LMFDB - Embedded newform 900.2.bj.f.127.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.9
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.872257 + 1.11318i) q^{2} +(-0.478336 - 1.94196i) q^{4} +(2.16662 - 0.552943i) q^{5} +(2.97520 - 2.97520i) q^{7} +(2.57898 + 1.16141i) q^{8} +O(q^{10})$	\(q+(-0.872257 + 1.11318i) q^{2} +(-0.478336 - 1.94196i) q^{4} +(2.16662 - 0.552943i) q^{5} +(2.97520 - 2.97520i) q^{7} +(2.57898 + 1.16141i) q^{8} +(-1.27433 + 2.89415i) q^{10} +(2.62851 + 3.61783i) q^{11} +(-1.97584 + 0.312943i) q^{13} +(0.716793 + 5.90707i) q^{14} +(-3.54239 + 1.85782i) q^{16} +(-0.276399 + 0.542463i) q^{17} +(-0.593603 - 1.82692i) q^{19} +(-2.11017 - 3.94299i) q^{20} +(-6.32003 - 0.229677i) q^{22} +(3.87093 + 0.613095i) q^{23} +(4.38851 - 2.39604i) q^{25} +(1.37508 - 2.47243i) q^{26} +(-7.20085 - 4.35456i) q^{28} +(-7.16789 - 2.32899i) q^{29} +(7.54161 - 2.45042i) q^{31} +(1.02179 - 5.56381i) q^{32} +(-0.362768 - 0.780848i) q^{34} +(4.80102 - 8.09125i) q^{35} +(-0.0557708 - 0.352123i) q^{37} +(2.55147 + 0.932759i) q^{38} +(6.22987 + 1.09031i) q^{40} +(-6.95445 - 5.05270i) q^{41} +(5.68128 + 5.68128i) q^{43} +(5.76836 - 6.83499i) q^{44} +(-4.05893 + 3.77426i) q^{46} +(0.299237 + 0.587287i) q^{47} -10.7036i q^{49} +(-1.16069 + 6.97516i) q^{50} +(1.55284 + 3.68731i) q^{52} +(3.58582 + 7.03757i) q^{53} +(7.69544 + 6.38506i) q^{55} +(11.1284 - 4.21754i) q^{56} +(8.84482 - 5.94767i) q^{58} +(-3.91416 - 2.84381i) q^{59} +(-0.162666 + 0.118184i) q^{61} +(-3.85047 + 10.5326i) q^{62} +(5.30225 + 5.99050i) q^{64} +(-4.10787 + 1.77056i) q^{65} +(-12.3429 - 6.28904i) q^{67} +(1.18565 + 0.277274i) q^{68} +(4.81929 + 12.4020i) q^{70} +(8.25771 + 2.68309i) q^{71} +(-2.42869 + 15.3341i) q^{73} +(0.440622 + 0.245059i) q^{74} +(-3.26386 + 2.02664i) q^{76} +(18.5841 + 2.94343i) q^{77} +(2.38682 - 7.34587i) q^{79} +(-6.64775 + 5.98393i) q^{80} +(11.6906 - 3.33429i) q^{82} +(-1.76165 + 3.45743i) q^{83} +(-0.298901 + 1.32815i) q^{85} +(-11.2798 + 1.36875i) q^{86} +(2.57708 + 12.3831i) q^{88} +(-1.32210 - 1.81971i) q^{89} +(-4.94746 + 6.80959i) q^{91} +(-0.661003 - 7.81045i) q^{92} +(-0.914767 - 0.179160i) q^{94} +(-2.29630 - 3.63002i) q^{95} +(0.154282 - 0.0786106i) q^{97} +(11.9150 + 9.33630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	−0.872257	+	1.11318i	−0.616779	+	0.787137i
$2$	−0.872257	+	1.11318i	−0.616779	+	0.787137i
$3$		0			0
$3$		0			0
$4$	−0.478336	−	1.94196i	−0.239168	−	0.970978i
$5$	2.16662	−	0.552943i	0.968943	−	0.247284i
$5$	2.16662	−	0.552943i	0.968943	−	0.247284i
$6$		0			0
$7$	2.97520	−	2.97520i	1.12452	−	1.12452i	0.133466	−	0.991053i	$-0.457389\pi$
$7$	2.97520	−	2.97520i	1.12452	−	1.12452i	0.991053	−	0.133466i	$-0.0426107\pi$
$8$	2.57898	+	1.16141i	0.911806	+	0.410621i
$9$		0			0
$10$	−1.27433	+	2.89415i	−0.402977	+	0.915210i
$11$	2.62851	+	3.61783i	0.792525	+	1.09082i	0.993789	+	0.111280i	$0.0354951\pi$
$11$	2.62851	+	3.61783i	0.792525	+	1.09082i	−0.201264	+	0.979537i	$0.564505\pi$
$12$		0			0
$13$	−1.97584	+	0.312943i	−0.548000	+	0.0867947i	−0.424295	−	0.905524i	$-0.639478\pi$
$13$	−1.97584	+	0.312943i	−0.548000	+	0.0867947i	−0.123706	+	0.992319i	$0.539478\pi$
$14$	0.716793	+	5.90707i	0.191571	+	1.57873i
$15$		0			0
$16$	−3.54239	+	1.85782i	−0.885597	+	0.464454i
$17$	−0.276399	+	0.542463i	−0.0670365	+	0.131567i	−0.922093	−	0.386968i	$-0.873522\pi$
$17$	−0.276399	+	0.542463i	−0.0670365	+	0.131567i	0.855057	+	0.518535i	$0.173522\pi$
$18$		0			0
$19$	−0.593603	−	1.82692i	−0.136182	−	0.419125i	0.859590	−	0.510984i	$-0.170719\pi$
$19$	−0.593603	−	1.82692i	−0.136182	−	0.419125i	−0.995772	+	0.0918594i	$0.970719\pi$
$20$	−2.11017	−	3.94299i	−0.471847	−	0.881680i
$21$		0			0
$22$	−6.32003	−	0.229677i	−1.34743	−	0.0489672i
$23$	3.87093	+	0.613095i	0.807145	+	0.127839i	0.546352	−	0.837556i	$-0.316016\pi$
$23$	3.87093	+	0.613095i	0.807145	+	0.127839i	0.260793	+	0.965395i	$0.416016\pi$
$24$		0			0
$25$	4.38851	−	2.39604i	0.877702	−	0.479208i
$26$	1.37508	−	2.47243i	0.269676	−	0.484884i
$27$		0			0
$28$	−7.20085	−	4.35456i	−1.36083	−	0.822934i
$29$	−7.16789	−	2.32899i	−1.33104	−	0.432482i	−0.444770	−	0.895645i	$-0.646715\pi$
$29$	−7.16789	−	2.32899i	−1.33104	−	0.432482i	−0.886274	+	0.463162i	$0.846715\pi$
$30$		0			0
$31$	7.54161	−	2.45042i	1.35451	−	0.440108i	0.460306	−	0.887760i	$-0.347740\pi$
$31$	7.54161	−	2.45042i	1.35451	−	0.440108i	0.894208	+	0.447652i	$0.147740\pi$
$32$	1.02179	−	5.56381i	0.180629	−	0.983551i
$33$		0			0
$34$	−0.362768	−	0.780848i	−0.0622142	−	0.133914i
$35$	4.80102	−	8.09125i	0.811520	−	1.36767i
$36$		0			0
$37$	−0.0557708	−	0.352123i	−0.00916866	−	0.0578887i	0.982680	−	0.185312i	$-0.0593294\pi$
$37$	−0.0557708	−	0.352123i	−0.00916866	−	0.0578887i	−0.991848	+	0.127423i	$0.959329\pi$
$38$	2.55147	+	0.932759i	0.413903	+	0.151313i
$39$		0			0
$40$	6.22987	+	1.09031i	0.985028	+	0.172393i
$41$	−6.95445	−	5.05270i	−1.08610	−	0.789099i	−0.107365	−	0.994220i	$-0.534241\pi$
$41$	−6.95445	−	5.05270i	−1.08610	−	0.789099i	−0.978737	+	0.205120i	$0.934241\pi$
$42$		0			0
$43$	5.68128	+	5.68128i	0.866387	+	0.866387i	0.992070	−	0.125684i	$-0.0401124\pi$
$43$	5.68128	+	5.68128i	0.866387	+	0.866387i	−0.125684	+	0.992070i	$0.540112\pi$
$44$	5.76836	−	6.83499i	0.869613	−	1.03041i
$45$		0			0
$46$	−4.05893	+	3.77426i	−0.598457	+	0.556485i
$47$	0.299237	+	0.587287i	0.0436483	+	0.0856646i	0.911801	−	0.410633i	$-0.134692\pi$
$47$	0.299237	+	0.587287i	0.0436483	+	0.0856646i	−0.868152	+	0.496298i	$0.834692\pi$
$48$		0			0
$49$		−	10.7036i		−	1.52909i
$50$	−1.16069	+	6.97516i	−0.164146	+	0.986436i
$51$		0			0
$52$	1.55284	+	3.68731i	0.215340	+	0.511338i
$53$	3.58582	+	7.03757i	0.492550	+	0.966685i	0.994789	+	0.101956i	$0.0325099\pi$
$53$	3.58582	+	7.03757i	0.492550	+	0.966685i	−0.502239	+	0.864729i	$0.667490\pi$
$54$		0			0
$55$	7.69544	+	6.38506i	1.03765	+	0.860961i
$56$	11.1284	−	4.21754i	1.48709	−	0.563593i
$57$		0			0
$58$	8.84482	−	5.94767i	1.16138	−	0.780968i
$59$	−3.91416	−	2.84381i	−0.509580	−	0.370232i	0.303084	−	0.952964i	$-0.401984\pi$
$59$	−3.91416	−	2.84381i	−0.509580	−	0.370232i	−0.812664	+	0.582732i	$0.801984\pi$
$60$		0			0
$61$	−0.162666	+	0.118184i	−0.0208272	+	0.0151319i	−0.598150	−	0.801384i	$-0.704097\pi$
$61$	−0.162666	+	0.118184i	−0.0208272	+	0.0151319i	0.577323	+	0.816516i	$0.304097\pi$
$62$	−3.85047	+	10.5326i	−0.489010	+	1.33764i
$63$		0			0
$64$	5.30225	+	5.99050i	0.662782	+	0.748813i
$65$	−4.10787	+	1.77056i	−0.509518	+	0.219611i
$66$		0			0
$67$	−12.3429	−	6.28904i	−1.50793	−	0.768328i	−0.512044	−	0.858959i	$-0.671112\pi$
$67$	−12.3429	−	6.28904i	−1.50793	−	0.768328i	−0.995885	+	0.0906310i	$0.971112\pi$
$68$	1.18565	+	0.277274i	0.143781	+	0.0336245i
$69$		0			0
$70$	4.81929	+	12.4020i	0.576015	+	1.48233i
$71$	8.25771	+	2.68309i	0.980010	+	0.318424i	0.754850	−	0.655897i	$-0.227710\pi$
$71$	8.25771	+	2.68309i	0.980010	+	0.318424i	0.225160	+	0.974322i	$0.427710\pi$
$72$		0			0
$73$	−2.42869	+	15.3341i	−0.284256	+	1.79472i	0.270509	+	0.962717i	$0.412808\pi$
$73$	−2.42869	+	15.3341i	−0.284256	+	1.79472i	−0.554766	+	0.832007i	$0.687192\pi$
$74$	0.440622	+	0.245059i	0.0512213	+	0.0284875i
$75$		0			0
$76$	−3.26386	+	2.02664i	−0.374391	+	0.232471i
$77$	18.5841	+	2.94343i	2.11785	+	0.335435i
$78$		0			0
$79$	2.38682	−	7.34587i	0.268538	−	0.826475i	−0.722319	−	0.691560i	$-0.756924\pi$
$79$	2.38682	−	7.34587i	0.268538	−	0.826475i	0.990857	−	0.134915i	$-0.0430762\pi$
$80$	−6.64775	+	5.98393i	−0.743241	+	0.669023i
$81$		0			0
$82$	11.6906	−	3.33429i	1.29101	−	0.368211i
$83$	−1.76165	+	3.45743i	−0.193366	+	0.379503i	−0.967250	−	0.253825i	$-0.918311\pi$
$83$	−1.76165	+	3.45743i	−0.193366	+	0.379503i	0.773884	+	0.633327i	$0.218311\pi$
$84$		0			0
$85$	−0.298901	+	1.32815i	−0.0324203	+	0.144058i
$86$	−11.2798	+	1.36875i	−1.21633	+	0.147596i
$87$		0			0
$88$	2.57708	+	12.3831i	0.274717	+	1.32004i
$89$	−1.32210	−	1.81971i	−0.140142	−	0.192889i	0.733177	−	0.680038i	$-0.238037\pi$
$89$	−1.32210	−	1.81971i	−0.140142	−	0.192889i	−0.873319	+	0.487149i	$0.838037\pi$
$90$		0			0
$91$	−4.94746	+	6.80959i	−0.518635	+	0.713839i
$92$	−0.661003	−	7.81045i	−0.0689143	−	0.814295i
$93$		0			0
$94$	−0.914767	−	0.179160i	−0.0943510	−	0.0184789i
$95$	−2.29630	−	3.63002i	−0.235595	−	0.372433i
$96$		0			0
$97$	0.154282	−	0.0786106i	0.0156650	−	0.00798170i	−0.446140	−	0.894963i	$-0.647202\pi$
$97$	0.154282	−	0.0786106i	0.0156650	−	0.00798170i	0.461805	+	0.886981i	$0.347202\pi$
$98$	11.9150	+	9.33630i	1.20360	+	0.943108i
$99$		0			0
$100$	−6.75218	−	7.37618i	−0.675218	−	0.737618i
$101$	−18.4043			−1.83130			−0.915650	−	0.401977i	$-0.868323\pi$
$101$	−18.4043			−1.83130			−0.915650	+	0.401977i	$0.868323\pi$
$102$		0			0
$103$	12.7706	−	6.50694i	1.25832	−	0.641147i	0.307696	−	0.951485i	$-0.400442\pi$
$103$	12.7706	−	6.50694i	1.25832	−	0.641147i	0.950627	+	0.310337i	$0.100442\pi$
$104$	−5.45911	−	1.48769i	−0.535310	−	0.145880i
$105$		0			0
$106$	−10.9618	−	2.14691i	−1.06471	−	0.208526i
$107$	1.33643	−	1.33643i	0.129198	−	0.129198i	−0.639551	−	0.768749i	$-0.720880\pi$
$107$	1.33643	−	1.33643i	0.129198	−	0.129198i	0.768749	+	0.639551i	$0.220880\pi$
$108$		0			0
$109$	11.1281	−	15.3165i	1.06588	−	1.46705i	0.191697	−	0.981454i	$-0.438601\pi$
$109$	11.1281	−	15.3165i	1.06588	−	1.46705i	0.874181	−	0.485601i	$-0.161399\pi$
$110$	−13.8201	+	2.99699i	−1.31770	+	0.285752i
$111$		0			0
$112$	−5.01194	+	16.0667i	−0.473583	+	1.51816i
$113$	15.8918	−	2.51702i	1.49498	−	0.236781i	0.645237	−	0.763982i	$-0.276758\pi$
$113$	15.8918	−	2.51702i	1.49498	−	0.236781i	0.849741	+	0.527201i	$0.176758\pi$
$114$		0			0
$115$	8.72586	−	0.812059i	0.813690	−	0.0757249i
$116$	−1.09413	+	15.0338i	−0.101588	+	1.39585i
$117$		0			0
$118$	6.57982	−	1.87664i	0.605721	−	0.172758i
$119$	0.791594	+	2.43628i	0.0725653	+	0.223333i
$120$		0			0
$121$	−2.78046	+	8.55737i	−0.252769	+	0.777943i
$122$	0.0103268	−	0.284163i	0.000934943	−	0.0257269i
$123$		0			0
$124$	−8.36603	−	13.4734i	−0.751292	−	1.20994i
$125$	8.18337	−	7.61791i	0.731943	−	0.681366i
$126$		0			0
$127$	−1.01246	+	6.39241i	−0.0898412	+	0.567235i	0.901171	+	0.433464i	$0.142709\pi$
$127$	−1.01246	+	6.39241i	−0.0898412	+	0.567235i	−0.991012	+	0.133771i	$0.957291\pi$
$128$	−11.2934	+	0.677101i	−0.998208	+	0.0598479i
$129$		0			0
$130$	1.61217	−	6.11717i	0.141396	−	0.536512i
$131$	−5.78251	+	1.87885i	−0.505220	+	0.164156i	−0.550527	−	0.834817i	$-0.685573\pi$
$131$	−5.78251	+	1.87885i	−0.505220	+	0.164156i	0.0453071	+	0.998973i	$0.485573\pi$
$132$		0			0
$133$	−7.20155	−	3.66937i	−0.624453	−	0.318175i
$134$	17.7670	−	8.25424i	1.53484	−	0.713058i
$135$		0			0
$136$	−1.34285	+	1.07799i	−0.115148	+	0.0924367i
$137$	2.40373	+	15.1766i	0.205365	+	1.29662i	0.847814	+	0.530293i	$0.177918\pi$
$137$	2.40373	+	15.1766i	0.205365	+	1.29662i	−0.642450	+	0.766328i	$0.722082\pi$
$138$		0			0
$139$	−3.62695	+	2.63514i	−0.307634	+	0.223509i	−0.730881	−	0.682505i	$-0.760890\pi$
$139$	−3.62695	+	2.63514i	−0.307634	+	0.223509i	0.423247	+	0.906015i	$0.360890\pi$
$140$	−18.0094	−	5.45303i	−1.52207	−	0.460865i
$141$		0			0
$142$	−10.1896	+	6.85196i	−0.855093	+	0.575004i
$143$	−6.32569	−	6.32569i	−0.528981	−	0.528981i
$144$		0			0
$145$	−16.8179	−	1.08260i	−1.39665	−	0.0899054i
$146$	−14.9512	−	16.0789i	−1.23737	−	1.33070i
$147$		0			0
$148$	−0.657130	+	0.276738i	−0.0540158	+	0.0227477i
$149$			3.78689i			0.310234i	0.987896	+	0.155117i	$0.0495755\pi$
$149$			3.78689i			0.310234i	−0.987896	+	0.155117i	$0.950425\pi$
$150$		0			0
$151$			11.2709i			0.917213i	0.888639	+	0.458606i	$0.151651\pi$
$151$			11.2709i			0.917213i	−0.888639	+	0.458606i	$0.848349\pi$
$152$	0.590918	−	5.40101i	0.0479297	−	0.438080i
$153$		0			0
$154$	−19.4867	+	18.1200i	−1.57028	+	1.46015i
$155$	14.9849	−	9.47922i	1.20362	−	0.761389i
$156$		0			0
$157$	−0.386372	−	0.386372i	−0.0308358	−	0.0308358i	0.691521	−	0.722357i	$-0.256941\pi$
$157$	−0.386372	−	0.386372i	−0.0308358	−	0.0308358i	−0.722357	+	0.691521i	$0.756941\pi$
$158$	6.09535	+	9.06444i	0.484920	+	0.721128i
$159$		0			0
$160$	−0.862637	−	12.6197i	−0.0681974	−	0.997672i
$161$	13.3409	−	9.69271i	1.05141	−	0.763893i
$162$		0			0
$163$	0.773723	+	4.88510i	0.0606027	+	0.382630i	0.999284	+	0.0378434i	$0.0120488\pi$
$163$	0.773723	+	4.88510i	0.0606027	+	0.382630i	−0.938681	+	0.344787i	$0.887951\pi$
$164$	−6.48556	+	15.9221i	−0.506437	+	1.24331i
$165$		0			0
$166$	−2.31213	−	4.97680i	−0.179456	−	0.386275i
$167$	6.33490	+	3.22779i	0.490209	+	0.249774i	0.681580	−	0.731744i	$-0.261293\pi$
$167$	6.33490	+	3.22779i	0.490209	+	0.249774i	−0.191371	+	0.981518i	$0.561293\pi$
$168$		0			0
$169$	−8.55771	+	2.78057i	−0.658285	+	0.213890i
$170$	−1.21775	−	1.49121i	−0.0933969	−	0.114371i
$171$		0			0
$172$	8.31523	−	13.7504i	0.634030	−	1.04845i
$173$	0.435575	−	2.75011i	0.0331162	−	0.209087i	−0.965582	−	0.260099i	$-0.916245\pi$
$173$	0.435575	−	2.75011i	0.0331162	−	0.209087i	0.998698	+	0.0510121i	$0.0162447\pi$
$174$		0			0
$175$	5.92799	−	20.1854i	0.448114	−	1.52587i
$176$	−16.0325	−	7.93248i	−1.20849	−	0.597933i
$177$		0			0
$178$	3.17887	+	0.115524i	0.238266	+	0.00865886i
$179$	4.61764	−	14.2116i	0.345139	−	1.06223i	−0.616371	−	0.787456i	$-0.711398\pi$
$179$	4.61764	−	14.2116i	0.345139	−	1.06223i	0.961510	−	0.274772i	$-0.0886023\pi$
$180$		0			0
$181$	1.26448	+	3.89168i	0.0939883	+	0.289266i	0.986989	−	0.160790i	$-0.0514040\pi$
$181$	1.26448	+	3.89168i	0.0939883	+	0.289266i	−0.893000	+	0.450056i	$0.851404\pi$
$182$	−3.26484	−	11.4471i	−0.242006	−	0.848517i
$183$		0			0
$184$	9.27099	+	6.07690i	0.683467	+	0.447995i
$185$	−0.315538	−	0.732080i	−0.0231988	−	0.0538236i
$186$		0			0
$187$	−2.68906	+	0.425905i	−0.196643	+	0.0311452i
$188$	0.997349	−	0.862027i	0.0727391	−	0.0628698i
$189$		0			0
$190$	6.04383	+	0.610121i	0.438465	+	0.0442628i
$191$	−14.5709	+	20.0552i	−1.05432	+	1.45114i	−0.169308	+	0.985563i	$0.554153\pi$
$191$	−14.5709	+	20.0552i	−1.05432	+	1.45114i	−0.885007	+	0.465577i	$0.845847\pi$
$192$		0			0
$193$	9.83381	−	9.83381i	0.707853	−	0.707853i	−0.258230	−	0.966083i	$-0.583139\pi$
$193$	9.83381	−	9.83381i	0.707853	−	0.707853i	0.966083	+	0.258230i	$0.0831393\pi$
$194$	−0.0470658	+	0.240312i	−0.00337913	+	0.0172534i
$195$		0			0
$196$	−20.7859	+	5.11993i	−1.48471	+	0.365709i
$197$	−5.20082	+	2.64995i	−0.370543	+	0.188801i	−0.629339	−	0.777131i	$-0.716674\pi$
$197$	−5.20082	+	2.64995i	−0.370543	+	0.188801i	0.258796	+	0.965932i	$0.416674\pi$
$198$		0			0
$199$	−18.7923			−1.33215			−0.666076	−	0.745884i	$-0.732027\pi$
$199$	−18.7923			−1.33215			−0.666076	+	0.745884i	$0.732027\pi$
$200$	14.1006	−	1.08247i	0.997066	−	0.0765422i
$201$		0			0
$202$	16.0533	−	20.4873i	1.12951	−	1.44148i
$203$	−28.2551	+	14.3967i	−1.98312	+	1.01045i
$204$		0			0
$205$	−17.8615	−	7.10188i	−1.24750	−	0.496017i
$206$	−3.89584	+	19.8917i	−0.271436	+	1.38592i
$207$		0			0
$208$	6.41781	−	4.77932i	0.444995	−	0.331386i
$209$	5.04921	−	6.94964i	0.349261	−	0.480717i
$210$		0			0
$211$	1.61602	+	2.22426i	0.111251	+	0.153124i	0.861012	−	0.508585i	$-0.169831\pi$
$211$	1.61602	+	2.22426i	0.111251	+	0.153124i	−0.749760	+	0.661709i	$0.769831\pi$
$212$	11.9514	−	10.3298i	0.820827	−	0.709456i
$213$		0			0
$214$	0.321977	+	2.65340i	0.0220099	+	0.181383i
$215$	15.4506	+	9.16776i	1.05372	+	0.625236i
$216$		0			0
$217$	15.1473	−	29.7283i	1.02827	−	2.01809i
$218$	7.34346	+	25.7475i	0.497362	+	1.74384i
$219$		0			0
$220$	8.71850	−	17.9984i	0.587801	−	1.21345i
$221$	0.376361	−	1.15832i	0.0253168	−	0.0779170i
$222$		0			0
$223$	−7.97469	−	1.26307i	−0.534025	−	0.0845812i	−0.116403	−	0.993202i	$-0.537136\pi$
$223$	−7.97469	−	1.26307i	−0.534025	−	0.0845812i	−0.417622	+	0.908621i	$0.637136\pi$
$224$	−13.5134	−	19.5935i	−0.902902	−	1.30914i
$225$		0			0
$226$	−11.0599	+	19.8859i	−0.735691	+	1.32279i
$227$	−0.687194	+	4.33877i	−0.0456107	+	0.287975i	−0.999942	−	0.0107760i	$-0.996570\pi$
$227$	−0.687194	+	4.33877i	−0.0456107	+	0.287975i	0.954331	+	0.298751i	$0.0965698\pi$
$228$		0			0
$229$	3.89153	+	1.26444i	0.257160	+	0.0835563i	0.434760	−	0.900547i	$-0.356833\pi$
$229$	3.89153	+	1.26444i	0.257160	+	0.0835563i	−0.177600	+	0.984103i	$0.556833\pi$
$230$	−6.70722	+	10.4218i	−0.442261	+	0.687191i
$231$		0			0
$232$	−15.7809	−	14.3313i	−1.03607	−	0.940894i
$233$	−23.3803	−	11.9128i	−1.53169	−	0.780436i	−0.533818	−	0.845599i	$-0.679243\pi$
$233$	−23.3803	−	11.9128i	−1.53169	−	0.780436i	−0.997875	+	0.0651628i	$0.979243\pi$
$234$		0			0
$235$	0.973071	+	1.10697i	0.0634761	+	0.0722106i
$236$	−3.65026	+	8.96143i	−0.237612	+	0.583339i
$237$		0			0
$238$	−3.40249	−	1.24387i	−0.220550	−	0.0806282i
$239$	−1.57633	+	1.14527i	−0.101964	+	0.0740815i	−0.637599	−	0.770368i	$-0.720072\pi$
$239$	−1.57633	+	1.14527i	−0.101964	+	0.0740815i	0.535635	+	0.844450i	$0.320072\pi$
$240$		0			0
$241$	−21.9199	−	15.9258i	−1.41199	−	1.02587i	−0.993030	−	0.117862i	$-0.962396\pi$
$241$	−21.9199	−	15.9258i	−1.41199	−	1.02587i	−0.418956	−	0.908006i	$-0.637604\pi$
$242$	−7.10062	−	10.5594i	−0.456445	−	0.678782i
$243$		0			0
$244$	0.307317	+	0.259359i	0.0196739	+	0.0166037i
$245$	−5.91849	−	23.1907i	−0.378118	−	1.48160i
$246$		0			0
$247$	1.74459	+	3.42395i	0.111006	+	0.217861i
$248$	22.2956	+	2.43933i	1.41577	+	0.154898i
$249$		0			0
$250$	1.34210	+	15.7543i	0.0848817	+	0.996391i
$251$		−	6.25683i		−	0.394928i	−0.980310	−	0.197464i	$-0.936729\pi$
$251$		−	6.25683i		−	0.394928i	0.980310	−	0.197464i	$-0.0632705\pi$
$252$		0			0
$253$	7.95670	+	15.6159i	0.500233	+	0.981763i
$254$	−6.23278	−	6.70287i	−0.391079	−	0.420576i
$255$		0			0
$256$	9.09703	−	13.1622i	0.568565	−	0.822639i
$257$	−10.4519	−	10.4519i	−0.651973	−	0.651973i	0.301495	−	0.953468i	$-0.402514\pi$
$257$	−10.4519	−	10.4519i	−0.651973	−	0.651973i	−0.953468	+	0.301495i	$0.902514\pi$
$258$		0			0
$259$	−1.21356	−	0.881706i	−0.0754073	−	0.0547866i
$260$	5.40329	+	7.13038i	0.335098	+	0.442207i
$261$		0			0
$262$	2.95234	−	8.07581i	0.182396	−	0.498925i
$263$	−4.88515	−	30.8437i	−0.301232	−	1.90190i	−0.417489	−	0.908682i	$-0.637090\pi$
$263$	−4.88515	−	30.8437i	−0.301232	−	1.90190i	0.116257	−	0.993219i	$-0.462910\pi$
$264$		0			0
$265$	11.6605	+	13.2650i	0.716299	+	0.814863i
$266$	10.3663	−	4.81598i	0.635596	−	0.295287i
$267$		0			0
$268$	−6.30896	+	26.9777i	−0.385381	+	1.64793i
$269$	−21.6924	+	7.04830i	−1.32261	+	0.429742i	−0.883391	−	0.468638i	$-0.844745\pi$
$269$	−21.6924	+	7.04830i	−1.32261	+	0.429742i	−0.439220	+	0.898380i	$0.644745\pi$
$270$		0			0
$271$	11.2228	+	3.64649i	0.681734	+	0.221509i	0.629354	−	0.777119i	$-0.283319\pi$
$271$	11.2228	+	3.64649i	0.681734	+	0.221509i	0.0523794	+	0.998627i	$0.483319\pi$
$272$	−0.0286852	−	2.43511i	−0.00173930	−	0.147650i
$273$		0			0
$274$	−18.9909	−	10.5621i	−1.14728	−	0.638078i
$275$	20.2037	+	9.57887i	1.21833	+	0.577628i
$276$		0			0
$277$	3.23443	+	0.512283i	0.194338	+	0.0307801i	0.252845	−	0.967507i	$-0.418634\pi$
$277$	3.23443	+	0.512283i	0.194338	+	0.0307801i	−0.0585067	+	0.998287i	$0.518634\pi$
$278$	0.230256	−	6.33596i	0.0138098	−	0.380006i
$279$		0			0
$280$	21.7790	−	15.2912i	1.30154	−	0.913824i
$281$	−3.60266	−	11.0878i	−0.214917	−	0.661445i	−0.999160	−	0.0409914i	$-0.986948\pi$
$281$	−3.60266	−	11.0878i	−0.214917	−	0.661445i	0.784243	−	0.620454i	$-0.213052\pi$
$282$		0			0
$283$	−9.86359	+	19.3584i	−0.586330	+	1.15074i	0.387162	+	0.922012i	$0.373456\pi$
$283$	−9.86359	+	19.3584i	−0.586330	+	1.15074i	−0.973491	+	0.228725i	$0.926544\pi$
$284$	1.26049	−	17.3195i	0.0747960	−	1.02772i
$285$		0			0
$286$	12.5593	−	1.52400i	0.742645	−	0.0901162i
$287$	−35.7236	+	5.65807i	−2.10870	+	0.333985i
$288$		0			0
$289$	9.77448	+	13.4534i	0.574969	+	0.791377i
$290$	15.8747	−	17.7770i	0.932193	−	1.04390i
$291$		0			0
$292$	30.9399	−	2.61847i	1.81062	−	0.153234i
$293$	−6.14531	+	6.14531i	−0.359013	+	0.359013i	−0.863449	−	0.504436i	$-0.831700\pi$
$293$	−6.14531	+	6.14531i	−0.359013	+	0.359013i	0.504436	+	0.863449i	$0.331700\pi$
$294$		0			0
$295$	−10.0530	−	3.99714i	−0.585307	−	0.232723i
$296$	0.265128	−	0.972890i	0.0154102	−	0.0565481i
$297$		0			0
$298$	−4.21549	−	3.30314i	−0.244197	−	0.191346i
$299$	−7.84022			−0.453412
$300$		0			0
$301$	33.8059			1.94854
$302$	−12.5465	−	9.83112i	−0.721972	−	0.565717i
$303$		0			0
$304$	5.49686	+	5.36887i	0.315267	+	0.307926i
$305$	−0.287087	+	0.346005i	−0.0164385	+	0.0198122i
$306$		0			0
$307$	−2.29000	+	2.29000i	−0.130697	+	0.130697i	−0.769429	−	0.638732i	$-0.779459\pi$
$307$	−2.29000	+	2.29000i	−0.130697	+	0.130697i	0.638732	+	0.769429i	$0.279459\pi$
$308$	−3.17343	−	37.4975i	−0.180823	−	2.13662i
$309$		0			0
$310$	−2.51860	+	24.9492i	−0.143047	+	1.41702i
$311$	6.35552	+	8.74762i	0.360388	+	0.496032i	0.950257	−	0.311467i	$-0.100820\pi$
$311$	6.35552	+	8.74762i	0.360388	+	0.496032i	−0.589869	+	0.807499i	$0.700820\pi$
$312$		0			0
$313$	−22.1314	+	3.50527i	−1.25094	+	0.198129i	−0.746540	−	0.665341i	$-0.768286\pi$
$313$	−22.1314	+	3.50527i	−1.25094	+	0.198129i	−0.504400	+	0.863470i	$0.668286\pi$
$314$	0.767117	−	0.0930858i	0.0432909	−	0.00525313i
$315$		0			0
$316$	−15.4071	−	1.12130i	−0.866715	−	0.0630780i
$317$	−12.6376	+	24.8027i	−0.709799	+	1.39306i	0.200744	+	0.979644i	$0.435664\pi$
$317$	−12.6376	+	24.8027i	−0.709799	+	1.39306i	−0.910543	+	0.413415i	$0.864336\pi$
$318$		0			0
$319$	−10.4150	−	32.0540i	−0.583126	−	1.79468i
$320$	14.8004	+	10.0473i	0.827367	+	0.561662i
$321$		0			0
$322$	−0.846940	+	23.3053i	−0.0471981	+	1.29875i
$323$	1.15511	+	0.182951i	0.0642720	+	0.0101797i
$324$		0			0
$325$	−7.92118	+	6.10755i	−0.439388	+	0.338786i
$326$	−6.11287	−	3.39976i	−0.338561	−	0.188296i
$327$		0			0
$328$	−12.0671	−	21.1078i	−0.666294	−	1.16548i
$329$	2.63759	+	0.857003i	0.145415	+	0.0472481i
$330$		0			0
$331$	−24.0903	+	7.82740i	−1.32412	+	0.430233i	−0.883908	−	0.467661i	$-0.845097\pi$
$331$	−24.0903	+	7.82740i	−1.32412	+	0.430233i	−0.440212	+	0.897894i	$0.645097\pi$
$332$	7.55685	+	1.76723i	0.414736	+	0.0969894i
$333$		0			0
$334$	−9.11877	+	4.23642i	−0.498957	+	0.231806i
$335$	−30.2199	−	6.80103i	−1.65109	−	0.371580i
$336$		0			0
$337$	4.33483	+	27.3690i	0.236133	+	1.49089i	0.766020	+	0.642817i	$0.222235\pi$
$337$	4.33483	+	27.3690i	0.236133	+	1.49089i	−0.529886	+	0.848069i	$0.677765\pi$
$338$	4.36925	−	11.9516i	0.237656	−	0.650083i
$339$		0			0
$340$	2.72218	−	0.0548485i	0.147631	−	0.00297458i
$341$	28.6884	+	20.8433i	1.55356	+	1.12873i
$342$		0			0
$343$	−11.0190	−	11.0190i	−0.594969	−	0.594969i
$344$	8.05359	+	21.2502i	0.434221	+	1.14573i
$345$		0			0
$346$	2.68144	+	2.88368i	0.144155	+	0.155027i
$347$	6.28919	+	12.3432i	0.337621	+	0.662619i	0.995930	−	0.0901287i	$-0.0287278\pi$
$347$	6.28919	+	12.3432i	0.337621	+	0.662619i	−0.658309	+	0.752748i	$0.728728\pi$
$348$		0			0
$349$			20.4056i			1.09229i	0.837692	+	0.546144i	$0.183905\pi$
$349$			20.4056i			1.09229i	−0.837692	+	0.546144i	$0.816095\pi$
$350$	17.2992	+	24.2057i	0.924681	+	1.29385i
$351$		0			0
$352$	22.8147	−	10.9279i	1.21603	−	0.582456i
$353$	−0.651505	−	1.27865i	−0.0346761	−	0.0680557i	0.873018	−	0.487687i	$-0.162159\pi$
$353$	−0.651505	−	1.27865i	−0.0346761	−	0.0680557i	−0.907695	+	0.419631i	$0.862159\pi$
$354$		0			0
$355$	19.3749	+	1.24721i	1.02831	+	0.0661948i
$356$	−2.90139	+	3.43789i	−0.153773	+	0.182208i
$357$		0			0
$358$	11.7923	+	17.5365i	0.623244	+	0.926831i
$359$	−3.09530	−	2.24886i	−0.163364	−	0.118691i	0.503100	−	0.864228i	$-0.332193\pi$
$359$	−3.09530	−	2.24886i	−0.163364	−	0.118691i	−0.666463	+	0.745538i	$0.732193\pi$
$360$		0			0
$361$	12.3860	−	8.99898i	0.651897	−	0.473631i
$362$	−5.43509	−	1.98695i	−0.285662	−	0.104432i
$363$		0			0
$364$	15.5905	+	6.35047i	0.817163	+	0.332855i
$365$	3.21685	+	34.5662i	0.168378	+	1.80928i
$366$		0			0
$367$	2.79735	+	1.42532i	0.146021	+	0.0744013i	0.525474	−	0.850810i	$-0.323888\pi$
$367$	2.79735	+	1.42532i	0.146021	+	0.0744013i	−0.379453	+	0.925211i	$0.623888\pi$
$368$	−14.8514	+	5.01966i	−0.774181	+	0.261668i
$369$		0			0
$370$	1.09017	+	0.287311i	0.0566750	+	0.0149366i
$371$	31.6067	+	10.2696i	1.64094	+	0.533173i
$372$		0			0
$373$	−4.32797	+	27.3257i	−0.224094	+	1.41487i	0.577201	+	0.816602i	$0.304145\pi$
$373$	−4.32797	+	27.3257i	−0.224094	+	1.41487i	−0.801295	+	0.598270i	$0.795855\pi$
$374$	1.87144	−	3.36490i	0.0967698	−	0.173995i
$375$		0			0
$376$	0.0896461	+	1.86214i	0.00462314	+	0.0960324i
$377$	14.8915	+	2.35858i	0.766950	+	0.121473i
$378$		0			0
$379$	−2.21616	+	6.82062i	−0.113836	+	0.350352i	−0.991703	−	0.128554i	$-0.958966\pi$
$379$	−2.21616	+	6.82062i	−0.113836	+	0.350352i	0.877866	+	0.478906i	$0.158966\pi$
$380$	−5.95094	+	6.19568i	−0.305277	+	0.317832i
$381$		0			0
$382$	−9.61540	−	33.7133i	−0.491967	−	1.72492i
$383$	−10.4506	+	20.5104i	−0.533999	+	1.04803i	0.453625	+	0.891193i	$0.350131\pi$
$383$	−10.4506	+	20.5104i	−0.533999	+	1.04803i	−0.987624	+	0.156840i	$0.949869\pi$
$384$		0			0
$385$	41.8923	−	3.89864i	2.13503	−	0.198693i
$386$	2.36919	+	19.5244i	0.120588	+	0.993766i
$387$		0			0
$388$	−0.226457	−	0.262007i	−0.0114966	−	0.0133014i
$389$	9.12189	+	12.5552i	0.462498	+	0.636574i	0.975025	−	0.222097i	$-0.0712902\pi$
$389$	9.12189	+	12.5552i	0.462498	+	0.636574i	−0.512526	+	0.858672i	$0.671290\pi$
$390$		0			0
$391$	−1.40250	+	1.93038i	−0.0709276	+	0.0976234i
$392$	12.4313	−	27.6044i	0.627875	−	1.39423i
$393$		0			0
$394$	1.58658	−	8.10088i	0.0799307	−	0.408116i
$395$	1.10949	−	17.2355i	0.0558243	−	0.867212i
$396$		0			0
$397$	−4.75804	+	2.42434i	−0.238799	+	0.121674i	−0.569295	−	0.822133i	$-0.692784\pi$
$397$	−4.75804	+	2.42434i	−0.238799	+	0.121674i	0.330496	+	0.943807i	$0.392784\pi$
$398$	16.3917	−	20.9192i	0.821643	−	1.04859i
$399$		0			0
$400$	−11.0944	+	16.6407i	−0.554720	+	0.832037i
$401$	15.4424			0.771156			0.385578	−	0.922675i	$-0.374002\pi$
$401$	15.4424			0.771156			0.385578	+	0.922675i	$0.374002\pi$
$402$		0			0
$403$	−14.1342	+	7.20174i	−0.704075	+	0.358744i
$404$	8.80346	+	35.7404i	0.437989	+	1.77815i
$405$		0			0
$406$	8.61960	−	44.0106i	0.427784	−	2.18421i
$407$	1.12733	−	1.12733i	0.0558795	−	0.0558795i
$408$		0			0
$409$	4.68229	−	6.44461i	0.231524	−	0.318666i	−0.677410	−	0.735606i	$-0.736898\pi$
$409$	4.68229	−	6.44461i	0.231524	−	0.318666i	0.908934	+	0.416940i	$0.136898\pi$
$410$	23.4855	−	13.6884i	1.15987	−	0.676022i
$411$		0			0
$412$	−18.7448	−	21.6874i	−0.923491	−	1.06846i
$413$	−20.1063	+	3.18452i	−0.989366	+	0.156700i
$414$		0			0
$415$	−1.90507	+	8.46505i	−0.0935161	+	0.415533i
$416$	−0.277742	+	11.3130i	−0.0136174	+	0.554664i
$417$		0			0
$418$	3.33199	+	11.6825i	0.162973	+	0.571412i
$419$	−9.73628	−	29.9652i	−0.475648	−	1.46390i	−0.845081	−	0.534638i	$-0.820448\pi$
$419$	−9.73628	−	29.9652i	−0.475648	−	1.46390i	0.369433	−	0.929257i	$-0.379552\pi$
$420$		0			0
$421$	2.55003	−	7.84818i	0.124281	−	0.382497i	−0.869489	−	0.493953i	$-0.835551\pi$
$421$	2.55003	−	7.84818i	0.124281	−	0.382497i	0.993769	+	0.111456i	$0.0355515\pi$
$422$	−3.88558	−	0.141206i	−0.189147	−	0.00687381i
$423$		0			0
$424$	1.07425	+	22.3143i	0.0521700	+	1.08368i
$425$	0.0867842	+	3.04286i	0.00420965	+	0.147601i
$426$		0			0
$427$	−0.132343	+	0.835584i	−0.00640455	+	0.0404367i
$428$	−3.23456	−	1.95603i	−0.156348	−	0.0945482i
$429$		0			0
$430$	−23.6823	+	9.20266i	−1.14206	+	0.443791i
$431$	−1.18372	+	0.384614i	−0.0570178	+	0.0185262i	−0.337387	−	0.941366i	$-0.609543\pi$
$431$	−1.18372	+	0.384614i	−0.0570178	+	0.0185262i	0.280369	+	0.959892i	$0.409543\pi$
$432$		0			0
$433$	6.80504	+	3.46734i	0.327030	+	0.166630i	0.609795	−	0.792559i	$-0.291252\pi$
$433$	6.80504	+	3.46734i	0.327030	+	0.166630i	−0.282765	+	0.959189i	$0.591252\pi$
$434$	19.8806	+	42.7924i	0.954297	+	2.05410i
$435$		0			0
$436$	−35.0670	−	14.2838i	−1.67940	−	0.684071i
$437$	−1.17772	−	7.43583i	−0.0563380	−	0.355704i
$438$		0			0
$439$	−14.0786	+	10.2287i	−0.671934	+	0.488189i	−0.870672	−	0.491864i	$-0.836316\pi$
$439$	−14.0786	+	10.2287i	−0.671934	+	0.488189i	0.198738	+	0.980053i	$0.436316\pi$
$440$	12.4307	+	25.4045i	0.592610	+	1.21111i
$441$		0			0
$442$	0.961133	+	1.42931i	0.0457165	+	0.0679853i
$443$	3.46818	+	3.46818i	0.164778	+	0.164778i	0.784680	−	0.619901i	$-0.212827\pi$
$443$	3.46818	+	3.46818i	0.164778	+	0.164778i	−0.619901	+	0.784680i	$0.712827\pi$
$444$		0			0
$445$	−3.87068	−	3.21158i	−0.183488	−	0.152244i
$446$	8.36200	−	7.77554i	0.395952	−	0.368182i
$447$		0			0
$448$	33.5982	+	2.04768i	1.58737	+	0.0967438i
$449$		−	21.8988i		−	1.03347i	−0.856146	−	0.516735i	$-0.827147\pi$
$449$		−	21.8988i		−	1.03347i	0.856146	−	0.516735i	$-0.172853\pi$
$450$		0			0
$451$		−	38.4411i		−	1.81012i
$452$	−12.4896	−	29.6573i	−0.587461	−	1.39496i
$453$		0			0
$454$	−4.23042	−	4.54950i	−0.198544	−	0.213518i
$455$	−6.95396	+	17.4895i	−0.326007	+	0.819920i
$456$		0			0
$457$	13.8191	+	13.8191i	0.646428	+	0.646428i	0.952128	−	0.305700i	$-0.0988904\pi$
$457$	13.8191	+	13.8191i	0.646428	+	0.646428i	−0.305700	+	0.952128i	$0.598890\pi$
$458$	−4.80196	+	3.22906i	−0.224381	+	0.150884i
$459$		0			0
$460$	−5.75088	−	16.5568i	−0.268136	−	0.771964i
$461$	13.8474	−	10.0607i	0.644936	−	0.468574i	−0.216606	−	0.976259i	$-0.569499\pi$
$461$	13.8474	−	10.0607i	0.644936	−	0.468574i	0.861543	+	0.507685i	$0.169499\pi$
$462$		0			0
$463$	−4.11100	−	25.9559i	−0.191055	−	1.20627i	−0.877675	−	0.479255i	$-0.840907\pi$
$463$	−4.11100	−	25.9559i	−0.191055	−	1.20627i	0.686621	−	0.727016i	$-0.259093\pi$
$464$	29.7183	−	5.06644i	1.37964	−	0.235204i
$465$		0			0
$466$	33.6547	−	15.6354i	1.55903	−	0.724295i
$467$	−1.86381	−	0.949661i	−0.0862471	−	0.0439451i	0.410335	−	0.911935i	$-0.365412\pi$
$467$	−1.86381	−	0.949661i	−0.0862471	−	0.0439451i	−0.496582	+	0.867990i	$0.665412\pi$
$468$		0			0
$469$	−55.4338	+	18.0115i	−2.55969	+	0.831695i
$470$	−2.08102	+	0.117643i	−0.0959903	+	0.00542645i
$471$		0			0
$472$	−6.79171	−	11.8801i	−0.312614	−	0.546824i
$473$	−5.62062	+	35.4872i	−0.258436	+	1.63170i
$474$		0			0
$475$	−6.98241	−	6.59517i	−0.320375	−	0.302607i
$476$	4.35249	−	2.70260i	0.199496	−	0.123873i
$477$		0			0
$478$	0.100073	−	2.75371i	0.00457723	−	0.125952i
$479$	−5.01981	+	15.4494i	−0.229361	+	0.705901i	0.768459	+	0.639900i	$0.221024\pi$
$479$	−5.01981	+	15.4494i	−0.229361	+	0.705901i	−0.997820	+	0.0660010i	$0.978976\pi$
$480$		0			0
$481$	0.220389	+	0.678287i	0.0100489	+	0.0309272i
$482$	36.8480	−	10.5095i	1.67838	−	0.478693i
$483$		0			0
$484$	17.9480	+	1.30623i	0.815820	+	0.0593740i
$485$	0.290804	−	0.255629i	0.0132047	−	0.0116075i
$486$		0			0
$487$	6.22862	−	0.986516i	0.282246	−	0.0447033i	−0.0137066	−	0.999906i	$-0.504363\pi$
$487$	6.22862	−	0.986516i	0.282246	−	0.0447033i	0.295952	+	0.955203i	$0.404363\pi$
$488$	−0.556772	+	0.115871i	−0.0252039	+	0.00524525i
$489$		0			0
$490$	30.9778	+	13.6399i	1.39944	+	0.616188i
$491$	1.68713	−	2.32213i	0.0761390	−	0.104796i	−0.769249	−	0.638949i	$-0.779369\pi$
$491$	1.68713	−	2.32213i	0.0761390	−	0.104796i	0.845388	+	0.534153i	$0.179369\pi$
$492$		0			0
$493$	3.24459	−	3.24459i	0.146129	−	0.146129i
$494$	−5.33320	−	1.04452i	−0.239952	−	0.0469953i
$495$		0			0
$496$	−22.1629	+	22.6913i	−0.995143	+	1.01887i
$497$	32.5510	−	16.5856i	1.46011	−	0.743965i
$498$		0			0
$499$	27.4468			1.22869			0.614345	−	0.789038i	$-0.289420\pi$
$499$	27.4468			1.22869			0.614345	+	0.789038i	$0.289420\pi$
$500$	−18.7080	−	12.2478i	−0.836649	−	0.547739i
$501$		0			0
$502$	6.96498	+	5.45757i	0.310862	+	0.243583i
$503$	28.9075	−	14.7291i	1.28892	−	0.656738i	0.330963	−	0.943644i	$-0.392627\pi$
$503$	28.9075	−	14.7291i	1.28892	−	0.656738i	0.957959	+	0.286906i	$0.0926266\pi$
$504$		0			0
$505$	−39.8752	+	10.1765i	−1.77443	+	0.452850i
$506$	−24.3236	−	4.76384i	−1.08132	−	0.211779i
$507$		0			0
$508$	12.8981	−	1.09157i	0.572260	−	0.0484307i
$509$	−16.3968	+	22.5682i	−0.726773	+	1.00032i	0.272498	+	0.962156i	$0.412150\pi$
$509$	−16.3968	+	22.5682i	−0.726773	+	1.00032i	−0.999272	+	0.0381615i	$0.987850\pi$
$510$		0			0
$511$	38.3963	+	52.8479i	1.69855	+	2.33785i
$512$	6.71696	+	21.6075i	0.296850	+	0.954924i
$513$		0			0
$514$	20.7516	−	2.51810i	0.915314	−	0.111069i
$515$	24.0711	−	21.1595i	1.06070	−	0.932398i
$516$		0			0
$517$	−1.33816	+	2.62628i	−0.0588520	+	0.115504i
$518$	2.04004	−	0.581841i	0.0896341	−	0.0255646i
$519$		0			0
$520$	−12.6504	−	0.204690i	−0.554759	−	0.00897624i
$521$	3.47813	−	10.7046i	0.152380	−	0.468976i	−0.845506	−	0.533965i	$-0.820701\pi$
$521$	3.47813	−	10.7046i	0.152380	−	0.468976i	0.997886	+	0.0649893i	$0.0207013\pi$
$522$		0			0
$523$	0.240669	+	0.0381182i	0.0105237	+	0.00166679i	0.161694	−	0.986841i	$-0.448304\pi$
$523$	0.240669	+	0.0381182i	0.0105237	+	0.00166679i	−0.151170	+	0.988508i	$0.548304\pi$
$524$	6.41463	+	10.3307i	0.280225	+	0.451297i
$525$		0			0
$526$	38.5956	+	21.4655i	1.68285	+	0.935942i
$527$	−0.755231	+	4.76834i	−0.0328984	+	0.207712i
$528$		0			0
$529$	−7.26607	−	2.36089i	−0.315916	−	0.102647i
$530$	−24.9373	+	1.40974i	−1.08321	+	0.0612350i
$531$		0			0
$532$	−3.68100	+	15.7403i	−0.159591	+	0.682428i
$533$	15.3221	+	7.80700i	0.663674	+	0.338159i
$534$		0			0
$535$	2.15657	−	3.63452i	0.0932368	−	0.157134i
$536$	−24.5280	−	30.5545i	−1.05945	−	1.31975i
$537$		0			0
$538$	11.0753	−	30.2955i	0.477492	−	1.30613i
$539$	38.7239	−	28.1345i	1.66795	−	1.21184i
$540$		0			0
$541$	−8.89390	−	6.46179i	−0.382378	−	0.277814i	0.379947	−	0.925008i	$-0.375942\pi$
$541$	−8.89390	−	6.46179i	−0.382378	−	0.277814i	−0.762325	+	0.647194i	$0.775942\pi$
$542$	−13.8483	+	9.31226i	−0.594836	+	0.399996i
$543$		0			0
$544$	2.73574	+	2.09211i	0.117294	+	0.0896986i
$545$	15.6412	−	39.3383i	0.669996	−	1.68507i
$546$		0			0
$547$	−2.33918	−	4.59090i	−0.100016	−	0.196293i	0.835576	−	0.549374i	$-0.185134\pi$
$547$	−2.33918	−	4.59090i	−0.100016	−	0.196293i	−0.935593	+	0.353081i	$0.885134\pi$
$548$	28.3224	−	11.9274i	1.20987	−	0.509515i
$549$		0			0
$550$	−28.2858	+	14.1351i	−1.20611	+	0.602722i
$551$			14.4777i			0.616770i
$552$		0			0
$553$	−14.7542	−	28.9567i	−0.627411	−	1.23136i
$554$	−3.39151	+	3.15365i	−0.144092	+	0.133986i
$555$		0			0
$556$	6.85222	+	5.78290i	0.290599	+	0.245250i
$557$	−10.4222	−	10.4222i	−0.441602	−	0.441602i	0.450948	−	0.892550i	$-0.351086\pi$
$557$	−10.4222	−	10.4222i	−0.441602	−	0.441602i	−0.892550	+	0.450948i	$0.851086\pi$
$558$		0			0
$559$	−13.0032	−	9.44740i	−0.549978	−	0.399582i
$560$	−1.97501	+	37.5818i	−0.0834595	+	1.58812i
$561$		0			0
$562$	15.4852	+	5.66104i	0.653204	+	0.238797i
$563$	−0.803478	−	5.07296i	−0.0338626	−	0.213800i	0.964955	−	0.262415i	$-0.0845191\pi$
$563$	−0.803478	−	5.07296i	−0.0338626	−	0.213800i	−0.998818	+	0.0486155i	$0.984519\pi$
$564$		0			0
$565$	33.0398	−	14.2407i	1.39000	−	0.599111i
$566$	−12.9458	−	27.8654i	−0.544151	−	1.17127i
$567$		0			0
$568$	18.1803	+	16.5102i	0.762827	+	0.692753i
$569$	−5.62370	+	1.82725i	−0.235758	+	0.0766024i	−0.424513	−	0.905422i	$-0.639555\pi$
$569$	−5.62370	+	1.82725i	−0.235758	+	0.0766024i	0.188755	+	0.982024i	$0.439555\pi$
$570$		0			0
$571$	−29.8755	−	9.70715i	−1.25025	−	0.406232i	−0.392241	−	0.919862i	$-0.628300\pi$
$571$	−29.8755	−	9.70715i	−1.25025	−	0.406232i	−0.858011	+	0.513631i	$0.828300\pi$
$572$	−9.25841	+	15.3100i	−0.387114	+	0.640145i
$573$		0			0
$574$	24.8617	−	44.7021i	1.03771	−	1.86583i
$575$	18.4566	−	6.58433i	0.769694	−	0.274585i
$576$		0			0
$577$	−7.16441	−	1.13473i	−0.298258	−	0.0472395i	0.00551184	−	0.999985i	$-0.498246\pi$
$577$	−7.16441	−	1.13473i	−0.298258	−	0.0472395i	−0.303770	+	0.952745i	$0.598246\pi$
$578$	−23.5019	−	0.854085i	−0.977551	−	0.0355253i
$579$		0			0
$580$	5.94225	+	33.1775i	0.246738	+	1.37762i
$581$	5.04529	+	15.5278i	0.209314	+	0.644202i
$582$		0			0
$583$	−16.0354	+	31.4712i	−0.664118	+	1.30340i
$584$	−24.0727	+	36.7257i	−0.996137	+	1.51972i
$585$		0			0
$586$	−1.48054	−	12.2011i	−0.0611607	−	0.504024i
$587$	−1.51204	+	0.239484i	−0.0624086	+	0.00988455i	−0.187561	−	0.982253i	$-0.560058\pi$
$587$	−1.51204	+	0.239484i	−0.0624086	+	0.00988455i	0.125152	+	0.992138i	$0.460058\pi$
$588$		0			0
$589$	−8.95345	−	12.3234i	−0.368921	−	0.507776i
$590$	13.2183	−	7.70423i	0.544189	−	0.317178i
$591$		0			0
$592$	0.851742	+	1.14374i	0.0350064	+	0.0470076i
$593$	−20.7780	+	20.7780i	−0.853251	+	0.853251i	−0.990532	−	0.137281i	$-0.956164\pi$
$593$	−20.7780	+	20.7780i	−0.853251	+	0.853251i	0.137281	+	0.990532i	$0.456164\pi$
$594$		0			0
$595$	3.06221	+	4.84078i	0.125538	+	0.198453i
$596$	7.35397	−	1.81141i	0.301231	−	0.0741981i
$597$		0			0
$598$	6.83868	−	8.72757i	0.279655	−	0.356897i
$599$	−4.16436			−0.170151			−0.0850756	−	0.996374i	$-0.527113\pi$
$599$	−4.16436			−0.170151			−0.0850756	+	0.996374i	$0.527113\pi$
$600$		0			0
$601$	−33.1465			−1.35207			−0.676037	−	0.736868i	$-0.736304\pi$
$601$	−33.1465			−1.35207			−0.676037	+	0.736868i	$0.736304\pi$
$602$	−29.4874	+	37.6320i	−1.20182	+	1.53376i
$603$		0			0
$604$	21.8876	−	5.39128i	0.890594	−	0.219368i
$605$	−1.29247	+	20.0780i	−0.0525462	+	0.816288i
$606$		0			0
$607$	−7.14827	+	7.14827i	−0.290139	+	0.290139i	−0.837135	−	0.546996i	$-0.815771\pi$
$607$	−7.14827	+	7.14827i	−0.290139	+	0.290139i	0.546996	+	0.837135i	$0.315771\pi$
$608$	−10.7712	+	1.43596i	−0.436829	+	0.0582360i
$609$		0			0
$610$	−0.134752	−	0.621384i	−0.00545594	−	0.0251591i
$611$	−0.775034	−	1.06674i	−0.0313545	−	0.0431558i
$612$		0			0
$613$	30.3792	−	4.81159i	1.22700	−	0.194338i	0.490905	−	0.871213i	$-0.336666\pi$
$613$	30.3792	−	4.81159i	1.22700	−	0.194338i	0.736098	+	0.676875i	$0.236666\pi$
$614$	−0.551714	−	4.54666i	−0.0222654	−	0.183488i
$615$		0			0
$616$	44.5094	+	29.1748i	1.79334	+	1.17549i
$617$	10.1605	−	19.9410i	0.409045	−	0.802795i	−0.590948	−	0.806710i	$-0.701246\pi$
$617$	10.1605	−	19.9410i	0.409045	−	0.802795i	0.999992	+	0.00391467i	$0.00124608\pi$
$618$		0			0
$619$	11.2635	+	34.6654i	0.452717	+	1.39332i	0.873794	+	0.486296i	$0.161652\pi$
$619$	11.2635	+	34.6654i	0.452717	+	1.39332i	−0.421077	+	0.907025i	$0.638348\pi$
$620$	−25.5760	−	24.5657i	−1.02716	−	0.986584i
$621$		0			0
$622$	−15.2813	−	0.555339i	−0.612725	−	0.0222671i
$623$	−9.34750	−	1.48050i	−0.374500	−	0.0593149i
$624$		0			0
$625$	13.5180	−	21.0301i	0.540720	−	0.841203i
$626$	15.4023	−	27.6937i	0.615598	−	1.10686i
$627$		0			0
$628$	−0.565502	+	0.935133i	−0.0225660	+	0.0373159i
$629$	0.206429	+	0.0670727i	0.00823085	+	0.00267437i
$630$		0			0
$631$	7.96006	−	2.58638i	0.316885	−	0.102962i	−0.146256	−	0.989247i	$-0.546722\pi$
$631$	7.96006	−	2.58638i	0.316885	−	0.102962i	0.463141	+	0.886285i	$0.346722\pi$
$632$	14.6871	−	16.1728i	0.584222	−	0.643318i
$633$		0			0
$634$	−16.5866	−	35.7023i	−0.658739	−	1.41792i
$635$	1.34102	+	14.4098i	0.0532169	+	0.571835i
$636$		0			0
$637$	3.34962	+	21.1487i	0.132717	+	0.837940i
$638$	44.7664	+	16.3656i	1.77232	+	0.647919i
$639$		0			0
$640$	−24.0942	+	7.71165i	−0.952407	+	0.304830i
$641$	22.9480	+	16.6727i	0.906390	+	0.658531i	0.940099	−	0.340901i	$-0.110732\pi$
$641$	22.9480	+	16.6727i	0.906390	+	0.658531i	−0.0337091	+	0.999432i	$0.510732\pi$
$642$		0			0
$643$	24.7384	+	24.7384i	0.975586	+	0.975586i	0.999709	−	0.0241234i	$-0.00767947\pi$
$643$	24.7384	+	24.7384i	0.975586	+	0.975586i	−0.0241234	+	0.999709i	$0.507679\pi$
$644$	−25.2042	−	21.2710i	−0.993186	−	0.838195i
$645$		0			0
$646$	−1.21121	+	1.12626i	−0.0476544	+	0.0443122i
$647$	−4.89479	−	9.60656i	−0.192434	−	0.377673i	0.774549	−	0.632514i	$-0.217977\pi$
$647$	−4.89479	−	9.60656i	−0.192434	−	0.377673i	−0.966983	+	0.254841i	$0.917977\pi$
$648$		0			0
$649$		−	21.6357i		−	0.849277i
$650$	0.110507	−	14.1450i	0.00433445	−	0.554814i
$651$		0			0
$652$	9.11654	−	3.83926i	0.357031	−	0.150357i
$653$	1.50600	+	2.95569i	0.0589343	+	0.115665i	0.918595	−	0.395201i	$-0.129325\pi$
$653$	1.50600	+	2.95569i	0.0589343	+	0.115665i	−0.859661	+	0.510866i	$0.829325\pi$
$654$		0			0
$655$	−11.4896	+	7.26816i	−0.448937	+	0.283991i
$656$	34.0223	+	4.97854i	1.32835	+	0.194379i
$657$		0			0
$658$	−3.25465	+	2.18858i	−0.126879	+	0.0853197i
$659$	−16.2441	−	11.8020i	−0.632779	−	0.459741i	0.224583	−	0.974455i	$-0.427898\pi$
$659$	−16.2441	−	11.8020i	−0.632779	−	0.459741i	−0.857362	+	0.514714i	$0.827898\pi$
$660$		0			0
$661$	−36.3648	+	26.4206i	−1.41443	+	1.02764i	−0.421766	+	0.906705i	$0.638590\pi$
$661$	−36.3648	+	26.4206i	−1.41443	+	1.02764i	−0.992660	+	0.120937i	$0.961410\pi$
$662$	12.2996	−	33.6443i	0.478037	−	1.30762i
$663$		0			0
$664$	−8.55876	+	6.87065i	−0.332144	+	0.266633i
$665$	−17.6320	−	3.96810i	−0.683739	−	0.153876i
$666$		0			0
$667$	−26.3185	−	13.4100i	−1.01906	−	0.519236i
$668$	3.23802	−	13.8461i	0.125283	−	0.535721i
$669$		0			0
$670$	33.9303	−	27.7080i	1.31084	−	1.07045i
$671$	−0.855138	−	0.277851i	−0.0330122	−	0.0107263i
$672$		0			0
$673$	5.35354	−	33.8009i	0.206364	−	1.30293i	−0.639194	−	0.769045i	$-0.720732\pi$
$673$	5.35354	−	33.8009i	0.206364	−	1.30293i	0.845558	−	0.533884i	$-0.179268\pi$
$674$	−34.2477	−	19.0474i	−1.31917	−	0.733678i
$675$		0			0
$676$	9.49321	+	15.2887i	0.365123	+	0.588025i
$677$	16.1587	+	2.55928i	0.621029	+	0.0983613i	0.459017	−	0.888428i	$-0.348202\pi$
$677$	16.1587	+	2.55928i	0.621029	+	0.0983613i	0.162012	+	0.986789i	$0.448202\pi$
$678$		0			0
$679$	0.225137	−	0.692902i	0.00863998	−	0.0265911i
$680$	−2.31338	+	3.07811i	−0.0887141	+	0.118040i
$681$		0			0
$682$	−48.2260	+	13.7546i	−1.84667	+	0.526690i
$683$	2.58511	−	5.07357i	0.0989167	−	0.194135i	−0.836245	−	0.548356i	$-0.815254\pi$
$683$	2.58511	−	5.07357i	0.0989167	−	0.194135i	0.935162	+	0.354221i	$0.115254\pi$
$684$		0			0
$685$	13.5998	+	31.5527i	0.519620	+	1.20557i
$686$	21.8775	−	2.65472i	0.835286	−	0.101358i
$687$		0			0
$688$	−30.6801	−	9.57052i	−1.16967	−	0.364873i
$689$	−9.28738	−	12.7830i	−0.353821	−	0.486993i
$690$		0			0
$691$	5.24350	−	7.21706i	0.199472	−	0.274550i	−0.697549	−	0.716537i	$-0.745726\pi$
$691$	5.24350	−	7.21706i	0.199472	−	0.274550i	0.897022	+	0.441987i	$0.145726\pi$
$692$	−5.54895	+	0.469611i	−0.210939	+	0.0178519i
$693$		0			0
$694$	−19.2260	−	3.76547i	−0.729810	−	0.142935i
$695$	−6.40116	+	7.71484i	−0.242810	+	0.292641i
$696$		0			0
$697$	4.66310	−	2.37597i	0.176628	−	0.0899963i
$698$	−22.7151	−	17.7989i	−0.859779	−	0.673699i
$699$		0			0
$700$	−42.0347	−	1.85651i	−1.58876	−	0.0701693i
$701$	−41.1910			−1.55576			−0.777880	−	0.628412i	$-0.783705\pi$
$701$	−41.1910			−1.55576			−0.777880	+	0.628412i	$0.783705\pi$
$702$		0			0
$703$	−0.610196	+	0.310910i	−0.0230140	+	0.0117262i
$704$	−7.73561	+	34.9287i	−0.291547	+	1.31643i
$705$		0			0
$706$	1.99165	+	0.390070i	0.0749566	+	0.0146805i
$707$	−54.7565	+	54.7565i	−2.05933	+	2.05933i
$708$		0			0
$709$	−21.9274	+	30.1804i	−0.823500	+	1.13345i	0.165598	+	0.986193i	$0.447044\pi$
$709$	−21.9274	+	30.1804i	−0.823500	+	1.13345i	−0.989098	+	0.147257i	$0.952956\pi$
$710$	−18.2883	+	20.4799i	−0.686347	+	0.768597i
$711$		0			0
$712$	−1.29623	−	6.22849i	−0.0485782	−	0.233422i
$713$	30.6954	−	4.86168i	1.14955	−	0.182071i
$714$		0			0
$715$	−17.2031	−	10.2076i	−0.643361	−	0.381744i
$716$	−29.8072	−	2.16931i	−1.11395	−	0.0810711i
$717$		0			0
$718$	5.20328	−	1.48403i	0.194185	−	0.0553836i
$719$	−14.0058	−	43.1054i	−0.522327	−	1.60756i	−0.769541	−	0.638597i	$-0.779515\pi$
$719$	−14.0058	−	43.1054i	−0.522327	−	1.60756i	0.247214	−	0.968961i	$-0.420485\pi$
$720$		0			0
$721$	18.6356	−	57.3544i	0.694025	−	2.13599i
$722$	−0.786323	+	21.6373i	−0.0292639	+	0.805257i
$723$		0			0
$724$	6.95263	−	4.31710i	0.258392	−	0.160444i
$725$	−37.0367	+	6.95375i	−1.37551	+	0.258256i
$726$		0			0
$727$	−3.93735	+	24.8594i	−0.146028	+	0.921985i	0.800493	+	0.599342i	$0.204571\pi$
$727$	−3.93735	+	24.8594i	−0.146028	+	0.921985i	−0.946521	+	0.322643i	$0.895429\pi$
$728$	−20.6681	+	11.8158i	−0.766011	+	0.437921i
$729$		0			0
$730$	−41.2843	−	26.5697i	−1.52800	−	0.983388i
$731$	−4.65218	+	1.51159i	−0.172067	+	0.0559080i
$732$		0			0
$733$	4.41985	+	2.25203i	0.163251	+	0.0831804i	0.533707	−	0.845670i	$-0.320799\pi$
$733$	4.41985	+	2.25203i	0.163251	+	0.0831804i	−0.370456	+	0.928850i	$0.620799\pi$
$734$	−4.02665	+	1.87071i	−0.148626	+	0.0690491i
$735$		0			0
$736$	7.36642	−	20.9107i	0.271530	−	0.770777i
$737$	−9.69082	−	61.1854i	−0.356966	−	2.25379i
$738$		0			0
$739$	38.2860	−	27.8164i	1.40837	−	1.02324i	0.414815	−	0.909906i	$-0.363846\pi$
$739$	38.2860	−	27.8164i	1.40837	−	1.02324i	0.993557	−	0.113336i	$-0.0361537\pi$
$740$	−1.27073	+	0.962942i	−0.0467131	+	0.0353984i
$741$		0			0
$742$	−39.0011	+	26.2262i	−1.43178	+	0.962793i
$743$	11.8611	+	11.8611i	0.435143	+	0.435143i	0.890373	−	0.455231i	$-0.150443\pi$
$743$	11.8611	+	11.8611i	0.435143	+	0.435143i	−0.455231	+	0.890373i	$0.650443\pi$
$744$		0			0
$745$	2.09393	+	8.20476i	0.0767158	+	0.300599i
$746$	−26.6433	−	28.6528i	−0.975481	−	1.04906i
$747$		0			0
$748$	2.11336	+	5.01830i	0.0772721	+	0.183487i
$749$		−	7.95230i		−	0.290571i
$750$		0			0
$751$		−	4.27171i		−	0.155877i	−0.996958	−	0.0779385i	$-0.975166\pi$
$751$		−	4.27171i		−	0.155877i	0.996958	−	0.0779385i	$-0.0248338\pi$
$752$	−2.15109	−	1.52447i	−0.0784421	−	0.0555917i
$753$		0			0
$754$	−15.6147	+	14.5196i	−0.568654	+	0.528772i
$755$	6.23217	+	24.4198i	0.226812	+	0.888727i
$756$		0			0
$757$	−7.67460	−	7.67460i	−0.278938	−	0.278938i	0.553747	−	0.832685i	$-0.313197\pi$
$757$	−7.67460	−	7.67460i	−0.278938	−	0.278938i	−0.832685	+	0.553747i	$0.813197\pi$
$758$	−5.65952	−	8.41631i	−0.205563	−	0.305694i
$759$		0			0
$760$	−1.70616	−	12.0287i	−0.0618888	−	0.436327i
$761$	0.148940	−	0.108211i	0.00539906	−	0.00392265i	−0.585082	−	0.810974i	$-0.698938\pi$
$761$	0.148940	−	0.108211i	0.00539906	−	0.00392265i	0.590482	+	0.807051i	$0.298938\pi$
$762$		0			0
$763$	−12.4614	−	78.6779i	−0.451131	−	2.84833i
$764$	45.9160	+	18.7030i	1.66118	+	0.676650i
$765$		0			0
$766$	−13.7162	−	29.5237i	−0.495585	−	1.06673i
$767$	8.62372	+	4.39400i	0.311384	+	0.158658i
$768$		0			0
$769$	32.7868	−	10.6531i	1.18232	−	0.384160i	0.349094	−	0.937088i	$-0.386489\pi$
$769$	32.7868	−	10.6531i	1.18232	−	0.384160i	0.833229	+	0.552928i	$0.186489\pi$
$770$	−32.2009	+	50.0342i	−1.16044	+	1.80311i
$771$		0			0
$772$	−23.8007	−	14.3930i	−0.856606	−	0.518014i
$773$	−2.09760	+	13.2437i	−0.0754454	+	0.476344i	0.920819	+	0.389990i	$0.127521\pi$
$773$	−2.09760	+	13.2437i	−0.0754454	+	0.476344i	−0.996265	+	0.0863536i	$0.972479\pi$
$774$		0			0
$775$	27.2251	−	28.8237i	0.977956	−	1.03538i
$776$	0.489189	−	0.0235503i	0.0175609	−	0.000845406i
$777$		0			0
$778$	−21.9328	−	0.797063i	−0.786330	−	0.0285761i
$779$	−5.10271	+	15.7045i	−0.182824	+	0.562673i
$780$		0			0
$781$	11.9985	+	36.9275i	0.429339	+	1.32137i
$782$	−0.925515	−	3.24502i	−0.0330964	−	0.116042i
$783$		0			0
$784$	19.8853	+	37.9164i	0.710191	+	1.35416i
$785$	−1.05076	−	0.623481i	−0.0375034	−	0.0222530i
$786$		0			0
$787$	−11.2133	+	1.77601i	−0.399710	+	0.0633079i	−0.353054	−	0.935603i	$-0.614857\pi$
$787$	−11.2133	+	1.77601i	−0.399710	+	0.0633079i	−0.0466566	+	0.998911i	$0.514857\pi$
$788$	7.63382	+	8.83219i	0.271944	+	0.314634i
$789$		0			0
$790$	18.2184	+	16.2688i	0.648183	+	0.578819i
$791$	39.7927	−	54.7700i	1.41487	−	1.94740i
$792$		0			0
$793$	0.284418	−	0.284418i	0.0101000	−	0.0101000i
$794$	1.45150	−	7.41120i	0.0515120	−	0.263014i
$795$		0			0
$796$	8.98904	+	36.4938i	0.318608	+	1.29349i
$797$	−14.6399	+	7.45942i	−0.518573	+	0.264226i	−0.693629	−	0.720332i	$-0.743989\pi$
$797$	−14.6399	+	7.45942i	−0.518573	+	0.264226i	0.175056	+	0.984559i	$0.443989\pi$
$798$		0			0
$799$	−0.401290			−0.0141966
$800$	−8.84696	−	26.8651i	−0.312787	−	0.949823i
$801$		0			0
$802$	−13.4697	+	17.1901i	−0.475633	+	0.607005i
$803$	−61.8601	+	31.5193i	−2.18300	+	1.11229i
$804$		0			0
$805$	23.5451	−	28.3772i	0.829856	−	1.00016i
$806$	4.31183	−	22.0157i	0.151878	−	0.775469i
$807$		0			0
$808$	−47.4644	−	21.3750i	−1.66979	−	0.751969i
$809$	4.40896	−	6.06841i	0.155011	−	0.213354i	−0.724448	−	0.689330i	$-0.757905\pi$
$809$	4.40896	−	6.06841i	0.155011	−	0.213354i	0.879458	+	0.475976i	$0.157905\pi$
$810$		0			0
$811$	14.2898	+	19.6682i	0.501782	+	0.690643i	0.982507	−	0.186228i	$-0.0596264\pi$
$811$	14.2898	+	19.6682i	0.501782	+	0.690643i	−0.480725	+	0.876872i	$0.659626\pi$
$812$	41.4732	+	47.9837i	1.45542	+	1.68390i
$813$		0			0
$814$	0.271599	+	2.23824i	0.00951953	+	0.0784501i
$815$	4.37755	+	10.1563i	0.153339	+	0.355761i
$816$		0			0
$817$	7.00683	−	13.7517i	0.245138	−	0.481110i
$818$	3.08986	+	10.8336i	0.108034	+	0.378787i
$819$		0			0
$820$	−5.24773	+	38.0834i	−0.183259	+	1.32993i
$821$	6.95848	−	21.4160i	0.242853	−	0.747424i	−0.753129	−	0.657872i	$-0.771457\pi$
$821$	6.95848	−	21.4160i	0.242853	−	0.747424i	0.995982	−	0.0895516i	$-0.0285434\pi$
$822$		0			0
$823$	−14.8281	−	2.34854i	−0.516876	−	0.0818651i	−0.107454	−	0.994210i	$-0.534270\pi$
$823$	−14.8281	−	2.34854i	−0.516876	−	0.0818651i	−0.409422	+	0.912345i	$0.634270\pi$
$824$	40.4923	−	1.94936i	1.41061	−	0.0679091i
$825$		0			0
$826$	13.9929	−	25.1596i	0.486875	−	0.875416i
$827$	1.70364	−	10.7563i	0.0592413	−	0.374035i	−0.940200	−	0.340622i	$-0.889362\pi$
$827$	1.70364	−	10.7563i	0.0592413	−	0.374035i	0.999442	−	0.0334128i	$-0.0106376\pi$
$828$		0			0
$829$	6.13294	+	1.99271i	0.213006	+	0.0692098i	0.413576	−	0.910469i	$-0.364280\pi$
$829$	6.13294	+	1.99271i	0.213006	+	0.0692098i	−0.200570	+	0.979679i	$0.564280\pi$
$830$	−7.76141	−	9.50438i	−0.269402	−	0.329902i
$831$		0			0
$832$	−12.3511	−	10.1770i	−0.428197	−	0.352824i
$833$	5.80631	+	2.95846i	0.201177	+	0.102505i
$834$		0			0
$835$	15.5101	+	3.49057i	0.536750	+	0.120796i
$836$	−15.9111	−	6.48108i	−0.550297	−	0.224153i
$837$		0			0
$838$	41.8492	+	15.2991i	1.44566	+	0.528499i
$839$	−0.865255	+	0.628644i	−0.0298719	+	0.0217032i	−0.602621	−	0.798028i	$-0.705877\pi$
$839$	−0.865255	+	0.628644i	−0.0298719	+	0.0217032i	0.572749	+	0.819731i	$0.305877\pi$
$840$		0			0
$841$	22.4930	+	16.3421i	0.775620	+	0.563521i
$842$	6.51215	+	9.68427i	0.224424	+	0.333742i
$843$		0			0
$844$	3.54641	−	4.20218i	0.122073	−	0.144645i
$845$	−17.0038	+	10.7564i	−0.584950	+	0.370030i
$846$		0			0
$847$	17.1875	+	33.7323i	0.590568	+	1.15906i
$848$	−25.7769	−	18.2680i	−0.885182	−	0.627326i
$849$		0			0
$850$	−3.46295	−	2.55755i	−0.118778	−	0.0877233i
$851$		−	1.39724i		−	0.0478967i
$852$		0			0
$853$	−16.5635	−	32.5077i	−0.567124	−	1.11304i	−0.979390	−	0.201980i	$-0.935262\pi$
$853$	−16.5635	−	32.5077i	−0.567124	−	1.11304i	0.412265	−	0.911064i	$-0.364738\pi$
$854$	−0.814717	−	0.876165i	−0.0278790	−	0.0299818i
$855$		0			0
$856$	4.99877	−	1.89448i	0.170855	−	0.0647521i
$857$	0.126626	+	0.126626i	0.00432545	+	0.00432545i	0.709266	−	0.704941i	$-0.249026\pi$
$857$	0.126626	+	0.126626i	0.00432545	+	0.00432545i	−0.704941	+	0.709266i	$0.749026\pi$
$858$		0			0
$859$	29.3912	+	21.3540i	1.00282	+	0.728588i	0.962690	−	0.270606i	$-0.0872241\pi$
$859$	29.3912	+	21.3540i	1.00282	+	0.728588i	0.0401258	+	0.999195i	$0.487224\pi$
$860$	10.4128	−	34.3897i	0.355074	−	1.17268i
$861$		0			0
$862$	0.604364	−	1.65318i	0.0205847	−	0.0563074i
$863$	−1.08585	−	6.85580i	−0.0369628	−	0.233374i	0.962290	−	0.272026i	$-0.0876936\pi$
$863$	−1.08585	−	6.85580i	−0.0369628	−	0.233374i	−0.999253	+	0.0386519i	$0.987694\pi$
$864$		0			0
$865$	−0.576929	−	6.19931i	−0.0196162	−	0.210783i
$866$	−9.79552	+	4.55082i	−0.332865	+	0.154643i
$867$		0			0
$868$	−64.9765	−	15.1953i	−2.20545	−	0.515762i
$869$	32.8499	−	10.6736i	1.11436	−	0.362076i
$870$		0			0
$871$	26.3558	+	8.56352i	0.893032	+	0.290164i
$872$	46.4878	−	26.5766i	1.57428	−	0.899999i
$873$		0			0
$874$	9.30469	+	5.17494i	0.314736	+	0.175045i
$875$	1.68236	−	47.0119i	0.0568742	−	1.58929i
$876$		0			0
$877$	−52.6769	−	8.34319i	−1.77877	−	0.281730i	−0.821350	−	0.570425i	$-0.806779\pi$
$877$	−52.6769	−	8.34319i	−1.77877	−	0.281730i	−0.957421	+	0.288695i	$0.906779\pi$
$878$	0.893774	−	24.5940i	0.0301634	−	0.830009i
$879$		0			0
$880$	−39.1225	−	8.32164i	−1.31882	−	0.280523i
$881$	−8.65792	−	26.6464i	−0.291693	−	0.897738i	−0.984312	−	0.176435i	$-0.943543\pi$
$881$	−8.65792	−	26.6464i	−0.291693	−	0.897738i	0.692619	−	0.721303i	$-0.256457\pi$
$882$		0			0
$883$	15.2558	−	29.9413i	0.513400	−	1.00760i	−0.478199	−	0.878251i	$-0.658710\pi$
$883$	15.2558	−	29.9413i	0.513400	−	1.00760i	0.991599	−	0.129352i	$-0.0412897\pi$
$884$	−2.42943	−	0.176810i	−0.0817106	−	0.00594676i
$885$		0			0
$886$	−6.88585	+	0.835564i	−0.231335	+	0.0280713i
$887$	34.2197	−	5.41987i	1.14899	−	0.181982i	0.447244	−	0.894412i	$-0.352406\pi$
$887$	34.2197	−	5.41987i	1.14899	−	0.181982i	0.701743	+	0.712430i	$0.252406\pi$
$888$		0			0
$889$	16.0064	+	22.0310i	0.536838	+	0.738895i
$890$	6.95129	−	1.50744i	0.233008	−	0.0505295i
$891$		0			0
$892$	1.36176	+	16.0907i	0.0455952	+	0.538755i
$893$	0.895299	−	0.895299i	0.0299600	−	0.0299600i
$894$		0			0
$895$	2.14646	−	33.3446i	0.0717482	−	1.11459i
$896$	−31.5857	+	35.6147i	−1.05520	+	1.18980i
$897$		0			0
$898$	24.3773	+	19.1014i	0.813482	+	0.637422i
$899$	−59.7645			−1.99326
$900$		0			0
$901$	−4.80874			−0.160202
$902$	42.7918	+	33.5305i	1.42481	+	1.11644i
$903$		0			0
$904$	43.9080	+	11.9656i	1.46036	+	0.397970i
$905$	4.89154	+	7.73262i	0.162600	+	0.257041i
$906$		0			0
$907$	33.1020	−	33.1020i	1.09913	−	1.09913i	0.104622	−	0.994512i	$-0.466637\pi$
$907$	33.1020	−	33.1020i	1.09913	−	1.09913i	0.994512	−	0.104622i	$-0.0333633\pi$
$908$	8.75442	−	0.740892i	0.290526	−	0.0245874i
$909$		0			0
$910$	−13.4033	−	22.9963i	−0.444315	−	0.762321i
$911$	13.7377	+	18.9083i	0.455149	+	0.626459i	0.973494	−	0.228713i	$-0.0734516\pi$
$911$	13.7377	+	18.9083i	0.455149	+	0.626459i	−0.518345	+	0.855172i	$0.673452\pi$
$912$		0			0
$913$	−17.1389	+	2.71454i	−0.567216	+	0.0898381i
$914$	−27.4369	+	3.32932i	−0.907531	+	0.110124i
$915$		0			0
$916$	0.594017	−	8.16201i	0.0196269	−	0.269680i
$917$	−11.6142	+	22.7941i	−0.383533	+	0.752727i
$918$		0			0
$919$	−0.383432	−	1.18008i	−0.0126483	−	0.0389273i	0.944533	−	0.328416i	$-0.106515\pi$
$919$	−0.383432	−	1.18008i	−0.0126483	−	0.0389273i	−0.957181	+	0.289489i	$0.906515\pi$
$920$	23.4469	+	8.04002i	0.773022	+	0.265072i
$921$		0			0
$922$	−0.879095	+	24.1901i	−0.0289514	+	0.796659i
$923$	−17.1556	−	2.71718i	−0.564683	−	0.0894370i
$924$		0			0
$925$	−1.08845	−	1.41167i	−0.0357880	−	0.0464153i
$926$	32.4794	+	18.0639i	1.06734	+	0.593616i
$927$		0			0
$928$	−20.2821	+	37.5010i	−0.665793	+	1.23103i
$929$	−5.53343	−	1.79792i	−0.181546	−	0.0589878i	0.216833	−	0.976209i	$-0.430427\pi$
$929$	−5.53343	−	1.79792i	−0.181546	−	0.0589878i	−0.398379	+	0.917221i	$0.630427\pi$
$930$		0			0
$931$	−19.5547	+	6.35370i	−0.640879	+	0.208234i
$932$	−11.9506	+	51.1018i	−0.391455	+	1.67390i
$933$		0			0
$934$	2.68287	−	1.24641i	0.0877861	−	0.0407838i
$935$	−5.59067	+	2.40967i	−0.182834	+	0.0788046i
$936$		0			0
$937$	2.60902	+	16.4727i	0.0852330	+	0.538140i	0.992948	+	0.118552i	$0.0378253\pi$
$937$	2.60902	+	16.4727i	0.0852330	+	0.538140i	−0.907715	+	0.419588i	$0.862175\pi$
$938$	28.3024	−	77.4184i	0.924107	−	2.52780i
$939$		0			0
$940$	1.68423	−	2.41916i	0.0549334	−	0.0789044i
$941$	13.7087	+	9.95998i	0.446892	+	0.324686i	0.788367	−	0.615205i	$-0.210927\pi$
$941$	13.7087	+	9.95998i	0.446892	+	0.324686i	−0.341475	+	0.939891i	$0.610927\pi$
$942$		0			0
$943$	−23.8224	−	23.8224i	−0.775764	−	0.775764i
$944$	19.1488	+	2.80207i	0.623239	+	0.0911995i
$945$		0			0
$946$	−34.6010	−	37.2107i	−1.12497	−	1.20982i
$947$	21.8024	+	42.7895i	0.708482	+	1.39047i	0.911501	+	0.411299i	$0.134925\pi$
$947$	21.8024	+	42.7895i	0.708482	+	1.39047i	−0.203019	+	0.979175i	$0.565075\pi$
$948$		0			0
$949$		−	31.0579i		−	1.00818i
$950$	13.4321	−	2.01999i	0.435794	−	0.0655372i
$951$		0			0
$952$	−0.788013	+	7.20247i	−0.0255396	+	0.233433i
$953$	−14.7001	−	28.8506i	−0.476183	−	0.934562i	−0.996736	−	0.0807326i	$-0.974274\pi$
$953$	−14.7001	−	28.8506i	−0.476183	−	0.934562i	0.520553	−	0.853830i	$-0.325726\pi$
$954$		0			0
$955$	−20.4803	+	51.5088i	−0.662728	+	1.66679i
$956$	2.97809	+	2.51334i	0.0963182	+	0.0812873i
$957$		0			0
$958$	−12.8194	−	19.0638i	−0.414175	−	0.615923i
$959$	52.3048	+	38.0017i	1.68901	+	1.22714i
$960$		0			0
$961$	25.7919	−	18.7389i	0.831995	−	0.604480i
$962$	−0.947290	−	0.346308i	−0.0305419	−	0.0111654i
$963$		0			0
$964$	−20.4420	+	50.1854i	−0.658393	+	1.61636i
$965$	15.8686	−	26.7437i	0.510829	−	0.860910i
$966$		0			0
$967$	33.4966	+	17.0674i	1.07718	+	0.548849i	0.900249	−	0.435375i	$-0.143384\pi$
$967$	33.4966	+	17.0674i	1.07718	+	0.548849i	0.176928	+	0.984224i	$0.443384\pi$
$968$	−17.1094	+	18.8400i	−0.549916	+	0.605541i
$969$		0			0
$970$	0.0309051	+	0.546690i	0.000992303	+	0.0175532i
$971$	38.7039	+	12.5757i	1.24207	+	0.403572i	0.855072	−	0.518509i	$-0.173513\pi$
$971$	38.7039	+	12.5757i	1.24207	+	0.403572i	0.386996	+	0.922081i	$0.373513\pi$
$972$		0			0
$973$	−2.95085	+	18.6310i	−0.0946000	+	0.597281i
$974$	−4.33478	+	7.79406i	−0.138895	+	0.249738i
$975$		0			0
$976$	0.356662	−	0.720856i	0.0114165	−	0.0230740i
$977$	2.97242	+	0.470785i	0.0950961	+	0.0150617i	0.203801	−	0.979012i	$-0.434670\pi$
$977$	2.97242	+	0.470785i	0.0950961	+	0.0150617i	−0.108705	+	0.994074i	$0.534670\pi$
$978$		0			0
$979$	3.10826	−	9.56625i	0.0993405	−	0.305739i
$980$	−42.2043	+	22.5864i	−1.34817	+	0.721496i
$981$		0			0
$982$	1.11334	+	3.90357i	0.0355281	+	0.124568i
$983$	12.7441	−	25.0117i	0.406474	−	0.797750i	−0.593501	−	0.804833i	$-0.702255\pi$
$983$	12.7441	−	25.0117i	0.406474	−	0.797750i	0.999975	+	0.00708356i	$0.00225479\pi$
$984$		0			0
$985$	−9.80293	+	8.61719i	−0.312347	+	0.274567i
$986$	0.781694	+	6.44192i	0.0248942	+	0.205152i
$987$		0			0
$988$	5.81466	−	5.02572i	0.184989	−	0.159889i
$989$	18.5087	+	25.4750i	0.588542	+	0.810058i
$990$		0			0
$991$	−12.6905	+	17.4669i	−0.403126	+	0.554855i	−0.961525	−	0.274717i	$-0.911416\pi$
$991$	−12.6905	+	17.4669i	−0.403126	+	0.554855i	0.558399	+	0.829572i	$0.311416\pi$
$992$	−5.92772	−	44.4639i	−0.188205	−	1.41173i
$993$		0			0
$994$	−9.93014	+	50.7020i	−0.314965	+	1.60817i
$995$	−40.7158	+	10.3911i	−1.29078	+	0.329419i
$996$		0			0
$997$	−34.9075	+	17.7863i	−1.10553	+	0.563297i	−0.908830	−	0.417166i	$-0.863023\pi$
$997$	−34.9075	+	17.7863i	−1.10553	+	0.563297i	−0.196702	+	0.980463i	$0.563023\pi$
$998$	−23.9407	+	30.5533i	−0.757830	+	0.967147i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.9		240
3.2	odd	2		300.2.w.a.127.22	yes	240
4.3	odd	2	inner	900.2.bj.f.127.12		240
12.11	even	2		300.2.w.a.127.19	✓	240
25.13	odd	20	inner	900.2.bj.f.163.12		240
75.38	even	20		300.2.w.a.163.19	yes	240
100.63	even	20	inner	900.2.bj.f.163.9		240
300.263	odd	20		300.2.w.a.163.22	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.19	✓	240	12.11	even	2
300.2.w.a.127.22	yes	240	3.2	odd	2
300.2.w.a.163.19	yes	240	75.38	even	20
300.2.w.a.163.22	yes	240	300.263	odd	20
900.2.bj.f.127.9		240	1.1	even	1	trivial
900.2.bj.f.127.12		240	4.3	odd	2	inner
900.2.bj.f.163.9		240	100.63	even	20	inner
900.2.bj.f.163.12		240	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.872257 + 1.11318i) q^{2} +(-0.478336 - 1.94196i) q^{4} +(2.16662 - 0.552943i) q^{5} +(2.97520 - 2.97520i) q^{7} +(2.57898 + 1.16141i) q^{8} +O(q^{10})\)	\(q+(-0.872257 + 1.11318i) q^{2} +(-0.478336 - 1.94196i) q^{4} +(2.16662 - 0.552943i) q^{5} +(2.97520 - 2.97520i) q^{7} +(2.57898 + 1.16141i) q^{8} +(-1.27433 + 2.89415i) q^{10} +(2.62851 + 3.61783i) q^{11} +(-1.97584 + 0.312943i) q^{13} +(0.716793 + 5.90707i) q^{14} +(-3.54239 + 1.85782i) q^{16} +(-0.276399 + 0.542463i) q^{17} +(-0.593603 - 1.82692i) q^{19} +(-2.11017 - 3.94299i) q^{20} +(-6.32003 - 0.229677i) q^{22} +(3.87093 + 0.613095i) q^{23} +(4.38851 - 2.39604i) q^{25} +(1.37508 - 2.47243i) q^{26} +(-7.20085 - 4.35456i) q^{28} +(-7.16789 - 2.32899i) q^{29} +(7.54161 - 2.45042i) q^{31} +(1.02179 - 5.56381i) q^{32} +(-0.362768 - 0.780848i) q^{34} +(4.80102 - 8.09125i) q^{35} +(-0.0557708 - 0.352123i) q^{37} +(2.55147 + 0.932759i) q^{38} +(6.22987 + 1.09031i) q^{40} +(-6.95445 - 5.05270i) q^{41} +(5.68128 + 5.68128i) q^{43} +(5.76836 - 6.83499i) q^{44} +(-4.05893 + 3.77426i) q^{46} +(0.299237 + 0.587287i) q^{47} -10.7036i q^{49} +(-1.16069 + 6.97516i) q^{50} +(1.55284 + 3.68731i) q^{52} +(3.58582 + 7.03757i) q^{53} +(7.69544 + 6.38506i) q^{55} +(11.1284 - 4.21754i) q^{56} +(8.84482 - 5.94767i) q^{58} +(-3.91416 - 2.84381i) q^{59} +(-0.162666 + 0.118184i) q^{61} +(-3.85047 + 10.5326i) q^{62} +(5.30225 + 5.99050i) q^{64} +(-4.10787 + 1.77056i) q^{65} +(-12.3429 - 6.28904i) q^{67} +(1.18565 + 0.277274i) q^{68} +(4.81929 + 12.4020i) q^{70} +(8.25771 + 2.68309i) q^{71} +(-2.42869 + 15.3341i) q^{73} +(0.440622 + 0.245059i) q^{74} +(-3.26386 + 2.02664i) q^{76} +(18.5841 + 2.94343i) q^{77} +(2.38682 - 7.34587i) q^{79} +(-6.64775 + 5.98393i) q^{80} +(11.6906 - 3.33429i) q^{82} +(-1.76165 + 3.45743i) q^{83} +(-0.298901 + 1.32815i) q^{85} +(-11.2798 + 1.36875i) q^{86} +(2.57708 + 12.3831i) q^{88} +(-1.32210 - 1.81971i) q^{89} +(-4.94746 + 6.80959i) q^{91} +(-0.661003 - 7.81045i) q^{92} +(-0.914767 - 0.179160i) q^{94} +(-2.29630 - 3.63002i) q^{95} +(0.154282 - 0.0786106i) q^{97} +(11.9150 + 9.33630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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