LMFDB - Embedded newform 567.2.ba.a.521.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			521.13
Character	$\chi$	$=$	567.521
Dual form			567.2.ba.a.530.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.408566 + 0.0720413i) q^{2} +(-1.71765 - 0.625173i) q^{4} +(-0.0312679 - 0.177329i) q^{5} +(1.82229 + 1.91814i) q^{7} +(-1.37531 - 0.794036i) q^{8} -0.0747032i q^{10} +(-1.56303 - 0.275605i) q^{11} +(3.21910 + 3.83638i) q^{13} +(0.606342 + 0.914967i) q^{14} +(2.29578 + 1.92639i) q^{16} +7.76129 q^{17} -4.34679i q^{19} +(-0.0571540 + 0.324137i) q^{20} +(-0.618747 - 0.225206i) q^{22} +(1.56305 + 1.86277i) q^{23} +(4.66800 - 1.69901i) q^{25} +(1.03884 + 1.79932i) q^{26} +(-1.93089 - 4.43393i) q^{28} +(-2.81590 + 3.35586i) q^{29} +(0.459948 - 1.26370i) q^{31} +(2.84078 + 3.38551i) q^{32} +(3.17100 + 0.559134i) q^{34} +(0.283162 - 0.383121i) q^{35} +(2.09041 - 3.62070i) q^{37} +(0.313148 - 1.77595i) q^{38} +(-0.0978025 + 0.268710i) q^{40} +(-8.48927 + 7.12335i) q^{41} +(-0.714703 + 0.260131i) q^{43} +(2.51244 + 1.45056i) q^{44} +(0.504413 + 0.873669i) q^{46} +(8.67893 - 3.15887i) q^{47} +(-0.358507 + 6.99081i) q^{49} +(2.02959 - 0.357871i) q^{50} +(-3.13089 - 8.60205i) q^{52} +(8.42703 + 4.86535i) q^{53} +0.285788i q^{55} +(-0.983146 - 4.08500i) q^{56} +(-1.39224 + 1.16823i) q^{58} +(-1.51017 + 1.26718i) q^{59} +(-0.916897 - 2.51916i) q^{61} +(0.278957 - 0.483169i) q^{62} +(-2.08017 - 3.60297i) q^{64} +(0.579646 - 0.690796i) q^{65} +(-0.722307 - 4.09641i) q^{67} +(-13.3312 - 4.85215i) q^{68} +(0.143291 - 0.136131i) q^{70} +(-5.04844 + 2.91472i) q^{71} +(-7.42228 + 4.28526i) q^{73} +(1.11491 - 1.32870i) q^{74} +(-2.71749 + 7.46625i) q^{76} +(-2.31965 - 3.50034i) q^{77} +(-0.884454 + 5.01599i) q^{79} +(0.269820 - 0.467342i) q^{80} +(-3.98161 + 2.29878i) q^{82} +(-10.1615 - 8.52653i) q^{83} +(-0.242679 - 1.37630i) q^{85} +(-0.310744 + 0.0547926i) q^{86} +(1.93081 + 1.62014i) q^{88} -8.19131 q^{89} +(-1.49256 + 13.1657i) q^{91} +(-1.52022 - 4.17676i) q^{92} +(3.77349 - 0.665368i) q^{94} +(-0.770811 + 0.135915i) q^{95} +(1.63818 + 4.50085i) q^{97} +(-0.650101 + 2.83038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.408566	+	0.0720413i	0.288900	+	0.0509409i	0.316220	−	0.948686i	$-0.397586\pi$
$2$	0.408566	+	0.0720413i	0.288900	+	0.0509409i	−0.0273200	+	0.999627i	$0.508697\pi$
$3$		0			0
$3$		0			0
$4$	−1.71765	−	0.625173i	−0.858824	−	0.312586i
$5$	−0.0312679	−	0.177329i	−0.0139834	−	0.0793039i	0.977017	−	0.213159i	$-0.0683753\pi$
$5$	−0.0312679	−	0.177329i	−0.0139834	−	0.0793039i	−0.991001	+	0.133855i	$0.957264\pi$
$6$		0			0
$7$	1.82229	+	1.91814i	0.688761	+	0.724988i
$7$	1.82229	+	1.91814i	0.688761	+	0.724988i
$8$	−1.37531	−	0.794036i	−0.486246	−	0.280734i
$9$		0			0
$10$		−	0.0747032i		−	0.0236232i
$11$	−1.56303	−	0.275605i	−0.471272	−	0.0830979i	−0.0670317	−	0.997751i	$-0.521353\pi$
$11$	−1.56303	−	0.275605i	−0.471272	−	0.0830979i	−0.404240	+	0.914653i	$0.632464\pi$
$12$		0			0
$13$	3.21910	+	3.83638i	0.892819	+	1.06402i	0.997580	+	0.0695228i	$0.0221477\pi$
$13$	3.21910	+	3.83638i	0.892819	+	1.06402i	−0.104761	+	0.994497i	$0.533408\pi$
$14$	0.606342	+	0.914967i	0.162052	+	0.244535i
$15$		0			0
$16$	2.29578	+	1.92639i	0.573944	+	0.481597i
$17$	7.76129			1.88239			0.941195	−	0.337864i	$-0.109704\pi$
$17$	7.76129			1.88239			0.941195	+	0.337864i	$0.109704\pi$
$18$		0			0
$19$		−	4.34679i		−	0.997221i	−0.866826	−	0.498611i	$-0.833844\pi$
$19$		−	4.34679i		−	0.997221i	0.866826	−	0.498611i	$-0.166156\pi$
$20$	−0.0571540	+	0.324137i	−0.0127800	+	0.0724791i
$21$		0			0
$22$	−0.618747	−	0.225206i	−0.131917	−	0.0480140i
$23$	1.56305	+	1.86277i	0.325918	+	0.388414i	0.903977	−	0.427581i	$-0.140634\pi$
$23$	1.56305	+	1.86277i	0.325918	+	0.388414i	−0.578059	+	0.815995i	$0.696190\pi$
$24$		0			0
$25$	4.66800	−	1.69901i	0.933599	−	0.339802i
$26$	1.03884	+	1.79932i	0.203733	+	0.352877i
$27$		0			0
$28$	−1.93089	−	4.43393i	−0.364904	−	0.837935i
$29$	−2.81590	+	3.35586i	−0.522899	+	0.623167i	−0.961264	−	0.275630i	$-0.911113\pi$
$29$	−2.81590	+	3.35586i	−0.522899	+	0.623167i	0.438365	+	0.898797i	$0.355558\pi$
$30$		0			0
$31$	0.459948	−	1.26370i	0.0826090	−	0.226966i	−0.891510	−	0.453000i	$-0.850354\pi$
$31$	0.459948	−	1.26370i	0.0826090	−	0.226966i	0.974119	+	0.226034i	$0.0725759\pi$
$32$	2.84078	+	3.38551i	0.502184	+	0.598480i
$33$		0			0
$34$	3.17100	+	0.559134i	0.543823	+	0.0958906i
$35$	0.283162	−	0.383121i	0.0478631	−	0.0647593i
$36$		0			0
$37$	2.09041	−	3.62070i	0.343662	−	0.595240i	−0.641448	−	0.767167i	$-0.721666\pi$
$37$	2.09041	−	3.62070i	0.343662	−	0.595240i	0.985110	+	0.171927i	$0.0549992\pi$
$38$	0.313148	−	1.77595i	0.0507993	−	0.288097i
$39$		0			0
$40$	−0.0978025	+	0.268710i	−0.0154639	+	0.0424868i
$41$	−8.48927	+	7.12335i	−1.32580	+	1.11248i	−0.340763	+	0.940149i	$0.610685\pi$
$41$	−8.48927	+	7.12335i	−1.32580	+	1.11248i	−0.985039	+	0.172331i	$0.944870\pi$
$42$		0			0
$43$	−0.714703	+	0.260131i	−0.108991	+	0.0396696i	−0.395940	−	0.918276i	$-0.629581\pi$
$43$	−0.714703	+	0.260131i	−0.108991	+	0.0396696i	0.286949	+	0.957946i	$0.407359\pi$
$44$	2.51244	+	1.45056i	0.378764	+	0.218680i
$45$		0			0
$46$	0.504413	+	0.873669i	0.0743716	+	0.128815i
$47$	8.67893	−	3.15887i	1.26595	−	0.460769i	0.380190	−	0.924908i	$-0.375859\pi$
$47$	8.67893	−	3.15887i	1.26595	−	0.460769i	0.885762	+	0.464139i	$0.153636\pi$
$48$		0			0
$49$	−0.358507	+	6.99081i	−0.0512153	+	0.998688i
$50$	2.02959	−	0.357871i	0.287027	−	0.0506106i
$51$		0			0
$52$	−3.13089	−	8.60205i	−0.434176	−	1.19289i
$53$	8.42703	+	4.86535i	1.15754	+	0.668307i	0.950714	−	0.310071i	$-0.100353\pi$
$53$	8.42703	+	4.86535i	1.15754	+	0.668307i	0.206828	+	0.978377i	$0.433686\pi$
$54$		0			0
$55$			0.285788i			0.0385357i
$56$	−0.983146	−	4.08500i	−0.131378	−	0.545881i
$57$		0			0
$58$	−1.39224	+	1.16823i	−0.182810	+	0.153396i
$59$	−1.51017	+	1.26718i	−0.196608	+	0.164973i	−0.735777	−	0.677224i	$-0.763183\pi$
$59$	−1.51017	+	1.26718i	−0.196608	+	0.164973i	0.539169	+	0.842197i	$0.318738\pi$
$60$		0			0
$61$	−0.916897	−	2.51916i	−0.117397	−	0.322545i	0.867052	−	0.498218i	$-0.166012\pi$
$61$	−0.916897	−	2.51916i	−0.117397	−	0.322545i	−0.984449	+	0.175673i	$0.943790\pi$
$62$	0.278957	−	0.483169i	0.0354276	−	0.0613625i
$63$		0			0
$64$	−2.08017	−	3.60297i	−0.260022	−	0.450371i
$65$	0.579646	−	0.690796i	0.0718963	−	0.0856827i
$66$		0			0
$67$	−0.722307	−	4.09641i	−0.0882438	−	0.500456i	−0.996609	−	0.0822786i	$-0.973780\pi$
$67$	−0.722307	−	4.09641i	−0.0882438	−	0.500456i	0.908366	−	0.418177i	$-0.137331\pi$
$68$	−13.3312	−	4.85215i	−1.61664	−	0.588410i
$69$		0			0
$70$	0.143291	−	0.136131i	0.0171266	−	0.0162708i
$71$	−5.04844	+	2.91472i	−0.599139	+	0.345913i	−0.768703	−	0.639606i	$-0.779097\pi$
$71$	−5.04844	+	2.91472i	−0.599139	+	0.345913i	0.169564	+	0.985519i	$0.445764\pi$
$72$		0			0
$73$	−7.42228	+	4.28526i	−0.868712	+	0.501551i	−0.866920	−	0.498447i	$-0.833904\pi$
$73$	−7.42228	+	4.28526i	−0.868712	+	0.501551i	−0.00179209	+	0.999998i	$0.500570\pi$
$74$	1.11491	−	1.32870i	0.129606	−	0.154458i
$75$		0			0
$76$	−2.71749	+	7.46625i	−0.311718	+	0.856438i
$77$	−2.31965	−	3.50034i	−0.264349	−	0.398901i
$78$		0			0
$79$	−0.884454	+	5.01599i	−0.0995088	+	0.564343i	0.893763	+	0.448539i	$0.148055\pi$
$79$	−0.884454	+	5.01599i	−0.0995088	+	0.564343i	−0.993272	+	0.115804i	$0.963056\pi$
$80$	0.269820	−	0.467342i	0.0301668	−	0.0522504i
$81$		0			0
$82$	−3.98161	+	2.29878i	−0.439695	+	0.253858i
$83$	−10.1615	−	8.52653i	−1.11537	−	0.935909i	−0.117011	−	0.993131i	$-0.537331\pi$
$83$	−10.1615	−	8.52653i	−1.11537	−	0.935909i	−0.998361	+	0.0572219i	$0.981776\pi$
$84$		0			0
$85$	−0.242679	−	1.37630i	−0.0263222	−	0.149281i
$86$	−0.310744	+	0.0547926i	−0.0335084	+	0.00590843i
$87$		0			0
$88$	1.93081	+	1.62014i	0.205825	+	0.172708i
$89$	−8.19131			−0.868278			−0.434139	−	0.900846i	$-0.642947\pi$
$89$	−8.19131			−0.868278			−0.434139	+	0.900846i	$0.642947\pi$
$90$		0			0
$91$	−1.49256	+	13.1657i	−0.156463	+	1.38014i
$92$	−1.52022	−	4.17676i	−0.158493	−	0.435457i
$93$		0			0
$94$	3.77349	−	0.665368i	0.389206	−	0.0686275i
$95$	−0.770811	+	0.135915i	−0.0790835	+	0.0139446i
$96$		0			0
$97$	1.63818	+	4.50085i	0.166332	+	0.456993i	0.994655	−	0.103258i	$-0.0329269\pi$
$97$	1.63818	+	4.50085i	0.166332	+	0.456993i	−0.828323	+	0.560251i	$0.810705\pi$
$98$	−0.650101	+	2.83038i	−0.0656701	+	0.285912i
$99$		0			0
$100$	−9.08015			−0.908015
$101$	−9.59097	−	8.04778i	−0.954337	−	0.800784i	0.0256856	−	0.999670i	$-0.491823\pi$
$101$	−9.59097	−	8.04778i	−0.954337	−	0.800784i	−0.980023	+	0.198886i	$0.936268\pi$
$102$		0			0
$103$	2.76125	−	0.486882i	0.272074	−	0.0479739i	−0.0359467	−	0.999354i	$-0.511445\pi$
$103$	2.76125	−	0.486882i	0.272074	−	0.0479739i	0.308020	+	0.951380i	$0.400334\pi$
$104$	−1.38104	−	7.83229i	−0.135423	−	0.768020i
$105$		0			0
$106$	3.09250	+	2.59491i	0.300370	+	0.252040i
$107$	6.82463	−	3.94020i	0.659762	−	0.380913i	−0.132425	−	0.991193i	$-0.542276\pi$
$107$	6.82463	−	3.94020i	0.659762	−	0.380913i	0.792186	+	0.610280i	$0.208943\pi$
$108$		0			0
$109$	8.69846	−	15.0662i	0.833161	−	1.44308i	−0.0623578	−	0.998054i	$-0.519862\pi$
$109$	8.69846	−	15.0662i	0.833161	−	1.44308i	0.895519	−	0.445024i	$-0.146805\pi$
$110$	−0.0205886	+	0.116764i	−0.00196304	+	0.0111330i
$111$		0			0
$112$	0.488502	+	7.91406i	0.0461591	+	0.747808i
$113$	−1.02719	+	2.82219i	−0.0966304	+	0.265490i	−0.978585	−	0.205845i	$-0.934006\pi$
$113$	−1.02719	+	2.82219i	−0.0966304	+	0.265490i	0.881954	+	0.471335i	$0.156228\pi$
$114$		0			0
$115$	0.281450	−	0.335419i	0.0262453	−	0.0312779i
$116$	6.93471	−	4.00376i	0.643872	−	0.371740i
$117$		0			0
$118$	−0.708295	+	0.408934i	−0.0652038	+	0.0376455i
$119$	14.1433	+	14.8872i	1.29652	+	1.36471i
$120$		0			0
$121$	−7.96951	−	2.90066i	−0.724501	−	0.263697i
$122$	−0.193130	−	1.09530i	−0.0174852	−	0.0991635i
$123$		0			0
$124$	−1.58006	+	1.88304i	−0.141893	+	0.169102i
$125$	−0.897403	−	1.55435i	−0.0802662	−	0.139025i
$126$		0			0
$127$	5.25357	−	9.09945i	0.466179	−	0.807446i	−0.533075	−	0.846068i	$-0.678964\pi$
$127$	5.25357	−	9.09945i	0.466179	−	0.807446i	0.999254	+	0.0386222i	$0.0122969\pi$
$128$	−3.61343	−	9.92780i	−0.319385	−	0.877502i
$129$		0			0
$130$	0.286590	−	0.240477i	0.0251356	−	0.0210913i
$131$	11.1700	−	9.37272i	0.975925	−	0.818898i	−0.00754465	−	0.999972i	$-0.502402\pi$
$131$	11.1700	−	9.37272i	0.975925	−	0.818898i	0.983470	+	0.181073i	$0.0579571\pi$
$132$		0			0
$133$	8.33774	−	7.92111i	0.722973	−	0.686848i
$134$		−	1.72569i		−	0.149077i
$135$		0			0
$136$	−10.6742	−	6.16274i	−0.915304	−	0.528451i
$137$	2.17300	+	5.97027i	0.185652	+	0.510075i	0.997247	−	0.0741452i	$-0.0236228\pi$
$137$	2.17300	+	5.97027i	0.185652	+	0.510075i	−0.811595	+	0.584220i	$0.801401\pi$
$138$		0			0
$139$	−15.1483	+	2.67106i	−1.28487	+	0.226556i	−0.774045	−	0.633131i	$-0.781769\pi$
$139$	−15.1483	+	2.67106i	−1.28487	+	0.226556i	−0.510821	+	0.859687i	$0.670658\pi$
$140$	−0.725890	+	0.481042i	−0.0613489	+	0.0406555i
$141$		0			0
$142$	−2.27260	+	0.827159i	−0.190713	+	0.0694137i
$143$	−3.97424	−	6.88358i	−0.332343	−	0.575634i
$144$		0			0
$145$	0.683138	+	0.394410i	0.0567315	+	0.0327539i
$146$	−3.34121	+	1.21610i	−0.276521	+	0.100645i
$147$		0			0
$148$	−5.85416	+	4.91223i	−0.481209	+	0.403783i
$149$	−5.96220	+	16.3810i	−0.488442	+	1.34198i	0.413648	+	0.910437i	$0.364254\pi$
$149$	−5.96220	+	16.3810i	−0.488442	+	1.34198i	−0.902090	+	0.431547i	$0.857968\pi$
$150$		0			0
$151$	0.399188	−	2.26391i	0.0324854	−	0.184234i	−0.964247	−	0.265004i	$-0.914627\pi$
$151$	0.399188	−	2.26391i	0.0324854	−	0.184234i	0.996733	+	0.0807699i	$0.0257379\pi$
$152$	−3.45150	+	5.97818i	−0.279954	+	0.484894i
$153$		0			0
$154$	−0.695563	−	1.59723i	−0.0560500	−	0.128709i
$155$	−0.238471	−	0.0420489i	−0.0191545	−	0.00337745i
$156$		0			0
$157$	−3.60935	−	4.30145i	−0.288057	−	0.343293i	0.602538	−	0.798090i	$-0.294156\pi$
$157$	−3.60935	−	4.30145i	−0.288057	−	0.343293i	−0.890595	+	0.454797i	$0.849712\pi$
$158$	−0.722716	+	1.98565i	−0.0574962	+	0.157970i
$159$		0			0
$160$	0.511524	−	0.609611i	0.0404395	−	0.0481940i
$161$	−0.724718	+	6.39265i	−0.0571157	+	0.503811i
$162$		0			0
$163$	9.58450	+	16.6008i	0.750716	+	1.30028i	0.947476	+	0.319827i	$0.103625\pi$
$163$	9.58450	+	16.6008i	0.750716	+	1.30028i	−0.196760	+	0.980452i	$0.563042\pi$
$164$	19.0349	−	6.92814i	1.48638	−	0.540997i
$165$		0			0
$166$	−3.53740	−	4.21571i	−0.274555	−	0.327202i
$167$	8.84469	+	3.21920i	0.684422	+	0.249109i	0.660745	−	0.750610i	$-0.270240\pi$
$167$	8.84469	+	3.21920i	0.684422	+	0.249109i	0.0236772	+	0.999720i	$0.492463\pi$
$168$		0			0
$169$	−2.09775	+	11.8969i	−0.161365	+	0.915147i
$170$		−	0.579794i		−	0.0444681i
$171$		0			0
$172$	1.39024			0.106005
$173$	−4.11126	−	3.44976i	−0.312573	−	0.262280i	0.472981	−	0.881072i	$-0.343178\pi$
$173$	−4.11126	−	3.44976i	−0.312573	−	0.262280i	−0.785555	+	0.618792i	$0.787622\pi$
$174$		0			0
$175$	11.7654	+	5.85777i	0.889380	+	0.442805i
$176$	−3.05745	−	3.64373i	−0.230464	−	0.274656i
$177$		0			0
$178$	−3.34670	−	0.590113i	−0.250846	−	0.0442308i
$179$		−	14.8693i		−	1.11138i	−0.831389	−	0.555691i	$-0.812454\pi$
$179$		−	14.8693i		−	1.11138i	0.831389	−	0.555691i	$-0.187546\pi$
$180$		0			0
$181$	−5.48950	−	3.16937i	−0.408031	−	0.235577i	0.281912	−	0.959440i	$-0.409031\pi$
$181$	−5.48950	−	3.16937i	−0.408031	−	0.235577i	−0.689944	+	0.723863i	$0.742365\pi$
$182$	−1.55828	+	5.27153i	−0.115508	+	0.390752i
$183$		0			0
$184$	−0.670572	−	3.80300i	−0.0494352	−	0.280361i
$185$	−0.707418	−	0.257479i	−0.0520104	−	0.0189302i
$186$		0			0
$187$	−12.1311	−	2.13905i	−0.887117	−	0.156423i
$188$	−16.8822			−1.23126
$189$		0			0
$190$	−0.324719			−0.0235576
$191$	−16.6883	−	2.94260i	−1.20752	−	0.212919i	−0.466575	−	0.884482i	$-0.654512\pi$
$191$	−16.6883	−	2.94260i	−1.20752	−	0.212919i	−0.740947	+	0.671563i	$0.765623\pi$
$192$		0			0
$193$	11.5156	+	4.19135i	0.828915	+	0.301700i	0.721413	−	0.692505i	$-0.243493\pi$
$193$	11.5156	+	4.19135i	0.828915	+	0.301700i	0.107501	+	0.994205i	$0.465715\pi$
$194$	0.345057	+	1.95691i	0.0247736	+	0.140498i
$195$		0			0
$196$	4.98626	−	11.7836i	0.356161	−	0.841688i
$197$	11.7644	+	6.79216i	0.838176	+	0.483921i	0.856644	−	0.515908i	$-0.172545\pi$
$197$	11.7644	+	6.79216i	0.838176	+	0.483921i	−0.0184676	+	0.999829i	$0.505879\pi$
$198$		0			0
$199$		−	7.03966i		−	0.499028i	−0.968371	−	0.249514i	$-0.919729\pi$
$199$		−	7.03966i		−	0.499028i	0.968371	−	0.249514i	$-0.0802709\pi$
$200$	−7.76902	−	1.36989i	−0.549352	−	0.0968657i
$201$		0			0
$202$	−3.33878	−	3.97900i	−0.234915	−	0.279961i
$203$	−11.5684	+	0.714068i	−0.811941	+	0.0501177i
$204$		0			0
$205$	1.52862	+	1.28266i	0.106763	+	0.0895850i
$206$	1.16323			0.0810459
$207$		0			0
$208$			15.0087i			1.04067i
$209$	−1.19799	+	6.79417i	−0.0828670	+	0.469962i
$210$		0			0
$211$	−12.4387	−	4.52733i	−0.856318	−	0.311674i	−0.123704	−	0.992319i	$-0.539477\pi$
$211$	−12.4387	−	4.52733i	−0.856318	−	0.311674i	−0.732613	+	0.680645i	$0.761700\pi$
$212$	−11.4330	−	13.6253i	−0.785221	−	0.935790i
$213$		0			0
$214$	3.07217	−	1.11818i	0.210009	−	0.0764371i
$215$	0.0684760	+	0.118604i	0.00467002	+	0.00808871i
$216$		0			0
$217$	3.26210	−	1.42058i	0.221446	−	0.0964352i
$218$	4.63928	−	5.52888i	0.314212	−	0.374463i
$219$		0			0
$220$	0.178667	−	0.490884i	0.0120457	−	0.0330954i
$221$	24.9844	+	29.7753i	1.68063	+	2.00290i
$222$		0			0
$223$	−12.9495	−	2.28334i	−0.867162	−	0.152904i	−0.277668	−	0.960677i	$-0.589562\pi$
$223$	−12.9495	−	2.28334i	−0.867162	−	0.152904i	−0.589494	+	0.807773i	$0.700673\pi$
$224$	−1.31715	+	11.6184i	−0.0880056	+	0.776288i
$225$		0			0
$226$	−0.622992	+	1.07905i	−0.0414408	+	0.0717776i
$227$	1.26546	−	7.17680i	0.0839918	−	0.476341i	−0.913578	−	0.406664i	$-0.866692\pi$
$227$	1.26546	−	7.17680i	0.0839918	−	0.476341i	0.997570	−	0.0696770i	$-0.0221969\pi$
$228$		0			0
$229$	1.41178	−	3.87883i	0.0932930	−	0.256321i	−0.884265	−	0.466985i	$-0.845340\pi$
$229$	1.41178	−	3.87883i	0.0932930	−	0.256321i	0.977559	+	0.210664i	$0.0675626\pi$
$230$	0.139155	−	0.116765i	0.00917560	−	0.00769924i
$231$		0			0
$232$	6.53740	−	2.37942i	0.429202	−	0.156217i
$233$	12.6906	+	7.32691i	0.831388	+	0.480002i	0.854328	−	0.519735i	$-0.173969\pi$
$233$	12.6906	+	7.32691i	0.831388	+	0.480002i	−0.0229398	+	0.999737i	$0.507303\pi$
$234$		0			0
$235$	−0.831531	−	1.44025i	−0.0542431	−	0.0939518i
$236$	3.38615	−	1.23246i	0.220420	−	0.0802262i
$237$		0			0
$238$	4.70600	+	7.10133i	0.305045	+	0.460311i
$239$	22.4643	−	3.96107i	1.45310	−	0.256220i	0.609324	−	0.792921i	$-0.291441\pi$
$239$	22.4643	−	3.96107i	1.45310	−	0.256220i	0.843773	+	0.536701i	$0.180330\pi$
$240$		0			0
$241$	0.269437	+	0.740271i	0.0173559	+	0.0476851i	0.948068	−	0.318068i	$-0.103034\pi$
$241$	0.269437	+	0.740271i	0.0173559	+	0.0476851i	−0.930712	+	0.365753i	$0.880812\pi$
$242$	−3.04711	−	1.75925i	−0.195875	−	0.113089i
$243$		0			0
$244$			4.90024i			0.313706i
$245$	1.25088	−	0.155014i	0.0799160	−	0.00990349i
$246$		0			0
$247$	16.6759	−	13.9928i	1.06106	−	0.890338i
$248$	−1.63599	+	1.37276i	−0.103885	+	0.0871703i
$249$		0			0
$250$	−0.254672	−	0.699705i	−0.0161069	−	0.0442532i
$251$	5.78209	−	10.0149i	0.364962	−	0.632133i	−0.623808	−	0.781578i	$-0.714415\pi$
$251$	5.78209	−	10.0149i	0.364962	−	0.632133i	0.988770	+	0.149444i	$0.0477485\pi$
$252$		0			0
$253$	−1.92971	−	3.34235i	−0.121320	−	0.210132i
$254$	2.80197	−	3.33926i	0.175811	−	0.209524i
$255$		0			0
$256$	0.683760	+	3.87780i	0.0427350	+	0.242362i
$257$	−9.55906	−	3.47921i	−0.596278	−	0.217027i	0.0262107	−	0.999656i	$-0.491656\pi$
$257$	−9.55906	−	3.47921i	−0.596278	−	0.217027i	−0.622488	+	0.782629i	$0.713878\pi$
$258$		0			0
$259$	10.7544	−	2.58827i	0.668243	−	0.160828i
$260$	−1.42750	+	0.824165i	−0.0885295	+	0.0511125i
$261$		0			0
$262$	5.23890	−	3.02468i	0.323660	−	0.186865i
$263$	−11.0604	+	13.1813i	−0.682014	+	0.812793i	−0.990365	−	0.138480i	$-0.955778\pi$
$263$	−11.0604	+	13.1813i	−0.682014	+	0.812793i	0.308351	+	0.951273i	$0.400223\pi$
$264$		0			0
$265$	0.599271	−	1.64648i	0.0368129	−	0.101143i
$266$	3.97717	−	2.63564i	0.243856	−	0.161601i
$267$		0			0
$268$	−1.32029	+	7.48775i	−0.0806497	+	0.457387i
$269$	5.09560	−	8.82584i	0.310684	−	0.538121i	−0.667826	−	0.744317i	$-0.732775\pi$
$269$	5.09560	−	8.82584i	0.310684	−	0.538121i	0.978511	+	0.206196i	$0.0661085\pi$
$270$		0			0
$271$	−6.85061	+	3.95520i	−0.416145	+	0.240261i	−0.693426	−	0.720527i	$-0.743900\pi$
$271$	−6.85061	+	3.95520i	−0.416145	+	0.240261i	0.277282	+	0.960789i	$0.410566\pi$
$272$	17.8182	+	14.9512i	1.08039	+	0.906552i
$273$		0			0
$274$	0.457709	+	2.59580i	0.0276512	+	0.156818i
$275$	−7.76448	+	1.36909i	−0.468216	+	0.0825591i
$276$		0			0
$277$	10.5255	+	8.83194i	0.632416	+	0.530660i	0.901679	−	0.432407i	$-0.142336\pi$
$277$	10.5255	+	8.83194i	0.632416	+	0.530660i	−0.269263	+	0.963067i	$0.586780\pi$
$278$	−6.38153			−0.382739
$279$		0			0
$280$	−0.693648	+	0.302069i	−0.0414534	+	0.0180521i
$281$	−0.953112	−	2.61865i	−0.0568579	−	0.156216i	0.908012	−	0.418944i	$-0.137600\pi$
$281$	−0.953112	−	2.61865i	−0.0568579	−	0.156216i	−0.964870	+	0.262729i	$0.915378\pi$
$282$		0			0
$283$	−16.1660	+	2.85051i	−0.960972	+	0.169445i	−0.632063	−	0.774917i	$-0.717792\pi$
$283$	−16.1660	+	2.85051i	−0.960972	+	0.169445i	−0.328908	+	0.944362i	$0.606681\pi$
$284$	10.4936	−	1.85031i	0.622683	−	0.109796i
$285$		0			0
$286$	−1.12784	−	3.09871i	−0.0666905	−	0.183231i
$287$	−29.1335	−	3.30279i	−1.71970	−	0.194957i
$288$		0			0
$289$	43.2377			2.54339
$290$	0.250693	+	0.210357i	0.0147212	+	0.0123526i
$291$		0			0
$292$	15.4279	−	2.72035i	0.902849	−	0.159197i
$293$	0.270460	+	1.53385i	0.0158004	+	0.0896087i	0.991688	−	0.128664i	$-0.0410689\pi$
$293$	0.270460	+	1.53385i	0.0158004	+	0.0896087i	−0.975888	+	0.218273i	$0.929958\pi$
$294$		0			0
$295$	0.271928	+	0.228175i	0.0158323	+	0.0132849i
$296$	−5.74994	+	3.31973i	−0.334208	+	0.192955i
$297$		0			0
$298$	−3.61606	+	6.26320i	−0.209473	+	0.362818i
$299$	−2.11467	+	11.9929i	−0.122295	+	0.693567i
$300$		0			0
$301$	−1.80136	−	0.896866i	−0.103829	−	0.0516945i
$302$	0.326189	−	0.896198i	0.0187701	−	0.0515704i
$303$		0			0
$304$	8.37359	−	9.97926i	0.480258	−	0.572350i
$305$	−0.418050	+	0.241361i	−0.0239375	+	0.0138203i
$306$		0			0
$307$	1.41615	−	0.817613i	0.0808238	−	0.0466637i	−0.459043	−	0.888414i	$-0.651808\pi$
$307$	1.41615	−	0.817613i	0.0808238	−	0.0466637i	0.539867	+	0.841750i	$0.318474\pi$
$308$	1.79603	+	7.46254i	0.102338	+	0.425218i
$309$		0			0
$310$	−0.0944022	−	0.0343596i	−0.00536168	−	0.00195149i
$311$	−2.06271	−	11.6982i	−0.116965	−	0.663344i	−0.985758	−	0.168168i	$-0.946215\pi$
$311$	−2.06271	−	11.6982i	−0.116965	−	0.663344i	0.868793	−	0.495176i	$-0.164896\pi$
$312$		0			0
$313$	−1.19230	+	1.42093i	−0.0673929	+	0.0803157i	−0.798688	−	0.601746i	$-0.794472\pi$
$313$	−1.19230	+	1.42093i	−0.0673929	+	0.0803157i	0.731295	+	0.682062i	$0.238916\pi$
$314$	−1.16478	−	2.01745i	−0.0657321	−	0.113851i
$315$		0			0
$316$	4.65504	−	8.06276i	0.261866	−	0.453566i
$317$	7.22432	+	19.8487i	0.405758	+	1.11481i	0.959398	+	0.282055i	$0.0910162\pi$
$317$	7.22432	+	19.8487i	0.405758	+	1.11481i	−0.553640	+	0.832756i	$0.686762\pi$
$318$		0			0
$319$	5.32623	−	4.46924i	0.298212	−	0.250229i
$320$	−0.573867	+	0.481532i	−0.0320802	+	0.0269184i
$321$		0			0
$322$	−0.756630	+	2.55961i	−0.0421653	+	0.142642i
$323$		−	33.7367i		−	1.87716i
$324$		0			0
$325$	21.5448	+	12.4389i	1.19509	+	0.689986i
$326$	2.71996	+	7.47303i	0.150645	+	0.413893i
$327$		0			0
$328$	17.3316	−	3.05602i	0.956976	−	0.168741i
$329$	21.8747	+	10.8910i	1.20599	+	0.600440i
$330$		0			0
$331$	−23.4181	+	8.52351i	−1.28718	+	0.468494i	−0.892800	−	0.450454i	$-0.851262\pi$
$331$	−23.4181	+	8.52351i	−1.28718	+	0.468494i	−0.394378	+	0.918948i	$0.629040\pi$
$332$	12.1234	+	20.9983i	0.665357	+	1.15243i
$333$		0			0
$334$	3.38173	+	1.95244i	0.185040	+	0.106833i
$335$	−0.703826	+	0.256172i	−0.0384541	+	0.0139962i
$336$		0			0
$337$	4.61488	−	3.87234i	0.251388	−	0.210940i	−0.508382	−	0.861132i	$-0.669756\pi$
$337$	4.61488	−	3.87234i	0.251388	−	0.210940i	0.759770	+	0.650192i	$0.225312\pi$
$338$	−1.71414	+	4.70955i	−0.0932368	+	0.256166i
$339$		0			0
$340$	−0.443589	+	2.51572i	−0.0240570	+	0.136434i
$341$	−1.06719	+	1.84843i	−0.0577918	+	0.100098i
$342$		0			0
$343$	−14.0627	+	12.0516i	−0.759312	+	0.650727i
$344$	1.18949	+	0.209740i	0.0641331	+	0.0113084i
$345$		0			0
$346$	−1.43120	−	1.70563i	−0.0769416	−	0.0916955i
$347$	11.1036	−	30.5068i	0.596071	−	1.63769i	−0.162958	−	0.986633i	$-0.552103\pi$
$347$	11.1036	−	30.5068i	0.596071	−	1.63769i	0.759028	−	0.651057i	$-0.225674\pi$
$348$		0			0
$349$	−6.71581	+	8.00359i	−0.359489	+	0.428422i	−0.915229	−	0.402934i	$-0.867990\pi$
$349$	−6.71581	+	8.00359i	−0.359489	+	0.428422i	0.555740	+	0.831356i	$0.312435\pi$
$350$	4.38494	+	3.24088i	0.234385	+	0.173232i
$351$		0			0
$352$	−3.50717	−	6.07460i	−0.186933	−	0.323777i
$353$	−4.68991	+	1.70699i	−0.249618	+	0.0908537i	−0.463799	−	0.885940i	$-0.653514\pi$
$353$	−4.68991	+	1.70699i	−0.249618	+	0.0908537i	0.214181	+	0.976794i	$0.431292\pi$
$354$		0			0
$355$	0.674717	+	0.804097i	0.0358103	+	0.0426770i
$356$	14.0698	+	5.12099i	0.745698	+	0.271412i
$357$		0			0
$358$	1.07120	−	6.07508i	0.0566148	−	0.321078i
$359$			16.1906i			0.854506i	0.904132	+	0.427253i	$0.140519\pi$
$359$			16.1906i			0.854506i	−0.904132	+	0.427253i	$0.859481\pi$
$360$		0			0
$361$	0.105445			0.00554976
$362$	−2.01450	−	1.69037i	−0.105880	−	0.0888437i
$363$		0			0
$364$	10.7945	−	21.6809i	0.565787	−	1.13639i
$365$	0.991979	+	1.18219i	0.0519225	+	0.0618789i
$366$		0			0
$367$	−11.3391	−	1.99938i	−0.591895	−	0.104367i	−0.130326	−	0.991471i	$-0.541602\pi$
$367$	−11.3391	−	1.99938i	−0.591895	−	0.104367i	−0.461569	+	0.887104i	$0.652713\pi$
$368$			7.28754i			0.379889i
$369$		0			0
$370$	−0.270478	−	0.156161i	−0.0140615	−	0.00811841i
$371$	6.02409	+	25.0303i	0.312755	+	1.29951i
$372$		0			0
$373$	−5.79313	−	32.8545i	−0.299957	−	1.70114i	−0.646343	−	0.763047i	$-0.723702\pi$
$373$	−5.79313	−	32.8545i	−0.299957	−	1.70114i	0.346386	−	0.938092i	$-0.387409\pi$
$374$	−4.80228	−	1.74789i	−0.248320	−	0.0903811i
$375$		0			0
$376$	−14.4445	−	2.54695i	−0.744917	−	0.131349i
$377$	−21.9390			−1.12992
$378$		0			0
$379$	−12.4601			−0.640032			−0.320016	−	0.947412i	$-0.603688\pi$
$379$	−12.4601			−0.640032			−0.320016	+	0.947412i	$0.603688\pi$
$380$	1.40895	+	0.248436i	0.0722777	+	0.0127445i
$381$		0			0
$382$	−6.60629	−	2.40449i	−0.338007	−	0.123024i
$383$	−5.05101	−	28.6457i	−0.258094	−	1.46373i	−0.788003	−	0.615672i	$-0.788885\pi$
$383$	−5.05101	−	28.6457i	−0.258094	−	1.46373i	0.529908	−	0.848055i	$-0.322226\pi$
$384$		0			0
$385$	−0.548181	+	0.520790i	−0.0279379	+	0.0265419i
$386$	4.40296	+	2.54205i	0.224105	+	0.129387i
$387$		0			0
$388$		−	8.75503i		−	0.444469i
$389$	−10.6003	−	1.86913i	−0.537459	−	0.0947685i	−0.101671	−	0.994818i	$-0.532419\pi$
$389$	−10.6003	−	1.86913i	−0.537459	−	0.0947685i	−0.435788	+	0.900050i	$0.643530\pi$
$390$		0			0
$391$	12.1313	+	14.4575i	0.613505	+	0.731147i
$392$	6.04401	−	9.32987i	0.305269	−	0.471230i
$393$		0			0
$394$	4.31721	+	3.62257i	0.217498	+	0.182502i
$395$	0.917134			0.0461460
$396$		0			0
$397$			39.1821i			1.96650i	0.182275	+	0.983248i	$0.441654\pi$
$397$			39.1821i			1.96650i	−0.182275	+	0.983248i	$0.558346\pi$
$398$	0.507146	−	2.87617i	0.0254209	−	0.144169i
$399$		0			0
$400$	13.9896	+	5.09181i	0.699482	+	0.254590i
$401$	−6.65975	−	7.93679i	−0.332572	−	0.396344i	0.573681	−	0.819079i	$-0.305515\pi$
$401$	−6.65975	−	7.93679i	−0.332572	−	0.396344i	−0.906254	+	0.422734i	$0.861070\pi$
$402$		0			0
$403$	6.32864	−	2.30344i	0.315252	−	0.114742i
$404$	11.4427	+	19.8193i	0.569294	+	0.986045i
$405$		0			0
$406$	−4.77790	−	0.541657i	−0.237123	−	0.0268820i
$407$	−4.26527	+	5.08315i	−0.211421	+	0.251962i
$408$		0			0
$409$	8.09126	−	22.2306i	0.400087	−	1.09923i	−0.562154	−	0.827033i	$-0.690027\pi$
$409$	8.09126	−	22.2306i	0.400087	−	1.09923i	0.962241	−	0.272198i	$-0.0877506\pi$
$410$	0.532137	+	0.634176i	0.0262804	+	0.0313197i
$411$		0			0
$412$	−5.04723	−	0.889964i	−0.248659	−	0.0438454i
$413$	−5.18261	−	0.587538i	−0.255019	−	0.0289109i
$414$		0			0
$415$	−1.19427	+	2.06854i	−0.0586245	+	0.101541i
$416$	−3.84334	+	21.7966i	−0.188435	+	1.06867i
$417$		0			0
$418$	−0.978921	+	2.68956i	−0.0478806	+	0.131551i
$419$	−0.297747	+	0.249839i	−0.0145459	+	0.0122054i	−0.650032	−	0.759907i	$-0.725244\pi$
$419$	−0.297747	+	0.249839i	−0.0145459	+	0.0122054i	0.635486	+	0.772113i	$0.280800\pi$
$420$		0			0
$421$	−29.2829	+	10.6581i	−1.42716	+	0.519444i	−0.936116	−	0.351691i	$-0.885607\pi$
$421$	−29.2829	+	10.6581i	−1.42716	+	0.519444i	−0.491044	+	0.871135i	$0.663385\pi$
$422$	−4.75590	−	2.74582i	−0.231513	−	0.133664i
$423$		0			0
$424$	−7.72652	−	13.3827i	−0.375233	−	0.649922i
$425$	36.2297	−	13.1865i	1.75740	−	0.639640i
$426$		0			0
$427$	3.16123	−	6.34937i	0.152983	−	0.307268i
$428$	−14.1856	+	2.50131i	−0.685688	+	0.120905i
$429$		0			0
$430$	0.0194326	+	0.0533907i	0.000937124	+	0.00257473i
$431$	−20.9763	−	12.1107i	−1.01039	−	0.583352i	−0.0990874	−	0.995079i	$-0.531592\pi$
$431$	−20.9763	−	12.1107i	−1.01039	−	0.583352i	−0.911307	+	0.411727i	$0.864926\pi$
$432$		0			0
$433$			10.0296i			0.481991i	0.970526	+	0.240995i	$0.0774739\pi$
$433$			10.0296i			0.481991i	−0.970526	+	0.240995i	$0.922526\pi$
$434$	1.43513	−	0.345395i	0.0688882	−	0.0165795i
$435$		0			0
$436$	−24.3599	+	20.4403i	−1.16663	+	0.978915i
$437$	8.09706	−	6.79424i	0.387335	−	0.325013i
$438$		0			0
$439$	−14.0388	−	38.5712i	−0.670034	−	1.84090i	−0.524200	−	0.851595i	$-0.675636\pi$
$439$	−14.0388	−	38.5712i	−0.670034	−	1.84090i	−0.145834	−	0.989309i	$-0.546587\pi$
$440$	0.226926	−	0.393048i	0.0108183	−	0.0187378i
$441$		0			0
$442$	8.06274	+	13.9651i	0.383506	+	0.664251i
$443$	22.4132	−	26.7110i	1.06488	−	1.26908i	0.103273	−	0.994653i	$-0.467068\pi$
$443$	22.4132	−	26.7110i	1.06488	−	1.26908i	0.961609	−	0.274424i	$-0.0884872\pi$
$444$		0			0
$445$	0.256125	+	1.45256i	0.0121415	+	0.0688578i
$446$	−5.12623	−	1.86580i	−0.242734	−	0.0883480i
$447$		0			0
$448$	3.12030	−	10.5557i	0.147420	−	0.498711i
$449$	−0.655683	+	0.378559i	−0.0309436	+	0.0178653i	−0.515392	−	0.856955i	$-0.672354\pi$
$449$	−0.655683	+	0.378559i	−0.0309436	+	0.0178653i	0.484448	+	0.874820i	$0.339020\pi$
$450$		0			0
$451$	15.2322	−	8.79433i	0.717258	−	0.414109i
$452$	3.52872	−	4.20536i	0.165977	−	0.197804i
$453$		0			0
$454$	1.03405	−	2.84103i	0.0485305	−	0.133336i
$455$	2.38133	−	0.146989i	0.111638	−	0.00689096i
$456$		0			0
$457$	−5.45161	+	30.9176i	−0.255015	+	1.44626i	0.541018	+	0.841011i	$0.318039\pi$
$457$	−5.45161	+	30.9176i	−0.255015	+	1.44626i	−0.796033	+	0.605253i	$0.793072\pi$
$458$	0.856242	−	1.48305i	0.0400096	−	0.0692986i
$459$		0			0
$460$	−0.693126	+	0.400177i	−0.0323172	+	0.0186583i
$461$	8.35408	+	7.00990i	0.389088	+	0.326484i	0.816258	−	0.577688i	$-0.196045\pi$
$461$	8.35408	+	7.00990i	0.389088	+	0.326484i	−0.427170	+	0.904171i	$0.640489\pi$
$462$		0			0
$463$	1.23596	+	7.00945i	0.0574397	+	0.325757i	0.999965	−	0.00837823i	$-0.00266690\pi$
$463$	1.23596	+	7.00945i	0.0574397	+	0.325757i	−0.942525	+	0.334135i	$0.891556\pi$
$464$	−12.9294	+	2.27979i	−0.600230	+	0.105837i
$465$		0			0
$466$	4.65711	+	3.90778i	0.215736	+	0.181024i
$467$	−13.2274			−0.612090			−0.306045	−	0.952017i	$-0.599006\pi$
$467$	−13.2274			−0.612090			−0.306045	+	0.952017i	$0.599006\pi$
$468$		0			0
$469$	6.54122	−	8.85033i	0.302045	−	0.408670i
$470$	−0.235978	−	0.648344i	−0.0108849	−	0.0299059i
$471$		0			0
$472$	3.08314	−	0.543641i	0.141913	−	0.0250231i
$473$	1.18880	−	0.209617i	0.0546610	−	0.00963820i
$474$		0			0
$475$	−7.38524	−	20.2908i	−0.338858	−	0.931005i
$476$	−14.9862	−	34.4131i	−0.686891	−	1.57732i
$477$		0			0
$478$	9.46353			0.432852
$479$	−1.52575	−	1.28025i	−0.0697132	−	0.0584963i	0.607265	−	0.794499i	$-0.292267\pi$
$479$	−1.52575	−	1.28025i	−0.0697132	−	0.0584963i	−0.676978	+	0.736003i	$0.736711\pi$
$480$		0			0
$481$	20.6197	−	3.63580i	0.940175	−	0.165778i
$482$	0.0567527	+	0.321861i	0.00258501	+	0.0146603i
$483$		0			0
$484$	11.8754	+	9.96464i	0.539791	+	0.452938i
$485$	0.746909	−	0.431228i	0.0339154	−	0.0195811i
$486$		0			0
$487$	−7.16028	+	12.4020i	−0.324463	+	0.561987i	−0.981404	−	0.191956i	$-0.938517\pi$
$487$	−7.16028	+	12.4020i	−0.324463	+	0.561987i	0.656940	+	0.753943i	$0.271850\pi$
$488$	−0.739281	+	4.19267i	−0.0334657	+	0.189793i
$489$		0			0
$490$	0.522236	+	0.0267816i	0.0235922	+	0.00120987i
$491$	−9.11592	+	25.0458i	−0.411396	+	1.13030i	0.545053	+	0.838401i	$0.316509\pi$
$491$	−9.11592	+	25.0458i	−0.411396	+	1.13030i	−0.956449	+	0.291899i	$0.905713\pi$
$492$		0			0
$493$	−21.8550	+	26.0458i	−0.984300	+	1.17304i
$494$	7.82128	−	4.51562i	0.351896	−	0.203167i
$495$		0			0
$496$	3.49030	−	2.01513i	0.156719	−	0.0904819i
$497$	−14.7906	−	4.37214i	−0.663447	−	0.196117i
$498$		0			0
$499$	−20.0327	−	7.29129i	−0.896785	−	0.326403i	−0.147821	−	0.989014i	$-0.547226\pi$
$499$	−20.0327	−	7.29129i	−0.896785	−	0.326403i	−0.748964	+	0.662611i	$0.769448\pi$
$500$	0.569687	+	3.23086i	0.0254772	+	0.144488i
$501$		0			0
$502$	3.08385	−	3.67519i	0.137639	−	0.164032i
$503$	6.74300	+	11.6792i	0.300655	+	0.520751i	0.976285	−	0.216491i	$-0.0694612\pi$
$503$	6.74300	+	11.6792i	0.300655	+	0.520751i	−0.675629	+	0.737242i	$0.736128\pi$
$504$		0			0
$505$	−1.12721	+	1.95239i	−0.0501604	+	0.0868803i
$506$	−0.547626	−	1.50459i	−0.0243450	−	0.0668872i
$507$		0			0
$508$	−14.7125	+	12.3453i	−0.652763	+	0.547733i
$509$	6.79910	−	5.70512i	0.301365	−	0.252875i	−0.479547	−	0.877516i	$-0.659199\pi$
$509$	6.79910	−	5.70512i	0.301365	−	0.252875i	0.780912	+	0.624641i	$0.214755\pi$
$510$		0			0
$511$	−21.7453	−	6.42797i	−0.961954	−	0.284357i
$512$			22.7635i			1.00601i
$513$		0			0
$514$	−3.65486	−	2.11014i	−0.161209	−	0.0930741i
$515$	−0.172677	−	0.474425i	−0.00760904	−	0.0209057i
$516$		0			0
$517$	−14.4360	+	2.54546i	−0.634897	+	0.111949i
$518$	4.58033	−	0.282725i	0.201248	−	0.0124222i
$519$		0			0
$520$	−1.34571	+	0.489798i	−0.0590133	+	0.0214791i
$521$	−21.3144	−	36.9177i	−0.933802	−	1.61739i	−0.776756	−	0.629802i	$-0.783136\pi$
$521$	−21.3144	−	36.9177i	−0.933802	−	1.61739i	−0.157046	−	0.987591i	$-0.550197\pi$
$522$		0			0
$523$	−19.7089	−	11.3789i	−0.861809	−	0.497565i	0.00280898	−	0.999996i	$-0.499106\pi$
$523$	−19.7089	−	11.3789i	−0.861809	−	0.497565i	−0.864617	+	0.502431i	$0.832439\pi$
$524$	−25.0457	+	9.11587i	−1.09412	+	0.398229i
$525$		0			0
$526$	−5.46851	+	4.58862i	−0.238438	+	0.200074i
$527$	3.56979	−	9.80791i	0.155502	−	0.427239i
$528$		0			0
$529$	2.96712	−	16.8274i	0.129005	−	0.731625i
$530$	0.363457	−	0.629526i	0.0157876	−	0.0273449i
$531$		0			0
$532$	−19.2734	+	8.39316i	−0.835606	+	0.363890i
$533$	−54.6557	−	9.63728i	−2.36740	−	0.417437i
$534$		0			0
$535$	−0.912103	−	1.08700i	−0.0394336	−	0.0469952i
$536$	−2.25930	+	6.20737i	−0.0975867	+	0.268117i
$537$		0			0
$538$	2.71772	−	3.23885i	0.117169	−	0.139637i
$539$	2.48706	−	10.8281i	0.107125	−	0.466397i
$540$		0			0
$541$	−1.69482	−	2.93552i	−0.0728660	−	0.126208i	0.827290	−	0.561775i	$-0.189881\pi$
$541$	−1.69482	−	2.93552i	−0.0728660	−	0.126208i	−0.900156	+	0.435567i	$0.856548\pi$
$542$	−3.08387	+	1.12244i	−0.132463	+	0.0482127i
$543$		0			0
$544$	22.0482	+	26.2760i	0.945307	+	1.12657i
$545$	−2.94365	−	1.07140i	−0.126092	−	0.0458938i
$546$		0			0
$547$	−0.794100	+	4.50356i	−0.0339532	+	0.192558i	−0.997067	−	0.0765371i	$-0.975614\pi$
$547$	−0.794100	+	4.50356i	−0.0339532	+	0.192558i	0.963113	+	0.269096i	$0.0867247\pi$
$548$		−	11.6133i		−	0.496097i
$549$		0			0
$550$	−3.27094			−0.139473
$551$	14.5872	+	12.2401i	0.621435	+	0.521446i
$552$		0			0
$553$	−11.2331	+	7.44408i	−0.477679	+	0.316555i
$554$	3.66410	+	4.36671i	0.155673	+	0.185524i
$555$		0			0
$556$	27.6894	+	4.88239i	1.17429	+	0.207059i
$557$		−	28.3433i		−	1.20094i	−0.799646	−	0.600472i	$-0.794979\pi$
$557$		−	28.3433i		−	1.20094i	0.799646	−	0.600472i	$-0.205021\pi$
$558$		0			0
$559$	−3.29867	−	1.90449i	−0.139519	−	0.0805511i
$560$	1.38812	−	0.334081i	0.0586586	−	0.0141175i
$561$		0			0
$562$	−0.200758	−	1.13856i	−0.00846848	−	0.0480271i
$563$	−4.56240	−	1.66058i	−0.192282	−	0.0699851i	0.244084	−	0.969754i	$-0.421513\pi$
$563$	−4.56240	−	1.66058i	−0.192282	−	0.0699851i	−0.436367	+	0.899769i	$0.643735\pi$
$564$		0			0
$565$	0.532575	+	0.0939073i	0.0224056	+	0.00395071i
$566$	−6.81026			−0.286257
$567$		0			0
$568$	9.25755			0.388438
$569$	−24.0084	−	4.23332i	−1.00648	−	0.177470i	−0.353978	−	0.935254i	$-0.615171\pi$
$569$	−24.0084	−	4.23332i	−1.00648	−	0.177470i	−0.652506	+	0.757784i	$0.726282\pi$
$570$		0			0
$571$	6.78414	+	2.46923i	0.283908	+	0.103334i	0.480049	−	0.877242i	$-0.340619\pi$
$571$	6.78414	+	2.46923i	0.283908	+	0.103334i	−0.196141	+	0.980576i	$0.562841\pi$
$572$	2.52292	+	14.3082i	0.105488	+	0.598254i
$573$		0			0
$574$	−11.6650	−	3.44822i	−0.486889	−	0.143926i
$575$	10.4612	+	6.03976i	0.436261	+	0.251875i
$576$		0			0
$577$			26.1510i			1.08868i	0.838864	+	0.544340i	$0.183220\pi$
$577$			26.1510i			1.08868i	−0.838864	+	0.544340i	$0.816780\pi$
$578$	17.6655	+	3.11490i	0.734786	+	0.129563i
$579$		0			0
$580$	−0.926816	−	1.10454i	−0.0384839	−	0.0458634i
$581$	−2.16220	−	35.0290i	−0.0897030	−	1.45325i
$582$		0			0
$583$	−11.8308	−	9.92722i	−0.489982	−	0.411143i
$584$	13.6106			0.563210
$585$		0			0
$586$			0.646165i			0.0266928i
$587$	3.34943	−	18.9956i	0.138246	−	0.784031i	−0.834298	−	0.551313i	$-0.814127\pi$
$587$	3.34943	−	18.9956i	0.138246	−	0.784031i	0.972544	−	0.232718i	$-0.0747619\pi$
$588$		0			0
$589$	−5.49302	−	1.99929i	−0.226336	−	0.0823795i
$590$	0.0946628	+	0.112815i	0.00389720	+	0.00464451i
$591$		0			0
$592$	11.7740	−	4.28539i	0.483908	−	0.176128i
$593$	19.5311	+	33.8289i	0.802047	+	1.38919i	0.918266	+	0.395963i	$0.129589\pi$
$593$	19.5311	+	33.8289i	0.802047	+	1.38919i	−0.116219	+	0.993224i	$0.537078\pi$
$594$		0			0
$595$	2.19770	−	2.97351i	0.0900971	−	0.121902i
$596$	20.4819	−	24.4094i	0.838972	−	0.999848i
$597$		0			0
$598$	−1.72797	+	4.74755i	−0.0706618	+	0.194142i
$599$	−5.53430	−	6.59552i	−0.226125	−	0.269486i	0.641038	−	0.767509i	$-0.278504\pi$
$599$	−5.53430	−	6.59552i	−0.226125	−	0.269486i	−0.867164	+	0.498023i	$0.834059\pi$
$600$		0			0
$601$	41.3305	+	7.28768i	1.68591	+	0.297271i	0.932737	−	0.360557i	$-0.117413\pi$
$601$	41.3305	+	7.28768i	1.68591	+	0.297271i	0.753168	+	0.657828i	$0.228525\pi$
$602$	−0.671366	−	0.496202i	−0.0273628	−	0.0202237i
$603$		0			0
$604$	−2.10100	+	3.63903i	−0.0854883	+	0.148070i
$605$	−0.265182	+	1.50392i	−0.0107812	+	0.0611431i
$606$		0			0
$607$	15.1581	−	41.6466i	0.615249	−	1.69038i	−0.103073	−	0.994674i	$-0.532868\pi$
$607$	15.1581	−	41.6466i	0.615249	−	1.69038i	0.718323	−	0.695710i	$-0.244910\pi$
$608$	14.7161	−	12.3483i	0.596817	−	0.500789i
$609$		0			0
$610$	−0.188189	+	0.0684952i	−0.00761955	+	0.00277329i
$611$	40.0570	+	23.1269i	1.62053	+	0.935615i
$612$		0			0
$613$	−22.3176	−	38.6553i	−0.901401	−	1.56127i	−0.825677	−	0.564143i	$-0.809207\pi$
$613$	−22.3176	−	38.6553i	−0.901401	−	1.56127i	−0.0757236	−	0.997129i	$-0.524127\pi$
$614$	0.637493	−	0.232028i	0.0257271	−	0.00936390i
$615$		0			0
$616$	0.410843	+	6.65594i	0.0165534	+	0.268176i
$617$	−26.5556	+	4.68248i	−1.06909	+	0.188509i	−0.680386	−	0.732854i	$-0.738188\pi$
$617$	−26.5556	+	4.68248i	−1.06909	+	0.188509i	−0.388703	+	0.921363i	$0.627077\pi$
$618$		0			0
$619$	13.2165	+	36.3120i	0.531215	+	1.45950i	0.857626	+	0.514274i	$0.171939\pi$
$619$	13.2165	+	36.3120i	0.531215	+	1.45950i	−0.326411	+	0.945228i	$0.605839\pi$
$620$	0.383322	+	0.221311i	0.0153946	+	0.00888807i
$621$		0			0
$622$		−	4.92809i		−	0.197599i
$623$	−14.9270	−	15.7121i	−0.598036	−	0.629491i
$624$		0			0
$625$	18.7794	−	15.7577i	0.751174	−	0.630310i
$626$	−0.589500	+	0.494650i	−0.0235612	+	0.0197702i
$627$		0			0
$628$	3.51044	+	9.64485i	0.140082	+	0.384871i
$629$	16.2243	−	28.1013i	0.646906	−	1.12047i
$630$		0			0
$631$	−5.01811	−	8.69163i	−0.199768	−	0.346008i	0.748685	−	0.662926i	$-0.230686\pi$
$631$	−5.01811	−	8.69163i	−0.199768	−	0.346008i	−0.948453	+	0.316917i	$0.897352\pi$
$632$	5.19927	−	6.19625i	0.206816	−	0.246474i
$633$		0			0
$634$	1.52169	+	8.62995i	0.0604341	+	0.342739i
$635$	−1.77786	−	0.647090i	−0.0705524	−	0.0256790i
$636$		0			0
$637$	−27.9735	+	21.1288i	−1.10835	+	0.837153i
$638$	2.49809	−	1.44227i	0.0989002	−	0.0571001i
$639$		0			0
$640$	−1.64750	+	0.951186i	−0.0651233	+	0.0375989i
$641$	−20.4966	+	24.4269i	−0.809567	+	0.964804i	−0.999857	−	0.0169239i	$-0.994613\pi$
$641$	−20.4966	+	24.4269i	−0.809567	+	0.964804i	0.190290	+	0.981728i	$0.439057\pi$
$642$		0			0
$643$	−4.12226	+	11.3258i	−0.162566	+	0.446646i	−0.994053	−	0.108898i	$-0.965268\pi$
$643$	−4.12226	+	11.3258i	−0.162566	+	0.446646i	0.831487	+	0.555544i	$0.187490\pi$
$644$	5.24132	−	10.5273i	0.206537	−	0.414832i
$645$		0			0
$646$	2.43043	−	13.7837i	0.0956242	−	0.542312i
$647$	−21.3692	+	37.0126i	−0.840111	+	1.45512i	0.0496886	+	0.998765i	$0.484177\pi$
$647$	−21.3692	+	37.0126i	−0.840111	+	1.45512i	−0.889800	+	0.456351i	$0.849156\pi$
$648$		0			0
$649$	2.70969	−	1.56444i	0.106365	−	0.0614096i
$650$	7.90637	+	6.63424i	0.310114	+	0.260216i
$651$		0			0
$652$	−6.08441	−	34.5064i	−0.238284	−	1.35137i
$653$	−14.0027	+	2.46906i	−0.547970	+	0.0966218i	−0.440777	−	0.897616i	$-0.645297\pi$
$653$	−14.0027	+	2.46906i	−0.547970	+	0.0966218i	−0.107192	+	0.994238i	$0.534186\pi$
$654$		0			0
$655$	−2.01132	−	1.68769i	−0.0785886	−	0.0659437i
$656$	−33.2118			−1.29670
$657$		0			0
$658$	8.15267	+	6.02558i	0.317824	+	0.234902i
$659$	−0.747205	−	2.05293i	−0.0291070	−	0.0799707i	0.924288	−	0.381696i	$-0.124660\pi$
$659$	−0.747205	−	2.05293i	−0.0291070	−	0.0799707i	−0.953395	+	0.301725i	$0.902438\pi$
$660$		0			0
$661$	−19.1020	+	3.36819i	−0.742980	+	0.131007i	−0.532310	−	0.846550i	$-0.678676\pi$
$661$	−19.1020	+	3.36819i	−0.742980	+	0.131007i	−0.210670	+	0.977557i	$0.567565\pi$
$662$	−10.1819	+	1.79535i	−0.395731	+	0.0697781i
$663$		0			0
$664$	7.20488	+	19.7952i	0.279604	+	0.768204i
$665$	−1.66535	−	1.23085i	−0.0645793	−	0.0477301i
$666$		0			0
$667$	−10.6526			−0.412469
$668$	−13.1795	−	11.0589i	−0.509930	−	0.427882i
$669$		0			0
$670$	−0.306015	+	0.0539587i	−0.0118224	+	0.00208460i
$671$	0.738849	+	4.19022i	0.0285229	+	0.161762i
$672$		0			0
$673$	−8.85877	−	7.43339i	−0.341480	−	0.286536i	0.455878	−	0.890042i	$-0.349325\pi$
$673$	−8.85877	−	7.43339i	−0.341480	−	0.286536i	−0.797358	+	0.603506i	$0.793770\pi$
$674$	2.16445	−	1.24965i	0.0833716	−	0.0481346i
$675$		0			0
$676$	11.0408	−	19.1233i	0.424647	−	0.735510i
$677$	2.04862	−	11.6183i	0.0787348	−	0.446527i	−0.919799	−	0.392390i	$-0.871648\pi$
$677$	2.04862	−	11.6183i	0.0787348	−	0.446527i	0.998534	−	0.0541367i	$-0.0172407\pi$
$678$		0			0
$679$	−5.64802	+	11.3441i	−0.216751	+	0.435347i
$680$	−0.759073	+	2.08554i	−0.0291091	+	0.0799767i
$681$		0			0
$682$	−0.569183	+	0.678326i	−0.0217951	+	0.0259744i
$683$	−20.5498	+	11.8644i	−0.786317	+	0.453980i	−0.838664	−	0.544648i	$-0.816663\pi$
$683$	−20.5498	+	11.8644i	−0.786317	+	0.453980i	0.0523472	+	0.998629i	$0.483330\pi$
$684$		0			0
$685$	0.990756	−	0.572013i	0.0378549	−	0.0218555i
$686$	−6.61374	+	3.91080i	−0.252514	+	0.149315i
$687$		0			0
$688$	−2.14191	−	0.779592i	−0.0816596	−	0.0297217i
$689$	8.46217	+	47.9913i	0.322383	+	1.82832i
$690$		0			0
$691$	−4.08371	+	4.86678i	−0.155352	+	0.185141i	−0.838107	−	0.545507i	$-0.816337\pi$
$691$	−4.08371	+	4.86678i	−0.155352	+	0.185141i	0.682755	+	0.730648i	$0.260782\pi$
$692$	4.90500	+	8.49571i	0.186460	+	0.322959i
$693$		0			0
$694$	6.73429	−	11.6641i	0.255630	−	0.442765i
$695$	0.947313	+	2.60272i	0.0359336	+	0.0987268i
$696$		0			0
$697$	−65.8877	+	55.2864i	−2.49568	+	2.09412i
$698$	−3.32044	+	2.78618i	−0.125681	+	0.105459i
$699$		0			0
$700$	−16.5467	−	17.4170i	−0.625406	−	0.658300i
$701$		−	30.6664i		−	1.15825i	−0.815238	−	0.579126i	$-0.803394\pi$
$701$		−	30.6664i		−	1.15825i	0.815238	−	0.579126i	$-0.196606\pi$
$702$		0			0
$703$	−15.7384	−	9.08659i	−0.593586	−	0.342707i
$704$	2.25838	+	6.20485i	0.0851160	+	0.233854i
$705$		0			0
$706$	−2.03911	+	0.359550i	−0.0767430	+	0.0135319i
$707$	−2.04079	−	33.0622i	−0.0767518	−	1.24343i
$708$		0			0
$709$	13.9023	−	5.06001i	0.522111	−	0.190033i	−0.0675015	−	0.997719i	$-0.521503\pi$
$709$	13.9023	−	5.06001i	0.522111	−	0.190033i	0.589612	+	0.807686i	$0.299281\pi$
$710$	0.217739	+	0.377134i	0.00817159	+	0.0141536i
$711$		0			0
$712$	11.2656	+	6.50420i	0.422196	+	0.243755i
$713$	3.07289	−	1.11844i	0.115081	−	0.0418860i
$714$		0			0
$715$	−1.09639	+	0.919982i	−0.0410027	+	0.0344054i
$716$	−9.29587	+	25.5402i	−0.347403	+	0.954481i
$717$		0			0
$718$	−1.16639	+	6.61492i	−0.0435293	+	0.246867i
$719$	4.89820	−	8.48393i	0.182672	−	0.316397i	−0.760118	−	0.649786i	$-0.774859\pi$
$719$	4.89820	−	8.48393i	0.182672	−	0.316397i	0.942790	+	0.333388i	$0.108192\pi$
$720$		0			0
$721$	5.96570	+	4.40921i	0.222174	+	0.164208i
$722$	0.0430815	+	0.00759643i	0.00160333	+	0.000282710i
$723$		0			0
$724$	7.44763	+	8.87574i	0.276789	+	0.329864i
$725$	−7.44296	+	20.4494i	−0.276425	+	0.759470i
$726$		0			0
$727$	29.0898	−	34.6679i	1.07888	−	1.28576i	0.122873	−	0.992422i	$-0.460789\pi$
$727$	29.0898	−	34.6679i	1.07888	−	1.28576i	0.956009	−	0.293339i	$-0.0947663\pi$
$728$	12.5068	−	16.9218i	0.463531	−	0.627162i
$729$		0			0
$730$	0.320122	+	0.554468i	0.0118483	+	0.0205218i
$731$	−5.54702	+	2.01895i	−0.205164	+	0.0746736i
$732$		0			0
$733$	−15.4136	−	18.3692i	−0.569315	−	0.678483i	0.402175	−	0.915563i	$-0.368254\pi$
$733$	−15.4136	−	18.3692i	−0.569315	−	0.678483i	−0.971490	+	0.237079i	$0.923810\pi$
$734$	−4.48873	−	1.63376i	−0.165682	−	0.0603033i
$735$		0			0
$736$	−1.86615	+	10.5834i	−0.0687871	+	0.390111i
$737$			6.60188i			0.243184i
$738$		0			0
$739$	−22.3128			−0.820790			−0.410395	−	0.911908i	$-0.634609\pi$
$739$	−22.3128			−0.820790			−0.410395	+	0.911908i	$0.634609\pi$
$740$	1.05413	+	0.884518i	0.0387505	+	0.0325155i
$741$		0			0
$742$	0.658029	+	10.6605i	0.0241570	+	0.391360i
$743$	28.1973	+	33.6043i	1.03446	+	1.23282i	0.972051	+	0.234770i	$0.0754337\pi$
$743$	28.1973	+	33.6043i	1.03446	+	1.23282i	0.0624085	+	0.998051i	$0.480122\pi$
$744$		0			0
$745$	3.09125	+	0.545071i	0.113255	+	0.0199699i
$746$		−	13.8406i		−	0.506739i
$747$		0			0
$748$	19.4998	+	11.2582i	0.712982	+	0.411641i
$749$	19.9943	+	5.91038i	0.730576	+	0.215961i
$750$		0			0
$751$	−3.23209	−	18.3301i	−0.117941	−	0.668875i	−0.985252	−	0.171109i	$-0.945265\pi$
$751$	−3.23209	−	18.3301i	−0.117941	−	0.668875i	0.867311	−	0.497766i	$-0.165846\pi$
$752$	26.0101	+	9.46690i	0.948491	+	0.345222i
$753$		0			0
$754$	−8.96354	−	1.58051i	−0.326433	−	0.0575589i
$755$	−0.413938			−0.0150647
$756$		0			0
$757$	26.2705			0.954819			0.477410	−	0.878681i	$-0.341576\pi$
$757$	26.2705			0.954819			0.477410	+	0.878681i	$0.341576\pi$
$758$	−5.09078	−	0.897641i	−0.184905	−	0.0326038i
$759$		0			0
$760$	1.16803	+	0.425126i	0.0423687	+	0.0154210i
$761$	−2.11972	−	12.0216i	−0.0768399	−	0.435781i	−0.998821	−	0.0485459i	$-0.984541\pi$
$761$	−2.11972	−	12.0216i	−0.0768399	−	0.435781i	0.921981	−	0.387235i	$-0.126570\pi$
$762$		0			0
$763$	44.7501	−	10.7701i	1.62006	−	0.389904i
$764$	26.8250	+	15.4874i	0.970494	+	0.560315i
$765$		0			0
$766$		−	12.0676i		−	0.436018i
$767$	−9.72280	−	1.71439i	−0.351070	−	0.0619031i
$768$		0			0
$769$	5.10850	+	6.08807i	0.184217	+	0.219541i	0.850247	−	0.526383i	$-0.176452\pi$
$769$	5.10850	+	6.08807i	0.184217	+	0.219541i	−0.666030	+	0.745925i	$0.732008\pi$
$770$	−0.261487	+	0.173285i	−0.00942333	+	0.00624478i
$771$		0			0
$772$	−17.1595	−	14.3985i	−0.617585	−	0.518215i
$773$	−7.78940			−0.280165			−0.140083	−	0.990140i	$-0.544737\pi$
$773$	−7.78940			−0.280165			−0.140083	+	0.990140i	$0.544737\pi$
$774$		0			0
$775$		−	6.68038i		−	0.239966i
$776$	1.32084	−	7.49084i	0.0474153	−	0.268906i
$777$		0			0
$778$	−4.19629	−	1.52733i	−0.150444	−	0.0547573i
$779$	30.9637	+	36.9011i	1.10939	+	1.32212i
$780$		0			0
$781$	8.69418	−	3.16442i	0.311102	−	0.113232i
$782$	3.91490	+	6.78080i	0.139996	+	0.242481i
$783$		0			0
$784$	−14.2901	+	15.3587i	−0.510359	+	0.548526i
$785$	−0.649915	+	0.774539i	−0.0231965	+	0.0276445i
$786$		0			0
$787$	−8.13240	+	22.3436i	−0.289889	+	0.796463i	0.706193	+	0.708020i	$0.250411\pi$
$787$	−8.13240	+	22.3436i	−0.289889	+	0.796463i	−0.996081	+	0.0884429i	$0.971811\pi$
$788$	−15.9608	−	19.0213i	−0.568579	−	0.677606i
$789$		0			0
$790$	0.374710	+	0.0660715i	0.0133316	+	0.00235072i
$791$	−7.28521	+	3.17256i	−0.259032	+	0.112803i
$792$		0			0
$793$	6.71285	−	11.6270i	0.238380	−	0.412887i
$794$	−2.82273	+	16.0085i	−0.100175	+	0.568121i
$795$		0			0
$796$	−4.40101	+	12.0917i	−0.155989	+	0.428578i
$797$	10.6111	−	8.90378i	0.375865	−	0.315388i	−0.435212	−	0.900328i	$-0.643326\pi$
$797$	10.6111	−	8.90378i	0.375865	−	0.315388i	0.811077	+	0.584940i	$0.198882\pi$
$798$		0			0
$799$	67.3597	−	24.5169i	2.38302	−	0.867347i
$800$	19.0128	+	10.9770i	0.672204	+	0.388097i
$801$		0			0
$802$	−2.14918	−	3.72248i	−0.0758900	−	0.131445i
$803$	12.7823	−	4.65238i	0.451077	−	0.164179i
$804$		0			0
$805$	1.15626	−	0.0713712i	0.0407529	−	0.00251551i
$806$	2.75161	−	0.485183i	0.0969214	−	0.0170899i
$807$		0			0
$808$	6.80033	+	18.6838i	0.239235	+	0.657292i
$809$	28.3326	+	16.3578i	0.996122	+	0.575111i	0.907099	−	0.420918i	$-0.138292\pi$
$809$	28.3326	+	16.3578i	0.996122	+	0.575111i	0.0890233	+	0.996030i	$0.471625\pi$
$810$		0			0
$811$		−	47.6172i		−	1.67207i	−0.548679	−	0.836033i	$-0.684869\pi$
$811$		−	47.6172i		−	1.67207i	0.548679	−	0.836033i	$-0.315131\pi$
$812$	20.3168	+	6.00572i	0.712981	+	0.210760i
$813$		0			0
$814$	−2.10884	+	1.76953i	−0.0739149	+	0.0620219i
$815$	2.64412	−	2.21868i	0.0926196	−	0.0777171i
$816$		0			0
$817$	1.13073	+	3.10666i	0.0395593	+	0.108688i
$818$	4.90734	−	8.49976i	0.171581	−	0.297187i
$819$		0			0
$820$	−1.82374	−	3.15881i	−0.0636878	−	0.110311i
$821$	31.4248	−	37.4506i	1.09673	−	1.30703i	0.148691	−	0.988884i	$-0.452494\pi$
$821$	31.4248	−	37.4506i	1.09673	−	1.30703i	0.948040	−	0.318150i	$-0.103062\pi$
$822$		0			0
$823$	3.43354	+	19.4726i	0.119686	+	0.678771i	0.984323	+	0.176375i	$0.0564371\pi$
$823$	3.43354	+	19.4726i	0.119686	+	0.678771i	−0.864637	+	0.502396i	$0.832452\pi$
$824$	−4.18417	−	1.52291i	−0.145762	−	0.0530532i
$825$		0			0
$826$	−2.07511	−	0.613410i	−0.0722024	−	0.0213433i
$827$	−33.5168	+	19.3510i	−1.16549	+	0.672899i	−0.952615	−	0.304180i	$-0.901618\pi$
$827$	−33.5168	+	19.3510i	−1.16549	+	0.672899i	−0.212880	+	0.977078i	$0.568284\pi$
$828$		0			0
$829$	11.1500	−	6.43746i	0.387256	−	0.223582i	−0.293715	−	0.955893i	$-0.594892\pi$
$829$	11.1500	−	6.43746i	0.387256	−	0.223582i	0.680970	+	0.732311i	$0.261558\pi$
$830$	−0.636960	+	0.759099i	−0.0221092	+	0.0263487i
$831$		0			0
$832$	7.12605	−	19.5787i	0.247051	−	0.678768i
$833$	−2.78248	+	54.2577i	−0.0964072	+	1.87992i
$834$		0			0
$835$	0.294303	−	1.66908i	0.0101848	−	0.0577608i
$836$	6.30526	−	10.9210i	0.218072	−	0.377712i
$837$		0			0
$838$	−0.139648	+	0.0806258i	−0.00482406	+	0.00278517i
$839$	−10.7228	−	8.99751i	−0.370193	−	0.310628i	0.438645	−	0.898660i	$-0.355459\pi$
$839$	−10.7228	−	8.99751i	−0.370193	−	0.310628i	−0.808838	+	0.588032i	$0.799903\pi$
$840$		0			0
$841$	1.70331	+	9.65992i	0.0587347	+	0.333101i
$842$	−12.7318	+	2.24496i	−0.438768	+	0.0773666i
$843$		0			0
$844$	18.5350	+	15.5527i	0.638001	+	0.535347i
$845$	2.17526			0.0748312
$846$		0			0
$847$	−8.95889	−	20.5725i	−0.307831	−	0.706879i
$848$	9.97405	+	27.4035i	0.342510	+	0.941039i
$849$		0			0
$850$	15.7522	−	2.77754i	0.540296	−	0.0952688i
$851$	10.0120	−	1.76538i	0.343205	−	0.0605164i
$852$		0			0
$853$	1.21924	+	3.34982i	0.0417458	+	0.114696i	0.958814	−	0.284035i	$-0.0916731\pi$
$853$	1.21924	+	3.34982i	0.0417458	+	0.114696i	−0.917068	+	0.398730i	$0.869451\pi$
$854$	1.74899	−	2.36640i	0.0598492	−	0.0809766i
$855$		0			0
$856$	−12.5146			−0.427741
$857$	22.6428	+	18.9996i	0.773464	+	0.649013i	0.941593	−	0.336752i	$-0.109328\pi$
$857$	22.6428	+	18.9996i	0.773464	+	0.649013i	−0.168130	+	0.985765i	$0.553773\pi$
$858$		0			0
$859$	26.8449	−	4.73347i	0.915935	−	0.161504i	0.304238	−	0.952596i	$-0.401598\pi$
$859$	26.8449	−	4.73347i	0.915935	−	0.161504i	0.611697	+	0.791092i	$0.290487\pi$
$860$	−0.0434697	−	0.246529i	−0.00148231	−	0.00840657i
$861$		0			0
$862$	−7.69776	−	6.45919i	−0.262187	−	0.220001i
$863$	23.1530	−	13.3674i	0.788136	−	0.455031i	−0.0511699	−	0.998690i	$-0.516295\pi$
$863$	23.1530	−	13.3674i	0.788136	−	0.455031i	0.839306	+	0.543659i	$0.182962\pi$
$864$		0			0
$865$	−0.483191	+	0.836911i	−0.0164290	+	0.0284558i
$866$	−0.722544	+	4.09775i	−0.0245530	+	0.139247i
$867$		0			0
$868$	−6.49125	+	0.400678i	−0.220327	+	0.0135999i
$869$	2.76486	−	7.59639i	0.0937914	−	0.257690i
$870$		0			0
$871$	13.3902	−	15.9578i	0.453709	−	0.540710i
$872$	−23.9262	+	13.8138i	−0.810242	+	0.467793i
$873$		0			0
$874$	3.79765	−	2.19258i	0.128458	−	0.0741650i
$875$	1.34612	−	4.55382i	0.0455073	−	0.153947i
$876$		0			0
$877$	39.7412	+	14.4646i	1.34196	+	0.488435i	0.910430	−	0.413662i	$-0.135751\pi$
$877$	39.7412	+	14.4646i	1.34196	+	0.488435i	0.431533	+	0.902097i	$0.357973\pi$
$878$	−2.95705	−	16.7703i	−0.0997957	−	0.565970i
$879$		0			0
$880$	−0.550539	+	0.656106i	−0.0185587	+	0.0221173i
$881$	24.9251	+	43.1715i	0.839747	+	1.45448i	0.890106	+	0.455753i	$0.150630\pi$
$881$	24.9251	+	43.1715i	0.839747	+	1.45448i	−0.0503592	+	0.998731i	$0.516037\pi$
$882$		0			0
$883$	−19.7615	+	34.2280i	−0.665028	+	1.15186i	0.314249	+	0.949340i	$0.398247\pi$
$883$	−19.7615	+	34.2280i	−0.665028	+	1.15186i	−0.979278	+	0.202522i	$0.935086\pi$
$884$	−24.2997	−	66.7630i	−0.817289	−	2.24548i
$885$		0			0
$886$	11.0816	−	9.29854i	0.372293	−	0.312391i
$887$	−28.4361	+	23.8607i	−0.954791	+	0.801165i	−0.980098	−	0.198515i	$-0.936388\pi$
$887$	−28.4361	+	23.8607i	−0.954791	+	0.801165i	0.0253071	+	0.999680i	$0.491944\pi$
$888$		0			0
$889$	27.0275	−	6.50478i	0.906475	−	0.218163i
$890$			0.611918i			0.0205115i
$891$		0			0
$892$	20.8152	+	12.0176i	0.696944	+	0.402381i
$893$	−13.7309	−	37.7255i	−0.459489	−	1.26243i
$894$		0			0
$895$	−2.63675	+	0.464930i	−0.0881369	+	0.0155409i
$896$	12.4582	−	25.0224i	0.416199	−	0.835940i
$897$		0			0
$898$	−0.295162	+	0.107430i	−0.00984968	+	0.00358499i
$899$	2.94562	+	5.10196i	0.0982418	+	0.170160i
$900$		0			0
$901$	65.4046	+	37.7614i	2.17894	+	1.25801i
$902$	6.85694	−	2.49572i	0.228311	−	0.0830984i
$903$		0			0
$904$	3.65363	−	3.06576i	0.121518	−	0.101966i
$905$	−0.390375	+	1.07255i	−0.0129765	+	0.0356527i
$906$		0			0
$907$	−5.56403	+	31.5552i	−0.184751	+	1.04777i	0.741525	+	0.670926i	$0.234103\pi$
$907$	−5.56403	+	31.5552i	−0.184751	+	1.04777i	−0.926275	+	0.376847i	$0.877008\pi$
$908$	−6.66036	+	11.5361i	−0.221032	+	0.382838i
$909$		0			0
$910$	0.983519	+	0.111499i	0.0326034	+	0.00369615i
$911$	17.5085	+	3.08722i	0.580082	+	0.102284i	0.455988	−	0.889986i	$-0.349286\pi$
$911$	17.5085	+	3.08722i	0.580082	+	0.102284i	0.124095	+	0.992270i	$0.460397\pi$
$912$		0			0
$913$	13.5328	+	16.1278i	0.447872	+	0.533753i
$914$	−4.45469	+	12.2392i	−0.147348	+	0.404835i
$915$		0			0
$916$	−4.84988	+	5.77987i	−0.160245	+	0.190972i
$917$	38.3331	+	4.34572i	1.26587	+	0.143508i
$918$		0			0
$919$	10.1037	+	17.5002i	0.333292	+	0.577279i	0.983155	−	0.182773i	$-0.0585072\pi$
$919$	10.1037	+	17.5002i	0.333292	+	0.577279i	−0.649863	+	0.760051i	$0.725174\pi$
$920$	−0.653415	+	0.237823i	−0.0215424	+	0.00784081i
$921$		0			0
$922$	2.90819	+	3.46585i	0.0957762	+	0.114142i
$923$	−27.4334	−	9.98494i	−0.902981	−	0.328658i
$924$		0			0
$925$	3.60643	−	20.4531i	0.118579	−	0.672493i
$926$			2.95287i			0.0970373i
$927$		0			0
$928$	−19.3607			−0.635545
$929$	5.15862	+	4.32860i	0.169249	+	0.142017i	0.723478	−	0.690348i	$-0.242542\pi$
$929$	5.15862	+	4.32860i	0.169249	+	0.142017i	−0.554229	+	0.832364i	$0.686987\pi$
$930$		0			0
$931$	30.3876	+	1.55835i	0.995913	+	0.0510730i
$932$	−17.2174	−	20.5189i	−0.563974	−	0.672118i
$933$		0			0
$934$	−5.40427	−	0.952918i	−0.176833	−	0.0311804i
$935$			2.21809i			0.0725392i
$936$		0			0
$937$	−37.6538	−	21.7394i	−1.23009	−	0.710196i	−0.263045	−	0.964784i	$-0.584727\pi$
$937$	−37.6538	−	21.7394i	−1.23009	−	0.710196i	−0.967050	+	0.254588i	$0.918060\pi$
$938$	3.31011	−	3.14471i	0.108079	−	0.102678i
$939$		0			0
$940$	0.527870	+	2.99370i	0.0172172	+	0.0976438i
$941$	−11.5099	−	4.18926i	−0.375212	−	0.136566i	0.147529	−	0.989058i	$-0.452868\pi$
$941$	−11.5099	−	4.18926i	−0.375212	−	0.136566i	−0.522741	+	0.852492i	$0.675090\pi$
$942$		0			0
$943$	−26.5383	−	4.67942i	−0.864206	−	0.152383i
$944$	−5.90810			−0.192292
$945$		0			0
$946$	0.500804			0.0162825
$947$	13.5396	+	2.38739i	0.439977	+	0.0775798i	0.389249	−	0.921133i	$-0.372735\pi$
$947$	13.5396	+	2.38739i	0.439977	+	0.0775798i	0.0507283	+	0.998712i	$0.483846\pi$
$948$		0			0
$949$	−40.3330	−	14.6800i	−1.30926	−	0.476533i
$950$	−1.55559	−	8.82217i	−0.0504699	−	0.286229i
$951$		0			0
$952$	−7.63048	−	31.7049i	−0.247305	−	1.02756i
$953$	41.3778	+	23.8895i	1.34036	+	0.773857i	0.986860	−	0.161578i	$-0.0516584\pi$
$953$	41.3778	+	23.8895i	1.34036	+	0.773857i	0.353499	+	0.935435i	$0.384992\pi$
$954$		0			0
$955$			3.05132i			0.0987385i
$956$	−41.0622	−	7.24037i	−1.32805	−	0.234170i
$957$		0			0
$958$	−0.531138	−	0.632986i	−0.0171603	−	0.0204508i
$959$	−7.49196	+	15.0477i	−0.241928	+	0.485915i
$960$		0			0
$961$	22.3620	+	18.7639i	0.721355	+	0.605289i
$962$	8.68643			0.280062
$963$		0			0
$964$		−	1.43997i		−	0.0463783i
$965$	0.383178	−	2.17311i	0.0123349	−	0.0699550i
$966$		0			0
$967$	42.4888	+	15.4647i	1.36635	+	0.497310i	0.918011	−	0.396555i	$-0.129795\pi$
$967$	42.4888	+	15.4647i	1.36635	+	0.497310i	0.448336	+	0.893865i	$0.352017\pi$
$968$	8.65731	+	10.3174i	0.278257	+	0.331613i
$969$		0			0
$970$	0.336228	−	0.122377i	0.0107956	−	0.00392929i
$971$	7.07273	+	12.2503i	0.226975	+	0.393132i	0.956910	−	0.290384i	$-0.0937832\pi$
$971$	7.07273	+	12.2503i	0.226975	+	0.393132i	−0.729935	+	0.683516i	$0.760450\pi$
$972$		0			0
$973$	−32.7282	−	24.1892i	−1.04922	−	0.775469i
$974$	−3.81890	+	4.55119i	−0.122366	+	0.145830i
$975$		0			0
$976$	2.74787	−	7.54972i	0.0879573	−	0.241661i
$977$	−23.6226	−	28.1523i	−0.755753	−	0.900672i	0.241818	−	0.970322i	$-0.422256\pi$
$977$	−23.6226	−	28.1523i	−0.755753	−	0.900672i	−0.997572	+	0.0696497i	$0.977812\pi$
$978$		0			0
$979$	12.8033	+	2.25756i	0.409195	+	0.0721521i
$980$	−2.24549	−	0.515758i	−0.0717295	−	0.0164753i
$981$		0			0
$982$	−5.52879	+	9.57614i	−0.176431	+	0.305587i
$983$	−1.70439	+	9.66609i	−0.0543617	+	0.308300i	−0.999849	−	0.0173575i	$-0.994475\pi$
$983$	−1.70439	+	9.66609i	−0.0543617	+	0.308300i	0.945488	+	0.325658i	$0.105586\pi$
$984$		0			0
$985$	0.836600	−	2.29854i	0.0266563	−	0.0732375i
$986$	−10.8056	+	9.06697i	−0.344120	+	0.288751i
$987$		0			0
$988$	−37.3913	+	13.6093i	−1.18957	+	0.432970i
$989$	−1.60168	−	0.924730i	−0.0509305	−	0.0294047i
$990$		0			0
$991$	15.3744	+	26.6292i	0.488384	+	0.845905i	0.999911	−	0.0133618i	$-0.00425333\pi$
$991$	15.3744	+	26.6292i	0.488384	+	0.845905i	−0.511527	+	0.859267i	$0.670920\pi$
$992$	5.58487	−	2.03273i	0.177320	−	0.0645392i
$993$		0			0
$994$	−5.72795	−	2.85184i	−0.181680	−	0.0904548i
$995$	−1.24834	+	0.220115i	−0.0395749	+	0.00697812i
$996$		0			0
$997$	−14.3109	−	39.3189i	−0.453231	−	1.24524i	−0.930437	−	0.366451i	$-0.880573\pi$
$997$	−14.3109	−	39.3189i	−0.453231	−	1.24524i	0.477206	−	0.878791i	$-0.341650\pi$
$998$	−7.65940	−	4.42216i	−0.242454	−	0.139981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.521.13		132
3.2	odd	2		189.2.ba.a.38.10	yes	132
7.5	odd	6		567.2.bd.a.278.10		132
21.5	even	6		189.2.bd.a.173.13	yes	132
27.5	odd	18		567.2.bd.a.206.10		132
27.22	even	9		189.2.bd.a.59.13	yes	132
189.5	even	18	inner	567.2.ba.a.530.13		132
189.103	odd	18		189.2.ba.a.5.10	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.10	✓	132	189.103	odd	18
189.2.ba.a.38.10	yes	132	3.2	odd	2
189.2.bd.a.59.13	yes	132	27.22	even	9
189.2.bd.a.173.13	yes	132	21.5	even	6
567.2.ba.a.521.13		132	1.1	even	1	trivial
567.2.ba.a.530.13		132	189.5	even	18	inner
567.2.bd.a.206.10		132	27.5	odd	18
567.2.bd.a.278.10		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.408566 + 0.0720413i) q^{2} +(-1.71765 - 0.625173i) q^{4} +(-0.0312679 - 0.177329i) q^{5} +(1.82229 + 1.91814i) q^{7} +(-1.37531 - 0.794036i) q^{8} -0.0747032i q^{10} +(-1.56303 - 0.275605i) q^{11} +(3.21910 + 3.83638i) q^{13} +(0.606342 + 0.914967i) q^{14} +(2.29578 + 1.92639i) q^{16} +7.76129 q^{17} -4.34679i q^{19} +(-0.0571540 + 0.324137i) q^{20} +(-0.618747 - 0.225206i) q^{22} +(1.56305 + 1.86277i) q^{23} +(4.66800 - 1.69901i) q^{25} +(1.03884 + 1.79932i) q^{26} +(-1.93089 - 4.43393i) q^{28} +(-2.81590 + 3.35586i) q^{29} +(0.459948 - 1.26370i) q^{31} +(2.84078 + 3.38551i) q^{32} +(3.17100 + 0.559134i) q^{34} +(0.283162 - 0.383121i) q^{35} +(2.09041 - 3.62070i) q^{37} +(0.313148 - 1.77595i) q^{38} +(-0.0978025 + 0.268710i) q^{40} +(-8.48927 + 7.12335i) q^{41} +(-0.714703 + 0.260131i) q^{43} +(2.51244 + 1.45056i) q^{44} +(0.504413 + 0.873669i) q^{46} +(8.67893 - 3.15887i) q^{47} +(-0.358507 + 6.99081i) q^{49} +(2.02959 - 0.357871i) q^{50} +(-3.13089 - 8.60205i) q^{52} +(8.42703 + 4.86535i) q^{53} +0.285788i q^{55} +(-0.983146 - 4.08500i) q^{56} +(-1.39224 + 1.16823i) q^{58} +(-1.51017 + 1.26718i) q^{59} +(-0.916897 - 2.51916i) q^{61} +(0.278957 - 0.483169i) q^{62} +(-2.08017 - 3.60297i) q^{64} +(0.579646 - 0.690796i) q^{65} +(-0.722307 - 4.09641i) q^{67} +(-13.3312 - 4.85215i) q^{68} +(0.143291 - 0.136131i) q^{70} +(-5.04844 + 2.91472i) q^{71} +(-7.42228 + 4.28526i) q^{73} +(1.11491 - 1.32870i) q^{74} +(-2.71749 + 7.46625i) q^{76} +(-2.31965 - 3.50034i) q^{77} +(-0.884454 + 5.01599i) q^{79} +(0.269820 - 0.467342i) q^{80} +(-3.98161 + 2.29878i) q^{82} +(-10.1615 - 8.52653i) q^{83} +(-0.242679 - 1.37630i) q^{85} +(-0.310744 + 0.0547926i) q^{86} +(1.93081 + 1.62014i) q^{88} -8.19131 q^{89} +(-1.49256 + 13.1657i) q^{91} +(-1.52022 - 4.17676i) q^{92} +(3.77349 - 0.665368i) q^{94} +(-0.770811 + 0.135915i) q^{95} +(1.63818 + 4.50085i) q^{97} +(-0.650101 + 2.83038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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