LMFDB - Embedded newform 900.2.bj.f.127.12

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			127.12
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.485574 - 1.32824i) q^{2} +(-1.52844 + 1.28992i) q^{4} +(2.16662 - 0.552943i) q^{5} +(-2.97520 + 2.97520i) q^{7} +(2.45549 + 1.40378i) q^{8} +O(q^{10})$	\(q+(-0.485574 - 1.32824i) q^{2} +(-1.52844 + 1.28992i) q^{4} +(2.16662 - 0.552943i) q^{5} +(-2.97520 + 2.97520i) q^{7} +(2.45549 + 1.40378i) q^{8} +(-1.78650 - 2.60930i) q^{10} +(-2.62851 - 3.61783i) q^{11} +(-1.97584 + 0.312943i) q^{13} +(5.39645 + 2.50709i) q^{14} +(0.672230 - 3.94311i) q^{16} +(-0.276399 + 0.542463i) q^{17} +(0.593603 + 1.82692i) q^{19} +(-2.59829 + 3.63990i) q^{20} +(-3.52901 + 5.24801i) q^{22} +(-3.87093 - 0.613095i) q^{23} +(4.38851 - 2.39604i) q^{25} +(1.37508 + 2.47243i) q^{26} +(0.709641 - 8.38516i) q^{28} +(-7.16789 - 2.32899i) q^{29} +(-7.54161 + 2.45042i) q^{31} +(-5.56381 + 1.02179i) q^{32} +(0.854732 + 0.103717i) q^{34} +(-4.80102 + 8.09125i) q^{35} +(-0.0557708 - 0.352123i) q^{37} +(2.13835 - 1.67555i) q^{38} +(6.09632 + 1.68371i) q^{40} +(-6.95445 - 5.05270i) q^{41} +(-5.68128 - 5.68128i) q^{43} +(8.68421 + 2.13907i) q^{44} +(1.06529 + 5.43922i) q^{46} +(-0.299237 - 0.587287i) q^{47} -10.7036i q^{49} +(-5.31346 - 4.66553i) q^{50} +(2.61628 - 3.02699i) q^{52} +(3.58582 + 7.03757i) q^{53} +(-7.69544 - 6.38506i) q^{55} +(-11.4821 + 3.12904i) q^{56} +(0.387089 + 10.6516i) q^{58} +(3.91416 + 2.84381i) q^{59} +(-0.162666 + 0.118184i) q^{61} +(6.91675 + 8.82720i) q^{62} +(4.05882 + 6.89391i) q^{64} +(-4.10787 + 1.77056i) q^{65} +(12.3429 + 6.28904i) q^{67} +(-0.277274 - 1.18565i) q^{68} +(13.0784 + 2.44800i) q^{70} +(-8.25771 - 2.68309i) q^{71} +(-2.42869 + 15.3341i) q^{73} +(-0.440622 + 0.245059i) q^{74} +(-3.26386 - 2.02664i) q^{76} +(18.5841 + 2.94343i) q^{77} +(-2.38682 + 7.34587i) q^{79} +(-0.723845 - 8.91493i) q^{80} +(-3.33429 + 11.6906i) q^{82} +(1.76165 - 3.45743i) q^{83} +(-0.298901 + 1.32815i) q^{85} +(-4.78741 + 10.3048i) q^{86} +(-1.37564 - 12.5734i) q^{88} +(-1.32210 - 1.81971i) q^{89} +(4.94746 - 6.80959i) q^{91} +(6.70731 - 4.05610i) q^{92} +(-0.634755 + 0.682630i) q^{94} +(2.29630 + 3.63002i) q^{95} +(0.154282 - 0.0786106i) q^{97} +(-14.2170 + 5.19740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.485574	−	1.32824i	−0.343353	−	0.939207i
$2$	−0.485574	−	1.32824i	−0.343353	−	0.939207i
$3$		0			0
$3$		0			0
$4$	−1.52844	+	1.28992i	−0.764218	+	0.644958i
$5$	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	$0.542611\pi$
$7$	−2.97520	+	2.97520i	−1.12452	+	1.12452i	−0.991053	+	0.133466i	$0.957389\pi$
$8$	2.45549	+	1.40378i	0.868145	+	0.496310i
$9$		0			0
$10$	−1.78650	−	2.60930i	−0.564940	−	0.825132i
$11$	−2.62851	−	3.61783i	−0.792525	−	1.09082i	−0.993789	−	0.111280i	$-0.964505\pi$
$11$	−2.62851	−	3.61783i	−0.792525	−	1.09082i	0.201264	−	0.979537i	$-0.435495\pi$
$12$		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	$0.539478\pi$
$14$	5.39645	+	2.50709i	1.44226	+	0.670049i
$15$		0			0
$16$	0.672230	−	3.94311i	0.168058	−	0.985777i
$17$	−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	0.995772	−	0.0918594i	$-0.0292810\pi$
$19$	0.593603	+	1.82692i	0.136182	+	0.419125i	−0.859590	+	0.510984i	$0.829281\pi$
$20$	−2.59829	+	3.63990i	−0.580996	+	0.813906i
$21$		0			0
$22$	−3.52901	+	5.24801i	−0.752387	+	1.11888i
$23$	−3.87093	−	0.613095i	−0.807145	−	0.127839i	−0.260793	−	0.965395i	$-0.583984\pi$
$23$	−3.87093	−	0.613095i	−0.807145	−	0.127839i	−0.546352	+	0.837556i	$0.683984\pi$
$24$		0			0
$25$	4.38851	−	2.39604i	0.877702	−	0.479208i
$26$	1.37508	+	2.47243i	0.269676	+	0.484884i
$27$		0			0
$28$	0.709641	−	8.38516i	0.134110	−	1.58465i
$29$	−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	−0.894208	−	0.447652i	$-0.852260\pi$
$31$	−7.54161	+	2.45042i	−1.35451	+	0.440108i	−0.460306	+	0.887760i	$0.652260\pi$
$32$	−5.56381	+	1.02179i	−0.983551	+	0.180629i
$33$		0			0
$34$	0.854732	+	0.103717i	0.146585	+	0.0177874i
$35$	−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	$0.959329\pi$
$38$	2.13835	−	1.67555i	0.346886	−	0.271811i
$39$		0			0
$40$	6.09632	+	1.68371i	0.963913	+	0.266218i
$41$	−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	0.125684	−	0.992070i	$-0.459888\pi$
$43$	−5.68128	−	5.68128i	−0.866387	−	0.866387i	−0.992070	+	0.125684i	$0.959888\pi$
$44$	8.68421	+	2.13907i	1.30919	+	0.322476i
$45$		0			0
$46$	1.06529	+	5.43922i	0.157068	+	0.801970i
$47$	−0.299237	−	0.587287i	−0.0436483	−	0.0856646i	0.868152	−	0.496298i	$-0.165308\pi$
$47$	−0.299237	−	0.587287i	−0.0436483	−	0.0856646i	−0.911801	+	0.410633i	$0.865308\pi$
$48$		0			0
$49$		−	10.7036i		−	1.52909i
$50$	−5.31346	−	4.66553i	−0.751436	−	0.659806i
$51$		0			0
$52$	2.61628	−	3.02699i	0.362813	−	0.419767i
$53$	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
$56$	−11.4821	+	3.12904i	−1.53436	+	0.418136i
$57$		0			0
$58$	0.387089	+	10.6516i	0.0508273	+	1.39862i
$59$	3.91416	+	2.84381i	0.509580	+	0.370232i	0.812664	−	0.582732i	$-0.198016\pi$
$59$	3.91416	+	2.84381i	0.509580	+	0.370232i	−0.303084	+	0.952964i	$0.598016\pi$
$60$		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	$0.304097\pi$
$62$	6.91675	+	8.82720i	0.878429	+	1.12106i
$63$		0			0
$64$	4.05882	+	6.89391i	0.507353	+	0.861739i
$65$	−4.10787	+	1.77056i	−0.509518	+	0.219611i
$66$		0			0
$67$	12.3429	+	6.28904i	1.50793	+	0.768328i	0.995885	−	0.0906310i	$-0.0288884\pi$
$67$	12.3429	+	6.28904i	1.50793	+	0.768328i	0.512044	+	0.858959i	$0.328888\pi$
$68$	−0.277274	−	1.18565i	−0.0336245	−	0.143781i
$69$		0			0
$70$	13.0784	+	2.44800i	1.56316	+	0.292591i
$71$	−8.25771	−	2.68309i	−0.980010	−	0.318424i	−0.225160	−	0.974322i	$-0.572290\pi$
$71$	−8.25771	−	2.68309i	−0.980010	−	0.318424i	−0.754850	+	0.655897i	$0.772290\pi$
$72$		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	$0.243076\pi$
$79$	−2.38682	+	7.34587i	−0.268538	+	0.826475i	−0.990857	+	0.134915i	$0.956924\pi$
$80$	−0.723845	−	8.91493i	−0.0809283	−	0.996720i
$81$		0			0
$82$	−3.33429	+	11.6906i	−0.368211	+	1.29101i
$83$	1.76165	−	3.45743i	0.193366	−	0.379503i	−0.773884	−	0.633327i	$-0.781689\pi$
$83$	1.76165	−	3.45743i	0.193366	−	0.379503i	0.967250	+	0.253825i	$0.0816887\pi$
$84$		0			0
$85$	−0.298901	+	1.32815i	−0.0324203	+	0.144058i
$86$	−4.78741	+	10.3048i	−0.516240	+	1.11119i
$87$		0			0
$88$	−1.37564	−	12.5734i	−0.146643	−	1.34033i
$89$	−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
$92$	6.70731	−	4.05610i	0.699286	−	0.422878i
$93$		0			0
$94$	−0.634755	+	0.682630i	−0.0654700	+	0.0704079i
$95$	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	$0.347202\pi$
$98$	−14.2170	+	5.19740i	−1.43613	+	0.525016i
$99$		0			0
$100$	−3.61686	+	9.32300i	−0.361686	+	0.932300i
$101$	−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	−0.950627	−	0.310337i	$-0.899558\pi$
$103$	−12.7706	+	6.50694i	−1.25832	+	0.641147i	−0.307696	+	0.951485i	$0.599558\pi$
$104$	−5.29096	−	2.00522i	−0.518821	−	0.196628i
$105$		0			0
$106$	7.60639	−	8.18009i	0.738798	−	0.794520i
$107$	−1.33643	+	1.33643i	−0.129198	+	0.129198i	−0.768749	−	0.639551i	$-0.779120\pi$
$107$	−1.33643	+	1.33643i	−0.129198	+	0.129198i	0.639551	+	0.768749i	$0.279120\pi$
$108$		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	$-0.161399\pi$
$110$	−4.74418	+	13.3218i	−0.452339	+	1.27018i
$111$		0			0
$112$	9.73151	+	13.7315i	0.919541	+	1.29751i
$113$	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
$116$	13.9599	−	5.68627i	1.29614	−	0.527957i
$117$		0			0
$118$	1.87664	−	6.57982i	0.172758	−	0.605721i
$119$	−0.791594	−	2.43628i	−0.0725653	−	0.223333i
$120$		0			0
$121$	−2.78046	+	8.55737i	−0.252769	+	0.777943i
$122$	0.235963	+	0.158672i	0.0213630	+	0.0143655i
$123$		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	$-0.857291\pi$
$127$	1.01246	−	6.39241i	0.0898412	−	0.567235i	0.991012	−	0.133771i	$-0.0427087\pi$
$128$	7.18590	−	8.73859i	0.635150	−	0.772389i
$129$		0			0
$130$	4.34640	+	4.59649i	0.381204	+	0.403139i
$131$	5.78251	−	1.87885i	0.505220	−	0.164156i	−0.0453071	−	0.998973i	$-0.514427\pi$
$131$	5.78251	−	1.87885i	0.505220	−	0.164156i	0.550527	+	0.834817i	$0.314427\pi$
$132$		0			0
$133$	−7.20155	−	3.66937i	−0.624453	−	0.318175i
$134$	2.35993	−	19.4481i	0.203867	−	1.68006i
$135$		0			0
$136$	−1.44019	+	0.944008i	−0.123495	+	0.0809480i
$137$	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	−0.423247	−	0.906015i	$-0.639110\pi$
$139$	3.62695	−	2.63514i	0.307634	−	0.223509i	0.730881	+	0.682505i	$0.239110\pi$
$140$	−3.09899	−	18.5599i	−0.261912	−	1.56859i
$141$		0			0
$142$	0.445943	+	12.2710i	0.0374227	+	1.02976i
$143$	6.32569	+	6.32569i	0.528981	+	0.528981i
$144$		0			0
$145$	−16.8179	−	1.08260i	−1.39665	−	0.0899054i
$146$	21.5467	−	4.21998i	1.78322	−	0.349248i
$147$		0			0
$148$	0.539451	+	0.466258i	0.0443426	+	0.0383261i
$149$			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	$-0.848349\pi$
$151$		−	11.2709i		−	0.917213i	0.888639	−	0.458606i	$-0.151651\pi$
$152$	−1.10701	+	5.31927i	−0.0897902	+	0.431450i
$153$		0			0
$154$	−5.11438	−	26.1134i	−0.412128	−	2.10428i
$155$	−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	$0.756941\pi$
$158$	10.9160	−	0.396701i	0.868434	−	0.0315598i
$159$		0			0
$160$	−11.4897	+	5.29030i	−0.908339	+	0.418235i
$161$	13.3409	−	9.69271i	1.05141	−	0.763893i
$162$		0			0
$163$	−0.773723	−	4.88510i	−0.0606027	−	0.382630i	−0.999284	−	0.0378434i	$-0.987951\pi$
$163$	−0.773723	−	4.88510i	−0.0606027	−	0.382630i	0.938681	−	0.344787i	$-0.112049\pi$
$164$	17.1470	−	1.24793i	1.33895	−	0.0974468i
$165$		0			0
$166$	−5.44771	−	0.661052i	−0.422824	−	0.0513076i
$167$	−6.33490	−	3.22779i	−0.490209	−	0.249774i	0.191371	−	0.981518i	$-0.438707\pi$
$167$	−6.33490	−	3.22779i	−0.490209	−	0.249774i	−0.681580	+	0.731744i	$0.738707\pi$
$168$		0			0
$169$	−8.55771	+	2.78057i	−0.658285	+	0.213890i
$170$	1.90923	−	0.247902i	0.146431	−	0.0190132i
$171$		0			0
$172$	16.0118	+	1.35509i	1.22089	+	0.103325i
$173$	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
$178$	−1.77503	+	2.63966i	−0.133044	+	0.197851i
$179$	−4.61764	+	14.2116i	−0.345139	+	1.06223i	0.616371	+	0.787456i	$0.288602\pi$
$179$	−4.61764	+	14.2116i	−0.345139	+	1.06223i	−0.961510	+	0.274772i	$0.911398\pi$
$180$		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	$0.851404\pi$
$182$	−11.4471	−	3.26484i	−0.848517	−	0.242006i
$183$		0			0
$184$	−8.64437	−	6.93937i	−0.637271	−	0.511577i
$185$	−0.315538	−	0.732080i	−0.0231988	−	0.0538236i
$186$		0			0
$187$	2.68906	−	0.425905i	0.196643	−	0.0311452i
$188$	1.21492	+	0.511638i	0.0886069	+	0.0373151i
$189$		0			0
$190$	3.70651	−	4.81268i	0.268899	−	0.349148i
$191$	14.5709	−	20.0552i	1.05432	−	1.45114i	0.169308	−	0.985563i	$-0.445847\pi$
$191$	14.5709	−	20.0552i	1.05432	−	1.45114i	0.885007	−	0.465577i	$-0.154153\pi$
$192$		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	$0.0831393\pi$
$194$	−0.179329	−	0.166752i	−0.0128751	−	0.0119721i
$195$		0			0
$196$	13.8068	+	16.3598i	0.986198	+	1.16856i
$197$	−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	$-0.267973\pi$
$199$	18.7923			1.33215			0.666076	+	0.745884i	$0.267973\pi$
$200$	14.1394	+	0.277049i	0.999808	+	0.0195903i
$201$		0			0
$202$	8.93667	+	24.4453i	0.628782	+	1.71997i
$203$	28.2551	−	14.3967i	1.98312	−	1.01045i
$204$		0			0
$205$	−17.8615	−	7.10188i	−1.24750	−	0.496017i
$206$	14.8438	+	13.8028i	1.03422	+	0.961685i
$207$		0			0
$208$	−0.0942543	+	8.00133i	−0.00653536	+	0.554793i
$209$	5.04921	−	6.94964i	0.349261	−	0.480717i
$210$		0			0
$211$	−1.61602	−	2.22426i	−0.111251	−	0.153124i	0.749760	−	0.661709i	$-0.230169\pi$
$211$	−1.61602	−	2.22426i	−0.111251	−	0.153124i	−0.861012	+	0.508585i	$0.830169\pi$
$212$	−14.5586	−	6.13106i	−0.999887	−	0.421083i
$213$		0			0
$214$	2.42404	+	1.12616i	0.165704	+	0.0769830i
$215$	−15.4506	−	9.16776i	−1.05372	−	0.625236i
$216$		0			0
$217$	15.1473	−	29.7283i	1.02827	−	2.01809i
$218$	−25.7475	−	7.34346i	−1.74384	−	0.497362i
$219$		0			0
$220$	19.9982	−	0.167324i	1.34828	−	0.0112810i
$221$	0.376361	−	1.15832i	0.0253168	−	0.0779170i
$222$		0			0
$223$	7.97469	+	1.26307i	0.534025	+	0.0845812i	0.417622	−	0.908621i	$-0.362864\pi$
$223$	7.97469	+	1.26307i	0.534025	+	0.0845812i	0.116403	+	0.993202i	$0.462864\pi$
$224$	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	−0.954331	−	0.298751i	$-0.903430\pi$
$227$	0.687194	−	4.33877i	0.0456107	−	0.287975i	0.999942	+	0.0107760i	$0.00343016\pi$
$228$		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	$0.556833\pi$
$230$	5.31566	+	11.1957i	0.350504	+	0.738223i
$231$		0			0
$232$	−14.3313	−	15.7809i	−0.940894	−	1.03607i
$233$	−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
$236$	−9.65082	+	0.702370i	−0.628215	+	0.0457204i
$237$		0			0
$238$	−2.85158	+	2.23442i	−0.184840	+	0.144836i
$239$	1.57633	−	1.14527i	0.101964	−	0.0740815i	−0.535635	−	0.844450i	$-0.679928\pi$
$239$	1.57633	−	1.14527i	0.101964	−	0.0740815i	0.637599	+	0.770368i	$0.279928\pi$
$240$		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	$-0.637604\pi$
$242$	12.7164	−	0.462126i	0.817438	−	0.0297066i
$243$		0			0
$244$	0.0961773	−	0.390462i	0.00615712	−	0.0249968i
$245$	−5.91849	−	23.1907i	−0.378118	−	1.48160i
$246$		0			0
$247$	−1.74459	−	3.42395i	−0.111006	−	0.217861i
$248$	−21.9582	−	4.56978i	−1.39434	−	0.290181i
$249$		0			0
$250$	−14.0920	−	7.17041i	−0.891258	−	0.453496i
$251$			6.25683i			0.394928i	0.980310	+	0.197464i	$0.0632705\pi$
$251$			6.25683i			0.394928i	−0.980310	+	0.197464i	$0.936729\pi$
$252$		0			0
$253$	7.95670	+	15.6159i	0.500233	+	0.981763i
$254$	−8.98227	+	1.75920i	−0.563598	+	0.110382i
$255$		0			0
$256$	−15.0962	−	5.30136i	−0.943513	−	0.331335i
$257$	−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
$260$	3.99474	−	8.00499i	0.247743	−	0.496448i
$261$		0			0
$262$	−5.30340	−	6.76823i	−0.327645	−	0.418143i
$263$	4.88515	+	30.8437i	0.301232	+	1.90190i	0.417489	+	0.908682i	$0.362910\pi$
$263$	4.88515	+	30.8437i	0.301232	+	1.90190i	−0.116257	+	0.993219i	$0.537090\pi$
$264$		0			0
$265$	11.6605	+	13.2650i	0.716299	+	0.814863i
$266$	−1.37692	+	11.3471i	−0.0844241	+	0.695737i
$267$		0			0
$268$	−26.9777	+	6.30896i	−1.64793	+	0.385381i
$269$	−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	−0.0523794	−	0.998627i	$-0.516681\pi$
$271$	−11.2228	−	3.64649i	−0.681734	−	0.221509i	−0.629354	+	0.777119i	$0.716681\pi$
$272$	1.95319	+	1.45453i	0.118429	+	0.0881939i
$273$		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	$0.518634\pi$
$278$	−5.26124	−	3.53790i	−0.315548	−	0.212189i
$279$		0			0
$280$	−23.1471	+	13.1284i	−1.38331	+	0.784571i
$281$	−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	$-0.626544\pi$
$283$	9.86359	−	19.3584i	0.586330	−	1.15074i	0.973491	−	0.228725i	$-0.0734555\pi$
$284$	16.0823	−	6.55082i	0.954311	−	0.388720i
$285$		0			0
$286$	5.33044	−	11.4736i	0.315195	−	0.678450i
$287$	35.7236	−	5.65807i	2.10870	−	0.333985i
$288$		0			0
$289$	9.77448	+	13.4534i	0.574969	+	0.791377i
$290$	6.72839	+	22.8639i	0.395104	+	1.34261i
$291$		0			0
$292$	−16.0677	−	26.5700i	−0.940288	−	1.55489i
$293$	−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
$296$	0.357358	−	0.942923i	0.0207710	−	0.0548063i
$297$		0			0
$298$	5.02989	−	1.83882i	0.291374	−	0.106520i
$299$	7.84022			0.453412
$300$		0			0
$301$	33.8059			1.94854
$302$	−14.9704	+	5.47286i	−0.861452	+	0.314928i
$303$		0			0
$304$	7.60279	−	1.11253i	0.436050	−	0.0638079i
$305$	−0.287087	+	0.346005i	−0.0164385	+	0.0198122i
$306$		0			0
$307$	2.29000	−	2.29000i	0.130697	−	0.130697i	−0.638732	−	0.769429i	$-0.720541\pi$
$307$	2.29000	−	2.29000i	0.130697	−	0.130697i	0.769429	+	0.638732i	$0.220541\pi$
$308$	−32.2014	+	19.4731i	−1.83484	+	1.10958i
$309$		0			0
$310$	19.8669	+	15.3006i	1.12837	+	0.869018i
$311$	−6.35552	−	8.74762i	−0.360388	−	0.496032i	0.589869	−	0.807499i	$-0.299180\pi$
$311$	−6.35552	−	8.74762i	−0.360388	−	0.496032i	−0.950257	+	0.311467i	$0.899180\pi$
$312$		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	$0.668286\pi$
$314$	−0.325582	+	0.700807i	−0.0183737	+	0.0395488i
$315$		0			0
$316$	−5.82746	−	14.3065i	−0.327820	−	0.804803i
$317$	−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
$320$	12.6059	+	12.6922i	0.704690	+	0.709516i
$321$		0			0
$322$	−19.3522	−	13.0133i	−1.07846	−	0.725205i
$323$	−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
$328$	−9.98368	−	22.1693i	−0.551256	−	1.22410i
$329$	2.63759	+	0.857003i	0.145415	+	0.0472481i
$330$		0			0
$331$	24.0903	−	7.82740i	1.32412	−	0.430233i	0.440212	−	0.897894i	$-0.354903\pi$
$331$	24.0903	−	7.82740i	1.32412	−	0.430233i	0.883908	+	0.467661i	$0.154903\pi$
$332$	1.76723	+	7.55685i	0.0969894	+	0.414736i
$333$		0			0
$334$	−1.21122	+	9.98159i	−0.0662748	+	0.546168i
$335$	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	$0.677765\pi$
$338$	7.84866	+	10.0165i	0.426911	+	0.544826i
$339$		0			0
$340$	−1.25635	−	2.41554i	−0.0681350	−	0.131001i
$341$	28.6884	+	20.8433i	1.55356	+	1.12873i
$342$		0			0
$343$	11.0190	+	11.0190i	0.594969	+	0.594969i
$344$	−5.97505	−	21.9255i	−0.322153	−	1.18215i
$345$		0			0
$346$	−3.86431	+	0.756836i	−0.207747	+	0.0406878i
$347$	−6.28919	−	12.3432i	−0.337621	−	0.662619i	0.658309	−	0.752748i	$-0.271272\pi$
$347$	−6.28919	−	12.3432i	−0.337621	−	0.662619i	−0.995930	+	0.0901287i	$0.971272\pi$
$348$		0			0
$349$			20.4056i			1.09229i	0.837692	+	0.546144i	$0.183905\pi$
$349$			20.4056i			1.09229i	−0.837692	+	0.546144i	$0.816095\pi$
$350$	29.6895	−	1.92770i	1.58697	−	0.103040i
$351$		0			0
$352$	18.3212	+	17.4431i	0.976522	+	0.929722i
$353$	−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
$356$	4.36801	+	1.07592i	0.231504	+	0.0570234i
$357$		0			0
$358$	21.1187	−	0.767475i	1.11616	−	0.0405623i
$359$	3.09530	+	2.24886i	0.163364	+	0.118691i	0.666463	−	0.745538i	$-0.267807\pi$
$359$	3.09530	+	2.24886i	0.163364	+	0.118691i	−0.503100	+	0.864228i	$0.667807\pi$
$360$		0			0
$361$	12.3860	−	8.99898i	0.651897	−	0.473631i
$362$	4.55508	−	3.56924i	0.239410	−	0.187595i
$363$		0			0
$364$	1.22193	+	16.7898i	0.0640468	+	0.880026i
$365$	3.21685	+	34.5662i	0.168378	+	1.80928i
$366$		0			0
$367$	−2.79735	−	1.42532i	−0.146021	−	0.0744013i	0.379453	−	0.925211i	$-0.376112\pi$
$367$	−2.79735	−	1.42532i	−0.146021	−	0.0744013i	−0.525474	+	0.850810i	$0.676112\pi$
$368$	−5.01966	+	14.8514i	−0.261668	+	0.774181i
$369$		0			0
$370$	−0.819159	+	0.774589i	−0.0425861	+	0.0402690i
$371$	−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	−0.877866	−	0.478906i	$-0.841034\pi$
$379$	2.21616	−	6.82062i	0.113836	−	0.350352i	0.991703	+	0.128554i	$0.0410335\pi$
$380$	−8.19217	−	2.58622i	−0.420250	−	0.132670i
$381$		0			0
$382$	−33.7133	−	9.61540i	−1.72492	−	0.491967i
$383$	10.4506	−	20.5104i	0.533999	−	1.04803i	−0.453625	−	0.891193i	$-0.649869\pi$
$383$	10.4506	−	20.5104i	0.533999	−	1.04803i	0.987624	−	0.156840i	$-0.0501306\pi$
$384$		0			0
$385$	41.8923	−	3.89864i	2.13503	−	0.198693i
$386$	−17.8367	−	8.28660i	−0.907864	−	0.421777i
$387$		0			0
$388$	−0.134409	+	0.319162i	−0.00682358	+	0.0162030i
$389$	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
$392$	15.0255	−	26.2826i	0.758902	−	1.32747i
$393$		0			0
$394$	6.04514	+	5.62118i	0.304550	+	0.283191i
$395$	−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	$0.392784\pi$
$398$	−9.12506	−	24.9607i	−0.457398	−	1.25117i
$399$		0			0
$400$	−6.49775	−	18.9151i	−0.324888	−	0.945753i
$401$	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
$404$	28.1298	−	23.7401i	1.39951	−	1.18111i
$405$		0			0
$406$	−32.8422	−	30.5389i	−1.62993	−	1.51562i
$407$	−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	$0.136898\pi$
$410$	−0.759905	+	27.1728i	−0.0375290	+	1.34197i
$411$		0			0
$412$	11.1256	−	26.4184i	0.548119	−	1.30154i
$413$	−20.1063	+	3.18452i	−0.989366	+	0.156700i
$414$		0			0
$415$	1.90507	−	8.46505i	0.0935161	−	0.415533i
$416$	10.6734	−	3.76005i	0.523309	−	0.184352i
$417$		0			0
$418$	−11.6825	−	3.33199i	−0.571412	−	0.162973i
$419$	9.73628	+	29.9652i	0.475648	+	1.46390i	0.845081	+	0.534638i	$0.179552\pi$
$419$	9.73628	+	29.9652i	0.475648	+	1.46390i	−0.369433	+	0.929257i	$0.620448\pi$
$420$		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	$0.0355515\pi$
$422$	−2.16965	+	3.22650i	−0.105617	+	0.157064i
$423$		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
$428$	0.318764	−	3.76654i	0.0154081	−	0.182062i
$429$		0			0
$430$	−4.67456	+	24.9737i	−0.225427	+	1.20434i
$431$	1.18372	−	0.384614i	0.0570178	−	0.0185262i	−0.280369	−	0.959892i	$-0.590457\pi$
$431$	1.18372	−	0.384614i	0.0570178	−	0.0185262i	0.337387	+	0.941366i	$0.390457\pi$
$432$		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	$0.591252\pi$
$434$	−46.8414	−	5.68397i	−2.24846	−	0.272839i
$435$		0			0
$436$	2.74844	+	37.7646i	0.131626	+	1.80860i
$437$	−1.17772	−	7.43583i	−0.0563380	−	0.355704i
$438$		0			0
$439$	14.0786	−	10.2287i	0.671934	−	0.488189i	−0.198738	−	0.980053i	$-0.563684\pi$
$439$	14.0786	−	10.2287i	0.671934	−	0.488189i	0.870672	+	0.491864i	$0.163684\pi$
$440$	−9.93284	−	26.4811i	−0.473530	−	1.26244i
$441$		0			0
$442$	−1.72127	+	0.0625530i	−0.0818727	+	0.00297534i
$443$	−3.46818	−	3.46818i	−0.164778	−	0.164778i	0.619901	−	0.784680i	$-0.287173\pi$
$443$	−3.46818	−	3.46818i	−0.164778	−	0.164778i	−0.784680	+	0.619901i	$0.787173\pi$
$444$		0			0
$445$	−3.87068	−	3.21158i	−0.183488	−	0.152244i
$446$	−2.19465	−	11.2056i	−0.103920	−	0.530601i
$447$		0			0
$448$	−32.5865	−	8.43495i	−1.53957	−	0.398514i
$449$		−	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
$452$	−21.0429	+	24.3462i	−0.989775	+	1.14515i
$453$		0			0
$454$	−6.09661	+	1.19404i	−0.286128	+	0.0560390i
$455$	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	$0.598890\pi$
$458$	−0.210155	−	5.78286i	−0.00981992	−	0.270215i
$459$		0			0
$460$	12.2894	−	12.4968i	0.572997	−	0.582667i
$461$	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	$0.159093\pi$
$463$	4.11100	+	25.9559i	0.191055	+	1.20627i	−0.686621	+	0.727016i	$0.740907\pi$
$464$	−14.0019	+	26.6982i	−0.650023	+	1.23943i
$465$		0			0
$466$	−4.47024	+	36.8392i	−0.207080	+	1.70654i
$467$	1.86381	+	0.949661i	0.0862471	+	0.0439451i	0.496582	−	0.867990i	$-0.334588\pi$
$467$	1.86381	+	0.949661i	0.0862471	+	0.0439451i	−0.410335	+	0.911935i	$0.634588\pi$
$468$		0			0
$469$	−55.4338	+	18.0115i	−2.55969	+	0.831695i
$470$	−0.997819	+	1.82998i	−0.0460259	+	0.0844109i
$471$		0			0
$472$	5.61910	+	12.4775i	0.258640	+	0.574325i
$473$	−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
$478$	−2.28662	−	1.53763i	−0.104588	−	0.0703296i
$479$	5.01981	−	15.4494i	0.229361	−	0.705901i	−0.768459	−	0.639900i	$-0.778976\pi$
$479$	5.01981	−	15.4494i	0.229361	−	0.705901i	0.997820	−	0.0660010i	$-0.0210241\pi$
$480$		0			0
$481$	0.220389	+	0.678287i	0.0100489	+	0.0309272i
$482$	−10.5095	+	36.8480i	−0.478693	+	1.67838i
$483$		0			0
$484$	−6.78855	−	16.6660i	−0.308570	−	0.757543i
$485$	0.290804	−	0.255629i	0.0132047	−	0.0116075i
$486$		0			0
$487$	−6.22862	+	0.986516i	−0.282246	+	0.0447033i	−0.295952	−	0.955203i	$-0.595637\pi$
$487$	−6.22862	+	0.986516i	−0.282246	+	0.0447033i	0.0137066	+	0.999906i	$0.495637\pi$
$488$	−0.565328	+	0.0618518i	−0.0255912	+	0.00279990i
$489$		0			0
$490$	−27.9289	+	19.1220i	−1.26170	+	0.863842i
$491$	−1.68713	+	2.32213i	−0.0761390	+	0.104796i	−0.845388	−	0.534153i	$-0.820631\pi$
$491$	−1.68713	+	2.32213i	−0.0761390	+	0.104796i	0.769249	+	0.638949i	$0.220631\pi$
$492$		0			0
$493$	3.24459	−	3.24459i	0.146129	−	0.146129i
$494$	−3.70069	+	3.97981i	−0.166502	+	0.179060i
$495$		0			0
$496$	4.59257	+	31.3846i	0.206212	+	1.40921i
$497$	32.5510	−	16.5856i	1.46011	−	0.743965i
$498$		0			0
$499$	−27.4468			−1.22869			−0.614345	−	0.789038i	$-0.710580\pi$
$499$	−27.4468			−1.22869			−0.614345	+	0.789038i	$0.710580\pi$
$500$	−2.68129	+	22.1993i	−0.119911	+	0.992785i
$501$		0			0
$502$	8.31057	−	3.03816i	0.370919	−	0.135600i
$503$	−28.9075	+	14.7291i	−1.28892	+	0.656738i	−0.957959	−	0.286906i	$-0.907373\pi$
$503$	−28.9075	+	14.7291i	−1.28892	+	0.656738i	−0.330963	+	0.943644i	$0.607373\pi$
$504$		0			0
$505$	−39.8752	+	10.1765i	−1.77443	+	0.452850i
$506$	16.8781	−	18.1511i	0.750322	−	0.806914i
$507$		0			0
$508$	6.69820	+	11.0764i	0.297185	+	0.491435i
$509$	−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
$512$	0.288866	+	22.6256i	0.0127662	+	0.999919i
$513$		0			0
$514$	−8.80746	+	18.9578i	−0.388480	+	0.836194i
$515$	−24.0711	+	21.1595i	−1.06070	+	0.932398i
$516$		0			0
$517$	−1.33816	+	2.62628i	−0.0588520	+	0.115504i
$518$	0.581841	−	2.04004i	0.0255646	−	0.0896341i
$519$		0			0
$520$	−12.5723	−	1.41895i	−0.551331	−	0.0622251i
$521$	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	0.151170	−	0.988508i	$-0.451696\pi$
$523$	−0.240669	−	0.0381182i	−0.0105237	−	0.00166679i	−0.161694	+	0.986841i	$0.551696\pi$
$524$	−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
$530$	11.9571	−	21.9291i	0.519381	−	0.952538i
$531$		0			0
$532$	15.7403	−	3.68100i	0.682428	−	0.159591i
$533$	15.3221	+	7.80700i	0.663674	+	0.338159i
$534$		0			0
$535$	−2.15657	+	3.63452i	−0.0932368	+	0.157134i
$536$	21.4795	+	32.7694i	0.927772	+	1.41542i
$537$		0			0
$538$	19.8951	+	25.3902i	0.857738	+	1.09465i
$539$	−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	$0.775942\pi$
$542$	0.606065	+	16.6771i	0.0260327	+	0.716344i
$543$		0			0
$544$	0.983546	−	3.30058i	0.0421692	−	0.141511i
$545$	15.6412	−	39.3383i	0.669996	−	1.68507i
$546$		0			0
$547$	2.33918	+	4.59090i	0.100016	+	0.196293i	0.935593	−	0.353081i	$-0.114866\pi$
$547$	2.33918	+	4.59090i	0.100016	+	0.196293i	−0.835576	+	0.549374i	$0.814866\pi$
$548$	−23.2504	−	20.0958i	−0.993210	−	0.858449i
$549$		0			0
$550$	−2.91264	+	31.4866i	−0.124195	+	1.34259i
$551$		−	14.4777i		−	0.616770i
$552$		0			0
$553$	−14.7542	−	28.9567i	−0.627411	−	1.23136i
$554$	−0.890120	−	4.54484i	−0.0378176	−	0.193092i
$555$		0			0
$556$	−2.14446	+	8.70610i	−0.0909453	+	0.369221i
$557$	−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
$560$	28.6773	+	24.3701i	1.21184	+	1.02983i
$561$		0			0
$562$	−12.9779	+	10.1692i	−0.547442	+	0.428960i
$563$	0.803478	+	5.07296i	0.0338626	+	0.213800i	0.998818	−	0.0486155i	$-0.0154809\pi$
$563$	0.803478	+	5.07296i	0.0338626	+	0.213800i	−0.964955	+	0.262415i	$0.915481\pi$
$564$		0			0
$565$	33.0398	−	14.2407i	1.39000	−	0.599111i
$566$	−30.5021	−	3.70127i	−1.28210	−	0.155576i
$567$		0			0
$568$	−16.5102	−	18.1803i	−0.692753	−	0.762827i
$569$	−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	0.858011	−	0.513631i	$-0.171700\pi$
$571$	29.8755	+	9.70715i	1.25025	+	0.406232i	0.392241	+	0.919862i	$0.371700\pi$
$572$	−17.8280	−	1.50880i	−0.745428	−	0.0630860i
$573$		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	$0.598246\pi$
$578$	13.1231	−	19.5155i	0.545850	−	0.811737i
$579$		0			0
$580$	27.1016	−	20.0390i	1.12533	−	0.832075i
$581$	5.04529	+	15.5278i	0.209314	+	0.644202i
$582$		0			0
$583$	16.0354	−	31.4712i	0.664118	−	1.30340i
$584$	−27.4893	+	34.2434i	−1.13752	+	1.41700i
$585$		0			0
$586$	11.1464	+	5.17844i	0.460455	+	0.213919i
$587$	1.51204	−	0.239484i	0.0624086	−	0.00988455i	−0.125152	−	0.992138i	$-0.539942\pi$
$587$	1.51204	−	0.239484i	0.0624086	−	0.00988455i	0.187561	+	0.982253i	$0.439942\pi$
$588$		0			0
$589$	−8.95345	−	12.3234i	−0.368921	−	0.507776i
$590$	0.427696	−	15.2937i	0.0176080	−	0.629630i
$591$		0			0
$592$	−1.42595	−	0.0167974i	−0.0586062	−	0.000690371i
$593$	−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
$596$	−4.88477	−	5.78802i	−0.200088	−	0.237086i
$597$		0			0
$598$	−3.80701	−	10.4137i	−0.155680	−	0.425847i
$599$	4.16436			0.170151			0.0850756	−	0.996374i	$-0.472887\pi$
$599$	4.16436			0.170151			0.0850756	+	0.996374i	$0.472887\pi$
$600$		0			0
$601$	−33.1465			−1.35207			−0.676037	−	0.736868i	$-0.736304\pi$
$601$	−33.1465			−1.35207			−0.676037	+	0.736868i	$0.736304\pi$
$602$	−16.4152	−	44.9022i	−0.669036	−	1.83008i
$603$		0			0
$604$	14.5385	+	17.2268i	0.591564	+	0.700950i
$605$	−1.29247	+	20.0780i	−0.0525462	+	0.816288i
$606$		0			0
$607$	7.14827	−	7.14827i	0.290139	−	0.290139i	−0.546996	−	0.837135i	$-0.684229\pi$
$607$	7.14827	−	7.14827i	0.290139	−	0.290139i	0.837135	+	0.546996i	$0.184229\pi$
$608$	−5.16942	−	9.55811i	−0.209648	−	0.387633i
$609$		0			0
$610$	0.598979	+	0.213309i	0.0242519	+	0.00863663i
$611$	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	$0.236666\pi$
$614$	−4.15364	−	1.92971i	−0.167627	−	0.0778766i
$615$		0			0
$616$	41.5011	+	33.3155i	1.67213	+	1.34232i
$617$	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	$-0.838348\pi$
$619$	−11.2635	−	34.6654i	−0.452717	−	1.39332i	0.421077	−	0.907025i	$-0.361652\pi$
$620$	10.6760	−	33.8176i	0.428760	−	1.35815i
$621$		0			0
$622$	−8.53285	+	12.6893i	−0.342136	+	0.508793i
$623$	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
$628$	1.08893	+	0.0921571i	0.0434531	+	0.00367747i
$629$	0.206429	+	0.0670727i	0.00823085	+	0.00267437i
$630$		0			0
$631$	−7.96006	+	2.58638i	−0.316885	+	0.102962i	−0.463141	−	0.886285i	$-0.653278\pi$
$631$	−7.96006	+	2.58638i	−0.316885	+	0.102962i	0.146256	+	0.989247i	$0.453278\pi$
$632$	−16.1728	+	14.6871i	−0.643318	+	0.584222i
$633$		0			0
$634$	39.0804	+	4.74221i	1.55208	+	0.188337i
$635$	−1.34102	−	14.4098i	−0.0532169	−	0.571835i
$636$		0			0
$637$	3.34962	+	21.1487i	0.132717	+	0.837940i
$638$	37.5181	−	29.3982i	1.48536	−	1.16388i
$639$		0			0
$640$	10.7372	−	22.9066i	0.424425	−	0.905463i
$641$	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	0.0241234	−	0.999709i	$-0.492321\pi$
$643$	−24.7384	−	24.7384i	−0.975586	−	0.975586i	−0.999709	+	0.0241234i	$0.992321\pi$
$644$	−7.88787	+	32.0233i	−0.310826	+	1.26189i
$645$		0			0
$646$	0.317888	+	1.62310i	0.0125071	+	0.0638599i
$647$	4.89479	+	9.60656i	0.192434	+	0.377673i	0.966983	−	0.254841i	$-0.0820231\pi$
$647$	4.89479	+	9.60656i	0.192434	+	0.377673i	−0.774549	+	0.632514i	$0.782023\pi$
$648$		0			0
$649$		−	21.6357i		−	0.849277i
$650$	11.9586	+	7.55555i	0.469055	+	0.296353i
$651$		0			0
$652$	7.48395	+	6.46852i	0.293094	+	0.253327i
$653$	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
$656$	−24.5983	+	24.0256i	−0.960404	+	0.938040i
$657$		0			0
$658$	−0.142438	−	3.91948i	−0.00555282	−	0.152797i
$659$	16.2441	+	11.8020i	0.632779	+	0.459741i	0.857362	−	0.514714i	$-0.172102\pi$
$659$	16.2441	+	11.8020i	0.632779	+	0.459741i	−0.224583	+	0.974455i	$0.572102\pi$
$660$		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	$0.961410\pi$
$662$	−22.0943	−	28.1968i	−0.858718	−	1.09590i
$663$		0			0
$664$	9.17917	−	6.01671i	0.356221	−	0.233494i
$665$	−17.6320	−	3.96810i	−0.683739	−	0.153876i
$666$		0			0
$667$	26.3185	+	13.4100i	1.01906	+	0.519236i
$668$	13.8461	−	3.23802i	0.535721	−	0.125283i
$669$		0			0
$670$	−5.64063	−	43.4417i	−0.217917	−	1.67830i
$671$	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
$680$	−2.59837	+	2.84165i	−0.0996428	+	0.108972i
$681$		0			0
$682$	13.7546	−	48.2260i	0.526690	−	1.84667i
$683$	−2.58511	+	5.07357i	−0.0989167	+	0.194135i	−0.935162	−	0.354221i	$-0.884746\pi$
$683$	−2.58511	+	5.07357i	−0.0989167	+	0.194135i	0.836245	+	0.548356i	$0.184746\pi$
$684$		0			0
$685$	13.5998	+	31.5527i	0.519620	+	1.20557i
$686$	9.28530	−	19.9864i	0.354515	−	0.763083i
$687$		0			0
$688$	−26.2210	+	18.5828i	−0.999667	+	0.708461i
$689$	−9.28738	−	12.7830i	−0.353821	−	0.486993i
$690$		0			0
$691$	−5.24350	+	7.21706i	−0.199472	+	0.274550i	−0.897022	−	0.441987i	$-0.854274\pi$
$691$	−5.24350	+	7.21706i	−0.199472	+	0.274550i	0.697549	+	0.716537i	$0.254274\pi$
$692$	2.88167	+	4.76523i	0.109545	+	0.181147i
$693$		0			0
$694$	−13.3409	+	14.3471i	−0.506413	+	0.544608i
$695$	6.40116	−	7.71484i	0.242810	−	0.292641i
$696$		0			0
$697$	4.66310	−	2.37597i	0.176628	−	0.0899963i
$698$	27.1035	−	9.90843i	1.02588	−	0.375040i
$699$		0			0
$700$	−16.9769	−	38.4987i	−0.641666	−	1.45511i
$701$	−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
$704$	14.2724	−	32.8048i	0.537910	−	1.23638i
$705$		0			0
$706$	−1.38200	+	1.48623i	−0.0520122	+	0.0559352i
$707$	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	$0.952956\pi$
$710$	7.75138	+	26.3401i	0.290904	+	0.988528i
$711$		0			0
$712$	−0.691923	−	6.32420i	−0.0259309	−	0.237009i
$713$	30.6954	−	4.86168i	1.14955	−	0.182071i
$714$		0			0
$715$	17.2031	+	10.2076i	0.643361	+	0.381744i
$716$	−11.2741	−	27.6779i	−0.421331	−	1.03437i
$717$		0			0
$718$	1.48403	−	5.20328i	0.0553836	−	0.194185i
$719$	14.0058	+	43.1054i	0.522327	+	1.60756i	0.769541	+	0.638597i	$0.220485\pi$
$719$	14.0058	+	43.1054i	0.522327	+	1.60756i	−0.247214	+	0.968961i	$0.579515\pi$
$720$		0			0
$721$	18.6356	−	57.3544i	0.694025	−	2.13599i
$722$	−17.9671	−	12.0819i	−0.668668	−	0.449643i
$723$		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	$-0.795429\pi$
$727$	3.93735	−	24.8594i	0.146028	−	0.921985i	0.946521	−	0.322643i	$-0.104571\pi$
$728$	21.7076	−	9.77573i	0.804536	−	0.362313i
$729$		0			0
$730$	44.3501	−	21.0572i	1.64147	−	0.779362i
$731$	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	$0.620799\pi$
$734$	−0.534847	+	4.40765i	−0.0197415	+	0.162690i
$735$		0			0
$736$	22.1636	−	0.544132i	0.816960	−	0.0200570i
$737$	−9.69082	−	61.1854i	−0.356966	−	2.25379i
$738$		0			0
$739$	−38.2860	+	27.8164i	−1.40837	+	1.02324i	−0.414815	+	0.909906i	$0.636154\pi$
$739$	−38.2860	+	27.8164i	−1.40837	+	1.02324i	−0.993557	+	0.113336i	$0.963846\pi$
$740$	1.42660	+	0.711918i	0.0524429	+	0.0261706i
$741$		0			0
$742$	1.70686	+	46.9679i	0.0626610	+	1.72425i
$743$	−11.8611	−	11.8611i	−0.435143	−	0.435143i	0.455231	−	0.890373i	$-0.349557\pi$
$743$	−11.8611	−	11.8611i	−0.435143	−	0.435143i	−0.890373	+	0.455231i	$0.849557\pi$
$744$		0			0
$745$	2.09393	+	8.20476i	0.0767158	+	0.300599i
$746$	38.3966	−	7.52009i	1.40580	−	0.275330i
$747$		0			0
$748$	−3.56067	+	4.11963i	−0.130191	+	0.150628i
$749$		−	7.95230i		−	0.290571i
$750$		0			0
$751$			4.27171i			0.155877i	0.996958	+	0.0779385i	$0.0248338\pi$
$751$			4.27171i			0.155877i	−0.996958	+	0.0779385i	$0.975166\pi$
$752$	−2.51689	+	0.785134i	−0.0917816	+	0.0286309i
$753$		0			0
$754$	−4.09816	−	20.9247i	−0.149246	−	0.762032i
$755$	−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	$0.813197\pi$
$758$	−10.1355	+	0.368336i	−0.368139	+	0.0133786i
$759$		0			0
$760$	0.542785	+	12.1370i	0.0196889	+	0.440254i
$761$	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
$764$	3.59876	+	49.4483i	0.130199	+	1.78898i
$765$		0			0
$766$	−32.3172	−	3.92153i	−1.16767	−	0.141691i
$767$	−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	$0.186489\pi$
$770$	−25.5201	−	53.7499i	−0.919682	−	1.93701i
$771$		0			0
$772$	−2.34555	+	27.7151i	−0.0844182	+	0.997490i
$773$	−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
$778$	12.2470	−	18.2125i	0.439075	−	0.652951i
$779$	5.10271	−	15.7045i	0.182824	−	0.562673i
$780$		0			0
$781$	11.9985	+	36.9275i	0.429339	+	1.32137i
$782$	−3.24502	−	0.925515i	−0.116042	−	0.0330964i
$783$		0			0
$784$	−42.2055	−	7.19529i	−1.50734	−	0.256975i
$785$	−1.05076	−	0.623481i	−0.0375034	−	0.0222530i
$786$		0			0
$787$	11.2133	−	1.77601i	0.399710	−	0.0633079i	0.0466566	−	0.998911i	$-0.485143\pi$
$787$	11.2133	−	1.77601i	0.399710	−	0.0633079i	0.353054	+	0.935603i	$0.385143\pi$
$788$	4.53090	−	10.7589i	0.161407	−	0.383270i
$789$		0			0
$790$	23.4316	−	6.89545i	0.833659	−	0.245329i
$791$	−39.7927	+	54.7700i	−1.41487	+	1.94740i
$792$		0			0
$793$	0.284418	−	0.284418i	0.0101000	−	0.0101000i
$794$	5.53048	+	5.14261i	0.196270	+	0.182505i
$795$		0			0
$796$	−28.7228	+	24.2405i	−1.01805	+	0.859182i
$797$	−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
$800$	−21.9686	+	17.8152i	−0.776706	+	0.629863i
$801$		0			0
$802$	−7.49842	−	20.5112i	−0.264779	−	0.724275i
$803$	61.8601	−	31.5193i	2.18300	−	1.11229i
$804$		0			0
$805$	23.5451	−	28.3772i	0.829856	−	1.00016i
$806$	−16.4288	−	15.2766i	−0.578681	−	0.538096i
$807$		0			0
$808$	−45.1916	−	25.8356i	−1.58983	−	0.908893i
$809$	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	0.480725	−	0.876872i	$-0.340374\pi$
$811$	−14.2898	−	19.6682i	−0.501782	−	0.690643i	−0.982507	+	0.186228i	$0.940374\pi$
$812$	−24.6156	+	58.4511i	−0.863837	+	2.05123i
$813$		0			0
$814$	2.04476	+	0.949959i	0.0716688	+	0.0332960i
$815$	−4.37755	−	10.1563i	−0.153339	−	0.355761i
$816$		0			0
$817$	7.00683	−	13.7517i	0.245138	−	0.481110i
$818$	−10.8336	−	3.08986i	−0.378787	−	0.108034i
$819$		0			0
$820$	36.4610	−	12.1851i	1.27327	−	0.425522i
$821$	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	0.409422	−	0.912345i	$-0.365730\pi$
$823$	14.8281	+	2.34854i	0.516876	+	0.0818651i	0.107454	+	0.994210i	$0.465730\pi$
$824$	−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	$0.110638\pi$
$827$	−1.70364	+	10.7563i	−0.0592413	+	0.374035i	−0.999442	+	0.0334128i	$0.989362\pi$
$828$		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	$0.564280\pi$
$830$	−12.1687	+	1.58002i	−0.422380	+	0.0548434i
$831$		0			0
$832$	−10.1770	−	12.3511i	−0.352824	−	0.428197i
$833$	5.80631	+	2.95846i	0.201177	+	0.102505i
$834$		0			0
$835$	−15.5101	−	3.49057i	−0.536750	−	0.120796i
$836$	1.24707	+	17.1351i	0.0431306	+	0.592631i
$837$		0			0
$838$	35.0732	−	27.4824i	1.21158	−	0.949364i
$839$	0.865255	−	0.628644i	0.0298719	−	0.0217032i	−0.572749	−	0.819731i	$-0.694123\pi$
$839$	0.865255	−	0.628644i	0.0298719	−	0.0217032i	0.602621	+	0.798028i	$0.294123\pi$
$840$		0			0
$841$	22.4930	+	16.3421i	0.775620	+	0.563521i
$842$	−11.6625	+	0.423827i	−0.401916	+	0.0146060i
$843$		0			0
$844$	5.33909	+	1.31511i	0.183779	+	0.0452679i
$845$	−17.0038	+	10.7564i	−0.584950	+	0.370030i
$846$		0			0
$847$	−17.1875	−	33.7323i	−0.590568	−	1.15906i
$848$	30.1604	−	9.40841i	1.03571	−	0.323086i
$849$		0			0
$850$	3.99951	−	1.59281i	0.137182	−	0.0546328i
$851$			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	$-0.364738\pi$
$854$	−1.17412	+	0.229954i	−0.0401775	+	0.00786887i
$855$		0			0
$856$	−5.15764	+	1.40554i	−0.176285	+	0.0480403i
$857$	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	−0.0401258	−	0.999195i	$-0.512776\pi$
$859$	−29.3912	−	21.3540i	−1.00282	−	0.728588i	−0.962690	+	0.270606i	$0.912776\pi$
$860$	35.4409	−	5.91766i	1.20852	−	0.201791i
$861$		0			0
$862$	−1.08564	−	1.38551i	−0.0369772	−	0.0471905i
$863$	1.08585	+	6.85580i	0.0369628	+	0.233374i	0.999253	−	0.0386519i	$-0.0123064\pi$
$863$	1.08585	+	6.85580i	0.0369628	+	0.233374i	−0.962290	+	0.272026i	$0.912306\pi$
$864$		0			0
$865$	−0.576929	−	6.19931i	−0.0196162	−	0.210783i
$866$	1.30111	−	10.7224i	0.0442134	−	0.364361i
$867$		0			0
$868$	15.1953	+	64.9765i	0.515762	+	2.20545i
$869$	32.8499	−	10.6736i	1.11436	−	0.362076i
$870$		0			0
$871$	−26.3558	−	8.56352i	−0.893032	−	0.290164i
$872$	48.8258	−	21.9881i	1.65345	−	0.744611i
$873$		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	$0.906779\pi$
$878$	−20.4223	−	13.7329i	−0.689221	−	0.463464i
$879$		0			0
$880$	−30.3501	+	26.0517i	−1.02310	+	0.878203i
$881$	−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	$0.341290\pi$
$883$	−15.2558	+	29.9413i	−0.513400	+	1.00760i	−0.991599	+	0.129352i	$0.958710\pi$
$884$	0.918892	+	2.25589i	0.0309057	+	0.0758738i
$885$		0			0
$886$	−2.92251	+	6.29063i	−0.0981838	+	0.211338i
$887$	−34.2197	+	5.41987i	−1.14899	+	0.181982i	−0.701743	−	0.712430i	$-0.747594\pi$
$887$	−34.2197	+	5.41987i	−1.14899	+	0.181982i	−0.447244	+	0.894412i	$0.647594\pi$
$888$		0			0
$889$	16.0064	+	22.0310i	0.536838	+	0.738895i
$890$	−2.38624	+	6.70065i	−0.0799871	+	0.224606i
$891$		0			0
$892$	−13.8180	+	8.35617i	−0.462662	+	0.279785i
$893$	0.895299	−	0.895299i	0.0299600	−	0.0299600i
$894$		0			0
$895$	−2.14646	+	33.3446i	−0.0717482	+	1.11459i
$896$	4.61956	+	47.3785i	0.154329	+	1.58280i
$897$		0			0
$898$	−29.0869	+	10.6335i	−0.970641	+	0.354845i
$899$	59.7645			1.99326
$900$		0			0
$901$	−4.80874			−0.160202
$902$	51.0589	−	18.6660i	1.70008	−	0.621509i
$903$		0			0
$904$	42.5555	+	16.1281i	1.41538	+	0.536412i
$905$	4.89154	+	7.73262i	0.162600	+	0.257041i
$906$		0			0
$907$	−33.1020	+	33.1020i	−1.09913	+	1.09913i	−0.104622	+	0.994512i	$0.533363\pi$
$907$	−33.1020	+	33.1020i	−1.09913	+	1.09913i	−0.994512	+	0.104622i	$0.966637\pi$
$908$	4.54632	+	7.51796i	0.150875	+	0.249492i
$909$		0			0
$910$	−26.6069	−	0.744077i	−0.882009	−	0.0246659i
$911$	−13.7377	−	18.9083i	−0.455149	−	0.626459i	0.518345	−	0.855172i	$-0.326548\pi$
$911$	−13.7377	−	18.9083i	−0.455149	−	0.626459i	−0.973494	+	0.228713i	$0.926548\pi$
$912$		0			0
$913$	−17.1389	+	2.71454i	−0.567216	+	0.0898381i
$914$	11.6448	−	25.0652i	0.385177	−	0.829083i
$915$		0			0
$916$	−7.57897	+	3.08714i	−0.250416	+	0.102002i
$917$	−11.6142	+	22.7941i	−0.383533	+	0.752727i
$918$		0			0
$919$	0.383432	+	1.18008i	0.0126483	+	0.0389273i	0.957181	−	0.289489i	$-0.0934852\pi$
$919$	0.383432	+	1.18008i	0.0126483	+	0.0389273i	−0.944533	+	0.328416i	$0.893485\pi$
$920$	−22.5662	−	10.2552i	−0.743984	−	0.338102i
$921$		0			0
$922$	−20.0869	−	13.5074i	−0.661528	−	0.444842i
$923$	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
$928$	42.2605	+	5.63397i	1.38727	+	0.184944i
$929$	−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
$932$	51.1018	−	11.9506i	1.67390	−	0.391455i
$933$		0			0
$934$	0.356356	−	2.93672i	0.0116603	−	0.0960925i
$935$	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	$0.862175\pi$
$938$	50.8408	+	64.8834i	1.66001	+	2.11852i
$939$		0			0
$940$	2.91517	+	0.436748i	0.0950824	+	0.0142451i
$941$	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
$944$	13.8447	−	13.5223i	0.450605	−	0.440113i
$945$		0			0
$946$	49.8647	−	9.76614i	1.62124	−	0.317525i
$947$	−21.8024	−	42.7895i	−0.708482	−	1.39047i	−0.911501	−	0.411299i	$-0.865075\pi$
$947$	−21.8024	−	42.7895i	−0.708482	−	1.39047i	0.203019	−	0.979175i	$-0.434925\pi$
$948$		0			0
$949$		−	31.0579i		−	1.00818i
$950$	5.36948	−	12.4768i	0.174209	−	0.404799i
$951$		0			0
$952$	1.47624	−	7.09346i	0.0478452	−	0.229900i
$953$	−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
$956$	−0.932016	+	3.78381i	−0.0301436	+	0.122377i
$957$		0			0
$958$	−22.9580	+	0.834317i	−0.741738	+	0.0269556i
$959$	−52.3048	−	38.0017i	−1.68901	−	1.22714i
$960$		0			0
$961$	25.7919	−	18.7389i	0.831995	−	0.604480i
$962$	0.793911	−	0.622087i	0.0255967	−	0.0200569i
$963$		0			0
$964$	54.0461	−	3.93338i	1.74071	−	0.126686i
$965$	15.8686	−	26.7437i	0.510829	−	0.860910i
$966$		0			0
$967$	−33.4966	−	17.0674i	−1.07718	−	0.548849i	−0.176928	−	0.984224i	$-0.556616\pi$
$967$	−33.4966	−	17.0674i	−1.07718	−	0.548849i	−0.900249	+	0.435375i	$0.856616\pi$
$968$	−18.8400	+	17.1094i	−0.605541	+	0.549916i
$969$		0			0
$970$	−0.480743	−	0.262130i	−0.0154357	−	0.00841649i
$971$	−38.7039	−	12.5757i	−1.24207	−	0.403572i	−0.386996	−	0.922081i	$-0.626487\pi$
$971$	−38.7039	−	12.5757i	−1.24207	−	0.403572i	−0.855072	+	0.518509i	$0.826487\pi$
$972$		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
$980$	38.9601	+	27.8111i	1.24453	+	0.888394i
$981$		0			0
$982$	3.90357	+	1.11334i	0.124568	+	0.0355281i
$983$	−12.7441	+	25.0117i	−0.406474	+	0.797750i	−0.999975	−	0.00708356i	$-0.997745\pi$
$983$	−12.7441	+	25.0117i	−0.406474	+	0.797750i	0.593501	+	0.804833i	$0.297745\pi$
$984$		0			0
$985$	−9.80293	+	8.61719i	−0.312347	+	0.274567i
$986$	−5.88507	−	2.73410i	−0.187419	−	0.0870714i
$987$		0			0
$988$	7.08310	+	2.98291i	0.225343	+	0.0948991i
$989$	18.5087	+	25.4750i	0.588542	+	0.810058i
$990$		0			0
$991$	12.6905	−	17.4669i	0.403126	−	0.554855i	−0.558399	−	0.829572i	$-0.688584\pi$
$991$	12.6905	−	17.4669i	0.403126	−	0.554855i	0.961525	+	0.274717i	$0.0885842\pi$
$992$	39.4563	−	21.3396i	1.25274	−	0.677533i
$993$		0			0
$994$	−37.8356	−	35.1820i	−1.20007	−	1.11591i
$995$	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	$0.563023\pi$
$998$	13.3275	+	36.4560i	0.421874	+	1.15399i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.485574 - 1.32824i) q^{2} +(-1.52844 + 1.28992i) q^{4} +(2.16662 - 0.552943i) q^{5} +(-2.97520 + 2.97520i) q^{7} +(2.45549 + 1.40378i) q^{8} +O(q^{10})\)	\(q+(-0.485574 - 1.32824i) q^{2} +(-1.52844 + 1.28992i) q^{4} +(2.16662 - 0.552943i) q^{5} +(-2.97520 + 2.97520i) q^{7} +(2.45549 + 1.40378i) q^{8} +(-1.78650 - 2.60930i) q^{10} +(-2.62851 - 3.61783i) q^{11} +(-1.97584 + 0.312943i) q^{13} +(5.39645 + 2.50709i) q^{14} +(0.672230 - 3.94311i) q^{16} +(-0.276399 + 0.542463i) q^{17} +(0.593603 + 1.82692i) q^{19} +(-2.59829 + 3.63990i) q^{20} +(-3.52901 + 5.24801i) q^{22} +(-3.87093 - 0.613095i) q^{23} +(4.38851 - 2.39604i) q^{25} +(1.37508 + 2.47243i) q^{26} +(0.709641 - 8.38516i) q^{28} +(-7.16789 - 2.32899i) q^{29} +(-7.54161 + 2.45042i) q^{31} +(-5.56381 + 1.02179i) q^{32} +(0.854732 + 0.103717i) q^{34} +(-4.80102 + 8.09125i) q^{35} +(-0.0557708 - 0.352123i) q^{37} +(2.13835 - 1.67555i) q^{38} +(6.09632 + 1.68371i) q^{40} +(-6.95445 - 5.05270i) q^{41} +(-5.68128 - 5.68128i) q^{43} +(8.68421 + 2.13907i) q^{44} +(1.06529 + 5.43922i) q^{46} +(-0.299237 - 0.587287i) q^{47} -10.7036i q^{49} +(-5.31346 - 4.66553i) q^{50} +(2.61628 - 3.02699i) q^{52} +(3.58582 + 7.03757i) q^{53} +(-7.69544 - 6.38506i) q^{55} +(-11.4821 + 3.12904i) q^{56} +(0.387089 + 10.6516i) q^{58} +(3.91416 + 2.84381i) q^{59} +(-0.162666 + 0.118184i) q^{61} +(6.91675 + 8.82720i) q^{62} +(4.05882 + 6.89391i) q^{64} +(-4.10787 + 1.77056i) q^{65} +(12.3429 + 6.28904i) q^{67} +(-0.277274 - 1.18565i) q^{68} +(13.0784 + 2.44800i) q^{70} +(-8.25771 - 2.68309i) q^{71} +(-2.42869 + 15.3341i) q^{73} +(-0.440622 + 0.245059i) q^{74} +(-3.26386 - 2.02664i) q^{76} +(18.5841 + 2.94343i) q^{77} +(-2.38682 + 7.34587i) q^{79} +(-0.723845 - 8.91493i) q^{80} +(-3.33429 + 11.6906i) q^{82} +(1.76165 - 3.45743i) q^{83} +(-0.298901 + 1.32815i) q^{85} +(-4.78741 + 10.3048i) q^{86} +(-1.37564 - 12.5734i) q^{88} +(-1.32210 - 1.81971i) q^{89} +(4.94746 - 6.80959i) q^{91} +(6.70731 - 4.05610i) q^{92} +(-0.634755 + 0.682630i) q^{94} +(2.29630 + 3.63002i) q^{95} +(0.154282 - 0.0786106i) q^{97} +(-14.2170 + 5.19740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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