LMFDB - Embedded newform 900.2.bj.f.127.10

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			127.10
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.729889 + 1.21131i) q^{2} +(-0.934525 - 1.76824i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(1.89964 - 1.89964i) q^{7} +(2.82398 + 0.158622i) q^{8} +O(q^{10})$	\(q+(-0.729889 + 1.21131i) q^{2} +(-0.934525 - 1.76824i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(1.89964 - 1.89964i) q^{7} +(2.82398 + 0.158622i) q^{8} +(3.15025 - 0.275559i) q^{10} +(-0.371763 - 0.511688i) q^{11} +(-1.67521 + 0.265328i) q^{13} +(0.914521 + 3.68758i) q^{14} +(-2.25333 + 3.30492i) q^{16} +(0.541217 - 1.06220i) q^{17} +(-0.913372 - 2.81107i) q^{19} +(-1.96554 + 4.01704i) q^{20} +(0.891157 - 0.0768435i) q^{22} +(-4.19377 - 0.664227i) q^{23} +(-1.53335 + 4.75908i) q^{25} +(0.901327 - 2.22286i) q^{26} +(-5.13429 - 1.58376i) q^{28} +(5.22865 + 1.69889i) q^{29} +(-7.39865 + 2.40397i) q^{31} +(-2.35859 - 5.14170i) q^{32} +(0.891619 + 1.43087i) q^{34} +(-5.93440 - 0.932412i) q^{35} +(0.788923 + 4.98106i) q^{37} +(4.07173 + 0.945396i) q^{38} +(-3.43124 - 5.31287i) q^{40} +(-6.93315 - 5.03723i) q^{41} +(-6.55061 - 6.55061i) q^{43} +(-0.557364 + 1.13555i) q^{44} +(3.86557 - 4.59512i) q^{46} +(-3.03945 - 5.96526i) q^{47} -0.217294i q^{49} +(-4.64553 - 5.33095i) q^{50} +(2.03469 + 2.71422i) q^{52} +(-4.62574 - 9.07852i) q^{53} +(-0.435374 + 1.34559i) q^{55} +(5.66587 - 5.06322i) q^{56} +(-5.87421 + 5.09350i) q^{58} +(5.41851 + 3.93677i) q^{59} +(10.3079 - 7.48916i) q^{61} +(2.48825 - 10.7167i) q^{62} +(7.94968 + 0.895887i) q^{64} +(2.68507 + 2.67845i) q^{65} +(-4.48471 - 2.28507i) q^{67} +(-2.38400 + 0.0356501i) q^{68} +(5.46089 - 6.50782i) q^{70} +(-10.6460 - 3.45911i) q^{71} +(-1.16618 + 7.36296i) q^{73} +(-6.60942 - 2.68000i) q^{74} +(-4.11707 + 4.24207i) q^{76} +(-1.67824 - 0.265808i) q^{77} +(2.84085 - 8.74324i) q^{79} +(8.93994 - 0.278475i) q^{80} +(11.1621 - 4.72155i) q^{82} +(-1.18719 + 2.32999i) q^{83} +(-2.63235 + 0.420254i) q^{85} +(12.7160 - 3.15358i) q^{86} +(-0.968686 - 1.50396i) q^{88} +(9.57838 + 13.1835i) q^{89} +(-2.67828 + 3.68634i) q^{91} +(2.74467 + 8.03631i) q^{92} +(9.44421 + 0.672270i) q^{94} +(-3.87820 + 5.35176i) q^{95} +(-14.4118 + 7.34318i) q^{97} +(0.263210 + 0.158601i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.729889	+	1.21131i	−0.516109	+	0.856523i
$2$	−0.729889	+	1.21131i	−0.516109	+	0.856523i
$3$		0			0
$3$		0			0
$4$	−0.934525	−	1.76824i	−0.467262	−	0.884119i
$5$	−1.31656	−	1.80739i	−0.588783	−	0.808291i
$5$	−1.31656	−	1.80739i	−0.588783	−	0.808291i
$6$		0			0
$7$	1.89964	−	1.89964i	0.717998	−	0.717998i	−0.250197	−	0.968195i	$-0.580495\pi$
$7$	1.89964	−	1.89964i	0.717998	−	0.717998i	0.968195	+	0.250197i	$0.0804954\pi$
$8$	2.82398	+	0.158622i	0.998426	+	0.0560812i
$9$		0			0
$10$	3.15025	−	0.275559i	0.996196	−	0.0871395i
$11$	−0.371763	−	0.511688i	−0.112091	−	0.154280i	0.749286	−	0.662247i	$-0.230397\pi$
$11$	−0.371763	−	0.511688i	−0.112091	−	0.154280i	−0.861376	+	0.507967i	$0.830397\pi$
$12$		0			0
$13$	−1.67521	+	0.265328i	−0.464621	+	0.0735887i	−0.384356	−	0.923185i	$-0.625577\pi$
$13$	−1.67521	+	0.265328i	−0.464621	+	0.0735887i	−0.0802646	+	0.996774i	$0.525577\pi$
$14$	0.914521	+	3.68758i	0.244416	+	0.985547i
$15$		0			0
$16$	−2.25333	+	3.30492i	−0.563332	+	0.826231i
$17$	0.541217	−	1.06220i	0.131264	−	0.257621i	−0.816014	−	0.578032i	$-0.803821\pi$
$17$	0.541217	−	1.06220i	0.131264	−	0.257621i	0.947279	+	0.320411i	$0.103821\pi$
$18$		0			0
$19$	−0.913372	−	2.81107i	−0.209542	−	0.644904i	−0.999496	−	0.0317382i	$-0.989896\pi$
$19$	−0.913372	−	2.81107i	−0.209542	−	0.644904i	0.789954	−	0.613166i	$-0.210104\pi$
$20$	−1.96554	+	4.01704i	−0.439509	+	0.898238i
$21$		0			0
$22$	0.891157	−	0.0768435i	0.189995	−	0.0163831i
$23$	−4.19377	−	0.664227i	−0.874461	−	0.138501i	−0.296959	−	0.954890i	$-0.595972\pi$
$23$	−4.19377	−	0.664227i	−0.874461	−	0.138501i	−0.577502	+	0.816389i	$0.695972\pi$
$24$		0			0
$25$	−1.53335	+	4.75908i	−0.306669	+	0.951816i
$26$	0.901327	−	2.22286i	0.176765	−	0.435938i
$27$		0			0
$28$	−5.13429	−	1.58376i	−0.970289	−	0.299302i
$29$	5.22865	+	1.69889i	0.970936	+	0.315476i	0.751194	−	0.660082i	$-0.229478\pi$
$29$	5.22865	+	1.69889i	0.970936	+	0.315476i	0.219742	+	0.975558i	$0.429478\pi$
$30$		0			0
$31$	−7.39865	+	2.40397i	−1.32884	+	0.431765i	−0.885520	−	0.464601i	$-0.846198\pi$
$31$	−7.39865	+	2.40397i	−1.32884	+	0.431765i	−0.443316	+	0.896366i	$0.646198\pi$
$32$	−2.35859	−	5.14170i	−0.416944	−	0.908932i
$33$		0			0
$34$	0.891619	+	1.43087i	0.152911	+	0.245392i
$35$	−5.93440	−	0.932412i	−1.00310	−	0.157606i
$36$		0			0
$37$	0.788923	+	4.98106i	0.129698	+	0.818882i	0.963674	+	0.267081i	$0.0860592\pi$
$37$	0.788923	+	4.98106i	0.129698	+	0.818882i	−0.833976	+	0.551801i	$0.813941\pi$
$38$	4.07173	+	0.945396i	0.660522	+	0.153363i
$39$		0			0
$40$	−3.43124	−	5.31287i	−0.542527	−	0.840039i
$41$	−6.93315	−	5.03723i	−1.08278	−	0.786683i	−0.104612	−	0.994513i	$-0.533360\pi$
$41$	−6.93315	−	5.03723i	−1.08278	−	0.786683i	−0.978165	+	0.207830i	$0.933360\pi$
$42$		0			0
$43$	−6.55061	−	6.55061i	−0.998959	−	0.998959i	0.00104006	−	0.999999i	$-0.499669\pi$
$43$	−6.55061	−	6.55061i	−0.998959	−	0.998959i	−0.999999	+	0.00104006i	$0.999669\pi$
$44$	−0.557364	+	1.13555i	−0.0840258	+	0.171191i
$45$		0			0
$46$	3.86557	−	4.59512i	0.569947	−	0.677514i
$47$	−3.03945	−	5.96526i	−0.443349	−	0.870122i	−0.999244	−	0.0388697i	$-0.987624\pi$
$47$	−3.03945	−	5.96526i	−0.443349	−	0.870122i	0.555895	−	0.831253i	$-0.312376\pi$
$48$		0			0
$49$		−	0.217294i		−	0.0310420i
$50$	−4.64553	−	5.33095i	−0.656977	−	0.753910i
$51$		0			0
$52$	2.03469	+	2.71422i	0.282161	+	0.376395i
$53$	−4.62574	−	9.07852i	−0.635394	−	1.24703i	−0.954188	−	0.299207i	$-0.903278\pi$
$53$	−4.62574	−	9.07852i	−0.635394	−	1.24703i	0.318794	−	0.947824i	$-0.396722\pi$
$54$		0			0
$55$	−0.435374	+	1.34559i	−0.0587058	+	0.181439i
$56$	5.66587	−	5.06322i	0.757134	−	0.676602i
$57$		0			0
$58$	−5.87421	+	5.09350i	−0.771322	+	0.668809i
$59$	5.41851	+	3.93677i	0.705429	+	0.512524i	0.881696	−	0.471818i	$-0.156402\pi$
$59$	5.41851	+	3.93677i	0.705429	+	0.512524i	−0.176267	+	0.984342i	$0.556402\pi$
$60$		0			0
$61$	10.3079	−	7.48916i	1.31980	−	0.958889i	0.319863	−	0.947464i	$-0.396363\pi$
$61$	10.3079	−	7.48916i	1.31980	−	0.958889i	0.999935	−	0.0114249i	$-0.00363674\pi$
$62$	2.48825	−	10.7167i	0.316008	−	1.36102i
$63$		0			0
$64$	7.94968	+	0.895887i	0.993710	+	0.111986i
$65$	2.68507	+	2.67845i	0.333042	+	0.332221i
$66$		0			0
$67$	−4.48471	−	2.28507i	−0.547894	−	0.279166i	0.158053	−	0.987431i	$-0.449478\pi$
$67$	−4.48471	−	2.28507i	−0.547894	−	0.279166i	−0.705947	+	0.708265i	$0.749478\pi$
$68$	−2.38400	+	0.0356501i	−0.289102	+	0.00432321i
$69$		0			0
$70$	5.46089	−	6.50782i	0.652701	−	0.777833i
$71$	−10.6460	−	3.45911i	−1.26345	−	0.410520i	−0.400728	−	0.916197i	$-0.631243\pi$
$71$	−10.6460	−	3.45911i	−1.26345	−	0.410520i	−0.862723	+	0.505677i	$0.831243\pi$
$72$		0			0
$73$	−1.16618	+	7.36296i	−0.136491	+	0.861770i	0.820499	+	0.571648i	$0.193696\pi$
$73$	−1.16618	+	7.36296i	−0.136491	+	0.861770i	−0.956990	+	0.290121i	$0.906304\pi$
$74$	−6.60942	−	2.68000i	−0.768329	−	0.311543i
$75$		0			0
$76$	−4.11707	+	4.24207i	−0.472261	+	0.486599i
$77$	−1.67824	−	0.265808i	−0.191254	−	0.0302916i
$78$		0			0
$79$	2.84085	−	8.74324i	0.319621	−	0.983691i	−0.654190	−	0.756330i	$-0.726990\pi$
$79$	2.84085	−	8.74324i	0.319621	−	0.983691i	0.973811	−	0.227361i	$-0.0730097\pi$
$80$	8.93994	−	0.278475i	0.999515	−	0.0311345i
$81$		0			0
$82$	11.1621	−	4.72155i	1.23264	−	0.521408i
$83$	−1.18719	+	2.32999i	−0.130311	+	0.255749i	−0.946938	−	0.321416i	$-0.895841\pi$
$83$	−1.18719	+	2.32999i	−0.130311	+	0.255749i	0.816627	+	0.577165i	$0.195841\pi$
$84$		0			0
$85$	−2.63235	+	0.420254i	−0.285519	+	0.0455830i
$86$	12.7160	−	3.15358i	1.37120	−	0.340059i
$87$		0			0
$88$	−0.968686	−	1.50396i	−0.103262	−	0.160323i
$89$	9.57838	+	13.1835i	1.01531	+	1.39745i	0.915443	+	0.402447i	$0.131840\pi$
$89$	9.57838	+	13.1835i	1.01531	+	1.39745i	0.0998628	+	0.995001i	$0.468160\pi$
$90$		0			0
$91$	−2.67828	+	3.68634i	−0.280760	+	0.386433i
$92$	2.74467	+	8.03631i	0.286151	+	0.837844i
$93$		0			0
$94$	9.44421	+	0.672270i	0.974096	+	0.0693394i
$95$	−3.87820	+	5.35176i	−0.397895	+	0.549079i
$96$		0			0
$97$	−14.4118	+	7.34318i	−1.46330	+	0.745587i	−0.990748	−	0.135716i	$-0.956666\pi$
$97$	−14.4118	+	7.34318i	−1.46330	+	0.745587i	−0.472550	+	0.881304i	$0.656666\pi$
$98$	0.263210	+	0.158601i	0.0265882	+	0.0160211i
$99$		0			0
$100$	9.84813	−	1.73616i	0.984813	−	0.173616i
$101$	5.68594			0.565772			0.282886	−	0.959154i	$-0.408708\pi$
$101$	5.68594			0.565772			0.282886	+	0.959154i	$0.408708\pi$
$102$		0			0
$103$	−6.63638	+	3.38140i	−0.653902	+	0.333180i	−0.749272	−	0.662262i	$-0.769597\pi$
$103$	−6.63638	+	3.38140i	−0.653902	+	0.333180i	0.0953702	+	0.995442i	$0.469597\pi$
$104$	−4.77285	+	0.483554i	−0.468016	+	0.0474164i
$105$		0			0
$106$	14.3731	+	1.02313i	1.39604	+	0.0993749i
$107$	12.5222	−	12.5222i	1.21057	−	1.21057i	0.239731	−	0.970839i	$-0.422941\pi$
$107$	12.5222	−	12.5222i	1.21057	−	1.21057i	0.970839	−	0.239731i	$-0.0770594\pi$
$108$		0			0
$109$	8.30989	−	11.4376i	0.795943	−	1.09552i	−0.197400	−	0.980323i	$-0.563250\pi$
$109$	8.30989	−	11.4376i	0.795943	−	1.09552i	0.993343	−	0.115198i	$-0.0367504\pi$
$110$	−1.31215	−	1.50950i	−0.125108	−	0.143925i
$111$		0			0
$112$	1.99766	+	10.5587i	0.188761	+	0.997703i
$113$	−13.0323	+	2.06411i	−1.22598	+	0.194175i	−0.735649	−	0.677363i	$-0.763123\pi$
$113$	−13.0323	+	2.06411i	−1.22598	+	0.194175i	−0.490327	+	0.871539i	$0.663123\pi$
$114$		0			0
$115$	4.32082	+	8.45428i	0.402919	+	0.788366i
$116$	−1.88226	−	10.8332i	−0.174763	−	1.00583i
$117$		0			0
$118$	−8.72355	+	3.69006i	−0.803068	+	0.339698i
$119$	−0.989679	−	3.04592i	−0.0907237	−	0.279219i
$120$		0			0
$121$	3.27557	−	10.0812i	0.297779	−	0.916470i
$122$	1.54801	+	17.9523i	0.140150	+	1.62533i
$123$		0			0
$124$	11.1650	+	10.8360i	1.00265	+	0.973101i
$125$	10.6203	−	3.49425i	0.949906	−	0.312535i
$126$		0			0
$127$	−0.370148	+	2.33702i	−0.0328453	+	0.207377i	−0.998653	−	0.0518815i	$-0.983478\pi$
$127$	−0.370148	+	2.33702i	−0.0328453	+	0.207377i	0.965808	+	0.259259i	$0.0834782\pi$
$128$	−6.88757	+	8.97560i	−0.608781	+	0.793338i
$129$		0			0
$130$	−5.20423	+	1.29747i	−0.456441	+	0.113796i
$131$	6.46861	−	2.10178i	0.565165	−	0.183633i	−0.0124790	−	0.999922i	$-0.503972\pi$
$131$	6.46861	−	2.10178i	0.565165	−	0.183633i	0.577644	+	0.816289i	$0.303972\pi$
$132$		0			0
$133$	−7.07512	−	3.60495i	−0.613490	−	0.312589i
$134$	6.04126	−	3.76451i	0.521886	−	0.325204i
$135$		0			0
$136$	1.69687	−	2.91377i	0.145506	−	0.249854i
$137$	2.37978	+	15.0253i	0.203318	+	1.28370i	0.852364	+	0.522950i	$0.175168\pi$
$137$	2.37978	+	15.0253i	0.203318	+	1.28370i	−0.649046	+	0.760749i	$0.724832\pi$
$138$		0			0
$139$	−7.83437	+	5.69201i	−0.664503	+	0.482790i	−0.868181	−	0.496248i	$-0.834711\pi$
$139$	−7.83437	+	5.69201i	−0.664503	+	0.482790i	0.203678	+	0.979038i	$0.434711\pi$
$140$	3.89712	+	11.3648i	0.329366	+	0.960500i
$141$		0			0
$142$	11.9605	−	10.3708i	1.00370	−	0.870301i
$143$	0.758548	+	0.758548i	0.0634330	+	0.0634330i
$144$		0			0
$145$	−3.81326	−	11.6869i	−0.316674	−	0.970546i
$146$	−8.06762	−	6.78674i	−0.667681	−	0.561675i
$147$		0			0
$148$	8.07044	−	6.04993i	0.663386	−	0.497301i
$149$			1.52894i			0.125256i	0.998037	+	0.0626280i	$0.0199482\pi$
$149$			1.52894i			0.125256i	−0.998037	+	0.0626280i	$0.980052\pi$
$150$		0			0
$151$		−	21.1225i		−	1.71893i	−0.511199	−	0.859463i	$-0.670798\pi$
$151$		−	21.1225i		−	1.71893i	0.511199	−	0.859463i	$-0.329202\pi$
$152$	−2.13345	−	8.08328i	−0.173045	−	0.655640i
$153$		0			0
$154$	1.54691	−	1.83886i	0.124653	−	0.148179i
$155$	14.0857	+	10.2073i	1.13139	+	0.819870i
$156$		0			0
$157$	−10.5994	−	10.5994i	−0.845925	−	0.845925i	0.143697	−	0.989622i	$-0.454101\pi$
$157$	−10.5994	−	10.5994i	−0.845925	−	0.845925i	−0.989622	+	0.143697i	$0.954101\pi$
$158$	8.51723	+	9.82273i	0.677595	+	0.781455i
$159$		0			0
$160$	−6.18784	+	11.0323i	−0.489192	+	0.872176i
$161$	−9.22846	+	6.70487i	−0.727305	+	0.528418i
$162$		0			0
$163$	−1.90252	−	12.0120i	−0.149017	−	0.940854i	−0.942971	−	0.332876i	$-0.891981\pi$
$163$	−1.90252	−	12.0120i	−0.149017	−	0.940854i	0.793954	−	0.607978i	$-0.208019\pi$
$164$	−2.42782	+	16.9669i	−0.189581	+	1.32489i
$165$		0			0
$166$	−1.95581	−	3.13868i	−0.151800	−	0.243609i
$167$	−8.22079	−	4.18870i	−0.636144	−	0.324132i	0.106006	−	0.994366i	$-0.466194\pi$
$167$	−8.22079	−	4.18870i	−0.636144	−	0.324132i	−0.742150	+	0.670234i	$0.766194\pi$
$168$		0			0
$169$	−9.62779	+	3.12826i	−0.740599	+	0.240635i
$170$	1.41227	−	3.49533i	0.108316	−	0.268079i
$171$		0			0
$172$	−5.46133	+	17.7048i	−0.416423	+	1.34997i
$173$	−1.12169	+	7.08206i	−0.0852803	+	0.538439i	0.907649	+	0.419730i	$0.137875\pi$
$173$	−1.12169	+	7.08206i	−0.0852803	+	0.538439i	−0.992929	+	0.118708i	$0.962125\pi$
$174$		0			0
$175$	6.12775	+	11.9534i	0.463214	+	0.903590i
$176$	2.52879	−	0.0756476i	0.190615	−	0.00570216i
$177$		0			0
$178$	−22.9604	+	1.97985i	−1.72096	+	0.148396i
$179$	−0.835280	+	2.57073i	−0.0624318	+	0.192145i	−0.977407	−	0.211364i	$-0.932210\pi$
$179$	−0.835280	+	2.57073i	−0.0624318	+	0.192145i	0.914976	+	0.403509i	$0.132210\pi$
$180$		0			0
$181$	1.34525	+	4.14024i	0.0999914	+	0.307742i	0.988522	−	0.151075i	$-0.0482735\pi$
$181$	1.34525	+	4.14024i	0.0999914	+	0.307742i	−0.888531	+	0.458817i	$0.848273\pi$
$182$	−2.51044	−	5.93483i	−0.186086	−	0.439919i
$183$		0			0
$184$	−11.7377	−	2.54098i	−0.865317	−	0.187324i
$185$	7.96408	−	7.98376i	0.585531	−	0.586978i
$186$		0			0
$187$	−0.744719	+	0.117952i	−0.0544592	+	0.00862550i
$188$	−7.70755	+	10.9492i	−0.562131	+	0.798549i
$189$		0			0
$190$	−3.65197	−	8.60389i	−0.264942	−	0.624191i
$191$	−10.3534	+	14.2503i	−0.749148	+	1.03111i	0.248892	+	0.968531i	$0.419934\pi$
$191$	−10.3534	+	14.2503i	−0.749148	+	1.03111i	−0.998040	+	0.0625824i	$0.980066\pi$
$192$		0			0
$193$	5.57116	−	5.57116i	0.401021	−	0.401021i	−0.477572	−	0.878593i	$-0.658483\pi$
$193$	5.57116	−	5.57116i	0.401021	−	0.401021i	0.878593	+	0.477572i	$0.158483\pi$
$194$	1.62418	−	22.8168i	0.116609	−	1.63815i
$195$		0			0
$196$	−0.384228	+	0.203067i	−0.0274448	+	0.0145048i
$197$	−6.63385	+	3.38011i	−0.472642	+	0.240823i	−0.674052	−	0.738684i	$-0.735448\pi$
$197$	−6.63385	+	3.38011i	−0.472642	+	0.240823i	0.201410	+	0.979507i	$0.435448\pi$
$198$		0			0
$199$	11.2356			0.796467			0.398234	−	0.917284i	$-0.369623\pi$
$199$	11.2356			0.796467			0.398234	+	0.917284i	$0.369623\pi$
$200$	−5.08502	+	13.1963i	−0.359565	+	0.933120i
$201$		0			0
$202$	−4.15010	+	6.88741i	−0.292000	+	0.484597i
$203$	13.1599	−	6.70529i	0.923642	−	0.470619i
$204$		0			0
$205$	0.0236448	+	19.1628i	0.00165143	+	1.33838i
$206$	0.747904	−	10.5067i	0.0521089	−	0.732039i
$207$		0			0
$208$	2.89792	−	6.13432i	0.200934	−	0.425339i
$209$	−1.09883	+	1.51241i	−0.0760079	+	0.104616i
$210$		0			0
$211$	−8.18653	−	11.2678i	−0.563584	−	0.775706i	0.428193	−	0.903687i	$-0.359150\pi$
$211$	−8.18653	−	11.2678i	−0.563584	−	0.775706i	−0.991777	+	0.127981i	$0.959150\pi$
$212$	−11.7301	+	16.6635i	−0.805628	+	1.14445i
$213$		0			0
$214$	6.02842	+	24.3081i	0.412094	+	1.66167i
$215$	−3.21527	+	20.4638i	−0.219280	+	1.39562i
$216$		0			0
$217$	−9.48811	+	18.6215i	−0.644095	+	1.26411i
$218$	7.78911	+	18.4140i	0.527545	+	1.24715i
$219$		0			0
$220$	2.78619	−	0.487643i	0.187845	−	0.0328769i
$221$	−0.624824	+	1.92301i	−0.0420302	+	0.129356i
$222$		0			0
$223$	21.4198	+	3.39257i	1.43438	+	0.227183i	0.824747	−	0.565502i	$-0.191318\pi$
$223$	21.4198	+	3.39257i	1.43438	+	0.227183i	0.609631	+	0.792685i	$0.291318\pi$
$224$	−14.2479	−	5.28690i	−0.951977	−	0.353246i
$225$		0			0
$226$	7.01186	−	17.2927i	0.466422	−	1.15029i
$227$	0.210388	−	1.32834i	0.0139640	−	0.0881651i	−0.979722	−	0.200361i	$-0.935788\pi$
$227$	0.210388	−	1.32834i	0.0139640	−	0.0881651i	0.993686	+	0.112196i	$0.0357885\pi$
$228$		0			0
$229$	12.7082	+	4.12914i	0.839781	+	0.272862i	0.697160	−	0.716916i	$-0.254447\pi$
$229$	12.7082	+	4.12914i	0.839781	+	0.272862i	0.142622	+	0.989777i	$0.454447\pi$
$230$	−13.3944	−	0.936851i	−0.883203	−	0.0617741i
$231$		0			0
$232$	14.4961	+	5.62701i	0.951716	+	0.369431i
$233$	−12.2616	−	6.24760i	−0.803284	−	0.409294i	0.00360719	−	0.999993i	$-0.498852\pi$
$233$	−12.2616	−	6.24760i	−0.803284	−	0.409294i	−0.806891	+	0.590700i	$0.798852\pi$
$234$		0			0
$235$	−6.77995	+	13.3471i	−0.442275	+	0.870669i
$236$	1.89743	−	13.2602i	0.123512	−	0.863167i
$237$		0			0
$238$	4.41189	+	1.02438i	0.285981	+	0.0664006i
$239$	23.3147	−	16.9391i	1.50810	−	1.09570i	0.541089	−	0.840965i	$-0.318012\pi$
$239$	23.3147	−	16.9391i	1.50810	−	1.09570i	0.967011	−	0.254734i	$-0.0819879\pi$
$240$		0			0
$241$	15.2138	+	11.0535i	0.980007	+	0.712017i	0.957710	−	0.287734i	$-0.0929021\pi$
$241$	15.2138	+	11.0535i	0.980007	+	0.712017i	0.0222970	+	0.999751i	$0.492902\pi$
$242$	9.82058	+	11.3258i	0.631291	+	0.728053i
$243$		0			0
$244$	−22.8756	−	11.2281i	−1.46446	−	0.718805i
$245$	−0.392736	+	0.286081i	−0.0250910	+	0.0182770i
$246$		0			0
$247$	2.27595	+	4.46680i	0.144815	+	0.284216i
$248$	−21.2749	+	5.61516i	−1.35096	+	0.356563i
$249$		0			0
$250$	−3.51901	+	15.4148i	−0.222562	+	0.974919i
$251$			5.19716i			0.328042i	0.986457	+	0.164021i	$0.0524465\pi$
$251$			5.19716i			0.328042i	−0.986457	+	0.164021i	$0.947554\pi$
$252$		0			0
$253$	1.21921	+	2.39284i	0.0766511	+	0.150436i
$254$	−2.56068	−	2.15413i	−0.160671	−	0.135162i
$255$		0			0
$256$	−5.84503	−	14.8941i	−0.365314	−	0.930884i
$257$	2.26286	+	2.26286i	0.141153	+	0.141153i	0.774152	−	0.632999i	$-0.218176\pi$
$257$	2.26286	+	2.26286i	0.141153	+	0.141153i	−0.632999	+	0.774152i	$0.718176\pi$
$258$		0			0
$259$	10.9609	+	7.96358i	0.681079	+	0.494833i
$260$	2.22687	−	7.25092i	0.138105	−	0.449683i
$261$		0			0
$262$	−2.17547	+	9.36952i	−0.134401	+	0.578851i
$263$	−3.31222	−	20.9126i	−0.204240	−	1.28952i	−0.850325	−	0.526258i	$-0.823595\pi$
$263$	−3.31222	−	20.9126i	−0.204240	−	1.28952i	0.646085	−	0.763266i	$-0.276405\pi$
$264$		0			0
$265$	−10.3184	+	20.3129i	−0.633855	+	1.24781i
$266$	9.53075	−	5.93892i	0.584368	−	0.364138i
$267$		0			0
$268$	0.150518	+	10.0655i	0.00919438	+	0.614848i
$269$	1.93497	−	0.628710i	0.117977	−	0.0383331i	−0.249433	−	0.968392i	$-0.580244\pi$
$269$	1.93497	−	0.628710i	0.117977	−	0.0383331i	0.367411	+	0.930059i	$0.380244\pi$
$270$		0			0
$271$	6.63734	+	2.15660i	0.403190	+	0.131004i	0.503590	−	0.863943i	$-0.332012\pi$
$271$	6.63734	+	2.15660i	0.403190	+	0.131004i	−0.100400	+	0.994947i	$0.532012\pi$
$272$	2.29094	+	4.18216i	0.138909	+	0.253581i
$273$		0			0
$274$	−19.9372	−	8.08417i	−1.20445	−	0.488383i
$275$	3.00521	−	0.984657i	0.181221	−	0.0593770i
$276$		0			0
$277$	16.9639	+	2.68682i	1.01926	+	0.161435i	0.643633	−	0.765335i	$-0.277427\pi$
$277$	16.9639	+	2.68682i	1.01926	+	0.161435i	0.375629	+	0.926770i	$0.377427\pi$
$278$	−1.17654	−	13.6444i	−0.0705641	−	0.818334i
$279$		0			0
$280$	−16.6107	−	3.57443i	−0.992679	−	0.213613i
$281$	4.69025	+	14.4351i	0.279797	+	0.861126i	0.987910	+	0.155027i	$0.0495465\pi$
$281$	4.69025	+	14.4351i	0.279797	+	0.861126i	−0.708113	+	0.706099i	$0.750454\pi$
$282$		0			0
$283$	−3.45853	+	6.78774i	−0.205588	+	0.403489i	−0.970660	−	0.240455i	$-0.922703\pi$
$283$	−3.45853	+	6.78774i	−0.205588	+	0.403489i	0.765072	+	0.643945i	$0.222703\pi$
$284$	3.83246	+	22.0573i	0.227415	+	1.30886i
$285$		0			0
$286$	−1.47249	+	0.365178i	−0.0870701	+	0.0215934i
$287$	−22.7395	+	3.60158i	−1.34227	+	0.212594i
$288$		0			0
$289$	9.15700	+	12.6035i	0.538647	+	0.741384i
$290$	16.9397	+	3.91113i	0.994733	+	0.229669i
$291$		0			0
$292$	14.1093	−	4.81879i	0.825684	−	0.281998i
$293$	9.90518	−	9.90518i	0.578667	−	0.578667i	−0.355869	−	0.934536i	$-0.615815\pi$
$293$	9.90518	−	9.90518i	0.578667	−	0.578667i	0.934536	+	0.355869i	$0.115815\pi$
$294$		0			0
$295$	−0.0184793	−	14.9764i	−0.00107591	−	0.871958i
$296$	1.43780	+	14.1915i	0.0835702	+	0.824867i
$297$		0			0
$298$	−1.85202	−	1.11596i	−0.107285	−	0.0646458i
$299$	7.20169			0.416485
$300$		0			0
$301$	−24.8877			−1.43450
$302$	25.5858	+	15.4171i	1.47230	+	0.887153i
$303$		0			0
$304$	11.3485	+	3.31564i	0.650881	+	0.190165i
$305$	−27.1069	−	8.77060i	−1.55214	−	0.502203i
$306$		0			0
$307$	0.395752	−	0.395752i	0.0225868	−	0.0225868i	−0.695723	−	0.718310i	$-0.744916\pi$
$307$	0.395752	−	0.395752i	0.0225868	−	0.0225868i	0.718310	+	0.695723i	$0.244916\pi$
$308$	1.09835	+	3.21594i	0.0625842	+	0.183245i
$309$		0			0
$310$	−22.6451	+	9.61185i	−1.28616	+	0.545917i
$311$	7.94526	+	10.9357i	0.450535	+	0.620108i	0.972512	−	0.232851i	$-0.0748056\pi$
$311$	7.94526	+	10.9357i	0.450535	+	0.620108i	−0.521978	+	0.852959i	$0.674806\pi$
$312$		0			0
$313$	24.5092	−	3.88187i	1.38534	−	0.219416i	0.581154	−	0.813793i	$-0.302601\pi$
$313$	24.5092	−	3.88187i	1.38534	−	0.219416i	0.804187	+	0.594377i	$0.202601\pi$
$314$	20.5755	−	5.10274i	1.16114	−	0.287964i
$315$		0			0
$316$	−18.1150	+	3.14747i	−1.01905	+	0.177059i
$317$	9.93010	−	19.4889i	0.557730	−	1.09461i	−0.424236	−	0.905551i	$-0.639457\pi$
$317$	9.93010	−	19.4889i	0.557730	−	1.09461i	0.981966	−	0.189055i	$-0.0605425\pi$
$318$		0			0
$319$	−1.07452	−	3.30703i	−0.0601614	−	0.185158i
$320$	−8.84700	−	15.5477i	−0.494562	−	0.869142i
$321$		0			0
$322$	−1.38590	−	16.0723i	−0.0772331	−	0.895674i
$323$	−3.48025	−	0.551217i	−0.193646	−	0.0306705i
$324$		0			0
$325$	1.30596	−	8.37932i	0.0724419	−	0.464801i
$326$	15.9389	+	6.46291i	0.882772	+	0.357947i
$327$		0			0
$328$	−18.7800	−	15.3248i	−1.03695	−	0.846169i
$329$	−17.1057	−	5.55799i	−0.943070	−	0.306422i
$330$		0			0
$331$	−23.9793	+	7.79135i	−1.31802	+	0.428251i	−0.881815	−	0.471595i	$-0.843678\pi$
$331$	−23.9793	+	7.79135i	−1.31802	+	0.428251i	−0.436207	+	0.899846i	$0.643678\pi$
$332$	5.22943	−	0.0782004i	0.287002	−	0.00429180i
$333$		0			0
$334$	11.0741	−	6.90061i	0.605946	−	0.377584i
$335$	1.77436	+	11.1141i	0.0969434	+	0.607226i
$336$		0			0
$337$	−1.74034	−	10.9881i	−0.0948026	−	0.598560i	−0.988656	−	0.150200i	$-0.952008\pi$
$337$	−1.74034	−	10.9881i	−0.0948026	−	0.598560i	0.893853	−	0.448360i	$-0.147992\pi$
$338$	3.23794	−	13.9455i	0.176121	−	0.758534i
$339$		0			0
$340$	3.20311	+	4.26189i	0.173713	+	0.231133i
$341$	3.98063	+	2.89209i	0.215563	+	0.156616i
$342$		0			0
$343$	12.8847	+	12.8847i	0.695710	+	0.695710i
$344$	−17.4597	−	19.5378i	−0.941364	−	1.05341i
$345$		0			0
$346$	−7.75983	−	6.52782i	−0.417171	−	0.350938i
$347$	3.35501	+	6.58458i	0.180106	+	0.353479i	0.963355	−	0.268230i	$-0.0864387\pi$
$347$	3.35501	+	6.58458i	0.180106	+	0.353479i	−0.783248	+	0.621709i	$0.786439\pi$
$348$		0			0
$349$		−	16.4473i		−	0.880406i	−0.897898	−	0.440203i	$-0.854907\pi$
$349$		−	16.4473i		−	0.880406i	0.897898	−	0.440203i	$-0.145093\pi$
$350$	−18.9518	−	1.30205i	−1.01301	−	0.0695976i
$351$		0			0
$352$	−1.75411	+	3.11836i	−0.0934942	+	0.166209i
$353$	−5.94902	−	11.6756i	−0.316634	−	0.621430i	0.676757	−	0.736206i	$-0.263385\pi$
$353$	−5.94902	−	11.6756i	−0.316634	−	0.621430i	−0.993391	+	0.114777i	$0.963385\pi$
$354$		0			0
$355$	7.76416	+	23.7957i	0.412079	+	1.26294i
$356$	14.3603	−	29.2572i	0.761096	−	1.55063i
$357$		0			0
$358$	−2.50428	−	2.88813i	−0.132355	−	0.152642i
$359$	22.2780	+	16.1859i	1.17579	+	0.854259i	0.991690	−	0.128649i	$-0.0410639\pi$
$359$	22.2780	+	16.1859i	1.17579	+	0.854259i	0.184097	+	0.982908i	$0.441064\pi$
$360$		0			0
$361$	8.30345	−	6.03281i	0.437024	−	0.317516i
$362$	−5.99698	−	1.39241i	−0.315194	−	0.0731835i
$363$		0			0
$364$	9.02124	+	1.29086i	0.472841	+	0.0676597i
$365$	14.8431	−	7.58603i	0.776924	−	0.397071i
$366$		0			0
$367$	25.1586	+	12.8189i	1.31327	+	0.669143i	0.963504	−	0.267696i	$-0.0862621\pi$
$367$	25.1586	+	12.8189i	1.31327	+	0.669143i	0.349763	+	0.936838i	$0.386262\pi$
$368$	11.6452	−	12.3634i	0.607046	−	0.644484i
$369$		0			0
$370$	3.85788	+	15.4742i	0.200562	+	0.804465i
$371$	−26.0332	−	8.45871i	−1.35158	−	0.439154i
$372$		0			0
$373$	1.69813	−	10.7216i	0.0879257	−	0.555141i	−0.903921	−	0.427700i	$-0.859324\pi$
$373$	1.69813	−	10.7216i	0.0879257	−	0.555141i	0.991846	−	0.127440i	$-0.0406762\pi$
$374$	0.400686	−	0.988174i	0.0207190	−	0.0510973i
$375$		0			0
$376$	−7.63712	−	17.3279i	−0.393854	−	0.893616i
$377$	−9.20987	−	1.45870i	−0.474333	−	0.0751269i
$378$		0			0
$379$	1.53707	−	4.73061i	0.0789539	−	0.242995i	−0.903787	−	0.427983i	$-0.859224\pi$
$379$	1.53707	−	4.73061i	0.0789539	−	0.242995i	0.982741	+	0.184988i	$0.0592245\pi$
$380$	13.0875	+	1.85623i	0.671373	+	0.0952226i
$381$		0			0
$382$	−9.70459	−	22.9423i	−0.496530	−	1.17383i
$383$	10.6272	−	20.8571i	0.543025	−	1.06575i	−0.442587	−	0.896725i	$-0.645939\pi$
$383$	10.6272	−	20.8571i	0.543025	−	1.06575i	0.985612	−	0.169021i	$-0.0540606\pi$
$384$		0			0
$385$	1.72909	+	3.38320i	0.0881224	+	0.172424i
$386$	2.68205	+	10.8147i	0.136513	+	0.550454i
$387$		0			0
$388$	26.4527	+	18.6211i	1.34293	+	0.945344i
$389$	−16.0951	−	22.1530i	−0.816053	−	1.12320i	−0.990361	−	0.138510i	$-0.955769\pi$
$389$	−16.0951	−	22.1530i	−0.816053	−	1.12320i	0.174308	−	0.984691i	$-0.444231\pi$
$390$		0			0
$391$	−2.97528	+	4.09512i	−0.150466	+	0.207099i
$392$	0.0344675	−	0.613633i	0.00174087	−	0.0309932i
$393$		0			0
$394$	0.747618	−	10.5027i	0.0376645	−	0.529120i
$395$	−19.5426	+	6.37645i	−0.983296	+	0.320834i
$396$		0			0
$397$	14.3256	−	7.29924i	0.718980	−	0.366338i	−0.0559093	−	0.998436i	$-0.517806\pi$
$397$	14.3256	−	7.29924i	0.718980	−	0.366338i	0.774889	+	0.632097i	$0.217806\pi$
$398$	−8.20070	+	13.6097i	−0.411064	+	0.682192i
$399$		0			0
$400$	−12.2733	−	15.7914i	−0.613663	−	0.789568i
$401$	27.2043			1.35852			0.679259	−	0.733898i	$-0.262301\pi$
$401$	27.2043			1.35852			0.679259	+	0.733898i	$0.262301\pi$
$402$		0			0
$403$	11.7565	−	5.99022i	0.585632	−	0.298394i
$404$	−5.31365	−	10.0541i	−0.264364	−	0.500210i
$405$		0			0
$406$	−1.48309	+	20.8347i	−0.0736043	+	1.03401i
$407$	2.25546	−	2.25546i	0.111799	−	0.111799i
$408$		0			0
$409$	7.09641	−	9.76738i	0.350895	−	0.482966i	−0.596689	−	0.802473i	$-0.703517\pi$
$409$	7.09641	−	9.76738i	0.350895	−	0.482966i	0.947584	+	0.319507i	$0.103517\pi$
$410$	−23.2292	−	13.9580i	−1.14721	−	0.689338i
$411$		0			0
$412$	12.1810	+	8.57469i	0.600114	+	0.422445i
$413$	17.7717	−	2.81476i	0.874488	−	0.138505i
$414$		0			0
$415$	5.77421	−	0.921849i	0.283445	−	0.0452518i
$416$	5.31538	+	7.98764i	0.260608	+	0.391626i
$417$		0			0
$418$	−1.02997	−	2.43492i	−0.0503775	−	0.119096i
$419$	3.46650	+	10.6688i	0.169350	+	0.521205i	0.999330	−	0.0365872i	$-0.0116487\pi$
$419$	3.46650	+	10.6688i	0.169350	+	0.521205i	−0.829981	+	0.557792i	$0.811649\pi$
$420$		0			0
$421$	−0.470464	+	1.44794i	−0.0229290	+	0.0705682i	−0.961866	−	0.273520i	$-0.911812\pi$
$421$	−0.470464	+	1.44794i	−0.0229290	+	0.0705682i	0.938937	+	0.344088i	$0.111812\pi$
$422$	19.6240	−	1.69216i	0.955281	−	0.0823729i
$423$		0			0
$424$	−11.6229	−	26.3713i	−0.564459	−	1.28070i
$425$	4.22522	+	4.20441i	0.204953	+	0.203944i
$426$		0			0
$427$	5.35469	−	33.8082i	0.259132	−	1.63609i
$428$	−33.8446	−	10.4400i	−1.63594	−	0.504634i
$429$		0			0
$430$	−22.4411	−	18.8310i	−1.08221	−	0.908111i
$431$	−36.0071	+	11.6994i	−1.73440	+	0.563541i	−0.994074	−	0.108708i	$-0.965329\pi$
$431$	−36.0071	+	11.6994i	−1.73440	+	0.563541i	−0.740326	+	0.672248i	$0.765329\pi$
$432$		0			0
$433$	−33.3181	−	16.9764i	−1.60116	−	0.815834i	−0.999859	−	0.0168151i	$-0.994647\pi$
$433$	−33.3181	−	16.9764i	−1.60116	−	0.815834i	−0.601306	−	0.799019i	$-0.705353\pi$
$434$	−15.6310	−	25.0846i	−0.750313	−	1.20410i
$435$		0			0
$436$	−27.9902	−	4.00516i	−1.34049	−	0.191812i
$437$	1.96328	+	12.3957i	0.0939165	+	0.592965i
$438$		0			0
$439$	3.13332	−	2.27649i	0.149545	−	0.108651i	−0.510497	−	0.859880i	$-0.670538\pi$
$439$	3.13332	−	2.27649i	0.149545	−	0.108651i	0.660042	+	0.751229i	$0.270538\pi$
$440$	−1.44293	+	3.73085i	−0.0687888	+	0.177862i
$441$		0			0
$442$	−1.87330	−	2.16044i	−0.0891038	−	0.102761i
$443$	14.4860	+	14.4860i	0.688250	+	0.688250i	0.961845	−	0.273595i	$-0.0882129\pi$
$443$	14.4860	+	14.4860i	0.688250	+	0.688250i	−0.273595	+	0.961845i	$0.588213\pi$
$444$		0			0
$445$	11.2173	−	34.6688i	0.531750	−	1.64346i
$446$	−19.7435	+	23.4698i	−0.934883	+	1.11133i
$447$		0			0
$448$	16.8034	−	13.3997i	0.793887	−	0.633076i
$449$		−	23.1164i		−	1.09093i	−0.838134	−	0.545465i	$-0.816353\pi$
$449$		−	23.1164i		−	1.09093i	0.838134	−	0.545465i	$-0.183647\pi$
$450$		0			0
$451$			5.42027i			0.255231i
$452$	15.8288	+	21.1152i	0.744526	+	0.993177i
$453$		0			0
$454$	1.45547	+	1.22439i	0.0683084	+	0.0574633i
$455$	10.1888	−	0.0125719i	0.477657	−	0.000589379i
$456$		0			0
$457$	−5.45027	−	5.45027i	−0.254953	−	0.254953i	0.568045	−	0.822998i	$-0.307700\pi$
$457$	−5.45027	−	5.45027i	−0.254953	−	0.254953i	−0.822998	+	0.568045i	$0.807700\pi$
$458$	−14.2772	+	12.3797i	−0.667131	+	0.578465i
$459$		0			0
$460$	10.9113	−	15.5410i	0.508741	−	0.724602i
$461$	11.7401	−	8.52968i	0.546791	−	0.397267i	−0.279810	−	0.960055i	$-0.590272\pi$
$461$	11.7401	−	8.52968i	0.546791	−	0.397267i	0.826601	+	0.562789i	$0.190272\pi$
$462$		0			0
$463$	0.0468495	+	0.295796i	0.00217728	+	0.0137468i	0.988753	−	0.149557i	$-0.0477848\pi$
$463$	0.0468495	+	0.295796i	0.00217728	+	0.0137468i	−0.986576	+	0.163304i	$0.947785\pi$
$464$	−17.3966	+	13.4521i	−0.807616	+	0.624500i
$465$		0			0
$466$	16.5174	−	10.2925i	0.765152	−	0.476791i
$467$	−24.4141	−	12.4396i	−1.12975	−	0.575636i	−0.213779	−	0.976882i	$-0.568577\pi$
$467$	−24.4141	−	12.4396i	−1.12975	−	0.575636i	−0.915970	+	0.401246i	$0.868577\pi$
$468$		0			0
$469$	−12.8602	+	4.17852i	−0.593828	+	0.192946i
$470$	−11.2188	−	17.9545i	−0.517485	−	0.828179i
$471$		0			0
$472$	14.6773	+	11.9768i	0.675576	+	0.551279i
$473$	−0.916595	+	5.78715i	−0.0421451	+	0.266093i
$474$		0			0
$475$	14.7786	−	0.0364706i	0.678090	−	0.00167339i
$476$	−4.46103	+	4.59647i	−0.204471	+	0.210679i
$477$		0			0
$478$	3.50132	+	40.6049i	0.160146	+	1.85722i
$479$	−0.998874	+	3.07422i	−0.0456397	+	0.140465i	−0.971280	−	0.237941i	$-0.923528\pi$
$479$	−0.998874	+	3.07422i	−0.0456397	+	0.140465i	0.925640	+	0.378406i	$0.123528\pi$
$480$		0			0
$481$	−2.64323	−	8.13502i	−0.120521	−	0.370925i
$482$	−24.4935	+	10.3608i	−1.11565	+	0.471920i
$483$		0			0
$484$	−20.8870	+	3.62911i	−0.949409	+	0.164960i
$485$	32.2460	+	16.3801i	1.46422	+	0.743781i
$486$		0			0
$487$	−8.61334	+	1.36422i	−0.390308	+	0.0618187i	−0.348504	−	0.937307i	$-0.613310\pi$
$487$	−8.61334	+	1.36422i	−0.390308	+	0.0618187i	−0.0418035	+	0.999126i	$0.513310\pi$
$488$	30.2973	−	19.5141i	1.37150	−	0.883364i
$489$		0			0
$490$	−0.0598774	−	0.684531i	−0.00270498	−	0.0309239i
$491$	9.14226	−	12.5832i	0.412585	−	0.567874i	−0.551262	−	0.834332i	$-0.685853\pi$
$491$	9.14226	−	12.5832i	0.412585	−	0.567874i	0.963846	+	0.266458i	$0.0858535\pi$
$492$		0			0
$493$	4.63440	−	4.63440i	0.208723	−	0.208723i
$494$	−7.07185	−	0.503398i	−0.318178	−	0.0226489i
$495$		0			0
$496$	8.72665	−	29.8689i	0.391838	−	1.34115i
$497$	−26.7947	+	13.6526i	−1.20191	+	0.612403i
$498$		0			0
$499$	17.8406			0.798657			0.399328	−	0.916808i	$-0.369243\pi$
$499$	17.8406			0.798657			0.399328	+	0.916808i	$0.369243\pi$
$500$	−16.1036	−	15.5137i	−0.720174	−	0.693794i
$501$		0			0
$502$	−6.29535	−	3.79335i	−0.280975	−	0.169306i
$503$	−6.24965	+	3.18436i	−0.278658	+	0.141983i	−0.587735	−	0.809054i	$-0.699980\pi$
$503$	−6.24965	+	3.18436i	−0.278658	+	0.141983i	0.309076	+	0.951037i	$0.399980\pi$
$504$		0			0
$505$	−7.48587	−	10.2767i	−0.333117	−	0.457308i
$506$	−3.78835	−	0.269667i	−0.168413	−	0.0119882i
$507$		0			0
$508$	4.47832	−	1.52949i	0.198693	−	0.0678604i
$509$	16.3845	−	22.5514i	0.726231	−	0.999571i	−0.273063	−	0.961996i	$-0.588037\pi$
$509$	16.3845	−	22.5514i	0.726231	−	0.999571i	0.999294	−	0.0375751i	$-0.0119633\pi$
$510$		0			0
$511$	11.7717	+	16.2023i	0.520749	+	0.716749i
$512$	22.3076	+	3.79095i	0.985866	+	0.167538i
$513$		0			0
$514$	−4.39264	+	1.08938i	−0.193751	+	0.0480504i
$515$	14.8487	+	7.54273i	0.654313	+	0.332373i
$516$		0			0
$517$	−1.92240	+	3.77291i	−0.0845469	+	0.165933i
$518$	−17.6466	+	7.46451i	−0.775346	+	0.327972i
$519$		0			0
$520$	7.15771	+	7.98979i	0.313886	+	0.350376i
$521$	−3.19880	+	9.84488i	−0.140142	+	0.431312i	−0.996354	−	0.0853117i	$-0.972811\pi$
$521$	−3.19880	+	9.84488i	−0.140142	+	0.431312i	0.856213	+	0.516624i	$0.172811\pi$
$522$		0			0
$523$	−21.5896	−	3.41946i	−0.944049	−	0.149523i	−0.334611	−	0.942356i	$-0.608605\pi$
$523$	−21.5896	−	3.41946i	−0.944049	−	0.149523i	−0.609438	+	0.792834i	$0.708605\pi$
$524$	−9.76151	−	9.47387i	−0.426434	−	0.413868i
$525$		0			0
$526$	27.7491	+	11.2517i	1.20992	+	0.490599i
$527$	−1.45078	+	9.15990i	−0.0631972	+	0.399011i
$528$		0			0
$529$	−4.72781	−	1.53616i	−0.205557	−	0.0667896i
$530$	−17.0739	−	27.3249i	−0.741643	−	1.18692i
$531$		0			0
$532$	0.237459	+	15.8794i	0.0102952	+	0.688459i
$533$	12.9510	+	6.59888i	0.560972	+	0.285829i
$534$		0			0
$535$	−39.1189	−	6.14635i	−1.69126	−	0.265730i
$536$	−12.3022	−	7.16436i	−0.531376	−	0.309453i
$537$		0			0
$538$	−0.650753	+	2.80273i	−0.0280560	+	0.120834i
$539$	−0.111187	+	0.0807820i	−0.00478916	+	0.00347953i
$540$		0			0
$541$	21.4851	+	15.6098i	0.923715	+	0.671118i	0.944446	−	0.328667i	$-0.106599\pi$
$541$	21.4851	+	15.6098i	0.923715	+	0.671118i	−0.0207309	+	0.999785i	$0.506599\pi$
$542$	−7.45682	+	6.46577i	−0.320298	+	0.277728i
$543$		0			0
$544$	−6.73801	−	0.277479i	−0.288890	−	0.0118968i
$545$	−31.6127	+	0.0390067i	−1.35414	+	0.00167087i
$546$		0			0
$547$	−5.65554	−	11.0996i	−0.241814	−	0.474586i	0.737921	−	0.674887i	$-0.235808\pi$
$547$	−5.65554	−	11.0996i	−0.241814	−	0.474586i	−0.979734	+	0.200302i	$0.935808\pi$
$548$	24.3444	−	18.2495i	1.03994	−	0.779581i
$549$		0			0
$550$	−1.00075	+	4.35892i	−0.0426720	+	0.185865i
$551$		−	16.2498i		−	0.692266i
$552$		0			0
$553$	−11.2124	−	22.0056i	−0.476801	−	0.935775i
$554$	−15.6363	+	18.5874i	−0.664324	+	0.789703i
$555$		0			0
$556$	17.3862	+	8.53371i	0.737341	+	0.361910i
$557$	25.7954	+	25.7954i	1.09299	+	1.09299i	0.995208	+	0.0977791i	$0.0311739\pi$
$557$	25.7954	+	25.7954i	1.09299	+	1.09299i	0.0977791	+	0.995208i	$0.468826\pi$
$558$		0			0
$559$	12.7117	+	9.23562i	0.537649	+	0.390625i
$560$	16.4537	−	17.5117i	0.695295	−	0.740004i
$561$		0			0
$562$	−20.9087	−	4.85469i	−0.881979	−	0.204783i
$563$	−6.27661	−	39.6289i	−0.264527	−	1.67016i	−0.659681	−	0.751545i	$-0.729309\pi$
$563$	−6.27661	−	39.6289i	−0.264527	−	1.67016i	0.395154	−	0.918615i	$-0.370691\pi$
$564$		0			0
$565$	20.8885	+	20.8370i	0.878784	+	0.876618i
$566$	−5.69769	−	9.14363i	−0.239492	−	0.384335i
$567$		0			0
$568$	−29.5154	−	11.4571i	−1.23844	−	0.480730i
$569$	10.0584	−	3.26818i	0.421671	−	0.137009i	−0.0904926	−	0.995897i	$-0.528844\pi$
$569$	10.0584	−	3.26818i	0.421671	−	0.137009i	0.512164	+	0.858888i	$0.328844\pi$
$570$		0			0
$571$	33.2285	+	10.7966i	1.39057	+	0.451823i	0.906129	−	0.423002i	$-0.139024\pi$
$571$	33.2285	+	10.7966i	1.39057	+	0.451823i	0.484439	+	0.874825i	$0.339024\pi$
$572$	0.632411	−	2.05017i	0.0264424	−	0.0857221i
$573$		0			0
$574$	12.2347	−	30.1732i	0.510665	−	1.25941i
$575$	9.59161	−	18.9400i	0.399998	−	0.789852i
$576$		0			0
$577$	42.9968	+	6.81002i	1.78998	+	0.283505i	0.961156	−	0.276005i	$-0.0890107\pi$
$577$	42.9968	+	6.81002i	1.78998	+	0.283505i	0.828824	+	0.559510i	$0.189011\pi$
$578$	−21.9503	+	1.89275i	−0.913013	+	0.0787282i
$579$		0			0
$580$	−17.1017	+	17.6645i	−0.710108	+	0.733477i
$581$	2.17091	+	6.68138i	0.0900646	+	0.277190i
$582$		0			0
$583$	−2.92569	+	5.74200i	−0.121170	+	0.237809i
$584$	−4.46118	+	20.6078i	−0.184605	+	0.852759i
$585$		0			0
$586$	4.76852	+	19.2279i	0.196986	+	0.794297i
$587$	13.4305	−	2.12719i	0.554338	−	0.0877985i	0.127020	−	0.991900i	$-0.459459\pi$
$587$	13.4305	−	2.12719i	0.554338	−	0.0877985i	0.427317	+	0.904102i	$0.359459\pi$
$588$		0			0
$589$	13.5154	+	18.6024i	0.556894	+	0.766499i
$590$	18.1545	+	10.9087i	0.747407	+	0.449104i
$591$		0			0
$592$	−18.2397	−	8.61664i	−0.749649	−	0.354142i
$593$	−8.49730	+	8.49730i	−0.348942	+	0.348942i	−0.859715	−	0.510773i	$-0.829359\pi$
$593$	−8.49730	+	8.49730i	−0.348942	+	0.348942i	0.510773	+	0.859715i	$0.329359\pi$
$594$		0			0
$595$	−4.20220	+	5.79887i	−0.172274	+	0.237731i
$596$	2.70354	−	1.42884i	0.110741	−	0.0585274i
$597$		0			0
$598$	−5.25644	+	8.72346i	−0.214952	+	0.356729i
$599$	32.3191			1.32052			0.660261	−	0.751036i	$-0.270446\pi$
$599$	32.3191			1.32052			0.660261	+	0.751036i	$0.270446\pi$
$600$		0			0
$601$	−29.2439			−1.19288			−0.596441	−	0.802657i	$-0.703419\pi$
$601$	−29.2439			−1.19288			−0.596441	+	0.802657i	$0.703419\pi$
$602$	18.1652	−	30.1466i	0.740360	−	1.22868i
$603$		0			0
$604$	−37.3496	+	19.7395i	−1.51973	+	0.803189i
$605$	−22.5331	+	7.35221i	−0.916102	+	0.298910i
$606$		0			0
$607$	3.02390	−	3.02390i	0.122737	−	0.122737i	−0.643070	−	0.765807i	$-0.722340\pi$
$607$	3.02390	−	3.02390i	0.122737	−	0.122737i	0.765807	+	0.643070i	$0.222340\pi$
$608$	−12.2994	+	11.3265i	−0.498806	+	0.459349i
$609$		0			0
$610$	30.4089	−	26.4332i	1.23122	−	1.07025i
$611$	6.67448	+	9.18663i	0.270020	+	0.371651i
$612$		0			0
$613$	−30.0602	+	4.76106i	−1.21412	+	0.192297i	−0.730458	−	0.682958i	$-0.760693\pi$
$613$	−30.0602	+	4.76106i	−1.21412	+	0.192297i	−0.483661	+	0.875255i	$0.660693\pi$
$614$	0.190522	+	0.768232i	0.00768884	+	0.0310033i
$615$		0			0
$616$	−4.69716	−	1.01684i	−0.189254	−	0.0409696i
$617$	6.53005	−	12.8160i	0.262890	−	0.515951i	−0.721398	−	0.692521i	$-0.756500\pi$
$617$	6.53005	−	12.8160i	0.262890	−	0.515951i	0.984288	+	0.176570i	$0.0565001\pi$
$618$		0			0
$619$	−0.651133	−	2.00398i	−0.0261713	−	0.0805469i	0.937118	−	0.349013i	$-0.113483\pi$
$619$	−0.651133	−	2.00398i	−0.0261713	−	0.0805469i	−0.963289	+	0.268466i	$0.913483\pi$
$620$	4.88554	−	34.4458i	0.196208	−	1.38338i
$621$		0			0
$622$	−19.0457	+	1.64229i	−0.763661	+	0.0658497i
$623$	43.2395	+	6.84846i	1.73235	+	0.274378i
$624$		0			0
$625$	−20.2977	−	14.5946i	−0.811908	−	0.583785i
$626$	−13.1868	+	32.5215i	−0.527052	+	1.29982i
$627$		0			0
$628$	−8.83686	+	28.6477i	−0.352629	+	1.14317i
$629$	5.71786	+	1.85784i	0.227986	+	0.0740771i
$630$		0			0
$631$	−28.3045	+	9.19668i	−1.12678	+	0.366114i	−0.812353	−	0.583166i	$-0.801814\pi$
$631$	−28.3045	+	9.19668i	−1.12678	+	0.366114i	−0.314431	+	0.949280i	$0.601814\pi$
$632$	9.40936	−	24.2401i	0.374284	−	0.964218i
$633$		0			0
$634$	16.3592	+	26.2531i	0.649706	+	1.04265i
$635$	4.71124	−	2.40782i	0.186960	−	0.0955516i
$636$		0			0
$637$	0.0576542	+	0.364014i	0.00228434	+	0.0144228i
$638$	4.79010	+	1.11219i	0.189642	+	0.0440321i
$639$		0			0
$640$	25.2903	+	0.631660i	0.999688	+	0.0249685i
$641$	−10.3700	−	7.53427i	−0.409592	−	0.297586i	0.363845	−	0.931460i	$-0.381464\pi$
$641$	−10.3700	−	7.53427i	−0.409592	−	0.297586i	−0.773437	+	0.633874i	$0.781464\pi$
$642$		0			0
$643$	−1.49163	−	1.49163i	−0.0588243	−	0.0588243i	0.677083	−	0.735907i	$-0.263244\pi$
$643$	−1.49163	−	1.49163i	−0.0588243	−	0.0588243i	−0.735907	+	0.677083i	$0.763244\pi$
$644$	20.4800	+	10.0522i	0.807026	+	0.396114i
$645$		0			0
$646$	3.20789	−	3.81332i	0.126213	−	0.150033i
$647$	−10.0385	−	19.7017i	−0.394654	−	0.774552i	0.605113	−	0.796140i	$-0.293128\pi$
$647$	−10.0385	−	19.7017i	−0.394654	−	0.774552i	−0.999767	+	0.0215874i	$0.993128\pi$
$648$		0			0
$649$		−	4.23613i		−	0.166283i
$650$	9.19671	+	7.69789i	0.360725	+	0.301936i
$651$		0			0
$652$	−19.4622	+	14.5896i	−0.762197	+	0.571374i
$653$	−10.1505	−	19.9215i	−0.397220	−	0.779589i	0.602610	−	0.798036i	$-0.294128\pi$
$653$	−10.1505	−	19.9215i	−0.397220	−	0.779589i	−0.999830	+	0.0184475i	$0.994128\pi$
$654$		0			0
$655$	−12.3150	−	8.92420i	−0.481188	−	0.348698i
$656$	32.2703	−	11.5630i	1.25994	−	0.451460i
$657$		0			0
$658$	19.2177	−	16.6636i	0.749185	−	0.649614i
$659$	−21.7105	−	15.7736i	−0.845720	−	0.614451i	0.0782429	−	0.996934i	$-0.475069\pi$
$659$	−21.7105	−	15.7736i	−0.845720	−	0.614451i	−0.923962	+	0.382483i	$0.875069\pi$
$660$		0			0
$661$	−26.7479	+	19.4335i	−1.04037	+	0.755875i	−0.970358	−	0.241671i	$-0.922304\pi$
$661$	−26.7479	+	19.4335i	−1.04037	+	0.755875i	−0.0700142	+	0.997546i	$0.522304\pi$
$662$	8.06452	−	34.7331i	0.313437	−	1.34994i
$663$		0			0
$664$	−3.72217	+	6.39151i	−0.144448	+	0.248039i
$665$	2.79924	+	17.5337i	0.108550	+	0.679926i
$666$		0			0
$667$	−20.7993	−	10.5978i	−0.805352	−	0.410347i
$668$	0.275911	+	18.4508i	0.0106753	+	0.713881i
$669$		0			0
$670$	−14.7576	−	5.96275i	−0.570137	−	0.230361i
$671$	−7.66423	−	2.49026i	−0.295874	−	0.0961354i
$672$		0			0
$673$	−0.968440	+	6.11449i	−0.0373306	+	0.235696i	−0.999298	−	0.0374688i	$-0.988071\pi$
$673$	−0.968440	+	6.11449i	−0.0373306	+	0.235696i	0.961967	+	0.273165i	$0.0880705\pi$
$674$	14.5802	+	5.91200i	0.561609	+	0.227722i
$675$		0			0
$676$	14.5289	+	14.1008i	0.558804	+	0.542338i
$677$	−37.8109	−	5.98865i	−1.45319	−	0.230163i	−0.620632	−	0.784102i	$-0.713124\pi$
$677$	−37.8109	−	5.98865i	−1.45319	−	0.230163i	−0.832557	+	0.553939i	$0.813124\pi$
$678$		0			0
$679$	−13.4279	+	41.3267i	−0.515315	+	1.58598i
$680$	−7.50037	+	0.769240i	−0.287626	+	0.0294990i
$681$		0			0
$682$	−6.40862	+	2.71085i	−0.245399	+	0.103804i
$683$	−21.0947	+	41.4007i	−0.807166	+	1.58415i	0.00447006	+	0.999990i	$0.498577\pi$
$683$	−21.0947	+	41.4007i	−0.807166	+	1.58415i	−0.811636	+	0.584163i	$0.801423\pi$
$684$		0			0
$685$	24.0235	−	24.0829i	0.917892	−	0.920160i
$686$	−25.0118	+	6.20293i	−0.954954	+	0.236829i
$687$		0			0
$688$	36.4100	−	6.88859i	1.38812	−	0.262625i
$689$	10.1579	+	13.9811i	0.386985	+	0.532639i
$690$		0			0
$691$	−20.3465	+	28.0045i	−0.774016	+	1.06534i	0.221901	+	0.975069i	$0.428774\pi$
$691$	−20.3465	+	28.0045i	−0.774016	+	1.06534i	−0.995917	+	0.0902726i	$0.971226\pi$
$692$	13.5710	−	4.63495i	0.515892	−	0.176194i
$693$		0			0
$694$	−10.4247	−	0.742066i	−0.395717	−	0.0281684i
$695$	20.6021	+	6.66594i	0.781483	+	0.252853i
$696$		0			0
$697$	−9.10288	+	4.63815i	−0.344796	+	0.175682i
$698$	19.9228	+	12.0047i	0.754087	+	0.454386i
$699$		0			0
$700$	15.4099	−	22.0060i	0.582438	−	0.831750i
$701$	1.62441			0.0613530			0.0306765	−	0.999529i	$-0.490234\pi$
$701$	1.62441			0.0613530			0.0306765	+	0.999529i	$0.490234\pi$
$702$		0			0
$703$	13.2815	−	6.76729i	0.500923	−	0.255233i
$704$	−2.49698	−	4.40081i	−0.0941086	−	0.165862i
$705$		0			0
$706$	18.4849	+	1.31581i	0.695687	+	0.0495213i
$707$	10.8013	−	10.8013i	0.406223	−	0.406223i
$708$		0			0
$709$	−8.33878	+	11.4774i	−0.313170	+	0.431041i	−0.936366	−	0.351024i	$-0.885834\pi$
$709$	−8.33878	+	11.4774i	−0.313170	+	0.431041i	0.623197	+	0.782065i	$0.285834\pi$
$710$	−34.4908	−	7.96343i	−1.29442	−	0.298862i
$711$		0			0
$712$	24.9579	+	38.7492i	0.935337	+	1.45219i
$713$	32.6250	−	5.16729i	1.22181	−	0.193516i
$714$		0			0
$715$	0.372322	−	2.36967i	0.0139240	−	0.0886206i
$716$	5.32625	−	0.925435i	0.199051	−	0.0345851i
$717$		0			0
$718$	−35.8665	+	15.1716i	−1.33853	+	0.566197i
$719$	−5.07697	−	15.6253i	−0.189339	−	0.582725i	0.810657	−	0.585521i	$-0.199110\pi$
$719$	−5.07697	−	15.6253i	−0.189339	−	0.582725i	−0.999996	+	0.00279590i	$0.999110\pi$
$720$		0			0
$721$	−6.18329	+	19.0302i	−0.230278	+	0.708723i
$722$	1.24698	+	14.4613i	0.0464079	+	0.538194i
$723$		0			0
$724$	6.06377	−	6.24787i	0.225358	−	0.232200i
$725$	−16.1025	+	22.2786i	−0.598032	+	0.827406i
$726$		0			0
$727$	−1.57474	+	9.94253i	−0.0584039	+	0.368748i	0.941125	+	0.338059i	$0.109770\pi$
$727$	−1.57474	+	9.94253i	−0.0584039	+	0.368748i	−0.999529	+	0.0306893i	$0.990230\pi$
$728$	−8.14813	+	9.98530i	−0.301990	+	0.370080i
$729$		0			0
$730$	−1.64482	+	23.5165i	−0.0608776	+	0.870385i
$731$	−10.5034	+	3.41275i	−0.388481	+	0.126225i
$732$		0			0
$733$	30.7430	+	15.6644i	1.13552	+	0.578576i	0.917645	−	0.397400i	$-0.130088\pi$
$733$	30.7430	+	15.6644i	1.13552	+	0.578576i	0.217875	+	0.975977i	$0.430088\pi$
$734$	−33.8906	+	21.1183i	−1.25093	+	0.779492i
$735$		0			0
$736$	6.47614	+	23.1297i	0.238714	+	0.852573i
$737$	0.498005	+	3.14428i	0.0183442	+	0.115821i
$738$		0			0
$739$	33.3131	−	24.2034i	1.22544	−	0.890335i	0.228902	−	0.973450i	$-0.426487\pi$
$739$	33.3131	−	24.2034i	1.22544	−	0.890335i	0.996540	+	0.0831141i	$0.0264866\pi$
$740$	−21.5598	−	6.62137i	−0.792554	−	0.243406i
$741$		0			0
$742$	29.2474	−	25.3603i	1.07371	−	0.931005i
$743$	11.4340	+	11.4340i	0.419473	+	0.419473i	0.885022	−	0.465549i	$-0.154143\pi$
$743$	11.4340	+	11.4340i	0.419473	+	0.419473i	−0.465549	+	0.885022i	$0.654143\pi$
$744$		0			0
$745$	2.76341	−	2.01295i	0.101243	−	0.0737486i
$746$	11.7476	+	9.88249i	0.430111	+	0.361824i
$747$		0			0
$748$	0.904525	+	1.20661i	0.0330727	+	0.0441181i
$749$		−	47.5756i		−	1.73837i
$750$		0			0
$751$		−	39.8961i		−	1.45583i	−0.685668	−	0.727915i	$-0.740490\pi$
$751$		−	39.8961i		−	1.45583i	0.685668	−	0.727915i	$-0.259510\pi$
$752$	26.5636	+	3.39653i	0.968675	+	0.123859i
$753$		0			0
$754$	8.48912	−	10.0913i	0.309155	−	0.367503i
$755$	−38.1767	+	27.8090i	−1.38939	+	1.01207i
$756$		0			0
$757$	−2.42176	−	2.42176i	−0.0880204	−	0.0880204i	0.661726	−	0.749746i	$-0.269824\pi$
$757$	−2.42176	−	2.42176i	−0.0880204	−	0.0880204i	−0.749746	+	0.661726i	$0.769824\pi$
$758$	4.60832	+	5.31468i	0.167382	+	0.193038i
$759$		0			0
$760$	−11.8009	+	14.4981i	−0.428062	+	0.525901i
$761$	−16.8140	+	12.2161i	−0.609507	+	0.442833i	−0.849241	−	0.528006i	$-0.822940\pi$
$761$	−16.8140	+	12.2161i	−0.609507	+	0.442833i	0.239733	+	0.970839i	$0.422940\pi$
$762$		0			0
$763$	−5.94150	−	37.5132i	−0.215097	−	1.35807i
$764$	34.8734	+	4.99009i	1.26168	+	0.180535i
$765$		0			0
$766$	17.5076	+	28.0961i	0.632576	+	1.01515i
$767$	−10.1217	−	5.15726i	−0.365473	−	0.186218i
$768$		0			0
$769$	−9.52824	+	3.09591i	−0.343597	+	0.111641i	−0.475732	−	0.879590i	$-0.657817\pi$
$769$	−9.52824	+	3.09591i	−0.343597	+	0.111641i	0.132135	+	0.991232i	$0.457817\pi$
$770$	−5.36013	−	0.374905i	−0.193166	−	0.0135106i
$771$		0			0
$772$	−15.0575	−	4.64475i	−0.541932	−	0.167168i
$773$	−4.80098	+	30.3122i	−0.172679	+	1.09025i	0.737289	+	0.675577i	$0.236106\pi$
$773$	−4.80098	+	30.3122i	−0.172679	+	1.09025i	−0.909968	+	0.414677i	$0.863894\pi$
$774$		0			0
$775$	−0.0959895	−	38.8969i	−0.00344804	−	1.39722i
$776$	−41.8634	+	18.4510i	−1.50281	+	0.662351i
$777$		0			0
$778$	38.5817	−	3.32686i	1.38322	−	0.119274i
$779$	−7.82747	+	24.0905i	−0.280448	+	0.863130i
$780$		0			0
$781$	2.18782	+	6.73342i	0.0782863	+	0.240941i
$782$	−2.78882	−	6.59296i	−0.0997281	−	0.235764i
$783$		0			0
$784$	0.718140	+	0.489635i	0.0256479	+	0.0174870i
$785$	−5.20256	+	33.1120i	−0.185687	+	1.18182i
$786$		0			0
$787$	−34.3093	+	5.43407i	−1.22300	+	0.193704i	−0.734345	−	0.678776i	$-0.762511\pi$
$787$	−34.3093	+	5.43407i	−1.22300	+	0.193704i	−0.488651	+	0.872480i	$0.662511\pi$
$788$	12.1763	+	8.57142i	0.433764	+	0.305344i
$789$		0			0
$790$	6.54011	−	28.3262i	0.232687	−	1.00780i
$791$	−20.8356	+	28.6778i	−0.740830	+	1.01967i
$792$		0			0
$793$	−15.2809	+	15.2809i	−0.542642	+	0.542642i
$794$	−1.61446	+	22.6803i	−0.0572949	+	0.804893i
$795$		0			0
$796$	−10.4999	−	19.8671i	−0.372159	−	0.704171i
$797$	18.2016	−	9.27416i	0.644732	−	0.328508i	−0.100869	−	0.994900i	$-0.532162\pi$
$797$	18.2016	−	9.27416i	0.644732	−	0.328508i	0.745601	+	0.666392i	$0.232162\pi$
$798$		0			0
$799$	−7.98129			−0.282358
$800$	28.0863	−	3.34075i	0.993000	−	0.118113i
$801$		0			0
$802$	−19.8561	+	32.9527i	−0.701144	+	1.16360i
$803$	4.20108	−	2.14056i	0.148253	−	0.0755387i
$804$		0			0
$805$	24.2682	+	7.85211i	0.855340	+	0.276750i
$806$	−1.32493	+	18.6129i	−0.0466685	+	0.655611i
$807$		0			0
$808$	16.0570	+	0.901912i	0.564882	+	0.0317292i
$809$	−20.5456	+	28.2786i	−0.722344	+	0.994222i	0.277098	+	0.960842i	$0.410627\pi$
$809$	−20.5456	+	28.2786i	−0.722344	+	0.994222i	−0.999443	+	0.0333800i	$0.989373\pi$
$810$		0			0
$811$	20.4028	+	28.0820i	0.716438	+	0.986093i	0.999635	+	0.0270307i	$0.00860518\pi$
$811$	20.4028	+	28.0820i	0.716438	+	0.986093i	−0.283196	+	0.959062i	$0.591395\pi$
$812$	−24.1548	−	17.0035i	−0.847666	−	0.596706i
$813$		0			0
$814$	1.08582	+	4.37829i	0.0380579	+	0.153459i
$815$	−19.2057	+	19.2531i	−0.672745	+	0.674408i
$816$		0			0
$817$	−12.4311	+	24.3974i	−0.434909	+	0.853557i
$818$	6.65169	+	15.7250i	0.232571	+	0.549813i
$819$		0			0
$820$	33.8622	−	17.9499i	1.18252	−	0.626837i
$821$	11.4445	−	35.2226i	0.399416	−	1.22928i	−0.526053	−	0.850452i	$-0.676329\pi$
$821$	11.4445	−	35.2226i	0.399416	−	1.22928i	0.925469	−	0.378824i	$-0.123671\pi$
$822$		0			0
$823$	−39.2887	−	6.22271i	−1.36952	−	0.216910i	−0.572023	−	0.820237i	$-0.693841\pi$
$823$	−39.2887	−	6.22271i	−1.36952	−	0.216910i	−0.797494	+	0.603327i	$0.793841\pi$
$824$	−19.2773	+	8.49633i	−0.671558	+	0.295984i
$825$		0			0
$826$	−9.56183	+	23.5814i	−0.332699	+	0.820503i
$827$	0.257318	−	1.62464i	0.00894782	−	0.0564943i	−0.982810	−	0.184618i	$-0.940895\pi$
$827$	0.257318	−	1.62464i	0.00894782	−	0.0564943i	0.991758	+	0.128123i	$0.0408953\pi$
$828$		0			0
$829$	−35.6026	−	11.5680i	−1.23653	−	0.401773i	−0.383454	−	0.923560i	$-0.625265\pi$
$829$	−35.6026	−	11.5680i	−1.23653	−	0.401773i	−0.853076	+	0.521787i	$0.825265\pi$
$830$	−3.09789	+	7.66718i	−0.107529	+	0.266132i
$831$		0			0
$832$	−13.5551	+	0.608469i	−0.469939	+	0.0210949i
$833$	−0.230809	−	0.117603i	−0.00799708	−	0.00407471i
$834$		0			0
$835$	3.25252	+	20.3729i	0.112558	+	0.705033i
$836$	3.70120	+	0.529610i	0.128009	+	0.0183169i
$837$		0			0
$838$	−15.4533	−	3.58804i	−0.533827	−	0.123947i
$839$	−24.8408	+	18.0479i	−0.857600	+	0.623083i	−0.927231	−	0.374490i	$-0.877818\pi$
$839$	−24.8408	+	18.0479i	−0.857600	+	0.623083i	0.0696306	+	0.997573i	$0.477818\pi$
$840$		0			0
$841$	0.991078	+	0.720060i	0.0341751	+	0.0248297i
$842$	−1.41051	−	1.62671i	−0.0486094	−	0.0560601i
$843$		0			0
$844$	−12.2736	+	25.0057i	−0.422475	+	0.860733i
$845$	18.3296	+	13.2827i	0.630556	+	0.456938i
$846$		0			0
$847$	−12.9282	−	25.3730i	−0.444219	−	0.871828i
$848$	40.4271	+	5.16918i	1.38827	+	0.177510i
$849$		0			0
$850$	−8.17677	+	2.04927i	−0.280461	+	0.0702895i
$851$		−	21.4134i		−	0.734044i
$852$		0			0
$853$	3.51179	+	6.89228i	0.120241	+	0.235987i	0.943280	−	0.331999i	$-0.107723\pi$
$853$	3.51179	+	6.89228i	0.120241	+	0.235987i	−0.823038	+	0.567986i	$0.807723\pi$
$854$	37.0437	+	31.1624i	1.26761	+	1.06635i
$855$		0			0
$856$	37.3488	−	33.3762i	1.27656	−	1.14078i
$857$	−15.0616	−	15.0616i	−0.514495	−	0.514495i	0.401406	−	0.915900i	$-0.368522\pi$
$857$	−15.0616	−	15.0616i	−0.514495	−	0.514495i	−0.915900	+	0.401406i	$0.868522\pi$
$858$		0			0
$859$	6.76410	+	4.91440i	0.230788	+	0.167677i	0.697169	−	0.716906i	$-0.254443\pi$
$859$	6.76410	+	4.91440i	0.230788	+	0.167677i	−0.466381	+	0.884584i	$0.654443\pi$
$860$	39.1896	−	13.4386i	1.33636	−	0.458252i
$861$		0			0
$862$	12.1096	−	52.1548i	0.412454	−	1.77640i
$863$	−5.82961	−	36.8067i	−0.198442	−	1.25291i	−0.862818	−	0.505515i	$-0.831302\pi$
$863$	−5.82961	−	36.8067i	−0.198442	−	1.25291i	0.664375	−	0.747399i	$-0.268698\pi$
$864$		0			0
$865$	14.2768	−	7.29661i	0.485427	−	0.248092i
$866$	44.8821	−	27.9675i	1.52516	−	0.950374i
$867$		0			0
$868$	41.7941	−	0.624985i	1.41858	−	0.0212134i
$869$	−5.52994	+	1.79679i	−0.187590	+	0.0609518i
$870$		0			0
$871$	8.11914	+	2.63807i	0.275107	+	0.0893875i
$872$	25.2812	−	30.9813i	0.856128	−	1.04916i
$873$		0			0
$874$	−16.4479	−	6.66932i	−0.556359	−	0.225593i
$875$	13.5369	−	26.8126i	0.457631	−	0.906430i
$876$		0			0
$877$	22.5291	+	3.56825i	0.760753	+	0.120491i	0.524745	−	0.851260i	$-0.324161\pi$
$877$	22.5291	+	3.56825i	0.760753	+	0.120491i	0.236008	+	0.971751i	$0.424161\pi$
$878$	0.470551	+	5.45700i	0.0158803	+	0.184165i
$879$		0			0
$880$	−3.46603	−	4.47093i	−0.116840	−	0.150715i
$881$	5.60391	+	17.2470i	0.188800	+	0.581068i	0.999993	−	0.00371110i	$-0.00118128\pi$
$881$	5.60391	+	17.2470i	0.188800	+	0.581068i	−0.811193	+	0.584779i	$0.801181\pi$
$882$		0			0
$883$	12.3251	−	24.1893i	0.414772	−	0.814035i	−0.585223	−	0.810872i	$-0.698993\pi$
$883$	12.3251	−	24.1893i	0.414772	−	0.814035i	0.999995	−	0.00316320i	$-0.00100688\pi$
$884$	3.98425	−	0.692263i	0.134005	−	0.0232833i
$885$		0			0
$886$	−28.1201	+	6.97380i	−0.944714	+	0.234289i
$887$	12.4877	−	1.97785i	0.419295	−	0.0664098i	0.0567776	−	0.998387i	$-0.481917\pi$
$887$	12.4877	−	1.97785i	0.419295	−	0.0664098i	0.362517	+	0.931977i	$0.381917\pi$
$888$		0			0
$889$	3.73636	+	5.14266i	0.125313	+	0.172479i
$890$	33.8071	+	38.8919i	1.13322	+	1.30366i
$891$		0			0
$892$	−14.0185	−	41.0458i	−0.469374	−	1.37431i
$893$	−13.9926	+	13.9926i	−0.468245	+	0.468245i
$894$		0			0
$895$	5.74601	−	1.87483i	0.192068	−	0.0626688i
$896$	3.96650	+	30.1344i	0.132511	+	1.00672i
$897$		0			0
$898$	28.0010	+	16.8724i	0.934405	+	0.563039i
$899$	−42.7690			−1.42643
$900$		0			0
$901$	−12.1467			−0.404666
$902$	−6.56561	−	3.95620i	−0.218611	−	0.131727i
$903$		0			0
$904$	−37.1303	+	3.76180i	−1.23494	+	0.125116i
$905$	5.71195	−	7.88226i	0.189872	−	0.262015i
$906$		0			0
$907$	−18.7242	+	18.7242i	−0.621728	+	0.621728i	−0.945973	−	0.324245i	$-0.894890\pi$
$907$	−18.7242	+	18.7242i	−0.621728	+	0.621728i	0.324245	+	0.945973i	$0.394890\pi$
$908$	−2.54544	+	0.869350i	−0.0844732	+	0.0288504i
$909$		0			0
$910$	−7.42145	+	12.3509i	−0.246019	+	0.409429i
$911$	−14.3129	−	19.7000i	−0.474207	−	0.652690i	0.503172	−	0.864186i	$-0.332166\pi$
$911$	−14.3129	−	19.7000i	−0.474207	−	0.652690i	−0.977379	+	0.211497i	$0.932166\pi$
$912$		0			0
$913$	1.63358	−	0.258734i	0.0540636	−	0.00856283i
$914$	10.5800	−	2.62386i	0.349957	−	0.0867894i
$915$		0			0
$916$	−4.57482	−	26.3299i	−0.151156	−	0.869964i
$917$	8.29542	−	16.2807i	0.273939	−	0.537635i
$918$		0			0
$919$	−10.9466	−	33.6902i	−0.361095	−	1.11134i	−0.952390	−	0.304881i	$-0.901383\pi$
$919$	−10.9466	−	33.6902i	−0.361095	−	1.11134i	0.591296	−	0.806455i	$-0.298617\pi$
$920$	10.8609	+	24.5601i	0.358072	+	0.809721i
$921$		0			0
$922$	1.76309	+	20.4466i	0.0580641	+	0.673372i
$923$	18.7522	+	2.97005i	0.617235	+	0.0977605i
$924$		0			0
$925$	−24.9150	−	3.88314i	−0.819200	−	0.127677i
$926$	−0.392494	−	0.159149i	−0.0128982	−	0.00522997i
$927$		0			0
$928$	−3.59708	−	30.8911i	−0.118080	−	1.01405i
$929$	−13.7959	−	4.48257i	−0.452630	−	0.147068i	0.0738256	−	0.997271i	$-0.476479\pi$
$929$	−13.7959	−	4.48257i	−0.452630	−	0.147068i	−0.526455	+	0.850203i	$0.676479\pi$
$930$		0			0
$931$	−0.610829	+	0.198471i	−0.0200191	+	0.00650461i
$932$	0.411531	+	27.5200i	0.0134801	+	0.901446i
$933$		0			0
$934$	32.8877	−	20.4934i	1.07612	−	0.670565i
$935$	1.19365	+	1.19071i	0.0390366	+	0.0389404i
$936$		0			0
$937$	2.14371	+	13.5349i	0.0700320	+	0.442165i	0.997643	+	0.0686172i	$0.0218587\pi$
$937$	2.14371	+	13.5349i	0.0700320	+	0.442165i	−0.927611	+	0.373547i	$0.878141\pi$
$938$	4.32503	−	18.6275i	0.141217	−	0.608208i
$939$		0			0
$940$	29.9369	−	0.484621i	0.976433	−	0.0158066i
$941$	−16.3885	−	11.9070i	−0.534251	−	0.388156i	0.287694	−	0.957722i	$-0.407111\pi$
$941$	−16.3885	−	11.9070i	−0.534251	−	0.388156i	−0.821945	+	0.569566i	$0.807111\pi$
$942$		0			0
$943$	25.7302	+	25.7302i	0.837890	+	0.837890i
$944$	−25.2204	+	9.03690i	−0.820854	+	0.294126i
$945$		0			0
$946$	−6.34100	−	5.33425i	−0.206164	−	0.173432i
$947$	8.14549	+	15.9864i	0.264693	+	0.519489i	0.984652	−	0.174527i	$-0.0558397\pi$
$947$	8.14549	+	15.9864i	0.264693	+	0.519489i	−0.719960	+	0.694016i	$0.755840\pi$
$948$		0			0
$949$		−	12.6440i		−	0.410440i
$950$	−10.7426	+	17.9281i	−0.348535	+	0.581663i
$951$		0			0
$952$	−2.31168	−	8.75858i	−0.0749220	−	0.283867i
$953$	−3.40557	−	6.68381i	−0.110317	−	0.216510i	0.829247	−	0.558882i	$-0.188770\pi$
$953$	−3.40557	−	6.68381i	−0.110317	−	0.216510i	−0.939564	+	0.342372i	$0.888770\pi$
$954$		0			0
$955$	39.3868	−	0.0485992i	1.27453	−	0.00157263i
$956$	−51.7405	−	25.3959i	−1.67341	−	0.821361i
$957$		0			0
$958$	−2.99475	−	3.45378i	−0.0967561	−	0.111587i
$959$	33.0635	+	24.0220i	1.06768	+	0.775711i
$960$		0			0
$961$	23.8814	−	17.3508i	0.770367	−	0.559704i
$962$	11.7833	+	2.73590i	0.379908	+	0.0882091i
$963$		0			0
$964$	5.32750	−	37.2314i	0.171587	−	1.19914i
$965$	−17.4040	−	2.73452i	−0.560256	−	0.0880273i
$966$		0			0
$967$	6.58765	+	3.35657i	0.211844	+	0.107940i	0.556693	−	0.830718i	$-0.312070\pi$
$967$	6.58765	+	3.35657i	0.211844	+	0.107940i	−0.344849	+	0.938658i	$0.612070\pi$
$968$	10.8492	−	27.9494i	0.348707	−	0.898328i
$969$		0			0
$970$	−43.3773	+	27.1042i	−1.39276	+	0.870262i
$971$	33.1625	+	10.7751i	1.06424	+	0.345791i	0.788240	−	0.615368i	$-0.210993\pi$
$971$	33.1625	+	10.7751i	1.06424	+	0.345791i	0.275995	+	0.961159i	$0.410993\pi$
$972$		0			0
$973$	−4.06974	+	25.6953i	−0.130470	+	0.823754i
$974$	4.63430	−	11.4291i	0.148492	−	0.366213i
$975$		0			0
$976$	1.52392	+	50.9425i	0.0487795	+	1.63063i
$977$	−61.5368	−	9.74647i	−1.96874	−	0.311817i	−0.997184	−	0.0749929i	$-0.976107\pi$
$977$	−61.5368	−	9.74647i	−1.96874	−	0.311817i	−0.971552	−	0.236824i	$-0.923893\pi$
$978$		0			0
$979$	3.18496	−	9.80228i	0.101792	−	0.313282i
$980$	0.872880	+	0.427101i	0.0278831	+	0.0136433i
$981$		0			0
$982$	8.56933	+	20.2584i	0.273458	+	0.646473i
$983$	17.3594	−	34.0698i	0.553679	−	1.08666i	−0.429338	−	0.903144i	$-0.641253\pi$
$983$	17.3594	−	34.0698i	0.553679	−	1.08666i	0.983017	−	0.183513i	$-0.0587470\pi$
$984$		0			0
$985$	14.8430	+	7.53985i	0.472939	+	0.240240i
$986$	2.23108	+	8.99627i	0.0710520	+	0.286499i
$987$		0			0
$988$	5.77144	−	8.19876i	0.183614	−	0.260837i
$989$	23.1207	+	31.8229i	0.735194	+	1.01191i
$990$		0			0
$991$	16.5933	−	22.8387i	0.527103	−	0.725495i	−0.459582	−	0.888135i	$-0.652001\pi$
$991$	16.5933	−	22.8387i	0.527103	−	0.725495i	0.986686	+	0.162640i	$0.0520009\pi$
$992$	29.8109	+	32.3716i	0.946496	+	1.02780i
$993$		0			0
$994$	3.01970	−	42.4215i	0.0957791	−	1.34553i
$995$	−14.7923	−	20.3071i	−0.468946	−	0.643777i
$996$		0			0
$997$	23.7517	−	12.1021i	0.752224	−	0.383277i	−0.0354484	−	0.999372i	$-0.511286\pi$
$997$	23.7517	−	12.1021i	0.752224	−	0.383277i	0.787672	+	0.616094i	$0.211286\pi$
$998$	−13.0217	+	21.6105i	−0.412194	+	0.684068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.10		240
3.2	odd	2		300.2.w.a.127.21	yes	240
4.3	odd	2	inner	900.2.bj.f.127.13		240
12.11	even	2		300.2.w.a.127.18	✓	240
25.13	odd	20	inner	900.2.bj.f.163.13		240
75.38	even	20		300.2.w.a.163.18	yes	240
100.63	even	20	inner	900.2.bj.f.163.10		240
300.263	odd	20		300.2.w.a.163.21	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.18	✓	240	12.11	even	2
300.2.w.a.127.21	yes	240	3.2	odd	2
300.2.w.a.163.18	yes	240	75.38	even	20
300.2.w.a.163.21	yes	240	300.263	odd	20
900.2.bj.f.127.10		240	1.1	even	1	trivial
900.2.bj.f.127.13		240	4.3	odd	2	inner
900.2.bj.f.163.10		240	100.63	even	20	inner
900.2.bj.f.163.13		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)

\(f(q)\)	\(=\)	\(q+(-0.729889 + 1.21131i) q^{2} +(-0.934525 - 1.76824i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(1.89964 - 1.89964i) q^{7} +(2.82398 + 0.158622i) q^{8} +O(q^{10})\)	\(q+(-0.729889 + 1.21131i) q^{2} +(-0.934525 - 1.76824i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(1.89964 - 1.89964i) q^{7} +(2.82398 + 0.158622i) q^{8} +(3.15025 - 0.275559i) q^{10} +(-0.371763 - 0.511688i) q^{11} +(-1.67521 + 0.265328i) q^{13} +(0.914521 + 3.68758i) q^{14} +(-2.25333 + 3.30492i) q^{16} +(0.541217 - 1.06220i) q^{17} +(-0.913372 - 2.81107i) q^{19} +(-1.96554 + 4.01704i) q^{20} +(0.891157 - 0.0768435i) q^{22} +(-4.19377 - 0.664227i) q^{23} +(-1.53335 + 4.75908i) q^{25} +(0.901327 - 2.22286i) q^{26} +(-5.13429 - 1.58376i) q^{28} +(5.22865 + 1.69889i) q^{29} +(-7.39865 + 2.40397i) q^{31} +(-2.35859 - 5.14170i) q^{32} +(0.891619 + 1.43087i) q^{34} +(-5.93440 - 0.932412i) q^{35} +(0.788923 + 4.98106i) q^{37} +(4.07173 + 0.945396i) q^{38} +(-3.43124 - 5.31287i) q^{40} +(-6.93315 - 5.03723i) q^{41} +(-6.55061 - 6.55061i) q^{43} +(-0.557364 + 1.13555i) q^{44} +(3.86557 - 4.59512i) q^{46} +(-3.03945 - 5.96526i) q^{47} -0.217294i q^{49} +(-4.64553 - 5.33095i) q^{50} +(2.03469 + 2.71422i) q^{52} +(-4.62574 - 9.07852i) q^{53} +(-0.435374 + 1.34559i) q^{55} +(5.66587 - 5.06322i) q^{56} +(-5.87421 + 5.09350i) q^{58} +(5.41851 + 3.93677i) q^{59} +(10.3079 - 7.48916i) q^{61} +(2.48825 - 10.7167i) q^{62} +(7.94968 + 0.895887i) q^{64} +(2.68507 + 2.67845i) q^{65} +(-4.48471 - 2.28507i) q^{67} +(-2.38400 + 0.0356501i) q^{68} +(5.46089 - 6.50782i) q^{70} +(-10.6460 - 3.45911i) q^{71} +(-1.16618 + 7.36296i) q^{73} +(-6.60942 - 2.68000i) q^{74} +(-4.11707 + 4.24207i) q^{76} +(-1.67824 - 0.265808i) q^{77} +(2.84085 - 8.74324i) q^{79} +(8.93994 - 0.278475i) q^{80} +(11.1621 - 4.72155i) q^{82} +(-1.18719 + 2.32999i) q^{83} +(-2.63235 + 0.420254i) q^{85} +(12.7160 - 3.15358i) q^{86} +(-0.968686 - 1.50396i) q^{88} +(9.57838 + 13.1835i) q^{89} +(-2.67828 + 3.68634i) q^{91} +(2.74467 + 8.03631i) q^{92} +(9.44421 + 0.672270i) q^{94} +(-3.87820 + 5.35176i) q^{95} +(-14.4118 + 7.34318i) q^{97} +(0.263210 + 0.158601i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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