LMFDB - Embedded newform 396.2.r.b.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.r (of order $10$, degree $4$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	396.19
Dual form			396.2.r.b.271.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989218 + 1.01067i) q^{2} +(-0.0428958 + 1.99954i) q^{4} +(-2.66345 - 1.93511i) q^{5} +(-1.40437 + 4.32221i) q^{7} +(-2.06330 + 1.93463i) q^{8} +O(q^{10})$	\(q+(0.989218 + 1.01067i) q^{2} +(-0.0428958 + 1.99954i) q^{4} +(-2.66345 - 1.93511i) q^{5} +(-1.40437 + 4.32221i) q^{7} +(-2.06330 + 1.93463i) q^{8} +(-0.678982 - 4.60611i) q^{10} +(1.46412 + 2.97596i) q^{11} +(-0.838793 - 1.15450i) q^{13} +(-5.75754 + 2.85626i) q^{14} +(-3.99632 - 0.171544i) q^{16} +(-1.93604 + 2.66473i) q^{17} +(-0.989336 - 3.04486i) q^{19} +(3.98358 - 5.24267i) q^{20} +(-1.55938 + 4.42361i) q^{22} +3.51482i q^{23} +(1.80424 + 5.55287i) q^{25} +(0.337066 - 1.98979i) q^{26} +(-8.58219 - 2.99350i) q^{28} +(3.38012 + 1.09827i) q^{29} +(1.57372 + 2.16604i) q^{31} +(-3.77986 - 4.20864i) q^{32} +(-4.60833 + 0.679308i) q^{34} +(12.1044 - 8.79438i) q^{35} +(0.140713 - 0.433070i) q^{37} +(2.09867 - 4.01192i) q^{38} +(9.23923 - 1.16007i) q^{40} +(8.53807 - 2.77419i) q^{41} +10.5057 q^{43} +(-6.01336 + 2.79990i) q^{44} +(-3.55232 + 3.47693i) q^{46} +(-3.26990 + 1.06246i) q^{47} +(-11.0461 - 8.02547i) q^{49} +(-3.82732 + 7.31649i) q^{50} +(2.34445 - 1.62768i) q^{52} +(-1.87204 + 1.36012i) q^{53} +(1.85922 - 10.7596i) q^{55} +(-5.46422 - 11.6350i) q^{56} +(2.23369 + 4.50260i) q^{58} +(2.50457 + 0.813785i) q^{59} +(0.697794 - 0.960431i) q^{61} +(-0.632394 + 3.73320i) q^{62} +(0.514433 - 7.98344i) q^{64} +4.69811i q^{65} +6.30893i q^{67} +(-5.24519 - 3.98550i) q^{68} +(20.8621 + 3.53399i) q^{70} +(-0.379984 + 0.523003i) q^{71} +(6.49205 + 2.10940i) q^{73} +(0.576885 - 0.286187i) q^{74} +(6.13076 - 1.84760i) q^{76} +(-14.9189 + 2.14886i) q^{77} +(-7.83975 + 5.69591i) q^{79} +(10.3121 + 8.19022i) q^{80} +(11.2498 + 5.88487i) q^{82} +(0.906427 + 0.658558i) q^{83} +(10.3131 - 3.35093i) q^{85} +(10.3925 + 10.6178i) q^{86} +(-8.77830 - 3.30779i) q^{88} +16.2562 q^{89} +(6.16797 - 2.00409i) q^{91} +(-7.02803 - 0.150771i) q^{92} +(-4.30843 - 2.25378i) q^{94} +(-3.25710 + 10.0243i) q^{95} +(-9.60184 + 6.97614i) q^{97} +(-2.81593 - 19.1029i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	0.989218	+	1.01067i	0.699483	+	0.714650i
$2$	0.989218	+	1.01067i	0.699483	+	0.714650i
$3$		0			0
$3$		0			0
$4$	−0.0428958	+	1.99954i	−0.0214479	+	0.999770i
$5$	−2.66345	−	1.93511i	−1.19113	−	0.865408i	−0.197749	−	0.980253i	$-0.563363\pi$
$5$	−2.66345	−	1.93511i	−1.19113	−	0.865408i	−0.993383	+	0.114844i	$0.963363\pi$
$6$		0			0
$7$	−1.40437	+	4.32221i	−0.530802	+	1.63364i	0.221746	+	0.975104i	$0.428824\pi$
$7$	−1.40437	+	4.32221i	−0.530802	+	1.63364i	−0.752548	+	0.658537i	$0.771176\pi$
$8$	−2.06330	+	1.93463i	−0.729488	+	0.683994i
$9$		0			0
$10$	−0.678982	−	4.60611i	−0.214713	−	1.45658i
$11$	1.46412	+	2.97596i	0.441448	+	0.897287i
$11$	1.46412	+	2.97596i	0.441448	+	0.897287i
$12$		0			0
$13$	−0.838793	−	1.15450i	−0.232639	−	0.320201i	0.676698	−	0.736261i	$-0.263410\pi$
$13$	−0.838793	−	1.15450i	−0.232639	−	0.320201i	−0.909337	+	0.416060i	$0.863410\pi$
$14$	−5.75754	+	2.85626i	−1.53877	+	0.763366i
$15$		0			0
$16$	−3.99632	−	0.171544i	−0.999080	−	0.0428859i
$17$	−1.93604	+	2.66473i	−0.469559	+	0.646293i	−0.976457	−	0.215714i	$-0.930792\pi$
$17$	−1.93604	+	2.66473i	−0.469559	+	0.646293i	0.506898	+	0.862006i	$0.330792\pi$
$18$		0			0
$19$	−0.989336	−	3.04486i	−0.226969	−	0.698539i	−0.998086	−	0.0618453i	$-0.980301\pi$
$19$	−0.989336	−	3.04486i	−0.226969	−	0.698539i	0.771117	−	0.636694i	$-0.219699\pi$
$20$	3.98358	−	5.24267i	0.890756	−	1.17230i
$21$		0			0
$22$	−1.55938	+	4.42361i	−0.332461	+	0.943117i
$23$			3.51482i			0.732891i	0.930439	+	0.366446i	$0.119425\pi$
$23$			3.51482i			0.732891i	−0.930439	+	0.366446i	$0.880575\pi$
$24$		0			0
$25$	1.80424	+	5.55287i	0.360848	+	1.11057i
$26$	0.337066	−	1.98979i	0.0661040	−	0.390230i
$27$		0			0
$28$	−8.58219	−	2.99350i	−1.62188	−	0.565718i
$29$	3.38012	+	1.09827i	0.627672	+	0.203943i	0.605543	−	0.795812i	$-0.292956\pi$
$29$	3.38012	+	1.09827i	0.627672	+	0.203943i	0.0221282	+	0.999755i	$0.492956\pi$
$30$		0			0
$31$	1.57372	+	2.16604i	0.282649	+	0.389033i	0.926609	−	0.376026i	$-0.122710\pi$
$31$	1.57372	+	2.16604i	0.282649	+	0.389033i	−0.643960	+	0.765059i	$0.722710\pi$
$32$	−3.77986	−	4.20864i	−0.668191	−	0.743990i
$33$		0			0
$34$	−4.60833	+	0.679308i	−0.790321	+	0.116500i
$35$	12.1044	−	8.79438i	2.04602	−	1.48652i
$36$		0			0
$37$	0.140713	−	0.433070i	0.0231331	−	0.0711962i	−0.938824	−	0.344399i	$-0.888083\pi$
$37$	0.140713	−	0.433070i	0.0231331	−	0.0711962i	0.961957	+	0.273202i	$0.0880829\pi$
$38$	2.09867	−	4.01192i	0.340450	−	0.650820i
$39$		0			0
$40$	9.23923	−	1.16007i	1.46085	−	0.183423i
$41$	8.53807	−	2.77419i	1.33342	−	0.433255i	0.446339	−	0.894864i	$-0.352728\pi$
$41$	8.53807	−	2.77419i	1.33342	−	0.433255i	0.887084	+	0.461609i	$0.152728\pi$
$42$		0			0
$43$	10.5057			1.60211			0.801055	−	0.598591i	$-0.204273\pi$
$43$	10.5057			1.60211			0.801055	+	0.598591i	$0.204273\pi$
$44$	−6.01336	+	2.79990i	−0.906549	+	0.422101i
$45$		0			0
$46$	−3.55232	+	3.47693i	−0.523760	+	0.512645i
$47$	−3.26990	+	1.06246i	−0.476964	+	0.154975i	−0.537626	−	0.843183i	$-0.680679\pi$
$47$	−3.26990	+	1.06246i	−0.476964	+	0.154975i	0.0606621	+	0.998158i	$0.480679\pi$
$48$		0			0
$49$	−11.0461	−	8.02547i	−1.57802	−	1.14650i
$50$	−3.82732	+	7.31649i	−0.541265	+	1.03471i
$51$		0			0
$52$	2.34445	−	1.62768i	0.325117	−	0.225718i
$53$	−1.87204	+	1.36012i	−0.257145	+	0.186827i	−0.708887	−	0.705322i	$-0.750803\pi$
$53$	−1.87204	+	1.36012i	−0.257145	+	0.186827i	0.451743	+	0.892148i	$0.350803\pi$
$54$		0			0
$55$	1.85922	−	10.7596i	0.250697	−	1.45082i
$56$	−5.46422	−	11.6350i	−0.730187	−	1.55479i
$57$		0			0
$58$	2.23369	+	4.50260i	0.293298	+	0.591220i
$59$	2.50457	+	0.813785i	0.326067	+	0.105946i	0.467476	−	0.884006i	$-0.345163\pi$
$59$	2.50457	+	0.813785i	0.326067	+	0.105946i	−0.141409	+	0.989951i	$0.545163\pi$
$60$		0			0
$61$	0.697794	−	0.960431i	0.0893434	−	0.122971i	−0.762005	−	0.647571i	$-0.775785\pi$
$61$	0.697794	−	0.960431i	0.0893434	−	0.122971i	0.851349	+	0.524600i	$0.175785\pi$
$62$	−0.632394	+	3.73320i	−0.0803141	+	0.474117i
$63$		0			0
$64$	0.514433	−	7.98344i	0.0643042	−	0.997930i
$65$			4.69811i			0.582729i
$66$		0			0
$67$			6.30893i			0.770759i	0.922758	+	0.385379i	$0.125929\pi$
$67$			6.30893i			0.770759i	−0.922758	+	0.385379i	$0.874071\pi$
$68$	−5.24519	−	3.98550i	−0.636073	−	0.483313i
$69$		0			0
$70$	20.8621	+	3.53399i	2.49350	+	0.422392i
$71$	−0.379984	+	0.523003i	−0.0450958	+	0.0620690i	−0.830969	−	0.556318i	$-0.812214\pi$
$71$	−0.379984	+	0.523003i	−0.0450958	+	0.0620690i	0.785874	+	0.618387i	$0.212214\pi$
$72$		0			0
$73$	6.49205	+	2.10940i	0.759837	+	0.246886i	0.663209	−	0.748434i	$-0.269194\pi$
$73$	6.49205	+	2.10940i	0.759837	+	0.246886i	0.0966285	+	0.995321i	$0.469194\pi$
$74$	0.576885	−	0.286187i	0.0670615	−	0.0332685i
$75$		0			0
$76$	6.13076	−	1.84760i	0.703247	−	0.211935i
$77$	−14.9189	+	2.14886i	−1.70017	+	0.244885i
$78$		0			0
$79$	−7.83975	+	5.69591i	−0.882041	+	0.640840i	−0.933791	−	0.357820i	$-0.883520\pi$
$79$	−7.83975	+	5.69591i	−0.882041	+	0.640840i	0.0517498	+	0.998660i	$0.483520\pi$
$80$	10.3121	+	8.19022i	1.15292	+	0.915695i
$81$		0			0
$82$	11.2498	+	5.88487i	1.24233	+	0.649875i
$83$	0.906427	+	0.658558i	0.0994933	+	0.0722861i	0.636420	−	0.771343i	$-0.280415\pi$
$83$	0.906427	+	0.658558i	0.0994933	+	0.0722861i	−0.536926	+	0.843629i	$0.680415\pi$
$84$		0			0
$85$	10.3131	−	3.35093i	1.11861	−	0.363460i
$86$	10.3925	+	10.6178i	1.12065	+	1.14495i
$87$		0			0
$88$	−8.77830	−	3.30779i	−0.935770	−	0.352612i
$89$	16.2562			1.72316			0.861579	−	0.507624i	$-0.169476\pi$
$89$	16.2562			1.72316			0.861579	+	0.507624i	$0.169476\pi$
$90$		0			0
$91$	6.16797	−	2.00409i	0.646579	−	0.210086i
$92$	−7.02803	−	0.150771i	−0.732723	−	0.0157190i
$93$		0			0
$94$	−4.30843	−	2.25378i	−0.444381	−	0.232460i
$95$	−3.25710	+	10.0243i	−0.334171	+	1.02847i
$96$		0			0
$97$	−9.60184	+	6.97614i	−0.974919	+	0.708320i	−0.956567	−	0.291512i	$-0.905842\pi$
$97$	−9.60184	+	6.97614i	−0.974919	+	0.708320i	−0.0183516	+	0.999832i	$0.505842\pi$
$98$	−2.81593	−	19.1029i	−0.284452	−	1.92968i
$99$		0			0
$100$	−11.1806	+	3.36945i	−1.11806	+	0.336945i
$101$	−5.24907	−	7.22473i	−0.522302	−	0.718887i	0.463631	−	0.886028i	$-0.346546\pi$
$101$	−5.24907	−	7.22473i	−0.522302	−	0.718887i	−0.985933	+	0.167141i	$0.946546\pi$
$102$		0			0
$103$	−16.7188	−	5.43226i	−1.64735	−	0.535256i	−0.669187	−	0.743094i	$-0.733357\pi$
$103$	−16.7188	−	5.43226i	−1.64735	−	0.535256i	−0.978163	+	0.207838i	$0.933357\pi$
$104$	3.96421	+	0.759330i	0.388723	+	0.0744584i
$105$		0			0
$106$	−3.22648	−	0.546558i	−0.313384	−	0.0530864i
$107$	−0.159322	−	0.490341i	−0.0154022	−	0.0474031i	0.943060	−	0.332623i	$-0.107934\pi$
$107$	−0.159322	−	0.490341i	−0.0154022	−	0.0474031i	−0.958462	+	0.285219i	$0.907934\pi$
$108$		0			0
$109$			1.15068i			0.110215i	0.998480	+	0.0551077i	$0.0175502\pi$
$109$			1.15068i			0.110215i	−0.998480	+	0.0551077i	$0.982450\pi$
$110$	12.7135	−	8.76451i	1.21219	−	0.835663i
$111$		0			0
$112$	6.35376	−	17.0320i	0.600374	−	1.60937i
$113$	2.25825	+	6.95019i	0.212439	+	0.653819i	0.999326	+	0.0367218i	$0.0116915\pi$
$113$	2.25825	+	6.95019i	0.212439	+	0.653819i	−0.786887	+	0.617097i	$0.788308\pi$
$114$		0			0
$115$	6.80157	−	9.36156i	0.634250	−	0.872970i
$116$	−2.34102	+	6.71156i	−0.217358	+	0.623153i
$117$		0			0
$118$	1.65510	+	3.33630i	0.152364	+	0.307131i
$119$	−8.79861	−	12.1103i	−0.806567	−	1.11014i
$120$		0			0
$121$	−6.71273	+	8.71432i	−0.610248	+	0.792211i
$122$	1.66095	−	0.244838i	0.150375	−	0.0221666i
$123$		0			0
$124$	−4.39860	+	3.05381i	−0.395006	+	0.274240i
$125$	0.853187	−	2.62584i	0.0763113	−	0.234862i
$126$		0			0
$127$	9.54190	+	6.93260i	0.846707	+	0.615168i	0.924236	−	0.381822i	$-0.124703\pi$
$127$	9.54190	+	6.93260i	0.846707	+	0.615168i	−0.0775294	+	0.996990i	$0.524703\pi$
$128$	8.57749	−	7.37744i	0.758150	−	0.652080i
$129$		0			0
$130$	−4.74823	+	4.64746i	−0.416447	+	0.407609i
$131$	−1.62443			−0.141927			−0.0709635	−	0.997479i	$-0.522607\pi$
$131$	−1.62443			−0.141927			−0.0709635	+	0.997479i	$0.522607\pi$
$132$		0			0
$133$	14.5499			1.26164
$134$	−6.37623	+	6.24091i	−0.550822	+	0.539132i
$135$		0			0
$136$	−1.16063	−	9.24367i	−0.0995228	−	0.792638i
$137$	−8.56610	−	6.22364i	−0.731852	−	0.531721i	0.158297	−	0.987392i	$-0.449400\pi$
$137$	−8.56610	−	6.22364i	−0.731852	−	0.531721i	−0.890149	+	0.455670i	$0.849400\pi$
$138$		0			0
$139$	2.31508	−	7.12509i	0.196363	−	0.604342i	−0.803595	−	0.595176i	$-0.797082\pi$
$139$	2.31508	−	7.12509i	0.196363	−	0.604342i	0.999958	−	0.00916624i	$-0.00291774\pi$
$140$	17.0655	+	24.5805i	1.44230	+	2.07743i
$141$		0			0
$142$	−0.904468	+	0.133327i	−0.0759013	+	0.0111885i
$143$	2.20766	−	4.18654i	0.184614	−	0.350096i
$144$		0			0
$145$	−6.87751	−	9.46608i	−0.571146	−	0.786115i
$146$	4.29016	+	8.64796i	0.355056	+	0.715710i
$147$		0			0
$148$	0.859904	+	0.299938i	0.0706837	+	0.0246547i
$149$	1.52127	−	2.09385i	0.124628	−	0.171535i	−0.742144	−	0.670240i	$-0.766191\pi$
$149$	1.52127	−	2.09385i	0.124628	−	0.171535i	0.866772	+	0.498705i	$0.166191\pi$
$150$		0			0
$151$	2.79066	+	8.58877i	0.227101	+	0.698944i	0.998072	+	0.0620737i	$0.0197714\pi$
$151$	2.79066	+	8.58877i	0.227101	+	0.698944i	−0.770971	+	0.636870i	$0.780229\pi$
$152$	7.93197	+	4.36848i	0.643368	+	0.354330i
$153$		0			0
$154$	−16.9298	−	12.9524i	−1.36424	−	1.04373i
$155$		−	8.81448i		−	0.707996i
$156$		0			0
$157$	5.48646	+	16.8856i	0.437867	+	1.34762i	0.890120	+	0.455727i	$0.150621\pi$
$157$	5.48646	+	16.8856i	0.437867	+	1.34762i	−0.452252	+	0.891890i	$0.649379\pi$
$158$	−13.5119	−	2.28888i	−1.07495	−	0.182093i
$159$		0			0
$160$	1.92328	+	18.5240i	0.152049	+	1.46445i
$161$	−15.1918	−	4.93611i	−1.19728	−	0.389020i
$162$		0			0
$163$	5.78224	+	7.95857i	0.452900	+	0.623363i	0.973017	−	0.230731i	$-0.0741119\pi$
$163$	5.78224	+	7.95857i	0.452900	+	0.623363i	−0.520118	+	0.854095i	$0.674112\pi$
$164$	5.18085	+	17.1912i	0.404556	+	1.34241i
$165$		0			0
$166$	0.231071	+	1.56755i	0.0179346	+	0.121666i
$167$	−6.02021	+	4.37394i	−0.465858	+	0.338466i	−0.795825	−	0.605527i	$-0.792962\pi$
$167$	−6.02021	+	4.37394i	−0.465858	+	0.338466i	0.329967	+	0.943993i	$0.392962\pi$
$168$		0			0
$169$	3.38793	−	10.4270i	0.260610	−	0.802074i
$170$	13.5886	+	7.10832i	1.04220	+	0.545183i
$171$		0			0
$172$	−0.450651	+	21.0066i	−0.0343618	+	1.60174i
$173$	6.78760	−	2.20542i	0.516052	−	0.167675i	−0.0394011	−	0.999223i	$-0.512545\pi$
$173$	6.78760	−	2.20542i	0.516052	−	0.167675i	0.555453	+	0.831548i	$0.312545\pi$
$174$		0			0
$175$	−26.5345			−2.00582
$176$	−5.34057	−	12.1441i	−0.402561	−	0.915393i
$177$		0			0
$178$	16.0810	+	16.4296i	1.20532	+	1.23145i
$179$	−21.7851	+	7.07840i	−1.62829	+	0.529064i	−0.973878	−	0.227072i	$-0.927085\pi$
$179$	−21.7851	+	7.07840i	−1.62829	+	0.529064i	−0.654414	+	0.756136i	$0.727085\pi$
$180$		0			0
$181$	8.57223	+	6.22809i	0.637169	+	0.462930i	0.858876	−	0.512183i	$-0.171163\pi$
$181$	8.57223	+	6.22809i	0.637169	+	0.462930i	−0.221707	+	0.975113i	$0.571163\pi$
$182$	8.12693	+	4.25127i	0.602408	+	0.315125i
$183$		0			0
$184$	−6.79987	−	7.25214i	−0.501293	−	0.534635i
$185$	−1.21282	+	0.881166i	−0.0891683	+	0.0647846i
$186$		0			0
$187$	−10.7647	−	1.86011i	−0.787196	−	0.136025i
$188$	−1.98416	−	6.58387i	−0.144709	−	0.480178i
$189$		0			0
$190$	−13.3532	+	6.62440i	−0.968745	+	0.480584i
$191$	10.1007	+	3.28193i	0.730863	+	0.237472i	0.650727	−	0.759312i	$-0.274464\pi$
$191$	10.1007	+	3.28193i	0.730863	+	0.237472i	0.0801365	+	0.996784i	$0.474464\pi$
$192$		0			0
$193$	14.9881	−	20.6293i	1.07887	−	1.48493i	0.218102	−	0.975926i	$-0.430014\pi$
$193$	14.9881	−	20.6293i	1.07887	−	1.48493i	0.860764	−	0.509005i	$-0.169986\pi$
$194$	−16.5489	−	2.80333i	−1.18814	−	0.201268i
$195$		0			0
$196$	16.5211	−	21.7429i	1.18008	−	1.55306i
$197$		−	7.36121i		−	0.524464i	−0.965005	−	0.262232i	$-0.915541\pi$
$197$		−	7.36121i		−	0.524464i	0.965005	−	0.262232i	$-0.0844586\pi$
$198$		0			0
$199$		−	15.2259i		−	1.07934i	−0.841878	−	0.539668i	$-0.818550\pi$
$199$		−	15.2259i		−	1.07934i	0.841878	−	0.539668i	$-0.181450\pi$
$200$	−14.4654	−	7.96673i	−1.02286	−	0.563333i
$201$		0			0
$202$	2.10932	−	12.4519i	0.148411	−	0.876112i
$203$	−9.49387	+	13.0672i	−0.666339	+	0.917137i
$204$		0			0
$205$	−28.1091	−	9.13320i	−1.96323	−	0.637891i
$206$	−11.0483	−	22.2708i	−0.769772	−	1.55168i
$207$		0			0
$208$	3.15404	+	4.75764i	0.218693	+	0.329883i
$209$	7.61290	−	7.40226i	0.526595	−	0.512025i
$210$		0			0
$211$	−11.6671	+	8.47664i	−0.803196	+	0.583556i	−0.911850	−	0.410524i	$-0.865346\pi$
$211$	−11.6671	+	8.47664i	−0.803196	+	0.583556i	0.108654	+	0.994080i	$0.465346\pi$
$212$	−2.63931	−	3.80157i	−0.181268	−	0.261093i
$213$		0			0
$214$	0.337968	−	0.646076i	0.0231030	−	0.0441648i
$215$	−27.9815	−	20.3298i	−1.90832	−	1.38648i
$216$		0			0
$217$	−11.5722	+	3.76003i	−0.785571	+	0.255247i
$218$	−1.16296	+	1.13828i	−0.0787653	+	0.0770937i
$219$		0			0
$220$	21.4344	+	4.17912i	1.44511	+	0.281756i
$221$	4.70037			0.316181
$222$		0			0
$223$	−20.9700	+	6.81357i	−1.40425	+	0.456270i	−0.910564	−	0.413368i	$-0.864352\pi$
$223$	−20.9700	+	6.81357i	−1.40425	+	0.456270i	−0.493691	+	0.869638i	$0.664352\pi$
$224$	23.4990	−	10.4268i	1.57009	−	0.696673i
$225$		0			0
$226$	−4.79042	+	9.15760i	−0.318654	+	0.609154i
$227$	7.04025	−	21.6676i	0.467278	−	1.43813i	−0.388818	−	0.921315i	$-0.627116\pi$
$227$	7.04025	−	21.6676i	0.467278	−	1.43813i	0.856095	−	0.516818i	$-0.172884\pi$
$228$		0			0
$229$	5.40049	−	3.92369i	0.356875	−	0.259285i	−0.394873	−	0.918736i	$-0.629211\pi$
$229$	5.40049	−	3.92369i	0.356875	−	0.259285i	0.751747	+	0.659451i	$0.229211\pi$
$230$	16.1897	−	2.38650i	1.06751	−	0.157361i
$231$		0			0
$232$	−9.09894	+	4.27321i	−0.597374	+	0.280550i
$233$	2.93304	+	4.03698i	0.192150	+	0.264471i	0.894212	−	0.447645i	$-0.147737\pi$
$233$	2.93304	+	4.03698i	0.192150	+	0.264471i	−0.702062	+	0.712116i	$0.747737\pi$
$234$		0			0
$235$	10.7652	+	3.49782i	0.702244	+	0.228173i
$236$	−1.73463	+	4.97308i	−0.112915	+	0.323720i
$237$		0			0
$238$	3.53569	−	20.8721i	0.229185	−	1.35294i
$239$	0.333992	+	1.02792i	0.0216042	+	0.0664908i	0.961277	−	0.275583i	$-0.0888708\pi$
$239$	0.333992	+	1.02792i	0.0216042	+	0.0664908i	−0.939673	+	0.342074i	$0.888871\pi$
$240$		0			0
$241$		−	1.92559i		−	0.124038i	−0.998075	−	0.0620192i	$-0.980246\pi$
$241$		−	1.92559i		−	0.124038i	0.998075	−	0.0620192i	$-0.0197540\pi$
$242$	−15.4476	+	1.83603i	−0.993011	+	0.118024i
$243$		0			0
$244$	1.89049	+	1.43647i	0.121026	+	0.0919603i
$245$	13.8906	+	42.7509i	0.887439	+	2.73126i
$246$		0			0
$247$	−2.68544	+	3.69620i	−0.170871	+	0.235183i
$248$	−7.43755	−	1.42464i	−0.472285	−	0.0904644i
$249$		0			0
$250$	3.49784	−	1.73524i	0.221223	−	0.109746i
$251$	7.31555	+	10.0690i	0.461754	+	0.635549i	0.974871	−	0.222769i	$-0.0715095\pi$
$251$	7.31555	+	10.0690i	0.461754	+	0.635549i	−0.513118	+	0.858318i	$0.671510\pi$
$252$		0			0
$253$	−10.4600	+	5.14611i	−0.657614	+	0.323533i
$254$	2.43247	+	16.5015i	0.152627	+	1.03540i
$255$		0			0
$256$	15.9411	+	1.37109i	0.996322	+	0.0856929i
$257$	−2.72942	+	8.40029i	−0.170257	+	0.523996i	−0.999385	−	0.0350621i	$-0.988837\pi$
$257$	−2.72942	+	8.40029i	−0.170257	+	0.523996i	0.829129	+	0.559058i	$0.188837\pi$
$258$		0			0
$259$	1.67421	+	1.21638i	0.104030	+	0.0755822i
$260$	−9.39407	−	0.201529i	−0.582595	−	0.0124983i
$261$		0			0
$262$	−1.60692	−	1.64176i	−0.0992755	−	0.101428i
$263$	−1.43738			−0.0886326			−0.0443163	−	0.999018i	$-0.514111\pi$
$263$	−1.43738			−0.0886326			−0.0443163	+	0.999018i	$0.514111\pi$
$264$		0			0
$265$	7.61808			0.467975
$266$	14.3930	+	14.7051i	0.882494	+	0.901629i
$267$		0			0
$268$	−12.6150	−	0.270626i	−0.770581	−	0.0165311i
$269$	−1.66385	−	1.20886i	−0.101447	−	0.0737055i	0.535905	−	0.844278i	$-0.319970\pi$
$269$	−1.66385	−	1.20886i	−0.101447	−	0.0737055i	−0.637352	+	0.770573i	$0.719970\pi$
$270$		0			0
$271$	2.13419	−	6.56835i	0.129643	−	0.398999i	−0.865076	−	0.501641i	$-0.832730\pi$
$271$	2.13419	−	6.56835i	0.129643	−	0.398999i	0.994718	+	0.102642i	$0.0327297\pi$
$272$	8.19416	−	10.3170i	0.496844	−	0.625561i
$273$		0			0
$274$	−2.18372	−	14.8140i	−0.131923	−	0.894947i
$275$	−13.8835	+	13.4994i	−0.837209	+	0.814045i
$276$		0			0
$277$	−11.0982	−	15.2753i	−0.666824	−	0.917804i	0.332859	−	0.942976i	$-0.391987\pi$
$277$	−11.0982	−	15.2753i	−0.666824	−	0.917804i	−0.999683	+	0.0251724i	$0.991987\pi$
$278$	9.49122	−	4.70849i	0.569245	−	0.282397i
$279$		0			0
$280$	−7.96125	+	41.5630i	−0.475775	+	2.48387i
$281$	7.98872	−	10.9955i	0.476567	−	0.655938i	−0.501274	−	0.865289i	$-0.667135\pi$
$281$	7.98872	−	10.9955i	0.476567	−	0.655938i	0.977841	+	0.209350i	$0.0671349\pi$
$282$		0			0
$283$	5.97209	+	18.3802i	0.355004	+	1.09259i	0.956007	+	0.293344i	$0.0947680\pi$
$283$	5.97209	+	18.3802i	0.355004	+	1.09259i	−0.601003	+	0.799247i	$0.705232\pi$
$284$	−1.02947	−	0.782227i	−0.0610875	−	0.0464166i
$285$		0			0
$286$	6.41505	−	1.91019i	0.379330	−	0.112952i
$287$			40.7993i			2.40831i
$288$		0			0
$289$	1.90074	+	5.84989i	0.111809	+	0.344111i
$290$	2.76370	−	16.3149i	0.162290	−	0.958043i
$291$		0			0
$292$	−4.49630	+	12.8906i	−0.263126	+	0.754367i
$293$	−15.0360	−	4.88550i	−0.878414	−	0.285414i	−0.165115	−	0.986274i	$-0.552800\pi$
$293$	−15.0360	−	4.88550i	−0.878414	−	0.285414i	−0.713298	+	0.700860i	$0.752800\pi$
$294$		0			0
$295$	−5.09604	−	7.01410i	−0.296703	−	0.408377i
$296$	0.547495	+	1.16578i	0.0318225	+	0.0677596i
$297$		0			0
$298$	3.62106	−	0.533776i	0.209762	−	0.0309208i
$299$	4.05786	−	2.94821i	0.234672	−	0.170499i
$300$		0			0
$301$	−14.7539	+	45.4080i	−0.850403	+	2.61727i
$302$	−5.91981	+	11.3166i	−0.340647	+	0.651197i
$303$		0			0
$304$	3.43138	+	12.3380i	0.196803	+	0.707630i
$305$	−3.71708	+	1.20775i	−0.212840	+	0.0691558i
$306$		0			0
$307$	25.7118			1.46745			0.733725	−	0.679446i	$-0.237780\pi$
$307$	25.7118			1.46745			0.733725	+	0.679446i	$0.237780\pi$
$308$	−3.65677	−	29.9231i	−0.208364	−	1.70503i
$309$		0			0
$310$	8.90851	−	8.71944i	0.505969	−	0.495231i
$311$	29.4939	−	9.58316i	1.67245	−	0.543411i	0.689025	−	0.724738i	$-0.258039\pi$
$311$	29.4939	−	9.58316i	1.67245	−	0.543411i	0.983423	+	0.181326i	$0.0580390\pi$
$312$		0			0
$313$	−9.77635	−	7.10293i	−0.552592	−	0.401481i	0.276148	−	0.961115i	$-0.410942\pi$
$313$	−9.77635	−	7.10293i	−0.552592	−	0.401481i	−0.828740	+	0.559634i	$0.810942\pi$
$314$	−11.6384	+	22.2485i	−0.656793	+	1.25556i
$315$		0			0
$316$	−11.0529	−	15.9202i	−0.621775	−	0.895583i
$317$	27.1151	−	19.7003i	1.52294	−	1.10648i	0.562929	−	0.826505i	$-0.309674\pi$
$317$	27.1151	−	19.7003i	1.52294	−	1.10648i	0.960008	−	0.279974i	$-0.0903257\pi$
$318$		0			0
$319$	1.68048	+	11.6671i	0.0940889	+	0.653232i
$320$	−16.8190	+	20.2680i	−0.940212	+	1.13302i
$321$		0			0
$322$	−10.0392	−	20.2367i	−0.559464	−	1.12775i
$323$	10.0291	+	3.25866i	0.558036	+	0.181317i
$324$		0			0
$325$	4.89741	−	6.74071i	0.271659	−	0.373907i
$326$	−2.32357	+	13.7167i	−0.128691	+	0.759697i
$327$		0			0
$328$	−12.2496	+	22.2420i	−0.676371	+	1.22811i
$329$		−	15.6253i		−	0.861449i
$330$		0			0
$331$		−	24.0830i		−	1.32372i	−0.749626	−	0.661861i	$-0.769767\pi$
$331$		−	24.0830i		−	1.32372i	0.749626	−	0.661861i	$-0.230233\pi$
$332$	−1.35569	+	1.78419i	−0.0744034	+	0.0979200i
$333$		0			0
$334$	−10.3759	−	1.75765i	−0.567744	−	0.0961744i
$335$	12.2085	−	16.8035i	0.667021	−	0.918075i
$336$		0			0
$337$	−8.75821	−	2.84572i	−0.477090	−	0.155016i	0.0605937	−	0.998163i	$-0.480701\pi$
$337$	−8.75821	−	2.84572i	−0.477090	−	0.155016i	−0.537684	+	0.843147i	$0.680701\pi$
$338$	13.8896	−	6.89047i	0.755494	−	0.374792i
$339$		0			0
$340$	6.25794	+	20.7652i	0.339384	+	1.12615i
$341$	−4.14195	+	7.85468i	−0.224299	+	0.425355i
$342$		0			0
$343$	24.4638	−	17.7740i	1.32092	−	0.959704i
$344$	−21.6765	+	20.3247i	−1.16872	+	1.09583i
$345$		0			0
$346$	8.94336	+	4.67836i	0.480798	+	0.251510i
$347$	27.8132	+	20.2074i	1.49309	+	1.08479i	0.973035	+	0.230659i	$0.0740883\pi$
$347$	27.8132	+	20.2074i	1.49309	+	1.08479i	0.520054	+	0.854133i	$0.325912\pi$
$348$		0			0
$349$	16.7485	−	5.44191i	0.896525	−	0.291299i	0.175723	−	0.984440i	$-0.443774\pi$
$349$	16.7485	−	5.44191i	0.896525	−	0.291299i	0.720802	+	0.693141i	$0.243774\pi$
$350$	−26.2484	−	26.8175i	−1.40304	−	1.43346i
$351$		0			0
$352$	6.99062	−	17.4107i	0.372601	−	0.927992i
$353$	−28.4766			−1.51565			−0.757827	−	0.652455i	$-0.773739\pi$
$353$	−28.4766			−1.51565			−0.757827	+	0.652455i	$0.773739\pi$
$354$		0			0
$355$	2.02414	−	0.657682i	0.107430	−	0.0349061i
$356$	−0.697324	+	32.5050i	−0.0369581	+	1.72276i
$357$		0			0
$358$	−28.7041	−	15.0154i	−1.51706	−	0.793587i
$359$	6.72849	−	20.7082i	0.355116	−	1.09294i	−0.600826	−	0.799380i	$-0.705161\pi$
$359$	6.72849	−	20.7082i	0.355116	−	1.09294i	0.955942	−	0.293556i	$-0.0948386\pi$
$360$		0			0
$361$	7.07892	−	5.14314i	0.372575	−	0.270692i
$362$	2.18528	+	14.8246i	0.114856	+	0.779164i
$363$		0			0
$364$	3.74269	+	12.4191i	0.196170	+	0.650936i
$365$	−13.2094	−	18.1811i	−0.691409	−	0.951643i
$366$		0			0
$367$	27.1565	+	8.82369i	1.41756	+	0.460593i	0.914826	−	0.403848i	$-0.132328\pi$
$367$	27.1565	+	8.82369i	1.41756	+	0.460593i	0.502734	+	0.864441i	$0.332328\pi$
$368$	0.602945	−	14.0464i	0.0314307	−	0.732217i
$369$		0			0
$370$	−2.09031	−	0.354093i	−0.108670	−	0.0184084i
$371$	−3.24967	−	10.0015i	−0.168715	−	0.519250i
$372$		0			0
$373$		−	32.5424i		−	1.68498i	−0.538712	−	0.842490i	$-0.681089\pi$
$373$		−	32.5424i		−	1.68498i	0.538712	−	0.842490i	$-0.318911\pi$
$374$	−8.76872	−	12.7196i	−0.453420	−	0.657716i
$375$		0			0
$376$	4.69134	−	8.51821i	0.241937	−	0.439293i
$377$	−1.56727	−	4.82356i	−0.0807185	−	0.248426i
$378$		0			0
$379$	9.49522	−	13.0690i	0.487737	−	0.671312i	−0.492232	−	0.870464i	$-0.663819\pi$
$379$	9.49522	−	13.0690i	0.487737	−	0.671312i	0.979969	+	0.199152i	$0.0638188\pi$
$380$	−19.9043	−	6.94270i	−1.02107	−	0.356153i
$381$		0			0
$382$	6.67489	+	13.4550i	0.341517	+	0.688418i
$383$	−10.2544	−	14.1139i	−0.523974	−	0.721188i	0.462223	−	0.886764i	$-0.347052\pi$
$383$	−10.2544	−	14.1139i	−0.523974	−	0.721188i	−0.986197	+	0.165575i	$0.947052\pi$
$384$		0			0
$385$	43.8941	+	23.1464i	2.23705	+	1.17965i
$386$	35.6758	−	5.25894i	1.81585	−	0.267673i
$387$		0			0
$388$	−13.5372	−	19.4985i	−0.687247	−	0.989887i
$389$	−10.7040	+	32.9437i	−0.542717	+	1.67031i	0.183641	+	0.982993i	$0.441211\pi$
$389$	−10.7040	+	32.9437i	−0.542717	+	1.67031i	−0.726358	+	0.687317i	$0.758789\pi$
$390$		0			0
$391$	−9.36606	−	6.80484i	−0.473662	−	0.344136i
$392$	38.3178	−	4.81114i	1.93534	−	0.242999i
$393$		0			0
$394$	7.43973	−	7.28184i	0.374808	−	0.366854i
$395$	31.9030			1.60522
$396$		0			0
$397$	34.3247			1.72271			0.861354	−	0.508005i	$-0.169617\pi$
$397$	34.3247			1.72271			0.861354	+	0.508005i	$0.169617\pi$
$398$	15.3883	−	15.0617i	0.771347	−	0.754977i
$399$		0			0
$400$	−6.25775	−	22.5006i	−0.312888	−	1.12503i
$401$	18.7900	+	13.6517i	0.938329	+	0.681736i	0.948018	−	0.318217i	$-0.103084\pi$
$401$	18.7900	+	13.6517i	0.938329	+	0.681736i	−0.00968917	+	0.999953i	$0.503084\pi$
$402$		0			0
$403$	1.18067	−	3.63372i	0.0588133	−	0.181009i
$404$	14.6713	−	10.1858i	0.729924	−	0.506763i
$405$		0			0
$406$	−22.5981	+	3.33116i	−1.12152	+	0.165323i
$407$	1.49482	−	0.215308i	0.0740955	−	0.0106724i
$408$		0			0
$409$	18.0110	+	24.7900i	0.890588	+	1.22579i	0.973374	+	0.229222i	$0.0736181\pi$
$409$	18.0110	+	24.7900i	0.890588	+	1.22579i	−0.0827865	+	0.996567i	$0.526382\pi$
$410$	−18.5754	−	37.4437i	−0.917374	−	1.84921i
$411$		0			0
$412$	11.5792	−	33.1968i	0.570465	−	1.63549i
$413$	−7.03470	+	9.68243i	−0.346155	+	0.476441i
$414$		0			0
$415$	−1.13984	−	3.50807i	−0.0559527	−	0.172205i
$416$	−1.68836	+	7.89403i	−0.0827786	+	0.387036i
$417$		0			0
$418$	15.0120	+	0.371657i	0.734263	+	0.0181784i
$419$		−	19.7469i		−	0.964701i	−0.875978	−	0.482350i	$-0.839783\pi$
$419$		−	19.7469i		−	0.964701i	0.875978	−	0.482350i	$-0.160217\pi$
$420$		0			0
$421$	6.95732	+	21.4124i	0.339079	+	1.04358i	0.964678	+	0.263433i	$0.0848548\pi$
$421$	6.95732	+	21.4124i	0.339079	+	1.04358i	−0.625599	+	0.780145i	$0.715145\pi$
$422$	−20.1084	−	3.40630i	−0.978860	−	0.165816i
$423$		0			0
$424$	1.23127	−	6.42804i	0.0597956	−	0.312173i
$425$	−18.2900	−	5.94278i	−0.887196	−	0.288267i
$426$		0			0
$427$	3.17122	+	4.36481i	0.153466	+	0.211228i
$428$	0.987292	−	0.297536i	0.0477225	−	0.0143820i
$429$		0			0
$430$	−7.13320	−	48.3906i	−0.343993	−	2.33360i
$431$	−5.38269	+	3.91076i	−0.259275	+	0.188374i	−0.709827	−	0.704376i	$-0.751227\pi$
$431$	−5.38269	+	3.91076i	−0.259275	+	0.188374i	0.450552	+	0.892750i	$0.351227\pi$
$432$		0			0
$433$	−5.78193	+	17.7950i	−0.277862	+	0.855171i	0.710586	+	0.703610i	$0.248430\pi$
$433$	−5.78193	+	17.7950i	−0.277862	+	0.855171i	−0.988448	+	0.151561i	$0.951570\pi$
$434$	−15.2475	−	7.97613i	−0.731906	−	0.382867i
$435$		0			0
$436$	−2.30083	−	0.0493594i	−0.110190	−	0.00236389i
$437$	10.7021	−	3.47734i	0.511953	−	0.166344i
$438$		0			0
$439$	−35.7973			−1.70851			−0.854256	−	0.519853i	$-0.825987\pi$
$439$	−35.7973			−1.70851			−0.854256	+	0.519853i	$0.825987\pi$
$440$	16.9796	+	25.7971i	0.809472	+	1.22983i
$441$		0			0
$442$	4.64969	+	4.75051i	0.221163	+	0.225959i
$443$	1.11072	−	0.360895i	0.0527719	−	0.0171466i	−0.282512	−	0.959264i	$-0.591168\pi$
$443$	1.11072	−	0.360895i	0.0527719	−	0.0171466i	0.335284	+	0.942117i	$0.391168\pi$
$444$		0			0
$445$	−43.2977	−	31.4576i	−2.05251	−	1.49123i
$446$	−27.6301	−	14.4536i	−1.30833	−	0.684397i
$447$		0			0
$448$	33.7837	+	13.4352i	1.59613	+	0.634754i
$449$	−10.6588	+	7.74407i	−0.503020	+	0.365465i	−0.810169	−	0.586196i	$-0.800625\pi$
$449$	−10.6588	+	7.74407i	−0.503020	+	0.365465i	0.307149	+	0.951661i	$0.400625\pi$
$450$		0			0
$451$	20.7566	+	21.3473i	0.977391	+	1.00520i
$452$	−13.9941	+	4.21734i	−0.658225	+	0.198367i
$453$		0			0
$454$	28.8631	−	14.3187i	1.35461	−	0.672009i
$455$	−20.3062	−	6.59789i	−0.951971	−	0.309314i
$456$		0			0
$457$	−4.63542	+	6.38011i	−0.216836	+	0.298449i	−0.903554	−	0.428475i	$-0.859051\pi$
$457$	−4.63542	+	6.38011i	−0.216836	+	0.298449i	0.686718	+	0.726924i	$0.259051\pi$
$458$	9.30781	+	1.57672i	0.434925	+	0.0736752i
$459$		0			0
$460$	18.4271	+	14.0016i	0.859166	+	0.652827i
$461$		−	15.7440i		−	0.733269i	−0.930365	−	0.366635i	$-0.880510\pi$
$461$		−	15.7440i		−	0.733269i	0.930365	−	0.366635i	$-0.119490\pi$
$462$		0			0
$463$			28.0352i			1.30291i	0.758688	+	0.651454i	$0.225841\pi$
$463$			28.0352i			1.30291i	−0.758688	+	0.651454i	$0.774159\pi$
$464$	−13.3196	−	4.96886i	−0.618348	−	0.230674i
$465$		0			0
$466$	−1.17863	+	6.95777i	−0.0545989	+	0.322313i
$467$	−1.46797	+	2.02049i	−0.0679297	+	0.0934973i	−0.841630	−	0.540054i	$-0.818404\pi$
$467$	−1.46797	+	2.02049i	−0.0679297	+	0.0934973i	0.773700	+	0.633552i	$0.218404\pi$
$468$		0			0
$469$	−27.2685	−	8.86008i	−1.25914	−	0.409120i
$470$	7.11399	+	14.3401i	0.328144	+	0.661461i
$471$		0			0
$472$	−6.74206	+	3.16633i	−0.310328	+	0.145742i
$473$	15.3816	+	31.2647i	0.707247	+	1.43755i
$474$		0			0
$475$	15.1227	−	10.9873i	0.693879	−	0.504132i
$476$	24.5924	−	17.0737i	1.12719	−	0.782572i
$477$		0			0
$478$	−0.708496	+	1.35439i	−0.0324059	+	0.0619485i
$479$	5.94112	+	4.31647i	0.271457	+	0.197225i	0.715182	−	0.698938i	$-0.246344\pi$
$479$	5.94112	+	4.31647i	0.271457	+	0.197225i	−0.443726	+	0.896163i	$0.646344\pi$
$480$		0			0
$481$	−0.618008	+	0.200803i	−0.0281787	+	0.00915583i
$482$	1.94613	−	1.90483i	0.0886440	−	0.0867627i
$483$		0			0
$484$	−17.1367	−	13.7962i	−0.778940	−	0.627099i
$485$	39.0737			1.77424
$486$		0			0
$487$	16.4772	−	5.35378i	0.746655	−	0.242603i	0.0891135	−	0.996021i	$-0.471597\pi$
$487$	16.4772	−	5.35378i	0.746655	−	0.242603i	0.657541	+	0.753419i	$0.271597\pi$
$488$	0.418316	+	3.33163i	0.0189363	+	0.150816i
$489$		0			0
$490$	−29.4661	+	56.3288i	−1.33114	+	2.54467i
$491$	−3.30378	+	10.1680i	−0.149098	+	0.458875i	−0.997515	−	0.0704524i	$-0.977556\pi$
$491$	−3.30378	+	10.1680i	−0.149098	+	0.458875i	0.848418	+	0.529328i	$0.177556\pi$
$492$		0			0
$493$	−9.47063	+	6.88082i	−0.426536	+	0.309896i
$494$	−6.39211	+	0.942254i	−0.287595	+	0.0423940i
$495$		0			0
$496$	−5.91753	−	8.92616i	−0.265705	−	0.400797i
$497$	−1.72689	−	2.37686i	−0.0774616	−	0.106617i
$498$		0			0
$499$	−36.1595	−	11.7489i	−1.61872	−	0.525955i	−0.647083	−	0.762420i	$-0.724011\pi$
$499$	−36.1595	−	11.7489i	−1.61872	−	0.525955i	−0.971640	+	0.236465i	$0.924011\pi$
$500$	5.21387	+	1.81862i	0.233171	+	0.0813311i
$501$		0			0
$502$	−2.93973	+	17.3540i	−0.131206	+	0.774548i
$503$	13.5200	+	41.6103i	0.602828	+	1.85531i	0.511085	+	0.859530i	$0.329244\pi$
$503$	13.5200	+	41.6103i	0.602828	+	1.85531i	0.0917431	+	0.995783i	$0.470756\pi$
$504$		0			0
$505$			29.4003i			1.30829i
$506$	−15.5482	−	5.48094i	−0.691202	−	0.243657i
$507$		0			0
$508$	−14.2713	+	18.7820i	−0.633187	+	0.833318i
$509$	−9.53129	−	29.3343i	−0.422467	−	1.30022i	−0.905399	−	0.424562i	$-0.860428\pi$
$509$	−9.53129	−	29.3343i	−0.422467	−	1.30022i	0.482932	−	0.875658i	$-0.339572\pi$
$510$		0			0
$511$	−18.2345	+	25.0976i	−0.806647	+	1.11025i
$512$	14.3836	+	17.4675i	0.635669	+	0.771961i
$513$		0			0
$514$	−11.1899	+	5.55118i	−0.493565	+	0.244852i
$515$	34.0176	+	46.8213i	1.49900	+	2.06319i
$516$		0			0
$517$	−7.94934	−	8.17555i	−0.349612	−	0.359560i
$518$	0.426797	+	2.89533i	0.0187524	+	0.127213i
$519$		0			0
$520$	−9.08910	−	9.69363i	−0.398583	−	0.425094i
$521$	5.30038	−	16.3129i	0.232214	−	0.714681i	−0.765265	−	0.643715i	$-0.777392\pi$
$521$	5.30038	−	16.3129i	0.232214	−	0.714681i	0.997479	−	0.0709652i	$-0.0226079\pi$
$522$		0			0
$523$	−5.52497	−	4.01412i	−0.241590	−	0.175525i	0.460401	−	0.887711i	$-0.347705\pi$
$523$	−5.52497	−	4.01412i	−0.241590	−	0.175525i	−0.701991	+	0.712186i	$0.747705\pi$
$524$	0.0696812	−	3.24811i	0.00304404	−	0.141894i
$525$		0			0
$526$	−1.42188	−	1.45271i	−0.0619969	−	0.0633412i
$527$	−8.81872			−0.384149
$528$		0			0
$529$	10.6460			0.462871
$530$	7.53594	+	7.69934i	0.327340	+	0.334438i
$531$		0			0
$532$	−0.624130	+	29.0932i	−0.0270595	+	1.26135i
$533$	−10.3645	−	7.53023i	−0.448935	−	0.326170i
$534$		0			0
$535$	−0.524520	+	1.61431i	−0.0226770	+	0.0697925i
$536$	−12.2054	−	13.0172i	−0.527194	−	0.562259i
$537$		0			0
$538$	−0.424158	−	2.87743i	−0.0182868	−	0.124055i
$539$	7.71072	−	44.6231i	0.332124	−	1.92205i
$540$		0			0
$541$	−16.6098	−	22.8614i	−0.714111	−	0.982890i	−0.999699	−	0.0245371i	$-0.992189\pi$
$541$	−16.6098	−	22.8614i	−0.714111	−	0.982890i	0.285588	−	0.958353i	$-0.407811\pi$
$542$	8.74960	−	4.34058i	0.375827	−	0.186444i
$543$		0			0
$544$	18.5329	−	1.92420i	0.794590	−	0.0824995i
$545$	2.22670	−	3.06479i	0.0953813	−	0.131281i
$546$		0			0
$547$	−5.25161	−	16.1628i	−0.224543	−	0.691071i	−0.998338	−	0.0576351i	$-0.981644\pi$
$547$	−5.25161	−	16.1628i	−0.224543	−	0.691071i	0.773795	−	0.633436i	$-0.218356\pi$
$548$	12.8119	−	16.8613i	0.547296	−	0.720279i
$549$		0			0
$550$	−27.3772	−	0.677786i	−1.16737	−	0.0289009i
$551$		−	11.3785i		−	0.484742i
$552$		0			0
$553$	−13.6090	−	41.8842i	−0.578714	−	1.78110i
$554$	4.45975	−	26.3271i	0.189477	−	1.11853i
$555$		0			0
$556$	14.1476	+	4.93474i	0.599992	+	0.209279i
$557$	23.7257	+	7.70896i	1.00529	+	0.326639i	0.764978	−	0.644056i	$-0.222750\pi$
$557$	23.7257	+	7.70896i	1.00529	+	0.326639i	0.240314	+	0.970695i	$0.422750\pi$
$558$		0			0
$559$	−8.81214	−	12.1289i	−0.372714	−	0.512996i
$560$	−49.8818	+	33.0687i	−2.10789	+	1.39741i
$561$		0			0
$562$	19.0154	−	2.80304i	0.802117	−	0.118239i
$563$	−17.5519	+	12.7522i	−0.739724	+	0.537441i	−0.892625	−	0.450800i	$-0.851139\pi$
$563$	−17.5519	+	12.7522i	−0.739724	+	0.537441i	0.152900	+	0.988242i	$0.451139\pi$
$564$		0			0
$565$	7.43465	−	22.8815i	0.312778	−	0.962631i
$566$	−12.6686	+	24.2178i	−0.532500	+	1.01795i
$567$		0			0
$568$	−0.227794	−	1.81424i	−0.00955803	−	0.0761238i
$569$	−26.6537	+	8.66031i	−1.11738	+	0.363059i	−0.808768	−	0.588128i	$-0.799865\pi$
$569$	−26.6537	+	8.66031i	−1.11738	+	0.363059i	−0.308614	+	0.951187i	$0.599865\pi$
$570$		0			0
$571$	30.5486			1.27842			0.639209	−	0.769033i	$-0.279262\pi$
$571$	30.5486			1.27842			0.639209	+	0.769033i	$0.279262\pi$
$572$	8.27646	+	4.59389i	0.346056	+	0.192080i
$573$		0			0
$574$	−41.2345	+	40.3594i	−1.72110	+	1.68457i
$575$	−19.5174	+	6.34158i	−0.813930	+	0.264462i
$576$		0			0
$577$	10.7807	+	7.83261i	0.448805	+	0.326076i	0.789124	−	0.614234i	$-0.210535\pi$
$577$	10.7807	+	7.83261i	0.448805	+	0.326076i	−0.340319	+	0.940310i	$0.610535\pi$
$578$	−4.03204	+	7.70784i	−0.167711	+	0.320604i
$579$		0			0
$580$	19.2228	−	13.3458i	0.798184	−	0.554154i
$581$	−4.11938	+	2.99291i	−0.170901	+	0.124167i
$582$		0			0
$583$	−6.78855	−	3.57976i	−0.281153	−	0.148258i
$584$	−17.4760	+	8.20738i	−0.723160	+	0.339624i
$585$		0			0
$586$	−9.93629	−	20.0292i	−0.410464	−	0.827400i
$587$	−28.4389	−	9.24035i	−1.17380	−	0.381390i	−0.343739	−	0.939065i	$-0.611694\pi$
$587$	−28.4389	−	9.24035i	−1.17380	−	0.381390i	−0.830059	+	0.557675i	$0.811694\pi$
$588$		0			0
$589$	5.03836	−	6.93471i	0.207602	−	0.285740i
$590$	2.04782	−	12.0889i	0.0843076	−	0.497691i
$591$		0			0
$592$	−0.636624	+	1.70655i	−0.0261651	+	0.0701387i
$593$			22.1335i			0.908914i	0.890769	+	0.454457i	$0.150167\pi$
$593$			22.1335i			0.908914i	−0.890769	+	0.454457i	$0.849833\pi$
$594$		0			0
$595$			49.2814i			2.02034i
$596$	4.12149	+	3.13166i	0.168823	+	0.128278i
$597$		0			0
$598$	6.99377	+	1.18473i	0.285996	+	0.0484470i
$599$	21.8597	−	30.0873i	0.893162	−	1.22933i	−0.0794359	−	0.996840i	$-0.525312\pi$
$599$	21.8597	−	30.0873i	0.893162	−	1.22933i	0.972598	−	0.232492i	$-0.0746881\pi$
$600$		0			0
$601$	−6.83308	−	2.22020i	−0.278727	−	0.0905640i	0.166318	−	0.986072i	$-0.446812\pi$
$601$	−6.83308	−	2.22020i	−0.278727	−	0.0905640i	−0.445045	+	0.895508i	$0.646812\pi$
$602$	−60.4872	+	30.0071i	−2.46527	+	1.22300i
$603$		0			0
$604$	−17.2933	+	5.21161i	−0.703654	+	0.212058i
$605$	34.7422	−	10.2203i	1.41247	−	0.415514i
$606$		0			0
$607$	−2.80811	+	2.04021i	−0.113978	+	0.0828098i	−0.643314	−	0.765602i	$-0.722441\pi$
$607$	−2.80811	+	2.04021i	−0.113978	+	0.0828098i	0.529336	+	0.848412i	$0.322441\pi$
$608$	−9.07519	+	15.6729i	−0.368047	+	0.635620i
$609$		0			0
$610$	−4.89764	−	2.56200i	−0.198300	−	0.103732i
$611$	3.96937	+	2.88392i	0.160584	+	0.116671i
$612$		0			0
$613$	−25.6464	+	8.33301i	−1.03585	+	0.336567i	−0.777100	−	0.629378i	$-0.783310\pi$
$613$	−25.6464	+	8.33301i	−1.03585	+	0.336567i	−0.258748	+	0.965945i	$0.583310\pi$
$614$	25.4346	+	25.9861i	1.02646	+	1.04871i
$615$		0			0
$616$	26.6250	−	33.2963i	1.07275	−	1.34154i
$617$	2.41944			0.0974030			0.0487015	−	0.998813i	$-0.484492\pi$
$617$	2.41944			0.0974030			0.0487015	+	0.998813i	$0.484492\pi$
$618$		0			0
$619$	4.31562	−	1.40223i	0.173459	−	0.0563604i	−0.221000	−	0.975274i	$-0.570932\pi$
$619$	4.31562	−	1.40223i	0.173459	−	0.0563604i	0.394459	+	0.918913i	$0.370932\pi$
$620$	17.6249	+	0.378104i	0.707833	+	0.0151850i
$621$		0			0
$622$	38.8613	+	20.3287i	1.55820	+	0.815107i
$623$	−22.8298	+	70.2628i	−0.914656	+	2.81502i
$624$		0			0
$625$	16.2641	−	11.8165i	0.650563	−	0.472662i
$626$	−2.49224	−	16.9070i	−0.0996099	−	0.675739i
$627$		0			0
$628$	−33.9988	+	10.2461i	−1.35670	+	0.408863i
$629$	0.881589	+	1.21340i	0.0351513	+	0.0483816i
$630$		0			0
$631$	−8.11153	−	2.63559i	−0.322915	−	0.104921i	0.143074	−	0.989712i	$-0.454301\pi$
$631$	−8.11153	−	2.63559i	−0.322915	−	0.104921i	−0.465989	+	0.884791i	$0.654301\pi$
$632$	5.15631	−	26.9194i	0.205107	−	1.07080i
$633$		0			0
$634$	46.7332	+	7.91648i	1.85601	+	0.314404i
$635$	−11.9991	−	36.9293i	−0.476168	−	1.46549i
$636$		0			0
$637$			19.4844i			0.772002i
$638$	−10.1292	+	13.2397i	−0.401018	+	0.524165i
$639$		0			0
$640$	−37.1219	+	3.05107i	−1.46737	+	0.120604i
$641$	2.68980	+	8.27836i	0.106241	+	0.326976i	0.990020	−	0.140929i	$-0.0450090\pi$
$641$	2.68980	+	8.27836i	0.106241	+	0.326976i	−0.883779	+	0.467905i	$0.845009\pi$
$642$		0			0
$643$	−2.43194	+	3.34728i	−0.0959065	+	0.132004i	−0.854273	−	0.519824i	$-0.825998\pi$
$643$	−2.43194	+	3.34728i	−0.0959065	+	0.132004i	0.758367	+	0.651828i	$0.225998\pi$
$644$	10.5216	−	30.1649i	0.414610	−	1.18866i
$645$		0			0
$646$	6.62758	+	13.3597i	0.260759	+	0.525628i
$647$	5.69838	+	7.84315i	0.224027	+	0.308346i	0.906204	−	0.422840i	$-0.138967\pi$
$647$	5.69838	+	7.84315i	0.224027	+	0.308346i	−0.682178	+	0.731186i	$0.738967\pi$
$648$		0			0
$649$	1.24519	+	8.64499i	0.0488780	+	0.339346i
$650$	11.6572	−	1.71838i	0.457234	−	0.0674003i
$651$		0			0
$652$	−16.1615	+	11.2204i	−0.632934	+	0.439426i
$653$	−7.76856	+	23.9092i	−0.304007	+	0.935638i	0.676039	+	0.736866i	$0.263695\pi$
$653$	−7.76856	+	23.9092i	−0.304007	+	0.935638i	−0.980046	+	0.198772i	$0.936305\pi$
$654$		0			0
$655$	4.32659	+	3.14345i	0.169054	+	0.122825i
$656$	−34.5968	+	9.62189i	−1.35078	+	0.375672i
$657$		0			0
$658$	15.7920	−	15.4568i	0.615634	−	0.602569i
$659$	−32.9528			−1.28366			−0.641830	−	0.766847i	$-0.721825\pi$
$659$	−32.9528			−1.28366			−0.641830	+	0.766847i	$0.721825\pi$
$660$		0			0
$661$	−17.1205			−0.665910			−0.332955	−	0.942943i	$-0.608046\pi$
$661$	−17.1205			−0.665910			−0.332955	+	0.942943i	$0.608046\pi$
$662$	24.3399	−	23.8234i	0.945998	−	0.925921i
$663$		0			0
$664$	−3.14430	+	0.394795i	−0.122022	+	0.0153210i
$665$	−38.7530	−	28.1557i	−1.50278	−	1.09183i
$666$		0			0
$667$	−3.86021	+	11.8805i	−0.149468	+	0.460015i
$668$	−8.48763	−	12.2253i	−0.328396	−	0.473010i
$669$		0			0
$670$	29.0596	−	4.28365i	1.12267	−	0.165492i
$671$	3.87986	+	0.670427i	0.149780	+	0.0258816i
$672$		0			0
$673$	−11.4758	−	15.7951i	−0.442359	−	0.608855i	0.528375	−	0.849011i	$-0.322801\pi$
$673$	−11.4758	−	15.7951i	−0.442359	−	0.608855i	−0.970734	+	0.240156i	$0.922801\pi$
$674$	−5.78771	−	11.6667i	−0.222934	−	0.449383i
$675$		0			0
$676$	20.7038	+	7.22156i	0.796300	+	0.277752i
$677$	7.60174	−	10.4629i	0.292159	−	0.402122i	−0.637555	−	0.770405i	$-0.720054\pi$
$677$	7.60174	−	10.4629i	0.292159	−	0.402122i	0.929714	+	0.368283i	$0.120054\pi$
$678$		0			0
$679$	−16.6678	−	51.2982i	−0.639652	−	1.96865i
$680$	−14.7963	+	26.8660i	−0.567411	+	1.03026i
$681$		0			0
$682$	−12.0358	+	3.58385i	−0.460873	+	0.137233i
$683$		−	33.9625i		−	1.29954i	−0.760132	−	0.649769i	$-0.774866\pi$
$683$		−	33.9625i		−	1.29954i	0.760132	−	0.649769i	$-0.225134\pi$
$684$		0			0
$685$	10.7720	+	33.1527i	0.411576	+	1.26670i
$686$	42.1636	+	7.14240i	1.60981	+	0.272698i
$687$		0			0
$688$	−41.9843	−	1.80219i	−1.60064	−	0.0687079i
$689$	3.14051	+	1.02041i	0.119644	+	0.0388747i
$690$		0			0
$691$	−8.46306	−	11.6484i	−0.321950	−	0.443126i	0.617111	−	0.786876i	$-0.288303\pi$
$691$	−8.46306	−	11.6484i	−0.321950	−	0.443126i	−0.939061	+	0.343750i	$0.888303\pi$
$692$	4.11868	+	13.6667i	0.156569	+	0.519529i
$693$		0			0
$694$	7.09028	+	48.0994i	0.269143	+	1.82583i
$695$	−19.9540	+	14.4974i	−0.756897	+	0.549918i
$696$		0			0
$697$	−9.13759	+	28.1226i	−0.346111	+	1.06522i
$698$	22.0678	+	11.5439i	0.835280	+	0.436943i
$699$		0			0
$700$	1.13822	−	53.0568i	0.0430206	−	2.00536i
$701$	−13.7481	+	4.46702i	−0.519257	+	0.168717i	−0.556908	−	0.830574i	$-0.688013\pi$
$701$	−13.7481	+	4.46702i	−0.519257	+	0.168717i	0.0376508	+	0.999291i	$0.488013\pi$
$702$		0			0
$703$	−1.45785			−0.0549839
$704$	24.5116	−	10.1578i	0.923817	−	0.382835i
$705$		0			0
$706$	−28.1695	−	28.7803i	−1.06017	−	1.08316i
$707$	38.5984	−	12.5414i	1.45164	−	0.471667i
$708$		0			0
$709$	11.2242	+	8.15483i	0.421532	+	0.306261i	0.778254	−	0.627950i	$-0.216106\pi$
$709$	11.2242	+	8.15483i	0.421532	+	0.306261i	−0.356722	+	0.934211i	$0.616106\pi$
$710$	2.66701	+	1.39514i	0.100091	+	0.0523586i
$711$		0			0
$712$	−33.5415	+	31.4498i	−1.25702	+	1.17863i
$713$	−7.61326	+	5.53135i	−0.285119	+	0.207151i
$714$		0			0
$715$	−13.9814	+	6.87859i	−0.522875	+	0.257245i
$716$	−13.2190	−	43.8637i	−0.494019	−	1.63926i
$717$		0			0
$718$	27.5850	−	13.6846i	1.02946	−	0.510706i
$719$	−40.9937	−	13.3196i	−1.52881	−	0.496739i	−0.580544	−	0.814229i	$-0.697160\pi$
$719$	−40.9937	−	13.3196i	−1.52881	−	0.496739i	−0.948262	+	0.317490i	$0.897160\pi$
$720$		0			0
$721$	46.9587	−	64.6331i	1.74883	−	2.40706i
$722$	12.2006	+	2.06675i	0.454059	+	0.0769164i
$723$		0			0
$724$	−12.8210	+	16.8734i	−0.476490	+	0.627094i
$725$			20.7509i			0.770669i
$726$		0			0
$727$			53.1309i			1.97052i	0.171070	+	0.985259i	$0.445278\pi$
$727$			53.1309i			1.97052i	−0.171070	+	0.985259i	$0.554722\pi$
$728$	−8.84920	+	16.0678i	−0.327973	+	0.595511i
$729$		0			0
$730$	5.30813	−	31.3354i	0.196463	−	1.15977i
$731$	−20.3395	+	27.9950i	−0.752285	+	1.03543i
$732$		0			0
$733$	32.2964	+	10.4937i	1.19290	+	0.387595i	0.837143	−	0.546985i	$-0.184224\pi$
$733$	32.2964	+	10.4937i	1.19290	+	0.387595i	0.355753	+	0.934580i	$0.384224\pi$
$734$	17.9459	+	36.1748i	0.662396	+	1.33524i
$735$		0			0
$736$	14.7926	−	13.2855i	0.545264	−	0.489711i
$737$	−18.7752	+	9.23701i	−0.691592	+	0.340250i
$738$		0			0
$739$	19.0365	−	13.8309i	0.700271	−	0.508776i	−0.179750	−	0.983712i	$-0.557529\pi$
$739$	19.0365	−	13.8309i	0.700271	−	0.508776i	0.880020	+	0.474936i	$0.157529\pi$
$740$	−1.70990	−	2.46288i	−0.0628572	−	0.0905373i
$741$		0			0
$742$	6.89352	−	13.1780i	0.253069	−	0.483778i
$743$	9.47180	+	6.88167i	0.347487	+	0.252464i	0.747814	−	0.663908i	$-0.231104\pi$
$743$	9.47180	+	6.88167i	0.347487	+	0.252464i	−0.400327	+	0.916372i	$0.631104\pi$
$744$		0			0
$745$	−8.10368	+	2.63304i	−0.296896	+	0.0964673i
$746$	32.8895	−	32.1915i	1.20417	−	1.17861i
$747$		0			0
$748$	4.18113	−	21.4447i	0.152877	−	0.784097i
$749$	2.34310			0.0856152
$750$		0			0
$751$	−12.9484	+	4.20718i	−0.472493	+	0.153522i	−0.535578	−	0.844486i	$-0.679906\pi$
$751$	−12.9484	+	4.20718i	−0.472493	+	0.153522i	0.0630847	+	0.998008i	$0.479906\pi$
$752$	13.2498	−	3.68498i	0.483171	−	0.134377i
$753$		0			0
$754$	3.32464	−	6.35554i	0.121076	−	0.231455i
$755$	9.18744	−	28.2760i	0.334365	−	1.02907i
$756$		0			0
$757$	−3.81262	+	2.77003i	−0.138572	+	0.100678i	−0.654912	−	0.755705i	$-0.727294\pi$
$757$	−3.81262	+	2.77003i	−0.138572	+	0.100678i	0.516340	+	0.856384i	$0.327294\pi$
$758$	22.6013	−	3.33163i	0.820916	−	0.121010i
$759$		0			0
$760$	−12.6729	−	26.9845i	−0.459696	−	0.978830i
$761$	5.49260	+	7.55992i	0.199107	+	0.274047i	0.896882	−	0.442270i	$-0.145827\pi$
$761$	5.49260	+	7.55992i	0.199107	+	0.274047i	−0.697775	+	0.716317i	$0.745827\pi$
$762$		0			0
$763$	−4.97349	−	1.61598i	−0.180052	−	0.0585026i
$764$	−6.99562	+	20.0560i	−0.253093	+	0.725602i
$765$		0			0
$766$	4.12068	−	24.3255i	0.148886	−	0.878917i
$767$	−1.16130	−	3.57412i	−0.0419322	−	0.129054i
$768$		0			0
$769$			24.7915i			0.894004i	0.894533	+	0.447002i	$0.147508\pi$
$769$			24.7915i			0.894004i	−0.894533	+	0.447002i	$0.852492\pi$
$770$	20.0275	+	67.2591i	0.721743	+	2.42385i
$771$		0			0
$772$	40.6062	+	30.8542i	1.46145	+	1.11047i
$773$	−8.40986	−	25.8829i	−0.302482	−	0.930943i	−0.980605	−	0.195995i	$-0.937206\pi$
$773$	−8.40986	−	25.8829i	−0.302482	−	0.930943i	0.678123	−	0.734948i	$-0.262794\pi$
$774$		0			0
$775$	−9.18840	+	12.6467i	−0.330057	+	0.454284i
$776$	6.31526	−	32.9699i	0.226704	−	1.18355i
$777$		0			0
$778$	−43.8837	+	21.7702i	−1.57331	+	0.780501i
$779$	−16.8940	−	23.2526i	−0.605292	−	0.833112i
$780$		0			0
$781$	−2.11278	−	0.365081i	−0.0756011	−	0.0130636i
$782$	−2.38765	−	16.1974i	−0.0853821	−	0.579219i
$783$		0			0
$784$	42.7671	+	33.9672i	1.52740	+	1.21312i
$785$	18.0626	−	55.5909i	0.644681	−	1.98412i
$786$		0			0
$787$	−16.6876	−	12.1242i	−0.594848	−	0.432183i	0.249198	−	0.968452i	$-0.419833\pi$
$787$	−16.6876	−	12.1242i	−0.594848	−	0.432183i	−0.844047	+	0.536270i	$0.819833\pi$
$788$	14.7190	+	0.315765i	0.524344	+	0.0112486i
$789$		0			0
$790$	31.5590	+	32.2433i	1.12282	+	1.14717i
$791$	−33.2116			−1.18087
$792$		0			0
$793$	−1.69412			−0.0601600
$794$	33.9546	+	34.6909i	1.20500	+	1.23113i
$795$		0			0
$796$	30.4448	+	0.653127i	1.07909	+	0.0231495i
$797$	13.0728	+	9.49798i	0.463064	+	0.336436i	0.794732	−	0.606960i	$-0.207611\pi$
$797$	13.0728	+	9.49798i	0.463064	+	0.336436i	−0.331668	+	0.943396i	$0.607611\pi$
$798$		0			0
$799$	3.49951	−	10.7704i	0.123804	−	0.381028i
$800$	16.5503	−	28.5825i	0.585141	−	1.01054i
$801$		0			0
$802$	4.79005	+	32.4950i	0.169143	+	1.14744i
$803$	3.22763	+	22.4085i	0.113901	+	0.790779i
$804$		0			0
$805$	30.9107	+	42.5449i	1.08946	+	1.49951i
$806$	4.84042	−	2.40128i	0.170497	−	0.0845816i
$807$		0			0
$808$	24.8076	+	4.75180i	0.872727	+	0.167168i
$809$	29.6885	−	40.8627i	1.04379	−	1.43666i	0.149722	−	0.988728i	$-0.452162\pi$
$809$	29.6885	−	40.8627i	1.04379	−	1.43666i	0.894070	−	0.447928i	$-0.147838\pi$
$810$		0			0
$811$	−7.20764	−	22.1828i	−0.253095	−	0.778945i	−0.994199	−	0.107555i	$-0.965698\pi$
$811$	−7.20764	−	22.1828i	−0.253095	−	0.778945i	0.741105	−	0.671390i	$-0.234302\pi$
$812$	−25.7211	−	19.5439i	−0.902635	−	0.685856i
$813$		0			0
$814$	1.69631	+	1.29778i	0.0594556	+	0.0454871i
$815$		−	32.3866i		−	1.13445i
$816$		0			0
$817$	−10.3937	−	31.9885i	−0.363629	−	1.11914i
$818$	−7.23766	+	42.7259i	−0.253059	+	1.49388i
$819$		0			0
$820$	19.4680	−	55.8135i	0.679851	−	1.94909i
$821$	−15.0235	−	4.88144i	−0.524325	−	0.170363i	0.0348825	−	0.999391i	$-0.488894\pi$
$821$	−15.0235	−	4.88144i	−0.524325	−	0.170363i	−0.559207	+	0.829028i	$0.688894\pi$
$822$		0			0
$823$	−6.21791	−	8.55821i	−0.216743	−	0.298321i	0.686776	−	0.726869i	$-0.259025\pi$
$823$	−6.21791	−	8.55821i	−0.216743	−	0.298321i	−0.903519	+	0.428548i	$0.859025\pi$
$824$	45.0053	−	21.1362i	1.56783	−	0.736315i
$825$		0			0
$826$	−16.7446	+	2.46830i	−0.582618	+	0.0858830i
$827$	3.28348	−	2.38559i	0.114178	−	0.0829550i	−0.529231	−	0.848478i	$-0.677520\pi$
$827$	3.28348	−	2.38559i	0.114178	−	0.0829550i	0.643409	+	0.765523i	$0.277520\pi$
$828$		0			0
$829$	4.59857	−	14.1529i	0.159715	−	0.491552i	−0.838893	−	0.544296i	$-0.816797\pi$
$829$	4.59857	−	14.1529i	0.159715	−	0.491552i	0.998608	+	0.0527441i	$0.0167968\pi$
$830$	2.41794	−	4.62225i	0.0839280	−	0.160441i
$831$		0			0
$832$	−9.64839	+	6.10254i	−0.334498	+	0.211568i
$833$	42.7715	−	13.8973i	1.48194	−	0.481513i
$834$		0			0
$835$	24.4986			0.847810
$836$	14.4746	+	15.5398i	0.500613	+	0.537456i
$837$		0			0
$838$	19.9576	−	19.5340i	0.689423	−	0.674791i
$839$	−12.3827	+	4.02337i	−0.427497	+	0.138902i	−0.514860	−	0.857274i	$-0.672156\pi$
$839$	−12.3827	+	4.02337i	−0.427497	+	0.138902i	0.0873629	+	0.996177i	$0.472156\pi$
$840$		0			0
$841$	−13.2425	−	9.62124i	−0.456638	−	0.331767i
$842$	−14.7585	+	28.2131i	−0.508613	+	0.972288i
$843$		0			0
$844$	−16.4489	−	23.6924i	−0.566195	−	0.815527i
$845$	−29.2009	+	21.2157i	−1.00454	+	0.729842i
$846$		0			0
$847$	−28.2379	−	41.2519i	−0.970267	−	1.41743i
$848$	7.71460	−	5.11433i	0.264920	−	0.175627i
$849$		0			0
$850$	−12.0866	−	24.3638i	−0.414568	−	0.835672i
$851$	1.52216	+	0.494581i	0.0521791	+	0.0169540i
$852$		0			0
$853$	−12.1213	+	16.6835i	−0.415025	+	0.571233i	−0.964435	−	0.264320i	$-0.914852\pi$
$853$	−12.1213	+	16.6835i	−0.415025	+	0.571233i	0.549410	+	0.835553i	$0.314852\pi$
$854$	−1.27434	+	7.52280i	−0.0436071	+	0.257425i
$855$		0			0
$856$	1.27736	+	0.703495i	0.0436592	+	0.0240450i
$857$			26.3263i			0.899290i	0.893207	+	0.449645i	$0.148450\pi$
$857$			26.3263i			0.899290i	−0.893207	+	0.449645i	$0.851550\pi$
$858$		0			0
$859$		−	50.2269i		−	1.71372i	−0.515550	−	0.856860i	$-0.672412\pi$
$859$		−	50.2269i		−	1.71372i	0.515550	−	0.856860i	$-0.327588\pi$
$860$	41.8505	−	55.0781i	1.42709	−	1.87815i
$861$		0			0
$862$	−9.27713	−	1.57152i	−0.315980	−	0.0535262i
$863$	11.9210	−	16.4079i	0.405796	−	0.558531i	−0.556391	−	0.830921i	$-0.687814\pi$
$863$	11.9210	−	16.4079i	0.405796	−	0.558531i	0.962187	+	0.272390i	$0.0878141\pi$
$864$		0			0
$865$	−22.3462	−	7.26072i	−0.759793	−	0.246872i
$866$	−23.7044	+	11.7595i	−0.805507	+	0.399604i
$867$		0			0
$868$	−7.02193	−	23.3003i	−0.238340	−	0.790865i
$869$	−28.4291	−	14.9913i	−0.964392	−	0.508546i
$870$		0			0
$871$	7.28366	−	5.29189i	0.246797	−	0.179309i
$872$	−2.22614	−	2.37420i	−0.0753866	−	0.0804007i
$873$		0			0
$874$	14.1012	+	7.37646i	0.476980	+	0.249513i
$875$	10.1512	+	7.37530i	0.343174	+	0.249331i
$876$		0			0
$877$	48.9484	−	15.9043i	1.65287	−	0.537050i	0.673511	−	0.739178i	$-0.264786\pi$
$877$	48.9484	−	15.9043i	1.65287	−	0.537050i	0.979359	+	0.202128i	$0.0647855\pi$
$878$	−35.4113	−	36.1791i	−1.19507	−	1.22099i
$879$		0			0
$880$	−9.27577	+	42.6797i	−0.312686	+	1.43873i
$881$	−6.44252			−0.217054			−0.108527	−	0.994094i	$-0.534613\pi$
$881$	−6.44252			−0.217054			−0.108527	+	0.994094i	$0.534613\pi$
$882$		0			0
$883$	−37.8694	+	12.3045i	−1.27441	+	0.414080i	−0.866607	−	0.498992i	$-0.833704\pi$
$883$	−37.8694	+	12.3045i	−1.27441	+	0.414080i	−0.407800	+	0.913071i	$0.633704\pi$
$884$	−0.201626	+	9.39858i	−0.00678142	+	0.316109i
$885$		0			0
$886$	1.46349	+	0.765565i	0.0491669	+	0.0257197i
$887$	10.0922	−	31.0606i	0.338863	−	1.04291i	−0.625924	−	0.779884i	$-0.715278\pi$
$887$	10.0922	−	31.0606i	0.338863	−	1.04291i	0.964788	−	0.263030i	$-0.0847219\pi$
$888$		0			0
$889$	−43.3645	+	31.5061i	−1.45440	+	1.05668i
$890$	−11.0377	−	74.8780i	−0.369984	−	2.50992i
$891$		0			0
$892$	−12.7245	−	42.2226i	−0.426047	−	1.41372i
$893$	6.47006	+	8.90527i	0.216512	+	0.298004i
$894$		0			0
$895$	71.7210	+	23.3036i	2.39737	+	0.778952i
$896$	19.8409	+	47.4344i	0.662837	+	1.58467i
$897$		0			0
$898$	−18.3706	−	3.11192i	−0.613033	−	0.103846i
$899$	2.94047	+	9.04984i	0.0980702	+	0.301829i
$900$		0			0
$901$		−	7.62174i		−	0.253917i
$902$	−1.04216	+	42.0951i	−0.0347002	+	1.40161i
$903$		0			0
$904$	−18.1055	−	9.97147i	−0.602180	−	0.331646i
$905$	−10.7797	−	33.1765i	−0.358329	−	1.10282i
$906$		0			0
$907$	12.5516	−	17.2757i	0.416768	−	0.573632i	−0.548085	−	0.836423i	$-0.684643\pi$
$907$	12.5516	−	17.2757i	0.416768	−	0.573632i	0.964853	+	0.262791i	$0.0846430\pi$
$908$	43.0233	+	15.0067i	1.42778	+	0.498015i
$909$		0			0
$910$	−13.4190	−	27.0496i	−0.444836	−	0.896685i
$911$	−14.5327	−	20.0025i	−0.481489	−	0.662713i	0.497301	−	0.867578i	$-0.334324\pi$
$911$	−14.5327	−	20.0025i	−0.481489	−	0.662713i	−0.978790	+	0.204865i	$0.934324\pi$
$912$		0			0
$913$	−0.632730	+	3.66170i	−0.0209403	+	0.121185i
$914$	−11.0336	+	1.62645i	−0.364960	+	0.0537983i
$915$		0			0
$916$	7.61391	+	10.9668i	0.251571	+	0.362354i
$917$	2.28130	−	7.02112i	0.0753352	−	0.231858i
$918$		0			0
$919$	25.1196	+	18.2505i	0.828621	+	0.602028i	0.919169	−	0.393864i	$-0.128862\pi$
$919$	25.1196	+	18.2505i	0.828621	+	0.602028i	−0.0905481	+	0.995892i	$0.528862\pi$
$920$	4.07743	+	32.4742i	0.134429	+	1.07064i
$921$		0			0
$922$	15.9119	−	15.5742i	0.524030	−	0.512909i
$923$	0.922534			0.0303656
$924$		0			0
$925$	2.65866			0.0874163
$926$	−28.3343	+	27.7330i	−0.931123	+	0.911362i
$927$		0			0
$928$	−8.15415	−	18.3770i	−0.267673	−	0.603254i
$929$	18.7373	+	13.6135i	0.614752	+	0.446643i	0.851084	−	0.525029i	$-0.175945\pi$
$929$	18.7373	+	13.6135i	0.614752	+	0.446643i	−0.236333	+	0.971672i	$0.575945\pi$
$930$		0			0
$931$	−13.5081	+	41.5738i	−0.442711	+	1.36253i
$932$	−8.19791	+	5.69155i	−0.268532	+	0.186433i
$933$		0			0
$934$	−3.49419	+	0.515075i	−0.114333	+	0.0168538i
$935$	25.0719	+	25.7853i	0.819937	+	0.843269i
$936$		0			0
$937$	−5.74761	−	7.91091i	−0.187766	−	0.258438i	0.704748	−	0.709458i	$-0.251060\pi$
$937$	−5.74761	−	7.91091i	−0.187766	−	0.258438i	−0.892514	+	0.451020i	$0.851060\pi$
$938$	−18.0199	−	36.3239i	−0.588371	−	1.18602i
$939$		0			0
$940$	−7.45582	+	21.3754i	−0.243182	+	0.697189i
$941$	4.80526	−	6.61387i	0.156647	−	0.215606i	−0.723479	−	0.690347i	$-0.757458\pi$
$941$	4.80526	−	6.61387i	0.156647	−	0.215606i	0.880126	+	0.474740i	$0.157458\pi$
$942$		0			0
$943$	9.75077	+	30.0098i	0.317529	+	0.977253i
$944$	−9.86947	−	3.68179i	−0.321224	−	0.119832i
$945$		0			0
$946$	−16.3824	+	46.4733i	−0.532638	+	1.51098i
$947$			51.1326i			1.66159i	0.556581	+	0.830794i	$0.312113\pi$
$947$			51.1326i			1.66159i	−0.556581	+	0.830794i	$0.687887\pi$
$948$		0			0
$949$	−3.01019	−	9.26442i	−0.0977150	−	0.300736i
$950$	26.0642	+	4.41521i	0.845634	+	0.143248i
$951$		0			0
$952$	41.5830	+	7.96507i	1.34771	+	0.258149i
$953$	36.1108	+	11.7331i	1.16974	+	0.380073i	0.828547	−	0.559920i	$-0.189168\pi$
$953$	36.1108	+	11.7331i	1.16974	+	0.380073i	0.341196	+	0.939992i	$0.389168\pi$
$954$		0			0
$955$	−20.5519	−	28.2873i	−0.665045	−	0.915355i
$956$	−2.06970	+	0.623737i	−0.0669388	+	0.0201731i
$957$		0			0
$958$	1.51454	+	10.2744i	0.0489326	+	0.331952i
$959$	38.9298	−	28.2842i	1.25711	−	0.913344i
$960$		0			0
$961$	7.36439	−	22.6653i	0.237561	−	0.731137i
$962$	−0.814290	−	0.425962i	−0.0262537	−	0.0137336i
$963$		0			0
$964$	3.85030	+	0.0825998i	0.124010	+	0.00266036i
$965$	−79.8401	+	25.9416i	−2.57014	+	0.835090i
$966$		0			0
$967$	31.7381			1.02063			0.510314	−	0.859988i	$-0.329529\pi$
$967$	31.7381			1.02063			0.510314	+	0.859988i	$0.329529\pi$
$968$	−3.00857	−	30.9669i	−0.0966991	−	0.995314i
$969$		0			0
$970$	38.6524	+	39.4905i	1.24105	+	1.26796i
$971$	−26.3894	+	8.57442i	−0.846875	+	0.275166i	−0.700137	−	0.714009i	$-0.746878\pi$
$971$	−26.3894	+	8.57442i	−0.846875	+	0.275166i	−0.146738	+	0.989175i	$0.546878\pi$
$972$		0			0
$973$	27.5449	+	20.0125i	0.883049	+	0.641573i
$974$	21.7105	+	11.3569i	0.695648	+	0.363900i
$975$		0			0
$976$	−2.95336	+	3.71849i	−0.0945349	+	0.119026i
$977$	−35.5201	+	25.8069i	−1.13639	+	0.825636i	−0.986612	−	0.163084i	$-0.947856\pi$
$977$	−35.5201	+	25.8069i	−1.13639	+	0.825636i	−0.149778	+	0.988720i	$0.547856\pi$
$978$		0			0
$979$	23.8010	+	48.3780i	0.760684	+	1.54617i
$980$	−86.0780	+	25.9410i	−2.74966	+	0.828655i
$981$		0			0
$982$	−13.5446	+	6.71934i	−0.432226	+	0.214423i
$983$	14.9235	+	4.84893i	0.475985	+	0.154657i	0.537178	−	0.843469i	$-0.319490\pi$
$983$	14.9235	+	4.84893i	0.475985	+	0.154657i	−0.0611928	+	0.998126i	$0.519490\pi$
$984$		0			0
$985$	−14.2448	+	19.6062i	−0.453876	+	0.624706i
$986$	−16.3227	−	2.76503i	−0.519822	−	0.0880564i
$987$		0			0
$988$	−7.27550	−	5.52820i	−0.231464	−	0.175876i
$989$			36.9258i			1.17417i
$990$		0			0
$991$		−	27.8527i		−	0.884770i	−0.896825	−	0.442385i	$-0.854133\pi$
$991$		−	27.8527i		−	0.884770i	0.896825	−	0.442385i	$-0.145867\pi$
$992$	3.16765	−	14.8106i	0.100573	−	0.470236i
$993$		0			0
$994$	0.693943	−	4.09654i	0.0220105	−	0.129934i
$995$	−29.4638	+	40.5535i	−0.934066	+	1.28563i
$996$		0			0
$997$	44.8898	+	14.5856i	1.42167	+	0.461930i	0.916134	−	0.400873i	$-0.131293\pi$
$997$	44.8898	+	14.5856i	1.42167	+	0.461930i	0.505540	+	0.862803i	$0.331293\pi$
$998$	−23.8954	−	48.1675i	−0.756395	−	1.52472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.b.19.9		48
3.2	odd	2		132.2.j.a.19.4	yes	48
4.3	odd	2	inner	396.2.r.b.19.7		48
11.7	odd	10	inner	396.2.r.b.271.7		48
12.11	even	2		132.2.j.a.19.6	yes	48
33.29	even	10		132.2.j.a.7.6	yes	48
44.7	even	10	inner	396.2.r.b.271.9		48
132.95	odd	10		132.2.j.a.7.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.4	✓	48	132.95	odd	10
132.2.j.a.7.6	yes	48	33.29	even	10
132.2.j.a.19.4	yes	48	3.2	odd	2
132.2.j.a.19.6	yes	48	12.11	even	2
396.2.r.b.19.7		48	4.3	odd	2	inner
396.2.r.b.19.9		48	1.1	even	1	trivial
396.2.r.b.271.7		48	11.7	odd	10	inner
396.2.r.b.271.9		48	44.7	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989218 + 1.01067i) q^{2} +(-0.0428958 + 1.99954i) q^{4} +(-2.66345 - 1.93511i) q^{5} +(-1.40437 + 4.32221i) q^{7} +(-2.06330 + 1.93463i) q^{8} +O(q^{10})\)	\(q+(0.989218 + 1.01067i) q^{2} +(-0.0428958 + 1.99954i) q^{4} +(-2.66345 - 1.93511i) q^{5} +(-1.40437 + 4.32221i) q^{7} +(-2.06330 + 1.93463i) q^{8} +(-0.678982 - 4.60611i) q^{10} +(1.46412 + 2.97596i) q^{11} +(-0.838793 - 1.15450i) q^{13} +(-5.75754 + 2.85626i) q^{14} +(-3.99632 - 0.171544i) q^{16} +(-1.93604 + 2.66473i) q^{17} +(-0.989336 - 3.04486i) q^{19} +(3.98358 - 5.24267i) q^{20} +(-1.55938 + 4.42361i) q^{22} +3.51482i q^{23} +(1.80424 + 5.55287i) q^{25} +(0.337066 - 1.98979i) q^{26} +(-8.58219 - 2.99350i) q^{28} +(3.38012 + 1.09827i) q^{29} +(1.57372 + 2.16604i) q^{31} +(-3.77986 - 4.20864i) q^{32} +(-4.60833 + 0.679308i) q^{34} +(12.1044 - 8.79438i) q^{35} +(0.140713 - 0.433070i) q^{37} +(2.09867 - 4.01192i) q^{38} +(9.23923 - 1.16007i) q^{40} +(8.53807 - 2.77419i) q^{41} +10.5057 q^{43} +(-6.01336 + 2.79990i) q^{44} +(-3.55232 + 3.47693i) q^{46} +(-3.26990 + 1.06246i) q^{47} +(-11.0461 - 8.02547i) q^{49} +(-3.82732 + 7.31649i) q^{50} +(2.34445 - 1.62768i) q^{52} +(-1.87204 + 1.36012i) q^{53} +(1.85922 - 10.7596i) q^{55} +(-5.46422 - 11.6350i) q^{56} +(2.23369 + 4.50260i) q^{58} +(2.50457 + 0.813785i) q^{59} +(0.697794 - 0.960431i) q^{61} +(-0.632394 + 3.73320i) q^{62} +(0.514433 - 7.98344i) q^{64} +4.69811i q^{65} +6.30893i q^{67} +(-5.24519 - 3.98550i) q^{68} +(20.8621 + 3.53399i) q^{70} +(-0.379984 + 0.523003i) q^{71} +(6.49205 + 2.10940i) q^{73} +(0.576885 - 0.286187i) q^{74} +(6.13076 - 1.84760i) q^{76} +(-14.9189 + 2.14886i) q^{77} +(-7.83975 + 5.69591i) q^{79} +(10.3121 + 8.19022i) q^{80} +(11.2498 + 5.88487i) q^{82} +(0.906427 + 0.658558i) q^{83} +(10.3131 - 3.35093i) q^{85} +(10.3925 + 10.6178i) q^{86} +(-8.77830 - 3.30779i) q^{88} +16.2562 q^{89} +(6.16797 - 2.00409i) q^{91} +(-7.02803 - 0.150771i) q^{92} +(-4.30843 - 2.25378i) q^{94} +(-3.25710 + 10.0243i) q^{95} +(-9.60184 + 6.97614i) q^{97} +(-2.81593 - 19.1029i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

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