LMFDB - Embedded newform 576.2.bd.a.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	576.109
Dual form			576.2.bd.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809383 - 1.15970i) q^{2} +(-0.689800 - 1.87728i) q^{4} +(0.159018 + 0.799435i) q^{5} +(-0.742008 - 1.79137i) q^{7} +(-2.73539 - 0.719478i) q^{8} +O(q^{10})$	\(q+(0.809383 - 1.15970i) q^{2} +(-0.689800 - 1.87728i) q^{4} +(0.159018 + 0.799435i) q^{5} +(-0.742008 - 1.79137i) q^{7} +(-2.73539 - 0.719478i) q^{8} +(1.05581 + 0.462637i) q^{10} +(-1.29226 - 0.863458i) q^{11} +(1.07211 - 5.38985i) q^{13} +(-2.67801 - 0.589395i) q^{14} +(-3.04835 + 2.58989i) q^{16} +(-1.43298 - 1.43298i) q^{17} +(0.0883441 + 0.0175727i) q^{19} +(1.39107 - 0.849970i) q^{20} +(-2.04728 + 0.799759i) q^{22} +(-3.31519 - 1.37320i) q^{23} +(4.00559 - 1.65917i) q^{25} +(-5.38285 - 5.60577i) q^{26} +(-2.85106 + 2.62864i) q^{28} +(1.04042 - 0.695186i) q^{29} -2.58743i q^{31} +(0.536209 + 5.63138i) q^{32} +(-2.82165 + 0.501994i) q^{34} +(1.31409 - 0.878046i) q^{35} +(1.60572 - 0.319397i) q^{37} +(0.0918832 - 0.0882294i) q^{38} +(0.140201 - 2.30118i) q^{40} +(-0.605183 - 0.250675i) q^{41} +(-5.04263 + 7.54683i) q^{43} +(-0.729554 + 3.02154i) q^{44} +(-4.27576 + 2.73318i) q^{46} +(3.86580 + 3.86580i) q^{47} +(2.29133 - 2.29133i) q^{49} +(1.31792 - 5.98817i) q^{50} +(-10.8578 + 1.70527i) q^{52} +(8.70867 + 5.81895i) q^{53} +(0.484787 - 1.17038i) q^{55} +(0.740832 + 5.43394i) q^{56} +(0.0358915 - 1.76924i) q^{58} +(-1.17041 - 5.88407i) q^{59} +(3.52821 + 5.28034i) q^{61} +(-3.00064 - 2.09422i) q^{62} +(6.96470 + 3.93610i) q^{64} +4.47932 q^{65} +(3.15404 + 4.72036i) q^{67} +(-1.70163 + 3.67856i) q^{68} +(0.0453323 - 2.23462i) q^{70} +(-5.01419 - 12.1053i) q^{71} +(-1.75399 + 4.23450i) q^{73} +(0.929237 - 2.12066i) q^{74} +(-0.0279508 - 0.177968i) q^{76} +(-0.587905 + 2.95560i) q^{77} +(7.46021 - 7.46021i) q^{79} +(-2.55519 - 2.02512i) q^{80} +(-0.780532 + 0.498937i) q^{82} +(2.65306 + 0.527725i) q^{83} +(0.917704 - 1.37344i) q^{85} +(4.67063 + 11.9562i) q^{86} +(2.91358 + 3.29164i) q^{88} +(-7.09322 + 2.93811i) q^{89} +(-10.4507 + 2.07877i) q^{91} +(-0.291057 + 7.17078i) q^{92} +(7.61208 - 1.35425i) q^{94} +0.0734197i q^{95} +11.4524i q^{97} +(-0.802689 - 4.51182i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.809383	−	1.15970i	0.572320	−	0.820030i
$2$	0.809383	−	1.15970i	0.572320	−	0.820030i
$3$		0			0
$3$		0			0
$4$	−0.689800	−	1.87728i	−0.344900	−	0.938640i
$5$	0.159018	+	0.799435i	0.0711148	+	0.357518i	0.999915	−	0.0130634i	$-0.00415834\pi$
$5$	0.159018	+	0.799435i	0.0711148	+	0.357518i	−0.928800	+	0.370582i	$0.879158\pi$
$6$		0			0
$7$	−0.742008	−	1.79137i	−0.280453	−	0.677073i	0.719394	−	0.694603i	$-0.244420\pi$
$7$	−0.742008	−	1.79137i	−0.280453	−	0.677073i	−0.999846	+	0.0175299i	$0.994420\pi$
$8$	−2.73539	−	0.719478i	−0.967106	−	0.254374i
$9$		0			0
$10$	1.05581	+	0.462637i	0.333876	+	0.146299i
$11$	−1.29226	−	0.863458i	−0.389630	−	0.260342i	0.345290	−	0.938496i	$-0.387780\pi$
$11$	−1.29226	−	0.863458i	−0.389630	−	0.260342i	−0.734920	+	0.678154i	$0.762780\pi$
$12$		0			0
$13$	1.07211	−	5.38985i	0.297349	−	1.49487i	−0.486367	−	0.873755i	$-0.661678\pi$
$13$	1.07211	−	5.38985i	0.297349	−	1.49487i	0.783716	−	0.621119i	$-0.213322\pi$
$14$	−2.67801	−	0.589395i	−0.715729	−	0.157522i
$15$		0			0
$16$	−3.04835	+	2.58989i	−0.762088	+	0.647473i
$17$	−1.43298	−	1.43298i	−0.347548	−	0.347548i	0.511648	−	0.859195i	$-0.329035\pi$
$17$	−1.43298	−	1.43298i	−0.347548	−	0.347548i	−0.859195	+	0.511648i	$0.829035\pi$
$18$		0			0
$19$	0.0883441	+	0.0175727i	0.0202675	+	0.00403146i	0.205214	−	0.978717i	$-0.434211\pi$
$19$	0.0883441	+	0.0175727i	0.0202675	+	0.00403146i	−0.184946	+	0.982749i	$0.559211\pi$
$20$	1.39107	−	0.849970i	0.311053	−	0.190059i
$21$		0			0
$22$	−2.04728	+	0.799759i	−0.436481	+	0.170509i
$23$	−3.31519	−	1.37320i	−0.691266	−	0.286332i	0.00926165	−	0.999957i	$-0.497052\pi$
$23$	−3.31519	−	1.37320i	−0.691266	−	0.286332i	−0.700527	+	0.713625i	$0.747052\pi$
$24$		0			0
$25$	4.00559	−	1.65917i	0.801118	−	0.331834i
$26$	−5.38285	−	5.60577i	−1.05566	−	1.09938i
$27$		0			0
$28$	−2.85106	+	2.62864i	−0.538799	+	0.496766i
$29$	1.04042	−	0.695186i	0.193201	−	0.129093i	−0.455207	−	0.890385i	$-0.650435\pi$
$29$	1.04042	−	0.695186i	0.193201	−	0.129093i	0.648409	+	0.761293i	$0.275435\pi$
$30$		0			0
$31$		−	2.58743i		−	0.464717i	−0.972630	−	0.232358i	$-0.925356\pi$
$31$		−	2.58743i		−	0.464717i	0.972630	−	0.232358i	$-0.0746442\pi$
$32$	0.536209	+	5.63138i	0.0947893	+	0.995497i
$33$		0			0
$34$	−2.82165	+	0.501994i	−0.483908	+	0.0860912i
$35$	1.31409	−	0.878046i	0.222122	−	0.148417i
$36$		0			0
$37$	1.60572	−	0.319397i	0.263979	−	0.0525086i	−0.0613263	−	0.998118i	$-0.519533\pi$
$37$	1.60572	−	0.319397i	0.263979	−	0.0525086i	0.325305	+	0.945609i	$0.394533\pi$
$38$	0.0918832	−	0.0882294i	0.0149054	−	0.0143127i
$39$		0			0
$40$	0.140201	−	2.30118i	0.0221677	−	0.363848i
$41$	−0.605183	−	0.250675i	−0.0945137	−	0.0391488i	0.334926	−	0.942245i	$-0.391289\pi$
$41$	−0.605183	−	0.250675i	−0.0945137	−	0.0391488i	−0.429439	+	0.903096i	$0.641289\pi$
$42$		0			0
$43$	−5.04263	+	7.54683i	−0.768994	+	1.15088i	0.215678	+	0.976465i	$0.430804\pi$
$43$	−5.04263	+	7.54683i	−0.768994	+	1.15088i	−0.984672	+	0.174416i	$0.944196\pi$
$44$	−0.729554	+	3.02154i	−0.109984	+	0.455514i
$45$		0			0
$46$	−4.27576	+	2.73318i	−0.630426	+	0.402986i
$47$	3.86580	+	3.86580i	0.563885	+	0.563885i	0.930409	−	0.366524i	$-0.119452\pi$
$47$	3.86580	+	3.86580i	0.563885	+	0.563885i	−0.366524	+	0.930409i	$0.619452\pi$
$48$		0			0
$49$	2.29133	−	2.29133i	0.327333	−	0.327333i
$50$	1.31792	−	5.98817i	0.186382	−	0.846856i
$51$		0			0
$52$	−10.8578	+	1.70527i	−1.50570	+	0.236478i
$53$	8.70867	+	5.81895i	1.19623	+	0.799294i	0.984042	−	0.177935i	$-0.0569417\pi$
$53$	8.70867	+	5.81895i	1.19623	+	0.799294i	0.212186	+	0.977229i	$0.431942\pi$
$54$		0			0
$55$	0.484787	−	1.17038i	0.0653687	−	0.157814i
$56$	0.740832	+	5.43394i	0.0989979	+	0.726141i
$57$		0			0
$58$	0.0358915	−	1.76924i	0.00471278	−	0.232313i
$59$	−1.17041	−	5.88407i	−0.152375	−	0.766040i	−0.979091	−	0.203421i	$-0.934794\pi$
$59$	−1.17041	−	5.88407i	−0.152375	−	0.766040i	0.826716	−	0.562619i	$-0.190206\pi$
$60$		0			0
$61$	3.52821	+	5.28034i	0.451741	+	0.676078i	0.985523	−	0.169544i	$-0.0542296\pi$
$61$	3.52821	+	5.28034i	0.451741	+	0.676078i	−0.533782	+	0.845622i	$0.679230\pi$
$62$	−3.00064	−	2.09422i	−0.381082	−	0.265967i
$63$		0			0
$64$	6.96470	+	3.93610i	0.870588	+	0.492013i
$65$	4.47932			0.555591
$66$		0			0
$67$	3.15404	+	4.72036i	0.385328	+	0.576684i	0.972536	−	0.232752i	$-0.0747731\pi$
$67$	3.15404	+	4.72036i	0.385328	+	0.576684i	−0.587208	+	0.809436i	$0.699773\pi$
$68$	−1.70163	+	3.67856i	−0.206353	+	0.446091i
$69$		0			0
$70$	0.0453323	−	2.23462i	0.00541824	−	0.267088i
$71$	−5.01419	−	12.1053i	−0.595075	−	1.43664i	−0.878546	−	0.477657i	$-0.841486\pi$
$71$	−5.01419	−	12.1053i	−0.595075	−	1.43664i	0.283471	−	0.958981i	$-0.408514\pi$
$72$		0			0
$73$	−1.75399	+	4.23450i	−0.205289	+	0.495611i	−0.992670	−	0.120855i	$-0.961436\pi$
$73$	−1.75399	+	4.23450i	−0.205289	+	0.495611i	0.787381	+	0.616466i	$0.211436\pi$
$74$	0.929237	−	2.12066i	0.108022	−	0.246522i
$75$		0			0
$76$	−0.0279508	−	0.177968i	−0.00320617	−	0.0204143i
$77$	−0.587905	+	2.95560i	−0.0669979	+	0.336821i
$78$		0			0
$79$	7.46021	−	7.46021i	0.839340	−	0.839340i	−0.149432	−	0.988772i	$-0.547745\pi$
$79$	7.46021	−	7.46021i	0.839340	−	0.839340i	0.988772	+	0.149432i	$0.0477446\pi$
$80$	−2.55519	−	2.02512i	−0.285679	−	0.226416i
$81$		0			0
$82$	−0.780532	+	0.498937i	−0.0861953	+	0.0550984i
$83$	2.65306	+	0.527725i	0.291211	+	0.0579254i	0.338534	−	0.940954i	$-0.390069\pi$
$83$	2.65306	+	0.527725i	0.291211	+	0.0579254i	−0.0473232	+	0.998880i	$0.515069\pi$
$84$		0			0
$85$	0.917704	−	1.37344i	0.0995389	−	0.148971i
$86$	4.67063	+	11.9562i	0.503647	+	1.28927i
$87$		0			0
$88$	2.91358	+	3.29164i	0.310589	+	0.350890i
$89$	−7.09322	+	2.93811i	−0.751880	+	0.311439i	−0.725508	−	0.688213i	$-0.758395\pi$
$89$	−7.09322	+	2.93811i	−0.751880	+	0.311439i	−0.0263716	+	0.999652i	$0.508395\pi$
$90$		0			0
$91$	−10.4507	+	2.07877i	−1.09553	+	0.217915i
$92$	−0.291057	+	7.17078i	−0.0303448	+	0.747605i
$93$		0			0
$94$	7.61208	−	1.35425i	0.785126	−	0.139680i
$95$			0.0734197i			0.00753271i
$96$		0			0
$97$			11.4524i			1.16281i	0.813614	+	0.581406i	$0.197497\pi$
$97$			11.4524i			1.16281i	−0.813614	+	0.581406i	$0.802503\pi$
$98$	−0.802689	−	4.51182i	−0.0810838	−	0.455762i
$99$		0			0
$100$	−5.87778	−	6.37511i	−0.587778	−	0.637511i
$101$	11.4055	−	2.26869i	1.13489	−	0.225743i	0.408319	−	0.912839i	$-0.366115\pi$
$101$	11.4055	−	2.26869i	1.13489	−	0.225743i	0.726566	+	0.687097i	$0.241115\pi$
$102$		0			0
$103$	12.3890	−	5.13170i	1.22073	−	0.505641i	0.323086	−	0.946370i	$-0.395280\pi$
$103$	12.3890	−	5.13170i	1.22073	−	0.505641i	0.897640	+	0.440729i	$0.145280\pi$
$104$	−6.81050	+	13.9720i	−0.667825	+	1.37006i
$105$		0			0
$106$	13.7969	−	5.38968i	1.34007	−	0.523492i
$107$	−5.26269	+	7.87617i	−0.508764	+	0.761419i	−0.993572	−	0.113202i	$-0.963889\pi$
$107$	−5.26269	+	7.87617i	−0.508764	+	0.761419i	0.484808	+	0.874620i	$0.338889\pi$
$108$		0			0
$109$	16.8083	+	3.34339i	1.60995	+	0.320238i	0.916428	−	0.400200i	$-0.131059\pi$
$109$	16.8083	+	3.34339i	1.60995	+	0.320238i	0.693519	+	0.720438i	$0.256059\pi$
$110$	−0.964909	−	1.50949i	−0.0920004	−	0.143924i
$111$		0			0
$112$	6.90135	+	3.53900i	0.652116	+	0.334404i
$113$	9.98074	−	9.98074i	0.938909	−	0.938909i	−0.0593295	−	0.998238i	$-0.518896\pi$
$113$	9.98074	−	9.98074i	0.938909	−	0.938909i	0.998238	+	0.0593295i	$0.0188963\pi$
$114$		0			0
$115$	0.570609	−	2.86865i	0.0532096	−	0.267503i
$116$	−2.02274	−	1.47362i	−0.187807	−	0.136822i
$117$		0			0
$118$	−7.77105	−	3.40513i	−0.715383	−	0.313468i
$119$	−1.50371	+	3.63027i	−0.137844	+	0.332786i
$120$		0			0
$121$	−3.28515	−	7.93106i	−0.298650	−	0.721005i
$122$	8.97927	+	0.182156i	0.812945	+	0.0164917i
$123$		0			0
$124$	−4.85733	+	1.78481i	−0.436201	+	0.160281i
$125$	4.22757	+	6.32701i	0.378126	+	0.565905i
$126$		0			0
$127$	−9.01235			−0.799717			−0.399858	−	0.916577i	$-0.630941\pi$
$127$	−9.01235			−0.799717			−0.399858	+	0.916577i	$0.630941\pi$
$128$	10.2018	−	4.89114i	0.901720	−	0.432320i
$129$		0			0
$130$	3.62548	−	5.19465i	0.317976	−	0.455601i
$131$	−4.77693	−	7.14918i	−0.417362	−	0.624627i	0.561904	−	0.827202i	$-0.310069\pi$
$131$	−4.77693	−	7.14918i	−0.417362	−	0.624627i	−0.979267	+	0.202575i	$0.935069\pi$
$132$		0			0
$133$	−0.0340728	−	0.171296i	−0.00295449	−	0.0148532i
$134$	8.02702	+	0.162839i	0.693429	+	0.0140671i
$135$		0			0
$136$	2.88875	+	4.95074i	0.247709	+	0.424523i
$137$	−1.16308	+	2.80792i	−0.0993685	+	0.239897i	−0.965744	−	0.259496i	$-0.916444\pi$
$137$	−1.16308	+	2.80792i	−0.0993685	+	0.239897i	0.866376	+	0.499393i	$0.166444\pi$
$138$		0			0
$139$	6.85100	+	4.57769i	0.581094	+	0.388275i	0.811094	−	0.584916i	$-0.198873\pi$
$139$	6.85100	+	4.57769i	0.581094	+	0.388275i	−0.230000	+	0.973191i	$0.573873\pi$
$140$	−2.55480	−	1.86124i	−0.215920	−	0.157303i
$141$		0			0
$142$	−18.0969	−	3.98289i	−1.51866	−	0.334237i
$143$	−6.03934	+	6.03934i	−0.505035	+	0.505035i
$144$		0			0
$145$	0.721201	+	0.721201i	0.0598925	+	0.0598925i
$146$	3.49109	+	5.46142i	0.288925	+	0.451991i
$147$		0			0
$148$	−1.70722	−	2.79406i	−0.140333	−	0.229671i
$149$	8.41009	−	12.5866i	0.688982	−	1.03113i	−0.307838	−	0.951439i	$-0.599605\pi$
$149$	8.41009	−	12.5866i	0.688982	−	1.03113i	0.996819	−	0.0796950i	$-0.0253946\pi$
$150$		0			0
$151$	−15.1739	−	6.28523i	−1.23483	−	0.511485i	−0.332738	−	0.943019i	$-0.607972\pi$
$151$	−15.1739	−	6.28523i	−1.23483	−	0.511485i	−0.902096	+	0.431534i	$0.857972\pi$
$152$	−0.229012	−	0.111630i	−0.0185753	−	0.00905438i
$153$		0			0
$154$	2.95176	+	3.07400i	0.237860	+	0.247710i
$155$	2.06848	−	0.411447i	0.166145	−	0.0330482i
$156$		0			0
$157$	−3.65930	+	2.44507i	−0.292044	+	0.195138i	−0.692958	−	0.720978i	$-0.743693\pi$
$157$	−3.65930	+	2.44507i	−0.292044	+	0.195138i	0.400914	+	0.916116i	$0.368693\pi$
$158$	−2.61343	−	14.6898i	−0.207913	−	1.16865i
$159$		0			0
$160$	−4.41666	+	1.32415i	−0.349168	+	0.104684i
$161$			6.95765i			0.548340i
$162$		0			0
$163$	3.89914	−	2.60532i	0.305404	−	0.204065i	−0.393418	−	0.919360i	$-0.628708\pi$
$163$	3.89914	−	2.60532i	0.305404	−	0.204065i	0.698823	+	0.715295i	$0.253708\pi$
$164$	−0.0531320	+	1.30901i	−0.00414891	+	0.102217i
$165$		0			0
$166$	2.75934	−	2.64961i	0.214166	−	0.205650i
$167$	−9.51475	+	3.94114i	−0.736274	+	0.304975i	−0.719127	−	0.694878i	$-0.755458\pi$
$167$	−9.51475	+	3.94114i	−0.736274	+	0.304975i	−0.0171464	+	0.999853i	$0.505458\pi$
$168$		0			0
$169$	−15.8906	−	6.58210i	−1.22235	−	0.506315i
$170$	−0.850003	−	2.17590i	−0.0651923	−	0.166884i
$171$		0			0
$172$	17.6459	+	4.26063i	1.34549	+	0.324870i
$173$	10.2124	+	2.03137i	0.776434	+	0.154442i	0.567374	−	0.823460i	$-0.307960\pi$
$173$	10.2124	+	2.03137i	0.776434	+	0.154442i	0.209060	+	0.977903i	$0.432960\pi$
$174$		0			0
$175$	−5.94436	−	5.94436i	−0.449351	−	0.449351i
$176$	6.17551	−	0.714679i	0.465497	−	0.0538710i
$177$		0			0
$178$	−2.33381	+	10.6040i	−0.174927	+	0.794807i
$179$	−4.62243	+	23.2385i	−0.345497	+	1.73693i	0.283003	+	0.959119i	$0.408669\pi$
$179$	−4.62243	+	23.2385i	−0.345497	+	1.73693i	−0.628500	+	0.777810i	$0.716331\pi$
$180$		0			0
$181$	−6.85149	−	4.57802i	−0.509267	−	0.340282i	0.274243	−	0.961660i	$-0.411573\pi$
$181$	−6.85149	−	4.57802i	−0.509267	−	0.340282i	−0.783510	+	0.621379i	$0.786573\pi$
$182$	−6.04786	+	13.8022i	−0.448298	+	1.02309i
$183$		0			0
$184$	8.08036	+	6.14144i	0.595692	+	0.452753i
$185$	0.510675	+	1.23288i	0.0375456	+	0.0906431i
$186$		0			0
$187$	0.614458	+	3.08909i	0.0449336	+	0.225896i
$188$	4.59056	−	9.92382i	0.334801	−	0.723769i
$189$		0			0
$190$	0.0851447	+	0.0594247i	0.00617705	+	0.00431112i
$191$	2.15250			0.155750			0.0778748	−	0.996963i	$-0.475187\pi$
$191$	2.15250			0.155750			0.0778748	+	0.996963i	$0.475187\pi$
$192$		0			0
$193$	−5.53246			−0.398236			−0.199118	−	0.979976i	$-0.563808\pi$
$193$	−5.53246			−0.398236			−0.199118	+	0.979976i	$0.563808\pi$
$194$	13.2813	+	9.26935i	0.953541	+	0.665500i
$195$		0			0
$196$	−5.88203	−	2.72091i	−0.420145	−	0.194351i
$197$	−2.86767	−	14.4167i	−0.204313	−	1.02715i	−0.937728	−	0.347370i	$-0.887075\pi$
$197$	−2.86767	−	14.4167i	−0.204313	−	1.02715i	0.733415	−	0.679781i	$-0.237925\pi$
$198$		0			0
$199$	0.633559	+	1.52955i	0.0449118	+	0.108427i	0.944743	−	0.327811i	$-0.106311\pi$
$199$	0.633559	+	1.52955i	0.0449118	+	0.108427i	−0.899832	+	0.436237i	$0.856311\pi$
$200$	−12.1506	+	1.65654i	−0.859175	+	0.117135i
$201$		0			0
$202$	6.60039	−	15.0631i	0.464402	−	1.05984i
$203$	−2.01733	−	1.34794i	−0.141589	−	0.0946068i
$204$		0			0
$205$	0.104164	−	0.523666i	0.00727511	−	0.0365744i
$206$	4.07623	−	18.5210i	0.284005	−	1.29042i
$207$		0			0
$208$	10.6910	+	19.2068i	0.741285	+	1.33175i
$209$	−0.0989898	−	0.0989898i	−0.00684727	−	0.00684727i
$210$		0			0
$211$	8.05837	+	1.60291i	0.554761	+	0.110349i	0.464506	−	0.885570i	$-0.346232\pi$
$211$	8.05837	+	1.60291i	0.554761	+	0.110349i	0.0902547	+	0.995919i	$0.471232\pi$
$212$	4.91655	−	20.3625i	0.337670	−	1.39850i
$213$		0			0
$214$	4.87445	+	12.4780i	0.333211	+	0.852977i
$215$	−6.83507	−	2.83118i	−0.466148	−	0.193085i
$216$		0			0
$217$	−4.63504	+	1.91990i	−0.314647	+	0.130331i
$218$	17.4817	−	16.7865i	1.18401	−	1.13693i
$219$		0			0
$220$	−2.53153	−	0.102753i	−0.170676	−	0.00692763i
$221$	−9.25983	+	6.18722i	−0.622883	+	0.416197i
$222$		0			0
$223$		−	1.76595i		−	0.118256i	−0.998250	−	0.0591282i	$-0.981168\pi$
$223$		−	1.76595i		−	0.118256i	0.998250	−	0.0591282i	$-0.0188321\pi$
$224$	9.69000	−	5.13908i	0.647440	−	0.343369i
$225$		0			0
$226$	−3.49641	−	19.6529i	−0.232578	−	1.30729i
$227$	6.55957	−	4.38296i	0.435374	−	0.290908i	−0.318505	−	0.947921i	$-0.603181\pi$
$227$	6.55957	−	4.38296i	0.435374	−	0.290908i	0.753879	+	0.657014i	$0.228181\pi$
$228$		0			0
$229$	22.3445	−	4.44460i	1.47657	−	0.293707i	0.609853	−	0.792515i	$-0.291228\pi$
$229$	22.3445	−	4.44460i	1.47657	−	0.293707i	0.866713	+	0.498807i	$0.166228\pi$
$230$	−2.86492	−	2.98357i	−0.188907	−	0.196731i
$231$		0			0
$232$	−3.34612	+	1.15305i	−0.219684	+	0.0757011i
$233$	−3.96025	−	1.64039i	−0.259445	−	0.107466i	0.249170	−	0.968460i	$-0.419842\pi$
$233$	−3.96025	−	1.64039i	−0.259445	−	0.107466i	−0.508615	+	0.860994i	$0.669842\pi$
$234$		0			0
$235$	−2.47573	+	3.70519i	−0.161499	+	0.241700i
$236$	−10.2387	+	6.25602i	−0.666482	+	0.407232i
$237$		0			0
$238$	2.99294	+	4.68212i	0.194003	+	0.303497i
$239$	2.96983	+	2.96983i	0.192103	+	0.192103i	0.796604	−	0.604501i	$-0.206628\pi$
$239$	2.96983	+	2.96983i	0.192103	+	0.192103i	−0.604501	+	0.796604i	$0.706628\pi$
$240$		0			0
$241$	−16.9923	+	16.9923i	−1.09457	+	1.09457i	−0.0995381	+	0.995034i	$0.531737\pi$
$241$	−16.9923	+	16.9923i	−1.09457	+	1.09457i	−0.995034	+	0.0995381i	$0.968263\pi$
$242$	−11.8566	−	2.60948i	−0.762170	−	0.167744i
$243$		0			0
$244$	7.47891	−	10.2658i	0.478788	−	0.657201i
$245$	2.19613	+	1.46741i	0.140306	+	0.0937493i
$246$		0			0
$247$	0.189429	−	0.457321i	0.0120531	−	0.0290986i
$248$	−1.86160	+	7.07763i	−0.118212	+	0.449430i
$249$		0			0
$250$	10.7592	+	0.218264i	0.680468	+	0.0138042i
$251$	1.88276	+	9.46528i	0.118839	+	0.597443i	0.993606	+	0.112900i	$0.0360141\pi$
$251$	1.88276	+	9.46528i	0.118839	+	0.597443i	−0.874767	+	0.484543i	$0.838986\pi$
$252$		0			0
$253$	3.09838	+	4.63705i	0.194793	+	0.291529i
$254$	−7.29444	+	10.4516i	−0.457694	+	0.655792i
$255$		0			0
$256$	2.58492	−	15.7898i	0.161557	−	0.986863i
$257$	4.05808			0.253136			0.126568	−	0.991958i	$-0.459604\pi$
$257$	4.05808			0.253136			0.126568	+	0.991958i	$0.459604\pi$
$258$		0			0
$259$	−1.76361	−	2.63944i	−0.109586	−	0.164007i
$260$	−3.08983	−	8.40893i	−0.191623	−	0.521499i
$261$		0			0
$262$	−12.1573	−	0.246626i	−0.751078	−	0.0152366i
$263$	−8.26702	−	19.9584i	−0.509766	−	1.23068i	−0.944018	−	0.329893i	$-0.892987\pi$
$263$	−8.26702	−	19.9584i	−0.509766	−	1.23068i	0.434252	−	0.900791i	$-0.357013\pi$
$264$		0			0
$265$	−3.26704	+	7.88734i	−0.200693	+	0.484515i
$266$	−0.226229	−	0.0991296i	−0.0138710	−	0.00607802i
$267$		0			0
$268$	6.68577	−	9.17712i	0.408399	−	0.560582i
$269$	−4.65173	+	23.3858i	−0.283621	+	1.42586i	0.531741	+	0.846907i	$0.321538\pi$
$269$	−4.65173	+	23.3858i	−0.283621	+	1.42586i	−0.815362	+	0.578952i	$0.803462\pi$
$270$		0			0
$271$	−5.40955	+	5.40955i	−0.328607	+	0.328607i	−0.852057	−	0.523450i	$-0.824645\pi$
$271$	−5.40955	+	5.40955i	−0.328607	+	0.328607i	0.523450	+	0.852057i	$0.324645\pi$
$272$	8.07947	+	0.656964i	0.489890	+	0.0398343i
$273$		0			0
$274$	2.31496	+	3.62150i	0.139852	+	0.218783i
$275$	−6.60887	−	1.31458i	−0.398530	−	0.0792725i
$276$		0			0
$277$	−10.2748	+	15.3773i	−0.617351	+	0.923931i	0.382649	+	0.923894i	$0.375012\pi$
$277$	−10.2748	+	15.3773i	−0.617351	+	0.923931i	−1.00000		3.72366e-5i	$0.999988\pi$
$278$	10.8538	−	4.23999i	0.650969	−	0.254297i
$279$		0			0
$280$	−4.22628	+	1.45634i	−0.252568	+	0.0870329i
$281$	−22.5624	+	9.34566i	−1.34596	+	0.557515i	−0.935165	−	0.354212i	$-0.884749\pi$
$281$	−22.5624	+	9.34566i	−1.34596	+	0.557515i	−0.410796	+	0.911727i	$0.634749\pi$
$282$		0			0
$283$	−30.7342	+	6.11341i	−1.82696	+	0.363405i	−0.984504	−	0.175362i	$-0.943890\pi$
$283$	−30.7342	+	6.11341i	−1.82696	+	0.363405i	−0.842455	+	0.538767i	$0.818890\pi$
$284$	−19.2663	+	17.7633i	−1.14324	+	1.05406i
$285$		0			0
$286$	2.11567	+	11.8919i	0.125102	+	0.703186i
$287$			1.27011i			0.0749720i
$288$		0			0
$289$		−	12.8932i		−	0.758421i
$290$	1.42010	−	0.252648i	0.0833914	−	0.0148360i
$291$		0			0
$292$	9.15924	+	0.371768i	0.536004	+	0.0217561i
$293$	−11.5609	+	2.29960i	−0.675394	+	0.134344i	−0.520858	−	0.853643i	$-0.674388\pi$
$293$	−11.5609	+	2.29960i	−0.675394	+	0.134344i	−0.154535	+	0.987987i	$0.549388\pi$
$294$		0			0
$295$	4.51781	−	1.87134i	0.263037	−	0.108954i
$296$	−4.62207	−	0.281603i	−0.268652	−	0.0163679i
$297$		0			0
$298$	−7.78967	−	19.9405i	−0.451243	−	1.15512i
$299$	−10.9556	+	16.3962i	−0.633577	+	0.948215i
$300$		0			0
$301$	17.2608	+	3.43339i	0.994897	+	0.197897i
$302$	−19.5705	+	12.5100i	−1.12615	+	0.719868i
$303$		0			0
$304$	−0.314815	+	0.175234i	−0.0180559	+	0.0100503i
$305$	−3.66024	+	3.66024i	−0.209585	+	0.209585i
$306$		0			0
$307$	−3.01807	+	15.1728i	−0.172250	+	0.865960i	0.793914	+	0.608031i	$0.208040\pi$
$307$	−3.01807	+	15.1728i	−0.172250	+	0.865960i	−0.966164	+	0.257929i	$0.916960\pi$
$308$	5.95401	−	0.935108i	0.339261	−	0.0532827i
$309$		0			0
$310$	1.19704	−	2.73184i	0.0679874	−	0.155158i
$311$	11.7272	−	28.3120i	0.664989	−	1.60543i	−0.124895	−	0.992170i	$-0.539859\pi$
$311$	11.7272	−	28.3120i	0.664989	−	1.60543i	0.789884	−	0.613256i	$-0.210141\pi$
$312$		0			0
$313$	−6.18242	−	14.9257i	−0.349451	−	0.843649i	−0.996685	−	0.0813577i	$-0.974074\pi$
$313$	−6.18242	−	14.9257i	−0.349451	−	0.843649i	0.647234	−	0.762291i	$-0.275926\pi$
$314$	−0.126235	+	6.22268i	−0.00712387	+	0.351166i
$315$		0			0
$316$	−19.1510	−	8.85885i	−1.07733	−	0.498349i
$317$	−15.9809	−	23.9172i	−0.897579	−	1.34332i	−0.938905	−	0.344176i	$-0.888158\pi$
$317$	−15.9809	−	23.9172i	−0.897579	−	1.34332i	0.0413265	−	0.999146i	$-0.486842\pi$
$318$		0			0
$319$	−1.94475			−0.108885
$320$	−2.03915	+	6.19374i	−0.113992	+	0.346241i
$321$		0			0
$322$	8.06878	+	5.63140i	0.449655	+	0.313826i
$323$	−0.101414	−	0.151776i	−0.00564281	−	0.00844506i
$324$		0			0
$325$	−4.64824	−	23.3683i	−0.257838	−	1.29624i
$326$	0.134509	−	6.63053i	0.00744977	−	0.367231i
$327$		0			0
$328$	1.47506	+	1.12111i	0.0814463	+	0.0619029i
$329$	4.05661	−	9.79352i	0.223648	−	0.539934i
$330$		0			0
$331$	17.2884	+	11.5517i	0.950256	+	0.634941i	0.931057	−	0.364875i	$-0.118888\pi$
$331$	17.2884	+	11.5517i	0.950256	+	0.634941i	0.0191998	+	0.999816i	$0.493888\pi$
$332$	−0.839388	−	5.34455i	−0.0460674	−	0.293320i
$333$		0			0
$334$	−3.13054	+	14.2241i	−0.171296	+	0.778310i
$335$	−3.27207	+	3.27207i	−0.178772	+	0.178772i
$336$		0			0
$337$	−0.552793	−	0.552793i	−0.0301125	−	0.0301125i	0.691890	−	0.722003i	$-0.256778\pi$
$337$	−0.552793	−	0.552793i	−0.0301125	−	0.0301125i	−0.722003	+	0.691890i	$0.756778\pi$
$338$	−20.4948	+	13.1008i	−1.11477	+	0.712592i
$339$		0			0
$340$	−3.21136	−	0.775387i	−0.174161	−	0.0420513i
$341$	−2.23414	+	3.34362i	−0.120985	+	0.181067i
$342$		0			0
$343$	−18.3444	−	7.59848i	−0.990502	−	0.410280i
$344$	19.2233	−	17.0155i	1.03645	−	0.917412i
$345$		0			0
$346$	10.6215	−	10.1991i	0.571016	−	0.548309i
$347$	−20.3020	+	4.03831i	−1.08987	+	0.216788i	−0.707140	−	0.707074i	$-0.750015\pi$
$347$	−20.3020	+	4.03831i	−1.08987	+	0.216788i	−0.382726	+	0.923862i	$0.625015\pi$
$348$		0			0
$349$	−24.9728	+	16.6863i	−1.33676	+	0.893195i	−0.998848	−	0.0479825i	$-0.984721\pi$
$349$	−24.9728	+	16.6863i	−1.33676	+	0.893195i	−0.337913	+	0.941177i	$0.609721\pi$
$350$	−11.7049	+	2.08240i	−0.625654	+	0.111309i
$351$		0			0
$352$	4.16954	−	7.74018i	0.222237	−	0.412553i
$353$			14.1087i			0.750928i	0.926837	+	0.375464i	$0.122517\pi$
$353$			14.1087i			0.750928i	−0.926837	+	0.375464i	$0.877483\pi$
$354$		0			0
$355$	8.88008	−	5.93348i	0.471306	−	0.314916i
$356$	10.4085	+	11.2892i	0.551652	+	0.598329i
$357$		0			0
$358$	23.2084	+	24.1695i	1.22660	+	1.27740i
$359$	21.9299	−	9.08367i	1.15742	−	0.479418i	0.280403	−	0.959882i	$-0.409532\pi$
$359$	21.9299	−	9.08367i	1.15742	−	0.479418i	0.877014	+	0.480465i	$0.159532\pi$
$360$		0			0
$361$	−17.5462	−	7.26788i	−0.923485	−	0.382520i
$362$	−10.8546	+	4.24029i	−0.570505	+	0.222865i
$363$		0			0
$364$	11.1113	+	18.1849i	0.582392	+	0.953150i
$365$	−3.66412	−	0.728839i	−0.191789	−	0.0381492i
$366$		0			0
$367$	11.6037	+	11.6037i	0.605711	+	0.605711i	0.941822	−	0.336111i	$-0.109112\pi$
$367$	11.6037	+	11.6037i	0.605711	+	0.605711i	−0.336111	+	0.941822i	$0.609112\pi$
$368$	13.6623	−	4.40000i	0.712198	−	0.229366i
$369$		0			0
$370$	1.84310	+	0.405642i	0.0958181	+	0.0210883i
$371$	3.96196	−	19.9181i	0.205695	−	1.03410i
$372$		0			0
$373$	12.5475	+	8.38398i	0.649685	+	0.434106i	0.836259	−	0.548335i	$-0.184738\pi$
$373$	12.5475	+	8.38398i	0.649685	+	0.434106i	−0.186573	+	0.982441i	$0.559738\pi$
$374$	4.07974	+	1.78767i	0.210958	+	0.0924381i
$375$		0			0
$376$	−7.79311	−	13.3558i	−0.401899	−	0.688774i
$377$	−2.63150	−	6.35301i	−0.135529	−	0.327197i
$378$		0			0
$379$	−0.563697	−	2.83390i	−0.0289552	−	0.145567i	0.963603	−	0.267336i	$-0.0861434\pi$
$379$	−0.563697	−	2.83390i	−0.0289552	−	0.145567i	−0.992559	+	0.121769i	$0.961143\pi$
$380$	0.137829	−	0.0506449i	0.00707050	−	0.00259803i
$381$		0			0
$382$	1.74220	−	2.49625i	0.0891386	−	0.127719i
$383$	34.7104			1.77362			0.886808	−	0.462137i	$-0.152917\pi$
$383$	34.7104			1.77362			0.886808	+	0.462137i	$0.152917\pi$
$384$		0			0
$385$	−2.45629			−0.125184
$386$	−4.47788	+	6.41599i	−0.227918	+	0.326565i
$387$		0			0
$388$	21.4993	−	7.89984i	1.09146	−	0.401053i
$389$	−6.28614	−	31.6026i	−0.318720	−	1.60231i	−0.725123	−	0.688619i	$-0.758217\pi$
$389$	−6.28614	−	31.6026i	−0.318720	−	1.60231i	0.406403	−	0.913694i	$-0.366783\pi$
$390$		0			0
$391$	2.78283	+	6.71836i	0.140734	+	0.339762i
$392$	−7.91624	+	4.61912i	−0.399831	+	0.233301i
$393$		0			0
$394$	−19.0401	−	8.34303i	−0.959227	−	0.420316i
$395$	7.15026	+	4.77765i	0.359769	+	0.240390i
$396$		0			0
$397$	−0.587551	+	2.95382i	−0.0294883	+	0.148248i	−0.992724	−	0.120408i	$-0.961580\pi$
$397$	−0.587551	+	2.95382i	−0.0294883	+	0.148248i	0.963236	+	0.268656i	$0.0865796\pi$
$398$	2.28661	+	0.503252i	0.114617	+	0.0252257i
$399$		0			0
$400$	−7.91338	+	15.4318i	−0.395669	+	0.771589i
$401$	−14.8685	−	14.8685i	−0.742498	−	0.742498i	0.230560	−	0.973058i	$-0.425944\pi$
$401$	−14.8685	−	14.8685i	−0.742498	−	0.742498i	−0.973058	+	0.230560i	$0.925944\pi$
$402$		0			0
$403$	−13.9459	−	2.77400i	−0.694693	−	0.138183i
$404$	−12.1264	−	19.8463i	−0.603313	−	0.987390i
$405$		0			0
$406$	−3.19600	+	1.24850i	−0.158615	+	0.0619620i
$407$	−2.35079	−	0.973727i	−0.116524	−	0.0482659i
$408$		0			0
$409$	14.6721	−	6.07739i	0.725490	−	0.300508i	0.0107925	−	0.999942i	$-0.496565\pi$
$409$	14.6721	−	6.07739i	0.725490	−	0.300508i	0.714697	+	0.699434i	$0.246565\pi$
$410$	−0.522986	−	0.544645i	−0.0258285	−	0.0268981i
$411$		0			0
$412$	−18.1796	−	19.7178i	−0.895643	−	0.971426i
$413$	−9.67206	+	6.46266i	−0.475931	+	0.318007i
$414$		0			0
$415$			2.20486i			0.108232i
$416$	30.9272	+	3.14736i	1.51633	+	0.154312i
$417$		0			0
$418$	−0.194919	+	0.0346777i	−0.00953380	+	0.00169614i
$419$	21.4066	−	14.3034i	1.04578	−	0.698768i	0.0909301	−	0.995857i	$-0.471016\pi$
$419$	21.4066	−	14.3034i	1.04578	−	0.698768i	0.954850	+	0.297090i	$0.0960160\pi$
$420$		0			0
$421$	11.3448	−	2.25662i	0.552911	−	0.109981i	0.0892757	−	0.996007i	$-0.471545\pi$
$421$	11.3448	−	2.25662i	0.552911	−	0.109981i	0.463635	+	0.886026i	$0.346545\pi$
$422$	8.38119	−	8.04790i	0.407990	−	0.391766i
$423$		0			0
$424$	−19.6350	−	22.1828i	−0.953560	−	1.07729i
$425$	−8.11746	−	3.36236i	−0.393755	−	0.163099i
$426$		0			0
$427$	6.84106	−	10.2384i	0.331062	−	0.495469i
$428$	18.4160	+	4.44656i	0.890170	+	0.214933i
$429$		0			0
$430$	−8.81550	+	5.63511i	−0.425121	+	0.271749i
$431$	16.7738	+	16.7738i	0.807965	+	0.807965i	0.984326	−	0.176361i	$-0.0564326\pi$
$431$	16.7738	+	16.7738i	0.807965	+	0.807965i	−0.176361	+	0.984326i	$0.556433\pi$
$432$		0			0
$433$	14.5447	−	14.5447i	0.698975	−	0.698975i	−0.265215	−	0.964189i	$-0.585443\pi$
$433$	14.5447	−	14.5447i	0.698975	−	0.698975i	0.964189	+	0.265215i	$0.0854428\pi$
$434$	−1.52502	+	6.92918i	−0.0732033	+	0.332611i
$435$		0			0
$436$	−5.31791	−	33.8602i	−0.254682	−	1.62161i
$437$	−0.268747	−	0.179571i	−0.0128559	−	0.00859004i
$438$		0			0
$439$	5.28898	−	12.7687i	0.252429	−	0.609418i	−0.745970	−	0.665980i	$-0.768014\pi$
$439$	5.28898	−	12.7687i	0.252429	−	0.609418i	0.998399	+	0.0565614i	$0.0180137\pi$
$440$	−2.16814	+	2.85265i	−0.103362	+	0.135995i
$441$		0			0
$442$	−0.319437	+	15.7464i	−0.0151941	+	0.748981i
$443$	2.91450	+	14.6522i	0.138472	+	0.696147i	0.986179	+	0.165682i	$0.0529826\pi$
$443$	2.91450	+	14.6522i	0.138472	+	0.696147i	−0.847707	+	0.530465i	$0.822017\pi$
$444$		0			0
$445$	−3.47677	−	5.20336i	−0.164815	−	0.246663i
$446$	−2.04796	−	1.42933i	−0.0969739	−	0.0676805i
$447$		0			0
$448$	1.88314	−	15.3970i	0.0889698	−	0.727438i
$449$	32.7646			1.54626			0.773130	−	0.634248i	$-0.218690\pi$
$449$	32.7646			1.54626			0.773130	+	0.634248i	$0.218690\pi$
$450$		0			0
$451$	0.565604	+	0.846486i	0.0266332	+	0.0398595i
$452$	−25.6213	−	11.8519i	−1.20513	−	0.557468i
$453$		0			0
$454$	0.226286	−	11.1546i	0.0106201	−	0.523512i
$455$	−3.32369	−	8.02409i	−0.155817	−	0.376175i
$456$		0			0
$457$	−10.4684	+	25.2729i	−0.489691	+	1.18222i	0.465185	+	0.885213i	$0.345988\pi$
$457$	−10.4684	+	25.2729i	−0.489691	+	1.18222i	−0.954876	+	0.297005i	$0.904012\pi$
$458$	12.9309	−	29.5103i	0.604219	−	1.37892i
$459$		0			0
$460$	−5.77885	+	0.907598i	−0.269440	+	0.0423170i
$461$	−1.87909	+	9.44683i	−0.0875181	+	0.439983i	0.912036	+	0.410111i	$0.134510\pi$
$461$	−1.87909	+	9.44683i	−0.0875181	+	0.439983i	−0.999554	+	0.0298721i	$0.990490\pi$
$462$		0			0
$463$	−2.57440	+	2.57440i	−0.119643	+	0.119643i	−0.764393	−	0.644751i	$-0.776961\pi$
$463$	−2.57440	+	2.57440i	−0.119643	+	0.119643i	0.644751	+	0.764393i	$0.276961\pi$
$464$	−1.37111	+	4.81375i	−0.0636521	+	0.223473i
$465$		0			0
$466$	−5.10772	+	3.26499i	−0.236610	+	0.151248i
$467$	29.4251	+	5.85303i	1.36163	+	0.270846i	0.821248	−	0.570572i	$-0.193278\pi$
$467$	29.4251	+	5.85303i	1.36163	+	0.270846i	0.540386	+	0.841417i	$0.318278\pi$
$468$		0			0
$469$	6.11557	−	9.15259i	0.282391	−	0.422627i
$470$	2.29309	+	5.87001i	0.105772	+	0.270763i
$471$		0			0
$472$	−1.03192	+	16.9373i	−0.0474979	+	0.779602i
$473$	13.0327	−	5.39834i	0.599246	−	0.248216i
$474$		0			0
$475$	0.383026	−	0.0761886i	0.0175744	−	0.00349577i
$476$	7.85228	+	0.318719i	0.359909	+	0.0146085i
$477$		0			0
$478$	5.84784	−	1.04038i	0.267474	−	0.0475858i
$479$		−	13.1017i		−	0.598630i	−0.954154	−	0.299315i	$-0.903242\pi$
$479$		−	13.1017i		−	0.598630i	0.954154	−	0.299315i	$-0.0967582\pi$
$480$		0			0
$481$		−	8.99701i		−	0.410228i
$482$	5.95267	+	33.4593i	0.271137	+	1.52403i
$483$		0			0
$484$	−12.6227	+	11.6380i	−0.573760	+	0.528999i
$485$	−9.15542	+	1.82113i	−0.415726	+	0.0826931i
$486$		0			0
$487$	8.42271	−	3.48880i	0.381670	−	0.158093i	−0.183596	−	0.983002i	$-0.558774\pi$
$487$	8.42271	−	3.48880i	0.381670	−	0.158093i	0.565265	+	0.824909i	$0.308774\pi$
$488$	−5.85194	−	16.9822i	−0.264905	−	0.768750i
$489$		0			0
$490$	3.47926	−	1.35916i	0.157177	−	0.0614004i
$491$	6.91581	−	10.3502i	0.312106	−	0.467100i	−0.641942	−	0.766753i	$-0.721871\pi$
$491$	6.91581	−	10.3502i	0.312106	−	0.467100i	0.954048	+	0.299654i	$0.0968711\pi$
$492$		0			0
$493$	−2.48708	−	0.494711i	−0.112013	−	0.0222807i
$494$	−0.377034	−	0.589828i	−0.0169636	−	0.0265376i
$495$		0			0
$496$	6.70117	+	7.88741i	0.300892	+	0.354155i
$497$	−17.9645	+	17.9645i	−0.805818	+	0.805818i
$498$		0			0
$499$	−0.940281	+	4.72711i	−0.0420927	+	0.211615i	−0.996108	−	0.0881445i	$-0.971906\pi$
$499$	−0.940281	+	4.72711i	−0.0420927	+	0.211615i	0.954015	+	0.299759i	$0.0969063\pi$
$500$	8.96139	−	12.3007i	0.400766	−	0.550104i
$501$		0			0
$502$	12.5007	+	5.47760i	0.557936	+	0.244477i
$503$	−10.6536	+	25.7202i	−0.475022	+	1.14680i	0.486894	+	0.873461i	$0.338130\pi$
$503$	−10.6536	+	25.7202i	−0.475022	+	1.14680i	−0.961916	+	0.273344i	$0.911870\pi$
$504$		0			0
$505$	3.62734	+	8.75716i	0.161414	+	0.389689i
$506$	7.88536	+	0.159965i	0.350547	+	0.00711131i
$507$		0			0
$508$	6.21671	+	16.9187i	0.275822	+	0.750646i
$509$	13.0686	+	19.5585i	0.579256	+	0.866917i	0.999174	−	0.0406446i	$-0.0129411\pi$
$509$	13.0686	+	19.5585i	0.579256	+	0.866917i	−0.419918	+	0.907562i	$0.637941\pi$
$510$		0			0
$511$	8.88701			0.393138
$512$	−16.2192	−	15.7777i	−0.716796	−	0.697283i
$513$		0			0
$514$	3.28454	−	4.70615i	0.144875	−	0.207579i
$515$	6.07253	+	9.08818i	0.267588	+	0.400473i
$516$		0			0
$517$	−1.65765	−	8.33356i	−0.0729033	−	0.366510i
$518$	−4.48839	−	0.0910529i	−0.197208	−	0.00400064i
$519$		0			0
$520$	−12.2527	−	3.22277i	−0.537315	−	0.141328i
$521$	−7.67162	+	18.5209i	−0.336100	+	0.811417i	0.661983	+	0.749519i	$0.269715\pi$
$521$	−7.67162	+	18.5209i	−0.336100	+	0.811417i	−0.998083	+	0.0618976i	$0.980285\pi$
$522$		0			0
$523$	23.7322	+	15.8574i	1.03774	+	0.693394i	0.952988	−	0.303008i	$-0.0979908\pi$
$523$	23.7322	+	15.8574i	1.03774	+	0.693394i	0.0847500	+	0.996402i	$0.472991\pi$
$524$	−10.1259	+	13.8991i	−0.442351	+	0.607187i
$525$		0			0
$526$	−29.8368	−	6.56670i	−1.30095	−	0.286322i
$527$	−3.70773	+	3.70773i	−0.161511	+	0.161511i
$528$		0			0
$529$	−7.15862	−	7.15862i	−0.311244	−	0.311244i
$530$	6.50264	+	10.1727i	0.282457	+	0.441872i
$531$		0			0
$532$	−0.298066	+	0.182124i	−0.0129228	+	0.00789607i
$533$	−1.99992	+	2.99309i	−0.0866261	+	0.129645i
$534$		0			0
$535$	−7.13335	−	2.95473i	−0.308402	−	0.127744i
$536$	−5.23134	−	15.1813i	−0.225960	−	0.655732i
$537$		0			0
$538$	23.3555	+	24.3227i	1.00693	+	1.04863i
$539$	−4.93945	+	0.982518i	−0.212757	+	0.0423201i
$540$		0			0
$541$	9.15217	−	6.11529i	0.393483	−	0.262917i	−0.343052	−	0.939316i	$-0.611461\pi$
$541$	9.15217	−	6.11529i	0.393483	−	0.262917i	0.736535	+	0.676400i	$0.236461\pi$
$542$	1.89505	+	10.6518i	0.0813994	+	0.457536i
$543$		0			0
$544$	7.30127	−	8.83802i	0.313039	−	0.378927i
$545$			13.9688i			0.598359i
$546$		0			0
$547$	22.1909	−	14.8275i	0.948813	−	0.633976i	0.0181423	−	0.999835i	$-0.494225\pi$
$547$	22.1909	−	14.8275i	0.948813	−	0.633976i	0.930670	+	0.365859i	$0.119225\pi$
$548$	6.07354	+	0.246521i	0.259449	+	0.0105309i
$549$		0			0
$550$	−6.87362	+	6.60029i	−0.293092	+	0.281437i
$551$	0.104131	−	0.0431326i	0.00443614	−	0.00183751i
$552$		0			0
$553$	−18.8995	−	7.82843i	−0.803689	−	0.332899i
$554$	9.51678	+	24.3617i	0.404329	+	1.03503i
$555$		0			0
$556$	3.86779	−	16.0189i	0.164031	−	0.679354i
$557$	3.07874	+	0.612399i	0.130450	+	0.0259482i	0.259884	−	0.965640i	$-0.416316\pi$
$557$	3.07874	+	0.612399i	0.130450	+	0.0259482i	−0.129433	+	0.991588i	$0.541316\pi$
$558$		0			0
$559$	35.2700	+	35.2700i	1.49176	+	1.49176i
$560$	−1.73176	+	6.07994i	−0.0731803	+	0.256924i
$561$		0			0
$562$	−7.42349	+	33.7298i	−0.313141	+	1.42281i
$563$	−3.12631	+	15.7170i	−0.131758	+	0.662394i	0.857294	+	0.514827i	$0.172144\pi$
$563$	−3.12631	+	15.7170i	−0.131758	+	0.662394i	−0.989052	+	0.147566i	$0.952856\pi$
$564$		0			0
$565$	9.56607	+	6.39184i	0.402447	+	0.268907i
$566$	−17.7860	+	40.5905i	−0.747602	+	1.70615i
$567$		0			0
$568$	5.00625	+	36.7204i	0.210057	+	1.54075i
$569$	−9.52243	−	22.9892i	−0.399201	−	0.963756i	−0.987856	−	0.155372i	$-0.950342\pi$
$569$	−9.52243	−	22.9892i	−0.399201	−	0.963756i	0.588655	−	0.808384i	$-0.299658\pi$
$570$		0			0
$571$	−1.30200	−	6.54559i	−0.0544870	−	0.273924i	0.943932	−	0.330141i	$-0.107096\pi$
$571$	−1.30200	−	6.54559i	−0.0544870	−	0.273924i	−0.998419	+	0.0562165i	$0.982096\pi$
$572$	15.5035	+	7.17159i	0.648232	+	0.299859i
$573$		0			0
$574$	1.47294	+	1.02800i	0.0614794	+	0.0429080i
$575$	−15.5577			−0.648800
$576$		0			0
$577$	41.6755			1.73497			0.867487	−	0.497460i	$-0.165734\pi$
$577$	41.6755			1.73497			0.867487	+	0.497460i	$0.165734\pi$
$578$	−14.9522	−	10.4355i	−0.621928	−	0.434059i
$579$		0			0
$580$	0.856412	−	1.85138i	0.0355606	−	0.0768744i
$581$	−1.02324	−	5.14417i	−0.0424511	−	0.213416i
$582$		0			0
$583$	−6.22942	−	15.0391i	−0.257996	−	0.622858i
$584$	7.84446	−	10.3210i	0.324606	−	0.427088i
$585$		0			0
$586$	−6.69033	+	15.2684i	−0.276375	+	0.630731i
$587$	−8.51613	−	5.69029i	−0.351498	−	0.234864i	0.367268	−	0.930115i	$-0.380293\pi$
$587$	−8.51613	−	5.69029i	−0.351498	−	0.234864i	−0.718767	+	0.695251i	$0.755293\pi$
$588$		0			0
$589$	0.0454683	−	0.228584i	0.00187349	−	0.00941865i
$590$	1.48645	−	6.75393i	0.0611962	−	0.278055i
$591$		0			0
$592$	−4.06759	+	5.13228i	−0.167177	+	0.210935i
$593$	17.7593	+	17.7593i	0.729285	+	0.729285i	0.970477	−	0.241192i	$-0.0775384\pi$
$593$	17.7593	+	17.7593i	0.729285	+	0.729285i	−0.241192	+	0.970477i	$0.577538\pi$
$594$		0			0
$595$	−3.14128	−	0.624839i	−0.128780	−	0.0256159i
$596$	−29.4298	−	7.10587i	−1.20549	−	0.291068i
$597$		0			0
$598$	10.1474	+	25.9759i	0.414956	+	1.06223i
$599$	23.1403	+	9.58504i	0.945488	+	0.391634i	0.801533	−	0.597950i	$-0.204018\pi$
$599$	23.1403	+	9.58504i	0.945488	+	0.391634i	0.143955	+	0.989584i	$0.454018\pi$
$600$		0			0
$601$	10.7219	−	4.44117i	0.437356	−	0.181159i	−0.153131	−	0.988206i	$-0.548936\pi$
$601$	10.7219	−	4.44117i	0.437356	−	0.181159i	0.590487	+	0.807047i	$0.298936\pi$
$602$	17.9523	−	17.2384i	0.731681	−	0.702585i
$603$		0			0
$604$	−1.33219	+	32.8212i	−0.0542061	+	1.33548i
$605$	5.81797	−	3.88744i	0.236534	−	0.158047i
$606$		0			0
$607$		−	23.5570i		−	0.956147i	−0.878320	−	0.478074i	$-0.841335\pi$
$607$		−	23.5570i		−	0.956147i	0.878320	−	0.478074i	$-0.158665\pi$
$608$	−0.0515879	+	0.506922i	−0.00209216	+	0.0205584i
$609$		0			0
$610$	1.28224	+	7.20731i	0.0519163	+	0.291815i
$611$	24.9806	−	16.6915i	1.01061	−	0.675267i
$612$		0			0
$613$	−7.55995	+	1.50377i	−0.305343	+	0.0607366i	−0.345384	−	0.938461i	$-0.612251\pi$
$613$	−7.55995	+	1.50377i	−0.305343	+	0.0607366i	0.0400405	+	0.999198i	$0.487251\pi$
$614$	15.1532	+	15.7807i	0.611531	+	0.636857i
$615$		0			0
$616$	3.73463	−	7.66172i	0.150473	−	0.308699i
$617$	−41.1541	−	17.0466i	−1.65680	−	0.686270i	−0.658975	−	0.752165i	$-0.729010\pi$
$617$	−41.1541	−	17.0466i	−1.65680	−	0.686270i	−0.997827	+	0.0658956i	$0.979010\pi$
$618$		0			0
$619$	25.0137	−	37.4356i	1.00538	−	1.50466i	0.148662	−	0.988888i	$-0.452503\pi$
$619$	25.0137	−	37.4356i	1.00538	−	1.50466i	0.856723	−	0.515777i	$-0.172497\pi$
$620$	−2.19924	−	3.59931i	−0.0883236	−	0.144552i
$621$		0			0
$622$	−23.3416	−	36.5153i	−0.935912	−	1.46413i
$623$	10.5265	+	10.5265i	0.421734	+	0.421734i
$624$		0			0
$625$	10.9429	−	10.9429i	0.437718	−	0.437718i
$626$	−22.3132	−	4.91084i	−0.891815	−	0.196277i
$627$		0			0
$628$	7.11425	+	5.18292i	0.283890	+	0.206821i
$629$	−2.75865	−	1.84327i	−0.109994	−	0.0734960i
$630$		0			0
$631$	−14.4914	+	34.9853i	−0.576893	+	1.39274i	0.318694	+	0.947858i	$0.396756\pi$
$631$	−14.4914	+	34.9853i	−0.576893	+	1.39274i	−0.895587	+	0.444886i	$0.853244\pi$
$632$	−25.7740	+	15.0391i	−1.02524	+	0.598224i
$633$		0			0
$634$	−40.6714	−	0.825073i	−1.61527	−	0.0327678i
$635$	−1.43312	−	7.20479i	−0.0568717	−	0.285913i
$636$		0			0
$637$	−9.89337	−	14.8065i	−0.391989	−	0.586654i
$638$	−1.57405	+	2.25533i	−0.0623172	+	0.0892892i
$639$		0			0
$640$	5.53241	+	7.37790i	0.218688	+	0.291637i
$641$	7.36049			0.290722			0.145361	−	0.989379i	$-0.453566\pi$
$641$	7.36049			0.290722			0.145361	+	0.989379i	$0.453566\pi$
$642$		0			0
$643$	5.65643	+	8.46545i	0.223068	+	0.333845i	0.926076	−	0.377337i	$-0.123160\pi$
$643$	5.65643	+	8.46545i	0.223068	+	0.333845i	−0.703008	+	0.711182i	$0.748160\pi$
$644$	13.0615	−	4.79938i	0.514693	−	0.189122i
$645$		0			0
$646$	−0.258097	−	0.00523585i	−0.0101547	−	0.000206002i
$647$	15.0418	+	36.3142i	0.591356	+	1.42766i	0.882194	+	0.470886i	$0.156066\pi$
$647$	15.0418	+	36.3142i	0.591356	+	1.42766i	−0.290838	+	0.956772i	$0.593934\pi$
$648$		0			0
$649$	−3.56817	+	8.61432i	−0.140063	+	0.338142i
$650$	−30.8624	−	13.5233i	−1.21052	−	0.530429i
$651$		0			0
$652$	−7.58054	−	5.52262i	−0.296877	−	0.216283i
$653$	−0.411603	+	2.06927i	−0.0161073	+	0.0809767i	−0.988003	−	0.154436i	$-0.950644\pi$
$653$	−0.411603	+	2.06927i	−0.0161073	+	0.0809767i	0.971896	+	0.235412i	$0.0756441\pi$
$654$		0			0
$655$	4.95569	−	4.95569i	0.193635	−	0.193635i
$656$	2.49403	−	0.803213i	0.0973756	−	0.0313602i
$657$		0			0
$658$	−8.07418	−	12.6312i	−0.314764	−	0.492414i
$659$	13.9933	+	2.78344i	0.545101	+	0.108427i	0.459957	−	0.887941i	$-0.347865\pi$
$659$	13.9933	+	2.78344i	0.545101	+	0.108427i	0.0851445	+	0.996369i	$0.472865\pi$
$660$		0			0
$661$	−2.17698	+	3.25808i	−0.0846746	+	0.126724i	−0.871389	−	0.490593i	$-0.836780\pi$
$661$	−2.17698	+	3.25808i	−0.0846746	+	0.126724i	0.786715	+	0.617317i	$0.211780\pi$
$662$	27.3895	−	10.6995i	1.06452	−	0.415850i
$663$		0			0
$664$	−6.87745	−	3.35235i	−0.266897	−	0.130096i
$665$	0.131522	−	0.0544780i	0.00510019	−	0.00211257i
$666$		0			0
$667$	−4.40382	+	0.875975i	−0.170517	+	0.0339179i
$668$	13.9619	+	15.1432i	0.540202	+	0.585910i
$669$		0			0
$670$	1.14626	+	6.44298i	0.0442838	+	0.248914i
$671$		−	9.87001i		−	0.381027i
$672$		0			0
$673$			36.5991i			1.41079i	0.708813	+	0.705397i	$0.249231\pi$
$673$			36.5991i			1.41079i	−0.708813	+	0.705397i	$0.750769\pi$
$674$	−1.08849	+	0.193652i	−0.0419272	+	0.00745919i
$675$		0			0
$676$	−1.39511	+	34.3714i	−0.0536582	+	1.32198i
$677$	16.1895	−	3.22028i	0.622211	−	0.123766i	0.126090	−	0.992019i	$-0.459757\pi$
$677$	16.1895	−	3.22028i	0.622211	−	0.123766i	0.496121	+	0.868253i	$0.334757\pi$
$678$		0			0
$679$	20.5154	−	8.49775i	0.787308	−	0.326114i
$680$	−3.49844	+	3.09663i	−0.134159	+	0.118750i
$681$		0			0
$682$	2.06932	+	5.29720i	0.0792384	+	0.202840i
$683$	−13.9637	+	20.8982i	−0.534307	+	0.799647i	−0.996182	−	0.0872981i	$-0.972177\pi$
$683$	−13.9637	+	20.8982i	−0.534307	+	0.799647i	0.461875	+	0.886945i	$0.347177\pi$
$684$		0			0
$685$	−2.42970	−	0.483297i	−0.0928341	−	0.0184658i
$686$	−23.6596	+	15.1238i	−0.903326	+	0.577431i
$687$		0			0
$688$	−4.17376	−	36.0653i	−0.159123	−	1.37498i
$689$	40.6999	−	40.6999i	1.55054	−	1.55054i
$690$		0			0
$691$	−0.174353	+	0.876532i	−0.00663270	+	0.0333449i	−0.983960	−	0.178390i	$-0.942911\pi$
$691$	−0.174353	+	0.876532i	−0.00663270	+	0.0333449i	0.977327	+	0.211735i	$0.0679112\pi$
$692$	−3.23105	−	20.5727i	−0.122826	−	0.782059i
$693$		0			0
$694$	−11.7488	+	26.8127i	−0.445979	+	1.01780i
$695$	−2.57014	+	6.20486i	−0.0974909	+	0.235364i
$696$		0			0
$697$	0.508002	+	1.22642i	0.0192419	+	0.0464541i
$698$	−0.861488	+	42.4664i	−0.0326078	+	1.60738i
$699$		0			0
$700$	−7.05880	+	15.2596i	−0.266798	+	0.576760i
$701$	2.15514	+	3.22540i	0.0813986	+	0.121822i	0.869935	−	0.493167i	$-0.164161\pi$
$701$	2.15514	+	3.22540i	0.0813986	+	0.121822i	−0.788536	+	0.614988i	$0.789161\pi$
$702$		0			0
$703$	0.147468			0.00556188
$704$	−5.60152	−	11.1002i	−0.211115	−	0.418354i
$705$		0			0
$706$	16.3618	+	11.4193i	0.615784	+	0.429771i
$707$	−12.5270	−	18.7480i	−0.471126	−	0.705090i
$708$		0			0
$709$	−2.60789	−	13.1108i	−0.0979414	−	0.492385i	−0.998354	−	0.0573482i	$-0.981735\pi$
$709$	−2.60789	−	13.1108i	−0.0979414	−	0.492385i	0.900413	−	0.435036i	$-0.143265\pi$
$710$	0.306337	−	15.1007i	0.0114966	−	0.566718i
$711$		0			0
$712$	21.5166	−	2.93345i	0.806369	−	0.109936i
$713$	−3.55306	+	8.57784i	−0.133063	+	0.321243i
$714$		0			0
$715$	−5.78842	−	3.86770i	−0.216475	−	0.144644i
$716$	46.8137	−	7.35233i	1.74951	−	0.274770i
$717$		0			0
$718$	7.21538	−	32.7842i	0.269276	−	1.22350i
$719$	−5.54087	+	5.54087i	−0.206640	+	0.206640i	−0.802838	−	0.596198i	$-0.796677\pi$
$719$	−5.54087	+	5.54087i	−0.206640	+	0.206640i	0.596198	+	0.802838i	$0.296677\pi$
$720$		0			0
$721$	−18.3855	−	18.3855i	−0.684712	−	0.684712i
$722$	−22.6301	+	14.4658i	−0.842207	+	0.538362i
$723$		0			0
$724$	−3.86807	+	16.0201i	−0.143756	+	0.595381i
$725$	3.01406	−	4.51086i	0.111939	−	0.167529i
$726$		0			0
$727$	−1.51607	−	0.627975i	−0.0562278	−	0.0232903i	0.354392	−	0.935097i	$-0.384688\pi$
$727$	−1.51607	−	0.627975i	−0.0562278	−	0.0232903i	−0.410620	+	0.911807i	$0.634688\pi$
$728$	30.0824	+	1.83279i	1.11493	+	0.0679278i
$729$		0			0
$730$	−3.81091	+	3.65937i	−0.141048	+	0.135439i
$731$	18.0404	−	3.58846i	0.667248	−	0.132724i
$732$		0			0
$733$	−35.6822	+	23.8421i	−1.31795	+	0.880628i	−0.997771	−	0.0667277i	$-0.978744\pi$
$733$	−35.6822	+	23.8421i	−1.31795	+	0.880628i	−0.320182	+	0.947356i	$0.603744\pi$
$734$	22.8487	−	4.06497i	0.843362	−	0.150041i
$735$		0			0
$736$	5.95537	−	19.4055i	0.219518	−	0.715294i
$737$		−	8.82329i		−	0.325010i
$738$		0			0
$739$	2.79111	−	1.86496i	0.102673	−	0.0686036i	−0.503174	−	0.864185i	$-0.667835\pi$
$739$	2.79111	−	1.86496i	0.102673	−	0.0686036i	0.605847	+	0.795581i	$0.292835\pi$
$740$	1.96219	−	1.80912i	0.0721317	−	0.0665045i
$741$		0			0
$742$	−19.8923	−	20.7161i	−0.730268	−	0.760511i
$743$	5.81769	−	2.40977i	0.213430	−	0.0884058i	−0.273407	−	0.961899i	$-0.588151\pi$
$743$	5.81769	−	2.40977i	0.213430	−	0.0884058i	0.486837	+	0.873493i	$0.338151\pi$
$744$		0			0
$745$	11.3995	+	4.72184i	0.417646	+	0.172995i
$746$	19.8786	−	7.76548i	0.727808	−	0.284314i
$747$		0			0
$748$	5.37523	−	3.28436i	0.196538	−	0.120088i
$749$	18.0141	+	3.58322i	0.658220	+	0.130928i
$750$		0			0
$751$	24.4261	+	24.4261i	0.891321	+	0.891321i	0.994648	−	0.103326i	$-0.0329486\pi$
$751$	24.4261	+	24.4261i	0.891321	+	0.891321i	−0.103326	+	0.994648i	$0.532949\pi$
$752$	−21.7963	−	1.77232i	−0.794831	−	0.0646298i
$753$		0			0
$754$	−9.49747	−	2.09027i	−0.345878	−	0.0761231i
$755$	2.61172	−	13.1300i	0.0950503	−	0.477850i
$756$		0			0
$757$	−14.3344	−	9.57795i	−0.520993	−	0.348116i	0.267104	−	0.963668i	$-0.413933\pi$
$757$	−14.3344	−	9.57795i	−0.520993	−	0.348116i	−0.788097	+	0.615551i	$0.788933\pi$
$758$	−3.74271	−	1.63999i	−0.135941	−	0.0595670i
$759$		0			0
$760$	0.0528239	−	0.200832i	0.00191612	−	0.00728493i
$761$	−14.8711	−	35.9019i	−0.539076	−	1.30144i	−0.925369	−	0.379068i	$-0.876245\pi$
$761$	−14.8711	−	35.9019i	−0.539076	−	1.30144i	0.386293	−	0.922376i	$-0.373755\pi$
$762$		0			0
$763$	−6.48269	−	32.5907i	−0.234689	−	1.17986i
$764$	−1.48480	−	4.04085i	−0.0537180	−	0.146193i
$765$		0			0
$766$	28.0940	−	40.2535i	1.01508	−	1.45442i
$767$	−32.9690			−1.19044
$768$		0			0
$769$	13.8807			0.500550			0.250275	−	0.968175i	$-0.419479\pi$
$769$	13.8807			0.500550			0.250275	+	0.968175i	$0.419479\pi$
$770$	−1.98808	+	2.84856i	−0.0716455	+	0.102655i
$771$		0			0
$772$	3.81629	+	10.3860i	0.137351	+	0.373800i
$773$	−0.0884866	−	0.444852i	−0.00318264	−	0.0160002i	0.979161	−	0.203084i	$-0.0650964\pi$
$773$	−0.0884866	−	0.444852i	−0.00318264	−	0.0160002i	−0.982344	+	0.187084i	$0.940096\pi$
$774$		0			0
$775$	−4.29299	−	10.3642i	−0.154209	−	0.372293i
$776$	8.23972	−	31.3267i	0.295789	−	1.12456i
$777$		0			0
$778$	−41.7373	−	18.2885i	−1.49636	−	0.655676i
$779$	−0.0490593	−	0.0327804i	−0.00175773	−	0.00117448i
$780$		0			0
$781$	−3.97282	+	19.9727i	−0.142159	+	0.714680i
$782$	10.0436	+	2.21047i	0.359160	+	0.0790464i
$783$		0			0
$784$	−1.05049	+	12.9191i	−0.0375173	+	0.461396i
$785$	−2.53656	−	2.53656i	−0.0905339	−	0.0905339i
$786$		0			0
$787$	−9.18877	−	1.82776i	−0.327544	−	0.0651526i	0.0285792	−	0.999592i	$-0.490902\pi$
$787$	−9.18877	−	1.82776i	−0.327544	−	0.0651526i	−0.356123	+	0.934439i	$0.615902\pi$
$788$	−25.0861	+	15.3281i	−0.893657	+	0.546040i
$789$		0			0
$790$	11.3279	−	4.42520i	0.403030	−	0.157441i
$791$	−25.2849	−	10.4734i	−0.899029	−	0.372390i
$792$		0			0
$793$	32.2428	−	13.3554i	1.14498	−	0.474265i
$794$	2.94998	+	3.07215i	0.104691	+	0.109027i
$795$		0			0
$796$	2.43436	−	2.24445i	0.0862836	−	0.0795524i
$797$	−14.6345	+	9.77843i	−0.518379	+	0.346370i	−0.787077	−	0.616855i	$-0.788407\pi$
$797$	−14.6345	+	9.77843i	−0.518379	+	0.346370i	0.268698	+	0.963224i	$0.413407\pi$
$798$		0			0
$799$		−	11.0792i		−	0.391954i
$800$	11.4912	+	21.6673i	0.406277	+	0.766056i
$801$		0			0
$802$	−29.2773	+	5.20867i	−1.03382	+	0.183925i
$803$	5.92291	−	3.95756i	0.209015	−	0.139659i
$804$		0			0
$805$	−5.56219	+	1.10639i	−0.196041	+	0.0389951i
$806$	−14.5045	+	13.9278i	−0.510901	+	0.490584i
$807$		0			0
$808$	−32.8306	−	2.00023i	−1.15498	−	0.0703680i
$809$	−4.53116	−	1.87687i	−0.159307	−	0.0659871i	0.301605	−	0.953433i	$-0.402478\pi$
$809$	−4.53116	−	1.87687i	−0.159307	−	0.0659871i	−0.460912	+	0.887446i	$0.652478\pi$
$810$		0			0
$811$	−21.6476	+	32.3980i	−0.760151	+	1.13765i	0.226375	+	0.974040i	$0.427313\pi$
$811$	−21.6476	+	32.3980i	−0.760151	+	1.13765i	−0.986526	+	0.163606i	$0.947687\pi$
$812$	−1.13890	+	4.71690i	−0.0399676	+	0.165531i
$813$		0			0
$814$	−3.03192	+	1.93808i	−0.106269	+	0.0679298i
$815$	2.70282	+	2.70282i	0.0946756	+	0.0946756i
$816$		0			0
$817$	−0.578105	+	0.578105i	−0.0202253	+	0.0202253i
$818$	4.82742	−	21.9342i	0.168787	−	0.766910i
$819$		0			0
$820$	−1.05492	+	0.165680i	−0.0368394	+	0.00578581i
$821$	−15.4667	−	10.3345i	−0.539792	−	0.360678i	0.255590	−	0.966785i	$-0.417730\pi$
$821$	−15.4667	−	10.3345i	−0.539792	−	0.360678i	−0.795383	+	0.606107i	$0.792730\pi$
$822$		0			0
$823$	−1.39014	+	3.35609i	−0.0484571	+	0.116986i	−0.946255	−	0.323423i	$-0.895166\pi$
$823$	−1.39014	+	3.35609i	−0.0484571	+	0.116986i	0.897797	+	0.440409i	$0.145166\pi$
$824$	−37.5809	+	5.12357i	−1.30919	+	0.178488i
$825$		0			0
$826$	−0.333658	+	16.4474i	−0.0116095	+	0.572280i
$827$	−7.68456	−	38.6329i	−0.267218	−	1.34340i	−0.848284	−	0.529541i	$-0.822364\pi$
$827$	−7.68456	−	38.6329i	−0.267218	−	1.34340i	0.581066	−	0.813857i	$-0.302636\pi$
$828$		0			0
$829$	−6.04482	−	9.04671i	−0.209945	−	0.314205i	0.711520	−	0.702666i	$-0.248007\pi$
$829$	−6.04482	−	9.04671i	−0.209945	−	0.314205i	−0.921465	+	0.388460i	$0.873007\pi$
$830$	2.55698	+	1.78458i	0.0887539	+	0.0619436i
$831$		0			0
$832$	28.6819	−	33.3187i	0.994366	−	1.15512i
$833$	−6.56685			−0.227528
$834$		0			0
$835$	−4.66370	−	6.97972i	−0.161394	−	0.241543i
$836$	−0.117548	+	0.254115i	−0.00406550	+	0.00878874i
$837$		0			0
$838$	0.738465	−	36.4021i	0.0255099	−	1.25749i
$839$	−4.57390	−	11.0424i	−0.157909	−	0.381225i	0.825048	−	0.565063i	$-0.191148\pi$
$839$	−4.57390	−	11.0424i	−0.157909	−	0.381225i	−0.982957	+	0.183837i	$0.941148\pi$
$840$		0			0
$841$	−10.4986	+	25.3459i	−0.362022	+	0.873998i
$842$	6.56528	−	14.9830i	0.226254	−	0.516348i
$843$		0			0
$844$	−2.54955	−	16.2335i	−0.0877591	−	0.558780i
$845$	2.73508	−	13.7502i	0.0940895	−	0.473020i
$846$		0			0
$847$	−11.7698	+	11.7698i	−0.404416	+	0.404416i
$848$	−41.6176	+	4.81631i	−1.42915	+	0.165393i
$849$		0			0
$850$	−10.4695	+	6.69237i	−0.359100	+	0.229546i
$851$	−5.76187	−	1.14611i	−0.197514	−	0.0392880i
$852$		0			0
$853$	−15.0788	+	22.5670i	−0.516287	+	0.772678i	−0.994407	−	0.105617i	$-0.966318\pi$
$853$	−15.0788	+	22.5670i	−0.516287	+	0.772678i	0.478120	+	0.878294i	$0.341318\pi$
$854$	−6.33638	−	16.2203i	−0.216827	−	0.555048i
$855$		0			0
$856$	20.0622	−	17.7580i	0.685713	−	0.606956i
$857$	36.9477	−	15.3043i	1.26211	−	0.522783i	0.351554	−	0.936168i	$-0.385653\pi$
$857$	36.9477	−	15.3043i	1.26211	−	0.522783i	0.910557	+	0.413384i	$0.135653\pi$
$858$		0			0
$859$	−4.65397	+	0.925733i	−0.158792	+	0.0315856i	−0.273846	−	0.961774i	$-0.588296\pi$
$859$	−4.65397	+	0.925733i	−0.158792	+	0.0315856i	0.115054	+	0.993359i	$0.463296\pi$
$860$	−0.600084	+	14.7843i	−0.0204627	+	0.504140i
$861$		0			0
$862$	33.0289	−	5.87612i	1.12497	−	0.200141i
$863$			10.4034i			0.354136i	0.984199	+	0.177068i	$0.0566612\pi$
$863$			10.4034i			0.354136i	−0.984199	+	0.177068i	$0.943339\pi$
$864$		0			0
$865$			8.48717i			0.288572i
$866$	−5.09524	−	28.6397i	−0.173143	−	0.973218i
$867$		0			0
$868$	6.80143	+	7.37692i	0.230856	+	0.250389i
$869$	−16.0821	+	3.19892i	−0.545547	+	0.108516i
$870$		0			0
$871$	28.8235	−	11.9391i	0.976646	−	0.404540i
$872$	−43.5718	−	21.2387i	−1.47553	−	0.719233i
$873$		0			0
$874$	−0.425767	+	0.166324i	−0.0144018	+	0.00562598i
$875$	8.19710	−	12.2678i	0.277113	−	0.414728i
$876$		0			0
$877$	−40.0008	−	7.95665i	−1.35073	−	0.268677i	−0.533896	−	0.845550i	$-0.679273\pi$
$877$	−40.0008	−	7.95665i	−1.35073	−	0.268677i	−0.816834	+	0.576873i	$0.804273\pi$
$878$	−10.5271	−	16.4684i	−0.355271	−	0.555782i
$879$		0			0
$880$	1.55335	+	4.82328i	0.0523636	+	0.162593i
$881$	−26.7291	+	26.7291i	−0.900526	+	0.900526i	−0.995482	−	0.0949554i	$-0.969729\pi$
$881$	−26.7291	+	26.7291i	−0.900526	+	0.900526i	0.0949554	+	0.995482i	$0.469729\pi$
$882$		0			0
$883$	−1.51668	+	7.62487i	−0.0510404	+	0.256597i	−0.997878	−	0.0651152i	$-0.979259\pi$
$883$	−1.51668	+	7.62487i	−0.0510404	+	0.256597i	0.946837	+	0.321713i	$0.104259\pi$
$884$	18.0026	+	13.1153i	0.605492	+	0.441117i
$885$		0			0
$886$	19.3511	+	8.47929i	0.650112	+	0.284867i
$887$	−7.40725	+	17.8827i	−0.248711	+	0.600442i	−0.998095	−	0.0616939i	$-0.980350\pi$
$887$	−7.40725	+	17.8827i	−0.248711	+	0.600442i	0.749384	+	0.662136i	$0.230350\pi$
$888$		0			0
$889$	6.68724	+	16.1444i	0.224283	+	0.541466i
$890$	−8.84837	−	0.179501i	−0.296598	−	0.00601688i
$891$		0			0
$892$	−3.31517	+	1.21815i	−0.111000	+	0.0407866i
$893$	0.273588	+	0.409453i	0.00915527	+	0.0137018i
$894$		0			0
$895$	−19.3127			−0.645554
$896$	−16.3316	−	14.6459i	−0.545602	−	0.489285i
$897$		0			0
$898$	26.5191	−	37.9971i	0.884955	−	1.26798i
$899$	−1.79875	−	2.69202i	−0.0599916	−	0.0897838i
$900$		0			0
$901$	−4.14091	−	20.8177i	−0.137954	−	0.693540i
$902$	1.43946	+	0.0292013i	0.0479287	+	0.000972298i
$903$		0			0
$904$	−34.4821	+	20.1203i	−1.14686	+	0.669191i
$905$	2.57032	−	6.20531i	0.0854404	−	0.206271i
$906$		0			0
$907$	−22.2411	−	14.8611i	−0.738505	−	0.493453i	0.128527	−	0.991706i	$-0.458975\pi$
$907$	−22.2411	−	14.8611i	−0.738505	−	0.493453i	−0.867032	+	0.498253i	$0.833975\pi$
$908$	−12.7528	−	9.29078i	−0.423218	−	0.308325i
$909$		0			0
$910$	−11.9957	−	2.64009i	−0.397652	−	0.0875180i
$911$	0.418109	−	0.418109i	0.0138526	−	0.0138526i	−0.700147	−	0.713999i	$-0.746882\pi$
$911$	0.418109	−	0.418109i	0.0138526	−	0.0138526i	0.713999	+	0.700147i	$0.246882\pi$
$912$		0			0
$913$	−2.97276	−	2.97276i	−0.0983839	−	0.0983839i
$914$	20.8360	+	32.5956i	0.689195	+	1.07817i
$915$		0			0
$916$	−23.7570	−	38.8810i	−0.784952	−	1.28466i
$917$	−9.26228	+	13.8620i	−0.305868	+	0.457763i
$918$		0			0
$919$	−12.8012	−	5.30244i	−0.422274	−	0.174911i	0.161419	−	0.986886i	$-0.448393\pi$
$919$	−12.8012	−	5.30244i	−0.422274	−	0.174911i	−0.583693	+	0.811974i	$0.698393\pi$
$920$	−3.62476	+	7.43632i	−0.119505	+	0.245168i
$921$		0			0
$922$	9.43457	+	9.82528i	0.310711	+	0.323578i
$923$	−70.6216	+	14.0475i	−2.32454	+	0.462379i
$924$		0			0
$925$	5.90192	−	3.94353i	0.194054	−	0.129663i
$926$	0.901852	+	5.06920i	0.0296367	+	0.166584i
$927$		0			0
$928$	4.47274	+	5.48624i	0.146825	+	0.180095i
$929$			26.2072i			0.859830i	0.902869	+	0.429915i	$0.141456\pi$
$929$			26.2072i			0.859830i	−0.902869	+	0.429915i	$0.858544\pi$
$930$		0			0
$931$	0.242690	−	0.162161i	0.00795386	−	0.00531460i
$932$	−0.347690	+	8.56604i	−0.0113890	+	0.280590i
$933$		0			0
$934$	30.6039	−	29.3870i	1.00139	−	0.961570i
$935$	−2.37182	+	0.982438i	−0.0775666	+	0.0321292i
$936$		0			0
$937$	15.5675	+	6.44825i	0.508567	+	0.210655i	0.622186	−	0.782869i	$-0.286245\pi$
$937$	15.5675	+	6.44825i	0.508567	+	0.210655i	−0.113620	+	0.993524i	$0.536245\pi$
$938$	−5.66441	−	14.5002i	−0.184950	−	0.473447i
$939$		0			0
$940$	8.66343	+	2.09179i	0.282570	+	0.0682268i
$941$	−1.05016	−	0.208890i	−0.0342342	−	0.00680961i	0.177944	−	0.984041i	$-0.443056\pi$
$941$	−1.05016	−	0.208890i	−0.0342342	−	0.00680961i	−0.212178	+	0.977231i	$0.568056\pi$
$942$		0			0
$943$	1.66207	+	1.66207i	0.0541245	+	0.0541245i
$944$	18.8069	+	14.9055i	0.612114	+	0.485132i
$945$		0			0
$946$	4.28803	−	19.4834i	0.139416	−	0.633459i
$947$	5.64778	−	28.3933i	0.183528	−	0.922658i	−0.773750	−	0.633491i	$-0.781622\pi$
$947$	5.64778	−	28.3933i	0.183528	−	0.922658i	0.957278	−	0.289168i	$-0.0933785\pi$
$948$		0			0
$949$	20.9428	+	13.9936i	0.679833	+	0.454250i
$950$	0.221659	−	0.505860i	0.00719156	−	0.0164123i
$951$		0			0
$952$	6.72512	−	8.84831i	0.217962	−	0.286775i
$953$	17.8099	+	42.9968i	0.576918	+	1.39280i	0.895565	+	0.444930i	$0.146771\pi$
$953$	17.8099	+	42.9968i	0.576918	+	1.39280i	−0.318647	+	0.947873i	$0.603229\pi$
$954$		0			0
$955$	0.342286	+	1.72079i	0.0110761	+	0.0556834i
$956$	3.52662	−	7.62380i	0.114059	−	0.246571i
$957$		0			0
$958$	−15.1940	−	10.6043i	−0.490895	−	0.342608i
$959$	5.89303			0.190296
$960$		0			0
$961$	24.3052			0.784038
$962$	−10.4338	−	7.28202i	−0.336400	−	0.234782i
$963$		0			0
$964$	43.6206	+	20.1780i	1.40493	+	0.649891i
$965$	−0.879759	−	4.42285i	−0.0283204	−	0.142376i
$966$		0			0
$967$	4.72582	+	11.4091i	0.151972	+	0.366893i	0.981470	−	0.191617i	$-0.0613732\pi$
$967$	4.72582	+	11.4091i	0.151972	+	0.366893i	−0.829498	+	0.558510i	$0.811373\pi$
$968$	3.27995	+	24.0581i	0.105421	+	0.773257i
$969$		0			0
$970$	−5.29828	+	12.0915i	−0.170118	+	0.388235i
$971$	11.8130	+	7.89320i	0.379097	+	0.253305i	0.730490	−	0.682923i	$-0.239292\pi$
$971$	11.8130	+	7.89320i	0.379097	+	0.253305i	−0.351393	+	0.936228i	$0.614292\pi$
$972$		0			0
$973$	3.11682	−	15.6693i	0.0999208	−	0.502336i
$974$	2.77124	−	12.5916i	0.0887963	−	0.403460i
$975$		0			0
$976$	−24.4307	−	6.95865i	−0.782009	−	0.222741i
$977$	−11.6219	−	11.6219i	−0.371817	−	0.371817i	0.496322	−	0.868139i	$-0.334684\pi$
$977$	−11.6219	−	11.6219i	−0.371817	−	0.371817i	−0.868139	+	0.496322i	$0.834684\pi$
$978$		0			0
$979$	11.7032	+	2.32791i	0.374035	+	0.0744003i
$980$	1.23984	−	5.13497i	0.0396054	−	0.164031i
$981$		0			0
$982$	−6.40562	−	16.3975i	−0.204411	−	0.523267i
$983$	−52.2673	−	21.6498i	−1.66707	−	0.690522i	−0.668485	−	0.743726i	$-0.733057\pi$
$983$	−52.2673	−	21.6498i	−1.66707	−	0.690522i	−0.998584	+	0.0532035i	$0.983057\pi$
$984$		0			0
$985$	11.0692	−	4.58503i	0.352695	−	0.146091i
$986$	−2.58672	+	2.48385i	−0.0823779	+	0.0791020i
$987$		0			0
$988$	−0.989187	−	0.0401505i	−0.0314702	−	0.00127736i
$989$	27.0806	−	18.0947i	0.861113	−	0.575377i
$990$		0			0
$991$		−	15.7589i		−	0.500597i	−0.968169	−	0.250299i	$-0.919471\pi$
$991$		−	15.7589i		−	0.500597i	0.968169	−	0.250299i	$-0.0805288\pi$
$992$	14.5708	−	1.38740i	0.462624	−	0.0440502i
$993$		0			0
$994$	6.29324	+	35.3736i	0.199610	+	1.12198i
$995$	−1.12203	+	0.749715i	−0.0355707	+	0.0237676i
$996$		0			0
$997$	−28.9525	+	5.75900i	−0.916934	+	0.182390i	−0.630931	−	0.775839i	$-0.717327\pi$
$997$	−28.9525	+	5.75900i	−0.916934	+	0.182390i	−0.286003	+	0.958229i	$0.592327\pi$
$998$	4.72097	+	4.91648i	0.149440	+	0.155629i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.109.5		56
3.2	odd	2		64.2.i.a.45.3	yes	56
12.11	even	2		256.2.i.a.17.7		56
24.5	odd	2		512.2.i.b.289.7		56
24.11	even	2		512.2.i.a.289.1		56
64.37	even	16	inner	576.2.bd.a.37.5		56
192.5	odd	16		512.2.i.b.225.7		56
192.59	even	16		512.2.i.a.225.1		56
192.101	odd	16		64.2.i.a.37.3	✓	56
192.155	even	16		256.2.i.a.241.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.3	✓	56	192.101	odd	16
64.2.i.a.45.3	yes	56	3.2	odd	2
256.2.i.a.17.7		56	12.11	even	2
256.2.i.a.241.7		56	192.155	even	16
512.2.i.a.225.1		56	192.59	even	16
512.2.i.a.289.1		56	24.11	even	2
512.2.i.b.225.7		56	192.5	odd	16
512.2.i.b.289.7		56	24.5	odd	2
576.2.bd.a.37.5		56	64.37	even	16	inner
576.2.bd.a.109.5		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809383 - 1.15970i) q^{2} +(-0.689800 - 1.87728i) q^{4} +(0.159018 + 0.799435i) q^{5} +(-0.742008 - 1.79137i) q^{7} +(-2.73539 - 0.719478i) q^{8} +O(q^{10})\)	\(q+(0.809383 - 1.15970i) q^{2} +(-0.689800 - 1.87728i) q^{4} +(0.159018 + 0.799435i) q^{5} +(-0.742008 - 1.79137i) q^{7} +(-2.73539 - 0.719478i) q^{8} +(1.05581 + 0.462637i) q^{10} +(-1.29226 - 0.863458i) q^{11} +(1.07211 - 5.38985i) q^{13} +(-2.67801 - 0.589395i) q^{14} +(-3.04835 + 2.58989i) q^{16} +(-1.43298 - 1.43298i) q^{17} +(0.0883441 + 0.0175727i) q^{19} +(1.39107 - 0.849970i) q^{20} +(-2.04728 + 0.799759i) q^{22} +(-3.31519 - 1.37320i) q^{23} +(4.00559 - 1.65917i) q^{25} +(-5.38285 - 5.60577i) q^{26} +(-2.85106 + 2.62864i) q^{28} +(1.04042 - 0.695186i) q^{29} -2.58743i q^{31} +(0.536209 + 5.63138i) q^{32} +(-2.82165 + 0.501994i) q^{34} +(1.31409 - 0.878046i) q^{35} +(1.60572 - 0.319397i) q^{37} +(0.0918832 - 0.0882294i) q^{38} +(0.140201 - 2.30118i) q^{40} +(-0.605183 - 0.250675i) q^{41} +(-5.04263 + 7.54683i) q^{43} +(-0.729554 + 3.02154i) q^{44} +(-4.27576 + 2.73318i) q^{46} +(3.86580 + 3.86580i) q^{47} +(2.29133 - 2.29133i) q^{49} +(1.31792 - 5.98817i) q^{50} +(-10.8578 + 1.70527i) q^{52} +(8.70867 + 5.81895i) q^{53} +(0.484787 - 1.17038i) q^{55} +(0.740832 + 5.43394i) q^{56} +(0.0358915 - 1.76924i) q^{58} +(-1.17041 - 5.88407i) q^{59} +(3.52821 + 5.28034i) q^{61} +(-3.00064 - 2.09422i) q^{62} +(6.96470 + 3.93610i) q^{64} +4.47932 q^{65} +(3.15404 + 4.72036i) q^{67} +(-1.70163 + 3.67856i) q^{68} +(0.0453323 - 2.23462i) q^{70} +(-5.01419 - 12.1053i) q^{71} +(-1.75399 + 4.23450i) q^{73} +(0.929237 - 2.12066i) q^{74} +(-0.0279508 - 0.177968i) q^{76} +(-0.587905 + 2.95560i) q^{77} +(7.46021 - 7.46021i) q^{79} +(-2.55519 - 2.02512i) q^{80} +(-0.780532 + 0.498937i) q^{82} +(2.65306 + 0.527725i) q^{83} +(0.917704 - 1.37344i) q^{85} +(4.67063 + 11.9562i) q^{86} +(2.91358 + 3.29164i) q^{88} +(-7.09322 + 2.93811i) q^{89} +(-10.4507 + 2.07877i) q^{91} +(-0.291057 + 7.17078i) q^{92} +(7.61208 - 1.35425i) q^{94} +0.0734197i q^{95} +11.4524i q^{97} +(-0.802689 - 4.51182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Introduction

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