LMFDB - Embedded newform 738.2.u.c.613.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [738,2,Mod(289,738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(738, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("738.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (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:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			613.3
Character	$\chi$	$=$	738.613
Dual form			738.2.u.c.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.846136 + 1.16461i) q^{5} +(0.790595 - 0.402828i) q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.846136 + 1.16461i) q^{5} +(0.790595 - 0.402828i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.16461 - 0.846136i) q^{10} +(-0.893820 - 5.64336i) q^{11} +(2.42371 - 4.75681i) q^{13} +(-0.627420 + 0.627420i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-6.91240 + 1.09482i) q^{17} +(-1.58063 - 3.10217i) q^{19} +(1.36908 + 0.444840i) q^{20} +(2.59397 + 5.09095i) q^{22} +(1.38107 + 4.25050i) q^{23} +(0.904723 - 2.78445i) q^{25} +(-0.835155 + 5.27296i) q^{26} +(0.402828 - 0.790595i) q^{28} +(4.45414 + 0.705466i) q^{29} +(0.563629 + 0.409501i) q^{31} +1.00000i q^{32} +(6.23577 - 3.17728i) q^{34} +(1.13809 + 0.579885i) q^{35} +(7.84252 - 5.69793i) q^{37} +(2.46190 + 2.46190i) q^{38} -1.43953 q^{40} +(3.59523 - 5.29852i) q^{41} +(-11.8768 + 3.85901i) q^{43} +(-4.04020 - 4.04020i) q^{44} +(-2.62695 - 3.61569i) q^{46} +(-1.53521 - 0.782229i) q^{47} +(-3.65173 + 5.02617i) q^{49} +2.92774i q^{50} +(-0.835155 - 5.27296i) q^{52} +(0.911637 + 0.144389i) q^{53} +(5.81600 - 5.81600i) q^{55} +(-0.138805 + 0.876381i) q^{56} +(-4.45414 + 0.705466i) q^{58} +(-3.38300 - 10.4118i) q^{59} +(12.8112 + 4.16262i) q^{61} +(-0.662586 - 0.215287i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(7.59060 - 1.20223i) q^{65} +(2.20927 - 13.9488i) q^{67} +(-4.94874 + 4.94874i) q^{68} +(-1.26158 - 0.199815i) q^{70} +(-1.93701 - 12.2298i) q^{71} +10.3536i q^{73} +(-5.69793 + 7.84252i) q^{74} +(-3.10217 - 1.58063i) q^{76} +(-2.97995 - 4.10156i) q^{77} +(8.39002 + 8.39002i) q^{79} +(1.36908 - 0.444840i) q^{80} +(-1.78194 + 6.15018i) q^{82} +12.1920 q^{83} +(-7.12387 - 7.12387i) q^{85} +(10.1030 - 7.34026i) q^{86} +(5.09095 + 2.59397i) q^{88} +(-0.841889 + 0.428964i) q^{89} -4.73705i q^{91} +(3.61569 + 2.62695i) q^{92} +(1.70179 + 0.269538i) q^{94} +(2.27538 - 4.46568i) q^{95} +(0.0457970 - 0.289151i) q^{97} +(1.91983 - 5.90862i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4}+O(q^{10}) $ 24 * q + 6 * q^4	$ 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) $ 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.846136	+	1.16461i	0.378404	+	0.520828i	0.955161	−	0.296088i	$-0.0956821\pi$
$5$	0.846136	+	1.16461i	0.378404	+	0.520828i	−0.576757	+	0.816916i	$0.695682\pi$
$6$		0			0
$7$	0.790595	−	0.402828i	0.298817	−	0.152255i	−0.298154	−	0.954518i	$-0.596371\pi$
$7$	0.790595	−	0.402828i	0.298817	−	0.152255i	0.596971	+	0.802263i	$0.296371\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$		0			0
$10$	−1.16461	−	0.846136i	−0.368281	−	0.267572i
$11$	−0.893820	−	5.64336i	−0.269497	−	1.70154i	−0.636467	−	0.771304i	$-0.719605\pi$
$11$	−0.893820	−	5.64336i	−0.269497	−	1.70154i	0.366970	−	0.930233i	$-0.380395\pi$
$12$		0			0
$13$	2.42371	−	4.75681i	0.672217	−	1.31930i	−0.262852	−	0.964836i	$-0.584663\pi$
$13$	2.42371	−	4.75681i	0.672217	−	1.31930i	0.935069	−	0.354464i	$-0.115337\pi$
$14$	−0.627420	+	0.627420i	−0.167685	+	0.167685i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.91240	+	1.09482i	−1.67650	+	0.265532i	−0.920986	−	0.389595i	$-0.872615\pi$
$17$	−6.91240	+	1.09482i	−1.67650	+	0.265532i	−0.755518	+	0.655128i	$0.772615\pi$
$18$		0			0
$19$	−1.58063	−	3.10217i	−0.362622	−	0.711687i	0.635554	−	0.772057i	$-0.280772\pi$
$19$	−1.58063	−	3.10217i	−0.362622	−	0.711687i	−0.998176	+	0.0603701i	$0.980772\pi$
$20$	1.36908	+	0.444840i	0.306135	+	0.0994693i
$21$		0			0
$22$	2.59397	+	5.09095i	0.553036	+	1.08539i
$23$	1.38107	+	4.25050i	0.287973	+	0.886290i	0.985492	+	0.169723i	$0.0542874\pi$
$23$	1.38107	+	4.25050i	0.287973	+	0.886290i	−0.697519	+	0.716566i	$0.745713\pi$
$24$		0			0
$25$	0.904723	−	2.78445i	0.180945	−	0.556890i
$26$	−0.835155	+	5.27296i	−0.163787	+	1.03411i
$27$		0			0
$28$	0.402828	−	0.790595i	0.0761274	−	0.149408i
$29$	4.45414	+	0.705466i	0.827112	+	0.131002i	0.555617	−	0.831438i	$-0.312482\pi$
$29$	4.45414	+	0.705466i	0.827112	+	0.131002i	0.271495	+	0.962440i	$0.412482\pi$
$30$		0			0
$31$	0.563629	+	0.409501i	0.101231	+	0.0735485i	0.637249	−	0.770658i	$-0.280072\pi$
$31$	0.563629	+	0.409501i	0.101231	+	0.0735485i	−0.536018	+	0.844206i	$0.680072\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	6.23577	−	3.17728i	1.06943	−	0.544900i
$35$	1.13809	+	0.579885i	0.192372	+	0.0980184i
$36$		0			0
$37$	7.84252	−	5.69793i	1.28930	−	0.936733i	0.289512	−	0.957174i	$-0.406507\pi$
$37$	7.84252	−	5.69793i	1.28930	−	0.936733i	0.999791	+	0.0204413i	$0.00650711\pi$
$38$	2.46190	+	2.46190i	0.399372	+	0.399372i
$39$		0			0
$40$	−1.43953			−0.227610
$41$	3.59523	−	5.29852i	0.561481	−	0.827489i
$41$	3.59523	−	5.29852i	0.561481	−	0.827489i
$42$		0			0
$43$	−11.8768	+	3.85901i	−1.81119	+	0.588493i	−0.811201	+	0.584767i	$0.801186\pi$
$43$	−11.8768	+	3.85901i	−1.81119	+	0.588493i	−0.999993	+	0.00372596i	$0.998814\pi$
$44$	−4.04020	−	4.04020i	−0.609083	−	0.609083i
$45$		0			0
$46$	−2.62695	−	3.61569i	−0.387323	−	0.533104i
$47$	−1.53521	−	0.782229i	−0.223933	−	0.114100i	0.338425	−	0.940993i	$-0.390106\pi$
$47$	−1.53521	−	0.782229i	−0.223933	−	0.114100i	−0.562358	+	0.826894i	$0.690106\pi$
$48$		0			0
$49$	−3.65173	+	5.02617i	−0.521675	+	0.718024i
$50$			2.92774i			0.414045i
$51$		0			0
$52$	−0.835155	−	5.27296i	−0.115815	−	0.731228i
$53$	0.911637	+	0.144389i	0.125223	+	0.0198334i	0.218731	−	0.975785i	$-0.429808\pi$
$53$	0.911637	+	0.144389i	0.125223	+	0.0198334i	−0.0935084	+	0.995618i	$0.529808\pi$
$54$		0			0
$55$	5.81600	−	5.81600i	0.784230	−	0.784230i
$56$	−0.138805	+	0.876381i	−0.0185486	+	0.117111i
$57$		0			0
$58$	−4.45414	+	0.705466i	−0.584857	+	0.0926322i
$59$	−3.38300	−	10.4118i	−0.440429	−	1.35550i	−0.887420	−	0.460962i	$-0.847504\pi$
$59$	−3.38300	−	10.4118i	−0.440429	−	1.35550i	0.446991	−	0.894538i	$-0.352496\pi$
$60$		0			0
$61$	12.8112	+	4.16262i	1.64031	+	0.532969i	0.976608	−	0.215029i	$-0.0689847\pi$
$61$	12.8112	+	4.16262i	1.64031	+	0.532969i	0.663701	+	0.747998i	$0.268985\pi$
$62$	−0.662586	−	0.215287i	−0.0841485	−	0.0273415i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	7.59060	−	1.20223i	0.941498	−	0.149119i
$66$		0			0
$67$	2.20927	−	13.9488i	0.269905	−	1.70411i	−0.364574	−	0.931174i	$-0.618786\pi$
$67$	2.20927	−	13.9488i	0.269905	−	1.70411i	0.634480	−	0.772940i	$-0.281214\pi$
$68$	−4.94874	+	4.94874i	−0.600122	+	0.600122i
$69$		0			0
$70$	−1.26158	−	0.199815i	−0.150788	−	0.0238824i
$71$	−1.93701	−	12.2298i	−0.229881	−	1.45141i	−0.784925	−	0.619591i	$-0.787299\pi$
$71$	−1.93701	−	12.2298i	−0.229881	−	1.45141i	0.555044	−	0.831821i	$-0.312701\pi$
$72$		0			0
$73$			10.3536i			1.21180i	0.795541	+	0.605899i	$0.207187\pi$
$73$			10.3536i			1.21180i	−0.795541	+	0.605899i	$0.792813\pi$
$74$	−5.69793	+	7.84252i	−0.662370	+	0.911675i
$75$		0			0
$76$	−3.10217	−	1.58063i	−0.355843	−	0.181311i
$77$	−2.97995	−	4.10156i	−0.339597	−	0.467416i
$78$		0			0
$79$	8.39002	+	8.39002i	0.943951	+	0.943951i	0.998511	−	0.0545599i	$-0.0173756\pi$
$79$	8.39002	+	8.39002i	0.943951	+	0.943951i	−0.0545599	+	0.998511i	$0.517376\pi$
$80$	1.36908	−	0.444840i	0.153068	−	0.0497347i
$81$		0			0
$82$	−1.78194	+	6.15018i	−0.196782	+	0.679174i
$83$	12.1920			1.33824			0.669120	−	0.743154i	$-0.266671\pi$
$83$	12.1920			1.33824			0.669120	+	0.743154i	$0.266671\pi$
$84$		0			0
$85$	−7.12387	−	7.12387i	−0.772692	−	0.772692i
$86$	10.1030	−	7.34026i	1.08944	−	0.791521i
$87$		0			0
$88$	5.09095	+	2.59397i	0.542697	+	0.276518i
$89$	−0.841889	+	0.428964i	−0.0892400	+	0.0454701i	−0.498041	−	0.867154i	$-0.665947\pi$
$89$	−0.841889	+	0.428964i	−0.0892400	+	0.0454701i	0.408801	+	0.912624i	$0.365947\pi$
$90$		0			0
$91$		−	4.73705i		−	0.496578i
$92$	3.61569	+	2.62695i	0.376961	+	0.273879i
$93$		0			0
$94$	1.70179	+	0.269538i	0.175527	+	0.0278007i
$95$	2.27538	−	4.46568i	0.233449	−	0.458169i
$96$		0			0
$97$	0.0457970	−	0.289151i	0.00464998	−	0.0293588i	−0.985254	−	0.171097i	$-0.945269\pi$
$97$	0.0457970	−	0.289151i	0.00464998	−	0.0293588i	0.989904	+	0.141738i	$0.0452690\pi$
$98$	1.91983	−	5.90862i	0.193932	−	0.596861i
$99$		0			0
$100$	−0.904723	−	2.78445i	−0.0904723	−	0.278445i
$101$	1.24717	+	2.44771i	0.124098	+	0.243556i	0.944694	−	0.327952i	$-0.106358\pi$
$101$	1.24717	+	2.44771i	0.124098	+	0.243556i	−0.820596	+	0.571508i	$0.806358\pi$
$102$		0			0
$103$	4.87199	+	1.58301i	0.480052	+	0.155978i	0.539040	−	0.842280i	$-0.318787\pi$
$103$	4.87199	+	1.58301i	0.480052	+	0.155978i	−0.0589878	+	0.998259i	$0.518787\pi$
$104$	2.42371	+	4.75681i	0.237665	+	0.466443i
$105$		0			0
$106$	−0.911637	+	0.144389i	−0.0885460	+	0.0140243i
$107$	0.889379	−	2.73723i	0.0859795	−	0.264618i	−0.898819	−	0.438321i	$-0.855573\pi$
$107$	0.889379	−	2.73723i	0.0859795	−	0.264618i	0.984798	+	0.173703i	$0.0555733\pi$
$108$		0			0
$109$	−8.16258	+	8.16258i	−0.781833	+	0.781833i	−0.980140	−	0.198307i	$-0.936456\pi$
$109$	−8.16258	+	8.16258i	−0.781833	+	0.781833i	0.198307	+	0.980140i	$0.436456\pi$
$110$	−3.73410	+	7.32859i	−0.356033	+	0.698754i
$111$		0			0
$112$	−0.138805	−	0.876381i	−0.0131159	−	0.0828103i
$113$	7.75953	+	5.63763i	0.729955	+	0.530343i	0.889549	−	0.456839i	$-0.151019\pi$
$113$	7.75953	+	5.63763i	0.729955	+	0.530343i	−0.159594	+	0.987183i	$0.551019\pi$
$114$		0			0
$115$	−3.78158	+	5.20490i	−0.352634	+	0.485360i
$116$	4.01813	−	2.04734i	0.373074	−	0.190091i
$117$		0			0
$118$	6.43484	+	8.85680i	0.592375	+	0.815335i
$119$	−5.02389	+	3.65007i	−0.460539	+	0.334601i
$120$		0			0
$121$	−20.5870	+	6.68911i	−1.87154	+	0.608101i
$122$	−13.4705			−1.21956
$123$		0			0
$124$	0.696684			0.0625641
$125$	10.8537	−	3.52658i	0.970784	−	0.315427i
$126$		0			0
$127$	−9.71963	+	7.06173i	−0.862478	+	0.626627i	−0.928558	−	0.371187i	$-0.878951\pi$
$127$	−9.71963	+	7.06173i	−0.862478	+	0.626627i	0.0660800	+	0.997814i	$0.478951\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$		0			0
$130$	−6.84758	+	3.48902i	−0.600573	+	0.306007i
$131$	−2.56863	+	3.53541i	−0.224422	+	0.308890i	−0.906349	−	0.422530i	$-0.861142\pi$
$131$	−2.56863	+	3.53541i	−0.224422	+	0.308890i	0.681927	+	0.731420i	$0.261142\pi$
$132$		0			0
$133$	−2.49928	−	1.81584i	−0.216715	−	0.157453i
$134$	2.20927	+	13.9488i	0.190852	+	1.20499i
$135$		0			0
$136$	3.17728	−	6.23577i	0.272450	−	0.534713i
$137$	−9.96448	+	9.96448i	−0.851323	+	0.851323i	−0.990296	−	0.138973i	$-0.955620\pi$
$137$	−9.96448	+	9.96448i	−0.851323	+	0.851323i	0.138973	+	0.990296i	$0.455620\pi$
$138$		0			0
$139$	−1.67948	+	5.16891i	−0.142452	+	0.438421i	−0.996675	−	0.0814858i	$-0.974033\pi$
$139$	−1.67948	+	5.16891i	−0.142452	+	0.438421i	0.854223	+	0.519907i	$0.174033\pi$
$140$	1.26158	−	0.199815i	0.106623	−	0.0168874i
$141$		0			0
$142$	5.62143	+	11.0327i	0.471740	+	0.925841i
$143$	−29.0107	−	9.42616i	−2.42600	−	0.788255i
$144$		0			0
$145$	2.94722	+	5.78424i	0.244753	+	0.480355i
$146$	−3.19944	−	9.84687i	−0.264788	−	0.814933i
$147$		0			0
$148$	2.99558	−	9.21944i	0.246235	−	0.757833i
$149$	1.47039	−	9.28367i	0.120459	−	0.760548i	−0.851319	−	0.524649i	$-0.824197\pi$
$149$	1.47039	−	9.28367i	0.120459	−	0.760548i	0.971778	−	0.235899i	$-0.0758034\pi$
$150$		0			0
$151$	1.55451	−	3.05089i	0.126504	−	0.248278i	−0.819064	−	0.573702i	$-0.805507\pi$
$151$	1.55451	−	3.05089i	0.126504	−	0.248278i	0.945568	+	0.325424i	$0.105507\pi$
$152$	3.43878	+	0.544650i	0.278922	+	0.0441769i
$153$		0			0
$154$	4.10156	+	2.97995i	0.330513	+	0.240132i
$155$			1.00290i			0.0805548i
$156$		0			0
$157$	4.56140	−	2.32415i	0.364039	−	0.185487i	−0.262397	−	0.964960i	$-0.584513\pi$
$157$	4.56140	−	2.32415i	0.364039	−	0.185487i	0.626436	+	0.779473i	$0.284513\pi$
$158$	−10.5720	−	5.38672i	−0.841066	−	0.428545i
$159$		0			0
$160$	−1.16461	+	0.846136i	−0.0920703	+	0.0668930i
$161$	2.80409	+	2.80409i	0.220993	+	0.220993i
$162$		0			0
$163$	−0.387993			−0.0303899			−0.0151950	−	0.999885i	$-0.504837\pi$
$163$	−0.387993			−0.0303899			−0.0151950	+	0.999885i	$0.504837\pi$
$164$	−0.205785	−	6.39982i	−0.0160691	−	0.499742i
$165$		0			0
$166$	−11.5952	+	3.76752i	−0.899965	+	0.292416i
$167$	6.00649	+	6.00649i	0.464796	+	0.464796i	0.900224	−	0.435427i	$-0.143403\pi$
$167$	6.00649	+	6.00649i	0.464796	+	0.464796i	−0.435427	+	0.900224i	$0.643403\pi$
$168$		0			0
$169$	−9.11160	−	12.5410i	−0.700893	−	0.964696i
$170$	8.97660	+	4.57381i	0.688474	+	0.350795i
$171$		0			0
$172$	−7.34026	+	10.1030i	−0.559690	+	0.770347i
$173$			22.2430i			1.69111i	0.533891	+	0.845553i	$0.320729\pi$
$173$			22.2430i			1.69111i	−0.533891	+	0.845553i	$0.679271\pi$
$174$		0			0
$175$	−0.406386	−	2.56582i	−0.0307199	−	0.193958i
$176$	−5.64336	−	0.893820i	−0.425384	−	0.0673742i
$177$		0			0
$178$	0.668127	−	0.668127i	0.0500782	−	0.0500782i
$179$	1.69137	−	10.6789i	0.126419	−	0.798176i	−0.840260	−	0.542184i	$-0.817598\pi$
$179$	1.69137	−	10.6789i	0.126419	−	0.798176i	0.966679	−	0.255993i	$-0.0824023\pi$
$180$		0			0
$181$	−16.4597	+	2.60697i	−1.22344	+	0.193774i	−0.734541	−	0.678565i	$-0.762602\pi$
$181$	−16.4597	+	2.60697i	−1.22344	+	0.193774i	−0.488902	+	0.872339i	$0.662602\pi$
$182$	1.46383	+	4.50520i	0.108506	+	0.333948i
$183$		0			0
$184$	−4.25050	−	1.38107i	−0.313351	−	0.101814i
$185$	13.2717	+	4.31223i	0.975754	+	0.317042i
$186$		0			0
$187$	12.3569	+	38.0306i	0.903626	+	2.78107i
$188$	−1.70179	+	0.269538i	−0.124116	+	0.0196581i
$189$		0			0
$190$	−0.784041	+	4.95024i	−0.0568803	+	0.359128i
$191$	8.24003	−	8.24003i	0.596228	−	0.596228i	−0.343079	−	0.939307i	$-0.611470\pi$
$191$	8.24003	−	8.24003i	0.596228	−	0.596228i	0.939307	+	0.343079i	$0.111470\pi$
$192$		0			0
$193$	3.03339	+	0.480441i	0.218348	+	0.0345829i	0.264650	−	0.964345i	$-0.414744\pi$
$193$	3.03339	+	0.480441i	0.218348	+	0.0345829i	−0.0463019	+	0.998927i	$0.514744\pi$
$194$	0.0457970	+	0.289151i	0.00328804	+	0.0207598i
$195$		0			0
$196$			6.21269i			0.443763i
$197$	−3.12304	+	4.29849i	−0.222507	+	0.306255i	−0.905647	−	0.424033i	$-0.860614\pi$
$197$	−3.12304	+	4.29849i	−0.222507	+	0.306255i	0.683140	+	0.730288i	$0.260614\pi$
$198$		0			0
$199$	−3.96702	−	2.02130i	−0.281215	−	0.143286i	0.307695	−	0.951485i	$-0.400442\pi$
$199$	−3.96702	−	2.02130i	−0.281215	−	0.143286i	−0.588909	+	0.808199i	$0.700442\pi$
$200$	1.72088	+	2.36859i	0.121685	+	0.167485i
$201$		0			0
$202$	−1.94251	−	1.94251i	−0.136675	−	0.136675i
$203$	3.80560	−	1.23651i	0.267101	−	0.0867863i
$204$		0			0
$205$	9.21275	−	0.296234i	0.643446	−	0.0206899i
$206$	−5.12272			−0.356917
$207$		0			0
$208$	−3.77502	−	3.77502i	−0.261751	−	0.261751i
$209$	−16.0939	+	11.6929i	−1.11324	+	0.808813i
$210$		0			0
$211$	−3.72596	−	1.89847i	−0.256506	−	0.130696i	0.321010	−	0.947076i	$-0.395978\pi$
$211$	−3.72596	−	1.89847i	−0.256506	−	0.130696i	−0.577516	+	0.816380i	$0.695978\pi$
$212$	0.822399	−	0.419033i	0.0564826	−	0.0287793i
$213$		0			0
$214$			2.87809i			0.196742i
$215$	−14.5436	−	10.5666i	−0.991866	−	0.720633i
$216$		0			0
$217$	0.610561	+	0.0967033i	0.0414476	+	0.00656465i
$218$	5.24070	−	10.2855i	0.354945	−	0.696619i
$219$		0			0
$220$	1.28668	−	8.12380i	0.0867482	−	0.547707i
$221$	−11.5459	+	35.5345i	−0.776658	+	2.39031i
$222$		0			0
$223$	3.14137	+	9.66814i	0.210362	+	0.647426i	0.999450	+	0.0331473i	$0.0105530\pi$
$223$	3.14137	+	9.66814i	0.210362	+	0.647426i	−0.789089	+	0.614279i	$0.789447\pi$
$224$	0.402828	+	0.790595i	0.0269151	+	0.0528239i
$225$		0			0
$226$	−9.12187	−	2.96388i	−0.606778	−	0.197154i
$227$	1.57821	+	3.09741i	0.104749	+	0.205582i	0.937432	−	0.348168i	$-0.113196\pi$
$227$	1.57821	+	3.09741i	0.104749	+	0.205582i	−0.832683	+	0.553750i	$0.813196\pi$
$228$		0			0
$229$	−22.1550	+	3.50900i	−1.46404	+	0.231881i	−0.837042	−	0.547138i	$-0.815717\pi$
$229$	−22.1550	+	3.50900i	−1.46404	+	0.231881i	−0.626999	+	0.779020i	$0.715717\pi$
$230$	1.98810	−	6.11873i	0.131091	−	0.403457i
$231$		0			0
$232$	−3.18881	+	3.18881i	−0.209356	+	0.209356i
$233$	−5.97422	+	11.7251i	−0.391384	+	0.768134i	−0.999673	−	0.0255816i	$-0.991856\pi$
$233$	−5.97422	+	11.7251i	−0.391384	+	0.768134i	0.608289	+	0.793716i	$0.291856\pi$
$234$		0			0
$235$	−0.388009	−	2.44979i	−0.0253109	−	0.159807i
$236$	−8.85680	−	6.43484i	−0.576529	−	0.418873i
$237$		0			0
$238$	3.65007	−	5.02389i	0.236599	−	0.325650i
$239$	5.14915	−	2.62362i	0.333071	−	0.169708i	−0.279455	−	0.960159i	$-0.590154\pi$
$239$	5.14915	−	2.62362i	0.333071	−	0.169708i	0.612526	+	0.790451i	$0.290154\pi$
$240$		0			0
$241$	4.55085	+	6.26371i	0.293146	+	0.403481i	0.930033	−	0.367476i	$-0.119778\pi$
$241$	4.55085	+	6.26371i	0.293146	+	0.403481i	−0.636887	+	0.770957i	$0.719778\pi$
$242$	17.5123	−	12.7234i	1.12573	−	0.817894i
$243$		0			0
$244$	12.8112	−	4.16262i	0.820154	−	0.266484i
$245$	−8.94337			−0.571371
$246$		0			0
$247$	−18.5874			−1.18269
$248$	−0.662586	+	0.215287i	−0.0420742	+	0.0136707i
$249$		0			0
$250$	−9.23271	+	6.70795i	−0.583928	+	0.424248i
$251$	−13.1223	−	18.0613i	−0.828273	−	1.14002i	−0.988242	−	0.152898i	$-0.951139\pi$
$251$	−13.1223	−	18.0613i	−0.828273	−	1.14002i	0.159969	−	0.987122i	$-0.448861\pi$
$252$		0			0
$253$	22.7526	−	11.5931i	1.43045	−	0.728849i
$254$	7.06173	−	9.71963i	0.443092	−	0.609864i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.60599	−	29.0811i	−0.287314	−	1.81403i	−0.534623	−	0.845091i	$-0.679546\pi$
$257$	−4.60599	−	29.0811i	−0.287314	−	1.81403i	0.247309	−	0.968937i	$-0.420454\pi$
$258$		0			0
$259$	3.90497	−	7.66394i	0.242643	−	0.476214i
$260$	5.43427	−	5.43427i	0.337019	−	0.337019i
$261$		0			0
$262$	1.35041	−	4.15613i	0.0834284	−	0.256766i
$263$	2.64972	−	0.419674i	0.163389	−	0.0258782i	−0.0742041	−	0.997243i	$-0.523642\pi$
$263$	2.64972	−	0.419674i	0.163389	−	0.0258782i	0.237593	+	0.971365i	$0.423642\pi$
$264$		0			0
$265$	0.603213	+	1.18387i	0.0370551	+	0.0727246i
$266$	2.93808	+	0.954641i	0.180146	+	0.0585328i
$267$		0			0
$268$	−6.41155	−	12.5834i	−0.391648	−	0.768652i
$269$	5.93792	+	18.2750i	0.362041	+	1.11425i	0.951813	+	0.306679i	$0.0992177\pi$
$269$	5.93792	+	18.2750i	0.362041	+	1.11425i	−0.589772	+	0.807570i	$0.700782\pi$
$270$		0			0
$271$	4.71424	−	14.5089i	0.286369	−	0.881354i	−0.699615	−	0.714520i	$-0.746645\pi$
$271$	4.71424	−	14.5089i	0.286369	−	0.881354i	0.985985	−	0.166835i	$-0.0533547\pi$
$272$	−1.09482	+	6.91240i	−0.0663831	+	0.419126i
$273$		0			0
$274$	6.39759	−	12.5560i	0.386493	−	0.758534i
$275$	−16.5223	−	2.61688i	−0.996333	−	0.157804i
$276$		0			0
$277$	19.8093	+	14.3923i	1.19022	+	0.864747i	0.993288	−	0.115669i	$-0.0369013\pi$
$277$	19.8093	+	14.3923i	1.19022	+	0.864747i	0.196935	+	0.980417i	$0.436901\pi$
$278$		−	5.43492i		−	0.325965i
$279$		0			0
$280$	−1.13809	+	0.579885i	−0.0680138	+	0.0346547i
$281$	13.9568	+	7.11133i	0.832592	+	0.424227i	0.817688	−	0.575662i	$-0.195256\pi$
$281$	13.9568	+	7.11133i	0.832592	+	0.424227i	0.0149041	+	0.999889i	$0.495256\pi$
$282$		0			0
$283$	−15.6965	+	11.4042i	−0.933060	+	0.677908i	−0.946740	−	0.321998i	$-0.895645\pi$
$283$	−15.6965	+	11.4042i	−0.933060	+	0.677908i	0.0136798	+	0.999906i	$0.495645\pi$
$284$	−8.75558	−	8.75558i	−0.519548	−	0.519548i
$285$		0			0
$286$	30.5037			1.80372
$287$	0.707982	−	5.63724i	0.0417908	−	0.332756i
$288$		0			0
$289$	30.4148	−	9.88235i	1.78910	−	0.581315i
$290$	−4.59040	−	4.59040i	−0.269557	−	0.269557i
$291$		0			0
$292$	6.08570	+	8.37625i	0.356139	+	0.490183i
$293$	6.94136	+	3.53680i	0.405518	+	0.206622i	0.644839	−	0.764319i	$-0.276925\pi$
$293$	6.94136	+	3.53680i	0.405518	+	0.206622i	−0.239320	+	0.970941i	$0.576925\pi$
$294$		0			0
$295$	9.26317	−	12.7497i	0.539323	−	0.742314i
$296$			9.69389i			0.563446i
$297$		0			0
$298$	1.47039	+	9.28367i	0.0851773	+	0.537788i
$299$	23.5661	+	3.73250i	1.36286	+	0.215856i
$300$		0			0
$301$	−7.83522	+	7.83522i	−0.451615	+	0.451615i
$302$	−0.535646	+	3.38194i	−0.0308230	+	0.194609i
$303$		0			0
$304$	−3.43878	+	0.544650i	−0.197228	+	0.0312378i
$305$	5.99223	+	18.4422i	0.343114	+	1.05600i
$306$		0			0
$307$	5.01133	+	1.62828i	0.286012	+	0.0929308i	0.448509	−	0.893778i	$-0.351955\pi$
$307$	5.01133	+	1.62828i	0.286012	+	0.0929308i	−0.162498	+	0.986709i	$0.551955\pi$
$308$	−4.82167	−	1.56666i	−0.274740	−	0.0892685i
$309$		0			0
$310$	−0.309913	−	0.953814i	−0.0176019	−	0.0541730i
$311$	−16.6566	+	2.63814i	−0.944507	+	0.149595i	−0.609647	−	0.792673i	$-0.708689\pi$
$311$	−16.6566	+	2.63814i	−0.944507	+	0.149595i	−0.334860	+	0.942268i	$0.608689\pi$
$312$		0			0
$313$	1.15232	−	7.27549i	0.0651332	−	0.411235i	−0.933482	−	0.358624i	$-0.883246\pi$
$313$	1.15232	−	7.27549i	0.0651332	−	0.411235i	0.998615	−	0.0526103i	$-0.0167541\pi$
$314$	−3.61995	+	3.61995i	−0.204286	+	0.204286i
$315$		0			0
$316$	11.7192	+	1.85614i	0.659256	+	0.104416i
$317$	0.181174	+	1.14389i	0.0101757	+	0.0642471i	0.992254	−	0.124228i	$-0.0396455\pi$
$317$	0.181174	+	1.14389i	0.0101757	+	0.0642471i	−0.982078	+	0.188475i	$0.939645\pi$
$318$		0			0
$319$		−	25.7669i		−	1.44267i
$320$	0.846136	−	1.16461i	0.0473005	−	0.0651035i
$321$		0			0
$322$	−3.53336	−	1.80033i	−0.196906	−	0.100329i
$323$	14.3223	+	19.7129i	0.796914	+	1.09686i
$324$		0			0
$325$	−11.0523	−	11.0523i	−0.613071	−	0.613071i
$326$	0.369003	−	0.119896i	0.0204372	−	0.00664045i
$327$		0			0
$328$	2.17336	+	6.02300i	0.120004	+	0.332564i
$329$	−1.52883			−0.0842873
$330$		0			0
$331$	−14.2677	−	14.2677i	−0.784224	−	0.784224i	0.196317	−	0.980541i	$-0.437102\pi$
$331$	−14.2677	−	14.2677i	−0.784224	−	0.784224i	−0.980541	+	0.196317i	$0.937102\pi$
$332$	9.86349	−	7.16625i	0.541330	−	0.393299i
$333$		0			0
$334$	−7.56862	−	3.85641i	−0.414137	−	0.211013i
$335$	18.1142	−	9.22964i	0.989683	−	0.504269i
$336$		0			0
$337$		−	10.9837i		−	0.598319i	−0.954203	−	0.299160i	$-0.903294\pi$
$337$		−	10.9837i		−	0.598319i	0.954203	−	0.299160i	$-0.0967063\pi$
$338$	12.5410	+	9.11160i	0.682143	+	0.495606i
$339$		0			0
$340$	−9.95064	−	1.57603i	−0.539649	−	0.0854720i
$341$	1.80718	−	3.54678i	0.0978640	−	0.192069i
$342$		0			0
$343$	−1.83399	+	11.5794i	−0.0990261	+	0.625226i
$344$	3.85901	−	11.8768i	0.208064	−	0.640354i
$345$		0			0
$346$	−6.87348	−	21.1544i	−0.369520	−	1.13727i
$347$	15.8032	+	31.0156i	0.848361	+	1.66500i	0.741724	+	0.670705i	$0.234008\pi$
$347$	15.8032	+	31.0156i	0.848361	+	1.66500i	0.106637	+	0.994298i	$0.465992\pi$
$348$		0			0
$349$	−3.17427	−	1.03138i	−0.169915	−	0.0552086i	0.222824	−	0.974859i	$-0.428472\pi$
$349$	−3.17427	−	1.03138i	−0.169915	−	0.0552086i	−0.392739	+	0.919650i	$0.628472\pi$
$350$	1.17938	+	2.31466i	0.0630404	+	0.123724i
$351$		0			0
$352$	5.64336	−	0.893820i	0.300792	−	0.0476408i
$353$	3.43437	−	10.5699i	0.182793	−	0.562580i	−0.817110	−	0.576482i	$-0.804425\pi$
$353$	3.43437	−	10.5699i	0.182793	−	0.562580i	0.999903	+	0.0139018i	$0.00442521\pi$
$354$		0			0
$355$	12.6039	−	12.6039i	0.668948	−	0.668948i
$356$	−0.428964	+	0.841889i	−0.0227350	+	0.0446200i
$357$		0			0
$358$	1.69137	+	10.6789i	0.0893915	+	0.564396i
$359$	−9.80178	−	7.12141i	−0.517318	−	0.375854i	0.298275	−	0.954480i	$-0.403589\pi$
$359$	−9.80178	−	7.12141i	−0.517318	−	0.375854i	−0.815593	+	0.578627i	$0.803589\pi$
$360$		0			0
$361$	4.04287	−	5.56453i	0.212782	−	0.292870i
$362$	14.8485	−	7.56571i	0.780422	−	0.397645i
$363$		0			0
$364$	−2.78437	−	3.83235i	−0.145940	−	0.200870i
$365$	−12.0579	+	8.76057i	−0.631139	+	0.458549i
$366$		0			0
$367$	17.0683	−	5.54583i	0.890958	−	0.289490i	0.172458	−	0.985017i	$-0.444829\pi$
$367$	17.0683	−	5.54583i	0.890958	−	0.289490i	0.718500	+	0.695527i	$0.244829\pi$
$368$	4.46924			0.232975
$369$		0			0
$370$	−13.9547			−0.725469
$371$	0.778899	−	0.253080i	0.0404384	−	0.0131392i
$372$		0			0
$373$	2.77571	−	2.01667i	0.143721	−	0.104419i	−0.513601	−	0.858029i	$-0.671689\pi$
$373$	2.77571	−	2.01667i	0.143721	−	0.104419i	0.657322	+	0.753610i	$0.271689\pi$
$374$	−23.5042	−	32.3508i	−1.21537	−	1.67282i
$375$		0			0
$376$	1.53521	−	0.782229i	0.0791724	−	0.0403404i
$377$	14.1513	−	19.4776i	0.728830	−	1.00315i
$378$		0			0
$379$	26.8692	+	19.5216i	1.38018	+	1.00276i	0.996864	+	0.0791397i	$0.0252173\pi$
$379$	26.8692	+	19.5216i	1.38018	+	1.00276i	0.383314	+	0.923618i	$0.374783\pi$
$380$	−0.784041	−	4.95024i	−0.0402205	−	0.253942i
$381$		0			0
$382$	−5.29043	+	10.3830i	−0.270682	+	0.531243i
$383$	4.32953	−	4.32953i	0.221228	−	0.221228i	−0.587787	−	0.809016i	$-0.700001\pi$
$383$	4.32953	−	4.32953i	0.221228	−	0.221228i	0.809016	+	0.587787i	$0.200001\pi$
$384$		0			0
$385$	2.25525	−	6.94095i	0.114938	−	0.353744i
$386$	−3.03339	+	0.480441i	−0.154395	+	0.0244538i
$387$		0			0
$388$	−0.132908	−	0.260847i	−0.00674739	−	0.0132425i
$389$	29.9212	+	9.72199i	1.51707	+	0.492924i	0.944941	−	0.327242i	$-0.106119\pi$
$389$	29.9212	+	9.72199i	1.51707	+	0.492924i	0.572125	+	0.820167i	$0.306119\pi$
$390$		0			0
$391$	−14.2000	−	27.8691i	−0.718126	−	1.40940i
$392$	−1.91983	−	5.90862i	−0.0969659	−	0.298430i
$393$		0			0
$394$	1.64188	−	5.05318i	0.0827166	−	0.254575i
$395$	−2.67197	+	16.8702i	−0.134442	+	0.848830i
$396$		0			0
$397$	−14.9392	+	29.3197i	−0.749774	+	1.47152i	0.127660	+	0.991818i	$0.459253\pi$
$397$	−14.9392	+	29.3197i	−0.749774	+	1.47152i	−0.877434	+	0.479697i	$0.840747\pi$
$398$	4.39748	+	0.696492i	0.220426	+	0.0349120i
$399$		0			0
$400$	−2.36859	−	1.72088i	−0.118430	−	0.0860442i
$401$			1.47694i			0.0737549i	0.999320	+	0.0368775i	$0.0117411\pi$
$401$			1.47694i			0.0737549i	−0.999320	+	0.0368775i	$0.988259\pi$
$402$		0			0
$403$	3.31399	−	1.68856i	0.165082	−	0.0841133i
$404$	2.44771	+	1.24717i	0.121778	+	0.0620490i
$405$		0			0
$406$	−3.23724	+	2.35199i	−0.160661	+	0.116727i
$407$	−39.1653	−	39.1653i	−1.94135	−	1.94135i
$408$		0			0
$409$	3.88842			0.192270			0.0961350	−	0.995368i	$-0.469352\pi$
$409$	3.88842			0.192270			0.0961350	+	0.995368i	$0.469352\pi$
$410$	−8.67030	+	3.12863i	−0.428196	+	0.154512i
$411$		0			0
$412$	4.87199	−	1.58301i	0.240026	−	0.0779891i
$413$	−6.86875	−	6.86875i	−0.337989	−	0.337989i
$414$		0			0
$415$	10.3161	+	14.1988i	0.506395	+	0.696993i
$416$	4.75681	+	2.42371i	0.233222	+	0.118832i
$417$		0			0
$418$	11.6929	−	16.0939i	0.571917	−	0.787176i
$419$		−	14.8830i		−	0.727082i	−0.931578	−	0.363541i	$-0.881568\pi$
$419$		−	14.8830i		−	0.727082i	0.931578	−	0.363541i	$-0.118432\pi$
$420$		0			0
$421$	−1.78083	−	11.2437i	−0.0867924	−	0.547986i	−0.992320	−	0.123698i	$-0.960525\pi$
$421$	−1.78083	−	11.2437i	−0.0867924	−	0.547986i	0.905528	−	0.424288i	$-0.139475\pi$
$422$	4.13026	+	0.654169i	0.201058	+	0.0318444i
$423$		0			0
$424$	−0.652660	+	0.652660i	−0.0316960	+	0.0316960i
$425$	−3.20534	+	20.2377i	−0.155482	+	0.981675i
$426$		0			0
$427$	11.8053	−	1.86978i	0.571299	−	0.0904849i
$428$	−0.889379	−	2.73723i	−0.0429897	−	0.132309i
$429$		0			0
$430$	17.0970	+	5.55517i	0.824493	+	0.267894i
$431$	−36.2549	−	11.7799i	−1.74634	−	0.567419i	−0.750692	−	0.660652i	$-0.770280\pi$
$431$	−36.2549	−	11.7799i	−1.74634	−	0.567419i	−0.995644	+	0.0932334i	$0.970280\pi$
$432$		0			0
$433$	0.361107	+	1.11137i	0.0173537	+	0.0534092i	0.959358	−	0.282191i	$-0.0910610\pi$
$433$	0.361107	+	1.11137i	0.0173537	+	0.0534092i	−0.942005	+	0.335600i	$0.891061\pi$
$434$	−0.610561	+	0.0967033i	−0.0293079	+	0.00464191i
$435$		0			0
$436$	−1.80582	+	11.4015i	−0.0864832	+	0.546033i
$437$	11.0028	−	11.0028i	0.526335	−	0.526335i
$438$		0			0
$439$	33.0879	+	5.24060i	1.57920	+	0.250120i	0.883576	−	0.468288i	$-0.155129\pi$
$439$	33.0879	+	5.24060i	1.57920	+	0.250120i	0.695622	+	0.718408i	$0.255129\pi$
$440$	1.28668	+	8.12380i	0.0613403	+	0.387287i
$441$		0			0
$442$		−	37.3632i		−	1.77718i
$443$	−12.1480	+	16.7203i	−0.577170	+	0.794406i	−0.993381	−	0.114862i	$-0.963357\pi$
$443$	−12.1480	+	16.7203i	−0.577170	+	0.794406i	0.416212	+	0.909268i	$0.363357\pi$
$444$		0			0
$445$	−1.21193	−	0.617508i	−0.0574508	−	0.0292727i
$446$	−5.97524	−	8.22421i	−0.282936	−	0.389428i
$447$		0			0
$448$	−0.627420	−	0.627420i	−0.0296428	−	0.0296428i
$449$	−18.7157	+	6.08109i	−0.883248	+	0.286985i	−0.715305	−	0.698812i	$-0.753712\pi$
$449$	−18.7157	+	6.08109i	−0.883248	+	0.286985i	−0.167943	+	0.985797i	$0.553712\pi$
$450$		0			0
$451$	−33.1149	−	15.5533i	−1.55932	−	0.732375i
$452$	9.59130			0.451137
$453$		0			0
$454$	−2.45812	−	2.45812i	−0.115365	−	0.115365i
$455$	5.51680	−	4.00819i	0.258632	−	0.187907i
$456$		0			0
$457$	8.59021	+	4.37693i	0.401833	+	0.204744i	0.643214	−	0.765686i	$-0.277600\pi$
$457$	8.59021	+	4.37693i	0.401833	+	0.204744i	−0.241381	+	0.970430i	$0.577600\pi$
$458$	19.9863	−	10.1835i	0.933898	−	0.475845i
$459$		0			0
$460$			6.43361i			0.299969i
$461$	−21.7334	−	15.7902i	−1.01223	−	0.735425i	−0.0475506	−	0.998869i	$-0.515142\pi$
$461$	−21.7334	−	15.7902i	−1.01223	−	0.735425i	−0.964675	+	0.263444i	$0.915142\pi$
$462$		0			0
$463$	−18.6786	−	2.95841i	−0.868070	−	0.137489i	−0.293515	−	0.955954i	$-0.594825\pi$
$463$	−18.6786	−	2.95841i	−0.868070	−	0.137489i	−0.574556	+	0.818466i	$0.694825\pi$
$464$	2.04734	−	4.01813i	0.0950455	−	0.186537i
$465$		0			0
$466$	2.05857	−	12.9973i	0.0953616	−	0.602090i
$467$	−1.76825	+	5.44211i	−0.0818248	+	0.251831i	−0.983597	−	0.180381i	$-0.942267\pi$
$467$	−1.76825	+	5.44211i	−0.0818248	+	0.251831i	0.901772	+	0.432212i	$0.142267\pi$
$468$		0			0
$469$	−3.87232	−	11.9178i	−0.178807	−	0.550312i
$470$	1.12604	+	2.20999i	0.0519406	+	0.101939i
$471$		0			0
$472$	10.4118	+	3.38300i	0.479242	+	0.155715i
$473$	32.3935	+	63.5758i	1.48945	+	2.92322i
$474$		0			0
$475$	−10.0679	+	1.59459i	−0.461946	+	0.0731650i
$476$	−1.91896	+	5.90594i	−0.0879552	+	0.270698i
$477$		0			0
$478$	−4.08639	+	4.08639i	−0.186907	+	0.186907i
$479$	−6.40032	+	12.5613i	−0.292438	+	0.573942i	−0.989747	−	0.142828i	$-0.954380\pi$
$479$	−6.40032	+	12.5613i	−0.292438	+	0.573942i	0.697310	+	0.716770i	$0.254380\pi$
$480$		0			0
$481$	−8.09590	−	51.1155i	−0.369141	−	2.33067i
$482$	−6.26371	−	4.55085i	−0.285304	−	0.207286i
$483$		0			0
$484$	−12.7234	+	17.5123i	−0.578339	+	0.796015i
$485$	0.375498	−	0.191326i	0.0170505	−	0.00868765i
$486$		0			0
$487$	0.0646026	+	0.0889178i	0.00292742	+	0.00402925i	0.810478	−	0.585769i	$-0.199207\pi$
$487$	0.0646026	+	0.0889178i	0.00292742	+	0.00402925i	−0.807551	+	0.589798i	$0.799207\pi$
$488$	−10.8979	+	7.91777i	−0.493324	+	0.358421i
$489$		0			0
$490$	8.50565	−	2.76365i	0.384246	−	0.124849i
$491$	0.236875			0.0106900			0.00534502	−	0.999986i	$-0.498299\pi$
$491$	0.236875			0.0106900			0.00534502	+	0.999986i	$0.498299\pi$
$492$		0			0
$493$	−31.5612			−1.42144
$494$	17.6777	−	5.74383i	0.795357	−	0.258427i
$495$		0			0
$496$	0.563629	−	0.409501i	0.0253077	−	0.0183871i
$497$	−6.45791	−	8.88855i	−0.289677	−	0.398706i
$498$		0			0
$499$	20.4628	−	10.4263i	0.916039	−	0.466745i	0.0686040	−	0.997644i	$-0.478146\pi$
$499$	20.4628	−	10.4263i	0.916039	−	0.466745i	0.847435	+	0.530899i	$0.178146\pi$
$500$	6.70795	−	9.23271i	0.299989	−	0.412899i
$501$		0			0
$502$	18.0613	+	13.1223i	0.806116	+	0.585677i
$503$	−0.534822	−	3.37673i	−0.0238465	−	0.150561i	0.972892	−	0.231260i	$-0.0742848\pi$
$503$	−0.534822	−	3.37673i	−0.0238465	−	0.150561i	−0.996739	+	0.0806989i	$0.974285\pi$
$504$		0			0
$505$	−1.79534	+	3.52356i	−0.0798917	+	0.156796i
$506$	−18.0566	+	18.0566i	−0.802714	+	0.802714i
$507$		0			0
$508$	−3.71257	+	11.4261i	−0.164719	+	0.506952i
$509$	29.7901	−	4.71828i	1.32042	−	0.209134i	0.543860	−	0.839176i	$-0.316962\pi$
$509$	29.7901	−	4.71828i	1.32042	−	0.209134i	0.776561	+	0.630042i	$0.216962\pi$
$510$		0			0
$511$	4.17073	+	8.18551i	0.184502	+	0.362106i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$		0			0
$514$	13.3671	+	26.2344i	0.589598	+	1.15715i
$515$	2.27879	+	7.01340i	0.100416	+	0.309047i
$516$		0			0
$517$	−3.04220	+	9.36292i	−0.133796	+	0.411781i
$518$	−1.34556	+	8.49555i	−0.0591206	+	0.373273i
$519$		0			0
$520$	−3.48902	+	6.84758i	−0.153003	+	0.300286i
$521$	−8.22561	−	1.30281i	−0.360370	−	0.0570771i	−0.0263759	−	0.999652i	$-0.508397\pi$
$521$	−8.22561	−	1.30281i	−0.360370	−	0.0570771i	−0.333994	+	0.942575i	$0.608397\pi$
$522$		0			0
$523$	13.4663	+	9.78383i	0.588840	+	0.427817i	0.841900	−	0.539633i	$-0.181437\pi$
$523$	13.4663	+	9.78383i	0.588840	+	0.427817i	−0.253060	+	0.967450i	$0.581437\pi$
$524$			4.37001i			0.190905i
$525$		0			0
$526$	−2.39035	+	1.21794i	−0.104224	+	0.0531048i
$527$	−4.34436	−	2.21356i	−0.189243	−	0.0964243i
$528$		0			0
$529$	2.44803	−	1.77860i	0.106436	−	0.0773304i
$530$	−0.939526	−	0.939526i	−0.0408104	−	0.0408104i
$531$		0			0
$532$	−3.08928			−0.133937
$533$	−16.4902	−	29.9439i	−0.714270	−	1.29702i
$534$		0			0
$535$	3.94033	−	1.28029i	0.170355	−	0.0553518i
$536$	9.98622	+	9.98622i	0.431339	+	0.431339i
$537$		0			0
$538$	−11.2946	−	15.5457i	−0.486944	−	0.670222i
$539$	31.6285	+	16.1155i	1.36233	+	0.694144i
$540$		0			0
$541$	9.34004	−	12.8555i	0.401560	−	0.552700i	−0.559575	−	0.828780i	$-0.689036\pi$
$541$	9.34004	−	12.8555i	0.401560	−	0.552700i	0.961135	+	0.276080i	$0.0890355\pi$
$542$			15.2556i			0.655284i
$543$		0			0
$544$	−1.09482	−	6.91240i	−0.0469399	−	0.296367i
$545$	−16.4129	−	2.59954i	−0.703049	−	0.111352i
$546$		0			0
$547$	10.1365	−	10.1365i	0.433407	−	0.433407i	−0.456379	−	0.889786i	$-0.650854\pi$
$547$	10.1365	−	10.1365i	0.433407	−	0.433407i	0.889786	+	0.456379i	$0.150854\pi$
$548$	−2.20446	+	13.9184i	−0.0941698	+	0.594565i
$549$		0			0
$550$	16.5223	−	2.61688i	0.704514	−	0.111584i
$551$	−4.85189	−	14.9326i	−0.206697	−	0.636149i
$552$		0			0
$553$	10.0128	+	3.25337i	0.425789	+	0.138347i
$554$	−23.2872	−	7.56646i	−0.989377	−	0.321468i
$555$		0			0
$556$	1.67948	+	5.16891i	0.0712259	+	0.219211i
$557$	9.91497	−	1.57038i	0.420111	−	0.0665390i	0.0571997	−	0.998363i	$-0.481783\pi$
$557$	9.91497	−	1.57038i	0.420111	−	0.0665390i	0.362911	+	0.931824i	$0.381783\pi$
$558$		0			0
$559$	−10.4294	+	65.8487i	−0.441117	+	2.78510i
$560$	0.903192	−	0.903192i	0.0381668	−	0.0381668i
$561$		0			0
$562$	−15.4712	−	2.45040i	−0.652614	−	0.103364i
$563$	4.18180	+	26.4028i	0.176242	+	1.11275i	0.904195	+	0.427120i	$0.140472\pi$
$563$	4.18180	+	26.4028i	0.176242	+	1.11275i	−0.727953	+	0.685627i	$0.759528\pi$
$564$		0			0
$565$			13.8070i			0.580865i
$566$	11.4042	−	15.6965i	0.479353	−	0.659773i
$567$		0			0
$568$	11.0327	+	5.62143i	0.462921	+	0.235870i
$569$	2.79788	+	3.85095i	0.117293	+	0.161440i	0.863627	−	0.504132i	$-0.168188\pi$
$569$	2.79788	+	3.85095i	0.117293	+	0.161440i	−0.746333	+	0.665572i	$0.768188\pi$
$570$		0			0
$571$	−23.0433	−	23.0433i	−0.964332	−	0.964332i	0.0350537	−	0.999385i	$-0.488840\pi$
$571$	−23.0433	−	23.0433i	−0.964332	−	0.964332i	−0.999385	+	0.0350537i	$0.988840\pi$
$572$	−29.0107	+	9.42616i	−1.21300	+	0.394127i
$573$		0			0
$574$	1.06867	+	5.58012i	0.0446056	+	0.232910i
$575$	13.0848			0.545673
$576$		0			0
$577$	15.7064	+	15.7064i	0.653868	+	0.653868i	0.953922	−	0.300054i	$-0.0970048\pi$
$577$	15.7064	+	15.7064i	0.653868	+	0.653868i	−0.300054	+	0.953922i	$0.597005\pi$
$578$	−25.8723	+	18.7974i	−1.07615	+	0.781867i
$579$		0			0
$580$	5.78424	+	2.94722i	0.240177	+	0.122377i
$581$	9.63890	−	4.91126i	0.399889	−	0.203754i
$582$		0			0
$583$		−	5.27375i		−	0.218416i
$584$	−8.37625	−	6.08570i	−0.346612	−	0.251828i
$585$		0			0
$586$	−7.69455	−	1.21870i	−0.317859	−	0.0503439i
$587$	−4.19204	+	8.22735i	−0.173024	+	0.339579i	−0.961192	−	0.275882i	$-0.911030\pi$
$587$	−4.19204	+	8.22735i	−0.173024	+	0.339579i	0.788167	+	0.615461i	$0.211030\pi$
$588$		0			0
$589$	0.379449	−	2.39574i	0.0156349	−	0.0987149i
$590$	−4.86994	+	14.9881i	−0.200492	+	0.617051i
$591$		0			0
$592$	−2.99558	−	9.21944i	−0.123117	−	0.378917i
$593$	−7.12391	−	13.9815i	−0.292544	−	0.574150i	0.697221	−	0.716856i	$-0.254420\pi$
$593$	−7.12391	−	13.9815i	−0.292544	−	0.574150i	−0.989765	+	0.142706i	$0.954420\pi$
$594$		0			0
$595$	−8.50179	−	2.76240i	−0.348540	−	0.113247i
$596$	−4.26723	−	8.37492i	−0.174793	−	0.343050i
$597$		0			0
$598$	−23.5661	+	3.73250i	−0.963689	+	0.152633i
$599$	−1.28943	+	3.96845i	−0.0526846	+	0.162147i	−0.973937	−	0.226819i	$-0.927167\pi$
$599$	−1.28943	+	3.96845i	−0.0526846	+	0.162147i	0.921252	+	0.388965i	$0.127167\pi$
$600$		0			0
$601$	−6.21228	+	6.21228i	−0.253404	+	0.253404i	−0.822365	−	0.568960i	$-0.807346\pi$
$601$	−6.21228	+	6.21228i	−0.253404	+	0.253404i	0.568960	+	0.822365i	$0.307346\pi$
$602$	5.03052	−	9.87295i	0.205029	−	0.402392i
$603$		0			0
$604$	−0.535646	−	3.38194i	−0.0217951	−	0.137609i
$605$	−25.2096	−	18.3158i	−1.02491	−	0.744644i
$606$		0			0
$607$	−12.6189	+	17.3685i	−0.512187	+	0.704965i	−0.984286	−	0.176581i	$-0.943496\pi$
$607$	−12.6189	+	17.3685i	−0.512187	+	0.704965i	0.472099	+	0.881545i	$0.343496\pi$
$608$	3.10217	−	1.58063i	0.125810	−	0.0641032i
$609$		0			0
$610$	−11.3979	−	15.6879i	−0.461487	−	0.635183i
$611$	−7.44182	+	5.40680i	−0.301064	+	0.218736i
$612$		0			0
$613$	25.7445	−	8.36490i	1.03981	−	0.337855i	0.261149	−	0.965298i	$-0.415899\pi$
$613$	25.7445	−	8.36490i	1.03981	−	0.337855i	0.778662	+	0.627443i	$0.215899\pi$
$614$	−5.26922			−0.212649
$615$		0			0
$616$	5.06980			0.204268
$617$	30.6813	−	9.96895i	1.23518	−	0.401335i	0.382593	−	0.923917i	$-0.375031\pi$
$617$	30.6813	−	9.96895i	1.23518	−	0.401335i	0.852589	+	0.522582i	$0.175031\pi$
$618$		0			0
$619$	−3.67000	+	2.66641i	−0.147510	+	0.107172i	−0.659092	−	0.752062i	$-0.729059\pi$
$619$	−3.67000	+	2.66641i	−0.147510	+	0.107172i	0.511583	+	0.859234i	$0.329059\pi$
$620$	0.589490	+	0.811363i	0.0236745	+	0.0325851i
$621$		0			0
$622$	15.0261	−	7.65618i	0.602492	−	0.306985i
$623$	−0.492794	+	0.678273i	−0.0197434	+	0.0271744i
$624$		0			0
$625$	1.44782	+	1.05190i	0.0579126	+	0.0420760i
$626$	1.15232	+	7.27549i	0.0460561	+	0.290787i
$627$		0			0
$628$	2.32415	−	4.56140i	0.0927437	−	0.182020i
$629$	−47.9725	+	47.9725i	−1.91279	+	1.91279i
$630$		0			0
$631$	10.5536	−	32.4805i	0.420131	−	1.29303i	−0.487449	−	0.873151i	$-0.662073\pi$
$631$	10.5536	−	32.4805i	0.420131	−	1.29303i	0.907580	−	0.419879i	$-0.137927\pi$
$632$	−11.7192	+	1.85614i	−0.466165	+	0.0738332i
$633$		0			0
$634$	−0.525788	−	1.03192i	−0.0208817	−	0.0409826i
$635$	−16.4483	−	5.34437i	−0.652730	−	0.212085i
$636$		0			0
$637$	15.0578	+	29.5526i	0.596611	+	1.17091i
$638$	7.96240	+	24.5057i	0.315234	+	0.970191i
$639$		0			0
$640$	−0.444840	+	1.36908i	−0.0175839	+	0.0541175i
$641$	1.01860	−	6.43116i	0.0402321	−	0.254016i	−0.959372	−	0.282144i	$-0.908955\pi$
$641$	1.01860	−	6.43116i	0.0402321	−	0.254016i	0.999604	+	0.0281279i	$0.00895456\pi$
$642$		0			0
$643$	−21.9635	+	43.1057i	−0.866155	+	1.69992i	−0.165762	+	0.986166i	$0.553009\pi$
$643$	−21.9635	+	43.1057i	−0.866155	+	1.69992i	−0.700392	+	0.713758i	$0.746991\pi$
$644$	3.91676	+	0.620353i	0.154342	+	0.0244453i
$645$		0			0
$646$	−19.7129	−	14.3223i	−0.775596	−	0.563503i
$647$		−	23.3541i		−	0.918145i	−0.888399	−	0.459073i	$-0.848182\pi$
$647$		−	23.3541i		−	0.918145i	0.888399	−	0.459073i	$-0.151818\pi$
$648$		0			0
$649$	−55.7337	+	28.3977i	−2.18774	+	1.11471i
$650$	13.9267	+	7.09601i	0.546250	+	0.278328i
$651$		0			0
$652$	−0.313893	+	0.228056i	−0.0122930	+	0.00893138i
$653$	20.6352	+	20.6352i	0.807517	+	0.807517i	0.984258	−	0.176740i	$-0.0565552\pi$
$653$	20.6352	+	20.6352i	0.807517	+	0.807517i	−0.176740	+	0.984258i	$0.556555\pi$
$654$		0			0
$655$	−6.29077			−0.245801
$656$	−3.92820	−	5.05660i	−0.153370	−	0.197427i
$657$		0			0
$658$	1.45401	−	0.472436i	0.0566831	−	0.0184175i
$659$	5.14680	+	5.14680i	0.200491	+	0.200491i	0.800210	−	0.599720i	$-0.204721\pi$
$659$	5.14680	+	5.14680i	0.200491	+	0.200491i	−0.599720	+	0.800210i	$0.704721\pi$
$660$		0			0
$661$	24.7194	+	34.0234i	0.961475	+	1.32336i	0.946237	+	0.323473i	$0.104850\pi$
$661$	24.7194	+	34.0234i	0.961475	+	1.32336i	0.0152376	+	0.999884i	$0.495150\pi$
$662$	17.9784	+	9.16043i	0.698748	+	0.356030i
$663$		0			0
$664$	−7.16625	+	9.86349i	−0.278104	+	0.382778i
$665$		−	4.44713i		−	0.172452i
$666$		0			0
$667$	3.15289	+	19.9066i	0.122081	+	0.770786i
$668$	8.38988	+	1.32883i	0.324614	+	0.0514139i
$669$		0			0
$670$	−14.3755	+	14.3755i	−0.555374	+	0.555374i
$671$	12.0402	−	76.0190i	0.464807	−	2.93468i
$672$		0			0
$673$	−12.3697	+	1.95917i	−0.476817	+	0.0755205i	−0.390218	−	0.920723i	$-0.627600\pi$
$673$	−12.3697	+	1.95917i	−0.476817	+	0.0755205i	−0.0866000	+	0.996243i	$0.527600\pi$
$674$	3.39414	+	10.4461i	0.130738	+	0.402369i
$675$		0			0
$676$	−14.7429	−	4.79025i	−0.567034	−	0.184241i
$677$	−11.7194	−	3.80786i	−0.450413	−	0.146348i	0.0750221	−	0.997182i	$-0.476097\pi$
$677$	−11.7194	−	3.80786i	−0.450413	−	0.146348i	−0.525435	+	0.850834i	$0.676097\pi$
$678$		0			0
$679$	−0.0802713	−	0.247050i	−0.00308053	−	0.00948090i
$680$	9.95064	−	1.57603i	0.381590	−	0.0604378i
$681$		0			0
$682$	−0.622710	+	3.93164i	−0.0238448	+	0.150550i
$683$	24.9321	−	24.9321i	0.954000	−	0.954000i	−0.0449875	−	0.998988i	$-0.514325\pi$
$683$	24.9321	−	24.9321i	0.954000	−	0.954000i	0.998988	+	0.0449875i	$0.0143248\pi$
$684$		0			0
$685$	−20.0360	−	3.17339i	−0.765537	−	0.121249i
$686$	−1.83399	−	11.5794i	−0.0700220	−	0.442102i
$687$		0			0
$688$			12.4880i			0.476101i
$689$	2.89638	−	3.98652i	0.110343	−	0.151874i
$690$		0			0
$691$	0.318112	+	0.162086i	0.0121015	+	0.00616605i	0.460031	−	0.887903i	$-0.347838\pi$
$691$	0.318112	+	0.162086i	0.0121015	+	0.00616605i	−0.447929	+	0.894069i	$0.647838\pi$
$692$	13.0741	+	17.9950i	0.497004	+	0.684067i
$693$		0			0
$694$	−24.6141	−	24.6141i	−0.934338	−	0.934338i
$695$	−7.44082	+	2.41767i	−0.282246	+	0.0917074i
$696$		0			0
$697$	−19.0508	+	40.5616i	−0.721601	+	1.53638i
$698$	3.33762			0.126331
$699$		0			0
$700$	−1.83692	−	1.83692i	−0.0694292	−	0.0694292i
$701$	23.2081	−	16.8617i	0.876557	−	0.636856i	−0.0557812	−	0.998443i	$-0.517765\pi$
$701$	23.2081	−	16.8617i	0.876557	−	0.636856i	0.932338	+	0.361587i	$0.117765\pi$
$702$		0			0
$703$	−30.0721	−	15.3225i	−1.13419	−	0.577899i
$704$	−5.09095	+	2.59397i	−0.191872	+	0.0977638i
$705$		0			0
$706$			11.1139i			0.418276i
$707$	1.97201	+	1.43275i	0.0741652	+	0.0538842i
$708$		0			0
$709$	31.5253	+	4.99312i	1.18396	+	0.187521i	0.717202	−	0.696865i	$-0.245423\pi$
$709$	31.5253	+	4.99312i	1.18396	+	0.187521i	0.466756	+	0.884386i	$0.345423\pi$
$710$	−8.09223	+	15.8819i	−0.303696	+	0.596037i
$711$		0			0
$712$	0.147811	−	0.933241i	0.00553944	−	0.0349747i
$713$	−0.962169	+	2.96125i	−0.0360335	+	0.110900i
$714$		0			0
$715$	−13.5693	−	41.7619i	−0.507462	−	1.56181i
$716$	−4.90854	−	9.63355i	−0.183441	−	0.360023i
$717$		0			0
$718$	11.5227	+	3.74395i	0.430023	+	0.139723i
$719$	19.4885	+	38.2483i	0.726797	+	1.42642i	0.897462	+	0.441091i	$0.145408\pi$
$719$	19.4885	+	38.2483i	0.726797	+	1.42642i	−0.170665	+	0.985329i	$0.554592\pi$
$720$		0			0
$721$	4.48945	−	0.711060i	0.167196	−	0.0264812i
$722$	−2.12546	+	6.54150i	−0.0791015	+	0.243449i
$723$		0			0
$724$	−11.7839	+	11.7839i	−0.437944	+	0.437944i
$725$	5.99409	−	11.7641i	0.222615	−	0.436907i
$726$		0			0
$727$	2.01036	+	12.6929i	0.0745601	+	0.470754i	0.996512	+	0.0834495i	$0.0265937\pi$
$727$	2.01036	+	12.6929i	0.0745601	+	0.470754i	−0.921952	+	0.387304i	$0.873406\pi$
$728$	3.83235	+	2.78437i	0.142036	+	0.103195i
$729$		0			0
$730$	8.76057	−	12.0579i	0.324243	−	0.446282i
$731$	77.8723	−	39.6779i	2.88021	−	1.46754i
$732$		0			0
$733$	11.5177	+	15.8527i	0.425416	+	0.585534i	0.966893	−	0.255181i	$-0.0821350\pi$
$733$	11.5177	+	15.8527i	0.425416	+	0.585534i	−0.541478	+	0.840715i	$0.682135\pi$
$734$	−14.5192	+	10.5488i	−0.535912	+	0.389363i
$735$		0			0
$736$	−4.25050	+	1.38107i	−0.156675	+	0.0509069i
$737$	−80.6926			−2.97235
$738$		0			0
$739$	−20.5990			−0.757746			−0.378873	−	0.925449i	$-0.623688\pi$
$739$	−20.5990			−0.757746			−0.378873	+	0.925449i	$0.623688\pi$
$740$	13.2717	−	4.31223i	0.487877	−	0.158521i
$741$		0			0
$742$	−0.662571	+	0.481386i	−0.0243238	+	0.0176722i
$743$	−10.5820	−	14.5649i	−0.388216	−	0.534334i	0.569522	−	0.821976i	$-0.307128\pi$
$743$	−10.5820	−	14.5649i	−0.388216	−	0.534334i	−0.957738	+	0.287643i	$0.907128\pi$
$744$		0			0
$745$	12.0560	−	6.14283i	0.441697	−	0.225056i
$746$	−2.01667	+	2.77571i	−0.0738356	+	0.101626i
$747$		0			0
$748$	32.3508	+	23.5042i	1.18286	+	0.859399i
$749$	−0.399494	−	2.52230i	−0.0145972	−	0.0921630i
$750$		0			0
$751$	−16.5819	+	32.5438i	−0.605082	+	1.18754i	0.361786	+	0.932261i	$0.382167\pi$
$751$	−16.5819	+	32.5438i	−0.605082	+	1.18754i	−0.966868	+	0.255279i	$0.917833\pi$
$752$	−1.21835	+	1.21835i	−0.0444287	+	0.0444287i
$753$		0			0
$754$	−7.43979	+	22.8973i	−0.270941	+	0.833871i
$755$	4.86841	−	0.771081i	0.177180	−	0.0280625i
$756$		0			0
$757$	−23.1130	−	45.3618i	−0.840057	−	1.64870i	−0.758165	−	0.652062i	$-0.773904\pi$
$757$	−23.1130	−	45.3618i	−0.840057	−	1.64870i	−0.0818913	−	0.996641i	$-0.526096\pi$
$758$	−31.5866	−	10.2631i	−1.14728	−	0.372773i
$759$		0			0
$760$	2.27538	+	4.46568i	0.0825366	+	0.161987i
$761$	3.56039	+	10.9578i	0.129064	+	0.397218i	0.994620	−	0.103595i	$-0.0330345\pi$
$761$	3.56039	+	10.9578i	0.129064	+	0.397218i	−0.865556	+	0.500813i	$0.833034\pi$
$762$		0			0
$763$	−3.16518	+	9.74141i	−0.114587	+	0.352663i
$764$	1.82296	−	11.5097i	0.0659523	−	0.416406i
$765$		0			0
$766$	−2.77973	+	5.45552i	−0.100436	+	0.197116i
$767$	−57.7263	−	9.14295i	−2.08438	−	0.330133i
$768$		0			0
$769$	16.8722	+	12.2584i	0.608428	+	0.442049i	0.848860	−	0.528617i	$-0.177289\pi$
$769$	16.8722	+	12.2584i	0.608428	+	0.442049i	−0.240433	+	0.970666i	$0.577289\pi$
$770$			7.29815i			0.263007i
$771$		0			0
$772$	2.73646	−	1.39429i	0.0984872	−	0.0501817i
$773$	5.75467	+	2.93215i	0.206981	+	0.105462i	0.554408	−	0.832245i	$-0.312945\pi$
$773$	5.75467	+	2.93215i	0.206981	+	0.105462i	−0.347427	+	0.937707i	$0.612945\pi$
$774$		0			0
$775$	1.65016	−	1.19891i	0.0592756	−	0.0430662i
$776$	0.207009	+	0.207009i	0.00743120	+	0.00743120i
$777$		0			0
$778$	−31.4610			−1.12793
$779$	−22.1197	−	2.77801i	−0.792519	−	0.0995325i
$780$		0			0
$781$	−67.2859	+	21.8625i	−2.40768	+	0.782302i
$782$	22.1171	+	22.1171i	0.790905	+	0.790905i
$783$		0			0
$784$	3.65173	+	5.02617i	0.130419	+	0.179506i
$785$	6.56629	+	3.34569i	0.234361	+	0.119413i
$786$		0			0
$787$	11.5225	−	15.8594i	0.410734	−	0.565327i	−0.552663	−	0.833405i	$-0.686388\pi$
$787$	11.5225	−	15.8594i	0.410734	−	0.565327i	0.963397	+	0.268078i	$0.0863884\pi$
$788$			5.31323i			0.189276i
$789$		0			0
$790$	−2.67197	−	16.8702i	−0.0950645	−	0.600214i
$791$	8.40564	+	1.33132i	0.298870	+	0.0473364i
$792$		0			0
$793$	50.8515	−	50.8515i	1.80579	−	1.80579i
$794$	5.14768	−	32.5012i	0.182684	−	1.15342i
$795$		0			0
$796$	−4.39748	+	0.696492i	−0.155864	+	0.0246865i
$797$	3.43343	+	10.5670i	0.121618	+	0.374303i	0.993270	−	0.115824i	$-0.0369507\pi$
$797$	3.43343	+	10.5670i	0.121618	+	0.374303i	−0.871652	+	0.490126i	$0.836951\pi$
$798$		0			0
$799$	11.4684	+	3.72631i	0.405723	+	0.131827i
$800$	2.78445	+	0.904723i	0.0984452	+	0.0319868i
$801$		0			0
$802$	−0.456400	−	1.40465i	−0.0161160	−	0.0496001i
$803$	58.4292	−	9.25427i	2.06192	−	0.326576i
$804$		0			0
$805$	−0.893019	+	5.63830i	−0.0314748	+	0.198724i
$806$	−2.63000	+	2.63000i	−0.0926377	+	0.0926377i
$807$		0			0
$808$	−2.71331	−	0.429746i	−0.0954538	−	0.0151184i
$809$	−6.70564	−	42.3377i	−0.235758	−	1.48851i	−0.767193	−	0.641416i	$-0.778347\pi$
$809$	−6.70564	−	42.3377i	−0.235758	−	1.48851i	0.531436	−	0.847099i	$-0.321653\pi$
$810$		0			0
$811$		−	12.7480i		−	0.447643i	−0.974630	−	0.223822i	$-0.928147\pi$
$811$		−	12.7480i		−	0.447643i	0.974630	−	0.223822i	$-0.0718533\pi$
$812$	2.35199	−	3.23724i	0.0825387	−	0.113605i
$813$		0			0
$814$	49.3511	+	25.1456i	1.72975	+	0.881354i
$815$	−0.328295	−	0.451859i	−0.0114997	−	0.0158279i
$816$		0			0
$817$	30.7442	+	30.7442i	1.07560	+	1.07560i
$818$	−3.69811	+	1.20159i	−0.129301	+	0.0420125i
$819$		0			0
$820$	7.27915	−	5.65478i	0.254199	−	0.197473i
$821$	−4.49594			−0.156909			−0.0784547	−	0.996918i	$-0.524999\pi$
$821$	−4.49594			−0.156909			−0.0784547	+	0.996918i	$0.524999\pi$
$822$		0			0
$823$	29.3864	+	29.3864i	1.02435	+	1.02435i	0.999696	+	0.0246494i	$0.00784694\pi$
$823$	29.3864	+	29.3864i	1.02435	+	1.02435i	0.0246494	+	0.999696i	$0.492153\pi$
$824$	−4.14436	+	3.01106i	−0.144376	+	0.104895i
$825$		0			0
$826$	8.65513	+	4.41001i	0.301150	+	0.153444i
$827$	4.19255	−	2.13621i	0.145789	−	0.0742833i	−0.379574	−	0.925161i	$-0.623929\pi$
$827$	4.19255	−	2.13621i	0.145789	−	0.0742833i	0.525363	+	0.850878i	$0.323929\pi$
$828$		0			0
$829$		−	14.2233i		−	0.493994i	−0.969016	−	0.246997i	$-0.920556\pi$
$829$		−	14.2233i		−	0.493994i	0.969016	−	0.246997i	$-0.0794439\pi$
$830$	−14.1988	−	10.3161i	−0.492849	−	0.358075i
$831$		0			0
$832$	−5.27296	−	0.835155i	−0.182807	−	0.0289538i
$833$	19.7395	−	38.7409i	0.683932	−	1.34229i
$834$		0			0
$835$	−1.91289	+	12.0775i	−0.0661983	+	0.417960i
$836$	−6.14731	+	18.9195i	−0.212609	+	0.654343i
$837$		0			0
$838$	4.59910	+	14.1546i	0.158873	+	0.488961i
$839$	5.17891	+	10.1642i	0.178796	+	0.350907i	0.962959	−	0.269648i	$-0.0869074\pi$
$839$	5.17891	+	10.1642i	0.178796	+	0.350907i	−0.784163	+	0.620555i	$0.786907\pi$
$840$		0			0
$841$	−8.23899	−	2.67701i	−0.284103	−	0.0923107i
$842$	5.16817	+	10.1431i	0.178107	+	0.349555i
$843$		0			0
$844$	−4.13026	+	0.654169i	−0.142169	+	0.0225174i
$845$	6.89573	−	21.2229i	0.237220	−	0.730089i
$846$		0			0
$847$	−13.5814	+	13.5814i	−0.466662	+	0.466662i
$848$	0.419033	−	0.822399i	0.0143897	−	0.0282413i
$849$		0			0
$850$	−3.20534	−	20.2377i	−0.109942	−	0.694149i
$851$	35.0501	+	25.4654i	1.20150	+	0.872942i
$852$		0			0
$853$	6.49985	−	8.94627i	0.222551	−	0.306315i	−0.683112	−	0.730314i	$-0.739374\pi$
$853$	6.49985	−	8.94627i	0.222551	−	0.306315i	0.905663	+	0.423999i	$0.139374\pi$
$854$	−10.6497	+	5.42630i	−0.364426	+	0.185684i
$855$		0			0
$856$	1.69170	+	2.32842i	0.0578211	+	0.0795839i
$857$	39.7812	−	28.9027i	1.35890	−	0.987298i	0.360385	−	0.932804i	$-0.382645\pi$
$857$	39.7812	−	28.9027i	1.35890	−	0.987298i	0.998514	−	0.0544938i	$-0.0173545\pi$
$858$		0			0
$859$	−7.92453	+	2.57484i	−0.270382	+	0.0878523i	−0.441070	−	0.897473i	$-0.645401\pi$
$859$	−7.92453	+	2.57484i	−0.270382	+	0.0878523i	0.170688	+	0.985325i	$0.445401\pi$
$860$	−17.9769			−0.613007
$861$		0			0
$862$	38.1206			1.29839
$863$	−28.6259	+	9.30111i	−0.974436	+	0.316613i	−0.752605	−	0.658472i	$-0.771203\pi$
$863$	−28.6259	+	9.30111i	−0.974436	+	0.316613i	−0.221831	+	0.975085i	$0.571203\pi$
$864$		0			0
$865$	−25.9044	+	18.8206i	−0.880776	+	0.639921i
$866$	−0.686866	−	0.945390i	−0.0233407	−	0.0321257i
$867$		0			0
$868$	0.550795	−	0.280644i	0.0186952	−	0.00952568i
$869$	39.8487	−	54.8470i	1.35177	−	1.86056i
$870$		0			0
$871$	−60.9970	−	44.3169i	−2.06680	−	1.50162i
$872$	−1.80582	−	11.4015i	−0.0611528	−	0.386104i
$873$		0			0
$874$	−7.06423	+	13.8643i	−0.238951	+	0.468968i
$875$	7.16027	−	7.16027i	0.242061	−	0.242061i
$876$		0			0
$877$	0.339590	−	1.04515i	0.0114671	−	0.0352922i	−0.945159	−	0.326610i	$-0.894094\pi$
$877$	0.339590	−	1.04515i	0.0114671	−	0.0352922i	0.956626	+	0.291318i	$0.0940937\pi$
$878$	−33.0879	+	5.24060i	−1.11666	+	0.176862i
$879$		0			0
$880$	−3.73410	−	7.32859i	−0.125877	−	0.247047i
$881$	29.8271	+	9.69141i	1.00490	+	0.326512i	0.764822	−	0.644242i	$-0.222827\pi$
$881$	29.8271	+	9.69141i	1.00490	+	0.326512i	0.240078	+	0.970754i	$0.422827\pi$
$882$		0			0
$883$	−8.56215	−	16.8042i	−0.288139	−	0.565505i	0.700882	−	0.713277i	$-0.252790\pi$
$883$	−8.56215	−	16.8042i	−0.288139	−	0.565505i	−0.989021	+	0.147772i	$0.952790\pi$
$884$	11.5459	+	35.5345i	0.388329	+	1.19515i
$885$		0			0
$886$	6.38659	−	19.6559i	0.214562	−	0.660353i
$887$	−6.06019	+	38.2625i	−0.203481	+	1.28473i	0.648523	+	0.761195i	$0.275387\pi$
$887$	−6.06019	+	38.2625i	−0.203481	+	1.28473i	−0.852004	+	0.523535i	$0.824613\pi$
$888$		0			0
$889$	−4.83963	+	9.49831i	−0.162316	+	0.318563i
$890$	1.34343	+	0.212779i	0.0450319	+	0.00713235i
$891$		0			0
$892$	8.22421	+	5.97524i	0.275367	+	0.200066i
$893$			5.99890i			0.200746i
$894$		0			0
$895$	13.8678	−	7.06600i	0.463550	−	0.236190i
$896$	0.790595	+	0.402828i	0.0264119	+	0.0134575i
$897$		0			0
$898$	15.9205	−	11.5669i	0.531274	−	0.385993i
$899$	2.22159	+	2.22159i	0.0740943	+	0.0740943i
$900$		0			0
$901$	−6.45968			−0.215203
$902$	36.3004	+	4.55897i	1.20867	+	0.151797i
$903$		0			0
$904$	−9.12187	+	2.96388i	−0.303389	+	0.0985770i
$905$	−16.9633	−	16.9633i	−0.563878	−	0.563878i
$906$		0			0
$907$	−10.0659	−	13.8545i	−0.334233	−	0.460032i	0.608513	−	0.793544i	$-0.291766\pi$
$907$	−10.0659	−	13.8545i	−0.334233	−	0.460032i	−0.942746	+	0.333512i	$0.891766\pi$
$908$	3.09741	+	1.57821i	0.102791	+	0.0523747i
$909$		0			0
$910$	−4.00819	+	5.51680i	−0.132870	+	0.182880i
$911$			38.3984i			1.27220i	0.771609	+	0.636098i	$0.219452\pi$
$911$			38.3984i			1.27220i	−0.771609	+	0.636098i	$0.780548\pi$
$912$		0			0
$913$	−10.8974	−	68.8036i	−0.360652	−	2.27707i
$914$	−9.52232	−	1.50819i	−0.314970	−	0.0498864i
$915$		0			0
$916$	−15.8612	+	15.8612i	−0.524069	+	0.524069i
$917$	−0.606580	+	3.82979i	−0.0200310	+	0.126471i
$918$		0			0
$919$	−37.3447	+	5.91481i	−1.23189	+	0.195112i	−0.738232	−	0.674547i	$-0.764339\pi$
$919$	−37.3447	+	5.91481i	−1.23189	+	0.195112i	−0.493654	+	0.869658i	$0.664339\pi$
$920$	−1.98810	−	6.11873i	−0.0655456	−	0.201729i
$921$		0			0
$922$	25.5491	+	8.30142i	0.841416	+	0.273393i
$923$	−62.8696	−	20.4276i	−2.06938	−	0.672382i
$924$		0			0
$925$	−8.77028	−	26.9922i	−0.288365	−	0.887496i
$926$	18.6786	−	2.95841i	0.613819	−	0.0972193i
$927$		0			0
$928$	−0.705466	+	4.45414i	−0.0231581	+	0.146214i
$929$	−23.6519	+	23.6519i	−0.775993	+	0.775993i	−0.979147	−	0.203154i	$-0.934881\pi$
$929$	−23.6519	+	23.6519i	−0.775993	+	0.775993i	0.203154	+	0.979147i	$0.434881\pi$
$930$		0			0
$931$	21.3641	+	3.38374i	0.700179	+	0.110898i
$932$	2.05857	+	12.9973i	0.0674309	+	0.425742i
$933$		0			0
$934$		−	5.72218i		−	0.187235i
$935$	−33.8351	+	46.5700i	−1.10653	+	1.52300i
$936$		0			0
$937$	38.6876	+	19.7123i	1.26387	+	0.643974i	0.951985	−	0.306146i	$-0.0990394\pi$
$937$	38.6876	+	19.7123i	1.26387	+	0.643974i	0.311886	+	0.950120i	$0.399039\pi$
$938$	7.36560	+	10.1379i	0.240495	+	0.331013i
$939$		0			0
$940$	−1.75386	−	1.75386i	−0.0572045	−	0.0572045i
$941$	3.62097	−	1.17652i	0.118040	−	0.0383536i	−0.249401	−	0.968400i	$-0.580234\pi$
$941$	3.62097	−	1.17652i	0.118040	−	0.0383536i	0.367442	+	0.930047i	$0.380234\pi$
$942$		0			0
$943$	27.4866	+	7.96391i	0.895087	+	0.259340i
$944$	−10.9476			−0.356314
$945$		0			0
$946$	−50.4540	−	50.4540i	−1.64040	−	1.64040i
$947$	46.0059	−	33.4252i	1.49499	−	1.08617i	0.522666	−	0.852538i	$-0.324938\pi$
$947$	46.0059	−	33.4252i	1.49499	−	1.08617i	0.972324	−	0.233636i	$-0.0750624\pi$
$948$		0			0
$949$	49.2501	+	25.0942i	1.59873	+	0.814592i
$950$	9.08236	−	4.62769i	0.294671	−	0.150142i
$951$		0			0
$952$		−	6.20987i		−	0.201263i
$953$	32.6273	+	23.7051i	1.05690	+	0.767884i	0.973513	−	0.228634i	$-0.0734258\pi$
$953$	32.6273	+	23.7051i	1.05690	+	0.767884i	0.0833885	+	0.996517i	$0.473426\pi$
$954$		0			0
$955$	16.5686	+	2.62421i	0.536147	+	0.0849173i
$956$	2.62362	−	5.14915i	0.0848541	−	0.166535i
$957$		0			0
$958$	2.20540	−	13.9243i	0.0712532	−	0.449875i
$959$	−3.86389	+	11.8918i	−0.124772	+	0.384008i
$960$		0			0
$961$	−9.42954	−	29.0211i	−0.304179	−	0.936166i
$962$	23.4952	+	46.1120i	0.757516	+	1.48671i
$963$		0			0
$964$	7.36343	+	2.39252i	0.237160	+	0.0770580i
$965$	2.00713	+	3.93922i	0.0646119	+	0.126808i
$966$		0			0
$967$	−5.28018	+	0.836298i	−0.169799	+	0.0268935i	−0.240755	−	0.970586i	$-0.577395\pi$
$967$	−5.28018	+	0.836298i	−0.169799	+	0.0268935i	0.0709560	+	0.997479i	$0.477395\pi$
$968$	6.68911	−	20.5870i	0.214996	−	0.661690i
$969$		0			0
$970$	−0.297997	+	0.297997i	−0.00956810	+	0.00956810i
$971$	−27.0680	+	53.1240i	−0.868654	+	1.70483i	−0.174939	+	0.984579i	$0.555973\pi$
$971$	−27.0680	+	53.1240i	−0.868654	+	1.70483i	−0.693715	+	0.720250i	$0.744027\pi$
$972$		0			0
$973$	0.754394	+	4.76306i	0.0241848	+	0.152697i
$974$	−0.0889178	−	0.0646026i	−0.00284911	−	0.00207000i
$975$		0			0
$976$	7.91777	−	10.8979i	0.253442	−	0.348832i
$977$	−5.55375	+	2.82977i	−0.177680	+	0.0905325i	−0.540568	−	0.841300i	$-0.681791\pi$
$977$	−5.55375	+	2.82977i	−0.177680	+	0.0905325i	0.362888	+	0.931833i	$0.381791\pi$
$978$		0			0
$979$	3.17329	+	4.36766i	0.101419	+	0.139591i
$980$	−7.23534	+	5.25678i	−0.231124	+	0.167922i
$981$		0			0
$982$	−0.225282	+	0.0731985i	−0.00718903	+	0.00233586i
$983$	−24.2574			−0.773689			−0.386845	−	0.922145i	$-0.626435\pi$
$983$	−24.2574			−0.773689			−0.386845	+	0.922145i	$0.626435\pi$
$984$		0			0
$985$	−7.64857			−0.243704
$986$	30.0164	−	9.75293i	0.955918	−	0.310597i
$987$		0			0
$988$	−15.0375	+	10.9254i	−0.478408	+	0.347584i
$989$	−32.8054	−	45.1527i	−1.04315	−	1.43577i
$990$		0			0
$991$	43.2334	−	22.0285i	1.37335	−	0.699759i	0.397382	−	0.917653i	$-0.369919\pi$
$991$	43.2334	−	22.0285i	1.37335	−	0.699759i	0.975972	+	0.217895i	$0.0699190\pi$
$992$	−0.409501	+	0.563629i	−0.0130017	+	0.0178952i
$993$		0			0
$994$	8.88855	+	6.45791i	0.281928	+	0.204832i
$995$	−1.00262	−	6.33031i	−0.0317853	−	0.200684i
$996$		0			0
$997$	13.9018	−	27.2838i	0.440274	−	0.864086i	−0.559114	−	0.829091i	$-0.688858\pi$
$997$	13.9018	−	27.2838i	0.440274	−	0.864086i	0.999387	−	0.0349949i	$-0.0111415\pi$
$998$	−16.2393	+	16.2393i	−0.514047	+	0.514047i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.c.613.3	yes	24
3.2	odd	2		738.2.u.d.613.1	yes	24
41.20	even	20	inner	738.2.u.c.307.3	✓	24
123.20	odd	20		738.2.u.d.307.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.307.3	✓	24	41.20	even	20	inner
738.2.u.c.613.3	yes	24	1.1	even	1	trivial
738.2.u.d.307.1	yes	24	123.20	odd	20
738.2.u.d.613.1	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.846136 + 1.16461i) q^{5} +(0.790595 - 0.402828i) q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.846136 + 1.16461i) q^{5} +(0.790595 - 0.402828i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.16461 - 0.846136i) q^{10} +(-0.893820 - 5.64336i) q^{11} +(2.42371 - 4.75681i) q^{13} +(-0.627420 + 0.627420i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-6.91240 + 1.09482i) q^{17} +(-1.58063 - 3.10217i) q^{19} +(1.36908 + 0.444840i) q^{20} +(2.59397 + 5.09095i) q^{22} +(1.38107 + 4.25050i) q^{23} +(0.904723 - 2.78445i) q^{25} +(-0.835155 + 5.27296i) q^{26} +(0.402828 - 0.790595i) q^{28} +(4.45414 + 0.705466i) q^{29} +(0.563629 + 0.409501i) q^{31} +1.00000i q^{32} +(6.23577 - 3.17728i) q^{34} +(1.13809 + 0.579885i) q^{35} +(7.84252 - 5.69793i) q^{37} +(2.46190 + 2.46190i) q^{38} -1.43953 q^{40} +(3.59523 - 5.29852i) q^{41} +(-11.8768 + 3.85901i) q^{43} +(-4.04020 - 4.04020i) q^{44} +(-2.62695 - 3.61569i) q^{46} +(-1.53521 - 0.782229i) q^{47} +(-3.65173 + 5.02617i) q^{49} +2.92774i q^{50} +(-0.835155 - 5.27296i) q^{52} +(0.911637 + 0.144389i) q^{53} +(5.81600 - 5.81600i) q^{55} +(-0.138805 + 0.876381i) q^{56} +(-4.45414 + 0.705466i) q^{58} +(-3.38300 - 10.4118i) q^{59} +(12.8112 + 4.16262i) q^{61} +(-0.662586 - 0.215287i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(7.59060 - 1.20223i) q^{65} +(2.20927 - 13.9488i) q^{67} +(-4.94874 + 4.94874i) q^{68} +(-1.26158 - 0.199815i) q^{70} +(-1.93701 - 12.2298i) q^{71} +10.3536i q^{73} +(-5.69793 + 7.84252i) q^{74} +(-3.10217 - 1.58063i) q^{76} +(-2.97995 - 4.10156i) q^{77} +(8.39002 + 8.39002i) q^{79} +(1.36908 - 0.444840i) q^{80} +(-1.78194 + 6.15018i) q^{82} +12.1920 q^{83} +(-7.12387 - 7.12387i) q^{85} +(10.1030 - 7.34026i) q^{86} +(5.09095 + 2.59397i) q^{88} +(-0.841889 + 0.428964i) q^{89} -4.73705i q^{91} +(3.61569 + 2.62695i) q^{92} +(1.70179 + 0.269538i) q^{94} +(2.27538 - 4.46568i) q^{95} +(0.0457970 - 0.289151i) q^{97} +(1.91983 - 5.90862i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4}+O(q^{10}) \) 24 * q + 6 * q^4	\( 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) \) 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

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