LMFDB - Embedded newform 990.2.bh.c.217.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(73,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 14]))

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

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

chi := DirichletCharacter("990.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bh (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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			217.5
Character	$\chi$	$=$	990.217
Dual form			990.2.bh.c.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.923903 + 2.03627i) q^{5} +(1.49255 + 2.92930i) q^{7} +(-0.453990 + 0.891007i) q^{8} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.923903 + 2.03627i) q^{5} +(1.49255 + 2.92930i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.86667 + 1.23107i) q^{10} +(3.16916 - 0.977970i) q^{11} +(-6.10433 - 0.966831i) q^{13} +(3.12672 - 1.01593i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-5.30072 + 0.839551i) q^{17} +(-0.213692 - 0.657676i) q^{19} +(1.50793 - 1.65111i) q^{20} +(-0.470163 - 3.28313i) q^{22} +(-3.92788 + 3.92788i) q^{23} +(-3.29281 - 3.76263i) q^{25} +(-1.90986 + 5.87793i) q^{26} +(-0.514298 - 3.24715i) q^{28} +(0.689338 - 2.12156i) q^{29} +(-4.63905 + 3.37046i) q^{31} +(0.707107 - 0.707107i) q^{32} +5.36679i q^{34} +(-7.34382 + 0.332855i) q^{35} +(-2.91923 + 1.48742i) q^{37} +(-0.683008 + 0.108178i) q^{38} +(-1.39489 - 1.74765i) q^{40} +(-1.24362 + 0.404076i) q^{41} +(4.38796 + 4.38796i) q^{43} +(-3.31626 - 0.0492198i) q^{44} +(3.26507 + 4.49398i) q^{46} +(-0.800329 + 1.57073i) q^{47} +(-2.23857 + 3.08113i) q^{49} +(-4.23142 + 2.66366i) q^{50} +(5.50680 + 2.80585i) q^{52} +(0.489889 - 3.09304i) q^{53} +(-0.936583 + 7.35682i) q^{55} -3.28763 q^{56} +(-1.98761 - 1.01274i) q^{58} +(0.820602 + 0.266630i) q^{59} +(-5.96441 + 8.20931i) q^{61} +(2.60326 + 5.10919i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(7.60854 - 11.5368i) q^{65} +(9.05603 + 9.05603i) q^{67} +(5.30072 + 0.839551i) q^{68} +(-0.820069 + 7.30547i) q^{70} +(-1.58734 - 1.15327i) q^{71} +(-2.99208 + 1.52454i) q^{73} +(1.01244 + 3.11597i) q^{74} +0.691521i q^{76} +(7.59490 + 7.82374i) q^{77} +(3.40098 - 2.47096i) q^{79} +(-1.94434 + 1.10432i) q^{80} +(0.204556 + 1.29152i) q^{82} +(-0.944728 - 5.96478i) q^{83} +(3.18779 - 11.5694i) q^{85} +(5.02037 - 3.64751i) q^{86} +(-0.567391 + 3.26773i) q^{88} +4.90528i q^{89} +(-6.27889 - 19.3244i) q^{91} +(4.94942 - 2.52186i) q^{92} +(1.42620 + 1.03619i) q^{94} +(1.53664 + 0.172494i) q^{95} +(14.9105 + 2.36159i) q^{97} +(2.69301 + 2.69301i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q + 8 * q^5 - 20 * q^7	$ 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47} - 40 q^{50} + 40 q^{52} + 96 q^{55} + 8 q^{56} + 48 q^{58} + 80 q^{61} - 40 q^{62} - 20 q^{68} - 56 q^{70} + 56 q^{71} - 20 q^{73} + 96 q^{77} + 12 q^{80} - 80 q^{85} + 56 q^{86} - 4 q^{88} - 68 q^{91} + 12 q^{92} - 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−0.923903	+	2.03627i	−0.413182	+	0.910649i
$5$	−0.923903	+	2.03627i	−0.413182	+	0.910649i
$6$		0			0
$7$	1.49255	+	2.92930i	0.564131	+	1.10717i	0.980232	+	0.197851i	$0.0633964\pi$
$7$	1.49255	+	2.92930i	0.564131	+	1.10717i	−0.416101	+	0.909319i	$0.636604\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$		0			0
$10$	1.86667	+	1.23107i	0.590293	+	0.389299i
$11$	3.16916	−	0.977970i	0.955538	−	0.294869i
$11$	3.16916	−	0.977970i	0.955538	−	0.294869i
$12$		0			0
$13$	−6.10433	−	0.966831i	−1.69304	−	0.268151i	−0.765924	−	0.642931i	$-0.777718\pi$
$13$	−6.10433	−	0.966831i	−1.69304	−	0.268151i	−0.927114	+	0.374781i	$0.877718\pi$
$14$	3.12672	−	1.01593i	0.835651	−	0.271519i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−5.30072	+	0.839551i	−1.28561	+	0.203621i	−0.761577	−	0.648075i	$-0.775574\pi$
$17$	−5.30072	+	0.839551i	−1.28561	+	0.203621i	−0.524036	+	0.851696i	$0.675574\pi$
$18$		0			0
$19$	−0.213692	−	0.657676i	−0.0490243	−	0.150881i	0.923548	−	0.383484i	$-0.125276\pi$
$19$	−0.213692	−	0.657676i	−0.0490243	−	0.150881i	−0.972572	+	0.232603i	$0.925276\pi$
$20$	1.50793	−	1.65111i	0.337183	−	0.369199i
$21$		0			0
$22$	−0.470163	−	3.28313i	−0.100239	−	0.699966i
$23$	−3.92788	+	3.92788i	−0.819020	+	0.819020i	−0.985966	−	0.166946i	$-0.946609\pi$
$23$	−3.92788	+	3.92788i	−0.819020	+	0.819020i	0.166946	+	0.985966i	$0.446609\pi$
$24$		0			0
$25$	−3.29281	−	3.76263i	−0.658562	−	0.752527i
$26$	−1.90986	+	5.87793i	−0.374554	+	1.15276i
$27$		0			0
$28$	−0.514298	−	3.24715i	−0.0971932	−	0.613654i
$29$	0.689338	−	2.12156i	0.128007	−	0.393965i	−0.866430	−	0.499298i	$-0.833591\pi$
$29$	0.689338	−	2.12156i	0.128007	−	0.393965i	0.994437	+	0.105334i	$0.0335911\pi$
$30$		0			0
$31$	−4.63905	+	3.37046i	−0.833197	+	0.605353i	−0.920462	−	0.390832i	$-0.872187\pi$
$31$	−4.63905	+	3.37046i	−0.833197	+	0.605353i	0.0872648	+	0.996185i	$0.472187\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			5.36679i			0.920397i
$35$	−7.34382	+	0.332855i	−1.24133	+	0.0562628i
$36$		0			0
$37$	−2.91923	+	1.48742i	−0.479918	+	0.244530i	−0.677176	−	0.735821i	$-0.736796\pi$
$37$	−2.91923	+	1.48742i	−0.479918	+	0.244530i	0.197258	+	0.980352i	$0.436796\pi$
$38$	−0.683008	+	0.108178i	−0.110798	+	0.0175488i
$39$		0			0
$40$	−1.39489	−	1.74765i	−0.220551	−	0.276328i
$41$	−1.24362	+	0.404076i	−0.194220	+	0.0631060i	−0.404512	−	0.914533i	$-0.632559\pi$
$41$	−1.24362	+	0.404076i	−0.194220	+	0.0631060i	0.210292	+	0.977639i	$0.432559\pi$
$42$		0			0
$43$	4.38796	+	4.38796i	0.669158	+	0.669158i	0.957521	−	0.288363i	$-0.0931111\pi$
$43$	4.38796	+	4.38796i	0.669158	+	0.669158i	−0.288363	+	0.957521i	$0.593111\pi$
$44$	−3.31626	−	0.0492198i	−0.499945	−	0.00742017i
$45$		0			0
$46$	3.26507	+	4.49398i	0.481408	+	0.662601i
$47$	−0.800329	+	1.57073i	−0.116740	+	0.229115i	−0.941981	−	0.335665i	$-0.891039\pi$
$47$	−0.800329	+	1.57073i	−0.116740	+	0.229115i	0.825241	+	0.564780i	$0.191039\pi$
$48$		0			0
$49$	−2.23857	+	3.08113i	−0.319796	+	0.440161i
$50$	−4.23142	+	2.66366i	−0.598413	+	0.376699i
$51$		0			0
$52$	5.50680	+	2.80585i	0.763655	+	0.389102i
$53$	0.489889	−	3.09304i	0.0672915	−	0.424862i	−0.930927	−	0.365204i	$-0.880999\pi$
$53$	0.489889	−	3.09304i	0.0672915	−	0.424862i	0.998219	−	0.0596574i	$-0.0190008\pi$
$54$		0			0
$55$	−0.936583	+	7.35682i	−0.126289	+	0.991994i
$56$	−3.28763			−0.439328
$57$		0			0
$58$	−1.98761	−	1.01274i	−0.260986	−	0.132979i
$59$	0.820602	+	0.266630i	0.106833	+	0.0347122i	0.361946	−	0.932199i	$-0.382113\pi$
$59$	0.820602	+	0.266630i	0.106833	+	0.0347122i	−0.255113	+	0.966911i	$0.582113\pi$
$60$		0			0
$61$	−5.96441	+	8.20931i	−0.763665	+	1.05109i	0.233236	+	0.972420i	$0.425069\pi$
$61$	−5.96441	+	8.20931i	−0.763665	+	1.05109i	−0.996900	+	0.0786740i	$0.974931\pi$
$62$	2.60326	+	5.10919i	0.330615	+	0.648868i
$63$		0			0
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	7.60854	−	11.5368i	0.943723	−	1.43097i
$66$		0			0
$67$	9.05603	+	9.05603i	1.10637	+	1.10637i	0.993624	+	0.112746i	$0.0359646\pi$
$67$	9.05603	+	9.05603i	1.10637	+	1.10637i	0.112746	+	0.993624i	$0.464035\pi$
$68$	5.30072	+	0.839551i	0.642807	+	0.101811i
$69$		0			0
$70$	−0.820069	+	7.30547i	−0.0980170	+	0.873171i
$71$	−1.58734	−	1.15327i	−0.188383	−	0.136868i	0.489596	−	0.871949i	$-0.337144\pi$
$71$	−1.58734	−	1.15327i	−0.188383	−	0.136868i	−0.677979	+	0.735081i	$0.737144\pi$
$72$		0			0
$73$	−2.99208	+	1.52454i	−0.350196	+	0.178434i	−0.620236	−	0.784415i	$-0.712963\pi$
$73$	−2.99208	+	1.52454i	−0.350196	+	0.178434i	0.270040	+	0.962849i	$0.412963\pi$
$74$	1.01244	+	3.11597i	0.117694	+	0.362224i
$75$		0			0
$76$			0.691521i			0.0793229i
$77$	7.59490	+	7.82374i	0.865519	+	0.891598i
$78$		0			0
$79$	3.40098	−	2.47096i	0.382640	−	0.278004i	−0.379793	−	0.925072i	$-0.624005\pi$
$79$	3.40098	−	2.47096i	0.382640	−	0.278004i	0.762433	+	0.647067i	$0.224005\pi$
$80$	−1.94434	+	1.10432i	−0.217384	+	0.123467i
$81$		0			0
$82$	0.204556	+	1.29152i	0.0225895	+	0.142624i
$83$	−0.944728	−	5.96478i	−0.103697	−	0.654720i	−0.983709	−	0.179768i	$-0.942465\pi$
$83$	−0.944728	−	5.96478i	−0.103697	−	0.654720i	0.880012	−	0.474952i	$-0.157535\pi$
$84$		0			0
$85$	3.18779	−	11.5694i	0.345765	−	1.25487i
$86$	5.02037	−	3.64751i	0.541360	−	0.393321i
$87$		0			0
$88$	−0.567391	+	3.26773i	−0.0604841	+	0.348341i
$89$			4.90528i			0.519959i	0.965614	+	0.259979i	$0.0837158\pi$
$89$			4.90528i			0.519959i	−0.965614	+	0.259979i	$0.916284\pi$
$90$		0			0
$91$	−6.27889	−	19.3244i	−0.658207	−	2.02575i
$92$	4.94942	−	2.52186i	0.516013	−	0.262922i
$93$		0			0
$94$	1.42620	+	1.03619i	0.147101	+	0.106875i
$95$	1.53664	+	0.172494i	0.157656	+	0.0176975i
$96$		0			0
$97$	14.9105	+	2.36159i	1.51393	+	0.239783i	0.857453	−	0.514563i	$-0.172046\pi$
$97$	14.9105	+	2.36159i	1.51393	+	0.239783i	0.656477	+	0.754346i	$0.272046\pi$
$98$	2.69301	+	2.69301i	0.272035	+	0.272035i
$99$		0			0
$100$	1.96893	+	4.59601i	0.196893	+	0.459601i
$101$	7.97621	+	10.9783i	0.793663	+	1.09238i	0.993642	+	0.112583i	$0.0359125\pi$
$101$	7.97621	+	10.9783i	0.793663	+	1.09238i	−0.199979	+	0.979800i	$0.564087\pi$
$102$		0			0
$103$	−0.0786923	−	0.154442i	−0.00775378	−	0.0152176i	0.887097	−	0.461583i	$-0.152718\pi$
$103$	−0.0786923	−	0.154442i	−0.00775378	−	0.0152176i	−0.894851	+	0.446365i	$0.852718\pi$
$104$	3.63276	−	5.00007i	0.356222	−	0.490297i
$105$		0			0
$106$	−2.97832	−	0.967716i	−0.289280	−	0.0939929i
$107$	−4.68320	−	2.38621i	−0.452742	−	0.230684i	0.212723	−	0.977113i	$-0.431767\pi$
$107$	−4.68320	−	2.38621i	−0.452742	−	0.230684i	−0.665465	+	0.746429i	$0.731767\pi$
$108$		0			0
$109$	−6.31752			−0.605109			−0.302554	−	0.953132i	$-0.597839\pi$
$109$	−6.31752			−0.605109			−0.302554	+	0.953132i	$0.597839\pi$
$110$	7.11973	+	2.07591i	0.678840	+	0.197930i
$111$		0			0
$112$	−0.514298	+	3.24715i	−0.0485966	+	0.306827i
$113$	−13.6344	−	6.94709i	−1.28262	−	0.653527i	−0.326139	−	0.945322i	$-0.605748\pi$
$113$	−13.6344	−	6.94709i	−1.28262	−	0.653527i	−0.956481	+	0.291794i	$0.905748\pi$
$114$		0			0
$115$	−4.36926	−	11.6272i	−0.407435	−	1.08424i
$116$	−1.31120	+	1.80471i	−0.121742	+	0.167563i
$117$		0			0
$118$	0.391717	−	0.768789i	0.0360605	−	0.0707727i
$119$	−10.3709	−	14.2743i	−0.950698	−	1.30852i
$120$		0			0
$121$	9.08715	−	6.19869i	0.826105	−	0.563517i
$122$	7.17520	+	7.17520i	0.649612	+	0.649612i
$123$		0			0
$124$	5.45353	−	1.77196i	0.489741	−	0.159127i
$125$	10.7040	−	3.22874i	0.957393	−	0.288788i
$126$		0			0
$127$	−12.9179	+	2.04599i	−1.14628	+	0.181552i	−0.700540	−	0.713613i	$-0.747058\pi$
$127$	−12.9179	+	2.04599i	−1.14628	+	0.181552i	−0.445735	+	0.895165i	$0.647058\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$		0			0
$130$	−10.2045	−	9.31962i	−0.894998	−	0.817385i
$131$			3.15120i			0.275322i	0.990479	+	0.137661i	$0.0439584\pi$
$131$			3.15120i			0.275322i	−0.990479	+	0.137661i	$0.956042\pi$
$132$		0			0
$133$	1.60758	−	1.60758i	0.139395	−	0.139395i
$134$	10.3612	−	7.52786i	0.895072	−	0.650308i
$135$		0			0
$136$	1.65843	−	5.10412i	0.142209	−	0.437675i
$137$	1.86611	+	11.7822i	0.159432	+	1.00662i	0.929545	+	0.368709i	$0.120200\pi$
$137$	1.86611	+	11.7822i	0.159432	+	1.00662i	−0.770112	+	0.637908i	$0.779800\pi$
$138$		0			0
$139$	2.70056	−	8.31147i	0.229059	−	0.704970i	−0.768796	−	0.639494i	$-0.779144\pi$
$139$	2.70056	−	8.31147i	0.229059	−	0.704970i	0.997854	−	0.0654751i	$-0.0208563\pi$
$140$	7.08724	+	1.95280i	0.598981	+	0.165042i
$141$		0			0
$142$	−1.38739	+	1.38739i	−0.116427	+	0.116427i
$143$	−20.2911	+	2.90581i	−1.69683	+	0.242996i
$144$		0			0
$145$	3.68320	+	3.36380i	0.305873	+	0.279348i
$146$	1.03771	+	3.19373i	0.0858812	+	0.264315i
$147$		0			0
$148$	3.23599	−	0.512530i	0.265997	−	0.0421297i
$149$	5.78912	+	4.20604i	0.474263	+	0.344572i	0.799100	−	0.601198i	$-0.205310\pi$
$149$	5.78912	+	4.20604i	0.474263	+	0.344572i	−0.324837	+	0.945770i	$0.605310\pi$
$150$		0			0
$151$	−9.35240	+	3.03878i	−0.761087	+	0.247292i	−0.663745	−	0.747959i	$-0.731034\pi$
$151$	−9.35240	+	3.03878i	−0.761087	+	0.247292i	−0.0973420	+	0.995251i	$0.531034\pi$
$152$	0.683008	+	0.108178i	0.0553992	+	0.00877438i
$153$		0			0
$154$	8.91552	−	6.27749i	0.718433	−	0.505854i
$155$	−2.57715	−	12.5603i	−0.207002	−	1.00887i
$156$		0			0
$157$	−4.49794	+	8.82771i	−0.358975	+	0.704528i	−0.997902	−	0.0647390i	$-0.979379\pi$
$157$	−4.49794	+	8.82771i	−0.358975	+	0.704528i	0.638927	+	0.769267i	$0.279379\pi$
$158$	−1.90850	−	3.74565i	−0.151832	−	0.297988i
$159$		0			0
$160$	0.786564	+	2.09316i	0.0621833	+	0.165479i
$161$	−17.3685	−	5.64337i	−1.36883	−	0.444760i
$162$		0			0
$163$	−0.641060	+	4.04749i	−0.0502117	+	0.317024i	0.949780	+	0.312919i	$0.101307\pi$
$163$	−0.641060	+	4.04749i	−0.0502117	+	0.317024i	−0.999992	+	0.00410528i	$0.998693\pi$
$164$	1.30762			0.102108
$165$		0			0
$166$	−6.03913			−0.468728
$167$	0.974586	−	6.15330i	0.0754158	−	0.476156i	−0.920857	−	0.389900i	$-0.872510\pi$
$167$	0.974586	−	6.15330i	0.0754158	−	0.476156i	0.996273	−	0.0862564i	$-0.0274904\pi$
$168$		0			0
$169$	23.9644	+	7.78650i	1.84341	+	0.598961i
$170$	−10.9282	−	4.95839i	−0.838159	−	0.380291i
$171$		0			0
$172$	−2.81724	−	5.52915i	−0.214813	−	0.421594i
$173$	−9.67972	+	18.9975i	−0.735936	+	1.44436i	0.153906	+	0.988085i	$0.450815\pi$
$173$	−9.67972	+	18.9975i	−0.735936	+	1.44436i	−0.889842	+	0.456270i	$0.849185\pi$
$174$		0			0
$175$	6.10719	−	15.2615i	0.461660	−	1.15366i
$176$	3.13874	+	1.07159i	0.236591	+	0.0807742i
$177$		0			0
$178$	4.84489	+	0.767355i	0.363140	+	0.0575157i
$179$	24.3710	−	7.91861i	1.82157	−	0.591864i	0.821816	−	0.569753i	$-0.192961\pi$
$179$	24.3710	−	7.91861i	1.82157	−	0.591864i	0.999756	−	0.0221110i	$-0.00703873\pi$
$180$		0			0
$181$	16.4629	+	11.9610i	1.22368	+	0.889056i	0.996400	−	0.0847729i	$-0.0270165\pi$
$181$	16.4629	+	11.9610i	1.22368	+	0.889056i	0.227281	+	0.973829i	$0.427016\pi$
$182$	−20.0688	+	3.17858i	−1.48760	+	0.235612i
$183$		0			0
$184$	−1.71655	−	5.28299i	−0.126546	−	0.389467i
$185$	−0.331711	−	7.31857i	−0.0243879	−	0.538072i
$186$		0			0
$187$	−15.9778	+	7.84461i	−1.16841	+	0.573655i
$188$	1.24654	−	1.24654i	0.0909134	−	0.0909134i
$189$		0			0
$190$	0.410753	−	1.49074i	0.0297992	−	0.108149i
$191$	0.225845	−	0.695079i	0.0163416	−	0.0502942i	−0.942553	−	0.334056i	$-0.891583\pi$
$191$	0.225845	−	0.695079i	0.0163416	−	0.0502942i	0.958895	+	0.283762i	$0.0915825\pi$
$192$		0			0
$193$	−2.57474	−	16.2563i	−0.185334	−	1.17015i	−0.888414	−	0.459043i	$-0.848192\pi$
$193$	−2.57474	−	16.2563i	−0.185334	−	1.17015i	0.703080	−	0.711111i	$-0.251808\pi$
$194$	4.66503	−	14.3575i	0.334929	−	1.03081i
$195$		0			0
$196$	3.08113	−	2.23857i	0.220081	−	0.159898i
$197$	−8.59023	+	8.59023i	−0.612028	+	0.612028i	−0.943474	−	0.331446i	$-0.892464\pi$
$197$	−8.59023	+	8.59023i	−0.612028	+	0.612028i	0.331446	+	0.943474i	$0.392464\pi$
$198$		0			0
$199$		−	13.9785i		−	0.990907i	−0.868634	−	0.495453i	$-0.835002\pi$
$199$		−	13.9785i		−	0.990907i	0.868634	−	0.495453i	$-0.164998\pi$
$200$	4.84744	−	1.22571i	0.342765	−	0.0866710i
$201$		0			0
$202$	12.0909	−	6.16063i	0.850714	−	0.433460i
$203$	7.24356	−	1.14727i	0.508398	−	0.0805224i
$204$		0			0
$205$	0.326173	−	2.90567i	0.0227809	−	0.202941i
$206$	−0.164851	+	0.0535633i	−0.0114857	+	0.00373193i
$207$		0			0
$208$	−4.37022	−	4.37022i	−0.303020	−	0.303020i
$209$	−1.32041	−	1.87530i	−0.0913347	−	0.129717i
$210$		0			0
$211$	3.00713	+	4.13896i	0.207019	+	0.284938i	0.899883	−	0.436131i	$-0.143651\pi$
$211$	3.00713	+	4.13896i	0.207019	+	0.284938i	−0.692864	+	0.721068i	$0.743651\pi$
$212$	−1.42171	+	2.79027i	−0.0976437	+	0.191637i
$213$		0			0
$214$	−3.08945	+	4.25226i	−0.211190	+	0.290678i
$215$	−12.9891	+	4.88103i	−0.885851	+	0.332884i
$216$		0			0
$217$	−16.7971	−	8.55855i	−1.14026	−	0.580992i
$218$	−0.988278	+	6.23974i	−0.0669346	+	0.422609i
$219$		0			0
$220$	3.16413	−	6.70733i	0.213325	−	0.452208i
$221$	33.1691			2.23119
$222$		0			0
$223$	10.4336	+	5.31616i	0.698682	+	0.355996i	0.766982	−	0.641668i	$-0.221757\pi$
$223$	10.4336	+	5.31616i	0.698682	+	0.355996i	−0.0682998	+	0.997665i	$0.521757\pi$
$224$	3.12672	+	1.01593i	0.208913	+	0.0678798i
$225$		0			0
$226$	−8.99446	+	12.3798i	−0.598302	+	0.823493i
$227$	3.50856	+	6.88595i	0.232872	+	0.457036i	0.977640	−	0.210287i	$-0.0674399\pi$
$227$	3.50856	+	6.88595i	0.232872	+	0.457036i	−0.744768	+	0.667323i	$0.767440\pi$
$228$		0			0
$229$	−11.1724	−	15.3775i	−0.738292	−	1.01617i	−0.998715	−	0.0506768i	$-0.983862\pi$
$229$	−11.1724	−	15.3775i	−0.738292	−	1.01617i	0.260423	−	0.965495i	$-0.416138\pi$
$230$	−12.1676	+	2.49657i	−0.802306	+	0.164619i
$231$		0			0
$232$	1.57737	+	1.57737i	0.103560	+	0.103560i
$233$	20.8711	+	3.30566i	1.36731	+	0.216561i	0.796559	−	0.604561i	$-0.206651\pi$
$233$	20.8711	+	3.30566i	1.36731	+	0.216561i	0.570753	+	0.821122i	$0.306651\pi$
$234$		0			0
$235$	−2.45902	−	3.08089i	−0.160409	−	0.200975i
$236$	−0.698046	−	0.507160i	−0.0454389	−	0.0330133i
$237$		0			0
$238$	−15.7209	+	8.01021i	−1.01904	+	0.519225i
$239$	−6.55831	−	20.1844i	−0.424222	−	1.30562i	−0.903737	−	0.428088i	$-0.859187\pi$
$239$	−6.55831	−	20.1844i	−0.424222	−	1.30562i	0.479515	−	0.877534i	$-0.340813\pi$
$240$		0			0
$241$		−	12.6447i		−	0.814517i	−0.913313	−	0.407259i	$-0.866485\pi$
$241$		−	12.6447i		−	0.814517i	0.913313	−	0.407259i	$-0.133515\pi$
$242$	−4.70083	−	9.94496i	−0.302181	−	0.639286i
$243$		0			0
$244$	8.20931	−	5.96441i	0.525547	−	0.381832i
$245$	−4.20580	−	7.40500i	−0.268698	−	0.473088i
$246$		0			0
$247$	0.668585	+	4.22128i	0.0425410	+	0.268593i
$248$	−0.897023	−	5.66358i	−0.0569610	−	0.359638i
$249$		0			0
$250$	−1.51452	−	11.0773i	−0.0957868	−	0.700589i
$251$	−20.8486	+	15.1474i	−1.31595	+	0.956094i	−0.315977	+	0.948767i	$0.602332\pi$
$251$	−20.8486	+	15.1474i	−1.31595	+	0.956094i	−0.999973	+	0.00732735i	$0.997668\pi$
$252$		0			0
$253$	−8.60674	+	16.2894i	−0.541101	+	1.02411i
$254$			13.0789i			0.820643i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	3.69199	−	1.88116i	0.230300	−	0.117344i	−0.335033	−	0.942206i	$-0.608748\pi$
$257$	3.69199	−	1.88116i	0.230300	−	0.117344i	0.565333	+	0.824863i	$0.308748\pi$
$258$		0			0
$259$	−8.71419	−	6.33123i	−0.541474	−	0.393404i
$260$	−10.8012	+	8.62100i	−0.669864	+	0.534652i
$261$		0			0
$262$	3.11241	+	0.492957i	0.192285	+	0.0304550i
$263$	9.62879	+	9.62879i	0.593736	+	0.593736i	0.938639	−	0.344902i	$-0.112088\pi$
$263$	9.62879	+	9.62879i	0.593736	+	0.593736i	−0.344902	+	0.938639i	$0.612088\pi$
$264$		0			0
$265$	5.84566	+	3.85522i	0.359096	+	0.236824i
$266$	−1.33631	−	1.83927i	−0.0819343	−	0.112773i
$267$		0			0
$268$	−5.81433	−	11.4113i	−0.355167	−	0.697054i
$269$	−9.43066	+	12.9802i	−0.574997	+	0.791416i	−0.993136	−	0.116967i	$-0.962683\pi$
$269$	−9.43066	+	12.9802i	−0.574997	+	0.791416i	0.418138	+	0.908383i	$0.362683\pi$
$270$		0			0
$271$	11.0157	+	3.57921i	0.669155	+	0.217422i	0.623841	−	0.781551i	$-0.285571\pi$
$271$	11.0157	+	3.57921i	0.669155	+	0.217422i	0.0453136	+	0.998973i	$0.485571\pi$
$272$	−4.78185	−	2.43647i	−0.289942	−	0.147733i
$273$		0			0
$274$	11.9290			0.720658
$275$	−14.1152	−	8.70412i	−0.851177	−	0.524878i
$276$		0			0
$277$	1.31072	−	8.27557i	0.0787537	−	0.497231i	−0.916509	−	0.400013i	$-0.869006\pi$
$277$	1.31072	−	8.27557i	0.0787537	−	0.497231i	0.995263	−	0.0972180i	$-0.0309944\pi$
$278$	−7.78668	−	3.96751i	−0.467014	−	0.237956i
$279$		0			0
$280$	3.03745	−	6.69450i	0.181522	−	0.400073i
$281$	15.2667	−	21.0128i	0.910736	−	1.25352i	−0.0561786	−	0.998421i	$-0.517892\pi$
$281$	15.2667	−	21.0128i	0.910736	−	1.25352i	0.966915	−	0.255100i	$-0.0821084\pi$
$282$		0			0
$283$	−5.90173	+	11.5828i	−0.350822	+	0.688526i	−0.997223	−	0.0744712i	$-0.976273\pi$
$283$	−5.90173	+	11.5828i	−0.350822	+	0.688526i	0.646402	+	0.762997i	$0.276273\pi$
$284$	1.15327	+	1.58734i	0.0684341	+	0.0941914i
$285$		0			0
$286$	−0.304199	+	20.4959i	−0.0179877	+	1.21195i
$287$	−3.03982	−	3.03982i	−0.179435	−	0.179435i
$288$		0			0
$289$	11.2248	−	3.64716i	0.660283	−	0.214539i
$290$	3.89856	−	3.11164i	0.228932	−	0.182722i
$291$		0			0
$292$	3.31675	−	0.525321i	0.194098	−	0.0307421i
$293$	13.8261	−	7.04473i	0.807727	−	0.411557i	−0.000812545	−	1.00000i	$-0.500259\pi$
$293$	13.8261	−	7.04473i	0.807727	−	0.411557i	0.808539	+	0.588442i	$0.200259\pi$
$294$		0			0
$295$	−1.30109	+	1.42463i	−0.0757522	+	0.0829451i
$296$		−	3.27633i		−	0.190433i
$297$		0			0
$298$	5.05988	−	5.05988i	0.293111	−	0.293111i
$299$	27.7747	−	20.1795i	1.60625	−	1.16701i
$300$		0			0
$301$	−6.30438	+	19.4029i	−0.363379	+	1.11836i
$302$	1.53833	+	9.71262i	0.0885208	+	0.558899i
$303$		0			0
$304$	0.213692	−	0.657676i	0.0122561	−	0.0377203i
$305$	−11.2058	−	19.7298i	−0.641645	−	1.12972i
$306$		0			0
$307$	16.0844	−	16.0844i	0.917983	−	0.917983i	−0.0788993	−	0.996883i	$-0.525141\pi$
$307$	16.0844	−	16.0844i	0.917983	−	0.917983i	0.996883	+	0.0788993i	$0.0251406\pi$
$308$	−4.80551	−	9.78777i	−0.273819	−	0.557710i
$309$		0			0
$310$	−12.8089	+	0.580556i	−0.727494	+	0.0329734i
$311$	1.79145	+	5.51353i	0.101584	+	0.312643i	0.988914	−	0.148492i	$-0.0474421\pi$
$311$	1.79145	+	5.51353i	0.101584	+	0.312643i	−0.887330	+	0.461136i	$0.847442\pi$
$312$		0			0
$313$	5.07254	−	0.803412i	0.286717	−	0.0454115i	−0.0114194	−	0.999935i	$-0.503635\pi$
$313$	5.07254	−	0.803412i	0.286717	−	0.0454115i	0.298136	+	0.954523i	$0.403635\pi$
$314$	8.01540	+	5.82353i	0.452335	+	0.328641i
$315$		0			0
$316$	−3.99809	+	1.29906i	−0.224910	+	0.0730777i
$317$	1.80129	+	0.285296i	0.101171	+	0.0160238i	0.206814	−	0.978380i	$-0.433690\pi$
$317$	1.80129	+	0.285296i	0.101171	+	0.0160238i	−0.105644	+	0.994404i	$0.533690\pi$
$318$		0			0
$319$	0.109797	−	7.39773i	0.00614744	−	0.414193i
$320$	2.19044	−	0.449438i	0.122449	−	0.0251243i
$321$		0			0
$322$	−8.29092	+	16.2718i	−0.462035	+	0.906795i
$323$	1.68487	+	3.30675i	0.0937489	+	0.183992i
$324$		0			0
$325$	16.4626	+	26.1520i	0.913179	+	1.45065i
$326$	3.89738	+	1.26633i	0.215856	+	0.0701358i
$327$		0			0
$328$	0.204556	−	1.29152i	0.0112947	−	0.0713121i
$329$	−5.79568			−0.319526
$330$		0			0
$331$	−20.3356			−1.11775			−0.558873	−	0.829254i	$-0.688766\pi$
$331$	−20.3356			−1.11775			−0.558873	+	0.829254i	$0.688766\pi$
$332$	−0.944728	+	5.96478i	−0.0518487	+	0.327360i
$333$		0			0
$334$	−5.92508	−	1.92518i	−0.324206	−	0.105341i
$335$	−26.8074	+	10.0736i	−1.46465	+	0.550382i
$336$		0			0
$337$	−11.4824	−	22.5356i	−0.625488	−	1.22759i	−0.958614	−	0.284708i	$-0.908103\pi$
$337$	−11.4824	−	22.5356i	−0.625488	−	1.22759i	0.333126	−	0.942882i	$-0.391897\pi$
$338$	11.4395	−	22.4513i	0.622226	−	1.22119i
$339$		0			0
$340$	−6.60690	+	10.0180i	−0.358310	+	0.543305i
$341$	−11.4057	+	15.2184i	−0.617651	+	0.824122i
$342$		0			0
$343$	10.3633	+	1.64139i	0.559567	+	0.0886267i
$344$	−5.90179	+	1.91761i	−0.318203	+	0.103391i
$345$		0			0
$346$	17.2494	+	12.5324i	0.927333	+	0.673747i
$347$	−0.371062	+	0.0587704i	−0.0199196	+	0.00315496i	−0.166386	−	0.986061i	$-0.553210\pi$
$347$	−0.371062	+	0.0587704i	−0.0199196	+	0.00315496i	0.146467	+	0.989216i	$0.453210\pi$
$348$		0			0
$349$	−4.40564	−	13.5592i	−0.235828	−	0.725805i	−0.997010	−	0.0772669i	$-0.975381\pi$
$349$	−4.40564	−	13.5592i	−0.235828	−	0.725805i	0.761182	−	0.648538i	$-0.224619\pi$
$350$	−14.1183	−	8.41943i	−0.754653	−	0.450037i
$351$		0			0
$352$	1.54941	−	2.93246i	0.0825836	−	0.156301i
$353$	−8.09648	+	8.09648i	−0.430932	+	0.430932i	−0.888945	−	0.458013i	$-0.848561\pi$
$353$	−8.09648	+	8.09648i	−0.430932	+	0.430932i	0.458013	+	0.888945i	$0.348561\pi$
$354$		0			0
$355$	3.81492	−	2.16675i	0.202475	−	0.114999i
$356$	1.51582	−	4.66520i	0.0803381	−	0.247255i
$357$		0			0
$358$	−4.00866	−	25.3097i	−0.211864	−	1.33766i
$359$	0.556243	−	1.71194i	0.0293574	−	0.0903528i	−0.935304	−	0.353845i	$-0.884874\pi$
$359$	0.556243	−	1.71194i	0.0293574	−	0.0903528i	0.964662	+	0.263492i	$0.0848742\pi$
$360$		0			0
$361$	14.9844	−	10.8868i	0.788655	−	0.572992i
$362$	14.3891	−	14.3891i	0.756277	−	0.756277i
$363$		0			0
$364$			20.3189i			1.06500i
$365$	−0.339989	−	7.50122i	−0.0177959	−	0.392632i
$366$		0			0
$367$	3.77605	−	1.92399i	0.197108	−	0.100432i	−0.352651	−	0.935755i	$-0.614720\pi$
$367$	3.77605	−	1.92399i	0.197108	−	0.100432i	0.549759	+	0.835323i	$0.314720\pi$
$368$	−5.48648	+	0.868972i	−0.286002	+	0.0452983i
$369$		0			0
$370$	−7.28036	−	0.817250i	−0.378488	−	0.0424868i
$371$	9.79161	−	3.18149i	0.508355	−	0.165175i
$372$		0			0
$373$	0.763112	+	0.763112i	0.0395124	+	0.0395124i	0.726587	−	0.687075i	$-0.241105\pi$
$373$	0.763112	+	0.763112i	0.0395124	+	0.0395124i	−0.687075	+	0.726587i	$0.741105\pi$
$374$	5.24856	+	17.0082i	0.271397	+	0.879474i
$375$		0			0
$376$	−1.03619	−	1.42620i	−0.0534376	−	0.0735505i
$377$	−6.25914	+	12.2843i	−0.322362	+	0.632671i
$378$		0			0
$379$	−9.39910	+	12.9368i	−0.482799	+	0.664516i	−0.979040	−	0.203669i	$-0.934713\pi$
$379$	−9.39910	+	12.9368i	−0.482799	+	0.664516i	0.496240	+	0.868185i	$0.334713\pi$
$380$	−1.40813	−	0.638899i	−0.0722353	−	0.0327748i
$381$		0			0
$382$	−0.651192	−	0.331799i	−0.0333179	−	0.0169763i
$383$	4.73547	−	29.8986i	0.241971	−	1.52775i	−0.505133	−	0.863041i	$-0.668557\pi$
$383$	4.73547	−	29.8986i	0.241971	−	1.52775i	0.747105	−	0.664706i	$-0.231443\pi$
$384$		0			0
$385$	−22.9482	+	8.23690i	−1.16955	+	0.419791i
$386$	−16.4589			−0.837738
$387$		0			0
$388$	−13.4509	−	6.85359i	−0.682868	−	0.347939i
$389$	31.4274	+	10.2114i	1.59343	+	0.517737i	0.965472	−	0.260508i	$-0.0838902\pi$
$389$	31.4274	+	10.2114i	1.59343	+	0.517737i	0.627960	+	0.778246i	$0.283890\pi$
$390$		0			0
$391$	17.5229	−	24.1183i	0.886173	−	1.21971i
$392$	−1.72902	−	3.39339i	−0.0873285	−	0.171392i
$393$		0			0
$394$	7.14066	+	9.82828i	0.359741	+	0.495141i
$395$	1.88936	+	9.20824i	0.0950642	+	0.463317i
$396$		0			0
$397$	24.0891	+	24.0891i	1.20900	+	1.20900i	0.971352	+	0.237647i	$0.0763760\pi$
$397$	24.0891	+	24.0891i	1.20900	+	1.20900i	0.237647	+	0.971352i	$0.423624\pi$
$398$	−13.8064	−	2.18671i	−0.692051	−	0.109610i
$399$		0			0
$400$	−0.452316	−	4.97950i	−0.0226158	−	0.248975i
$401$	18.1981	+	13.2217i	0.908772	+	0.660262i	0.940704	−	0.339228i	$-0.110166\pi$
$401$	18.1981	+	13.2217i	0.908772	+	0.660262i	−0.0319319	+	0.999490i	$0.510166\pi$
$402$		0			0
$403$	31.5769	−	16.0893i	1.57296	−	0.801463i
$404$	−4.19334	−	12.9058i	−0.208627	−	0.642087i
$405$		0			0
$406$		−	7.33385i		−	0.363973i
$407$	−7.79685	+	7.56879i	−0.386475	+	0.375171i
$408$		0			0
$409$	−20.4850	+	14.8832i	−1.01292	+	0.735928i	−0.964819	−	0.262915i	$-0.915316\pi$
$409$	−20.4850	+	14.8832i	−1.01292	+	0.735928i	−0.0480988	+	0.998843i	$0.515316\pi$
$410$	−2.81887	−	0.776704i	−0.139214	−	0.0383587i
$411$		0			0
$412$	0.0271155	+	0.171201i	0.00133588	+	0.00843445i
$413$	0.443753	+	2.80174i	0.0218356	+	0.137865i
$414$		0			0
$415$	13.0188	+	3.58715i	0.639065	+	0.176086i
$416$	−5.00007	+	3.63276i	−0.245149	+	0.178111i
$417$		0			0
$418$	−2.05877	+	1.01079i	−0.100698	+	0.0494395i
$419$			31.5445i			1.54105i	0.637409	+	0.770526i	$0.280006\pi$
$419$			31.5445i			1.54105i	−0.637409	+	0.770526i	$0.719994\pi$
$420$		0			0
$421$	−3.43588	−	10.5745i	−0.167454	−	0.515372i	0.831754	−	0.555144i	$-0.187337\pi$
$421$	−3.43588	−	10.5745i	−0.167454	−	0.515372i	−0.999209	+	0.0397722i	$0.987337\pi$
$422$	4.55842	−	2.32263i	0.221900	−	0.113064i
$423$		0			0
$424$	2.53351	+	1.84071i	0.123038	+	0.0893925i
$425$	20.6132	+	17.1802i	0.999886	+	0.833361i
$426$		0			0
$427$	−32.9497	−	5.21872i	−1.59455	−	0.252551i
$428$	3.71661	+	3.71661i	0.179649	+	0.179649i
$429$		0			0
$430$	2.78899	+	13.5928i	0.134497	+	0.655502i
$431$	−12.2800	−	16.9020i	−0.591508	−	0.814141i	0.403389	−	0.915028i	$-0.367832\pi$
$431$	−12.2800	−	16.9020i	−0.591508	−	0.814141i	−0.994898	+	0.100887i	$0.967832\pi$
$432$		0			0
$433$	16.0627	+	31.5249i	0.771925	+	1.51499i	0.855106	+	0.518454i	$0.173492\pi$
$433$	16.0627	+	31.5249i	0.771925	+	1.51499i	−0.0831808	+	0.996534i	$0.526508\pi$
$434$	−11.0808	+	15.2514i	−0.531897	+	0.732093i
$435$		0			0
$436$	6.00832	+	1.95222i	0.287746	+	0.0934945i
$437$	3.42263	+	1.74392i	0.163727	+	0.0834229i
$438$		0			0
$439$	−9.73788			−0.464764			−0.232382	−	0.972625i	$-0.574652\pi$
$439$	−9.73788			−0.464764			−0.232382	+	0.972625i	$0.574652\pi$
$440$	−6.12978	−	4.17443i	−0.292226	−	0.199008i
$441$		0			0
$442$	5.18878	−	32.7607i	0.246805	−	1.55827i
$443$	6.66885	+	3.39795i	0.316847	+	0.161442i	0.605180	−	0.796089i	$-0.293101\pi$
$443$	6.66885	+	3.39795i	0.316847	+	0.161442i	−0.288333	+	0.957530i	$0.593101\pi$
$444$		0			0
$445$	−9.98849	−	4.53200i	−0.473500	−	0.214838i
$446$	6.88288	−	9.47347i	0.325914	−	0.448582i
$447$		0			0
$448$	1.49255	−	2.92930i	0.0705164	−	0.138396i
$449$	3.57047	+	4.91433i	0.168501	+	0.231921i	0.884914	−	0.465755i	$-0.154217\pi$
$449$	3.57047	+	4.91433i	0.168501	+	0.231921i	−0.716413	+	0.697677i	$0.754217\pi$
$450$		0			0
$451$	−3.54605	+	2.49680i	−0.166977	+	0.117570i
$452$	10.8203	+	10.8203i	0.508946	+	0.508946i
$453$		0			0
$454$	7.35003	−	2.38817i	0.344954	−	0.112082i
$455$	45.1509	+	5.06837i	2.11671	+	0.237609i
$456$		0			0
$457$	−11.2557	+	1.78273i	−0.526520	+	0.0833926i	−0.414035	−	0.910261i	$-0.635881\pi$
$457$	−11.2557	+	1.78273i	−0.526520	+	0.0833926i	−0.112485	+	0.993653i	$0.535881\pi$
$458$	−16.9359	+	8.62926i	−0.791362	+	0.403219i
$459$		0			0
$460$	0.562402	+	12.4083i	0.0262221	+	0.578541i
$461$			16.0054i			0.745447i	0.927943	+	0.372723i	$0.121576\pi$
$461$			16.0054i			0.745447i	−0.927943	+	0.372723i	$0.878424\pi$
$462$		0			0
$463$	−25.6272	+	25.6272i	−1.19100	+	1.19100i	−0.214208	+	0.976788i	$0.568717\pi$
$463$	−25.6272	+	25.6272i	−1.19100	+	1.19100i	−0.976788	+	0.214208i	$0.931283\pi$
$464$	1.80471	−	1.31120i	0.0837816	−	0.0608709i
$465$		0			0
$466$	6.52992	−	20.0970i	0.302493	−	0.930977i
$467$	0.242904	+	1.53364i	0.0112403	+	0.0709682i	0.992671	−	0.120849i	$-0.0385618\pi$
$467$	0.242904	+	1.53364i	0.0112403	+	0.0709682i	−0.981431	+	0.191818i	$0.938562\pi$
$468$		0			0
$469$	−13.0112	+	40.0444i	−0.600802	+	1.84908i
$470$	−3.42764	+	1.94678i	−0.158105	+	0.0897984i
$471$		0			0
$472$	−0.610114	+	0.610114i	−0.0280828	+	0.0280828i
$473$	18.1974	+	9.61486i	0.836719	+	0.442092i
$474$		0			0
$475$	−1.77095	+	2.96964i	−0.0812567	+	0.136257i
$476$	5.45230	+	16.7804i	0.249906	+	0.769131i
$477$		0			0
$478$	−20.9619	+	3.32003i	−0.958773	+	0.151855i
$479$	−28.0212	−	20.3586i	−1.28032	−	0.930209i	−0.280760	−	0.959778i	$-0.590586\pi$
$479$	−28.0212	−	20.3586i	−1.28032	−	0.930209i	−0.999563	+	0.0295692i	$0.990586\pi$
$480$		0			0
$481$	19.2580	−	6.25731i	0.878090	−	0.285309i
$482$	−12.4890	−	1.97807i	−0.568860	−	0.0900985i
$483$		0			0
$484$	−10.5579	+	3.08722i	−0.479904	+	0.140328i
$485$	−18.5847	+	28.1799i	−0.843886	+	1.27958i
$486$		0			0
$487$	−14.4231	+	28.3070i	−0.653575	+	1.28271i	0.291723	+	0.956503i	$0.405772\pi$
$487$	−14.4231	+	28.3070i	−0.653575	+	1.28271i	−0.945297	+	0.326210i	$0.894228\pi$
$488$	−4.60676	−	9.04128i	−0.208538	−	0.409279i
$489$		0			0
$490$	−7.97177	+	2.99562i	−0.360128	+	0.135328i
$491$	8.90838	+	2.89451i	0.402030	+	0.130627i	0.503051	−	0.864257i	$-0.332211\pi$
$491$	8.90838	+	2.89451i	0.402030	+	0.130627i	−0.101021	+	0.994884i	$0.532211\pi$
$492$		0			0
$493$	−1.87282	+	11.8245i	−0.0843478	+	0.532551i
$494$	4.27390			0.192292
$495$		0			0
$496$	−5.73418			−0.257472
$497$	1.00908	−	6.37111i	0.0452636	−	0.285783i
$498$		0			0
$499$	35.8360	+	11.6438i	1.60424	+	0.521249i	0.968151	−	0.250366i	$-0.0805509\pi$
$499$	35.8360	+	11.6438i	1.60424	+	0.521249i	0.636090	+	0.771615i	$0.280551\pi$
$500$	−11.1778	−	0.236994i	−0.499888	−	0.0105987i
$501$		0			0
$502$	11.6995	+	22.9615i	0.522172	+	1.02482i
$503$	−9.04689	+	17.7555i	−0.403381	+	0.791679i	−0.999941	−	0.0108892i	$-0.996534\pi$
$503$	−9.04689	+	17.7555i	−0.403381	+	0.791679i	0.596560	+	0.802569i	$0.296534\pi$
$504$		0			0
$505$	−29.7241	+	6.09885i	−1.32270	+	0.271395i
$506$	14.7425	+	11.0490i	0.655384	+	0.491188i
$507$		0			0
$508$	12.9179	+	2.04599i	0.573138	+	0.0907761i
$509$	−22.4047	+	7.27974i	−0.993072	+	0.322669i	−0.760094	−	0.649813i	$-0.774847\pi$
$509$	−22.4047	+	7.27974i	−0.993072	+	0.322669i	−0.232978	+	0.972482i	$0.574847\pi$
$510$		0			0
$511$	−8.93166	−	6.48923i	−0.395113	−	0.287067i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$		0			0
$514$	−1.28045	−	3.94081i	−0.0564781	−	0.173822i
$515$	0.387190	−	0.0175492i	0.0170616	−	0.000773312i
$516$		0			0
$517$	−1.00024	+	5.76061i	−0.0439905	+	0.253351i
$518$	−7.61648	+	7.61648i	−0.334649	+	0.334649i
$519$		0			0
$520$	6.82518	+	12.0169i	0.299304	+	0.526975i
$521$	−1.58405	+	4.87520i	−0.0693984	+	0.213586i	−0.979741	−	0.200270i	$-0.935818\pi$
$521$	−1.58405	+	4.87520i	−0.0693984	+	0.213586i	0.910342	+	0.413856i	$0.135818\pi$
$522$		0			0
$523$	−3.01976	−	19.0660i	−0.132045	−	0.833698i	−0.961436	−	0.275030i	$-0.911312\pi$
$523$	−3.01976	−	19.0660i	−0.132045	−	0.833698i	0.829391	−	0.558669i	$-0.188688\pi$
$524$	0.973775	−	2.99697i	0.0425396	−	0.130923i
$525$		0			0
$526$	11.0165	−	8.00397i	0.480343	−	0.348989i
$527$	21.7606	−	21.7606i	0.947907	−	0.947907i
$528$		0			0
$529$		−	7.85653i		−	0.341588i
$530$	4.72221	−	5.17060i	0.205120	−	0.224597i
$531$		0			0
$532$	−2.02567	+	1.03213i	−0.0878240	+	0.0447486i
$533$	7.98213	−	1.26424i	0.345744	−	0.0547605i
$534$		0			0
$535$	9.18580	−	7.33165i	0.397137	−	0.316975i
$536$	−12.1803	+	3.95763i	−0.526110	+	0.170944i
$537$		0			0
$538$	11.3451	+	11.3451i	0.489122	+	0.489122i
$539$	−4.08114	+	11.9538i	−0.175787	+	0.514889i
$540$		0			0
$541$	8.73481	+	12.0224i	0.375539	+	0.516885i	0.954396	−	0.298544i	$-0.0965011\pi$
$541$	8.73481	+	12.0224i	0.375539	+	0.516885i	−0.578857	+	0.815429i	$0.696501\pi$
$542$	5.25838	−	10.3201i	0.225867	−	0.443288i
$543$		0			0
$544$	−3.15452	+	4.34183i	−0.135249	+	0.186154i
$545$	5.83678	−	12.8642i	0.250020	−	0.551041i
$546$		0			0
$547$	13.6214	+	6.94045i	0.582409	+	0.296752i	0.720264	−	0.693700i	$-0.244021\pi$
$547$	13.6214	+	6.94045i	0.582409	+	0.296752i	−0.137855	+	0.990452i	$0.544021\pi$
$548$	1.86611	−	11.7822i	0.0797162	−	0.503309i
$549$		0			0
$550$	−10.8051	+	12.5798i	−0.460729	+	0.536403i
$551$	−1.54261			−0.0657173
$552$		0			0
$553$	12.3143	+	6.27445i	0.523657	+	0.266817i
$554$	−7.96865	−	2.58917i	−0.338555	−	0.110003i
$555$		0			0
$556$	−5.13677	+	7.07016i	−0.217848	+	0.299841i
$557$	−11.9233	−	23.4008i	−0.505206	−	0.991523i	−0.992950	−	0.118536i	$-0.962180\pi$
$557$	−11.9233	−	23.4008i	−0.505206	−	0.991523i	0.487744	−	0.872987i	$-0.337820\pi$
$558$		0			0
$559$	−22.5432	−	31.0280i	−0.953474	−	1.31234i
$560$	−6.13692	−	4.04730i	−0.259332	−	0.171030i
$561$		0			0
$562$	−18.3659	−	18.3659i	−0.774718	−	0.774718i
$563$	−8.44742	−	1.33794i	−0.356016	−	0.0563874i	−0.0241352	−	0.999709i	$-0.507683\pi$
$563$	−8.44742	−	1.33794i	−0.356016	−	0.0563874i	−0.331881	+	0.943321i	$0.607683\pi$
$564$		0			0
$565$	26.7431	−	21.3450i	1.12509	−	0.897990i
$566$	10.5170	+	7.64102i	0.442061	+	0.321176i
$567$		0			0
$568$	1.74821	−	0.890758i	0.0733533	−	0.0373754i
$569$	3.86425	+	11.8929i	0.161998	+	0.498578i	0.998803	−	0.0489236i	$-0.0155791\pi$
$569$	3.86425	+	11.8929i	0.161998	+	0.498578i	−0.836805	+	0.547501i	$0.815579\pi$
$570$		0			0
$571$			12.4922i			0.522784i	0.965233	+	0.261392i	$0.0841815\pi$
$571$			12.4922i			0.522784i	−0.965233	+	0.261392i	$0.915818\pi$
$572$	20.1960	+	3.50672i	0.844436	+	0.146623i
$573$		0			0
$574$	−3.47793	+	2.52686i	−0.145166	+	0.105469i
$575$	27.7129	+	1.84542i	1.15571	+	0.0769595i
$576$		0			0
$577$	−1.16108	−	7.33080i	−0.0483366	−	0.305185i	0.951662	−	0.307149i	$-0.0993749\pi$
$577$	−1.16108	−	7.33080i	−0.0483366	−	0.305185i	−0.999998	+	0.00196373i	$0.999375\pi$
$578$	−1.84631	−	11.6572i	−0.0767965	−	0.484874i
$579$		0			0
$580$	−2.46346	−	4.33733i	−0.102290	−	0.180098i
$581$	16.0626	−	11.6701i	0.666387	−	0.484158i
$582$		0			0
$583$	−1.47236	−	10.2814i	−0.0609790	−	0.425813i
$584$		−	3.35809i		−	0.138959i
$585$		0			0
$586$	−4.79512	−	14.7579i	−0.198085	−	0.609642i
$587$	−28.6196	+	14.5824i	−1.18126	+	0.601881i	−0.930544	−	0.366180i	$-0.880665\pi$
$587$	−28.6196	+	14.5824i	−1.18126	+	0.601881i	−0.250714	+	0.968061i	$0.580665\pi$
$588$		0			0
$589$	3.20800	+	2.33075i	0.132183	+	0.0960368i
$590$	1.20355	+	1.50793i	0.0495495	+	0.0620805i
$591$		0			0
$592$	−3.23599	−	0.512530i	−0.132998	−	0.0210649i
$593$	−10.2796	−	10.2796i	−0.422131	−	0.422131i	0.463806	−	0.885937i	$-0.346483\pi$
$593$	−10.2796	−	10.2796i	−0.422131	−	0.422131i	−0.885937	+	0.463806i	$0.846483\pi$
$594$		0			0
$595$	38.6481	−	7.92988i	1.58442	−	0.325093i
$596$	−4.20604	−	5.78912i	−0.172286	−	0.237132i
$597$		0			0
$598$	−15.5861	−	30.5895i	−0.637365	−	1.25090i
$599$	13.2708	−	18.2657i	0.542232	−	0.746318i	−0.446701	−	0.894683i	$-0.647401\pi$
$599$	13.2708	−	18.2657i	0.542232	−	0.746318i	0.988933	+	0.148365i	$0.0474011\pi$
$600$		0			0
$601$	14.7655	+	4.79760i	0.602298	+	0.195698i	0.594265	−	0.804269i	$-0.297443\pi$
$601$	14.7655	+	4.79760i	0.602298	+	0.195698i	0.00803271	+	0.999968i	$0.497443\pi$
$602$	18.1778	+	9.26205i	0.740871	+	0.377493i
$603$		0			0
$604$	9.83369			0.400127
$605$	4.22657	+	24.2309i	0.171834	+	0.985126i
$606$		0			0
$607$	−2.00517	+	12.6602i	−0.0813875	+	0.513861i	0.912991	+	0.407979i	$0.133766\pi$
$607$	−2.00517	+	12.6602i	−0.0813875	+	0.513861i	−0.994379	+	0.105881i	$0.966234\pi$
$608$	−0.616150	−	0.313944i	−0.0249882	−	0.0127321i
$609$		0			0
$610$	−21.2398	+	7.98147i	−0.859976	+	0.323160i
$611$	6.40411	−	8.81450i	0.259083	−	0.356597i
$612$		0			0
$613$	−15.3402	+	30.1068i	−0.619584	+	1.21600i	0.341535	+	0.939869i	$0.389053\pi$
$613$	−15.3402	+	30.1068i	−0.619584	+	1.21600i	−0.961119	+	0.276134i	$0.910947\pi$
$614$	−13.3702	−	18.4025i	−0.539577	−	0.742664i
$615$		0			0
$616$	−10.4190	+	3.21520i	−0.419794	+	0.129544i
$617$	4.79584	+	4.79584i	0.193073	+	0.193073i	0.797023	−	0.603949i	$-0.206407\pi$
$617$	4.79584	+	4.79584i	0.193073	+	0.193073i	−0.603949	+	0.797023i	$0.706407\pi$
$618$		0			0
$619$	−1.03088	+	0.334954i	−0.0414346	+	0.0134629i	−0.329661	−	0.944099i	$-0.606934\pi$
$619$	−1.03088	+	0.334954i	−0.0414346	+	0.0134629i	0.288226	+	0.957562i	$0.406934\pi$
$620$	−1.43034	+	12.7420i	−0.0574438	+	0.511730i
$621$		0			0
$622$	5.72589	−	0.906892i	0.229587	−	0.0363631i
$623$	−14.3690	+	7.32138i	−0.575683	+	0.293325i
$624$		0			0
$625$	−3.31483	+	24.7793i	−0.132593	+	0.991171i
$626$		−	5.13577i		−	0.205267i
$627$		0			0
$628$	7.00571	−	7.00571i	0.279558	−	0.279558i
$629$	14.2252	−	10.3352i	0.567197	−	0.412093i
$630$		0			0
$631$	0.413885	−	1.27381i	0.0164765	−	0.0507094i	−0.942480	−	0.334262i	$-0.891513\pi$
$631$	0.413885	−	1.27381i	0.0164765	−	0.0507094i	0.958957	+	0.283552i	$0.0915130\pi$
$632$	0.657626	+	4.15208i	0.0261589	+	0.165161i
$633$		0			0
$634$	0.563568	−	1.73448i	0.0223821	−	0.0688851i
$635$	7.76866	−	28.1946i	0.308290	−	1.11887i
$636$		0			0
$637$	16.6439	−	16.6439i	0.659456	−	0.659456i
$638$	−7.28947	−	1.26570i	−0.288593	−	0.0501097i
$639$		0			0
$640$	−0.101245	−	2.23377i	−0.00400205	−	0.0882977i
$641$	−4.00585	−	12.3287i	−0.158222	−	0.486956i	0.840252	−	0.542197i	$-0.182407\pi$
$641$	−4.00585	−	12.3287i	−0.158222	−	0.486956i	−0.998473	+	0.0552410i	$0.982407\pi$
$642$		0			0
$643$	−40.7047	+	6.44700i	−1.60524	+	0.254245i	−0.893787	−	0.448491i	$-0.851962\pi$
$643$	−40.7047	+	6.44700i	−1.60524	+	0.254245i	−0.711451	+	0.702736i	$0.751962\pi$
$644$	14.7745	+	10.7343i	0.582198	+	0.422992i
$645$		0			0
$646$	3.52961	−	1.14684i	0.138871	−	0.0451218i
$647$	−7.49301	−	1.18678i	−0.294581	−	0.0466570i	0.00739486	−	0.999973i	$-0.497646\pi$
$647$	−7.49301	−	1.18678i	−0.294581	−	0.0466570i	−0.301976	+	0.953316i	$0.597646\pi$
$648$		0			0
$649$	2.86137	+	0.0424684i	0.112319	+	0.00166703i
$650$	28.4053	−	12.1688i	1.11415	−	0.477300i
$651$		0			0
$652$	1.86043	−	3.65130i	0.0728600	−	0.142996i
$653$	13.0321	+	25.5769i	0.509984	+	1.00090i	0.992177	+	0.124836i	$0.0398403\pi$
$653$	13.0321	+	25.5769i	0.509984	+	1.00090i	−0.482193	+	0.876065i	$0.660160\pi$
$654$		0			0
$655$	−6.41671	−	2.91141i	−0.250721	−	0.113758i
$656$	−1.24362	−	0.404076i	−0.0485551	−	0.0157765i
$657$		0			0
$658$	−0.906644	+	5.72432i	−0.0353447	+	0.223157i
$659$	−32.7832			−1.27705			−0.638526	−	0.769600i	$-0.720456\pi$
$659$	−32.7832			−1.27705			−0.638526	+	0.769600i	$0.720456\pi$
$660$		0			0
$661$	19.2907			0.750323			0.375162	−	0.926959i	$-0.377587\pi$
$661$	19.2907			0.750323			0.375162	+	0.926959i	$0.377587\pi$
$662$	−3.18119	+	20.0852i	−0.123640	+	0.780634i
$663$		0			0
$664$	5.74356	+	1.86619i	0.222893	+	0.0724224i
$665$	1.78822	+	4.75872i	0.0693444	+	0.184535i
$666$		0			0
$667$	5.62562	+	11.0409i	0.217825	+	0.427505i
$668$	−2.82836	+	5.55097i	−0.109433	+	0.214773i
$669$		0			0
$670$	5.75602	+	28.0532i	0.222374	+	1.08379i
$671$	−10.8737	+	31.8496i	−0.419775	+	1.22954i
$672$		0			0
$673$	5.42946	+	0.859942i	0.209290	+	0.0331483i	0.260199	−	0.965555i	$-0.416212\pi$
$673$	5.42946	+	0.859942i	0.209290	+	0.0331483i	−0.0509088	+	0.998703i	$0.516212\pi$
$674$	−24.0544	+	7.81573i	−0.926539	+	0.301051i
$675$		0			0
$676$	−20.3853	−	14.8108i	−0.784051	−	0.569646i
$677$	−30.3025	+	4.79944i	−1.16462	+	0.184457i	−0.708664	−	0.705546i	$-0.750702\pi$
$677$	−30.3025	+	4.79944i	−1.16462	+	0.184457i	−0.455954	+	0.890003i	$0.650702\pi$
$678$		0			0
$679$	15.3369	+	47.2020i	0.588575	+	1.81145i
$680$	8.86116	+	8.09273i	0.339810	+	0.310342i
$681$		0			0
$682$	13.2468	+	13.6459i	0.507246	+	0.522529i
$683$	12.8058	−	12.8058i	0.489999	−	0.489999i	−0.418307	−	0.908306i	$-0.637376\pi$
$683$	12.8058	−	12.8058i	0.489999	−	0.489999i	0.908306	+	0.418307i	$0.137376\pi$
$684$		0			0
$685$	−25.7158	−	7.08565i	−0.982549	−	0.270729i
$686$	3.24236	−	9.97897i	0.123794	−	0.380999i
$687$		0			0
$688$	0.970756	+	6.12911i	0.0370097	+	0.233670i
$689$	−5.98089	+	18.4073i	−0.227854	+	0.701262i
$690$		0			0
$691$	−28.6104	+	20.7867i	−1.08839	+	0.790763i	−0.979127	−	0.203249i	$-0.934850\pi$
$691$	−28.6104	+	20.7867i	−1.08839	+	0.790763i	−0.109265	+	0.994013i	$0.534850\pi$
$692$	15.0765	−	15.0765i	0.573123	−	0.573123i
$693$		0			0
$694$			0.375687i			0.0142609i
$695$	14.4294	+	13.1781i	0.547337	+	0.499872i
$696$		0			0
$697$	6.25282	−	3.18597i	0.236843	−	0.120677i
$698$	−14.0814	+	2.23028i	−0.532990	+	0.0844172i
$699$		0			0
$700$	−10.5244	+	12.6274i	−0.397783	+	0.477269i
$701$	−37.5754	+	12.2090i	−1.41920	+	0.461127i	−0.915349	−	0.402661i	$-0.868085\pi$
$701$	−37.5754	+	12.2090i	−1.41920	+	0.461127i	−0.503855	+	0.863788i	$0.668085\pi$
$702$		0			0
$703$	1.60206	+	1.60206i	0.0604227	+	0.0604227i
$704$	−2.65398	−	1.98907i	−0.100026	−	0.0749658i
$705$		0			0
$706$	6.73023	+	9.26336i	0.253295	+	0.348631i
$707$	−20.2538	+	39.7504i	−0.761724	+	1.49497i
$708$		0			0
$709$	8.24861	−	11.3532i	0.309783	−	0.426380i	−0.625531	−	0.780200i	$-0.715117\pi$
$709$	8.24861	−	11.3532i	0.309783	−	0.426380i	0.935314	+	0.353820i	$0.115117\pi$
$710$	−1.54329	−	4.10691i	−0.0579186	−	0.154130i
$711$		0			0
$712$	−4.37064	−	2.22695i	−0.163797	−	0.0834585i
$713$	4.98284	−	31.4604i	0.186609	−	1.17820i
$714$		0			0
$715$	12.8300	−	44.0030i	0.479815	−	1.64562i
$716$	−25.6251			−0.957657
$717$		0			0
$718$	−1.60385	−	0.817202i	−0.0598551	−	0.0304977i
$719$	17.2499	+	5.60484i	0.643314	+	0.209025i	0.612464	−	0.790499i	$-0.290179\pi$
$719$	17.2499	+	5.60484i	0.643314	+	0.209025i	0.0308501	+	0.999524i	$0.490179\pi$
$720$		0			0
$721$	0.334955	−	0.461026i	0.0124744	−	0.0171695i
$722$	−8.40872	−	16.5030i	−0.312940	−	0.614180i
$723$		0			0
$724$	−11.9610	−	16.4629i	−0.444528	−	0.611841i
$725$	−10.2525	+	4.39218i	−0.380769	+	0.163121i
$726$		0			0
$727$	−33.9484	−	33.9484i	−1.25908	−	1.25908i	−0.951534	−	0.307543i	$-0.900493\pi$
$727$	−33.9484	−	33.9484i	−1.25908	−	1.25908i	−0.307543	−	0.951534i	$-0.599507\pi$
$728$	20.0688	+	3.17858i	0.743798	+	0.117806i
$729$		0			0
$730$	−7.46205	−	0.837645i	−0.276183	−	0.0310026i
$731$	−26.9433	−	19.5754i	−0.996533	−	0.724023i
$732$		0			0
$733$	19.6845	−	10.0298i	0.727064	−	0.370458i	−0.0509529	−	0.998701i	$-0.516226\pi$
$733$	19.6845	−	10.0298i	0.727064	−	0.370458i	0.778017	+	0.628244i	$0.216226\pi$
$734$	−1.30960	−	4.03054i	−0.0483383	−	0.148770i
$735$		0			0
$736$			5.55487i			0.204755i
$737$	37.5565	+	19.8435i	1.38341	+	0.730944i
$738$		0			0
$739$	16.6360	−	12.0867i	0.611963	−	0.444617i	−0.238142	−	0.971230i	$-0.576538\pi$
$739$	16.6360	−	12.0867i	0.611963	−	0.444617i	0.850105	+	0.526613i	$0.176538\pi$
$740$	−1.94609	+	7.06288i	−0.0715396	+	0.259637i
$741$		0			0
$742$	−1.61057	−	10.1688i	−0.0591260	−	0.373307i
$743$	2.17935	+	13.7599i	0.0799525	+	0.504800i	0.994870	+	0.101160i	$0.0322553\pi$
$743$	2.17935	+	13.7599i	0.0799525	+	0.504800i	−0.914918	+	0.403640i	$0.867745\pi$
$744$		0			0
$745$	−13.9132	+	7.90225i	−0.509741	+	0.289516i
$746$	0.873094	−	0.634340i	0.0319662	−	0.0232248i
$747$		0			0
$748$	17.6199	−	2.52327i	0.644247	−	0.0922599i
$749$		−	17.2800i		−	0.631398i
$750$		0			0
$751$	10.2437	+	31.5269i	0.373798	+	1.15043i	0.944286	+	0.329127i	$0.106754\pi$
$751$	10.2437	+	31.5269i	0.373798	+	1.15043i	−0.570487	+	0.821306i	$0.693246\pi$
$752$	−1.57073	+	0.800329i	−0.0572788	+	0.0291850i
$753$		0			0
$754$	11.1539	+	8.10376i	0.406200	+	0.295122i
$755$	2.45293	−	21.8516i	0.0892711	−	0.795260i
$756$		0			0
$757$	14.4411	+	2.28724i	0.524869	+	0.0831311i	0.413246	−	0.910620i	$-0.364395\pi$
$757$	14.4411	+	2.28724i	0.524869	+	0.0831311i	0.111623	+	0.993751i	$0.464395\pi$
$758$	11.3071	+	11.3071i	0.410694	+	0.410694i
$759$		0			0
$760$	−0.851312	+	1.29084i	−0.0308803	+	0.0468238i
$761$	−6.58319	−	9.06098i	−0.238640	−	0.328460i	0.672852	−	0.739777i	$-0.265069\pi$
$761$	−6.58319	−	9.06098i	−0.238640	−	0.328460i	−0.911493	+	0.411317i	$0.865069\pi$
$762$		0			0
$763$	−9.42922	−	18.5059i	−0.341361	−	0.669958i
$764$	−0.429583	+	0.591270i	−0.0155418	+	0.0213914i
$765$		0			0
$766$	−28.7897	−	9.35435i	−1.04021	−	0.337986i
$767$	−4.75144	−	2.42098i	−0.171565	−	0.0874165i
$768$		0			0
$769$	−37.2217			−1.34225			−0.671125	−	0.741345i	$-0.734188\pi$
$769$	−37.2217			−1.34225			−0.671125	+	0.741345i	$0.734188\pi$
$770$	4.54560	+	23.9542i	0.163812	+	0.863250i
$771$		0			0
$772$	−2.57474	+	16.2563i	−0.0926671	+	0.585077i
$773$	−23.4625	−	11.9548i	−0.843889	−	0.429983i	−0.0220869	−	0.999756i	$-0.507031\pi$
$773$	−23.4625	−	11.9548i	−0.843889	−	0.429983i	−0.821802	+	0.569773i	$0.807031\pi$
$774$		0			0
$775$	27.9573	+	6.35674i	1.00426	+	0.228341i
$776$	−8.87341	+	12.2132i	−0.318537	+	0.438428i
$777$		0			0
$778$	15.0020	−	29.4430i	0.537847	−	1.05558i
$779$	0.531502	+	0.731549i	0.0190430	+	0.0262105i
$780$		0			0
$781$	−6.15840	−	2.10253i	−0.220365	−	0.0752344i
$782$	−21.0801	−	21.0801i	−0.753824	−	0.753824i
$783$		0			0
$784$	−3.62208	+	1.17689i	−0.129360	+	0.0420317i
$785$	−13.8200	−	17.3150i	−0.493256	−	0.617998i
$786$		0			0
$787$	−38.3678	+	6.07686i	−1.36766	+	0.216617i	−0.796709	−	0.604364i	$-0.793427\pi$
$787$	−38.3678	+	6.07686i	−1.36766	+	0.216617i	−0.570956	+	0.820981i	$0.693427\pi$
$788$	10.8243	−	5.51527i	0.385600	−	0.196473i
$789$		0			0
$790$	9.39043	−	0.425617i	0.334097	−	0.0151428i
$791$		−	50.3082i		−	1.78875i
$792$		0			0
$793$	44.3458	−	44.3458i	1.57476	−	1.57476i
$794$	27.5609	−	20.0242i	0.978100	−	0.710631i
$795$		0			0
$796$	−4.31958	+	13.2943i	−0.153104	+	0.471204i
$797$	−6.36654	−	40.1968i	−0.225515	−	1.42384i	−0.797371	−	0.603489i	$-0.793777\pi$
$797$	−6.36654	−	40.1968i	−0.225515	−	1.42384i	0.571856	−	0.820354i	$-0.306223\pi$
$798$		0			0
$799$	2.92361	−	8.99794i	0.103430	−	0.318324i
$800$	−4.98895	−	0.332218i	−0.176386	−	0.0117457i
$801$		0			0
$802$	15.9058	−	15.9058i	0.561652	−	0.561652i
$803$	−7.99142	+	7.75768i	−0.282011	+	0.273762i
$804$		0			0
$805$	27.5382	−	30.1531i	0.970595	−	1.06276i
$806$	−10.9515	−	33.7051i	−0.385748	−	1.18721i
$807$		0			0
$808$	−13.4029	+	2.12281i	−0.471512	+	0.0746801i
$809$	−39.9952	−	29.0582i	−1.40615	−	1.02163i	−0.993868	−	0.110577i	$-0.964730\pi$
$809$	−39.9952	−	29.0582i	−1.40615	−	1.02163i	−0.412287	−	0.911054i	$-0.635270\pi$
$810$		0			0
$811$	−33.0590	+	10.7415i	−1.16086	+	0.377186i	−0.825224	−	0.564805i	$-0.808951\pi$
$811$	−33.0590	+	10.7415i	−1.16086	+	0.377186i	−0.335636	+	0.941992i	$0.608951\pi$
$812$	−7.24356	−	1.14727i	−0.254199	−	0.0402612i
$813$		0			0
$814$	6.25591	+	8.88487i	0.219270	+	0.311415i
$815$	−7.64952	−	5.04486i	−0.267951	−	0.176714i
$816$		0			0
$817$	1.94818	−	3.82353i	0.0681584	−	0.133768i
$818$	11.4954	+	22.5610i	0.401928	+	0.788828i
$819$		0			0
$820$	−1.20811	+	2.66266i	−0.0421890	+	0.0929842i
$821$	13.1314	+	4.26664i	0.458288	+	0.148907i	0.529058	−	0.848586i	$-0.322546\pi$
$821$	13.1314	+	4.26664i	0.458288	+	0.148907i	−0.0707697	+	0.997493i	$0.522546\pi$
$822$		0			0
$823$	2.41578	−	15.2526i	0.0842087	−	0.531673i	−0.909137	−	0.416498i	$-0.863257\pi$
$823$	2.41578	−	15.2526i	0.0842087	−	0.531673i	0.993345	−	0.115175i	$-0.0367428\pi$
$824$	0.173335			0.00603840
$825$		0			0
$826$	2.83667			0.0987003
$827$	7.49561	−	47.3254i	0.260648	−	1.64567i	−0.416004	−	0.909363i	$-0.636570\pi$
$827$	7.49561	−	47.3254i	0.260648	−	1.64567i	0.676652	−	0.736303i	$-0.263430\pi$
$828$		0			0
$829$	−42.1108	−	13.6826i	−1.46257	−	0.475218i	−0.533716	−	0.845664i	$-0.679205\pi$
$829$	−42.1108	−	13.6826i	−1.46257	−	0.475218i	−0.928854	+	0.370446i	$0.879205\pi$
$830$	5.57957	−	12.2973i	0.193670	−	0.426846i
$831$		0			0
$832$	2.80585	+	5.50680i	0.0972755	+	0.190914i
$833$	9.27927	−	18.2116i	0.321508	−	0.630994i
$834$		0			0
$835$	11.6294	+	7.66957i	0.402451	+	0.265416i
$836$	0.676287	+	2.19154i	0.0233899	+	0.0757961i
$837$		0			0
$838$	31.1562	+	4.93465i	1.07627	+	0.170465i
$839$	6.92949	−	2.25153i	0.239233	−	0.0777314i	−0.186947	−	0.982370i	$-0.559859\pi$
$839$	6.92949	−	2.25153i	0.239233	−	0.0777314i	0.426179	+	0.904639i	$0.359859\pi$
$840$		0			0
$841$	19.4356	+	14.1208i	0.670195	+	0.486925i
$842$	−10.9818	+	1.73935i	−0.378459	+	0.0599420i
$843$		0			0
$844$	−1.58094	−	4.86564i	−0.0544182	−	0.167482i
$845$	−37.9962	+	41.6040i	−1.30711	+	1.43122i
$846$		0			0
$847$	31.7208	+	17.3671i	1.08994	+	0.596741i
$848$	2.21437	−	2.21437i	0.0760418	−	0.0760418i
$849$		0			0
$850$	20.1933	−	17.6718i	0.692624	−	0.606138i
$851$	5.62397	−	17.3088i	0.192787	−	0.593338i
$852$		0			0
$853$	1.09044	+	6.88475i	0.0373358	+	0.235729i	0.999298	−	0.0374520i	$-0.0119241\pi$
$853$	1.09044	+	6.88475i	0.0373358	+	0.235729i	−0.961963	+	0.273181i	$0.911924\pi$
$854$	−10.3089	+	31.7276i	−0.352764	+	1.08570i
$855$		0			0
$856$	4.25226	−	3.08945i	0.145339	−	0.105595i
$857$	22.8797	−	22.8797i	0.781554	−	0.781554i	−0.198539	−	0.980093i	$-0.563620\pi$
$857$	22.8797	−	22.8797i	0.781554	−	0.781554i	0.980093	+	0.198539i	$0.0636196\pi$
$858$		0			0
$859$			53.1298i			1.81276i	0.422459	+	0.906382i	$0.361167\pi$
$859$			53.1298i			1.81276i	−0.422459	+	0.906382i	$0.638833\pi$
$860$	13.8617	−	0.628276i	0.472681	−	0.0214240i
$861$		0			0
$862$	−18.6149	+	9.48479i	−0.634028	+	0.323053i
$863$	19.4487	−	3.08038i	0.662042	−	0.104857i	0.183634	−	0.982995i	$-0.441214\pi$
$863$	19.4487	−	3.08038i	0.662042	−	0.104857i	0.478408	+	0.878138i	$0.341214\pi$
$864$		0			0
$865$	−29.7410	−	37.2624i	−1.01122	−	1.26696i
$866$	33.6495	−	10.9334i	1.14346	−	0.371532i
$867$		0			0
$868$	13.3303	+	13.3303i	0.452458	+	0.452458i
$869$	8.36173	−	11.1569i	0.283652	−	0.378472i
$870$		0			0
$871$	−46.5254	−	64.0367i	−1.57645	−	2.16980i
$872$	2.86809	−	5.62895i	0.0971259	−	0.190620i
$873$		0			0
$874$	2.25786	−	3.10768i	0.0763734	−	0.105119i
$875$	25.4342	+	26.5361i	0.859832	+	0.897083i
$876$		0			0
$877$	−16.4202	−	8.36653i	−0.554472	−	0.282518i	0.154219	−	0.988037i	$-0.450714\pi$
$877$	−16.4202	−	8.36653i	−0.554472	−	0.282518i	−0.708691	+	0.705519i	$0.750714\pi$
$878$	−1.52334	+	9.61799i	−0.0514103	+	0.324592i
$879$		0			0
$880$	−5.08194	+	5.40128i	−0.171312	+	0.182077i
$881$	8.88945			0.299493			0.149747	−	0.988724i	$-0.452154\pi$
$881$	8.88945			0.299493			0.149747	+	0.988724i	$0.452154\pi$
$882$		0			0
$883$	−18.7495	−	9.55336i	−0.630972	−	0.321496i	0.109093	−	0.994032i	$-0.465205\pi$
$883$	−18.7495	−	9.55336i	−0.630972	−	0.321496i	−0.740065	+	0.672535i	$0.765205\pi$
$884$	−31.5456	−	10.2498i	−1.06099	−	0.344738i
$885$		0			0
$886$	4.39936	−	6.05519i	0.147799	−	0.203428i
$887$	8.27236	+	16.2354i	0.277759	+	0.545132i	0.987172	−	0.159661i	$-0.0510400\pi$
$887$	8.27236	+	16.2354i	0.277759	+	0.545132i	−0.709413	+	0.704793i	$0.751040\pi$
$888$		0			0
$889$	−25.2739	−	34.7865i	−0.847659	−	1.16670i
$890$	−6.03875	+	9.15655i	−0.202419	+	0.306928i
$891$		0			0
$892$	−8.28012	−	8.28012i	−0.277239	−	0.277239i
$893$	1.20406	+	0.190704i	0.0402923	+	0.00638167i
$894$		0			0
$895$	−6.39196	+	56.9419i	−0.213660	+	1.90336i
$896$	−2.65975	−	1.93242i	−0.0888559	−	0.0645576i
$897$		0			0
$898$	5.41237	−	2.75774i	0.180613	−	0.0920269i
$899$	3.95278	+	12.1654i	0.131833	+	0.405739i
$900$		0			0
$901$			16.8066i			0.559910i
$902$	1.91134	+	3.89298i	0.0636406	+	0.129622i
$903$		0			0
$904$	12.3798	−	8.99446i	0.411746	−	0.299151i
$905$	−39.5661	+	22.4722i	−1.31522	+	0.747001i
$906$		0			0
$907$	−5.12613	−	32.3651i	−0.170211	−	1.07467i	−0.913840	−	0.406075i	$-0.866897\pi$
$907$	−5.12613	−	32.3651i	−0.170211	−	1.07467i	0.743629	−	0.668592i	$-0.233103\pi$
$908$	−1.20897	−	7.63313i	−0.0401210	−	0.253314i
$909$		0			0
$910$	12.0691	−	43.8022i	0.400088	−	1.45203i
$911$	6.48533	−	4.71187i	0.214869	−	0.156111i	−0.475145	−	0.879907i	$-0.657604\pi$
$911$	6.48533	−	4.71187i	0.214869	−	0.156111i	0.690014	+	0.723796i	$0.257604\pi$
$912$		0			0
$913$	−8.82737	−	17.9794i	−0.292143	−	0.595032i
$914$			11.3960i			0.376947i
$915$		0			0
$916$	5.87367	+	18.0773i	0.194071	+	0.597291i
$917$	−9.23081	+	4.70333i	−0.304828	+	0.155318i
$918$		0			0
$919$	−12.3712	−	8.98820i	−0.408088	−	0.296493i	0.364739	−	0.931110i	$-0.381158\pi$
$919$	−12.3712	−	8.98820i	−0.408088	−	0.296493i	−0.772827	+	0.634616i	$0.781158\pi$
$920$	12.3435	+	1.38561i	0.406954	+	0.0456822i
$921$		0			0
$922$	15.8084	+	2.50380i	0.520621	+	0.0824582i
$923$	8.57464	+	8.57464i	0.282238	+	0.282238i
$924$		0			0
$925$	15.2091	+	6.08620i	0.500071	+	0.200113i
$926$	21.3027	+	29.3206i	0.700050	+	0.963536i
$927$		0			0
$928$	−1.01274	−	1.98761i	−0.0332447	−	0.0652464i
$929$	−9.74393	+	13.4114i	−0.319688	+	0.440013i	−0.938372	−	0.345627i	$-0.887666\pi$
$929$	−9.74393	+	13.4114i	−0.319688	+	0.440013i	0.618684	+	0.785640i	$0.287666\pi$
$930$		0			0
$931$	2.50475	+	0.813842i	0.0820898	+	0.0266726i
$932$	−18.8281	−	9.59340i	−0.616735	−	0.314242i
$933$		0			0
$934$	1.55275			0.0508076
$935$	−1.21187	−	39.7827i	−0.0396323	−	1.30103i
$936$		0			0
$937$	2.84529	−	17.9644i	0.0929514	−	0.586872i	−0.896617	−	0.442807i	$-0.853983\pi$
$937$	2.84529	−	17.9644i	0.0929514	−	0.586872i	0.989568	−	0.144065i	$-0.0460174\pi$
$938$	37.5160	+	19.1153i	1.22494	+	0.624138i
$939$		0			0
$940$	1.38661	+	3.68998i	0.0452264	+	0.120354i
$941$	−1.89175	+	2.60377i	−0.0616692	+	0.0848804i	−0.838738	−	0.544536i	$-0.816706\pi$
$941$	−1.89175	+	2.60377i	−0.0616692	+	0.0848804i	0.777068	+	0.629416i	$0.216706\pi$
$942$		0			0
$943$	3.29762	−	6.47194i	0.107385	−	0.210756i
$944$	0.507160	+	0.698046i	0.0165066	+	0.0227195i
$945$		0			0
$946$	12.3432	−	16.4693i	0.401312	−	0.535463i
$947$	11.9236	+	11.9236i	0.387464	+	0.387464i	0.873782	−	0.486318i	$-0.161660\pi$
$947$	11.9236	+	11.9236i	0.387464	+	0.387464i	−0.486318	+	0.873782i	$0.661660\pi$
$948$		0			0
$949$	19.7386	−	6.41347i	0.640743	−	0.208190i
$950$	2.65605	+	2.21370i	0.0861735	+	0.0718219i
$951$		0			0
$952$	17.4268	−	2.76013i	0.564805	−	0.0894564i
$953$	−9.25387	+	4.71508i	−0.299762	+	0.152736i	−0.597402	−	0.801942i	$-0.703800\pi$
$953$	−9.25387	+	4.71508i	−0.299762	+	0.152736i	0.297640	+	0.954678i	$0.403800\pi$
$954$		0			0
$955$	1.20671	+	1.10207i	0.0390483	+	0.0356621i
$956$			21.2231i			0.686406i
$957$		0			0
$958$	−24.4915	+	24.4915i	−0.791283	+	0.791283i
$959$	−31.7281	+	23.0518i	−1.02456	+	0.744383i
$960$		0			0
$961$	0.581191	−	1.78872i	0.0187481	−	0.0577007i
$962$	−3.16765	−	19.9998i	−0.102129	−	0.644819i
$963$		0			0
$964$	−3.90743	+	12.0258i	−0.125850	+	0.387326i
$965$	35.4811	+	9.77636i	1.14218	+	0.314712i
$966$		0			0
$967$	20.8838	−	20.8838i	0.671577	−	0.671577i	−0.286502	−	0.958080i	$-0.592493\pi$
$967$	20.8838	−	20.8838i	0.671577	−	0.671577i	0.958080	+	0.286502i	$0.0924926\pi$
$968$	1.39759	+	10.9109i	0.0449202	+	0.350688i
$969$		0			0
$970$	24.9257	+	22.7642i	0.800316	+	0.730913i
$971$	4.09100	+	12.5908i	0.131286	+	0.404058i	0.994994	−	0.0999353i	$-0.0318636\pi$
$971$	4.09100	+	12.5908i	0.131286	+	0.404058i	−0.863708	+	0.503993i	$0.831864\pi$
$972$		0			0
$973$	28.3775	−	4.49455i	0.909740	−	0.144089i
$974$	25.7022	+	18.6738i	0.823552	+	0.598346i
$975$		0			0
$976$	−9.65062	+	3.13568i	−0.308909	+	0.100371i
$977$	−26.0175	−	4.12077i	−0.832374	−	0.131835i	−0.274319	−	0.961639i	$-0.588452\pi$
$977$	−26.0175	−	4.12077i	−0.832374	−	0.131835i	−0.558055	+	0.829804i	$0.688452\pi$
$978$		0			0
$979$	4.79722	+	15.5456i	0.153320	+	0.496840i
$980$	1.71168	+	8.34224i	0.0546775	+	0.266483i
$981$		0			0
$982$	4.25245	−	8.34590i	0.135701	−	0.266328i
$983$	25.8499	+	50.7333i	0.824483	+	1.61814i	0.785469	+	0.618901i	$0.212422\pi$
$983$	25.8499	+	50.7333i	0.824483	+	1.61814i	0.0390141	+	0.999239i	$0.487578\pi$
$984$		0			0
$985$	−9.55551	−	25.4286i	−0.304464	−	0.810222i
$986$	11.3860	+	3.69953i	0.362604	+	0.117817i
$987$		0			0
$988$	0.668585	−	4.22128i	0.0212705	−	0.134297i
$989$	−34.4708			−1.09611
$990$		0			0
$991$	−15.2937			−0.485820			−0.242910	−	0.970049i	$-0.578102\pi$
$991$	−15.2937			−0.485820			−0.242910	+	0.970049i	$0.578102\pi$
$992$	−0.897023	+	5.66358i	−0.0284805	+	0.179819i
$993$		0			0
$994$	−6.13482	−	1.99332i	−0.194585	−	0.0632244i
$995$	28.4640	+	12.9147i	0.902368	+	0.409425i
$996$		0			0
$997$	−2.83827	−	5.57042i	−0.0898889	−	0.176417i	0.841685	−	0.539969i	$-0.181564\pi$
$997$	−2.83827	−	5.57042i	−0.0898889	−	0.176417i	−0.931574	+	0.363552i	$0.881564\pi$
$998$	17.1065	−	33.5733i	0.541496	−	1.06275i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.c.217.5		48
3.2	odd	2		110.2.k.a.107.2	yes	48
5.3	odd	4	inner	990.2.bh.c.613.3		48
11.7	odd	10	inner	990.2.bh.c.667.3		48
12.11	even	2		880.2.cm.c.657.3		48
15.2	even	4		550.2.bh.b.393.2		48
15.8	even	4		110.2.k.a.63.5	yes	48
15.14	odd	2		550.2.bh.b.107.5		48
33.29	even	10		110.2.k.a.7.5	✓	48
55.18	even	20	inner	990.2.bh.c.73.5		48
60.23	odd	4		880.2.cm.c.833.4		48
132.95	odd	10		880.2.cm.c.337.4		48
165.29	even	10		550.2.bh.b.7.2		48
165.62	odd	20		550.2.bh.b.293.5		48
165.128	odd	20		110.2.k.a.73.2	yes	48
660.623	even	20		880.2.cm.c.513.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.5	✓	48	33.29	even	10
110.2.k.a.63.5	yes	48	15.8	even	4
110.2.k.a.73.2	yes	48	165.128	odd	20
110.2.k.a.107.2	yes	48	3.2	odd	2
550.2.bh.b.7.2		48	165.29	even	10
550.2.bh.b.107.5		48	15.14	odd	2
550.2.bh.b.293.5		48	165.62	odd	20
550.2.bh.b.393.2		48	15.2	even	4
880.2.cm.c.337.4		48	132.95	odd	10
880.2.cm.c.513.3		48	660.623	even	20
880.2.cm.c.657.3		48	12.11	even	2
880.2.cm.c.833.4		48	60.23	odd	4
990.2.bh.c.73.5		48	55.18	even	20	inner
990.2.bh.c.217.5		48	1.1	even	1	trivial
990.2.bh.c.613.3		48	5.3	odd	4	inner
990.2.bh.c.667.3		48	11.7	odd	10	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.923903 + 2.03627i) q^{5} +(1.49255 + 2.92930i) q^{7} +(-0.453990 + 0.891007i) q^{8} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.923903 + 2.03627i) q^{5} +(1.49255 + 2.92930i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.86667 + 1.23107i) q^{10} +(3.16916 - 0.977970i) q^{11} +(-6.10433 - 0.966831i) q^{13} +(3.12672 - 1.01593i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-5.30072 + 0.839551i) q^{17} +(-0.213692 - 0.657676i) q^{19} +(1.50793 - 1.65111i) q^{20} +(-0.470163 - 3.28313i) q^{22} +(-3.92788 + 3.92788i) q^{23} +(-3.29281 - 3.76263i) q^{25} +(-1.90986 + 5.87793i) q^{26} +(-0.514298 - 3.24715i) q^{28} +(0.689338 - 2.12156i) q^{29} +(-4.63905 + 3.37046i) q^{31} +(0.707107 - 0.707107i) q^{32} +5.36679i q^{34} +(-7.34382 + 0.332855i) q^{35} +(-2.91923 + 1.48742i) q^{37} +(-0.683008 + 0.108178i) q^{38} +(-1.39489 - 1.74765i) q^{40} +(-1.24362 + 0.404076i) q^{41} +(4.38796 + 4.38796i) q^{43} +(-3.31626 - 0.0492198i) q^{44} +(3.26507 + 4.49398i) q^{46} +(-0.800329 + 1.57073i) q^{47} +(-2.23857 + 3.08113i) q^{49} +(-4.23142 + 2.66366i) q^{50} +(5.50680 + 2.80585i) q^{52} +(0.489889 - 3.09304i) q^{53} +(-0.936583 + 7.35682i) q^{55} -3.28763 q^{56} +(-1.98761 - 1.01274i) q^{58} +(0.820602 + 0.266630i) q^{59} +(-5.96441 + 8.20931i) q^{61} +(2.60326 + 5.10919i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(7.60854 - 11.5368i) q^{65} +(9.05603 + 9.05603i) q^{67} +(5.30072 + 0.839551i) q^{68} +(-0.820069 + 7.30547i) q^{70} +(-1.58734 - 1.15327i) q^{71} +(-2.99208 + 1.52454i) q^{73} +(1.01244 + 3.11597i) q^{74} +0.691521i q^{76} +(7.59490 + 7.82374i) q^{77} +(3.40098 - 2.47096i) q^{79} +(-1.94434 + 1.10432i) q^{80} +(0.204556 + 1.29152i) q^{82} +(-0.944728 - 5.96478i) q^{83} +(3.18779 - 11.5694i) q^{85} +(5.02037 - 3.64751i) q^{86} +(-0.567391 + 3.26773i) q^{88} +4.90528i q^{89} +(-6.27889 - 19.3244i) q^{91} +(4.94942 - 2.52186i) q^{92} +(1.42620 + 1.03619i) q^{94} +(1.53664 + 0.172494i) q^{95} +(14.9105 + 2.36159i) q^{97} +(2.69301 + 2.69301i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q + 8 * q^5 - 20 * q^7	\( 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47} - 40 q^{50} + 40 q^{52} + 96 q^{55} + 8 q^{56} + 48 q^{58} + 80 q^{61} - 40 q^{62} - 20 q^{68} - 56 q^{70} + 56 q^{71} - 20 q^{73} + 96 q^{77} + 12 q^{80} - 80 q^{85} + 56 q^{86} - 4 q^{88} - 68 q^{91} + 12 q^{92} - 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

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