LMFDB - Embedded newform 900.2.bj.f.127.6

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			127.6
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18105 - 0.777895i) q^{2} +(0.789760 + 1.83747i) q^{4} +(-2.16584 + 0.556007i) q^{5} +(3.13412 - 3.13412i) q^{7} +(0.496609 - 2.78449i) q^{8} +O(q^{10})$	\(q+(-1.18105 - 0.777895i) q^{2} +(0.789760 + 1.83747i) q^{4} +(-2.16584 + 0.556007i) q^{5} +(3.13412 - 3.13412i) q^{7} +(0.496609 - 2.78449i) q^{8} +(2.99048 + 1.02812i) q^{10} +(-0.0527296 - 0.0725760i) q^{11} +(-5.12177 + 0.811209i) q^{13} +(-6.13957 + 1.26354i) q^{14} +(-2.75256 + 2.90231i) q^{16} +(1.36594 - 2.68082i) q^{17} +(0.464955 + 1.43098i) q^{19} +(-2.73213 - 3.54054i) q^{20} +(0.00581977 + 0.126734i) q^{22} +(-2.09335 - 0.331555i) q^{23} +(4.38171 - 2.40844i) q^{25} +(6.68011 + 3.02612i) q^{26} +(8.23404 + 3.28364i) q^{28} +(6.04881 + 1.96538i) q^{29} +(-3.95945 + 1.28650i) q^{31} +(5.50860 - 1.28658i) q^{32} +(-3.69864 + 2.10362i) q^{34} +(-5.04540 + 8.53059i) q^{35} +(-1.26010 - 7.95598i) q^{37} +(0.564019 - 2.05175i) q^{38} +(0.472619 + 6.30687i) q^{40} +(-8.23695 - 5.98450i) q^{41} +(-7.85946 - 7.85946i) q^{43} +(0.0917123 - 0.154206i) q^{44} +(2.21444 + 2.01999i) q^{46} +(3.49688 + 6.86301i) q^{47} -12.6454i q^{49} +(-7.04854 - 0.564022i) q^{50} +(-5.53554 - 8.77042i) q^{52} +(-1.47153 - 2.88805i) q^{53} +(0.154557 + 0.127870i) q^{55} +(-7.17049 - 10.2834i) q^{56} +(-5.61510 - 7.02655i) q^{58} +(-11.4383 - 8.31042i) q^{59} +(-9.26103 + 6.72853i) q^{61} +(5.67708 + 1.56061i) q^{62} +(-7.50676 - 2.76560i) q^{64} +(10.6419 - 4.60469i) q^{65} +(1.84223 + 0.938661i) q^{67} +(6.00467 + 0.392675i) q^{68} +(12.5948 - 6.15026i) q^{70} +(2.37497 + 0.771676i) q^{71} +(1.16183 - 7.33551i) q^{73} +(-4.70067 + 10.3766i) q^{74} +(-2.26218 + 1.98447i) q^{76} +(-0.392723 - 0.0622012i) q^{77} +(-0.395606 + 1.21755i) q^{79} +(4.34789 - 7.81638i) q^{80} +(5.07295 + 13.4755i) q^{82} +(-1.03260 + 2.02659i) q^{83} +(-1.46786 + 6.56569i) q^{85} +(3.16858 + 15.3962i) q^{86} +(-0.228273 + 0.110783i) q^{88} +(-7.66814 - 10.5543i) q^{89} +(-13.5098 + 18.5947i) q^{91} +(-1.04403 - 4.10831i) q^{92} +(1.20871 - 10.8258i) q^{94} +(-1.80265 - 2.84076i) q^{95} +(3.93972 - 2.00739i) q^{97} +(-9.83679 + 14.9349i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.18105	−	0.777895i	−0.835129	−	0.550055i
$2$	−1.18105	−	0.777895i	−0.835129	−	0.550055i
$3$		0			0
$3$		0			0
$4$	0.789760	+	1.83747i	0.394880	+	0.918733i
$5$	−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	$-0.433941\pi$
$7$	3.13412	−	3.13412i	1.18459	−	1.18459i	0.978543	−	0.206043i	$-0.0660586\pi$
$8$	0.496609	−	2.78449i	0.175578	−	0.984466i
$9$		0			0
$10$	2.99048	+	1.02812i	0.945672	+	0.325121i
$11$	−0.0527296	−	0.0725760i	−0.0158986	−	0.0218825i	0.800994	−	0.598673i	$-0.204305\pi$
$11$	−0.0527296	−	0.0725760i	−0.0158986	−	0.0218825i	−0.816892	+	0.576790i	$0.804305\pi$
$12$		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	$0.705453\pi$
$14$	−6.13957	+	1.26354i	−1.64087	+	0.337695i
$15$		0			0
$16$	−2.75256	+	2.90231i	−0.688140	+	0.725578i
$17$	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	0.990118	−	0.140235i	$-0.0447857\pi$
$19$	0.464955	+	1.43098i	0.106668	+	0.328290i	−0.883450	+	0.468525i	$0.844786\pi$
$20$	−2.73213	−	3.54054i	−0.610924	−	0.791689i
$21$		0			0
$22$	0.00581977	+	0.126734i	0.00124078	+	0.0270198i
$23$	−2.09335	−	0.331555i	−0.436494	−	0.0691339i	−0.0656796	−	0.997841i	$-0.520922\pi$
$23$	−2.09335	−	0.331555i	−0.436494	−	0.0691339i	−0.370815	+	0.928707i	$0.620922\pi$
$24$		0			0
$25$	4.38171	−	2.40844i	0.876343	−	0.481688i
$26$	6.68011	+	3.02612i	1.31008	+	0.593471i
$27$		0			0
$28$	8.23404	+	3.28364i	1.55609	+	0.620549i
$29$	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	−0.642177	−	0.766556i	$-0.721969\pi$
$31$	−3.95945	+	1.28650i	−0.711139	+	0.231063i	−0.0689619	+	0.997619i	$0.521969\pi$
$32$	5.50860	−	1.28658i	0.973793	−	0.227436i
$33$		0			0
$34$	−3.69864	+	2.10362i	−0.634312	+	0.360768i
$35$	−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	$-0.280347\pi$
$38$	0.564019	−	2.05175i	0.0914960	−	0.332838i
$39$		0			0
$40$	0.472619	+	6.30687i	0.0747277	+	0.997204i
$41$	−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	$-0.928103\pi$
$43$	−7.85946	−	7.85946i	−1.19856	−	1.19856i	−0.223957	−	0.974599i	$-0.571897\pi$
$44$	0.0917123	−	0.154206i	0.0138261	−	0.0232475i
$45$		0			0
$46$	2.21444	+	2.01999i	0.326501	+	0.297831i
$47$	3.49688	+	6.86301i	0.510072	+	1.00107i	0.992163	+	0.124952i	$0.0398776\pi$
$47$	3.49688	+	6.86301i	0.510072	+	1.00107i	−0.482091	+	0.876121i	$0.660122\pi$
$48$		0			0
$49$		−	12.6454i		−	1.80649i
$50$	−7.04854	−	0.564022i	−0.996814	−	0.0797647i
$51$		0			0
$52$	−5.53554	−	8.77042i	−0.767641	−	1.21624i
$53$	−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
$56$	−7.17049	−	10.2834i	−0.958197	−	1.37417i
$57$		0			0
$58$	−5.61510	−	7.02655i	−0.737298	−	0.922632i
$59$	−11.4383	−	8.31042i	−1.48914	−	1.08192i	−0.974465	−	0.224539i	$-0.927912\pi$
$59$	−11.4383	−	8.31042i	−1.48914	−	1.08192i	−0.514676	−	0.857385i	$-0.672088\pi$
$60$		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	$0.561804\pi$
$62$	5.67708	+	1.56061i	0.720990	+	0.198198i
$63$		0			0
$64$	−7.50676	−	2.76560i	−0.938345	−	0.345701i
$65$	10.6419	−	4.60469i	1.31996	−	0.571141i
$66$		0			0
$67$	1.84223	+	0.938661i	0.225064	+	0.114676i	0.562887	−	0.826534i	$-0.309691\pi$
$67$	1.84223	+	0.938661i	0.225064	+	0.114676i	−0.337823	+	0.941210i	$0.609691\pi$
$68$	6.00467	+	0.392675i	0.728174	+	0.0476188i
$69$		0			0
$70$	12.5948	−	6.15026i	1.50536	−	0.735096i
$71$	2.37497	+	0.771676i	0.281857	+	0.0915810i	0.446534	−	0.894767i	$-0.352658\pi$
$71$	2.37497	+	0.771676i	0.281857	+	0.0915810i	−0.164677	+	0.986348i	$0.552658\pi$
$72$		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	−0.970842	−	0.239722i	$-0.922944\pi$
$79$	−0.395606	+	1.21755i	−0.0445091	+	0.136985i	0.926332	+	0.376707i	$0.122944\pi$
$80$	4.34789	−	7.81638i	0.486109	−	0.873898i
$81$		0			0
$82$	5.07295	+	13.4755i	0.560213	+	1.48812i
$83$	−1.03260	+	2.02659i	−0.113343	+	0.222447i	−0.940709	−	0.339216i	$-0.889838\pi$
$83$	−1.03260	+	2.02659i	−0.113343	+	0.222447i	0.827366	+	0.561663i	$0.189838\pi$
$84$		0			0
$85$	−1.46786	+	6.56569i	−0.159212	+	0.712149i
$86$	3.16858	+	15.3962i	0.341677	+	1.66022i
$87$		0			0
$88$	−0.228273	+	0.110783i	−0.0243340	+	0.0118095i
$89$	−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
$92$	−1.04403	−	4.10831i	−0.108847	−	0.428321i
$93$		0			0
$94$	1.20871	−	10.8258i	0.124669	−	1.11659i
$95$	−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	$0.277933\pi$
$98$	−9.83679	+	14.9349i	−0.993666	+	1.50865i
$99$		0			0
$100$	7.88593	+	6.14916i	0.788593	+	0.614916i
$101$	−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	$-0.688923\pi$
$103$	−2.20599	+	1.12401i	−0.217363	+	0.110752i	0.341919	+	0.939729i	$0.388923\pi$
$104$	−0.284716	+	14.6644i	−0.0279187	+	1.43796i
$105$		0			0
$106$	−0.508641	+	4.55562i	−0.0494036	+	0.442481i
$107$	−2.71179	+	2.71179i	−0.262159	+	0.262159i	−0.825931	−	0.563772i	$-0.809350\pi$
$107$	−2.71179	+	2.71179i	−0.262159	+	0.262159i	0.563772	+	0.825931i	$0.309350\pi$
$108$		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	$0.0931344\pi$
$110$	−0.0830696	−	0.271250i	−0.00792038	−	0.0258626i
$111$		0			0
$112$	0.469342	+	17.7230i	0.0443487	+	1.67467i
$113$	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
$116$	1.16579	+	12.6667i	0.108241	+	1.17607i
$117$		0			0
$118$	7.04459	+	18.7128i	0.648507	+	1.72265i
$119$	−4.12097	−	12.6830i	−0.377768	−	1.16265i
$120$		0			0
$121$	3.39670	−	10.4540i	0.308791	−	0.950361i
$122$	16.1718	−	0.742628i	1.46413	−	0.0672344i
$123$		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	$-0.910637\pi$
$127$	0.434901	−	2.74586i	0.0385912	−	0.243655i	0.999442	+	0.0334122i	$0.0106374\pi$
$128$	6.71451	+	9.10579i	0.593485	+	0.804845i
$129$		0			0
$130$	−16.1506	−	2.83991i	−1.41650	−	0.249076i
$131$	11.7429	−	3.81550i	1.02598	−	0.333361i	0.252781	−	0.967524i	$-0.418655\pi$
$131$	11.7429	−	3.81550i	1.02598	−	0.333361i	0.773200	+	0.634162i	$0.218655\pi$
$132$		0			0
$133$	5.94209	+	3.02765i	0.515245	+	0.262530i
$134$	−1.44558	−	2.54166i	−0.124879	−	0.219566i
$135$		0			0
$136$	−6.78636	−	5.13477i	−0.581926	−	0.440303i
$137$	−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	−0.981805	−	0.189889i	$-0.939187\pi$
$139$	−13.0231	+	9.46183i	−1.10460	+	0.802542i	−0.122799	+	0.992432i	$0.539187\pi$
$140$	−19.6593	−	2.53365i	−1.66152	−	0.214132i
$141$		0			0
$142$	−2.20468	−	2.75887i	−0.185013	−	0.231519i
$143$	0.328943	+	0.328943i	0.0275076	+	0.0275076i
$144$		0			0
$145$	−14.1935	−	0.893513i	−1.17871	−	0.0742022i
$146$	−7.07843	+	7.75982i	−0.585815	+	0.642207i
$147$		0			0
$148$	13.6237	−	8.59871i	1.11986	−	0.706810i
$149$			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	$-0.947693\pi$
$151$		−	4.02046i		−	0.327180i	0.986528	−	0.163590i	$-0.0523075\pi$
$152$	4.21546	−	0.584022i	0.341919	−	0.0473704i
$153$		0			0
$154$	0.415439	+	0.378960i	0.0334771	+	0.0305374i
$155$	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	$0.791700\pi$
$158$	1.41436	−	1.13025i	0.112520	−	0.0899176i
$159$		0			0
$160$	−11.2154	+	5.84933i	−0.886656	+	0.462430i
$161$	−7.59995	+	5.52169i	−0.598960	+	0.435170i
$162$		0			0
$163$	1.04062	+	6.57021i	0.0815075	+	0.514618i	0.994337	+	0.106276i	$0.0338929\pi$
$163$	1.04062	+	6.57021i	0.0815075	+	0.514618i	−0.912829	+	0.408342i	$0.866107\pi$
$164$	4.49109	−	19.8614i	0.350696	−	1.55092i
$165$		0			0
$166$	2.79603	−	1.59025i	0.217014	−	0.123428i
$167$	−2.62863	−	1.33936i	−0.203410	−	0.103642i	0.349318	−	0.937004i	$-0.386413\pi$
$167$	−2.62863	−	1.33936i	−0.203410	−	0.103642i	−0.552728	+	0.833362i	$0.686413\pi$
$168$		0			0
$169$	13.2108	−	4.29244i	1.01621	−	0.330187i
$170$	6.84103	−	6.61257i	0.524683	−	0.507161i
$171$		0			0
$172$	8.23440	−	20.6486i	0.627867	−	1.57444i
$173$	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
$178$	0.846333	+	18.4302i	0.0634354	+	1.38140i
$179$	2.84051	−	8.74220i	0.212310	−	0.653423i	−0.787024	−	0.616923i	$-0.788379\pi$
$179$	2.84051	−	8.74220i	0.212310	−	0.653423i	0.999334	−	0.0364999i	$-0.0116209\pi$
$180$		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	$0.845329\pi$
$182$	30.4205	−	11.4520i	2.25492	−	0.848881i
$183$		0			0
$184$	−1.96279	+	5.66427i	−0.144699	+	0.417575i
$185$	7.15276	+	16.5307i	0.525881	+	1.21536i
$186$		0			0
$187$	−0.266589	+	0.0422235i	−0.0194949	+	0.00308769i
$188$	−9.84885	+	11.8455i	−0.718302	+	0.863924i
$189$		0			0
$190$	−0.0807892	+	4.75735i	−0.00586107	+	0.345135i
$191$	2.40696	−	3.31289i	0.174161	−	0.239712i	−0.713009	−	0.701155i	$-0.752668\pi$
$191$	2.40696	−	3.31289i	0.174161	−	0.239712i	0.887170	+	0.461443i	$0.152668\pi$
$192$		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	$0.447908\pi$
$194$	−6.21454	−	0.693861i	−0.446178	−	0.0498164i
$195$		0			0
$196$	23.2355	−	9.98683i	1.65968	−	0.713345i
$197$	−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	$-0.227030\pi$
$199$	21.3364			1.51250			0.756249	+	0.654284i	$0.227030\pi$
$200$	−4.53028	−	13.3969i	−0.320339	−	0.947303i
$201$		0			0
$202$	8.05270	+	5.30388i	0.566586	+	0.373180i
$203$	25.1174	−	12.7980i	1.76290	−	0.898242i
$204$		0			0
$205$	21.1673	+	8.38165i	1.47839	+	0.585400i
$206$	3.47975	+	0.388518i	0.242445	+	0.0270693i
$207$		0			0
$208$	11.7436	−	17.0979i	0.814272	−	1.18553i
$209$	0.0793382	−	0.109200i	0.00548794	−	0.00755350i
$210$		0			0
$211$	15.1542	+	20.8580i	1.04326	+	1.43592i	0.894511	+	0.447047i	$0.147524\pi$
$211$	15.1542	+	20.8580i	1.04326	+	1.43592i	0.148748	+	0.988875i	$0.452476\pi$
$212$	4.14453	−	4.98475i	0.284647	−	0.342354i
$213$		0			0
$214$	5.31225	−	1.09327i	0.363138	−	0.0747347i
$215$	21.3922	+	12.6524i	1.45894	+	0.862887i
$216$		0			0
$217$	−8.37734	+	16.4415i	−0.568691	+	1.11612i
$218$	−9.10493	+	3.42762i	−0.616664	+	0.232148i
$219$		0			0
$220$	−0.112894	+	0.384979i	−0.00761133	+	0.0259553i
$221$	−4.82135	+	14.8386i	−0.324319	+	0.998152i
$222$		0			0
$223$	24.4327	+	3.86975i	1.63613	+	0.259138i	0.905722	−	0.423872i	$-0.139329\pi$
$223$	24.4327	+	3.86975i	1.63613	+	0.259138i	0.730410	+	0.683009i	$0.239329\pi$
$224$	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	$-0.733062\pi$
$227$	2.96964	−	18.7496i	0.197102	−	1.24445i	0.865598	−	0.500739i	$-0.166938\pi$
$228$		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	$0.557558\pi$
$230$	−5.91925	−	3.14373i	−0.390304	−	0.207291i
$231$		0			0
$232$	8.47647	−	15.8668i	0.556508	−	1.04171i
$233$	−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
$236$	6.23659	−	27.5807i	0.405968	−	1.79535i
$237$		0			0
$238$	−4.99899	+	18.1850i	−0.324037	+	1.17876i
$239$	−16.3162	+	11.8544i	−1.05541	+	0.766798i	−0.973233	−	0.229820i	$-0.926186\pi$
$239$	−16.3162	+	11.8544i	−1.05541	+	0.766798i	−0.0821734	+	0.996618i	$0.526186\pi$
$240$		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	$0.630519\pi$
$242$	−12.1438	+	9.70439i	−0.780630	+	0.623822i
$243$		0			0
$244$	−19.6774	−	11.7029i	−1.25972	−	0.749201i
$245$	7.03093	+	27.3879i	0.449190	+	1.74975i
$246$		0			0
$247$	−3.54222	−	6.95199i	−0.225386	−	0.442345i
$248$	1.61596	+	11.6639i	0.102613	+	0.740662i
$249$		0			0
$250$	15.5796	−	2.69745i	0.985340	−	0.170602i
$251$			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
$254$	−2.64963	+	2.90469i	−0.166252	+	0.182256i
$255$		0			0
$256$	−0.846832	−	15.9776i	−0.0529270	−	0.998598i
$257$	−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
$260$	16.8655	+	15.9175i	1.04595	+	0.987163i
$261$		0			0
$262$	−16.8370	−	4.62844i	−1.04019	−	0.285946i
$263$	2.36297	+	14.9192i	0.145707	+	0.919957i	0.946895	+	0.321544i	$0.104202\pi$
$263$	2.36297	+	14.9192i	0.145707	+	0.919957i	−0.801188	+	0.598413i	$0.795798\pi$
$264$		0			0
$265$	4.79287	+	5.43686i	0.294424	+	0.333984i
$266$	−4.66272	−	8.19813i	−0.285890	−	0.502659i
$267$		0			0
$268$	−0.269842	+	4.12634i	−0.0164832	+	0.252057i
$269$	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	0.139412	−	0.990234i	$-0.455479\pi$
$271$	−5.42995	−	1.76430i	−0.329846	−	0.107173i	−0.469258	+	0.883061i	$0.655479\pi$
$272$	4.02072	+	11.3435i	0.243792	+	0.687801i
$273$		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	$0.434930\pi$
$278$	22.7412	−	1.04430i	1.36393	−	0.0626331i
$279$		0			0
$280$	21.2477	+	18.2852i	1.26979	+	1.09275i
$281$	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	$0.334496\pi$
$283$	−8.36586	+	16.4189i	−0.497299	+	0.976004i	−0.994134	+	0.108159i	$0.965504\pi$
$284$	0.457731	+	4.97337i	0.0271613	+	0.295115i
$285$		0			0
$286$	−0.132615	−	0.644382i	−0.00784171	−	0.0381031i
$287$	−44.5717	+	7.05947i	−2.63099	+	0.416707i
$288$		0			0
$289$	4.67138	+	6.42960i	0.274787	+	0.378212i
$290$	16.0682	+	12.0963i	0.943557	+	0.710322i
$291$		0			0
$292$	14.3963	−	3.65846i	0.842480	−	0.214095i
$293$	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
$296$	−22.7791	−	0.442267i	−1.32401	−	0.0257062i
$297$		0			0
$298$	2.25693	−	3.42662i	0.130740	−	0.198499i
$299$	10.9906			0.635605
$300$		0			0
$301$	−49.2649			−2.83958
$302$	−3.12749	+	4.74837i	−0.179967	+	0.273238i
$303$		0			0
$304$	−5.43297	−	2.58942i	−0.311602	−	0.148514i
$305$	16.3168	−	19.7221i	0.934296	−	1.12928i
$306$		0			0
$307$	22.4411	−	22.4411i	1.28078	−	1.28078i	0.340557	−	0.940224i	$-0.389384\pi$
$307$	22.4411	−	22.4411i	1.28078	−	1.28078i	0.940224	−	0.340557i	$-0.110616\pi$
$308$	−0.195864	−	0.770739i	−0.0111604	−	0.0439169i
$309$		0			0
$310$	−13.1634	−	0.223540i	−0.747628	−	0.0126962i
$311$	8.54043	+	11.7549i	0.484284	+	0.666559i	0.979321	−	0.202312i	$-0.0648457\pi$
$311$	8.54043	+	11.7549i	0.484284	+	0.666559i	−0.495037	+	0.868872i	$0.664846\pi$
$312$		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	$0.470292\pi$
$314$	0.933204	+	4.53446i	0.0526637	+	0.255895i
$315$		0			0
$316$	−2.54964	+	0.234659i	−0.143428	+	0.0132006i
$317$	−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
$320$	17.7961	+	1.81605i	0.994833	+	0.101520i
$321$		0			0
$322$	13.2712	−	0.609429i	0.739576	−	0.0339621i
$323$	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
$328$	−20.7543	+	19.9638i	−1.14597	+	1.10231i
$329$	32.4691	+	10.5499i	1.79008	+	0.581633i
$330$		0			0
$331$	29.8062	−	9.68463i	1.63830	−	0.532316i	0.662141	−	0.749379i	$-0.269648\pi$
$331$	29.8062	−	9.68463i	1.63830	−	0.532316i	0.976157	+	0.217064i	$0.0696479\pi$
$332$	−4.53930	−	0.296847i	−0.249126	−	0.0162916i
$333$		0			0
$334$	2.06267	+	3.62665i	0.112864	+	0.198441i
$335$	−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	$-0.386973\pi$
$338$	−18.9416	−	5.20700i	−1.03029	−	0.283223i
$339$		0			0
$340$	−13.2235	+	2.48817i	−0.717144	+	0.134940i
$341$	0.302150	+	0.219525i	0.0163623	+	0.0118879i
$342$		0			0
$343$	−17.6934	−	17.6934i	−0.955352	−	0.955352i
$344$	−25.7876	+	17.9815i	−1.39038	+	0.969497i
$345$		0			0
$346$	−6.20029	+	6.79715i	−0.333330	+	0.365417i
$347$	−4.47490	−	8.78249i	−0.240225	−	0.471469i	0.739144	−	0.673548i	$-0.235230\pi$
$347$	−4.47490	−	8.78249i	−0.240225	−	0.471469i	−0.979369	+	0.202079i	$0.935230\pi$
$348$		0			0
$349$			19.1891i			1.02717i	0.858039	+	0.513585i	$0.171683\pi$
$349$			19.1891i			1.02717i	−0.858039	+	0.513585i	$0.828317\pi$
$350$	−23.8587	+	20.3232i	−1.27530	+	1.08632i
$351$		0			0
$352$	−0.383841	−	0.331952i	−0.0204588	−	0.0176931i
$353$	−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
$356$	13.3372	−	22.4253i	0.706868	−	1.18854i
$357$		0			0
$358$	−10.1553	+	8.11536i	−0.536724	+	0.428910i
$359$	−0.644378	−	0.468168i	−0.0340090	−	0.0247090i	0.570651	−	0.821193i	$-0.306691\pi$
$359$	−0.644378	−	0.468168i	−0.0340090	−	0.0247090i	−0.604660	+	0.796484i	$0.706691\pi$
$360$		0			0
$361$	13.5398	−	9.83724i	0.712621	−	0.517749i
$362$	1.72386	−	6.27093i	0.0906041	−	0.329593i
$363$		0			0
$364$	−44.8366	−	10.1385i	−2.35008	−	0.531402i
$365$	1.56225	+	16.5335i	0.0817721	+	0.865403i
$366$		0			0
$367$	−24.8460	−	12.6597i	−1.29695	−	0.660830i	−0.337135	−	0.941456i	$-0.609458\pi$
$367$	−24.8460	−	12.6597i	−1.29695	−	0.660830i	−0.959817	+	0.280626i	$0.909458\pi$
$368$	6.72435	−	5.16294i	0.350531	−	0.269137i
$369$		0			0
$370$	4.41141	−	25.0877i	0.229338	−	1.30425i
$371$	−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	$-0.741037\pi$
$379$	5.76200	−	17.7336i	0.295974	−	0.910915i	0.982893	−	0.184180i	$-0.0589630\pi$
$380$	3.79614	−	5.55583i	0.194738	−	0.285008i
$381$		0			0
$382$	−5.41982	+	2.04033i	−0.277302	+	0.104392i
$383$	−8.53445	+	16.7498i	−0.436090	+	0.855875i	0.563468	+	0.826138i	$0.309467\pi$
$383$	−8.53445	+	16.7498i	−0.436090	+	0.855875i	−0.999558	+	0.0297370i	$0.990533\pi$
$384$		0			0
$385$	0.885158	−	0.0836387i	0.0451118	−	0.00426262i
$386$	22.4171	−	4.61349i	1.14100	−	0.234820i
$387$		0			0
$388$	6.79994	+	5.65374i	0.345214	+	0.287025i
$389$	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
$392$	−35.2110	−	6.27982i	−1.77842	−	0.317179i
$393$		0			0
$394$	12.1047	+	1.35150i	0.609825	+	0.0680878i
$395$	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	$0.273107\pi$
$398$	−25.1994	−	16.5975i	−1.26313	−	0.831956i
$399$		0			0
$400$	−5.07088	+	19.3465i	−0.253544	+	0.967324i
$401$	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
$404$	−5.38478	−	12.5283i	−0.267903	−	0.623307i
$405$		0			0
$406$	−39.6204	−	4.42367i	−1.96633	−	0.219543i
$407$	−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	$0.311620\pi$
$410$	−18.4796	−	26.3651i	−0.912644	−	1.30208i
$411$		0			0
$412$	−3.80753	−	3.16573i	−0.187583	−	0.155965i
$413$	−61.8949	+	9.80318i	−3.04565	+	0.482383i
$414$		0			0
$415$	1.10965	−	4.96341i	0.0544704	−	0.243644i
$416$	−27.1701	+	11.0582i	−1.33213	+	0.542172i
$417$		0			0
$418$	−0.178648	+	0.0672535i	−0.00873797	+	0.00328948i
$419$	6.15217	+	18.9344i	0.300553	+	0.925007i	0.981299	+	0.192488i	$0.0616556\pi$
$419$	6.15217	+	18.9344i	0.300553	+	0.925007i	−0.680746	+	0.732519i	$0.738344\pi$
$420$		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	$0.0913234\pi$
$422$	−1.67257	−	36.4227i	−0.0814195	−	1.77303i
$423$		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
$428$	−7.12449	−	2.84116i	−0.344375	−	0.137333i
$429$		0			0
$430$	−15.4231	−	31.5840i	−0.743766	−	1.52312i
$431$	−8.32624	+	2.70536i	−0.401061	+	0.130313i	−0.502600	−	0.864519i	$-0.667623\pi$
$431$	−8.32624	+	2.70536i	−0.401061	+	0.130313i	0.101539	+	0.994832i	$0.467623\pi$
$432$		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	$0.522922\pi$
$434$	22.6838	−	12.9015i	1.08886	−	0.619292i
$435$		0			0
$436$	13.4197	+	3.03448i	0.642688	+	0.145325i
$437$	−0.498865	−	3.14971i	−0.0238640	−	0.150671i
$438$		0			0
$439$	−25.5000	+	18.5268i	−1.21705	+	0.884236i	−0.995852	−	0.0909931i	$-0.970996\pi$
$439$	−25.5000	+	18.5268i	−1.21705	+	0.884236i	−0.221195	+	0.975229i	$0.570996\pi$
$440$	0.432807	−	0.366860i	0.0206333	−	0.0174893i
$441$		0			0
$442$	17.2371	−	13.7746i	0.819887	−	0.655192i
$443$	−22.7614	−	22.7614i	−1.08143	−	1.08143i	−0.996377	−	0.0850506i	$-0.972895\pi$
$443$	−22.7614	−	22.7614i	−1.08143	−	1.08143i	−0.0850506	−	0.996377i	$-0.527105\pi$
$444$		0			0
$445$	22.4762	+	18.5954i	1.06547	+	0.881504i
$446$	−25.8459	−	23.5764i	−1.22384	−	1.11638i
$447$		0			0
$448$	−32.1948	+	14.8593i	−1.52106	+	0.702038i
$449$		−	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
$452$	12.3887	+	19.6284i	0.582714	+	0.923242i
$453$		0			0
$454$	−18.0925	+	19.8341i	−0.849124	+	0.930862i
$455$	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	$0.795581\pi$
$458$	−3.55221	−	4.44512i	−0.165984	−	0.207707i
$459$		0			0
$460$	4.54544	+	8.31746i	0.211932	+	0.387803i
$461$	−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	$0.344001\pi$
$463$	6.36230	+	40.1700i	0.295681	+	1.86686i	−0.175019	+	0.984565i	$0.555999\pi$
$464$	−22.3539	+	12.1457i	−1.03775	+	0.563851i
$465$		0			0
$466$	3.23708	+	5.69153i	0.149955	+	0.263655i
$467$	22.9322	+	11.6845i	1.06118	+	0.540696i	0.895306	−	0.445452i	$-0.146957\pi$
$467$	22.9322	+	11.6845i	1.06118	+	0.540696i	0.165870	+	0.986148i	$0.446957\pi$
$468$		0			0
$469$	8.71563	−	2.83188i	0.402450	−	0.130764i
$470$	3.40133	+	24.1189i	0.156891	+	1.11252i
$471$		0			0
$472$	−28.8206	+	27.7228i	−1.32658	+	1.27605i
$473$	−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
$478$	28.4917	−	1.30837i	1.30318	−	0.0598435i
$479$	4.89353	−	15.0607i	0.223591	−	0.688142i	−0.774841	−	0.632157i	$-0.782170\pi$
$479$	4.89353	−	15.0607i	0.223591	−	0.688142i	0.998432	−	0.0559855i	$-0.0178301\pi$
$480$		0			0
$481$	12.9079	+	39.7265i	0.588551	+	1.81137i
$482$	−3.35003	−	8.89882i	−0.152590	−	0.405330i
$483$		0			0
$484$	21.8914	−	2.01480i	0.995063	−	0.0915819i
$485$	−7.41667	+	6.53819i	−0.336774	+	0.296884i
$486$		0			0
$487$	−18.8395	+	2.98389i	−0.853701	+	0.135213i	−0.567922	−	0.823083i	$-0.692252\pi$
$487$	−18.8395	+	2.98389i	−0.853701	+	0.135213i	−0.285779	+	0.958295i	$0.592252\pi$
$488$	14.1364	+	29.1287i	0.639925	+	1.31859i
$489$		0			0
$490$	13.0010	−	37.8158i	0.587327	−	1.70834i
$491$	4.08602	−	5.62393i	0.184400	−	0.253804i	−0.706802	−	0.707411i	$-0.749863\pi$
$491$	4.08602	−	5.62393i	0.184400	−	0.253804i	0.891202	+	0.453607i	$0.149863\pi$
$492$		0			0
$493$	13.5312	−	13.5312i	0.609413	−	0.609413i
$494$	−1.22438	+	10.9661i	−0.0550876	+	0.493389i
$495$		0			0
$496$	7.16480	−	15.0328i	0.321709	−	0.674991i
$497$	9.86197	−	5.02493i	0.442370	−	0.225399i
$498$		0			0
$499$	0.252832			0.0113183			0.00565916	−	0.999984i	$-0.498199\pi$
$499$	0.252832			0.0113183			0.00565916	+	0.999984i	$0.498199\pi$
$500$	−20.4986	−	8.93346i	−0.916726	−	0.399516i
$501$		0			0
$502$	21.0566	−	31.9695i	0.939803	−	1.42687i
$503$	−15.9788	+	8.14160i	−0.712459	+	0.363016i	−0.772357	−	0.635189i	$-0.780922\pi$
$503$	−15.9788	+	8.14160i	−0.712459	+	0.363016i	0.0598984	+	0.998204i	$0.480922\pi$
$504$		0			0
$505$	14.7672	−	3.79099i	0.657133	−	0.168697i
$506$	0.0298364	−	0.267229i	0.00132639	−	0.0118798i
$507$		0			0
$508$	5.38888	−	1.36945i	0.239093	−	0.0607596i
$509$	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
$512$	−11.4287	+	19.5291i	−0.505083	+	0.863071i
$513$		0			0
$514$	0.147109	+	0.714805i	0.00648868	+	0.0315287i
$515$	4.15286	−	3.66097i	0.182997	−	0.161321i
$516$		0			0
$517$	0.313701	−	0.615673i	0.0137966	−	0.0270773i
$518$	17.7892	+	47.2541i	0.781611	+	2.07623i
$519$		0			0
$520$	−7.53684	−	31.9190i	−0.330512	−	1.39974i
$521$	−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	−0.275171	−	0.961395i	$-0.588735\pi$
$523$	−19.0721	−	3.02072i	−0.833963	−	0.132087i	−0.558791	+	0.829308i	$0.688735\pi$
$524$	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
$530$	−1.43132	−	10.1496i	−0.0621727	−	0.440869i
$531$		0			0
$532$	−0.870373	+	13.3095i	−0.0377355	+	0.577040i
$533$	47.0425	+	23.9693i	2.03764	+	1.03823i
$534$		0			0
$535$	4.36553	−	7.38108i	0.188738	−	0.319112i
$536$	3.52856	−	4.66351i	0.152410	−	0.201433i
$537$		0			0
$538$	−27.1339	−	7.45902i	−1.16982	−	0.321581i
$539$	−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	$0.664892\pi$
$542$	5.04060	+	6.30765i	0.216512	+	0.270937i
$543$		0			0
$544$	4.07537	−	16.5249i	0.174730	−	0.708501i
$545$	−5.66321	+	14.3021i	−0.242585	+	0.612633i
$546$		0			0
$547$	8.45520	+	16.5943i	0.361518	+	0.709520i	0.998095	−	0.0616937i	$-0.0196502\pi$
$547$	8.45520	+	16.5943i	0.361518	+	0.709520i	−0.636577	+	0.771213i	$0.719650\pi$
$548$	7.69126	−	4.85442i	0.328554	−	0.207370i
$549$		0			0
$550$	0.330732	+	0.541296i	0.0141025	+	0.0230809i
$551$			9.56956i			0.407677i
$552$		0			0
$553$	2.57607	+	5.05582i	0.109546	+	0.214995i
$554$	−12.3005	−	11.2204i	−0.522598	−	0.476709i
$555$		0			0
$556$	−27.6709	−	16.4569i	−1.17351	−	0.697929i
$557$	−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
$560$	−10.8706	−	38.1243i	−0.459369	−	1.61105i
$561$		0			0
$562$	2.91188	−	10.5926i	0.122830	−	0.446823i
$563$	0.604217	+	3.81487i	0.0254647	+	0.160778i	0.997144	−	0.0755266i	$-0.0240638\pi$
$563$	0.604217	+	3.81487i	0.0254647	+	0.160778i	−0.971679	+	0.236304i	$0.924064\pi$
$564$		0			0
$565$	−23.8168	+	10.3054i	−1.00198	+	0.433551i
$566$	22.6527	−	12.8838i	0.952164	−	0.541547i
$567$		0			0
$568$	3.32816	−	6.22987i	0.139646	−	0.261399i
$569$	−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	0.259687	−	0.965693i	$-0.416381\pi$
$571$	−2.33800	−	0.759663i	−0.0978424	−	0.0317909i	−0.357529	+	0.933902i	$0.616381\pi$
$572$	−0.344636	+	0.864208i	−0.0144099	+	0.0361344i
$573$		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	$0.596693\pi$
$578$	−0.515580	−	11.2275i	−0.0214453	−	0.467003i
$579$		0			0
$580$	−9.56767	−	26.7858i	−0.397276	−	1.11222i
$581$	3.11529	+	9.58788i	0.129244	+	0.397772i
$582$		0			0
$583$	−0.132010	+	0.259083i	−0.00546728	+	0.0107301i
$584$	−19.8487	−	6.87798i	−0.821343	−	0.284613i
$585$		0			0
$586$	−32.3973	+	6.66745i	−1.33832	+	0.275430i
$587$	19.2103	−	3.04261i	0.792893	−	0.125582i	0.253167	−	0.967423i	$-0.418528\pi$
$587$	19.2103	−	3.04261i	0.792893	−	0.125582i	0.539726	+	0.841841i	$0.318528\pi$
$588$		0			0
$589$	−3.68193	−	5.06775i	−0.151711	−	0.208813i
$590$	−25.6619	−	36.6121i	−1.05648	−	1.50730i
$591$		0			0
$592$	26.5592	+	18.2421i	1.09158	+	0.749746i
$593$	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
$596$	−5.33109	+	2.29135i	−0.218370	+	0.0938575i
$597$		0			0
$598$	−12.9805	−	8.54956i	−0.530812	−	0.349618i
$599$	41.8236			1.70887			0.854434	−	0.519561i	$-0.173904\pi$
$599$	41.8236			1.70887			0.854434	+	0.519561i	$0.173904\pi$
$600$		0			0
$601$	−37.3005			−1.52152			−0.760759	−	0.649034i	$-0.775173\pi$
$601$	−37.3005			−1.52152			−0.760759	+	0.649034i	$0.775173\pi$
$602$	58.1844	+	38.3229i	2.37142	+	1.56193i
$603$		0			0
$604$	7.38746	−	3.17520i	0.300591	−	0.129197i
$605$	−1.54423	+	24.5302i	−0.0627818	+	0.997294i
$606$		0			0
$607$	6.86710	−	6.86710i	0.278727	−	0.278727i	−0.553874	−	0.832601i	$-0.686851\pi$
$607$	6.86710	−	6.86710i	0.278727	−	0.278727i	0.832601	+	0.553874i	$0.186851\pi$
$608$	4.40232	+	7.28452i	0.178538	+	0.295426i
$609$		0			0
$610$	−34.6127	+	10.6001i	−1.40143	+	0.429184i
$611$	−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	$0.514467\pi$
$614$	−43.9609	+	9.04725i	−1.77412	+	0.365117i
$615$		0			0
$616$	−0.368228	+	1.06264i	−0.0148363	+	0.0428151i
$617$	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	$-0.866529\pi$
$619$	−10.2938	−	31.6812i	−0.413744	−	1.27337i	0.499625	−	0.866242i	$-0.333471\pi$
$620$	15.3727	+	10.5037i	0.617382	+	0.421839i
$621$		0			0
$622$	−0.942608	−	20.5267i	−0.0377951	−	0.823045i
$623$	−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
$628$	2.42518	−	6.08136i	0.0967750	−	0.242673i
$629$	−23.0498	−	7.48932i	−0.919054	−	0.298619i
$630$		0			0
$631$	−4.13387	+	1.34318i	−0.164567	+	0.0534710i	−0.390142	−	0.920755i	$-0.627574\pi$
$631$	−4.13387	+	1.34318i	−0.164567	+	0.0534710i	0.225575	+	0.974226i	$0.427574\pi$
$632$	3.19379	+	1.70621i	0.127042	+	0.0678692i
$633$		0			0
$634$	9.76201	−	5.55218i	0.387699	−	0.220505i
$635$	0.584789	+	6.18889i	0.0232066	+	0.245599i
$636$		0			0
$637$	10.2581	+	64.7669i	0.406439	+	2.56616i
$638$	−0.213878	+	0.778029i	−0.00846750	+	0.0308024i
$639$		0			0
$640$	−19.6054	−	15.9884i	−0.774972	−	0.631995i
$641$	−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	0.599272	−	0.800545i	$-0.295457\pi$
$643$	−5.10377	−	5.10377i	−0.201273	−	0.201273i	−0.800545	+	0.599272i	$0.795457\pi$
$644$	−16.1480	−	9.60384i	−0.636322	−	0.378444i
$645$		0			0
$646$	−4.72994	−	4.31461i	−0.186097	−	0.169756i
$647$	8.71938	+	17.1127i	0.342794	+	0.672771i	0.996465	−	0.0840074i	$-0.0267720\pi$
$647$	8.71938	+	17.1127i	0.342794	+	0.672771i	−0.653671	+	0.756779i	$0.726772\pi$
$648$		0			0
$649$			1.26835i			0.0497872i
$650$	36.5585	−	2.82905i	1.43394	−	0.110964i
$651$		0			0
$652$	−11.2507	+	7.10098i	−0.440611	+	0.278096i
$653$	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
$656$	40.0416	−	7.43352i	1.56336	−	0.290230i
$657$		0			0
$658$	−30.1410	−	37.7175i	−1.17502	−	1.47038i
$659$	27.2711	+	19.8136i	1.06233	+	0.771830i	0.974518	−	0.224307i	$-0.0720119\pi$
$659$	27.2711	+	19.8136i	1.06233	+	0.771830i	0.0878139	+	0.996137i	$0.472012\pi$
$660$		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	$-0.0369389\pi$
$662$	−42.7363	−	11.7481i	−1.66099	−	0.456602i
$663$		0			0
$664$	5.13023	+	3.88169i	0.199091	+	0.150639i
$665$	−14.5530	−	3.25355i	−0.564341	−	0.126167i
$666$		0			0
$667$	−12.0107	−	6.11974i	−0.465055	−	0.236957i
$668$	0.385031	−	5.88779i	0.0148973	−	0.227806i
$669$		0			0
$670$	4.54408	+	4.70108i	0.175553	+	0.181619i
$671$	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
$680$	17.5531	+	7.34783i	0.673132	+	0.281776i
$681$		0			0
$682$	−0.186087	−	0.494310i	−0.00712564	−	0.0189281i
$683$	1.48416	−	2.91283i	0.0567898	−	0.111456i	−0.860867	−	0.508830i	$-0.830078\pi$
$683$	1.48416	−	2.91283i	0.0567898	−	0.111456i	0.917657	+	0.397373i	$0.130078\pi$
$684$		0			0
$685$	4.03810	+	9.33246i	0.154288	+	0.356575i
$686$	7.13318	+	34.6603i	0.272346	+	1.32334i
$687$		0			0
$688$	44.4442	−	1.17697i	1.69442	−	0.0448717i
$689$	9.87967	+	13.5982i	0.376385	+	0.518050i
$690$		0			0
$691$	16.4783	−	22.6804i	0.626864	−	0.862805i	−0.370966	−	0.928647i	$-0.620973\pi$
$691$	16.4783	−	22.6804i	0.626864	−	0.862805i	0.997830	+	0.0658420i	$0.0209733\pi$
$692$	12.6103	−	3.20460i	0.479373	−	0.121821i
$693$		0			0
$694$	−1.54677	+	13.8536i	−0.0587145	+	0.525874i
$695$	22.9451	−	27.7337i	0.870356	−	1.05200i
$696$		0			0
$697$	−27.2946	+	13.9073i	−1.03385	+	0.526775i
$698$	14.9271	−	22.6633i	0.564999	−	0.857819i
$699$		0			0
$700$	43.9876	−	5.44324i	1.66258	−	0.205735i
$701$	−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
$704$	0.195112	+	0.690640i	0.00735355	+	0.0260295i
$705$		0			0
$706$	−5.56838	+	49.8729i	−0.209569	+	1.87699i
$707$	−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	$-0.0572302\pi$
$710$	6.30893	+	4.74944i	0.236770	+	0.178243i
$711$		0			0
$712$	−33.1964	+	16.1105i	−1.24409	+	0.603766i
$713$	8.71508	−	1.38033i	0.326382	−	0.0516939i
$714$		0			0
$715$	−0.895333	−	0.529543i	−0.0334835	−	0.0198038i
$716$	18.3068	−	1.68489i	0.684158	−	0.0629673i
$717$		0			0
$718$	0.396857	+	1.05419i	0.0148106	+	0.0393420i
$719$	−3.78332	−	11.6439i	−0.141094	−	0.434243i	0.855394	−	0.517978i	$-0.173315\pi$
$719$	−3.78332	−	11.6439i	−0.141094	−	0.434243i	−0.996488	+	0.0837350i	$0.973315\pi$
$720$		0			0
$721$	−3.39106	+	10.4366i	−0.126290	+	0.388680i
$722$	−23.6435	+	1.08574i	−0.879920	+	0.0404069i
$723$		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	$0.371492\pi$
$727$	−7.14374	+	45.1038i	−0.264947	+	1.67281i	−0.657789	+	0.753202i	$0.728508\pi$
$728$	45.0676	+	46.8522i	1.67032	+	1.73646i
$729$		0			0
$730$	11.0162	−	20.7422i	0.407729	−	0.767702i
$731$	−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	$0.936101\pi$
$734$	19.4965	+	34.2793i	0.719629	+	1.26527i
$735$		0			0
$736$	−11.9580	+	0.866853i	−0.440779	+	0.0319526i
$737$	−0.0290155	−	0.183197i	−0.00106880	−	0.00674814i
$738$		0			0
$739$	8.08428	−	5.87357i	0.297385	−	0.216063i	−0.429080	−	0.903267i	$-0.641162\pi$
$739$	8.08428	−	5.87357i	0.297385	−	0.216063i	0.726465	+	0.687204i	$0.241162\pi$
$740$	−24.7257	+	26.1983i	−0.908935	+	0.963067i
$741$		0			0
$742$	12.6837	+	15.8720i	0.465634	+	0.582680i
$743$	−16.3290	−	16.3290i	−0.599053	−	0.599053i	0.341008	−	0.940060i	$-0.389232\pi$
$743$	−16.3290	−	16.3290i	−0.599053	−	0.599053i	−0.940060	+	0.341008i	$0.889232\pi$
$744$		0			0
$745$	−1.61316	−	6.28381i	−0.0591015	−	0.230221i
$746$	−5.26708	+	5.77410i	−0.192841	+	0.211405i
$747$		0			0
$748$	−0.288125	−	0.456501i	−0.0105349	−	0.0166913i
$749$			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	$-0.284361\pi$
$752$	−29.5440	−	8.74181i	−1.07736	−	0.318781i
$753$		0			0
$754$	34.4593	+	31.4334i	1.25493	+	1.14474i
$755$	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	$0.813865\pi$
$758$	−20.6001	+	16.4621i	−0.748229	+	0.597929i
$759$		0			0
$760$	−8.80528	+	3.60872i	−0.319401	+	0.130902i
$761$	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
$764$	7.98824	+	1.80631i	0.289004	+	0.0653501i
$765$		0			0
$766$	23.1092	−	13.1435i	0.834970	−	0.474893i
$767$	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	$0.493950\pi$
$770$	−1.11048	−	0.589778i	−0.0400189	−	0.0212541i
$771$		0			0
$772$	−30.0645	−	11.9894i	−1.08205	−	0.431507i
$773$	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
$778$	−0.418881	−	9.12175i	−0.0150176	−	0.327031i
$779$	4.73390	−	14.5695i	0.169610	−	0.522005i
$780$		0			0
$781$	−0.0692262	−	0.213056i	−0.00247711	−	0.00762375i
$782$	8.44003	−	3.17731i	0.301815	−	0.113621i
$783$		0			0
$784$	36.7009	+	34.8072i	1.31075	+	1.24312i
$785$	6.30039	+	3.72636i	0.224870	+	0.132999i
$786$		0			0
$787$	17.4691	−	2.76683i	0.622705	−	0.0986268i	0.162894	−	0.986644i	$-0.447917\pi$
$787$	17.4691	−	2.76683i	0.622705	−	0.0986268i	0.459811	+	0.888017i	$0.347917\pi$
$788$	−13.2449	−	11.0124i	−0.471831	−	0.392299i
$789$		0			0
$790$	−2.43484	+	3.23432i	−0.0866277	+	0.115072i
$791$	30.2353	−	41.6153i	1.07504	−	1.47967i
$792$		0			0
$793$	41.9746	−	41.9746i	1.49056	−	1.49056i
$794$	−13.3984	−	1.49595i	−0.475491	−	0.0530892i
$795$		0			0
$796$	16.8506	+	39.2049i	0.597255	+	1.38958i
$797$	−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
$800$	21.0385	−	18.9046i	0.743823	−	0.668377i
$801$		0			0
$802$	−16.8241	−	11.0811i	−0.594080	−	0.391289i
$803$	−0.593645	+	0.302477i	−0.0209493	+	0.0106742i
$804$		0			0
$805$	13.3902	−	16.1847i	0.471941	−	0.570436i
$806$	−30.3427	−	3.38780i	−1.06878	−	0.119330i
$807$		0			0
$808$	−3.38601	+	18.9854i	−0.119119	+	0.667902i
$809$	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	0.987386	−	0.158333i	$-0.0506120\pi$
$811$	15.1413	+	20.8402i	0.531683	+	0.731799i	−0.455703	+	0.890132i	$0.650612\pi$
$812$	43.3526	+	36.0451i	1.52138	+	1.26494i
$813$		0			0
$814$	1.00096	−	0.206000i	0.0350836	−	0.00722029i
$815$	−5.90689	−	13.6514i	−0.206909	−	0.478188i
$816$		0			0
$817$	7.59246	−	14.9010i	0.265626	−	0.521321i
$818$	18.3900	−	6.92304i	0.642990	−	0.242058i
$819$		0			0
$820$	1.31610	+	45.5137i	0.0459603	+	1.58941i
$821$	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	0.0876604	−	0.996150i	$-0.472061\pi$
$823$	−3.92443	−	0.621568i	−0.136797	−	0.0216665i	−0.224457	+	0.974484i	$0.572061\pi$
$824$	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	$-0.779817\pi$
$827$	4.58447	−	28.9452i	0.159418	−	1.00652i	0.929565	−	0.368658i	$-0.120183\pi$
$828$		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	$0.393366\pi$
$830$	−5.17156	+	4.99884i	−0.179507	+	0.173512i
$831$		0			0
$832$	40.6914	+	8.07525i	1.41072	+	0.279959i
$833$	−33.9000	−	17.2729i	−1.17457	−	0.598471i
$834$		0			0
$835$	6.43789	+	1.43929i	0.222792	+	0.0498087i
$836$	0.263309	+	0.0595397i	0.00910672	+	0.00205923i
$837$		0			0
$838$	7.46297	−	27.1482i	0.257804	−	0.937821i
$839$	−21.2823	+	15.4625i	−0.734746	+	0.533824i	−0.891061	−	0.453883i	$-0.850038\pi$
$839$	−21.2823	+	15.4625i	−0.734746	+	0.533824i	0.156315	+	0.987707i	$0.450038\pi$
$840$		0			0
$841$	9.26395	+	6.73065i	0.319447	+	0.232092i
$842$	−1.23565	+	0.987435i	−0.0425831	+	0.0340293i
$843$		0			0
$844$	−26.3576	+	44.3181i	−0.907267	+	1.52549i
$845$	−26.2258	+	16.6420i	−0.902194	+	0.572502i
$846$		0			0
$847$	−22.1183	−	43.4096i	−0.759994	−	1.49157i
$848$	12.4325	+	3.67867i	0.426934	+	0.126326i
$849$		0			0
$850$	−11.1399	+	18.1254i	−0.382097	+	0.621696i
$851$			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	$-0.472984\pi$
$854$	48.3569	−	53.0119i	1.65474	−	1.81403i
$855$		0			0
$856$	6.20425	+	8.89765i	0.212057	+	0.304116i
$857$	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	0.437325	−	0.899304i	$-0.355926\pi$
$859$	−8.28918	−	6.02244i	−0.282823	−	0.205483i	−0.720148	+	0.693821i	$0.755926\pi$
$860$	−6.35364	+	49.2998i	−0.216657	+	1.68111i
$861$		0			0
$862$	11.9382	+	3.28177i	0.406616	+	0.111778i
$863$	3.08157	+	19.4563i	0.104898	+	0.662299i	0.982969	+	0.183769i	$0.0588299\pi$
$863$	3.08157	+	19.4563i	0.104898	+	0.662299i	−0.878072	+	0.478529i	$0.841170\pi$
$864$		0			0
$865$	1.36844	+	14.4824i	0.0465285	+	0.492416i
$866$	−11.3103	−	19.8862i	−0.384341	−	0.675759i
$867$		0			0
$868$	−36.8267	−	2.40828i	−1.24998	−	0.0817423i
$869$	0.109225	−	0.0354894i	0.00370521	−	0.00120389i
$870$		0			0
$871$	−10.1969	−	3.31318i	−0.345509	−	0.112263i
$872$	−13.4888	−	14.0230i	−0.456790	−	0.474879i
$873$		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	$0.810585\pi$
$878$	44.5287	−	2.04481i	1.50277	−	0.0690088i
$879$		0			0
$880$	−0.796545	+	0.0966015i	−0.0268515	+	0.00325644i
$881$	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	$-0.595927\pi$
$883$	19.3210	−	37.9195i	0.650202	−	1.27609i	0.947025	−	0.321161i	$-0.104073\pi$
$884$	−31.0731	+	2.85986i	−1.04510	+	0.0961873i
$885$		0			0
$886$	9.17639	+	44.5884i	0.308287	+	1.49797i
$887$	9.67782	−	1.53282i	0.324949	−	0.0514669i	0.00817134	−	0.999967i	$-0.497399\pi$
$887$	9.67782	−	1.53282i	0.324949	−	0.0514669i	0.316778	+	0.948500i	$0.397399\pi$
$888$		0			0
$889$	−7.24281	−	9.96887i	−0.242916	−	0.334345i
$890$	−12.0803	−	39.4462i	−0.404933	−	1.32224i
$891$		0			0
$892$	12.1854	+	47.9503i	0.407997	+	1.60550i
$893$	−8.19496	+	8.19496i	−0.274234	+	0.274234i
$894$		0			0
$895$	−1.29137	+	20.5135i	−0.0431658	+	0.685692i
$896$	49.5827	+	7.49454i	1.65644	+	0.250375i
$897$		0			0
$898$	−2.50148	+	3.79792i	−0.0834756	+	0.126738i
$899$	−26.4785			−0.883107
$900$		0			0
$901$	−9.75235			−0.324898
$902$	0.710502	−	1.07873i	0.0236571	−	0.0359178i
$903$		0			0
$904$	0.637200	−	32.8192i	0.0211929	−	1.09155i
$905$	−5.50960	−	8.68246i	−0.183145	−	0.288615i
$906$		0			0
$907$	−18.8705	+	18.8705i	−0.626584	+	0.626584i	−0.947207	−	0.320623i	$-0.896108\pi$
$907$	−18.8705	+	18.8705i	−0.626584	+	0.626584i	0.320623	+	0.947207i	$0.396108\pi$
$908$	36.7970	−	9.35105i	1.22115	−	0.310326i
$909$		0			0
$910$	−59.5184	+	41.7172i	−1.97302	+	1.38291i
$911$	9.42916	+	12.9781i	0.312402	+	0.429984i	0.936128	−	0.351658i	$-0.114382\pi$
$911$	9.42916	+	12.9781i	0.312402	+	0.429984i	−0.623726	+	0.781643i	$0.714382\pi$
$912$		0			0
$913$	0.201531	−	0.0319193i	0.00666969	−	0.00105638i
$914$	1.73936	+	8.45161i	0.0575329	+	0.279554i
$915$		0			0
$916$	0.737502	+	8.01316i	0.0243677	+	0.264762i
$917$	24.8454	−	48.7618i	0.820467	−	1.61026i
$918$		0			0
$919$	−4.00489	−	12.3258i	−0.132109	−	0.406591i	0.863020	−	0.505170i	$-0.168570\pi$
$919$	−4.00489	−	12.3258i	−0.132109	−	0.406591i	−0.995129	+	0.0985793i	$0.968570\pi$
$920$	1.10171	−	13.3592i	0.0363224	−	0.440440i
$921$		0			0
$922$	33.8522	−	1.55453i	1.11486	−	0.0511957i
$923$	−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
$928$	35.8491	+	3.04424i	1.17681	+	0.0999321i
$929$	−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
$932$	0.604254	−	9.24009i	0.0197930	−	0.302669i
$933$		0			0
$934$	−17.9947	−	31.6389i	−0.588806	−	1.03526i
$935$	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	$-0.224195\pi$
$938$	−12.4965	−	3.43525i	−0.408025	−	0.112165i
$939$		0			0
$940$	14.7448	−	31.1315i	0.480924	−	1.01540i
$941$	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
$944$	55.6040	−	10.3226i	1.80976	−	0.335973i
$945$		0			0
$946$	0.950320	−	1.04180i	0.0308976	−	0.0338719i
$947$	−14.5982	−	28.6506i	−0.474377	−	0.931018i	−0.996922	−	0.0784058i	$-0.975017\pi$
$947$	−14.5982	−	28.6506i	−0.474377	−	0.931018i	0.522544	−	0.852612i	$-0.324983\pi$
$948$		0			0
$949$			38.5133i			1.25019i
$950$	−2.47014	−	10.3486i	−0.0801421	−	0.335752i
$951$		0			0
$952$	−37.3623	+	5.17628i	−1.21092	+	0.167764i
$953$	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
$956$	−34.6679	−	20.6183i	−1.12124	−	0.666844i
$957$		0			0
$958$	−17.4952	+	13.9808i	−0.565243	+	0.451700i
$959$	−16.3067	−	11.8475i	−0.526570	−	0.382576i
$960$		0			0
$961$	−11.0573	+	8.03363i	−0.356688	+	0.259149i
$962$	15.6581	−	56.9600i	0.504839	−	1.83647i
$963$		0			0
$964$	−2.96579	+	13.1159i	−0.0955217	+	0.422435i
$965$	18.4220	−	31.1473i	0.593026	−	1.00267i
$966$		0			0
$967$	−8.41681	−	4.28858i	−0.270666	−	0.137911i	0.313390	−	0.949625i	$-0.398535\pi$
$967$	−8.41681	−	4.28858i	−0.270666	−	0.137911i	−0.584056	+	0.811713i	$0.698535\pi$
$968$	−27.4221	−	14.6496i	−0.881381	−	0.470856i
$969$		0			0
$970$	13.8455	−	1.95253i	0.444552	−	0.0626921i
$971$	49.9618	+	16.2336i	1.60335	+	0.520960i	0.967933	−	0.251209i	$-0.0808282\pi$
$971$	49.9618	+	16.2336i	1.60335	+	0.520960i	0.635417	+	0.772169i	$0.280828\pi$
$972$		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
$980$	−44.7716	+	34.5489i	−1.43018	+	1.10363i
$981$		0			0
$982$	−9.20063	+	3.46365i	−0.293604	+	0.110529i
$983$	4.87976	−	9.57708i	0.155640	−	0.305461i	−0.799999	−	0.600002i	$-0.795167\pi$
$983$	4.87976	−	9.57708i	0.155640	−	0.305461i	0.955639	+	0.294540i	$0.0951666\pi$
$984$		0			0
$985$	14.4462	−	12.7351i	0.460294	−	0.405774i
$986$	−26.5068	+	5.45516i	−0.844149	+	0.173728i
$987$		0			0
$988$	9.97655	−	11.9991i	0.317396	−	0.381742i
$989$	13.8468	+	19.0585i	0.440302	+	0.606024i
$990$		0			0
$991$	−9.46784	+	13.0314i	−0.300756	+	0.413955i	−0.932470	−	0.361246i	$-0.882351\pi$
$991$	−9.46784	+	13.0314i	−0.300756	+	0.413955i	0.631715	+	0.775201i	$0.282351\pi$
$992$	−20.1559	+	12.1810i	−0.639950	+	0.386747i
$993$		0			0
$994$	−15.5563	−	1.73689i	−0.493417	−	0.0550907i
$995$	−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	$0.293714\pi$
$998$	−0.298608	−	0.196677i	−0.00945226	−	0.00622570i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.18105 - 0.777895i) q^{2} +(0.789760 + 1.83747i) q^{4} +(-2.16584 + 0.556007i) q^{5} +(3.13412 - 3.13412i) q^{7} +(0.496609 - 2.78449i) q^{8} +O(q^{10})\)	\(q+(-1.18105 - 0.777895i) q^{2} +(0.789760 + 1.83747i) q^{4} +(-2.16584 + 0.556007i) q^{5} +(3.13412 - 3.13412i) q^{7} +(0.496609 - 2.78449i) q^{8} +(2.99048 + 1.02812i) q^{10} +(-0.0527296 - 0.0725760i) q^{11} +(-5.12177 + 0.811209i) q^{13} +(-6.13957 + 1.26354i) q^{14} +(-2.75256 + 2.90231i) q^{16} +(1.36594 - 2.68082i) q^{17} +(0.464955 + 1.43098i) q^{19} +(-2.73213 - 3.54054i) q^{20} +(0.00581977 + 0.126734i) q^{22} +(-2.09335 - 0.331555i) q^{23} +(4.38171 - 2.40844i) q^{25} +(6.68011 + 3.02612i) q^{26} +(8.23404 + 3.28364i) q^{28} +(6.04881 + 1.96538i) q^{29} +(-3.95945 + 1.28650i) q^{31} +(5.50860 - 1.28658i) q^{32} +(-3.69864 + 2.10362i) q^{34} +(-5.04540 + 8.53059i) q^{35} +(-1.26010 - 7.95598i) q^{37} +(0.564019 - 2.05175i) q^{38} +(0.472619 + 6.30687i) q^{40} +(-8.23695 - 5.98450i) q^{41} +(-7.85946 - 7.85946i) q^{43} +(0.0917123 - 0.154206i) q^{44} +(2.21444 + 2.01999i) q^{46} +(3.49688 + 6.86301i) q^{47} -12.6454i q^{49} +(-7.04854 - 0.564022i) q^{50} +(-5.53554 - 8.77042i) q^{52} +(-1.47153 - 2.88805i) q^{53} +(0.154557 + 0.127870i) q^{55} +(-7.17049 - 10.2834i) q^{56} +(-5.61510 - 7.02655i) q^{58} +(-11.4383 - 8.31042i) q^{59} +(-9.26103 + 6.72853i) q^{61} +(5.67708 + 1.56061i) q^{62} +(-7.50676 - 2.76560i) q^{64} +(10.6419 - 4.60469i) q^{65} +(1.84223 + 0.938661i) q^{67} +(6.00467 + 0.392675i) q^{68} +(12.5948 - 6.15026i) q^{70} +(2.37497 + 0.771676i) q^{71} +(1.16183 - 7.33551i) q^{73} +(-4.70067 + 10.3766i) q^{74} +(-2.26218 + 1.98447i) q^{76} +(-0.392723 - 0.0622012i) q^{77} +(-0.395606 + 1.21755i) q^{79} +(4.34789 - 7.81638i) q^{80} +(5.07295 + 13.4755i) q^{82} +(-1.03260 + 2.02659i) q^{83} +(-1.46786 + 6.56569i) q^{85} +(3.16858 + 15.3962i) q^{86} +(-0.228273 + 0.110783i) q^{88} +(-7.66814 - 10.5543i) q^{89} +(-13.5098 + 18.5947i) q^{91} +(-1.04403 - 4.10831i) q^{92} +(1.20871 - 10.8258i) q^{94} +(-1.80265 - 2.84076i) q^{95} +(3.93972 - 2.00739i) q^{97} +(-9.83679 + 14.9349i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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