LMFDB - Embedded newform 819.2.et.c.271.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.4
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.556084 - 0.556084i) q^{2} -1.38154i q^{4} +(-0.542987 - 2.02645i) q^{5} +(-0.405927 + 2.61443i) q^{7} +(-1.88042 + 1.88042i) q^{8} +O(q^{10})$	\(q+(-0.556084 - 0.556084i) q^{2} -1.38154i q^{4} +(-0.542987 - 2.02645i) q^{5} +(-0.405927 + 2.61443i) q^{7} +(-1.88042 + 1.88042i) q^{8} +(-0.824932 + 1.42882i) q^{10} +(0.632763 + 2.36150i) q^{11} +(1.96880 + 3.02057i) q^{13} +(1.67957 - 1.22811i) q^{14} -0.671737 q^{16} -6.55339 q^{17} +(-7.74006 - 2.07394i) q^{19} +(-2.79963 + 0.750158i) q^{20} +(0.961326 - 1.66506i) q^{22} +3.84618i q^{23} +(0.518448 - 0.299326i) q^{25} +(0.584868 - 2.77451i) q^{26} +(3.61194 + 0.560804i) q^{28} +(1.25425 + 2.17242i) q^{29} +(-0.457027 - 0.122460i) q^{31} +(4.13438 + 4.13438i) q^{32} +(3.64424 + 3.64424i) q^{34} +(5.51843 - 0.597007i) q^{35} +(-5.00037 + 5.00037i) q^{37} +(3.15084 + 5.45741i) q^{38} +(4.83163 + 2.78954i) q^{40} +(11.0034 + 2.94834i) q^{41} +(0.810492 + 0.467938i) q^{43} +(3.26252 - 0.874188i) q^{44} +(2.13880 - 2.13880i) q^{46} +(-7.03848 + 1.88596i) q^{47} +(-6.67045 - 2.12253i) q^{49} +(-0.454751 - 0.121850i) q^{50} +(4.17303 - 2.71998i) q^{52} +(1.08341 + 1.87652i) q^{53} +(4.44190 - 2.56453i) q^{55} +(-4.15291 - 5.67954i) q^{56} +(0.510581 - 1.90552i) q^{58} +(3.92820 + 3.92820i) q^{59} +(8.13407 - 4.69621i) q^{61} +(0.186047 + 0.322243i) q^{62} -3.25466i q^{64} +(5.05200 - 5.62981i) q^{65} +(-11.1395 + 2.98482i) q^{67} +9.05378i q^{68} +(-3.40069 - 2.73672i) q^{70} +(-9.44098 + 2.52970i) q^{71} +(2.62580 - 9.79963i) q^{73} +5.56125 q^{74} +(-2.86524 + 10.6932i) q^{76} +(-6.43083 + 0.695715i) q^{77} +(1.07540 - 1.86264i) q^{79} +(0.364744 + 1.36124i) q^{80} +(-4.47927 - 7.75833i) q^{82} +(-1.52436 + 1.52436i) q^{83} +(3.55840 + 13.2801i) q^{85} +(-0.190489 - 0.710914i) q^{86} +(-5.63048 - 3.25076i) q^{88} +(-4.45304 - 4.45304i) q^{89} +(-8.69623 + 3.92116i) q^{91} +5.31366 q^{92} +(4.96274 + 2.86524i) q^{94} +16.8110i q^{95} +(4.17950 + 15.5981i) q^{97} +(2.52902 + 4.88964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.556084	−	0.556084i	−0.393211	−	0.393211i	0.482619	−	0.875830i	$-0.339685\pi$
$2$	−0.556084	−	0.556084i	−0.393211	−	0.393211i	−0.875830	+	0.482619i	$0.839685\pi$
$3$		0			0
$3$		0			0
$4$		−	1.38154i		−	0.690770i
$5$	−0.542987	−	2.02645i	−0.242831	−	0.906258i	−0.974461	−	0.224556i	$-0.927907\pi$
$5$	−0.542987	−	2.02645i	−0.242831	−	0.906258i	0.731630	−	0.681702i	$-0.238760\pi$
$6$		0			0
$7$	−0.405927	+	2.61443i	−0.153426	+	0.988160i
$7$	−0.405927	+	2.61443i	−0.153426	+	0.988160i
$8$	−1.88042	+	1.88042i	−0.664829	+	0.664829i
$9$		0			0
$10$	−0.824932	+	1.42882i	−0.260867	+	0.451834i
$11$	0.632763	+	2.36150i	0.190785	+	0.712020i	0.993318	+	0.115412i	$0.0368188\pi$
$11$	0.632763	+	2.36150i	0.190785	+	0.712020i	−0.802532	+	0.596608i	$0.796515\pi$
$12$		0			0
$13$	1.96880	+	3.02057i	0.546048	+	0.837754i
$13$	1.96880	+	3.02057i	0.546048	+	0.837754i
$14$	1.67957	−	1.22811i	0.448884	−	0.328227i
$15$		0			0
$16$	−0.671737			−0.167934
$17$	−6.55339			−1.58943			−0.794715	−	0.606983i	$-0.792380\pi$
$17$	−6.55339			−1.58943			−0.794715	+	0.606983i	$0.792380\pi$
$18$		0			0
$19$	−7.74006	−	2.07394i	−1.77569	−	0.475795i	−0.785905	−	0.618347i	$-0.787803\pi$
$19$	−7.74006	−	2.07394i	−1.77569	−	0.475795i	−0.989787	+	0.142552i	$0.954469\pi$
$20$	−2.79963	+	0.750158i	−0.626016	+	0.167740i
$21$		0			0
$22$	0.961326	−	1.66506i	0.204955	−	0.354993i
$23$			3.84618i			0.801984i	0.916082	+	0.400992i	$0.131335\pi$
$23$			3.84618i			0.801984i	−0.916082	+	0.400992i	$0.868665\pi$
$24$		0			0
$25$	0.518448	−	0.299326i	0.103690	−	0.0598652i
$26$	0.584868	−	2.77451i	0.114702	−	0.544126i
$27$		0			0
$28$	3.61194	+	0.560804i	0.682592	+	0.105982i
$29$	1.25425	+	2.17242i	0.232908	+	0.403408i	0.958663	−	0.284545i	$-0.0918426\pi$
$29$	1.25425	+	2.17242i	0.232908	+	0.403408i	−0.725755	+	0.687954i	$0.758509\pi$
$30$		0			0
$31$	−0.457027	−	0.122460i	−0.0820844	−	0.0219945i	0.217543	−	0.976051i	$-0.430196\pi$
$31$	−0.457027	−	0.122460i	−0.0820844	−	0.0219945i	−0.299628	+	0.954056i	$0.596862\pi$
$32$	4.13438	+	4.13438i	0.730863	+	0.730863i
$33$		0			0
$34$	3.64424	+	3.64424i	0.624981	+	0.624981i
$35$	5.51843	−	0.597007i	0.932784	−	0.100913i
$36$		0			0
$37$	−5.00037	+	5.00037i	−0.822055	+	0.822055i	−0.986403	−	0.164347i	$-0.947448\pi$
$37$	−5.00037	+	5.00037i	−0.822055	+	0.822055i	0.164347	+	0.986403i	$0.447448\pi$
$38$	3.15084	+	5.45741i	0.511134	+	0.885309i
$39$		0			0
$40$	4.83163	+	2.78954i	0.763948	+	0.441065i
$41$	11.0034	+	2.94834i	1.71844	+	0.460454i	0.977468	−	0.211084i	$-0.0676993\pi$
$41$	11.0034	+	2.94834i	1.71844	+	0.460454i	0.740970	+	0.671538i	$0.234366\pi$
$42$		0			0
$43$	0.810492	+	0.467938i	0.123599	+	0.0713598i	0.560525	−	0.828138i	$-0.310599\pi$
$43$	0.810492	+	0.467938i	0.123599	+	0.0713598i	−0.436926	+	0.899497i	$0.643933\pi$
$44$	3.26252	−	0.874188i	0.491843	−	0.131789i
$45$		0			0
$46$	2.13880	−	2.13880i	0.315349	−	0.315349i
$47$	−7.03848	+	1.88596i	−1.02667	+	0.275095i	−0.732578	−	0.680683i	$-0.761683\pi$
$47$	−7.03848	+	1.88596i	−1.02667	+	0.275095i	−0.294090	+	0.955778i	$0.595017\pi$
$48$		0			0
$49$	−6.67045	−	2.12253i	−0.952921	−	0.303219i
$50$	−0.454751	−	0.121850i	−0.0643115	−	0.0172322i
$51$		0			0
$52$	4.17303	−	2.71998i	0.578696	−	0.377194i
$53$	1.08341	+	1.87652i	0.148818	+	0.257760i	0.930791	−	0.365552i	$-0.119120\pi$
$53$	1.08341	+	1.87652i	0.148818	+	0.257760i	−0.781973	+	0.623312i	$0.785787\pi$
$54$		0			0
$55$	4.44190	−	2.56453i	0.598945	−	0.345801i
$56$	−4.15291	−	5.67954i	−0.554956	−	0.758960i
$57$		0			0
$58$	0.510581	−	1.90552i	0.0670426	−	0.250206i
$59$	3.92820	+	3.92820i	0.511408	+	0.511408i	0.914958	−	0.403550i	$-0.132224\pi$
$59$	3.92820	+	3.92820i	0.511408	+	0.511408i	−0.403550	+	0.914958i	$0.632224\pi$
$60$		0			0
$61$	8.13407	−	4.69621i	1.04146	−	0.601288i	0.121214	−	0.992626i	$-0.461321\pi$
$61$	8.13407	−	4.69621i	1.04146	−	0.601288i	0.920247	+	0.391339i	$0.127988\pi$
$62$	0.186047	+	0.322243i	0.0236280	+	0.0409249i
$63$		0			0
$64$		−	3.25466i		−	0.406832i
$65$	5.05200	−	5.62981i	0.626624	−	0.698293i
$66$		0			0
$67$	−11.1395	+	2.98482i	−1.36091	+	0.364653i	−0.864149	−	0.503237i	$-0.832142\pi$
$67$	−11.1395	+	2.98482i	−1.36091	+	0.364653i	−0.496756	+	0.867890i	$0.665476\pi$
$68$			9.05378i			1.09793i
$69$		0			0
$70$	−3.40069	−	2.73672i	−0.406461	−	0.327101i
$71$	−9.44098	+	2.52970i	−1.12044	+	0.300221i	−0.771061	−	0.636762i	$-0.780274\pi$
$71$	−9.44098	+	2.52970i	−1.12044	+	0.300221i	−0.349377	+	0.936982i	$0.613607\pi$
$72$		0			0
$73$	2.62580	−	9.79963i	0.307327	−	1.14696i	−0.623597	−	0.781746i	$-0.714329\pi$
$73$	2.62580	−	9.79963i	0.307327	−	1.14696i	0.930924	−	0.365214i	$-0.119004\pi$
$74$	5.56125			0.646482
$75$		0			0
$76$	−2.86524	+	10.6932i	−0.328665	+	1.22660i
$77$	−6.43083	+	0.695715i	−0.732862	+	0.0792841i
$78$		0			0
$79$	1.07540	−	1.86264i	0.120992	−	0.209564i	−0.799167	−	0.601109i	$-0.794726\pi$
$79$	1.07540	−	1.86264i	0.120992	−	0.209564i	0.920159	+	0.391545i	$0.128059\pi$
$80$	0.364744	+	1.36124i	0.0407796	+	0.152192i
$81$		0			0
$82$	−4.47927	−	7.75833i	−0.494653	−	0.856764i
$83$	−1.52436	+	1.52436i	−0.167320	+	0.167320i	−0.785801	−	0.618480i	$-0.787749\pi$
$83$	−1.52436	+	1.52436i	−0.167320	+	0.167320i	0.618480	+	0.785801i	$0.287749\pi$
$84$		0			0
$85$	3.55840	+	13.2801i	0.385963	+	1.44043i
$86$	−0.190489	−	0.710914i	−0.0205409	−	0.0766598i
$87$		0			0
$88$	−5.63048	−	3.25076i	−0.600212	−	0.346532i
$89$	−4.45304	−	4.45304i	−0.472021	−	0.472021i	0.430547	−	0.902568i	$-0.358321\pi$
$89$	−4.45304	−	4.45304i	−0.472021	−	0.472021i	−0.902568	+	0.430547i	$0.858321\pi$
$90$		0			0
$91$	−8.69623	+	3.92116i	−0.911613	+	0.411050i
$92$	5.31366			0.553987
$93$		0			0
$94$	4.96274	+	2.86524i	0.511867	+	0.295527i
$95$			16.8110i			1.72477i
$96$		0			0
$97$	4.17950	+	15.5981i	0.424363	+	1.58375i	0.765309	+	0.643663i	$0.222586\pi$
$97$	4.17950	+	15.5981i	0.424363	+	1.58375i	−0.340946	+	0.940083i	$0.610747\pi$
$98$	2.52902	+	4.88964i	0.255470	+	0.493928i
$99$		0			0
$100$	−0.413531	−	0.716257i	−0.0413531	−	0.0716257i
$101$	1.76991	−	3.06558i	0.176113	−	0.305037i	−0.764433	−	0.644703i	$-0.776981\pi$
$101$	1.76991	−	3.06558i	0.176113	−	0.305037i	0.940546	+	0.339667i	$0.110314\pi$
$102$		0			0
$103$	−4.58234	+	7.93684i	−0.451511	+	0.782041i	−0.998480	−	0.0551124i	$-0.982448\pi$
$103$	−4.58234	+	7.93684i	−0.451511	+	0.782041i	0.546969	+	0.837153i	$0.315782\pi$
$104$	−9.38211	−	1.97776i	−0.919992	−	0.193935i
$105$		0			0
$106$	0.441036	−	1.64597i	0.0428372	−	0.159871i
$107$	2.01759			0.195048			0.0975240	−	0.995233i	$-0.468908\pi$
$107$	2.01759			0.195048			0.0975240	+	0.995233i	$0.468908\pi$
$108$		0			0
$109$	−1.45769	+	5.44016i	−0.139621	+	0.521073i	0.860315	+	0.509763i	$0.170267\pi$
$109$	−1.45769	+	5.44016i	−0.139621	+	0.521073i	−0.999936	+	0.0113102i	$0.996400\pi$
$110$	−3.89616	−	1.04397i	−0.371485	−	0.0995390i
$111$		0			0
$112$	0.272676	−	1.75621i	0.0257655	−	0.165946i
$113$	6.20648	−	10.7499i	0.583857	−	1.01127i	−0.411160	−	0.911563i	$-0.634876\pi$
$113$	6.20648	−	10.7499i	0.583857	−	1.01127i	0.995017	−	0.0997064i	$-0.0317904\pi$
$114$		0			0
$115$	7.79411	−	2.08842i	0.726804	−	0.194747i
$116$	3.00129	−	1.73279i	0.278663	−	0.160886i
$117$		0			0
$118$		−	4.36881i		−	0.402182i
$119$	2.66020	−	17.1334i	0.243860	−	1.57061i
$120$		0			0
$121$	4.34997	−	2.51145i	0.395451	−	0.228314i
$122$	−7.13471	−	1.91174i	−0.645947	−	0.173081i
$123$		0			0
$124$	−0.169183	+	0.631401i	−0.0151931	+	0.0567015i
$125$	−8.30541	−	8.30541i	−0.742859	−	0.742859i
$126$		0			0
$127$	−9.05461	+	5.22768i	−0.803467	+	0.463882i	−0.844682	−	0.535269i	$-0.820210\pi$
$127$	−9.05461	+	5.22768i	−0.803467	+	0.463882i	0.0412153	+	0.999150i	$0.486877\pi$
$128$	6.45891	−	6.45891i	0.570892	−	0.570892i
$129$		0			0
$130$	−5.93999	+	0.321313i	−0.520971	+	0.0281810i
$131$	−18.0680	−	10.4315i	−1.57860	−	0.911408i	−0.995055	−	0.0993303i	$-0.968330\pi$
$131$	−18.0680	−	10.4315i	−1.57860	−	0.911408i	−0.583550	−	0.812077i	$-0.698337\pi$
$132$		0			0
$133$	8.56407	−	19.3940i	0.742599	−	1.68167i
$134$	7.85430	+	4.53468i	0.678508	+	0.391737i
$135$		0			0
$136$	12.3231	−	12.3231i	1.05670	−	1.05670i
$137$	−7.97181	+	7.97181i	−0.681078	+	0.681078i	−0.960243	−	0.279165i	$-0.909942\pi$
$137$	−7.97181	+	7.97181i	−0.681078	+	0.681078i	0.279165	+	0.960243i	$0.409942\pi$
$138$		0			0
$139$	−8.83314	−	5.09981i	−0.749217	−	0.432561i	0.0761940	−	0.997093i	$-0.475723\pi$
$139$	−8.83314	−	5.09981i	−0.749217	−	0.432561i	−0.825411	+	0.564532i	$0.809057\pi$
$140$	−0.824789	−	7.62393i	−0.0697074	−	0.644340i
$141$		0			0
$142$	6.65671	+	3.84325i	0.558618	+	0.322518i
$143$	−5.88729	+	6.56064i	−0.492320	+	0.548628i
$144$		0			0
$145$	3.72127	−	3.72127i	0.309035	−	0.309035i
$146$	−6.90958	+	3.98925i	−0.571841	+	0.330153i
$147$		0			0
$148$	6.90821	+	6.90821i	0.567852	+	0.567852i
$149$	1.21789	−	4.54523i	0.0997734	−	0.372359i	−0.897926	−	0.440145i	$-0.854927\pi$
$149$	1.21789	−	4.54523i	0.0997734	−	0.372359i	0.997700	+	0.0677861i	$0.0215935\pi$
$150$		0			0
$151$	0.563961	+	0.151113i	0.0458945	+	0.0122974i	0.281693	−	0.959505i	$-0.409104\pi$
$151$	0.563961	+	0.151113i	0.0458945	+	0.0122974i	−0.235799	+	0.971802i	$0.575771\pi$
$152$	18.4545	−	10.6547i	1.49685	−	0.864210i
$153$		0			0
$154$	3.96296	+	3.18921i	0.319344	+	0.256994i
$155$			0.992638i			0.0797306i
$156$		0			0
$157$	−9.61395	+	5.55061i	−0.767276	+	0.442987i	−0.831902	−	0.554922i	$-0.812748\pi$
$157$	−9.61395	+	5.55061i	−0.767276	+	0.442987i	0.0646257	+	0.997910i	$0.479415\pi$
$158$	−1.63380	+	0.437774i	−0.129978	+	0.0348275i
$159$		0			0
$160$	6.13322	−	10.6231i	0.484874	−	0.839826i
$161$	−10.0556	−	1.56127i	−0.792489	−	0.123045i
$162$		0			0
$163$	15.9158	+	4.26463i	1.24662	+	0.334031i	0.821031	−	0.570884i	$-0.193399\pi$
$163$	15.9158	+	4.26463i	1.24662	+	0.334031i	0.425592	+	0.904915i	$0.360066\pi$
$164$	4.07326	−	15.2016i	0.318068	−	1.18705i
$165$		0			0
$166$	1.69535			0.131584
$167$	−0.00245012	+	0.00914399i	−0.000189596	+	0.000707583i	−0.966021	−	0.258465i	$-0.916783\pi$
$167$	−0.00245012	+	0.00914399i	−0.000189596	+	0.000707583i	0.965831	+	0.259173i	$0.0834499\pi$
$168$		0			0
$169$	−5.24763	+	11.8938i	−0.403664	+	0.914907i
$170$	5.40610	−	9.36364i	0.414629	−	0.718159i
$171$		0			0
$172$	0.646475	−	1.11973i	0.0492933	−	0.0853784i
$173$	−10.4806	−	18.1529i	−0.796823	−	1.38014i	−0.921675	−	0.387963i	$-0.873179\pi$
$173$	−10.4806	−	18.1529i	−0.796823	−	1.38014i	0.124852	−	0.992175i	$-0.460154\pi$
$174$		0			0
$175$	0.572114	+	1.47695i	0.0432478	+	0.111647i
$176$	−0.425051	−	1.58631i	−0.0320394	−	0.119573i
$177$		0			0
$178$			4.95253i			0.371208i
$179$	8.35625	+	4.82448i	0.624576	+	0.360599i	0.778648	−	0.627461i	$-0.215906\pi$
$179$	8.35625	+	4.82448i	0.624576	+	0.360599i	−0.154073	+	0.988060i	$0.549239\pi$
$180$		0			0
$181$	1.25766			0.0934813			0.0467407	−	0.998907i	$-0.485117\pi$
$181$	1.25766			0.0934813			0.0467407	+	0.998907i	$0.485117\pi$
$182$	7.01633	+	2.65534i	0.520085	+	0.196827i
$183$		0			0
$184$	−7.23244	−	7.23244i	−0.533183	−	0.533183i
$185$	12.8481	+	7.41788i	0.944614	+	0.545373i
$186$		0			0
$187$	−4.14674	−	15.4759i	−0.303240	−	1.13171i
$188$	2.60552	+	9.72395i	0.190027	+	0.709192i
$189$		0			0
$190$	9.34833	−	9.34833i	0.678199	−	0.678199i
$191$	1.22251	+	2.11745i	0.0884578	+	0.153213i	0.906859	−	0.421433i	$-0.138473\pi$
$191$	1.22251	+	2.11745i	0.0884578	+	0.153213i	−0.818402	+	0.574647i	$0.805139\pi$
$192$		0			0
$193$	4.45444	+	16.6242i	0.320638	+	1.19664i	0.918625	+	0.395131i	$0.129301\pi$
$193$	4.45444	+	16.6242i	0.320638	+	1.19664i	−0.597987	+	0.801506i	$0.704033\pi$
$194$	6.34970	−	10.9980i	0.455882	−	0.789610i
$195$		0			0
$196$	−2.93236	+	9.21550i	−0.209454	+	0.658250i
$197$	−6.05858	+	22.6109i	−0.431656	+	1.61096i	0.317287	+	0.948329i	$0.397228\pi$
$197$	−6.05858	+	22.6109i	−0.431656	+	1.61096i	−0.748944	+	0.662634i	$0.769439\pi$
$198$		0			0
$199$	−18.6415			−1.32146			−0.660732	−	0.750622i	$-0.729754\pi$
$199$	−18.6415			−1.32146			−0.660732	+	0.750622i	$0.729754\pi$
$200$	−0.412042	+	1.53776i	−0.0291357	+	0.108736i
$201$		0			0
$202$	−2.68894	+	0.720500i	−0.189193	+	0.0506942i
$203$	−6.18877	+	2.39729i	−0.434366	+	0.168257i
$204$		0			0
$205$		−	23.8987i		−	1.66916i
$206$	6.96172	−	1.86539i	0.485046	−	0.129968i
$207$		0			0
$208$	−1.32252	−	2.02903i	−0.0917002	−	0.140688i
$209$		−	19.5905i		−	1.35510i
$210$		0			0
$211$	−5.61294	−	9.72190i	−0.386411	−	0.669283i	0.605553	−	0.795805i	$-0.292952\pi$
$211$	−5.61294	−	9.72190i	−0.386411	−	0.669283i	−0.991964	+	0.126522i	$0.959619\pi$
$212$	2.59249	−	1.49677i	0.178053	−	0.102799i
$213$		0			0
$214$	−1.12195	−	1.12195i	−0.0766950	−	0.0766950i
$215$	0.508168	−	1.89651i	0.0346567	−	0.129341i
$216$		0			0
$217$	0.505682	−	1.14515i	0.0343279	−	0.0777381i
$218$	3.83579	−	2.21459i	0.259792	−	0.149991i
$219$		0			0
$220$	−3.54300	−	6.13666i	−0.238869	−	0.413734i
$221$	−12.9023	−	19.7949i	−0.867905	−	1.33155i
$222$		0			0
$223$	9.81982	+	2.63121i	0.657584	+	0.176199i	0.572155	−	0.820145i	$-0.306107\pi$
$223$	9.81982	+	2.63121i	0.657584	+	0.176199i	0.0854284	+	0.996344i	$0.472774\pi$
$224$	−12.4873	+	9.13079i	−0.834343	+	0.610076i
$225$		0			0
$226$	−9.42920	+	2.52655i	−0.627221	+	0.168063i
$227$	4.65548	−	4.65548i	0.308995	−	0.308995i	−0.535524	−	0.844520i	$-0.679886\pi$
$227$	4.65548	−	4.65548i	0.308995	−	0.308995i	0.844520	+	0.535524i	$0.179886\pi$
$228$		0			0
$229$	1.20056	−	0.321690i	0.0793354	−	0.0212578i	−0.218933	−	0.975740i	$-0.570258\pi$
$229$	1.20056	−	0.321690i	0.0793354	−	0.0212578i	0.298268	+	0.954482i	$0.403591\pi$
$230$	−5.49552	−	3.17284i	−0.362364	−	0.209211i
$231$		0			0
$232$	−6.44358	−	1.72655i	−0.423042	−	0.113354i
$233$	−12.6928	−	7.32822i	−0.831536	−	0.480088i	0.0228423	−	0.999739i	$-0.492728\pi$
$233$	−12.6928	−	7.32822i	−0.831536	−	0.480088i	−0.854378	+	0.519652i	$0.826062\pi$
$234$		0			0
$235$	7.64360	+	13.2391i	0.498614	+	0.863624i
$236$	5.42696	−	5.42696i	0.353265	−	0.353265i
$237$		0			0
$238$	−11.0069	+	8.04829i	−0.713470	+	0.521693i
$239$	4.85743	+	4.85743i	0.314201	+	0.314201i	0.846535	−	0.532334i	$-0.178685\pi$
$239$	4.85743	+	4.85743i	0.314201	+	0.314201i	−0.532334	+	0.846535i	$0.678685\pi$
$240$		0			0
$241$	−13.5158	−	13.5158i	−0.870627	−	0.870627i	0.121914	−	0.992541i	$-0.461097\pi$
$241$	−13.5158	−	13.5158i	−0.870627	−	0.870627i	−0.992541	+	0.121914i	$0.961097\pi$
$242$	−3.81553	−	1.02237i	−0.245271	−	0.0657202i
$243$		0			0
$244$	−6.48800	−	11.2375i	−0.415352	−	0.719410i
$245$	−0.679246	+	14.6699i	−0.0433955	+	0.937223i
$246$		0			0
$247$	−8.97418	−	27.4626i	−0.571013	−	1.74740i
$248$	1.08968	−	0.629127i	0.0691947	−	0.0399496i
$249$		0			0
$250$			9.23702i			0.584200i
$251$	1.37023	−	2.37330i	0.0864880	−	0.149802i	−0.819536	−	0.573027i	$-0.805769\pi$
$251$	1.37023	−	2.37330i	0.0864880	−	0.149802i	0.906024	+	0.423226i	$0.139102\pi$
$252$		0			0
$253$	−9.08277	+	2.43372i	−0.571029	+	0.153007i
$254$	7.94215	+	2.12809i	0.498335	+	0.133528i
$255$		0			0
$256$	−13.6927			−0.855794
$257$	10.9615			0.683758			0.341879	−	0.939744i	$-0.388937\pi$
$257$	10.9615			0.683758			0.341879	+	0.939744i	$0.388937\pi$
$258$		0			0
$259$	−11.0433	−	15.1029i	−0.686198	−	0.938447i
$260$	−7.77782	−	6.97955i	−0.482360	−	0.432853i
$261$		0			0
$262$	4.24649	+	15.8481i	0.262349	+	0.979100i
$263$	−11.0595	+	19.1556i	−0.681958	+	1.18119i	0.292425	+	0.956289i	$0.405538\pi$
$263$	−11.0595	+	19.1556i	−0.681958	+	1.18119i	−0.974383	+	0.224897i	$0.927795\pi$
$264$		0			0
$265$	3.21440	−	3.21440i	0.197459	−	0.197459i
$266$	−15.5470	+	6.02233i	−0.953249	+	0.369252i
$267$		0			0
$268$	4.12365	+	15.3897i	0.251892	+	0.940073i
$269$			9.12867i			0.556585i	0.960496	+	0.278292i	$0.0897684\pi$
$269$			9.12867i			0.556585i	−0.960496	+	0.278292i	$0.910232\pi$
$270$		0			0
$271$	13.7284	+	13.7284i	0.833942	+	0.833942i	0.988053	−	0.154112i	$-0.0492516\pi$
$271$	13.7284	+	13.7284i	0.833942	+	0.833942i	−0.154112	+	0.988053i	$0.549252\pi$
$272$	4.40216			0.266920
$273$		0			0
$274$	8.86600			0.535614
$275$	1.03491	+	1.03491i	0.0624077	+	0.0624077i
$276$		0			0
$277$		−	28.0822i		−	1.68730i	−0.536896	−	0.843649i	$-0.680403\pi$
$277$		−	28.0822i		−	1.68730i	0.536896	−	0.843649i	$-0.319597\pi$
$278$	2.07604	+	7.74789i	0.124513	+	0.464688i
$279$		0			0
$280$	−9.25434	+	11.4996i	−0.553053	+	0.687232i
$281$	−3.79779	+	3.79779i	−0.226557	+	0.226557i	−0.811253	−	0.584695i	$-0.801214\pi$
$281$	−3.79779	+	3.79779i	−0.226557	+	0.226557i	0.584695	+	0.811253i	$0.301214\pi$
$282$		0			0
$283$	0.692540	−	1.19951i	0.0411672	−	0.0713037i	−0.844708	−	0.535228i	$-0.820226\pi$
$283$	0.692540	−	1.19951i	0.0411672	−	0.0713037i	0.885875	+	0.463924i	$0.153559\pi$
$284$	3.49489	+	13.0431i	0.207383	+	0.773966i
$285$		0			0
$286$	6.92210	−	0.374439i	0.409312	−	0.0221410i
$287$	−12.1748	+	27.5707i	−0.718655	+	1.62745i
$288$		0			0
$289$	25.9469			1.52629
$290$	−4.13868			−0.243032
$291$		0			0
$292$	−13.5386	−	3.62765i	−0.792286	−	0.212292i
$293$	17.3288	−	4.64324i	1.01236	−	0.271261i	0.285745	−	0.958306i	$-0.407759\pi$
$293$	17.3288	−	4.64324i	1.01236	−	0.271261i	0.726615	+	0.687045i	$0.241092\pi$
$294$		0			0
$295$	5.82735	−	10.0933i	0.339281	−	0.587653i
$296$		−	18.8056i		−	1.09305i
$297$		0			0
$298$	−3.20478	+	1.85028i	−0.185648	+	0.107184i
$299$	−11.6176	+	7.57237i	−0.671866	+	0.437922i
$300$		0			0
$301$	−1.55239	+	1.92902i	−0.0894782	+	0.111187i
$302$	−0.229578	−	0.397641i	−0.0132107	−	0.0228817i
$303$		0			0
$304$	5.19929	+	1.39315i	0.298200	+	0.0799024i
$305$	−13.9333	−	13.9333i	−0.797820	−	0.797820i
$306$		0			0
$307$	−5.47242	−	5.47242i	−0.312327	−	0.312327i	0.533483	−	0.845811i	$-0.320883\pi$
$307$	−5.47242	−	5.47242i	−0.312327	−	0.312327i	−0.845811	+	0.533483i	$0.820883\pi$
$308$	0.961159	+	8.88446i	0.0547671	+	0.506239i
$309$		0			0
$310$	0.551990	−	0.551990i	0.0313509	−	0.0313509i
$311$	−3.27357	−	5.66998i	−0.185627	−	0.321515i	0.758161	−	0.652068i	$-0.226098\pi$
$311$	−3.27357	−	5.66998i	−0.185627	−	0.321515i	−0.943788	+	0.330553i	$0.892765\pi$
$312$		0			0
$313$	−14.8538	−	8.57583i	−0.839585	−	0.484735i	0.0175379	−	0.999846i	$-0.494417\pi$
$313$	−14.8538	−	8.57583i	−0.839585	−	0.484735i	−0.857123	+	0.515111i	$0.827751\pi$
$314$	8.43277	+	2.25955i	0.475889	+	0.127514i
$315$		0			0
$316$	−2.57332	−	1.48570i	−0.144760	−	0.0835774i
$317$	15.5081	−	4.15537i	0.871019	−	0.233389i	0.204491	−	0.978869i	$-0.434446\pi$
$317$	15.5081	−	4.15537i	0.871019	−	0.233389i	0.666528	+	0.745480i	$0.267780\pi$
$318$		0			0
$319$	−4.33654	+	4.33654i	−0.242800	+	0.242800i
$320$	−6.59541	+	1.76723i	−0.368695	+	0.0987914i
$321$		0			0
$322$	4.72354	+	6.45993i	0.263233	+	0.359998i
$323$	50.7236	+	13.5914i	2.82234	+	0.756243i
$324$		0			0
$325$	1.92486	+	0.976692i	0.106772	+	0.0541771i
$326$	−6.47904	−	11.2220i	−0.358841	−	0.621530i
$327$		0			0
$328$	−26.2351	+	15.1468i	−1.44859	+	0.836345i
$329$	−2.07358	−	19.1672i	−0.114320	−	1.05672i
$330$		0			0
$331$	−1.47690	+	5.51186i	−0.0811776	+	0.302959i	−0.994563	−	0.104137i	$-0.966792\pi$
$331$	−1.47690	+	5.51186i	−0.0811776	+	0.302959i	0.913385	+	0.407096i	$0.133459\pi$
$332$	2.10597	+	2.10597i	0.115580	+	0.115580i
$333$		0			0
$334$	0.00644730	−	0.00372235i	0.000352781	−	0.000203678i
$335$	12.0972	+	20.9529i	0.660940	+	1.14478i
$336$		0			0
$337$			6.54996i			0.356799i	0.983958	+	0.178399i	$0.0570919\pi$
$337$			6.54996i			0.356799i	−0.983958	+	0.178399i	$0.942908\pi$
$338$	9.53207	−	3.69583i	0.518476	−	0.201027i
$339$		0			0
$340$	18.3471	−	4.91608i	0.995009	−	0.266612i
$341$		−	1.15676i		−	0.0626420i
$342$		0			0
$343$	8.25691	−	16.5778i	0.445831	−	0.895117i
$344$	−2.40399	+	0.644146i	−0.129614	+	0.0347300i
$345$		0			0
$346$	−4.26645	+	15.9226i	−0.229366	+	0.856005i
$347$	22.8051			1.22424			0.612120	−	0.790765i	$-0.290317\pi$
$347$	22.8051			1.22424			0.612120	+	0.790765i	$0.290317\pi$
$348$		0			0
$349$	−0.529316	+	1.97543i	−0.0283336	+	0.105743i	−0.978645	−	0.205560i	$-0.934099\pi$
$349$	−0.529316	+	1.97543i	−0.0283336	+	0.105743i	0.950311	+	0.311302i	$0.100765\pi$
$350$	0.503164	−	1.13945i	0.0268953	−	0.0609062i
$351$		0			0
$352$	−7.14728	+	12.3795i	−0.380951	+	0.659827i
$353$	−6.69454	−	24.9843i	−0.356314	−	1.32978i	−0.878823	−	0.477149i	$-0.841670\pi$
$353$	−6.69454	−	24.9843i	−0.356314	−	1.32978i	0.522508	−	0.852634i	$-0.324996\pi$
$354$		0			0
$355$	10.2527	+	17.7581i	0.544154	+	0.942503i
$356$	−6.15206	+	6.15206i	−0.326058	+	0.326058i
$357$		0			0
$358$	−1.96396	−	7.32960i	−0.103798	−	0.387381i
$359$	3.89528	+	14.5374i	0.205585	+	0.767255i	0.989270	+	0.146096i	$0.0466709\pi$
$359$	3.89528	+	14.5374i	0.205585	+	0.767255i	−0.783685	+	0.621158i	$0.786662\pi$
$360$		0			0
$361$	39.1529	+	22.6049i	2.06068	+	1.18973i
$362$	−0.699366	−	0.699366i	−0.0367579	−	0.0367579i
$363$		0			0
$364$	5.41725	+	12.0142i	0.283941	+	0.629715i
$365$	−21.2843			−1.11407
$366$		0			0
$367$	13.2477	+	7.64858i	0.691526	+	0.399253i	0.804184	−	0.594381i	$-0.202603\pi$
$367$	13.2477	+	7.64858i	0.691526	+	0.399253i	−0.112657	+	0.993634i	$0.535936\pi$
$368$		−	2.58362i		−	0.134681i
$369$		0			0
$370$	−3.01968	−	11.2696i	−0.156986	−	0.585879i
$371$	−5.34581	+	2.07076i	−0.277540	+	0.107509i
$372$		0			0
$373$	10.2210	+	17.7032i	0.529221	+	0.916638i	0.999419	+	0.0340771i	$0.0108492\pi$
$373$	10.2210	+	17.7032i	0.529221	+	0.916638i	−0.470198	+	0.882561i	$0.655817\pi$
$374$	−6.29994	+	10.9118i	−0.325762	+	0.564237i
$375$		0			0
$376$	9.68892	−	16.7817i	0.499668	−	0.865450i
$377$	−4.09257	+	8.06561i	−0.210778	+	0.415400i
$378$		0			0
$379$	−1.64237	+	6.12940i	−0.0843628	+	0.314846i	−0.995193	−	0.0979355i	$-0.968776\pi$
$379$	−1.64237	+	6.12940i	−0.0843628	+	0.314846i	0.910830	+	0.412782i	$0.135443\pi$
$380$	23.2251			1.19142
$381$		0			0
$382$	0.497662	−	1.85730i	0.0254626	−	0.0950277i
$383$	6.04679	+	1.62023i	0.308976	+	0.0827899i	0.409975	−	0.912097i	$-0.365537\pi$
$383$	6.04679	+	1.62023i	0.308976	+	0.0827899i	−0.100999	+	0.994887i	$0.532204\pi$
$384$		0			0
$385$	4.90169	+	12.6540i	0.249813	+	0.644909i
$386$	6.76741	−	11.7215i	0.344452	−	0.596609i
$387$		0			0
$388$	21.5494	−	5.77414i	1.09400	−	0.293138i
$389$	−4.72095	+	2.72564i	−0.239362	+	0.138196i	−0.614883	−	0.788618i	$-0.710797\pi$
$389$	−4.72095	+	2.72564i	−0.239362	+	0.138196i	0.375522	+	0.926814i	$0.377464\pi$
$390$		0			0
$391$		−	25.2055i		−	1.27470i
$392$	16.5345	−	8.55200i	0.835118	−	0.431941i
$393$		0			0
$394$	15.9427	−	9.20450i	0.803180	−	0.463716i
$395$	−4.35848	−	1.16785i	−0.219299	−	0.0587610i
$396$		0			0
$397$	2.48129	−	9.26032i	0.124533	−	0.464762i	−0.875290	−	0.483598i	$-0.839330\pi$
$397$	2.48129	−	9.26032i	0.124533	−	0.464762i	0.999823	+	0.0188365i	$0.00599620\pi$
$398$	10.3663	+	10.3663i	0.519614	+	0.519614i
$399$		0			0
$400$	−0.348261	+	0.201069i	−0.0174130	+	0.0100534i
$401$	−26.5226	+	26.5226i	−1.32447	+	1.32447i	−0.414362	+	0.910112i	$0.635995\pi$
$401$	−26.5226	+	26.5226i	−1.32447	+	1.32447i	−0.910112	+	0.414362i	$0.864005\pi$
$402$		0			0
$403$	−0.529898	−	1.62158i	−0.0263961	−	0.0807766i
$404$	−4.23523	−	2.44521i	−0.210710	−	0.121654i
$405$		0			0
$406$	4.77457	+	2.10838i	0.236958	+	0.104637i
$407$	−14.9724	−	8.64434i	−0.742156	−	0.428484i
$408$		0			0
$409$	−21.7339	+	21.7339i	−1.07467	+	1.07467i	−0.0776962	+	0.996977i	$0.524756\pi$
$409$	−21.7339	+	21.7339i	−1.07467	+	1.07467i	−0.996977	+	0.0776962i	$0.975244\pi$
$410$	−13.2897	+	13.2897i	−0.656332	+	0.656332i
$411$		0			0
$412$	10.9651	+	6.33069i	0.540210	+	0.311891i
$413$	−11.8645	+	8.67542i	−0.583816	+	0.426889i
$414$		0			0
$415$	3.91676	+	2.26134i	0.192266	+	0.111005i
$416$	−4.34839	+	20.6280i	−0.213197	+	1.01137i
$417$		0			0
$418$	−10.8940	+	10.8940i	−0.532842	+	0.532842i
$419$	−20.2493	+	11.6909i	−0.989241	+	0.571138i	−0.905047	−	0.425311i	$-0.860165\pi$
$419$	−20.2493	+	11.6909i	−0.989241	+	0.571138i	−0.0841936	+	0.996449i	$0.526831\pi$
$420$		0			0
$421$	14.1492	+	14.1492i	0.689589	+	0.689589i	0.962141	−	0.272552i	$-0.0878676\pi$
$421$	14.1492	+	14.1492i	0.689589	+	0.689589i	−0.272552	+	0.962141i	$0.587868\pi$
$422$	−2.28493	+	8.52747i	−0.111229	+	0.415111i
$423$		0			0
$424$	−5.56591	−	1.49138i	−0.270305	−	0.0724279i
$425$	−3.39759	+	1.96160i	−0.164807	+	0.0951516i
$426$		0			0
$427$	8.97605	+	23.1722i	0.434382	+	1.12138i
$428$		−	2.78739i		−	0.134733i
$429$		0			0
$430$	−1.33720	+	0.772034i	−0.0644856	+	0.0372308i
$431$	12.7388	−	3.41335i	0.613606	−	0.164415i	0.0613869	−	0.998114i	$-0.480448\pi$
$431$	12.7388	−	3.41335i	0.613606	−	0.164415i	0.552220	+	0.833699i	$0.313781\pi$
$432$		0			0
$433$	−5.53868	+	9.59327i	−0.266172	+	0.461023i	−0.967870	−	0.251451i	$-0.919092\pi$
$433$	−5.53868	+	9.59327i	−0.266172	+	0.461023i	0.701698	+	0.712474i	$0.252426\pi$
$434$	−0.918003	+	0.355600i	−0.0440656	+	0.0170693i
$435$		0			0
$436$	7.51581	+	2.01385i	0.359942	+	0.0964462i
$437$	7.97676	−	29.7697i	0.381580	−	1.42408i
$438$		0			0
$439$	13.2330			0.631578			0.315789	−	0.948829i	$-0.397731\pi$
$439$	13.2330			0.631578			0.315789	+	0.948829i	$0.397731\pi$
$440$	−3.53024	+	13.1750i	−0.168298	+	0.628095i
$441$		0			0
$442$	−3.83287	+	18.1824i	−0.182311	+	0.864850i
$443$	−2.45582	+	4.25360i	−0.116679	+	0.202095i	−0.918450	−	0.395537i	$-0.870558\pi$
$443$	−2.45582	+	4.25360i	−0.116679	+	0.202095i	0.801770	+	0.597632i	$0.203892\pi$
$444$		0			0
$445$	−6.60594	+	11.4418i	−0.313151	+	0.542394i
$446$	−3.99747	−	6.92382i	−0.189286	−	0.327852i
$447$		0			0
$448$	8.50906	+	1.32115i	0.402015	+	0.0624186i
$449$	−0.246197	−	0.918821i	−0.0116188	−	0.0433618i	0.959873	−	0.280435i	$-0.0904786\pi$
$449$	−0.246197	−	0.918821i	−0.0116188	−	0.0433618i	−0.971492	+	0.237073i	$0.923812\pi$
$450$		0			0
$451$			27.8501i			1.31141i
$452$	−14.8515	−	8.57451i	−0.698555	−	0.403311i
$453$		0			0
$454$	−5.17768			−0.243001
$455$	12.6680	+	15.4934i	0.593885	+	0.726341i
$456$		0			0
$457$	−13.6046	−	13.6046i	−0.636394	−	0.636394i	0.313270	−	0.949664i	$-0.398576\pi$
$457$	−13.6046	−	13.6046i	−0.636394	−	0.636394i	−0.949664	+	0.313270i	$0.898576\pi$
$458$	−0.846500	−	0.488727i	−0.0395543	−	0.0228367i
$459$		0			0
$460$	−2.88524	−	10.7679i	−0.134525	−	0.502055i
$461$	−1.66867	−	6.22758i	−0.0777179	−	0.290047i	0.916118	−	0.400909i	$-0.131306\pi$
$461$	−1.66867	−	6.22758i	−0.0777179	−	0.290047i	−0.993836	+	0.110862i	$0.964639\pi$
$462$		0			0
$463$	7.67988	−	7.67988i	0.356914	−	0.356914i	−0.505760	−	0.862674i	$-0.668788\pi$
$463$	7.67988	−	7.67988i	0.356914	−	0.356914i	0.862674	+	0.505760i	$0.168788\pi$
$464$	−0.842525	−	1.45930i	−0.0391132	−	0.0677461i
$465$		0			0
$466$	2.98318	+	11.1334i	0.138193	+	0.515745i
$467$	10.7238	−	18.5741i	0.496236	−	0.859507i	−0.503754	−	0.863847i	$-0.668048\pi$
$467$	10.7238	−	18.5741i	0.496236	−	0.859507i	0.999991	+	0.00434034i	$0.00138158\pi$
$468$		0			0
$469$	−3.28177	−	30.3350i	−0.151538	−	1.40074i
$470$	3.11157	−	11.6125i	0.143526	−	0.535647i
$471$		0			0
$472$	−14.7733			−0.679997
$473$	−0.592187	+	2.21007i	−0.0272288	+	0.101619i
$474$		0			0
$475$	−4.63361	+	1.24157i	−0.212604	+	0.0569672i
$476$	−23.6704	−	3.67517i	−1.08493	−	0.168451i
$477$		0			0
$478$		−	5.40228i		−	0.247095i
$479$	17.4860	−	4.68536i	0.798956	−	0.214080i	0.163831	−	0.986489i	$-0.447615\pi$
$479$	17.4860	−	4.68536i	0.798956	−	0.214080i	0.635126	+	0.772409i	$0.280948\pi$
$480$		0			0
$481$	−24.9487	−	5.25920i	−1.13756	−	0.239799i
$482$			15.0318i			0.684680i
$483$		0			0
$484$	−3.46968	−	6.00966i	−0.157713	−	0.273166i
$485$	29.3394	−	16.9391i	1.33223	−	0.769165i
$486$		0			0
$487$	5.09200	+	5.09200i	0.230740	+	0.230740i	0.813002	−	0.582261i	$-0.197832\pi$
$487$	5.09200	+	5.09200i	0.230740	+	0.230740i	−0.582261	+	0.813002i	$0.697832\pi$
$488$	−6.46463	+	24.1263i	−0.292640	+	1.09215i
$489$		0			0
$490$	8.53539	−	7.77996i	0.385590	−	0.351463i
$491$	24.3966	−	14.0854i	1.10101	−	0.635666i	0.164520	−	0.986374i	$-0.447392\pi$
$491$	24.3966	−	14.0854i	1.10101	−	0.635666i	0.936485	+	0.350708i	$0.114059\pi$
$492$		0			0
$493$	−8.21957	−	14.2367i	−0.370191	−	0.641190i
$494$	−10.2811	+	20.2619i	−0.462568	+	0.911625i
$495$		0			0
$496$	0.307002	+	0.0822609i	0.0137848	+	0.00369362i
$497$	−2.78138	−	25.7096i	−0.124762	−	1.15323i
$498$		0			0
$499$	−20.3207	+	5.44491i	−0.909678	+	0.243748i	−0.683168	−	0.730261i	$-0.739398\pi$
$499$	−20.3207	+	5.44491i	−0.909678	+	0.243748i	−0.226510	+	0.974009i	$0.572732\pi$
$500$	−11.4743	+	11.4743i	−0.513145	+	0.513145i
$501$		0			0
$502$	−2.08172	+	0.557794i	−0.0929116	+	0.0248956i
$503$	18.9822	+	10.9594i	0.846374	+	0.488655i	0.859426	−	0.511260i	$-0.170821\pi$
$503$	18.9822	+	10.9594i	0.846374	+	0.488655i	−0.0130514	+	0.999915i	$0.504155\pi$
$504$		0			0
$505$	−7.17330	−	1.92208i	−0.319208	−	0.0855314i
$506$	6.40414	+	3.69743i	0.284699	+	0.164371i
$507$		0			0
$508$	7.22226	+	12.5093i	0.320436	+	0.555011i
$509$	2.12967	−	2.12967i	0.0943961	−	0.0943961i	−0.658332	−	0.752728i	$-0.728738\pi$
$509$	2.12967	−	2.12967i	0.0943961	−	0.0943961i	0.752728	+	0.658332i	$0.228738\pi$
$510$		0			0
$511$	24.5545	+	10.8429i	1.08623	+	0.479661i
$512$	−5.30352	−	5.30352i	−0.234385	−	0.234385i
$513$		0			0
$514$	−6.09550	−	6.09550i	−0.268861	−	0.268861i
$515$	18.5718	+	4.97630i	0.818371	+	0.219282i
$516$		0			0
$517$	−8.90738	−	15.4280i	−0.391746	−	0.678525i
$518$	−2.25746	+	14.5395i	−0.0991871	+	0.638828i
$519$		0			0
$520$	1.08653	+	20.0863i	0.0476476	+	0.880843i
$521$	−20.7786	+	11.9965i	−0.910328	+	0.525578i	−0.880537	−	0.473978i	$-0.842818\pi$
$521$	−20.7786	+	11.9965i	−0.910328	+	0.525578i	−0.0297912	+	0.999556i	$0.509484\pi$
$522$		0			0
$523$			9.58298i			0.419034i	0.977805	+	0.209517i	$0.0671892\pi$
$523$			9.58298i			0.419034i	−0.977805	+	0.209517i	$0.932811\pi$
$524$	−14.4116	+	24.9616i	−0.629573	+	1.09045i
$525$		0			0
$526$	16.8021	−	4.50212i	0.732608	−	0.196302i
$527$	2.99507	+	0.802528i	0.130467	+	0.0349587i
$528$		0			0
$529$	8.20689			0.356821
$530$	−3.57496			−0.155286
$531$		0			0
$532$	−26.7935	−	11.8316i	−1.16165	−	0.512966i
$533$	12.7578	+	39.0411i	0.552602	+	1.69106i
$534$		0			0
$535$	−1.09553	−	4.08856i	−0.0473637	−	0.176764i
$536$	15.3342	−	26.5596i	0.662337	−	1.14720i
$537$		0			0
$538$	5.07631	−	5.07631i	0.218855	−	0.218855i
$539$	0.791552	−	17.0953i	0.0340946	−	0.736349i
$540$		0			0
$541$	−5.61424	−	20.9526i	−0.241375	−	0.900823i	−0.975171	−	0.221454i	$-0.928920\pi$
$541$	−5.61424	−	20.9526i	−0.241375	−	0.900823i	0.733796	−	0.679370i	$-0.237747\pi$
$542$		−	15.2683i		−	0.655830i
$543$		0			0
$544$	−27.0942	−	27.0942i	−1.16166	−	1.16166i
$545$	11.8157			0.506131
$546$		0			0
$547$	−24.6132			−1.05238			−0.526191	−	0.850366i	$-0.676380\pi$
$547$	−24.6132			−1.05238			−0.526191	+	0.850366i	$0.676380\pi$
$548$	11.0134	+	11.0134i	0.470468	+	0.470468i
$549$		0			0
$550$		−	1.15100i		−	0.0490788i
$551$	−5.20248	−	19.4159i	−0.221633	−	0.827146i
$552$		0			0
$553$	4.43321	+	3.56764i	0.188519	+	0.151712i
$554$	−15.6161	+	15.6161i	−0.663464	+	0.663464i
$555$		0			0
$556$	−7.04560	+	12.2033i	−0.298800	+	0.517537i
$557$	−0.132844	−	0.495782i	−0.00562880	−	0.0210070i	0.963054	−	0.269307i	$-0.0867947\pi$
$557$	−0.132844	−	0.495782i	−0.00562880	−	0.0210070i	−0.968683	+	0.248300i	$0.920128\pi$
$558$		0			0
$559$	0.182263	+	3.36942i	0.00770889	+	0.142511i
$560$	−3.70693	+	0.401032i	−0.156646	+	0.0169467i
$561$		0			0
$562$	4.22379			0.178170
$563$	43.2008			1.82070			0.910349	−	0.413842i	$-0.135813\pi$
$563$	43.2008			1.82070			0.910349	+	0.413842i	$0.135813\pi$
$564$		0			0
$565$	−25.1543	−	6.74007i	−1.05825	−	0.283557i
$566$	−1.05214	+	0.281920i	−0.0442248	+	0.0118500i
$567$		0			0
$568$	12.9961	−	22.5099i	0.545305	−	0.944496i
$569$			30.7249i			1.28805i	0.765003	+	0.644027i	$0.222737\pi$
$569$			30.7249i			1.28805i	−0.765003	+	0.644027i	$0.777263\pi$
$570$		0			0
$571$	18.1885	−	10.5012i	0.761167	−	0.439460i	−0.0685475	−	0.997648i	$-0.521836\pi$
$571$	18.1885	−	10.5012i	0.761167	−	0.439460i	0.829715	+	0.558188i	$0.188503\pi$
$572$	9.06379	+	8.13353i	0.378976	+	0.340080i
$573$		0			0
$574$	22.1018	−	8.56142i	0.922513	−	0.357347i
$575$	1.15126	+	1.99405i	0.0480110	+	0.0831574i
$576$		0			0
$577$	−8.56673	−	2.29545i	−0.356638	−	0.0955608i	0.0760516	−	0.997104i	$-0.475769\pi$
$577$	−8.56673	−	2.29545i	−0.356638	−	0.0955608i	−0.432689	+	0.901543i	$0.642435\pi$
$578$	−14.4287	−	14.4287i	−0.600153	−	0.600153i
$579$		0			0
$580$	−5.14109	−	5.14109i	−0.213472	−	0.213472i
$581$	−3.36655	−	4.60411i	−0.139668	−	0.191011i
$582$		0			0
$583$	−3.74587	+	3.74587i	−0.155138	+	0.155138i
$584$	13.4898	+	23.3650i	0.558212	+	0.966852i
$585$		0			0
$586$	−12.2183	−	7.05424i	−0.504734	−	0.291408i
$587$	−30.5954	−	8.19801i	−1.26281	−	0.338368i	−0.435536	−	0.900171i	$-0.643441\pi$
$587$	−30.5954	−	8.19801i	−1.26281	−	0.338368i	−0.827271	+	0.561803i	$0.810108\pi$
$588$		0			0
$589$	3.28344	+	1.89570i	0.135292	+	0.0781108i
$590$	−8.85320	+	2.37221i	−0.364480	+	0.0976622i
$591$		0			0
$592$	3.35893	−	3.35893i	0.138051	−	0.138051i
$593$	5.48978	−	1.47098i	0.225438	−	0.0604060i	−0.144332	−	0.989529i	$-0.546103\pi$
$593$	5.48978	−	1.47098i	0.225438	−	0.0604060i	0.369770	+	0.929123i	$0.379437\pi$
$594$		0			0
$595$	−36.1644	+	3.91242i	−1.48260	+	0.160393i
$596$	−6.27941	−	1.68256i	−0.257215	−	0.0689205i
$597$		0			0
$598$	10.6713	+	2.24951i	0.436380	+	0.0919892i
$599$	−5.44521	−	9.43138i	−0.222485	−	0.385356i	0.733077	−	0.680146i	$-0.238084\pi$
$599$	−5.44521	−	9.43138i	−0.222485	−	0.385356i	−0.955562	+	0.294790i	$0.904750\pi$
$600$		0			0
$601$	−1.42936	+	0.825243i	−0.0583049	+	0.0336624i	−0.528869	−	0.848703i	$-0.677384\pi$
$601$	−1.42936	+	0.825243i	−0.0583049	+	0.0336624i	0.470564	+	0.882366i	$0.344050\pi$
$602$	1.93596	−	0.209440i	0.0789037	−	0.00853614i
$603$		0			0
$604$	0.208769	−	0.779135i	0.00849468	−	0.0317026i
$605$	−7.45132	−	7.45132i	−0.302939	−	0.302939i
$606$		0			0
$607$	22.6877	−	13.0987i	0.920865	−	0.531662i	0.0369540	−	0.999317i	$-0.488234\pi$
$607$	22.6877	−	13.0987i	0.920865	−	0.531662i	0.883911	+	0.467655i	$0.154901\pi$
$608$	−23.4259	−	40.5749i	−0.950046	−	1.64553i
$609$		0			0
$610$			15.4962i			0.627423i
$611$	−19.5540	−	17.5471i	−0.791072	−	0.709880i
$612$		0			0
$613$	22.6882	−	6.07928i	0.916367	−	0.245540i	0.230335	−	0.973111i	$-0.426018\pi$
$613$	22.6882	−	6.07928i	0.916367	−	0.245540i	0.686032	+	0.727571i	$0.259351\pi$
$614$			6.08625i			0.245621i
$615$		0			0
$616$	10.7844	−	13.4009i	0.434517	−	0.539938i
$617$	7.41451	−	1.98671i	0.298497	−	0.0799820i	−0.106462	−	0.994317i	$-0.533952\pi$
$617$	7.41451	−	1.98671i	0.298497	−	0.0799820i	0.404959	+	0.914335i	$0.367286\pi$
$618$		0			0
$619$	−7.36942	+	27.5031i	−0.296202	+	1.10544i	0.644056	+	0.764978i	$0.277250\pi$
$619$	−7.36942	+	27.5031i	−0.296202	+	1.10544i	−0.940258	+	0.340463i	$0.889416\pi$
$620$	1.37137			0.0550755
$621$		0			0
$622$	−1.33261	+	4.97337i	−0.0534328	+	0.199414i
$623$	13.4498	−	9.83454i	0.538853	−	0.394012i
$624$		0			0
$625$	−10.8242	+	18.7480i	−0.432967	+	0.749921i
$626$	3.49107	+	13.0288i	0.139531	+	0.520737i
$627$		0			0
$628$	7.66840	+	13.2821i	0.306003	+	0.530012i
$629$	32.7694	−	32.7694i	1.30660	−	1.30660i
$630$		0			0
$631$	−2.62809	−	9.80818i	−0.104623	−	0.390458i	0.893679	−	0.448706i	$-0.148115\pi$
$631$	−2.62809	−	9.80818i	−0.104623	−	0.390458i	−0.998302	+	0.0582487i	$0.981448\pi$
$632$	1.48035	+	5.52475i	0.0588852	+	0.219763i
$633$		0			0
$634$	−10.9345	−	6.31305i	−0.434265	−	0.250723i
$635$	15.5102	+	15.5102i	0.615503	+	0.615503i
$636$		0			0
$637$	−6.72156	−	24.3274i	−0.266318	−	0.963885i
$638$	4.82296			0.190943
$639$		0			0
$640$	−16.5958	−	9.58157i	−0.656005	−	0.378745i
$641$			23.1705i			0.915180i	0.889163	+	0.457590i	$0.151287\pi$
$641$			23.1705i			0.915180i	−0.889163	+	0.457590i	$0.848713\pi$
$642$		0			0
$643$	6.46488	+	24.1273i	0.254950	+	0.951486i	0.968118	+	0.250493i	$0.0805928\pi$
$643$	6.46488	+	24.1273i	0.254950	+	0.951486i	−0.713168	+	0.700993i	$0.752741\pi$
$644$	−2.15696	+	13.8922i	−0.0849959	+	0.547428i
$645$		0			0
$646$	−20.6487	−	35.7646i	−0.812411	−	1.40714i
$647$	−2.29221	+	3.97022i	−0.0901160	+	0.156085i	−0.907560	−	0.419923i	$-0.862057\pi$
$647$	−2.29221	+	3.97022i	−0.0901160	+	0.156085i	0.817444	+	0.576008i	$0.195390\pi$
$648$		0			0
$649$	−6.79083	+	11.7621i	−0.266564	+	0.461702i
$650$	−0.527259	−	1.61350i	−0.0206808	−	0.0632869i
$651$		0			0
$652$	5.89176	−	21.9883i	0.230739	−	0.861130i
$653$	25.4566			0.996192			0.498096	−	0.867122i	$-0.334033\pi$
$653$	25.4566			0.996192			0.498096	+	0.867122i	$0.334033\pi$
$654$		0			0
$655$	−11.3284	+	42.2780i	−0.442636	+	1.65194i
$656$	−7.39138	−	1.98051i	−0.288585	−	0.0773260i
$657$		0			0
$658$	−9.50546	+	11.8116i	−0.370561	+	0.460465i
$659$	6.21741	−	10.7689i	0.242196	−	0.419496i	−0.719144	−	0.694861i	$-0.755466\pi$
$659$	6.21741	−	10.7689i	0.242196	−	0.419496i	0.961339	+	0.275366i	$0.0887990\pi$
$660$		0			0
$661$	36.4077	−	9.75540i	1.41609	−	0.379441i	0.531998	−	0.846746i	$-0.321442\pi$
$661$	36.4077	−	9.75540i	1.41609	−	0.379441i	0.884096	+	0.467305i	$0.154775\pi$
$662$	3.88634	−	2.24378i	0.151047	−	0.0872069i
$663$		0			0
$664$		−	5.73288i		−	0.222479i
$665$	−43.9511	−	6.82403i	−1.70435	−	0.264625i
$666$		0			0
$667$	−8.35552	+	4.82406i	−0.323527	+	0.186788i
$668$	0.0126328	+	0.00338495i	0.000488778	+	0.000130968i
$669$		0			0
$670$	4.92454	−	18.3786i	0.190252	−	0.710029i
$671$	16.2371	+	16.2371i	0.626825	+	0.626825i
$672$		0			0
$673$	21.1591	−	12.2162i	0.815624	−	0.470901i	−0.0332811	−	0.999446i	$-0.510596\pi$
$673$	21.1591	−	12.2162i	0.815624	−	0.470901i	0.848905	+	0.528545i	$0.177262\pi$
$674$	3.64233	−	3.64233i	0.140297	−	0.140297i
$675$		0			0
$676$	16.4318	+	7.24981i	0.631991	+	0.278839i
$677$	3.00229	+	1.73338i	0.115388	+	0.0666190i	0.556583	−	0.830792i	$-0.312112\pi$
$677$	3.00229	+	1.73338i	0.115388	+	0.0666190i	−0.441195	+	0.897411i	$0.645445\pi$
$678$		0			0
$679$	−42.4766	+	4.59530i	−1.63010	+	0.176351i
$680$	−31.6635	−	18.2810i	−1.21424	−	0.701043i
$681$		0			0
$682$	−0.643255	+	0.643255i	−0.0246315	+	0.0246315i
$683$	−26.9394	+	26.9394i	−1.03081	+	1.03081i	−0.0312978	+	0.999510i	$0.509964\pi$
$683$	−26.9394	+	26.9394i	−1.03081	+	1.03081i	−0.999510	+	0.0312978i	$0.990036\pi$
$684$		0			0
$685$	20.4831	+	11.8259i	0.782619	+	0.451845i
$686$	−13.8102	+	4.62711i	−0.527275	+	0.176664i
$687$		0			0
$688$	−0.544437	−	0.314331i	−0.0207565	−	0.0119838i
$689$	−3.53513	+	6.96700i	−0.134678	+	0.265422i
$690$		0			0
$691$	15.8802	−	15.8802i	0.604110	−	0.604110i	−0.337290	−	0.941401i	$-0.609510\pi$
$691$	15.8802	−	15.8802i	0.604110	−	0.604110i	0.941401	+	0.337290i	$0.109510\pi$
$692$	−25.0789	+	14.4793i	−0.953359	+	0.550422i
$693$		0			0
$694$	−12.6815	−	12.6815i	−0.481384	−	0.481384i
$695$	−5.53826	+	20.6691i	−0.210078	+	0.784023i
$696$		0			0
$697$	−72.1094	−	19.3217i	−2.73134	−	0.731860i
$698$	1.39285	−	0.804163i	0.0527202	−	0.0304380i
$699$		0			0
$700$	2.04047	−	0.790399i	0.0771223	−	0.0298743i
$701$		−	43.0296i		−	1.62520i	−0.582819	−	0.812602i	$-0.698050\pi$
$701$		−	43.0296i		−	1.62520i	0.582819	−	0.812602i	$-0.301950\pi$
$702$		0			0
$703$	49.0736	−	28.3327i	1.85085	−	1.06859i
$704$	7.68589	−	2.05943i	0.289673	−	0.0776176i
$705$		0			0
$706$	−10.1707	+	17.6161i	−0.382778	+	0.662992i
$707$	7.29628	+	5.87171i	0.274405	+	0.220829i
$708$		0			0
$709$	19.1430	+	5.12936i	0.718932	+	0.192637i	0.599695	−	0.800228i	$-0.295288\pi$
$709$	19.1430	+	5.12936i	0.718932	+	0.192637i	0.119237	+	0.992866i	$0.461955\pi$
$710$	4.17367	−	15.5763i	0.156635	−	0.584570i
$711$		0			0
$712$	16.7472			0.627627
$713$	0.471003	−	1.75781i	0.0176392	−	0.0658304i
$714$		0			0
$715$	16.4916	+	8.36798i	0.616749	+	0.312945i
$716$	6.66522	−	11.5445i	0.249091	−	0.431438i
$717$		0			0
$718$	5.91791	−	10.2501i	0.220854	−	0.382531i
$719$	−23.2898	−	40.3391i	−0.868563	−	1.50440i	−0.863465	−	0.504408i	$-0.831711\pi$
$719$	−23.2898	−	40.3391i	−0.868563	−	1.50440i	−0.00509796	−	0.999987i	$-0.501623\pi$
$720$		0			0
$721$	−18.8902	−	15.2020i	−0.703508	−	0.566151i
$722$	−9.20205	−	34.3425i	−0.342465	−	1.27810i
$723$		0			0
$724$		−	1.73751i		−	0.0645742i
$725$	1.30052	+	0.750858i	0.0483003	+	0.0278862i
$726$		0			0
$727$	38.0896			1.41266			0.706332	−	0.707880i	$-0.250348\pi$
$727$	38.0896			1.41266			0.706332	+	0.707880i	$0.250348\pi$
$728$	8.97914	−	23.7260i	0.332789	−	0.879345i
$729$		0			0
$730$	11.8358	+	11.8358i	0.438064	+	0.438064i
$731$	−5.31147	−	3.06658i	−0.196452	−	0.113421i
$732$		0			0
$733$	8.16549	+	30.4740i	0.301599	+	1.12558i	0.935833	+	0.352443i	$0.114649\pi$
$733$	8.16549	+	30.4740i	0.301599	+	1.12558i	−0.634234	+	0.773141i	$0.718684\pi$
$734$	−3.11360	−	11.6201i	−0.114925	−	0.428906i
$735$		0			0
$736$	−15.9016	+	15.9016i	−0.586140	+	0.586140i
$737$	−14.0973	−	24.4173i	−0.519281	−	0.899422i
$738$		0			0
$739$	−7.67265	−	28.6347i	−0.282243	−	1.05335i	−0.950830	−	0.309712i	$-0.899767\pi$
$739$	−7.67265	−	28.6347i	−0.282243	−	1.05335i	0.668587	−	0.743634i	$-0.266899\pi$
$740$	10.2481	−	17.7502i	0.376728	−	0.652512i
$741$		0			0
$742$	4.12424	+	1.82120i	0.151405	+	0.0668583i
$743$	−6.49849	+	24.2527i	−0.238406	+	0.889745i	0.738177	+	0.674607i	$0.235687\pi$
$743$	−6.49849	+	24.2527i	−0.238406	+	0.889745i	−0.976584	+	0.215138i	$0.930980\pi$
$744$		0			0
$745$	−9.87198			−0.361682
$746$	4.16077	−	15.5282i	0.152337	−	0.568528i
$747$		0			0
$748$	−21.3805	+	5.72890i	−0.781750	+	0.209469i
$749$	−0.818995	+	5.27485i	−0.0299254	+	0.192739i
$750$		0			0
$751$			31.1328i			1.13605i	0.823011	+	0.568025i	$0.192293\pi$
$751$			31.1328i			1.13605i	−0.823011	+	0.568025i	$0.807707\pi$
$752$	4.72801	−	1.26687i	0.172413	−	0.0461979i
$753$		0			0
$754$	6.76097	−	2.20934i	0.246220	−	0.0804595i
$755$		−	1.22489i		−	0.0445784i
$756$		0			0
$757$	1.51455	+	2.62328i	0.0550472	+	0.0953446i	0.892236	−	0.451570i	$-0.149136\pi$
$757$	1.51455	+	2.62328i	0.0550472	+	0.0953446i	−0.837189	+	0.546914i	$0.815802\pi$
$758$	4.32176	−	2.49517i	0.156973	−	0.0906286i
$759$		0			0
$760$	−31.6118	−	31.6118i	−1.14668	−	1.14668i
$761$	−7.59236	+	28.3351i	−0.275223	+	1.02715i	0.680469	+	0.732777i	$0.261776\pi$
$761$	−7.59236	+	28.3351i	−0.275223	+	1.02715i	−0.955692	+	0.294369i	$0.904890\pi$
$762$		0			0
$763$	−13.6312	−	6.01932i	−0.493482	−	0.217914i
$764$	2.92535	−	1.68895i	0.105835	−	0.0611040i
$765$		0			0
$766$	−2.46154	−	4.26351i	−0.0889389	−	0.154047i
$767$	−4.13153	+	19.5992i	−0.149181	+	0.707687i
$768$		0			0
$769$	−30.9694	−	8.29823i	−1.11679	−	0.299242i	−0.347203	−	0.937790i	$-0.612869\pi$
$769$	−30.9694	−	8.29823i	−1.11679	−	0.299242i	−0.769582	+	0.638548i	$0.779535\pi$
$770$	4.31095	−	9.76245i	0.155356	−	0.351814i
$771$		0			0
$772$	22.9670	−	6.15399i	0.826601	−	0.221487i
$773$	31.5168	−	31.5168i	1.13358	−	1.13358i	0.144005	−	0.989577i	$-0.454002\pi$
$773$	31.5168	−	31.5168i	1.13358	−	1.13358i	0.989577	−	0.144005i	$-0.0459983\pi$
$774$		0			0
$775$	−0.273600	+	0.0733109i	−0.00982801	+	0.00263341i
$776$	−37.1902	−	21.4718i	−1.33505	−	0.770791i
$777$		0			0
$778$	4.14094	+	1.10956i	0.148460	+	0.0397797i
$779$	−79.0521	−	45.6408i	−2.83234	−	1.63525i
$780$		0			0
$781$	−11.9478	−	20.6942i	−0.427526	−	0.740497i
$782$	−14.0164	+	14.0164i	−0.501225	+	0.501225i
$783$		0			0
$784$	4.48079	+	1.42578i	0.160028	+	0.0509208i
$785$	16.4683	+	16.4683i	0.587779	+	0.587779i
$786$		0			0
$787$	13.0345	+	13.0345i	0.464631	+	0.464631i	0.900170	−	0.435539i	$-0.143442\pi$
$787$	13.0345	+	13.0345i	0.464631	+	0.464631i	−0.435539	+	0.900170i	$0.643442\pi$
$788$	31.2379	+	8.37018i	1.11281	+	0.298175i
$789$		0			0
$790$	1.77426	+	3.07311i	0.0631253	+	0.109336i
$791$	25.5856	+	20.5901i	0.909718	+	0.732099i
$792$		0			0
$793$	30.1996	+	15.3236i	1.07242	+	0.544156i
$794$	−6.52932	+	3.76971i	−0.231717	+	0.133782i
$795$		0			0
$796$			25.7540i			0.912828i
$797$	6.45241	−	11.1759i	0.228556	−	0.395871i	−0.728824	−	0.684701i	$-0.759933\pi$
$797$	6.45241	−	11.1759i	0.228556	−	0.395871i	0.957380	+	0.288830i	$0.0932662\pi$
$798$		0			0
$799$	46.1259	−	12.3594i	1.63182	−	0.437244i
$800$	3.38099	+	0.905934i	0.119536	+	0.0320296i
$801$		0			0
$802$	29.4976			1.04160
$803$	24.8034			0.875292
$804$		0			0
$805$	2.29620	+	21.2249i	0.0809303	+	0.748078i
$806$	−0.607067	+	1.19640i	−0.0213830	+	0.0421415i
$807$		0			0
$808$	2.43640	+	9.09277i	0.0857123	+	0.319883i
$809$	19.0726	−	33.0347i	0.670558	−	1.16144i	−0.307189	−	0.951649i	$-0.599388\pi$
$809$	19.0726	−	33.0347i	0.670558	−	1.16144i	0.977746	−	0.209791i	$-0.0672784\pi$
$810$		0			0
$811$	−10.6932	+	10.6932i	−0.375490	+	0.375490i	−0.869472	−	0.493982i	$-0.835541\pi$
$811$	−10.6932	+	10.6932i	−0.375490	+	0.375490i	0.493982	+	0.869472i	$0.335541\pi$
$812$	3.31196	+	8.55003i	0.116227	+	0.300047i
$813$		0			0
$814$	3.51895	+	13.1329i	0.123339	+	0.460308i
$815$		−	34.5683i		−	1.21087i
$816$		0			0
$817$	−5.30278	−	5.30278i	−0.185521	−	0.185521i
$818$	24.1718			0.845146
$819$		0			0
$820$	−33.0171			−1.15301
$821$	17.3195	+	17.3195i	0.604455	+	0.604455i	0.941492	−	0.337036i	$-0.109425\pi$
$821$	17.3195	+	17.3195i	0.604455	+	0.604455i	−0.337036	+	0.941492i	$0.609425\pi$
$822$		0			0
$823$		−	13.5237i		−	0.471408i	−0.971825	−	0.235704i	$-0.924260\pi$
$823$		−	13.5237i		−	0.471408i	0.971825	−	0.235704i	$-0.0757396\pi$
$824$	−6.30788	−	23.5413i	−0.219746	−	0.820101i
$825$		0			0
$826$	11.4219	+	1.77342i	0.397420	+	0.0617051i
$827$	−24.6131	+	24.6131i	−0.855881	+	0.855881i	−0.990850	−	0.134969i	$-0.956906\pi$
$827$	−24.6131	+	24.6131i	−0.855881	+	0.855881i	0.134969	+	0.990850i	$0.456906\pi$
$828$		0			0
$829$	9.85463	−	17.0687i	0.342266	−	0.592821i	−0.642588	−	0.766212i	$-0.722139\pi$
$829$	9.85463	−	17.0687i	0.342266	−	0.592821i	0.984853	+	0.173391i	$0.0554724\pi$
$830$	−0.920551	−	3.43554i	−0.0319528	−	0.119249i
$831$		0			0
$832$	9.83090	−	6.40778i	0.340825	−	0.222150i
$833$	43.7140	+	13.9098i	1.51460	+	0.481945i
$834$		0			0
$835$	0.0198603			0.000687292
$836$	−27.0651			−0.936066
$837$		0			0
$838$	17.7614	+	4.75916i	0.613558	+	0.164402i
$839$	−22.4087	+	6.00440i	−0.773635	+	0.207295i	−0.623977	−	0.781443i	$-0.714484\pi$
$839$	−22.4087	+	6.00440i	−0.773635	+	0.207295i	−0.149658	+	0.988738i	$0.547817\pi$
$840$		0			0
$841$	11.3537	−	19.6652i	0.391508	−	0.678111i
$842$		−	15.7363i		−	0.542308i
$843$		0			0
$844$	−13.4312	+	7.75451i	−0.462321	+	0.266921i
$845$	26.9516	+	4.17590i	0.927164	+	0.143655i
$846$		0			0
$847$	4.80024	+	12.3921i	0.164938	+	0.425799i
$848$	−0.727766	−	1.26053i	−0.0249916	−	0.0432867i
$849$		0			0
$850$	2.98016	+	0.798532i	0.102219	+	0.0273894i
$851$	−19.2323	−	19.2323i	−0.659275	−	0.659275i
$852$		0			0
$853$	−25.2631	−	25.2631i	−0.864993	−	0.864993i	0.126920	−	0.991913i	$-0.459491\pi$
$853$	−25.2631	−	25.2631i	−0.864993	−	0.864993i	−0.991913	+	0.126920i	$0.959491\pi$
$854$	7.89427	−	17.8772i	0.270137	−	0.611744i
$855$		0			0
$856$	−3.79392	+	3.79392i	−0.129674	+	0.129674i
$857$	3.17108	+	5.49248i	0.108322	+	0.187619i	0.915091	−	0.403248i	$-0.132119\pi$
$857$	3.17108	+	5.49248i	0.108322	+	0.187619i	−0.806769	+	0.590868i	$0.798786\pi$
$858$		0			0
$859$	12.1601	+	7.02065i	0.414898	+	0.239541i	0.692892	−	0.721041i	$-0.256336\pi$
$859$	12.1601	+	7.02065i	0.414898	+	0.239541i	−0.277994	+	0.960583i	$0.589670\pi$
$860$	−2.62010	−	0.702054i	−0.0893448	−	0.0239399i
$861$		0			0
$862$	−8.98196	−	5.18573i	−0.305927	−	0.176627i
$863$	−33.5781	+	8.99722i	−1.14301	+	0.306269i	−0.780161	−	0.625579i	$-0.784863\pi$
$863$	−33.5781	+	8.99722i	−1.14301	+	0.306269i	−0.362850	+	0.931848i	$0.618196\pi$
$864$		0			0
$865$	−31.0952	+	31.0952i	−1.05727	+	1.05727i
$866$	8.41464	−	2.25470i	0.285941	−	0.0766177i
$867$		0			0
$868$	−1.58208	−	0.698620i	−0.0536991	−	0.0237127i
$869$	5.07911	+	1.36094i	0.172297	+	0.0461668i
$870$		0			0
$871$	−30.9473	−	27.7710i	−1.04861	−	0.940986i
$872$	−7.48873	−	12.9709i	−0.253600	−	0.439249i
$873$		0			0
$874$	−20.9902	+	12.1187i	−0.710004	+	0.409921i
$875$	25.0853	−	18.3425i	0.848037	−	0.620090i
$876$		0			0
$877$	7.21350	−	26.9211i	0.243583	−	0.909062i	−0.730508	−	0.682904i	$-0.760717\pi$
$877$	7.21350	−	26.9211i	0.243583	−	0.909062i	0.974091	−	0.226158i	$-0.0726167\pi$
$878$	−7.35868	−	7.35868i	−0.248343	−	0.248343i
$879$		0			0
$880$	−2.98379	+	1.72269i	−0.100583	+	0.0580719i
$881$	−4.46832	−	7.73936i	−0.150542	−	0.260746i	0.780885	−	0.624675i	$-0.214768\pi$
$881$	−4.46832	−	7.73936i	−0.150542	−	0.260746i	−0.931427	+	0.363929i	$0.881435\pi$
$882$		0			0
$883$			17.8140i			0.599488i	0.954020	+	0.299744i	$0.0969012\pi$
$883$			17.8140i			0.599488i	−0.954020	+	0.299744i	$0.903099\pi$
$884$	−27.3475	+	17.8251i	−0.919797	+	0.599523i
$885$		0			0
$886$	3.73100	−	0.999719i	0.125345	−	0.0335862i
$887$			43.3313i			1.45492i	0.686149	+	0.727461i	$0.259300\pi$
$887$			43.3313i			1.45492i	−0.686149	+	0.727461i	$0.740700\pi$
$888$		0			0
$889$	−9.99188	−	25.7947i	−0.335117	−	0.865125i
$890$	10.0361	−	2.68916i	0.336410	−	0.0901407i
$891$		0			0
$892$	3.63513	−	13.5665i	0.121713	−	0.454239i
$893$	58.3897			1.95394
$894$		0			0
$895$	5.23926	−	19.5532i	0.175129	−	0.653591i
$896$	14.2645	+	19.5082i	0.476543	+	0.651722i
$897$		0			0
$898$	−0.374035	+	0.647848i	−0.0124817	+	0.0216190i
$899$	−0.307190	−	1.14645i	−0.0102454	−	0.0382362i
$900$		0			0
$901$	−7.10000	−	12.2976i	−0.236535	−	0.409691i
$902$	15.4870	−	15.4870i	0.515661	−	0.515661i
$903$		0			0
$904$	8.54362	+	31.8852i	0.284157	+	1.06049i
$905$	−0.682894	−	2.54860i	−0.0227002	−	0.0847182i
$906$		0			0
$907$	30.7649	+	17.7621i	1.02153	+	0.589781i	0.914547	−	0.404480i	$-0.132547\pi$
$907$	30.7649	+	17.7621i	1.02153	+	0.589781i	0.106984	+	0.994261i	$0.465881\pi$
$908$	−6.43174	−	6.43174i	−0.213445	−	0.213445i
$909$		0			0
$910$	1.57115	−	15.6601i	0.0520831	−	0.519127i
$911$	56.1740			1.86113			0.930564	−	0.366130i	$-0.119318\pi$
$911$	56.1740			1.86113			0.930564	+	0.366130i	$0.119318\pi$
$912$		0			0
$913$	−4.56435	−	2.63523i	−0.151058	−	0.0872133i
$914$			15.1306i			0.500474i
$915$		0			0
$916$	−0.444427	−	1.65863i	−0.0146843	−	0.0548025i
$917$	34.6067	−	43.0029i	1.14282	−	1.42008i
$918$		0			0
$919$	21.2328	+	36.7763i	0.700405	+	1.21314i	0.968324	+	0.249696i	$0.0803306\pi$
$919$	21.2328	+	36.7763i	0.700405	+	1.21314i	−0.267919	+	0.963441i	$0.586336\pi$
$920$	−10.7291	+	18.5833i	−0.353727	+	0.612674i
$921$		0			0
$922$	−2.53513	+	4.39098i	−0.0834902	+	0.144609i
$923$	−26.2286	−	23.5366i	−0.863324	−	0.774717i
$924$		0			0
$925$	−1.09569	+	4.08917i	−0.0360261	+	0.134451i
$926$	−8.54132			−0.280685
$927$		0			0
$928$	−3.79608	+	14.1672i	−0.124612	+	0.465060i
$929$	−27.8702	−	7.46779i	−0.914391	−	0.245010i	−0.229205	−	0.973378i	$-0.573612\pi$
$929$	−27.8702	−	7.46779i	−0.914391	−	0.245010i	−0.685186	+	0.728368i	$0.740279\pi$
$930$		0			0
$931$	47.2277	+	30.2627i	1.54782	+	0.991818i
$932$	−10.1242	+	17.5357i	−0.331630	+	0.574400i
$933$		0			0
$934$	−16.2921	+	4.36545i	−0.533093	+	0.142842i
$935$	−29.1095	+	16.8064i	−0.951982	+	0.549627i
$936$		0			0
$937$			15.4230i			0.503847i	0.967747	+	0.251923i	$0.0810631\pi$
$937$			15.4230i			0.503847i	−0.967747	+	0.251923i	$0.918937\pi$
$938$	−15.0439	+	18.6937i	−0.491200	+	0.610372i
$939$		0			0
$940$	18.2904	−	10.5599i	0.596566	−	0.344428i
$941$	−31.8491	−	8.53393i	−1.03825	−	0.278198i	−0.300862	−	0.953668i	$-0.597274\pi$
$941$	−31.8491	−	8.53393i	−1.03825	−	0.278198i	−0.737388	+	0.675470i	$0.763941\pi$
$942$		0			0
$943$	−11.3399	+	42.3210i	−0.369277	+	1.37816i
$944$	−2.63872	−	2.63872i	−0.0858829	−	0.0858829i
$945$		0			0
$946$	1.55829	−	0.899681i	0.0506645	−	0.0292511i
$947$	17.4962	−	17.4962i	0.568550	−	0.568550i	−0.363172	−	0.931722i	$-0.618306\pi$
$947$	17.4962	−	17.4962i	0.568550	−	0.568550i	0.931722	+	0.363172i	$0.118306\pi$
$948$		0			0
$949$	34.7701	−	11.3621i	1.12869	−	0.368830i
$950$	3.26709	+	1.88626i	0.105998	+	0.0611983i
$951$		0			0
$952$	27.2156	+	37.2202i	0.882064	+	1.20631i
$953$	−38.7397	−	22.3663i	−1.25490	−	0.724517i	−0.282822	−	0.959172i	$-0.591271\pi$
$953$	−38.7397	−	22.3663i	−1.25490	−	0.724517i	−0.972079	+	0.234655i	$0.924604\pi$
$954$		0			0
$955$	3.62711	−	3.62711i	0.117371	−	0.117371i
$956$	6.71074	−	6.71074i	0.217041	−	0.217041i
$957$		0			0
$958$	−12.3291	−	7.11824i	−0.398337	−	0.229980i
$959$	−17.6057	−	24.0777i	−0.568519	−	0.777509i
$960$		0			0
$961$	−26.6529	−	15.3881i	−0.859771	−	0.496389i
$962$	10.9490	+	16.7981i	0.353010	+	0.541593i
$963$		0			0
$964$	−18.6726	+	18.6726i	−0.601403	+	0.601403i
$965$	31.2695	−	18.0534i	1.00660	−	0.581161i
$966$		0			0
$967$	−7.27104	−	7.27104i	−0.233821	−	0.233821i	0.580465	−	0.814285i	$-0.302871\pi$
$967$	−7.27104	−	7.27104i	−0.233821	−	0.233821i	−0.814285	+	0.580465i	$0.802871\pi$
$968$	−3.45718	+	12.9024i	−0.111118	+	0.414697i
$969$		0			0
$970$	−25.7347	−	6.89560i	−0.826293	−	0.221404i
$971$	−18.9111	+	10.9184i	−0.606887	+	0.350387i	−0.771746	−	0.635931i	$-0.780616\pi$
$971$	−18.9111	+	10.9184i	−0.606887	+	0.350387i	0.164859	+	0.986317i	$0.447283\pi$
$972$		0			0
$973$	16.9187	−	21.0234i	0.542388	−	0.673980i
$974$		−	5.66316i		−	0.181459i
$975$		0			0
$976$	−5.46396	+	3.15462i	−0.174897	+	0.100977i
$977$	3.64839	−	0.977584i	0.116722	−	0.0312757i	−0.199985	−	0.979799i	$-0.564089\pi$
$977$	3.64839	−	0.977584i	0.116722	−	0.0312757i	0.316707	+	0.948523i	$0.397423\pi$
$978$		0			0
$979$	7.69815	−	13.3336i	0.246034	−	0.426143i
$980$	20.2670	+	0.938407i	0.647406	+	0.0299763i
$981$		0			0
$982$	−21.3993	−	5.73392i	−0.682878	−	0.182977i
$983$	−12.2540	+	45.7327i	−0.390843	+	1.45865i	0.437903	+	0.899022i	$0.355721\pi$
$983$	−12.2540	+	45.7327i	−0.390843	+	1.45865i	−0.828746	+	0.559625i	$0.810945\pi$
$984$		0			0
$985$	49.1098			1.56477
$986$	−3.34604	+	12.4876i	−0.106560	+	0.397686i
$987$		0			0
$988$	−37.9406	+	12.3982i	−1.20705	+	0.394439i
$989$	−1.79977	+	3.11730i	−0.0572294	+	0.0991243i
$990$		0			0
$991$	5.24867	−	9.09095i	0.166729	−	0.288784i	−0.770539	−	0.637393i	$-0.780013\pi$
$991$	5.24867	−	9.09095i	0.166729	−	0.288784i	0.937268	+	0.348610i	$0.113346\pi$
$992$	−1.38323	−	2.39582i	−0.0439175	−	0.0760674i
$993$		0			0
$994$	−12.7500	+	15.8434i	−0.404406	+	0.502522i
$995$	10.1221	+	37.7762i	0.320892	+	1.19759i
$996$		0			0
$997$		−	37.0853i		−	1.17450i	−0.809405	−	0.587251i	$-0.800210\pi$
$997$		−	37.0853i		−	1.17450i	0.809405	−	0.587251i	$-0.199790\pi$
$998$	14.3278	+	8.27218i	0.453540	+	0.261851i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.4		36
3.2	odd	2		273.2.bt.a.271.6	yes	36
7.3	odd	6		819.2.gh.c.388.6		36
13.6	odd	12		819.2.gh.c.19.6		36
21.17	even	6		273.2.cg.a.115.4	yes	36
39.32	even	12		273.2.cg.a.19.4	yes	36
91.45	even	12	inner	819.2.et.c.136.4		36
273.227	odd	12		273.2.bt.a.136.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.6	✓	36	273.227	odd	12
273.2.bt.a.271.6	yes	36	3.2	odd	2
273.2.cg.a.19.4	yes	36	39.32	even	12
273.2.cg.a.115.4	yes	36	21.17	even	6
819.2.et.c.136.4		36	91.45	even	12	inner
819.2.et.c.271.4		36	1.1	even	1	trivial
819.2.gh.c.19.6		36	13.6	odd	12
819.2.gh.c.388.6		36	7.3	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.556084 - 0.556084i) q^{2} -1.38154i q^{4} +(-0.542987 - 2.02645i) q^{5} +(-0.405927 + 2.61443i) q^{7} +(-1.88042 + 1.88042i) q^{8} +O(q^{10})\)	\(q+(-0.556084 - 0.556084i) q^{2} -1.38154i q^{4} +(-0.542987 - 2.02645i) q^{5} +(-0.405927 + 2.61443i) q^{7} +(-1.88042 + 1.88042i) q^{8} +(-0.824932 + 1.42882i) q^{10} +(0.632763 + 2.36150i) q^{11} +(1.96880 + 3.02057i) q^{13} +(1.67957 - 1.22811i) q^{14} -0.671737 q^{16} -6.55339 q^{17} +(-7.74006 - 2.07394i) q^{19} +(-2.79963 + 0.750158i) q^{20} +(0.961326 - 1.66506i) q^{22} +3.84618i q^{23} +(0.518448 - 0.299326i) q^{25} +(0.584868 - 2.77451i) q^{26} +(3.61194 + 0.560804i) q^{28} +(1.25425 + 2.17242i) q^{29} +(-0.457027 - 0.122460i) q^{31} +(4.13438 + 4.13438i) q^{32} +(3.64424 + 3.64424i) q^{34} +(5.51843 - 0.597007i) q^{35} +(-5.00037 + 5.00037i) q^{37} +(3.15084 + 5.45741i) q^{38} +(4.83163 + 2.78954i) q^{40} +(11.0034 + 2.94834i) q^{41} +(0.810492 + 0.467938i) q^{43} +(3.26252 - 0.874188i) q^{44} +(2.13880 - 2.13880i) q^{46} +(-7.03848 + 1.88596i) q^{47} +(-6.67045 - 2.12253i) q^{49} +(-0.454751 - 0.121850i) q^{50} +(4.17303 - 2.71998i) q^{52} +(1.08341 + 1.87652i) q^{53} +(4.44190 - 2.56453i) q^{55} +(-4.15291 - 5.67954i) q^{56} +(0.510581 - 1.90552i) q^{58} +(3.92820 + 3.92820i) q^{59} +(8.13407 - 4.69621i) q^{61} +(0.186047 + 0.322243i) q^{62} -3.25466i q^{64} +(5.05200 - 5.62981i) q^{65} +(-11.1395 + 2.98482i) q^{67} +9.05378i q^{68} +(-3.40069 - 2.73672i) q^{70} +(-9.44098 + 2.52970i) q^{71} +(2.62580 - 9.79963i) q^{73} +5.56125 q^{74} +(-2.86524 + 10.6932i) q^{76} +(-6.43083 + 0.695715i) q^{77} +(1.07540 - 1.86264i) q^{79} +(0.364744 + 1.36124i) q^{80} +(-4.47927 - 7.75833i) q^{82} +(-1.52436 + 1.52436i) q^{83} +(3.55840 + 13.2801i) q^{85} +(-0.190489 - 0.710914i) q^{86} +(-5.63048 - 3.25076i) q^{88} +(-4.45304 - 4.45304i) q^{89} +(-8.69623 + 3.92116i) q^{91} +5.31366 q^{92} +(4.96274 + 2.86524i) q^{94} +16.8110i q^{95} +(4.17950 + 15.5981i) q^{97} +(2.52902 + 4.88964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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