LMFDB - Embedded newform 855.2.bs.c.586.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			586.2
Root			$0.154946 + 0.268374i$ of defining polynomial
Character	$\chi$	$=$	855.586
Dual form			855.2.bs.c.766.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528654 - 0.443593i) q^{2} +(-0.264596 - 1.50060i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(1.16732 + 2.02186i) q^{7} +(-1.21589 + 2.10598i) q^{8} +O(q^{10})$	\(q+(-0.528654 - 0.443593i) q^{2} +(-0.264596 - 1.50060i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(1.16732 + 2.02186i) q^{7} +(-1.21589 + 2.10598i) q^{8} +(0.528654 - 0.443593i) q^{10} +(2.28929 - 3.96516i) q^{11} +(-1.20379 - 0.438145i) q^{13} +(0.279774 - 1.58668i) q^{14} +(-1.28673 + 0.468333i) q^{16} +(0.501495 + 0.420805i) q^{17} +(3.67523 - 2.34365i) q^{19} +1.52375 q^{20} +(-2.96916 + 1.08069i) q^{22} +(0.966645 + 5.48212i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(0.442032 + 0.765622i) q^{26} +(2.72513 - 2.28666i) q^{28} +(3.62387 - 3.04079i) q^{29} +(2.24045 + 3.88057i) q^{31} +(5.45822 + 1.98663i) q^{32} +(-0.0784514 - 0.444920i) q^{34} +(-2.19385 + 0.798495i) q^{35} +7.79252 q^{37} +(-2.98255 - 0.391324i) q^{38} +(-1.86284 - 1.56311i) q^{40} +(8.17440 - 2.97524i) q^{41} +(1.66494 - 9.44233i) q^{43} +(-6.55586 - 2.38614i) q^{44} +(1.92081 - 3.32694i) q^{46} +(-4.84673 + 4.06689i) q^{47} +(0.774723 - 1.34186i) q^{49} +(0.345054 + 0.597652i) q^{50} +(-0.338961 + 1.92235i) q^{52} +(-1.14634 - 6.50124i) q^{53} +(3.50739 + 2.94305i) q^{55} -5.67731 q^{56} -3.26464 q^{58} +(-4.51420 - 3.78786i) q^{59} +(-1.30132 - 7.38016i) q^{61} +(0.536973 - 3.04533i) q^{62} +(-0.634941 - 1.09975i) q^{64} +(0.640526 - 1.10942i) q^{65} +(10.0048 - 8.39500i) q^{67} +(0.498766 - 0.863888i) q^{68} +(1.51399 + 0.551048i) q^{70} +(-0.651454 + 3.69458i) q^{71} +(-7.48353 + 2.72378i) q^{73} +(-4.11955 - 3.45671i) q^{74} +(-4.48934 - 4.89493i) q^{76} +10.6893 q^{77} +(-5.92896 + 2.15796i) q^{79} +(-0.237779 - 1.34851i) q^{80} +(-5.64122 - 2.05324i) q^{82} +(-4.91848 - 8.51905i) q^{83} +(-0.501495 + 0.420805i) q^{85} +(-5.06873 + 4.25317i) q^{86} +(5.56702 + 9.64236i) q^{88} +(11.4439 + 4.16525i) q^{89} +(-0.519346 - 2.94536i) q^{91} +(7.97070 - 2.90110i) q^{92} +4.36629 q^{94} +(1.66985 + 4.02636i) q^{95} +(3.22485 + 2.70597i) q^{97} +(-1.00480 + 0.365717i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.528654	−	0.443593i	−0.373815	−	0.313668i	0.436454	−	0.899727i	$-0.356234\pi$
$2$	−0.528654	−	0.443593i	−0.373815	−	0.313668i	−0.810268	+	0.586059i	$0.800679\pi$
$3$		0			0
$3$		0			0
$4$	−0.264596	−	1.50060i	−0.132298	−	0.750300i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$		0			0
$7$	1.16732	+	2.02186i	0.441206	+	0.764191i	0.997779	−	0.0666074i	$-0.0212175\pi$
$7$	1.16732	+	2.02186i	0.441206	+	0.764191i	−0.556573	+	0.830798i	$0.687884\pi$
$8$	−1.21589	+	2.10598i	−0.429880	+	0.744575i
$9$		0			0
$10$	0.528654	−	0.443593i	0.167175	−	0.140277i
$11$	2.28929	−	3.96516i	0.690246	−	1.19554i	−0.281511	−	0.959558i	$-0.590836\pi$
$11$	2.28929	−	3.96516i	0.690246	−	1.19554i	0.971757	−	0.235983i	$-0.0758310\pi$
$12$		0			0
$13$	−1.20379	−	0.438145i	−0.333872	−	0.121520i	0.169644	−	0.985505i	$-0.445738\pi$
$13$	−1.20379	−	0.438145i	−0.333872	−	0.121520i	−0.503516	+	0.863986i	$0.667961\pi$
$14$	0.279774	−	1.58668i	0.0747729	−	0.424058i
$15$		0			0
$16$	−1.28673	+	0.468333i	−0.321683	+	0.117083i
$17$	0.501495	+	0.420805i	0.121631	+	0.102060i	0.701574	−	0.712597i	$-0.252481\pi$
$17$	0.501495	+	0.420805i	0.121631	+	0.102060i	−0.579944	+	0.814657i	$0.696925\pi$
$18$		0			0
$19$	3.67523	−	2.34365i	0.843155	−	0.537671i
$19$	3.67523	−	2.34365i	0.843155	−	0.537671i
$20$	1.52375			0.340721
$21$		0			0
$22$	−2.96916	+	1.08069i	−0.633027	+	0.230403i
$23$	0.966645	+	5.48212i	0.201559	+	1.14310i	0.902763	+	0.430139i	$0.141535\pi$
$23$	0.966645	+	5.48212i	0.201559	+	1.14310i	−0.701203	+	0.712961i	$0.747353\pi$
$24$		0			0
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	0.442032	+	0.765622i	0.0866897	+	0.150151i
$27$		0			0
$28$	2.72513	−	2.28666i	0.515002	−	0.432138i
$29$	3.62387	−	3.04079i	0.672935	−	0.564660i	−0.240997	−	0.970526i	$-0.577474\pi$
$29$	3.62387	−	3.04079i	0.672935	−	0.564660i	0.913933	+	0.405866i	$0.133030\pi$
$30$		0			0
$31$	2.24045	+	3.88057i	0.402396	+	0.696971i	0.994015	−	0.109248i	$-0.0348441\pi$
$31$	2.24045	+	3.88057i	0.402396	+	0.696971i	−0.591618	+	0.806218i	$0.701511\pi$
$32$	5.45822	+	1.98663i	0.964886	+	0.351190i
$33$		0			0
$34$	−0.0784514	−	0.444920i	−0.0134543	−	0.0763032i
$35$	−2.19385	+	0.798495i	−0.370828	+	0.134970i
$36$		0			0
$37$	7.79252			1.28108			0.640541	−	0.767924i	$-0.278710\pi$
$37$	7.79252			1.28108			0.640541	+	0.767924i	$0.278710\pi$
$38$	−2.98255	−	0.391324i	−0.483834	−	0.0634812i
$39$		0			0
$40$	−1.86284	−	1.56311i	−0.294542	−	0.247150i
$41$	8.17440	−	2.97524i	1.27663	−	0.464654i	0.387311	−	0.921949i	$-0.373404\pi$
$41$	8.17440	−	2.97524i	1.27663	−	0.464654i	0.889315	+	0.457295i	$0.151182\pi$
$42$		0			0
$43$	1.66494	−	9.44233i	0.253901	−	1.43994i	−0.544979	−	0.838450i	$-0.683462\pi$
$43$	1.66494	−	9.44233i	0.253901	−	1.43994i	0.798879	−	0.601491i	$-0.205427\pi$
$44$	−6.55586	−	2.38614i	−0.988333	−	0.359724i
$45$		0			0
$46$	1.92081	−	3.32694i	0.283208	−	0.490531i
$47$	−4.84673	+	4.06689i	−0.706968	+	0.593217i	−0.923747	−	0.383004i	$-0.874889\pi$
$47$	−4.84673	+	4.06689i	−0.706968	+	0.593217i	0.216779	+	0.976221i	$0.430445\pi$
$48$		0			0
$49$	0.774723	−	1.34186i	0.110675	−	0.191694i
$50$	0.345054	+	0.597652i	0.0487981	+	0.0845207i
$51$		0			0
$52$	−0.338961	+	1.92235i	−0.0470055	+	0.266581i
$53$	−1.14634	−	6.50124i	−0.157462	−	0.893013i	−0.956500	−	0.291732i	$-0.905768\pi$
$53$	−1.14634	−	6.50124i	−0.157462	−	0.893013i	0.799038	−	0.601281i	$-0.205343\pi$
$54$		0			0
$55$	3.50739	+	2.94305i	0.472936	+	0.396841i
$56$	−5.67731			−0.758663
$57$		0			0
$58$	−3.26464			−0.428669
$59$	−4.51420	−	3.78786i	−0.587699	−	0.493138i	0.299766	−	0.954013i	$-0.403091\pi$
$59$	−4.51420	−	3.78786i	−0.587699	−	0.493138i	−0.887465	+	0.460875i	$0.847536\pi$
$60$		0			0
$61$	−1.30132	−	7.38016i	−0.166617	−	0.944932i	−0.947381	−	0.320107i	$-0.896281\pi$
$61$	−1.30132	−	7.38016i	−0.166617	−	0.944932i	0.780764	−	0.624826i	$-0.214830\pi$
$62$	0.536973	−	3.04533i	0.0681956	−	0.386757i
$63$		0			0
$64$	−0.634941	−	1.09975i	−0.0793676	−	0.137469i
$65$	0.640526	−	1.10942i	0.0794474	−	0.137607i
$66$		0			0
$67$	10.0048	−	8.39500i	1.22228	−	1.02561i	0.223574	−	0.974687i	$-0.428227\pi$
$67$	10.0048	−	8.39500i	1.22228	−	1.02561i	0.998702	−	0.0509251i	$-0.0162170\pi$
$68$	0.498766	−	0.863888i	0.0604842	−	0.104762i
$69$		0			0
$70$	1.51399	+	0.551048i	0.180957	+	0.0658629i
$71$	−0.651454	+	3.69458i	−0.0773134	+	0.438466i	0.921439	+	0.388524i	$0.127015\pi$
$71$	−0.651454	+	3.69458i	−0.0773134	+	0.438466i	−0.998752	+	0.0499424i	$0.984096\pi$
$72$		0			0
$73$	−7.48353	+	2.72378i	−0.875881	+	0.318795i	−0.740546	−	0.672005i	$-0.765433\pi$
$73$	−7.48353	+	2.72378i	−0.875881	+	0.318795i	−0.135335	+	0.990800i	$0.543211\pi$
$74$	−4.11955	−	3.45671i	−0.478888	−	0.401834i
$75$		0			0
$76$	−4.48934	−	4.89493i	−0.514963	−	0.561486i
$77$	10.6893			1.21816
$78$		0			0
$79$	−5.92896	+	2.15796i	−0.667060	+	0.242790i	−0.653281	−	0.757115i	$-0.726608\pi$
$79$	−5.92896	+	2.15796i	−0.667060	+	0.242790i	−0.0137784	+	0.999905i	$0.504386\pi$
$80$	−0.237779	−	1.34851i	−0.0265845	−	0.150768i
$81$		0			0
$82$	−5.64122	−	2.05324i	−0.622969	−	0.226742i
$83$	−4.91848	−	8.51905i	−0.539873	−	0.935088i	−0.998910	−	0.0466706i	$-0.985139\pi$
$83$	−4.91848	−	8.51905i	−0.539873	−	0.935088i	0.459037	−	0.888417i	$-0.348194\pi$
$84$		0			0
$85$	−0.501495	+	0.420805i	−0.0543948	+	0.0456427i
$86$	−5.06873	+	4.25317i	−0.546575	+	0.458631i
$87$		0			0
$88$	5.56702	+	9.64236i	0.593446	+	1.02788i
$89$	11.4439	+	4.16525i	1.21305	+	0.441516i	0.867762	−	0.496979i	$-0.165558\pi$
$89$	11.4439	+	4.16525i	1.21305	+	0.441516i	0.345292	+	0.938495i	$0.387780\pi$
$90$		0			0
$91$	−0.519346	−	2.94536i	−0.0544423	−	0.308758i
$92$	7.97070	−	2.90110i	0.831003	−	0.302460i
$93$		0			0
$94$	4.36629			0.450348
$95$	1.66985	+	4.02636i	0.171323	+	0.413096i
$96$		0			0
$97$	3.22485	+	2.70597i	0.327434	+	0.274750i	0.791653	−	0.610971i	$-0.209221\pi$
$97$	3.22485	+	2.70597i	0.327434	+	0.274750i	−0.464219	+	0.885720i	$0.653665\pi$
$98$	−1.00480	+	0.365717i	−0.101500	+	0.0369430i
$99$		0			0
$100$	−0.264596	+	1.50060i	−0.0264596	+	0.150060i
$101$	−0.0536285	−	0.0195192i	−0.00533623	−	0.00194223i	0.339351	−	0.940660i	$-0.389793\pi$
$101$	−0.0536285	−	0.0195192i	−0.00533623	−	0.00194223i	−0.344687	+	0.938718i	$0.612015\pi$
$102$		0			0
$103$	−3.62170	+	6.27298i	−0.356857	+	0.618095i	−0.987434	−	0.158032i	$-0.949485\pi$
$103$	−3.62170	+	6.27298i	−0.356857	+	0.618095i	0.630577	+	0.776127i	$0.282818\pi$
$104$	2.38640	−	2.00243i	0.234006	−	0.196354i
$105$		0			0
$106$	−2.27789	+	3.94541i	−0.221248	+	0.383213i
$107$	7.42998	+	12.8691i	0.718283	+	1.24410i	0.961680	+	0.274176i	$0.0884050\pi$
$107$	7.42998	+	12.8691i	0.718283	+	1.24410i	−0.243396	+	0.969927i	$0.578262\pi$
$108$		0			0
$109$	−2.33021	+	13.2153i	−0.223193	+	1.26579i	0.642916	+	0.765937i	$0.277724\pi$
$109$	−2.33021	+	13.2153i	−0.223193	+	1.26579i	−0.866109	+	0.499855i	$0.833387\pi$
$110$	−0.548678	−	3.11171i	−0.0523144	−	0.296690i
$111$		0			0
$112$	−2.44893	−	2.05490i	−0.231403	−	0.194170i
$113$	4.23499			0.398395			0.199197	−	0.979959i	$-0.436167\pi$
$113$	4.23499			0.398395			0.199197	+	0.979959i	$0.436167\pi$
$114$		0			0
$115$	−5.56669			−0.519096
$116$	−5.52187	−	4.63340i	−0.512693	−	0.430200i
$117$		0			0
$118$	0.706178	+	4.00494i	0.0650090	+	0.368684i
$119$	−0.265402	+	1.50517i	−0.0243293	+	0.137978i
$120$		0			0
$121$	−4.98166	−	8.62850i	−0.452879	−	0.784409i
$122$	−2.58584	+	4.47881i	−0.234111	+	0.405492i
$123$		0			0
$124$	5.23037	−	4.38880i	0.469701	−	0.394126i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	17.1659	+	6.24787i	1.52323	+	0.554409i	0.961951	−	0.273221i	$-0.0880892\pi$
$127$	17.1659	+	6.24787i	1.52323	+	0.554409i	0.561274	+	0.827630i	$0.310311\pi$
$128$	1.86510	−	10.5775i	0.164853	−	0.934928i
$129$		0			0
$130$	−0.830749	+	0.302368i	−0.0728615	+	0.0265194i
$131$	−6.43888	−	5.40286i	−0.562568	−	0.472050i	0.316602	−	0.948558i	$-0.397458\pi$
$131$	−6.43888	−	5.40286i	−0.562568	−	0.472050i	−0.879170	+	0.476508i	$0.841902\pi$
$132$		0			0
$133$	9.02871	+	4.69500i	0.782888	+	0.407108i
$134$	−9.01302			−0.778607
$135$		0			0
$136$	−1.49596	+	0.544487i	−0.128278	+	0.0466894i
$137$	2.05932	+	11.6790i	0.175940	+	0.997804i	0.937054	+	0.349186i	$0.113542\pi$
$137$	2.05932	+	11.6790i	0.175940	+	0.997804i	−0.761114	+	0.648618i	$0.775347\pi$
$138$		0			0
$139$	−0.0351557	−	0.0127956i	−0.00298187	−	0.00108531i	0.340529	−	0.940234i	$-0.389394\pi$
$139$	−0.0351557	−	0.0127956i	−0.00298187	−	0.00108531i	−0.343511	+	0.939149i	$0.611616\pi$
$140$	1.77871	+	3.08081i	0.150328	+	0.260376i
$141$		0			0
$142$	1.98329	−	1.66417i	0.166434	−	0.139654i
$143$	−4.49315	+	3.77020i	−0.375736	+	0.315280i
$144$		0			0
$145$	2.36531	+	4.09684i	0.196428	+	0.340224i
$146$	5.16445	+	1.87971i	0.427413	+	0.155566i
$147$		0			0
$148$	−2.06187	−	11.6935i	−0.169485	−	0.961197i
$149$	−9.11593	+	3.31793i	−0.746806	+	0.271815i	−0.687261	−	0.726410i	$-0.741187\pi$
$149$	−9.11593	+	3.31793i	−0.746806	+	0.271815i	−0.0595451	+	0.998226i	$0.518965\pi$
$150$		0			0
$151$	4.60766			0.374966			0.187483	−	0.982268i	$-0.439967\pi$
$151$	4.60766			0.374966			0.187483	+	0.982268i	$0.439967\pi$
$152$	0.467022	+	10.5895i	0.0378805	+	0.858926i
$153$		0			0
$154$	−5.65096	−	4.74172i	−0.455367	−	0.382098i
$155$	−4.21066	+	1.53256i	−0.338209	+	0.123098i
$156$		0			0
$157$	−3.54300	+	20.0934i	−0.282762	+	1.60362i	0.430409	+	0.902634i	$0.358369\pi$
$157$	−3.54300	+	20.0934i	−0.282762	+	1.60362i	−0.713171	+	0.700990i	$0.752742\pi$
$158$	4.09163	+	1.48923i	0.325512	+	0.118477i
$159$		0			0
$160$	−2.90426	+	5.03032i	−0.229602	+	0.397682i
$161$	−9.95568	+	8.35381i	−0.784618	+	0.658373i
$162$		0			0
$163$	1.89681	−	3.28537i	0.148569	−	0.257330i	−0.782130	−	0.623116i	$-0.785866\pi$
$163$	1.89681	−	3.28537i	0.148569	−	0.257330i	0.930699	+	0.365786i	$0.119200\pi$
$164$	−6.62756	−	11.4793i	−0.517525	−	0.896380i
$165$		0			0
$166$	−1.17882	+	6.68544i	−0.0914944	+	0.518890i
$167$	−2.69126	−	15.2629i	−0.208256	−	1.18108i	−0.892233	−	0.451576i	$-0.850862\pi$
$167$	−2.69126	−	15.2629i	−0.208256	−	1.18108i	0.683977	−	0.729504i	$-0.260249\pi$
$168$		0			0
$169$	−8.70143	−	7.30137i	−0.669341	−	0.561643i
$170$	0.451784			0.0346502
$171$		0			0
$172$	−14.6097			−1.11398
$173$	−12.9585	−	10.8734i	−0.985214	−	0.826693i	−0.000346094	−	1.00000i	$-0.500110\pi$
$173$	−12.9585	−	10.8734i	−0.985214	−	0.826693i	−0.984868	+	0.173307i	$0.944555\pi$
$174$		0			0
$175$	−0.405406	−	2.29917i	−0.0306458	−	0.173801i
$176$	−1.08869	+	6.17425i	−0.0820629	+	0.465402i
$177$		0			0
$178$	−4.20220	−	7.27843i	−0.314968	−	0.545541i
$179$	1.52632	−	2.64366i	0.114082	−	0.197597i	−0.803330	−	0.595534i	$-0.796941\pi$
$179$	1.52632	−	2.64366i	0.114082	−	0.197597i	0.917413	+	0.397937i	$0.130274\pi$
$180$		0			0
$181$	−18.7574	+	15.7394i	−1.39423	+	1.16990i	−0.430636	+	0.902526i	$0.641711\pi$
$181$	−18.7574	+	15.7394i	−1.39423	+	1.16990i	−0.963594	+	0.267371i	$0.913845\pi$
$182$	−1.03199	+	1.78745i	−0.0764960	+	0.132495i
$183$		0			0
$184$	−12.7205	−	4.62989i	−0.937770	−	0.341320i
$185$	−1.35316	+	7.67413i	−0.0994861	+	0.564214i
$186$		0			0
$187$	2.81662	−	1.02517i	0.205972	−	0.0749677i
$188$	7.38520	+	6.19692i	0.538621	+	0.451957i
$189$		0			0
$190$	0.903294	−	2.86929i	0.0655318	−	0.208160i
$191$	1.69095			0.122353			0.0611765	−	0.998127i	$-0.480515\pi$
$191$	1.69095			0.122353			0.0611765	+	0.998127i	$0.480515\pi$
$192$		0			0
$193$	−16.7180	+	6.08486i	−1.20339	+	0.437997i	−0.864406	−	0.502795i	$-0.832305\pi$
$193$	−16.7180	+	6.08486i	−1.20339	+	0.437997i	−0.338983	+	0.940793i	$0.610083\pi$
$194$	−0.504479	−	2.86104i	−0.0362195	−	0.205411i
$195$		0			0
$196$	−2.21858	−	0.807498i	−0.158470	−	0.0576785i
$197$	7.25076	+	12.5587i	0.516595	+	0.894769i	0.999814	+	0.0192697i	$0.00613411\pi$
$197$	7.25076	+	12.5587i	0.516595	+	0.894769i	−0.483219	+	0.875499i	$0.660533\pi$
$198$		0			0
$199$	−9.21831	+	7.73508i	−0.653469	+	0.548325i	−0.908121	−	0.418707i	$-0.862483\pi$
$199$	−9.21831	+	7.73508i	−0.653469	+	0.548325i	0.254652	+	0.967033i	$0.418039\pi$
$200$	1.86284	−	1.56311i	0.131723	−	0.110529i
$201$		0			0
$202$	0.0196923	+	0.0341081i	0.00138555	+	0.00239984i
$203$	10.3783	+	3.77738i	0.728411	+	0.265120i
$204$		0			0
$205$	1.51057	+	8.56685i	0.105503	+	0.598335i
$206$	4.69728	−	1.70967i	0.327275	−	0.119118i
$207$		0			0
$208$	1.75416			0.121629
$209$	−0.879316	−	19.9382i	−0.0608235	−	1.37915i
$210$		0			0
$211$	6.18615	+	5.19079i	0.425872	+	0.357349i	0.830391	−	0.557180i	$-0.188117\pi$
$211$	6.18615	+	5.19079i	0.425872	+	0.357349i	−0.404520	+	0.914529i	$0.632561\pi$
$212$	−9.45244	+	3.44041i	−0.649196	+	0.236288i
$213$		0			0
$214$	1.78076	−	10.0992i	0.121730	−	0.690366i
$215$	9.00976	+	3.27929i	0.614461	+	0.223645i
$216$		0			0
$217$	−5.23064	+	9.05974i	−0.355079	+	0.615015i
$218$	7.09407	−	5.95263i	0.480471	−	0.403163i
$219$		0			0
$220$	3.48830	−	6.04191i	0.235181	−	0.407346i
$221$	−0.419324	−	0.726290i	−0.0282068	−	0.0488556i
$222$		0			0
$223$	2.63587	−	14.9488i	0.176511	−	1.00104i	−0.759874	−	0.650070i	$-0.774739\pi$
$223$	2.63587	−	14.9488i	0.176511	−	1.00104i	0.936385	−	0.350974i	$-0.114149\pi$
$224$	2.35481	+	13.3548i	0.157337	+	0.892304i
$225$		0			0
$226$	−2.23885	−	1.87862i	−0.148926	−	0.124964i
$227$	20.9433			1.39005			0.695026	−	0.718984i	$-0.255393\pi$
$227$	20.9433			1.39005			0.695026	+	0.718984i	$0.255393\pi$
$228$		0			0
$229$	28.1530			1.86040			0.930200	−	0.367054i	$-0.119633\pi$
$229$	28.1530			1.86040			0.930200	+	0.367054i	$0.119633\pi$
$230$	2.94285	+	2.46935i	0.194046	+	0.162824i
$231$		0			0
$232$	1.99761	+	11.3290i	0.131150	+	0.743787i
$233$	−3.62673	+	20.5682i	−0.237595	+	1.34747i	0.599483	+	0.800387i	$0.295373\pi$
$233$	−3.62673	+	20.5682i	−0.237595	+	1.34747i	−0.837079	+	0.547083i	$0.815738\pi$
$234$		0			0
$235$	−3.16348	−	5.47930i	−0.206363	−	0.357430i
$236$	−4.48963	+	7.77626i	−0.292250	+	0.506192i
$237$		0			0
$238$	0.807988	−	0.677982i	0.0523741	−	0.0439471i
$239$	−0.619806	+	1.07353i	−0.0400919	+	0.0694412i	−0.885375	−	0.464877i	$-0.846098\pi$
$239$	−0.619806	+	1.07353i	−0.0400919	+	0.0694412i	0.845283	+	0.534319i	$0.179432\pi$
$240$		0			0
$241$	−1.10023	−	0.400452i	−0.0708723	−	0.0257954i	0.306341	−	0.951922i	$-0.400895\pi$
$241$	−1.10023	−	0.400452i	−0.0708723	−	0.0257954i	−0.377213	+	0.926127i	$0.623118\pi$
$242$	−1.19397	+	6.77132i	−0.0767511	+	0.435277i
$243$		0			0
$244$	−10.7303	+	3.90553i	−0.686940	+	0.250026i
$245$	1.18694	+	0.995964i	0.0758311	+	0.0636298i
$246$		0			0
$247$	−5.45108	+	1.21099i	−0.346844	+	0.0770537i
$248$	−10.8965			−0.691929
$249$		0			0
$250$	−0.648490	+	0.236031i	−0.0410141	+	0.0149279i
$251$	−3.81928	−	21.6602i	−0.241071	−	1.36718i	−0.829444	−	0.558590i	$-0.811343\pi$
$251$	−3.81928	−	21.6602i	−0.241071	−	1.36718i	0.588373	−	0.808589i	$-0.299769\pi$
$252$		0			0
$253$	23.9504	+	8.71723i	1.50575	+	0.548048i
$254$	−6.30330	−	10.9176i	−0.395504	−	0.685033i
$255$		0			0
$256$	−7.62367	+	6.39702i	−0.476480	+	0.399814i
$257$	−12.7665	+	10.7123i	−0.796350	+	0.668217i	−0.947308	−	0.320323i	$-0.896208\pi$
$257$	−12.7665	+	10.7123i	−0.796350	+	0.668217i	0.150959	+	0.988540i	$0.451764\pi$
$258$		0			0
$259$	9.09637	+	15.7554i	0.565221	+	0.978992i
$260$	−1.83428	−	0.667624i	−0.113757	−	0.0414043i
$261$		0			0
$262$	1.00727	+	5.71249i	0.0622291	+	0.352919i
$263$	−4.06239	+	1.47859i	−0.250498	+	0.0911737i	−0.464217	−	0.885721i	$-0.653664\pi$
$263$	−4.06239	+	1.47859i	−0.250498	+	0.0911737i	0.213720	+	0.976895i	$0.431442\pi$
$264$		0			0
$265$	6.60153			0.405529
$266$	−2.69039	−	6.48710i	−0.164959	−	0.397750i
$267$		0			0
$268$	−15.2448	−	12.7919i	−0.931222	−	0.781388i
$269$	−22.8324	+	8.31030i	−1.39211	+	0.506688i	−0.925828	−	0.377946i	$-0.876631\pi$
$269$	−22.8324	+	8.31030i	−1.39211	+	0.506688i	−0.466286	+	0.884634i	$0.654408\pi$
$270$		0			0
$271$	−1.42694	+	8.09260i	−0.0866807	+	0.491591i	0.910301	+	0.413948i	$0.135850\pi$
$271$	−1.42694	+	8.09260i	−0.0866807	+	0.491591i	−0.996981	+	0.0776427i	$0.975261\pi$
$272$	−0.842368	−	0.306597i	−0.0510760	−	0.0185902i
$273$		0			0
$274$	4.09206	−	7.08765i	0.247210	−	0.428181i
$275$	−3.50739	+	2.94305i	−0.211504	+	0.177473i
$276$		0			0
$277$	−9.66010	+	16.7318i	−0.580419	+	1.00532i	0.415011	+	0.909817i	$0.363778\pi$
$277$	−9.66010	+	16.7318i	−0.580419	+	1.00532i	−0.995430	+	0.0954986i	$0.969555\pi$
$278$	0.0129091	+	0.0223593i	0.000774239	+	0.00134102i
$279$		0			0
$280$	0.985855	−	5.59106i	0.0589161	−	0.334130i
$281$	−1.37960	−	7.82413i	−0.0823003	−	0.466748i	−0.997907	−	0.0646721i	$-0.979400\pi$
$281$	−1.37960	−	7.82413i	−0.0823003	−	0.466748i	0.915606	−	0.402076i	$-0.131711\pi$
$282$		0			0
$283$	−12.9560	−	10.8714i	−0.770154	−	0.646236i	0.170594	−	0.985341i	$-0.445431\pi$
$283$	−12.9560	−	10.8714i	−0.770154	−	0.646236i	−0.940748	+	0.339105i	$0.889876\pi$
$284$	5.71646			0.339210
$285$		0			0
$286$	4.04775			0.239349
$287$	15.5577	+	13.0544i	0.918339	+	0.770578i
$288$		0			0
$289$	−2.87760	−	16.3197i	−0.169270	−	0.959981i
$290$	0.566900	−	3.21505i	0.0332895	−	0.188794i
$291$		0			0
$292$	6.06742	+	10.5091i	0.355069	+	0.614998i
$293$	−2.41533	+	4.18348i	−0.141105	+	0.244402i	−0.927913	−	0.372797i	$-0.878399\pi$
$293$	−2.41533	+	4.18348i	−0.141105	+	0.244402i	0.786808	+	0.617198i	$0.211732\pi$
$294$		0			0
$295$	4.51420	−	3.78786i	0.262827	−	0.220538i
$296$	−9.47481	+	16.4109i	−0.550712	+	0.953861i
$297$		0			0
$298$	6.29099	+	2.28973i	0.364427	+	0.132641i
$299$	1.23832	−	7.02287i	0.0716140	−	0.406143i
$300$		0			0
$301$	21.0346	−	7.65596i	1.21241	−	0.441282i
$302$	−2.43586	−	2.04393i	−0.140168	−	0.117615i
$303$		0			0
$304$	−3.63143	+	4.73689i	−0.208277	+	0.271679i
$305$	7.49401			0.429106
$306$		0			0
$307$	5.78211	−	2.10452i	0.330003	−	0.120111i	−0.171705	−	0.985148i	$-0.554928\pi$
$307$	5.78211	−	2.10452i	0.330003	−	0.120111i	0.501708	+	0.865037i	$0.332705\pi$
$308$	−2.82836	−	16.0404i	−0.161161	−	0.913988i
$309$		0			0
$310$	2.90582	+	1.05763i	0.165039	+	0.0600694i
$311$	1.43076	+	2.47815i	0.0811311	+	0.140523i	0.903736	−	0.428090i	$-0.140813\pi$
$311$	1.43076	+	2.47815i	0.0811311	+	0.140523i	−0.822605	+	0.568613i	$0.807480\pi$
$312$		0			0
$313$	−4.96486	+	4.16601i	−0.280630	+	0.235477i	−0.772228	−	0.635346i	$-0.780858\pi$
$313$	−4.96486	+	4.16601i	−0.280630	+	0.235477i	0.491597	+	0.870823i	$0.336413\pi$
$314$	10.7863	−	9.05078i	0.608706	−	0.510765i
$315$		0			0
$316$	4.80702	+	8.32601i	0.270416	+	0.468375i
$317$	−29.1565	−	10.6121i	−1.63759	−	0.596034i	−0.650975	−	0.759099i	$-0.725640\pi$
$317$	−29.1565	−	10.6121i	−1.63759	−	0.596034i	−0.986615	+	0.163065i	$0.947862\pi$
$318$		0			0
$319$	−3.76113	−	21.3304i	−0.210583	−	1.19428i
$320$	1.19330	−	0.434325i	0.0667074	−	0.0242795i
$321$		0			0
$322$	8.96881			0.499812
$323$	2.82933	+	0.371221i	0.157428	+	0.0206553i
$324$		0			0
$325$	0.981342	+	0.823444i	0.0544351	+	0.0456764i
$326$	−2.46012	+	0.895411i	−0.136254	+	0.0495922i
$327$		0			0
$328$	−3.67335	+	20.8326i	−0.202827	+	1.15029i
$329$	−13.8804	−	5.05204i	−0.765249	−	0.278528i
$330$		0			0
$331$	−8.80238	+	15.2462i	−0.483823	+	0.838005i	−0.999827	−	0.0185804i	$-0.994085\pi$
$331$	−8.80238	+	15.2462i	−0.483823	+	0.838005i	0.516005	+	0.856586i	$0.327419\pi$
$332$	−11.4823	+	9.63478i	−0.630172	+	0.528777i
$333$		0			0
$334$	−5.34778	+	9.26262i	−0.292617	+	0.506828i
$335$	6.53015	+	11.3105i	0.356780	+	0.617961i
$336$		0			0
$337$	4.80448	−	27.2476i	0.261717	−	1.48427i	−0.516507	−	0.856283i	$-0.672768\pi$
$337$	4.80448	−	27.2476i	0.261717	−	1.48427i	0.778224	−	0.627987i	$-0.216121\pi$
$338$	1.36121	+	7.71979i	0.0740399	+	0.419901i
$339$		0			0
$340$	0.764154	+	0.641201i	0.0414420	+	0.0347740i
$341$	20.5161			1.11101
$342$		0			0
$343$	19.9599			1.07773
$344$	17.8609	+	14.9871i	0.962997	+	0.808050i
$345$		0			0
$346$	2.02716	+	11.4966i	0.108981	+	0.618060i
$347$	3.69547	−	20.9581i	0.198383	−	1.12509i	−0.709134	−	0.705074i	$-0.750914\pi$
$347$	3.69547	−	20.9581i	0.198383	−	1.12509i	0.907517	−	0.420014i	$-0.137975\pi$
$348$		0			0
$349$	−9.82495	−	17.0173i	−0.525917	−	0.910916i	−0.999544	−	0.0301899i	$-0.990389\pi$
$349$	−9.82495	−	17.0173i	−0.525917	−	0.910916i	0.473627	−	0.880726i	$-0.342945\pi$
$350$	−0.805579	+	1.39530i	−0.0430600	+	0.0745821i
$351$		0			0
$352$	20.3727	−	17.0948i	1.08587	−	0.911153i
$353$	3.23301	−	5.59974i	0.172076	−	0.298044i	−0.767070	−	0.641564i	$-0.778286\pi$
$353$	3.23301	−	5.59974i	0.172076	−	0.298044i	0.939145	+	0.343520i	$0.111619\pi$
$354$		0			0
$355$	−3.52533	−	1.28311i	−0.187105	−	0.0681007i
$356$	3.22236	−	18.2749i	0.170784	−	0.968567i
$357$		0			0
$358$	−1.97960	+	0.720517i	−0.104625	+	0.0380805i
$359$	14.8577	+	12.4671i	0.784159	+	0.657988i	0.944292	−	0.329108i	$-0.106748\pi$
$359$	14.8577	+	12.4671i	0.784159	+	0.657988i	−0.160133	+	0.987095i	$0.551192\pi$
$360$		0			0
$361$	8.01458	−	17.2269i	0.421820	−	0.906680i
$362$	16.8981			0.888143
$363$		0			0
$364$	−4.28239	+	1.55866i	−0.224458	+	0.0816961i
$365$	−1.38290	−	7.84282i	−0.0723843	−	0.410512i
$366$		0			0
$367$	−28.2213	−	10.2717i	−1.47314	−	0.536179i	−0.524189	−	0.851602i	$-0.675632\pi$
$367$	−28.2213	−	10.2717i	−1.47314	−	0.536179i	−0.948951	+	0.315423i	$0.897854\pi$
$368$	−3.81127	−	6.60131i	−0.198676	−	0.344117i
$369$		0			0
$370$	4.11955	−	3.45671i	0.214165	−	0.179706i
$371$	11.8064	−	9.90678i	0.612960	−	0.514334i
$372$		0			0
$373$	2.47898	+	4.29372i	0.128357	+	0.222320i	0.923040	−	0.384704i	$-0.125696\pi$
$373$	2.47898	+	4.29372i	0.128357	+	0.222320i	−0.794683	+	0.607024i	$0.792363\pi$
$374$	−1.94378	−	0.707477i	−0.100510	−	0.0365828i
$375$		0			0
$376$	−2.67170	−	15.1520i	−0.137782	−	0.781403i
$377$	−5.69470	+	2.07270i	−0.293292	+	0.106749i
$378$		0			0
$379$	−4.05839			−0.208465			−0.104233	−	0.994553i	$-0.533239\pi$
$379$	−4.05839			−0.208465			−0.104233	+	0.994553i	$0.533239\pi$
$380$	5.60013	−	3.57114i	0.287280	−	0.183196i
$381$		0			0
$382$	−0.893928	−	0.750095i	−0.0457374	−	0.0383782i
$383$	−2.26407	+	0.824054i	−0.115689	+	0.0421072i	−0.399216	−	0.916857i	$-0.630718\pi$
$383$	−2.26407	+	0.824054i	−0.115689	+	0.0421072i	0.283527	+	0.958964i	$0.408495\pi$
$384$		0			0
$385$	−1.85618	+	10.5269i	−0.0945998	+	0.536502i
$386$	11.5372	+	4.19921i	0.587230	+	0.213734i
$387$		0			0
$388$	3.20730	−	5.55520i	0.162826	−	0.282023i
$389$	4.57546	−	3.83927i	0.231985	−	0.194659i	−0.519384	−	0.854541i	$-0.673838\pi$
$389$	4.57546	−	3.83927i	0.231985	−	0.194659i	0.751369	+	0.659883i	$0.229394\pi$
$390$		0			0
$391$	−1.82213	+	3.15602i	−0.0921492	+	0.159607i
$392$	1.88395	+	3.26309i	0.0951537	+	0.164811i
$393$		0			0
$394$	1.73781	−	9.85559i	0.0875494	−	0.496517i
$395$	−1.09563	−	6.21361i	−0.0551270	−	0.312641i
$396$		0			0
$397$	−21.7311	−	18.2346i	−1.09065	−	0.915168i	−0.0938929	−	0.995582i	$-0.529931\pi$
$397$	−21.7311	−	18.2346i	−1.09065	−	0.915168i	−0.996762	+	0.0804146i	$0.974376\pi$
$398$	8.30453			0.416268
$399$		0			0
$400$	1.36931			0.0684657
$401$	24.0310	+	20.1644i	1.20005	+	1.00696i	0.999629	+	0.0272515i	$0.00867549\pi$
$401$	24.0310	+	20.1644i	1.20005	+	1.00696i	0.200421	+	0.979710i	$0.435769\pi$
$402$		0			0
$403$	−0.996785	−	5.65305i	−0.0496534	−	0.281598i
$404$	−0.0151006	+	0.0856396i	−0.000751282	+	0.00426073i
$405$		0			0
$406$	−3.81089	−	6.60065i	−0.189131	−	0.327585i
$407$	17.8393	−	30.8986i	0.884262	−	1.53159i
$408$		0			0
$409$	−22.8163	+	19.1452i	−1.12820	+	0.946669i	−0.998989	−	0.0449489i	$-0.985687\pi$
$409$	−22.8163	+	19.1452i	−1.12820	+	0.946669i	−0.129207	+	0.991618i	$0.541243\pi$
$410$	3.00163	−	5.19898i	0.148240	−	0.256759i
$411$		0			0
$412$	10.3715	+	3.77493i	0.510968	+	0.185977i
$413$	2.38901	−	13.5487i	0.117555	−	0.666689i
$414$		0			0
$415$	9.24371	−	3.36444i	0.453756	−	0.165154i
$416$	−5.70014	−	4.78299i	−0.279472	−	0.234505i
$417$		0			0
$418$	−8.37958	+	10.9304i	−0.409859	+	0.534626i
$419$	−35.7692			−1.74744			−0.873719	−	0.486431i	$-0.838298\pi$
$419$	−35.7692			−1.74744			−0.873719	+	0.486431i	$0.838298\pi$
$420$		0			0
$421$	35.7451	−	13.0102i	1.74211	−	0.634077i	0.742741	−	0.669578i	$-0.233525\pi$
$421$	35.7451	−	13.0102i	1.74211	−	0.634077i	0.999370	+	0.0355017i	$0.0113029\pi$
$422$	−0.967730	−	5.48827i	−0.0471083	−	0.267165i
$423$		0			0
$424$	15.0853	+	5.49059i	0.732605	+	0.266646i
$425$	−0.327328	−	0.566949i	−0.0158777	−	0.0275010i
$426$		0			0
$427$	13.4026	−	11.2461i	0.648597	−	0.544237i
$428$	17.3454	−	14.5545i	0.838423	−	0.703521i
$429$		0			0
$430$	−3.30838	−	5.73028i	−0.159544	−	0.276339i
$431$	−7.88210	−	2.86885i	−0.379667	−	0.138188i	0.145135	−	0.989412i	$-0.453638\pi$
$431$	−7.88210	−	2.86885i	−0.379667	−	0.138188i	−0.524802	+	0.851224i	$0.675861\pi$
$432$		0			0
$433$	4.03137	+	22.8630i	0.193735	+	1.09873i	0.914209	+	0.405244i	$0.132813\pi$
$433$	4.03137	+	22.8630i	0.193735	+	1.09873i	−0.720474	+	0.693482i	$0.756076\pi$
$434$	6.78404	−	2.46919i	0.325644	−	0.118525i
$435$		0			0
$436$	20.4474			0.979252
$437$	16.4008	+	17.8825i	0.784558	+	0.855438i
$438$		0			0
$439$	13.5703	+	11.3869i	0.647677	+	0.543465i	0.906365	−	0.422495i	$-0.138846\pi$
$439$	13.5703	+	11.3869i	0.647677	+	0.543465i	−0.258688	+	0.965961i	$0.583290\pi$
$440$	−10.4626	+	3.80807i	−0.498784	+	0.181542i
$441$		0			0
$442$	−0.100500	+	0.569965i	−0.00478031	+	0.0271105i
$443$	1.67598	+	0.610008i	0.0796283	+	0.0289823i	0.381527	−	0.924358i	$-0.375398\pi$
$443$	1.67598	+	0.610008i	0.0796283	+	0.0289823i	−0.301899	+	0.953340i	$0.597620\pi$
$444$		0			0
$445$	−6.08919	+	10.5468i	−0.288655	+	0.499966i
$446$	−8.02464	+	6.73348i	−0.379978	+	0.318839i
$447$		0			0
$448$	1.48236	−	2.56752i	0.0700349	−	0.121304i
$449$	4.42844	+	7.67028i	0.208991	+	0.361983i	0.951397	−	0.307967i	$-0.0996488\pi$
$449$	4.42844	+	7.67028i	0.208991	+	0.361983i	−0.742406	+	0.669950i	$0.766315\pi$
$450$		0			0
$451$	6.91624	−	39.2240i	0.325673	−	1.84698i
$452$	−1.12056	−	6.35504i	−0.0527069	−	0.298916i
$453$		0			0
$454$	−11.0717	−	9.29029i	−0.519622	−	0.436015i
$455$	2.99080			0.140211
$456$		0			0
$457$	3.00530			0.140582			0.0702909	−	0.997527i	$-0.477607\pi$
$457$	3.00530			0.140582			0.0702909	+	0.997527i	$0.477607\pi$
$458$	−14.8832	−	12.4885i	−0.695445	−	0.583548i
$459$		0			0
$460$	1.47293	+	8.35337i	0.0686755	+	0.389478i
$461$	−3.49320	+	19.8109i	−0.162695	+	0.922686i	0.788715	+	0.614759i	$0.210747\pi$
$461$	−3.49320	+	19.8109i	−0.162695	+	0.922686i	−0.951410	+	0.307928i	$0.900365\pi$
$462$		0			0
$463$	−4.07718	−	7.06188i	−0.189483	−	0.328194i	0.755595	−	0.655039i	$-0.227348\pi$
$463$	−4.07718	−	7.06188i	−0.189483	−	0.328194i	−0.945078	+	0.326845i	$0.894014\pi$
$464$	−3.23885	+	5.60986i	−0.150360	+	0.260431i
$465$		0			0
$466$	11.0412	−	9.26468i	0.511475	−	0.429178i
$467$	−3.07873	+	5.33252i	−0.142467	+	0.246759i	−0.928425	−	0.371520i	$-0.878837\pi$
$467$	−3.07873	+	5.33252i	−0.142467	+	0.246759i	0.785958	+	0.618280i	$0.212170\pi$
$468$		0			0
$469$	28.6523	+	10.4286i	1.32304	+	0.481547i
$470$	−0.758198	+	4.29995i	−0.0349731	+	0.198342i
$471$		0			0
$472$	13.4659	−	4.90118i	0.619818	−	0.225595i
$473$	−33.6288	−	28.2179i	−1.54625	−	1.29746i
$474$		0			0
$475$	−4.25516	+	0.945312i	−0.195240	+	0.0433739i
$476$	2.32888			0.106744
$477$		0			0
$478$	0.803876	−	0.292587i	0.0367684	−	0.0133826i
$479$	−5.91976	−	33.5726i	−0.270481	−	1.53397i	−0.752960	−	0.658066i	$-0.771375\pi$
$479$	−5.91976	−	33.5726i	−0.270481	−	1.53397i	0.482479	−	0.875907i	$-0.339736\pi$
$480$		0			0
$481$	−9.38059	−	3.41426i	−0.427718	−	0.155677i
$482$	0.404005	+	0.699757i	0.0184019	+	0.0318731i
$483$		0			0
$484$	−11.6298	+	9.75856i	−0.528627	+	0.443571i
$485$	−3.22485	+	2.70597i	−0.146433	+	0.122872i
$486$		0			0
$487$	−14.2860	−	24.7441i	−0.647360	−	1.12126i	−0.983751	−	0.179538i	$-0.942540\pi$
$487$	−14.2860	−	24.7441i	−0.647360	−	1.12126i	0.336391	−	0.941723i	$-0.390794\pi$
$488$	17.1247	+	6.23288i	0.775198	+	0.282149i
$489$		0			0
$490$	−0.185680	−	1.05304i	−0.00838815	−	0.0475715i
$491$	−4.92500	+	1.79255i	−0.222262	+	0.0808968i	−0.450751	−	0.892650i	$-0.648844\pi$
$491$	−4.92500	+	1.79255i	−0.222262	+	0.0808968i	0.228489	+	0.973547i	$0.426622\pi$
$492$		0			0
$493$	3.09693			0.139479
$494$	3.41892	+	1.77787i	0.153825	+	0.0799899i
$495$		0			0
$496$	−4.70026	−	3.94398i	−0.211048	−	0.177090i
$497$	−8.23038	+	2.99561i	−0.369183	+	0.134372i
$498$		0			0
$499$	6.57832	−	37.3075i	0.294486	−	1.67011i	−0.374798	−	0.927107i	$-0.622288\pi$
$499$	6.57832	−	37.3075i	0.294486	−	1.67011i	0.669284	−	0.743007i	$-0.266601\pi$
$500$	−1.43186	−	0.521153i	−0.0640346	−	0.0233067i
$501$		0			0
$502$	−7.58924	+	13.1450i	−0.338725	+	0.586688i
$503$	−11.4325	+	9.59297i	−0.509748	+	0.427729i	−0.861040	−	0.508536i	$-0.830187\pi$
$503$	−11.4325	+	9.59297i	−0.509748	+	0.427729i	0.351292	+	0.936266i	$0.385742\pi$
$504$		0			0
$505$	0.0285351	−	0.0494243i	0.00126980	−	0.00219935i
$506$	−8.79457	−	15.2326i	−0.390966	−	0.677173i
$507$		0			0
$508$	4.83353	−	27.4123i	0.214453	−	1.21622i
$509$	2.27541	+	12.9045i	0.100856	+	0.571982i	0.992795	+	0.119826i	$0.0382338\pi$
$509$	2.27541	+	12.9045i	0.100856	+	0.571982i	−0.891939	+	0.452156i	$0.850655\pi$
$510$		0			0
$511$	−14.2428	−	11.9511i	−0.630064	−	0.528686i
$512$	−14.6134			−0.645827
$513$		0			0
$514$	11.5010			0.507285
$515$	−5.54877	−	4.65597i	−0.244508	−	0.205167i
$516$		0			0
$517$	5.03031	+	28.5283i	0.221233	+	1.25467i
$518$	2.18015	−	12.3642i	0.0957902	−	0.543253i
$519$		0			0
$520$	1.55761	+	2.69786i	0.0683058	+	0.118309i
$521$	2.05831	−	3.56509i	0.0901761	−	0.156190i	−0.817409	−	0.576058i	$-0.804590\pi$
$521$	2.05831	−	3.56509i	0.0901761	−	0.156190i	0.907585	+	0.419868i	$0.137924\pi$
$522$		0			0
$523$	−6.37125	+	5.34611i	−0.278595	+	0.233769i	−0.771369	−	0.636388i	$-0.780428\pi$
$523$	−6.37125	+	5.34611i	−0.278595	+	0.233769i	0.492774	+	0.870158i	$0.335983\pi$
$524$	−6.40384	+	11.0918i	−0.279753	+	0.484546i
$525$		0			0
$526$	2.80349	+	1.02039i	0.122238	+	0.0444910i
$527$	−0.509387	+	2.88888i	−0.0221892	+	0.125841i
$528$		0			0
$529$	−7.50627	+	2.73206i	−0.326360	+	0.118785i
$530$	−3.48992	−	2.92839i	−0.151593	−	0.127201i
$531$		0			0
$532$	4.65635	−	14.7908i	0.201878	−	0.641261i
$533$	−11.1439			−0.482695
$534$		0			0
$535$	−13.9638	+	5.08240i	−0.603707	+	0.219731i
$536$	5.51500	+	31.2771i	0.238212	+	1.35097i
$537$		0			0
$538$	15.7568	+	5.73501i	0.679325	+	0.247254i
$539$	−3.54712	−	6.14380i	−0.152785	−	0.264632i
$540$		0			0
$541$	−30.7437	+	25.7970i	−1.32177	+	1.10910i	−0.335848	+	0.941916i	$0.609023\pi$
$541$	−30.7437	+	25.7970i	−1.32177	+	1.10910i	−0.985926	+	0.167184i	$0.946533\pi$
$542$	4.34418	−	3.64520i	0.186599	−	0.156575i
$543$		0			0
$544$	1.90129	+	3.29313i	0.0815171	+	0.141192i
$545$	−12.6098	−	4.58961i	−0.540146	−	0.196597i
$546$		0			0
$547$	4.40095	+	24.9590i	0.188171	+	1.06717i	0.921813	+	0.387635i	$0.126708\pi$
$547$	4.40095	+	24.9590i	0.188171	+	1.06717i	−0.733642	+	0.679536i	$0.762181\pi$
$548$	16.9806	−	6.18044i	0.725376	−	0.264015i
$549$		0			0
$550$	3.15971			0.134731
$551$	6.19199	−	19.6687i	0.263787	−	0.837913i
$552$		0			0
$553$	−11.2841	−	9.46848i	−0.479849	−	0.402641i
$554$	12.5290	−	4.56017i	0.532304	−	0.193743i
$555$		0			0
$556$	−0.00989906	+	0.0561403i	−0.000419814	+	0.00238088i
$557$	10.9782	+	3.99573i	0.465160	+	0.169304i	0.563959	−	0.825803i	$-0.309278\pi$
$557$	10.9782	+	3.99573i	0.465160	+	0.169304i	−0.0987986	+	0.995107i	$0.531500\pi$
$558$		0			0
$559$	−6.14135	+	10.6371i	−0.259752	+	0.449903i
$560$	2.44893	−	2.05490i	0.103486	−	0.0868354i
$561$		0			0
$562$	−2.74140	+	4.74824i	−0.115639	+	0.200292i
$563$	8.40055	+	14.5502i	0.354041	+	0.613217i	0.986953	−	0.161007i	$-0.0514741\pi$
$563$	8.40055	+	14.5502i	0.354041	+	0.613217i	−0.632912	+	0.774223i	$0.718141\pi$
$564$		0			0
$565$	−0.735399	+	4.17066i	−0.0309385	+	0.175461i
$566$	2.02677	+	11.4944i	0.0851916	+	0.483145i
$567$		0			0
$568$	−6.98860	−	5.86414i	−0.293235	−	0.246054i
$569$	36.3784			1.52506			0.762530	−	0.646953i	$-0.223957\pi$
$569$	36.3784			1.52506			0.762530	+	0.646953i	$0.223957\pi$
$570$		0			0
$571$	33.6369			1.40766			0.703831	−	0.710368i	$-0.251471\pi$
$571$	33.6369			1.40766			0.703831	+	0.710368i	$0.251471\pi$
$572$	6.84643	+	5.74484i	0.286264	+	0.240204i
$573$		0			0
$574$	−2.43376	−	13.8025i	−0.101583	−	0.576107i
$575$	0.966645	−	5.48212i	0.0403119	−	0.228620i
$576$		0			0
$577$	−13.4247	−	23.2522i	−0.558876	−	0.968002i	−0.997591	−	0.0693753i	$-0.977899\pi$
$577$	−13.4247	−	23.2522i	−0.558876	−	0.968002i	0.438715	−	0.898626i	$-0.355434\pi$
$578$	−5.71804	+	9.90394i	−0.237839	+	0.411950i
$579$		0			0
$580$	5.52187	−	4.63340i	0.229283	−	0.192391i
$581$	11.4829	−	19.8889i	0.476390	−	0.825132i
$582$		0			0
$583$	−28.4028	−	10.3378i	−1.17632	−	0.428146i
$584$	3.36290	−	19.0719i	0.139158	−	0.789202i
$585$		0			0
$586$	3.13264	−	1.14019i	0.129408	−	0.0471007i
$587$	−13.1076	−	10.9986i	−0.541010	−	0.453962i	0.330873	−	0.943675i	$-0.392657\pi$
$587$	−13.1076	−	10.9986i	−0.541010	−	0.453962i	−0.871883	+	0.489714i	$0.837101\pi$
$588$		0			0
$589$	17.3289	+	9.01113i	0.714023	+	0.371297i
$590$	−4.06672			−0.167424
$591$		0			0
$592$	−10.0269	+	3.64949i	−0.412103	+	0.149993i
$593$	7.07542	+	40.1267i	0.290553	+	1.64781i	0.684749	+	0.728779i	$0.259912\pi$
$593$	7.07542	+	40.1267i	0.290553	+	1.64781i	−0.394196	+	0.919026i	$0.628977\pi$
$594$		0			0
$595$	−1.43621	−	0.522739i	−0.0588790	−	0.0214302i
$596$	7.39093	+	12.8015i	0.302744	+	0.524368i
$597$		0			0
$598$	−3.76994	+	3.16336i	−0.154164	+	0.129359i
$599$	−9.21441	+	7.73181i	−0.376490	+	0.315913i	−0.811323	−	0.584598i	$-0.801252\pi$
$599$	−9.21441	+	7.73181i	−0.376490	+	0.315913i	0.434832	+	0.900511i	$0.356808\pi$
$600$		0			0
$601$	6.29815	+	10.9087i	0.256907	+	0.444976i	0.965412	−	0.260730i	$-0.0839632\pi$
$601$	6.29815	+	10.9087i	0.256907	+	0.444976i	−0.708505	+	0.705706i	$0.750630\pi$
$602$	−14.5161	−	5.28344i	−0.591634	−	0.215337i
$603$		0			0
$604$	−1.21917	−	6.91426i	−0.0496073	−	0.281337i
$605$	9.36247	−	3.40766i	0.380638	−	0.138541i
$606$		0			0
$607$	5.16663			0.209707			0.104854	−	0.994488i	$-0.466563\pi$
$607$	5.16663			0.209707			0.104854	+	0.994488i	$0.466563\pi$
$608$	24.7162	−	5.49086i	1.00237	−	0.222684i
$609$		0			0
$610$	−3.96174	−	3.32429i	−0.160406	−	0.134597i
$611$	7.61635	−	2.77213i	0.308125	−	0.112148i
$612$		0			0
$613$	−0.0704640	+	0.399621i	−0.00284601	+	0.0161405i	−0.986198	−	0.165572i	$-0.947053\pi$
$613$	−0.0704640	+	0.399621i	−0.00284601	+	0.0161405i	0.983352	+	0.181713i	$0.0581641\pi$
$614$	−3.99029	−	1.45235i	−0.161035	−	0.0586119i
$615$		0			0
$616$	−12.9970	+	22.5115i	−0.523664	+	0.907013i
$617$	−7.69345	+	6.45557i	−0.309727	+	0.259892i	−0.784379	−	0.620282i	$-0.787018\pi$
$617$	−7.69345	+	6.45557i	−0.309727	+	0.259892i	0.474652	+	0.880173i	$0.342574\pi$
$618$		0			0
$619$	8.16582	−	14.1436i	0.328212	−	0.568480i	−0.653945	−	0.756542i	$-0.726887\pi$
$619$	8.16582	−	14.1436i	0.328212	−	0.568480i	0.982157	+	0.188062i	$0.0602206\pi$
$620$	3.41388	+	5.91301i	0.137105	+	0.237472i
$621$		0			0
$622$	0.342914	−	1.94476i	0.0137496	−	0.0779779i
$623$	4.93719	+	28.0002i	0.197804	+	1.12180i
$624$		0			0
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	4.47271			0.178765
$627$		0			0
$628$	31.0896			1.24061
$629$	3.90791	+	3.27913i	0.155819	+	0.130747i
$630$		0			0
$631$	0.803192	+	4.55513i	0.0319746	+	0.181337i	0.996612	−	0.0822422i	$-0.0262081\pi$
$631$	0.803192	+	4.55513i	0.0319746	+	0.181337i	−0.964638	+	0.263579i	$0.915097\pi$
$632$	2.66431	−	15.1101i	0.105981	−	0.601046i
$633$		0			0
$634$	10.7062	+	18.5437i	0.425199	+	0.736466i
$635$	−9.13377	+	15.8202i	−0.362463	+	0.627804i
$636$		0			0
$637$	−1.52054	+	1.27588i	−0.0602458	+	0.0505523i
$638$	−7.47371	+	12.9448i	−0.295887	+	0.512491i
$639$		0			0
$640$	10.0929	+	3.67353i	0.398958	+	0.145209i
$641$	4.67772	−	26.5287i	0.184759	−	1.04782i	−0.741506	−	0.670946i	$-0.765888\pi$
$641$	4.67772	−	26.5287i	0.184759	−	1.04782i	0.926265	−	0.376873i	$-0.123001\pi$
$642$		0			0
$643$	5.70932	−	2.07802i	0.225154	−	0.0819492i	−0.226980	−	0.973899i	$-0.572885\pi$
$643$	5.70932	−	2.07802i	0.225154	−	0.0819492i	0.452134	+	0.891950i	$0.350663\pi$
$644$	15.1700	+	12.7291i	0.597781	+	0.501598i
$645$		0			0
$646$	−1.33107	−	1.45132i	−0.0523701	−	0.0571014i
$647$	14.8936			0.585529			0.292765	−	0.956185i	$-0.405425\pi$
$647$	14.8936			0.585529			0.292765	+	0.956185i	$0.405425\pi$
$648$		0			0
$649$	−25.3538	+	9.22802i	−0.995223	+	0.362231i
$650$	−0.153516	−	0.870634i	−0.00602140	−	0.0341491i
$651$		0			0
$652$	−5.43191	−	1.97705i	−0.212730	−	0.0774274i
$653$	2.52297	+	4.36991i	0.0987315	+	0.171008i	0.911160	−	0.412053i	$-0.135188\pi$
$653$	2.52297	+	4.36991i	0.0987315	+	0.171008i	−0.812428	+	0.583061i	$0.801855\pi$
$654$		0			0
$655$	6.43888	−	5.40286i	0.251588	−	0.211107i
$656$	−9.12487	+	7.65668i	−0.356266	+	0.298943i
$657$		0			0
$658$	5.09686	+	8.82802i	0.198696	+	0.344152i
$659$	29.7179	+	10.8164i	1.15764	+	0.421348i	0.848256	−	0.529587i	$-0.177653\pi$
$659$	29.7179	+	10.8164i	1.15764	+	0.421348i	0.309389	+	0.950935i	$0.399875\pi$
$660$		0			0
$661$	−1.97045	−	11.1750i	−0.0766418	−	0.434657i	−0.998849	−	0.0479615i	$-0.984728\pi$
$661$	−1.97045	−	11.1750i	−0.0766418	−	0.434657i	0.922207	−	0.386696i	$-0.126384\pi$
$662$	11.4165	−	4.15527i	0.443715	−	0.161499i
$663$		0			0
$664$	23.9212			0.928323
$665$	−6.19149	+	8.07626i	−0.240096	+	0.313184i
$666$		0			0
$667$	20.1729	+	16.9271i	0.781099	+	0.655420i
$668$	−22.1914	+	8.07702i	−0.858612	+	0.312509i
$669$		0			0
$670$	1.56510	−	8.87610i	0.0604649	−	0.342914i
$671$	−32.2426	−	11.7354i	−1.24471	−	0.453038i
$672$		0			0
$673$	−3.76192	+	6.51584i	−0.145011	+	0.251167i	−0.929377	−	0.369131i	$-0.879655\pi$
$673$	−3.76192	+	6.51584i	−0.145011	+	0.251167i	0.784366	+	0.620299i	$0.212989\pi$
$674$	−14.6268	+	12.2733i	−0.563402	+	0.472750i
$675$		0			0
$676$	−8.65407	+	14.9893i	−0.332849	+	0.576511i
$677$	−9.11850	−	15.7937i	−0.350453	−	0.607002i	0.635876	−	0.771791i	$-0.280639\pi$
$677$	−9.11850	−	15.7937i	−0.350453	−	0.607002i	−0.986329	+	0.164789i	$0.947306\pi$
$678$		0			0
$679$	−1.70666	+	9.67893i	−0.0654954	+	0.371443i
$680$	−0.276443	−	1.56779i	−0.0106011	−	0.0601219i
$681$		0			0
$682$	−10.8459	−	9.10081i	−0.415312	−	0.348488i
$683$	−28.9640			−1.10828			−0.554139	−	0.832424i	$-0.686952\pi$
$683$	−28.9640			−1.10828			−0.554139	+	0.832424i	$0.686952\pi$
$684$		0			0
$685$	−11.8592			−0.453115
$686$	−10.5519	−	8.85408i	−0.402873	−	0.338050i
$687$		0			0
$688$	2.27982	+	12.9295i	0.0869174	+	0.492933i
$689$	−1.46852	+	8.32842i	−0.0559463	+	0.317287i
$690$		0			0
$691$	16.3005	+	28.2333i	0.620100	+	1.07404i	0.989467	+	0.144761i	$0.0462413\pi$
$691$	16.3005	+	28.2333i	0.620100	+	1.07404i	−0.369367	+	0.929284i	$0.620425\pi$
$692$	−12.8879	+	22.3226i	−0.489926	+	0.848576i
$693$		0			0
$694$	−11.2505	+	9.44028i	−0.427063	+	0.358348i
$695$	0.0187060	−	0.0323997i	0.000709557	−	0.00122899i
$696$		0			0
$697$	5.35142	+	1.94776i	0.202699	+	0.0737765i
$698$	−2.35477	+	13.3545i	−0.0891292	+	0.505477i
$699$		0			0
$700$	−3.34287	+	1.21671i	−0.126349	+	0.0459872i
$701$	0.701156	+	0.588339i	0.0264823	+	0.0222213i	0.655933	−	0.754819i	$-0.272275\pi$
$701$	0.701156	+	0.588339i	0.0264823	+	0.0222213i	−0.629450	+	0.777041i	$0.716720\pi$
$702$		0			0
$703$	28.6393	−	18.2630i	1.08015	−	0.688801i
$704$	−5.81424			−0.219133
$705$		0			0
$706$	−4.19315	+	1.52618i	−0.157811	+	0.0574386i
$707$	−0.0231366	−	0.131214i	−0.000870142	−	0.00493482i
$708$		0			0
$709$	−15.0820	−	5.48939i	−0.566415	−	0.206158i	0.0429098	−	0.999079i	$-0.486337\pi$
$709$	−15.0820	−	5.48939i	−0.566415	−	0.206158i	−0.609325	+	0.792921i	$0.708559\pi$
$710$	1.29450	+	2.24214i	0.0485816	+	0.0841459i
$711$		0			0
$712$	−22.6864	+	19.0362i	−0.850210	+	0.713411i
$713$	−19.1080	+	16.0335i	−0.715601	+	0.600460i
$714$		0			0
$715$	−2.93269	−	5.07957i	−0.109676	−	0.189965i
$716$	−4.37094	−	1.59089i	−0.163350	−	0.0594544i
$717$		0			0
$718$	−2.32426	−	13.1815i	−0.0867407	−	0.491931i
$719$	−30.9864	+	11.2781i	−1.15560	+	0.420603i	−0.847523	−	0.530759i	$-0.821907\pi$
$719$	−30.9864	+	11.2781i	−1.15560	+	0.420603i	−0.308075	+	0.951362i	$0.599685\pi$
$720$		0			0
$721$	−16.9108			−0.629790
$722$	−11.8787	+	5.55186i	−0.442079	+	0.206619i
$723$		0			0
$724$	28.5816	+	23.9828i	1.06223	+	0.891315i
$725$	−4.44533	+	1.61797i	−0.165095	+	0.0600898i
$726$		0			0
$727$	1.64266	−	9.31601i	0.0609230	−	0.345512i	−0.939075	−	0.343711i	$-0.888316\pi$
$727$	1.64266	−	9.31601i	0.0609230	−	0.345512i	0.999998	−	0.00180034i	$-0.000573066\pi$
$728$	6.83432	+	2.48749i	0.253297	+	0.0921925i
$729$		0			0
$730$	−2.74795	+	4.75958i	−0.101706	+	0.176160i
$731$	4.80833	−	4.03467i	0.177843	−	0.149228i
$732$		0			0
$733$	−5.22951	+	9.05778i	−0.193156	+	0.334557i	−0.946295	−	0.323306i	$-0.895206\pi$
$733$	−5.22951	+	9.05778i	−0.193156	+	0.334557i	0.753138	+	0.657862i	$0.228539\pi$
$734$	10.3628	+	17.9490i	0.382500	+	0.662509i
$735$		0			0
$736$	−5.61477	+	31.8430i	−0.206963	+	1.17375i
$737$	−10.3837	−	58.8891i	−0.382490	−	2.16921i
$738$		0			0
$739$	−5.97281	−	5.01178i	−0.219713	−	0.184361i	0.526287	−	0.850307i	$-0.323584\pi$
$739$	−5.97281	−	5.01178i	−0.219713	−	0.184361i	−0.746000	+	0.665946i	$0.768028\pi$
$740$	11.8739			0.436491
$741$		0			0
$742$	−10.6361			−0.390463
$743$	−15.6403	−	13.1238i	−0.573787	−	0.481464i	0.309113	−	0.951025i	$-0.399968\pi$
$743$	−15.6403	−	13.1238i	−0.573787	−	0.481464i	−0.882900	+	0.469561i	$0.844412\pi$
$744$		0			0
$745$	−1.68456	−	9.55359i	−0.0617174	−	0.350017i
$746$	0.594143	−	3.36955i	0.0217531	−	0.123368i
$747$		0			0
$748$	−2.28364	−	3.95537i	−0.0834980	−	0.144623i
$749$	−17.3463	+	30.0447i	−0.633821	+	1.09781i
$750$		0			0
$751$	26.8265	−	22.5101i	0.978914	−	0.821407i	−0.00501107	−	0.999987i	$-0.501595\pi$
$751$	26.8265	−	22.5101i	0.978914	−	0.821407i	0.983925	+	0.178581i	$0.0571506\pi$
$752$	4.33179	−	7.50288i	0.157964	−	0.273602i
$753$		0			0
$754$	3.92996	+	1.43039i	0.143121	+	0.0520917i
$755$	−0.800112	+	4.53766i	−0.0291190	+	0.165142i
$756$		0			0
$757$	−33.3503	+	12.1385i	−1.21214	+	0.441182i	−0.867444	−	0.497534i	$-0.834239\pi$
$757$	−33.3503	+	12.1385i	−1.21214	+	0.441182i	−0.344692	+	0.938716i	$0.612017\pi$
$758$	2.14548	+	1.80027i	0.0779275	+	0.0653889i
$759$		0			0
$760$	−10.5098	−	1.37893i	−0.381229	−	0.0500190i
$761$	24.2563			0.879290			0.439645	−	0.898172i	$-0.355104\pi$
$761$	24.2563			0.879290			0.439645	+	0.898172i	$0.355104\pi$
$762$		0			0
$763$	−29.4395	+	10.7151i	−1.06578	+	0.387912i
$764$	−0.447420	−	2.53744i	−0.0161871	−	0.0918015i
$765$		0			0
$766$	1.56245	+	0.568687i	0.0564538	+	0.0205475i
$767$	3.77453	+	6.53768i	0.136290	+	0.236062i
$768$		0			0
$769$	−19.7393	+	16.5633i	−0.711819	+	0.597287i	−0.925109	−	0.379702i	$-0.876027\pi$
$769$	−19.7393	+	16.5633i	−0.711819	+	0.597287i	0.213290	+	0.976989i	$0.431582\pi$
$770$	5.65096	−	4.74172i	0.203646	−	0.170880i
$771$		0			0
$772$	13.5545	+	23.4770i	0.487836	+	0.844956i
$773$	35.6601	+	12.9792i	1.28260	+	0.466829i	0.891292	−	0.453429i	$-0.149800\pi$
$773$	35.6601	+	12.9792i	1.28260	+	0.466829i	0.391311	+	0.920259i	$0.372022\pi$
$774$		0			0
$775$	−0.778099	−	4.41282i	−0.0279501	−	0.158513i
$776$	−9.61975	+	3.50130i	−0.345329	+	0.125689i
$777$		0			0
$778$	−4.12191			−0.147778
$779$	23.0698	−	30.0926i	0.826562	−	1.07818i
$780$		0			0
$781$	13.1582	+	11.0411i	0.470839	+	0.395081i
$782$	2.36327	−	0.860160i	0.0845103	−	0.0307592i
$783$		0			0
$784$	−0.368425	+	2.08944i	−0.0131580	+	0.0746230i
$785$	−19.1729	−	6.97835i	−0.684308	−	0.249068i
$786$		0			0
$787$	3.32256	−	5.75484i	0.118437	−	0.205138i	−0.800712	−	0.599050i	$-0.795545\pi$
$787$	3.32256	−	5.75484i	0.118437	−	0.205138i	0.919148	+	0.393912i	$0.128878\pi$
$788$	16.9270	−	14.2035i	0.603001	−	0.505978i
$789$		0			0
$790$	−2.17711	+	3.77086i	−0.0774580	+	0.134161i
$791$	4.94360	+	8.56256i	0.175774	+	0.304450i
$792$		0			0
$793$	−1.66706	+	9.45436i	−0.0591990	+	0.335734i
$794$	3.39951	+	19.2796i	0.120644	+	0.684206i
$795$		0			0
$796$	14.0464	+	11.7863i	0.497862	+	0.417755i
$797$	−15.3836			−0.544916			−0.272458	−	0.962168i	$-0.587837\pi$
$797$	−15.3836			−0.544916			−0.272458	+	0.962168i	$0.587837\pi$
$798$		0			0
$799$	−4.14198			−0.146533
$800$	−4.44958	−	3.73364i	−0.157316	−	0.132004i
$801$		0			0
$802$	−3.75928	−	21.3200i	−0.132745	−	0.752834i
$803$	−6.33171	+	35.9089i	−0.223441	+	1.26720i
$804$		0			0
$805$	−6.49811	−	11.2551i	−0.229028	−	0.396689i
$806$	−1.98070	+	3.43067i	−0.0697672	+	0.120840i
$807$		0			0
$808$	0.106313	−	0.0892071i	0.00374008	−	0.00313830i
$809$	6.12735	−	10.6129i	0.215426	−	0.373129i	−0.737978	−	0.674825i	$-0.764219\pi$
$809$	6.12735	−	10.6129i	0.215426	−	0.373129i	0.953404	+	0.301695i	$0.0975526\pi$
$810$		0			0
$811$	−47.3559	−	17.2361i	−1.66289	−	0.605243i	−0.672078	−	0.740481i	$-0.734598\pi$
$811$	−47.3559	−	17.2361i	−1.66289	−	0.605243i	−0.990813	+	0.135238i	$0.956820\pi$
$812$	2.92229	−	16.5731i	0.102552	−	0.581602i
$813$		0			0
$814$	−23.1372	+	8.42126i	−0.810960	+	0.295165i
$815$	2.90608	+	2.43849i	0.101795	+	0.0854165i
$816$		0			0
$817$	−16.0105	−	38.6047i	−0.560137	−	1.35061i
$818$	20.5546			0.718676
$819$		0			0
$820$	12.4557	−	4.53352i	0.434973	−	0.158317i
$821$	1.07376	+	6.08959i	0.0374745	+	0.212528i	0.997795	−	0.0663702i	$-0.0211418\pi$
$821$	1.07376	+	6.08959i	0.0374745	+	0.212528i	−0.960321	+	0.278898i	$0.910031\pi$
$822$		0			0
$823$	−27.0925	−	9.86085i	−0.944384	−	0.343728i	−0.176488	−	0.984303i	$-0.556474\pi$
$823$	−27.0925	−	9.86085i	−0.944384	−	0.343728i	−0.767896	+	0.640575i	$0.778696\pi$
$824$	−8.80715	−	15.2544i	−0.306812	−	0.531414i
$825$		0			0
$826$	−7.27308	+	6.10284i	−0.253063	+	0.212345i
$827$	15.7181	−	13.1891i	0.546572	−	0.458629i	−0.327206	−	0.944953i	$-0.606107\pi$
$827$	15.7181	−	13.1891i	0.546572	−	0.458629i	0.873778	+	0.486324i	$0.161663\pi$
$828$		0			0
$829$	4.29107	+	7.43236i	0.149035	+	0.258136i	0.930871	−	0.365348i	$-0.119050\pi$
$829$	4.29107	+	7.43236i	0.149035	+	0.258136i	−0.781836	+	0.623484i	$0.785717\pi$
$830$	−6.37917	−	2.32183i	−0.221424	−	0.0805918i
$831$		0			0
$832$	0.282488	+	1.60207i	0.00979350	+	0.0555417i
$833$	0.953180	−	0.346929i	0.0330257	−	0.0120204i
$834$		0			0
$835$	15.4984			0.536343
$836$	−29.6865	+	6.59507i	−1.02673	+	0.228095i
$837$		0			0
$838$	18.9095	+	15.8670i	0.653218	+	0.548115i
$839$	39.4563	−	14.3609i	1.36218	−	0.495794i	0.445455	−	0.895305i	$-0.353042\pi$
$839$	39.4563	−	14.3609i	1.36218	−	0.495794i	0.916729	+	0.399510i	$0.130820\pi$
$840$		0			0
$841$	−1.14976	+	6.52061i	−0.0396469	+	0.224849i
$842$	−24.6680	−	8.97843i	−0.850116	−	0.309417i
$843$		0			0
$844$	6.15248	−	10.6564i	0.211777	−	0.366808i
$845$	8.70143	−	7.30137i	0.299338	−	0.251175i
$846$		0			0
$847$	11.6304	−	20.1445i	0.399625	−	0.692172i
$848$	4.51978	+	7.82849i	0.155210	+	0.268831i
$849$		0			0
$850$	−0.0784514	+	0.444920i	−0.00269086	+	0.0152606i
$851$	7.53260	+	42.7195i	0.258214	+	1.46441i
$852$		0			0
$853$	−11.8447	−	9.93891i	−0.405556	−	0.340302i	0.417081	−	0.908869i	$-0.363053\pi$
$853$	−11.8447	−	9.93891i	−0.405556	−	0.340302i	−0.822636	+	0.568568i	$0.807498\pi$
$854$	−12.0740			−0.413165
$855$		0			0
$856$	−36.1360			−1.23510
$857$	−20.3501	−	17.0757i	−0.695144	−	0.583295i	0.225243	−	0.974303i	$-0.427682\pi$
$857$	−20.3501	−	17.0757i	−0.695144	−	0.583295i	−0.920388	+	0.391007i	$0.872127\pi$
$858$		0			0
$859$	4.03858	+	22.9039i	0.137795	+	0.781471i	0.972873	+	0.231340i	$0.0743111\pi$
$859$	4.03858	+	22.9039i	0.137795	+	0.781471i	−0.835078	+	0.550131i	$0.814578\pi$
$860$	2.53695	−	14.3877i	0.0865092	−	0.490618i
$861$		0			0
$862$	2.89430	+	5.01307i	0.0985802	+	0.170746i
$863$	−0.0573750	+	0.0993764i	−0.00195307	+	0.00338281i	−0.867000	−	0.498308i	$-0.833955\pi$
$863$	−0.0573750	+	0.0993764i	−0.00195307	+	0.00338281i	0.865047	+	0.501690i	$0.167288\pi$
$864$		0			0
$865$	12.9585	−	10.8734i	0.440601	−	0.369708i
$866$	8.01068	−	13.8749i	0.272214	−	0.471489i
$867$		0			0
$868$	14.9791	+	5.45193i	0.508422	+	0.185051i
$869$	−5.01641	+	28.4495i	−0.170170	+	0.965082i
$870$		0			0
$871$	−15.7219	+	5.72231i	−0.532717	+	0.193893i
$872$	−24.9977	−	20.9756i	−0.846530	−	0.710323i
$873$		0			0
$874$	−0.737784	−	16.7290i	−0.0249559	−	0.565866i
$875$	2.33464			0.0789253
$876$		0			0
$877$	−21.7949	+	7.93269i	−0.735961	+	0.267868i	−0.682686	−	0.730712i	$-0.739188\pi$
$877$	−21.7949	+	7.93269i	−0.735961	+	0.267868i	−0.0532749	+	0.998580i	$0.516966\pi$
$878$	−2.12288	−	12.0394i	−0.0716436	−	0.406311i
$879$		0			0
$880$	−5.89140	−	2.14430i	−0.198599	−	0.0722842i
$881$	4.15319	+	7.19353i	0.139924	+	0.242356i	0.927468	−	0.373903i	$-0.121981\pi$
$881$	4.15319	+	7.19353i	0.139924	+	0.242356i	−0.787543	+	0.616259i	$0.788647\pi$
$882$		0			0
$883$	−22.7800	+	19.1147i	−0.766609	+	0.643261i	−0.939838	−	0.341620i	$-0.889024\pi$
$883$	−22.7800	+	19.1147i	−0.766609	+	0.643261i	0.173229	+	0.984882i	$0.444580\pi$
$884$	−0.978920	+	0.821411i	−0.0329246	+	0.0276270i
$885$		0			0
$886$	−0.615419	−	1.06594i	−0.0206754	−	0.0358109i
$887$	−10.7996	−	3.93072i	−0.362614	−	0.131981i	0.154287	−	0.988026i	$-0.450692\pi$
$887$	−10.7996	−	3.93072i	−0.362614	−	0.131981i	−0.516901	+	0.856045i	$0.672914\pi$
$888$		0			0
$889$	7.40578	+	42.0003i	0.248382	+	1.40864i
$890$	7.89756	−	2.87448i	0.264727	−	0.0963527i
$891$		0			0
$892$	−23.1296			−0.774436
$893$	−8.28145	+	26.3058i	−0.277128	+	0.880290i
$894$		0			0
$895$	2.33846	+	1.96220i	0.0781659	+	0.0655890i
$896$	23.5634	−	8.57637i	0.787198	−	0.286517i
$897$		0			0
$898$	1.06137	−	6.01935i	0.0354185	−	0.200868i
$899$	19.9191	+	7.24994i	0.664338	+	0.241799i
$900$		0			0
$901$	2.16086	−	3.74273i	0.0719888	−	0.124688i
$902$	−21.0558	+	17.6679i	−0.701081	+	0.588277i
$903$		0			0
$904$	−5.14927	+	8.91879i	−0.171262	+	0.296635i
$905$	−12.2430	−	21.2056i	−0.406973	−	0.704897i
$906$		0			0
$907$	4.13253	−	23.4367i	0.137218	−	0.778204i	−0.836071	−	0.548621i	$-0.815153\pi$
$907$	4.13253	−	23.4367i	0.137218	−	0.778204i	0.973289	−	0.229582i	$-0.0737360\pi$
$908$	−5.54151	−	31.4275i	−0.183901	−	1.04296i
$909$		0			0
$910$	−1.58110	−	1.32670i	−0.0524128	−	0.0439796i
$911$	−23.2831			−0.771405			−0.385702	−	0.922623i	$-0.626041\pi$
$911$	−23.2831			−0.771405			−0.385702	+	0.922623i	$0.626041\pi$
$912$		0			0
$913$	−45.0392			−1.49058
$914$	−1.58876	−	1.33313i	−0.0525515	−	0.0440960i
$915$		0			0
$916$	−7.44917	−	42.2463i	−0.246128	−	1.39586i
$917$	3.40759	−	19.3254i	0.112528	−	0.638181i
$918$		0			0
$919$	−18.5406	−	32.1133i	−0.611599	−	1.05932i	−0.990971	−	0.134077i	$-0.957193\pi$
$919$	−18.5406	−	32.1133i	−0.611599	−	1.05932i	0.379372	−	0.925244i	$-0.376140\pi$
$920$	6.76845	−	11.7233i	0.223149	−	0.386506i
$921$		0			0
$922$	10.6347	−	8.92356i	0.350235	−	0.293882i
$923$	2.40298	−	4.16208i	0.0790951	−	0.136997i
$924$		0			0
$925$	−7.32257	−	2.66520i	−0.240765	−	0.0876312i
$926$	−0.977187	+	5.54190i	−0.0321124	+	0.182118i
$927$		0			0
$928$	25.8208	−	9.39800i	0.847609	−	0.308504i
$929$	−15.3901	−	12.9139i	−0.504934	−	0.423690i	0.354408	−	0.935091i	$-0.384682\pi$
$929$	−15.3901	−	12.9139i	−0.504934	−	0.423690i	−0.859342	+	0.511401i	$0.829127\pi$
$930$		0			0
$931$	−0.297571	−	6.74732i	−0.00975250	−	0.221134i
$932$	31.8243			1.04244
$933$		0			0
$934$	3.99305	−	1.45335i	0.130657	−	0.0475551i
$935$	0.520491	+	2.95185i	0.0170219	+	0.0965359i
$936$		0			0
$937$	18.8820	+	6.87247i	0.616847	+	0.224514i	0.631496	−	0.775379i	$-0.282441\pi$
$937$	18.8820	+	6.87247i	0.616847	+	0.224514i	−0.0146495	+	0.999893i	$0.504663\pi$
$938$	−10.5211	−	18.2231i	−0.343526	−	0.595004i
$939$		0			0
$940$	−7.38520	+	6.19692i	−0.240879	+	0.202121i
$941$	−3.26137	+	2.73661i	−0.106318	+	0.0892111i	−0.694397	−	0.719592i	$-0.744329\pi$
$941$	−3.26137	+	2.73661i	−0.106318	+	0.0892111i	0.588079	+	0.808803i	$0.299884\pi$
$942$		0			0
$943$	24.2123	+	41.9370i	0.788462	+	1.36566i
$944$	7.58255	+	2.75982i	0.246791	+	0.0898246i
$945$		0			0
$946$	5.26072	+	29.8350i	0.171041	+	0.970021i
$947$	−41.1890	+	14.9916i	−1.33846	+	0.487160i	−0.909328	−	0.416080i	$-0.863404\pi$
$947$	−41.1890	+	14.9916i	−1.33846	+	0.487160i	−0.429134	+	0.903241i	$0.641181\pi$
$948$		0			0
$949$	10.2020			0.331172
$950$	2.66884	+	1.38782i	0.0865886	+	0.0450267i
$951$		0			0
$952$	−2.84715	−	2.38904i	−0.0922766	−	0.0774292i
$953$	28.3499	−	10.3185i	0.918343	−	0.334250i	0.160764	−	0.986993i	$-0.448604\pi$
$953$	28.3499	−	10.3185i	0.918343	−	0.334250i	0.757579	+	0.652743i	$0.226382\pi$
$954$		0			0
$955$	−0.293631	+	1.66526i	−0.00950167	+	0.0538866i
$956$	1.77495	+	0.646027i	0.0574058	+	0.0208940i
$957$		0			0
$958$	−11.7631	+	20.3743i	−0.380048	+	0.658263i
$959$	−21.2094	+	17.7968i	−0.684887	+	0.574689i
$960$		0			0
$961$	5.46080	−	9.45838i	0.176155	−	0.305109i
$962$	3.44455	+	5.96613i	0.111057	+	0.192356i
$963$		0			0
$964$	−0.309801	+	1.75697i	−0.00997803	+	0.0565882i
$965$	−3.08936	−	17.5206i	−0.0994501	−	0.564009i
$966$		0			0
$967$	9.52967	+	7.99635i	0.306454	+	0.257145i	0.783024	−	0.621991i	$-0.213676\pi$
$967$	9.52967	+	7.99635i	0.306454	+	0.257145i	−0.476571	+	0.879136i	$0.658120\pi$
$968$	24.2285			0.778735
$969$		0			0
$970$	2.90518			0.0932797
$971$	22.6566	+	19.0111i	0.727084	+	0.610096i	0.929335	−	0.369238i	$-0.120381\pi$
$971$	22.6566	+	19.0111i	0.727084	+	0.610096i	−0.202251	+	0.979334i	$0.564826\pi$
$972$		0			0
$973$	−0.0151670	−	0.0860165i	−0.000486233	−	0.00275756i
$974$	−3.42396	+	19.4182i	−0.109711	+	0.622200i
$975$		0			0
$976$	5.13082	+	8.88685i	0.164234	+	0.284461i
$977$	−19.6892	+	34.1028i	−0.629915	+	1.09104i	0.357654	+	0.933854i	$0.383577\pi$
$977$	−19.6892	+	34.1028i	−0.629915	+	1.09104i	−0.987568	+	0.157190i	$0.949757\pi$
$978$		0			0
$979$	42.7143	−	35.8416i	1.36516	−	1.14550i
$980$	1.18048	−	2.04466i	0.0377092	−	0.0653142i
$981$		0			0
$982$	3.39879	+	1.23706i	0.108460	+	0.0394761i
$983$	6.67169	−	37.8370i	0.212794	−	1.20681i	−0.671900	−	0.740642i	$-0.734522\pi$
$983$	6.67169	−	37.8370i	0.212794	−	1.20681i	0.884694	−	0.466172i	$-0.154367\pi$
$984$		0			0
$985$	−13.6270	+	4.95981i	−0.434191	+	0.158033i
$986$	−1.63720	−	1.37378i	−0.0521392	−	0.0437500i
$987$		0			0
$988$	3.25955	+	7.85947i	0.103700	+	0.250043i
$989$	53.3733			1.69717
$990$		0			0
$991$	−9.83853	+	3.58093i	−0.312531	+	0.113752i	−0.493524	−	0.869732i	$-0.664291\pi$
$991$	−9.83853	+	3.58093i	−0.312531	+	0.113752i	0.180992	+	0.983485i	$0.442069\pi$
$992$	4.51960	+	25.6319i	0.143497	+	0.813815i
$993$		0			0
$994$	5.67986	+	2.06730i	0.180154	+	0.0655708i
$995$	−6.01683	−	10.4214i	−0.190746	−	0.330382i
$996$		0			0
$997$	−2.76477	+	2.31992i	−0.0875612	+	0.0734725i	−0.685518	−	0.728056i	$-0.740424\pi$
$997$	−2.76477	+	2.31992i	−0.0875612	+	0.0734725i	0.597956	+	0.801529i	$0.295980\pi$
$998$	−20.0270	+	16.8047i	−0.633944	+	0.531942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.586.2		18
3.2	odd	2		95.2.k.a.16.2	yes	18
15.2	even	4		475.2.u.b.149.2		36
15.8	even	4		475.2.u.b.149.5		36
15.14	odd	2		475.2.l.c.301.2		18
19.6	even	9	inner	855.2.bs.c.766.2		18
57.5	odd	18		1805.2.a.v.1.5		9
57.14	even	18		1805.2.a.s.1.5		9
57.44	odd	18		95.2.k.a.6.2	✓	18
285.14	even	18		9025.2.a.cf.1.5		9
285.44	odd	18		475.2.l.c.101.2		18
285.119	odd	18		9025.2.a.cc.1.5		9
285.158	even	36		475.2.u.b.424.2		36
285.272	even	36		475.2.u.b.424.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.2	✓	18	57.44	odd	18
95.2.k.a.16.2	yes	18	3.2	odd	2
475.2.l.c.101.2		18	285.44	odd	18
475.2.l.c.301.2		18	15.14	odd	2
475.2.u.b.149.2		36	15.2	even	4
475.2.u.b.149.5		36	15.8	even	4
475.2.u.b.424.2		36	285.158	even	36
475.2.u.b.424.5		36	285.272	even	36
855.2.bs.c.586.2		18	1.1	even	1	trivial
855.2.bs.c.766.2		18	19.6	even	9	inner
1805.2.a.s.1.5		9	57.14	even	18
1805.2.a.v.1.5		9	57.5	odd	18
9025.2.a.cc.1.5		9	285.119	odd	18
9025.2.a.cf.1.5		9	285.14	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.528654 - 0.443593i) q^{2} +(-0.264596 - 1.50060i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(1.16732 + 2.02186i) q^{7} +(-1.21589 + 2.10598i) q^{8} +O(q^{10})\)	\(q+(-0.528654 - 0.443593i) q^{2} +(-0.264596 - 1.50060i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(1.16732 + 2.02186i) q^{7} +(-1.21589 + 2.10598i) q^{8} +(0.528654 - 0.443593i) q^{10} +(2.28929 - 3.96516i) q^{11} +(-1.20379 - 0.438145i) q^{13} +(0.279774 - 1.58668i) q^{14} +(-1.28673 + 0.468333i) q^{16} +(0.501495 + 0.420805i) q^{17} +(3.67523 - 2.34365i) q^{19} +1.52375 q^{20} +(-2.96916 + 1.08069i) q^{22} +(0.966645 + 5.48212i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(0.442032 + 0.765622i) q^{26} +(2.72513 - 2.28666i) q^{28} +(3.62387 - 3.04079i) q^{29} +(2.24045 + 3.88057i) q^{31} +(5.45822 + 1.98663i) q^{32} +(-0.0784514 - 0.444920i) q^{34} +(-2.19385 + 0.798495i) q^{35} +7.79252 q^{37} +(-2.98255 - 0.391324i) q^{38} +(-1.86284 - 1.56311i) q^{40} +(8.17440 - 2.97524i) q^{41} +(1.66494 - 9.44233i) q^{43} +(-6.55586 - 2.38614i) q^{44} +(1.92081 - 3.32694i) q^{46} +(-4.84673 + 4.06689i) q^{47} +(0.774723 - 1.34186i) q^{49} +(0.345054 + 0.597652i) q^{50} +(-0.338961 + 1.92235i) q^{52} +(-1.14634 - 6.50124i) q^{53} +(3.50739 + 2.94305i) q^{55} -5.67731 q^{56} -3.26464 q^{58} +(-4.51420 - 3.78786i) q^{59} +(-1.30132 - 7.38016i) q^{61} +(0.536973 - 3.04533i) q^{62} +(-0.634941 - 1.09975i) q^{64} +(0.640526 - 1.10942i) q^{65} +(10.0048 - 8.39500i) q^{67} +(0.498766 - 0.863888i) q^{68} +(1.51399 + 0.551048i) q^{70} +(-0.651454 + 3.69458i) q^{71} +(-7.48353 + 2.72378i) q^{73} +(-4.11955 - 3.45671i) q^{74} +(-4.48934 - 4.89493i) q^{76} +10.6893 q^{77} +(-5.92896 + 2.15796i) q^{79} +(-0.237779 - 1.34851i) q^{80} +(-5.64122 - 2.05324i) q^{82} +(-4.91848 - 8.51905i) q^{83} +(-0.501495 + 0.420805i) q^{85} +(-5.06873 + 4.25317i) q^{86} +(5.56702 + 9.64236i) q^{88} +(11.4439 + 4.16525i) q^{89} +(-0.519346 - 2.94536i) q^{91} +(7.97070 - 2.90110i) q^{92} +4.36629 q^{94} +(1.66985 + 4.02636i) q^{95} +(3.22485 + 2.70597i) q^{97} +(-1.00480 + 0.365717i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

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