LMFDB - Embedded newform 972.2.p.a.395.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(35,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 31]))

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

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

chi := DirichletCharacter("972.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.p (of order $54$, degree $18$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	no (minimal twist has level 324)
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			395.30
Character	$\chi$	$=$	972.395
Dual form			972.2.p.a.251.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456796 + 1.33841i) q^{2} +(-1.58267 + 1.22276i) q^{4} +(0.874721 - 3.69074i) q^{5} +(2.85958 + 2.12888i) q^{7} +(-2.35951 - 1.55971i) q^{8} +O(q^{10})$	\(q+(0.456796 + 1.33841i) q^{2} +(-1.58267 + 1.22276i) q^{4} +(0.874721 - 3.69074i) q^{5} +(2.85958 + 2.12888i) q^{7} +(-2.35951 - 1.55971i) q^{8} +(5.33928 - 0.515181i) q^{10} +(0.253209 + 0.268386i) q^{11} +(1.86762 - 0.937956i) q^{13} +(-1.54306 + 4.79975i) q^{14} +(1.00972 - 3.87046i) q^{16} +(-2.09840 - 5.76530i) q^{17} +(1.03264 - 2.83716i) q^{19} +(3.12849 + 6.91081i) q^{20} +(-0.243545 + 0.461494i) q^{22} +(-3.75651 - 5.04586i) q^{23} +(-8.38825 - 4.21274i) q^{25} +(2.10849 + 2.07119i) q^{26} +(-7.12890 + 0.127258i) q^{28} +(3.89902 + 5.92817i) q^{29} +(2.55754 + 1.10321i) q^{31} +(5.64149 - 0.416598i) q^{32} +(6.75779 - 5.44208i) q^{34} +(10.3585 - 8.69179i) q^{35} +(-0.159326 - 0.133690i) q^{37} +(4.26898 + 0.0860925i) q^{38} +(-7.82041 + 7.34403i) q^{40} +(10.2366 + 0.596211i) q^{41} +(7.05296 + 2.11152i) q^{43} +(-0.728918 - 0.115154i) q^{44} +(5.03747 - 7.33267i) q^{46} +(2.93833 + 6.81180i) q^{47} +(1.63746 + 5.46949i) q^{49} +(1.80664 - 13.1513i) q^{50} +(-1.80895 + 3.76814i) q^{52} +(-6.38357 - 3.68555i) q^{53} +(1.21203 - 0.699765i) q^{55} +(-3.42678 - 9.48325i) q^{56} +(-6.15326 + 7.92645i) q^{58} +(-2.92703 + 3.10247i) q^{59} +(-1.15413 - 0.134898i) q^{61} +(-0.308278 + 3.92697i) q^{62} +(3.13459 + 7.36032i) q^{64} +(-1.82810 - 7.71336i) q^{65} +(4.04241 - 6.14618i) q^{67} +(10.3707 + 6.55876i) q^{68} +(16.3649 + 9.89349i) q^{70} +(0.398446 - 2.25970i) q^{71} +(0.219535 + 1.24504i) q^{73} +(0.106153 - 0.274312i) q^{74} +(1.83483 + 5.75297i) q^{76} +(0.152711 + 1.30652i) q^{77} +(0.0782584 - 0.00455803i) q^{79} +(-13.4016 - 7.11218i) q^{80} +(3.87804 + 13.9730i) q^{82} +(0.294342 + 5.05366i) q^{83} +(-23.1137 + 2.70161i) q^{85} +(0.395692 + 10.4043i) q^{86} +(-0.178845 - 1.02819i) q^{88} +(8.23009 - 1.45119i) q^{89} +(7.33742 + 1.29379i) q^{91} +(12.1152 + 3.39266i) q^{92} +(-7.77476 + 7.04429i) q^{94} +(-9.56793 - 6.29293i) q^{95} +(-12.4281 + 2.94552i) q^{97} +(-6.57243 + 4.69003i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8}+O(q^{10}) $ 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8	$ 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8} - 18 q^{10} - 36 q^{13} + 18 q^{14} - 18 q^{16} + 36 q^{17} + 18 q^{20} - 18 q^{22} - 36 q^{25} + 27 q^{26} - 9 q^{28} + 36 q^{29} + 18 q^{32} - 18 q^{34} - 36 q^{37} + 18 q^{38} - 18 q^{40} + 36 q^{41} + 90 q^{44} - 18 q^{46} - 36 q^{49} + 135 q^{50} - 18 q^{52} + 54 q^{53} + 144 q^{56} - 18 q^{58} - 36 q^{61} + 117 q^{62} - 18 q^{64} + 36 q^{65} + 63 q^{68} - 18 q^{70} - 36 q^{73} + 18 q^{74} - 18 q^{76} + 36 q^{77} - 36 q^{82} - 36 q^{85} + 18 q^{86} - 18 q^{88} + 54 q^{89} - 72 q^{92} - 18 q^{94} - 36 q^{97} - 153 q^{98}+O(q^{100}) $ 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8 - 18 * q^10 - 36 * q^13 + 18 * q^14 - 18 * q^16 + 36 * q^17 + 18 * q^20 - 18 * q^22 - 36 * q^25 + 27 * q^26 - 9 * q^28 + 36 * q^29 + 18 * q^32 - 18 * q^34 - 36 * q^37 + 18 * q^38 - 18 * q^40 + 36 * q^41 + 90 * q^44 - 18 * q^46 - 36 * q^49 + 135 * q^50 - 18 * q^52 + 54 * q^53 + 144 * q^56 - 18 * q^58 - 36 * q^61 + 117 * q^62 - 18 * q^64 + 36 * q^65 + 63 * q^68 - 18 * q^70 - 36 * q^73 + 18 * q^74 - 18 * q^76 + 36 * q^77 - 36 * q^82 - 36 * q^85 + 18 * q^86 - 18 * q^88 + 54 * q^89 - 72 * q^92 - 18 * q^94 - 36 * q^97 - 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{53}{54}\right)$	$-1$

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 $

$2$	0.456796	+	1.33841i	0.323004	+	0.946398i
$2$	0.456796	+	1.33841i	0.323004	+	0.946398i
$3$		0			0
$3$		0			0
$4$	−1.58267	+	1.22276i	−0.791337	+	0.611380i
$5$	0.874721	−	3.69074i	0.391187	−	1.65055i	−0.319905	−	0.947450i	$-0.603651\pi$
$5$	0.874721	−	3.69074i	0.391187	−	1.65055i	0.711092	−	0.703099i	$-0.248201\pi$
$6$		0			0
$7$	2.85958	+	2.12888i	1.08082	+	0.804641i	0.981700	−	0.190434i	$-0.0609896\pi$
$7$	2.85958	+	2.12888i	1.08082	+	0.804641i	0.0991206	+	0.995075i	$0.468397\pi$
$8$	−2.35951	−	1.55971i	−0.834213	−	0.551442i
$9$		0			0
$10$	5.33928	−	0.515181i	1.68843	−	0.162915i
$11$	0.253209	+	0.268386i	0.0763453	+	0.0809213i	0.764420	−	0.644718i	$-0.223025\pi$
$11$	0.253209	+	0.268386i	0.0763453	+	0.0809213i	−0.688075	+	0.725640i	$0.741544\pi$
$12$		0			0
$13$	1.86762	−	0.937956i	0.517986	−	0.260142i	−0.170544	−	0.985350i	$-0.554553\pi$
$13$	1.86762	−	0.937956i	0.517986	−	0.260142i	0.688530	+	0.725208i	$0.258256\pi$
$14$	−1.54306	+	4.79975i	−0.412401	+	1.28279i
$15$		0			0
$16$	1.00972	−	3.87046i	0.252429	−	0.967615i
$17$	−2.09840	−	5.76530i	−0.508936	−	1.39829i	−0.882336	−	0.470620i	$-0.844030\pi$
$17$	−2.09840	−	5.76530i	−0.508936	−	1.39829i	0.373399	−	0.927671i	$-0.378192\pi$
$18$		0			0
$19$	1.03264	−	2.83716i	0.236904	−	0.650888i	−0.763085	−	0.646298i	$-0.776316\pi$
$19$	1.03264	−	2.83716i	0.236904	−	0.650888i	0.999989	−	0.00459076i	$-0.00146129\pi$
$20$	3.12849	+	6.91081i	0.699551	+	1.54530i
$21$		0			0
$22$	−0.243545	+	0.461494i	−0.0519239	+	0.0983909i
$23$	−3.75651	−	5.04586i	−0.783286	−	1.05214i	−0.997163	−	0.0752748i	$-0.976017\pi$
$23$	−3.75651	−	5.04586i	−0.783286	−	1.05214i	0.213877	−	0.976861i	$-0.431391\pi$
$24$		0			0
$25$	−8.38825	−	4.21274i	−1.67765	−	0.842547i
$26$	2.10849	+	2.07119i	0.413509	+	0.406194i
$27$		0			0
$28$	−7.12890	+	0.127258i	−1.34723	+	0.0240495i
$29$	3.89902	+	5.92817i	0.724030	+	1.10083i	0.990570	+	0.137010i	$0.0437493\pi$
$29$	3.89902	+	5.92817i	0.724030	+	1.10083i	−0.266540	+	0.963824i	$0.585880\pi$
$30$		0			0
$31$	2.55754	+	1.10321i	0.459347	+	0.198143i	0.613163	−	0.789957i	$-0.289897\pi$
$31$	2.55754	+	1.10321i	0.459347	+	0.198143i	−0.153816	+	0.988100i	$0.549156\pi$
$32$	5.64149	−	0.416598i	0.997285	−	0.0736448i
$33$		0			0
$34$	6.75779	−	5.44208i	1.15895	−	0.933309i
$35$	10.3585	−	8.69179i	1.75090	−	1.46918i
$36$		0			0
$37$	−0.159326	−	0.133690i	−0.0261930	−	0.0219785i	0.629597	−	0.776922i	$-0.283220\pi$
$37$	−0.159326	−	0.133690i	−0.0261930	−	0.0219785i	−0.655790	+	0.754943i	$0.727664\pi$
$38$	4.26898	+	0.0860925i	0.692520	+	0.0139661i
$39$		0			0
$40$	−7.82041	+	7.34403i	−1.23651	+	1.16119i
$41$	10.2366	+	0.596211i	1.59868	+	0.0931125i	0.834173	−	0.551502i	$-0.185945\pi$
$41$	10.2366	+	0.596211i	1.59868	+	0.0931125i	0.764507	+	0.644615i	$0.222982\pi$
$42$		0			0
$43$	7.05296	+	2.11152i	1.07557	+	0.322003i	0.775132	−	0.631799i	$-0.217683\pi$
$43$	7.05296	+	2.11152i	1.07557	+	0.322003i	0.300434	+	0.953803i	$0.402869\pi$
$44$	−0.728918	−	0.115154i	−0.109889	−	0.0173601i
$45$		0			0
$46$	5.03747	−	7.33267i	0.742734	−	1.08114i
$47$	2.93833	+	6.81180i	0.428599	+	0.993604i	0.986510	+	0.163703i	$0.0523438\pi$
$47$	2.93833	+	6.81180i	0.428599	+	0.993604i	−0.557911	+	0.829901i	$0.688397\pi$
$48$		0			0
$49$	1.63746	+	5.46949i	0.233923	+	0.781356i
$50$	1.80664	−	13.1513i	0.255498	−	1.85987i
$51$		0			0
$52$	−1.80895	+	3.76814i	−0.250856	+	0.522546i
$53$	−6.38357	−	3.68555i	−0.876850	−	0.506250i	−0.00723169	−	0.999974i	$-0.502302\pi$
$53$	−6.38357	−	3.68555i	−0.876850	−	0.506250i	−0.869619	+	0.493724i	$0.835635\pi$
$54$		0			0
$55$	1.21203	−	0.699765i	0.163430	−	0.0943563i
$56$	−3.42678	−	9.48325i	−0.457922	−	1.26725i
$57$		0			0
$58$	−6.15326	+	7.92645i	−0.807963	+	1.04079i
$59$	−2.92703	+	3.10247i	−0.381067	+	0.403908i	−0.889309	−	0.457307i	$-0.848814\pi$
$59$	−2.92703	+	3.10247i	−0.381067	+	0.403908i	0.508242	+	0.861214i	$0.330296\pi$
$60$		0			0
$61$	−1.15413	−	0.134898i	−0.147771	−	0.0172719i	0.0418860	−	0.999122i	$-0.486663\pi$
$61$	−1.15413	−	0.134898i	−0.147771	−	0.0172719i	−0.189657	+	0.981850i	$0.560737\pi$
$62$	−0.308278	+	3.92697i	−0.0391513	+	0.498726i
$63$		0			0
$64$	3.13459	+	7.36032i	0.391824	+	0.920040i
$65$	−1.82810	−	7.71336i	−0.226748	−	0.956725i
$66$		0			0
$67$	4.04241	−	6.14618i	0.493858	−	0.750875i	−0.499453	−	0.866341i	$-0.666466\pi$
$67$	4.04241	−	6.14618i	0.493858	−	0.750875i	0.993311	+	0.115466i	$0.0368360\pi$
$68$	10.3707	+	6.55876i	1.25763	+	0.795366i
$69$		0			0
$70$	16.3649	+	9.89349i	1.95598	+	1.18250i
$71$	0.398446	−	2.25970i	0.0472869	−	0.268177i	−0.951993	−	0.306120i	$-0.900969\pi$
$71$	0.398446	−	2.25970i	0.0472869	−	0.268177i	0.999280	+	0.0379425i	$0.0120804\pi$
$72$		0			0
$73$	0.219535	+	1.24504i	0.0256946	+	0.145721i	0.994956	−	0.100312i	$-0.0319840\pi$
$73$	0.219535	+	1.24504i	0.0256946	+	0.145721i	−0.969261	+	0.246033i	$0.920873\pi$
$74$	0.106153	−	0.274312i	0.0123400	−	0.0318882i
$75$		0			0
$76$	1.83483	+	5.75297i	0.210469	+	0.659910i
$77$	0.152711	+	1.30652i	0.0174030	+	0.148892i
$78$		0			0
$79$	0.0782584	−	0.00455803i	0.00880476	−	0.000512819i	−0.0537419	−	0.998555i	$-0.517115\pi$
$79$	0.0782584	−	0.00455803i	0.00880476	−	0.000512819i	0.0625466	+	0.998042i	$0.480078\pi$
$80$	−13.4016	−	7.11218i	−1.49835	−	0.795165i
$81$		0			0
$82$	3.87804	+	13.9730i	0.428258	+	1.54306i
$83$	0.294342	+	5.05366i	0.0323083	+	0.554711i	0.975160	+	0.221500i	$0.0710953\pi$
$83$	0.294342	+	5.05366i	0.0323083	+	0.554711i	−0.942852	+	0.333211i	$0.891868\pi$
$84$		0			0
$85$	−23.1137	+	2.70161i	−2.50704	+	0.293031i
$86$	0.395692	+	10.4043i	0.0426686	+	1.12192i
$87$		0			0
$88$	−0.178845	−	1.02819i	−0.0190649	−	0.109606i
$89$	8.23009	−	1.45119i	0.872387	−	0.153825i	0.280508	−	0.959852i	$-0.409497\pi$
$89$	8.23009	−	1.45119i	0.872387	−	0.153825i	0.591880	+	0.806026i	$0.298386\pi$
$90$		0			0
$91$	7.33742	+	1.29379i	0.769171	+	0.135626i
$92$	12.1152	+	3.39266i	1.26310	+	0.353709i
$93$		0			0
$94$	−7.77476	+	7.04429i	−0.801905	+	0.726563i
$95$	−9.56793	−	6.29293i	−0.981649	−	0.645641i
$96$		0			0
$97$	−12.4281	+	2.94552i	−1.26188	+	0.299072i	−0.806506	−	0.591226i	$-0.798644\pi$
$97$	−12.4281	+	2.94552i	−1.26188	+	0.299072i	−0.455378	+	0.890298i	$0.650496\pi$
$98$	−6.57243	+	4.69003i	−0.663915	+	0.473764i
$99$		0			0
$100$	18.4270	−	3.58942i	1.84270	−	0.358942i
$101$	−0.0948622	+	0.811598i	−0.00943914	+	0.0807570i	−0.997137	−	0.0756184i	$-0.975907\pi$
$101$	−0.0948622	+	0.811598i	−0.00943914	+	0.0807570i	0.987698	+	0.156375i	$0.0499810\pi$
$102$		0			0
$103$	−7.31110	−	6.89767i	−0.720384	−	0.679647i	0.236002	−	0.971753i	$-0.424163\pi$
$103$	−7.31110	−	6.89767i	−0.720384	−	0.679647i	−0.956386	+	0.292105i	$0.905644\pi$
$104$	−5.86963	−	0.699839i	−0.575564	−	0.0686249i
$105$		0			0
$106$	2.01679	−	10.2274i	0.195888	−	0.993370i
$107$	9.81977	+	17.0083i	0.949313	+	1.64426i	0.746877	+	0.664963i	$0.231552\pi$
$107$	9.81977	+	17.0083i	0.949313	+	1.64426i	0.202436	+	0.979295i	$0.435114\pi$
$108$		0			0
$109$	0.261103	−	0.452244i	0.0250091	−	0.0433171i	−0.853250	−	0.521502i	$-0.825372\pi$
$109$	0.261103	−	0.452244i	0.0250091	−	0.0433171i	0.878259	+	0.478185i	$0.158705\pi$
$110$	1.49022	+	1.30254i	0.142087	+	0.124192i
$111$		0			0
$112$	11.1271	−	8.91834i	1.05141	−	0.842704i
$113$	−19.3462	+	5.79188i	−1.81994	+	0.544854i	−0.999634	−	0.0270702i	$-0.991382\pi$
$113$	−19.3462	+	5.79188i	−1.81994	+	0.544854i	−0.820306	+	0.571924i	$0.806197\pi$
$114$		0			0
$115$	−21.9089	+	9.45056i	−2.04301	+	0.881269i
$116$	−13.4196	−	4.61480i	−1.24598	−	0.428474i
$117$		0			0
$118$	−5.48943	−	2.50037i	−0.505343	−	0.230177i
$119$	6.27309	−	20.9536i	0.575054	−	1.92081i
$120$		0			0
$121$	0.631677	−	10.8455i	0.0574252	−	0.985952i
$122$	−0.346652	−	1.60631i	−0.0313844	−	0.145429i
$123$		0			0
$124$	−5.39671	+	1.38123i	−0.484639	+	0.124038i
$125$	−10.6951	+	12.7459i	−0.956598	+	1.14003i
$126$		0			0
$127$	−2.72655	−	3.24937i	−0.241942	−	0.288335i	0.631385	−	0.775469i	$-0.282487\pi$
$127$	−2.72655	−	3.24937i	−0.241942	−	0.288335i	−0.873327	+	0.487134i	$0.838042\pi$
$128$	−8.41925	+	7.55753i	−0.744163	+	0.667998i
$129$		0			0
$130$	9.48856	−	5.97018i	0.832202	−	0.523620i
$131$	−5.26366	+	12.2025i	−0.459888	+	1.06614i	0.517690	+	0.855568i	$0.326792\pi$
$131$	−5.26366	+	12.2025i	−0.459888	+	1.06614i	−0.977578	+	0.210572i	$0.932467\pi$
$132$		0			0
$133$	8.99289	−	5.91471i	0.779782	−	0.512871i
$134$	10.0727	+	2.60284i	0.870145	+	0.224851i
$135$		0			0
$136$	−4.04102	+	16.8762i	−0.346515	+	1.44712i
$137$	8.19288	−	16.3134i	0.699965	−	1.39374i	−0.209435	−	0.977823i	$-0.567163\pi$
$137$	8.19288	−	16.3134i	0.699965	−	1.39374i	0.909400	−	0.415922i	$-0.136541\pi$
$138$		0			0
$139$	−10.0551	+	7.48577i	−0.852866	+	0.634935i	−0.932212	−	0.361912i	$-0.882124\pi$
$139$	−10.0551	+	7.48577i	−0.852866	+	0.634935i	0.0793465	+	0.996847i	$0.474717\pi$
$140$	−5.76612	+	26.4222i	−0.487326	+	2.23308i
$141$		0			0
$142$	3.20641	−	0.498939i	0.269076	−	0.0418700i
$143$	0.724633	+	0.263745i	0.0605969	+	0.0220555i
$144$		0			0
$145$	25.2899	−	9.20477i	2.10021	−	0.764414i
$146$	−1.56610	+	0.862559i	−0.129611	+	0.0713859i
$147$		0			0
$148$	0.415632	+	0.0167709i	0.0341647	+	0.00137856i
$149$	1.62011	+	3.22591i	0.132725	+	0.264277i	0.950172	−	0.311727i	$-0.100908\pi$
$149$	1.62011	+	3.22591i	0.132725	+	0.264277i	−0.817447	+	0.576004i	$0.804611\pi$
$150$		0			0
$151$	5.22213	−	4.92682i	0.424971	−	0.400939i	−0.443822	−	0.896115i	$-0.646378\pi$
$151$	5.22213	−	4.92682i	0.424971	−	0.400939i	0.868793	+	0.495176i	$0.164896\pi$
$152$	−6.86168	+	5.08368i	−0.556555	+	0.412341i
$153$		0			0
$154$	−1.67890	+	0.801203i	−0.135290	+	0.0645628i
$155$	6.30881	−	8.47420i	0.506735	−	0.680664i
$156$		0			0
$157$	7.89799	+	1.87186i	0.630328	+	0.149390i	0.533348	−	0.845896i	$-0.320934\pi$
$157$	7.89799	+	1.87186i	0.630328	+	0.149390i	0.0969799	+	0.995286i	$0.469082\pi$
$158$	0.0418487	+	0.102660i	0.00332930	+	0.00816716i
$159$		0			0
$160$	3.39718	−	21.1857i	0.268571	−	1.67488i
$161$		−	22.4262i		−	1.76743i
$162$		0			0
$163$			7.68098i			0.601621i	0.953684	+	0.300810i	$0.0972571\pi$
$163$			7.68098i			0.601621i	−0.953684	+	0.300810i	$0.902743\pi$
$164$	−16.9302	+	11.5732i	−1.32202	+	0.903718i
$165$		0			0
$166$	−6.62941	+	2.70244i	−0.514542	+	0.209750i
$167$	−0.436113	−	0.103361i	−0.0337474	−	0.00799828i	0.213707	−	0.976898i	$-0.431446\pi$
$167$	−0.436113	−	0.103361i	−0.0337474	−	0.00799828i	−0.247455	+	0.968899i	$0.579594\pi$
$168$		0			0
$169$	−5.15480	+	6.92410i	−0.396523	+	0.532623i
$170$	−14.1741	−	29.7015i	−1.08711	−	2.27800i
$171$		0			0
$172$	−13.7444	+	5.28223i	−1.04800	+	0.402766i
$173$	5.36388	−	5.06056i	0.407808	−	0.384747i	−0.454822	−	0.890582i	$-0.650297\pi$
$173$	5.36388	−	5.06056i	0.407808	−	0.384747i	0.862630	+	0.505835i	$0.168816\pi$
$174$		0			0
$175$	−15.0185	−	29.9042i	−1.13529	−	2.26055i
$176$	1.29445	−	0.709041i	0.0975725	−	0.0534460i
$177$		0			0
$178$	5.70175	+	10.3523i	0.427364	+	0.775939i
$179$	−20.8808	+	7.59999i	−1.56070	+	0.568050i	−0.970898	−	0.239495i	$-0.923018\pi$
$179$	−20.8808	+	7.59999i	−1.56070	+	0.568050i	−0.589807	+	0.807545i	$0.700796\pi$
$180$		0			0
$181$	−15.8404	−	5.76543i	−1.17741	−	0.428541i	−0.322121	−	0.946698i	$-0.604396\pi$
$181$	−15.8404	−	5.76543i	−1.17741	−	0.428541i	−0.855285	+	0.518158i	$0.826618\pi$
$182$	1.62009	+	10.4115i	0.120089	+	0.771749i
$183$		0			0
$184$	0.993422	+	17.7648i	0.0732360	+	1.30964i
$185$	−0.632782	+	0.471088i	−0.0465230	+	0.0346351i
$186$		0			0
$187$	1.01599	−	2.02301i	0.0742966	−	0.147937i
$188$	−12.9796	−	7.18800i	−0.946635	−	0.524239i
$189$		0			0
$190$	4.05191	−	15.6804i	0.293957	−	1.13757i
$191$	−6.08575	+	4.00266i	−0.440349	+	0.289622i	−0.750259	−	0.661144i	$-0.770071\pi$
$191$	−6.08575	+	4.00266i	−0.440349	+	0.289622i	0.309910	+	0.950766i	$0.399701\pi$
$192$		0			0
$193$	5.19455	−	12.0423i	0.373912	−	0.866826i	−0.622534	−	0.782593i	$-0.713897\pi$
$193$	5.19455	−	12.0423i	0.373912	−	0.866826i	0.996446	−	0.0842331i	$-0.0268440\pi$
$194$	−9.61943	−	15.2884i	−0.690634	−	1.09764i
$195$		0			0
$196$	−9.27943	−	6.65420i	−0.662817	−	0.475300i
$197$	11.4542	+	13.6505i	0.816076	+	0.972561i	0.999946	−	0.0103894i	$-0.00330712\pi$
$197$	11.4542	+	13.6505i	0.816076	+	0.972561i	−0.183870	+	0.982950i	$0.558863\pi$
$198$		0			0
$199$	−8.13451	+	9.69433i	−0.576640	+	0.687213i	−0.972980	−	0.230891i	$-0.925836\pi$
$199$	−8.13451	+	9.69433i	−0.576640	+	0.687213i	0.396340	+	0.918104i	$0.370280\pi$
$200$	13.2215	+	23.0233i	0.934902	+	1.62799i
$201$		0			0
$202$	−1.12958	+	0.243770i	−0.0794771	+	0.0171516i
$203$	−1.47080	+	25.2526i	−0.103230	+	1.77239i
$204$		0			0
$205$	11.1546	−	37.2589i	0.779070	−	2.60228i
$206$	5.89221	−	12.9361i	0.410530	−	0.901298i
$207$		0			0
$208$	−1.74455	−	8.17564i	−0.120963	−	0.566879i
$209$	1.02293	−	0.441247i	0.0707573	−	0.0305217i
$210$		0			0
$211$	−3.55626	+	1.06468i	−0.244823	+	0.0732953i	−0.406864	−	0.913489i	$-0.633378\pi$
$211$	−3.55626	+	1.06468i	−0.244823	+	0.0732953i	0.162041	+	0.986784i	$0.448192\pi$
$212$	14.6097	−	1.97254i	1.00340	−	0.135474i
$213$		0			0
$214$	−18.2785	+	20.9122i	−1.24949	+	1.42953i
$215$	13.9624	−	24.1836i	0.952229	−	1.64931i
$216$		0			0
$217$	4.96488	+	8.59942i	0.337038	+	0.583767i
$218$	0.724557	+	0.142879i	0.0490732	+	0.00967700i
$219$		0			0
$220$	−1.06260	+	2.58952i	−0.0716406	+	0.174585i
$221$	−9.32662	−	8.79921i	−0.627377	−	0.591899i
$222$		0			0
$223$	−1.09225	+	9.34481i	−0.0731426	+	0.625775i	0.906097	+	0.423070i	$0.139047\pi$
$223$	−1.09225	+	9.34481i	−0.0731426	+	0.625775i	−0.979240	+	0.202705i	$0.935027\pi$
$224$	17.0192	+	10.8188i	1.13714	+	0.722859i
$225$		0			0
$226$	−16.5892	−	23.2474i	−1.10350	−	1.54640i
$227$	4.88161	−	1.15696i	0.324004	−	0.0767904i	−0.0653952	−	0.997859i	$-0.520831\pi$
$227$	4.88161	−	1.15696i	0.324004	−	0.0767904i	0.389399	+	0.921069i	$0.372683\pi$
$228$		0			0
$229$	3.99822	+	2.62967i	0.264210	+	0.173774i	0.674701	−	0.738091i	$-0.264272\pi$
$229$	3.99822	+	2.62967i	0.264210	+	0.173774i	−0.410491	+	0.911865i	$0.634643\pi$
$230$	−22.6566	−	25.0060i	−1.49393	−	1.64885i
$231$		0			0
$232$	0.0464631	−	20.0689i	0.00305045	−	1.31759i
$233$	−9.17615	−	1.61800i	−0.601149	−	0.105999i	−0.135212	−	0.990817i	$-0.543172\pi$
$233$	−9.17615	−	1.61800i	−0.601149	−	0.105999i	−0.465937	+	0.884818i	$0.654283\pi$
$234$		0			0
$235$	27.7108	−	4.88616i	1.80765	−	0.318738i
$236$	0.838960	−	8.48926i	0.0546116	−	0.552604i
$237$		0			0
$238$	30.9100	−	1.17556i	2.00360	−	0.0762002i
$239$	16.2720	−	1.90192i	1.05255	−	0.123025i	0.427816	−	0.903866i	$-0.359283\pi$
$239$	16.2720	−	1.90192i	1.05255	−	0.123025i	0.624730	+	0.780841i	$0.285209\pi$
$240$		0			0
$241$	0.619928	+	10.6438i	0.0399331	+	0.685625i	0.957569	+	0.288203i	$0.0930579\pi$
$241$	0.619928	+	10.6438i	0.0399331	+	0.685625i	−0.917636	+	0.397422i	$0.869905\pi$
$242$	14.8042	−	4.10873i	0.951651	−	0.264119i
$243$		0			0
$244$	1.99155	−	1.19772i	0.127496	−	0.0766761i
$245$	21.6188	−	1.25915i	1.38117	−	0.0804442i
$246$		0			0
$247$	−0.732544	−	6.26732i	−0.0466107	−	0.398780i
$248$	−4.31384	−	6.59207i	−0.273929	−	0.418597i
$249$		0			0
$250$	−21.9447	−	8.49212i	−1.38791	−	0.537089i
$251$	3.47543	+	19.7101i	0.219367	+	1.24409i	0.873165	+	0.487424i	$0.162063\pi$
$251$	3.47543	+	19.7101i	0.219367	+	1.24409i	−0.653798	+	0.756669i	$0.726825\pi$
$252$		0			0
$253$	0.403057	−	2.28585i	0.0253400	−	0.143710i
$254$	3.10351	−	5.13354i	0.194732	−	0.322107i
$255$		0			0
$256$	−13.9609	−	7.81614i	−0.872559	−	0.488509i
$257$	6.90020	−	10.4912i	0.430423	−	0.654426i	−0.553536	−	0.832826i	$-0.686722\pi$
$257$	6.90020	−	10.4912i	0.430423	−	0.654426i	0.983958	+	0.178400i	$0.0570921\pi$
$258$		0			0
$259$	−0.170995	−	0.721484i	−0.0106251	−	0.0448308i
$260$	12.3249	+	9.97242i	0.764357	+	0.618463i
$261$		0			0
$262$	−18.7364	−	1.47085i	−1.15754	−	0.0908697i
$263$	−12.1229	−	1.41697i	−0.747531	−	0.0873739i	−0.266206	−	0.963916i	$-0.585770\pi$
$263$	−12.1229	−	1.41697i	−0.747531	−	0.0873739i	−0.481325	+	0.876542i	$0.659844\pi$
$264$		0			0
$265$	−19.1863	+	20.3362i	−1.17860	+	1.24925i
$266$	12.0242	+	9.33434i	0.737252	+	0.572325i
$267$		0			0
$268$	1.11749	+	14.6703i	0.0682615	+	0.896131i
$269$	−13.4840	+	7.78500i	−0.822135	+	0.474660i	−0.851152	−	0.524919i	$-0.824096\pi$
$269$	−13.4840	+	7.78500i	−0.822135	+	0.474660i	0.0290174	+	0.999579i	$0.490762\pi$
$270$		0			0
$271$	27.8391	+	16.0729i	1.69110	+	0.976360i	0.953628	+	0.300987i	$0.0973160\pi$
$271$	27.8391	+	16.0729i	1.69110	+	0.976360i	0.737476	+	0.675373i	$0.236017\pi$
$272$	−24.4332	+	2.30045i	−1.48148	+	0.139485i
$273$		0			0
$274$	25.5764	+	3.51354i	1.54513	+	0.212261i
$275$	−0.993340	−	3.31799i	−0.0599007	−	0.200082i
$276$		0			0
$277$	4.88948	+	11.3351i	0.293781	+	0.681060i	0.999627	−	0.0273048i	$-0.00869247\pi$
$277$	4.88948	+	11.3351i	0.293781	+	0.681060i	−0.705847	+	0.708365i	$0.749433\pi$
$278$	−14.6122	−	10.0384i	−0.876380	−	0.602064i
$279$		0			0
$280$	−37.9977	+	4.35214i	−2.27079	+	0.260090i
$281$	−11.6621	−	3.49140i	−0.695702	−	0.208279i	−0.0806225	−	0.996745i	$-0.525691\pi$
$281$	−11.6621	−	3.49140i	−0.695702	−	0.208279i	−0.615079	+	0.788465i	$0.710876\pi$
$282$		0			0
$283$	1.56653	+	0.0912401i	0.0931206	+	0.00542366i	0.104642	−	0.994510i	$-0.466630\pi$
$283$	1.56653	+	0.0912401i	0.0931206	+	0.00542366i	−0.0115212	+	0.999934i	$0.503667\pi$
$284$	2.13246	+	4.06357i	0.126538	+	0.241129i
$285$		0			0
$286$	−0.0219887	+	1.09033i	−0.00130022	+	0.0644727i
$287$	28.0030	+	23.4973i	1.65296	+	1.38700i
$288$		0			0
$289$	−15.8127	+	13.2684i	−0.930157	+	0.780495i
$290$	23.8721	+	29.6435i	1.40182	+	1.74073i
$291$		0			0
$292$	−1.86984	−	1.70206i	−0.109424	−	0.0996056i
$293$	−1.49400	−	0.644447i	−0.0872802	−	0.0376490i	0.351992	−	0.936003i	$-0.385504\pi$
$293$	−1.49400	−	0.644447i	−0.0872802	−	0.0376490i	−0.439272	+	0.898354i	$0.644764\pi$
$294$		0			0
$295$	8.89008	+	13.5167i	0.517600	+	0.786973i
$296$	0.167413	+	0.563946i	0.00973067	+	0.0327787i
$297$		0			0
$298$	−3.57753	+	3.64196i	−0.207240	+	0.210973i
$299$	−11.7485	−	5.90034i	−0.679436	−	0.341226i
$300$		0			0
$301$	15.6733	+	21.0530i	0.903396	+	1.21347i
$302$	8.97955	+	4.73878i	0.516715	+	0.272686i
$303$		0			0
$304$	−9.93843	−	6.86152i	−0.570008	−	0.393535i
$305$	−1.50741	+	4.14158i	−0.0863141	+	0.237146i
$306$		0			0
$307$	−1.69558	−	4.65857i	−0.0967719	−	0.265879i	0.881856	−	0.471520i	$-0.156294\pi$
$307$	−1.69558	−	4.65857i	−0.0967719	−	0.265879i	−0.978628	+	0.205641i	$0.934072\pi$
$308$	−1.83925	−	1.88107i	−0.104801	−	0.107184i
$309$		0			0
$310$	14.2238	+	4.57278i	0.807856	+	0.259716i
$311$	−21.5229	+	10.8092i	−1.22045	+	0.612933i	−0.938095	−	0.346377i	$-0.887412\pi$
$311$	−21.5229	+	10.8092i	−1.22045	+	0.612933i	−0.282354	+	0.959310i	$0.591115\pi$
$312$		0			0
$313$	−3.49585	−	3.70539i	−0.197597	−	0.209441i	0.620997	−	0.783813i	$-0.286728\pi$
$313$	−3.49585	−	3.70539i	−0.197597	−	0.209441i	−0.818594	+	0.574372i	$0.805246\pi$
$314$	1.10246	+	11.4258i	0.0622155	+	0.644795i
$315$		0			0
$316$	−0.118284	+	0.102905i	−0.00665401	+	0.00578887i
$317$	−10.7411	−	7.99645i	−0.603280	−	0.449125i	0.251686	−	0.967809i	$-0.419015\pi$
$317$	−10.7411	−	7.99645i	−0.603280	−	0.449125i	−0.854966	+	0.518683i	$0.826422\pi$
$318$		0			0
$319$	−0.603770	+	2.54751i	−0.0338046	+	0.142633i
$320$	29.9069	−	5.13073i	1.67185	−	0.286816i
$321$		0			0
$322$	30.0154	−	10.2442i	1.67269	−	0.570887i
$323$	−18.5240			−1.03070
$324$		0			0
$325$	−19.6175			−1.08818
$326$	−10.2803	+	3.50864i	−0.569372	+	0.194326i
$327$		0			0
$328$	−23.2233	−	17.3728i	−1.28229	−	0.959255i
$329$	−6.09913	+	25.7343i	−0.336256	+	1.41878i
$330$		0			0
$331$	−26.8006	−	19.9523i	−1.47309	−	1.09668i	−0.973028	−	0.230687i	$-0.925903\pi$
$331$	−26.8006	−	19.9523i	−1.47309	−	1.09668i	−0.500064	−	0.865989i	$-0.666690\pi$
$332$	−6.64526	−	7.63839i	−0.364706	−	0.419211i
$333$		0			0
$334$	−0.0608759	−	0.630912i	−0.00333098	−	0.0345219i
$335$	−19.1480	−	20.2957i	−1.04616	−	1.10887i
$336$		0			0
$337$	20.4222	−	10.2564i	1.11247	−	0.558703i	0.204974	−	0.978767i	$-0.434289\pi$
$337$	20.4222	−	10.2564i	1.11247	−	0.558703i	0.907494	+	0.420065i	$0.137993\pi$
$338$	−11.6220	−	3.73633i	−0.632152	−	0.203229i
$339$		0			0
$340$	33.2781	−	32.5383i	1.80476	−	1.76464i
$341$	0.351504	+	0.965750i	0.0190350	+	0.0522983i
$342$		0			0
$343$	1.57371	−	4.32373i	0.0849723	−	0.233460i
$344$	−13.3482	−	15.9827i	−0.719685	−	0.861731i
$345$		0			0
$346$	9.22330	+	4.86742i	0.495848	+	0.261674i
$347$	2.31099	+	3.10420i	0.124060	+	0.166642i	0.859814	−	0.510607i	$-0.170579\pi$
$347$	2.31099	+	3.10420i	0.124060	+	0.166642i	−0.735754	+	0.677249i	$0.763172\pi$
$348$		0			0
$349$	−11.2338	−	5.64183i	−0.601332	−	0.302000i	0.121968	−	0.992534i	$-0.461079\pi$
$349$	−11.2338	−	5.64183i	−0.601332	−	0.302000i	−0.723300	+	0.690534i	$0.757376\pi$
$350$	33.1637	−	33.7610i	1.77268	−	1.80460i
$351$		0			0
$352$	1.54028	+	1.40861i	0.0820974	+	0.0750791i
$353$	11.3170	+	17.2067i	0.602344	+	0.915819i	0.999999	−	0.00171576i	$-0.000546142\pi$
$353$	11.3170	+	17.2067i	0.602344	+	0.915819i	−0.397655	+	0.917535i	$0.630176\pi$
$354$		0			0
$355$	−7.99143	−	3.44717i	−0.424141	−	0.182957i
$356$	−11.2511	+	12.3602i	−0.596307	+	0.655088i
$357$		0			0
$358$	−19.7102	−	24.4754i	−1.04171	−	1.29356i
$359$	18.7882	−	15.7651i	0.991601	−	0.832052i	0.00580232	−	0.999983i	$-0.498153\pi$
$359$	18.7882	−	15.7651i	0.991601	−	0.832052i	0.985799	+	0.167931i	$0.0537086\pi$
$360$		0			0
$361$	7.57173	+	6.35344i	0.398512	+	0.334392i
$362$	0.480671	−	23.8345i	0.0252635	−	1.25271i
$363$		0			0
$364$	−13.1947	+	6.92426i	−0.691592	+	0.362930i
$365$	4.78717	+	0.278821i	0.250572	+	0.0145941i
$366$		0			0
$367$	−7.46037	−	2.23349i	−0.389428	−	0.116587i	0.0861026	−	0.996286i	$-0.472559\pi$
$367$	−7.46037	−	2.23349i	−0.389428	−	0.116587i	−0.475531	+	0.879699i	$0.657744\pi$
$368$	−23.3228	+	9.44452i	−1.21579	+	0.492330i
$369$		0			0
$370$	−0.919561	−	0.631729i	−0.0478057	−	0.0328420i
$371$	−10.4082	−	24.1290i	−0.540368	−	1.25271i
$372$		0			0
$373$	2.70087	+	9.02152i	0.139846	+	0.467117i	0.999005	−	0.0445906i	$-0.0141983\pi$
$373$	2.70087	+	9.02152i	0.139846	+	0.467117i	−0.859160	+	0.511707i	$0.829013\pi$
$374$	3.17171	+	0.435710i	0.164005	+	0.0225301i
$375$		0			0
$376$	3.69145	−	20.6555i	0.190372	−	1.06522i
$377$	12.8423	+	7.41449i	0.661411	+	0.381866i
$378$		0			0
$379$	1.00647	−	0.581088i	0.0516991	−	0.0298485i	−0.473928	−	0.880564i	$-0.657164\pi$
$379$	1.00647	−	0.581088i	0.0516991	−	0.0298485i	0.525627	+	0.850715i	$0.323831\pi$
$380$	22.8377	−	1.73963i	1.17155	−	0.0892409i
$381$		0			0
$382$	−8.13714	−	6.31682i	−0.416332	−	0.323196i
$383$	−18.3800	+	19.4816i	−0.939172	+	0.995464i	−0.999996	−	0.00268457i	$-0.999145\pi$
$383$	−18.3800	+	19.4816i	−0.939172	+	0.995464i	0.0608246	+	0.998148i	$0.480627\pi$
$384$		0			0
$385$	4.95561	+	0.579228i	0.252561	+	0.0295202i
$386$	18.4904	+	1.45154i	0.941137	+	0.0738817i
$387$		0			0
$388$	16.0680	−	19.8584i	0.815729	−	1.00816i
$389$	2.27968	+	9.61872i	0.115584	+	0.487688i	0.999788	+	0.0205871i	$0.00655353\pi$
$389$	2.27968	+	9.61872i	0.115584	+	0.487688i	−0.884204	+	0.467101i	$0.845298\pi$
$390$		0			0
$391$	−21.2083	+	32.2456i	−1.07255	+	1.63073i
$392$	4.66723	−	15.4593i	0.235731	−	0.780812i
$393$		0			0
$394$	−13.0378	+	21.5659i	−0.656834	+	1.08647i
$395$	0.0516318	−	0.292818i	0.00259788	−	0.0147333i
$396$		0			0
$397$	2.49961	+	14.1760i	0.125452	+	0.711472i	0.981039	+	0.193813i	$0.0620854\pi$
$397$	2.49961	+	14.1760i	0.125452	+	0.711472i	−0.855587	+	0.517659i	$0.826803\pi$
$398$	−16.6908	−	6.45896i	−0.836633	−	0.323758i
$399$		0			0
$400$	−24.7750	+	28.2127i	−1.23875	+	1.41064i
$401$	−0.316914	−	2.71138i	−0.0158259	−	0.135400i	0.983015	−	0.183523i	$-0.0587501\pi$
$401$	−0.316914	−	2.71138i	−0.0158259	−	0.135400i	−0.998841	+	0.0481231i	$0.984676\pi$
$402$		0			0
$403$	5.81129	−	0.338469i	0.289481	−	0.0168603i
$404$	−0.842253	−	1.40049i	−0.0419037	−	0.0696769i
$405$		0			0
$406$	−34.4702	+	9.56678i	−1.71073	+	0.474792i
$407$	−0.00446216	−	0.0766123i	−0.000221181	−	0.00379753i
$408$		0			0
$409$	24.5810	−	2.87310i	1.21545	−	0.142066i	0.515900	−	0.856649i	$-0.327458\pi$
$409$	24.5810	−	2.87310i	1.21545	−	0.142066i	0.699551	+	0.714583i	$0.253384\pi$
$410$	54.9630	−	2.09034i	2.71443	−	0.103234i
$411$		0			0
$412$	20.0053	+	1.97704i	0.985589	+	0.0974019i
$413$	−14.9749	+	2.64048i	−0.736866	+	0.129929i
$414$		0			0
$415$	18.9092	+	3.33420i	0.928217	+	0.163670i
$416$	10.1454	−	6.06952i	0.497421	−	0.297583i
$417$		0			0
$418$	1.05784	+	1.16753i	0.0517405	+	0.0571059i
$419$	−7.64662	−	5.02926i	−0.373562	−	0.245696i	0.348820	−	0.937190i	$-0.386582\pi$
$419$	−7.64662	−	5.02926i	−0.373562	−	0.245696i	−0.722382	+	0.691494i	$0.756953\pi$
$420$		0			0
$421$	15.3360	−	3.63470i	0.747430	−	0.177144i	0.160786	−	0.986989i	$-0.448597\pi$
$421$	15.3360	−	3.63470i	0.747430	−	0.177144i	0.586644	+	0.809845i	$0.300449\pi$
$422$	−3.04946	−	4.27339i	−0.148445	−	0.208026i
$423$		0			0
$424$	9.31369	+	18.6526i	0.452313	+	0.905852i
$425$	−6.68581	+	57.2008i	−0.324310	+	2.77465i
$426$		0			0
$427$	−3.01313	−	2.84275i	−0.145816	−	0.137570i
$428$	−36.3386	−	14.9114i	−1.75649	−	0.720772i
$429$		0			0
$430$	38.7456	+	7.64044i	1.86848	+	0.368455i
$431$	−13.6704	−	23.6778i	−0.658479	−	1.14052i	−0.981009	−	0.193960i	$-0.937867\pi$
$431$	−13.6704	−	23.6778i	−0.658479	−	1.14052i	0.322530	−	0.946559i	$-0.395467\pi$
$432$		0			0
$433$	−13.5032	+	23.3882i	−0.648922	+	1.12397i	0.334458	+	0.942411i	$0.391447\pi$
$433$	−13.5032	+	23.3882i	−0.648922	+	1.12397i	−0.983381	+	0.181556i	$0.941887\pi$
$434$	−9.24160	+	10.5732i	−0.443611	+	0.507531i
$435$		0			0
$436$	0.139744	+	1.03502i	0.00669254	+	0.0495685i
$437$	−18.1950	+	5.44723i	−0.870386	+	0.260577i
$438$		0			0
$439$	6.55305	−	2.82671i	0.312760	−	0.134911i	−0.233913	−	0.972257i	$-0.575153\pi$
$439$	6.55305	−	2.82671i	0.312760	−	0.134911i	0.546673	+	0.837346i	$0.315894\pi$
$440$	−3.95123	−	0.239313i	−0.188367	−	0.0114088i
$441$		0			0
$442$	7.51658	−	16.5023i	0.357527	−	0.784933i
$443$	1.77205	−	5.91905i	0.0841926	−	0.281223i	−0.905518	−	0.424308i	$-0.860517\pi$
$443$	1.77205	−	5.91905i	0.0841926	−	0.281223i	0.989710	+	0.143086i	$0.0457024\pi$
$444$		0			0
$445$	1.84308	−	31.6445i	0.0873704	−	1.50009i
$446$	−13.0061	+	2.80679i	−0.615857	+	0.132906i
$447$		0			0
$448$	−6.70562	+	27.7206i	−0.316811	+	1.30968i
$449$	14.9846	−	17.8579i	0.707166	−	0.842768i	−0.286151	−	0.958185i	$-0.592376\pi$
$449$	14.9846	−	17.8579i	0.707166	−	0.842768i	0.993317	+	0.115417i	$0.0368204\pi$
$450$		0			0
$451$	2.43197	+	2.89831i	0.114517	+	0.136476i
$452$	23.5367	−	32.8224i	1.10707	−	1.54384i
$453$		0			0
$454$	3.77839	+	6.00509i	0.177329	+	0.281833i
$455$	11.1932	−	25.9488i	0.524746	−	1.21650i
$456$		0			0
$457$	−27.6280	+	18.1712i	−1.29238	+	0.850014i	−0.994515	−	0.104594i	$-0.966646\pi$
$457$	−27.6280	+	18.1712i	−1.29238	+	0.850014i	−0.297868	+	0.954607i	$0.596275\pi$
$458$	−1.69320	+	6.55248i	−0.0791182	+	0.306177i
$459$		0			0
$460$	23.1188	−	41.7464i	1.07792	−	1.94644i
$461$	−0.466380	+	0.928638i	−0.0217215	+	0.0432510i	−0.904232	−	0.427042i	$-0.859556\pi$
$461$	−0.466380	+	0.928638i	−0.0217215	+	0.0432510i	0.882510	+	0.470293i	$0.155852\pi$
$462$		0			0
$463$	18.2791	−	13.6083i	0.849501	−	0.632430i	−0.0818131	−	0.996648i	$-0.526071\pi$
$463$	18.2791	−	13.6083i	0.849501	−	0.632430i	0.931314	+	0.364218i	$0.118664\pi$
$464$	26.8817	−	9.10523i	1.24795	−	0.422700i
$465$		0			0
$466$	−2.02608	−	13.0205i	−0.0938564	−	0.603164i
$467$	−10.0689	−	3.66477i	−0.465932	−	0.169585i	0.0983769	−	0.995149i	$-0.468635\pi$
$467$	−10.0689	−	3.66477i	−0.465932	−	0.169585i	−0.564309	+	0.825564i	$0.690857\pi$
$468$		0			0
$469$	24.6441	−	8.96971i	1.13796	−	0.414183i
$470$	19.1979	+	34.8564i	0.885532	+	1.60781i
$471$		0			0
$472$	11.7453	−	2.75499i	0.540623	−	0.126809i
$473$	1.21917	+	2.42757i	0.0560575	+	0.111620i
$474$		0			0
$475$	−20.6142	+	19.4485i	−0.945846	+	0.892360i
$476$	15.6929	+	40.8332i	0.719285	+	1.87159i
$477$		0			0
$478$	9.97851	+	20.9097i	0.456407	+	0.956389i
$479$	7.69314	−	10.3337i	0.351508	−	0.472158i	−0.590841	−	0.806788i	$-0.701204\pi$
$479$	7.69314	−	10.3337i	0.351508	−	0.472158i	0.942350	+	0.334630i	$0.108611\pi$
$480$		0			0
$481$	−0.422957	−	0.100243i	−0.0192852	−	0.00457067i
$482$	−13.9625	+	5.69175i	−0.635975	+	0.259252i
$483$		0			0
$484$	12.2617	+	17.9372i	0.557349	+	0.815329i
$485$			48.4454i			2.19979i
$486$		0			0
$487$			21.1052i			0.956369i	0.878259	+	0.478185i	$0.158705\pi$
$487$			21.1052i			0.956369i	−0.878259	+	0.478185i	$0.841295\pi$
$488$	2.51277	+	2.11840i	0.113748	+	0.0958953i
$489$		0			0
$490$	11.5606	+	28.3596i	0.522256	+	1.28115i
$491$	14.1512	+	3.35389i	0.638633	+	0.151359i	0.537161	−	0.843480i	$-0.319497\pi$
$491$	14.1512	+	3.35389i	0.638633	+	0.151359i	0.101472	+	0.994838i	$0.467645\pi$
$492$		0			0
$493$	25.9960	−	34.9187i	1.17080	−	1.57266i
$494$	8.05360	−	3.84333i	0.362349	−	0.172920i
$495$		0			0
$496$	6.85234	−	8.78491i	0.307679	−	0.394454i
$497$	5.95002	−	5.61355i	0.266895	−	0.251802i
$498$		0			0
$499$	−4.99823	−	9.95230i	−0.223752	−	0.445526i	0.753547	−	0.657395i	$-0.228342\pi$
$499$	−4.99823	−	9.95230i	−0.223752	−	0.445526i	−0.977298	+	0.211868i	$0.932045\pi$
$500$	1.34166	−	33.2502i	0.0600008	−	1.48699i
$501$		0			0
$502$	−24.7927	+	13.6551i	−1.10655	+	0.609455i
$503$	22.2568	−	8.10083i	0.992384	−	0.361198i	0.205741	−	0.978607i	$-0.434040\pi$
$503$	22.2568	−	8.10083i	0.992384	−	0.361198i	0.786643	+	0.617408i	$0.211817\pi$
$504$		0			0
$505$	2.91242	+	1.06003i	0.129601	+	0.0471709i
$506$	3.24352	−	0.504713i	0.144192	−	0.0224372i
$507$		0			0
$508$	8.28844	+	1.80879i	0.367740	+	0.0802520i
$509$	21.4334	−	15.9566i	0.950018	−	0.707262i	−0.00618061	−	0.999981i	$-0.501967\pi$
$509$	21.4334	−	15.9566i	0.950018	−	0.707262i	0.956199	+	0.292719i	$0.0945600\pi$
$510$		0			0
$511$	−2.02277	+	4.02767i	−0.0894822	+	0.178174i
$512$	4.08389	−	22.2558i	0.180484	−	0.983578i
$513$		0			0
$514$	17.1936	+	4.44292i	0.758375	+	0.195969i
$515$	−31.8527	+	20.9498i	−1.40360	+	0.923159i
$516$		0			0
$517$	−1.08418	+	2.51341i	−0.0476822	+	0.110540i
$518$	0.887530	−	0.558432i	0.0389959	−	0.0245361i
$519$		0			0
$520$	−7.71721	+	21.0511i	−0.338422	+	0.923151i
$521$	15.7683	+	18.7919i	0.690823	+	0.823290i	0.991455	−	0.130450i	$-0.0416422\pi$
$521$	15.7683	+	18.7919i	0.690823	+	0.823290i	−0.300632	+	0.953740i	$0.597198\pi$
$522$		0			0
$523$	−15.0537	+	17.9403i	−0.658253	+	0.784475i	−0.987134	−	0.159896i	$-0.948884\pi$
$523$	−15.0537	+	17.9403i	−0.658253	+	0.784475i	0.328881	+	0.944371i	$0.393329\pi$
$524$	−6.59011	−	25.7488i	−0.287890	−	1.12484i
$525$		0			0
$526$	−3.64122	−	16.8727i	−0.158765	−	0.735684i
$527$	0.993629	−	17.0600i	0.0432832	−	0.743143i
$528$		0			0
$529$	−4.75293	+	15.8759i	−0.206649	+	0.690256i
$530$	−35.9824	−	16.3895i	−1.56298	−	0.711916i
$531$		0			0
$532$	−7.00054	+	20.3572i	−0.303512	+	0.882597i
$533$	19.6773	−	8.48794i	0.852317	−	0.367654i
$534$		0			0
$535$	71.3629	−	21.3646i	3.08529	−	0.923674i
$536$	−19.1244	+	8.19699i	−0.826047	+	0.354056i
$537$		0			0
$538$	−16.5790	−	14.4910i	−0.714769	−	0.624750i
$539$	−1.05331	+	1.82439i	−0.0453694	+	0.0785822i
$540$		0			0
$541$	21.2815	+	36.8606i	0.914962	+	1.58476i	0.806957	+	0.590610i	$0.201113\pi$
$541$	21.2815	+	36.8606i	0.914962	+	1.58476i	0.108004	+	0.994150i	$0.465554\pi$
$542$	−8.79533	+	44.6021i	−0.377792	+	1.91583i
$543$		0			0
$544$	−14.2399	−	31.6507i	−0.610531	−	1.35701i
$545$	−1.44072	−	1.35925i	−0.0617137	−	0.0582239i
$546$		0			0
$547$	−3.55324	+	30.3999i	−0.151926	+	1.29981i	0.675135	+	0.737694i	$0.264085\pi$
$547$	−3.55324	+	30.3999i	−0.151926	+	1.29981i	−0.827061	+	0.562112i	$0.809989\pi$
$548$	6.98066	+	35.8367i	0.298199	+	1.53087i
$549$		0			0
$550$	3.98707	−	2.84514i	0.170009	−	0.121317i
$551$	20.8454	−	4.94046i	0.888046	−	0.210471i
$552$		0			0
$553$	0.233490	+	0.153569i	0.00992900	+	0.00653041i
$554$	−12.9375	+	11.7220i	−0.549661	+	0.498018i
$555$		0			0
$556$	6.76071	−	24.1426i	0.286718	−	1.02387i
$557$	6.28172	+	1.10764i	0.266165	+	0.0469320i	0.305138	−	0.952308i	$-0.401297\pi$
$557$	6.28172	+	1.10764i	0.266165	+	0.0469320i	−0.0389729	+	0.999240i	$0.512409\pi$
$558$		0			0
$559$	15.1528	−	2.67184i	0.640894	−	0.113007i
$560$	−23.1821	−	48.8683i	−0.979623	−	2.06506i
$561$		0			0
$562$	−0.654278	−	17.2035i	−0.0275991	−	0.725686i
$563$	−5.15676	+	0.602739i	−0.217332	+	0.0254024i	−0.224062	−	0.974575i	$-0.571932\pi$
$563$	−5.15676	+	0.602739i	−0.217332	+	0.0254024i	0.00673023	+	0.999977i	$0.497858\pi$
$564$		0			0
$565$	4.45376	+	76.4681i	0.187371	+	3.21704i
$566$	0.593469	+	2.13834i	0.0249454	+	0.0898810i
$567$		0			0
$568$	−4.46462	+	4.71033i	−0.187331	+	0.197641i
$569$	−35.7367	+	2.08142i	−1.49816	+	0.0872578i	−0.787516	−	0.616295i	$-0.788633\pi$
$569$	−35.7367	+	2.08142i	−1.49816	+	0.0872578i	−0.710643	+	0.703552i	$0.751596\pi$
$570$		0			0
$571$	1.26983	+	10.8641i	0.0531407	+	0.454647i	0.993445	+	0.114312i	$0.0364664\pi$
$571$	1.26983	+	10.8641i	0.0531407	+	0.454647i	−0.940304	+	0.340335i	$0.889459\pi$
$572$	−1.46935	+	0.468630i	−0.0614368	+	0.0195944i
$573$		0			0
$574$	−18.6573	+	48.2129i	−0.778742	+	2.01237i
$575$	10.2536	+	58.1511i	0.427605	+	2.42507i
$576$		0			0
$577$	1.60819	−	9.12049i	0.0669498	−	0.379691i	−0.932861	−	0.360237i	$-0.882696\pi$
$577$	1.60819	−	9.12049i	0.0669498	−	0.379691i	0.999811	−	0.0194545i	$-0.00619295\pi$
$578$	−24.9817	−	15.1029i	−1.03910	−	0.628196i
$579$		0			0
$580$	−28.7705	+	45.4916i	−1.19463	+	1.88894i
$581$	−9.91694	+	15.0780i	−0.411424	+	0.625540i
$582$		0			0
$583$	−0.627225	−	2.64647i	−0.0259770	−	0.109606i
$584$	1.42392	−	3.28011i	0.0589221	−	0.135732i
$585$		0			0
$586$	0.180082	−	2.29396i	0.00743911	−	0.0947626i
$587$	18.4325	+	2.15446i	0.760793	+	0.0889239i	0.487638	−	0.873046i	$-0.337859\pi$
$587$	18.4325	+	2.15446i	0.760793	+	0.0889239i	0.273155	+	0.961970i	$0.411933\pi$
$588$		0			0
$589$	5.77101	−	6.11691i	0.237790	−	0.252043i
$590$	−14.0299	+	18.0729i	−0.577603	+	0.744051i
$591$		0			0
$592$	−0.678317	+	0.481675i	−0.0278787	+	0.0197967i
$593$	5.66767	−	3.27223i	0.232743	−	0.134374i	−0.379094	−	0.925358i	$-0.623764\pi$
$593$	5.66767	−	3.27223i	0.232743	−	0.134374i	0.611837	+	0.790984i	$0.290431\pi$
$594$		0			0
$595$	−71.8470	−	41.4809i	−2.94544	−	1.70055i
$596$	−6.50863	−	3.12456i	−0.266604	−	0.127987i
$597$		0			0
$598$	2.53038	−	18.4196i	0.103475	−	0.753234i
$599$	−0.528274	−	1.76456i	−0.0215847	−	0.0720979i	0.946519	−	0.322649i	$-0.104573\pi$
$599$	−0.528274	−	1.76456i	−0.0215847	−	0.0720979i	−0.968103	+	0.250551i	$0.919388\pi$
$600$		0			0
$601$	4.82735	+	11.1910i	0.196912	+	0.456492i	0.987851	−	0.155402i	$-0.0496672\pi$
$601$	4.82735	+	11.1910i	0.196912	+	0.456492i	−0.790940	+	0.611894i	$0.790408\pi$
$602$	−21.0179	+	30.5942i	−0.856627	+	1.24693i
$603$		0			0
$604$	−2.24061	+	14.1830i	−0.0911690	+	0.577096i
$605$	−39.4753	−	11.8181i	−1.60490	−	0.480475i
$606$		0			0
$607$	35.1472	+	2.04709i	1.42658	+	0.0830890i	0.753972	−	0.656907i	$-0.228136\pi$
$607$	35.1472	+	2.04709i	1.42658	+	0.0830890i	0.672611	+	0.739996i	$0.265173\pi$
$608$	4.64368	−	16.4360i	0.188326	−	0.666568i
$609$		0			0
$610$	−6.23170	−	0.125675i	−0.252314	−	0.00508842i
$611$	11.8769	+	9.96587i	0.480486	+	0.403176i
$612$		0			0
$613$	27.2490	−	22.8647i	1.10058	−	0.923495i	0.103115	−	0.994669i	$-0.467119\pi$
$613$	27.2490	−	22.8647i	1.10058	−	0.923495i	0.997464	+	0.0711743i	$0.0226747\pi$
$614$	5.46053	−	4.39740i	0.220369	−	0.177464i
$615$		0			0
$616$	1.67748	−	3.32094i	0.0675875	−	0.133804i
$617$	40.8912	+	17.6387i	1.64622	+	0.710108i	0.998652	−	0.0519027i	$-0.0165286\pi$
$617$	40.8912	+	17.6387i	1.64622	+	0.710108i	0.647564	+	0.762011i	$0.275788\pi$
$618$		0			0
$619$	18.2520	+	27.7508i	0.733609	+	1.11540i	0.988907	+	0.148536i	$0.0474561\pi$
$619$	18.2520	+	27.7508i	0.733609	+	1.11540i	−0.255298	+	0.966862i	$0.582174\pi$
$620$	0.377121	+	21.1260i	0.0151455	+	0.848442i
$621$		0			0
$622$	−24.2987	−	23.8688i	−0.974288	−	0.957051i
$623$	26.6240	+	13.3711i	1.06667	+	0.535701i
$624$		0			0
$625$	9.65991	+	12.9755i	0.386396	+	0.519020i
$626$	3.36243	−	6.37149i	0.134390	−	0.254656i
$627$		0			0
$628$	−14.7888	+	6.69480i	−0.590136	+	0.267152i
$629$	−0.436436	+	1.19910i	−0.0174018	+	0.0478111i
$630$		0			0
$631$	−12.5396	−	34.4522i	−0.499193	−	1.37152i	−0.892056	−	0.451925i	$-0.850738\pi$
$631$	−12.5396	−	34.4522i	−0.499193	−	1.37152i	0.392863	−	0.919597i	$-0.371485\pi$
$632$	−0.191761	−	0.111306i	−0.00762784	−	0.00442751i
$633$		0			0
$634$	5.79602	−	18.0287i	0.230190	−	0.716012i
$635$	−14.3776	+	7.22068i	−0.570556	+	0.286544i
$636$		0			0
$637$	8.18830	+	8.67909i	0.324432	+	0.343878i
$638$	−3.68541	+	0.355600i	−0.145907	+	0.0140783i
$639$		0			0
$640$	20.5284	+	37.6840i	0.811455	+	1.48959i
$641$	6.61816	+	4.92704i	0.261402	+	0.194606i	0.719879	−	0.694100i	$-0.244197\pi$
$641$	6.61816	+	4.92704i	0.261402	+	0.194606i	−0.458477	+	0.888706i	$0.651605\pi$
$642$		0			0
$643$	−0.0807862	+	0.340864i	−0.00318590	+	0.0134424i	−0.974615	−	0.223889i	$-0.928125\pi$
$643$	−0.0807862	+	0.340864i	−0.00318590	+	0.0134424i	0.971429	+	0.237332i	$0.0762728\pi$
$644$	27.4219	+	35.4934i	1.08057	+	1.39864i
$645$		0			0
$646$	−8.46167	−	24.7926i	−0.332920	−	0.975453i
$647$	−1.81191			−0.0712337			−0.0356168	−	0.999366i	$-0.511340\pi$
$647$	−1.81191			−0.0712337			−0.0356168	+	0.999366i	$0.511340\pi$
$648$		0			0
$649$	−1.57381			−0.0617774
$650$	−8.96118	−	26.2562i	−0.351487	−	1.02985i
$651$		0			0
$652$	−9.39199	−	12.1565i	−0.367819	−	0.476085i
$653$	9.69506	−	40.9067i	0.379397	−	1.60080i	−0.363631	−	0.931543i	$-0.618463\pi$
$653$	9.69506	−	40.9067i	0.379397	−	1.60080i	0.743029	−	0.669260i	$-0.233389\pi$
$654$		0			0
$655$	40.4321	+	30.1006i	1.57981	+	1.17613i
$656$	12.6436	−	39.0182i	0.493651	−	1.52340i
$657$		0			0
$658$	−37.2290	+	3.59218i	−1.45134	+	0.140038i
$659$	30.5270	+	32.3568i	1.18916	+	1.26044i	0.957756	+	0.287583i	$0.0928519\pi$
$659$	30.5270	+	32.3568i	1.18916	+	1.26044i	0.231408	+	0.972857i	$0.425667\pi$
$660$		0			0
$661$	−0.0414178	+	0.0208008i	−0.00161097	+	0.000809058i	−0.449604	−	0.893228i	$-0.648435\pi$
$661$	−0.0414178	+	0.0208008i	−0.00161097	+	0.000809058i	0.447994	+	0.894037i	$0.352139\pi$
$662$	14.4619	−	44.9842i	0.562078	−	1.74836i
$663$		0			0
$664$	7.18776	−	12.3833i	0.278939	−	0.480564i
$665$	−13.9634	−	38.3641i	−0.541477	−	1.48770i
$666$		0			0
$667$	15.2661	−	41.9432i	0.591104	−	1.62405i
$668$	0.816610	−	0.369675i	0.0315956	−	0.0143031i
$669$		0			0
$670$	18.4172	−	34.8988i	0.711517	−	1.34826i
$671$	−0.256030	−	0.343908i	−0.00988393	−	0.0132764i
$672$		0			0
$673$	−26.0993	−	13.1076i	−1.00606	−	0.505260i	−0.132085	−	0.991238i	$-0.542167\pi$
$673$	−26.0993	−	13.1076i	−1.00606	−	0.505260i	−0.873971	+	0.485978i	$0.838463\pi$
$674$	23.0561	+	22.6482i	0.888086	+	0.872375i
$675$		0			0
$676$	−0.308138	−	17.2617i	−0.0118515	−	0.663911i
$677$	−24.0436	−	36.5565i	−0.924071	−	1.40498i	−0.914304	−	0.405029i	$-0.867261\pi$
$677$	−24.0436	−	36.5565i	−0.924071	−	1.40498i	−0.00976724	−	0.999952i	$-0.503109\pi$
$678$		0			0
$679$	−41.8099	−	18.0350i	−1.60452	−	0.692121i
$680$	58.7509	+	29.6763i	2.25299	+	1.13803i
$681$		0			0
$682$	−1.13200	+	0.911607i	−0.0433466	+	0.0349072i
$683$	24.5285	−	20.5819i	0.938557	−	0.787543i	−0.0387764	−	0.999248i	$-0.512346\pi$
$683$	24.5285	−	20.5819i	0.938557	−	0.787543i	0.977334	+	0.211705i	$0.0679016\pi$
$684$		0			0
$685$	−53.0419	−	44.5074i	−2.02663	−	1.70054i
$686$	6.50578	+	0.131202i	0.248392	+	0.00500932i
$687$		0			0
$688$	15.2940	−	25.1662i	0.583079	−	0.959451i
$689$	−15.3790	−	0.895725i	−0.585893	−	0.0341244i
$690$		0			0
$691$	−33.8395	−	10.1309i	−1.28732	−	0.385397i	−0.431235	−	0.902240i	$-0.641922\pi$
$691$	−33.8395	−	10.1309i	−1.28732	−	0.385397i	−0.856080	+	0.516843i	$0.827107\pi$
$692$	−2.30143	+	14.5680i	−0.0874872	+	0.553791i
$693$		0			0
$694$	−3.09903	+	4.51103i	−0.117638	+	0.171236i
$695$	18.8326	+	43.6589i	0.714361	+	1.65607i
$696$		0			0
$697$	−18.0430	−	60.2679i	−0.683428	−	2.28281i
$698$	2.41951	−	17.6126i	0.0915799	−	0.666646i
$699$		0			0
$700$	60.3351	+	28.9647i	2.28045	+	1.09476i
$701$	28.7233	+	16.5834i	1.08487	+	0.626347i	0.932205	−	0.361932i	$-0.117883\pi$
$701$	28.7233	+	16.5834i	1.08487	+	0.626347i	0.152660	+	0.988279i	$0.451216\pi$
$702$		0			0
$703$	−0.543827	+	0.313978i	−0.0205108	+	0.0118419i
$704$	−1.18170	+	2.70498i	−0.0445369	+	0.101948i
$705$		0			0
$706$	−17.8600	+	23.0067i	−0.672170	+	0.865870i
$707$	−1.99906	+	2.11888i	−0.0751824	+	0.0796887i
$708$		0			0
$709$	16.4678	+	1.92481i	0.618460	+	0.0722877i	0.419553	−	0.907731i	$-0.362187\pi$
$709$	16.4678	+	1.92481i	0.618460	+	0.0722877i	0.198907	+	0.980018i	$0.436261\pi$
$710$	0.963262	−	12.2705i	0.0361506	−	0.460502i
$711$		0			0
$712$	−21.6824	−	9.41248i	−0.812583	−	0.352748i
$713$	−4.04074	−	17.0492i	−0.151327	−	0.638498i
$714$		0			0
$715$	1.60727	−	2.44373i	0.0601083	−	0.0913902i
$716$	23.7545	−	37.5605i	0.887749	−	1.40370i
$717$		0			0
$718$	29.6826	+	17.9448i	1.10774	+	0.669693i
$719$	2.85237	−	16.1766i	0.106375	−	0.603284i	−0.884287	−	0.466944i	$-0.845355\pi$
$719$	2.85237	−	16.1766i	0.106375	−	0.603284i	0.990662	−	0.136340i	$-0.0435340\pi$
$720$		0			0
$721$	−6.22238	−	35.2889i	−0.231734	−	1.31423i
$722$	−5.04476	+	13.0363i	−0.187746	+	0.485161i
$723$		0			0
$724$	32.1199	−	10.2442i	1.19373	−	0.380722i
$725$	−7.73212	−	66.1526i	−0.287164	−	2.45684i
$726$		0			0
$727$	−31.9318	+	1.85982i	−1.18429	+	0.0689768i	−0.638955	−	0.769244i	$-0.720633\pi$
$727$	−31.9318	+	1.85982i	−1.18429	+	0.0689768i	−0.545331	+	0.838221i	$0.683596\pi$
$728$	−15.2948	−	14.4970i	−0.566863	−	0.537294i
$729$		0			0
$730$	1.81358	+	6.53455i	0.0671237	+	0.241854i
$731$	−2.62638	−	45.0932i	−0.0971402	−	1.66783i
$732$		0			0
$733$	19.3169	−	2.25782i	0.713485	−	0.0833944i	0.248396	−	0.968659i	$-0.420097\pi$
$733$	19.3169	−	2.25782i	0.713485	−	0.0833944i	0.465089	+	0.885264i	$0.346022\pi$
$734$	−0.418549	−	11.0053i	−0.0154489	−	0.406212i
$735$		0			0
$736$	−23.2944	−	26.9013i	−0.858643	−	0.991593i
$737$	2.67312	−	0.471343i	0.0984656	−	0.0173621i
$738$		0			0
$739$	−14.5280	−	2.56167i	−0.534420	−	0.0942326i	−0.100076	−	0.994980i	$-0.531909\pi$
$739$	−14.5280	−	2.56167i	−0.534420	−	0.0942326i	−0.434344	+	0.900747i	$0.643020\pi$
$740$	0.425459	−	1.51932i	0.0156402	−	0.0558513i
$741$		0			0
$742$	27.5400	−	24.9525i	1.01103	−	0.916035i
$743$	1.61301	+	1.06090i	0.0591758	+	0.0389205i	0.578752	−	0.815503i	$-0.303540\pi$
$743$	1.61301	+	1.06090i	0.0591758	+	0.0389205i	−0.519576	+	0.854424i	$0.673910\pi$
$744$		0			0
$745$	13.3231	−	3.15764i	0.488122	−	0.115687i
$746$	−10.8407	+	7.73586i	−0.396908	+	0.283230i
$747$		0			0
$748$	0.865666	+	4.44407i	0.0316519	+	0.162491i
$749$	−8.12828	+	69.5418i	−0.297001	+	2.54100i
$750$		0			0
$751$	18.4272	+	17.3851i	0.672417	+	0.634393i	0.944743	−	0.327812i	$-0.106311\pi$
$751$	18.4272	+	17.3851i	0.672417	+	0.634393i	−0.272326	+	0.962205i	$0.587793\pi$
$752$	29.3317	−	4.49468i	1.06962	−	0.163904i
$753$		0			0
$754$	−4.05732	+	20.5751i	−0.147759	+	0.749302i
$755$	−13.6157	−	23.5831i	−0.495526	−	0.858277i
$756$		0			0
$757$	−9.88889	+	17.1281i	−0.359418	+	0.622530i	−0.987864	−	0.155324i	$-0.950358\pi$
$757$	−9.88889	+	17.1281i	−0.359418	+	0.622530i	0.628446	+	0.777853i	$0.283691\pi$
$758$	1.23749	+	1.08164i	0.0449476	+	0.0392868i
$759$		0			0
$760$	12.7605	+	29.7715i	0.462871	+	1.07992i
$761$	−9.77015	+	2.92499i	−0.354168	+	0.106031i	−0.458944	−	0.888465i	$-0.651772\pi$
$761$	−9.77015	+	2.92499i	−0.354168	+	0.106031i	0.104777	+	0.994496i	$0.466587\pi$
$762$		0			0
$763$	1.70942	−	0.737371i	0.0618851	−	0.0266946i
$764$	4.73747	−	13.7763i	0.171396	−	0.498410i
$765$		0			0
$766$	−34.4702	−	15.7008i	−1.24546	−	0.567291i
$767$	−2.55661	+	8.53968i	−0.0923140	+	0.308350i
$768$		0			0
$769$	−2.97182	+	51.0242i	−0.107167	+	1.83998i	0.334024	+	0.942565i	$0.391593\pi$
$769$	−2.97182	+	51.0242i	−0.107167	+	1.83998i	−0.441190	+	0.897413i	$0.645444\pi$
$770$	1.48846	+	6.89722i	0.0536404	+	0.248559i
$771$		0			0
$772$	6.50359	+	25.4108i	0.234069	+	0.914554i
$773$	24.5742	−	29.2863i	0.883871	−	1.05336i	−0.114333	−	0.993443i	$-0.536473\pi$
$773$	24.5742	−	29.2863i	0.883871	−	1.05336i	0.998204	−	0.0599139i	$-0.0190826\pi$
$774$		0			0
$775$	−16.8057	−	20.0283i	−0.603679	−	0.719437i
$776$	33.9185	+	12.4343i	1.21760	+	0.446366i
$777$		0			0
$778$	−11.8324	+	7.44493i	−0.424213	+	0.266914i
$779$	12.2622	−	28.4270i	0.439340	−	1.01850i
$780$		0			0
$781$	0.707361	−	0.465239i	0.0253114	−	0.0166476i
$782$	−52.8457	−	13.6557i	−1.88976	−	0.488326i
$783$		0			0
$784$	22.8228	−	0.815080i	0.815101	−	0.0291100i
$785$	13.8171	−	27.5121i	0.493152	−	0.981947i
$786$		0			0
$787$	−22.7469	+	16.9344i	−0.810838	+	0.603647i	−0.920687	−	0.390302i	$-0.872371\pi$
$787$	−22.7469	+	16.9344i	−0.810838	+	0.603647i	0.109849	+	0.993948i	$0.464963\pi$
$788$	−34.8196	−	7.59867i	−1.24040	−	0.270692i
$789$		0			0
$790$	0.415496	−	0.0646539i	0.0147827	−	0.00230028i
$791$	−67.6523	−	24.6234i	−2.40544	−	0.875509i
$792$		0			0
$793$	−2.28200	+	0.830581i	−0.0810362	+	0.0294948i
$794$	−17.8314	+	9.82103i	−0.632814	+	0.348535i
$795$		0			0
$796$	1.02044	−	25.2895i	0.0361686	−	0.896363i
$797$	6.09784	+	12.1418i	0.215997	+	0.430085i	0.975371	−	0.220569i	$-0.0707913\pi$
$797$	6.09784	+	12.1418i	0.215997	+	0.430085i	−0.759375	+	0.650654i	$0.774495\pi$
$798$		0			0
$799$	33.1063	−	31.2342i	1.17122	−	1.10499i
$800$	−49.0773	−	20.2716i	−1.73514	−	0.716709i
$801$		0			0
$802$	3.48416	−	1.66271i	0.123030	−	0.0587122i
$803$	−0.278564	+	0.374176i	−0.00983031	+	0.0132044i
$804$		0			0
$805$	−82.7693	−	19.6167i	−2.91723	−	0.691397i
$806$	3.10758	+	7.62326i	0.109460	+	0.268518i
$807$		0			0
$808$	1.48969	−	1.76702i	0.0524071	−	0.0621634i
$809$			16.0043i			0.562683i	0.959608	+	0.281341i	$0.0907793\pi$
$809$			16.0043i			0.562683i	−0.959608	+	0.281341i	$0.909221\pi$
$810$		0			0
$811$			14.6868i			0.515725i	0.966182	+	0.257862i	$0.0830181\pi$
$811$			14.6868i			0.515725i	−0.966182	+	0.257862i	$0.916982\pi$
$812$	−28.5501	−	41.7652i	−1.00191	−	1.46567i
$813$		0			0
$814$	0.100500	−	0.0409684i	0.00352253	−	0.00143594i
$815$	28.3485	+	6.71871i	0.993004	+	0.235346i
$816$		0			0
$817$	13.2739	−	17.8299i	0.464394	−	0.623789i
$818$	15.0739	+	31.5869i	0.527046	+	1.10441i
$819$		0			0
$820$	27.9046	+	72.6081i	0.974472	+	2.53559i
$821$	7.19381	−	6.78701i	0.251066	−	0.236868i	−0.550412	−	0.834893i	$-0.685529\pi$
$821$	7.19381	−	6.78701i	0.251066	−	0.236868i	0.801477	+	0.598025i	$0.204048\pi$
$822$		0			0
$823$	−2.12742	−	4.23604i	−0.0741571	−	0.147659i	0.853499	−	0.521094i	$-0.174476\pi$
$823$	−2.12742	−	4.23604i	−0.0741571	−	0.147659i	−0.927656	+	0.373435i	$0.878180\pi$
$824$	6.49224	+	27.6783i	0.226168	+	0.964221i
$825$		0			0
$826$	−10.3745	−	18.8363i	−0.360975	−	0.655400i
$827$	−35.4582	+	12.9057i	−1.23300	+	0.448776i	−0.874624	−	0.484801i	$-0.838892\pi$
$827$	−35.4582	+	12.9057i	−1.23300	+	0.448776i	−0.358377	+	0.933577i	$0.616670\pi$
$828$		0			0
$829$	−24.4864	−	8.91232i	−0.850448	−	0.309538i	−0.120225	−	0.992747i	$-0.538362\pi$
$829$	−24.4864	−	8.91232i	−0.850448	−	0.309538i	−0.730223	+	0.683209i	$0.760584\pi$
$830$	4.17513	+	26.8313i	0.144921	+	0.931328i
$831$		0			0
$832$	12.7579	+	10.8062i	0.442301	+	0.374638i
$833$	28.0972	−	20.9176i	0.973511	−	0.724752i
$834$		0			0
$835$	−0.762954	+	1.51917i	−0.0264031	+	0.0525729i
$836$	−1.07942	+	1.94914i	−0.0373325	+	0.0674125i
$837$		0			0
$838$	3.23826	−	12.5317i	0.111864	−	0.432899i
$839$	15.7619	−	10.3667i	0.544160	−	0.357900i	−0.247475	−	0.968894i	$-0.579601\pi$
$839$	15.7619	−	10.3667i	0.544160	−	0.357900i	0.791635	+	0.610995i	$0.209230\pi$
$840$		0			0
$841$	−8.45457	+	19.5999i	−0.291537	+	0.675858i
$842$	11.8701	+	18.8655i	0.409072	+	0.650148i
$843$		0			0
$844$	4.32657	−	6.03349i	0.148927	−	0.207681i
$845$	21.0460	+	25.0817i	0.724005	+	0.862836i
$846$		0			0
$847$	24.8950	−	29.6688i	0.855404	−	1.01943i
$848$	−20.7104	+	20.9860i	−0.711198	+	0.720662i
$849$		0			0
$850$	−79.6121	+	17.1808i	−2.73067	+	0.589295i
$851$	−0.0760743	+	1.30615i	−0.00260779	+	0.0447741i
$852$		0			0
$853$	1.54855	−	5.17251i	0.0530213	−	0.177104i	−0.927377	−	0.374127i	$-0.877942\pi$
$853$	1.54855	−	5.17251i	0.0530213	−	0.177104i	0.980399	+	0.197024i	$0.0631276\pi$
$854$	2.42837	−	5.33136i	0.0830970	−	0.182435i
$855$		0			0
$856$	3.35827	−	55.4474i	0.114783	−	1.89515i
$857$	−31.1800	+	13.4498i	−1.06509	+	0.459435i	−0.855204	−	0.518291i	$-0.826568\pi$
$857$	−31.1800	+	13.4498i	−1.06509	+	0.459435i	−0.209885	+	0.977726i	$0.567309\pi$
$858$		0			0
$859$	−31.5742	+	9.45269i	−1.07730	+	0.322522i	−0.775822	−	0.630952i	$-0.782664\pi$
$859$	−31.5742	+	9.45269i	−1.07730	+	0.322522i	−0.301476	+	0.953474i	$0.597479\pi$
$860$	7.47279	+	55.3475i	0.254820	+	1.88733i
$861$		0			0
$862$	25.4460	−	29.1125i	0.866694	−	0.991575i
$863$	−16.8495	+	29.1842i	−0.573563	+	0.993441i	0.422633	+	0.906301i	$0.361106\pi$
$863$	−16.8495	+	29.1842i	−0.573563	+	0.993441i	−0.996196	+	0.0871400i	$0.972227\pi$
$864$		0			0
$865$	−13.9853	−	24.2233i	−0.475515	−	0.823616i
$866$	−37.4712	−	7.38914i	−1.27332	−	0.251093i
$867$		0			0
$868$	−18.3728	−	7.53923i	−0.623614	−	0.255898i
$869$	0.0210390	+	0.0198493i	0.000713700	+	0.000673342i
$870$		0			0
$871$	1.78485	−	15.2704i	0.0604773	−	0.517416i
$872$	−1.32145	+	0.659828i	−0.0447498	+	0.0223446i
$873$		0			0
$874$	−15.6020	−	21.8641i	−0.527747	−	0.739564i
$875$	−57.7180	+	13.6794i	−1.95123	+	0.462449i
$876$		0			0
$877$	−43.3803	−	28.5317i	−1.46485	−	0.963445i	−0.996816	−	0.0797337i	$-0.974593\pi$
$877$	−43.3803	−	28.5317i	−1.46485	−	0.963445i	−0.468031	−	0.883712i	$-0.655037\pi$
$878$	6.77670	+	7.47942i	0.228702	+	0.252418i
$879$		0			0
$880$	−1.48461	−	5.39767i	−0.0500461	−	0.181956i
$881$	−28.2935	−	4.98890i	−0.953232	−	0.168080i	−0.324659	−	0.945831i	$-0.605249\pi$
$881$	−28.2935	−	4.98890i	−0.953232	−	0.168080i	−0.628573	+	0.777751i	$0.716361\pi$
$882$		0			0
$883$	−25.5035	+	4.49695i	−0.858260	+	0.151334i	−0.585425	−	0.810727i	$-0.699072\pi$
$883$	−25.5035	+	4.49695i	−0.858260	+	0.151334i	−0.272835	+	0.962061i	$0.587961\pi$
$884$	25.5203	+	2.52207i	0.858342	+	0.0848265i
$885$		0			0
$886$	8.73158	−	0.332077i	0.293343	−	0.0111563i
$887$	−10.1567	+	1.18715i	−0.341028	+	0.0398604i	−0.284883	−	0.958562i	$-0.591955\pi$
$887$	−10.1567	+	1.18715i	−0.341028	+	0.0398604i	−0.0561446	+	0.998423i	$0.517881\pi$
$888$		0			0
$889$	−0.879262	−	15.0963i	−0.0294895	−	0.506315i
$890$	43.1951	−	11.9883i	1.44790	−	0.401848i
$891$		0			0
$892$	−9.69778	−	16.1254i	−0.324706	−	0.539917i
$893$	22.3604	−	1.30234i	0.748262	−	0.0435813i
$894$		0			0
$895$	9.78470	+	83.7134i	0.327066	+	2.79823i
$896$	−40.1646	+	3.68781i	−1.34181	+	0.123201i
$897$		0			0
$898$	30.7461	+	11.8981i	1.02601	+	0.397043i
$899$	3.43185	+	19.4630i	0.114459	+	0.649127i
$900$		0			0
$901$	−7.85307	+	44.5369i	−0.261624	+	1.48374i
$902$	−2.76821	+	4.57891i	−0.0921712	+	0.152461i
$903$		0			0
$904$	54.6813	+	16.5086i	1.81867	+	0.549066i
$905$	−35.1346	+	53.4196i	−1.16791	+	1.77573i
$906$		0			0
$907$	−10.5008	−	44.3062i	−0.348672	−	1.47116i	−0.811311	−	0.584615i	$-0.801246\pi$
$907$	−10.5008	−	44.3062i	−0.348672	−	1.47116i	0.462639	−	0.886547i	$-0.346903\pi$
$908$	−6.31131	+	7.80014i	−0.209448	+	0.258857i
$909$		0			0
$910$	39.8431	+	3.12779i	1.32079	+	0.103685i
$911$	−46.9874	−	5.49204i	−1.55676	−	0.181959i	−0.706267	−	0.707945i	$-0.749622\pi$
$911$	−46.9874	−	5.49204i	−1.55676	−	0.181959i	−0.850493	+	0.525986i	$0.823696\pi$
$912$		0			0
$913$	−1.28180	+	1.35863i	−0.0424214	+	0.0449640i
$914$	−36.9409	−	28.6770i	−1.22190	−	0.948551i
$915$		0			0
$916$	−9.54335	+	0.726951i	−0.315321	+	0.0240191i
$917$	−41.0296	+	23.6884i	−1.35492	+	0.782261i
$918$		0			0
$919$	27.4935	+	15.8734i	0.906928	+	0.523615i	0.879441	−	0.476007i	$-0.157916\pi$
$919$	27.4935	+	15.8734i	0.906928	+	0.523615i	0.0274862	+	0.999622i	$0.491250\pi$
$920$	66.4344	+	11.8728i	2.19028	+	0.391435i
$921$		0			0
$922$	−1.45594	−	0.200008i	−0.0479487	−	0.00658691i
$923$	−1.37535	−	4.59400i	−0.0452703	−	0.151213i
$924$		0			0
$925$	0.773263	+	1.79263i	0.0254247	+	0.0589412i
$926$	26.5632	+	18.2487i	0.872922	+	0.599688i
$927$		0			0
$928$	24.4660	+	31.8194i	0.803135	+	1.04452i
$929$	46.6009	+	13.9514i	1.52893	+	0.457730i	0.937312	−	0.348491i	$-0.113306\pi$
$929$	46.6009	+	13.9514i	1.52893	+	0.457730i	0.591614	+	0.806221i	$0.298491\pi$
$930$		0			0
$931$	17.2087	+	1.00229i	0.563992	+	0.0328488i
$932$	16.5013	−	8.65945i	0.540518	−	0.283650i
$933$		0			0
$934$	0.305536	−	15.1503i	0.00999746	−	0.495733i
$935$	−6.57767	−	5.51932i	−0.215113	−	0.180501i
$936$		0			0
$937$	19.2580	−	16.1594i	0.629132	−	0.527904i	−0.271527	−	0.962431i	$-0.587529\pi$
$937$	19.2580	−	16.1594i	0.629132	−	0.527904i	0.900659	+	0.434527i	$0.143084\pi$
$938$	23.2624	+	28.8865i	0.759546	+	0.943178i
$939$		0			0
$940$	−37.8826	+	41.6169i	−1.23559	+	1.35739i
$941$	−34.8606	−	15.0374i	−1.13642	−	0.490205i	−0.257078	−	0.966391i	$-0.582760\pi$
$941$	−34.8606	−	15.0374i	−1.13642	−	0.490205i	−0.879345	+	0.476186i	$0.842019\pi$
$942$		0			0
$943$	−35.4453	−	53.8919i	−1.15426	−	1.75496i
$944$	9.05253	+	14.4616i	0.294635	+	0.470684i
$945$		0			0
$946$	−2.69216	+	2.74065i	−0.0875298	+	0.0891062i
$947$	5.05797	+	2.54021i	0.164362	+	0.0825457i	0.529078	−	0.848573i	$-0.322538\pi$
$947$	5.05797	+	2.54021i	0.164362	+	0.0825457i	−0.364716	+	0.931119i	$0.618834\pi$
$948$		0			0
$949$	1.57781	+	2.11936i	0.0512178	+	0.0687974i
$950$	−35.4466	−	18.7063i	−1.15004	−	0.606911i
$951$		0			0
$952$	−47.4830	+	39.6560i	−1.53893	+	1.28526i
$953$	11.0342	−	30.3161i	0.357432	−	0.982035i	−0.622486	−	0.782631i	$-0.713877\pi$
$953$	11.0342	−	30.3161i	0.357432	−	0.982035i	0.979917	−	0.199404i	$-0.0639006\pi$
$954$		0			0
$955$	9.44944	+	25.9621i	0.305777	+	0.840114i
$956$	−23.4276	+	22.9068i	−0.757704	+	0.740859i
$957$		0			0
$958$	17.3449	+	5.57618i	0.560388	+	0.180158i
$959$	58.1574	−	29.2077i	1.87800	−	0.943167i
$960$		0			0
$961$	−15.9496	−	16.9056i	−0.514502	−	0.545341i
$962$	−0.0590395	−	0.611879i	−0.00190351	−	0.0197278i
$963$		0			0
$964$	−13.9959	−	16.0876i	−0.450778	−	0.518146i
$965$	−39.9013	−	29.7054i	−1.28447	−	0.956251i
$966$		0			0
$967$	6.73696	−	28.4255i	0.216646	−	0.914101i	−0.750700	−	0.660643i	$-0.770284\pi$
$967$	6.73696	−	28.4255i	0.216646	−	0.914101i	0.967346	−	0.253458i	$-0.0815681\pi$
$968$	−18.4063	+	24.6048i	−0.591600	+	0.790828i
$969$		0			0
$970$	−64.8398	+	22.1297i	−2.08188	+	0.710542i
$971$	−23.4277			−0.751829			−0.375915	−	0.926654i	$-0.622671\pi$
$971$	−23.4277			−0.751829			−0.375915	+	0.926654i	$0.622671\pi$
$972$		0			0
$973$	−44.6898			−1.43269
$974$	−28.2474	+	9.64079i	−0.905106	+	0.308911i
$975$		0			0
$976$	−1.68746	+	4.33079i	−0.0540142	+	0.138625i
$977$	−2.82117	+	11.9035i	−0.0902572	+	0.380825i	−0.999361	−	0.0357446i	$-0.988620\pi$
$977$	−2.82117	+	11.9035i	−0.0902572	+	0.380825i	0.909104	+	0.416570i	$0.136768\pi$
$978$		0			0
$979$	2.47341	+	1.84138i	0.0790504	+	0.0588509i
$980$	−32.6758	+	28.4274i	−1.04379	+	0.908080i
$981$		0			0
$982$	1.97533	+	20.4721i	0.0630352	+	0.653290i
$983$	−26.0766	−	27.6396i	−0.831715	−	0.881566i	0.162747	−	0.986668i	$-0.447965\pi$
$983$	−26.0766	−	27.6396i	−0.831715	−	0.881566i	−0.994461	+	0.105102i	$0.966483\pi$
$984$		0			0
$985$	60.3998	−	30.3339i	1.92450	−	0.966519i
$986$	58.6104	+	18.8426i	1.86653	+	0.600069i
$987$		0			0
$988$	8.82280	+	9.02339i	0.280691	+	0.287072i
$989$	−15.8400	−	43.5202i	−0.503684	−	1.38386i
$990$		0			0
$991$	−16.9022	+	46.4384i	−0.536916	+	1.47517i	0.313774	+	0.949498i	$0.398407\pi$
$991$	−16.9022	+	46.4384i	−0.536916	+	1.47517i	−0.850690	+	0.525668i	$0.823816\pi$
$992$	14.8879	+	5.15831i	0.472692	+	0.163776i
$993$		0			0
$994$	10.2312	+	5.39931i	0.324513	+	0.171256i
$995$	28.6638	+	38.5022i	0.908704	+	1.22060i
$996$		0			0
$997$	8.96485	+	4.50232i	0.283920	+	0.142590i	0.585060	−	0.810990i	$-0.301071\pi$
$997$	8.96485	+	4.50232i	0.283920	+	0.142590i	−0.301140	+	0.953580i	$0.597367\pi$
$998$	11.0371	−	11.2359i	0.349372	−	0.355665i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.p.a.395.30		936
3.2	odd	2		324.2.p.a.203.23	yes	936
4.3	odd	2	inner	972.2.p.a.395.29		936
12.11	even	2		324.2.p.a.203.24	yes	936
81.2	odd	54	inner	972.2.p.a.251.29		936
81.79	even	27		324.2.p.a.83.24	yes	936
324.79	odd	54		324.2.p.a.83.23	✓	936
324.83	even	54	inner	972.2.p.a.251.30		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.83.23	✓	936	324.79	odd	54
324.2.p.a.83.24	yes	936	81.79	even	27
324.2.p.a.203.23	yes	936	3.2	odd	2
324.2.p.a.203.24	yes	936	12.11	even	2
972.2.p.a.251.29		936	81.2	odd	54	inner
972.2.p.a.251.30		936	324.83	even	54	inner
972.2.p.a.395.29		936	4.3	odd	2	inner
972.2.p.a.395.30		936	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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.p (of order \(54\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.456796 + 1.33841i) q^{2} +(-1.58267 + 1.22276i) q^{4} +(0.874721 - 3.69074i) q^{5} +(2.85958 + 2.12888i) q^{7} +(-2.35951 - 1.55971i) q^{8} +O(q^{10})\)	\(q+(0.456796 + 1.33841i) q^{2} +(-1.58267 + 1.22276i) q^{4} +(0.874721 - 3.69074i) q^{5} +(2.85958 + 2.12888i) q^{7} +(-2.35951 - 1.55971i) q^{8} +(5.33928 - 0.515181i) q^{10} +(0.253209 + 0.268386i) q^{11} +(1.86762 - 0.937956i) q^{13} +(-1.54306 + 4.79975i) q^{14} +(1.00972 - 3.87046i) q^{16} +(-2.09840 - 5.76530i) q^{17} +(1.03264 - 2.83716i) q^{19} +(3.12849 + 6.91081i) q^{20} +(-0.243545 + 0.461494i) q^{22} +(-3.75651 - 5.04586i) q^{23} +(-8.38825 - 4.21274i) q^{25} +(2.10849 + 2.07119i) q^{26} +(-7.12890 + 0.127258i) q^{28} +(3.89902 + 5.92817i) q^{29} +(2.55754 + 1.10321i) q^{31} +(5.64149 - 0.416598i) q^{32} +(6.75779 - 5.44208i) q^{34} +(10.3585 - 8.69179i) q^{35} +(-0.159326 - 0.133690i) q^{37} +(4.26898 + 0.0860925i) q^{38} +(-7.82041 + 7.34403i) q^{40} +(10.2366 + 0.596211i) q^{41} +(7.05296 + 2.11152i) q^{43} +(-0.728918 - 0.115154i) q^{44} +(5.03747 - 7.33267i) q^{46} +(2.93833 + 6.81180i) q^{47} +(1.63746 + 5.46949i) q^{49} +(1.80664 - 13.1513i) q^{50} +(-1.80895 + 3.76814i) q^{52} +(-6.38357 - 3.68555i) q^{53} +(1.21203 - 0.699765i) q^{55} +(-3.42678 - 9.48325i) q^{56} +(-6.15326 + 7.92645i) q^{58} +(-2.92703 + 3.10247i) q^{59} +(-1.15413 - 0.134898i) q^{61} +(-0.308278 + 3.92697i) q^{62} +(3.13459 + 7.36032i) q^{64} +(-1.82810 - 7.71336i) q^{65} +(4.04241 - 6.14618i) q^{67} +(10.3707 + 6.55876i) q^{68} +(16.3649 + 9.89349i) q^{70} +(0.398446 - 2.25970i) q^{71} +(0.219535 + 1.24504i) q^{73} +(0.106153 - 0.274312i) q^{74} +(1.83483 + 5.75297i) q^{76} +(0.152711 + 1.30652i) q^{77} +(0.0782584 - 0.00455803i) q^{79} +(-13.4016 - 7.11218i) q^{80} +(3.87804 + 13.9730i) q^{82} +(0.294342 + 5.05366i) q^{83} +(-23.1137 + 2.70161i) q^{85} +(0.395692 + 10.4043i) q^{86} +(-0.178845 - 1.02819i) q^{88} +(8.23009 - 1.45119i) q^{89} +(7.33742 + 1.29379i) q^{91} +(12.1152 + 3.39266i) q^{92} +(-7.77476 + 7.04429i) q^{94} +(-9.56793 - 6.29293i) q^{95} +(-12.4281 + 2.94552i) q^{97} +(-6.57243 + 4.69003i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8}+O(q^{10}) \) 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8	\( 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8} - 18 q^{10} - 36 q^{13} + 18 q^{14} - 18 q^{16} + 36 q^{17} + 18 q^{20} - 18 q^{22} - 36 q^{25} + 27 q^{26} - 9 q^{28} + 36 q^{29} + 18 q^{32} - 18 q^{34} - 36 q^{37} + 18 q^{38} - 18 q^{40} + 36 q^{41} + 90 q^{44} - 18 q^{46} - 36 q^{49} + 135 q^{50} - 18 q^{52} + 54 q^{53} + 144 q^{56} - 18 q^{58} - 36 q^{61} + 117 q^{62} - 18 q^{64} + 36 q^{65} + 63 q^{68} - 18 q^{70} - 36 q^{73} + 18 q^{74} - 18 q^{76} + 36 q^{77} - 36 q^{82} - 36 q^{85} + 18 q^{86} - 18 q^{88} + 54 q^{89} - 72 q^{92} - 18 q^{94} - 36 q^{97} - 153 q^{98}+O(q^{100}) \) 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8 - 18 * q^10 - 36 * q^13 + 18 * q^14 - 18 * q^16 + 36 * q^17 + 18 * q^20 - 18 * q^22 - 36 * q^25 + 27 * q^26 - 9 * q^28 + 36 * q^29 + 18 * q^32 - 18 * q^34 - 36 * q^37 + 18 * q^38 - 18 * q^40 + 36 * q^41 + 90 * q^44 - 18 * q^46 - 36 * q^49 + 135 * q^50 - 18 * q^52 + 54 * q^53 + 144 * q^56 - 18 * q^58 - 36 * q^61 + 117 * q^62 - 18 * q^64 + 36 * q^65 + 63 * q^68 - 18 * q^70 - 36 * q^73 + 18 * q^74 - 18 * q^76 + 36 * q^77 - 36 * q^82 - 36 * q^85 + 18 * q^86 - 18 * q^88 + 54 * q^89 - 72 * q^92 - 18 * q^94 - 36 * q^97 - 153 * q^98

Introduction

L-functions

Modular forms

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