LMFDB - Embedded newform 297.2.n.b.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	297.235
Dual form			297.2.n.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41247 + 0.628870i) q^{2} +(0.261321 - 0.290226i) q^{4} +(-0.540848 - 0.240801i) q^{5} +(-0.706174 - 0.150102i) q^{7} +(0.768973 - 2.36665i) q^{8} +0.915362 q^{10} +(-3.10382 - 1.16888i) q^{11} +(0.164629 - 1.56634i) q^{13} +(1.09184 - 0.232078i) q^{14} +(0.483816 + 4.60320i) q^{16} +(3.71501 - 2.69911i) q^{17} +(0.775200 - 2.38582i) q^{19} +(-0.211222 + 0.0940420i) q^{20} +(5.11912 - 0.300892i) q^{22} +(-2.22600 - 3.85554i) q^{23} +(-3.11112 - 3.45525i) q^{25} +(0.752490 + 2.31593i) q^{26} +(-0.228102 + 0.165726i) q^{28} +(6.82612 + 1.45094i) q^{29} +(0.954161 - 9.07824i) q^{31} +(-1.08974 - 1.88749i) q^{32} +(-3.54993 + 6.14866i) q^{34} +(0.345788 + 0.251230i) q^{35} +(0.893583 + 2.75017i) q^{37} +(0.405428 + 3.85739i) q^{38} +(-0.985790 + 1.09483i) q^{40} +(-1.12890 + 0.239955i) q^{41} +(2.10724 - 3.64985i) q^{43} +(-1.15033 + 0.595357i) q^{44} +(5.56879 + 4.04596i) q^{46} +(0.152264 + 0.169107i) q^{47} +(-5.91867 - 2.63516i) q^{49} +(6.56726 + 2.92393i) q^{50} +(-0.411571 - 0.457096i) q^{52} +(-4.61430 - 3.35249i) q^{53} +(1.39723 + 1.37959i) q^{55} +(-0.898268 + 1.55585i) q^{56} +(-10.5541 + 2.24335i) q^{58} +(-4.77328 + 5.30126i) q^{59} +(-0.476541 - 4.53398i) q^{61} +(4.36131 + 13.4227i) q^{62} +(-4.76295 - 3.46049i) q^{64} +(-0.466215 + 0.807507i) q^{65} +(4.04571 + 7.00738i) q^{67} +(0.187456 - 1.78353i) q^{68} +(-0.646405 - 0.137398i) q^{70} +(-9.95852 + 7.23528i) q^{71} +(4.78461 + 14.7255i) q^{73} +(-2.99165 - 3.32257i) q^{74} +(-0.489852 - 0.848448i) q^{76} +(2.01639 + 1.29133i) q^{77} +(-13.3556 + 5.94631i) q^{79} +(0.846785 - 2.60614i) q^{80} +(1.44363 - 1.04886i) q^{82} +(-0.726787 - 6.91491i) q^{83} +(-2.65920 + 0.565231i) q^{85} +(-0.681124 + 6.48047i) q^{86} +(-5.15310 + 6.44683i) q^{88} -12.4803 q^{89} +(-0.351367 + 1.08140i) q^{91} +(-1.70068 - 0.361491i) q^{92} +(-0.321414 - 0.143103i) q^{94} +(-0.993774 + 1.10370i) q^{95} +(12.9545 - 5.76772i) q^{97} +10.0171 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.41247	+	0.628870i	−0.998764	+	0.444679i	−0.839970	−	0.542633i	$-0.817427\pi$
$2$	−1.41247	+	0.628870i	−0.998764	+	0.444679i	−0.158794	+	0.987312i	$0.550761\pi$
$3$		0			0
$3$		0			0
$4$	0.261321	−	0.290226i	0.130660	−	0.145113i
$5$	−0.540848	−	0.240801i	−0.241875	−	0.107690i	0.282220	−	0.959350i	$-0.408929\pi$
$5$	−0.540848	−	0.240801i	−0.241875	−	0.107690i	−0.524094	+	0.851660i	$0.675596\pi$
$6$		0			0
$7$	−0.706174	−	0.150102i	−0.266909	−	0.0567332i	0.0725131	−	0.997367i	$-0.476898\pi$
$7$	−0.706174	−	0.150102i	−0.266909	−	0.0567332i	−0.339422	+	0.940634i	$0.610231\pi$
$8$	0.768973	−	2.36665i	0.271873	−	0.836739i
$9$		0			0
$10$	0.915362			0.289463
$11$	−3.10382	−	1.16888i	−0.935837	−	0.352432i
$11$	−3.10382	−	1.16888i	−0.935837	−	0.352432i
$12$		0			0
$13$	0.164629	−	1.56634i	0.0456598	−	0.434424i	−0.947682	−	0.319217i	$-0.896580\pi$
$13$	0.164629	−	1.56634i	0.0456598	−	0.434424i	0.993342	−	0.115207i	$-0.0367531\pi$
$14$	1.09184	−	0.232078i	0.291807	−	0.0620255i
$15$		0			0
$16$	0.483816	+	4.60320i	0.120954	+	1.15080i
$17$	3.71501	−	2.69911i	0.901022	−	0.654631i	−0.0377065	−	0.999289i	$-0.512005\pi$
$17$	3.71501	−	2.69911i	0.901022	−	0.654631i	0.938728	+	0.344658i	$0.112005\pi$
$18$		0			0
$19$	0.775200	−	2.38582i	0.177843	−	0.547345i	−0.821909	−	0.569619i	$-0.807091\pi$
$19$	0.775200	−	2.38582i	0.177843	−	0.547345i	0.999752	+	0.0222743i	$0.00709072\pi$
$20$	−0.211222	+	0.0940420i	−0.0472306	+	0.0210284i
$21$		0			0
$22$	5.11912	−	0.300892i	1.09140	−	0.0641503i
$23$	−2.22600	−	3.85554i	−0.464153	−	0.803937i	0.535010	−	0.844846i	$-0.320308\pi$
$23$	−2.22600	−	3.85554i	−0.464153	−	0.803937i	−0.999163	+	0.0409092i	$0.986975\pi$
$24$		0			0
$25$	−3.11112	−	3.45525i	−0.622224	−	0.691050i
$26$	0.752490	+	2.31593i	0.147576	+	0.454191i
$27$		0			0
$28$	−0.228102	+	0.165726i	−0.0431072	+	0.0313192i
$29$	6.82612	+	1.45094i	1.26758	+	0.269432i	0.792152	−	0.610323i	$-0.208960\pi$
$29$	6.82612	+	1.45094i	1.26758	+	0.269432i	0.475426	+	0.879755i	$0.342294\pi$
$30$		0			0
$31$	0.954161	−	9.07824i	0.171372	−	1.63050i	−0.483912	−	0.875117i	$-0.660784\pi$
$31$	0.954161	−	9.07824i	0.171372	−	1.63050i	0.655284	−	0.755382i	$-0.272549\pi$
$32$	−1.08974	−	1.88749i	−0.192641	−	0.333664i
$33$		0			0
$34$	−3.54993	+	6.14866i	−0.608808	+	1.05449i
$35$	0.345788	+	0.251230i	0.0584489	+	0.0424656i
$36$		0			0
$37$	0.893583	+	2.75017i	0.146904	+	0.452125i	0.997251	−	0.0740981i	$-0.0236078\pi$
$37$	0.893583	+	2.75017i	0.146904	+	0.452125i	−0.850347	+	0.526223i	$0.823608\pi$
$38$	0.405428	+	3.85739i	0.0657691	+	0.625751i
$39$		0			0
$40$	−0.985790	+	1.09483i	−0.155867	+	0.173108i
$41$	−1.12890	+	0.239955i	−0.176304	+	0.0374747i	−0.295218	−	0.955430i	$-0.595392\pi$
$41$	−1.12890	+	0.239955i	−0.176304	+	0.0374747i	0.118913	+	0.992905i	$0.462059\pi$
$42$		0			0
$43$	2.10724	−	3.64985i	0.321351	−	0.556596i	−0.659416	−	0.751778i	$-0.729196\pi$
$43$	2.10724	−	3.64985i	0.321351	−	0.556596i	0.980767	+	0.195182i	$0.0625297\pi$
$44$	−1.15033	+	0.595357i	−0.173419	+	0.0897534i
$45$		0			0
$46$	5.56879	+	4.04596i	0.821073	+	0.596544i
$47$	0.152264	+	0.169107i	0.0222100	+	0.0246667i	0.754147	−	0.656705i	$-0.228050\pi$
$47$	0.152264	+	0.169107i	0.0222100	+	0.0246667i	−0.731937	+	0.681372i	$0.761384\pi$
$48$		0			0
$49$	−5.91867	−	2.63516i	−0.845524	−	0.376451i
$50$	6.56726	+	2.92393i	0.928751	+	0.413506i
$51$		0			0
$52$	−0.411571	−	0.457096i	−0.0570747	−	0.0633878i
$53$	−4.61430	−	3.35249i	−0.633823	−	0.460500i	0.223899	−	0.974612i	$-0.428121\pi$
$53$	−4.61430	−	3.35249i	−0.633823	−	0.460500i	−0.857723	+	0.514113i	$0.828121\pi$
$54$		0			0
$55$	1.39723	+	1.37959i	0.188402	+	0.186024i
$56$	−0.898268	+	1.55585i	−0.120036	+	0.207909i
$57$		0			0
$58$	−10.5541	+	2.24335i	−1.38582	+	0.294566i
$59$	−4.77328	+	5.30126i	−0.621428	+	0.690166i	−0.968880	−	0.247532i	$-0.920380\pi$
$59$	−4.77328	+	5.30126i	−0.621428	+	0.690166i	0.347452	+	0.937698i	$0.387047\pi$
$60$		0			0
$61$	−0.476541	−	4.53398i	−0.0610148	−	0.580517i	−0.981730	−	0.190281i	$-0.939060\pi$
$61$	−0.476541	−	4.53398i	−0.0610148	−	0.580517i	0.920715	−	0.390236i	$-0.127607\pi$
$62$	4.36131	+	13.4227i	0.553887	+	1.70469i
$63$		0			0
$64$	−4.76295	−	3.46049i	−0.595369	−	0.432561i
$65$	−0.466215	+	0.807507i	−0.0578268	+	0.100159i
$66$		0			0
$67$	4.04571	+	7.00738i	0.494262	+	0.856087i	0.999978	−	0.00661279i	$-0.00210493\pi$
$67$	4.04571	+	7.00738i	0.494262	+	0.856087i	−0.505716	+	0.862700i	$0.668772\pi$
$68$	0.187456	−	1.78353i	0.0227324	−	0.216284i
$69$		0			0
$70$	−0.646405	−	0.137398i	−0.0772602	−	0.0164222i
$71$	−9.95852	+	7.23528i	−1.18186	+	0.858670i	−0.992380	−	0.123215i	$-0.960680\pi$
$71$	−9.95852	+	7.23528i	−1.18186	+	0.858670i	−0.189478	+	0.981885i	$0.560680\pi$
$72$		0			0
$73$	4.78461	+	14.7255i	0.559996	+	1.72349i	0.682370	+	0.731007i	$0.260950\pi$
$73$	4.78461	+	14.7255i	0.559996	+	1.72349i	−0.122373	+	0.992484i	$0.539050\pi$
$74$	−2.99165	−	3.32257i	−0.347773	−	0.386241i
$75$		0			0
$76$	−0.489852	−	0.848448i	−0.0561899	−	0.0973237i
$77$	2.01639	+	1.29133i	0.229789	+	0.147160i
$78$		0			0
$79$	−13.3556	+	5.94631i	−1.50263	+	0.669012i	−0.982701	−	0.185200i	$-0.940707\pi$
$79$	−13.3556	+	5.94631i	−1.50263	+	0.669012i	−0.519925	+	0.854212i	$0.674040\pi$
$80$	0.846785	−	2.60614i	0.0946734	−	0.291375i
$81$		0			0
$82$	1.44363	−	1.04886i	0.159422	−	0.115827i
$83$	−0.726787	−	6.91491i	−0.0797752	−	0.759010i	−0.959153	−	0.282886i	$-0.908708\pi$
$83$	−0.726787	−	6.91491i	−0.0797752	−	0.759010i	0.879378	−	0.476124i	$-0.157959\pi$
$84$		0			0
$85$	−2.65920	+	0.565231i	−0.288431	+	0.0613079i
$86$	−0.681124	+	6.48047i	−0.0734475	+	0.698807i
$87$		0			0
$88$	−5.15310	+	6.44683i	−0.549322	+	0.687235i
$89$	−12.4803			−1.32291			−0.661453	−	0.749986i	$-0.730060\pi$
$89$	−12.4803			−1.32291			−0.661453	+	0.749986i	$0.730060\pi$
$90$		0			0
$91$	−0.351367	+	1.08140i	−0.0368332	+	0.113361i
$92$	−1.70068	−	0.361491i	−0.177308	−	0.0376880i
$93$		0			0
$94$	−0.321414	−	0.143103i	−0.0331514	−	0.0147599i
$95$	−0.993774	+	1.10370i	−0.101959	+	0.113237i
$96$		0			0
$97$	12.9545	−	5.76772i	1.31533	−	0.585623i	0.375360	−	0.926879i	$-0.377519\pi$
$97$	12.9545	−	5.76772i	1.31533	−	0.585623i	0.939970	+	0.341256i	$0.110852\pi$
$98$	10.0171			1.01188
$99$		0			0
$100$	−1.81581			−0.181581
$101$	13.1263	−	5.84421i	1.30612	−	0.581521i	0.368641	−	0.929572i	$-0.379823\pi$
$101$	13.1263	−	5.84421i	1.30612	−	0.581521i	0.937476	+	0.348051i	$0.113156\pi$
$102$		0			0
$103$	−2.96348	+	3.29128i	−0.292000	+	0.324299i	−0.871239	−	0.490859i	$-0.836683\pi$
$103$	−2.96348	+	3.29128i	−0.292000	+	0.324299i	0.579239	+	0.815158i	$0.303350\pi$
$104$	−3.58038	−	1.59409i	−0.351085	−	0.156313i
$105$		0			0
$106$	8.62583	+	1.83348i	0.837815	+	0.178083i
$107$	4.86529	−	14.9738i	0.470345	−	1.44757i	−0.381788	−	0.924250i	$-0.624692\pi$
$107$	4.86529	−	14.9738i	0.470345	−	1.44757i	0.852134	−	0.523324i	$-0.175308\pi$
$108$		0			0
$109$	−13.6970			−1.31194			−0.655969	−	0.754788i	$-0.727740\pi$
$109$	−13.6970			−1.31194			−0.655969	+	0.754788i	$0.727740\pi$
$110$	−2.84112	−	1.06995i	−0.270890	−	0.102016i
$111$		0			0
$112$	0.349291	−	3.32328i	0.0330049	−	0.314021i
$113$	7.85465	−	1.66956i	0.738904	−	0.157059i	0.176941	−	0.984221i	$-0.443380\pi$
$113$	7.85465	−	1.66956i	0.738904	−	0.157059i	0.561963	+	0.827163i	$0.310046\pi$
$114$		0			0
$115$	0.275508	+	2.62129i	0.0256913	+	0.244436i
$116$	2.20491	−	1.60196i	0.204721	−	0.148738i
$117$		0			0
$118$	3.40829	−	10.4896i	0.313758	−	0.965648i
$119$	−3.02858	+	1.34841i	−0.277630	+	0.123609i
$120$		0			0
$121$	8.26742	+	7.25602i	0.751583	+	0.659638i
$122$	3.52438	+	6.10441i	0.319083	+	0.552668i
$123$		0			0
$124$	−2.38540	−	2.64926i	−0.214215	−	0.237910i
$125$	1.76536	+	5.43321i	0.157898	+	0.485961i
$126$		0			0
$127$	9.70522	−	7.05126i	0.861199	−	0.625698i	−0.0670118	−	0.997752i	$-0.521347\pi$
$127$	9.70522	−	7.05126i	0.861199	−	0.625698i	0.928211	+	0.372054i	$0.121347\pi$
$128$	13.1674	+	2.79882i	1.16385	+	0.247383i
$129$		0			0
$130$	0.150695	−	1.43377i	0.0132168	−	0.125750i
$131$	−3.44555	−	5.96786i	−0.301039	−	0.521414i	0.675333	−	0.737513i	$-0.264000\pi$
$131$	−3.44555	−	5.96786i	−0.301039	−	0.521414i	−0.976372	+	0.216099i	$0.930667\pi$
$132$		0			0
$133$	−0.905543	+	1.56845i	−0.0785205	+	0.136002i
$134$	−10.1212	−	7.35345i	−0.874335	−	0.635242i
$135$		0			0
$136$	−3.53112	−	10.8677i	−0.302791	−	0.931896i
$137$	0.966528	+	9.19590i	0.0825760	+	0.785658i	0.954939	+	0.296801i	$0.0959196\pi$
$137$	0.966528	+	9.19590i	0.0825760	+	0.785658i	−0.872363	+	0.488858i	$0.837414\pi$
$138$		0			0
$139$	14.4608	−	16.0603i	1.22655	−	1.36222i	0.316029	−	0.948749i	$-0.397650\pi$
$139$	14.4608	−	16.0603i	1.22655	−	1.36222i	0.910518	−	0.413469i	$-0.135683\pi$
$140$	0.163275	−	0.0347052i	0.0137993	−	0.00293313i
$141$		0			0
$142$	9.51601	−	16.4822i	0.798566	−	1.38316i
$143$	−2.34184	+	4.66920i	−0.195835	+	0.390458i
$144$		0			0
$145$	−3.34251	−	2.42847i	−0.277580	−	0.201674i
$146$	−16.0185	−	17.7904i	−1.32570	−	1.47234i
$147$		0			0
$148$	1.03168	+	0.459335i	0.0848038	+	0.0377571i
$149$	1.04732	+	0.466296i	0.0857996	+	0.0382005i	0.449188	−	0.893437i	$-0.351713\pi$
$149$	1.04732	+	0.466296i	0.0857996	+	0.0382005i	−0.363388	+	0.931638i	$0.618380\pi$
$150$		0			0
$151$	0.589263	+	0.654443i	0.0479536	+	0.0532578i	0.766644	−	0.642072i	$-0.221925\pi$
$151$	0.589263	+	0.654443i	0.0479536	+	0.0532578i	−0.718691	+	0.695330i	$0.755258\pi$
$152$	−5.05031	−	3.66926i	−0.409634	−	0.297616i
$153$		0			0
$154$	−3.66015	−	0.555908i	−0.294944	−	0.0447963i
$155$	−2.70211	+	4.68018i	−0.217038	+	0.375921i
$156$		0			0
$157$	9.57236	−	2.03467i	0.763958	−	0.162384i	0.190576	−	0.981672i	$-0.438965\pi$
$157$	9.57236	−	2.03467i	0.763958	−	0.162384i	0.573382	+	0.819288i	$0.305631\pi$
$158$	15.1249	−	16.7979i	1.20327	−	1.33637i
$159$		0			0
$160$	0.134876	+	1.28326i	0.0106629	+	0.101450i
$161$	0.993219	+	3.05681i	0.0782766	+	0.240911i
$162$		0			0
$163$	−3.74555	−	2.72130i	−0.293374	−	0.213149i	0.431355	−	0.902182i	$-0.358035\pi$
$163$	−3.74555	−	2.72130i	−0.293374	−	0.213149i	−0.724730	+	0.689033i	$0.758035\pi$
$164$	−0.225364	+	0.390342i	−0.0175980	+	0.0304806i
$165$		0			0
$166$	5.37515	+	9.31002i	0.417192	+	0.722598i
$167$	−1.77566	+	16.8943i	−0.137405	+	1.30732i	0.680831	+	0.732440i	$0.261619\pi$
$167$	−1.77566	+	16.8943i	−0.137405	+	1.30732i	−0.818236	+	0.574882i	$0.805048\pi$
$168$		0			0
$169$	10.2896	+	2.18712i	0.791509	+	0.168240i
$170$	3.40058	−	2.47066i	0.260812	−	0.189491i
$171$		0			0
$172$	−0.508616	−	1.56536i	−0.0387816	−	0.119357i
$173$	0.395493	+	0.439240i	0.0300688	+	0.0333948i	0.757992	−	0.652264i	$-0.226181\pi$
$173$	0.395493	+	0.439240i	0.0300688	+	0.0333948i	−0.727923	+	0.685659i	$0.759514\pi$
$174$		0			0
$175$	1.67835	+	2.90699i	0.126872	+	0.219748i
$176$	3.87893	−	14.8530i	0.292385	−	1.11959i
$177$		0			0
$178$	17.6280	−	7.84848i	1.32127	−	0.588268i
$179$	2.97921	−	9.16907i	0.222677	−	0.685328i	−0.775842	−	0.630927i	$-0.782675\pi$
$179$	2.97921	−	9.16907i	0.222677	−	0.685328i	0.998519	−	0.0544017i	$-0.0173251\pi$
$180$		0			0
$181$	3.85243	−	2.79896i	0.286349	−	0.208045i	−0.435333	−	0.900270i	$-0.643369\pi$
$181$	3.85243	−	2.79896i	0.286349	−	0.208045i	0.721682	+	0.692225i	$0.243369\pi$
$182$	−0.183764	−	1.74840i	−0.0136215	−	0.129600i
$183$		0			0
$184$	−10.8365	+	2.30336i	−0.798875	+	0.169806i
$185$	0.178950	−	1.70260i	0.0131567	−	0.125178i
$186$		0			0
$187$	−14.6857	+	4.03514i	−1.07392	+	0.295079i
$188$	0.0888691			0.00648144
$189$		0			0
$190$	0.709589	−	2.18389i	0.0514790	−	0.158436i
$191$	−5.08444	−	1.08073i	−0.367897	−	0.0781989i	0.0202537	−	0.999795i	$-0.493553\pi$
$191$	−5.08444	−	1.08073i	−0.367897	−	0.0781989i	−0.388151	+	0.921596i	$0.626886\pi$
$192$		0			0
$193$	2.98551	+	1.32923i	0.214902	+	0.0956804i	0.511364	−	0.859364i	$-0.329140\pi$
$193$	2.98551	+	1.32923i	0.214902	+	0.0956804i	−0.296463	+	0.955044i	$0.595807\pi$
$194$	−14.6706	+	16.2934i	−1.05329	+	1.16980i
$195$		0			0
$196$	−2.31146	+	1.02913i	−0.165105	+	0.0735093i
$197$	22.4626			1.60039			0.800197	−	0.599737i	$-0.204728\pi$
$197$	22.4626			1.60039			0.800197	+	0.599737i	$0.204728\pi$
$198$		0			0
$199$	−20.8291			−1.47654			−0.738269	−	0.674507i	$-0.764356\pi$
$199$	−20.8291			−1.47654			−0.738269	+	0.674507i	$0.764356\pi$
$200$	−10.5698	+	4.70596i	−0.747394	+	0.332761i
$201$		0			0
$202$	−14.8652	+	16.5095i	−1.04591	+	1.16160i
$203$	−4.60264	−	2.04923i	−0.323042	−	0.143828i
$204$		0			0
$205$	0.668344	+	0.142061i	0.0466792	+	0.00992197i
$206$	2.11603	−	6.51246i	0.147431	−	0.453745i
$207$		0			0
$208$	7.28981			0.505457
$209$	−5.19483	+	6.49904i	−0.359334	+	0.449548i
$210$		0			0
$211$	−0.354563	+	3.37344i	−0.0244091	+	0.232237i	0.975515	+	0.219932i	$0.0705836\pi$
$211$	−0.354563	+	3.37344i	−0.0244091	+	0.232237i	−0.999924	+	0.0123051i	$0.996083\pi$
$212$	−2.17880	+	0.463117i	−0.149640	+	0.0318070i
$213$		0			0
$214$	2.54454	+	24.2096i	0.173941	+	1.65494i
$215$	−2.01858	+	1.46659i	−0.137666	+	0.100020i
$216$		0			0
$217$	−2.03646	+	6.26759i	−0.138244	+	0.425472i
$218$	19.3466	−	8.61366i	1.31032	−	0.583390i
$219$		0			0
$220$	0.765519	−	0.0449957i	0.0516113	−	0.00303361i
$221$	−3.61612	−	6.26330i	−0.243247	−	0.421315i
$222$		0			0
$223$	−7.37810	−	8.19420i	−0.494074	−	0.548725i	0.443607	−	0.896221i	$-0.353698\pi$
$223$	−7.37810	−	8.19420i	−0.494074	−	0.548725i	−0.937681	+	0.347497i	$0.887032\pi$
$224$	0.486232	+	1.49647i	0.0324877	+	0.0999870i
$225$		0			0
$226$	−10.0445	+	7.29775i	−0.668150	+	0.485439i
$227$	−5.83650	−	1.24059i	−0.387382	−	0.0823406i	0.0101037	−	0.999949i	$-0.496784\pi$
$227$	−5.83650	−	1.24059i	−0.387382	−	0.0823406i	−0.397486	+	0.917608i	$0.630117\pi$
$228$		0			0
$229$	−2.58715	+	24.6151i	−0.170964	+	1.62661i	0.486889	+	0.873464i	$0.338132\pi$
$229$	−2.58715	+	24.6151i	−0.170964	+	1.62661i	−0.657852	+	0.753147i	$0.728535\pi$
$230$	−2.03760	−	3.52922i	−0.134355	−	0.232710i
$231$		0			0
$232$	8.68297	−	15.0393i	0.570065	−	0.987381i
$233$	3.38850	+	2.46189i	0.221988	+	0.161284i	0.693221	−	0.720725i	$-0.256191\pi$
$233$	3.38850	+	2.46189i	0.221988	+	0.161284i	−0.471233	+	0.882009i	$0.656191\pi$
$234$		0			0
$235$	−0.0416308	−	0.128126i	−0.00271569	−	0.00835805i
$236$	0.291208	+	2.77066i	0.0189560	+	0.180355i
$237$		0			0
$238$	3.42980	−	3.80917i	0.222321	−	0.246912i
$239$	−7.21173	+	1.53290i	−0.466488	+	0.0991551i	−0.435158	−	0.900354i	$-0.643308\pi$
$239$	−7.21173	+	1.53290i	−0.466488	+	0.0991551i	−0.0313298	+	0.999509i	$0.509974\pi$
$240$		0			0
$241$	4.41462	−	7.64634i	0.284371	−	0.492544i	−0.688086	−	0.725629i	$-0.741549\pi$
$241$	4.41462	−	7.64634i	0.284371	−	0.492544i	0.972456	+	0.233085i	$0.0748821\pi$
$242$	−16.2405	−	5.04975i	−1.04398	−	0.324610i
$243$		0			0
$244$	−1.44041	−	1.04652i	−0.0922129	−	0.0669966i
$245$	2.56655	+	2.85044i	0.163971	+	0.182108i
$246$		0			0
$247$	−3.60938	−	1.60700i	−0.229659	−	0.102251i
$248$	−20.7513	−	9.23908i	−1.31771	−	0.586682i
$249$		0			0
$250$	−5.91029	−	6.56404i	−0.373799	−	0.415146i
$251$	16.6439	+	12.0925i	1.05056	+	0.763274i	0.972318	−	0.233661i	$-0.0750704\pi$
$251$	16.6439	+	12.0925i	1.05056	+	0.763274i	0.0782385	+	0.996935i	$0.475070\pi$
$252$		0			0
$253$	2.40242	+	14.5689i	0.151039	+	0.915936i
$254$	−9.27397	+	16.0630i	−0.581901	+	1.00788i
$255$		0			0
$256$	−8.84127	+	1.87927i	−0.552579	+	0.117454i
$257$	2.26326	−	2.51360i	0.141178	−	0.156794i	−0.668409	−	0.743794i	$-0.733024\pi$
$257$	2.26326	−	2.51360i	0.141178	−	0.156794i	0.809587	+	0.587000i	$0.199691\pi$
$258$		0			0
$259$	−0.218220	−	2.07623i	−0.0135595	−	0.129010i
$260$	0.112528	+	0.346326i	0.00697871	+	0.0214783i
$261$		0			0
$262$	8.61973	+	6.26260i	0.532528	+	0.386905i
$263$	−7.14112	+	12.3688i	−0.440341	+	0.762692i	−0.997715	−	0.0675692i	$-0.978476\pi$
$263$	−7.14112	+	12.3688i	−0.440341	+	0.762692i	0.557374	+	0.830262i	$0.311809\pi$
$264$		0			0
$265$	1.68836	+	2.92432i	0.103715	+	0.179639i
$266$	0.292699	−	2.78485i	0.0179465	−	0.170750i
$267$		0			0
$268$	3.09095	+	0.657003i	0.188810	+	0.0401328i
$269$	5.43693	−	3.95016i	0.331495	−	0.240845i	−0.409570	−	0.912279i	$-0.634321\pi$
$269$	5.43693	−	3.95016i	0.331495	−	0.240845i	0.741065	+	0.671433i	$0.234321\pi$
$270$		0			0
$271$	−1.23000	−	3.78554i	−0.0747170	−	0.229955i	0.906722	−	0.421728i	$-0.138576\pi$
$271$	−1.23000	−	3.78554i	−0.0747170	−	0.229955i	−0.981439	+	0.191773i	$0.938576\pi$
$272$	14.2219	+	15.7951i	0.862331	+	0.957716i
$273$		0			0
$274$	−7.14821	−	12.3811i	−0.431839	−	0.747968i
$275$	5.61758	+	14.3610i	0.338753	+	0.866002i
$276$		0			0
$277$	−11.9967	+	5.34127i	−0.720811	+	0.320926i	−0.734152	−	0.678985i	$-0.762420\pi$
$277$	−11.9967	+	5.34127i	−0.720811	+	0.320926i	0.0133410	+	0.999911i	$0.495753\pi$
$278$	−10.3255	+	31.7786i	−0.619282	+	1.90595i
$279$		0			0
$280$	0.860476	−	0.625172i	0.0514233	−	0.0373612i
$281$	−0.310227	−	2.95161i	−0.0185066	−	0.176078i	0.981364	−	0.192157i	$-0.0615484\pi$
$281$	−0.310227	−	2.95161i	−0.0185066	−	0.176078i	−0.999871	+	0.0160790i	$0.994882\pi$
$282$		0			0
$283$	−7.91593	+	1.68258i	−0.470553	+	0.100019i	−0.437084	−	0.899421i	$-0.643989\pi$
$283$	−7.91593	+	1.68258i	−0.470553	+	0.100019i	−0.0334689	+	0.999440i	$0.510655\pi$
$284$	−0.502499	+	4.78096i	−0.0298178	+	0.283697i
$285$		0			0
$286$	0.371456	−	8.06780i	0.0219646	−	0.477059i
$287$	0.833217			0.0491833
$288$		0			0
$289$	1.26279	−	3.88648i	0.0742820	−	0.228616i
$290$	6.24837	+	1.32813i	0.366917	+	0.0779906i
$291$		0			0
$292$	5.52405	+	2.45947i	0.323271	+	0.143929i
$293$	10.5158	−	11.6789i	0.614338	−	0.682292i	−0.353046	−	0.935606i	$-0.614854\pi$
$293$	10.5158	−	11.6789i	0.614338	−	0.682292i	0.967384	+	0.253314i	$0.0815207\pi$
$294$		0			0
$295$	3.85817	−	1.71777i	0.224631	−	0.100012i
$296$	7.19584			0.418249
$297$		0			0
$298$	−1.77254			−0.102681
$299$	−6.40554	+	2.85193i	−0.370442	+	0.164931i
$300$		0			0
$301$	−2.03593	+	2.26113i	−0.117349	+	0.130329i
$302$	−1.24387	−	0.553809i	−0.0715769	−	0.0318681i
$303$		0			0
$304$	11.3575	+	2.41410i	0.651395	+	0.138458i
$305$	−0.834052	+	2.56695i	−0.0477577	+	0.146983i
$306$		0			0
$307$	−3.51315			−0.200506			−0.100253	−	0.994962i	$-0.531965\pi$
$307$	−3.51315			−0.200506			−0.100253	+	0.994962i	$0.531965\pi$
$308$	0.901701	−	0.247758i	0.0513792	−	0.0141173i
$309$		0			0
$310$	0.873403	−	8.30987i	0.0496060	−	0.471969i
$311$	25.7589	−	5.47523i	1.46066	−	0.310472i	0.592020	−	0.805923i	$-0.298331\pi$
$311$	25.7589	−	5.47523i	1.46066	−	0.310472i	0.868636	+	0.495451i	$0.164997\pi$
$312$		0			0
$313$	0.257259	+	2.44766i	0.0145412	+	0.138350i	0.999384	−	0.0351004i	$-0.0111751\pi$
$313$	0.257259	+	2.44766i	0.0145412	+	0.138350i	−0.984843	+	0.173450i	$0.944508\pi$
$314$	−12.2411	+	8.89367i	−0.690805	+	0.501899i
$315$		0			0
$316$	−1.76433	+	5.43005i	−0.0992513	+	0.305464i
$317$	24.2155	−	10.7814i	1.36008	−	0.605545i	0.408444	−	0.912783i	$-0.366071\pi$
$317$	24.2155	−	10.7814i	1.36008	−	0.605545i	0.951633	+	0.307238i	$0.0994048\pi$
$318$		0			0
$319$	−19.4911	−	12.4824i	−1.09129	−	0.698880i
$320$	1.74274	+	3.01852i	0.0974224	+	0.168741i
$321$		0			0
$322$	−3.32523	−	3.69304i	−0.185308	−	0.205805i
$323$	−3.55972	−	10.9557i	−0.198068	−	0.609591i
$324$		0			0
$325$	−5.92427	+	4.30423i	−0.328619	+	0.238756i
$326$	7.00182	+	1.48828i	0.387795	+	0.0824283i
$327$		0			0
$328$	−0.300202	+	2.85623i	−0.0165759	+	0.157709i
$329$	−0.0821419	−	0.142274i	−0.00452863	−	0.00784382i
$330$		0			0
$331$	−4.05198	+	7.01824i	−0.222717	+	0.385757i	−0.955632	−	0.294563i	$-0.904826\pi$
$331$	−4.05198	+	7.01824i	−0.222717	+	0.385757i	0.732915	+	0.680320i	$0.238159\pi$
$332$	−2.19681	−	1.59608i	−0.120566	−	0.0875962i
$333$		0			0
$334$	−8.11627	−	24.9793i	−0.444103	−	1.36681i
$335$	−0.500731	−	4.76414i	−0.0273579	−	0.260293i
$336$		0			0
$337$	16.5413	−	18.3710i	0.901064	−	1.00073i	−0.0989203	−	0.995095i	$-0.531539\pi$
$337$	16.5413	−	18.3710i	0.901064	−	1.00073i	0.999984	−	0.00563738i	$-0.00179444\pi$
$338$	−15.9091	+	3.38159i	−0.865343	+	0.183934i
$339$		0			0
$340$	−0.530861	+	0.919478i	−0.0287900	+	0.0498657i
$341$	−13.5730	+	27.0619i	−0.735017	+	1.46549i
$342$		0			0
$343$	7.87256	+	5.71975i	0.425078	+	0.308837i
$344$	−7.01752	−	7.79374i	−0.378359	−	0.420210i
$345$		0			0
$346$	−0.834846	−	0.371697i	−0.0448816	−	0.0199826i
$347$	1.89071	+	0.841800i	0.101499	+	0.0451902i	0.456858	−	0.889540i	$-0.348975\pi$
$347$	1.89071	+	0.841800i	0.101499	+	0.0451902i	−0.355359	+	0.934730i	$0.615641\pi$
$348$		0			0
$349$	−3.48902	−	3.87495i	−0.186763	−	0.207422i	0.642491	−	0.766293i	$-0.277901\pi$
$349$	−3.48902	−	3.87495i	−0.186763	−	0.207422i	−0.829254	+	0.558872i	$0.811234\pi$
$350$	−4.19874	−	3.05056i	−0.224432	−	0.163059i
$351$		0			0
$352$	1.17611	+	7.13221i	0.0626868	+	0.380148i
$353$	10.8363	−	18.7689i	0.576756	−	0.998970i	−0.419093	−	0.907943i	$-0.637652\pi$
$353$	10.8363	−	18.7689i	0.576756	−	0.998970i	0.995848	−	0.0910266i	$-0.0290148\pi$
$354$		0			0
$355$	7.12831	−	1.51517i	0.378331	−	0.0804168i
$356$	−3.26136	+	3.62211i	−0.172852	+	0.191971i
$357$		0			0
$358$	1.55812	+	14.8245i	0.0823493	+	0.783501i
$359$	−2.70478	−	8.32446i	−0.142753	−	0.439348i	0.853962	−	0.520335i	$-0.174193\pi$
$359$	−2.70478	−	8.32446i	−0.142753	−	0.439348i	−0.996715	+	0.0809868i	$0.974193\pi$
$360$		0			0
$361$	10.2801	+	7.46894i	0.541059	+	0.393102i
$362$	−3.68125	+	6.37611i	−0.193482	+	0.335121i
$363$		0			0
$364$	0.222030	+	0.384567i	0.0116375	+	0.0201568i
$365$	0.958173	−	9.11641i	0.0501531	−	0.477175i
$366$		0			0
$367$	6.61837	+	1.40678i	0.345476	+	0.0734332i	0.377382	−	0.926058i	$-0.376824\pi$
$367$	6.61837	+	1.40678i	0.345476	+	0.0734332i	−0.0319060	+	0.999491i	$0.510158\pi$
$368$	16.6709	−	12.1121i	0.869029	−	0.631387i
$369$		0			0
$370$	0.817952	+	2.51740i	0.0425233	+	0.130873i
$371$	2.75529	+	3.06006i	0.143047	+	0.158870i
$372$		0			0
$373$	10.9467	+	18.9602i	0.566797	+	0.981722i	0.996880	+	0.0789323i	$0.0251511\pi$
$373$	10.9467	+	18.9602i	0.566797	+	0.981722i	−0.430083	+	0.902790i	$0.641516\pi$
$374$	18.2054	−	14.9349i	0.941380	−	0.772265i
$375$		0			0
$376$	0.517304	−	0.230319i	0.0266779	−	0.0118778i
$377$	3.39643	−	10.4531i	0.174925	−	0.538364i
$378$		0			0
$379$	27.3639	−	19.8810i	1.40559	−	1.02122i	0.411642	−	0.911346i	$-0.364955\pi$
$379$	27.3639	−	19.8810i	1.40559	−	1.02122i	0.993946	−	0.109873i	$-0.0350445\pi$
$380$	0.0606282	+	0.576839i	0.00311016	+	0.0295912i
$381$		0			0
$382$	7.86123	−	1.67096i	0.402216	−	0.0854936i
$383$	−1.92059	+	18.2732i	−0.0981378	+	0.933719i	0.829063	+	0.559155i	$0.188874\pi$
$383$	−1.92059	+	18.2732i	−0.0981378	+	0.933719i	−0.927201	+	0.374564i	$0.877792\pi$
$384$		0			0
$385$	−0.779606	−	1.18396i	−0.0397324	−	0.0603402i
$386$	−5.05284			−0.257183
$387$		0			0
$388$	1.71134	−	5.26696i	0.0868801	−	0.267390i
$389$	−30.1333	−	6.40504i	−1.52782	−	0.324748i	−0.634057	−	0.773286i	$-0.718612\pi$
$389$	−30.1333	−	6.40504i	−1.52782	−	0.324748i	−0.893764	+	0.448538i	$0.851945\pi$
$390$		0			0
$391$	−18.6761	−	8.31516i	−0.944493	−	0.420516i
$392$	−10.7878	+	11.9811i	−0.544867	+	0.605136i
$393$		0			0
$394$	−31.7277	+	14.1261i	−1.59842	+	0.711661i
$395$	8.65524			0.435493
$396$		0			0
$397$	−8.29578			−0.416353			−0.208177	−	0.978091i	$-0.566753\pi$
$397$	−8.29578			−0.416353			−0.208177	+	0.978091i	$0.566753\pi$
$398$	29.4204	−	13.0988i	1.47471	−	0.656584i
$399$		0			0
$400$	14.4000	−	15.9928i	0.720000	−	0.799641i
$401$	3.59354	+	1.59995i	0.179453	+	0.0798976i	0.494497	−	0.869180i	$-0.335352\pi$
$401$	3.59354	+	1.59995i	0.179453	+	0.0798976i	−0.315044	+	0.949077i	$0.602019\pi$
$402$		0			0
$403$	−14.0625	−	2.98907i	−0.700503	−	0.148896i
$404$	1.73404	−	5.33682i	0.0862716	−	0.265517i
$405$		0			0
$406$	7.78977			0.386600
$407$	0.441104	−	9.58052i	0.0218647	−	0.474889i
$408$		0			0
$409$	0.261766	−	2.49054i	0.0129435	−	0.123149i	−0.986142	−	0.165902i	$-0.946946\pi$
$409$	0.261766	−	2.49054i	0.0129435	−	0.123149i	0.999086	+	0.0427534i	$0.0136130\pi$
$410$	−1.03335	+	0.219646i	−0.0510336	+	0.0108475i
$411$		0			0
$412$	0.180796	+	1.72016i	0.00890719	+	0.0847462i
$413$	4.16650	−	3.02714i	0.205020	−	0.148956i
$414$		0			0
$415$	−1.27204	+	3.91493i	−0.0624419	+	0.192176i
$416$	−3.13585	+	1.39617i	−0.153747	+	0.0684528i
$417$		0			0
$418$	3.25047	−	12.4466i	0.158986	−	0.608781i
$419$	5.36970	+	9.30060i	0.262327	+	0.454364i	0.966860	−	0.255307i	$-0.0821767\pi$
$419$	5.36970	+	9.30060i	0.262327	+	0.454364i	−0.704533	+	0.709672i	$0.748843\pi$
$420$		0			0
$421$	14.8463	+	16.4885i	0.723564	+	0.803600i	0.986939	−	0.161094i	$-0.0515022\pi$
$421$	14.8463	+	16.4885i	0.723564	+	0.803600i	−0.263375	+	0.964694i	$0.584836\pi$
$422$	−1.62065	−	4.98785i	−0.0788920	−	0.242805i
$423$		0			0
$424$	−11.4825	+	8.34249i	−0.557637	+	0.405147i
$425$	−20.8839	−	4.43902i	−1.01302	−	0.215324i
$426$		0			0
$427$	−0.344039	+	3.27331i	−0.0166492	+	0.158407i
$428$	−3.07440	−	5.32501i	−0.148606	−	0.257394i
$429$		0			0
$430$	1.92889	−	3.34093i	0.0930192	−	0.161114i
$431$	−14.9330	−	10.8495i	−0.719297	−	0.522600i	0.166862	−	0.985980i	$-0.446636\pi$
$431$	−14.9330	−	10.8495i	−0.719297	−	0.522600i	−0.886160	+	0.463380i	$0.846636\pi$
$432$		0			0
$433$	4.67130	+	14.3768i	0.224488	+	0.690904i	0.998343	+	0.0575408i	$0.0183259\pi$
$433$	4.67130	+	14.3768i	0.224488	+	0.690904i	−0.773855	+	0.633363i	$0.781674\pi$
$434$	−1.06507	−	10.1334i	−0.0511249	−	0.486420i
$435$		0			0
$436$	−3.57932	+	3.97524i	−0.171418	+	0.190379i
$437$	−10.9242	+	2.32202i	−0.522577	+	0.111077i
$438$		0			0
$439$	−11.9777	+	20.7459i	−0.571663	+	0.990150i	0.424732	+	0.905319i	$0.360368\pi$
$439$	−11.9777	+	20.7459i	−0.571663	+	0.990150i	−0.996395	+	0.0848306i	$0.972965\pi$
$440$	4.33945	−	2.24589i	0.206875	−	0.107068i
$441$		0			0
$442$	9.04645	+	6.57263i	0.430296	+	0.312628i
$443$	−17.0613	−	18.9485i	−0.810607	−	0.900270i	0.186003	−	0.982549i	$-0.440447\pi$
$443$	−17.0613	−	18.9485i	−0.810607	−	0.900270i	−0.996609	+	0.0822794i	$0.973780\pi$
$444$		0			0
$445$	6.74993	+	3.00526i	0.319978	+	0.142463i
$446$	15.5744	+	6.93417i	0.737469	+	0.328342i
$447$		0			0
$448$	2.84405	+	3.15864i	0.134369	+	0.149231i
$449$	−18.1886	−	13.2148i	−0.858375	−	0.623646i	0.0690672	−	0.997612i	$-0.477998\pi$
$449$	−18.1886	−	13.2148i	−0.858375	−	0.623646i	−0.927442	+	0.373966i	$0.877998\pi$
$450$		0			0
$451$	3.78438	+	0.574776i	0.178200	+	0.0270651i
$452$	1.56804	−	2.71592i	0.0737542	−	0.127746i
$453$		0			0
$454$	9.02402	−	1.91812i	0.423518	−	0.0900216i
$455$	0.450437	−	0.500261i	0.0211168	−	0.0234526i
$456$		0			0
$457$	−2.26718	−	21.5708i	−0.106054	−	1.00904i	−0.910077	−	0.414439i	$-0.863978\pi$
$457$	−2.26718	−	21.5708i	−0.106054	−	1.00904i	0.804023	−	0.594598i	$-0.202689\pi$
$458$	−11.8254	−	36.3950i	−0.552566	−	1.70062i
$459$		0			0
$460$	0.832763	+	0.605037i	0.0388278	+	0.0282100i
$461$	−6.05182	+	10.4821i	−0.281861	+	0.488198i	−0.971843	−	0.235629i	$-0.924285\pi$
$461$	−6.05182	+	10.4821i	−0.281861	+	0.488198i	0.689982	+	0.723827i	$0.257618\pi$
$462$		0			0
$463$	−10.0154	−	17.3472i	−0.465455	−	0.806192i	0.533767	−	0.845632i	$-0.320776\pi$
$463$	−10.0154	−	17.3472i	−0.465455	−	0.806192i	−0.999222	+	0.0394398i	$0.987443\pi$
$464$	−3.37637	+	32.1240i	−0.156744	+	1.49132i
$465$		0			0
$466$	−6.33435	−	1.34641i	−0.293433	−	0.0623711i
$467$	4.90871	−	3.56639i	0.227148	−	0.165033i	−0.468390	−	0.883522i	$-0.655166\pi$
$467$	4.90871	−	3.56639i	0.227148	−	0.165033i	0.695538	+	0.718489i	$0.255166\pi$
$468$		0			0
$469$	−1.80516	−	5.55570i	−0.0833543	−	0.256538i
$470$	0.139377	+	0.154794i	0.00642898	+	0.00714011i
$471$		0			0
$472$	8.87574	+	15.3732i	0.408539	+	0.707610i
$473$	−10.8067	+	8.86535i	−0.496895	+	0.407629i
$474$		0			0
$475$	−10.6553	+	4.74407i	−0.488901	+	0.217673i
$476$	−0.400088	+	1.23134i	−0.0183380	+	0.0564385i
$477$		0			0
$478$	9.22233	−	6.70041i	0.421819	−	0.306470i
$479$	3.79154	+	36.0741i	0.173240	+	1.64827i	0.643286	+	0.765626i	$0.277571\pi$
$479$	3.79154	+	36.0741i	0.173240	+	1.64827i	−0.470046	+	0.882642i	$0.655763\pi$
$480$		0			0
$481$	4.45480	−	0.946896i	0.203121	−	0.0431747i
$482$	−1.42694	+	13.5764i	−0.0649953	+	0.618389i
$483$		0			0
$484$	4.26634	−	0.503273i	0.193924	−	0.0228760i
$485$	−8.39529			−0.381211
$486$		0			0
$487$	−2.68379	+	8.25986i	−0.121614	+	0.374290i	−0.993269	−	0.115830i	$-0.963047\pi$
$487$	−2.68379	+	8.25986i	−0.121614	+	0.374290i	0.871655	+	0.490120i	$0.163047\pi$
$488$	−11.0968	−	2.35870i	−0.502329	−	0.106773i
$489$		0			0
$490$	−5.41772	−	2.41213i	−0.244748	−	0.108969i
$491$	22.2133	−	24.6704i	1.00247	−	1.11336i	0.00892472	−	0.999960i	$-0.497159\pi$
$491$	22.2133	−	24.6704i	1.00247	−	1.11336i	0.993549	−	0.113400i	$-0.0361742\pi$
$492$		0			0
$493$	29.2753	−	13.0342i	1.31849	−	0.587032i
$494$	6.10872			0.274844
$495$		0			0
$496$	42.2506			1.89711
$497$	8.11848	−	3.61458i	0.364163	−	0.162136i
$498$		0			0
$499$	13.9694	−	15.5146i	0.625355	−	0.694527i	−0.344340	−	0.938845i	$-0.611897\pi$
$499$	13.9694	−	15.5146i	0.625355	−	0.694527i	0.969695	+	0.244318i	$0.0785641\pi$
$500$	2.03818	+	0.907458i	0.0911504	+	0.0405828i
$501$		0			0
$502$	−31.1136	−	6.61341i	−1.38867	−	0.295171i
$503$	−7.20593	+	22.1776i	−0.321297	+	0.988850i	0.651788	+	0.758401i	$0.274019\pi$
$503$	−7.20593	+	22.1776i	−0.321297	+	0.988850i	−0.973085	+	0.230448i	$0.925981\pi$
$504$		0			0
$505$	−8.50663			−0.378540
$506$	−12.5553	−	19.0672i	−0.558149	−	0.847641i
$507$		0			0
$508$	0.489718	−	4.65935i	0.0217277	−	0.206725i
$509$	6.33958	−	1.34752i	0.280997	−	0.0597278i	−0.0652572	−	0.997868i	$-0.520787\pi$
$509$	6.33958	−	1.34752i	0.280997	−	0.0597278i	0.346254	+	0.938141i	$0.387453\pi$
$510$		0			0
$511$	−1.16844	−	11.1170i	−0.0516887	−	0.491785i
$512$	−10.4751	+	7.61063i	−0.462940	+	0.336346i
$513$		0			0
$514$	−1.61605	+	4.97368i	−0.0712807	+	0.219379i
$515$	2.39534	−	1.06647i	0.105551	−	0.0469944i
$516$		0			0
$517$	−0.274935	−	0.702856i	−0.0120916	−	0.0309116i
$518$	1.61390	+	2.79537i	0.0709109	+	0.122821i
$519$		0			0
$520$	1.55258	+	1.72432i	0.0680854	+	0.0756164i
$521$	10.2625	+	31.5848i	0.449610	+	1.38376i	0.877348	+	0.479855i	$0.159311\pi$
$521$	10.2625	+	31.5848i	0.449610	+	1.38376i	−0.427738	+	0.903903i	$0.640689\pi$
$522$		0			0
$523$	32.4728	−	23.5929i	1.41994	−	1.03164i	0.428154	−	0.903706i	$-0.359164\pi$
$523$	32.4728	−	23.5929i	1.41994	−	1.03164i	0.991782	−	0.127938i	$-0.0408359\pi$
$524$	−2.63242	−	0.559539i	−0.114998	−	0.0244436i
$525$		0			0
$526$	2.30823	−	21.9613i	0.100644	−	0.957560i
$527$	−20.9585	−	36.3011i	−0.912965	−	1.58130i
$528$		0			0
$529$	1.58985	−	2.75370i	0.0691240	−	0.119726i
$530$	−4.22376	−	3.06874i	−0.183468	−	0.133298i
$531$		0			0
$532$	0.218567	+	0.672680i	0.00947608	+	0.0291644i
$533$	0.190001	+	1.80774i	0.00822986	+	0.0783019i
$534$		0			0
$535$	−6.23710	+	6.92700i	−0.269653	+	0.299480i
$536$	19.6951	−	4.18632i	0.850698	−	0.180821i
$537$		0			0
$538$	−5.19534	+	8.99859i	−0.223987	+	0.387957i
$539$	15.2903	+	15.0973i	0.658599	+	0.650287i
$540$		0			0
$541$	−19.9410	−	14.4880i	−0.857332	−	0.622888i	0.0698260	−	0.997559i	$-0.477756\pi$
$541$	−19.9410	−	14.4880i	−0.857332	−	0.622888i	−0.927158	+	0.374671i	$0.877756\pi$
$542$	4.11794	+	4.57344i	0.176881	+	0.196446i
$543$		0			0
$544$	−9.14294	−	4.07070i	−0.392000	−	0.174530i
$545$	7.40801	+	3.29826i	0.317324	+	0.141282i
$546$		0			0
$547$	17.2103	+	19.1139i	0.735858	+	0.817253i	0.988645	−	0.150269i	$-0.0480139\pi$
$547$	17.2103	+	19.1139i	0.735858	+	0.817253i	−0.252787	+	0.967522i	$0.581347\pi$
$548$	2.92147	+	2.12257i	0.124799	+	0.0906716i
$549$		0			0
$550$	−16.9659	−	16.7517i	−0.723427	−	0.714296i
$551$	8.75329	−	15.1611i	0.372902	−	0.645886i
$552$		0			0
$553$	10.3240	−	2.19442i	0.439019	−	0.0933164i
$554$	13.5859	−	15.0887i	0.577211	−	0.641058i
$555$		0			0
$556$	−0.882224	−	8.39380i	−0.0374146	−	0.355976i
$557$	−3.60979	−	11.1098i	−0.152952	−	0.470737i	0.844996	−	0.534773i	$-0.179603\pi$
$557$	−3.60979	−	11.1098i	−0.152952	−	0.470737i	−0.997948	+	0.0640357i	$0.979603\pi$
$558$		0			0
$559$	−5.36998	−	3.90152i	−0.227126	−	0.165017i
$560$	−0.989164	+	1.71328i	−0.0417998	+	0.0723994i
$561$		0			0
$562$	2.29436	+	3.97396i	0.0967819	+	0.167631i
$563$	0.848991	−	8.07761i	0.0357807	−	0.340431i	−0.961957	−	0.273201i	$-0.911917\pi$
$563$	0.848991	−	8.07761i	0.0357807	−	0.340431i	0.997738	−	0.0672292i	$-0.0214159\pi$
$564$		0			0
$565$	−4.65021	−	0.988432i	−0.195636	−	0.0415836i
$566$	10.1229	−	7.35468i	0.425495	−	0.309140i
$567$		0			0
$568$	9.46559	+	29.1321i	0.397167	+	1.22236i
$569$	12.0488	+	13.3815i	0.505111	+	0.560983i	0.940733	−	0.339147i	$-0.110138\pi$
$569$	12.0488	+	13.3815i	0.505111	+	0.560983i	−0.435622	+	0.900129i	$0.643472\pi$
$570$		0			0
$571$	1.30322	+	2.25725i	0.0545382	+	0.0944629i	0.892006	−	0.452024i	$-0.149298\pi$
$571$	1.30322	+	2.25725i	0.0545382	+	0.0944629i	−0.837467	+	0.546487i	$0.815965\pi$
$572$	0.743151	+	1.89982i	0.0310727	+	0.0794356i
$573$		0			0
$574$	−1.17689	+	0.523986i	−0.0491225	+	0.0218707i
$575$	−6.39652	+	19.6865i	−0.266753	+	0.820982i
$576$		0			0
$577$	−28.4684	+	20.6835i	−1.18515	+	0.861064i	−0.992744	−	0.120251i	$-0.961630\pi$
$577$	−28.4684	+	20.6835i	−1.18515	+	0.861064i	−0.192409	+	0.981315i	$0.561630\pi$
$578$	0.660439	+	6.28365i	0.0274706	+	0.261366i
$579$		0			0
$580$	−1.57827	+	0.335473i	−0.0655343	+	0.0139297i
$581$	−0.524704	+	4.99223i	−0.0217684	+	0.207112i
$582$		0			0
$583$	10.4033	+	15.7991i	0.430861	+	0.654333i
$584$	38.5294			1.59436
$585$		0			0
$586$	−7.50863	+	23.1092i	−0.310179	+	0.954631i
$587$	23.0377	+	4.89682i	0.950869	+	0.202113i	0.657134	−	0.753774i	$-0.271768\pi$
$587$	23.0377	+	4.89682i	0.950869	+	0.202113i	0.293735	+	0.955887i	$0.405102\pi$
$588$		0			0
$589$	−20.9194	−	9.31391i	−0.861968	−	0.383773i
$590$	−4.36928	+	4.85258i	−0.179880	+	0.199777i
$591$		0			0
$592$	−12.2272	+	5.44392i	−0.502536	+	0.223744i
$593$	−13.1828			−0.541354			−0.270677	−	0.962670i	$-0.587248\pi$
$593$	−13.1828			−0.541354			−0.270677	+	0.962670i	$0.587248\pi$
$594$		0			0
$595$	1.96270			0.0804630
$596$	0.409018	−	0.182106i	0.0167540	−	0.00745937i
$597$		0			0
$598$	7.25412	−	8.05651i	0.296643	−	0.329455i
$599$	−31.2582	−	13.9171i	−1.27718	−	0.568636i	−0.347731	−	0.937594i	$-0.613048\pi$
$599$	−31.2582	−	13.9171i	−1.27718	−	0.568636i	−0.929446	+	0.368958i	$0.879715\pi$
$600$		0			0
$601$	−28.3942	−	6.03537i	−1.15822	−	0.246188i	−0.411555	−	0.911385i	$-0.635014\pi$
$601$	−28.3942	−	6.03537i	−1.15822	−	0.246188i	−0.746668	+	0.665197i	$0.768347\pi$
$602$	1.45372	−	4.47410i	0.0592493	−	0.182351i
$603$		0			0
$604$	0.343924			0.0139941
$605$	−2.72416	−	5.91521i	−0.110753	−	0.240487i
$606$		0			0
$607$	0.329929	−	3.13906i	0.0133914	−	0.127411i	−0.985784	−	0.168019i	$-0.946263\pi$
$607$	0.329929	−	3.13906i	0.0133914	−	0.127411i	0.999175	+	0.0406085i	$0.0129296\pi$
$608$	−5.34798	+	1.13675i	−0.216889	+	0.0461012i
$609$		0			0
$610$	−0.436207	−	4.15024i	−0.0176615	−	0.168038i
$611$	0.289945	−	0.210657i	0.0117299	−	0.00852229i
$612$		0			0
$613$	10.4884	−	32.2798i	0.423620	−	1.30377i	−0.480689	−	0.876891i	$-0.659613\pi$
$613$	10.4884	−	32.2798i	0.423620	−	1.30377i	0.904309	−	0.426878i	$-0.140387\pi$
$614$	4.96221	−	2.20932i	0.200258	−	0.0891608i
$615$		0			0
$616$	4.60667	−	3.77910i	0.185608	−	0.152264i
$617$	−10.8039	−	18.7129i	−0.434948	−	0.753351i	0.562344	−	0.826904i	$-0.309900\pi$
$617$	−10.8039	−	18.7129i	−0.434948	−	0.753351i	−0.997291	+	0.0735523i	$0.976566\pi$
$618$		0			0
$619$	13.7256	+	15.2438i	0.551679	+	0.612701i	0.952902	−	0.303279i	$-0.0980815\pi$
$619$	13.7256	+	15.2438i	0.551679	+	0.612701i	−0.401223	+	0.915980i	$0.631415\pi$
$620$	0.652196	+	2.00725i	0.0261928	+	0.0806132i
$621$		0			0
$622$	−32.9404	+	23.9326i	−1.32079	+	0.959611i
$623$	8.81325	+	1.87331i	0.353095	+	0.0750527i
$624$		0			0
$625$	−2.07649	+	19.7565i	−0.0830597	+	0.790260i
$626$	−1.90263	−	3.29545i	−0.0760444	−	0.131713i
$627$		0			0
$628$	1.91094	−	3.30985i	0.0762550	−	0.132078i
$629$	10.7427	+	7.80501i	0.428339	+	0.311206i
$630$		0			0
$631$	9.22863	+	28.4028i	0.367386	+	1.13070i	0.948473	+	0.316857i	$0.102628\pi$
$631$	9.22863	+	28.4028i	0.367386	+	1.13070i	−0.581087	+	0.813841i	$0.697372\pi$
$632$	3.80275	+	36.1807i	0.151265	+	1.43919i
$633$		0			0
$634$	−27.4234	+	30.4568i	−1.08912	+	1.20959i
$635$	−6.94700	+	1.47663i	−0.275683	+	0.0585983i
$636$		0			0
$637$	−5.10193	+	8.83680i	−0.202146	+	0.350127i
$638$	35.3803	+	5.37360i	1.40072	+	0.212743i
$639$		0			0
$640$	−6.44762	−	4.68447i	−0.254864	−	0.185170i
$641$	25.5073	+	28.3287i	1.00748	+	1.11892i	0.992891	+	0.119024i	$0.0379764\pi$
$641$	25.5073	+	28.3287i	1.00748	+	1.11892i	0.0145863	+	0.999894i	$0.495357\pi$
$642$		0			0
$643$	−15.3705	−	6.84340i	−0.606154	−	0.269877i	0.0806235	−	0.996745i	$-0.474309\pi$
$643$	−15.3705	−	6.84340i	−0.606154	−	0.269877i	−0.686778	+	0.726867i	$0.740976\pi$
$644$	1.14672	+	0.510551i	0.0451870	+	0.0201185i
$645$		0			0
$646$	11.9177	+	13.2359i	0.468895	+	0.520761i
$647$	−16.9687	−	12.3285i	−0.667109	−	0.484683i	0.201947	−	0.979396i	$-0.435273\pi$
$647$	−16.9687	−	12.3285i	−0.667109	−	0.484683i	−0.869056	+	0.494713i	$0.835273\pi$
$648$		0			0
$649$	21.0120	−	10.8748i	0.824792	−	0.426872i
$650$	5.66102	−	9.80517i	0.222043	−	0.384591i
$651$		0			0
$652$	−1.76859	+	0.375925i	−0.0692632	+	0.0147223i
$653$	−13.2264	+	14.6894i	−0.517587	+	0.574839i	−0.944107	−	0.329639i	$-0.893073\pi$
$653$	−13.2264	+	14.6894i	−0.517587	+	0.574839i	0.426520	+	0.904478i	$0.359739\pi$
$654$		0			0
$655$	0.426450	+	4.05740i	0.0166628	+	0.158536i
$656$	−1.65074	−	5.08046i	−0.0644506	−	0.198358i
$657$		0			0
$658$	0.205494	+	0.149300i	0.00801101	+	0.00582034i
$659$	−5.90277	+	10.2239i	−0.229939	+	0.398267i	−0.957790	−	0.287469i	$-0.907186\pi$
$659$	−5.90277	+	10.2239i	−0.229939	+	0.398267i	0.727851	+	0.685736i	$0.240519\pi$
$660$		0			0
$661$	−8.90382	−	15.4219i	−0.346318	−	0.599841i	0.639274	−	0.768979i	$-0.279235\pi$
$661$	−8.90382	−	15.4219i	−0.346318	−	0.599841i	−0.985592	+	0.169138i	$0.945902\pi$
$662$	1.30972	−	12.4612i	0.0509039	−	0.484318i
$663$		0			0
$664$	−16.9241	−	3.59733i	−0.656782	−	0.139603i
$665$	0.867445	−	0.630235i	0.0336381	−	0.0244395i
$666$		0			0
$667$	−9.60079	−	29.5482i	−0.371744	−	1.14411i
$668$	4.43916	+	4.93019i	0.171756	+	0.190755i
$669$		0			0
$670$	3.70329	+	6.41429i	0.143071	+	0.247806i
$671$	−3.82060	+	14.6297i	−0.147493	+	0.564773i
$672$		0			0
$673$	18.0017	−	8.01486i	0.693913	−	0.308950i	−0.0293041	−	0.999571i	$-0.509329\pi$
$673$	18.0017	−	8.01486i	0.693913	−	0.308950i	0.723217	+	0.690620i	$0.242662\pi$
$674$	−11.8111	+	36.3508i	−0.454946	+	1.40018i
$675$		0			0
$676$	3.32365	−	2.41477i	0.127833	−	0.0928760i
$677$	−1.29761	−	12.3459i	−0.0498711	−	0.474492i	−0.990745	−	0.135735i	$-0.956660\pi$
$677$	−1.29761	−	12.3459i	−0.0498711	−	0.474492i	0.940874	−	0.338757i	$-0.110006\pi$
$678$		0			0
$679$	−10.0139	+	2.12852i	−0.384297	+	0.0816850i
$680$	−0.707148	+	6.72806i	−0.0271179	+	0.258010i
$681$		0			0
$682$	2.15290	−	46.7597i	0.0824387	−	1.79052i
$683$	−2.02837			−0.0776135			−0.0388068	−	0.999247i	$-0.512356\pi$
$683$	−2.02837			−0.0776135			−0.0388068	+	0.999247i	$0.512356\pi$
$684$		0			0
$685$	1.69164	−	5.20632i	0.0646341	−	0.198923i
$686$	−14.7167	−	3.12813i	−0.561886	−	0.119433i
$687$		0			0
$688$	17.8205	+	7.93420i	0.679400	+	0.302488i
$689$	−6.01077	+	6.67564i	−0.228992	+	0.254322i
$690$		0			0
$691$	2.14032	−	0.952931i	0.0814215	−	0.0362512i	−0.365622	−	0.930764i	$-0.619144\pi$
$691$	2.14032	−	0.952931i	0.0814215	−	0.0362512i	0.447043	+	0.894512i	$0.352477\pi$
$692$	0.230830			0.00877483
$693$		0			0
$694$	−3.19995			−0.121469
$695$	−11.6884	+	5.20402i	−0.443367	+	0.197400i
$696$		0			0
$697$	−3.54620	+	3.93846i	−0.134322	+	0.149180i
$698$	7.36497	+	3.27910i	0.278768	+	0.124116i
$699$		0			0
$700$	1.28228	+	0.272556i	0.0484655	+	0.0103016i
$701$	1.37008	−	4.21668i	0.0517473	−	0.159262i	−0.921843	−	0.387563i	$-0.873317\pi$
$701$	1.37008	−	4.21668i	0.0517473	−	0.159262i	0.973591	+	0.228301i	$0.0733170\pi$
$702$		0			0
$703$	7.25411			0.273594
$704$	10.7384	+	16.3081i	0.404720	+	0.614634i
$705$		0			0
$706$	−3.50261	+	33.3251i	−0.131822	+	1.25421i
$707$	−10.1467	+	2.15675i	−0.381606	+	0.0811128i
$708$		0			0
$709$	−3.12357	−	29.7188i	−0.117308	−	1.11611i	−0.881847	−	0.471536i	$-0.843700\pi$
$709$	−3.12357	−	29.7188i	−0.117308	−	1.11611i	0.764538	−	0.644578i	$-0.222967\pi$
$710$	−9.11565	+	6.62291i	−0.342104	+	0.248553i
$711$		0			0
$712$	−9.59699	+	29.5365i	−0.359662	+	1.10693i
$713$	−37.1255	+	16.5293i	−1.39036	+	0.619029i
$714$		0			0
$715$	2.39093	−	1.96141i	0.0894157	−	0.0733525i
$716$	−1.88258	−	3.26072i	−0.0703551	−	0.121859i
$717$		0			0
$718$	9.05541	+	10.0571i	0.337945	+	0.375326i
$719$	6.68469	+	20.5734i	0.249297	+	0.767257i	0.994900	+	0.100867i	$0.0321616\pi$
$719$	6.68469	+	20.5734i	0.249297	+	0.767257i	−0.745603	+	0.666390i	$0.767838\pi$
$720$		0			0
$721$	2.58676	−	1.87939i	0.0963360	−	0.0699922i
$722$	−19.2173	−	4.08477i	−0.715194	−	0.152019i
$723$		0			0
$724$	0.194391	−	1.84950i	0.00722447	−	0.0687363i
$725$	−16.2235	−	28.1000i	−0.602527	−	1.04361i
$726$		0			0
$727$	6.22109	−	10.7752i	0.230727	−	0.399631i	−0.727295	−	0.686325i	$-0.759223\pi$
$727$	6.22109	−	10.7752i	0.230727	−	0.399631i	0.958022	+	0.286694i	$0.0925561\pi$
$728$	2.28910	+	1.66313i	0.0848396	+	0.0616396i
$729$		0			0
$730$	4.37965	+	13.4792i	0.162098	+	0.498887i
$731$	−2.02293	−	19.2469i	−0.0748207	−	0.711872i
$732$		0			0
$733$	−35.0305	+	38.9053i	−1.29388	+	1.43700i	−0.457143	+	0.889393i	$0.651127\pi$
$733$	−35.0305	+	38.9053i	−1.29388	+	1.43700i	−0.836736	+	0.547606i	$0.815539\pi$
$734$	−10.2329	+	2.17507i	−0.377703	+	0.0802833i
$735$		0			0
$736$	−4.85153	+	8.40310i	−0.178830	+	0.309742i
$737$	−4.36635	−	26.4786i	−0.160837	−	0.975352i
$738$		0			0
$739$	37.7617	+	27.4355i	1.38909	+	1.00923i	0.995965	+	0.0897445i	$0.0286051\pi$
$739$	37.7617	+	27.4355i	1.38909	+	1.00923i	0.393122	+	0.919486i	$0.371395\pi$
$740$	−0.447375	−	0.496861i	−0.0164458	−	0.0182650i
$741$		0			0
$742$	−5.81613	−	2.58951i	−0.213517	−	0.0950638i
$743$	19.9810	+	8.89609i	0.733030	+	0.326366i	0.739082	−	0.673616i	$-0.235260\pi$
$743$	19.9810	+	8.89609i	0.733030	+	0.326366i	−0.00605180	+	0.999982i	$0.501926\pi$
$744$		0			0
$745$	−0.454155	−	0.504391i	−0.0166390	−	0.0184794i
$746$	−27.3853	−	19.8966i	−1.00265	−	0.728466i
$747$		0			0
$748$	−2.66657	+	5.31664i	−0.0974994	+	0.194395i
$749$	−5.68334	+	9.84384i	−0.207665	+	0.359686i
$750$		0			0
$751$	−38.7269	+	8.23167i	−1.41317	+	0.300378i	−0.850356	−	0.526208i	$-0.823613\pi$
$751$	−38.7269	+	8.23167i	−1.41317	+	0.300378i	−0.562810	+	0.826586i	$0.690280\pi$
$752$	−0.704764	+	0.782720i	−0.0257001	+	0.0285429i
$753$		0			0
$754$	1.77633	+	16.9006i	0.0646900	+	0.615484i
$755$	−0.161111	−	0.495850i	−0.00586344	−	0.0180458i
$756$		0			0
$757$	−18.7253	−	13.6047i	−0.680583	−	0.494472i	0.192968	−	0.981205i	$-0.438189\pi$
$757$	−18.7253	−	13.6047i	−0.680583	−	0.494472i	−0.873551	+	0.486733i	$0.838189\pi$
$758$	−26.1480	+	45.2896i	−0.949736	+	1.64499i
$759$		0			0
$760$	1.84789	+	3.20063i	0.0670299	+	0.116099i
$761$	−1.55673	+	14.8113i	−0.0564313	+	0.536908i	0.929389	+	0.369102i	$0.120335\pi$
$761$	−1.55673	+	14.8113i	−0.0564313	+	0.536908i	−0.985820	+	0.167806i	$0.946332\pi$
$762$		0			0
$763$	9.67249	+	2.05595i	0.350168	+	0.0744304i
$764$	−1.64233	+	1.19322i	−0.0594173	+	0.0431692i
$765$		0			0
$766$	−8.77872	−	27.0181i	−0.317188	−	0.976204i
$767$	7.51774	+	8.34930i	0.271450	+	0.301476i
$768$		0			0
$769$	−10.8117	−	18.7264i	−0.389879	−	0.675290i	0.602554	−	0.798078i	$-0.294150\pi$
$769$	−10.8117	−	18.7264i	−0.389879	−	0.675290i	−0.992433	+	0.122788i	$0.960816\pi$
$770$	1.84572	+	1.18203i	0.0665153	+	0.0425974i
$771$		0			0
$772$	1.16595	−	0.519116i	0.0419636	−	0.0186834i
$773$	1.87664	−	5.77569i	0.0674979	−	0.207737i	−0.911619	−	0.411037i	$-0.865167\pi$
$773$	1.87664	−	5.77569i	0.0674979	−	0.207737i	0.979117	+	0.203300i	$0.0651666\pi$
$774$		0			0
$775$	−34.3361	+	24.9466i	−1.23339	+	0.896109i
$776$	−3.68853	−	35.0941i	−0.132411	−	1.25980i
$777$		0			0
$778$	46.5903	−	9.90307i	1.67034	−	0.355042i
$779$	−0.302633	+	2.87936i	−0.0108430	+	0.103164i
$780$		0			0
$781$	39.3667	−	10.8167i	1.40865	−	0.387051i
$782$	31.6086			1.13032
$783$		0			0
$784$	9.26663	−	28.5197i	0.330951	−	1.01856i
$785$	−5.66714	−	1.20459i	−0.202269	−	0.0429936i
$786$		0			0
$787$	46.7328	+	20.8068i	1.66584	+	0.741681i	0.999990	−	0.00440228i	$-0.00140129\pi$
$787$	46.7328	+	20.8068i	1.66584	+	0.741681i	0.665853	+	0.746083i	$0.268068\pi$
$788$	5.86995	−	6.51924i	0.209108	−	0.232238i
$789$		0			0
$790$	−12.2252	+	5.44303i	−0.434954	+	0.193654i
$791$	−5.79736			−0.206130
$792$		0			0
$793$	−7.18019			−0.254976
$794$	11.7175	−	5.21697i	0.415839	−	0.185143i
$795$		0			0
$796$	−5.44309	+	6.04516i	−0.192925	+	0.214265i
$797$	23.0773	+	10.2747i	0.817439	+	0.363947i	0.772478	−	0.635041i	$-0.219017\pi$
$797$	23.0773	+	10.2747i	0.817439	+	0.363947i	0.0449609	+	0.998989i	$0.485684\pi$
$798$		0			0
$799$	1.02210	+	0.217254i	0.0361593	+	0.00768590i
$800$	−3.13143	+	9.63754i	−0.110713	+	0.340738i
$801$		0			0
$802$	−6.08192			−0.214760
$803$	2.36185	−	51.2980i	0.0833480	−	1.81027i
$804$		0			0
$805$	0.198903	−	1.89244i	0.00701042	−	0.0666997i
$806$	21.7425	−	4.62152i	0.765848	−	0.162786i
$807$		0			0
$808$	−3.73745	−	35.5595i	−0.131483	−	1.25098i
$809$	41.5248	−	30.1696i	1.45994	−	1.06071i	0.476556	−	0.879144i	$-0.341885\pi$
$809$	41.5248	−	30.1696i	1.45994	−	1.06071i	0.983380	−	0.181561i	$-0.0581150\pi$
$810$		0			0
$811$	1.40476	−	4.32339i	0.0493276	−	0.151815i	−0.923359	−	0.383939i	$-0.874567\pi$
$811$	1.40476	−	4.32339i	0.0493276	−	0.151815i	0.972686	+	0.232124i	$0.0745674\pi$
$812$	−1.79751	+	0.800302i	−0.0630801	+	0.0280851i
$813$		0			0
$814$	5.40186	+	13.8096i	0.189335	+	0.484025i
$815$	1.37048	+	2.37375i	0.0480059	+	0.0831487i
$816$		0			0
$817$	−7.07435	−	7.85686i	−0.247500	−	0.274877i
$818$	1.19649	+	3.68241i	0.0418342	+	0.128753i
$819$		0			0
$820$	0.215882	−	0.156848i	0.00753894	−	0.00547736i
$821$	10.6362	+	2.26079i	0.371205	+	0.0789021i	0.389737	−	0.920926i	$-0.372566\pi$
$821$	10.6362	+	2.26079i	0.371205	+	0.0789021i	−0.0185320	+	0.999828i	$0.505899\pi$
$822$		0			0
$823$	2.46856	−	23.4868i	0.0860486	−	0.818697i	−0.863346	−	0.504612i	$-0.831636\pi$
$823$	2.46856	−	23.4868i	0.0860486	−	0.818697i	0.949395	−	0.314085i	$-0.101698\pi$
$824$	5.51048	+	9.54444i	0.191967	+	0.332496i
$825$		0			0
$826$	−3.98136	+	6.89591i	−0.138529	+	0.239940i
$827$	−22.3321	−	16.2252i	−0.776564	−	0.564207i	0.127382	−	0.991854i	$-0.459343\pi$
$827$	−22.3321	−	16.2252i	−0.776564	−	0.564207i	−0.903946	+	0.427647i	$0.859343\pi$
$828$		0			0
$829$	−4.97546	−	15.3129i	−0.172805	−	0.531839i	0.826722	−	0.562611i	$-0.190203\pi$
$829$	−4.97546	−	15.3129i	−0.172805	−	0.531839i	−0.999526	+	0.0307727i	$0.990203\pi$
$830$	−0.665273	−	6.32965i	−0.0230920	−	0.219705i
$831$		0			0
$832$	−6.20441	+	6.89069i	−0.215099	+	0.238892i
$833$	−29.1005	+	6.18550i	−1.00827	+	0.214315i
$834$		0			0
$835$	5.02854	−	8.70968i	0.174020	−	0.301411i
$836$	0.528675	+	3.20601i	0.0182846	+	0.110882i
$837$		0			0
$838$	−13.4334	−	9.75993i	−0.464049	−	0.337151i
$839$	13.0025	+	14.4407i	0.448896	+	0.498549i	0.924538	−	0.381089i	$-0.124451\pi$
$839$	13.0025	+	14.4407i	0.448896	+	0.498549i	−0.475642	+	0.879639i	$0.657784\pi$
$840$		0			0
$841$	17.9979	+	8.01318i	0.620617	+	0.276317i
$842$	−31.3390	−	13.9530i	−1.08001	−	0.480853i
$843$		0			0
$844$	0.886407	+	0.984455i	0.0305114	+	0.0338863i
$845$	−5.03845	−	3.66065i	−0.173328	−	0.125930i
$846$		0			0
$847$	−4.74909	−	6.36497i	−0.163181	−	0.218703i
$848$	13.1997	−	22.8626i	0.453280	−	0.785103i
$849$		0			0
$850$	32.2894	−	6.86333i	1.10752	−	0.235410i
$851$	8.61427	−	9.56712i	0.295293	−	0.327957i
$852$		0			0
$853$	2.06815	+	19.6771i	0.0708121	+	0.673732i	0.971138	+	0.238517i	$0.0766611\pi$
$853$	2.06815	+	19.6771i	0.0708121	+	0.673732i	−0.900326	+	0.435215i	$0.856672\pi$
$854$	−1.57255	−	4.83980i	−0.0538114	−	0.165614i
$855$		0			0
$856$	−31.6966	−	23.0289i	−1.08337	−	0.787112i
$857$	−2.17032	+	3.75911i	−0.0741369	+	0.128409i	−0.900711	−	0.434420i	$-0.856953\pi$
$857$	−2.17032	+	3.75911i	−0.0741369	+	0.128409i	0.826574	+	0.562828i	$0.190287\pi$
$858$		0			0
$859$	2.58967	+	4.48545i	0.0883586	+	0.153042i	0.906817	−	0.421524i	$-0.138505\pi$
$859$	2.58967	+	4.48545i	0.0883586	+	0.153042i	−0.818459	+	0.574565i	$0.805171\pi$
$860$	−0.101856	+	0.969096i	−0.00347327	+	0.0330459i
$861$		0			0
$862$	27.9153	+	5.93357i	0.950797	+	0.202098i
$863$	−2.17943	+	1.58345i	−0.0741886	+	0.0539011i	−0.624261	−	0.781216i	$-0.714600\pi$
$863$	−2.17943	+	1.58345i	−0.0741886	+	0.0539011i	0.550073	+	0.835117i	$0.314600\pi$
$864$		0			0
$865$	−0.108132	−	0.332797i	−0.00367661	−	0.0113155i
$866$	−15.6392	−	17.3691i	−0.531441	−	0.590225i
$867$		0			0
$868$	1.28685	+	2.22889i	0.0436785	+	0.0756534i
$869$	48.4040	−	2.84509i	1.64199	−	0.0965132i
$870$		0			0
$871$	11.6420	−	5.18333i	0.394472	−	0.175630i
$872$	−10.5326	+	32.4161i	−0.356680	+	1.09775i
$873$		0			0
$874$	13.9699	−	10.1497i	0.472538	−	0.343319i
$875$	−0.431114	−	4.10177i	−0.0145743	−	0.138665i
$876$		0			0
$877$	20.3893	−	4.33387i	0.688497	−	0.146344i	0.149638	−	0.988741i	$-0.452189\pi$
$877$	20.3893	−	4.33387i	0.688497	−	0.146344i	0.538858	+	0.842396i	$0.318856\pi$
$878$	3.87155	−	36.8353i	0.130658	−	1.24313i
$879$		0			0
$880$	−5.67454	+	7.09919i	−0.191289	+	0.239314i
$881$	−11.5843			−0.390286			−0.195143	−	0.980775i	$-0.562517\pi$
$881$	−11.5843			−0.390286			−0.195143	+	0.980775i	$0.562517\pi$
$882$		0			0
$883$	4.75801	−	14.6437i	0.160120	−	0.492798i	−0.838524	−	0.544865i	$-0.816581\pi$
$883$	4.75801	−	14.6437i	0.160120	−	0.492798i	0.998644	+	0.0520667i	$0.0165808\pi$
$884$	−2.76274	−	0.587239i	−0.0929211	−	0.0197510i
$885$		0			0
$886$	36.0146	+	16.0348i	1.20994	+	0.538698i
$887$	3.95453	−	4.39196i	0.132780	−	0.147467i	−0.673088	−	0.739563i	$-0.735032\pi$
$887$	3.95453	−	4.39196i	0.132780	−	0.147467i	0.805868	+	0.592095i	$0.201699\pi$
$888$		0			0
$889$	−7.91198	+	3.52264i	−0.265359	+	0.118146i
$890$	−11.4240			−0.382932
$891$		0			0
$892$	−4.30623			−0.144183
$893$	0.521493	−	0.232184i	0.0174511	−	0.00776974i
$894$		0			0
$895$	−3.81922	+	4.24168i	−0.127663	+	0.141784i
$896$	−8.87838	−	3.95291i	−0.296606	−	0.132057i
$897$		0			0
$898$	34.0013	+	7.22719i	1.13464	+	0.241174i
$899$	19.6852	−	60.5847i	0.656537	−	2.02061i
$900$		0			0
$901$	−26.1909			−0.872546
$902$	−5.70677	+	1.56803i	−0.190015	+	0.0522098i
$903$		0			0
$904$	2.08875	−	19.8731i	0.0694707	−	0.660969i
$905$	−2.75757	+	0.586140i	−0.0916648	+	0.0194840i
$906$		0			0
$907$	0.772812	+	7.35282i	0.0256608	+	0.244146i	0.999832	+	0.0183351i	$0.00583657\pi$
$907$	0.772812	+	7.35282i	0.0256608	+	0.244146i	−0.974171	+	0.225811i	$0.927497\pi$
$908$	−1.88525	+	1.36971i	−0.0625642	+	0.0454556i
$909$		0			0
$910$	−0.321628	+	0.989869i	−0.0106619	+	0.0328138i
$911$	12.9713	−	5.77517i	0.429757	−	0.191340i	−0.180447	−	0.983585i	$-0.557754\pi$
$911$	12.9713	−	5.77517i	0.429757	−	0.191340i	0.610203	+	0.792245i	$0.291088\pi$
$912$		0			0
$913$	−5.82692	+	22.3122i	−0.192843	+	0.738426i
$914$	16.7675	+	29.0422i	0.554620	+	0.960631i
$915$		0			0
$916$	6.46787	+	7.18330i	0.213704	+	0.237343i
$917$	1.53737	+	4.73153i	0.0507684	+	0.156249i
$918$		0			0
$919$	33.6895	−	24.4769i	1.11132	−	0.807418i	0.128445	−	0.991717i	$-0.459001\pi$
$919$	33.6895	−	24.4769i	1.11132	−	0.807418i	0.982870	+	0.184299i	$0.0590013\pi$
$920$	6.41554	+	1.36366i	0.211514	+	0.0449587i
$921$		0			0
$922$	1.95613	−	18.6114i	0.0644218	−	0.612932i
$923$	9.69344	+	16.7895i	0.319063	+	0.552634i
$924$		0			0
$925$	6.72247	−	11.6437i	0.221033	−	0.382841i
$926$	25.0555	+	18.2039i	0.823376	+	0.598218i
$927$		0			0
$928$	−4.70008	−	14.4654i	−0.154288	−	0.474849i
$929$	−3.56785	−	33.9458i	−0.117057	−	1.11373i	−0.882530	−	0.470257i	$-0.844161\pi$
$929$	−3.56785	−	33.9458i	−0.117057	−	1.11373i	0.765473	−	0.643469i	$-0.222505\pi$
$930$		0			0
$931$	−10.8752	+	12.0781i	−0.356419	+	0.395844i
$932$	1.59999	−	0.340089i	0.0524094	−	0.0111400i
$933$		0			0
$934$	−4.69059	+	8.12434i	−0.153481	+	0.265837i
$935$	8.91439	+	1.35393i	0.291532	+	0.0442781i
$936$		0			0
$937$	−41.8118	−	30.3780i	−1.36593	−	0.992407i	−0.998043	−	0.0625376i	$-0.980081\pi$
$937$	−41.8118	−	30.3780i	−1.36593	−	0.992407i	−0.367889	−	0.929870i	$-0.619919\pi$
$938$	6.04353	+	6.71202i	0.197328	+	0.219155i
$939$		0			0
$940$	−0.0480647	−	0.0213998i	−0.00156770	−	0.000697984i
$941$	−16.4495	−	7.32378i	−0.536237	−	0.238748i	0.120706	−	0.992688i	$-0.461484\pi$
$941$	−16.4495	−	7.32378i	−0.536237	−	0.238748i	−0.656943	+	0.753940i	$0.728151\pi$
$942$		0			0
$943$	3.43809	+	3.81838i	0.111959	+	0.124344i
$944$	−26.7122	−	19.4075i	−0.869407	−	0.631661i
$945$		0			0
$946$	9.68901	−	19.3181i	0.315017	−	0.628084i
$947$	14.3151	−	24.7946i	0.465180	−	0.805715i	−0.534030	−	0.845466i	$-0.679323\pi$
$947$	14.3151	−	24.7946i	0.465180	−	0.805715i	0.999210	+	0.0397506i	$0.0126563\pi$
$948$		0			0
$949$	23.8528	−	5.07007i	0.774295	−	0.164581i
$950$	12.0669	−	13.4017i	0.391502	−	0.434808i
$951$		0			0
$952$	0.862328	+	8.20451i	0.0279482	+	0.265910i
$953$	−5.15728	−	15.8725i	−0.167061	−	0.514160i	0.832121	−	0.554594i	$-0.187126\pi$
$953$	−5.15728	−	15.8725i	−0.167061	−	0.514160i	−0.999182	+	0.0404331i	$0.987126\pi$
$954$		0			0
$955$	2.48967	+	1.80885i	0.0805637	+	0.0585330i
$956$	−1.43969	+	2.49361i	−0.0465628	+	0.0806492i
$957$		0			0
$958$	−28.0414	−	48.5690i	−0.905975	−	1.56919i
$959$	0.697785	−	6.63898i	0.0225327	−	0.214384i
$960$		0			0
$961$	−51.1814	−	10.8789i	−1.65101	−	0.350933i
$962$	−5.69677	+	4.13895i	−0.183671	+	0.133445i
$963$		0			0
$964$	−1.06554	−	3.27939i	−0.0343187	−	0.105622i
$965$	−1.29463	−	1.43783i	−0.0416755	−	0.0462853i
$966$		0			0
$967$	−12.1597	−	21.0612i	−0.391029	−	0.677281i	0.601557	−	0.798830i	$-0.294547\pi$
$967$	−12.1597	−	21.0612i	−0.391029	−	0.677281i	−0.992585	+	0.121549i	$0.961214\pi$
$968$	23.5299	−	13.9864i	0.756280	−	0.449541i
$969$		0			0
$970$	11.8581	−	5.27955i	0.380739	−	0.169516i
$971$	−2.33367	+	7.18229i	−0.0748910	+	0.230491i	−0.981494	−	0.191495i	$-0.938667\pi$
$971$	−2.33367	+	7.18229i	−0.0748910	+	0.230491i	0.906603	+	0.421985i	$0.138667\pi$
$972$		0			0
$973$	−12.6225	+	9.17079i	−0.404659	+	0.294002i
$974$	−1.40362	−	13.3545i	−0.0449748	−	0.427907i
$975$		0			0
$976$	20.6403	−	4.38723i	0.660679	−	0.140432i
$977$	0.212432	−	2.02115i	0.00679629	−	0.0646624i	−0.990598	−	0.136804i	$-0.956317\pi$
$977$	0.212432	−	2.02115i	0.00679629	−	0.0646624i	0.997394	+	0.0721420i	$0.0229835\pi$
$978$		0			0
$979$	38.7366	+	14.5880i	1.23803	+	0.466235i
$980$	1.49797			0.0478508
$981$		0			0
$982$	−15.8611	+	48.8154i	−0.506148	+	1.55776i
$983$	32.7089	+	6.95248i	1.04325	+	0.221750i	0.697506	−	0.716579i	$-0.254293\pi$
$983$	32.7089	+	6.95248i	1.04325	+	0.221750i	0.345745	+	0.938329i	$0.387626\pi$
$984$		0			0
$985$	−12.1489	−	5.40902i	−0.387095	−	0.172346i
$986$	−33.1536	+	36.8208i	−1.05583	+	1.17261i
$987$		0			0
$988$	−1.40960	+	0.627594i	−0.0448453	+	0.0199664i
$989$	−18.7629			−0.596624
$990$		0			0
$991$	40.1009			1.27385			0.636923	−	0.770927i	$-0.280207\pi$
$991$	40.1009			1.27385			0.636923	+	0.770927i	$0.280207\pi$
$992$	−18.1749	+	8.09197i	−0.577052	+	0.256920i
$993$		0			0
$994$	−9.19397	+	10.2109i	−0.291615	+	0.323871i
$995$	11.2654	+	5.01568i	0.357137	+	0.159008i
$996$		0			0
$997$	−15.7776	−	3.35364i	−0.499682	−	0.106211i	−0.0488260	−	0.998807i	$-0.515548\pi$
$997$	−15.7776	−	3.35364i	−0.499682	−	0.106211i	−0.450856	+	0.892597i	$0.648881\pi$
$998$	−9.97461	+	30.6987i	−0.315741	+	0.971750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.235.2		72
3.2	odd	2		99.2.m.b.70.8	yes	72
9.2	odd	6		891.2.f.f.730.2		36
9.4	even	3	inner	297.2.n.b.37.8		72
9.5	odd	6		99.2.m.b.4.2	✓	72
9.7	even	3		891.2.f.e.730.8		36
11.3	even	5	inner	297.2.n.b.289.8		72
33.5	odd	10		1089.2.e.p.727.4		36
33.14	odd	10		99.2.m.b.25.2	yes	72
33.17	even	10		1089.2.e.o.727.15		36
99.5	odd	30		1089.2.e.p.364.4		36
99.14	odd	30		99.2.m.b.58.8	yes	72
99.16	even	15		9801.2.a.cp.1.4		18
99.25	even	15		891.2.f.e.487.8		36
99.38	odd	30		9801.2.a.cm.1.15		18
99.47	odd	30		891.2.f.f.487.2		36
99.50	even	30		1089.2.e.o.364.15		36
99.58	even	15	inner	297.2.n.b.91.2		72
99.61	odd	30		9801.2.a.cn.1.15		18
99.83	even	30		9801.2.a.co.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.2	✓	72	9.5	odd	6
99.2.m.b.25.2	yes	72	33.14	odd	10
99.2.m.b.58.8	yes	72	99.14	odd	30
99.2.m.b.70.8	yes	72	3.2	odd	2
297.2.n.b.37.8		72	9.4	even	3	inner
297.2.n.b.91.2		72	99.58	even	15	inner
297.2.n.b.235.2		72	1.1	even	1	trivial
297.2.n.b.289.8		72	11.3	even	5	inner
891.2.f.e.487.8		36	99.25	even	15
891.2.f.e.730.8		36	9.7	even	3
891.2.f.f.487.2		36	99.47	odd	30
891.2.f.f.730.2		36	9.2	odd	6
1089.2.e.o.364.15		36	99.50	even	30
1089.2.e.o.727.15		36	33.17	even	10
1089.2.e.p.364.4		36	99.5	odd	30
1089.2.e.p.727.4		36	33.5	odd	10
9801.2.a.cm.1.15		18	99.38	odd	30
9801.2.a.cn.1.15		18	99.61	odd	30
9801.2.a.co.1.4		18	99.83	even	30
9801.2.a.cp.1.4		18	99.16	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41247 + 0.628870i) q^{2} +(0.261321 - 0.290226i) q^{4} +(-0.540848 - 0.240801i) q^{5} +(-0.706174 - 0.150102i) q^{7} +(0.768973 - 2.36665i) q^{8} +0.915362 q^{10} +(-3.10382 - 1.16888i) q^{11} +(0.164629 - 1.56634i) q^{13} +(1.09184 - 0.232078i) q^{14} +(0.483816 + 4.60320i) q^{16} +(3.71501 - 2.69911i) q^{17} +(0.775200 - 2.38582i) q^{19} +(-0.211222 + 0.0940420i) q^{20} +(5.11912 - 0.300892i) q^{22} +(-2.22600 - 3.85554i) q^{23} +(-3.11112 - 3.45525i) q^{25} +(0.752490 + 2.31593i) q^{26} +(-0.228102 + 0.165726i) q^{28} +(6.82612 + 1.45094i) q^{29} +(0.954161 - 9.07824i) q^{31} +(-1.08974 - 1.88749i) q^{32} +(-3.54993 + 6.14866i) q^{34} +(0.345788 + 0.251230i) q^{35} +(0.893583 + 2.75017i) q^{37} +(0.405428 + 3.85739i) q^{38} +(-0.985790 + 1.09483i) q^{40} +(-1.12890 + 0.239955i) q^{41} +(2.10724 - 3.64985i) q^{43} +(-1.15033 + 0.595357i) q^{44} +(5.56879 + 4.04596i) q^{46} +(0.152264 + 0.169107i) q^{47} +(-5.91867 - 2.63516i) q^{49} +(6.56726 + 2.92393i) q^{50} +(-0.411571 - 0.457096i) q^{52} +(-4.61430 - 3.35249i) q^{53} +(1.39723 + 1.37959i) q^{55} +(-0.898268 + 1.55585i) q^{56} +(-10.5541 + 2.24335i) q^{58} +(-4.77328 + 5.30126i) q^{59} +(-0.476541 - 4.53398i) q^{61} +(4.36131 + 13.4227i) q^{62} +(-4.76295 - 3.46049i) q^{64} +(-0.466215 + 0.807507i) q^{65} +(4.04571 + 7.00738i) q^{67} +(0.187456 - 1.78353i) q^{68} +(-0.646405 - 0.137398i) q^{70} +(-9.95852 + 7.23528i) q^{71} +(4.78461 + 14.7255i) q^{73} +(-2.99165 - 3.32257i) q^{74} +(-0.489852 - 0.848448i) q^{76} +(2.01639 + 1.29133i) q^{77} +(-13.3556 + 5.94631i) q^{79} +(0.846785 - 2.60614i) q^{80} +(1.44363 - 1.04886i) q^{82} +(-0.726787 - 6.91491i) q^{83} +(-2.65920 + 0.565231i) q^{85} +(-0.681124 + 6.48047i) q^{86} +(-5.15310 + 6.44683i) q^{88} -12.4803 q^{89} +(-0.351367 + 1.08140i) q^{91} +(-1.70068 - 0.361491i) q^{92} +(-0.321414 - 0.143103i) q^{94} +(-0.993774 + 1.10370i) q^{95} +(12.9545 - 5.76772i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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