LMFDB - Embedded newform 900.2.bj.f.127.2

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			127.2
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.2

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

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	−0.206043	+	0.978543i	$0.566059\pi$
$7$	−3.13412	+	3.13412i	−1.18459	+	1.18459i	−0.978543	+	0.206043i	$0.933941\pi$
$8$	−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	0.816892	−	0.576790i	$-0.195695\pi$
$11$	0.0527296	+	0.0725760i	0.0158986	+	0.0218825i	−0.800994	+	0.598673i	$0.795695\pi$
$12$		0			0
$13$	−5.12177	+	0.811209i	−1.42052	+	0.224989i	−0.818967	−	0.573841i	$-0.805453\pi$
$13$	−5.12177	+	0.811209i	−1.42052	+	0.224989i	−0.601557	+	0.798830i	$0.705453\pi$
$14$	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	−0.663936	−	0.747789i	$-0.731115\pi$
$17$	1.36594	−	2.68082i	0.331290	−	0.650193i	0.995226	+	0.0975960i	$0.0311153\pi$
$18$		0			0
$19$	−0.464955	−	1.43098i	−0.106668	−	0.328290i	0.883450	−	0.468525i	$-0.155214\pi$
$19$	−0.464955	−	1.43098i	−0.106668	−	0.328290i	−0.990118	+	0.140235i	$0.955214\pi$
$20$	−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	0.370815	−	0.928707i	$-0.379078\pi$
$23$	2.09335	+	0.331555i	0.436494	+	0.0691339i	0.0656796	+	0.997841i	$0.479078\pi$
$24$		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	0.811002	−	0.585043i	$-0.198922\pi$
$29$	6.04881	+	1.96538i	1.12324	+	0.364962i	0.312235	+	0.950005i	$0.398922\pi$
$30$		0			0
$31$	3.95945	−	1.28650i	0.711139	−	0.231063i	0.0689619	−	0.997619i	$-0.478031\pi$
$31$	3.95945	−	1.28650i	0.711139	−	0.231063i	0.642177	+	0.766556i	$0.278031\pi$
$32$	−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	−0.843743	−	0.536747i	$-0.819653\pi$
$37$	−1.26010	−	7.95598i	−0.207160	−	1.30796i	0.636583	−	0.771208i	$-0.280347\pi$
$38$	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	−0.286670	−	0.958029i	$-0.592548\pi$
$41$	−8.23695	−	5.98450i	−1.28640	−	0.934621i	−0.999726	+	0.0234081i	$0.992548\pi$
$42$		0			0
$43$	7.85946	+	7.85946i	1.19856	+	1.19856i	0.974599	+	0.223957i	$0.0718974\pi$
$43$	7.85946	+	7.85946i	1.19856	+	1.19856i	0.223957	+	0.974599i	$0.428103\pi$
$44$	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	−0.992163	−	0.124952i	$-0.960122\pi$
$47$	−3.49688	−	6.86301i	−0.510072	−	1.00107i	0.482091	−	0.876121i	$-0.339878\pi$
$48$		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	0.767583	−	0.640950i	$-0.221459\pi$
$53$	−1.47153	−	2.88805i	−0.202131	−	0.396704i	−0.969713	+	0.244246i	$0.921459\pi$
$54$		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	0.974465	+	0.224539i	$0.0720877\pi$
$59$	11.4383	+	8.31042i	1.48914	+	1.08192i	0.514676	+	0.857385i	$0.327912\pi$
$60$		0			0
$61$	−9.26103	+	6.72853i	−1.18575	+	0.861500i	−0.992809	−	0.119710i	$-0.961804\pi$
$61$	−9.26103	+	6.72853i	−1.18575	+	0.861500i	−0.192944	+	0.981210i	$0.561804\pi$
$62$	−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	0.337823	−	0.941210i	$-0.390309\pi$
$67$	−1.84223	−	0.938661i	−0.225064	−	0.114676i	−0.562887	+	0.826534i	$0.690309\pi$
$68$	−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	0.164677	−	0.986348i	$-0.447342\pi$
$71$	−2.37497	−	0.771676i	−0.281857	−	0.0915810i	−0.446534	+	0.894767i	$0.647342\pi$
$72$		0			0
$73$	1.16183	−	7.33551i	0.135982	−	0.858556i	−0.821531	−	0.570164i	$-0.806880\pi$
$73$	1.16183	−	7.33551i	0.135982	−	0.858556i	0.957513	−	0.288392i	$-0.0931205\pi$
$74$	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	−0.926332	−	0.376707i	$-0.877056\pi$
$79$	0.395606	−	1.21755i	0.0445091	−	0.136985i	0.970842	+	0.239722i	$0.0770563\pi$
$80$	−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	−0.827366	−	0.561663i	$-0.810162\pi$
$83$	1.03260	−	2.02659i	0.113343	−	0.222447i	0.940709	+	0.339216i	$0.110162\pi$
$84$		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	−0.990882	−	0.134733i	$-0.956982\pi$
$89$	−7.66814	−	10.5543i	−0.812821	−	1.11875i	0.178061	−	0.984020i	$-0.443018\pi$
$90$		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	−0.242396	−	0.970177i	$-0.577933\pi$
$97$	3.93972	−	2.00739i	0.400018	−	0.203819i	0.642413	+	0.766358i	$0.277933\pi$
$98$	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	−0.341919	−	0.939729i	$-0.611077\pi$
$103$	2.20599	−	1.12401i	0.217363	−	0.110752i	0.559282	+	0.828978i	$0.311077\pi$
$104$	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	−0.563772	−	0.825931i	$-0.690650\pi$
$107$	2.71179	−	2.71179i	0.262159	−	0.262159i	0.825931	+	0.563772i	$0.190650\pi$
$108$		0			0
$109$	4.04353	−	5.56544i	0.387300	−	0.533072i	−0.570200	−	0.821506i	$-0.693134\pi$
$109$	4.04353	−	5.56544i	0.387300	−	0.533072i	0.957500	+	0.288433i	$0.0931344\pi$
$110$	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	0.408086	−	0.912943i	$-0.366196\pi$
$113$	11.4626	−	1.81550i	1.07831	−	0.170788i	0.670228	+	0.742155i	$0.266196\pi$
$114$		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	−0.999442	−	0.0334122i	$-0.989363\pi$
$127$	−0.434901	+	2.74586i	−0.0385912	+	0.243655i	0.960850	+	0.277068i	$0.0893626\pi$
$128$	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	−0.773200	−	0.634162i	$-0.781345\pi$
$131$	−11.7429	+	3.81550i	−1.02598	+	0.333361i	−0.252781	+	0.967524i	$0.581345\pi$
$132$		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	−0.999262	−	0.0384157i	$-0.987769\pi$
$137$	−0.711394	−	4.49156i	−0.0607785	−	0.383740i	0.938483	−	0.345324i	$-0.112231\pi$
$138$		0			0
$139$	13.0231	−	9.46183i	1.10460	−	0.802542i	0.122799	−	0.992432i	$-0.460813\pi$
$139$	13.0231	−	9.46183i	1.10460	−	0.802542i	0.981805	+	0.189889i	$0.0608130\pi$
$140$	−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	$0.0379185\pi$
$149$			2.90133i			0.237686i	−0.992913	+	0.118843i	$0.962081\pi$
$150$		0			0
$151$			4.02046i			0.327180i	0.986528	+	0.163590i	$0.0523075\pi$
$151$			4.02046i			0.327180i	−0.986528	+	0.163590i	$0.947693\pi$
$152$	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	0.608679	−	0.793416i	$-0.291700\pi$
$157$	−2.31475	−	2.31475i	−0.184737	−	0.184737i	−0.793416	+	0.608679i	$0.791700\pi$
$158$	−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	−0.994337	−	0.106276i	$-0.966107\pi$
$163$	−1.04062	−	6.57021i	−0.0815075	−	0.514618i	0.912829	−	0.408342i	$-0.133893\pi$
$164$	−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	0.552728	−	0.833362i	$-0.313587\pi$
$167$	2.62863	+	1.33936i	0.203410	+	0.103642i	−0.349318	+	0.937004i	$0.613587\pi$
$168$		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	−0.918322	−	0.395835i	$-0.870455\pi$
$173$	1.01770	−	6.42548i	0.0773739	−	0.488520i	0.995696	−	0.0926847i	$-0.0295449\pi$
$174$		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	0.787024	+	0.616923i	$0.211621\pi$
$179$	−2.84051	+	8.74220i	−0.212310	+	0.653423i	−0.999334	+	0.0364999i	$0.988379\pi$
$180$		0			0
$181$	1.42108	+	4.37363i	0.105628	+	0.325090i	0.989877	−	0.141925i	$-0.0453293\pi$
$181$	1.42108	+	4.37363i	0.105628	+	0.325090i	−0.884249	+	0.467015i	$0.845329\pi$
$182$	−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	−0.887170	−	0.461443i	$-0.847332\pi$
$191$	−2.40696	+	3.31289i	−0.174161	+	0.239712i	0.713009	+	0.701155i	$0.247332\pi$
$192$		0			0
$193$	−11.4434	+	11.4434i	−0.823717	+	0.823717i	−0.986639	−	0.162922i	$-0.947908\pi$
$193$	−11.4434	+	11.4434i	−0.823717	+	0.823717i	0.162922	+	0.986639i	$0.447908\pi$
$194$	−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	−0.705463	−	0.708747i	$-0.749261\pi$
$197$	−7.67379	+	3.90999i	−0.546735	+	0.278575i	0.158728	+	0.987322i	$0.449261\pi$
$198$		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	−0.894511	−	0.447047i	$-0.852476\pi$
$211$	−15.1542	−	20.8580i	−1.04326	−	1.43592i	−0.148748	−	0.988875i	$-0.547524\pi$
$212$	−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	−0.730410	−	0.683009i	$-0.760671\pi$
$223$	−24.4327	−	3.86975i	−1.63613	−	0.259138i	−0.905722	+	0.423872i	$0.860671\pi$
$224$	−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	0.668496	+	0.743715i	$0.266938\pi$
$227$	−2.96964	+	18.7496i	−0.197102	+	1.24445i	−0.865598	+	0.500739i	$0.833062\pi$
$228$		0			0
$229$	3.82659	+	1.24333i	0.252868	+	0.0821618i	0.432708	−	0.901534i	$-0.357558\pi$
$229$	3.82659	+	1.24333i	0.252868	+	0.0821618i	−0.179840	+	0.983696i	$0.557558\pi$
$230$	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	0.313611	−	0.949552i	$-0.398461\pi$
$233$	−4.12528	−	2.10194i	−0.270256	−	0.137702i	−0.583867	+	0.811849i	$0.698461\pi$
$234$		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	0.0821734	−	0.996618i	$-0.473814\pi$
$239$	16.3162	−	11.8544i	1.05541	−	0.766798i	0.973233	+	0.229820i	$0.0738139\pi$
$240$		0			0
$241$	5.43945	+	3.95199i	0.350386	+	0.254570i	0.749031	−	0.662535i	$-0.230519\pi$
$241$	5.43945	+	3.95199i	0.350386	+	0.254570i	−0.398645	+	0.917105i	$0.630519\pi$
$242$	−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	$-0.673997\pi$
$251$		−	27.0687i		−	1.70856i	0.519811	−	0.854282i	$-0.326003\pi$
$252$		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	0.695635	−	0.718396i	$-0.255123\pi$
$257$	−0.364893	−	0.364893i	−0.0227614	−	0.0227614i	−0.718396	+	0.695635i	$0.755123\pi$
$258$		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	−0.946895	−	0.321544i	$-0.895798\pi$
$263$	−2.36297	−	14.9192i	−0.145707	−	0.919957i	0.801188	−	0.598413i	$-0.204202\pi$
$264$		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	0.331252	−	0.943542i	$-0.392529\pi$
$269$	18.9244	−	6.14891i	1.15384	−	0.374906i	0.822589	+	0.568636i	$0.192529\pi$
$270$		0			0
$271$	5.42995	+	1.76430i	0.329846	+	0.107173i	0.469258	−	0.883061i	$-0.344521\pi$
$271$	5.42995	+	1.76430i	0.329846	+	0.107173i	−0.139412	+	0.990234i	$0.544521\pi$
$272$	−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	0.495650	−	0.868522i	$-0.334930\pi$
$277$	11.6279	+	1.84168i	0.698653	+	0.110656i	0.203003	+	0.979178i	$0.434930\pi$
$278$	−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	0.996775	−	0.0802486i	$-0.0255714\pi$
$281$	2.40044	+	7.38779i	0.143198	+	0.440719i	−0.853577	+	0.520967i	$0.825571\pi$
$282$		0			0
$283$	8.36586	−	16.4189i	0.497299	−	0.976004i	−0.496835	−	0.867845i	$-0.665504\pi$
$283$	8.36586	−	16.4189i	0.497299	−	0.976004i	0.994134	−	0.108159i	$-0.0344955\pi$
$284$	−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	−0.0332770	−	0.999446i	$-0.510594\pi$
$293$	16.5382	−	16.5382i	0.966169	−	0.966169i	0.999446	+	0.0332770i	$0.0105943\pi$
$294$		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	−0.340557	+	0.940224i	$0.610616\pi$
$307$	−22.4411	+	22.4411i	−1.28078	+	1.28078i	−0.940224	+	0.340557i	$0.889384\pi$
$308$	−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	0.495037	−	0.868872i	$-0.335154\pi$
$311$	−8.54043	−	11.7549i	−0.484284	−	0.666559i	−0.979321	+	0.202312i	$0.935154\pi$
$312$		0			0
$313$	−2.22635	+	0.352619i	−0.125841	+	0.0199312i	−0.219037	−	0.975717i	$-0.570292\pi$
$313$	−2.22635	+	0.352619i	−0.125841	+	0.0199312i	0.0931963	+	0.995648i	$0.470292\pi$
$314$	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	−0.969812	−	0.243854i	$-0.921588\pi$
$317$	−3.60520	+	7.07561i	−0.202488	+	0.397406i	0.767323	+	0.641260i	$0.221588\pi$
$318$		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	−0.976157	−	0.217064i	$-0.930352\pi$
$331$	−29.8062	+	9.68463i	−1.63830	+	0.532316i	−0.662141	+	0.749379i	$0.730352\pi$
$332$	−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	−0.620393	−	0.784291i	$-0.713027\pi$
$337$	−5.00654	−	31.6100i	−0.272723	−	1.72191i	0.347669	−	0.937617i	$-0.386973\pi$
$338$	−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	0.979369	−	0.202079i	$-0.0647697\pi$
$347$	4.47490	+	8.78249i	0.240225	+	0.471469i	−0.739144	+	0.673548i	$0.764770\pi$
$348$		0			0
$349$			19.1891i			1.02717i	0.858039	+	0.513585i	$0.171683\pi$
$349$			19.1891i			1.02717i	−0.858039	+	0.513585i	$0.828317\pi$
$350$	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	−0.721862	−	0.692037i	$-0.756713\pi$
$353$	−16.1097	−	31.6170i	−0.857432	−	1.68281i	−0.135570	−	0.990768i	$-0.543287\pi$
$354$		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	0.604660	−	0.796484i	$-0.293309\pi$
$359$	0.644378	+	0.468168i	0.0340090	+	0.0247090i	−0.570651	+	0.821193i	$0.693309\pi$
$360$		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	0.959817	−	0.280626i	$-0.0905422\pi$
$367$	24.8460	+	12.6597i	1.29695	+	0.660830i	0.337135	+	0.941456i	$0.390542\pi$
$368$	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	−0.955146	−	0.296137i	$-0.904302\pi$
$373$	0.864521	−	5.45837i	0.0447632	−	0.282624i	0.999909	+	0.0135133i	$0.00430155\pi$
$374$	−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	0.686918	+	0.726735i	$0.258963\pi$
$379$	−5.76200	+	17.7336i	−0.295974	+	0.910915i	−0.982893	+	0.184180i	$0.941037\pi$
$380$	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	−0.563468	−	0.826138i	$-0.690533\pi$
$383$	8.53445	−	16.7498i	0.436090	−	0.855875i	0.999558	−	0.0297370i	$-0.00946699\pi$
$384$		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	0.894318	−	0.447431i	$-0.147661\pi$
$389$	3.79524	+	5.22370i	0.192426	+	0.264852i	−0.701892	+	0.712283i	$0.747661\pi$
$390$		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	−0.227660	−	0.973741i	$-0.573107\pi$
$397$	8.49393	−	4.32787i	0.426298	−	0.217210i	0.653958	+	0.756531i	$0.273107\pi$
$398$	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	−0.961701	−	0.274101i	$-0.911620\pi$
$409$	−8.16703	+	11.2410i	−0.403834	+	0.555829i	0.557867	+	0.829930i	$0.311620\pi$
$410$	−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	−0.981299	−	0.192488i	$-0.938344\pi$
$419$	−6.15217	−	18.9344i	−0.300553	−	0.925007i	0.680746	−	0.732519i	$-0.261656\pi$
$420$		0			0
$421$	0.345619	−	1.06371i	0.0168444	−	0.0518419i	−0.942281	−	0.334823i	$-0.891323\pi$
$421$	0.345619	−	1.06371i	0.0168444	−	0.0518419i	0.959125	+	0.282981i	$0.0913234\pi$
$422$	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	−0.101539	−	0.994832i	$-0.532377\pi$
$431$	8.32624	−	2.70536i	0.401061	−	0.130313i	0.502600	+	0.864519i	$0.332377\pi$
$432$		0			0
$433$	14.4137	+	7.34415i	0.692678	+	0.352937i	0.764629	−	0.644471i	$-0.222922\pi$
$433$	14.4137	+	7.34415i	0.692678	+	0.352937i	−0.0719504	+	0.997408i	$0.522922\pi$
$434$	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	0.221195	−	0.975229i	$-0.429004\pi$
$439$	25.5000	−	18.5268i	1.21705	−	0.884236i	0.995852	+	0.0909931i	$0.0290041\pi$
$440$	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	0.996377	+	0.0850506i	$0.0271052\pi$
$443$	22.7614	+	22.7614i	1.08143	+	1.08143i	0.0850506	+	0.996377i	$0.472895\pi$
$444$		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	$-0.975824\pi$
$449$		−	3.21571i		−	0.151759i	0.997117	−	0.0758794i	$-0.0241764\pi$
$450$		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	0.598961	−	0.800778i	$-0.295581\pi$
$457$	−4.31437	−	4.31437i	−0.201818	−	0.201818i	−0.800778	+	0.598961i	$0.795581\pi$
$458$	−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	−0.939207	−	0.343350i	$-0.888438\pi$
$461$	−19.3859	+	14.0847i	−0.902893	+	0.655990i	0.0363144	+	0.999340i	$0.488438\pi$
$462$		0			0
$463$	−6.36230	−	40.1700i	−0.295681	−	1.86686i	−0.470700	−	0.882293i	$-0.655999\pi$
$463$	−6.36230	−	40.1700i	−0.295681	−	1.86686i	0.175019	−	0.984565i	$-0.444001\pi$
$464$	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	−0.165870	−	0.986148i	$-0.553043\pi$
$467$	−22.9322	−	11.6845i	−1.06118	−	0.540696i	−0.895306	+	0.445452i	$0.853043\pi$
$468$		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	0.774841	+	0.632157i	$0.217830\pi$
$479$	−4.89353	+	15.0607i	−0.223591	+	0.688142i	−0.998432	+	0.0559855i	$0.982170\pi$
$480$		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	0.285779	−	0.958295i	$-0.407748\pi$
$487$	18.8395	−	2.98389i	0.853701	−	0.135213i	0.567922	+	0.823083i	$0.307748\pi$
$488$	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	−0.891202	−	0.453607i	$-0.850137\pi$
$491$	−4.08602	+	5.62393i	−0.184400	+	0.253804i	0.706802	+	0.707411i	$0.250137\pi$
$492$		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	−0.0598984	−	0.998204i	$-0.519078\pi$
$503$	15.9788	−	8.14160i	0.712459	−	0.363016i	0.772357	+	0.635189i	$0.219078\pi$
$504$		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	−0.438066	−	0.898943i	$-0.644336\pi$
$509$	12.4593	−	17.1488i	0.552249	−	0.760105i	0.990315	+	0.138837i	$0.0443365\pi$
$510$		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	−0.995407	−	0.0957313i	$-0.969481\pi$
$521$	−3.05487	+	9.40193i	−0.133836	+	0.411906i	0.861571	+	0.507637i	$0.169481\pi$
$522$		0			0
$523$	19.0721	+	3.02072i	0.833963	+	0.132087i	0.558791	−	0.829308i	$-0.311265\pi$
$523$	19.0721	+	3.02072i	0.833963	+	0.132087i	0.275171	+	0.961395i	$0.411265\pi$
$524$	−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	0.673264	−	0.739402i	$-0.264892\pi$
$541$	4.14253	+	3.00972i	0.178101	+	0.129398i	−0.495163	+	0.868800i	$0.664892\pi$
$542$	−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	0.636577	−	0.771213i	$-0.280350\pi$
$547$	−8.45520	−	16.5943i	−0.361518	−	0.709520i	−0.998095	+	0.0616937i	$0.980350\pi$
$548$	−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	0.0996610	−	0.995021i	$-0.468224\pi$
$557$	−21.1313	−	21.1313i	−0.895360	−	0.895360i	−0.995021	+	0.0996610i	$0.968224\pi$
$558$		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	0.971679	−	0.236304i	$-0.0759362\pi$
$563$	−0.604217	−	3.81487i	−0.0254647	−	0.160778i	−0.997144	+	0.0755266i	$0.975936\pi$
$564$		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	−0.359541	−	0.933129i	$-0.617067\pi$
$569$	−2.43157	+	0.790065i	−0.101937	+	0.0331213i	0.257605	+	0.966250i	$0.417067\pi$
$570$		0			0
$571$	2.33800	+	0.759663i	0.0978424	+	0.0317909i	0.357529	−	0.933902i	$-0.383619\pi$
$571$	2.33800	+	0.759663i	0.0978424	+	0.0317909i	−0.259687	+	0.965693i	$0.583619\pi$
$572$	−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	0.0103878	−	0.999946i	$-0.496693\pi$
$577$	−6.93561	−	1.09849i	−0.288733	−	0.0457308i	−0.299121	+	0.954215i	$0.596693\pi$
$578$	−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	−0.539726	−	0.841841i	$-0.681472\pi$
$587$	−19.2103	+	3.04261i	−0.792893	+	0.125582i	−0.253167	+	0.967423i	$0.581472\pi$
$588$		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	0.0834655	−	0.996511i	$-0.473401\pi$
$593$	26.2991	−	26.2991i	1.07998	−	1.07998i	0.996511	−	0.0834655i	$-0.0265988\pi$
$594$		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	−0.832601	−	0.553874i	$-0.813149\pi$
$607$	−6.86710	+	6.86710i	−0.278727	+	0.278727i	0.553874	+	0.832601i	$0.313149\pi$
$608$	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	−0.351908	−	0.936035i	$-0.614467\pi$
$613$	−9.83772	+	1.55814i	−0.397342	+	0.0629328i	−0.0454338	+	0.998967i	$0.514467\pi$
$614$	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	−0.430179	−	0.902743i	$-0.641550\pi$
$617$	13.7364	−	26.9593i	0.553008	−	1.08534i	0.983188	−	0.182597i	$-0.0584503\pi$
$618$		0			0
$619$	10.2938	+	31.6812i	0.413744	+	1.27337i	0.913369	+	0.407133i	$0.133471\pi$
$619$	10.2938	+	31.6812i	0.413744	+	1.27337i	−0.499625	+	0.866242i	$0.666529\pi$
$620$	−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	−0.225575	−	0.974226i	$-0.572426\pi$
$631$	4.13387	−	1.34318i	0.164567	−	0.0534710i	0.390142	+	0.920755i	$0.372426\pi$
$632$	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	0.00592940	−	0.999982i	$-0.498113\pi$
$641$	−23.8819	−	17.3512i	−0.943278	−	0.685332i	−0.949208	+	0.314651i	$0.898113\pi$
$642$		0			0
$643$	5.10377	+	5.10377i	0.201273	+	0.201273i	0.800545	−	0.599272i	$-0.204543\pi$
$643$	5.10377	+	5.10377i	0.201273	+	0.201273i	−0.599272	+	0.800545i	$0.704543\pi$
$644$	−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	0.653671	−	0.756779i	$-0.273228\pi$
$647$	−8.71938	−	17.1127i	−0.342794	−	0.672771i	−0.996465	+	0.0840074i	$0.973228\pi$
$648$		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	0.844045	+	0.536272i	$0.180168\pi$
$653$	19.9775	+	39.2081i	0.781781	+	1.53433i	−0.0622643	+	0.998060i	$0.519832\pi$
$654$		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	−0.0878139	−	0.996137i	$-0.527988\pi$
$659$	−27.2711	−	19.8136i	−1.06233	−	0.771830i	−0.974518	+	0.224307i	$0.927988\pi$
$660$		0			0
$661$	36.2595	−	26.3441i	1.41033	−	1.02467i	0.417058	−	0.908880i	$-0.363061\pi$
$661$	36.2595	−	26.3441i	1.41033	−	1.02467i	0.993274	−	0.115787i	$-0.0369389\pi$
$662$	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	−0.774972	−	0.631995i	$-0.782236\pi$
$673$	4.08246	−	25.7757i	0.157367	−	0.993579i	0.932340	−	0.361583i	$-0.117764\pi$
$674$	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	−0.0112789	−	0.999936i	$-0.503590\pi$
$677$	−8.61245	−	1.36408i	−0.331003	−	0.0524258i	−0.319724	+	0.947511i	$0.603590\pi$
$678$		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	−0.917657	−	0.397373i	$-0.869922\pi$
$683$	−1.48416	+	2.91283i	−0.0567898	+	0.111456i	0.860867	+	0.508830i	$0.169922\pi$
$684$		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	−0.997830	−	0.0658420i	$-0.979027\pi$
$691$	−16.4783	+	22.6804i	−0.626864	+	0.862805i	0.370966	+	0.928647i	$0.379027\pi$
$692$	−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	−0.133961	−	0.990987i	$-0.542770\pi$
$709$	22.6308	−	31.1487i	0.849919	−	1.16981i	0.983881	−	0.178827i	$-0.0572302\pi$
$710$	−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	0.996488	−	0.0837350i	$-0.0266849\pi$
$719$	3.78332	+	11.6439i	0.141094	+	0.434243i	−0.855394	+	0.517978i	$0.826685\pi$
$720$		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	−0.392842	−	0.919606i	$-0.628508\pi$
$727$	7.14374	−	45.1038i	0.264947	−	1.67281i	0.657789	−	0.753202i	$-0.271492\pi$
$728$	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	−0.414664	−	0.909974i	$-0.636101\pi$
$733$	−37.7569	−	19.2381i	−1.39458	−	0.710575i	−0.979918	+	0.199399i	$0.936101\pi$
$734$	−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	−0.726465	−	0.687204i	$-0.758838\pi$
$739$	−8.08428	+	5.87357i	−0.297385	+	0.216063i	0.429080	+	0.903267i	$0.358838\pi$
$740$	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	0.940060	−	0.341008i	$-0.110768\pi$
$743$	16.3290	+	16.3290i	0.599053	+	0.599053i	−0.341008	+	0.940060i	$0.610768\pi$
$744$		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	$0.284361\pi$
$751$			42.7056i			1.55835i	−0.626807	+	0.779174i	$0.715639\pi$
$752$	−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	0.552000	−	0.833844i	$-0.313865\pi$
$757$	−7.75454	−	7.75454i	−0.281844	−	0.281844i	−0.833844	+	0.552000i	$0.813865\pi$
$758$	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	−0.305847	−	0.952081i	$-0.598940\pi$
$761$	13.9344	−	10.1240i	0.505123	−	0.366993i	0.810970	+	0.585087i	$0.198940\pi$
$762$		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	−0.572304	−	0.820041i	$-0.693950\pi$
$769$	−15.3435	+	4.98540i	−0.553300	+	0.179778i	0.0190041	+	0.999819i	$0.493950\pi$
$770$	−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	−0.788091	−	0.615559i	$-0.788930\pi$
$773$	4.21620	−	26.6201i	0.151646	−	0.957457i	0.939737	−	0.341898i	$-0.111070\pi$
$774$		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	−0.459811	−	0.888017i	$-0.652083\pi$
$787$	−17.4691	+	2.76683i	−0.622705	+	0.0986268i	−0.162894	+	0.986644i	$0.552083\pi$
$788$	−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	−0.760682	−	0.649125i	$-0.775135\pi$
$797$	−19.2719	+	9.81954i	−0.682647	+	0.347826i	0.0780351	+	0.996951i	$0.475135\pi$
$798$		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	−0.385794	−	0.922585i	$-0.626072\pi$
$809$	17.3745	−	23.9139i	0.610854	−	0.840768i	0.996647	+	0.0818172i	$0.0260724\pi$
$810$		0			0
$811$	−15.1413	−	20.8402i	−0.531683	−	0.731799i	0.455703	−	0.890132i	$-0.349388\pi$
$811$	−15.1413	−	20.8402i	−0.531683	−	0.731799i	−0.987386	+	0.158333i	$0.949388\pi$
$812$	−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	−0.793512	−	0.608555i	$-0.791750\pi$
$821$	5.90690	−	18.1796i	0.206152	−	0.634471i	0.999664	−	0.0259166i	$-0.00825044\pi$
$822$		0			0
$823$	3.92443	+	0.621568i	0.136797	+	0.0216665i	0.224457	−	0.974484i	$-0.427939\pi$
$823$	3.92443	+	0.621568i	0.136797	+	0.0216665i	−0.0876604	+	0.996150i	$0.527939\pi$
$824$	−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	0.770147	+	0.637866i	$0.220183\pi$
$827$	−4.58447	+	28.9452i	−0.159418	+	1.00652i	−0.929565	+	0.368658i	$0.879817\pi$
$828$		0			0
$829$	33.1072	+	10.7572i	1.14986	+	0.373612i	0.821091	−	0.570798i	$-0.193366\pi$
$829$	33.1072	+	10.7572i	1.14986	+	0.373612i	0.328770	+	0.944410i	$0.393366\pi$
$830$	−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	−0.156315	−	0.987707i	$-0.549962\pi$
$839$	21.2823	−	15.4625i	0.734746	−	0.533824i	0.891061	+	0.453883i	$0.149962\pi$
$840$		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	−0.855933	−	0.517087i	$-0.827016\pi$
$853$	−22.5226	−	44.2032i	−0.771161	−	1.51349i	0.0847720	−	0.996400i	$-0.472984\pi$
$854$	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	0.730568	−	0.682840i	$-0.239255\pi$
$857$	1.39722	+	1.39722i	0.0477281	+	0.0477281i	−0.682840	+	0.730568i	$0.739255\pi$
$858$		0			0
$859$	8.28918	+	6.02244i	0.282823	+	0.205483i	0.720148	−	0.693821i	$-0.244074\pi$
$859$	8.28918	+	6.02244i	0.282823	+	0.205483i	−0.437325	+	0.899304i	$0.644074\pi$
$860$	−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	−0.982969	−	0.183769i	$-0.941170\pi$
$863$	−3.08157	−	19.4563i	−0.104898	−	0.662299i	0.878072	−	0.478529i	$-0.158830\pi$
$864$		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	−0.614357	−	0.789028i	$-0.710585\pi$
$877$	−42.7175	−	6.76579i	−1.44247	−	0.228465i	−0.828111	+	0.560564i	$0.810585\pi$
$878$	−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	0.968305	+	0.249771i	$0.0803553\pi$
$881$	9.84663	+	30.3048i	0.331741	+	1.02100i	−0.636564	+	0.771224i	$0.719645\pi$
$882$		0			0
$883$	−19.3210	+	37.9195i	−0.650202	+	1.27609i	0.296822	+	0.954933i	$0.404073\pi$
$883$	−19.3210	+	37.9195i	−0.650202	+	1.27609i	−0.947025	+	0.321161i	$0.895927\pi$
$884$	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	−0.316778	−	0.948500i	$-0.602601\pi$
$887$	−9.67782	+	1.53282i	−0.324949	+	0.0514669i	−0.00817134	+	0.999967i	$0.502601\pi$
$888$		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	−0.320623	−	0.947207i	$-0.603892\pi$
$907$	18.8705	−	18.8705i	0.626584	−	0.626584i	0.947207	+	0.320623i	$0.103892\pi$
$908$	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	0.623726	−	0.781643i	$-0.285618\pi$
$911$	−9.42916	−	12.9781i	−0.312402	−	0.429984i	−0.936128	+	0.351658i	$0.885618\pi$
$912$		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	0.995129	−	0.0985793i	$-0.0314298\pi$
$919$	4.00489	+	12.3258i	0.132109	+	0.406591i	−0.863020	+	0.505170i	$0.831430\pi$
$920$	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	0.0817736	−	0.996651i	$-0.473942\pi$
$929$	−13.3466	−	4.33657i	−0.437887	−	0.142278i	−0.519660	+	0.854373i	$0.673942\pi$
$930$		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	−0.924844	−	0.380347i	$-0.875805\pi$
$937$	−4.98334	−	31.4636i	−0.162799	−	1.02787i	0.762045	−	0.647524i	$-0.224195\pi$
$938$	−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	0.999820	+	0.0189631i	$0.00603650\pi$
$941$	40.7011	+	29.5711i	1.32682	+	0.963989i	0.326996	+	0.945026i	$0.393963\pi$
$942$		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	0.996922	+	0.0784058i	$0.0249830\pi$
$947$	14.5982	+	28.6506i	0.474377	+	0.931018i	−0.522544	+	0.852612i	$0.675017\pi$
$948$		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	0.942981	+	0.332846i	$0.108009\pi$
$953$	20.3126	+	39.8657i	0.657989	+	1.29138i	−0.284992	+	0.958530i	$0.591991\pi$
$954$		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	0.584056	−	0.811713i	$-0.301465\pi$
$967$	8.41681	+	4.28858i	0.270666	+	0.137911i	−0.313390	+	0.949625i	$0.601465\pi$
$968$	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	−0.635417	−	0.772169i	$-0.719172\pi$
$971$	−49.9618	−	16.2336i	−1.60335	−	0.520960i	−0.967933	+	0.251209i	$0.919172\pi$
$972$		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	0.0713675	−	0.997450i	$-0.477264\pi$
$977$	−5.28202	−	0.836590i	−0.168987	−	0.0267649i	−0.240354	+	0.970685i	$0.577264\pi$
$978$		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	−0.955639	−	0.294540i	$-0.904833\pi$
$983$	−4.87976	+	9.57708i	−0.155640	+	0.305461i	0.799999	+	0.600002i	$0.204833\pi$
$984$		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	−0.631715	−	0.775201i	$-0.717649\pi$
$991$	9.46784	−	13.0314i	0.300756	−	0.413955i	0.932470	+	0.361246i	$0.117649\pi$
$992$	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	−0.290176	−	0.956973i	$-0.593714\pi$
$997$	9.89793	−	5.04325i	0.313471	−	0.159721i	0.603647	+	0.797252i	$0.293714\pi$
$998$	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.127.2		240
3.2	odd	2		300.2.w.a.127.29	yes	240
4.3	odd	2	inner	900.2.bj.f.127.6		240
12.11	even	2		300.2.w.a.127.25	✓	240
25.13	odd	20	inner	900.2.bj.f.163.6		240
75.38	even	20		300.2.w.a.163.25	yes	240
100.63	even	20	inner	900.2.bj.f.163.2		240
300.263	odd	20		300.2.w.a.163.29	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.25	✓	240	12.11	even	2
300.2.w.a.127.29	yes	240	3.2	odd	2
300.2.w.a.163.25	yes	240	75.38	even	20
300.2.w.a.163.29	yes	240	300.263	odd	20
900.2.bj.f.127.2		240	1.1	even	1	trivial
900.2.bj.f.127.6		240	4.3	odd	2	inner
900.2.bj.f.163.2		240	100.63	even	20	inner
900.2.bj.f.163.6		240	25.13	odd	20	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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