143154	+	0.247951i	0.785528	+	0.618826i	$0.212391\pi$
$252$		0			0
$253$	13.8129	+	7.97487i	0.868408	+	0.501376i
$254$	5.27252	+	3.04409i	0.330827	+	0.191003i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.1494	+	17.5792i	0.633101	+	1.09656i	0.986914	+	0.161247i	$0.0515515\pi$
$257$	10.1494	+	17.5792i	0.633101	+	1.09656i	−0.353813	+	0.935316i	$0.615115\pi$
$258$		0			0
$259$	1.71896			0.106811
$260$	−11.7805	−	5.65061i	−0.730595	−	0.350436i
$261$		0			0
$262$	3.50640	−	2.02442i	0.216626	−	0.125069i
$263$	9.81314	+	16.9969i	0.605104	+	1.04807i	0.992035	+	0.125962i	$0.0402019\pi$
$263$	9.81314	+	16.9969i	0.605104	+	1.04807i	−0.386931	+	0.922109i	$0.626465\pi$
$264$		0			0
$265$			0.264942i			0.0162753i
$266$	2.40547	+	1.38880i	0.147489	+	0.0851528i
$267$		0			0
$268$			14.3076i			0.873973i
$269$	4.52417	−	7.83610i	0.275844	−	0.477775i	−0.694504	−	0.719489i	$-0.744376\pi$
$269$	4.52417	−	7.83610i	0.275844	−	0.477775i	0.970348	+	0.241714i	$0.0777095\pi$
$270$		0			0
$271$	19.6128	−	11.3234i	1.19139	−	0.687850i	0.232769	−	0.972532i	$-0.425221\pi$
$271$	19.6128	−	11.3234i	1.19139	−	0.687850i	0.958622	+	0.284682i	$0.0918880\pi$
$272$	−7.58108			−0.459670
$273$		0			0
$274$	8.52235			0.514854
$275$	−14.1967	+	8.19647i	−0.856093	+	0.494266i
$276$		0			0
$277$	−10.5587	+	18.2881i	−0.634409	+	1.09883i	0.352231	+	0.935913i	$0.385423\pi$
$277$	−10.5587	+	18.2881i	−0.634409	+	1.09883i	−0.986640	+	0.162915i	$0.947910\pi$
$278$			19.2126i			1.15230i
$279$		0			0
$280$	−3.13825	−	1.81187i	−0.187546	−	0.108280i
$281$		−	19.3644i		−	1.15518i	−0.816325	−	0.577592i	$-0.803992\pi$
$281$		−	19.3644i		−	1.15518i	0.816325	−	0.577592i	$-0.196008\pi$
$282$		0			0
$283$	−2.78361	−	4.82136i	−0.165469	−	0.286600i	0.771353	−	0.636407i	$-0.219580\pi$
$283$	−2.78361	−	4.82136i	−0.165469	−	0.286600i	−0.936822	+	0.349808i	$0.886247\pi$
$284$	−11.0728	+	6.39291i	−0.657052	+	0.379349i
$285$		0			0
$286$	−3.14358	+	6.55379i	−0.185884	+	0.387534i
$287$	−11.6259			−0.686258
$288$		0			0
$289$	−20.2364	−	35.0504i	−1.19038	−	2.06179i
$290$	10.2716	−	17.7910i	0.603172	−	1.04472i
$291$		0			0
$292$	4.15753	+	2.40035i	0.243301	+	0.140470i
$293$	27.2323	+	15.7226i	1.59093	+	0.918523i	0.993148	+	0.116864i	$0.0372841\pi$
$293$	27.2323	+	15.7226i	1.59093	+	0.918523i	0.597781	+	0.801659i	$0.296049\pi$
$294$		0			0
$295$	−2.42035	+	4.19217i	−0.140918	+	0.244078i
$296$	−0.859480	−	1.48866i	−0.0499562	−	0.0865267i
$297$		0			0
$298$	−0.153080			−0.00886770
$299$	16.1059	+	23.5441i	0.931426	+	1.36159i
$300$		0			0
$301$	−4.56813	+	2.63741i	−0.263303	+	0.152018i
$302$	5.88088	+	10.1860i	0.338407	+	0.586138i
$303$		0			0
$304$		−	2.77760i		−	0.159306i
$305$	−1.17865	−	0.680492i	−0.0674891	−	0.0389648i
$306$		0			0
$307$			13.6952i			0.781626i	0.920470	+	0.390813i	$0.127806\pi$
$307$			13.6952i			0.781626i	−0.920470	+	0.390813i	$0.872194\pi$
$308$	−1.00799	+	1.74589i	−0.0574356	+	0.0994813i
$309$		0			0
$310$	−18.3034	+	10.5675i	−1.03956	+	0.600193i
$311$	20.9665			1.18890			0.594451	−	0.804132i	$-0.297369\pi$
$311$	20.9665			1.18890			0.594451	+	0.804132i	$0.297369\pi$
$312$		0			0
$313$	−12.2102			−0.690163			−0.345082	−	0.938573i	$-0.612149\pi$
$313$	−12.2102			−0.690163			−0.345082	+	0.938573i	$0.612149\pi$
$314$	−20.3619	+	11.7559i	−1.14909	+	0.663426i
$315$		0			0
$316$	5.06841	−	8.77875i	0.285121	−	0.493843i
$317$			12.5110i			0.702686i	0.936247	+	0.351343i	$0.114275\pi$
$317$			12.5110i			0.702686i	−0.936247	+	0.351343i	$0.885725\pi$
$318$		0			0
$319$	−9.89759	−	5.71438i	−0.554159	−	0.319944i
$320$			3.62374i			0.202573i
$321$		0			0
$322$	3.95583	+	6.85169i	0.220450	+	0.381830i
$323$	18.2361	−	10.5286i	1.01468	−	0.585827i
$324$		0			0
$325$	−29.2331	+	2.23649i	−1.62156	+	0.124058i
$326$	−18.4831			−1.02368
$327$		0			0
$328$	5.81297	+	10.0684i	0.320968	+	0.555932i
$329$	−2.81829	+	4.88142i	−0.155377	+	0.269121i
$330$		0			0
$331$	−19.0473	−	10.9970i	−1.04693	−	0.604448i	−0.125145	−	0.992138i	$-0.539940\pi$
$331$	−19.0473	−	10.9970i	−1.04693	−	0.604448i	−0.921790	+	0.387690i	$0.873273\pi$
$332$	1.70687	+	0.985464i	0.0936769	+	0.0540844i
$333$		0			0
$334$	6.66706	−	11.5477i	0.364805	−	0.631861i
$335$	25.9234	+	44.9007i	1.41635	+	2.45319i
$336$		0			0
$337$	7.58788			0.413338			0.206669	−	0.978411i	$-0.433738\pi$
$337$	7.58788			0.413338			0.206669	+	0.978411i	$0.433738\pi$
$338$	−10.1385	+	8.13697i	−0.551463	+	0.442593i
$339$		0			0
$340$	−23.7913	+	13.7359i	−1.29027	+	0.744936i
$341$	5.87896	+	10.1827i	0.318364	+	0.551422i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	4.56813	+	2.63741i	0.246297	+	0.142200i
$345$		0			0
$346$		−	16.8307i		−	0.904825i
$347$	−3.75725	+	6.50774i	−0.201700	+	0.349354i	−0.949076	−	0.315047i	$-0.897980\pi$
$347$	−3.75725	+	6.50774i	−0.201700	+	0.349354i	0.747377	+	0.664401i	$0.231313\pi$
$348$		0			0
$349$	−19.9831	+	11.5373i	−1.06967	+	0.617575i	−0.928092	−	0.372352i	$-0.878551\pi$
$349$	−19.9831	+	11.5373i	−1.06967	+	0.617575i	−0.141580	+	0.989927i	$0.545218\pi$
$350$	−8.13150			−0.434647
$351$		0			0
$352$	2.01598			0.107452
$353$	−30.2137	+	17.4439i	−1.60811	+	0.928443i	−0.618318	+	0.785928i	$0.712186\pi$
$353$	−30.2137	+	17.4439i	−1.60811	+	0.928443i	−0.989793	+	0.142515i	$0.954481\pi$
$354$		0			0
$355$	−23.1662	+	40.1251i	−1.22954	+	2.12962i
$356$			13.6545i			0.723689i
$357$		0			0
$358$	−9.43642	−	5.44812i	−0.498731	−	0.287942i
$359$			4.29129i			0.226486i	0.993567	+	0.113243i	$0.0361238\pi$
$359$			4.29129i			0.226486i	−0.993567	+	0.113243i	$0.963876\pi$
$360$		0			0
$361$	−5.64247	−	9.77304i	−0.296972	−	0.514371i
$362$	−14.2289	+	8.21504i	−0.747853	+	0.431773i
$363$		0			0
$364$	−2.97588	+	2.03571i	−0.155979	+	0.106700i
$365$	17.3965			0.910575
$366$		0			0
$367$	−12.4286	−	21.5270i	−0.648767	−	1.12370i	−0.983418	−	0.181356i	$-0.941951\pi$
$367$	−12.4286	−	21.5270i	−0.648767	−	1.12370i	0.334650	−	0.942342i	$-0.391382\pi$
$368$	3.95583	−	6.85169i	0.206212	−	0.357169i
$369$		0			0
$370$	−5.39453	−	3.11453i	−0.280448	−	0.161917i
$371$	0.0633177	+	0.0365565i	0.00328729	+	0.00189792i
$372$		0			0
$373$	−17.2705	+	29.9134i	−0.894233	+	1.54886i	−0.0594830	+	0.998229i	$0.518945\pi$
$373$	−17.2705	+	29.9134i	−0.894233	+	1.54886i	−0.834750	+	0.550628i	$0.814388\pi$
$374$	7.64165	+	13.2357i	0.395140	+	0.684403i
$375$		0			0
$376$	5.63658			0.290684
$377$	−11.5406	−	16.8705i	−0.594373	−	0.868876i
$378$		0			0
$379$	23.5599	−	13.6023i	1.21019	−	0.698704i	0.247391	−	0.968916i	$-0.420427\pi$
$379$	23.5599	−	13.6023i	1.21019	−	0.698704i	0.962801	+	0.270211i	$0.0870936\pi$
$380$	−5.03265	−	8.71681i	−0.258170	−	0.447163i
$381$		0			0
$382$		−	6.99477i		−	0.357883i
$383$	−25.0615	−	14.4693i	−1.28058	−	0.739344i	−0.303627	−	0.952791i	$-0.598198\pi$
$383$	−25.0615	−	14.4693i	−1.28058	−	0.739344i	−0.976955	+	0.213447i	$0.931531\pi$
$384$		0			0
$385$			7.30539i			0.372317i
$386$	−2.69959	+	4.67583i	−0.137406	+	0.237993i
$387$		0			0
$388$	−13.6356	+	7.87254i	−0.692245	+	0.399668i
$389$	21.5418			1.09221			0.546106	−	0.837716i	$-0.316109\pi$
$389$	21.5418			1.09221			0.546106	+	0.837716i	$0.316109\pi$
$390$		0			0
$391$	59.9789			3.03326
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−1.98149	+	3.43204i	−0.0998259	+	0.172904i
$395$		−	36.7332i		−	1.84825i
$396$		0			0
$397$	2.96408	+	1.71131i	0.148763	+	0.0858883i	0.572534	−	0.819881i	$-0.305960\pi$
$397$	2.96408	+	1.71131i	0.148763	+	0.0858883i	−0.423771	+	0.905769i	$0.639294\pi$
$398$		−	25.4039i		−	1.27338i
$399$		0			0
$400$	4.06575	+	7.04209i	0.203288	+	0.352104i
$401$	6.45616	−	3.72747i	0.322405	−	0.186141i	−0.330059	−	0.943960i	$-0.607069\pi$
$401$	6.45616	−	3.72747i	0.322405	−	0.186141i	0.652464	+	0.757819i	$0.273735\pi$
$402$		0			0
$403$	1.60413	+	20.9676i	0.0799076	+	1.04447i
$404$	−0.320161			−0.0159286
$405$		0			0
$406$	−2.83454	−	4.90957i	−0.140676	−	0.243658i
$407$	−1.73269	+	3.00111i	−0.0858864	+	0.148760i
$408$		0			0
$409$	−5.65842	−	3.26689i	−0.279791	−	0.161537i	0.353538	−	0.935420i	$-0.384979\pi$
$409$	−5.65842	−	3.26689i	−0.279791	−	0.161537i	−0.633329	+	0.773883i	$0.718312\pi$
$410$	36.4851	+	21.0647i	1.80187	+	1.04031i
$411$		0			0
$412$	−0.0699850	+	0.121218i	−0.00344791	+	0.00597196i
$413$	0.667915	+	1.15686i	0.0328659	+	0.0569255i
$414$		0			0
$415$	7.14213			0.350594
$416$	3.25092	+	1.55933i	0.159390	+	0.0764525i
$417$		0			0
$418$	−4.84938	+	2.79979i	−0.237191	+	0.136942i
$419$	−8.61309	−	14.9183i	−0.420777	−	0.728807i	0.575239	−	0.817986i	$-0.304909\pi$
$419$	−8.61309	−	14.9183i	−0.420777	−	0.728807i	−0.996016	+	0.0891785i	$0.971576\pi$
$420$		0			0
$421$			2.95781i			0.144155i	0.997399	+	0.0720774i	$0.0229629\pi$
$421$			2.95781i			0.144155i	−0.997399	+	0.0720774i	$0.977037\pi$
$422$	1.90990	+	1.10268i	0.0929726	+	0.0536777i
$423$		0			0
$424$		−	0.0731130i		−	0.00355068i
$425$	−30.8228	+	53.3866i	−1.49512	+	2.58963i
$426$		0			0
$427$	−0.325257	+	0.187787i	−0.0157403	+	0.00908765i
$428$	1.38088			0.0667474
$429$		0			0
$430$	19.1146			0.921787
$431$	−17.3358	+	10.0088i	−0.835037	+	0.482109i	−0.855574	−	0.517680i	$-0.826796\pi$
$431$	−17.3358	+	10.0088i	−0.835037	+	0.482109i	0.0205370	+	0.999789i	$0.493462\pi$
$432$		0			0
$433$	16.9433	−	29.3466i	0.814241	−	1.41031i	−0.0956311	−	0.995417i	$-0.530487\pi$
$433$	16.9433	−	29.3466i	0.814241	−	1.41031i	0.909872	−	0.414890i	$-0.136180\pi$
$434$			5.83236i			0.279962i
$435$		0			0
$436$	−2.71622	−	1.56821i	−0.130083	−	0.0751036i
$437$			21.9754i			1.05123i
$438$		0			0
$439$	13.6418	+	23.6283i	0.651089	+	1.12772i	0.982859	+	0.184359i	$0.0590209\pi$
$439$	13.6418	+	23.6283i	0.651089	+	1.12772i	−0.331770	+	0.943360i	$0.607646\pi$
$440$	6.32665	−	3.65269i	0.301611	−	0.174135i
$441$		0			0
$442$	2.08510	+	27.2543i	0.0991781	+	1.29636i
$443$	−3.73740			−0.177569			−0.0887845	−	0.996051i	$-0.528298\pi$
$443$	−3.73740			−0.177569			−0.0887845	+	0.996051i	$0.528298\pi$
$444$		0			0
$445$	24.7402	+	42.8514i	1.17280	+	2.03135i
$446$	4.58265	−	7.93739i	0.216995	−	0.375846i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−2.67990	−	1.54724i	−0.126472	−	0.0730189i	0.435429	−	0.900223i	$-0.356597\pi$
$449$	−2.67990	−	1.54724i	−0.126472	−	0.0730189i	−0.561901	+	0.827204i	$0.689930\pi$
$450$		0			0
$451$	11.7188	−	20.2976i	0.551818	−	0.955777i
$452$	−6.23703	−	10.8029i	−0.293365	−	0.508124i
$453$		0			0
$454$	9.97359			0.468084
$455$	−5.65061	+	11.7805i	−0.264905	+	0.552278i
$456$		0			0
$457$	17.4469	−	10.0730i	0.816130	−	0.471193i	−0.0329500	−	0.999457i	$-0.510490\pi$
$457$	17.4469	−	10.0730i	0.816130	−	0.471193i	0.849080	+	0.528264i	$0.177157\pi$
$458$	−0.652628	−	1.13039i	−0.0304953	−	0.0528194i
$459$		0			0
$460$		−	28.6698i		−	1.33674i
$461$	−25.0527	−	14.4642i	−1.16682	−	0.673665i	−0.213892	−	0.976857i	$-0.568614\pi$
$461$	−25.0527	−	14.4642i	−1.16682	−	0.673665i	−0.952929	+	0.303192i	$0.901948\pi$
$462$		0			0
$463$			27.2704i			1.26736i	0.773594	+	0.633681i	$0.218457\pi$
$463$			27.2704i			1.26736i	−0.773594	+	0.633681i	$0.781543\pi$
$464$	−2.83454	+	4.90957i	−0.131590	+	0.227921i
$465$		0			0
$466$	23.7434	−	13.7083i	1.09989	−	0.635023i
$467$	15.5605			0.720055			0.360028	−	0.932942i	$-0.382767\pi$
$467$	15.5605			0.720055			0.360028	+	0.932942i	$0.382767\pi$
$468$		0			0
$469$	14.3076			0.660661
$470$	17.6890	−	10.2128i	0.815933	−	0.471079i
$471$		0			0
$472$	0.667915	−	1.15686i	0.0307433	−	0.0532489i
$473$		−	10.6339i		−	0.488949i
$474$		0			0
$475$	−19.5601	−	11.2930i	−0.897479	−	0.518160i
$476$			7.58108i			0.347478i
$477$		0			0
$478$	−0.171560	−	0.297151i	−0.00784699	−	0.0135914i
$479$	32.3400	−	18.6715i	1.47765	−	0.853122i	0.477970	−	0.878376i	$-0.341373\pi$
$479$	32.3400	−	18.6715i	1.47765	−	0.853122i	0.999681	+	0.0252536i	$0.00803931\pi$
$480$		0			0
$481$	−5.11542	+	3.49931i	−0.233243	+	0.159555i
$482$	−10.8526			−0.494321
$483$		0			0
$484$	3.46791	+	6.00660i	0.157632	+	0.273027i
$485$	−28.5281	+	49.4120i	−1.29539	+	2.24369i
$486$		0			0
$487$	23.6297	+	13.6426i	1.07076	+	0.618205i	0.928390	−	0.371608i	$-0.121194\pi$
$487$	23.6297	+	13.6426i	1.07076	+	0.618205i	0.142373	+	0.989813i	$0.454527\pi$
$488$	0.325257	+	0.187787i	0.0147237	+	0.00850072i
$489$		0			0
$490$	−1.81187	+	3.13825i	−0.0818520	+	0.141772i
$491$	−10.3161	−	17.8680i	−0.465559	−	0.806373i	0.533667	−	0.845695i	$-0.320814\pi$
$491$	−10.3161	−	17.8680i	−0.465559	−	0.806373i	−0.999227	+	0.0393220i	$0.987480\pi$
$492$		0			0
$493$	−42.9778			−1.93562
$494$	−9.98560	+	0.763951i	−0.449273	+	0.0343718i
$495$		0			0
$496$	5.05098	−	2.91618i	0.226796	−	0.130940i
$497$	6.39291	+	11.0728i	0.286761	+	0.496685i
$498$		0			0
$499$		−	18.9558i		−	0.848580i	−0.905526	−	0.424290i	$-0.860524\pi$
$499$		−	18.9558i		−	0.848580i	0.905526	−	0.424290i	$-0.139476\pi$
$500$	9.82744	+	5.67387i	0.439496	+	0.253743i
$501$		0			0
$502$		−	4.53598i		−	0.202451i
$503$	−7.30193	+	12.6473i	−0.325577	+	0.563916i	−0.981629	−	0.190800i	$-0.938892\pi$
$503$	−7.30193	+	12.6473i	−0.325577	+	0.563916i	0.656052	+	0.754716i	$0.272225\pi$
$504$		0			0
$505$	−1.00475	+	0.580091i	−0.0447106	+	0.0258137i
$506$	−15.9497			−0.709052
$507$		0			0
$508$	−6.08818			−0.270119
$509$	−26.0537	+	15.0421i	−1.15481	+	0.666730i	−0.950055	−	0.312083i	$-0.898973\pi$
$509$	−26.0537	+	15.0421i	−1.15481	+	0.666730i	−0.204756	+	0.978813i	$0.565640\pi$
$510$		0			0
$511$	2.40035	−	4.15753i	0.106185	−	0.183918i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−17.5792	−	10.1494i	−0.775387	−	0.447670i
$515$			0.507215i			0.0223506i
$516$		0			0
$517$	−5.68161	−	9.84085i	−0.249877	−	0.432800i
$518$	−1.48866	+	0.859480i	−0.0654081	+	0.0377634i
$519$		0			0
$520$	13.0275	−	0.996674i	0.571294	−	0.0437070i
$521$	3.62407			0.158773			0.0793867	−	0.996844i	$-0.474704\pi$
$521$	3.62407			0.158773			0.0793867	+	0.996844i	$0.474704\pi$
$522$		0			0
$523$	13.0474	+	22.5988i	0.570523	+	0.988174i	0.996512	+	0.0834464i	$0.0265927\pi$
$523$	13.0474	+	22.5988i	0.570523	+	0.988174i	−0.425989	+	0.904728i	$0.640074\pi$
$524$	−2.02442	+	3.50640i	−0.0884374	+	0.153178i
$525$		0			0
$526$	−16.9969	−	9.81314i	−0.741098	−	0.427873i
$527$	38.2919	+	22.1078i	1.66802	+	0.963031i
$528$		0			0
$529$	−19.7971	+	34.2896i	−0.860745	+	1.49085i
$530$	−0.132471	−	0.229447i	−0.00575418	−	0.00996654i
$531$		0			0
$532$	−2.77760			−0.120424
$533$	34.5974	−	23.6671i	1.49858	−	1.02514i
$534$		0			0
$535$	4.33355	−	2.50198i	0.187356	−	0.108170i
$536$	−7.15378	−	12.3907i	−0.308996	−	0.535197i
$537$		0			0
$538$			9.04835i			0.390102i
$539$	1.74589	+	1.00799i	0.0752008	+	0.0434172i
$540$		0			0
$541$		−	10.1512i		−	0.436436i	−0.975900	−	0.218218i	$-0.929976\pi$
$541$		−	10.1512i		−	0.436436i	0.975900	−	0.218218i	$-0.0700243\pi$
$542$	−11.3234	+	19.6128i	−0.486383	+	0.842441i
$543$		0			0
$544$	6.56541	−	3.79054i	0.281490	−	0.162518i
$545$	−11.3656			−0.486848
$546$		0			0
$547$	29.9605			1.28102			0.640509	−	0.767950i	$-0.278723\pi$
$547$	29.9605			1.28102			0.640509	+	0.767950i	$0.278723\pi$
$548$	−7.38057	+	4.26117i	−0.315282	+	0.182028i
$549$		0			0
$550$	8.19647	−	14.1967i	0.349499	−	0.605349i
$551$		−	15.7464i		−	0.670821i
$552$		0			0
$553$	−8.77875	−	5.06841i	−0.373310	−	0.215531i
$554$		−	21.1173i		−	0.897189i
$555$		0			0
$556$	−9.60631	−	16.6386i	−0.407398	−	0.705635i
$557$	3.62112	−	2.09066i	0.153432	−	0.0885839i	−0.421318	−	0.906913i	$-0.638433\pi$
$557$	3.62112	−	2.09066i	0.153432	−	0.0885839i	0.574750	+	0.818329i	$0.305099\pi$
$558$		0			0
$559$	8.22519	−	17.1480i	0.347889	−	0.725284i
$560$	3.62374			0.153131
$561$		0			0
$562$	9.68221	+	16.7701i	0.408419	+	0.707403i
$563$	13.4183	−	23.2412i	0.565514	−	0.979498i	−0.431488	−	0.902119i	$-0.642011\pi$
$563$	13.4183	−	23.2412i	0.565514	−	0.979498i	0.997002	−	0.0773798i	$-0.0246554\pi$
$564$		0			0
$565$	−39.1468	−	22.6014i	−1.64692	−	0.950848i
$566$	4.82136	+	2.78361i	0.202657	+	0.117004i
$567$		0			0
$568$	6.39291	−	11.0728i	0.268240	−	0.464606i
$569$	−7.77089	−	13.4596i	−0.325773	−	0.564255i	0.655896	−	0.754851i	$-0.272291\pi$
$569$	−7.77089	−	13.4596i	−0.325773	−	0.564255i	−0.981668	+	0.190597i	$0.938958\pi$
$570$		0			0
$571$	47.3351			1.98091			0.990457	−	0.137825i	$-0.0440112\pi$
$571$	47.3351			1.98091			0.990457	+	0.137825i	$0.0440112\pi$
$572$	−0.554475	−	7.24754i	−0.0231838	−	0.303035i
$573$		0			0
$574$	10.0684	−	5.81297i	0.420245	−	0.242629i
$575$	−32.1668	−	55.7145i	−1.34145	−	2.32346i
$576$		0			0
$577$			1.85520i			0.0772330i	0.999254	+	0.0386165i	$0.0122951\pi$
$577$			1.85520i			0.0772330i	−0.999254	+	0.0386165i	$0.987705\pi$
$578$	35.0504	+	20.2364i	1.45791	+	0.841723i
$579$		0			0
$580$			20.5433i			0.853014i
$581$	0.985464	−	1.70687i	0.0408839	−	0.0708131i
$582$		0			0
$583$	−0.127647	+	0.0736971i	−0.00528661	+	0.00305222i
$584$	−4.80070			−0.198655
$585$		0			0
$586$	−31.4452			−1.29899
$587$	−3.73652	+	2.15728i	−0.154223	+	0.0890405i	−0.575125	−	0.818065i	$-0.695047\pi$
$587$	−3.73652	+	2.15728i	−0.154223	+	0.0890405i	0.420903	+	0.907106i	$0.361713\pi$
$588$		0			0
$589$	−8.09999	+	14.0296i	−0.333754	+	0.578079i
$590$		−	4.84070i		−	0.199288i
$591$		0			0
$592$	1.48866	+	0.859480i	0.0611836	+	0.0353244i
$593$		−	13.8068i		−	0.566979i	−0.958975	−	0.283490i	$-0.908508\pi$
$593$		−	13.8068i		−	0.566979i	0.958975	−	0.283490i	$-0.0914921\pi$
$594$		0			0
$595$	13.7359	+	23.7913i	0.563118	+	0.975350i
$596$	0.132571	−	0.0765401i	0.00543034	−	0.00313521i
$597$		0			0
$598$	−25.7202	−	12.3369i	−1.05178	−	0.504493i
$599$	19.0317			0.777612			0.388806	−	0.921320i	$-0.372888\pi$
$599$	19.0317			0.777612			0.388806	+	0.921320i	$0.372888\pi$
$600$		0			0
$601$	7.20400	+	12.4777i	0.293857	+	0.508975i	0.974718	−	0.223437i	$-0.0717277\pi$
$601$	7.20400	+	12.4777i	0.293857	+	0.508975i	−0.680861	+	0.732412i	$0.738394\pi$
$602$	2.63741	−	4.56813i	0.107493	−	0.186183i
$603$		0			0
$604$	−10.1860	−	5.88088i	−0.414462	−	0.239290i
$605$	21.7664	+	12.5668i	0.884929	+	0.510914i
$606$		0			0
$607$	−19.1587	+	33.1839i	−0.777629	+	1.34689i	0.155676	+	0.987808i	$0.450244\pi$
$607$	−19.1587	+	33.1839i	−0.777629	+	1.34689i	−0.933305	+	0.359085i	$0.883089\pi$
$608$	1.38880	+	2.40547i	0.0563233	+	0.0975548i
$609$		0			0
$610$	1.36098			0.0551046
$611$	−1.55029	−	20.2638i	−0.0627178	−	0.819784i
$612$		0			0
$613$	−24.7425	+	14.2851i	−0.999339	+	0.576968i	−0.908053	−	0.418856i	$-0.862431\pi$
$613$	−24.7425	+	14.2851i	−0.999339	+	0.576968i	−0.0912860	+	0.995825i	$0.529098\pi$
$614$	−6.84760	−	11.8604i	−0.276346	−	0.478646i
$615$		0			0
$616$		−	2.01598i		−	0.0812261i
$617$	−2.64638	−	1.52789i	−0.106539	−	0.0615105i	0.445784	−	0.895141i	$-0.352925\pi$
$617$	−2.64638	−	1.52789i	−0.106539	−	0.0615105i	−0.552323	+	0.833630i	$0.686258\pi$
$618$		0			0
$619$			40.2175i			1.61648i	0.588856	+	0.808238i	$0.299579\pi$
$619$			40.2175i			1.61648i	−0.588856	+	0.808238i	$0.700421\pi$
$620$	10.5675	−	18.3034i	0.424401	−	0.735083i
$621$		0			0
$622$	−18.1575	+	10.4833i	−0.728051	+	0.420341i
$623$	13.6545			0.547057
$624$		0			0
$625$	0.463794			0.0185518
$626$	10.5744	−	6.10512i	0.422637	−	0.244010i
$627$		0			0
$628$	11.7559	−	20.3619i	0.469113	−	0.812527i
$629$			13.0316i			0.519603i
$630$		0			0
$631$	13.7571	+	7.94266i	0.547661	+	0.316192i	0.748178	−	0.663498i	$-0.230929\pi$
$631$	13.7571	+	7.94266i	0.547661	+	0.316192i	−0.200517	+	0.979690i	$0.564262\pi$
$632$			10.1368i			0.403221i
$633$		0			0
$634$	−6.25548	−	10.8348i	−0.248437	−	0.430305i
$635$	−19.1063	+	11.0310i	−0.758208	+	0.437752i
$636$		0			0
$637$	2.03571	+	2.97588i	0.0806579	+	0.117909i
$638$	11.4288			0.452469
$639$		0			0
$640$	−1.81187	−	3.13825i	−0.0716205	−	0.124050i
$641$	5.52325	−	9.56655i	0.218155	−	0.377856i	−0.736089	−	0.676885i	$-0.763329\pi$
$641$	5.52325	−	9.56655i	0.218155	−	0.377856i	0.954244	+	0.299029i	$0.0966628\pi$
$642$		0			0
$643$	−1.24600	−	0.719378i	−0.0491374	−	0.0283695i	0.475230	−	0.879862i	$-0.342365\pi$
$643$	−1.24600	−	0.719378i	−0.0491374	−	0.0283695i	−0.524367	+	0.851492i	$0.675698\pi$
$644$	−6.85169	−	3.95583i	−0.269995	−	0.155881i
$645$		0			0
$646$	−10.5286	+	18.2361i	−0.414242	+	0.717489i
$647$	10.6562	+	18.4571i	0.418940	+	0.725625i	0.995833	−	0.0911948i	$-0.0290686\pi$
$647$	10.6562	+	18.4571i	0.418940	+	0.725625i	−0.576894	+	0.816819i	$0.695735\pi$
$648$		0			0
$649$	−2.69301			−0.105710
$650$	24.1984	−	16.5534i	0.949138	−	0.649278i
$651$		0			0
$652$	16.0068	−	9.24154i	0.626875	−	0.361927i
$653$	15.5822	+	26.9891i	0.609778	+	1.05617i	0.991277	+	0.131797i	$0.0420746\pi$
$653$	15.5822	+	26.9891i	0.609778	+	1.05617i	−0.381499	+	0.924369i	$0.624592\pi$
$654$		0			0
$655$			14.6720i			0.573281i
$656$	−10.0684	−	5.81297i	−0.393104	−	0.226958i
$657$		0			0
$658$		−	5.63658i		−	0.219737i
$659$	−11.9888	+	20.7653i	−0.467019	+	0.808901i	−0.999290	−	0.0376733i	$-0.988005\pi$
$659$	−11.9888	+	20.7653i	−0.467019	+	0.808901i	0.532271	+	0.846574i	$0.321339\pi$
$660$		0			0
$661$	−5.12358	+	2.95810i	−0.199284	+	0.115057i	−0.596322	−	0.802746i	$-0.703372\pi$
$661$	−5.12358	+	2.95810i	−0.199284	+	0.115057i	0.397037	+	0.917802i	$0.370038\pi$
$662$	21.9939			0.854819
$663$		0			0
$664$	−1.97093			−0.0764869
$665$	−8.71681	+	5.03265i	−0.338023	+	0.195158i
$666$		0			0
$667$	22.4259	−	38.8428i	0.868335	−	1.50400i
$668$			13.3341i			0.515912i
$669$		0			0
$670$	−44.9007	−	25.9234i	−1.73467	−	1.00151i
$671$		−	0.757150i		−	0.0292294i
$672$		0			0
$673$	−2.01309	−	3.48677i	−0.0775987	−	0.134405i	0.824615	−	0.565695i	$-0.191392\pi$
$673$	−2.01309	−	3.48677i	−0.0775987	−	0.134405i	−0.902213	+	0.431290i	$0.858059\pi$
$674$	−6.57130	+	3.79394i	−0.253117	+	0.146137i
$675$		0			0
$676$	4.71173	−	12.1161i	0.181221	−	0.466003i
$677$	27.7397			1.06612			0.533061	−	0.846077i	$-0.321042\pi$
$677$	27.7397			1.06612			0.533061	+	0.846077i	$0.321042\pi$
$678$		0			0
$679$	7.87254	+	13.6356i	0.302120	+	0.523288i
$680$	13.7359	−	23.7913i	0.526749	−	0.912356i
$681$		0			0
$682$	−10.1827	−	5.87896i	−0.389914	−	0.225117i
$683$	−40.8116	−	23.5626i	−1.56161	−	0.901597i	−0.997094	−	0.0761765i	$-0.975729\pi$
$683$	−40.8116	−	23.5626i	−1.56161	−	0.901597i	−0.564518	−	0.825421i	$-0.690938\pi$
$684$		0			0
$685$	−15.4414	+	26.7453i	−0.589985	+	1.02188i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−5.27482			−0.201101
$689$	−0.262844	+	0.0201090i	−0.0100136	+	0.000766092i
$690$		0			0
$691$	9.13743	−	5.27550i	0.347604	−	0.200689i	−0.316025	−	0.948751i	$-0.602348\pi$
$691$	9.13743	−	5.27550i	0.347604	−	0.200689i	0.663630	+	0.748061i	$0.269015\pi$
$692$	8.41536	+	14.5758i	0.319904	+	0.554090i
$693$		0			0
$694$		−	7.51449i		−	0.285246i
$695$	−60.2940	−	34.8108i	−2.28708	−	1.32045i
$696$		0			0
$697$		−	88.1372i		−	3.33844i
$698$	11.5373	−	19.9831i	0.436691	−	0.756372i
$699$		0			0
$700$	7.04209	−	4.06575i	0.266166	−	0.153671i
$701$	43.5823			1.64608			0.823041	−	0.567982i	$-0.192276\pi$
$701$	43.5823			1.64608			0.823041	+	0.567982i	$0.192276\pi$
$702$		0			0
$703$	−4.77458			−0.180077
$704$	−1.74589	+	1.00799i	−0.0658007	+	0.0379900i
$705$		0			0
$706$	17.4439	−	30.2137i	0.656508	−	1.13711i
$707$			0.320161i			0.0120409i
$708$		0			0
$709$	17.0192	+	9.82602i	0.639168	+	0.369024i	0.784294	−	0.620389i	$-0.213025\pi$
$709$	17.0192	+	9.82602i	0.639168	+	0.369024i	−0.145126	+	0.989413i	$0.546359\pi$
$710$		−	46.3325i		−	1.73883i
$711$		0			0
$712$	−6.82727	−	11.8252i	−0.255863	−	0.443167i
$713$	−39.9616	+	23.0718i	−1.49657	+	0.864047i
$714$		0			0
$715$	−14.8717	−	21.7400i	−0.556170	−	0.813029i
$716$	10.8962			0.407212
$717$		0			0
$718$	−2.14565	−	3.71637i	−0.0800749	−	0.138694i
$719$	24.2207	−	41.9514i	0.903279	−	1.56452i	0.0800679	−	0.996789i	$-0.474486\pi$
$719$	24.2207	−	41.9514i	0.903279	−	1.56452i	0.823211	−	0.567736i	$-0.192180\pi$
$720$		0			0
$721$	0.121218	+	0.0699850i	0.00451438	+	0.00260638i
$722$	9.77304	+	5.64247i	0.363715	+	0.209991i
$723$		0			0
$724$	8.21504	−	14.2289i	0.305310	−	0.528812i
$725$	23.0491	+	39.9222i	0.856021	+	1.48267i
$726$		0			0
$727$	−29.0669			−1.07803			−0.539016	−	0.842295i	$-0.681204\pi$
$727$	−29.0669			−1.07803			−0.539016	+	0.842295i	$0.681204\pi$
$728$	1.55933	−	3.25092i	0.0577927	−	0.120487i
$729$		0			0
$730$	−15.0658	+	8.69825i	−0.557611	+	0.321937i
$731$	−19.9944	−	34.6313i	−0.739520	−	1.28089i
$732$		0			0
$733$			5.40128i			0.199501i	0.995012	+	0.0997505i	$0.0318045\pi$
$733$			5.40128i			0.199501i	−0.995012	+	0.0997505i	$0.968196\pi$
$734$	21.5270	+	12.4286i	0.794575	+	0.458748i
$735$		0			0
$736$			7.91165i			0.291627i
$737$	−14.4219	+	24.9794i	−0.531236	+	0.920128i
$738$		0			0
$739$	26.0102	−	15.0170i	0.956800	−	0.552409i	0.0616132	−	0.998100i	$-0.480375\pi$
$739$	26.0102	−	15.0170i	0.956800	−	0.552409i	0.895187	+	0.445691i	$0.147042\pi$
$740$	6.22906			0.228985
$741$		0			0
$742$	−0.0731130			−0.00268406
$743$	−20.2184	+	11.6731i	−0.741742	+	0.428245i	−0.822702	−	0.568473i	$-0.807535\pi$
$743$	−20.2184	+	11.6731i	−0.741742	+	0.428245i	0.0809605	+	0.996717i	$0.474201\pi$
$744$		0			0
$745$	0.277362	−	0.480405i	0.0101617	−	0.0176007i
$746$		−	34.5410i		−	1.26464i
$747$		0			0
$748$	−13.2357	−	7.64165i	−0.483946	−	0.279406i
$749$		−	1.38088i		−	0.0504563i
$750$		0			0
$751$	−17.0773	−	29.5788i	−0.623160	−	1.07934i	−0.988894	−	0.148625i	$-0.952515\pi$
$751$	−17.0773	−	29.5788i	−0.623160	−	1.07934i	0.365734	−	0.930719i	$-0.380818\pi$
$752$	−4.88142	+	2.81829i	−0.178007	+	0.102772i
$753$		0			0
$754$	18.4297	+	8.83998i	0.671172	+	0.321933i
$755$	−42.6216			−1.55116
$756$		0			0
$757$	9.63731	+	16.6923i	0.350274	+	0.606693i	0.986297	−	0.164977i	$-0.0527551\pi$
$757$	9.63731	+	16.6923i	0.350274	+	0.606693i	−0.636023	+	0.771670i	$0.719422\pi$
$758$	−13.6023	+	23.5599i	−0.494059	+	0.855735i
$759$		0			0
$760$	8.71681	+	5.03265i	0.316192	+	0.182553i
$761$	19.3565	+	11.1755i	0.701673	+	0.405111i	0.807970	−	0.589223i	$-0.200566\pi$
$761$	19.3565	+	11.1755i	0.701673	+	0.405111i	−0.106297	+	0.994334i	$0.533900\pi$
$762$		0			0
$763$	−1.56821	+	2.71622i	−0.0567730	+	0.0983338i
$764$	3.49738	+	6.05765i	0.126531	+	0.219158i
$765$		0			0
$766$	28.9385			1.04559
$767$	−4.34268	−	2.08300i	−0.156805	−	0.0752128i
$768$		0			0
$769$	35.4214	−	20.4505i	1.27733	−	0.737466i	0.300972	−	0.953633i	$-0.402689\pi$
$769$	35.4214	−	20.4505i	1.27733	−	0.737466i	0.976356	+	0.216168i	$0.0693557\pi$
$770$	−3.65269	−	6.32665i	−0.131634	−	0.227997i
$771$		0			0
$772$		−	5.39918i		−	0.194321i
$773$	12.5621	+	7.25272i	0.451827	+	0.260862i	0.708601	−	0.705609i	$-0.249327\pi$
$773$	12.5621	+	7.25272i	0.451827	+	0.260862i	−0.256775	+	0.966471i	$0.582660\pi$
$774$		0			0
$775$		−	47.4259i		−	1.70359i
$776$	7.87254	−	13.6356i	0.282608	−	0.489491i
$777$		0			0
$778$	−18.6557	+	10.7709i	−0.668841	+	0.386156i
$779$	32.2922			1.15699
$780$		0			0
$781$	−25.7759			−0.922335
$782$	−51.9432	+	29.9894i	−1.85749	+	1.07242i

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.62374i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.62374i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(1.81187 + 3.13825i) q^{10} +(1.74589 - 1.00799i) q^{11} +(3.59505 - 0.275040i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.79054 - 6.56541i) q^{17} +(2.40547 + 1.38880i) q^{19} +(-3.13825 - 1.81187i) q^{20} +(-1.00799 + 1.74589i) q^{22} +(3.95583 + 6.85169i) q^{23} -8.13150 q^{25} +(-2.97588 + 2.03571i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-2.83454 - 4.90957i) q^{29} +5.83236i q^{31} +(0.866025 + 0.500000i) q^{32} +7.58108i q^{34} +(-1.81187 + 3.13825i) q^{35} +(-1.48866 + 0.859480i) q^{37} -2.77760 q^{38} +3.62374 q^{40} +(10.0684 - 5.81297i) q^{41} +(2.63741 - 4.56813i) q^{43} -2.01598i q^{44} +(-6.85169 - 3.95583i) q^{46} -5.63658i q^{47} +(0.500000 + 0.866025i) q^{49} +(7.04209 - 4.06575i) q^{50} +(1.55933 - 3.25092i) q^{52} -0.0731130 q^{53} +(-3.65269 - 6.32665i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.90957 + 2.83454i) q^{58} +(-1.15686 - 0.667915i) q^{59} +(0.187787 - 0.325257i) q^{61} +(-2.91618 - 5.05098i) q^{62} -1.00000 q^{64} +(-0.996674 - 13.0275i) q^{65} +(-12.3907 + 7.15378i) q^{67} +(-3.79054 - 6.56541i) q^{68} -3.62374i q^{70} +(-11.0728 - 6.39291i) q^{71} +4.80070i q^{73} +(0.859480 - 1.48866i) q^{74} +(2.40547 - 1.38880i) q^{76} -2.01598 q^{77} +10.1368 q^{79} +(-3.13825 + 1.81187i) q^{80} +(-5.81297 + 10.0684i) q^{82} +1.97093i q^{83} +(-23.7913 - 13.7359i) q^{85} +5.27482i q^{86} +(1.00799 + 1.74589i) q^{88} +(-11.8252 + 6.82727i) q^{89} +(-3.25092 - 1.55933i) q^{91} +7.91165 q^{92} +(2.81829 + 4.88142i) q^{94} +(5.03265 - 8.71681i) q^{95} +(-13.6356 - 7.87254i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Introduction

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