LMFDB - Embedded newform 567.2.ba.a.143.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.21
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60395 - 1.91151i) q^{2} +(-0.733927 - 4.16231i) q^{4} +(0.273867 - 0.229802i) q^{5} +(2.61630 - 0.393657i) q^{7} +(-4.81149 - 2.77792i) q^{8} +O(q^{10})$	\(q+(1.60395 - 1.91151i) q^{2} +(-0.733927 - 4.16231i) q^{4} +(0.273867 - 0.229802i) q^{5} +(2.61630 - 0.393657i) q^{7} +(-4.81149 - 2.77792i) q^{8} -0.892090i q^{10} +(2.21304 - 2.63740i) q^{11} +(-0.362359 + 0.995572i) q^{13} +(3.44393 - 5.63249i) q^{14} +(-5.08414 + 1.85047i) q^{16} -5.82370 q^{17} +4.08644i q^{19} +(-1.15751 - 0.971262i) q^{20} +(-1.49181 - 8.46049i) q^{22} +(-0.737571 + 2.02646i) q^{23} +(-0.846047 + 4.79817i) q^{25} +(1.32184 + 2.28950i) q^{26} +(-3.55870 - 10.6009i) q^{28} +(-2.91124 - 7.99857i) q^{29} +(3.71733 - 0.655466i) q^{31} +(-0.817075 + 2.24489i) q^{32} +(-9.34090 + 11.1321i) q^{34} +(0.626056 - 0.709041i) q^{35} +(0.937031 - 1.62298i) q^{37} +(7.81127 + 6.55443i) q^{38} +(-1.95608 + 0.344910i) q^{40} +(-4.24450 - 1.54487i) q^{41} +(-1.24925 + 7.08485i) q^{43} +(-12.6019 - 7.27569i) q^{44} +(2.69057 + 4.66021i) q^{46} +(-2.12948 + 12.0769i) q^{47} +(6.69007 - 2.05985i) q^{49} +(7.81473 + 9.31324i) q^{50} +(4.40982 + 0.777571i) q^{52} +(7.91413 + 4.56923i) q^{53} -1.23086i q^{55} +(-13.6819 - 5.37379i) q^{56} +(-19.9588 - 7.26442i) q^{58} +(3.87534 + 1.41051i) q^{59} +(13.0904 + 2.30819i) q^{61} +(4.70948 - 8.15705i) q^{62} +(-2.42983 - 4.20859i) q^{64} +(0.129546 + 0.355925i) q^{65} +(3.53447 - 2.96577i) q^{67} +(4.27417 + 24.2400i) q^{68} +(-0.351177 - 2.33398i) q^{70} +(7.24109 - 4.18065i) q^{71} +(-6.45287 + 3.72557i) q^{73} +(-1.59940 - 4.39433i) q^{74} +(17.0090 - 2.99915i) q^{76} +(4.75175 - 7.77140i) q^{77} +(-10.2764 - 8.62293i) q^{79} +(-0.967136 + 1.67513i) q^{80} +(-9.76098 + 5.63551i) q^{82} +(-3.80912 + 1.38640i) q^{83} +(-1.59492 + 1.33830i) q^{85} +(11.5390 + 13.7517i) q^{86} +(-17.9745 + 6.54218i) q^{88} +11.5913 q^{89} +(-0.556126 + 2.74736i) q^{91} +(8.97607 + 1.58272i) q^{92} +(19.6695 + 23.4412i) q^{94} +(0.939071 + 1.11914i) q^{95} +(4.45675 + 0.785845i) q^{97} +(6.79310 - 16.0920i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.60395	−	1.91151i	1.13416	−	1.35164i	0.206401	−	0.978468i	$-0.433825\pi$
$2$	1.60395	−	1.91151i	1.13416	−	1.35164i	0.927761	−	0.373174i	$-0.121731\pi$
$3$		0			0
$3$		0			0
$4$	−0.733927	−	4.16231i	−0.366964	−	2.08115i
$5$	0.273867	−	0.229802i	0.122477	−	0.102771i	−0.579492	−	0.814978i	$-0.696749\pi$
$5$	0.273867	−	0.229802i	0.122477	−	0.102771i	0.701969	+	0.712208i	$0.252304\pi$
$6$		0			0
$7$	2.61630	−	0.393657i	0.988869	−	0.148788i
$7$	2.61630	−	0.393657i	0.988869	−	0.148788i
$8$	−4.81149	−	2.77792i	−1.70112	−	0.982141i
$9$		0			0
$10$		−	0.892090i		−	0.282104i
$11$	2.21304	−	2.63740i	0.667256	−	0.795205i	−0.321151	−	0.947028i	$-0.604070\pi$
$11$	2.21304	−	2.63740i	0.667256	−	0.795205i	0.988408	+	0.151823i	$0.0485143\pi$
$12$		0			0
$13$	−0.362359	+	0.995572i	−0.100500	+	0.276122i	−0.979745	−	0.200248i	$-0.935825\pi$
$13$	−0.362359	+	0.995572i	−0.100500	+	0.276122i	0.879245	+	0.476370i	$0.158048\pi$
$14$	3.44393	−	5.63249i	0.920429	−	1.50535i
$15$		0			0
$16$	−5.08414	+	1.85047i	−1.27103	+	0.462619i
$17$	−5.82370			−1.41245			−0.706227	−	0.707986i	$-0.749604\pi$
$17$	−5.82370			−1.41245			−0.706227	+	0.707986i	$0.749604\pi$
$18$		0			0
$19$			4.08644i			0.937493i	0.883333	+	0.468746i	$0.155294\pi$
$19$			4.08644i			0.937493i	−0.883333	+	0.468746i	$0.844706\pi$
$20$	−1.15751	−	0.971262i	−0.258826	−	0.217181i
$21$		0			0
$22$	−1.49181	−	8.46049i	−0.318056	−	1.80378i
$23$	−0.737571	+	2.02646i	−0.153794	+	0.422546i	−0.992531	−	0.121991i	$-0.961072\pi$
$23$	−0.737571	+	2.02646i	−0.153794	+	0.422546i	0.838737	+	0.544537i	$0.183294\pi$
$24$		0			0
$25$	−0.846047	+	4.79817i	−0.169209	+	0.959634i
$26$	1.32184	+	2.28950i	0.259235	+	0.449008i
$27$		0			0
$28$	−3.55870	−	10.6009i	−0.672530	−	2.00339i
$29$	−2.91124	−	7.99857i	−0.540604	−	1.48530i	−0.846058	−	0.533090i	$-0.821031\pi$
$29$	−2.91124	−	7.99857i	−0.540604	−	1.48530i	0.305455	−	0.952207i	$-0.401192\pi$
$30$		0			0
$31$	3.71733	−	0.655466i	0.667653	−	0.117725i	0.170459	−	0.985365i	$-0.445475\pi$
$31$	3.71733	−	0.655466i	0.667653	−	0.117725i	0.497194	+	0.867640i	$0.334364\pi$
$32$	−0.817075	+	2.24489i	−0.144440	+	0.396845i
$33$		0			0
$34$	−9.34090	+	11.1321i	−1.60195	+	1.90913i
$35$	0.626056	−	0.709041i	0.105823	−	0.119850i
$36$		0			0
$37$	0.937031	−	1.62298i	0.154047	−	0.266817i	−0.778665	−	0.627440i	$-0.784103\pi$
$37$	0.937031	−	1.62298i	0.154047	−	0.266817i	0.932712	+	0.360623i	$0.117436\pi$
$38$	7.81127	+	6.55443i	1.26715	+	1.06327i
$39$		0			0
$40$	−1.95608	+	0.344910i	−0.309283	+	0.0545350i
$41$	−4.24450	−	1.54487i	−0.662879	−	0.241268i	−0.0114001	−	0.999935i	$-0.503629\pi$
$41$	−4.24450	−	1.54487i	−0.662879	−	0.241268i	−0.651479	+	0.758667i	$0.725851\pi$
$42$		0			0
$43$	−1.24925	+	7.08485i	−0.190509	+	1.08043i	0.728162	+	0.685405i	$0.240375\pi$
$43$	−1.24925	+	7.08485i	−0.190509	+	1.08043i	−0.918671	+	0.395024i	$0.870736\pi$
$44$	−12.6019	−	7.27569i	−1.89980	−	1.09685i
$45$		0			0
$46$	2.69057	+	4.66021i	0.396703	+	0.687110i
$47$	−2.12948	+	12.0769i	−0.310617	+	1.76159i	0.285194	+	0.958470i	$0.407942\pi$
$47$	−2.12948	+	12.0769i	−0.310617	+	1.76159i	−0.595811	+	0.803125i	$0.703169\pi$
$48$		0			0
$49$	6.69007	−	2.05985i	0.955724	−	0.294264i
$50$	7.81473	+	9.31324i	1.10517	+	1.31709i
$51$		0			0
$52$	4.40982	+	0.777571i	0.611533	+	0.107830i
$53$	7.91413	+	4.56923i	1.08709	+	0.627631i	0.932800	−	0.360394i	$-0.117358\pi$
$53$	7.91413	+	4.56923i	1.08709	+	0.627631i	0.154289	+	0.988026i	$0.450691\pi$
$54$		0			0
$55$		−	1.23086i		−	0.165969i
$56$	−13.6819	−	5.37379i	−1.82832	−	0.718103i
$57$		0			0
$58$	−19.9588	−	7.26442i	−2.62072	−	0.953865i
$59$	3.87534	+	1.41051i	0.504527	+	0.183633i	0.581729	−	0.813383i	$-0.302376\pi$
$59$	3.87534	+	1.41051i	0.504527	+	0.183633i	−0.0772021	+	0.997015i	$0.524599\pi$
$60$		0			0
$61$	13.0904	+	2.30819i	1.67606	+	0.295534i	0.929235	−	0.369490i	$-0.120468\pi$
$61$	13.0904	+	2.30819i	1.67606	+	0.295534i	0.746822	+	0.665024i	$0.231579\pi$
$62$	4.70948	−	8.15705i	0.598104	−	1.03595i
$63$		0			0
$64$	−2.42983	−	4.20859i	−0.303729	−	0.526074i
$65$	0.129546	+	0.355925i	0.0160682	+	0.0441471i
$66$		0			0
$67$	3.53447	−	2.96577i	0.431804	−	0.362327i	−0.400828	−	0.916153i	$-0.631277\pi$
$67$	3.53447	−	2.96577i	0.431804	−	0.362327i	0.832632	+	0.553827i	$0.186833\pi$
$68$	4.27417	+	24.2400i	0.518319	+	2.93953i
$69$		0			0
$70$	−0.351177	−	2.33398i	−0.0419737	−	0.278964i
$71$	7.24109	−	4.18065i	0.859359	−	0.496151i	−0.00443842	−	0.999990i	$-0.501413\pi$
$71$	7.24109	−	4.18065i	0.859359	−	0.496151i	0.863798	+	0.503839i	$0.168079\pi$
$72$		0			0
$73$	−6.45287	+	3.72557i	−0.755251	+	0.436045i	−0.827588	−	0.561336i	$-0.810288\pi$
$73$	−6.45287	+	3.72557i	−0.755251	+	0.436045i	0.0723368	+	0.997380i	$0.476954\pi$
$74$	−1.59940	−	4.39433i	−0.185927	−	0.510830i
$75$		0			0
$76$	17.0090	−	2.99915i	1.95107	−	0.344026i
$77$	4.75175	−	7.77140i	0.541512	−	0.885634i
$78$		0			0
$79$	−10.2764	−	8.62293i	−1.15619	−	0.970156i	−0.156340	−	0.987703i	$-0.549970\pi$
$79$	−10.2764	−	8.62293i	−1.15619	−	0.970156i	−0.999846	+	0.0175477i	$0.994414\pi$
$80$	−0.967136	+	1.67513i	−0.108129	+	0.187285i
$81$		0			0
$82$	−9.76098	+	5.63551i	−1.07792	+	0.622338i
$83$	−3.80912	+	1.38640i	−0.418105	+	0.152178i	−0.542501	−	0.840055i	$-0.682523\pi$
$83$	−3.80912	+	1.38640i	−0.418105	+	0.152178i	0.124397	+	0.992233i	$0.460300\pi$
$84$		0			0
$85$	−1.59492	+	1.33830i	−0.172993	+	0.145159i
$86$	11.5390	+	13.7517i	1.24429	+	1.48288i
$87$		0			0
$88$	−17.9745	+	6.54218i	−1.91609	+	0.697398i
$89$	11.5913			1.22867			0.614337	−	0.789044i	$-0.289424\pi$
$89$	11.5913			1.22867			0.614337	+	0.789044i	$0.289424\pi$
$90$		0			0
$91$	−0.556126	+	2.74736i	−0.0582978	+	0.288002i
$92$	8.97607	+	1.58272i	0.935820	+	0.165010i
$93$		0			0
$94$	19.6695	+	23.4412i	2.02876	+	2.41778i
$95$	0.939071	+	1.11914i	0.0963466	+	0.114821i
$96$		0			0
$97$	4.45675	+	0.785845i	0.452515	+	0.0797905i	0.395260	−	0.918569i	$-0.370654\pi$
$97$	4.45675	+	0.785845i	0.452515	+	0.0797905i	0.0572541	+	0.998360i	$0.481765\pi$
$98$	6.79310	−	16.0920i	0.686206	−	1.62554i
$99$		0			0
$100$	20.5924			2.05924
$101$	2.02623	−	0.737486i	0.201617	−	0.0733826i	−0.239238	−	0.970961i	$-0.576898\pi$
$101$	2.02623	−	0.737486i	0.201617	−	0.0733826i	0.440855	+	0.897578i	$0.354675\pi$
$102$		0			0
$103$	−2.87110	−	3.42164i	−0.282898	−	0.337144i	0.605818	−	0.795603i	$-0.292846\pi$
$103$	−2.87110	−	3.42164i	−0.282898	−	0.337144i	−0.888715	+	0.458459i	$0.848402\pi$
$104$	4.50910	−	3.78359i	0.442154	−	0.371011i
$105$		0			0
$106$	21.4280	−	7.79914i	2.08127	−	0.757520i
$107$	−4.17439	+	2.41009i	−0.403554	+	0.232992i	−0.688016	−	0.725695i	$-0.741518\pi$
$107$	−4.17439	+	2.41009i	−0.403554	+	0.232992i	0.284463	+	0.958687i	$0.408185\pi$
$108$		0			0
$109$	−10.0905	+	17.4773i	−0.966494	+	1.67402i	−0.260949	+	0.965353i	$0.584036\pi$
$109$	−10.0905	+	17.4773i	−0.966494	+	1.67402i	−0.705545	+	0.708665i	$0.749298\pi$
$110$	−2.35280	−	1.97423i	−0.224330	−	0.188236i
$111$		0			0
$112$	−12.5732	+	6.84280i	−1.18805	+	0.646584i
$113$	−12.4855	+	2.20154i	−1.17454	+	0.207103i	−0.726664	−	0.686993i	$-0.758930\pi$
$113$	−12.4855	+	2.20154i	−1.17454	+	0.207103i	−0.447876	+	0.894096i	$0.647819\pi$
$114$		0			0
$115$	0.263688	+	0.724476i	0.0245890	+	0.0675578i
$116$	−31.1559	+	17.9879i	−2.89275	+	1.67013i
$117$		0			0
$118$	8.91205	−	5.14538i	0.820421	−	0.473670i
$119$	−15.2365	+	2.29254i	−1.39673	+	0.210156i
$120$		0			0
$121$	−0.148193	−	0.840442i	−0.0134721	−	0.0764039i
$122$	25.4085	−	21.3202i	2.30038	−	1.93024i
$123$		0			0
$124$	−5.45651	−	14.9916i	−0.490009	−	1.34629i
$125$	1.76469	+	3.05654i	0.157839	+	0.273385i
$126$		0			0
$127$	3.72128	−	6.44544i	0.330210	−	0.571940i	−0.652343	−	0.757924i	$-0.726214\pi$
$127$	3.72128	−	6.44544i	0.330210	−	0.571940i	0.982553	+	0.185984i	$0.0595471\pi$
$128$	−16.6474	−	2.93539i	−1.47144	−	0.259454i
$129$		0			0
$130$	0.888140	+	0.323257i	0.0778951	+	0.0283515i
$131$	−6.73738	−	2.45221i	−0.588648	−	0.214250i	0.0304869	−	0.999535i	$-0.490294\pi$
$131$	−6.73738	−	2.45221i	−0.588648	−	0.214250i	−0.619134	+	0.785285i	$0.712516\pi$
$132$		0			0
$133$	1.60865	+	10.6914i	0.139488	+	0.927058i
$134$		−	11.5131i		−	0.994582i
$135$		0			0
$136$	28.0207	+	16.1777i	2.40275	+	1.38723i
$137$	3.66765	+	0.646705i	0.313348	+	0.0552517i	0.328111	−	0.944639i	$-0.393588\pi$
$137$	3.66765	+	0.646705i	0.313348	+	0.0552517i	−0.0147625	+	0.999891i	$0.504699\pi$
$138$		0			0
$139$	−8.88294	−	10.5863i	−0.753441	−	0.897916i	0.243973	−	0.969782i	$-0.421549\pi$
$139$	−8.88294	−	10.5863i	−0.753441	−	0.897916i	−0.997414	+	0.0718657i	$0.977105\pi$
$140$	−3.41073	−	2.08546i	−0.288259	−	0.176253i
$141$		0			0
$142$	3.62298	−	20.5470i	0.304034	−	1.72426i
$143$	1.82381	+	3.15892i	0.152514	+	0.264163i
$144$		0			0
$145$	−2.63538	−	1.52154i	−0.218856	−	0.126357i
$146$	−3.22861	+	18.3103i	−0.267201	+	1.51537i
$147$		0			0
$148$	−7.44308	−	2.70906i	−0.611817	−	0.222683i
$149$	−9.28511	+	1.63721i	−0.760666	+	0.134126i	−0.540509	−	0.841339i	$-0.681768\pi$
$149$	−9.28511	+	1.63721i	−0.760666	+	0.134126i	−0.220157	+	0.975464i	$0.570657\pi$
$150$		0			0
$151$	−3.54028	−	2.97065i	−0.288104	−	0.241748i	0.487268	−	0.873252i	$-0.337993\pi$
$151$	−3.54028	−	2.97065i	−0.288104	−	0.241748i	−0.775372	+	0.631504i	$0.782438\pi$
$152$	11.3518	−	19.6619i	0.920751	−	1.59479i
$153$		0			0
$154$	−7.23356	−	21.5479i	−0.582897	−	1.73638i
$155$	0.867429	−	1.03376i	0.0696735	−	0.0830337i
$156$		0			0
$157$	0.399278	−	1.09701i	0.0318659	−	0.0875508i	−0.922739	−	0.385424i	$-0.874055\pi$
$157$	0.399278	−	1.09701i	0.0318659	−	0.0875508i	0.954605	+	0.297873i	$0.0962773\pi$
$158$	−32.9656	+	5.81273i	−2.62261	+	0.462436i
$159$		0			0
$160$	0.292111	+	0.802568i	0.0230934	+	0.0634486i
$161$	−1.13198	+	5.59218i	−0.0892124	+	0.440726i
$162$		0			0
$163$	3.53124	+	6.11629i	0.276588	+	0.479065i	0.970535	−	0.240962i	$-0.0774629\pi$
$163$	3.53124	+	6.11629i	0.276588	+	0.479065i	−0.693947	+	0.720027i	$0.744130\pi$
$164$	−3.31508	+	18.8007i	−0.258864	+	1.46809i
$165$		0			0
$166$	−3.45949	+	9.50488i	−0.268509	+	0.737722i
$167$	−2.87826	−	16.3234i	−0.222726	−	1.26314i	−0.866985	−	0.498335i	$-0.833945\pi$
$167$	−2.87826	−	16.3234i	−0.222726	−	1.26314i	0.644259	−	0.764808i	$-0.277166\pi$
$168$		0			0
$169$	9.09872	+	7.63473i	0.699901	+	0.587287i
$170$			5.19526i			0.398458i
$171$		0			0
$172$	30.4062			2.31845
$173$	−3.04449	+	1.10810i	−0.231468	+	0.0842475i	−0.455150	−	0.890415i	$-0.650414\pi$
$173$	−3.04449	+	1.10810i	−0.231468	+	0.0842475i	0.223682	+	0.974662i	$0.428192\pi$
$174$		0			0
$175$	−0.324682	+	12.8865i	−0.0245436	+	0.974128i
$176$	−6.37096	+	17.5041i	−0.480229	+	1.31942i
$177$		0			0
$178$	18.5918	−	22.1568i	1.39351	−	1.66073i
$179$			5.12037i			0.382714i	0.981520	+	0.191357i	$0.0612889\pi$
$179$			5.12037i			0.382714i	−0.981520	+	0.191357i	$0.938711\pi$
$180$		0			0
$181$	−3.60530	−	2.08152i	−0.267980	−	0.154718i	0.359990	−	0.932956i	$-0.382780\pi$
$181$	−3.60530	−	2.08152i	−0.267980	−	0.154718i	−0.627969	+	0.778238i	$0.716114\pi$
$182$	4.35961	+	5.46967i	0.323156	+	0.405439i
$183$		0			0
$184$	9.17815	−	7.70138i	0.676622	−	0.567753i
$185$	−0.116343	−	0.659814i	−0.00855371	−	0.0485105i
$186$		0			0
$187$	−12.8881	+	15.3594i	−0.942469	+	1.12319i
$188$	51.8306			3.78014
$189$		0			0
$190$	3.64547			0.264470
$191$	−1.92952	+	2.29952i	−0.139615	+	0.166387i	−0.831321	−	0.555792i	$-0.812415\pi$
$191$	−1.92952	+	2.29952i	−0.139615	+	0.166387i	0.691706	+	0.722179i	$0.256859\pi$
$192$		0			0
$193$	−2.87016	−	16.2775i	−0.206599	−	1.17168i	−0.894904	−	0.446259i	$-0.852756\pi$
$193$	−2.87016	−	16.2775i	−0.206599	−	1.17168i	0.688305	−	0.725422i	$-0.258355\pi$
$194$	8.65055	−	7.25867i	0.621073	−	0.521142i
$195$		0			0
$196$	−13.4838	−	26.3344i	−0.963125	−	1.88103i
$197$	2.93897	+	1.69681i	0.209393	+	0.120893i	0.601029	−	0.799227i	$-0.294758\pi$
$197$	2.93897	+	1.69681i	0.209393	+	0.120893i	−0.391636	+	0.920120i	$0.628091\pi$
$198$		0			0
$199$		−	4.20709i		−	0.298232i	−0.988820	−	0.149116i	$-0.952357\pi$
$199$		−	4.20709i		−	0.298232i	0.988820	−	0.149116i	$-0.0476429\pi$
$200$	17.3997	−	20.7361i	1.23034	−	1.46626i
$201$		0			0
$202$	1.84025	−	5.05604i	0.129479	−	0.355742i
$203$	−10.7654	−	19.7806i	−0.755581	−	1.38833i
$204$		0			0
$205$	−1.51744	+	0.552304i	−0.105983	+	0.0385746i
$206$	−11.1456			−0.776550
$207$		0			0
$208$		−	5.73216i		−	0.397454i
$209$	10.7776	+	9.04345i	0.745499	+	0.625548i
$210$		0			0
$211$	−3.10714	−	17.6215i	−0.213905	−	1.21311i	−0.882797	−	0.469754i	$-0.844343\pi$
$211$	−3.10714	−	17.6215i	−0.213905	−	1.21311i	0.668893	−	0.743359i	$-0.266768\pi$
$212$	13.2101	−	36.2945i	0.907275	−	2.49272i
$213$		0			0
$214$	−2.08860	+	11.8450i	−0.142774	+	0.809710i
$215$	1.28598	+	2.22739i	0.0877033	+	0.151907i
$216$		0			0
$217$	9.46764	−	3.17825i	0.642705	−	0.215754i
$218$	17.2233	+	47.3207i	1.16651	+	3.20496i
$219$		0			0
$220$	−5.12321	+	0.903360i	−0.345407	+	0.0609045i
$221$	2.11027	−	5.79791i	0.141952	−	0.390010i
$222$		0			0
$223$	−8.41245	+	10.0256i	−0.563339	+	0.671361i	−0.970250	−	0.242107i	$-0.922162\pi$
$223$	−8.41245	+	10.0256i	−0.563339	+	0.671361i	0.406911	+	0.913468i	$0.366606\pi$
$224$	−1.25400	+	6.19497i	−0.0837861	+	0.413919i
$225$		0			0
$226$	−15.8179	+	27.3974i	−1.05219	+	1.82245i
$227$	−0.859517	−	0.721220i	−0.0570481	−	0.0478691i	0.613818	−	0.789448i	$-0.289633\pi$
$227$	−0.859517	−	0.721220i	−0.0570481	−	0.0478691i	−0.670866	+	0.741579i	$0.734077\pi$
$228$		0			0
$229$	1.25625	−	0.221510i	0.0830151	−	0.0146378i	−0.131986	−	0.991252i	$-0.542136\pi$
$229$	1.25625	−	0.221510i	0.0830151	−	0.0146378i	0.215001	+	0.976614i	$0.431024\pi$
$230$	1.80778	+	0.657980i	0.119202	+	0.0433859i
$231$		0			0
$232$	−8.21194	+	46.5722i	−0.539140	+	3.05762i
$233$	16.2536	+	9.38404i	1.06481	+	0.614769i	0.926759	−	0.375656i	$-0.122583\pi$
$233$	16.2536	+	9.38404i	1.06481	+	0.614769i	0.138052	+	0.990425i	$0.455916\pi$
$234$		0			0
$235$	2.19210	+	3.79682i	0.142997	+	0.247677i
$236$	3.02676	−	17.1656i	0.197025	−	1.11738i
$237$		0			0
$238$	−20.0564	+	32.8019i	−1.30006	+	2.12623i
$239$	−8.01259	−	9.54904i	−0.518292	−	0.617676i	0.441884	−	0.897072i	$-0.354310\pi$
$239$	−8.01259	−	9.54904i	−0.518292	−	0.617676i	−0.960176	+	0.279396i	$0.909866\pi$
$240$		0			0
$241$	−20.2909	−	3.57784i	−1.30705	−	0.230469i	−0.523624	−	0.851950i	$-0.675420\pi$
$241$	−20.2909	−	3.57784i	−1.30705	−	0.230469i	−0.783429	+	0.621481i	$0.786531\pi$
$242$	−1.84421	−	1.06475i	−0.118550	−	0.0684450i
$243$		0			0
$244$		−	56.1804i		−	3.59658i
$245$	1.35883	−	2.10152i	0.0868127	−	0.134261i
$246$		0			0
$247$	−4.06834	−	1.48076i	−0.258862	−	0.0942182i
$248$	−19.7067	−	7.17267i	−1.25138	−	0.455465i
$249$		0			0
$250$	8.67309	+	1.52930i	0.548534	+	0.0967214i
$251$	−4.73924	+	8.20860i	−0.299138	+	0.518122i	−0.975939	−	0.218044i	$-0.930032\pi$
$251$	−4.73924	+	8.20860i	−0.299138	+	0.518122i	0.676801	+	0.736166i	$0.263366\pi$
$252$		0			0
$253$	3.71231	+	6.42990i	0.233391	+	0.404245i
$254$	−6.35179	−	17.4514i	−0.398547	−	1.09500i
$255$		0			0
$256$	−24.8672	+	20.8661i	−1.55420	+	1.30413i
$257$	2.78746	+	15.8084i	0.173877	+	0.986104i	0.939432	+	0.342734i	$0.111353\pi$
$257$	2.78746	+	15.8084i	0.173877	+	0.986104i	−0.765556	+	0.643370i	$0.777536\pi$
$258$		0			0
$259$	1.81266	−	4.61509i	0.112633	−	0.286767i
$260$	1.38639	−	0.800435i	0.0859805	−	0.0496409i
$261$		0			0
$262$	−15.4938	+	8.94536i	−0.957211	+	0.552646i
$263$	−4.56467	−	12.5413i	−0.281470	−	0.773331i	−0.997188	−	0.0749421i	$-0.976123\pi$
$263$	−4.56467	−	12.5413i	−0.281470	−	0.773331i	0.715718	−	0.698389i	$-0.246099\pi$
$264$		0			0
$265$	3.21744	−	0.567321i	0.197646	−	0.0348503i
$266$	23.0168	+	14.0734i	1.41125	+	0.862896i
$267$		0			0
$268$	−14.9385	−	12.5349i	−0.912515	−	0.765691i
$269$	−12.4472	+	21.5591i	−0.758916	+	1.31448i	0.184487	+	0.982835i	$0.440938\pi$
$269$	−12.4472	+	21.5591i	−0.758916	+	1.31448i	−0.943404	+	0.331647i	$0.892396\pi$
$270$		0			0
$271$	7.54919	−	4.35853i	0.458581	−	0.264762i	−0.252867	−	0.967501i	$-0.581373\pi$
$271$	7.54919	−	4.35853i	0.458581	−	0.264762i	0.711447	+	0.702739i	$0.248040\pi$
$272$	29.6085	−	10.7766i	1.79528	−	0.653427i
$273$		0			0
$274$	7.11889	−	5.97346i	0.430068	−	0.360870i
$275$	10.7823	+	12.8499i	0.650200	+	0.774878i
$276$		0			0
$277$	21.1896	−	7.71239i	1.27316	−	0.463393i	0.384996	−	0.922918i	$-0.374203\pi$
$277$	21.1896	−	7.71239i	1.27316	−	0.463393i	0.888165	+	0.459525i	$0.151980\pi$
$278$	−34.4835			−2.06819
$279$		0			0
$280$	−4.98192	+	1.67241i	−0.297727	+	0.0999457i
$281$	−11.7861	−	2.07821i	−0.703099	−	0.123975i	−0.189342	−	0.981911i	$-0.560636\pi$
$281$	−11.7861	−	2.07821i	−0.703099	−	0.123975i	−0.513757	+	0.857936i	$0.671747\pi$
$282$		0			0
$283$	−13.6417	−	16.2575i	−0.810915	−	0.966411i	0.188964	−	0.981984i	$-0.439487\pi$
$283$	−13.6417	−	16.2575i	−0.810915	−	0.966411i	−0.999879	+	0.0155731i	$0.995043\pi$
$284$	−22.7156	−	27.0714i	−1.34792	−	1.60639i
$285$		0			0
$286$	8.96361	+	1.58053i	0.530029	+	0.0934584i
$287$	−11.7130	−	2.37097i	−0.691398	−	0.139954i
$288$		0			0
$289$	16.9154			0.995025
$290$	−7.13544	+	2.59709i	−0.419008	+	0.152506i
$291$		0			0
$292$	20.2429	+	24.1245i	1.18463	+	1.41178i
$293$	−17.6180	+	14.7833i	−1.02926	+	0.863649i	−0.990762	−	0.135610i	$-0.956701\pi$
$293$	−17.6180	+	14.7833i	−1.02926	+	0.863649i	−0.0384944	+	0.999259i	$0.512256\pi$
$294$		0			0
$295$	1.38547	−	0.504269i	0.0806650	−	0.0293597i
$296$	−9.01703	+	5.20598i	−0.524104	+	0.302592i
$297$		0			0
$298$	−11.7633	+	20.3746i	−0.681428	+	1.18027i
$299$	−1.75022	−	1.46861i	−0.101218	−	0.0849319i
$300$		0			0
$301$	−0.479417	+	19.0279i	−0.0276331	+	1.09675i
$302$	−11.3569	+	2.00252i	−0.653513	+	0.115232i
$303$		0			0
$304$	−7.56185	−	20.7760i	−0.433702	−	1.19159i
$305$	4.11546	−	2.37606i	0.235651	−	0.136053i
$306$		0			0
$307$	−28.4532	+	16.4275i	−1.62391	+	0.937565i	−0.638051	+	0.769994i	$0.720259\pi$
$307$	−28.4532	+	16.4275i	−1.62391	+	0.937565i	−0.985860	+	0.167571i	$0.946408\pi$
$308$	−35.8344	−	14.0746i	−2.04186	−	0.801975i
$309$		0			0
$310$	−0.584735	−	3.31620i	−0.0332107	−	0.188347i
$311$	−7.37844	+	6.19125i	−0.418393	+	0.351073i	−0.827551	−	0.561390i	$-0.810267\pi$
$311$	−7.37844	+	6.19125i	−0.418393	+	0.351073i	0.409158	+	0.912463i	$0.365822\pi$
$312$		0			0
$313$	−3.68536	−	10.1254i	−0.208309	−	0.572324i	0.790906	−	0.611937i	$-0.209610\pi$
$313$	−3.68536	−	10.1254i	−0.208309	−	0.572324i	−0.999215	+	0.0396135i	$0.987387\pi$
$314$	−1.45652	−	2.52277i	−0.0821962	−	0.142368i
$315$		0			0
$316$	−28.3492	+	49.1022i	−1.59477	+	2.76221i
$317$	4.34468	+	0.766085i	0.244022	+	0.0430276i	0.294321	−	0.955707i	$-0.404906\pi$
$317$	4.34468	+	0.766085i	0.244022	+	0.0430276i	−0.0502994	+	0.998734i	$0.516018\pi$
$318$		0			0
$319$	−27.5381	−	10.0230i	−1.54184	−	0.561183i
$320$	−1.63259	−	0.594216i	−0.0912648	−	0.0332177i
$321$		0			0
$322$	8.87387	+	11.1334i	0.494522	+	0.620437i
$323$		−	23.7982i		−	1.32417i
$324$		0			0
$325$	−4.47035	−	2.58096i	−0.247970	−	0.143166i
$326$	17.3553	+	3.06020i	0.961219	+	0.169489i
$327$		0			0
$328$	16.1308	+	19.2240i	0.890676	+	1.06147i
$329$	−0.817217	+	32.4351i	−0.0450546	+	1.78820i
$330$		0			0
$331$	−2.39714	+	13.5948i	−0.131759	+	0.747240i	0.845304	+	0.534286i	$0.179420\pi$
$331$	−2.39714	+	13.5948i	−0.131759	+	0.747240i	−0.977062	+	0.212954i	$0.931692\pi$
$332$	8.56626	+	14.8372i	0.470134	+	0.814297i
$333$		0			0
$334$	−35.8189	−	20.6801i	−1.95992	−	1.13156i
$335$	0.286436	−	1.62446i	0.0156496	−	0.0887535i
$336$		0			0
$337$	6.81432	+	2.48021i	0.371200	+	0.135106i	0.520882	−	0.853628i	$-0.325603\pi$
$337$	6.81432	+	2.48021i	0.371200	+	0.135106i	−0.149683	+	0.988734i	$0.547825\pi$
$338$	29.1877	−	5.14658i	1.58760	−	0.279937i
$339$		0			0
$340$	6.74096	+	5.65633i	0.365580	+	0.306758i
$341$	6.49788	−	11.2547i	0.351880	−	0.609474i
$342$		0			0
$343$	16.6924	−	8.02278i	0.901303	−	0.433189i
$344$	25.6919	−	30.6184i	1.38521	−	1.65083i
$345$		0			0
$346$	−2.76505	+	7.59691i	−0.148650	+	0.408412i
$347$	17.6016	−	3.10363i	0.944901	−	0.166611i	0.320089	−	0.947387i	$-0.396287\pi$
$347$	17.6016	−	3.10363i	0.944901	−	0.166611i	0.624811	+	0.780776i	$0.285176\pi$
$348$		0			0
$349$	−11.7174	−	32.1932i	−0.627217	−	1.72326i	−0.688591	−	0.725150i	$-0.741770\pi$
$349$	−11.7174	−	32.1932i	−0.627217	−	1.72326i	0.0613741	−	0.998115i	$-0.480452\pi$
$350$	24.1119	+	21.2899i	1.28884	+	1.13799i
$351$		0			0
$352$	4.11246	+	7.12299i	0.219195	+	0.379657i
$353$	2.82122	−	15.9999i	0.150158	−	0.851589i	−0.812922	−	0.582373i	$-0.802124\pi$
$353$	2.82122	−	15.9999i	0.150158	−	0.851589i	0.963080	−	0.269216i	$-0.0867646\pi$
$354$		0			0
$355$	1.02238	−	2.80896i	0.0542621	−	0.149084i
$356$	−8.50716	−	48.2465i	−0.450878	−	2.55706i
$357$		0			0
$358$	9.78764	+	8.21280i	0.517293	+	0.434060i
$359$			17.5252i			0.924947i	0.886633	+	0.462473i	$0.153038\pi$
$359$			17.5252i			0.924947i	−0.886633	+	0.462473i	$0.846962\pi$
$360$		0			0
$361$	2.30103			0.121107
$362$	−9.76155	+	3.55291i	−0.513056	+	0.186737i
$363$		0			0
$364$	11.8435	+	0.298403i	0.620769	+	0.0156406i
$365$	−0.911088	+	2.50319i	−0.0476885	+	0.131023i
$366$		0			0
$367$	−5.56009	+	6.62625i	−0.290234	+	0.345888i	−0.891384	−	0.453249i	$-0.850265\pi$
$367$	−5.56009	+	6.62625i	−0.290234	+	0.345888i	0.601150	+	0.799136i	$0.294709\pi$
$368$		−	11.6677i		−	0.608218i
$369$		0			0
$370$	−1.44785	−	0.835916i	−0.0752701	−	0.0434572i
$371$	22.5045	+	8.83902i	1.16837	+	0.458899i
$372$		0			0
$373$	0.481953	−	0.404407i	0.0249546	−	0.0209394i	−0.630225	−	0.776413i	$-0.717037\pi$
$373$	0.481953	−	0.404407i	0.0249546	−	0.0209394i	0.655180	+	0.755473i	$0.272593\pi$
$374$	8.68787	+	49.2713i	0.449239	+	2.54776i
$375$		0			0
$376$	43.7945	−	52.1923i	2.25853	−	2.69161i
$377$	9.01807			0.464454
$378$		0			0
$379$	−5.41656			−0.278230			−0.139115	−	0.990276i	$-0.544426\pi$
$379$	−5.41656			−0.278230			−0.139115	+	0.990276i	$0.544426\pi$
$380$	3.96900	−	4.73007i	0.203605	−	0.242648i
$381$		0			0
$382$	1.30070	+	7.37661i	0.0665494	+	0.377420i
$383$	12.5526	−	10.5329i	0.641409	−	0.538206i	−0.263042	−	0.964784i	$-0.584726\pi$
$383$	12.5526	−	10.5329i	0.641409	−	0.538206i	0.904450	+	0.426579i	$0.140281\pi$
$384$		0			0
$385$	−0.484535	−	3.22029i	−0.0246942	−	0.164121i
$386$	−35.7182	−	20.6219i	−1.81801	−	1.04963i
$387$		0			0
$388$		−	19.1271i		−	0.971033i
$389$	−10.0311	+	11.9546i	−0.508598	+	0.606124i	−0.957846	−	0.287284i	$-0.907248\pi$
$389$	−10.0311	+	11.9546i	−0.508598	+	0.606124i	0.449247	+	0.893407i	$0.351692\pi$
$390$		0			0
$391$	4.29539	−	11.8015i	0.217227	−	0.596827i
$392$	−37.9113	−	8.67350i	−1.91481	−	0.438078i
$393$		0			0
$394$	7.95742	−	2.89627i	0.400889	−	0.145912i
$395$	−4.79594			−0.241310
$396$		0			0
$397$		−	6.56653i		−	0.329565i	−0.986330	−	0.164782i	$-0.947308\pi$
$397$		−	6.56653i		−	0.329565i	0.986330	−	0.164782i	$-0.0526921\pi$
$398$	−8.04189	−	6.74795i	−0.403104	−	0.338244i
$399$		0			0
$400$	−4.57747	−	25.9601i	−0.228874	−	1.29801i
$401$	12.0749	−	33.1756i	0.602993	−	1.65671i	−0.142183	−	0.989840i	$-0.545412\pi$
$401$	12.0749	−	33.1756i	0.602993	−	1.65671i	0.745176	−	0.666868i	$-0.232366\pi$
$402$		0			0
$403$	−0.694444	+	3.93839i	−0.0345927	+	0.196185i
$404$	−4.55675	−	7.89252i	−0.226707	−	0.392668i
$405$		0			0
$406$	−55.0780	−	11.1490i	−2.73347	−	0.553315i
$407$	−2.20677	−	6.06305i	−0.109386	−	0.300534i
$408$		0			0
$409$	17.1446	−	3.02306i	0.847748	−	0.149481i	0.267134	−	0.963659i	$-0.413923\pi$
$409$	17.1446	−	3.02306i	0.847748	−	0.149481i	0.580615	+	0.814179i	$0.302812\pi$
$410$	−1.37816	+	3.78647i	−0.0680627	+	0.187001i
$411$		0			0
$412$	−12.1347	+	14.4616i	−0.597836	+	0.712473i
$413$	10.6943	+	2.16476i	0.526233	+	0.106521i
$414$		0			0
$415$	−0.724594	+	1.25503i	−0.0355689	+	0.0616071i
$416$	−1.93888	−	1.62691i	−0.0950614	−	0.0797660i
$417$		0			0
$418$	34.5733	−	6.09620i	1.69103	−	0.298175i
$419$	−16.1147	−	5.86527i	−0.787254	−	0.286537i	−0.0830600	−	0.996545i	$-0.526469\pi$
$419$	−16.1147	−	5.86527i	−0.787254	−	0.286537i	−0.704194	+	0.710007i	$0.748692\pi$
$420$		0			0
$421$	4.49987	−	25.5201i	0.219310	−	1.24377i	−0.653958	−	0.756531i	$-0.726893\pi$
$421$	4.49987	−	25.5201i	0.219310	−	1.24377i	0.873268	−	0.487240i	$-0.161996\pi$
$422$	−38.6673	−	22.3246i	−1.88230	−	1.08674i
$423$		0			0
$424$	−25.3858	−	43.9696i	−1.23285	−	2.13535i
$425$	4.92712	−	27.9431i	0.239000	−	1.35544i
$426$		0			0
$427$	35.1571	+	0.885801i	1.70137	+	0.0428669i
$428$	13.0952	+	15.6063i	0.632981	+	0.754358i
$429$		0			0
$430$	6.32032	+	1.11444i	0.304793	+	0.0537432i
$431$	−10.4907	−	6.05678i	−0.505317	−	0.291745i	0.225590	−	0.974222i	$-0.427569\pi$
$431$	−10.4907	−	6.05678i	−0.505317	−	0.291745i	−0.730907	+	0.682478i	$0.760902\pi$
$432$		0			0
$433$		−	31.6375i		−	1.52040i	−0.649689	−	0.760200i	$-0.725101\pi$
$433$		−	31.6375i		−	1.52040i	0.649689	−	0.760200i	$-0.274899\pi$
$434$	9.11034	−	23.1952i	0.437310	−	1.11341i
$435$		0			0
$436$	80.1514	+	29.1727i	3.83856	+	1.39712i
$437$	−8.28100	−	3.01404i	−0.396134	−	0.144181i
$438$		0			0
$439$	3.83395	+	0.676028i	0.182984	+	0.0322651i	0.264389	−	0.964416i	$-0.414830\pi$
$439$	3.83395	+	0.676028i	0.182984	+	0.0322651i	−0.0814050	+	0.996681i	$0.525941\pi$
$440$	−3.41922	+	5.92226i	−0.163005	+	0.282333i
$441$		0			0
$442$	−7.69801	−	13.3333i	−0.366157	−	0.634202i
$443$	0.0712478	+	0.195752i	0.00338509	+	0.00930045i	0.941374	−	0.337366i	$-0.109536\pi$
$443$	0.0712478	+	0.195752i	0.00338509	+	0.00930045i	−0.937989	+	0.346666i	$0.887314\pi$
$444$		0			0
$445$	3.17447	−	2.66370i	0.150484	−	0.126271i
$446$	5.67084	+	32.1610i	0.268522	+	1.52287i
$447$		0			0
$448$	−8.01391	−	10.0544i	−0.378622	−	0.475027i
$449$	11.7985	−	6.81187i	0.556806	−	0.321472i	−0.195057	−	0.980792i	$-0.562489\pi$
$449$	11.7985	−	6.81187i	0.556806	−	0.321472i	0.751862	+	0.659320i	$0.229156\pi$
$450$		0			0
$451$	−13.4677	+	7.77556i	−0.634168	+	0.366137i
$452$	18.3269	+	50.3529i	0.862027	+	2.36840i
$453$		0			0
$454$	−2.75724	+	0.486176i	−0.129404	+	0.0228174i
$455$	0.479044	+	0.880211i	0.0224579	+	0.0412649i
$456$		0			0
$457$	15.2178	+	12.7693i	0.711859	+	0.597320i	0.925120	−	0.379675i	$-0.123964\pi$
$457$	15.2178	+	12.7693i	0.711859	+	0.597320i	−0.213261	+	0.976995i	$0.568409\pi$
$458$	1.59153	−	2.75662i	0.0743675	−	0.128808i
$459$		0			0
$460$	2.82197	−	1.62926i	0.131575	−	0.0759648i
$461$	−5.61005	+	2.04189i	−0.261286	+	0.0951003i	−0.469342	−	0.883017i	$-0.655509\pi$
$461$	−5.61005	+	2.04189i	−0.261286	+	0.0951003i	0.208056	+	0.978117i	$0.433286\pi$
$462$		0			0
$463$	21.0832	−	17.6909i	0.979822	−	0.822168i	−0.00424088	−	0.999991i	$-0.501350\pi$
$463$	21.0832	−	17.6909i	0.979822	−	0.822168i	0.984062	+	0.177823i	$0.0569055\pi$
$464$	29.6023	+	35.2786i	1.37425	+	1.63777i
$465$		0			0
$466$	44.0077	−	16.0175i	2.03862	−	0.741996i
$467$	15.8827			0.734962			0.367481	−	0.930031i	$-0.380220\pi$
$467$	15.8827			0.734962			0.367481	+	0.930031i	$0.380220\pi$
$468$		0			0
$469$	8.07975	−	9.15073i	0.373088	−	0.422541i
$470$	10.7737	+	1.89969i	0.496952	+	0.0876261i
$471$		0			0
$472$	−14.7279	−	17.5520i	−0.677907	−	0.807898i
$473$	15.9209	+	18.9738i	0.732045	+	0.872417i
$474$		0			0
$475$	−19.6074	−	3.45732i	−0.899650	−	0.158633i
$476$	20.7248	+	61.7366i	0.949918	+	2.82969i
$477$		0			0
$478$	−31.1049			−1.42270
$479$	−10.0828	+	3.66985i	−0.460696	+	0.167680i	−0.561933	−	0.827183i	$-0.689942\pi$
$479$	−10.0828	+	3.66985i	−0.460696	+	0.167680i	0.101237	+	0.994862i	$0.467720\pi$
$480$		0			0
$481$	1.27626	+	1.52098i	0.0581923	+	0.0693509i
$482$	−39.3846	+	33.0476i	−1.79392	+	1.50528i
$483$		0			0
$484$	−3.38942	+	1.23365i	−0.154064	+	0.0560749i
$485$	1.40115	−	0.808953i	0.0636228	−	0.0367326i
$486$		0			0
$487$	−4.54921	+	7.87946i	−0.206144	+	0.357052i	−0.950497	−	0.310735i	$-0.899425\pi$
$487$	−4.54921	+	7.87946i	−0.206144	+	0.357052i	0.744352	+	0.667787i	$0.232758\pi$
$488$	−56.5725	−	47.4699i	−2.56091	−	2.14886i
$489$		0			0
$490$	−1.83757	−	5.96815i	−0.0830130	−	0.269613i
$491$	−2.90320	+	0.511913i	−0.131020	+	0.0231023i	−0.238773	−	0.971075i	$-0.576745\pi$
$491$	−2.90320	+	0.511913i	−0.131020	+	0.0231023i	0.107754	+	0.994178i	$0.465634\pi$
$492$		0			0
$493$	16.9542	+	46.5812i	0.763578	+	2.09791i
$494$	−9.35589	+	5.40163i	−0.420941	+	0.243031i
$495$		0			0
$496$	−17.6865	+	10.2113i	−0.794148	+	0.458501i
$497$	17.2991	−	13.7883i	0.775972	−	0.618491i
$498$		0			0
$499$	1.84999	+	10.4918i	0.0828171	+	0.469679i	0.997806	+	0.0662008i	$0.0210878\pi$
$499$	1.84999	+	10.4918i	0.0828171	+	0.469679i	−0.914989	+	0.403478i	$0.867801\pi$
$500$	11.4271	−	9.58848i	0.511036	−	0.428810i
$501$		0			0
$502$	8.08933	+	22.2253i	0.361045	+	0.991962i
$503$	−8.22192	−	14.2408i	−0.366597	−	0.634965i	0.622434	−	0.782672i	$-0.286144\pi$
$503$	−8.22192	−	14.2408i	−0.366597	−	0.634965i	−0.989031	+	0.147707i	$0.952811\pi$
$504$		0			0
$505$	0.385441	−	0.667604i	0.0171519	−	0.0297080i
$506$	18.2452	+	3.21712i	0.811097	+	0.143018i
$507$		0			0
$508$	−29.5591	−	10.7586i	−1.31147	−	0.477337i
$509$	13.7090	+	4.98966i	0.607640	+	0.221163i	0.627470	−	0.778641i	$-0.284090\pi$
$509$	13.7090	+	4.98966i	0.607640	+	0.221163i	−0.0198304	+	0.999803i	$0.506313\pi$
$510$		0			0
$511$	−15.4161	+	12.2874i	−0.681966	+	0.543564i
$512$			47.1935i			2.08568i
$513$		0			0
$514$	34.6889	+	20.0277i	1.53006	+	0.883383i
$515$	−1.57260	−	0.277292i	−0.0692970	−	0.0122189i
$516$		0			0
$517$	27.1389	+	32.3429i	1.19357	+	1.42244i
$518$	−5.91438	−	10.8673i	−0.259863	−	0.477480i
$519$		0			0
$520$	0.365420	−	2.07240i	0.0160247	−	0.0908808i
$521$	−8.47444	−	14.6782i	−0.371272	−	0.643062i	0.618489	−	0.785793i	$-0.287745\pi$
$521$	−8.47444	−	14.6782i	−0.371272	−	0.643062i	−0.989762	+	0.142731i	$0.954412\pi$
$522$		0			0
$523$	27.0509	+	15.6178i	1.18285	+	0.682920i	0.956673	−	0.291165i	$-0.0940429\pi$
$523$	27.0509	+	15.6178i	1.18285	+	0.682920i	0.226180	+	0.974085i	$0.427376\pi$
$524$	−5.26209	+	29.8428i	−0.229875	+	1.30369i
$525$		0			0
$526$	−31.2944	−	11.3902i	−1.36450	−	0.496637i
$527$	−21.6486	+	3.81724i	−0.943029	+	0.166281i
$528$		0			0
$529$	14.0565	+	11.7948i	0.611152	+	0.512817i
$530$	4.07616	−	7.06012i	0.177057	−	0.306672i
$531$		0			0
$532$	43.3201	−	14.5424i	1.87816	−	0.630492i
$533$	3.07606	−	3.66591i	0.133239	−	0.158788i
$534$		0			0
$535$	−0.589387	+	1.61933i	−0.0254814	+	0.0700096i
$536$	−25.2447	+	4.45133i	−1.09041	+	0.192268i
$537$		0			0
$538$	21.2459	+	58.3725i	0.915974	+	2.51662i
$539$	9.37274	−	22.2029i	0.403713	−	0.956346i
$540$		0			0
$541$	19.0672	+	33.0253i	0.819762	+	1.41987i	0.905858	+	0.423582i	$0.139228\pi$
$541$	19.0672	+	33.0253i	0.819762	+	1.41987i	−0.0860957	+	0.996287i	$0.527439\pi$
$542$	3.77714	−	21.4212i	0.162242	−	0.920120i
$543$		0			0
$544$	4.75839	−	13.0736i	0.204014	−	0.560525i
$545$	1.25285	+	7.10526i	0.0536662	+	0.304356i
$546$		0			0
$547$	−26.5978	−	22.3182i	−1.13724	−	0.954257i	−0.137894	−	0.990447i	$-0.544033\pi$
$547$	−26.5978	−	22.3182i	−1.13724	−	0.954257i	−0.999345	+	0.0361899i	$0.988478\pi$
$548$		−	15.7405i		−	0.672401i
$549$		0			0
$550$	41.8570			1.78479
$551$	32.6856	−	11.8966i	1.39246	−	0.506812i
$552$		0			0
$553$	−30.2807	−	18.5148i	−1.28766	−	0.787330i
$554$	19.2447	−	52.8744i	0.817630	−	2.24642i
$555$		0			0
$556$	−37.5439	+	44.7431i	−1.59222	+	1.89753i
$557$			19.0242i			0.806081i	0.915182	+	0.403041i	$0.132047\pi$
$557$			19.0242i			0.806081i	−0.915182	+	0.403041i	$0.867953\pi$
$558$		0			0
$559$	−6.60080	−	3.81097i	−0.279184	−	0.161187i
$560$	−1.87089	+	4.76336i	−0.0790597	+	0.201289i
$561$		0			0
$562$	−22.8768	+	19.1959i	−0.964999	+	0.809730i
$563$	5.42674	+	30.7766i	0.228710	+	1.29708i	0.855465	+	0.517861i	$0.173272\pi$
$563$	5.42674	+	30.7766i	0.228710	+	1.29708i	−0.626755	+	0.779217i	$0.715617\pi$
$564$		0			0
$565$	−2.91346	+	3.47213i	−0.122570	+	0.146074i
$566$	−52.9570			−2.22595
$567$		0			0
$568$	−46.4539			−1.94916
$569$	−5.51067	+	6.56736i	−0.231019	+	0.275318i	−0.869084	−	0.494665i	$-0.835291\pi$
$569$	−5.51067	+	6.56736i	−0.231019	+	0.275318i	0.638065	+	0.769983i	$0.279735\pi$
$570$		0			0
$571$	2.20202	+	12.4883i	0.0921518	+	0.522619i	0.995583	+	0.0938856i	$0.0299288\pi$
$571$	2.20202	+	12.4883i	0.0921518	+	0.522619i	−0.903431	+	0.428733i	$0.858960\pi$
$572$	11.8099	−	9.90966i	0.493796	−	0.414344i
$573$		0			0
$574$	−23.3192	+	18.5867i	−0.973326	+	0.775792i
$575$	−9.09928	−	5.25347i	−0.379466	−	0.219085i
$576$		0			0
$577$		−	35.7244i		−	1.48723i	−0.668610	−	0.743613i	$-0.733110\pi$
$577$		−	35.7244i		−	1.48723i	0.668610	−	0.743613i	$-0.266890\pi$
$578$	27.1315	−	32.3340i	1.12852	−	1.34492i
$579$		0			0
$580$	−4.39893	+	12.0860i	−0.182656	+	0.501842i
$581$	−9.42003	+	5.12674i	−0.390809	+	0.212693i
$582$		0			0
$583$	29.5651	−	10.7608i	1.22446	−	0.445668i
$584$	41.3972			1.71303
$585$		0			0
$586$			57.3887i			2.37070i
$587$	−23.8827	−	20.0400i	−0.985744	−	0.827138i	−0.000798351	−	1.00000i	$-0.500254\pi$
$587$	−23.8827	−	20.0400i	−0.985744	−	0.827138i	−0.984946	+	0.172862i	$0.944699\pi$
$588$		0			0
$589$	2.67852	+	15.1906i	0.110367	+	0.625920i
$590$	1.25830	−	3.45716i	0.0518035	−	0.142329i
$591$		0			0
$592$	−1.76070	+	9.98543i	−0.0723643	+	0.410398i
$593$	7.36449	+	12.7557i	0.302423	+	0.523812i	0.976684	−	0.214681i	$-0.0688711\pi$
$593$	7.36449	+	12.7557i	0.302423	+	0.523812i	−0.674261	+	0.738493i	$0.735538\pi$
$594$		0			0
$595$	−3.64596	+	4.12924i	−0.149470	+	0.169282i
$596$	13.6292	+	37.4459i	0.558273	+	1.53384i
$597$		0			0
$598$	−5.61453	+	0.989993i	−0.229595	+	0.0404838i
$599$	4.92526	−	13.5320i	0.201241	−	0.552904i	−0.797487	−	0.603336i	$-0.793838\pi$
$599$	4.92526	−	13.5320i	0.201241	−	0.552904i	0.998727	+	0.0504321i	$0.0160598\pi$
$600$		0			0
$601$	23.1504	−	27.5895i	0.944324	−	1.12540i	−0.0476382	−	0.998865i	$-0.515169\pi$
$601$	23.1504	−	27.5895i	0.944324	−	1.12540i	0.991962	−	0.126537i	$-0.0403861\pi$
$602$	35.6030	+	31.4361i	1.45107	+	1.28124i
$603$		0			0
$604$	−9.76645	+	16.9160i	−0.397391	+	0.688302i
$605$	−0.233720	−	0.196115i	−0.00950209	−	0.00797320i
$606$		0			0
$607$	−2.31280	+	0.407809i	−0.0938737	+	0.0165525i	−0.220388	−	0.975412i	$-0.570732\pi$
$607$	−2.31280	+	0.407809i	−0.0938737	+	0.0165525i	0.126514	+	0.991965i	$0.459621\pi$
$608$	−9.17362	−	3.33892i	−0.372039	−	0.135411i
$609$		0			0
$610$	2.05912	−	11.6778i	0.0833712	−	0.472822i
$611$	−11.2518	−	6.49622i	−0.455198	−	0.262809i
$612$		0			0
$613$	−13.6890	−	23.7101i	−0.552895	−	0.957643i	−0.998064	−	0.0621960i	$-0.980190\pi$
$613$	−13.6890	−	23.7101i	−0.552895	−	0.957643i	0.445169	−	0.895447i	$-0.353144\pi$
$614$	−14.2362	+	80.7374i	−0.574526	+	3.25830i
$615$		0			0
$616$	−44.4513	+	24.1921i	−1.79099	+	0.974727i
$617$	−20.2153	−	24.0916i	−0.813837	−	0.969893i	0.186083	−	0.982534i	$-0.440421\pi$
$617$	−20.2153	−	24.0916i	−0.813837	−	0.969893i	−0.999920	+	0.0126410i	$0.995976\pi$
$618$		0			0
$619$	−13.5624	−	2.39142i	−0.545120	−	0.0961193i	−0.105695	−	0.994399i	$-0.533707\pi$
$619$	−13.5624	−	2.39142i	−0.545120	−	0.0961193i	−0.439425	+	0.898279i	$0.644818\pi$
$620$	−4.93946	−	2.85180i	−0.198374	−	0.114531i
$621$		0			0
$622$			24.0344i			0.963691i
$623$	30.3263	−	4.56298i	1.21500	−	0.182812i
$624$		0			0
$625$	−21.7061	−	7.90038i	−0.868244	−	0.316015i
$626$	−25.2660	−	9.19607i	−1.00983	−	0.367549i
$627$		0			0
$628$	−4.85913	−	0.856795i	−0.193900	−	0.0341899i
$629$	−5.45698	+	9.45177i	−0.217584	+	0.376867i
$630$		0			0
$631$	11.5471	+	20.0002i	0.459684	+	0.796197i	0.998944	−	0.0459427i	$-0.0146292\pi$
$631$	11.5471	+	20.0002i	0.459684	+	0.796197i	−0.539260	+	0.842140i	$0.681296\pi$
$632$	25.4911	+	70.0362i	1.01398	+	2.78589i
$633$		0			0
$634$	8.43303	−	7.07615i	0.334918	−	0.281030i
$635$	−0.462039	−	2.62035i	−0.0183354	−	0.103985i
$636$		0			0
$637$	−0.373476	+	7.40685i	−0.0147976	+	0.293470i
$638$	−63.3288	+	36.5629i	−2.50721	+	1.44754i
$639$		0			0
$640$	−5.23375	+	3.02170i	−0.206882	+	0.119443i
$641$	−8.39959	−	23.0777i	−0.331764	−	0.911514i	−0.987653	−	0.156657i	$-0.949928\pi$
$641$	−8.39959	−	23.0777i	−0.331764	−	0.911514i	0.655889	−	0.754857i	$-0.272294\pi$
$642$		0			0
$643$	−37.4315	+	6.60018i	−1.47615	+	0.260286i	−0.853040	−	0.521846i	$-0.825244\pi$
$643$	−37.4315	+	6.60018i	−1.47615	+	0.260286i	−0.623114	+	0.782131i	$0.714133\pi$
$644$	24.1072	+	0.607392i	0.949956	+	0.0239346i
$645$		0			0
$646$	−45.4904	−	38.1710i	−1.78980	−	1.50182i
$647$	1.12029	−	1.94040i	0.0440432	−	0.0762851i	−0.843163	−	0.537657i	$-0.819309\pi$
$647$	1.12029	−	1.94040i	0.0440432	−	0.0762851i	0.887207	+	0.461372i	$0.152643\pi$
$648$		0			0
$649$	12.2964	−	7.09931i	0.482674	−	0.278672i
$650$	−12.1037	+	4.40540i	−0.474748	+	0.172794i
$651$		0			0
$652$	22.8662	−	19.1870i	0.895509	−	0.751422i
$653$	29.1222	+	34.7064i	1.13964	+	1.35817i	0.924317	+	0.381625i	$0.124635\pi$
$653$	29.1222	+	34.7064i	1.13964	+	1.35817i	0.215321	+	0.976543i	$0.430920\pi$
$654$		0			0
$655$	−2.40867	+	0.876684i	−0.0941145	+	0.0342549i
$656$	24.4383			0.954157
$657$		0			0
$658$	60.6892	+	53.5863i	2.36591	+	2.08901i
$659$	43.6553	+	7.69760i	1.70057	+	0.299856i	0.937893	−	0.346926i	$-0.112774\pi$
$659$	43.6553	+	7.69760i	1.70057	+	0.299856i	0.762675	+	0.646782i	$0.223886\pi$
$660$		0			0
$661$	−16.8804	−	20.1173i	−0.656571	−	0.782470i	0.330319	−	0.943870i	$-0.392844\pi$
$661$	−16.8804	−	20.1173i	−0.656571	−	0.782470i	−0.986889	+	0.161399i	$0.948399\pi$
$662$	22.1418	+	26.3876i	0.860566	+	1.02558i
$663$		0			0
$664$	22.1788	+	3.91073i	0.860706	+	0.151766i
$665$	2.89745	+	2.55834i	0.112358	+	0.0992081i
$666$		0			0
$667$	18.3560			0.710748
$668$	−65.8306	+	23.9604i	−2.54706	+	0.927055i
$669$		0			0
$670$	−2.64574	−	3.15307i	−0.102214	−	0.121814i
$671$	35.0572	−	29.4165i	1.35337	−	1.13561i
$672$		0			0
$673$	−40.4246	+	14.7134i	−1.55825	+	0.567158i	−0.970336	−	0.241762i	$-0.922275\pi$
$673$	−40.4246	+	14.7134i	−1.55825	+	0.567158i	−0.587918	+	0.808920i	$0.700052\pi$
$674$	15.6708	−	9.04751i	0.603615	−	0.348497i
$675$		0			0
$676$	25.1003	−	43.4750i	0.965396	−	1.67212i
$677$	31.8275	+	26.7064i	1.22323	+	1.02641i	0.998649	+	0.0519559i	$0.0165455\pi$
$677$	31.8275	+	26.7064i	1.22323	+	1.02641i	0.224580	+	0.974456i	$0.427899\pi$
$678$		0			0
$679$	11.9696	+	0.301579i	0.459350	+	0.0115735i
$680$	11.3916	−	2.00865i	0.436848	−	0.0770282i
$681$		0			0
$682$	−11.0911	−	30.4726i	−0.424702	−	1.16686i
$683$	−7.54959	+	4.35876i	−0.288877	+	0.166783i	−0.637435	−	0.770504i	$-0.720005\pi$
$683$	−7.54959	+	4.35876i	−0.288877	+	0.166783i	0.348558	+	0.937287i	$0.386671\pi$
$684$		0			0
$685$	1.15306	−	0.665721i	0.0440562	−	0.0254359i
$686$	11.4381	−	44.7757i	0.436707	−	1.70955i
$687$		0			0
$688$	−6.75897	−	38.3320i	−0.257683	−	1.46139i
$689$	−7.41675	+	6.22339i	−0.282556	+	0.237092i
$690$		0			0
$691$	−15.2046	−	41.7744i	−0.578412	−	1.58917i	−0.790857	−	0.612001i	$-0.790365\pi$
$691$	−15.2046	−	41.7744i	−0.578412	−	1.58917i	0.212445	−	0.977173i	$-0.431857\pi$
$692$	6.84670	+	11.8588i	0.260273	+	0.450805i
$693$		0			0
$694$	22.2993	−	38.6236i	0.846472	−	1.46613i
$695$	−4.86549	−	0.857918i	−0.184559	−	0.0325427i
$696$		0			0
$697$	24.7187	+	8.99685i	0.936286	+	0.340780i
$698$	−80.3318	−	29.2384i	−3.04060	−	1.10669i
$699$		0			0
$700$	53.8759	−	8.10633i	2.03632	−	0.306391i
$701$			4.87126i			0.183985i	0.995760	+	0.0919925i	$0.0293236\pi$
$701$			4.87126i			0.183985i	−0.995760	+	0.0919925i	$0.970676\pi$
$702$		0			0
$703$	6.63222	+	3.82912i	0.250139	+	0.144418i
$704$	−16.4770	−	2.90535i	−0.621002	−	0.109499i
$705$		0			0
$706$	−26.0589	−	31.0558i	−0.980740	−	1.16880i
$707$	5.01091	−	2.72712i	0.188454	−	0.102564i
$708$		0			0
$709$	2.93571	−	16.6492i	0.110253	−	0.625275i	−0.878739	−	0.477303i	$-0.841614\pi$
$709$	2.93571	−	16.6492i	0.110253	−	0.625275i	0.988992	−	0.147972i	$-0.0472746\pi$
$710$	−3.72951	−	6.45971i	−0.139966	−	0.242428i
$711$		0			0
$712$	−55.7713	−	32.1996i	−2.09012	−	1.20673i
$713$	−1.41352	+	8.01648i	−0.0529368	+	0.300220i
$714$		0			0
$715$	1.22541	+	0.446012i	0.0458276	+	0.0166799i
$716$	21.3126	−	3.75798i	0.796488	−	0.140442i
$717$		0			0
$718$	33.4997	+	28.1096i	1.25020	+	1.04904i
$719$	2.77541	−	4.80714i	0.103505	−	0.179276i	−0.809621	−	0.586953i	$-0.800327\pi$
$719$	2.77541	−	4.80714i	0.103505	−	0.179276i	0.913126	+	0.407676i	$0.133661\pi$
$720$		0			0
$721$	−8.85861	−	7.82182i	−0.329912	−	0.291300i
$722$	3.69074	−	4.39845i	0.137355	−	0.163693i
$723$		0			0
$724$	−6.01790	+	16.5340i	−0.223653	+	0.614483i
$725$	40.8415	−	7.20146i	1.51682	−	0.267456i
$726$		0			0
$727$	11.3466	+	31.1745i	0.420822	+	1.15620i	0.951237	+	0.308461i	$0.0998139\pi$
$727$	11.3466	+	31.1745i	0.420822	+	1.15620i	−0.530415	+	0.847738i	$0.677964\pi$
$728$	10.3077	−	11.6740i	0.382030	−	0.432669i
$729$		0			0
$730$	3.32354	+	5.75654i	0.123010	+	0.213059i
$731$	7.27525	−	41.2600i	0.269085	−	1.52606i
$732$		0			0
$733$	−8.25356	+	22.6765i	−0.304852	+	0.837575i	0.688787	+	0.724964i	$0.258144\pi$
$733$	−8.25356	+	22.6765i	−0.304852	+	0.837575i	−0.993639	+	0.112611i	$0.964079\pi$
$734$	3.74806	+	21.2563i	0.138344	+	0.784585i
$735$		0			0
$736$	−3.94654	−	3.31154i	−0.145471	−	0.122065i
$737$		−	15.8852i		−	0.585138i
$738$		0			0
$739$	26.0657			0.958843			0.479422	−	0.877585i	$-0.340846\pi$
$739$	26.0657			0.958843			0.479422	+	0.877585i	$0.340846\pi$
$740$	−2.66096	+	0.968511i	−0.0978189	+	0.0356032i
$741$		0			0
$742$	52.9919	−	28.8402i	1.94539	−	1.05876i
$743$	−6.91069	+	18.9870i	−0.253528	+	0.696564i	0.746003	+	0.665943i	$0.231971\pi$
$743$	−6.91069	+	18.9870i	−0.253528	+	0.696564i	−0.999531	+	0.0306207i	$0.990252\pi$
$744$		0			0
$745$	−2.16665	+	2.58211i	−0.0793800	+	0.0946014i
$746$		−	1.56991i		−	0.0574783i
$747$		0			0
$748$	73.3895	+	42.3714i	2.68338	+	1.54925i
$749$	−9.97272	+	7.94879i	−0.364395	+	0.290442i
$750$		0			0
$751$	8.51983	−	7.14899i	0.310893	−	0.260870i	−0.473968	−	0.880542i	$-0.657179\pi$
$751$	8.51983	−	7.14899i	0.310893	−	0.260870i	0.784861	+	0.619672i	$0.212734\pi$
$752$	−11.5214	−	65.3411i	−0.420142	−	2.38274i
$753$		0			0
$754$	14.4645	−	17.2381i	0.526766	−	0.627776i
$755$	−1.65223			−0.0601307
$756$		0			0
$757$	52.3885			1.90409			0.952047	−	0.305952i	$-0.0989747\pi$
$757$	52.3885			1.90409			0.952047	+	0.305952i	$0.0989747\pi$
$758$	−8.68788	+	10.3538i	−0.315558	+	0.376067i
$759$		0			0
$760$	−1.40945	−	7.99340i	−0.0511262	−	0.289951i
$761$	9.61925	−	8.07151i	0.348698	−	0.292592i	−0.451569	−	0.892236i	$-0.649136\pi$
$761$	9.61925	−	8.07151i	0.348698	−	0.292592i	0.800267	+	0.599644i	$0.204691\pi$
$762$		0			0
$763$	−19.5197	+	49.6980i	−0.706662	+	1.79919i
$764$	10.9874	+	6.34360i	0.397511	+	0.229503i
$765$		0			0
$766$		−	40.8887i		−	1.47737i
$767$	−2.80853	+	3.34707i	−0.101410	+	0.120856i
$768$		0			0
$769$	5.13723	−	14.1144i	0.185253	−	0.508979i	−0.811949	−	0.583728i	$-0.801593\pi$
$769$	5.13723	−	14.1144i	0.185253	−	0.508979i	0.997202	+	0.0747491i	$0.0238156\pi$
$770$	−6.93279	−	4.23899i	−0.249841	−	0.152763i
$771$		0			0
$772$	−65.6455	+	23.8930i	−2.36263	+	0.859929i
$773$	18.8942			0.679576			0.339788	−	0.940502i	$-0.389645\pi$
$773$	18.8942			0.679576			0.339788	+	0.940502i	$0.389645\pi$
$774$		0			0
$775$			18.3909i			0.660622i
$776$	−19.2606	−	16.1616i	−0.691415	−	0.580166i
$777$		0			0
$778$	6.76200	+	38.3492i	0.242429	+	1.37489i
$779$	6.31301	−	17.3449i	0.226187	−	0.621444i
$780$		0			0
$781$	4.99879	−	28.3496i	0.178871	−	1.01443i
$782$	−15.6691	−	27.1396i	−0.560325	−	0.970512i
$783$		0			0
$784$	−30.2015	+	22.8524i	−1.07863	+	0.816155i
$785$	−0.142745	−	0.392190i	−0.00509480	−	0.0139978i
$786$		0			0
$787$	−1.36876	+	0.241349i	−0.0487910	+	0.00860317i	−0.197990	−	0.980204i	$-0.563441\pi$
$787$	−1.36876	+	0.241349i	−0.0487910	+	0.00860317i	0.149199	+	0.988807i	$0.452330\pi$
$788$	4.90567	−	13.4782i	0.174757	−	0.480142i
$789$		0			0
$790$	−7.69243	+	9.16748i	−0.273684	+	0.326164i
$791$	−31.7993	+	10.6749i	−1.13065	+	0.379556i
$792$		0			0
$793$	−7.04140	+	12.1961i	−0.250047	+	0.433095i
$794$	−12.5520	−	10.5324i	−0.445453	−	0.373780i
$795$		0			0
$796$	−17.5112	+	3.08770i	−0.620668	+	0.109440i
$797$	1.89028	+	0.688005i	0.0669571	+	0.0243704i	0.375282	−	0.926911i	$-0.377546\pi$
$797$	1.89028	+	0.688005i	0.0669571	+	0.0243704i	−0.308324	+	0.951281i	$0.599768\pi$
$798$		0			0
$799$	12.4014	−	70.3321i	0.438732	−	2.48817i
$800$	−10.0801	−	5.81975i	−0.356385	−	0.205759i
$801$		0			0
$802$	−44.0479	−	76.2932i	−1.55539	−	2.69401i
$803$	−4.45466	+	25.2636i	−0.157201	+	0.891534i
$804$		0			0
$805$	0.975082	+	1.79165i	0.0343671	+	0.0631472i
$806$	6.41442	+	7.64441i	0.225938	+	0.269263i
$807$		0			0
$808$	−11.7978	−	2.08028i	−0.415047	−	0.0731840i
$809$	−4.13482	−	2.38724i	−0.145373	−	0.0839309i	0.425550	−	0.904935i	$-0.360081\pi$
$809$	−4.13482	−	2.38724i	−0.145373	−	0.0839309i	−0.570922	+	0.821004i	$0.693414\pi$
$810$		0			0
$811$		−	17.2143i		−	0.604475i	−0.953233	−	0.302237i	$-0.902266\pi$
$811$		−	17.2143i		−	0.604475i	0.953233	−	0.302237i	$-0.0977336\pi$
$812$	−74.4321	+	59.3264i	−2.61206	+	2.08195i
$813$		0			0
$814$	−15.1291	−	5.50655i	−0.530276	−	0.193005i
$815$	2.37263	+	0.863565i	0.0831094	+	0.0302494i
$816$		0			0
$817$	−28.9518	−	5.10498i	−1.01289	−	0.178601i
$818$	21.7205	−	37.6210i	0.759439	−	1.31539i
$819$		0			0
$820$	3.41255	+	5.91071i	0.119171	+	0.206411i
$821$	2.98238	+	8.19401i	0.104086	+	0.285973i	0.980793	−	0.195051i	$-0.0624872\pi$
$821$	2.98238	+	8.19401i	0.104086	+	0.285973i	−0.876707	+	0.481024i	$0.840265\pi$
$822$		0			0
$823$	−9.30169	+	7.80505i	−0.324237	+	0.272067i	−0.790347	−	0.612660i	$-0.790100\pi$
$823$	−9.30169	+	7.80505i	−0.324237	+	0.272067i	0.466110	+	0.884727i	$0.345655\pi$
$824$	4.30923	+	24.4389i	0.150119	+	0.851368i
$825$		0			0
$826$	21.2911	−	16.9701i	0.740812	−	0.590467i
$827$	17.3220	−	10.0009i	0.602346	−	0.347765i	−0.167618	−	0.985852i	$-0.553607\pi$
$827$	17.3220	−	10.0009i	0.602346	−	0.347765i	0.769964	+	0.638087i	$0.220274\pi$
$828$		0			0
$829$	−12.8073	+	7.39429i	−0.444815	+	0.256814i	−0.705638	−	0.708572i	$-0.749340\pi$
$829$	−12.8073	+	7.39429i	−0.444815	+	0.256814i	0.260823	+	0.965387i	$0.416006\pi$
$830$	1.23680	+	3.39807i	0.0429299	+	0.117949i
$831$		0			0
$832$	5.07043	−	0.894053i	0.175785	−	0.0309957i
$833$	−38.9609	+	11.9959i	−1.34992	+	0.415635i
$834$		0			0
$835$	−4.53941	−	3.80902i	−0.157093	−	0.131816i
$836$	29.7317	−	51.4968i	1.02829	−	1.78105i
$837$		0			0
$838$	−37.0586	+	21.3958i	−1.28017	+	0.739106i
$839$	9.90483	−	3.60506i	0.341953	−	0.124461i	−0.165335	−	0.986238i	$-0.552870\pi$
$839$	9.90483	−	3.60506i	0.341953	−	0.124461i	0.507287	+	0.861777i	$0.330648\pi$
$840$		0			0
$841$	−33.2865	+	27.9307i	−1.14781	+	0.963127i
$842$	−41.5643	−	49.5344i	−1.43240	−	1.70707i
$843$		0			0
$844$	−71.0656	+	25.8658i	−2.44618	+	0.890337i
$845$	4.24632			0.146078
$846$		0			0
$847$	−0.718563	−	2.14051i	−0.0246901	−	0.0735489i
$848$	−48.6918	−	8.58567i	−1.67208	−	0.294833i
$849$		0			0
$850$	−45.5106	−	54.2375i	−1.56100	−	1.86033i
$851$	2.59779	+	3.09592i	0.0890510	+	0.106127i
$852$		0			0
$853$	−10.2716	−	1.81115i	−0.351691	−	0.0620126i	−0.00498807	−	0.999988i	$-0.501588\pi$
$853$	−10.2716	−	1.81115i	−0.351691	−	0.0620126i	−0.346703	+	0.937975i	$0.612699\pi$
$854$	58.0834	−	65.7824i	1.98757	−	2.25103i
$855$		0			0
$856$	26.7801			0.915324
$857$	44.2233	−	16.0960i	1.51064	−	0.549828i	0.551850	−	0.833943i	$-0.313922\pi$
$857$	44.2233	−	16.0960i	1.51064	−	0.549828i	0.958790	+	0.284115i	$0.0916999\pi$
$858$		0			0
$859$	2.65487	+	3.16395i	0.0905829	+	0.107952i	0.809432	−	0.587214i	$-0.199775\pi$
$859$	2.65487	+	3.16395i	0.0905829	+	0.107952i	−0.718849	+	0.695166i	$0.755331\pi$
$860$	8.32726	−	6.98740i	0.283957	−	0.238268i
$861$		0			0
$862$	−28.4040	+	10.3382i	−0.967446	+	0.352121i
$863$	−24.3038	+	14.0318i	−0.827311	+	0.477648i	−0.852931	−	0.522024i	$-0.825177\pi$
$863$	−24.3038	+	14.0318i	−0.827311	+	0.477648i	0.0256201	+	0.999672i	$0.491844\pi$
$864$		0			0
$865$	−0.579142	+	1.00310i	−0.0196914	+	0.0341065i
$866$	−60.4754	−	50.7448i	−2.05504	−	1.72438i
$867$		0			0
$868$	−20.1774	−	37.0746i	−0.684866	−	1.25839i
$869$	−45.4842	+	8.02009i	−1.54295	+	0.272063i
$870$		0			0
$871$	1.67190	+	4.59350i	0.0566500	+	0.155645i
$872$	97.1007	−	56.0611i	3.28824	−	1.89847i
$873$		0			0
$874$	−19.0437	+	10.9949i	−0.644161	+	0.371907i
$875$	5.82020	+	7.30215i	0.196759	+	0.246858i
$876$		0			0
$877$	2.77883	+	15.7595i	0.0938345	+	0.532162i	0.995098	+	0.0988910i	$0.0315295\pi$
$877$	2.77883	+	15.7595i	0.0938345	+	0.532162i	−0.901264	+	0.433271i	$0.857359\pi$
$878$	7.44168	−	6.24431i	0.251145	−	0.210735i
$879$		0			0
$880$	2.27767	+	6.25785i	0.0767802	+	0.210952i
$881$	12.7246	+	22.0396i	0.428702	+	0.742533i	0.996758	−	0.0804564i	$-0.0256378\pi$
$881$	12.7246	+	22.0396i	0.428702	+	0.742533i	−0.568056	+	0.822990i	$0.692304\pi$
$882$		0			0
$883$	−5.39480	+	9.34406i	−0.181549	+	0.314453i	−0.942408	−	0.334465i	$-0.891445\pi$
$883$	−5.39480	+	9.34406i	−0.181549	+	0.314453i	0.760859	+	0.648917i	$0.224778\pi$
$884$	−25.6815	−	4.52834i	−0.863761	−	0.152304i
$885$		0			0
$886$	0.488459	+	0.177785i	0.0164101	+	0.00597279i
$887$	−21.1469	−	7.69684i	−0.710043	−	0.258435i	−0.0383505	−	0.999264i	$-0.512210\pi$
$887$	−21.1469	−	7.69684i	−0.710043	−	0.258435i	−0.671693	+	0.740830i	$0.734433\pi$
$888$		0			0
$889$	7.19869	−	18.3281i	0.241436	−	0.614706i
$890$		−	10.3405i		−	0.346613i
$891$		0			0
$892$	47.9036	+	27.6572i	1.60393	+	0.926030i
$893$	−49.3514	−	8.70199i	−1.65148	−	0.291201i
$894$		0			0
$895$	1.17667	+	1.40230i	0.0393318	+	0.0468738i
$896$	−44.7102	−	1.12650i	−1.49366	−	0.0376336i
$897$		0			0
$898$	5.90322	−	33.4788i	0.196993	−	1.11720i
$899$	−16.0648	−	27.8251i	−0.535793	−	0.928020i
$900$		0			0
$901$	−46.0895	−	26.6098i	−1.53546	−	0.886500i
$902$	−6.73837	+	38.2152i	−0.224363	+	1.27243i
$903$		0			0
$904$	66.1897	+	24.0911i	2.20144	+	0.801257i
$905$	−1.46571	+	0.258444i	−0.0487218	+	0.00859097i
$906$		0			0
$907$	−13.2659	−	11.1314i	−0.440486	−	0.369611i	0.395405	−	0.918507i	$-0.370604\pi$
$907$	−13.2659	−	11.1314i	−0.440486	−	0.369611i	−0.835891	+	0.548895i	$0.815049\pi$
$908$	−2.37112	+	4.10690i	−0.0786883	+	0.136292i
$909$		0			0
$910$	2.45090	+	0.496115i	0.0812464	+	0.0164460i
$911$	−20.4723	+	24.3979i	−0.678277	+	0.808339i	−0.989885	−	0.141872i	$-0.954688\pi$
$911$	−20.4723	+	24.3979i	−0.678277	+	0.808339i	0.311608	+	0.950211i	$0.399132\pi$
$912$		0			0
$913$	−4.77322	+	13.1143i	−0.157971	+	0.434021i
$914$	48.8171	−	8.60777i	1.61473	−	0.284720i
$915$		0			0
$916$	−1.84399	−	5.06631i	−0.0609270	−	0.167396i
$917$	−18.5923	−	3.76349i	−0.613973	−	0.124282i
$918$		0			0
$919$	−9.28327	−	16.0791i	−0.306227	−	0.530401i	0.671307	−	0.741180i	$-0.265733\pi$
$919$	−9.28327	−	16.0791i	−0.306227	−	0.530401i	−0.977534	+	0.210779i	$0.932400\pi$
$920$	0.743802	−	4.21831i	0.0245224	−	0.139074i
$921$		0			0
$922$	−5.09513	+	13.9987i	−0.167799	+	0.461024i
$923$	1.53826	+	8.72392i	0.0506325	+	0.287151i
$924$		0			0
$925$	6.99458	+	5.86915i	0.229980	+	0.192977i
$926$		−	68.6762i		−	2.25684i
$927$		0			0
$928$	20.3346			0.667517
$929$	10.2172	−	3.71876i	0.335216	−	0.122008i	−0.168928	−	0.985628i	$-0.554031\pi$
$929$	10.2172	−	3.71876i	0.335216	−	0.122008i	0.504143	+	0.863620i	$0.331808\pi$
$930$		0			0
$931$	8.41744	+	27.3385i	0.275871	+	0.895985i
$932$	27.1303	−	74.5399i	0.888682	−	2.44163i
$933$		0			0
$934$	25.4749	−	30.3599i	0.833566	−	0.993405i
$935$			7.16814i			0.234423i
$936$		0			0
$937$	18.3316	+	10.5838i	0.598869	+	0.345757i	0.768596	−	0.639734i	$-0.220955\pi$
$937$	18.3316	+	10.5838i	0.598869	+	0.345757i	−0.169728	+	0.985491i	$0.554289\pi$
$938$	−4.53222	−	30.1218i	−0.147982	−	0.983512i
$939$		0			0
$940$	14.1947	−	11.9108i	0.462980	−	0.388487i
$941$	0.900013	+	5.10423i	0.0293396	+	0.166393i	0.995957	−	0.0898309i	$-0.0286327\pi$
$941$	0.900013	+	5.10423i	0.0293396	+	0.166393i	−0.966617	+	0.256224i	$0.917522\pi$
$942$		0			0
$943$	6.26123	−	7.46185i	0.203894	−	0.242991i
$944$	−22.3129			−0.726223
$945$		0			0
$946$	61.8050			2.00945
$947$	−19.2144	+	22.8988i	−0.624383	+	0.744111i	−0.981818	−	0.189827i	$-0.939207\pi$
$947$	−19.2144	+	22.8988i	−0.624383	+	0.744111i	0.357434	+	0.933938i	$0.383652\pi$
$948$		0			0
$949$	−1.37082	−	7.77429i	−0.0444986	−	0.252364i
$950$	−38.0580	+	31.9344i	−1.23476	+	1.03609i
$951$		0			0
$952$	79.6790	+	31.2953i	2.58241	+	1.01429i
$953$	29.6132	+	17.0972i	0.959267	+	0.553833i	0.895947	−	0.444160i	$-0.146498\pi$
$953$	29.6132	+	17.0972i	0.959267	+	0.553833i	0.0633195	+	0.997993i	$0.479831\pi$
$954$		0			0
$955$			1.07317i			0.0347270i
$956$	−33.8654	+	40.3592i	−1.09528	+	1.30531i
$957$		0			0
$958$	−9.15737	+	25.1597i	−0.295861	+	0.812872i
$959$	9.85025	+	0.248182i	0.318081	+	0.00801421i
$960$		0			0
$961$	−15.7415	+	5.72945i	−0.507792	+	0.184821i
$962$	4.95443			0.159737
$963$		0			0
$964$			87.0829i			2.80475i
$965$	−4.52665	−	3.79831i	−0.145718	−	0.122272i
$966$		0			0
$967$	7.82430	+	44.3738i	0.251612	+	1.42697i	0.804621	+	0.593789i	$0.202369\pi$
$967$	7.82430	+	44.3738i	0.251612	+	1.42697i	−0.553008	+	0.833176i	$0.686520\pi$
$968$	−1.62165	+	4.45545i	−0.0521218	+	0.143204i
$969$		0			0
$970$	0.701045	−	3.97582i	0.0225092	−	0.127656i
$971$	−16.1729	−	28.0122i	−0.519012	−	0.898955i	−0.999756	−	0.0220939i	$-0.992967\pi$
$971$	−16.1729	−	28.0122i	−0.519012	−	0.898955i	0.480744	−	0.876861i	$-0.340367\pi$
$972$		0			0
$973$	−27.4078	−	24.2001i	−0.878654	−	0.775818i
$974$	7.76498	+	21.3341i	0.248806	+	0.683589i
$975$		0			0
$976$	−70.8247	+	12.4883i	−2.26704	+	0.399741i
$977$	−10.5538	+	28.9962i	−0.337645	+	0.927672i	0.648416	+	0.761286i	$0.275432\pi$
$977$	−10.5538	+	28.9962i	−0.337645	+	0.927672i	−0.986061	+	0.166386i	$0.946790\pi$
$978$		0			0
$979$	25.6520	−	30.5708i	0.819840	−	0.977047i
$980$	−9.74444	−	4.11352i	−0.311275	−	0.131402i
$981$		0			0
$982$	−3.67806	+	6.37058i	−0.117371	+	0.203293i
$983$	−8.84591	−	7.42260i	−0.282141	−	0.236744i	0.490724	−	0.871315i	$-0.336732\pi$
$983$	−8.84591	−	7.42260i	−0.282141	−	0.236744i	−0.772865	+	0.634571i	$0.781177\pi$
$984$		0			0
$985$	1.19482	−	0.210679i	0.0380701	−	0.00671278i
$986$	116.234	+	42.3058i	3.70165	+	1.34729i
$987$		0			0
$988$	−3.17749	+	18.0205i	−0.101090	+	0.573307i
$989$	−13.4357	−	7.75713i	−0.427232	−	0.246662i
$990$		0			0
$991$	7.29987	+	12.6437i	0.231888	+	0.401642i	0.958364	−	0.285550i	$-0.0921764\pi$
$991$	7.29987	+	12.6437i	0.231888	+	0.401642i	−0.726476	+	0.687192i	$0.758843\pi$
$992$	−1.56589	+	8.88058i	−0.0497170	+	0.281959i
$993$		0			0
$994$	1.39037	−	55.1832i	0.0440998	−	1.75031i
$995$	−0.966797	−	1.15218i	−0.0306495	−	0.0365267i
$996$		0			0
$997$	39.4757	+	6.96063i	1.25021	+	0.220445i	0.759286	−	0.650758i	$-0.225549\pi$
$997$	39.4757	+	6.96063i	1.25021	+	0.220445i	0.490923	+	0.871203i	$0.336660\pi$
$998$	23.0225	+	13.2921i	0.728766	+	0.420753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.21		132
3.2	odd	2		189.2.ba.a.101.2	✓	132
7.5	odd	6		567.2.bd.a.467.2		132
21.5	even	6		189.2.bd.a.47.21	yes	132
27.4	even	9		189.2.bd.a.185.21	yes	132
27.23	odd	18		567.2.bd.a.17.2		132
189.131	even	18	inner	567.2.ba.a.341.21		132
189.166	odd	18		189.2.ba.a.131.2	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.2	✓	132	3.2	odd	2
189.2.ba.a.131.2	yes	132	189.166	odd	18
189.2.bd.a.47.21	yes	132	21.5	even	6
189.2.bd.a.185.21	yes	132	27.4	even	9
567.2.ba.a.143.21		132	1.1	even	1	trivial
567.2.ba.a.341.21		132	189.131	even	18	inner
567.2.bd.a.17.2		132	27.23	odd	18
567.2.bd.a.467.2		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60395 - 1.91151i) q^{2} +(-0.733927 - 4.16231i) q^{4} +(0.273867 - 0.229802i) q^{5} +(2.61630 - 0.393657i) q^{7} +(-4.81149 - 2.77792i) q^{8} +O(q^{10})\)	\(q+(1.60395 - 1.91151i) q^{2} +(-0.733927 - 4.16231i) q^{4} +(0.273867 - 0.229802i) q^{5} +(2.61630 - 0.393657i) q^{7} +(-4.81149 - 2.77792i) q^{8} -0.892090i q^{10} +(2.21304 - 2.63740i) q^{11} +(-0.362359 + 0.995572i) q^{13} +(3.44393 - 5.63249i) q^{14} +(-5.08414 + 1.85047i) q^{16} -5.82370 q^{17} +4.08644i q^{19} +(-1.15751 - 0.971262i) q^{20} +(-1.49181 - 8.46049i) q^{22} +(-0.737571 + 2.02646i) q^{23} +(-0.846047 + 4.79817i) q^{25} +(1.32184 + 2.28950i) q^{26} +(-3.55870 - 10.6009i) q^{28} +(-2.91124 - 7.99857i) q^{29} +(3.71733 - 0.655466i) q^{31} +(-0.817075 + 2.24489i) q^{32} +(-9.34090 + 11.1321i) q^{34} +(0.626056 - 0.709041i) q^{35} +(0.937031 - 1.62298i) q^{37} +(7.81127 + 6.55443i) q^{38} +(-1.95608 + 0.344910i) q^{40} +(-4.24450 - 1.54487i) q^{41} +(-1.24925 + 7.08485i) q^{43} +(-12.6019 - 7.27569i) q^{44} +(2.69057 + 4.66021i) q^{46} +(-2.12948 + 12.0769i) q^{47} +(6.69007 - 2.05985i) q^{49} +(7.81473 + 9.31324i) q^{50} +(4.40982 + 0.777571i) q^{52} +(7.91413 + 4.56923i) q^{53} -1.23086i q^{55} +(-13.6819 - 5.37379i) q^{56} +(-19.9588 - 7.26442i) q^{58} +(3.87534 + 1.41051i) q^{59} +(13.0904 + 2.30819i) q^{61} +(4.70948 - 8.15705i) q^{62} +(-2.42983 - 4.20859i) q^{64} +(0.129546 + 0.355925i) q^{65} +(3.53447 - 2.96577i) q^{67} +(4.27417 + 24.2400i) q^{68} +(-0.351177 - 2.33398i) q^{70} +(7.24109 - 4.18065i) q^{71} +(-6.45287 + 3.72557i) q^{73} +(-1.59940 - 4.39433i) q^{74} +(17.0090 - 2.99915i) q^{76} +(4.75175 - 7.77140i) q^{77} +(-10.2764 - 8.62293i) q^{79} +(-0.967136 + 1.67513i) q^{80} +(-9.76098 + 5.63551i) q^{82} +(-3.80912 + 1.38640i) q^{83} +(-1.59492 + 1.33830i) q^{85} +(11.5390 + 13.7517i) q^{86} +(-17.9745 + 6.54218i) q^{88} +11.5913 q^{89} +(-0.556126 + 2.74736i) q^{91} +(8.97607 + 1.58272i) q^{92} +(19.6695 + 23.4412i) q^{94} +(0.939071 + 1.11914i) q^{95} +(4.45675 + 0.785845i) q^{97} +(6.79310 - 16.0920i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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