LMFDB - Embedded newform 900.2.bj.f.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	900.163
Dual form			900.2.bj.f.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36363 - 0.374857i) q^{2} +(1.71896 + 1.02233i) q^{4} +(-2.16584 - 0.556007i) q^{5} +(-3.13412 - 3.13412i) q^{7} +(-1.96080 - 2.03845i) q^{8} +O(q^{10})$	\(q+(-1.36363 - 0.374857i) q^{2} +(1.71896 + 1.02233i) q^{4} +(-2.16584 - 0.556007i) q^{5} +(-3.13412 - 3.13412i) q^{7} +(-1.96080 - 2.03845i) q^{8} +(2.74498 + 1.57007i) q^{10} +(0.0527296 - 0.0725760i) q^{11} +(-5.12177 - 0.811209i) q^{13} +(3.09893 + 5.44862i) q^{14} +(1.90968 + 3.51470i) q^{16} +(1.36594 + 2.68082i) q^{17} +(-0.464955 + 1.43098i) q^{19} +(-3.15458 - 3.16996i) q^{20} +(-0.0991092 + 0.0792007i) q^{22} +(2.09335 - 0.331555i) q^{23} +(4.38171 + 2.40844i) q^{25} +(6.68011 + 3.02612i) q^{26} +(-2.18333 - 8.59155i) q^{28} +(6.04881 - 1.96538i) q^{29} +(3.95945 + 1.28650i) q^{31} +(-1.28658 - 5.50860i) q^{32} +(-0.857717 - 4.16767i) q^{34} +(5.04540 + 8.53059i) q^{35} +(-1.26010 + 7.95598i) q^{37} +(1.17044 - 1.77704i) q^{38} +(3.11339 + 5.50516i) q^{40} +(-8.23695 + 5.98450i) q^{41} +(7.85946 - 7.85946i) q^{43} +(0.164837 - 0.0708485i) q^{44} +(-2.97884 - 0.332591i) q^{46} +(-3.49688 + 6.86301i) q^{47} +12.6454i q^{49} +(-5.07221 - 4.92674i) q^{50} +(-7.97482 - 6.63059i) q^{52} +(-1.47153 + 2.88805i) q^{53} +(-0.154557 + 0.127870i) q^{55} +(-0.243356 + 12.5341i) q^{56} +(-8.98507 + 0.412604i) q^{58} +(11.4383 - 8.31042i) q^{59} +(-9.26103 - 6.72853i) q^{61} +(-4.91697 - 3.23854i) q^{62} +(-0.310530 + 7.99397i) q^{64} +(10.6419 + 4.60469i) q^{65} +(-1.84223 + 0.938661i) q^{67} +(-0.392675 + 6.00467i) q^{68} +(-3.68230 - 13.5239i) q^{70} +(-2.37497 + 0.771676i) q^{71} +(1.16183 + 7.33551i) q^{73} +(4.70067 - 10.3766i) q^{74} +(-2.26218 + 1.98447i) q^{76} +(-0.392723 + 0.0622012i) q^{77} +(0.395606 + 1.21755i) q^{79} +(-2.18185 - 8.67407i) q^{80} +(13.4755 - 5.07295i) q^{82} +(1.03260 + 2.02659i) q^{83} +(-1.46786 - 6.56569i) q^{85} +(-13.6636 + 7.77120i) q^{86} +(-0.251335 + 0.0348206i) q^{88} +(-7.66814 + 10.5543i) q^{89} +(13.5098 + 18.5947i) q^{91} +(3.93736 + 1.57017i) q^{92} +(7.34109 - 8.04777i) q^{94} +(1.80265 - 2.84076i) q^{95} +(3.93972 + 2.00739i) q^{97} +(4.74022 - 17.2436i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−1.36363	−	0.374857i	−0.964231	−	0.265064i
$2$	−1.36363	−	0.374857i	−0.964231	−	0.265064i
$3$		0			0
$3$		0			0
$4$	1.71896	+	1.02233i	0.859482	+	0.511166i
$5$	−2.16584	−	0.556007i	−0.968592	−	0.248654i
$5$	−2.16584	−	0.556007i	−0.968592	−	0.248654i
$6$		0			0
$7$	−3.13412	−	3.13412i	−1.18459	−	1.18459i	−0.978543	−	0.206043i	$-0.933941\pi$
$7$	−3.13412	−	3.13412i	−1.18459	−	1.18459i	−0.206043	−	0.978543i	$-0.566059\pi$
$8$	−1.96080	−	2.03845i	−0.693247	−	0.720700i
$9$		0			0
$10$	2.74498	+	1.57007i	0.868037	+	0.496499i
$11$	0.0527296	−	0.0725760i	0.0158986	−	0.0218825i	−0.800994	−	0.598673i	$-0.795695\pi$
$11$	0.0527296	−	0.0725760i	0.0158986	−	0.0218825i	0.816892	+	0.576790i	$0.195695\pi$
$12$		0			0
$13$	−5.12177	−	0.811209i	−1.42052	−	0.224989i	−0.601557	−	0.798830i	$-0.705453\pi$
$13$	−5.12177	−	0.811209i	−1.42052	−	0.224989i	−0.818967	+	0.573841i	$0.805453\pi$
$14$	3.09893	+	5.44862i	0.828223	+	1.45621i
$15$		0			0
$16$	1.90968	+	3.51470i	0.477419	+	0.878676i
$17$	1.36594	+	2.68082i	0.331290	+	0.650193i	0.995226	−	0.0975960i	$-0.0311153\pi$
$17$	1.36594	+	2.68082i	0.331290	+	0.650193i	−0.663936	+	0.747789i	$0.731115\pi$
$18$		0			0
$19$	−0.464955	+	1.43098i	−0.106668	+	0.328290i	−0.990118	−	0.140235i	$-0.955214\pi$
$19$	−0.464955	+	1.43098i	−0.106668	+	0.328290i	0.883450	+	0.468525i	$0.155214\pi$
$20$	−3.15458	−	3.16996i	−0.705385	−	0.708825i
$21$		0			0
$22$	−0.0991092	+	0.0792007i	−0.0211302	+	0.0168856i
$23$	2.09335	−	0.331555i	0.436494	−	0.0691339i	0.0656796	−	0.997841i	$-0.479078\pi$
$23$	2.09335	−	0.331555i	0.436494	−	0.0691339i	0.370815	+	0.928707i	$0.379078\pi$
$24$		0			0
$25$	4.38171	+	2.40844i	0.876343	+	0.481688i
$26$	6.68011	+	3.02612i	1.31008	+	0.593471i
$27$		0			0
$28$	−2.18333	−	8.59155i	−0.412610	−	1.62365i
$29$	6.04881	−	1.96538i	1.12324	−	0.364962i	0.312235	−	0.950005i	$-0.398922\pi$
$29$	6.04881	−	1.96538i	1.12324	−	0.364962i	0.811002	+	0.585043i	$0.198922\pi$
$30$		0			0
$31$	3.95945	+	1.28650i	0.711139	+	0.231063i	0.642177	−	0.766556i	$-0.278031\pi$
$31$	3.95945	+	1.28650i	0.711139	+	0.231063i	0.0689619	+	0.997619i	$0.478031\pi$
$32$	−1.28658	−	5.50860i	−0.227436	−	0.973793i
$33$		0			0
$34$	−0.857717	−	4.16767i	−0.147097	−	0.714750i
$35$	5.04540	+	8.53059i	0.852829	+	1.44193i
$36$		0			0
$37$	−1.26010	+	7.95598i	−0.207160	+	1.30796i	0.636583	+	0.771208i	$0.280347\pi$
$37$	−1.26010	+	7.95598i	−0.207160	+	1.30796i	−0.843743	+	0.536747i	$0.819653\pi$
$38$	1.17044	−	1.77704i	0.189870	−	0.288273i
$39$		0			0
$40$	3.11339	+	5.50516i	0.492269	+	0.870443i
$41$	−8.23695	+	5.98450i	−1.28640	+	0.934621i	−0.999726	−	0.0234081i	$-0.992548\pi$
$41$	−8.23695	+	5.98450i	−1.28640	+	0.934621i	−0.286670	+	0.958029i	$0.592548\pi$
$42$		0			0
$43$	7.85946	−	7.85946i	1.19856	−	1.19856i	0.223957	−	0.974599i	$-0.428103\pi$
$43$	7.85946	−	7.85946i	1.19856	−	1.19856i	0.974599	−	0.223957i	$-0.0718974\pi$
$44$	0.164837	−	0.0708485i	0.0248501	−	0.0106808i
$45$		0			0
$46$	−2.97884	−	0.332591i	−0.439206	−	0.0490379i
$47$	−3.49688	+	6.86301i	−0.510072	+	1.00107i	0.482091	+	0.876121i	$0.339878\pi$
$47$	−3.49688	+	6.86301i	−0.510072	+	1.00107i	−0.992163	+	0.124952i	$0.960122\pi$
$48$		0			0
$49$			12.6454i			1.80649i
$50$	−5.07221	−	4.92674i	−0.717318	−	0.696746i
$51$		0			0
$52$	−7.97482	−	6.63059i	−1.10591	−	0.919498i
$53$	−1.47153	+	2.88805i	−0.202131	+	0.396704i	−0.969713	−	0.244246i	$-0.921459\pi$
$53$	−1.47153	+	2.88805i	−0.202131	+	0.396704i	0.767583	+	0.640950i	$0.221459\pi$
$54$		0			0
$55$	−0.154557	+	0.127870i	−0.0208404	+	0.0172420i
$56$	−0.243356	+	12.5341i	−0.0325197	+	1.67494i
$57$		0			0
$58$	−8.98507	+	0.412604i	−1.17980	+	0.0541776i
$59$	11.4383	−	8.31042i	1.48914	−	1.08192i	0.514676	−	0.857385i	$-0.327912\pi$
$59$	11.4383	−	8.31042i	1.48914	−	1.08192i	0.974465	−	0.224539i	$-0.0720877\pi$
$60$		0			0
$61$	−9.26103	−	6.72853i	−1.18575	−	0.861500i	−0.192944	−	0.981210i	$-0.561804\pi$
$61$	−9.26103	−	6.72853i	−1.18575	−	0.861500i	−0.992809	+	0.119710i	$0.961804\pi$
$62$	−4.91697	−	3.23854i	−0.624456	−	0.411296i
$63$		0			0
$64$	−0.310530	+	7.99397i	−0.0388163	+	0.999246i
$65$	10.6419	+	4.60469i	1.31996	+	0.571141i
$66$		0			0
$67$	−1.84223	+	0.938661i	−0.225064	+	0.114676i	−0.562887	−	0.826534i	$-0.690309\pi$
$67$	−1.84223	+	0.938661i	−0.225064	+	0.114676i	0.337823	+	0.941210i	$0.390309\pi$
$68$	−0.392675	+	6.00467i	−0.0476188	+	0.728174i
$69$		0			0
$70$	−3.68230	−	13.5239i	−0.440120	−	1.61641i
$71$	−2.37497	+	0.771676i	−0.281857	+	0.0915810i	−0.446534	−	0.894767i	$-0.647342\pi$
$71$	−2.37497	+	0.771676i	−0.281857	+	0.0915810i	0.164677	+	0.986348i	$0.447342\pi$
$72$		0			0
$73$	1.16183	+	7.33551i	0.135982	+	0.858556i	0.957513	+	0.288392i	$0.0931205\pi$
$73$	1.16183	+	7.33551i	0.135982	+	0.858556i	−0.821531	+	0.570164i	$0.806880\pi$
$74$	4.70067	−	10.3766i	0.546442	−	1.20626i
$75$		0			0
$76$	−2.26218	+	1.98447i	−0.259490	+	0.227634i
$77$	−0.392723	+	0.0622012i	−0.0447549	+	0.00708848i
$78$		0			0
$79$	0.395606	+	1.21755i	0.0445091	+	0.136985i	0.970842	−	0.239722i	$-0.0770563\pi$
$79$	0.395606	+	1.21755i	0.0445091	+	0.136985i	−0.926332	+	0.376707i	$0.877056\pi$
$80$	−2.18185	−	8.67407i	−0.243938	−	0.969791i
$81$		0			0
$82$	13.4755	−	5.07295i	1.48812	−	0.560213i
$83$	1.03260	+	2.02659i	0.113343	+	0.222447i	0.940709	−	0.339216i	$-0.110162\pi$
$83$	1.03260	+	2.02659i	0.113343	+	0.222447i	−0.827366	+	0.561663i	$0.810162\pi$
$84$		0			0
$85$	−1.46786	−	6.56569i	−0.159212	−	0.712149i
$86$	−13.6636	+	7.77120i	−1.47338	+	0.837990i
$87$		0			0
$88$	−0.251335	+	0.0348206i	−0.0267924	+	0.00371189i
$89$	−7.66814	+	10.5543i	−0.812821	+	1.11875i	0.178061	+	0.984020i	$0.443018\pi$
$89$	−7.66814	+	10.5543i	−0.812821	+	1.11875i	−0.990882	+	0.134733i	$0.956982\pi$
$90$		0			0
$91$	13.5098	+	18.5947i	1.41621	+	1.94925i
$92$	3.93736	+	1.57017i	0.410498	+	0.163702i
$93$		0			0
$94$	7.34109	−	8.04777i	0.757176	−	0.830064i
$95$	1.80265	−	2.84076i	0.184948	−	0.291456i
$96$		0			0
$97$	3.93972	+	2.00739i	0.400018	+	0.203819i	0.642413	−	0.766358i	$-0.277933\pi$
$97$	3.93972	+	2.00739i	0.400018	+	0.203819i	−0.242396	+	0.970177i	$0.577933\pi$
$98$	4.74022	−	17.2436i	0.478835	−	1.74187i
$99$		0			0
$100$	5.06978	+	8.61959i	0.506978	+	0.861959i
$101$	−6.81825			−0.678442			−0.339221	−	0.940707i	$-0.610163\pi$
$101$	−6.81825			−0.678442			−0.339221	+	0.940707i	$0.610163\pi$
$102$		0			0
$103$	2.20599	+	1.12401i	0.217363	+	0.110752i	0.559282	−	0.828978i	$-0.311077\pi$
$103$	2.20599	+	1.12401i	0.217363	+	0.110752i	−0.341919	+	0.939729i	$0.611077\pi$
$104$	8.38916	+	12.0311i	0.822625	+	1.17974i
$105$		0			0
$106$	3.08923	−	3.38661i	0.300052	−	0.328936i
$107$	2.71179	+	2.71179i	0.262159	+	0.262159i	0.825931	−	0.563772i	$-0.190650\pi$
$107$	2.71179	+	2.71179i	0.262159	+	0.262159i	−0.563772	+	0.825931i	$0.690650\pi$
$108$		0			0
$109$	4.04353	+	5.56544i	0.387300	+	0.533072i	0.957500	−	0.288433i	$-0.0931344\pi$
$109$	4.04353	+	5.56544i	0.387300	+	0.533072i	−0.570200	+	0.821506i	$0.693134\pi$
$110$	0.258691	−	0.116431i	0.0246652	−	0.0111012i
$111$		0			0
$112$	5.03035	−	17.0006i	0.475323	−	1.60641i
$113$	11.4626	+	1.81550i	1.07831	+	0.170788i	0.670228	−	0.742155i	$-0.266196\pi$
$113$	11.4626	+	1.81550i	1.07831	+	0.170788i	0.408086	+	0.912943i	$0.366196\pi$
$114$		0			0
$115$	−4.71821	−	0.445824i	−0.439975	−	0.0415733i
$116$	12.4070	+	2.80548i	1.15196	+	0.260482i
$117$		0			0
$118$	−18.7128	+	7.04459i	−1.72265	+	0.648507i
$119$	4.12097	−	12.6830i	0.377768	−	1.16265i
$120$		0			0
$121$	3.39670	+	10.4540i	0.308791	+	0.950361i
$122$	10.1064	+	12.6468i	0.914987	+	1.14499i
$123$		0			0
$124$	5.49093	+	6.25933i	0.493100	+	0.562105i
$125$	−8.15097	−	7.65256i	−0.729045	−	0.684465i
$126$		0			0
$127$	−0.434901	−	2.74586i	−0.0385912	−	0.243655i	0.960850	−	0.277068i	$-0.0893626\pi$
$127$	−0.434901	−	2.74586i	−0.0385912	−	0.243655i	−0.999442	+	0.0334122i	$0.989363\pi$
$128$	3.42005	−	10.7844i	0.302292	−	0.953215i
$129$		0			0
$130$	−12.7855	−	10.2683i	−1.12136	−	0.900587i
$131$	−11.7429	−	3.81550i	−1.02598	−	0.333361i	−0.252781	−	0.967524i	$-0.581345\pi$
$131$	−11.7429	−	3.81550i	−1.02598	−	0.333361i	−0.773200	+	0.634162i	$0.781345\pi$
$132$		0			0
$133$	5.94209	−	3.02765i	0.515245	−	0.262530i
$134$	2.86398	−	0.589413i	0.247410	−	0.0509175i
$135$		0			0
$136$	2.78636	−	8.04095i	0.238928	−	0.689506i
$137$	−0.711394	+	4.49156i	−0.0607785	+	0.383740i	0.938483	+	0.345324i	$0.112231\pi$
$137$	−0.711394	+	4.49156i	−0.0607785	+	0.383740i	−0.999262	+	0.0384157i	$0.987769\pi$
$138$		0			0
$139$	13.0231	+	9.46183i	1.10460	+	0.802542i	0.981805	−	0.189889i	$-0.0608130\pi$
$139$	13.0231	+	9.46183i	1.10460	+	0.802542i	0.122799	+	0.992432i	$0.460813\pi$
$140$	−0.0482204	+	19.8219i	−0.00407537	+	1.67525i
$141$		0			0
$142$	3.52785	−	0.162003i	0.296051	−	0.0135950i
$143$	−0.328943	+	0.328943i	−0.0275076	+	0.0275076i
$144$		0			0
$145$	−14.1935	+	0.893513i	−1.17871	+	0.0742022i
$146$	1.16546	−	10.4384i	0.0964544	−	0.863890i
$147$		0			0
$148$	−10.2997	+	12.3878i	−0.846632	+	1.01827i
$149$		−	2.90133i		−	0.237686i	−0.992913	−	0.118843i	$-0.962081\pi$
$149$		−	2.90133i		−	0.237686i	0.992913	−	0.118843i	$-0.0379185\pi$
$150$		0			0
$151$		−	4.02046i		−	0.327180i	−0.986528	−	0.163590i	$-0.947693\pi$
$151$		−	4.02046i		−	0.327180i	0.986528	−	0.163590i	$-0.0523075\pi$
$152$	3.82866	−	1.85809i	0.310546	−	0.150711i
$153$		0			0
$154$	0.558844	+	0.0623957i	0.0450330	+	0.00502799i
$155$	−7.86024	−	4.98784i	−0.631349	−	0.400633i
$156$		0			0
$157$	−2.31475	+	2.31475i	−0.184737	+	0.184737i	−0.793416	−	0.608679i	$-0.791700\pi$
$157$	−2.31475	+	2.31475i	−0.184737	+	0.184737i	0.608679	+	0.793416i	$0.291700\pi$
$158$	−0.0830520	−	1.80858i	−0.00660726	−	0.143883i
$159$		0			0
$160$	−0.276307	+	12.6461i	−0.0218440	+	0.999761i
$161$	−7.59995	−	5.52169i	−0.598960	−	0.435170i
$162$		0			0
$163$	−1.04062	+	6.57021i	−0.0815075	+	0.514618i	0.912829	+	0.408342i	$0.133893\pi$
$163$	−1.04062	+	6.57021i	−0.0815075	+	0.514618i	−0.994337	+	0.106276i	$0.966107\pi$
$164$	−20.2772	+	1.86624i	−1.58338	+	0.145729i
$165$		0			0
$166$	−0.648400	−	3.15060i	−0.0503256	−	0.244534i
$167$	2.62863	−	1.33936i	0.203410	−	0.103642i	−0.349318	−	0.937004i	$-0.613587\pi$
$167$	2.62863	−	1.33936i	0.203410	−	0.103642i	0.552728	+	0.833362i	$0.313587\pi$
$168$		0			0
$169$	13.2108	+	4.29244i	1.01621	+	0.330187i
$170$	−0.459577	+	9.50340i	−0.0352479	+	0.728877i
$171$		0			0
$172$	21.5451	−	5.47515i	1.64280	−	0.417476i
$173$	1.01770	+	6.42548i	0.0773739	+	0.488520i	0.995696	+	0.0926847i	$0.0295449\pi$
$173$	1.01770	+	6.42548i	0.0773739	+	0.488520i	−0.918322	+	0.395835i	$0.870455\pi$
$174$		0			0
$175$	−6.18447	−	21.2812i	−0.467502	−	1.60870i
$176$	0.355780	+	0.0467322i	0.0268179	+	0.00352257i
$177$		0			0
$178$	14.4128	−	11.5177i	1.08029	−	0.863286i
$179$	−2.84051	−	8.74220i	−0.212310	−	0.653423i	−0.999334	−	0.0364999i	$-0.988379\pi$
$179$	−2.84051	−	8.74220i	−0.212310	−	0.653423i	0.787024	−	0.616923i	$-0.211621\pi$
$180$		0			0
$181$	1.42108	−	4.37363i	0.105628	−	0.325090i	−0.884249	−	0.467015i	$-0.845329\pi$
$181$	1.42108	−	4.37363i	0.105628	−	0.325090i	0.989877	+	0.141925i	$0.0453293\pi$
$182$	−11.4520	−	30.4205i	−0.848881	−	2.25492i
$183$		0			0
$184$	−4.78050	−	3.61708i	−0.352423	−	0.266654i
$185$	7.15276	−	16.5307i	0.525881	−	1.21536i
$186$		0			0
$187$	0.266589	+	0.0422235i	0.0194949	+	0.00308769i
$188$	−13.0273	+	8.22230i	−0.950112	+	0.599673i
$189$		0			0
$190$	−3.52303	+	3.19800i	−0.255587	+	0.232008i
$191$	−2.40696	−	3.31289i	−0.174161	−	0.239712i	0.713009	−	0.701155i	$-0.247332\pi$
$191$	−2.40696	−	3.31289i	−0.174161	−	0.239712i	−0.887170	+	0.461443i	$0.847332\pi$
$192$		0			0
$193$	−11.4434	−	11.4434i	−0.823717	−	0.823717i	0.162922	−	0.986639i	$-0.447908\pi$
$193$	−11.4434	−	11.4434i	−0.823717	−	0.823717i	−0.986639	+	0.162922i	$0.947908\pi$
$194$	−4.61983	−	4.21416i	−0.331684	−	0.302559i
$195$		0			0
$196$	−12.9278	+	21.7370i	−0.923414	+	1.55264i
$197$	−7.67379	−	3.90999i	−0.546735	−	0.278575i	0.158728	−	0.987322i	$-0.449261\pi$
$197$	−7.67379	−	3.90999i	−0.546735	−	0.278575i	−0.705463	+	0.708747i	$0.749261\pi$
$198$		0			0
$199$	−21.3364			−1.51250			−0.756249	−	0.654284i	$-0.772970\pi$
$199$	−21.3364			−1.51250			−0.756249	+	0.654284i	$0.772970\pi$
$200$	−3.68218	−	13.6544i	−0.260370	−	0.965509i
$201$		0			0
$202$	9.29756	+	2.55587i	0.654174	+	0.179831i
$203$	−25.1174	−	12.7980i	−1.76290	−	0.898242i
$204$		0			0
$205$	21.1673	−	8.38165i	1.47839	−	0.585400i
$206$	−2.58681	−	2.35966i	−0.180231	−	0.164405i
$207$		0			0
$208$	−6.92976	−	19.5507i	−0.480493	−	1.35559i
$209$	0.0793382	+	0.109200i	0.00548794	+	0.00755350i
$210$		0			0
$211$	−15.1542	+	20.8580i	−1.04326	+	1.43592i	−0.148748	+	0.988875i	$0.547524\pi$
$211$	−15.1542	+	20.8580i	−1.04326	+	1.43592i	−0.894511	+	0.447047i	$0.852476\pi$
$212$	−5.48205	+	3.46005i	−0.376509	+	0.237637i
$213$		0			0
$214$	−2.68134	−	4.71441i	−0.183293	−	0.322270i
$215$	−21.3922	+	12.6524i	−1.45894	+	0.862887i
$216$		0			0
$217$	−8.37734	−	16.4415i	−0.568691	−	1.11612i
$218$	−3.42762	−	9.10493i	−0.232148	−	0.616664i
$219$		0			0
$220$	−0.396403	+	0.0617959i	−0.0267255	+	0.00416628i
$221$	−4.82135	−	14.8386i	−0.324319	−	0.998152i
$222$		0			0
$223$	−24.4327	+	3.86975i	−1.63613	+	0.259138i	−0.905722	−	0.423872i	$-0.860671\pi$
$223$	−24.4327	+	3.86975i	−1.63613	+	0.259138i	−0.730410	+	0.683009i	$0.760671\pi$
$224$	−13.2323	+	21.2969i	−0.884123	+	1.42296i
$225$		0			0
$226$	−14.9502	−	6.77253i	−0.994474	−	0.450502i
$227$	−2.96964	−	18.7496i	−0.197102	−	1.24445i	−0.865598	−	0.500739i	$-0.833062\pi$
$227$	−2.96964	−	18.7496i	−0.197102	−	1.24445i	0.668496	−	0.743715i	$-0.266938\pi$
$228$		0			0
$229$	3.82659	−	1.24333i	0.252868	−	0.0821618i	−0.179840	−	0.983696i	$-0.557558\pi$
$229$	3.82659	−	1.24333i	0.252868	−	0.0821618i	0.432708	+	0.901534i	$0.357558\pi$
$230$	6.26677	+	2.37659i	0.413218	+	0.156708i
$231$		0			0
$232$	−15.8668	−	8.47647i	−1.04171	−	0.556508i
$233$	−4.12528	+	2.10194i	−0.270256	+	0.137702i	−0.583867	−	0.811849i	$-0.698461\pi$
$233$	−4.12528	+	2.10194i	−0.270256	+	0.137702i	0.313611	+	0.949552i	$0.398461\pi$
$234$		0			0
$235$	11.3896	−	12.9199i	0.742973	−	0.842801i
$236$	28.1580	−	2.59156i	1.83293	−	0.168696i
$237$		0			0
$238$	−10.3738	+	15.7502i	−0.672433	+	1.02093i
$239$	16.3162	+	11.8544i	1.05541	+	0.766798i	0.973233	−	0.229820i	$-0.0738139\pi$
$239$	16.3162	+	11.8544i	1.05541	+	0.766798i	0.0821734	+	0.996618i	$0.473814\pi$
$240$		0			0
$241$	5.43945	−	3.95199i	0.350386	−	0.254570i	−0.398645	−	0.917105i	$-0.630519\pi$
$241$	5.43945	−	3.95199i	0.350386	−	0.254570i	0.749031	+	0.662535i	$0.230519\pi$
$242$	−0.713091	−	15.5286i	−0.0458392	−	0.998216i
$243$		0			0
$244$	−9.04058	−	21.0339i	−0.578764	−	1.34656i
$245$	7.03093	−	27.3879i	0.449190	−	1.74975i
$246$		0			0
$247$	3.54222	−	6.95199i	0.225386	−	0.442345i
$248$	−5.14123	−	10.5937i	−0.326468	−	0.672702i
$249$		0			0
$250$	8.24628	+	13.4907i	0.521541	+	0.853226i
$251$			27.0687i			1.70856i	0.519811	+	0.854282i	$0.326003\pi$
$251$			27.0687i			1.70856i	−0.519811	+	0.854282i	$0.673997\pi$
$252$		0			0
$253$	0.0863187	−	0.169410i	0.00542681	−	0.0106507i
$254$	−0.436261	+	3.90735i	−0.0273734	+	0.245169i
$255$		0			0
$256$	−8.70628	+	13.4239i	−0.544143	+	0.838993i
$257$	−0.364893	+	0.364893i	−0.0227614	+	0.0227614i	−0.718396	−	0.695635i	$-0.755123\pi$
$257$	−0.364893	+	0.364893i	−0.0227614	+	0.0227614i	0.695635	+	0.718396i	$0.255123\pi$
$258$		0			0
$259$	28.8843	−	20.9857i	1.79478	−	1.30399i
$260$	13.5855	+	18.7948i	0.842538	+	1.16561i
$261$		0			0
$262$	14.5827	+	9.60483i	0.900920	+	0.593388i
$263$	−2.36297	+	14.9192i	−0.145707	+	0.919957i	0.801188	+	0.598413i	$0.204202\pi$
$263$	−2.36297	+	14.9192i	−0.145707	+	0.919957i	−0.946895	+	0.321544i	$0.895798\pi$
$264$		0			0
$265$	4.79287	−	5.43686i	0.294424	−	0.333984i
$266$	−9.23774	+	1.90115i	−0.566402	+	0.116567i
$267$		0			0
$268$	−4.12634	−	0.269842i	−0.252057	−	0.0164832i
$269$	18.9244	+	6.14891i	1.15384	+	0.374906i	0.822589	−	0.568636i	$-0.192529\pi$
$269$	18.9244	+	6.14891i	1.15384	+	0.374906i	0.331252	+	0.943542i	$0.392529\pi$
$270$		0			0
$271$	5.42995	−	1.76430i	0.329846	−	0.107173i	−0.139412	−	0.990234i	$-0.544521\pi$
$271$	5.42995	−	1.76430i	0.329846	−	0.107173i	0.469258	+	0.883061i	$0.344521\pi$
$272$	−6.81376	+	9.92038i	−0.413145	+	0.601511i
$273$		0			0
$274$	2.65377	−	5.85815i	0.160320	−	0.353904i
$275$	0.405841	−	0.191011i	0.0244731	−	0.0115184i
$276$		0			0
$277$	11.6279	−	1.84168i	0.698653	−	0.110656i	0.203003	−	0.979178i	$-0.434930\pi$
$277$	11.6279	−	1.84168i	0.698653	−	0.110656i	0.495650	+	0.868522i	$0.334930\pi$
$278$	−14.2118	−	17.7842i	−0.852368	−	1.06663i
$279$		0			0
$280$	7.49612	−	27.0116i	0.447979	−	1.61425i
$281$	2.40044	−	7.38779i	0.143198	−	0.440719i	−0.853577	−	0.520967i	$-0.825571\pi$
$281$	2.40044	−	7.38779i	0.143198	−	0.440719i	0.996775	+	0.0802486i	$0.0255714\pi$
$282$		0			0
$283$	8.36586	+	16.4189i	0.497299	+	0.976004i	0.994134	+	0.108159i	$0.0344955\pi$
$283$	8.36586	+	16.4189i	0.497299	+	0.976004i	−0.496835	+	0.867845i	$0.665504\pi$
$284$	−4.87140	−	1.10153i	−0.289065	−	0.0653637i
$285$		0			0
$286$	0.571863	−	0.325250i	0.0338150	−	0.0192324i
$287$	44.5717	+	7.05947i	2.63099	+	0.416707i
$288$		0			0
$289$	4.67138	−	6.42960i	0.274787	−	0.378212i
$290$	19.6896	+	4.10212i	1.15621	+	0.240885i
$291$		0			0
$292$	−5.50218	+	13.7972i	−0.321991	+	0.807423i
$293$	16.5382	+	16.5382i	0.966169	+	0.966169i	0.999446	−	0.0332770i	$-0.0105943\pi$
$293$	16.5382	+	16.5382i	0.966169	+	0.966169i	−0.0332770	+	0.999446i	$0.510594\pi$
$294$		0			0
$295$	−29.3942	+	11.6392i	−1.71139	+	0.677663i
$296$	18.6887	−	13.0314i	1.08626	−	0.757436i
$297$		0			0
$298$	−1.08758	+	3.95633i	−0.0630021	+	0.229184i
$299$	−10.9906			−0.635605
$300$		0			0
$301$	−49.2649			−2.83958
$302$	−1.50710	+	5.48241i	−0.0867238	+	0.315477i
$303$		0			0
$304$	−5.91739	+	1.09854i	−0.339386	+	0.0630053i
$305$	16.3168	+	19.7221i	0.934296	+	1.12928i
$306$		0			0
$307$	−22.4411	−	22.4411i	−1.28078	−	1.28078i	−0.940224	−	0.340557i	$-0.889384\pi$
$307$	−22.4411	−	22.4411i	−1.28078	−	1.28078i	−0.340557	−	0.940224i	$-0.610616\pi$
$308$	−0.738667	−	0.294571i	−0.0420894	−	0.0167848i
$309$		0			0
$310$	8.84871	+	9.74803i	0.502573	+	0.553651i
$311$	−8.54043	+	11.7549i	−0.484284	+	0.666559i	−0.979321	−	0.202312i	$-0.935154\pi$
$311$	−8.54043	+	11.7549i	−0.484284	+	0.666559i	0.495037	+	0.868872i	$0.335154\pi$
$312$		0			0
$313$	−2.22635	−	0.352619i	−0.125841	−	0.0199312i	0.0931963	−	0.995648i	$-0.470292\pi$
$313$	−2.22635	−	0.352619i	−0.125841	−	0.0199312i	−0.219037	+	0.975717i	$0.570292\pi$
$314$	4.02416	−	2.28876i	0.227096	−	0.129162i
$315$		0			0
$316$	−0.564707	+	2.49736i	−0.0317673	+	0.140488i
$317$	−3.60520	−	7.07561i	−0.202488	−	0.397406i	0.767323	−	0.641260i	$-0.221588\pi$
$317$	−3.60520	−	7.07561i	−0.202488	−	0.397406i	−0.969812	+	0.243854i	$0.921588\pi$
$318$		0			0
$319$	0.176312	−	0.542633i	0.00987158	−	0.0303816i
$320$	5.11726	−	17.1410i	0.286063	−	0.958211i
$321$		0			0
$322$	8.29366	+	10.3784i	0.462188	+	0.578367i
$323$	−4.47130	+	0.708185i	−0.248790	+	0.0394045i
$324$		0			0
$325$	−20.4884	−	15.8900i	−1.13649	−	0.881417i
$326$	3.88191	−	8.56924i	0.214999	−	0.474606i
$327$		0			0
$328$	28.3501	+	5.05619i	1.56537	+	0.279181i
$329$	32.4691	−	10.5499i	1.79008	−	0.581633i
$330$		0			0
$331$	−29.8062	−	9.68463i	−1.63830	−	0.532316i	−0.662141	−	0.749379i	$-0.730352\pi$
$331$	−29.8062	−	9.68463i	−1.63830	−	0.532316i	−0.976157	+	0.217064i	$0.930352\pi$
$332$	−0.296847	+	4.53930i	−0.0162916	+	0.249126i
$333$		0			0
$334$	−4.08655	+	0.841021i	−0.223606	+	0.0460186i
$335$	4.51187	−	1.00870i	0.246510	−	0.0551111i
$336$		0			0
$337$	−5.00654	+	31.6100i	−0.272723	+	1.72191i	0.347669	+	0.937617i	$0.386973\pi$
$337$	−5.00654	+	31.6100i	−0.272723	+	1.72191i	−0.620393	+	0.784291i	$0.713027\pi$
$338$	−16.4055	−	10.8054i	−0.892343	−	0.587738i
$339$		0			0
$340$	4.18911	−	12.7868i	0.227186	−	0.693463i
$341$	0.302150	−	0.219525i	0.0163623	−	0.0118879i
$342$		0			0
$343$	17.6934	−	17.6934i	0.955352	−	0.955352i
$344$	−31.4319	−	0.610265i	−1.69469	−	0.0329033i
$345$		0			0
$346$	1.02088	−	9.14345i	0.0548827	−	0.491555i
$347$	4.47490	−	8.78249i	0.240225	−	0.471469i	−0.739144	−	0.673548i	$-0.764770\pi$
$347$	4.47490	−	8.78249i	0.240225	−	0.471469i	0.979369	+	0.202079i	$0.0647697\pi$
$348$		0			0
$349$		−	19.1891i		−	1.02717i	−0.858039	−	0.513585i	$-0.828317\pi$
$349$		−	19.1891i		−	1.02717i	0.858039	−	0.513585i	$-0.171683\pi$
$350$	0.455925	+	31.3379i	0.0243702	+	1.67508i
$351$		0			0
$352$	−0.467633	−	0.197092i	−0.0249249	−	0.0105050i
$353$	−16.1097	+	31.6170i	−0.857432	+	1.68281i	−0.135570	+	0.990768i	$0.543287\pi$
$353$	−16.1097	+	31.6170i	−0.857432	+	1.68281i	−0.721862	+	0.692037i	$0.756713\pi$
$354$		0			0
$355$	5.57287	−	0.350824i	0.295777	−	0.0186198i
$356$	−23.9712	+	10.3031i	−1.27047	+	0.546061i
$357$		0			0
$358$	0.596327	+	12.9859i	0.0315168	+	0.686326i
$359$	0.644378	−	0.468168i	0.0340090	−	0.0247090i	−0.570651	−	0.821193i	$-0.693309\pi$
$359$	0.644378	−	0.468168i	0.0340090	−	0.0247090i	0.604660	+	0.796484i	$0.293309\pi$
$360$		0			0
$361$	13.5398	+	9.83724i	0.712621	+	0.517749i
$362$	−3.57731	+	5.43131i	−0.188019	+	0.285463i
$363$		0			0
$364$	4.21297	+	45.7751i	0.220820	+	2.39927i
$365$	1.56225	−	16.5335i	0.0817721	−	0.865403i
$366$		0			0
$367$	24.8460	−	12.6597i	1.29695	−	0.660830i	0.337135	−	0.941456i	$-0.390542\pi$
$367$	24.8460	−	12.6597i	1.29695	−	0.660830i	0.959817	+	0.280626i	$0.0905422\pi$
$368$	5.16294	+	6.72435i	0.269137	+	0.350531i
$369$		0			0
$370$	−15.9504	+	19.8605i	−0.829220	+	1.03250i
$371$	13.6634	−	4.43952i	0.709370	−	0.230488i
$372$		0			0
$373$	0.864521	+	5.45837i	0.0447632	+	0.282624i	0.999909	−	0.0135133i	$-0.00430155\pi$
$373$	0.864521	+	5.45837i	0.0447632	+	0.282624i	−0.955146	+	0.296137i	$0.904302\pi$
$374$	−0.347700	−	0.157510i	−0.0179791	−	0.00814464i
$375$		0			0
$376$	20.8466	−	6.32879i	1.07508	−	0.326382i
$377$	−32.5750	+	5.15937i	−1.67770	+	0.265721i
$378$		0			0
$379$	−5.76200	−	17.7336i	−0.295974	−	0.910915i	−0.982893	−	0.184180i	$-0.941037\pi$
$379$	−5.76200	−	17.7336i	−0.295974	−	0.910915i	0.686918	−	0.726735i	$-0.258963\pi$
$380$	6.00289	−	3.04026i	0.307942	−	0.155962i
$381$		0			0
$382$	2.04033	+	5.41982i	0.104392	+	0.277302i
$383$	8.53445	+	16.7498i	0.436090	+	0.855875i	0.999558	+	0.0297370i	$0.00946699\pi$
$383$	8.53445	+	16.7498i	0.436090	+	0.855875i	−0.563468	+	0.826138i	$0.690533\pi$
$384$		0			0
$385$	0.885158	+	0.0836387i	0.0451118	+	0.00426262i
$386$	11.3149	+	19.8943i	0.575916	+	1.01259i
$387$		0			0
$388$	4.72002	+	7.47833i	0.239623	+	0.379654i
$389$	3.79524	−	5.22370i	0.192426	−	0.264852i	−0.701892	−	0.712283i	$-0.747661\pi$
$389$	3.79524	−	5.22370i	0.192426	−	0.264852i	0.894318	+	0.447431i	$0.147661\pi$
$390$		0			0
$391$	3.74824	+	5.15901i	0.189557	+	0.260902i
$392$	25.7770	−	24.7951i	1.30193	−	1.25234i
$393$		0			0
$394$	8.99851	+	8.20835i	0.453338	+	0.413531i
$395$	−0.179853	−	2.85697i	−0.00904937	−	0.143750i
$396$		0			0
$397$	8.49393	+	4.32787i	0.426298	+	0.217210i	0.653958	−	0.756531i	$-0.273107\pi$
$397$	8.49393	+	4.32787i	0.426298	+	0.217210i	−0.227660	+	0.973741i	$0.573107\pi$
$398$	29.0949	+	7.99810i	1.45840	+	0.400909i
$399$		0			0
$400$	−0.0973070	+	19.9998i	−0.00486535	+	0.999988i
$401$	14.2450			0.711363			0.355682	−	0.934607i	$-0.384249\pi$
$401$	14.2450			0.711363			0.355682	+	0.934607i	$0.384249\pi$
$402$		0			0
$403$	−19.2358	−	9.80113i	−0.958204	−	0.488229i
$404$	−11.7203	−	6.97052i	−0.583108	−	0.346796i
$405$		0			0
$406$	29.4534	+	26.8671i	1.46175	+	1.33339i
$407$	0.510969	+	0.510969i	0.0253278	+	0.0253278i
$408$		0			0
$409$	−8.16703	−	11.2410i	−0.403834	−	0.555829i	0.557867	−	0.829930i	$-0.311620\pi$
$409$	−8.16703	−	11.2410i	−0.403834	−	0.555829i	−0.961701	+	0.274101i	$0.911620\pi$
$410$	−32.0063	+	3.49473i	−1.58068	+	0.172593i
$411$		0			0
$412$	2.64291	+	4.18738i	0.130207	+	0.206298i
$413$	−61.8949	−	9.80318i	−3.04565	−	0.482383i
$414$		0			0
$415$	−1.10965	−	4.96341i	−0.0544704	−	0.243644i
$416$	2.12091	+	29.2575i	0.103986	+	1.43447i
$417$		0			0
$418$	−0.0672535	−	0.178648i	−0.00328948	−	0.00873797i
$419$	−6.15217	+	18.9344i	−0.300553	+	0.925007i	0.680746	+	0.732519i	$0.261656\pi$
$419$	−6.15217	+	18.9344i	−0.300553	+	0.925007i	−0.981299	+	0.192488i	$0.938344\pi$
$420$		0			0
$421$	0.345619	+	1.06371i	0.0168444	+	0.0518419i	0.959125	−	0.282981i	$-0.0913234\pi$
$421$	0.345619	+	1.06371i	0.0168444	+	0.0518419i	−0.942281	+	0.334823i	$0.891323\pi$
$422$	28.4835	−	22.7619i	1.38655	−	1.10803i
$423$		0			0
$424$	8.77251	−	2.66324i	0.426031	−	0.129338i
$425$	−0.471412	+	15.0364i	−0.0228669	+	0.729371i
$426$		0			0
$427$	7.93715	+	50.1132i	0.384105	+	2.42515i
$428$	1.88912	+	7.43382i	0.0913141	+	0.359327i
$429$		0			0
$430$	33.9139	−	9.23415i	1.63547	−	0.445310i
$431$	8.32624	+	2.70536i	0.401061	+	0.130313i	0.502600	−	0.864519i	$-0.332377\pi$
$431$	8.32624	+	2.70536i	0.401061	+	0.130313i	−0.101539	+	0.994832i	$0.532377\pi$
$432$		0			0
$433$	14.4137	−	7.34415i	0.692678	−	0.352937i	−0.0719504	−	0.997408i	$-0.522922\pi$
$433$	14.4137	−	7.34415i	0.692678	−	0.352937i	0.764629	+	0.644471i	$0.222922\pi$
$434$	5.26038	+	25.5604i	0.252506	+	1.22694i
$435$		0			0
$436$	1.26095	+	13.7006i	0.0603887	+	0.656140i
$437$	−0.498865	+	3.14971i	−0.0238640	+	0.150671i
$438$		0			0
$439$	25.5000	+	18.5268i	1.21705	+	0.884236i	0.995852	−	0.0909931i	$-0.0290041\pi$
$439$	25.5000	+	18.5268i	1.21705	+	0.884236i	0.221195	+	0.975229i	$0.429004\pi$
$440$	0.563711	+	0.0643278i	0.0268738	+	0.00306671i
$441$		0			0
$442$	1.01218	+	22.0417i	0.0481444	+	1.04841i
$443$	22.7614	−	22.7614i	1.08143	−	1.08143i	0.0850506	−	0.996377i	$-0.472895\pi$
$443$	22.7614	−	22.7614i	1.08143	−	1.08143i	0.996377	−	0.0850506i	$-0.0271052\pi$
$444$		0			0
$445$	22.4762	−	18.5954i	1.06547	−	0.881504i
$446$	34.7677	+	3.88185i	1.64630	+	0.183811i
$447$		0			0
$448$	26.0273	−	24.0808i	1.22967	−	1.13771i
$449$			3.21571i			0.151759i	0.997117	+	0.0758794i	$0.0241764\pi$
$449$			3.21571i			0.151759i	−0.997117	+	0.0758794i	$0.975824\pi$
$450$		0			0
$451$			0.913365i			0.0430087i
$452$	17.8478	+	14.8394i	0.839491	+	0.697987i
$453$		0			0
$454$	−2.97893	+	26.6807i	−0.139808	+	1.25219i
$455$	−18.9213	−	47.7846i	−0.887046	−	2.24018i
$456$		0			0
$457$	−4.31437	+	4.31437i	−0.201818	+	0.201818i	−0.800778	−	0.598961i	$-0.795581\pi$
$457$	−4.31437	+	4.31437i	−0.201818	+	0.201818i	0.598961	+	0.800778i	$0.295581\pi$
$458$	−5.68412	+	0.261021i	−0.265601	+	0.0121967i
$459$		0			0
$460$	−7.65466	−	5.58993i	−0.356900	−	0.260632i
$461$	−19.3859	−	14.0847i	−0.902893	−	0.655990i	0.0363144	−	0.999340i	$-0.488438\pi$
$461$	−19.3859	−	14.0847i	−0.902893	−	0.655990i	−0.939207	+	0.343350i	$0.888438\pi$
$462$		0			0
$463$	−6.36230	+	40.1700i	−0.295681	+	1.86686i	0.175019	+	0.984565i	$0.444001\pi$
$463$	−6.36230	+	40.1700i	−0.295681	+	1.86686i	−0.470700	+	0.882293i	$0.655999\pi$
$464$	18.4590	+	17.5066i	0.856937	+	0.812721i
$465$		0			0
$466$	6.41328	−	1.31987i	0.297089	−	0.0611417i
$467$	−22.9322	+	11.6845i	−1.06118	+	0.540696i	−0.895306	−	0.445452i	$-0.853043\pi$
$467$	−22.9322	+	11.6845i	−1.06118	+	0.540696i	−0.165870	+	0.986148i	$0.553043\pi$
$468$		0			0
$469$	8.71563	+	2.83188i	0.402450	+	0.130764i
$470$	−20.3742	+	13.3485i	−0.939793	+	0.615719i
$471$		0			0
$472$	−39.3686	−	7.02132i	−1.81209	−	0.323182i
$473$	−0.155982	−	0.984834i	−0.00717208	−	0.0452827i
$474$		0			0
$475$	−5.48374	+	5.15034i	−0.251611	+	0.236314i
$476$	20.0501	−	17.5887i	0.918993	−	0.806176i
$477$		0			0
$478$	−17.8055	−	22.2812i	−0.814405	−	1.01912i
$479$	−4.89353	−	15.0607i	−0.223591	−	0.688142i	−0.998432	−	0.0559855i	$-0.982170\pi$
$479$	−4.89353	−	15.0607i	−0.223591	−	0.688142i	0.774841	−	0.632157i	$-0.217830\pi$
$480$		0			0
$481$	12.9079	−	39.7265i	0.588551	−	1.81137i
$482$	−8.89882	+	3.35003i	−0.405330	+	0.152590i
$483$		0			0
$484$	−4.84862	+	21.4426i	−0.220392	+	0.974661i
$485$	−7.41667	−	6.53819i	−0.336774	−	0.296884i
$486$		0			0
$487$	18.8395	+	2.98389i	0.853701	+	0.135213i	0.567922	−	0.823083i	$-0.307748\pi$
$487$	18.8395	+	2.98389i	0.853701	+	0.135213i	0.285779	+	0.958295i	$0.407748\pi$
$488$	4.44327	+	32.0714i	0.201137	+	1.45180i
$489$		0			0
$490$	−19.8541	+	34.7113i	−0.896918	+	1.56810i
$491$	−4.08602	−	5.62393i	−0.184400	−	0.253804i	0.706802	−	0.707411i	$-0.250137\pi$
$491$	−4.08602	−	5.62393i	−0.184400	−	0.253804i	−0.891202	+	0.453607i	$0.850137\pi$
$492$		0			0
$493$	13.5312	+	13.5312i	0.609413	+	0.609413i
$494$	−7.43627	+	8.15211i	−0.334574	+	0.366781i
$495$		0			0
$496$	3.03959	+	16.3731i	0.136482	+	0.735175i
$497$	9.86197	+	5.02493i	0.442370	+	0.225399i
$498$		0			0
$499$	−0.252832			−0.0113183			−0.00565916	−	0.999984i	$-0.501801\pi$
$499$	−0.252832			−0.0113183			−0.00565916	+	0.999984i	$0.501801\pi$
$500$	−6.18778	−	21.4875i	−0.276726	−	0.960949i
$501$		0			0
$502$	10.1469	−	36.9117i	0.452879	−	1.64745i
$503$	15.9788	+	8.14160i	0.712459	+	0.363016i	0.772357	−	0.635189i	$-0.219078\pi$
$503$	15.9788	+	8.14160i	0.712459	+	0.363016i	−0.0598984	+	0.998204i	$0.519078\pi$
$504$		0			0
$505$	14.7672	+	3.79099i	0.657133	+	0.168697i
$506$	−0.181211	+	0.198655i	−0.00805582	+	0.00883130i
$507$		0			0
$508$	2.05960	−	5.16464i	0.0913799	−	0.229144i
$509$	12.4593	+	17.1488i	0.552249	+	0.760105i	0.990315	−	0.138837i	$-0.0443365\pi$
$509$	12.4593	+	17.1488i	0.552249	+	0.760105i	−0.438066	+	0.898943i	$0.644336\pi$
$510$		0			0
$511$	19.3490	−	26.6317i	0.855951	−	1.17812i
$512$	16.9042	−	15.0416i	0.747066	−	0.664750i
$513$		0			0
$514$	0.634361	−	0.360795i	0.0279804	−	0.0159140i
$515$	−4.15286	−	3.66097i	−0.182997	−	0.161321i
$516$		0			0
$517$	0.313701	+	0.615673i	0.0137966	+	0.0270773i
$518$	−47.2541	+	17.7892i	−2.07623	+	0.781611i
$519$		0			0
$520$	−11.4802	−	30.7218i	−0.503441	−	1.34724i
$521$	−3.05487	−	9.40193i	−0.133836	−	0.411906i	0.861571	−	0.507637i	$-0.169481\pi$
$521$	−3.05487	−	9.40193i	−0.133836	−	0.411906i	−0.995407	+	0.0957313i	$0.969481\pi$
$522$		0			0
$523$	19.0721	−	3.02072i	0.833963	−	0.132087i	0.275171	−	0.961395i	$-0.411265\pi$
$523$	19.0721	−	3.02072i	0.833963	−	0.132087i	0.558791	+	0.829308i	$0.311265\pi$
$524$	−16.2849	−	18.5638i	−0.711409	−	0.810965i
$525$		0			0
$526$	8.81478	−	19.4585i	0.384343	−	0.848429i
$527$	1.95951	+	12.3719i	0.0853576	+	0.538927i
$528$		0			0
$529$	−17.6021	+	5.71927i	−0.765309	+	0.248664i
$530$	−8.57375	+	5.61721i	−0.372420	+	0.243996i
$531$		0			0
$532$	13.3095	+	0.870373i	0.577040	+	0.0377355i
$533$	47.0425	−	23.9693i	2.03764	−	1.03823i
$534$		0			0
$535$	−4.36553	−	7.38108i	−0.188738	−	0.319112i
$536$	5.52565	+	1.91475i	0.238672	+	0.0827047i
$537$		0			0
$538$	−23.5009	−	15.4788i	−1.01320	−	0.667338i
$539$	0.917753	+	0.666787i	0.0395304	+	0.0287205i
$540$		0			0
$541$	4.14253	−	3.00972i	0.178101	−	0.129398i	−0.495163	−	0.868800i	$-0.664892\pi$
$541$	4.14253	−	3.00972i	0.178101	−	0.129398i	0.673264	+	0.739402i	$0.264892\pi$
$542$	−8.06579	+	0.370390i	−0.346455	+	0.0159096i
$543$		0			0
$544$	13.0102	−	10.9735i	0.557806	−	0.470486i
$545$	−5.66321	−	14.3021i	−0.242585	−	0.612633i
$546$		0			0
$547$	−8.45520	+	16.5943i	−0.361518	+	0.709520i	−0.998095	−	0.0616937i	$-0.980350\pi$
$547$	−8.45520	+	16.5943i	−0.361518	+	0.709520i	0.636577	+	0.771213i	$0.280350\pi$
$548$	−5.81473	+	6.99355i	−0.248393	+	0.298750i
$549$		0			0
$550$	−0.625018	+	0.108336i	−0.0266509	+	0.00461946i
$551$			9.56956i			0.407677i
$552$		0			0
$553$	2.57607	−	5.05582i	0.109546	−	0.214995i
$554$	−16.5465	−	1.84744i	−0.702994	−	0.0784901i
$555$		0			0
$556$	12.7131	+	29.5785i	0.539155	+	1.25441i
$557$	−21.1313	+	21.1313i	−0.895360	+	0.895360i	−0.995021	−	0.0996610i	$-0.968224\pi$
$557$	−21.1313	+	21.1313i	−0.895360	+	0.895360i	0.0996610	+	0.995021i	$0.468224\pi$
$558$		0			0
$559$	−46.6300	+	33.8787i	−1.97224	+	1.43292i
$560$	−20.3474	+	34.0238i	−0.859835	+	1.43777i
$561$		0			0
$562$	−6.04267	+	9.17438i	−0.254895	+	0.386998i
$563$	−0.604217	+	3.81487i	−0.0254647	+	0.160778i	−0.997144	−	0.0755266i	$-0.975936\pi$
$563$	−0.604217	+	3.81487i	−0.0254647	+	0.160778i	0.971679	+	0.236304i	$0.0759362\pi$
$564$		0			0
$565$	−23.8168	−	10.3054i	−1.00198	−	0.433551i
$566$	−5.25317	−	25.5253i	−0.220807	−	1.07291i
$567$		0			0
$568$	6.22987	+	3.32816i	0.261399	+	0.139646i
$569$	−2.43157	−	0.790065i	−0.101937	−	0.0331213i	0.257605	−	0.966250i	$-0.417067\pi$
$569$	−2.43157	−	0.790065i	−0.101937	−	0.0331213i	−0.359541	+	0.933129i	$0.617067\pi$
$570$		0			0
$571$	2.33800	−	0.759663i	0.0978424	−	0.0317909i	−0.259687	−	0.965693i	$-0.583619\pi$
$571$	2.33800	−	0.759663i	0.0978424	−	0.0317909i	0.357529	+	0.933902i	$0.383619\pi$
$572$	−0.901731	+	0.229153i	−0.0377033	+	0.00958135i
$573$		0			0
$574$	−58.1330	−	26.3345i	−2.42642	−	1.09918i
$575$	9.97100	+	3.58894i	0.415820	+	0.149669i
$576$		0			0
$577$	−6.93561	+	1.09849i	−0.288733	+	0.0457308i	−0.299121	−	0.954215i	$-0.596693\pi$
$577$	−6.93561	+	1.09849i	−0.288733	+	0.0457308i	0.0103878	+	0.999946i	$0.496693\pi$
$578$	−8.78020	+	7.01648i	−0.365208	+	0.291847i
$579$		0			0
$580$	−25.3116	−	12.9746i	−1.05101	−	0.538740i
$581$	3.11529	−	9.58788i	0.129244	−	0.397772i
$582$		0			0
$583$	0.132010	+	0.259083i	0.00546728	+	0.0107301i
$584$	12.6749	−	16.7518i	0.524492	−	0.693194i
$585$		0			0
$586$	−16.3524	−	28.7513i	−0.675513	−	1.18771i
$587$	−19.2103	−	3.04261i	−0.792893	−	0.125582i	−0.253167	−	0.967423i	$-0.581472\pi$
$587$	−19.2103	−	3.04261i	−0.792893	−	0.125582i	−0.539726	+	0.841841i	$0.681472\pi$
$588$		0			0
$589$	−3.68193	+	5.06775i	−0.151711	+	0.208813i
$590$	44.4458	−	4.85299i	1.82980	−	0.199794i
$591$		0			0
$592$	−30.3693	+	10.7644i	−1.24817	+	0.442416i
$593$	26.2991	+	26.2991i	1.07998	+	1.07998i	0.996511	+	0.0834655i	$0.0265988\pi$
$593$	26.2991	+	26.2991i	1.07998	+	1.07998i	0.0834655	+	0.996511i	$0.473401\pi$
$594$		0			0
$595$	−15.9772	+	25.1781i	−0.655001	+	1.03220i
$596$	2.96612	−	4.98728i	0.121497	−	0.204287i
$597$		0			0
$598$	14.9871	+	4.11992i	0.612870	+	0.168476i
$599$	−41.8236			−1.70887			−0.854434	−	0.519561i	$-0.826096\pi$
$599$	−41.8236			−1.70887			−0.854434	+	0.519561i	$0.826096\pi$
$600$		0			0
$601$	−37.3005			−1.52152			−0.760759	−	0.649034i	$-0.775173\pi$
$601$	−37.3005			−1.52152			−0.760759	+	0.649034i	$0.775173\pi$
$602$	67.1791	+	18.4673i	2.73801	+	0.752672i
$603$		0			0
$604$	4.11024	−	6.91103i	0.167243	−	0.281206i
$605$	−1.54423	−	24.5302i	−0.0627818	−	0.997294i
$606$		0			0
$607$	−6.86710	−	6.86710i	−0.278727	−	0.278727i	0.553874	−	0.832601i	$-0.313149\pi$
$607$	−6.86710	−	6.86710i	−0.278727	−	0.278727i	−0.832601	+	0.553874i	$0.813149\pi$
$608$	8.48092	+	0.720184i	0.343947	+	0.0292073i
$609$		0			0
$610$	−14.8571	−	33.0101i	−0.601544	−	1.33654i
$611$	23.4776	−	32.3141i	0.949800	−	1.30729i
$612$		0			0
$613$	−9.83772	−	1.55814i	−0.397342	−	0.0629328i	−0.0454338	−	0.998967i	$-0.514467\pi$
$613$	−9.83772	−	1.55814i	−0.397342	−	0.0629328i	−0.351908	+	0.936035i	$0.614467\pi$
$614$	22.1891	+	39.0135i	0.895479	+	1.57446i
$615$		0			0
$616$	0.896844	+	0.678580i	0.0361349	+	0.0273408i
$617$	13.7364	+	26.9593i	0.553008	+	1.08534i	0.983188	+	0.182597i	$0.0584503\pi$
$617$	13.7364	+	26.9593i	0.553008	+	1.08534i	−0.430179	+	0.902743i	$0.641550\pi$
$618$		0			0
$619$	10.2938	−	31.6812i	0.413744	−	1.27337i	−0.499625	−	0.866242i	$-0.666529\pi$
$619$	10.2938	−	31.6812i	0.413744	−	1.27337i	0.913369	−	0.407133i	$-0.133471\pi$
$620$	−8.41223	−	16.6097i	−0.337843	−	0.667061i
$621$		0			0
$622$	16.0524	−	12.8279i	0.643642	−	0.514351i
$623$	57.1113	−	9.04554i	2.28811	−	0.362402i
$624$		0			0
$625$	13.3988	+	21.1062i	0.535953	+	0.844248i
$626$	2.90373	+	1.31541i	0.116057	+	0.0525742i
$627$		0			0
$628$	−6.34541	+	1.61253i	−0.253209	+	0.0643469i
$629$	−23.0498	+	7.48932i	−0.919054	+	0.298619i
$630$		0			0
$631$	4.13387	+	1.34318i	0.164567	+	0.0534710i	0.390142	−	0.920755i	$-0.372426\pi$
$631$	4.13387	+	1.34318i	0.164567	+	0.0534710i	−0.225575	+	0.974226i	$0.572426\pi$
$632$	1.70621	−	3.19379i	0.0678692	−	0.127042i
$633$		0			0
$634$	2.26381	+	10.9999i	0.0899076	+	0.436864i
$635$	−0.584789	+	6.18889i	−0.0232066	+	0.245599i
$636$		0			0
$637$	10.2581	−	64.7669i	0.406439	−	2.56616i
$638$	−0.443834	+	0.673857i	−0.0175716	+	0.0266783i
$639$		0			0
$640$	−13.4035	+	21.4557i	−0.529818	+	0.848111i
$641$	−23.8819	+	17.3512i	−0.943278	+	0.685332i	−0.949208	−	0.314651i	$-0.898113\pi$
$641$	−23.8819	+	17.3512i	−0.943278	+	0.685332i	0.00592940	+	0.999982i	$0.498113\pi$
$642$		0			0
$643$	5.10377	−	5.10377i	0.201273	−	0.201273i	−0.599272	−	0.800545i	$-0.704543\pi$
$643$	5.10377	−	5.10377i	0.201273	−	0.201273i	0.800545	+	0.599272i	$0.204543\pi$
$644$	−7.41904	−	17.2613i	−0.292351	−	0.680189i
$645$		0			0
$646$	6.36266	+	0.710400i	0.250336	+	0.0279503i
$647$	−8.71938	+	17.1127i	−0.342794	+	0.672771i	−0.996465	−	0.0840074i	$-0.973228\pi$
$647$	−8.71938	+	17.1127i	−0.342794	+	0.672771i	0.653671	+	0.756779i	$0.273228\pi$
$648$		0			0
$649$		−	1.26835i		−	0.0497872i
$650$	21.9821	+	29.3482i	0.862208	+	1.15113i
$651$		0			0
$652$	−8.50572	+	10.2301i	−0.333110	+	0.400641i
$653$	19.9775	−	39.2081i	0.781781	−	1.53433i	−0.0622643	−	0.998060i	$-0.519832\pi$
$653$	19.9775	−	39.2081i	0.781781	−	1.53433i	0.844045	−	0.536272i	$-0.180168\pi$
$654$		0			0
$655$	23.3118	+	14.7929i	0.910866	+	0.578005i
$656$	−36.7636	−	17.5220i	−1.43538	−	0.684119i
$657$		0			0
$658$	−48.2305	+	2.21480i	−1.88022	+	0.0863419i
$659$	−27.2711	+	19.8136i	−1.06233	+	0.771830i	−0.974518	−	0.224307i	$-0.927988\pi$
$659$	−27.2711	+	19.8136i	−1.06233	+	0.771830i	−0.0878139	+	0.996137i	$0.527988\pi$
$660$		0			0
$661$	36.2595	+	26.3441i	1.41033	+	1.02467i	0.993274	+	0.115787i	$0.0369389\pi$
$661$	36.2595	+	26.3441i	1.41033	+	1.02467i	0.417058	+	0.908880i	$0.363061\pi$
$662$	37.0143	+	24.3793i	1.43860	+	0.947529i
$663$		0			0
$664$	2.10638	−	6.07864i	0.0817433	−	0.235897i
$665$	−14.5530	+	3.25355i	−0.564341	+	0.126167i
$666$		0			0
$667$	12.0107	−	6.11974i	0.465055	−	0.236957i
$668$	5.88779	+	0.385031i	0.227806	+	0.0148973i
$669$		0			0
$670$	−6.53063	−	0.315816i	−0.252300	−	0.0122010i
$671$	−0.976660	+	0.317336i	−0.0377035	+	0.0122506i
$672$		0			0
$673$	4.08246	+	25.7757i	0.157367	+	0.993579i	0.932340	+	0.361583i	$0.117764\pi$
$673$	4.08246	+	25.7757i	0.157367	+	0.993579i	−0.774972	+	0.631995i	$0.782236\pi$
$674$	18.6763	−	41.2276i	0.719384	−	1.58803i
$675$		0			0
$676$	18.3205	+	20.8843i	0.704636	+	0.803243i
$677$	−8.61245	+	1.36408i	−0.331003	+	0.0524258i	−0.319724	−	0.947511i	$-0.603590\pi$
$677$	−8.61245	+	1.36408i	−0.331003	+	0.0524258i	−0.0112789	+	0.999936i	$0.503590\pi$
$678$		0			0
$679$	−6.05616	−	18.6389i	−0.232414	−	0.715297i
$680$	−10.5056	+	15.8662i	−0.402872	+	0.608439i
$681$		0			0
$682$	−0.494310	+	0.186087i	−0.0189281	+	0.00712564i
$683$	−1.48416	−	2.91283i	−0.0567898	−	0.111456i	0.860867	−	0.508830i	$-0.169922\pi$
$683$	−1.48416	−	2.91283i	−0.0567898	−	0.111456i	−0.917657	+	0.397373i	$0.869922\pi$
$684$		0			0
$685$	4.03810	−	9.33246i	0.154288	−	0.356575i
$686$	−30.7597	+	17.4947i	−1.17441	+	0.667950i
$687$		0			0
$688$	42.6327	+	12.6146i	1.62536	+	0.480929i
$689$	9.87967	−	13.5982i	0.376385	−	0.518050i
$690$		0			0
$691$	−16.4783	−	22.6804i	−0.626864	−	0.862805i	0.370966	−	0.928647i	$-0.379027\pi$
$691$	−16.4783	−	22.6804i	−0.626864	−	0.862805i	−0.997830	+	0.0658420i	$0.979027\pi$
$692$	−4.81959	+	12.0856i	−0.183213	+	0.459425i
$693$		0			0
$694$	−9.39429	+	10.2986i	−0.356602	+	0.390930i
$695$	−22.9451	−	27.7337i	−0.870356	−	1.05200i
$696$		0			0
$697$	−27.2946	−	13.9073i	−1.03385	−	0.526775i
$698$	−7.19318	+	26.1668i	−0.272266	+	0.990428i
$699$		0			0
$700$	11.1255	−	42.9041i	0.420505	−	1.62162i
$701$	−23.1470			−0.874250			−0.437125	−	0.899401i	$-0.644003\pi$
$701$	−23.1470			−0.874250			−0.437125	+	0.899401i	$0.644003\pi$
$702$		0			0
$703$	−10.7990	−	5.50236i	−0.407291	−	0.207525i
$704$	0.563797	+	0.444056i	0.0212489	+	0.0167360i
$705$		0			0
$706$	33.8195	−	37.0751i	1.27281	−	1.39534i
$707$	21.3692	+	21.3692i	0.803672	+	0.803672i
$708$		0			0
$709$	22.6308	+	31.1487i	0.849919	+	1.16981i	0.983881	+	0.178827i	$0.0572302\pi$
$709$	22.6308	+	31.1487i	0.849919	+	1.16981i	−0.133961	+	0.990987i	$0.542770\pi$
$710$	−7.73083	−	1.61064i	−0.290133	−	0.0604461i
$711$		0			0
$712$	36.5500	−	5.06375i	1.36977	−	0.189772i
$713$	8.71508	+	1.38033i	0.326382	+	0.0516939i
$714$		0			0
$715$	0.895333	−	0.529543i	0.0334835	−	0.0198038i
$716$	4.05469	−	17.9315i	0.151531	−	0.670131i
$717$		0			0
$718$	−1.05419	+	0.396857i	−0.0393420	+	0.0148106i
$719$	3.78332	−	11.6439i	0.141094	−	0.434243i	−0.855394	−	0.517978i	$-0.826685\pi$
$719$	3.78332	−	11.6439i	0.141094	−	0.434243i	0.996488	+	0.0837350i	$0.0266849\pi$
$720$		0			0
$721$	−3.39106	−	10.4366i	−0.126290	−	0.388680i
$722$	−14.7757	−	18.4898i	−0.549894	−	0.688120i
$723$		0			0
$724$	6.91409	−	6.06531i	0.256960	−	0.225415i
$725$	31.2377	+	5.95649i	1.16014	+	0.221218i
$726$		0			0
$727$	7.14374	+	45.1038i	0.264947	+	1.67281i	0.657789	+	0.753202i	$0.271492\pi$
$727$	7.14374	+	45.1038i	0.264947	+	1.67281i	−0.392842	+	0.919606i	$0.628508\pi$
$728$	11.4142	−	63.9995i	0.423038	−	2.37198i
$729$		0			0
$730$	−8.32804	+	21.9599i	−0.308234	+	0.812774i
$731$	31.8053	+	10.3342i	1.17636	+	0.382223i
$732$		0			0
$733$	−37.7569	+	19.2381i	−1.39458	+	0.710575i	−0.979918	−	0.199399i	$-0.936101\pi$
$733$	−37.7569	+	19.2381i	−1.39458	+	0.710575i	−0.414664	+	0.909974i	$0.636101\pi$
$734$	−38.6263	+	7.94939i	−1.42572	+	0.293417i
$735$		0			0
$736$	−4.51966	−	11.1049i	−0.166597	−	0.409331i
$737$	−0.0290155	+	0.183197i	−0.00106880	+	0.00674814i
$738$		0			0
$739$	−8.08428	−	5.87357i	−0.297385	−	0.216063i	0.429080	−	0.903267i	$-0.358838\pi$
$739$	−8.08428	−	5.87357i	−0.297385	−	0.216063i	−0.726465	+	0.687204i	$0.758838\pi$
$740$	29.1952	−	21.1033i	1.07324	−	0.775771i
$741$		0			0
$742$	−20.2960	+	0.932017i	−0.745091	+	0.0342154i
$743$	16.3290	−	16.3290i	0.599053	−	0.599053i	−0.341008	−	0.940060i	$-0.610768\pi$
$743$	16.3290	−	16.3290i	0.599053	−	0.599053i	0.940060	+	0.341008i	$0.110768\pi$
$744$		0			0
$745$	−1.61316	+	6.28381i	−0.0591015	+	0.230221i
$746$	0.867224	−	7.76726i	0.0317513	−	0.284379i
$747$		0			0
$748$	0.415090	+	0.345123i	0.0151772	+	0.0126189i
$749$		−	16.9982i		−	0.621099i
$750$		0			0
$751$		−	42.7056i		−	1.55835i	−0.626807	−	0.779174i	$-0.715639\pi$
$751$		−	42.7056i		−	1.55835i	0.626807	−	0.779174i	$-0.284361\pi$
$752$	−30.7994	+	0.815630i	−1.12314	+	0.0297430i
$753$		0			0
$754$	46.3542	+	5.17551i	1.68812	+	0.188481i
$755$	−2.23540	+	8.70767i	−0.0813546	+	0.316904i
$756$		0			0
$757$	−7.75454	+	7.75454i	−0.281844	+	0.281844i	−0.833844	−	0.552000i	$-0.813865\pi$
$757$	−7.75454	+	7.75454i	−0.281844	+	0.281844i	0.552000	+	0.833844i	$0.313865\pi$
$758$	1.20965	+	26.3420i	0.0439366	+	0.956784i
$759$		0			0
$760$	−9.32538	+	1.89555i	−0.338267	+	0.0687588i
$761$	13.9344	+	10.1240i	0.505123	+	0.366993i	0.810970	−	0.585087i	$-0.198940\pi$
$761$	13.9344	+	10.1240i	0.505123	+	0.366993i	−0.305847	+	0.952081i	$0.598940\pi$
$762$		0			0
$763$	4.76985	−	30.1156i	0.172680	−	1.09026i
$764$	−0.750597	−	8.15545i	−0.0271557	−	0.295054i
$765$		0			0
$766$	−5.35904	−	26.0397i	−0.193630	−	0.940853i
$767$	−65.3259	+	33.2852i	−2.35878	+	1.20186i
$768$		0			0
$769$	−15.3435	−	4.98540i	−0.553300	−	0.179778i	0.0190041	−	0.999819i	$-0.493950\pi$
$769$	−15.3435	−	4.98540i	−0.553300	−	0.179778i	−0.572304	+	0.820041i	$0.693950\pi$
$770$	−1.17567	−	0.445860i	−0.0423684	−	0.0160677i
$771$		0			0
$772$	−7.97187	−	31.3699i	−0.286914	−	1.12903i
$773$	4.21620	+	26.6201i	0.151646	+	0.957457i	0.939737	+	0.341898i	$0.111070\pi$
$773$	4.21620	+	26.6201i	0.151646	+	0.957457i	−0.788091	+	0.615559i	$0.788930\pi$
$774$		0			0
$775$	14.2507	+	15.1732i	0.511901	+	0.545038i
$776$	−3.63305	−	11.9670i	−0.130419	−	0.429590i
$777$		0			0
$778$	−7.13344	+	5.70051i	−0.255746	+	0.204373i
$779$	−4.73390	−	14.5695i	−0.169610	−	0.522005i
$780$		0			0
$781$	−0.0692262	+	0.213056i	−0.00247711	+	0.00762375i
$782$	−3.17731	−	8.44003i	−0.113621	−	0.301815i
$783$		0			0
$784$	−44.4448	+	24.1486i	−1.58732	+	0.862451i
$785$	6.30039	−	3.72636i	0.224870	−	0.132999i
$786$		0			0
$787$	−17.4691	−	2.76683i	−0.622705	−	0.0986268i	−0.162894	−	0.986644i	$-0.552083\pi$
$787$	−17.4691	−	2.76683i	−0.622705	−	0.0986268i	−0.459811	+	0.888017i	$0.652083\pi$
$788$	−9.19366	−	14.5663i	−0.327511	−	0.518903i
$789$		0			0
$790$	−0.825705	+	3.96327i	−0.0293773	+	0.141007i
$791$	−30.2353	−	41.6153i	−1.07504	−	1.47967i
$792$		0			0
$793$	41.9746	+	41.9746i	1.49056	+	1.49056i
$794$	−9.96023	−	9.08562i	−0.353475	−	0.322437i
$795$		0			0
$796$	−36.6765	−	21.8129i	−1.29996	−	0.773137i
$797$	−19.2719	−	9.81954i	−0.682647	−	0.347826i	0.0780351	−	0.996951i	$-0.475135\pi$
$797$	−19.2719	−	9.81954i	−0.682647	−	0.347826i	−0.760682	+	0.649125i	$0.775135\pi$
$798$		0			0
$799$	−23.1750			−0.819873
$800$	7.62975	−	27.2358i	0.269752	−	0.962930i
$801$		0			0
$802$	−19.4249	−	5.33986i	−0.685919	−	0.188557i
$803$	0.593645	+	0.302477i	0.0209493	+	0.0106742i
$804$		0			0
$805$	13.3902	+	16.1847i	0.471941	+	0.570436i
$806$	22.5565	+	20.5758i	0.794517	+	0.724751i
$807$		0			0
$808$	13.3692	+	13.8986i	0.470328	+	0.488953i
$809$	17.3745	+	23.9139i	0.610854	+	0.840768i	0.996647	−	0.0818172i	$-0.0260724\pi$
$809$	17.3745	+	23.9139i	0.610854	+	0.840768i	−0.385794	+	0.922585i	$0.626072\pi$
$810$		0			0
$811$	−15.1413	+	20.8402i	−0.531683	+	0.731799i	−0.987386	−	0.158333i	$-0.949388\pi$
$811$	−15.1413	+	20.8402i	−0.531683	+	0.731799i	0.455703	+	0.890132i	$0.349388\pi$
$812$	−30.0922	−	47.6776i	−1.05603	−	1.67316i
$813$		0			0
$814$	−0.505231	−	0.888312i	−0.0177083	−	0.0311353i
$815$	5.90689	−	13.6514i	0.206909	−	0.478188i
$816$		0			0
$817$	7.59246	+	14.9010i	0.265626	+	0.521321i
$818$	6.92304	+	18.3900i	0.242058	+	0.642990i
$819$		0			0
$820$	44.9547	+	7.23227i	1.56989	+	0.252562i
$821$	5.90690	+	18.1796i	0.206152	+	0.634471i	0.999664	+	0.0259166i	$0.00825044\pi$
$821$	5.90690	+	18.1796i	0.206152	+	0.634471i	−0.793512	+	0.608555i	$0.791750\pi$
$822$		0			0
$823$	3.92443	−	0.621568i	0.136797	−	0.0216665i	−0.0876604	−	0.996150i	$-0.527939\pi$
$823$	3.92443	−	0.621568i	0.136797	−	0.0216665i	0.224457	+	0.974484i	$0.427939\pi$
$824$	−2.03427	−	6.70075i	−0.0708673	−	0.233432i
$825$		0			0
$826$	80.7268	+	36.5696i	2.80884	+	1.27242i
$827$	−4.58447	−	28.9452i	−0.159418	−	1.00652i	−0.929565	−	0.368658i	$-0.879817\pi$
$827$	−4.58447	−	28.9452i	−0.159418	−	1.00652i	0.770147	−	0.637866i	$-0.220183\pi$
$828$		0			0
$829$	33.1072	−	10.7572i	1.14986	−	0.373612i	0.328770	−	0.944410i	$-0.393366\pi$
$829$	33.1072	−	10.7572i	1.14986	−	0.373612i	0.821091	+	0.570798i	$0.193366\pi$
$830$	−0.347422	+	7.18420i	−0.0120592	+	0.249367i
$831$		0			0
$832$	8.07525	−	40.6914i	0.279959	−	1.41072i
$833$	−33.9000	+	17.2729i	−1.17457	+	0.598471i
$834$		0			0
$835$	−6.43789	+	1.43929i	−0.222792	+	0.0498087i
$836$	0.0247412	+	0.268820i	0.000855693	+	0.00929735i
$837$		0			0
$838$	15.4870	−	23.5133i	0.534989	−	0.812255i
$839$	21.2823	+	15.4625i	0.734746	+	0.533824i	0.891061	−	0.453883i	$-0.149962\pi$
$839$	21.2823	+	15.4625i	0.734746	+	0.533824i	−0.156315	+	0.987707i	$0.549962\pi$
$840$		0			0
$841$	9.26395	−	6.73065i	0.319447	−	0.232092i
$842$	−0.0725580	−	1.58006i	−0.00250051	−	0.0544524i
$843$		0			0
$844$	−47.3733	+	20.3615i	−1.63066	+	0.700871i
$845$	−26.2258	−	16.6420i	−0.902194	−	0.572502i
$846$		0			0
$847$	22.1183	−	43.4096i	0.759994	−	1.49157i
$848$	−12.9608	+	0.343228i	−0.445075	+	0.0117865i
$849$		0			0
$850$	6.27932	−	20.3273i	0.215379	−	0.697221i
$851$			17.0725i			0.585237i
$852$		0			0
$853$	−22.5226	+	44.2032i	−0.771161	+	1.51349i	0.0847720	+	0.996400i	$0.472984\pi$
$853$	−22.5226	+	44.2032i	−0.771161	+	1.51349i	−0.855933	+	0.517087i	$0.827016\pi$
$854$	7.96197	−	71.3110i	0.272453	−	2.44021i
$855$		0			0
$856$	0.210563	−	10.8451i	0.00719689	−	0.370679i
$857$	1.39722	−	1.39722i	0.0477281	−	0.0477281i	−0.682840	−	0.730568i	$-0.739255\pi$
$857$	1.39722	−	1.39722i	0.0477281	−	0.0477281i	0.730568	+	0.682840i	$0.239255\pi$
$858$		0			0
$859$	8.28918	−	6.02244i	0.282823	−	0.205483i	−0.437325	−	0.899304i	$-0.644074\pi$
$859$	8.28918	−	6.02244i	0.282823	−	0.205483i	0.720148	+	0.693821i	$0.244074\pi$
$860$	−49.7074	−	0.120923i	−1.69501	−	0.00412343i
$861$		0			0
$862$	−10.3398	−	6.81026i	−0.352174	−	0.231958i
$863$	−3.08157	+	19.4563i	−0.104898	+	0.662299i	0.878072	+	0.478529i	$0.158830\pi$
$863$	−3.08157	+	19.4563i	−0.104898	+	0.662299i	−0.982969	+	0.183769i	$0.941170\pi$
$864$		0			0
$865$	1.36844	−	14.4824i	0.0465285	−	0.492416i
$866$	−22.4079	+	4.61161i	−0.761453	+	0.156709i
$867$		0			0
$868$	2.40828	−	36.8267i	0.0817423	−	1.24998i
$869$	0.109225	+	0.0354894i	0.00370521	+	0.00120389i
$870$		0			0
$871$	10.1969	−	3.31318i	0.345509	−	0.112263i
$872$	3.41630	−	19.1552i	0.115691	−	0.648678i
$873$		0			0
$874$	1.86096	−	4.10803i	0.0629479	−	0.138956i
$875$	1.56210	+	49.5301i	0.0528087	+	1.67442i
$876$		0			0
$877$	−42.7175	+	6.76579i	−1.44247	+	0.228465i	−0.828111	−	0.560564i	$-0.810585\pi$
$877$	−42.7175	+	6.76579i	−1.44247	+	0.228465i	−0.614357	+	0.789028i	$0.710585\pi$
$878$	−27.8276	−	34.8225i	−0.939135	−	1.17520i
$879$		0			0
$880$	−0.744578	−	0.299030i	−0.0250997	−	0.0100803i
$881$	9.84663	−	30.3048i	0.331741	−	1.02100i	−0.636564	−	0.771224i	$-0.719645\pi$
$881$	9.84663	−	30.3048i	0.331741	−	1.02100i	0.968305	−	0.249771i	$-0.0803553\pi$
$882$		0			0
$883$	−19.3210	−	37.9195i	−0.650202	−	1.27609i	−0.947025	−	0.321161i	$-0.895927\pi$
$883$	−19.3210	−	37.9195i	−0.650202	−	1.27609i	0.296822	−	0.954933i	$-0.404073\pi$
$884$	6.88224	−	30.4360i	0.231475	−	1.02367i
$885$		0			0
$886$	−39.5704	+	22.5058i	−1.32939	+	0.756098i
$887$	−9.67782	−	1.53282i	−0.324949	−	0.0514669i	−0.00817134	−	0.999967i	$-0.502601\pi$
$887$	−9.67782	−	1.53282i	−0.324949	−	0.0514669i	−0.316778	+	0.948500i	$0.602601\pi$
$888$		0			0
$889$	−7.24281	+	9.96887i	−0.242916	+	0.334345i
$890$	−37.6198	+	16.9318i	−1.26102	+	0.567555i
$891$		0			0
$892$	−45.9550	−	18.3263i	−1.53869	−	0.613611i
$893$	−8.19496	−	8.19496i	−0.274234	−	0.274234i
$894$		0			0
$895$	1.29137	+	20.5135i	0.0431658	+	0.685692i
$896$	−44.5184	+	23.0808i	−1.48726	+	0.771074i
$897$		0			0
$898$	1.20543	−	4.38503i	0.0402258	−	0.146330i
$899$	26.4785			0.883107
$900$		0			0
$901$	−9.75235			−0.324898
$902$	0.342382	−	1.24549i	0.0114001	−	0.0414703i
$903$		0			0
$904$	−18.7751	−	26.9258i	−0.624452	−	0.895540i
$905$	−5.50960	+	8.68246i	−0.183145	+	0.288615i
$906$		0			0
$907$	18.8705	+	18.8705i	0.626584	+	0.626584i	0.947207	−	0.320623i	$-0.103892\pi$
$907$	18.8705	+	18.8705i	0.626584	+	0.626584i	−0.320623	+	0.947207i	$0.603892\pi$
$908$	14.0636	−	35.2658i	0.466717	−	1.17034i
$909$		0			0
$910$	7.88925	+	72.2532i	0.261526	+	2.39517i
$911$	−9.42916	+	12.9781i	−0.312402	+	0.429984i	−0.936128	−	0.351658i	$-0.885618\pi$
$911$	−9.42916	+	12.9781i	−0.312402	+	0.429984i	0.623726	+	0.781643i	$0.285618\pi$
$912$		0			0
$913$	0.201531	+	0.0319193i	0.00666969	+	0.00105638i
$914$	7.50046	−	4.26592i	0.248093	−	0.141104i
$915$		0			0
$916$	7.84887	+	1.77480i	0.259334	+	0.0586409i
$917$	24.8454	+	48.7618i	0.820467	+	1.61026i
$918$		0			0
$919$	4.00489	−	12.3258i	0.132109	−	0.406591i	−0.863020	−	0.505170i	$-0.831430\pi$
$919$	4.00489	−	12.3258i	0.132109	−	0.406591i	0.995129	+	0.0985793i	$0.0314298\pi$
$920$	8.34268	+	10.4920i	0.275050	+	0.345911i
$921$		0			0
$922$	21.1555	+	26.4733i	0.696718	+	0.871850i
$923$	12.7901	−	2.02575i	0.420990	−	0.0666783i
$924$		0			0
$925$	−24.6829	+	31.8259i	−0.811570	+	1.04643i
$926$	23.7338	−	52.3920i	0.779942	−	1.72171i
$927$		0			0
$928$	−18.6087	−	30.7919i	−0.610862	−	1.01079i
$929$	−13.3466	+	4.33657i	−0.437887	+	0.142278i	−0.519660	−	0.854373i	$-0.673942\pi$
$929$	−13.3466	+	4.33657i	−0.437887	+	0.142278i	0.0817736	+	0.996651i	$0.473942\pi$
$930$		0			0
$931$	−18.0954	−	5.87954i	−0.593051	−	0.192694i
$932$	−9.24009	−	0.604254i	−0.302669	−	0.0197930i
$933$		0			0
$934$	35.6510	−	7.33707i	1.16654	−	0.240076i
$935$	−0.553912	−	0.239674i	−0.0181148	−	0.00783819i
$936$		0			0
$937$	−4.98334	+	31.4636i	−0.162799	+	1.02787i	0.762045	+	0.647524i	$0.224195\pi$
$937$	−4.98334	+	31.4636i	−0.162799	+	1.02787i	−0.924844	+	0.380347i	$0.875805\pi$
$938$	−10.8233	−	7.12875i	−0.353394	−	0.232762i
$939$		0			0
$940$	32.7867	−	10.5649i	1.06938	−	0.344590i
$941$	40.7011	−	29.5711i	1.32682	−	0.963989i	0.326996	−	0.945026i	$-0.393963\pi$
$941$	40.7011	−	29.5711i	1.32682	−	0.963989i	0.999820	−	0.0189631i	$-0.00603650\pi$
$942$		0			0
$943$	−15.2587	+	15.2587i	−0.496890	+	0.496890i
$944$	51.0521	+	24.3321i	1.66160	+	0.791941i
$945$		0			0
$946$	−0.156470	+	1.40142i	−0.00508728	+	0.0455641i
$947$	14.5982	−	28.6506i	0.474377	−	0.931018i	−0.522544	−	0.852612i	$-0.675017\pi$
$947$	14.5982	−	28.6506i	0.474377	−	0.931018i	0.996922	−	0.0784058i	$-0.0249830\pi$
$948$		0			0
$949$		−	38.5133i		−	1.25019i
$950$	9.40842	−	4.96753i	0.305249	−	0.161168i
$951$		0			0
$952$	−33.9341	+	16.4685i	−1.09981	+	0.533747i
$953$	20.3126	−	39.8657i	0.657989	−	1.29138i	−0.284992	−	0.958530i	$-0.591991\pi$
$953$	20.3126	−	39.8657i	0.657989	−	1.29138i	0.942981	−	0.332846i	$-0.108009\pi$
$954$		0			0
$955$	3.37109	+	8.51347i	0.109086	+	0.275489i
$956$	15.9278	+	37.0579i	0.515142	+	1.19854i
$957$		0			0
$958$	1.02733	+	22.3716i	0.0331915	+	0.722794i
$959$	16.3067	−	11.8475i	0.526570	−	0.382576i
$960$		0			0
$961$	−11.0573	−	8.03363i	−0.356688	−	0.259149i
$962$	−32.4934	+	49.3336i	−1.04763	+	1.59058i
$963$		0			0
$964$	13.3905	−	1.23241i	0.431278	−	0.0396932i
$965$	18.4220	+	31.1473i	0.593026	+	1.00267i
$966$		0			0
$967$	8.41681	−	4.28858i	0.270666	−	0.137911i	−0.313390	−	0.949625i	$-0.601465\pi$
$967$	8.41681	−	4.28858i	0.270666	−	0.137911i	0.584056	+	0.811713i	$0.301465\pi$
$968$	14.6496	−	27.4221i	0.470856	−	0.881381i
$969$		0			0
$970$	7.66270	+	11.6958i	0.246034	+	0.375531i
$971$	−49.9618	+	16.2336i	−1.60335	+	0.520960i	−0.967933	−	0.251209i	$-0.919172\pi$
$971$	−49.9618	+	16.2336i	−1.60335	+	0.520960i	−0.635417	+	0.772169i	$0.719172\pi$
$972$		0			0
$973$	−11.1614	−	70.4704i	−0.357819	−	2.25918i
$974$	−24.5716	−	11.1311i	−0.787325	−	0.356662i
$975$		0			0
$976$	5.96323	−	45.3991i	0.190878	−	1.45319i
$977$	−5.28202	+	0.836590i	−0.168987	+	0.0267649i	−0.240354	−	0.970685i	$-0.577264\pi$
$977$	−5.28202	+	0.836590i	−0.168987	+	0.0267649i	0.0713675	+	0.997450i	$0.477264\pi$
$978$		0			0
$979$	0.361651	+	1.11305i	0.0115584	+	0.0355731i
$980$	40.0854	−	39.8909i	1.28048	−	1.27427i
$981$		0			0
$982$	3.46365	+	9.20063i	0.110529	+	0.293604i
$983$	−4.87976	−	9.57708i	−0.155640	−	0.305461i	0.799999	−	0.600002i	$-0.204833\pi$
$983$	−4.87976	−	9.57708i	−0.155640	−	0.305461i	−0.955639	+	0.294540i	$0.904833\pi$
$984$		0			0
$985$	14.4462	+	12.7351i	0.460294	+	0.405774i
$986$	−13.3792	−	23.5237i	−0.426081	−	0.749148i
$987$		0			0
$988$	13.1962	−	8.32891i	0.419827	−	0.264978i
$989$	13.8468	−	19.0585i	0.440302	−	0.606024i
$990$		0			0
$991$	9.46784	+	13.0314i	0.300756	+	0.413955i	0.932470	−	0.361246i	$-0.117649\pi$
$991$	9.46784	+	13.0314i	0.300756	+	0.413955i	−0.631715	+	0.775201i	$0.717649\pi$
$992$	1.99271	−	23.4663i	0.0632686	−	0.745054i
$993$		0			0
$994$	−11.5644	−	10.5490i	−0.366802	−	0.334593i
$995$	46.2112	+	11.8632i	1.46499	+	0.376088i
$996$		0			0
$997$	9.89793	+	5.04325i	0.313471	+	0.159721i	0.603647	−	0.797252i	$-0.293714\pi$
$997$	9.89793	+	5.04325i	0.313471	+	0.159721i	−0.290176	+	0.956973i	$0.593714\pi$
$998$	0.344769	+	0.0947760i	0.0109135	+	0.00300008i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.163.2		240
3.2	odd	2		300.2.w.a.163.29	yes	240
4.3	odd	2	inner	900.2.bj.f.163.6		240
12.11	even	2		300.2.w.a.163.25	yes	240
25.2	odd	20	inner	900.2.bj.f.127.6		240
75.2	even	20		300.2.w.a.127.25	✓	240
100.27	even	20	inner	900.2.bj.f.127.2		240
300.227	odd	20		300.2.w.a.127.29	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.25	✓	240	75.2	even	20
300.2.w.a.127.29	yes	240	300.227	odd	20
300.2.w.a.163.25	yes	240	12.11	even	2
300.2.w.a.163.29	yes	240	3.2	odd	2
900.2.bj.f.127.2		240	100.27	even	20	inner
900.2.bj.f.127.6		240	25.2	odd	20	inner
900.2.bj.f.163.2		240	1.1	even	1	trivial
900.2.bj.f.163.6		240	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36363 - 0.374857i) q^{2} +(1.71896 + 1.02233i) q^{4} +(-2.16584 - 0.556007i) q^{5} +(-3.13412 - 3.13412i) q^{7} +(-1.96080 - 2.03845i) q^{8} +O(q^{10})\)	\(q+(-1.36363 - 0.374857i) q^{2} +(1.71896 + 1.02233i) q^{4} +(-2.16584 - 0.556007i) q^{5} +(-3.13412 - 3.13412i) q^{7} +(-1.96080 - 2.03845i) q^{8} +(2.74498 + 1.57007i) q^{10} +(0.0527296 - 0.0725760i) q^{11} +(-5.12177 - 0.811209i) q^{13} +(3.09893 + 5.44862i) q^{14} +(1.90968 + 3.51470i) q^{16} +(1.36594 + 2.68082i) q^{17} +(-0.464955 + 1.43098i) q^{19} +(-3.15458 - 3.16996i) q^{20} +(-0.0991092 + 0.0792007i) q^{22} +(2.09335 - 0.331555i) q^{23} +(4.38171 + 2.40844i) q^{25} +(6.68011 + 3.02612i) q^{26} +(-2.18333 - 8.59155i) q^{28} +(6.04881 - 1.96538i) q^{29} +(3.95945 + 1.28650i) q^{31} +(-1.28658 - 5.50860i) q^{32} +(-0.857717 - 4.16767i) q^{34} +(5.04540 + 8.53059i) q^{35} +(-1.26010 + 7.95598i) q^{37} +(1.17044 - 1.77704i) q^{38} +(3.11339 + 5.50516i) q^{40} +(-8.23695 + 5.98450i) q^{41} +(7.85946 - 7.85946i) q^{43} +(0.164837 - 0.0708485i) q^{44} +(-2.97884 - 0.332591i) q^{46} +(-3.49688 + 6.86301i) q^{47} +12.6454i q^{49} +(-5.07221 - 4.92674i) q^{50} +(-7.97482 - 6.63059i) q^{52} +(-1.47153 + 2.88805i) q^{53} +(-0.154557 + 0.127870i) q^{55} +(-0.243356 + 12.5341i) q^{56} +(-8.98507 + 0.412604i) q^{58} +(11.4383 - 8.31042i) q^{59} +(-9.26103 - 6.72853i) q^{61} +(-4.91697 - 3.23854i) q^{62} +(-0.310530 + 7.99397i) q^{64} +(10.6419 + 4.60469i) q^{65} +(-1.84223 + 0.938661i) q^{67} +(-0.392675 + 6.00467i) q^{68} +(-3.68230 - 13.5239i) q^{70} +(-2.37497 + 0.771676i) q^{71} +(1.16183 + 7.33551i) q^{73} +(4.70067 - 10.3766i) q^{74} +(-2.26218 + 1.98447i) q^{76} +(-0.392723 + 0.0622012i) q^{77} +(0.395606 + 1.21755i) q^{79} +(-2.18185 - 8.67407i) q^{80} +(13.4755 - 5.07295i) q^{82} +(1.03260 + 2.02659i) q^{83} +(-1.46786 - 6.56569i) q^{85} +(-13.6636 + 7.77120i) q^{86} +(-0.251335 + 0.0348206i) q^{88} +(-7.66814 + 10.5543i) q^{89} +(13.5098 + 18.5947i) q^{91} +(3.93736 + 1.57017i) q^{92} +(7.34109 - 8.04777i) q^{94} +(1.80265 - 2.84076i) q^{95} +(3.93972 + 2.00739i) q^{97} +(4.74022 - 17.2436i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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