LMFDB - Embedded newform 738.2.u.d.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [738,2,Mod(289,738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(738, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("738.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (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:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			415.1
Character	$\chi$	$=$	738.415
Dual form			738.2.u.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-3.17802 - 1.03260i) q^{5} +(-0.0295159 - 0.186356i) q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-3.17802 - 1.03260i) q^{5} +(-0.0295159 - 0.186356i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-1.03260 - 3.17802i) q^{10} +(1.66667 - 3.27102i) q^{11} +(5.44127 + 0.861812i) q^{13} +(0.133416 - 0.133416i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.15110 + 1.09604i) q^{17} +(2.44120 - 0.386648i) q^{19} +(1.96412 - 2.70338i) q^{20} +(3.62596 - 0.574295i) q^{22} +(4.08088 - 2.96494i) q^{23} +(4.98846 + 3.62433i) q^{25} +(2.50108 + 4.90864i) q^{26} +(0.186356 + 0.0295159i) q^{28} +(0.824791 - 0.420252i) q^{29} +(0.894416 + 2.75273i) q^{31} -1.00000i q^{32} +(0.377670 + 2.38452i) q^{34} +(-0.0986294 + 0.622721i) q^{35} +(-0.0598364 + 0.184157i) q^{37} +(1.74771 + 1.74771i) q^{38} +3.34157 q^{40} +(-0.312306 - 6.39550i) q^{41} +(-0.374552 - 0.515527i) q^{43} +(2.59590 + 2.59590i) q^{44} +(4.79737 + 1.55876i) q^{46} +(0.339165 - 2.14140i) q^{47} +(6.62354 - 2.15212i) q^{49} +6.16607i q^{50} +(-2.50108 + 4.90864i) q^{52} +(-7.80894 + 3.97885i) q^{53} +(-8.67437 + 8.67437i) q^{55} +(0.0856585 + 0.168114i) q^{56} +(0.824791 + 0.420252i) q^{58} +(0.834669 - 0.606422i) q^{59} +(5.01958 - 6.90887i) q^{61} +(-1.70128 + 2.34161i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-16.4025 - 8.35751i) q^{65} +(-5.92399 - 11.6265i) q^{67} +(-1.70712 + 1.70712i) q^{68} +(-0.561765 + 0.286234i) q^{70} +(-0.312899 + 0.614098i) q^{71} -6.55734i q^{73} +(-0.184157 + 0.0598364i) q^{74} +(-0.386648 + 2.44120i) q^{76} +(-0.658768 - 0.214047i) q^{77} +(10.1046 + 10.1046i) q^{79} +(1.96412 + 2.70338i) q^{80} +(4.99050 - 4.01184i) q^{82} -13.1883 q^{83} +(-5.70447 - 5.70447i) q^{85} +(0.196914 - 0.606038i) q^{86} +(-0.574295 + 3.62596i) q^{88} +(2.07242 + 13.0848i) q^{89} -1.03945i q^{91} +(1.55876 + 4.79737i) q^{92} +(1.93179 - 0.984294i) q^{94} +(-8.15744 - 1.29201i) q^{95} +(-2.00053 - 3.92626i) q^{97} +(5.63432 + 4.09357i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4}+O(q^{10}) $ 24 * q + 6 * q^4	$ 24 q + 6 q^{4} + 4 q^{10} + 4 q^{11} + 2 q^{13} - 6 q^{16} + 10 q^{17} - 8 q^{19} + 10 q^{20} + 4 q^{22} - 4 q^{23} + 6 q^{25} - 8 q^{26} - 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} + 8 q^{38} + 16 q^{40} + 4 q^{41} - 20 q^{43} - 4 q^{44} + 20 q^{46} - 12 q^{47} + 40 q^{49} + 8 q^{52} + 26 q^{53} - 4 q^{55} - 14 q^{58} - 8 q^{59} + 40 q^{61} + 6 q^{64} - 12 q^{65} + 8 q^{67} - 10 q^{68} - 60 q^{70} + 48 q^{71} - 10 q^{74} + 8 q^{76} - 20 q^{77} + 28 q^{79} + 10 q^{80} - 2 q^{82} - 80 q^{83} - 30 q^{85} - 8 q^{86} + 16 q^{88} + 58 q^{89} + 4 q^{92} - 8 q^{94} - 68 q^{95} - 86 q^{97} + 2 q^{98}+O(q^{100}) $ 24 * q + 6 * q^4 + 4 * q^10 + 4 * q^11 + 2 * q^13 - 6 * q^16 + 10 * q^17 - 8 * q^19 + 10 * q^20 + 4 * q^22 - 4 * q^23 + 6 * q^25 - 8 * q^26 - 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 + 8 * q^38 + 16 * q^40 + 4 * q^41 - 20 * q^43 - 4 * q^44 + 20 * q^46 - 12 * q^47 + 40 * q^49 + 8 * q^52 + 26 * q^53 - 4 * q^55 - 14 * q^58 - 8 * q^59 + 40 * q^61 + 6 * q^64 - 12 * q^65 + 8 * q^67 - 10 * q^68 - 60 * q^70 + 48 * q^71 - 10 * q^74 + 8 * q^76 - 20 * q^77 + 28 * q^79 + 10 * q^80 - 2 * q^82 - 80 * q^83 - 30 * q^85 - 8 * q^86 + 16 * q^88 + 58 * q^89 + 4 * q^92 - 8 * q^94 - 68 * q^95 - 86 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−3.17802	−	1.03260i	−1.42125	−	0.461793i	−0.505253	−	0.862971i	$-0.668601\pi$
$5$	−3.17802	−	1.03260i	−1.42125	−	0.461793i	−0.916000	+	0.401178i	$0.868601\pi$
$6$		0			0
$7$	−0.0295159	−	0.186356i	−0.0111560	−	0.0704360i	0.981482	−	0.191553i	$-0.0613524\pi$
$7$	−0.0295159	−	0.186356i	−0.0111560	−	0.0704360i	−0.992638	+	0.121117i	$0.961352\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		0			0
$10$	−1.03260	−	3.17802i	−0.326537	−	1.00498i
$11$	1.66667	−	3.27102i	0.502520	−	0.986251i	−0.490845	−	0.871247i	$-0.663312\pi$
$11$	1.66667	−	3.27102i	0.502520	−	0.986251i	0.993365	−	0.115004i	$-0.0366881\pi$
$12$		0			0
$13$	5.44127	+	0.861812i	1.50914	+	0.239024i	0.855507	−	0.517792i	$-0.173246\pi$
$13$	5.44127	+	0.861812i	1.50914	+	0.239024i	0.653629	+	0.756815i	$0.273246\pi$
$14$	0.133416	−	0.133416i	0.0356570	−	0.0356570i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.15110	+	1.09604i	0.521719	+	0.265829i	0.694958	−	0.719051i	$-0.255423\pi$
$17$	2.15110	+	1.09604i	0.521719	+	0.265829i	−0.173238	+	0.984880i	$0.555423\pi$
$18$		0			0
$19$	2.44120	−	0.386648i	0.560050	−	0.0887032i	0.130009	−	0.991513i	$-0.458499\pi$
$19$	2.44120	−	0.386648i	0.560050	−	0.0887032i	0.430041	+	0.902810i	$0.358499\pi$
$20$	1.96412	−	2.70338i	0.439191	−	0.604495i
$21$		0			0
$22$	3.62596	−	0.574295i	0.773057	−	0.122440i
$23$	4.08088	−	2.96494i	0.850923	−	0.618232i	−0.0744774	−	0.997223i	$-0.523729\pi$
$23$	4.08088	−	2.96494i	0.850923	−	0.618232i	0.925400	+	0.378991i	$0.123729\pi$
$24$		0			0
$25$	4.98846	+	3.62433i	0.997691	+	0.724865i
$26$	2.50108	+	4.90864i	0.490501	+	0.962663i
$27$		0			0
$28$	0.186356	+	0.0295159i	0.0352180	+	0.00557798i
$29$	0.824791	−	0.420252i	0.153160	−	0.0780389i	−0.375731	−	0.926729i	$-0.622608\pi$
$29$	0.824791	−	0.420252i	0.153160	−	0.0780389i	0.528891	+	0.848690i	$0.322608\pi$
$30$		0			0
$31$	0.894416	+	2.75273i	0.160642	+	0.494405i	0.998689	−	0.0511934i	$-0.0163025\pi$
$31$	0.894416	+	2.75273i	0.160642	+	0.494405i	−0.838047	+	0.545598i	$0.816303\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.377670	+	2.38452i	0.0647699	+	0.408941i
$35$	−0.0986294	+	0.622721i	−0.0166714	+	0.105259i
$36$		0			0
$37$	−0.0598364	+	0.184157i	−0.00983704	+	0.0302753i	−0.955855	−	0.293840i	$-0.905067\pi$
$37$	−0.0598364	+	0.184157i	−0.00983704	+	0.0302753i	0.946018	+	0.324115i	$0.105067\pi$
$38$	1.74771	+	1.74771i	0.283516	+	0.283516i
$39$		0			0
$40$	3.34157			0.528348
$41$	−0.312306	−	6.39550i	−0.0487740	−	0.998810i
$41$	−0.312306	−	6.39550i	−0.0487740	−	0.998810i
$42$		0			0
$43$	−0.374552	−	0.515527i	−0.0571186	−	0.0786171i	0.779502	−	0.626400i	$-0.215472\pi$
$43$	−0.374552	−	0.515527i	−0.0571186	−	0.0786171i	−0.836621	+	0.547782i	$0.815472\pi$
$44$	2.59590	+	2.59590i	0.391346	+	0.391346i
$45$		0			0
$46$	4.79737	+	1.55876i	0.707333	+	0.229826i
$47$	0.339165	−	2.14140i	0.0494722	−	0.312355i	−0.950526	−	0.310644i	$-0.899455\pi$
$47$	0.339165	−	2.14140i	0.0494722	−	0.312355i	0.999999	−	0.00171134i	$-0.000544737\pi$
$48$		0			0
$49$	6.62354	−	2.15212i	0.946220	−	0.307445i
$50$			6.16607i			0.872014i
$51$		0			0
$52$	−2.50108	+	4.90864i	−0.346837	+	0.680705i
$53$	−7.80894	+	3.97885i	−1.07264	+	0.546538i	−0.898855	−	0.438246i	$-0.855600\pi$
$53$	−7.80894	+	3.97885i	−1.07264	+	0.546538i	−0.173785	+	0.984784i	$0.555600\pi$
$54$		0			0
$55$	−8.67437	+	8.67437i	−1.16965	+	1.16965i
$56$	0.0856585	+	0.168114i	0.0114466	+	0.0224652i
$57$		0			0
$58$	0.824791	+	0.420252i	0.108300	+	0.0551818i
$59$	0.834669	−	0.606422i	0.108665	−	0.0789495i	−0.532126	−	0.846665i	$-0.678607\pi$
$59$	0.834669	−	0.606422i	0.108665	−	0.0789495i	0.640791	+	0.767716i	$0.278607\pi$
$60$		0			0
$61$	5.01958	−	6.90887i	0.642692	−	0.884590i	−0.356064	−	0.934462i	$-0.615881\pi$
$61$	5.01958	−	6.90887i	0.642692	−	0.884590i	0.998756	+	0.0498721i	$0.0158814\pi$
$62$	−1.70128	+	2.34161i	−0.216063	+	0.297385i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−16.4025	−	8.35751i	−2.03448	−	1.03662i
$66$		0			0
$67$	−5.92399	−	11.6265i	−0.723730	−	1.42040i	−0.899925	−	0.436045i	$-0.856379\pi$
$67$	−5.92399	−	11.6265i	−0.723730	−	1.42040i	0.176195	−	0.984355i	$-0.443621\pi$
$68$	−1.70712	+	1.70712i	−0.207019	+	0.207019i
$69$		0			0
$70$	−0.561765	+	0.286234i	−0.0671438	+	0.0342115i
$71$	−0.312899	+	0.614098i	−0.0371342	+	0.0728800i	−0.908828	−	0.417171i	$-0.863022\pi$
$71$	−0.312899	+	0.614098i	−0.0371342	+	0.0728800i	0.871694	+	0.490051i	$0.163022\pi$
$72$		0			0
$73$		−	6.55734i		−	0.767478i	−0.923442	−	0.383739i	$-0.874636\pi$
$73$		−	6.55734i		−	0.767478i	0.923442	−	0.383739i	$-0.125364\pi$
$74$	−0.184157	+	0.0598364i	−0.0214079	+	0.00695584i
$75$		0			0
$76$	−0.386648	+	2.44120i	−0.0443516	+	0.280025i
$77$	−0.658768	−	0.214047i	−0.0750736	−	0.0243929i
$78$		0			0
$79$	10.1046	+	10.1046i	1.13685	+	1.13685i	0.989011	+	0.147844i	$0.0472332\pi$
$79$	10.1046	+	10.1046i	1.13685	+	1.13685i	0.147844	+	0.989011i	$0.452767\pi$
$80$	1.96412	+	2.70338i	0.219596	+	0.302248i
$81$		0			0
$82$	4.99050	−	4.01184i	0.551109	−	0.443034i
$83$	−13.1883			−1.44761			−0.723804	−	0.690005i	$-0.757608\pi$
$83$	−13.1883			−1.44761			−0.723804	+	0.690005i	$0.757608\pi$
$84$		0			0
$85$	−5.70447	−	5.70447i	−0.618737	−	0.618737i
$86$	0.196914	−	0.606038i	0.0212337	−	0.0653507i
$87$		0			0
$88$	−0.574295	+	3.62596i	−0.0612201	+	0.386528i
$89$	2.07242	+	13.0848i	0.219676	+	1.38698i	0.813115	+	0.582103i	$0.197770\pi$
$89$	2.07242	+	13.0848i	0.219676	+	1.38698i	−0.593439	+	0.804879i	$0.702230\pi$
$90$		0			0
$91$		−	1.03945i		−	0.108964i
$92$	1.55876	+	4.79737i	0.162512	+	0.500160i
$93$		0			0
$94$	1.93179	−	0.984294i	0.199249	−	0.101522i
$95$	−8.15744	−	1.29201i	−0.836936	−	0.132558i
$96$		0			0
$97$	−2.00053	−	3.92626i	−0.203123	−	0.398651i	0.766864	−	0.641810i	$-0.221816\pi$
$97$	−2.00053	−	3.92626i	−0.203123	−	0.398651i	−0.969986	+	0.243159i	$0.921816\pi$
$98$	5.63432	+	4.09357i	0.569152	+	0.413513i
$99$		0			0
$100$	−4.98846	+	3.62433i	−0.498846	+	0.362433i
$101$	9.05758	−	1.43458i	0.901263	−	0.142746i	0.311428	−	0.950270i	$-0.399193\pi$
$101$	9.05758	−	1.43458i	0.901263	−	0.142746i	0.589835	+	0.807524i	$0.299193\pi$
$102$		0			0
$103$	6.41440	−	8.82866i	0.632029	−	0.869914i	−0.366130	−	0.930564i	$-0.619317\pi$
$103$	6.41440	−	8.82866i	0.632029	−	0.869914i	0.998159	+	0.0606499i	$0.0193173\pi$
$104$	−5.44127	+	0.861812i	−0.533560	+	0.0845076i
$105$		0			0
$106$	−7.80894	−	3.97885i	−0.758471	−	0.386460i
$107$	11.9565	+	8.68692i	1.15588	+	0.839797i	0.989252	−	0.146223i	$-0.0467117\pi$
$107$	11.9565	+	8.68692i	1.15588	+	0.839797i	0.166629	+	0.986020i	$0.446712\pi$
$108$		0			0
$109$	−12.1467	+	12.1467i	−1.16345	+	1.16345i	−0.179730	+	0.983716i	$0.557523\pi$
$109$	−12.1467	+	12.1467i	−1.16345	+	1.16345i	−0.983716	+	0.179730i	$0.942477\pi$
$110$	−12.1164	−	1.91905i	−1.15525	−	0.182974i
$111$		0			0
$112$	−0.0856585	+	0.168114i	−0.00809397	+	0.0158853i
$113$	−1.35334	−	4.16516i	−0.127312	−	0.391826i	0.867003	−	0.498302i	$-0.166043\pi$
$113$	−1.35334	−	4.16516i	−0.127312	−	0.391826i	−0.994315	+	0.106477i	$0.966043\pi$
$114$		0			0
$115$	−16.0307	+	5.20870i	−1.49487	+	0.485713i
$116$	0.144809	+	0.914288i	0.0134452	+	0.0848895i
$117$		0			0
$118$	0.981212	+	0.318815i	0.0903279	+	0.0293493i
$119$	0.140762	−	0.433222i	0.0129037	−	0.0397134i
$120$		0			0
$121$	−1.45617	−	2.00424i	−0.132379	−	0.182204i
$122$	8.53983			0.773160
$123$		0			0
$124$	−2.89439			−0.259924
$125$	−2.29031	−	3.15234i	−0.204852	−	0.281954i
$126$		0			0
$127$	−6.17483	+	19.0042i	−0.547928	+	1.68635i	0.165998	+	0.986126i	$0.446915\pi$
$127$	−6.17483	+	19.0042i	−0.547928	+	1.68635i	−0.713926	+	0.700221i	$0.753085\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$		0			0
$130$	−2.87980	−	18.1824i	−0.252575	−	1.59470i
$131$	15.4172	−	5.00937i	1.34701	−	0.437670i	0.455325	−	0.890325i	$-0.349523\pi$
$131$	15.4172	−	5.00937i	1.34701	−	0.437670i	0.891686	+	0.452655i	$0.149523\pi$
$132$		0			0
$133$	−0.144109	−	0.443521i	−0.0124958	−	0.0384581i
$134$	5.92399	−	11.6265i	0.511754	−	1.00437i
$135$		0			0
$136$	−2.38452	−	0.377670i	−0.204471	−	0.0323850i
$137$	−5.57819	+	5.57819i	−0.476577	+	0.476577i	−0.904035	−	0.427458i	$-0.859409\pi$
$137$	−5.57819	+	5.57819i	−0.476577	+	0.476577i	0.427458	+	0.904035i	$0.359409\pi$
$138$		0			0
$139$	−15.0914	−	10.9646i	−1.28004	−	0.930002i	−0.280484	−	0.959859i	$-0.590495\pi$
$139$	−15.0914	−	10.9646i	−1.28004	−	0.930002i	−0.999554	+	0.0298566i	$0.990495\pi$
$140$	−0.561765	−	0.286234i	−0.0474778	−	0.0241912i
$141$		0			0
$142$	−0.680733	+	0.107817i	−0.0571258	+	0.00904784i
$143$	11.8878	−	16.3622i	0.994108	−	1.36827i
$144$		0			0
$145$	−3.05516	+	0.483889i	−0.253717	+	0.0401848i
$146$	5.30500	−	3.85431i	0.439045	−	0.318985i
$147$		0			0
$148$	−0.156654	−	0.113816i	−0.0128769	−	0.00935558i
$149$	−6.35880	−	12.4798i	−0.520933	−	1.02239i	−0.990243	−	0.139355i	$-0.955497\pi$
$149$	−6.35880	−	12.4798i	−0.520933	−	1.02239i	0.469309	−	0.883034i	$-0.344503\pi$
$150$		0			0
$151$	−1.05288	−	0.166760i	−0.0856823	−	0.0135707i	0.113446	−	0.993544i	$-0.463811\pi$
$151$	−1.05288	−	0.166760i	−0.0856823	−	0.0135707i	−0.199128	+	0.979973i	$0.563811\pi$
$152$	−2.20224	+	1.12210i	−0.178625	+	0.0910141i
$153$		0			0
$154$	−0.214047	−	0.658768i	−0.0172484	−	0.0530851i
$155$		−	9.67180i		−	0.776858i
$156$		0			0
$157$	0.799722	+	5.04925i	0.0638248	+	0.402974i	0.998831	+	0.0483421i	$0.0153938\pi$
$157$	0.799722	+	5.04925i	0.0638248	+	0.402974i	−0.935006	+	0.354632i	$0.884606\pi$
$158$	−2.23545	+	14.1141i	−0.177843	+	1.12286i
$159$		0			0
$160$	−1.03260	+	3.17802i	−0.0816343	+	0.251244i
$161$	−0.672985	−	0.672985i	−0.0530386	−	0.0530386i
$162$		0			0
$163$	21.5791			1.69020			0.845102	−	0.534604i	$-0.179539\pi$
$163$	21.5791			1.69020			0.845102	+	0.534604i	$0.179539\pi$
$164$	6.17899	+	1.67930i	0.482498	+	0.131131i
$165$		0			0
$166$	−7.75191	−	10.6696i	−0.601665	−	0.828121i
$167$	9.92227	+	9.92227i	0.767808	+	0.767808i	0.977720	−	0.209912i	$-0.0673178\pi$
$167$	9.92227	+	9.92227i	0.767808	+	0.767808i	−0.209912	+	0.977720i	$0.567318\pi$
$168$		0			0
$169$	16.5009	+	5.36147i	1.26930	+	0.412421i
$170$	1.26201	−	7.96802i	0.0967918	−	0.611119i
$171$		0			0
$172$	0.606038	−	0.196914i	0.0462100	−	0.0150145i
$173$			8.84477i			0.672455i	0.941781	+	0.336228i	$0.109151\pi$
$173$			8.84477i			0.672455i	−0.941781	+	0.336228i	$0.890849\pi$
$174$		0			0
$175$	0.528176	−	1.03660i	0.0399264	−	0.0783599i
$176$	−3.27102	+	1.66667i	−0.246563	+	0.125630i
$177$		0			0
$178$	−9.36765	+	9.36765i	−0.702135	+	0.702135i
$179$	2.14495	+	4.20971i	0.160321	+	0.314648i	0.957168	−	0.289533i	$-0.0935001\pi$
$179$	2.14495	+	4.20971i	0.160321	+	0.314648i	−0.796847	+	0.604182i	$0.793500\pi$
$180$		0			0
$181$	−21.1196	−	10.7610i	−1.56980	−	0.799855i	−0.570041	−	0.821616i	$-0.693073\pi$
$181$	−21.1196	−	10.7610i	−1.56980	−	0.799855i	−0.999763	+	0.0217607i	$0.993073\pi$
$182$	0.840933	−	0.610973i	0.0623341	−	0.0452884i
$183$		0			0
$184$	−2.96494	+	4.08088i	−0.218578	+	0.300847i
$185$	0.380322	−	0.523469i	0.0279619	−	0.0384862i
$186$		0			0
$187$	7.17036	−	5.20957i	0.524348	−	0.380961i
$188$	1.93179	+	0.984294i	0.140890	+	0.0717870i
$189$		0			0
$190$	−3.74956	−	7.35893i	−0.272022	−	0.533873i
$191$	2.35072	−	2.35072i	0.170092	−	0.170092i	−0.616928	−	0.787020i	$-0.711623\pi$
$191$	2.35072	−	2.35072i	0.170092	−	0.170092i	0.787020	+	0.616928i	$0.211623\pi$
$192$		0			0
$193$	−20.8129	+	10.6047i	−1.49815	+	0.763343i	−0.994906	−	0.100803i	$-0.967859\pi$
$193$	−20.8129	+	10.6047i	−1.49815	+	0.763343i	−0.503240	+	0.864147i	$0.667859\pi$
$194$	2.00053	−	3.92626i	0.143630	−	0.281889i
$195$		0			0
$196$			6.96440i			0.497457i
$197$	−21.4788	+	6.97887i	−1.53030	+	0.497224i	−0.948680	−	0.316238i	$-0.897580\pi$
$197$	−21.4788	+	6.97887i	−1.53030	+	0.497224i	−0.581618	+	0.813462i	$0.697580\pi$
$198$		0			0
$199$	0.570612	−	3.60270i	0.0404496	−	0.255389i	−0.959174	−	0.282816i	$-0.908731\pi$
$199$	0.570612	−	3.60270i	0.0404496	−	0.255389i	0.999624	+	0.0274272i	$0.00873145\pi$
$200$	−5.86428	−	1.90542i	−0.414667	−	0.134734i
$201$		0			0
$202$	6.48451	+	6.48451i	0.456249	+	0.456249i
$203$	−0.102661	−	0.141301i	−0.00720539	−	0.00991737i
$204$		0			0
$205$	−5.61149	+	20.6475i	−0.391923	+	1.44209i
$206$	10.9128			0.760333
$207$		0			0
$208$	−3.89552	−	3.89552i	−0.270105	−	0.270105i
$209$	2.80394	−	8.62964i	0.193953	−	0.596925i
$210$		0			0
$211$	3.26768	−	20.6313i	0.224956	−	1.42032i	−0.573963	−	0.818881i	$-0.694595\pi$
$211$	3.26768	−	20.6313i	0.224956	−	1.42032i	0.798920	−	0.601438i	$-0.205405\pi$
$212$	−1.37102	−	8.65628i	−0.0941620	−	0.594515i
$213$		0			0
$214$			14.7791i			1.01028i
$215$	0.658000	+	2.02512i	0.0448752	+	0.138112i
$216$		0			0
$217$	0.486588	−	0.247929i	0.0330318	−	0.0168305i
$218$	−16.9666	−	2.68724i	−1.14912	−	0.182003i
$219$		0			0
$220$	−5.56929	−	10.9303i	−0.375481	−	0.736924i
$221$	10.7601	+	7.81770i	0.723805	+	0.525875i
$222$		0			0
$223$	−10.2913	+	7.47706i	−0.689156	+	0.500701i	−0.876382	−	0.481616i	$-0.840050\pi$
$223$	−10.2913	+	7.47706i	−0.689156	+	0.500701i	0.187227	+	0.982317i	$0.440050\pi$
$224$	−0.186356	+	0.0295159i	−0.0124514	+	0.00197211i
$225$		0			0
$226$	2.57421	−	3.54310i	0.171234	−	0.235684i
$227$	21.8290	−	3.45738i	1.44884	−	0.229474i	0.618087	−	0.786109i	$-0.287908\pi$
$227$	21.8290	−	3.45738i	1.44884	−	0.229474i	0.830757	+	0.556635i	$0.187908\pi$
$228$		0			0
$229$	−6.21657	−	3.16750i	−0.410803	−	0.209314i	0.236361	−	0.971665i	$-0.424045\pi$
$229$	−6.21657	−	3.16750i	−0.410803	−	0.209314i	−0.647164	+	0.762351i	$0.724045\pi$
$230$	−13.6365	−	9.90753i	−0.899167	−	0.653283i
$231$		0			0
$232$	−0.654558	+	0.654558i	−0.0429739	+	0.0429739i
$233$	−2.71839	−	0.430551i	−0.178088	−	0.0282063i	0.0667535	−	0.997769i	$-0.478736\pi$
$233$	−2.71839	−	0.430551i	−0.178088	−	0.0282063i	−0.244841	+	0.969563i	$0.578736\pi$
$234$		0			0
$235$	−3.28908	+	6.45519i	−0.214556	+	0.421090i
$236$	0.318815	+	0.981212i	0.0207531	+	0.0638715i
$237$		0			0
$238$	0.433222	−	0.140762i	0.0280816	−	0.00912426i
$239$	3.21128	+	20.2752i	0.207721	+	1.31150i	0.842455	+	0.538766i	$0.181109\pi$
$239$	3.21128	+	20.2752i	0.207721	+	1.31150i	−0.634735	+	0.772730i	$0.718891\pi$
$240$		0			0
$241$	−27.1757	−	8.82991i	−1.75054	−	0.568784i	−0.754386	−	0.656431i	$-0.772065\pi$
$241$	−27.1757	−	8.82991i	−1.75054	−	0.568784i	−0.996152	+	0.0876466i	$0.972065\pi$
$242$	0.765553	−	2.35613i	0.0492116	−	0.151458i
$243$		0			0
$244$	5.01958	+	6.90887i	0.321346	+	0.442295i
$245$	−23.2720			−1.48679
$246$		0			0
$247$	13.6164			0.866394
$248$	−1.70128	−	2.34161i	−0.108031	−	0.148692i
$249$		0			0
$250$	1.20409	−	3.70580i	0.0761532	−	0.234375i
$251$	−16.6877	−	5.42218i	−1.05332	−	0.342245i	−0.269350	−	0.963042i	$-0.586809\pi$
$251$	−16.6877	−	5.42218i	−1.05332	−	0.342245i	−0.783971	+	0.620798i	$0.786809\pi$
$252$		0			0
$253$	−2.89689	−	18.2902i	−0.182126	−	1.14990i
$254$	−19.0042	+	6.17483i	−1.19243	+	0.387443i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−5.63128	+	11.0520i	−0.351270	+	0.689406i	−0.997263	−	0.0739376i	$-0.976443\pi$
$257$	−5.63128	+	11.0520i	−0.351270	+	0.689406i	0.645993	+	0.763343i	$0.276443\pi$
$258$		0			0
$259$	0.0360850	+	0.00571530i	0.00224221	+	0.000355132i
$260$	13.0171	−	13.0171i	0.807288	−	0.807288i
$261$		0			0
$262$	13.1147	+	9.52838i	0.810228	+	0.588665i
$263$	8.64227	+	4.40346i	0.532905	+	0.271529i	0.699668	−	0.714468i	$-0.253331\pi$
$263$	8.64227	+	4.40346i	0.532905	+	0.271529i	−0.166763	+	0.985997i	$0.553331\pi$
$264$		0			0
$265$	28.9255	−	4.58135i	1.77688	−	0.281430i
$266$	0.274111	−	0.377281i	0.0168068	−	0.0231326i
$267$		0			0
$268$	12.8880	−	2.04127i	0.787263	−	0.124690i
$269$	1.80972	−	1.31484i	0.110341	−	0.0801671i	−0.531247	−	0.847217i	$-0.678276\pi$
$269$	1.80972	−	1.31484i	0.110341	−	0.0801671i	0.641587	+	0.767050i	$0.278276\pi$
$270$		0			0
$271$	−1.01376	−	0.736538i	−0.0615814	−	0.0447415i	0.556569	−	0.830802i	$-0.312118\pi$
$271$	−1.01376	−	0.736538i	−0.0615814	−	0.0447415i	−0.618150	+	0.786060i	$0.712118\pi$
$272$	−1.09604	−	2.15110i	−0.0664573	−	0.130430i
$273$		0			0
$274$	−7.79163	−	1.23407i	−0.470710	−	0.0745531i
$275$	20.1694	−	10.2768i	1.21626	−	0.619715i
$276$		0			0
$277$	6.16373	+	18.9700i	0.370343	+	1.13980i	0.946567	+	0.322506i	$0.104525\pi$
$277$	6.16373	+	18.9700i	0.370343	+	1.13980i	−0.576225	+	0.817291i	$0.695475\pi$
$278$		−	18.6540i		−	1.11879i
$279$		0			0
$280$	−0.0986294	−	0.622721i	−0.00589423	−	0.0372147i
$281$	−1.49711	+	9.45238i	−0.0893101	+	0.563882i	0.901938	+	0.431866i	$0.142145\pi$
$281$	−1.49711	+	9.45238i	−0.0893101	+	0.563882i	−0.991248	+	0.132015i	$0.957855\pi$
$282$		0			0
$283$	4.98294	−	15.3359i	0.296205	−	0.911625i	−0.686609	−	0.727027i	$-0.740902\pi$
$283$	4.98294	−	15.3359i	0.296205	−	0.911625i	0.982814	−	0.184599i	$-0.0590985\pi$
$284$	−0.487351	−	0.487351i	−0.0289190	−	0.0289190i
$285$		0			0
$286$	20.2247			1.19591
$287$	−1.18262	+	0.246969i	−0.0698080	+	0.0145781i
$288$		0			0
$289$	−6.56641	−	9.03789i	−0.386260	−	0.531641i
$290$	−2.18725	−	2.18725i	−0.128440	−	0.128440i
$291$		0			0
$292$	6.23640	+	2.02633i	0.364958	+	0.118582i
$293$	−2.59359	+	16.3753i	−0.151519	+	0.956653i	0.788377	+	0.615192i	$0.210922\pi$
$293$	−2.59359	+	16.3753i	−0.151519	+	0.956653i	−0.939896	+	0.341461i	$0.889078\pi$
$294$		0			0
$295$	−3.27879	+	1.06534i	−0.190898	+	0.0620266i
$296$		−	0.193635i		−	0.0112548i
$297$		0			0
$298$	6.35880	−	12.4798i	0.368355	−	0.722938i
$299$	24.7604	−	12.6160i	1.43193	−	0.729605i
$300$		0			0
$301$	−0.0850163	+	0.0850163i	−0.00490026	+	0.00490026i
$302$	−0.483956	−	0.949818i	−0.0278486	−	0.0546559i
$303$		0			0
$304$	−2.20224	−	1.12210i	−0.126307	−	0.0643567i
$305$	−23.0864	+	16.7733i	−1.32193	+	0.960435i
$306$		0			0
$307$	15.5549	−	21.4095i	0.887766	−	1.22191i	−0.0864429	−	0.996257i	$-0.527550\pi$
$307$	15.5549	−	21.4095i	0.887766	−	1.22191i	0.974209	−	0.225648i	$-0.0724500\pi$
$308$	0.407141	−	0.560382i	0.0231990	−	0.0319307i
$309$		0			0
$310$	7.82465	−	5.68494i	0.444410	−	0.322883i
$311$	8.61374	+	4.38892i	0.488440	+	0.248873i	0.680824	−	0.732447i	$-0.261622\pi$
$311$	8.61374	+	4.38892i	0.488440	+	0.248873i	−0.192384	+	0.981320i	$0.561622\pi$
$312$		0			0
$313$	−1.78085	−	3.49511i	−0.100660	−	0.197555i	0.835185	−	0.549970i	$-0.185361\pi$
$313$	−1.78085	−	3.49511i	−0.100660	−	0.197555i	−0.935844	+	0.352414i	$0.885361\pi$
$314$	−3.61486	+	3.61486i	−0.203998	+	0.203998i
$315$		0			0
$316$	−12.7325	+	6.48754i	−0.716260	+	0.364953i
$317$	11.4931	−	22.5564i	0.645516	−	1.26690i	−0.303849	−	0.952720i	$-0.598272\pi$
$317$	11.4931	−	22.5564i	0.645516	−	1.26690i	0.949365	−	0.314176i	$-0.101728\pi$
$318$		0			0
$319$		−	3.39833i		−	0.190270i
$320$	−3.17802	+	1.03260i	−0.177657	+	0.0577242i
$321$		0			0
$322$	0.148886	−	0.940027i	0.00829707	−	0.0523856i
$323$	5.67506	+	1.84394i	0.315769	+	0.102599i
$324$		0			0
$325$	24.0200	+	24.0200i	1.33239	+	1.33239i
$326$	12.6839	+	17.4579i	0.702495	+	0.966901i
$327$		0			0
$328$	2.27334	+	5.98598i	0.125524	+	0.330520i
$329$	−0.409074			−0.0225530
$330$		0			0
$331$	−3.65359	−	3.65359i	−0.200820	−	0.200820i	0.599532	−	0.800351i	$-0.295354\pi$
$331$	−3.65359	−	3.65359i	−0.200820	−	0.200820i	−0.800351	+	0.599532i	$0.795354\pi$
$332$	4.07542	−	12.5429i	0.223668	−	0.688379i
$333$		0			0
$334$	−2.19512	+	13.8594i	−0.120112	+	0.758355i
$335$	6.82103	+	43.0663i	0.372673	+	2.35296i
$336$		0			0
$337$			24.1672i			1.31647i	0.752811	+	0.658237i	$0.228697\pi$
$337$			24.1672i			1.31647i	−0.752811	+	0.658237i	$0.771303\pi$
$338$	5.36147	+	16.5009i	0.291626	+	0.897531i
$339$		0			0
$340$	7.18806	−	3.66250i	0.389827	−	0.198627i
$341$	10.4949	+	1.66223i	0.568333	+	0.0900151i
$342$		0			0
$343$	−1.19617	−	2.34761i	−0.0645871	−	0.126759i
$344$	0.515527	+	0.374552i	0.0277953	+	0.0201945i
$345$		0			0
$346$	−7.15557	+	5.19882i	−0.384686	+	0.279490i
$347$	7.08501	−	1.12215i	0.380343	−	0.0602404i	0.0366642	−	0.999328i	$-0.488327\pi$
$347$	7.08501	−	1.12215i	0.380343	−	0.0602404i	0.343679	+	0.939087i	$0.388327\pi$
$348$		0			0
$349$	0.00688816	−	0.00948074i	0.000368715	−	0.000507492i	−0.808833	−	0.588039i	$-0.799900\pi$
$349$	0.00688816	−	0.00948074i	0.000368715	−	0.000507492i	0.809201	+	0.587531i	$0.199900\pi$
$350$	1.14909	−	0.181997i	0.0614212	−	0.00972816i
$351$		0			0
$352$	−3.27102	−	1.66667i	−0.174346	−	0.0888338i
$353$	−14.4588	−	10.5049i	−0.769563	−	0.559120i	0.132266	−	0.991214i	$-0.457775\pi$
$353$	−14.4588	−	10.5049i	−0.769563	−	0.559120i	−0.901829	+	0.432094i	$0.857775\pi$
$354$		0			0
$355$	1.62852	−	1.62852i	0.0864327	−	0.0864327i
$356$	−13.0848	−	2.07242i	−0.693491	−	0.109838i
$357$		0			0
$358$	−2.14495	+	4.20971i	−0.113364	+	0.222490i
$359$	4.08702	+	12.5786i	0.215705	+	0.663871i	0.999103	+	0.0423509i	$0.0134847\pi$
$359$	4.08702	+	12.5786i	0.215705	+	0.663871i	−0.783398	+	0.621520i	$0.786515\pi$
$360$		0			0
$361$	−12.2601	+	3.98355i	−0.645269	+	0.209661i
$362$	−3.70797	−	23.4112i	−0.194887	−	1.23047i
$363$		0			0
$364$	0.988576	+	0.321208i	0.0518155	+	0.0168359i
$365$	−6.77111	+	20.8393i	−0.354416	+	1.09078i
$366$		0			0
$367$	7.87957	+	10.8453i	0.411310	+	0.566120i	0.963537	−	0.267574i	$-0.0862218\pi$
$367$	7.87957	+	10.8453i	0.411310	+	0.566120i	−0.552227	+	0.833694i	$0.686222\pi$
$368$	−5.04425			−0.262950
$369$		0			0
$370$	0.647043			0.0336382
$371$	0.971971	+	1.33780i	0.0504622	+	0.0694553i
$372$		0			0
$373$	2.59411	−	7.98386i	0.134318	−	0.413389i	−0.861165	−	0.508325i	$-0.830265\pi$
$373$	2.59411	−	7.98386i	0.134318	−	0.413389i	0.995483	+	0.0949365i	$0.0302648\pi$
$374$	8.42926	+	2.73883i	0.435867	+	0.141622i
$375$		0			0
$376$	0.339165	+	2.14140i	0.0174911	+	0.110434i
$377$	4.85009	−	1.57589i	0.249792	−	0.0811624i
$378$		0			0
$379$	6.33795	+	19.5062i	0.325558	+	1.00197i	0.971188	+	0.238315i	$0.0765950\pi$
$379$	6.33795	+	19.5062i	0.325558	+	1.00197i	−0.645630	+	0.763651i	$0.723405\pi$
$380$	3.74956	−	7.35893i	0.192349	−	0.377505i
$381$		0			0
$382$	3.28349	+	0.520053i	0.167998	+	0.0266083i
$383$	−9.35955	+	9.35955i	−0.478251	+	0.478251i	−0.904572	−	0.426321i	$-0.859809\pi$
$383$	−9.35955	+	9.35955i	−0.478251	+	0.478251i	0.426321	+	0.904572i	$0.359809\pi$
$384$		0			0
$385$	1.87255	+	1.36049i	0.0954342	+	0.0693370i
$386$	−20.8129	−	10.6047i	−1.05935	−	0.539765i
$387$		0			0
$388$	4.35229	−	0.689335i	0.220954	−	0.0349957i
$389$	−5.08926	+	7.00477i	−0.258036	+	0.355156i	−0.918305	−	0.395873i	$-0.870442\pi$
$389$	−5.08926	+	7.00477i	−0.258036	+	0.355156i	0.660269	+	0.751029i	$0.270442\pi$
$390$		0			0
$391$	12.0281	−	1.90506i	0.608287	−	0.0963432i
$392$	−5.63432	+	4.09357i	−0.284576	+	0.206757i
$393$		0			0
$394$	−18.2709	−	13.2746i	−0.920476	−	0.668765i
$395$	−21.6786	−	42.5466i	−1.09077	−	2.14075i
$396$		0			0
$397$	36.4796	+	5.77780i	1.83086	+	0.289979i	0.974163	−	0.225846i	$-0.0725145\pi$
$397$	36.4796	+	5.77780i	1.83086	+	0.289979i	0.856694	+	0.515825i	$0.172515\pi$
$398$	3.25004	−	1.65598i	0.162910	−	0.0830068i
$399$		0			0
$400$	−1.90542	−	5.86428i	−0.0952710	−	0.293214i
$401$			21.7437i			1.08583i	0.839788	+	0.542915i	$0.182679\pi$
$401$			21.7437i			1.08583i	−0.839788	+	0.542915i	$0.817321\pi$
$402$		0			0
$403$	2.49442	+	15.7491i	0.124256	+	0.784521i
$404$	−1.43458	+	9.05758i	−0.0713730	+	0.450631i
$405$		0			0
$406$	0.0539721	−	0.166109i	0.00267859	−	0.00824385i
$407$	0.502656	+	0.502656i	0.0249157	+	0.0249157i
$408$		0			0
$409$	28.3303			1.40084			0.700421	−	0.713729i	$-0.252995\pi$
$409$	28.3303			1.40084			0.700421	+	0.713729i	$0.252995\pi$
$410$	−20.0025	+	7.59652i	−0.987855	+	0.375165i
$411$		0			0
$412$	6.41440	+	8.82866i	0.316015	+	0.434957i
$413$	−0.137647	−	0.137647i	−0.00677314	−	0.00677314i
$414$		0			0
$415$	41.9128	+	13.6183i	2.05742	+	0.668496i
$416$	0.861812	−	5.44127i	0.0422538	−	0.266780i
$417$		0			0
$418$	8.62964	−	2.80394i	0.422090	−	0.137145i
$419$		−	36.1746i		−	1.76725i	−0.468199	−	0.883623i	$-0.655097\pi$
$419$		−	36.1746i		−	1.76725i	0.468199	−	0.883623i	$-0.344903\pi$
$420$		0			0
$421$	8.03166	−	15.7630i	0.391439	−	0.768243i	−0.608235	−	0.793757i	$-0.708122\pi$
$421$	8.03166	−	15.7630i	0.391439	−	0.768243i	0.999674	+	0.0255140i	$0.00812224\pi$
$422$	18.6118	−	9.48318i	0.906008	−	0.461634i
$423$		0			0
$424$	6.19721	−	6.19721i	0.300963	−	0.300963i
$425$	6.75827	+	13.2639i	0.327824	+	0.643391i
$426$		0			0
$427$	−1.43567	−	0.731509i	−0.0694768	−	0.0354002i
$428$	−11.9565	+	8.68692i	−0.577940	+	0.419898i
$429$		0			0
$430$	−1.25159	+	1.72267i	−0.0603571	+	0.0830744i
$431$	−23.3523	+	32.1417i	−1.12484	+	1.54821i	−0.327325	+	0.944912i	$0.606147\pi$
$431$	−23.3523	+	32.1417i	−1.12484	+	1.54821i	−0.797516	+	0.603298i	$0.793853\pi$
$432$		0			0
$433$	3.78342	−	2.74881i	0.181820	−	0.132100i	−0.493153	−	0.869943i	$-0.664156\pi$
$433$	3.78342	−	2.74881i	0.181820	−	0.132100i	0.674972	+	0.737843i	$0.264156\pi$
$434$	0.486588	+	0.247929i	0.0233570	+	0.0119010i
$435$		0			0
$436$	−7.79868	−	15.3058i	−0.373489	−	0.733014i
$437$	8.81587	−	8.81587i	0.421720	−	0.421720i
$438$		0			0
$439$	−6.56624	+	3.34567i	−0.313390	+	0.159680i	−0.603610	−	0.797280i	$-0.706271\pi$
$439$	−6.56624	+	3.34567i	−0.313390	+	0.159680i	0.290220	+	0.956960i	$0.406271\pi$
$440$	5.56929	−	10.9303i	0.265505	−	0.521084i
$441$		0			0
$442$			13.3003i			0.632629i
$443$	−27.4050	+	8.90444i	−1.30205	+	0.423063i	−0.876295	−	0.481775i	$-0.839992\pi$
$443$	−27.4050	+	8.90444i	−1.30205	+	0.423063i	−0.425758	+	0.904837i	$0.639992\pi$
$444$		0			0
$445$	6.92514	−	43.7236i	0.328283	−	2.07270i
$446$	−12.0981	−	3.93092i	−0.572863	−	0.186135i
$447$		0			0
$448$	−0.133416	−	0.133416i	−0.00630332	−	0.00630332i
$449$	−2.46964	−	3.39917i	−0.116549	−	0.160417i	0.746756	−	0.665098i	$-0.231610\pi$
$449$	−2.46964	−	3.39917i	−0.116549	−	0.160417i	−0.863306	+	0.504681i	$0.831610\pi$
$450$		0			0
$451$	−21.4404	−	9.63763i	−1.00959	−	0.453818i
$452$	4.37951			0.205995
$453$		0			0
$454$	15.6279	+	15.6279i	0.733452	+	0.733452i
$455$	−1.07334	+	3.30339i	−0.0503188	+	0.154865i
$456$		0			0
$457$	−5.01200	+	31.6445i	−0.234451	+	1.48027i	0.536785	+	0.843719i	$0.319639\pi$
$457$	−5.01200	+	31.6445i	−0.234451	+	1.48027i	−0.771236	+	0.636549i	$0.780361\pi$
$458$	−1.09145	−	6.89112i	−0.0510000	−	0.322001i
$459$		0			0
$460$		−	16.8557i		−	0.785901i
$461$	−2.10166	−	6.46826i	−0.0978842	−	0.301257i	0.890110	−	0.455745i	$-0.150627\pi$
$461$	−2.10166	−	6.46826i	−0.0978842	−	0.301257i	−0.987995	+	0.154488i	$0.950627\pi$
$462$		0			0
$463$	−11.0090	+	5.60935i	−0.511631	+	0.260689i	−0.690692	−	0.723149i	$-0.742694\pi$
$463$	−11.0090	+	5.60935i	−0.511631	+	0.260689i	0.179061	+	0.983838i	$0.442694\pi$
$464$	−0.914288	−	0.144809i	−0.0424448	−	0.00672259i
$465$		0			0
$466$	−1.24951	−	2.45230i	−0.0578824	−	0.113601i
$467$	−1.85811	−	1.35000i	−0.0859832	−	0.0624705i	0.543963	−	0.839109i	$-0.316923\pi$
$467$	−1.85811	−	1.35000i	−0.0859832	−	0.0624705i	−0.629946	+	0.776639i	$0.716923\pi$
$468$		0			0
$469$	−1.99181	+	1.44714i	−0.0919734	+	0.0668226i
$470$	−7.15564	+	1.13334i	−0.330065	+	0.0522771i
$471$		0			0
$472$	−0.606422	+	0.834669i	−0.0279129	+	0.0384187i
$473$	−2.31055	+	0.365956i	−0.106239	+	0.0168267i
$474$		0			0
$475$	13.5792	+	6.91893i	0.623055	+	0.317462i
$476$	0.368520	+	0.267746i	0.0168911	+	0.0122721i
$477$		0			0
$478$	−14.5155	+	14.5155i	−0.663922	+	0.663922i
$479$	34.0388	+	5.39122i	1.55527	+	0.246331i	0.874084	−	0.485775i	$-0.161463\pi$
$479$	34.0388	+	5.39122i	1.55527	+	0.246331i	0.681190	+	0.732107i	$0.261463\pi$
$480$		0			0
$481$	−0.484295	+	0.950482i	−0.0220819	+	0.0433382i
$482$	−8.82991	−	27.1757i	−0.402191	−	1.23782i
$483$		0			0
$484$	2.35613	−	0.765553i	0.107097	−	0.0347979i
$485$	2.30346	+	14.5435i	0.104595	+	0.660385i
$486$		0			0
$487$	16.4793	+	5.35445i	0.746748	+	0.242633i	0.657581	−	0.753384i	$-0.271580\pi$
$487$	16.4793	+	5.35445i	0.746748	+	0.242633i	0.0891666	+	0.996017i	$0.471580\pi$
$488$	−2.63895	+	8.12186i	−0.119460	+	0.367659i
$489$		0			0
$490$	−13.6789	−	18.8275i	−0.617952	−	0.850538i
$491$	30.4472			1.37406			0.687031	−	0.726628i	$-0.258914\pi$
$491$	30.4472			1.37406			0.687031	+	0.726628i	$0.258914\pi$
$492$		0			0
$493$	2.23483			0.100651
$494$	8.00355	+	11.0159i	0.360097	+	0.495630i
$495$		0			0
$496$	0.894416	−	2.75273i	0.0401605	−	0.123601i
$497$	0.123676	+	0.0401849i	0.00554764	+	0.00180254i
$498$		0			0
$499$	0.862810	+	5.44757i	0.0386247	+	0.243867i	0.999445	−	0.0333044i	$-0.0106031\pi$
$499$	0.862810	+	5.44757i	0.0386247	+	0.243867i	−0.960821	+	0.277171i	$0.910603\pi$
$500$	3.70580	−	1.20409i	0.165728	−	0.0538484i
$501$		0			0
$502$	−5.42218	−	16.6877i	−0.242004	−	0.744810i
$503$	−4.95912	+	9.73283i	−0.221116	+	0.433965i	−0.974741	−	0.223340i	$-0.928304\pi$
$503$	−4.95912	+	9.73283i	−0.221116	+	0.433965i	0.753624	+	0.657306i	$0.228304\pi$
$504$		0			0
$505$	−30.2665	−	4.79374i	−1.34684	−	0.213319i
$506$	13.0944	−	13.0944i	0.582115	−	0.582115i
$507$		0			0
$508$	−16.1659	−	11.7452i	−0.717246	−	0.521110i
$509$	−26.4370	−	13.4703i	−1.17180	−	0.597061i	−0.243866	−	0.969809i	$-0.578416\pi$
$509$	−26.4370	−	13.4703i	−1.17180	−	0.597061i	−0.927933	+	0.372748i	$0.878416\pi$
$510$		0			0
$511$	−1.22200	+	0.193546i	−0.0540581	+	0.00856196i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$		0			0
$514$	−12.2513	+	1.94041i	−0.540379	+	0.0855877i
$515$	−29.5016	+	21.4341i	−1.29999	+	0.944501i
$516$		0			0
$517$	−6.43930	−	4.67842i	−0.283200	−	0.205757i
$518$	0.0165864	+	0.0325527i	0.000728767	+	0.00143029i
$519$		0			0
$520$	18.1824	+	2.87980i	0.797349	+	0.126288i
$521$	30.6711	−	15.6277i	1.34372	−	0.684662i	0.373673	−	0.927561i	$-0.378098\pi$
$521$	30.6711	−	15.6277i	1.34372	−	0.684662i	0.970052	+	0.242899i	$0.0780984\pi$
$522$		0			0
$523$	9.10779	+	28.0309i	0.398256	+	1.22570i	0.926397	+	0.376548i	$0.122889\pi$
$523$	9.10779	+	28.0309i	0.398256	+	1.22570i	−0.528141	+	0.849156i	$0.677111\pi$
$524$			16.2106i			0.708166i
$525$		0			0
$526$	1.51733	+	9.58003i	0.0661586	+	0.417709i
$527$	−1.09313	+	6.90172i	−0.0476173	+	0.300644i
$528$		0			0
$529$	0.755376	−	2.32481i	0.0328424	−	0.101079i
$530$	20.7084	+	20.7084i	0.899515	+	0.899515i
$531$		0			0
$532$	0.466345			0.0202186
$533$	3.81238	−	35.0688i	0.165132	−	1.51900i
$534$		0			0
$535$	−29.0279	−	39.9535i	−1.25499	−	1.72734i
$536$	9.22682	+	9.22682i	0.398538	+	0.398538i
$537$		0			0
$538$	2.12745	+	0.691251i	0.0917210	+	0.0298020i
$539$	3.99962	−	25.2526i	0.172276	−	1.08771i
$540$		0			0
$541$	4.64295	−	1.50859i	0.199616	−	0.0648592i	−0.207503	−	0.978234i	$-0.566534\pi$
$541$	4.64295	−	1.50859i	0.199616	−	0.0648592i	0.407119	+	0.913375i	$0.366534\pi$
$542$		−	1.25307i		−	0.0538241i
$543$		0			0
$544$	1.09604	−	2.15110i	0.0469924	−	0.0922278i
$545$	51.1453	−	26.0598i	2.19082	−	1.11628i
$546$		0			0
$547$	−17.3535	+	17.3535i	−0.741980	+	0.741980i	−0.972959	−	0.230978i	$-0.925807\pi$
$547$	−17.3535	+	17.3535i	−0.741980	+	0.741980i	0.230978	+	0.972959i	$0.425807\pi$
$548$	−3.58142	−	7.02893i	−0.152991	−	0.300261i
$549$		0			0
$550$	20.1694	+	10.2768i	0.860025	+	0.438204i
$551$	1.85099	−	1.34482i	0.0788549	−	0.0572915i
$552$		0			0
$553$	1.58480	−	2.18130i	0.0673927	−	0.0927582i
$554$	−11.7241	+	16.1369i	−0.498110	+	0.685589i
$555$		0			0
$556$	15.0914	−	10.9646i	0.640019	−	0.465001i
$557$	−9.87211	−	5.03009i	−0.418295	−	0.213132i	0.232159	−	0.972678i	$-0.425421\pi$
$557$	−9.87211	−	5.03009i	−0.418295	−	0.213132i	−0.650454	+	0.759546i	$0.725421\pi$
$558$		0			0
$559$	−1.59375	−	3.12791i	−0.0674084	−	0.132297i
$560$	0.445819	−	0.445819i	0.0188393	−	0.0188393i
$561$		0			0
$562$	−8.52711	+	4.34478i	−0.359695	+	0.183274i
$563$	13.3810	−	26.2618i	0.563944	−	1.10680i	−0.416340	−	0.909209i	$-0.636688\pi$
$563$	13.3810	−	26.2618i	0.563944	−	1.10680i	0.980284	−	0.197593i	$-0.0633125\pi$
$564$		0			0
$565$			14.6344i			0.615675i
$566$	15.3359	−	4.98294i	0.644617	−	0.209449i
$567$		0			0
$568$	0.107817	−	0.680733i	0.00452392	−	0.0285629i
$569$	12.0321	+	3.90946i	0.504411	+	0.163893i	0.550159	−	0.835060i	$-0.314567\pi$
$569$	12.0321	+	3.90946i	0.504411	+	0.163893i	−0.0457478	+	0.998953i	$0.514567\pi$
$570$		0			0
$571$	−12.9232	−	12.9232i	−0.540818	−	0.540818i	0.382951	−	0.923769i	$-0.374908\pi$
$571$	−12.9232	−	12.9232i	−0.540818	−	0.540818i	−0.923769	+	0.382951i	$0.874908\pi$
$572$	11.8878	+	16.3622i	0.497054	+	0.684136i
$573$		0			0
$574$	−0.894931	−	0.811597i	−0.0373537	−	0.0338754i
$575$	31.1032			1.29709
$576$		0			0
$577$	−21.7134	−	21.7134i	−0.903941	−	0.903941i	0.0918333	−	0.995774i	$-0.470727\pi$
$577$	−21.7134	−	21.7134i	−0.903941	−	0.903941i	−0.995774	+	0.0918333i	$0.970727\pi$
$578$	3.45217	−	10.6247i	0.143591	−	0.441928i
$579$		0			0
$580$	0.483889	−	3.05516i	0.0200924	−	0.126858i
$581$	0.389266	+	2.45773i	0.0161495	+	0.101964i
$582$		0			0
$583$			32.1747i			1.33254i
$584$	2.02633	+	6.23640i	0.0838501	+	0.258064i
$585$		0			0
$586$	−14.7723	+	7.52688i	−0.610240	+	0.310933i
$587$	14.8919	+	2.35865i	0.614656	+	0.0973519i	0.455997	−	0.889981i	$-0.349283\pi$
$587$	14.8919	+	2.35865i	0.614656	+	0.0973519i	0.158659	+	0.987333i	$0.449283\pi$
$588$		0			0
$589$	3.24779	+	6.37414i	0.133823	+	0.262642i
$590$	−2.78910	−	2.02640i	−0.114826	−	0.0834256i
$591$		0			0
$592$	0.156654	−	0.113816i	0.00643843	−	0.00467779i
$593$	−43.2237	+	6.84596i	−1.77498	+	0.281130i	−0.956145	−	0.292893i	$-0.905382\pi$
$593$	−43.2237	+	6.84596i	−1.77498	+	0.281130i	−0.818839	+	0.574023i	$0.805382\pi$
$594$		0			0
$595$	−0.894691	+	1.23144i	−0.0366787	+	0.0504840i
$596$	13.8340	−	2.19109i	0.566663	−	0.0897506i
$597$		0			0
$598$	24.7604	+	12.6160i	1.01253	+	0.515908i
$599$	−24.6062	−	17.8774i	−1.00538	−	0.730452i	−0.0421457	−	0.999111i	$-0.513419\pi$
$599$	−24.6062	−	17.8774i	−1.00538	−	0.730452i	−0.963235	+	0.268659i	$0.913419\pi$
$600$		0			0
$601$	4.67274	−	4.67274i	0.190605	−	0.190605i	−0.605353	−	0.795957i	$-0.706968\pi$
$601$	4.67274	−	4.67274i	0.190605	−	0.190605i	0.795957	+	0.605353i	$0.206968\pi$
$602$	−0.118751	−	0.0188083i	−0.00483993	−	0.000766569i
$603$		0			0
$604$	0.483956	−	0.949818i	0.0196919	−	0.0386475i
$605$	2.55815	+	7.87317i	0.104003	+	0.320090i
$606$		0			0
$607$	1.26069	−	0.409622i	0.0511697	−	0.0166260i	−0.283320	−	0.959025i	$-0.591436\pi$
$607$	1.26069	−	0.409622i	0.0511697	−	0.0166260i	0.334490	+	0.942399i	$0.391436\pi$
$608$	−0.386648	−	2.44120i	−0.0156807	−	0.0990038i
$609$		0			0
$610$	−27.1397	−	8.81823i	−1.09886	−	0.357040i
$611$	3.69097	−	11.3596i	0.149321	−	0.459562i
$612$		0			0
$613$	−13.7949	−	18.9870i	−0.557170	−	0.766879i	0.433793	−	0.901012i	$-0.357175\pi$
$613$	−13.7949	−	18.9870i	−0.557170	−	0.766879i	−0.990963	+	0.134134i	$0.957175\pi$
$614$	26.4636			1.06798
$615$		0			0
$616$	0.692670			0.0279085
$617$	−9.71209	−	13.3675i	−0.390994	−	0.538157i	0.567461	−	0.823400i	$-0.307926\pi$
$617$	−9.71209	−	13.3675i	−0.390994	−	0.538157i	−0.958455	+	0.285243i	$0.907926\pi$
$618$		0			0
$619$	4.36790	−	13.4430i	0.175561	−	0.540320i	−0.824098	−	0.566447i	$-0.808318\pi$
$619$	4.36790	−	13.4430i	0.175561	−	0.540320i	0.999659	+	0.0261273i	$0.00831752\pi$
$620$	9.19843	+	2.98875i	0.369418	+	0.120031i
$621$		0			0
$622$	1.51232	+	9.54840i	0.0606384	+	0.382856i
$623$	2.37725	−	0.772417i	0.0952427	−	0.0309462i
$624$		0			0
$625$	−5.50357	−	16.9382i	−0.220143	−	0.677530i
$626$	1.78085	−	3.49511i	0.0711770	−	0.139693i
$627$		0			0
$628$	−5.04925	−	0.799722i	−0.201487	−	0.0319124i
$629$	−0.330558	+	0.330558i	−0.0131802	+	0.0131802i
$630$		0			0
$631$	−34.3090	−	24.9269i	−1.36582	−	0.992326i	−0.998051	−	0.0624085i	$-0.980122\pi$
$631$	−34.3090	−	24.9269i	−1.36582	−	0.992326i	−0.367769	−	0.929917i	$-0.619878\pi$
$632$	−12.7325	−	6.48754i	−0.506472	−	0.258061i
$633$		0			0
$634$	25.0040	−	3.96025i	0.993036	−	0.157281i
$635$	39.2475	−	54.0195i	1.55749	−	2.14370i
$636$		0			0
$637$	37.8951	−	6.00200i	1.50146	−	0.237808i
$638$	2.74931	−	1.99749i	0.108846	−	0.0790814i
$639$		0			0
$640$	−2.70338	−	1.96412i	−0.106861	−	0.0776388i
$641$	−15.5004	−	30.4213i	−0.612230	−	1.20157i	−0.964105	−	0.265522i	$-0.914456\pi$
$641$	−15.5004	−	30.4213i	−0.612230	−	1.20157i	0.351875	−	0.936047i	$-0.385544\pi$
$642$		0			0
$643$	−10.2584	−	1.62477i	−0.404552	−	0.0640747i	−0.0491571	−	0.998791i	$-0.515654\pi$
$643$	−10.2584	−	1.62477i	−0.404552	−	0.0640747i	−0.355395	+	0.934716i	$0.615654\pi$
$644$	0.848010	−	0.432083i	0.0334163	−	0.0170264i
$645$		0			0
$646$	1.84394	+	5.67506i	0.0725488	+	0.223282i
$647$			35.8164i			1.40809i	0.710156	+	0.704044i	$0.248624\pi$
$647$			35.8164i			1.40809i	−0.710156	+	0.704044i	$0.751376\pi$
$648$		0			0
$649$	−0.592505	−	3.74093i	−0.0232578	−	0.146844i
$650$	−5.31399	+	33.5512i	−0.208432	+	1.31599i
$651$		0			0
$652$	−6.66831	+	20.5229i	−0.261151	+	0.803740i
$653$	22.2976	+	22.2976i	0.872573	+	0.872573i	0.992752	−	0.120179i	$-0.0383469\pi$
$653$	22.2976	+	22.2976i	0.872573	+	0.872573i	−0.120179	+	0.992752i	$0.538347\pi$
$654$		0			0
$655$	−54.1690			−2.11656
$656$	−3.50652	+	5.35764i	−0.136907	+	0.209181i
$657$		0			0
$658$	−0.240448	−	0.330948i	−0.00937362	−	0.0129017i
$659$	−23.7601	−	23.7601i	−0.925562	−	0.925562i	0.0718533	−	0.997415i	$-0.477109\pi$
$659$	−23.7601	−	23.7601i	−0.925562	−	0.925562i	−0.997415	+	0.0718533i	$0.977109\pi$
$660$		0			0
$661$	−41.6593	−	13.5359i	−1.62036	−	0.526487i	−0.648332	−	0.761357i	$-0.724533\pi$
$661$	−41.6593	−	13.5359i	−1.62036	−	0.526487i	−0.972027	+	0.234871i	$0.924533\pi$
$662$	0.808290	−	5.10335i	0.0314151	−	0.198347i
$663$		0			0
$664$	12.5429	−	4.07542i	0.486757	−	0.158157i
$665$			1.55832i			0.0604292i
$666$		0			0
$667$	2.11986	−	4.16045i	0.0820812	−	0.161093i
$668$	−12.5028	+	6.37049i	−0.483747	+	0.246482i
$669$		0			0
$670$	−30.8321	+	30.8321i	−1.19115	+	1.19115i
$671$	−14.2331	−	27.9340i	−0.549462	−	1.07838i
$672$		0			0
$673$	−15.9149	−	8.10903i	−0.613473	−	0.312580i	0.119504	−	0.992834i	$-0.461870\pi$
$673$	−15.9149	−	8.10903i	−0.613473	−	0.312580i	−0.732977	+	0.680254i	$0.761870\pi$
$674$	−19.5517	+	14.2051i	−0.753104	+	0.547162i
$675$		0			0
$676$	−10.1981	+	14.0365i	−0.392236	+	0.539866i
$677$	−24.8457	+	34.1972i	−0.954899	+	1.31431i	−0.00558305	+	0.999984i	$0.501777\pi$
$677$	−24.8457	+	34.1972i	−0.954899	+	1.31431i	−0.949316	+	0.314322i	$0.898223\pi$
$678$		0			0
$679$	−0.672634	+	0.488698i	−0.0258133	+	0.0187545i
$680$	7.18806	+	3.66250i	0.275649	+	0.140450i
$681$		0			0
$682$	4.82399	+	9.46762i	0.184720	+	0.362534i
$683$	−21.7524	+	21.7524i	−0.832332	+	0.832332i	−0.987835	−	0.155503i	$-0.950300\pi$
$683$	−21.7524	+	21.7524i	−0.832332	+	0.832332i	0.155503	+	0.987835i	$0.450300\pi$
$684$		0			0
$685$	23.4876	−	11.9676i	0.897417	−	0.457257i
$686$	1.19617	−	2.34761i	0.0456700	−	0.0896323i
$687$		0			0
$688$			0.637226i			0.0242940i
$689$	−45.9195	+	14.9202i	−1.74939	+	0.568413i
$690$		0			0
$691$	2.72449	−	17.2018i	0.103645	−	0.654386i	−0.880097	−	0.474795i	$-0.842522\pi$
$691$	2.72449	−	17.2018i	0.103645	−	0.654386i	0.983741	−	0.179592i	$-0.0574776\pi$
$692$	−8.41187	−	2.73318i	−0.319771	−	0.103900i
$693$		0			0
$694$	5.07231	+	5.07231i	0.192542	+	0.192542i
$695$	36.6388	+	50.4290i	1.38979	+	1.91288i
$696$		0			0
$697$	6.33794	−	14.0997i	0.240066	−	0.534064i
$698$	0.0117188			0.000443565
$699$		0			0
$700$	0.822654	+	0.822654i	0.0310934	+	0.0310934i
$701$	−4.19956	+	12.9249i	−0.158615	+	0.488167i	−0.998509	−	0.0545831i	$-0.982617\pi$
$701$	−4.19956	+	12.9249i	−0.158615	+	0.488167i	0.839894	+	0.542750i	$0.182617\pi$
$702$		0			0
$703$	−0.0748685	+	0.472701i	−0.00282372	+	0.0178283i
$704$	−0.574295	−	3.62596i	−0.0216446	−	0.136658i
$705$		0			0
$706$		−	17.8720i		−	0.672623i
$707$	−0.534685	−	1.64559i	−0.0201089	−	0.0618889i
$708$		0			0
$709$	−23.8743	+	12.1645i	−0.896617	+	0.456849i	−0.840647	−	0.541583i	$-0.817825\pi$
$709$	−23.8743	+	12.1645i	−0.896617	+	0.456849i	−0.0559697	+	0.998432i	$0.517825\pi$
$710$	2.27471	+	0.360279i	0.0853685	+	0.0135210i
$711$		0			0
$712$	−6.01440	−	11.8039i	−0.225399	−	0.442371i
$713$	11.8117	+	8.58168i	0.442351	+	0.321386i
$714$		0			0
$715$	−54.6752	+	39.7239i	−2.04474	+	1.48559i
$716$	−4.66649	+	0.739100i	−0.174395	+	0.0276215i
$717$		0			0
$718$	−7.77398	+	10.7000i	−0.290122	+	0.399319i
$719$	−3.27883	+	0.519316i	−0.122280	+	0.0193672i	−0.217274	−	0.976111i	$-0.569717\pi$
$719$	−3.27883	+	0.519316i	−0.122280	+	0.0193672i	0.0949946	+	0.995478i	$0.469717\pi$
$720$		0			0
$721$	−1.83460	−	0.934776i	−0.0683241	−	0.0348129i
$722$	−10.4291	−	7.57716i	−0.388130	−	0.281993i
$723$		0			0
$724$	16.7606	−	16.7606i	0.622902	−	0.622902i
$725$	5.63757	+	0.892903i	0.209374	+	0.0331616i
$726$		0			0
$727$	0.223503	−	0.438650i	0.00828928	−	0.0162686i	−0.886825	−	0.462106i	$-0.847094\pi$
$727$	0.223503	−	0.438650i	0.00828928	−	0.0162686i	0.895114	+	0.445837i	$0.147094\pi$
$728$	0.321208	+	0.988576i	0.0119048	+	0.0366391i
$729$		0			0
$730$	−20.8393	+	6.77111i	−0.771299	+	0.250610i
$731$	−0.240661	−	1.51948i	−0.00890118	−	0.0561998i
$732$		0			0
$733$	22.4451	+	7.29286i	0.829029	+	0.269368i	0.692636	−	0.721287i	$-0.256449\pi$
$733$	22.4451	+	7.29286i	0.829029	+	0.269368i	0.136393	+	0.990655i	$0.456449\pi$
$734$	−4.14254	+	12.7494i	−0.152904	+	0.470590i
$735$		0			0
$736$	−2.96494	−	4.08088i	−0.109289	−	0.150423i
$737$	−47.9038			−1.76456
$738$		0			0
$739$	−18.2730			−0.672182			−0.336091	−	0.941830i	$-0.609105\pi$
$739$	−18.2730			−0.672182			−0.336091	+	0.941830i	$0.609105\pi$
$740$	0.380322	+	0.523469i	0.0139809	+	0.0192431i
$741$		0			0
$742$	−0.510996	+	1.57268i	−0.0187592	+	0.0577350i
$743$	−51.5726	−	16.7569i	−1.89201	−	0.614752i	−0.977809	−	0.209500i	$-0.932816\pi$
$743$	−51.5726	−	16.7569i	−1.89201	−	0.614752i	−0.914205	−	0.405252i	$-0.867184\pi$
$744$		0			0
$745$	7.32168	+	46.2273i	0.268246	+	1.69364i
$746$	7.98386	−	2.59411i	0.292310	−	0.0949773i
$747$		0			0
$748$	2.73883	+	8.42926i	0.100142	+	0.308204i
$749$	1.26595	−	2.48457i	0.0462569	−	0.0907844i
$750$		0			0
$751$	1.31559	+	0.208368i	0.0480064	+	0.00760347i	0.180391	−	0.983595i	$-0.442264\pi$
$751$	1.31559	+	0.208368i	0.0480064	+	0.00760347i	−0.132385	+	0.991198i	$0.542264\pi$
$752$	−1.53307	+	1.53307i	−0.0559055	+	0.0559055i
$753$		0			0
$754$	4.12573	+	2.99752i	0.150250	+	0.109163i
$755$	3.17388	+	1.61717i	0.115509	+	0.0588549i
$756$		0			0
$757$	−17.0784	+	2.70495i	−0.620723	+	0.0983129i	−0.458872	−	0.888502i	$-0.651746\pi$
$757$	−17.0784	+	2.70495i	−0.620723	+	0.0983129i	−0.161851	+	0.986815i	$0.551746\pi$
$758$	−12.0555	+	16.5930i	−0.437875	+	0.602683i
$759$		0			0
$760$	8.15744	−	1.29201i	0.295901	−	0.0468662i
$761$	14.3315	−	10.4125i	0.519517	−	0.377451i	−0.296905	−	0.954907i	$-0.595954\pi$
$761$	14.3315	−	10.4125i	0.519517	−	0.377451i	0.816422	+	0.577456i	$0.195954\pi$
$762$		0			0
$763$	2.62214	+	1.90510i	0.0949278	+	0.0689691i
$764$	1.50925	+	2.96208i	0.0546029	+	0.107164i
$765$		0			0
$766$	−13.0734	−	2.07063i	−0.472363	−	0.0748149i
$767$	5.06428	−	2.58038i	0.182860	−	0.0931720i
$768$		0			0
$769$	10.1379	+	31.2014i	0.365583	+	1.12515i	0.949615	+	0.313419i	$0.101474\pi$
$769$	10.1379	+	31.2014i	0.365583	+	1.12515i	−0.584032	+	0.811731i	$0.698526\pi$
$770$			2.31460i			0.0834125i
$771$		0			0
$772$	−3.65413	−	23.0713i	−0.131515	−	0.830354i
$773$	3.80592	−	24.0296i	0.136889	−	0.864285i	−0.819689	−	0.572809i	$-0.805854\pi$
$773$	3.80592	−	24.0296i	0.136889	−	0.864285i	0.956578	−	0.291476i	$-0.0941464\pi$
$774$		0			0
$775$	−5.51503	+	16.9735i	−0.198106	+	0.609707i
$776$	3.11589	+	3.11589i	0.111854	+	0.111854i
$777$		0			0
$778$	−8.65837			−0.310418
$779$	−3.23521	−	15.4920i	−0.115914	−	0.555057i
$780$		0			0
$781$	1.48723	+	2.04700i	0.0532173	+	0.0732473i
$782$	8.61116	+	8.61116i	0.307935	+	0.307935i
$783$		0			0
$784$	−6.62354	−	2.15212i	−0.236555	−	0.0768614i
$785$	2.67233	−	16.8724i	0.0953794	−	0.602202i
$786$		0			0
$787$	−2.52782	+	0.821338i	−0.0901070	+	0.0292776i	−0.353724	−	0.935350i	$-0.615085\pi$
$787$	−2.52782	+	0.821338i	−0.0901070	+	0.0292776i	0.263617	+	0.964628i	$0.415085\pi$
$788$		−	22.5841i		−	0.804525i
$789$		0			0
$790$	21.6786	−	42.5466i	0.771288	−	1.51374i
$791$	−0.736259	+	0.375142i	−0.0261783	+	0.0133385i
$792$		0			0
$793$	33.2670	−	33.2670i	1.18135	−	1.18135i
$794$	16.7678	+	32.9087i	0.595068	+	1.16789i
$795$		0			0
$796$	3.25004	+	1.65598i	0.115195	+	0.0586946i
$797$	−16.8491	+	12.2416i	−0.596827	+	0.433620i	−0.844751	−	0.535159i	$-0.820252\pi$
$797$	−16.8491	+	12.2416i	−0.596827	+	0.433620i	0.247924	+	0.968779i	$0.420252\pi$
$798$		0			0
$799$	3.07664	−	4.23464i	0.108844	−	0.149811i
$800$	3.62433	−	4.98846i	0.128139	−	0.176369i
$801$		0			0
$802$	−17.5910	+	12.7806i	−0.621161	+	0.451300i
$803$	−21.4492	−	10.9289i	−0.756926	−	0.385673i
$804$		0			0
$805$	1.44383	+	2.83368i	0.0508884	+	0.0998742i
$806$	−11.2751	+	11.2751i	−0.397150	+	0.397150i
$807$		0			0
$808$	−8.17096	+	4.16331i	−0.287453	+	0.146465i
$809$	15.3881	−	30.2008i	0.541015	−	1.06180i	−0.445060	−	0.895501i	$-0.646818\pi$
$809$	15.3881	−	30.2008i	0.541015	−	1.06180i	0.986075	−	0.166301i	$-0.0531825\pi$
$810$		0			0
$811$			2.85031i			0.100088i	0.998747	+	0.0500440i	$0.0159362\pi$
$811$			2.85031i			0.100088i	−0.998747	+	0.0500440i	$0.984064\pi$
$812$	0.166109	−	0.0539721i	0.00582928	−	0.00189405i
$813$		0			0
$814$	−0.111203	+	0.702111i	−0.00389768	+	0.0246090i
$815$	−68.5788	−	22.2826i	−2.40221	−	0.780525i
$816$		0			0
$817$	−1.11368	−	1.11368i	−0.0389629	−	0.0389629i
$818$	16.6521	+	22.9197i	0.582228	+	0.801368i
$819$		0			0
$820$	−17.9029	−	11.7173i	−0.625197	−	0.409185i
$821$	16.9213			0.590557			0.295278	−	0.955411i	$-0.404588\pi$
$821$	16.9213			0.590557			0.295278	+	0.955411i	$0.404588\pi$
$822$		0			0
$823$	13.6211	+	13.6211i	0.474802	+	0.474802i	0.903465	−	0.428663i	$-0.141015\pi$
$823$	13.6211	+	13.6211i	0.474802	+	0.474802i	−0.428663	+	0.903465i	$0.641015\pi$
$824$	−3.37225	+	10.3787i	−0.117478	+	0.361560i
$825$		0			0
$826$	0.0304518	−	0.192265i	0.00105955	−	0.00668975i
$827$	8.04493	+	50.7937i	0.279750	+	1.76627i	0.582143	+	0.813086i	$0.302214\pi$
$827$	8.04493	+	50.7937i	0.279750	+	1.76627i	−0.302393	+	0.953183i	$0.597786\pi$
$828$		0			0
$829$			28.2684i			0.981804i	0.871215	+	0.490902i	$0.163333\pi$
$829$			28.2684i			0.981804i	−0.871215	+	0.490902i	$0.836667\pi$
$830$	13.6183	+	41.9128i	0.472698	+	1.45481i
$831$		0			0
$832$	4.90864	−	2.50108i	0.170176	−	0.0867092i
$833$	16.6067	+	2.63025i	0.575389	+	0.0911326i
$834$		0			0
$835$	−21.2874	−	41.7789i	−0.736681	−	1.44582i
$836$	7.34081	+	5.33341i	0.253887	+	0.184460i
$837$		0			0
$838$	29.2659	−	21.2629i	1.01097	−	0.734515i
$839$	−7.01571	+	1.11118i	−0.242209	+	0.0383622i	−0.276359	−	0.961055i	$-0.589128\pi$
$839$	−7.01571	+	1.11118i	−0.242209	+	0.0383622i	0.0341495	+	0.999417i	$0.489128\pi$
$840$		0			0
$841$	−16.5421	+	22.7683i	−0.570417	+	0.785112i
$842$	17.4734	−	2.76752i	0.602175	−	0.0953751i
$843$		0			0
$844$	18.6118	+	9.48318i	0.640644	+	0.326424i
$845$	−46.9040	−	34.0777i	−1.61355	−	1.17231i
$846$		0			0
$847$	−0.330523	+	0.330523i	−0.0113569	+	0.0113569i
$848$	8.65628	+	1.37102i	0.297258	+	0.0470810i
$849$		0			0
$850$	−6.75827	+	13.2639i	−0.231807	+	0.454946i
$851$	0.301830	+	0.928936i	0.0103466	+	0.0318435i
$852$		0			0
$853$	−5.49384	+	1.78506i	−0.188106	+	0.0611192i	−0.401555	−	0.915835i	$-0.631530\pi$
$853$	−5.49384	+	1.78506i	−0.188106	+	0.0611192i	0.213449	+	0.976954i	$0.431530\pi$
$854$	−0.252061	−	1.59145i	−0.00862534	−	0.0544583i
$855$		0			0
$856$	−14.0557	−	4.56699i	−0.480415	−	0.156096i
$857$	−0.513931	+	1.58172i	−0.0175555	+	0.0540304i	−0.959451	−	0.281877i	$-0.909043\pi$
$857$	−0.513931	+	1.58172i	−0.0175555	+	0.0540304i	0.941895	+	0.335908i	$0.109043\pi$
$858$		0			0
$859$	22.1239	+	30.4510i	0.754859	+	1.03897i	0.997624	+	0.0688892i	$0.0219455\pi$
$859$	22.1239	+	30.4510i	0.754859	+	1.03897i	−0.242765	+	0.970085i	$0.578055\pi$
$860$	−2.12933			−0.0726097
$861$		0			0
$862$	−39.7293			−1.35319
$863$	1.42739	+	1.96464i	0.0485891	+	0.0668771i	0.832620	−	0.553844i	$-0.186840\pi$
$863$	1.42739	+	1.96464i	0.0485891	+	0.0668771i	−0.784031	+	0.620722i	$0.786840\pi$
$864$		0			0
$865$	9.13312	−	28.1088i	0.310535	−	0.955729i
$866$	4.44768	+	1.44514i	0.151138	+	0.0491078i
$867$		0			0
$868$	0.0854306	+	0.539387i	0.00289970	+	0.0183080i
$869$	49.8933	−	16.2113i	1.69252	−	0.549932i
$870$		0			0
$871$	−22.2141	−	68.3681i	−0.752698	−	2.31656i
$872$	7.79868	−	15.3058i	0.264097	−	0.518319i
$873$		0			0
$874$	12.3140	+	1.95035i	0.416528	+	0.0659716i
$875$	−0.519857	+	0.519857i	−0.0175744	+	0.0175744i
$876$		0			0
$877$	18.6352	+	13.5393i	0.629266	+	0.457189i	0.856146	−	0.516734i	$-0.172852\pi$
$877$	18.6352	+	13.5393i	0.629266	+	0.457189i	−0.226880	+	0.973923i	$0.572852\pi$
$878$	−6.56624	−	3.34567i	−0.221600	−	0.112911i
$879$		0			0
$880$	12.1164	−	1.91905i	0.408443	−	0.0646910i
$881$	−3.71080	+	5.10748i	−0.125020	+	0.172075i	−0.866939	−	0.498414i	$-0.833916\pi$
$881$	−3.71080	+	5.10748i	−0.125020	+	0.172075i	0.741919	+	0.670490i	$0.233916\pi$
$882$		0			0
$883$	1.91690	−	0.303607i	0.0645088	−	0.0102172i	−0.124097	−	0.992270i	$-0.539603\pi$
$883$	1.91690	−	0.303607i	0.0645088	−	0.0102172i	0.188605	+	0.982053i	$0.439603\pi$
$884$	−10.7601	+	7.81770i	−0.361903	+	0.262938i
$885$		0			0
$886$	−23.3121	−	16.9372i	−0.783186	−	0.569018i
$887$	15.0643	+	29.5653i	0.505809	+	0.992706i	0.992855	+	0.119329i	$0.0380744\pi$
$887$	15.0643	+	29.5653i	0.505809	+	0.992706i	−0.487046	+	0.873376i	$0.661926\pi$
$888$		0			0
$889$	3.72380	+	0.589792i	0.124892	+	0.0197810i
$890$	39.4436	−	20.0975i	1.32215	−	0.673671i
$891$		0			0
$892$	−3.93092	−	12.0981i	−0.131617	−	0.405076i
$893$		−	5.35873i		−	0.179323i
$894$		0			0
$895$	−2.46975	−	15.5934i	−0.0825547	−	0.521230i
$896$	0.0295159	−	0.186356i	0.000986057	−	0.00622572i
$897$		0			0
$898$	1.29837	−	3.99596i	0.0433270	−	0.133347i
$899$	1.89455	+	1.89455i	0.0631867	+	0.0631867i
$900$		0			0
$901$	−21.1588			−0.704902
$902$	−4.80532	−	23.0105i	−0.160000	−	0.766165i
$903$		0			0
$904$	2.57421	+	3.54310i	0.0856171	+	0.117842i
$905$	56.0066	+	56.0066i	1.86172	+	1.86172i
$906$		0			0
$907$	39.6329	+	12.8775i	1.31599	+	0.427591i	0.881116	−	0.472900i	$-0.156793\pi$
$907$	39.6329	+	12.8775i	1.31599	+	0.427591i	0.434874	+	0.900491i	$0.356793\pi$
$908$	−3.45738	+	21.8290i	−0.114737	+	0.724422i
$909$		0			0
$910$	−3.30339	+	1.07334i	−0.109506	+	0.0355808i
$911$		−	32.0723i		−	1.06260i	−0.847183	−	0.531301i	$-0.821703\pi$
$911$		−	32.0723i		−	1.06260i	0.847183	−	0.531301i	$-0.178297\pi$
$912$		0			0
$913$	−21.9806	+	43.1394i	−0.727452	+	1.42770i
$914$	−28.5469	+	14.5454i	−0.944249	+	0.481119i
$915$		0			0
$916$	4.93350	−	4.93350i	0.163007	−	0.163007i
$917$	−1.38858	−	2.72524i	−0.0458549	−	0.0899954i
$918$		0			0
$919$	26.4568	+	13.4804i	0.872728	+	0.444677i	0.832183	−	0.554501i	$-0.187091\pi$
$919$	26.4568	+	13.4804i	0.872728	+	0.444677i	0.0405447	+	0.999178i	$0.487091\pi$
$920$	13.6365	−	9.90753i	0.449584	−	0.326642i
$921$		0			0
$922$	3.99760	−	5.50223i	0.131654	−	0.181206i
$923$	−2.23180	+	3.07181i	−0.0734606	+	0.101110i
$924$		0			0
$925$	−0.965938	+	0.701795i	−0.0317598	+	0.0230749i
$926$	−11.0090	−	5.60935i	−0.361777	−	0.184335i
$927$		0			0
$928$	−0.420252	−	0.824791i	−0.0137955	−	0.0270751i
$929$	32.7111	−	32.7111i	1.07322	−	1.07322i	0.0761188	−	0.997099i	$-0.475747\pi$
$929$	32.7111	−	32.7111i	1.07322	−	1.07322i	0.997099	−	0.0761188i	$-0.0242528\pi$
$930$		0			0
$931$	15.3373	−	7.81473i	0.502659	−	0.256118i
$932$	1.24951	−	2.45230i	0.0409290	−	0.0803277i
$933$		0			0
$934$		−	2.29675i		−	0.0751521i
$935$	−28.1669	+	9.15199i	−0.921157	+	0.299302i
$936$		0			0
$937$	3.07185	−	19.3949i	0.100353	−	0.633603i	−0.885326	−	0.464971i	$-0.846065\pi$
$937$	3.07185	−	19.3949i	0.100353	−	0.633603i	0.985679	−	0.168632i	$-0.0539351\pi$
$938$	−2.34152	−	0.760805i	−0.0764532	−	0.0248412i
$939$		0			0
$940$	−5.12287	−	5.12287i	−0.167090	−	0.167090i
$941$	−9.06491	−	12.4768i	−0.295507	−	0.406731i	0.635286	−	0.772277i	$-0.280882\pi$
$941$	−9.06491	−	12.4768i	−0.295507	−	0.406731i	−0.930793	+	0.365546i	$0.880882\pi$
$942$		0			0
$943$	−20.2367	−	25.1733i	−0.658999	−	0.819757i
$944$	−1.03171			−0.0335792
$945$		0			0
$946$	−1.65417	−	1.65417i	−0.0537818	−	0.0537818i
$947$	9.69981	−	29.8529i	0.315201	−	0.970090i	−0.660470	−	0.750852i	$-0.729643\pi$
$947$	9.69981	−	29.8529i	0.315201	−	0.970090i	0.975671	−	0.219238i	$-0.0703570\pi$
$948$		0			0
$949$	5.65119	−	35.6802i	0.183445	−	1.15823i
$950$	2.38410	+	15.0526i	0.0773505	+	0.488372i
$951$		0			0
$952$			0.455516i			0.0147634i
$953$	11.3377	+	34.8939i	0.367265	+	1.13032i	0.948551	+	0.316625i	$0.102550\pi$
$953$	11.3377	+	34.8939i	0.367265	+	1.13032i	−0.581286	+	0.813699i	$0.697450\pi$
$954$		0			0
$955$	−9.89798	+	5.04327i	−0.320291	+	0.163197i
$956$	−20.2752	−	3.21128i	−0.655748	−	0.103860i
$957$		0			0
$958$	15.6459	+	30.7069i	0.505497	+	0.992094i
$959$	1.20418	+	0.874884i	0.0388848	+	0.0282515i
$960$		0			0
$961$	18.3020	−	13.2972i	0.590387	−	0.428941i
$962$	−1.05362	+	0.166877i	−0.0339700	+	0.00538032i
$963$		0			0
$964$	16.7955	−	23.1170i	0.540946	−	0.744548i
$965$	77.0943	−	12.2105i	2.48175	−	0.393071i
$966$		0			0
$967$	40.0388	+	20.4008i	1.28756	+	0.656045i	0.957641	−	0.287964i	$-0.0929783\pi$
$967$	40.0388	+	20.4008i	1.28756	+	0.656045i	0.329920	+	0.944009i	$0.392978\pi$
$968$	2.00424	+	1.45617i	0.0644189	+	0.0468030i
$969$		0			0
$970$	−10.4120	+	10.4120i	−0.334308	+	0.334308i
$971$	−57.9014	−	9.17068i	−1.85814	−	0.294301i	−0.875983	−	0.482342i	$-0.839786\pi$
$971$	−57.9014	−	9.17068i	−1.85814	−	0.294301i	−0.982161	+	0.188041i	$0.939786\pi$
$972$		0			0
$973$	−1.59788	+	3.13601i	−0.0512256	+	0.100536i
$974$	5.35445	+	16.4793i	0.171567	+	0.528030i
$975$		0			0
$976$	−8.12186	+	2.63895i	−0.259974	+	0.0844708i
$977$	1.44366	+	9.11491i	0.0461868	+	0.291612i	0.999960	−	0.00891457i	$-0.00283763\pi$
$977$	1.44366	+	9.11491i	0.0461868	+	0.291612i	−0.953773	+	0.300526i	$0.902838\pi$
$978$		0			0
$979$	46.2546	+	15.0290i	1.47830	+	0.480330i
$980$	7.19145	−	22.1330i	0.229722	−	0.707013i
$981$		0			0
$982$	17.8964	+	24.6323i	0.571097	+	0.786048i
$983$	3.57723			0.114096			0.0570480	−	0.998371i	$-0.481831\pi$
$983$	3.57723			0.114096			0.0570480	+	0.998371i	$0.481831\pi$
$984$		0			0
$985$	75.4663			2.40456
$986$	1.31360	+	1.80801i	0.0418335	+	0.0575788i
$987$		0			0
$988$	−4.20771	+	12.9500i	−0.133865	+	0.411995i
$989$	−3.05701	−	0.993281i	−0.0972071	−	0.0315845i
$990$		0			0
$991$	−5.73604	−	36.2160i	−0.182211	−	1.15044i	−0.894008	−	0.448052i	$-0.852118\pi$
$991$	−5.73604	−	36.2160i	−0.182211	−	1.15044i	0.711796	−	0.702386i	$-0.247882\pi$
$992$	2.75273	−	0.894416i	0.0873992	−	0.0283977i
$993$		0			0
$994$	0.0401849	+	0.123676i	0.00127459	+	0.00392278i
$995$	−5.53357	+	10.8602i	−0.175426	+	0.344293i
$996$		0			0
$997$	−51.3631	−	8.13511i	−1.62668	−	0.257642i	−0.724590	−	0.689180i	$-0.757971\pi$
$997$	−51.3631	−	8.13511i	−1.62668	−	0.257642i	−0.902095	+	0.431538i	$0.857971\pi$
$998$	−3.90003	+	3.90003i	−0.123453	+	0.123453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.d.415.1	yes	24
3.2	odd	2		738.2.u.c.415.3	yes	24
41.33	even	20	inner	738.2.u.d.361.1	yes	24
123.74	odd	20		738.2.u.c.361.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.361.3	✓	24	123.74	odd	20
738.2.u.c.415.3	yes	24	3.2	odd	2
738.2.u.d.361.1	yes	24	41.33	even	20	inner
738.2.u.d.415.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-3.17802 - 1.03260i) q^{5} +(-0.0295159 - 0.186356i) q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-3.17802 - 1.03260i) q^{5} +(-0.0295159 - 0.186356i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-1.03260 - 3.17802i) q^{10} +(1.66667 - 3.27102i) q^{11} +(5.44127 + 0.861812i) q^{13} +(0.133416 - 0.133416i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.15110 + 1.09604i) q^{17} +(2.44120 - 0.386648i) q^{19} +(1.96412 - 2.70338i) q^{20} +(3.62596 - 0.574295i) q^{22} +(4.08088 - 2.96494i) q^{23} +(4.98846 + 3.62433i) q^{25} +(2.50108 + 4.90864i) q^{26} +(0.186356 + 0.0295159i) q^{28} +(0.824791 - 0.420252i) q^{29} +(0.894416 + 2.75273i) q^{31} -1.00000i q^{32} +(0.377670 + 2.38452i) q^{34} +(-0.0986294 + 0.622721i) q^{35} +(-0.0598364 + 0.184157i) q^{37} +(1.74771 + 1.74771i) q^{38} +3.34157 q^{40} +(-0.312306 - 6.39550i) q^{41} +(-0.374552 - 0.515527i) q^{43} +(2.59590 + 2.59590i) q^{44} +(4.79737 + 1.55876i) q^{46} +(0.339165 - 2.14140i) q^{47} +(6.62354 - 2.15212i) q^{49} +6.16607i q^{50} +(-2.50108 + 4.90864i) q^{52} +(-7.80894 + 3.97885i) q^{53} +(-8.67437 + 8.67437i) q^{55} +(0.0856585 + 0.168114i) q^{56} +(0.824791 + 0.420252i) q^{58} +(0.834669 - 0.606422i) q^{59} +(5.01958 - 6.90887i) q^{61} +(-1.70128 + 2.34161i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-16.4025 - 8.35751i) q^{65} +(-5.92399 - 11.6265i) q^{67} +(-1.70712 + 1.70712i) q^{68} +(-0.561765 + 0.286234i) q^{70} +(-0.312899 + 0.614098i) q^{71} -6.55734i q^{73} +(-0.184157 + 0.0598364i) q^{74} +(-0.386648 + 2.44120i) q^{76} +(-0.658768 - 0.214047i) q^{77} +(10.1046 + 10.1046i) q^{79} +(1.96412 + 2.70338i) q^{80} +(4.99050 - 4.01184i) q^{82} -13.1883 q^{83} +(-5.70447 - 5.70447i) q^{85} +(0.196914 - 0.606038i) q^{86} +(-0.574295 + 3.62596i) q^{88} +(2.07242 + 13.0848i) q^{89} -1.03945i q^{91} +(1.55876 + 4.79737i) q^{92} +(1.93179 - 0.984294i) q^{94} +(-8.15744 - 1.29201i) q^{95} +(-2.00053 - 3.92626i) q^{97} +(5.63432 + 4.09357i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4}+O(q^{10}) \) 24 * q + 6 * q^4	\( 24 q + 6 q^{4} + 4 q^{10} + 4 q^{11} + 2 q^{13} - 6 q^{16} + 10 q^{17} - 8 q^{19} + 10 q^{20} + 4 q^{22} - 4 q^{23} + 6 q^{25} - 8 q^{26} - 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} + 8 q^{38} + 16 q^{40} + 4 q^{41} - 20 q^{43} - 4 q^{44} + 20 q^{46} - 12 q^{47} + 40 q^{49} + 8 q^{52} + 26 q^{53} - 4 q^{55} - 14 q^{58} - 8 q^{59} + 40 q^{61} + 6 q^{64} - 12 q^{65} + 8 q^{67} - 10 q^{68} - 60 q^{70} + 48 q^{71} - 10 q^{74} + 8 q^{76} - 20 q^{77} + 28 q^{79} + 10 q^{80} - 2 q^{82} - 80 q^{83} - 30 q^{85} - 8 q^{86} + 16 q^{88} + 58 q^{89} + 4 q^{92} - 8 q^{94} - 68 q^{95} - 86 q^{97} + 2 q^{98}+O(q^{100}) \) 24 * q + 6 * q^4 + 4 * q^10 + 4 * q^11 + 2 * q^13 - 6 * q^16 + 10 * q^17 - 8 * q^19 + 10 * q^20 + 4 * q^22 - 4 * q^23 + 6 * q^25 - 8 * q^26 - 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 + 8 * q^38 + 16 * q^40 + 4 * q^41 - 20 * q^43 - 4 * q^44 + 20 * q^46 - 12 * q^47 + 40 * q^49 + 8 * q^52 + 26 * q^53 - 4 * q^55 - 14 * q^58 - 8 * q^59 + 40 * q^61 + 6 * q^64 - 12 * q^65 + 8 * q^67 - 10 * q^68 - 60 * q^70 + 48 * q^71 - 10 * q^74 + 8 * q^76 - 20 * q^77 + 28 * q^79 + 10 * q^80 - 2 * q^82 - 80 * q^83 - 30 * q^85 - 8 * q^86 + 16 * q^88 + 58 * q^89 + 4 * q^92 - 8 * q^94 - 68 * q^95 - 86 * q^97 + 2 * q^98

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