LMFDB - Embedded newform 504.2.bk.c.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221012 + 1.39684i) q^{2} +(-1.90231 - 0.617436i) q^{4} +(-0.225540 + 0.390646i) q^{5} +(-0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +O(q^{10})$	\(q+(-0.221012 + 1.39684i) q^{2} +(-1.90231 - 0.617436i) q^{4} +(-0.225540 + 0.390646i) q^{5} +(-0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +(-0.495822 - 0.401380i) q^{10} +(0.360048 + 0.623622i) q^{11} +3.48975 q^{13} +(3.74111 - 0.0641172i) q^{14} +(3.23754 + 2.34911i) q^{16} +(3.55796 - 2.05419i) q^{17} +(3.97736 + 2.29633i) q^{19} +(0.670245 - 0.603872i) q^{20} +(-0.950673 + 0.365101i) q^{22} +(-0.0459022 - 0.0265016i) q^{23} +(2.39826 + 4.15391i) q^{25} +(-0.771279 + 4.87462i) q^{26} +(-0.737270 + 5.23989i) q^{28} -7.85260i q^{29} +(-4.58331 - 7.93852i) q^{31} +(-3.99686 + 4.00314i) q^{32} +(2.08301 + 5.42389i) q^{34} +(1.12128 + 0.408713i) q^{35} +(7.51467 + 4.33860i) q^{37} +(-4.08664 + 5.04820i) q^{38} +(0.695379 + 1.06969i) q^{40} +3.94348i q^{41} +5.17408 q^{43} +(-0.299875 - 1.40863i) q^{44} +(0.0471634 - 0.0582606i) q^{46} +(-0.460124 + 0.796959i) q^{47} +(-6.58011 + 2.38791i) q^{49} +(-6.33239 + 2.43192i) q^{50} +(-6.63858 - 2.15470i) q^{52} +(2.71489 - 1.56744i) q^{53} -0.324821 q^{55} +(-7.15632 - 2.18793i) q^{56} +(10.9688 + 1.73552i) q^{58} +(4.86409 - 2.80828i) q^{59} +(-2.54813 + 4.41348i) q^{61} +(12.1018 - 4.64762i) q^{62} +(-4.70838 - 6.46770i) q^{64} +(-0.787078 + 1.36326i) q^{65} +(-4.93346 - 8.54500i) q^{67} +(-8.03666 + 1.71088i) q^{68} +(-0.818721 + 1.47591i) q^{70} -11.1608i q^{71} +(-3.33103 + 1.92317i) q^{73} +(-7.72115 + 9.53788i) q^{74} +(-6.14832 - 6.82409i) q^{76} +(1.46004 - 1.22395i) q^{77} +(-8.40929 - 4.85511i) q^{79} +(-1.64786 + 0.734917i) q^{80} +(-5.50839 - 0.871557i) q^{82} +9.53613i q^{83} +1.85320i q^{85} +(-1.14353 + 7.22734i) q^{86} +(2.03390 - 0.107553i) q^{88} +(12.6107 + 7.28081i) q^{89} +(-1.59899 - 9.09351i) q^{91} +(0.0709569 + 0.0787559i) q^{92} +(-1.01153 - 0.818857i) q^{94} +(-1.79410 + 1.03583i) q^{95} -5.14572i q^{97} +(-1.88124 - 9.71910i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.221012	+	1.39684i	−0.156279	+	0.987713i
$2$	−0.221012	+	1.39684i	−0.156279	+	0.987713i
$3$		0			0
$3$		0			0
$4$	−1.90231	−	0.617436i	−0.951154	−	0.308718i
$5$	−0.225540	+	0.390646i	−0.100864	+	0.174702i	−0.912041	−	0.410099i	$-0.865494\pi$
$5$	−0.225540	+	0.390646i	−0.100864	+	0.174702i	0.811177	+	0.584801i	$0.198827\pi$
$6$		0			0
$7$	−0.458196	−	2.60577i	−0.173182	−	0.984890i
$7$	−0.458196	−	2.60577i	−0.173182	−	0.984890i
$8$	1.28289	−	2.52075i	0.453571	−	0.891220i
$9$		0			0
$10$	−0.495822	−	0.401380i	−0.156793	−	0.126927i
$11$	0.360048	+	0.623622i	0.108559	+	0.188029i	0.915187	−	0.403030i	$-0.132043\pi$
$11$	0.360048	+	0.623622i	0.108559	+	0.188029i	−0.806628	+	0.591060i	$0.798710\pi$
$12$		0			0
$13$	3.48975			0.967884			0.483942	−	0.875100i	$-0.339205\pi$
$13$	3.48975			0.967884			0.483942	+	0.875100i	$0.339205\pi$
$14$	3.74111	−	0.0641172i	0.999853	−	0.0171360i
$15$		0			0
$16$	3.23754	+	2.34911i	0.809386	+	0.587277i
$17$	3.55796	−	2.05419i	0.862931	−	0.498214i	−0.00206160	−	0.999998i	$-0.500656\pi$
$17$	3.55796	−	2.05419i	0.862931	−	0.498214i	0.864993	+	0.501784i	$0.167323\pi$
$18$		0			0
$19$	3.97736	+	2.29633i	0.912468	+	0.526814i	0.881225	−	0.472698i	$-0.156720\pi$
$19$	3.97736	+	2.29633i	0.912468	+	0.526814i	0.0312438	+	0.999512i	$0.490053\pi$
$20$	0.670245	−	0.603872i	0.149871	−	0.135030i
$21$		0			0
$22$	−0.950673	+	0.365101i	−0.202684	+	0.0778397i
$23$	−0.0459022	−	0.0265016i	−0.00957126	−	0.00552597i	0.495207	−	0.868775i	$-0.335092\pi$
$23$	−0.0459022	−	0.0265016i	−0.00957126	−	0.00552597i	−0.504778	+	0.863249i	$0.668426\pi$
$24$		0			0
$25$	2.39826	+	4.15391i	0.479653	+	0.830783i
$26$	−0.771279	+	4.87462i	−0.151260	+	0.955991i
$27$		0			0
$28$	−0.737270	+	5.23989i	−0.139331	+	0.990246i
$29$		−	7.85260i		−	1.45819i	−0.684411	−	0.729096i	$-0.739941\pi$
$29$		−	7.85260i		−	1.45819i	0.684411	−	0.729096i	$-0.260059\pi$
$30$		0			0
$31$	−4.58331	−	7.93852i	−0.823186	−	1.42580i	−0.903298	−	0.429015i	$-0.858861\pi$
$31$	−4.58331	−	7.93852i	−0.823186	−	1.42580i	0.0801113	−	0.996786i	$-0.474472\pi$
$32$	−3.99686	+	4.00314i	−0.706551	+	0.707662i
$33$		0			0
$34$	2.08301	+	5.42389i	0.357234	+	0.930189i
$35$	1.12128	+	0.408713i	0.189530	+	0.0690850i
$36$		0			0
$37$	7.51467	+	4.33860i	1.23540	+	0.713261i	0.968151	−	0.250366i	$-0.0805508\pi$
$37$	7.51467	+	4.33860i	1.23540	+	0.713261i	0.267253	+	0.963626i	$0.413884\pi$
$38$	−4.08664	+	5.04820i	−0.662941	+	0.818927i
$39$		0			0
$40$	0.695379	+	1.06969i	0.109949	+	0.169132i
$41$			3.94348i			0.615868i	0.951408	+	0.307934i	$0.0996375\pi$
$41$			3.94348i			0.615868i	−0.951408	+	0.307934i	$0.900362\pi$
$42$		0			0
$43$	5.17408			0.789039			0.394520	−	0.918888i	$-0.370911\pi$
$43$	5.17408			0.789039			0.394520	+	0.918888i	$0.370911\pi$
$44$	−0.299875	−	1.40863i	−0.0452079	−	0.212359i
$45$		0			0
$46$	0.0471634	−	0.0582606i	0.00695386	−	0.00859006i
$47$	−0.460124	+	0.796959i	−0.0671160	+	0.116248i	−0.897631	−	0.440748i	$-0.854713\pi$
$47$	−0.460124	+	0.796959i	−0.0671160	+	0.116248i	0.830515	+	0.556997i	$0.188046\pi$
$48$		0			0
$49$	−6.58011	+	2.38791i	−0.940016	+	0.341130i
$50$	−6.33239	+	2.43192i	−0.895535	+	0.343925i
$51$		0			0
$52$	−6.63858	−	2.15470i	−0.920606	−	0.298803i
$53$	2.71489	−	1.56744i	0.372919	−	0.215305i	−0.301814	−	0.953367i	$-0.597592\pi$
$53$	2.71489	−	1.56744i	0.372919	−	0.215305i	0.674733	+	0.738062i	$0.264259\pi$
$54$		0			0
$55$	−0.324821			−0.0437988
$56$	−7.15632	−	2.18793i	−0.956304	−	0.292374i
$57$		0			0
$58$	10.9688	+	1.73552i	1.44028	+	0.227885i
$59$	4.86409	−	2.80828i	0.633250	−	0.365607i	−0.148759	−	0.988873i	$-0.547528\pi$
$59$	4.86409	−	2.80828i	0.633250	−	0.365607i	0.782010	+	0.623266i	$0.214195\pi$
$60$		0			0
$61$	−2.54813	+	4.41348i	−0.326254	+	0.565089i	−0.981765	−	0.190097i	$-0.939120\pi$
$61$	−2.54813	+	4.41348i	−0.326254	+	0.565089i	0.655511	+	0.755185i	$0.272453\pi$
$62$	12.1018	−	4.64762i	1.53693	−	0.590249i
$63$		0			0
$64$	−4.70838	−	6.46770i	−0.588547	−	0.808463i
$65$	−0.787078	+	1.36326i	−0.0976250	+	0.169091i
$66$		0			0
$67$	−4.93346	−	8.54500i	−0.602718	−	1.04394i	−0.992408	−	0.122992i	$-0.960751\pi$
$67$	−4.93346	−	8.54500i	−0.602718	−	1.04394i	0.389690	−	0.920946i	$-0.372582\pi$
$68$	−8.03666	+	1.71088i	−0.974588	+	0.207475i
$69$		0			0
$70$	−0.818721	+	1.47591i	−0.0978559	+	0.176405i
$71$		−	11.1608i		−	1.32454i	−0.749266	−	0.662270i	$-0.769593\pi$
$71$		−	11.1608i		−	1.32454i	0.749266	−	0.662270i	$-0.230407\pi$
$72$		0			0
$73$	−3.33103	+	1.92317i	−0.389867	+	0.225090i	−0.682103	−	0.731256i	$-0.738934\pi$
$73$	−3.33103	+	1.92317i	−0.389867	+	0.225090i	0.292235	+	0.956346i	$0.405601\pi$
$74$	−7.72115	+	9.53788i	−0.897565	+	1.10876i
$75$		0			0
$76$	−6.14832	−	6.82409i	−0.705260	−	0.782776i
$77$	1.46004	−	1.22395i	0.166388	−	0.139482i
$78$		0			0
$79$	−8.40929	−	4.85511i	−0.946119	−	0.546242i	−0.0542460	−	0.998528i	$-0.517276\pi$
$79$	−8.40929	−	4.85511i	−0.946119	−	0.546242i	−0.891873	+	0.452285i	$0.850609\pi$
$80$	−1.64786	+	0.734917i	−0.184237	+	0.0821662i
$81$		0			0
$82$	−5.50839	−	0.871557i	−0.608300	−	0.0962474i
$83$			9.53613i			1.04673i	0.852110	+	0.523363i	$0.175323\pi$
$83$			9.53613i			1.04673i	−0.852110	+	0.523363i	$0.824677\pi$
$84$		0			0
$85$			1.85320i			0.201008i
$86$	−1.14353	+	7.22734i	−0.123311	+	0.779344i
$87$		0			0
$88$	2.03390	−	0.107553i	0.216814	−	0.0114652i
$89$	12.6107	+	7.28081i	1.33673	+	0.771764i	0.986322	−	0.164831i	$-0.0527078\pi$
$89$	12.6107	+	7.28081i	1.33673	+	0.771764i	0.350413	+	0.936595i	$0.386041\pi$
$90$		0			0
$91$	−1.59899	−	9.09351i	−0.167620	−	0.953259i
$92$	0.0709569	+	0.0787559i	0.00739777	+	0.00821087i
$93$		0			0
$94$	−1.01153	−	0.818857i	−0.104331	−	0.0844586i
$95$	−1.79410	+	1.03583i	−0.184071	+	0.106273i
$96$		0			0
$97$		−	5.14572i		−	0.522469i	−0.965275	−	0.261235i	$-0.915870\pi$
$97$		−	5.14572i		−	0.522469i	0.965275	−	0.261235i	$-0.0841296\pi$
$98$	−1.88124	−	9.71910i	−0.190034	−	0.981778i
$99$		0			0
$100$	−1.99746	−	9.38280i	−0.199746	−	0.938280i
$101$	7.14490	+	12.3753i	0.710944	+	1.23139i	0.964503	+	0.264072i	$0.0850656\pi$
$101$	7.14490	+	12.3753i	0.710944	+	1.23139i	−0.253559	+	0.967320i	$0.581601\pi$
$102$		0			0
$103$	−7.46214	+	12.9248i	−0.735267	+	1.27352i	0.219339	+	0.975649i	$0.429610\pi$
$103$	−7.46214	+	12.9248i	−0.735267	+	1.27352i	−0.954606	+	0.297871i	$0.903724\pi$
$104$	4.47698	−	8.79680i	0.439004	−	0.862598i
$105$		0			0
$106$	1.58944	+	4.13869i	0.154380	+	0.401985i
$107$	7.90786	−	13.6968i	0.764482	−	1.32412i	−0.176039	−	0.984383i	$-0.556328\pi$
$107$	7.90786	−	13.6968i	0.764482	−	1.32412i	0.940520	−	0.339738i	$-0.110338\pi$
$108$		0			0
$109$	0.208805	−	0.120553i	0.0199999	−	0.0115469i	−0.489967	−	0.871741i	$-0.662991\pi$
$109$	0.208805	−	0.120553i	0.0199999	−	0.0115469i	0.509967	+	0.860194i	$0.329658\pi$
$110$	0.0717893	−	0.453721i	0.00684485	−	0.0432606i
$111$		0			0
$112$	4.63781	−	9.51266i	0.438232	−	0.898862i
$113$	−13.3327			−1.25423			−0.627116	−	0.778926i	$-0.715765\pi$
$113$	−13.3327			−1.25423			−0.627116	+	0.778926i	$0.715765\pi$
$114$		0			0
$115$	0.0207055	−	0.0119543i	0.00193080	−	0.00111475i
$116$	−4.84848	+	14.9381i	−0.450170	+	1.38696i
$117$		0			0
$118$	2.84769	+	7.41500i	0.262151	+	0.682606i
$119$	−6.98299	−	8.33001i	−0.640130	−	0.763611i
$120$		0			0
$121$	5.24073	−	9.07721i	0.476430	−	0.825201i
$122$	−5.60175	−	4.53475i	−0.507159	−	0.410557i
$123$		0			0
$124$	3.81733	+	17.9314i	0.342806	+	1.61029i
$125$	−4.41901			−0.395248
$126$		0			0
$127$			0.517396i			0.0459115i	0.999736	+	0.0229557i	$0.00730768\pi$
$127$			0.517396i			0.0459115i	−0.999736	+	0.0229557i	$0.992692\pi$
$128$	10.0749	−	5.14740i	0.890507	−	0.454970i
$129$		0			0
$130$	−1.73030	−	1.40072i	−0.151757	−	0.122851i
$131$	−11.6665	−	6.73566i	−1.01931	−	0.588497i	−0.105404	−	0.994429i	$-0.533614\pi$
$131$	−11.6665	−	6.73566i	−1.01931	−	0.588497i	−0.913903	+	0.405932i	$0.866947\pi$
$132$		0			0
$133$	4.16130	−	11.4163i	0.360831	−	0.989915i
$134$	13.0263	−	5.00269i	1.12530	−	0.432166i
$135$		0			0
$136$	−0.613624	−	11.6040i	−0.0526178	−	0.995037i
$137$	−11.2294	−	19.4498i	−0.959389	−	1.66171i	−0.723989	−	0.689811i	$-0.757694\pi$
$137$	−11.2294	−	19.4498i	−0.959389	−	1.66171i	−0.235399	−	0.971899i	$-0.575640\pi$
$138$		0			0
$139$			1.05090i			0.0891361i	0.999006	+	0.0445681i	$0.0141912\pi$
$139$			1.05090i			0.0891361i	−0.999006	+	0.0445681i	$0.985809\pi$
$140$	−1.88066	−	1.46981i	−0.158945	−	0.124222i
$141$		0			0
$142$	15.5898	+	2.46667i	1.30826	+	0.206998i
$143$	1.25648	+	2.17629i	0.105072	+	0.181990i
$144$		0			0
$145$	3.06759	+	1.77107i	0.254749	+	0.147080i
$146$	−1.95016	−	5.07795i	−0.161396	−	0.420254i
$147$		0			0
$148$	−11.6164	−	12.8932i	−0.954862	−	1.05981i
$149$	10.9331	+	6.31222i	0.895673	+	0.517117i	0.875794	−	0.482685i	$-0.160339\pi$
$149$	10.9331	+	6.31222i	0.895673	+	0.517117i	0.0198791	+	0.999802i	$0.493672\pi$
$150$		0			0
$151$	2.86647	−	1.65496i	0.233270	−	0.134679i	−0.378810	−	0.925475i	$-0.623666\pi$
$151$	2.86647	−	1.65496i	0.233270	−	0.134679i	0.612080	+	0.790796i	$0.290333\pi$
$152$	10.8910	−	7.07999i	0.883376	−	0.574263i
$153$		0			0
$154$	1.38696	+	2.30995i	0.111765	+	0.186141i
$155$	4.13487			0.332121
$156$		0			0
$157$	1.75915	+	3.04694i	0.140396	+	0.243172i	0.927646	−	0.373462i	$-0.121829\pi$
$157$	1.75915	+	3.04694i	0.140396	+	0.243172i	−0.787250	+	0.616634i	$0.788496\pi$
$158$	8.64035	−	10.6734i	0.687389	−	0.849128i
$159$		0			0
$160$	−0.662361	−	2.46422i	−0.0523642	−	0.194814i
$161$	−0.0480250	+	0.131754i	−0.00378490	+	0.0103836i
$162$		0			0
$163$	−9.35173	+	16.1977i	−0.732484	+	1.26870i	0.223335	+	0.974742i	$0.428306\pi$
$163$	−9.35173	+	16.1977i	−0.732484	+	1.26870i	−0.955819	+	0.293957i	$0.905028\pi$
$164$	2.43485	−	7.50170i	0.190130	−	0.585785i
$165$		0			0
$166$	−13.3204	−	2.10760i	−1.03387	−	0.163582i
$167$	−23.5845			−1.82502			−0.912510	−	0.409054i	$-0.865859\pi$
$167$	−23.5845			−1.82502			−0.912510	+	0.409054i	$0.865859\pi$
$168$		0			0
$169$	−0.821615			−0.0632012
$170$	−2.58862	−	0.409581i	−0.198538	−	0.0314134i
$171$		0			0
$172$	−9.84268	−	3.19466i	−0.750497	−	0.243591i
$173$	−12.4108	+	21.4961i	−0.943572	+	1.63432i	−0.184988	+	0.982741i	$0.559225\pi$
$173$	−12.4108	+	21.4961i	−0.943572	+	1.63432i	−0.758585	+	0.651575i	$0.774109\pi$
$174$		0			0
$175$	9.72529	−	8.15264i	0.735163	−	0.616282i
$176$	−0.299283	+	2.86480i	−0.0225593	+	0.215942i
$177$		0			0
$178$	−12.9572	+	16.0060i	−0.971186	+	1.19970i
$179$	−0.498970	−	0.864242i	−0.0372948	−	0.0645965i	0.846776	−	0.531950i	$-0.178541\pi$
$179$	−0.498970	−	0.864242i	−0.0372948	−	0.0645965i	−0.884070	+	0.467354i	$0.845207\pi$
$180$		0			0
$181$	5.81455			0.432192			0.216096	−	0.976372i	$-0.430668\pi$
$181$	5.81455			0.432192			0.216096	+	0.976372i	$0.430668\pi$
$182$	13.0555	−	0.223753i	0.967742	−	0.0165857i
$183$		0			0
$184$	−0.125691	+	0.0817092i	−0.00926610	+	0.00602368i
$185$	−3.38971	+	1.95705i	−0.249216	+	0.143885i
$186$		0			0
$187$	2.56207	+	1.47921i	0.187357	+	0.108171i
$188$	1.36737	−	1.23196i	0.0997257	−	0.0898501i
$189$		0			0
$190$	−1.05036	−	2.73500i	−0.0762012	−	0.198418i
$191$	11.6440	+	6.72270i	0.842534	+	0.486437i	0.858125	−	0.513441i	$-0.171630\pi$
$191$	11.6440	+	6.72270i	0.842534	+	0.486437i	−0.0155908	+	0.999878i	$0.504963\pi$
$192$		0			0
$193$	3.70703	+	6.42076i	0.266838	+	0.462176i	0.968043	−	0.250783i	$-0.0806879\pi$
$193$	3.70703	+	6.42076i	0.266838	+	0.462176i	−0.701206	+	0.712959i	$0.747355\pi$
$194$	7.18774	+	1.13727i	0.516050	+	0.0816511i
$195$		0			0
$196$	13.9918	−	0.479739i	0.999413	−	0.0342670i
$197$			6.62804i			0.472228i	0.971725	+	0.236114i	$0.0758739\pi$
$197$			6.62804i			0.472228i	−0.971725	+	0.236114i	$0.924126\pi$
$198$		0			0
$199$	5.39583	+	9.34584i	0.382500	+	0.662509i	0.991419	−	0.130723i	$-0.0417299\pi$
$199$	5.39583	+	9.34584i	0.382500	+	0.662509i	−0.608919	+	0.793232i	$0.708397\pi$
$200$	13.5477	−	0.716406i	0.957967	−	0.0506575i
$201$		0			0
$202$	−18.8654	+	7.24516i	−1.32737	+	0.509768i
$203$	−20.4621	+	3.59803i	−1.43616	+	0.252532i
$204$		0			0
$205$	−1.54050	−	0.889410i	−0.107593	−	0.0621191i
$206$	−16.4046	−	13.2799i	−1.14296	−	0.925257i
$207$		0			0
$208$	11.2982	+	8.19781i	0.783392	+	0.568416i
$209$			3.30716i			0.228761i
$210$		0			0
$211$	5.17795			0.356465			0.178232	−	0.983988i	$-0.442962\pi$
$211$	5.17795			0.356465			0.178232	+	0.983988i	$0.442962\pi$
$212$	−6.13236	+	1.30549i	−0.421172	+	0.0896611i
$213$		0			0
$214$	17.3845	+	14.0732i	1.18838	+	0.962021i
$215$	−1.16696	+	2.02123i	−0.0795859	+	0.137847i
$216$		0			0
$217$	−18.5859	+	15.5805i	−1.26170	+	1.05767i
$218$	0.122245	+	0.318310i	0.00827948	+	0.0215587i
$219$		0			0
$220$	0.617908	+	0.200556i	0.0416594	+	0.0135215i
$221$	12.4164	−	7.16861i	0.835217	−	0.482213i
$222$		0			0
$223$	−19.0791			−1.27763			−0.638815	−	0.769361i	$-0.720575\pi$
$223$	−19.0791			−1.27763			−0.638815	+	0.769361i	$0.720575\pi$
$224$	12.2626	+	8.58068i	0.819331	+	0.573321i
$225$		0			0
$226$	2.94668	−	18.6236i	0.196010	−	1.23882i
$227$	2.06649	−	1.19309i	0.137158	−	0.0791879i	−0.429851	−	0.902900i	$-0.641434\pi$
$227$	2.06649	−	1.19309i	0.137158	−	0.0791879i	0.567009	+	0.823712i	$0.308101\pi$
$228$		0			0
$229$	−5.11149	+	8.85335i	−0.337776	+	0.585046i	−0.984014	−	0.178090i	$-0.943008\pi$
$229$	−5.11149	+	8.85335i	−0.337776	+	0.585046i	0.646238	+	0.763136i	$0.276341\pi$
$230$	0.0121221	+	0.0315643i	0.000799306	+	0.00208129i
$231$		0			0
$232$	−19.7945	−	10.0740i	−1.29957	−	0.661393i
$233$	−8.53778	+	14.7879i	−0.559328	+	0.968785i	0.438224	+	0.898866i	$0.355608\pi$
$233$	−8.53778	+	14.7879i	−0.559328	+	0.968785i	−0.997553	+	0.0699194i	$0.977726\pi$
$234$		0			0
$235$	−0.207553	−	0.359492i	−0.0135392	−	0.0234506i
$236$	−10.9869	+	2.33895i	−0.715188	+	0.152253i
$237$		0			0
$238$	13.1790	−	7.91306i	0.854267	−	0.512928i
$239$			29.9136i			1.93495i	0.252968	+	0.967475i	$0.418593\pi$
$239$			29.9136i			1.93495i	−0.252968	+	0.967475i	$0.581407\pi$
$240$		0			0
$241$	14.5829	−	8.41946i	0.939369	−	0.542345i	0.0496064	−	0.998769i	$-0.484203\pi$
$241$	14.5829	−	8.41946i	0.939369	−	0.542345i	0.889762	+	0.456424i	$0.150870\pi$
$242$	11.5211	+	9.32662i	0.740606	+	0.599538i
$243$		0			0
$244$	7.57236	−	6.82249i	0.484771	−	0.436765i
$245$	0.551248	−	3.10906i	0.0352179	−	0.198631i
$246$		0			0
$247$	13.8800	+	8.01362i	0.883163	+	0.509895i
$248$	−25.8909	+	1.36912i	−1.64408	+	0.0869391i
$249$		0			0
$250$	0.976656	−	6.17264i	0.0617691	−	0.390392i
$251$			23.1292i			1.45990i	0.683500	+	0.729951i	$0.260457\pi$
$251$			23.1292i			1.45990i	−0.683500	+	0.729951i	$0.739543\pi$
$252$		0			0
$253$		−	0.0381674i		−	0.00239957i
$254$	−0.722718	−	0.114351i	−0.0453473	−	0.00717501i
$255$		0			0
$256$	4.96339	+	15.2107i	0.310212	+	0.950667i
$257$	10.4388	+	6.02683i	0.651153	+	0.375943i	0.788898	−	0.614524i	$-0.210652\pi$
$257$	10.4388	+	6.02683i	0.651153	+	0.375943i	−0.137745	+	0.990468i	$0.543985\pi$
$258$		0			0
$259$	7.86221	−	21.5695i	0.488534	−	1.34026i
$260$	2.33899	−	2.10737i	0.145058	−	0.130693i
$261$		0			0
$262$	11.9871	−	14.8075i	0.740563	−	0.914813i
$263$	20.2875	−	11.7130i	1.25098	−	0.722254i	0.279677	−	0.960094i	$-0.409773\pi$
$263$	20.2875	−	11.7130i	1.25098	−	0.722254i	0.971304	+	0.237840i	$0.0764394\pi$
$264$		0			0
$265$			1.41408i			0.0868664i
$266$	15.0270	+	8.33579i	0.921362	+	0.511100i
$267$		0			0
$268$	4.10896	+	19.3013i	0.250995	+	1.17902i
$269$	−5.98880	−	10.3729i	−0.365144	−	0.632447i	0.623655	−	0.781699i	$-0.285647\pi$
$269$	−5.98880	−	10.3729i	−0.365144	−	0.632447i	−0.988799	+	0.149252i	$0.952313\pi$
$270$		0			0
$271$	3.99591	−	6.92112i	0.242734	−	0.420428i	−0.718758	−	0.695260i	$-0.755289\pi$
$271$	3.99591	−	6.92112i	0.242734	−	0.420428i	0.961492	+	0.274832i	$0.0886224\pi$
$272$	16.3445	+	1.70750i	0.991034	+	0.103532i
$273$		0			0
$274$	29.6500	−	11.3869i	1.79122	−	0.687910i
$275$	−1.72698	+	2.99122i	−0.104141	+	0.180377i
$276$		0			0
$277$	−7.54343	+	4.35520i	−0.453241	+	0.261679i	−0.709198	−	0.705009i	$-0.750943\pi$
$277$	−7.54343	+	4.35520i	−0.453241	+	0.261679i	0.255957	+	0.966688i	$0.417609\pi$
$278$	−1.46793	−	0.232262i	−0.0880409	−	0.0139301i
$279$		0			0
$280$	2.46874	−	2.30213i	0.147535	−	0.137578i
$281$	−6.82201			−0.406967			−0.203484	−	0.979078i	$-0.565226\pi$
$281$	−6.82201			−0.406967			−0.203484	+	0.979078i	$0.565226\pi$
$282$		0			0
$283$	−13.0126	+	7.51281i	−0.773517	+	0.446590i	−0.834128	−	0.551571i	$-0.814028\pi$
$283$	−13.0126	+	7.51281i	−0.773517	+	0.446590i	0.0606110	+	0.998161i	$0.480695\pi$
$284$	−6.89107	+	21.2312i	−0.408909	+	1.25984i
$285$		0			0
$286$	−3.31762	+	1.27411i	−0.196175	+	0.0753398i
$287$	10.2758	−	1.80689i	0.606562	−	0.106657i
$288$		0			0
$289$	−0.0606311	+	0.105016i	−0.00356654	+	0.00617742i
$290$	−3.15188	+	3.89349i	−0.185085	+	0.228634i
$291$		0			0
$292$	7.52407	−	1.60176i	0.440313	−	0.0937360i
$293$	2.77974			0.162394			0.0811971	−	0.996698i	$-0.474126\pi$
$293$	2.77974			0.162394			0.0811971	+	0.996698i	$0.474126\pi$
$294$		0			0
$295$			2.53352i			0.147507i
$296$	20.5770	−	13.3767i	1.19602	−	0.777503i
$297$		0			0
$298$	−11.2335	+	13.8767i	−0.650738	+	0.803853i
$299$	−0.160187	−	0.0924841i	−0.00926387	−	0.00534850i
$300$		0			0
$301$	−2.37074	−	13.4825i	−0.136647	−	0.777117i
$302$	1.67818	+	4.36976i	0.0965684	+	0.251451i
$303$		0			0
$304$	7.48255	+	16.7777i	0.429154	+	0.962267i
$305$	−1.14941	−	1.99083i	−0.0658148	−	0.113995i
$306$		0			0
$307$			24.7943i			1.41508i	0.706672	+	0.707542i	$0.250196\pi$
$307$			24.7943i			1.41508i	−0.706672	+	0.707542i	$0.749804\pi$
$308$	−3.53316	+	1.42684i	−0.201321	+	0.0813015i
$309$		0			0
$310$	−0.913857	+	5.77574i	−0.0519036	+	0.328040i
$311$	1.29417	+	2.24157i	0.0733858	+	0.127108i	0.900383	−	0.435098i	$-0.143286\pi$
$311$	1.29417	+	2.24157i	0.0733858	+	0.127108i	−0.826997	+	0.562206i	$0.809953\pi$
$312$		0			0
$313$	−2.50486	−	1.44618i	−0.141583	−	0.0817431i	0.427535	−	0.903999i	$-0.359382\pi$
$313$	−2.50486	−	1.44618i	−0.141583	−	0.0817431i	−0.569118	+	0.822256i	$0.692715\pi$
$314$	−4.64487	+	1.78384i	−0.262125	+	0.100668i
$315$		0			0
$316$	12.9993	+	14.4281i	0.731270	+	0.811645i
$317$	−29.4673	−	17.0130i	−1.65505	−	0.955543i	−0.974951	−	0.222421i	$-0.928604\pi$
$317$	−29.4673	−	17.0130i	−1.65505	−	0.955543i	−0.680098	−	0.733121i	$-0.738063\pi$
$318$		0			0
$319$	4.89706	−	2.82732i	0.274182	−	0.158299i
$320$	3.58851	−	0.380587i	0.200604	−	0.0212754i
$321$		0			0
$322$	−0.173424	−	0.0962023i	−0.00966455	−	0.00536114i
$323$	18.8684			1.04986
$324$		0			0
$325$	8.36935	+	14.4961i	0.464248	+	0.804101i
$326$	−20.5587	−	16.6427i	−1.13864	−	0.921755i
$327$		0			0
$328$	9.94053	+	5.05905i	0.548874	+	0.279339i
$329$	2.28752	+	0.833817i	0.126115	+	0.0459698i
$330$		0			0
$331$	1.22267	−	2.11772i	0.0672040	−	0.116401i	−0.830466	−	0.557070i	$-0.811926\pi$
$331$	1.22267	−	2.11772i	0.0672040	−	0.116401i	0.897670	+	0.440669i	$0.145259\pi$
$332$	5.88796	−	18.1407i	0.323144	−	0.995598i
$333$		0			0
$334$	5.21246	−	32.9436i	0.285213	−	1.80260i
$335$	4.45076			0.243171
$336$		0			0
$337$	−28.0906			−1.53019			−0.765097	−	0.643915i	$-0.777309\pi$
$337$	−28.0906			−1.53019			−0.765097	+	0.643915i	$0.777309\pi$
$338$	0.181587	−	1.14766i	0.00987704	−	0.0624246i
$339$		0			0
$340$	1.14423	−	3.52536i	0.0620548	−	0.191189i
$341$	3.30042	−	5.71650i	0.178728	−	0.309566i
$342$		0			0
$343$	9.23734	+	16.0522i	0.498769	+	0.866735i
$344$	6.63778	−	13.0426i	0.357885	−	0.703208i
$345$		0			0
$346$	−27.2836	−	22.0867i	−1.46677	−	1.18739i
$347$	−8.51021	−	14.7401i	−0.456852	−	0.791291i	0.541941	−	0.840417i	$-0.317690\pi$
$347$	−8.51021	−	14.7401i	−0.456852	−	0.791291i	−0.998793	+	0.0491260i	$0.984356\pi$
$348$		0			0
$349$	−28.1655			−1.50766			−0.753831	−	0.657068i	$-0.771796\pi$
$349$	−28.1655			−1.50766			−0.753831	+	0.657068i	$0.771796\pi$
$350$	9.23850	+	15.3865i	0.493819	+	0.822442i
$351$		0			0
$352$	−3.93551	−	1.05120i	−0.209763	−	0.0560294i
$353$	17.9835	−	10.3828i	0.957164	−	0.552619i	0.0618651	−	0.998085i	$-0.480295\pi$
$353$	17.9835	−	10.3828i	0.957164	−	0.552619i	0.895299	+	0.445466i	$0.146962\pi$
$354$		0			0
$355$	4.35991	+	2.51719i	0.231400	+	0.133599i
$356$	−19.4940	−	21.6367i	−1.03318	−	1.14674i
$357$		0			0
$358$	1.31748	−	0.505972i	0.0696312	−	0.0267415i
$359$	0.559584	+	0.323076i	0.0295337	+	0.0170513i	0.514694	−	0.857374i	$-0.327905\pi$
$359$	0.559584	+	0.323076i	0.0295337	+	0.0170513i	−0.485160	+	0.874425i	$0.661239\pi$
$360$		0			0
$361$	1.04625	+	1.81215i	0.0550656	+	0.0953764i
$362$	−1.28509	+	8.12197i	−0.0675427	+	0.426881i
$363$		0			0
$364$	−2.57289	+	18.2859i	−0.134856	+	0.958443i
$365$		−	1.73500i		−	0.0908143i
$366$		0			0
$367$	−3.69198	−	6.39470i	−0.192720	−	0.333801i	0.753431	−	0.657527i	$-0.228398\pi$
$367$	−3.69198	−	6.39470i	−0.192720	−	0.333801i	−0.946151	+	0.323726i	$0.895064\pi$
$368$	−0.0863551	−	0.193629i	−0.00450157	−	0.0100936i
$369$		0			0
$370$	−1.98451	−	5.16741i	−0.103170	−	0.268641i
$371$	−5.32836	−	6.35620i	−0.276634	−	0.329997i
$372$		0			0
$373$	9.22518	+	5.32616i	0.477662	+	0.275778i	0.719442	−	0.694553i	$-0.244398\pi$
$373$	9.22518	+	5.32616i	0.477662	+	0.275778i	−0.241780	+	0.970331i	$0.577731\pi$
$374$	−2.63247	+	3.25187i	−0.136122	+	0.168150i
$375$		0			0
$376$	1.41865	+	2.18227i	0.0731611	+	0.112542i
$377$		−	27.4037i		−	1.41136i
$378$		0			0
$379$	1.95468			0.100405			0.0502026	−	0.998739i	$-0.484013\pi$
$379$	1.95468			0.100405			0.0502026	+	0.998739i	$0.484013\pi$
$380$	4.05249	−	0.862714i	0.207888	−	0.0442563i
$381$		0			0
$382$	−11.9640	+	14.7790i	−0.612131	+	0.756161i
$383$	−2.21292	+	3.83290i	−0.113075	+	0.195852i	−0.917009	−	0.398867i	$-0.869403\pi$
$383$	−2.21292	+	3.83290i	−0.113075	+	0.195852i	0.803934	+	0.594719i	$0.202737\pi$
$384$		0			0
$385$	0.148832	+	0.846409i	0.00758516	+	0.0431370i
$386$	−9.78805	+	3.75905i	−0.498199	+	0.191330i
$387$		0			0
$388$	−3.17716	+	9.78875i	−0.161296	+	0.496948i
$389$	9.07706	−	5.24065i	0.460225	−	0.265711i	−0.251914	−	0.967750i	$-0.581060\pi$
$389$	9.07706	−	5.24065i	0.460225	−	0.265711i	0.712139	+	0.702038i	$0.247727\pi$
$390$		0			0
$391$	−0.217757			−0.0110125
$392$	−2.42224	+	19.6503i	−0.122342	+	0.992488i
$393$		0			0
$394$	−9.25829	−	1.46488i	−0.466426	−	0.0737995i
$395$	3.79326	−	2.19004i	0.190859	−	0.110193i
$396$		0			0
$397$	6.09656	−	10.5596i	0.305978	−	0.529969i	−0.671501	−	0.741004i	$-0.734350\pi$
$397$	6.09656	−	10.5596i	0.305978	−	0.529969i	0.977478	+	0.211035i	$0.0676834\pi$
$398$	−14.2472	+	5.47154i	−0.714146	+	0.274264i
$399$		0			0
$400$	−1.99351	+	19.0823i	−0.0996754	+	0.954113i
$401$	2.50405	−	4.33714i	0.125046	−	0.216586i	−0.796705	−	0.604369i	$-0.793425\pi$
$401$	2.50405	−	4.33714i	0.125046	−	0.216586i	0.921751	+	0.387782i	$0.126759\pi$
$402$		0			0
$403$	−15.9946	−	27.7035i	−0.796749	−	1.38001i
$404$	−5.95082	−	27.9532i	−0.296064	−	1.39072i
$405$		0			0
$406$	−0.503487	−	29.3774i	−0.0249876	−	1.45798i
$407$			6.24842i			0.309722i
$408$		0			0
$409$	26.3361	−	15.2051i	1.30223	−	0.751845i	0.321447	−	0.946928i	$-0.395831\pi$
$409$	26.3361	−	15.2051i	1.30223	−	0.751845i	0.980787	+	0.195082i	$0.0624974\pi$
$410$	1.58283	−	1.95526i	0.0781705	−	0.0965635i
$411$		0			0
$412$	22.1755	−	19.9796i	1.09251	−	0.984322i
$413$	−9.54646	−	11.3880i	−0.469750	−	0.560365i
$414$		0			0
$415$	−3.72525	−	2.15078i	−0.182865	−	0.105577i
$416$	−13.9481	+	13.9700i	−0.683859	+	0.684934i
$417$		0			0
$418$	−4.61956	−	0.730922i	−0.225950	−	0.0357506i
$419$			1.70610i			0.0833485i	0.999131	+	0.0416743i	$0.0132692\pi$
$419$			1.70610i			0.0833485i	−0.999131	+	0.0416743i	$0.986731\pi$
$420$		0			0
$421$		−	13.0483i		−	0.635937i	−0.948101	−	0.317969i	$-0.896999\pi$
$421$		−	13.0483i		−	0.635937i	0.948101	−	0.317969i	$-0.103001\pi$
$422$	−1.14439	+	7.23275i	−0.0557081	+	0.352085i
$423$		0			0
$424$	−0.468224	−	8.85443i	−0.0227390	−	0.430009i
$425$	17.0658	+	9.85296i	0.827815	+	0.477939i
$426$		0			0
$427$	12.6681	+	4.61760i	0.613051	+	0.223461i
$428$	−23.5001	+	21.1729i	−1.13592	+	1.02343i
$429$		0			0
$430$	−2.56542	−	2.07677i	−0.123715	−	0.100151i
$431$	1.95335	−	1.12777i	0.0940894	−	0.0543226i	−0.452217	−	0.891908i	$-0.649367\pi$
$431$	1.95335	−	1.12777i	0.0940894	−	0.0543226i	0.546306	+	0.837585i	$0.316033\pi$
$432$		0			0
$433$		−	7.41221i		−	0.356208i	−0.984012	−	0.178104i	$-0.943004\pi$
$433$		−	7.41221i		−	0.356208i	0.984012	−	0.178104i	$-0.0569963\pi$
$434$	−17.6556	−	29.4050i	−0.847498	−	1.41148i
$435$		0			0
$436$	−0.471645	+	0.100406i	−0.0225877	+	0.00480858i
$437$	−0.121713	−	0.210813i	−0.00582231	−	0.0100845i
$438$		0			0
$439$	5.12867	−	8.88312i	0.244778	−	0.423968i	−0.717291	−	0.696774i	$-0.754618\pi$
$439$	5.12867	−	8.88312i	0.244778	−	0.423968i	0.962069	+	0.272806i	$0.0879516\pi$
$440$	−0.416709	+	0.818792i	−0.0198658	+	0.0390344i
$441$		0			0
$442$	7.26920	+	18.9280i	0.345761	+	0.900314i
$443$	−10.6349	+	18.4201i	−0.505277	+	0.875166i	0.494704	+	0.869061i	$0.335276\pi$
$443$	−10.6349	+	18.4201i	−0.505277	+	0.875166i	−0.999981	+	0.00610446i	$0.998057\pi$
$444$		0			0
$445$	−5.68844	+	3.28422i	−0.269658	+	0.155687i
$446$	4.21671	−	26.6504i	0.199667	−	1.26193i
$447$		0			0
$448$	−14.6960	+	15.2324i	−0.694321	+	0.719665i
$449$	15.4114			0.727307			0.363654	−	0.931534i	$-0.381529\pi$
$449$	15.4114			0.727307			0.363654	+	0.931534i	$0.381529\pi$
$450$		0			0
$451$	−2.45924	+	1.41984i	−0.115801	+	0.0668577i
$452$	25.3628	+	8.23207i	1.19297	+	0.387204i
$453$		0			0
$454$	1.20983	+	3.15023i	0.0567801	+	0.147848i
$455$	3.91298	+	1.42631i	0.183443	+	0.0668663i
$456$		0			0
$457$	18.0425	−	31.2505i	0.843991	−	1.46184i	−0.0425032	−	0.999096i	$-0.513533\pi$
$457$	18.0425	−	31.2505i	0.843991	−	1.46184i	0.886494	−	0.462739i	$-0.153133\pi$
$458$	−11.2370	−	9.09661i	−0.525070	−	0.425057i
$459$		0			0
$460$	−0.0467693	+	0.00995647i	−0.00218063	+	0.000464223i
$461$	−30.9944			−1.44355			−0.721776	−	0.692127i	$-0.756674\pi$
$461$	−30.9944			−1.44355			−0.721776	+	0.692127i	$0.756674\pi$
$462$		0			0
$463$			4.76599i			0.221494i	0.993849	+	0.110747i	$0.0353244\pi$
$463$			4.76599i			0.221494i	−0.993849	+	0.110747i	$0.964676\pi$
$464$	18.4466	−	25.4232i	0.856363	−	1.18024i
$465$		0			0
$466$	−18.7693	−	15.1942i	−0.869470	−	0.703857i
$467$	−0.964225	−	0.556695i	−0.0446190	−	0.0257608i	0.477525	−	0.878618i	$-0.341534\pi$
$467$	−0.964225	−	0.556695i	−0.0446190	−	0.0257608i	−0.522144	+	0.852858i	$0.674867\pi$
$468$		0			0
$469$	−20.0059	+	16.7708i	−0.923784	+	0.774402i
$470$	0.548023	−	0.210465i	0.0252784	−	0.00970803i
$471$		0			0
$472$	−0.838886	−	15.8639i	−0.0386129	−	0.730194i
$473$	1.86292	+	3.22667i	0.0856570	+	0.148362i
$474$		0			0
$475$			22.0288i			1.01075i
$476$	8.14054	+	20.1578i	0.373121	+	0.923931i
$477$		0			0
$478$	−41.7844	−	6.61127i	−1.91117	−	0.302393i
$479$	13.3498	+	23.1224i	0.609966	+	1.05649i	0.991245	+	0.132032i	$0.0421501\pi$
$479$	13.3498	+	23.1224i	0.609966	+	1.05649i	−0.381280	+	0.924460i	$0.624517\pi$
$480$		0			0
$481$	26.2243	+	15.1406i	1.19573	+	0.690354i
$482$	8.53760	+	22.2308i	0.388877	+	1.01258i
$483$		0			0
$484$	−15.5741	+	14.0318i	−0.707913	+	0.637810i
$485$	2.01016	+	1.16056i	0.0912765	+	0.0526985i
$486$		0			0
$487$	19.3435	−	11.1680i	0.876536	−	0.506068i	0.00702114	−	0.999975i	$-0.497765\pi$
$487$	19.3435	−	11.1680i	0.876536	−	0.506068i	0.869515	+	0.493907i	$0.164432\pi$
$488$	7.85633	+	12.0852i	0.355639	+	0.547072i
$489$		0			0
$490$	4.22102	+	1.45714i	0.190686	+	0.0658271i
$491$	17.8395			0.805084			0.402542	−	0.915402i	$-0.368127\pi$
$491$	17.8395			0.805084			0.402542	+	0.915402i	$0.368127\pi$
$492$		0			0
$493$	−16.1307	−	27.9392i	−0.726491	−	1.25832i
$494$	−14.2614	+	17.6170i	−0.641650	+	0.792626i
$495$		0			0
$496$	3.80978	−	36.4680i	0.171064	−	1.63746i
$497$	−29.0824	+	5.11382i	−1.30453	+	0.229386i
$498$		0			0
$499$	−3.10223	+	5.37322i	−0.138875	+	0.240538i	−0.927071	−	0.374886i	$-0.877682\pi$
$499$	−3.10223	+	5.37322i	−0.138875	+	0.240538i	0.788196	+	0.615424i	$0.211015\pi$
$500$	8.40631	+	2.72846i	0.375942	+	0.122020i
$501$		0			0
$502$	−32.3077	−	5.11184i	−1.44196	−	0.228152i
$503$	5.86342			0.261437			0.130718	−	0.991420i	$-0.458272\pi$
$503$	5.86342			0.261437			0.130718	+	0.991420i	$0.458272\pi$
$504$		0			0
$505$	−6.44583			−0.286836
$506$	0.0533137	+	0.00843548i	0.00237008	+	0.000375003i
$507$		0			0
$508$	0.319459	−	0.984246i	0.0141737	−	0.0436688i
$509$	17.5030	−	30.3161i	0.775808	−	1.34374i	−0.158530	−	0.987354i	$-0.550676\pi$
$509$	17.5030	−	30.3161i	0.775808	−	1.34374i	0.934339	−	0.356386i	$-0.115991\pi$
$510$		0			0
$511$	6.53761	+	7.79872i	0.289207	+	0.344995i
$512$	−22.3438	+	3.57129i	−0.987466	+	0.157830i
$513$		0			0
$514$	−10.7256	+	13.2493i	−0.473086	+	0.584400i
$515$	−3.36602	−	5.83011i	−0.148324	−	0.256905i
$516$		0			0
$517$	−0.662668			−0.0291441
$518$	28.3914	+	15.7493i	1.24745	+	0.691986i
$519$		0			0
$520$	2.42670	+	3.73294i	0.106418	+	0.163700i
$521$	6.98875	−	4.03495i	0.306182	−	0.176775i	−0.339034	−	0.940774i	$-0.610100\pi$
$521$	6.98875	−	4.03495i	0.306182	−	0.176775i	0.645217	+	0.763999i	$0.276767\pi$
$522$		0			0
$523$	−26.9826	−	15.5784i	−1.17987	−	0.681196i	−0.223882	−	0.974616i	$-0.571873\pi$
$523$	−26.9826	−	15.5784i	−1.17987	−	0.681196i	−0.955984	+	0.293420i	$0.905206\pi$
$524$	18.0344	+	20.0166i	0.787838	+	0.874430i
$525$		0			0
$526$	11.8774	+	30.9271i	0.517877	+	1.34848i
$527$	−32.6144	−	18.8299i	−1.42071	−	0.820245i
$528$		0			0
$529$	−11.4986	−	19.9162i	−0.499939	−	0.865920i
$530$	−1.97524	−	0.312530i	−0.0857991	−	0.0135754i
$531$		0			0
$532$	−14.9649	+	19.1479i	−0.648810	+	0.830167i
$533$			13.7618i			0.596088i
$534$		0			0
$535$	3.56707	+	6.17835i	0.154218	+	0.267113i
$536$	−27.8689	+	1.47372i	−1.20375	+	0.0636548i
$537$		0			0
$538$	15.8129	−	6.07284i	0.681741	−	0.261819i
$539$	−3.85831	−	3.24374i	−0.166189	−	0.139718i
$540$		0			0
$541$	−21.2493	−	12.2683i	−0.913581	−	0.527456i	−0.0319992	−	0.999488i	$-0.510187\pi$
$541$	−21.2493	−	12.2683i	−0.913581	−	0.527456i	−0.881581	+	0.472032i	$0.843521\pi$
$542$	8.78453	+	7.11129i	0.377328	+	0.305456i
$543$		0			0
$544$	−5.99745	+	22.4533i	−0.257138	+	0.962677i
$545$			0.108758i			0.00465869i
$546$		0			0
$547$	30.8257			1.31801			0.659005	−	0.752138i	$-0.270977\pi$
$547$	30.8257			1.31801			0.659005	+	0.752138i	$0.270977\pi$
$548$	9.35266	+	43.9329i	0.399526	+	1.87672i
$549$		0			0
$550$	−3.79656	−	3.07341i	−0.161886	−	0.131051i
$551$	18.0322	−	31.2326i	0.768196	−	1.33055i
$552$		0			0
$553$	−8.79820	+	24.1373i	−0.374138	+	1.02642i
$554$	−4.41631	−	11.4995i	−0.187631	−	0.488567i
$555$		0			0
$556$	0.648863	−	1.99913i	0.0275179	−	0.0847821i
$557$	−33.2404	+	19.1914i	−1.40844	+	0.813164i	−0.995238	−	0.0974752i	$-0.968923\pi$
$557$	−33.2404	+	19.1914i	−1.40844	+	0.813164i	−0.413203	+	0.910639i	$0.635590\pi$
$558$		0			0
$559$	18.0563			0.763698
$560$	2.67007	+	3.95722i	0.112831	+	0.167223i
$561$		0			0
$562$	1.50775	−	9.52924i	0.0636006	−	0.401967i
$563$	0.879959	−	0.508045i	0.0370859	−	0.0214115i	−0.481342	−	0.876533i	$-0.659851\pi$
$563$	0.879959	−	0.508045i	0.0370859	−	0.0214115i	0.518428	+	0.855121i	$0.326517\pi$
$564$		0			0
$565$	3.00704	−	5.20835i	0.126507	−	0.219117i
$566$	−7.61823	−	19.8369i	−0.320218	−	0.833805i
$567$		0			0
$568$	−28.1335	−	14.3181i	−1.18046	−	0.600772i
$569$	−1.66552	+	2.88476i	−0.0698220	+	0.120935i	−0.898823	−	0.438312i	$-0.855576\pi$
$569$	−1.66552	+	2.88476i	−0.0698220	+	0.120935i	0.829001	+	0.559247i	$0.188910\pi$
$570$		0			0
$571$	3.34133	+	5.78735i	0.139830	+	0.242193i	0.927432	−	0.373991i	$-0.122011\pi$
$571$	3.34133	+	5.78735i	0.139830	+	0.242193i	−0.787602	+	0.616184i	$0.788678\pi$
$572$	−1.04649	−	4.91576i	−0.0437560	−	0.205538i
$573$		0			0
$574$	0.252845	+	14.7530i	0.0105535	+	0.615777i
$575$		−	0.254232i		−	0.0106022i
$576$		0			0
$577$	−0.561113	+	0.323959i	−0.0233595	+	0.0134866i	−0.511634	−	0.859203i	$-0.670960\pi$
$577$	−0.561113	+	0.323959i	−0.0233595	+	0.0134866i	0.488275	+	0.872690i	$0.337626\pi$
$578$	−0.133290	−	0.107902i	−0.00554414	−	0.00448812i
$579$		0			0
$580$	−4.74197	−	5.26317i	−0.196900	−	0.218541i
$581$	24.8490	−	4.36942i	1.03091	−	0.181274i
$582$		0			0
$583$	1.95498	+	1.12871i	0.0809672	+	0.0467464i
$584$	0.574487	+	10.8639i	0.0237724	+	0.449552i
$585$		0			0
$586$	−0.614357	+	3.88284i	−0.0253788	+	0.160399i
$587$			4.35212i			0.179631i	0.995958	+	0.0898157i	$0.0286278\pi$
$587$			4.35212i			0.179631i	−0.995958	+	0.0898157i	$0.971372\pi$
$588$		0			0
$589$		−	42.0991i		−	1.73466i
$590$	−3.53891	−	0.559938i	−0.145695	−	0.0230523i
$591$		0			0
$592$	14.1372	+	31.6992i	0.581037	+	1.30283i
$593$	−21.7338	−	12.5480i	−0.892502	−	0.515286i	−0.0177420	−	0.999843i	$-0.505648\pi$
$593$	−21.7338	−	12.5480i	−0.892502	−	0.515286i	−0.874760	+	0.484556i	$0.838981\pi$
$594$		0			0
$595$	4.82902	−	0.849130i	0.197971	−	0.0348109i
$596$	−16.9007	−	18.7583i	−0.692279	−	0.768368i
$597$		0			0
$598$	0.164589	−	0.203315i	0.00673053	−	0.00831418i
$599$	−20.4978	+	11.8344i	−0.837519	+	0.483542i	−0.856420	−	0.516279i	$-0.827317\pi$
$599$	−20.4978	+	11.8344i	−0.837519	+	0.483542i	0.0189009	+	0.999821i	$0.493983\pi$
$600$		0			0
$601$		−	14.8295i		−	0.604907i	−0.953164	−	0.302453i	$-0.902194\pi$
$601$		−	14.8295i		−	0.604907i	0.953164	−	0.302453i	$-0.0978057\pi$
$602$	19.3568	−	0.331747i	0.788923	−	0.0135210i
$603$		0			0
$604$	−6.47474	+	1.37837i	−0.263453	+	0.0560852i
$605$	2.36398	+	4.09454i	0.0961096	+	0.166467i
$606$		0			0
$607$	0.527187	−	0.913114i	0.0213979	−	0.0370622i	−0.855128	−	0.518417i	$-0.826522\pi$
$607$	0.527187	−	0.913114i	0.0213979	−	0.0370622i	0.876526	+	0.481354i	$0.159855\pi$
$608$	−25.0895	+	6.74382i	−1.01751	+	0.273498i
$609$		0			0
$610$	3.03490	−	1.16554i	0.122879	−	0.0471911i
$611$	−1.60572	+	2.78119i	−0.0649605	+	0.112515i
$612$		0			0
$613$	32.6152	−	18.8304i	1.31731	−	0.760552i	0.334019	−	0.942566i	$-0.391595\pi$
$613$	32.6152	−	18.8304i	1.31731	−	0.760552i	0.983296	+	0.182015i	$0.0582618\pi$
$614$	−34.6335	−	5.47984i	−1.39770	−	0.221148i
$615$		0			0
$616$	−1.21218	−	5.25060i	−0.0488403	−	0.211553i
$617$	−3.75729			−0.151263			−0.0756314	−	0.997136i	$-0.524097\pi$
$617$	−3.75729			−0.151263			−0.0756314	+	0.997136i	$0.524097\pi$
$618$		0			0
$619$	4.60049	−	2.65609i	0.184909	−	0.106757i	−0.404688	−	0.914455i	$-0.632620\pi$
$619$	4.60049	−	2.65609i	0.184909	−	0.106757i	0.589597	+	0.807697i	$0.299287\pi$
$620$	−7.86579	−	2.55302i	−0.315898	−	0.102532i
$621$		0			0
$622$	−3.41714	+	1.31233i	−0.137015	+	0.0526197i
$623$	13.1940	−	36.1968i	0.528605	−	1.45019i
$624$		0			0
$625$	−10.9947	+	19.0433i	−0.439786	+	0.761732i
$626$	2.57369	−	3.17926i	0.102865	−	0.127069i
$627$		0			0
$628$	−1.46515	−	6.88238i	−0.0584660	−	0.274637i
$629$	35.6492			1.42142
$630$		0			0
$631$			37.4896i			1.49244i	0.665702	+	0.746218i	$0.268132\pi$
$631$			37.4896i			1.49244i	−0.665702	+	0.746218i	$0.731868\pi$
$632$	−23.0267	+	14.9692i	−0.915954	+	0.595441i
$633$		0			0
$634$	30.2770	−	37.4009i	1.20245	−	1.48538i
$635$	−0.202119	−	0.116693i	−0.00802083	−	0.00463083i
$636$		0			0
$637$	−22.9630	+	8.33322i	−0.909826	+	0.330174i
$638$	2.86699	+	7.46526i	0.113505	+	0.295552i
$639$		0			0
$640$	−0.261487	+	5.09667i	−0.0103362	+	0.201464i
$641$	11.0865	+	19.2023i	0.437889	+	0.758445i	0.997526	−	0.0702920i	$-0.0223931\pi$
$641$	11.0865	+	19.2023i	0.437889	+	0.758445i	−0.559638	+	0.828737i	$0.689060\pi$
$642$		0			0
$643$			29.4039i			1.15958i	0.814767	+	0.579788i	$0.196865\pi$
$643$			29.4039i			1.15958i	−0.814767	+	0.579788i	$0.803135\pi$
$644$	0.172708	−	0.220983i	0.00680564	−	0.00870796i
$645$		0			0
$646$	−4.17014	+	26.3560i	−0.164072	+	1.03696i
$647$	−10.3938	−	18.0026i	−0.408623	−	0.707755i	0.586113	−	0.810229i	$-0.300657\pi$
$647$	−10.3938	−	18.0026i	−0.408623	−	0.707755i	−0.994736	+	0.102474i	$0.967324\pi$
$648$		0			0
$649$	3.50261	+	2.02223i	0.137490	+	0.0793796i
$650$	−22.0985	+	8.48679i	−0.866774	+	0.332879i
$651$		0			0
$652$	27.7909	−	25.0388i	1.08838	−	0.980597i
$653$	−3.36065	−	1.94027i	−0.131512	−	0.0759287i	0.432800	−	0.901490i	$-0.357525\pi$
$653$	−3.36065	−	1.94027i	−0.131512	−	0.0759287i	−0.564313	+	0.825561i	$0.690859\pi$
$654$		0			0
$655$	5.26252	−	3.03832i	0.205624	−	0.118717i
$656$	−9.26365	+	12.7672i	−0.361685	+	0.498475i
$657$		0			0
$658$	−1.67028	+	3.01101i	−0.0651142	+	0.117381i
$659$	25.0314			0.975087			0.487543	−	0.873099i	$-0.337893\pi$
$659$	25.0314			0.975087			0.487543	+	0.873099i	$0.337893\pi$
$660$		0			0
$661$	2.76963	+	4.79715i	0.107726	+	0.186587i	0.914849	−	0.403797i	$-0.132310\pi$
$661$	2.76963	+	4.79715i	0.107726	+	0.186587i	−0.807122	+	0.590384i	$0.798976\pi$
$662$	2.68789	+	2.17591i	0.104468	+	0.0845692i
$663$		0			0
$664$	24.0382	+	12.2338i	0.932864	+	0.474764i
$665$	3.52118	+	4.20041i	0.136545	+	0.162885i
$666$		0			0
$667$	−0.208107	+	0.360451i	−0.00805793	+	0.0139567i
$668$	44.8649	+	14.5619i	1.73587	+	0.563417i
$669$		0			0
$670$	−0.983673	+	6.21699i	−0.0380026	+	0.240183i
$671$	−3.66979			−0.141671
$672$		0			0
$673$	−6.26781			−0.241606			−0.120803	−	0.992676i	$-0.538547\pi$
$673$	−6.26781			−0.241606			−0.120803	+	0.992676i	$0.538547\pi$
$674$	6.20838	−	39.2380i	0.239138	−	1.51139i
$675$		0			0
$676$	1.56296	+	0.507295i	0.0601140	+	0.0195114i
$677$	−22.2551	+	38.5470i	−0.855333	+	1.48148i	0.0210020	+	0.999779i	$0.493314\pi$
$677$	−22.2551	+	38.5470i	−0.855333	+	1.48148i	−0.876335	+	0.481701i	$0.840019\pi$
$678$		0			0
$679$	−13.4086	+	2.35775i	−0.514575	+	0.0904822i
$680$	4.67146	+	2.37746i	0.179142	+	0.0911713i
$681$		0			0
$682$	7.25559	+	5.87357i	0.277831	+	0.224911i
$683$	8.00201	+	13.8599i	0.306189	+	0.530334i	0.977525	−	0.210818i	$-0.0676129\pi$
$683$	8.00201	+	13.8599i	0.306189	+	0.530334i	−0.671337	+	0.741153i	$0.734280\pi$
$684$		0			0
$685$	10.1307			0.387073
$686$	−24.4638	+	9.35533i	−0.934032	+	0.357188i
$687$		0			0
$688$	16.7513	+	12.1545i	0.638637	+	0.463384i
$689$	9.47431	−	5.46999i	0.360942	−	0.208390i
$690$		0			0
$691$	−32.1161	−	18.5422i	−1.22175	−	0.705380i	−0.256462	−	0.966554i	$-0.582557\pi$
$691$	−32.1161	−	18.5422i	−1.22175	−	0.705380i	−0.965292	+	0.261175i	$0.915890\pi$
$692$	36.8815	−	33.2293i	1.40203	−	1.26319i
$693$		0			0
$694$	22.4704	−	8.62963i	0.852965	−	0.327576i
$695$	−0.410530	−	0.237019i	−0.0155723	−	0.00899066i
$696$		0			0
$697$	8.10064	+	14.0307i	0.306834	+	0.531451i
$698$	6.22491	−	39.3425i	0.235616	−	1.48914i
$699$		0			0
$700$	−23.5342	+	9.50408i	−0.889510	+	0.359220i
$701$		−	21.0727i		−	0.795906i	−0.917406	−	0.397953i	$-0.869721\pi$
$701$		−	21.0727i		−	0.795906i	0.917406	−	0.397953i	$-0.130279\pi$
$702$		0			0
$703$	19.9257	+	34.5123i	0.751511	+	1.30166i
$704$	2.33816	−	5.26493i	0.0881226	−	0.198430i
$705$		0			0
$706$	10.5285	+	27.4147i	0.396244	+	1.03177i
$707$	28.9736	−	24.2883i	1.08966	−	0.913457i
$708$		0			0
$709$	−16.4705	−	9.50925i	−0.618563	−	0.357127i	0.157746	−	0.987480i	$-0.449577\pi$
$709$	−16.4705	−	9.50925i	−0.618563	−	0.357127i	−0.776309	+	0.630352i	$0.782910\pi$
$710$	−4.47970	+	5.53375i	−0.168120	+	0.207678i
$711$		0			0
$712$	34.5313	−	22.4480i	1.29412	−	0.841276i
$713$			0.485860i			0.0181956i
$714$		0			0
$715$	−1.13354			−0.0423921
$716$	0.415580	+	1.95214i	0.0155310	+	0.0729548i
$717$		0			0
$718$	−0.574959	+	0.710244i	−0.0214573	+	0.0265061i
$719$	−1.02572	+	1.77660i	−0.0382529	+	0.0662559i	−0.884518	−	0.466506i	$-0.845513\pi$
$719$	−1.02572	+	1.77660i	−0.0382529	+	0.0662559i	0.846265	+	0.532762i	$0.178846\pi$
$720$		0			0
$721$	37.0983	+	13.5226i	1.38161	+	0.503606i
$722$	−2.76251	+	1.06093i	−0.102810	+	0.0394837i
$723$		0			0
$724$	−11.0611	−	3.59011i	−0.411081	−	0.133426i
$725$	32.6191	−	18.8326i	1.21144	−	0.699426i
$726$		0			0
$727$	−29.6614			−1.10008			−0.550039	−	0.835139i	$-0.685387\pi$
$727$	−29.6614			−1.10008			−0.550039	+	0.835139i	$0.685387\pi$
$728$	−24.9738	−	7.63532i	−0.925591	−	0.282984i
$729$		0			0
$730$	2.42352	+	0.383457i	0.0896984	+	0.0141924i
$731$	18.4091	−	10.6285i	0.680886	−	0.393110i
$732$		0			0
$733$	−13.8269	+	23.9490i	−0.510710	+	0.884575i	0.489213	+	0.872164i	$0.337284\pi$
$733$	−13.8269	+	23.9490i	−0.510710	+	0.884575i	−0.999923	+	0.0124107i	$0.996049\pi$
$734$	9.74833	−	3.74379i	0.359818	−	0.138186i
$735$		0			0
$736$	0.289554	−	0.0778295i	0.0106731	−	0.00286883i
$737$	3.55257	−	6.15323i	0.130860	−	0.226657i
$738$		0			0
$739$	1.43287	+	2.48180i	0.0527090	+	0.0912946i	0.891176	−	0.453658i	$-0.149881\pi$
$739$	1.43287	+	2.48180i	0.0527090	+	0.0912946i	−0.838467	+	0.544952i	$0.816548\pi$
$740$	7.65663	−	1.62998i	0.281463	−	0.0599192i
$741$		0			0
$742$	10.0562	−	6.03805i	0.369175	−	0.221664i
$743$		−	3.95558i		−	0.145116i	−0.997364	−	0.0725581i	$-0.976884\pi$
$743$		−	3.95558i		−	0.145116i	0.997364	−	0.0725581i	$-0.0231163\pi$
$744$		0			0
$745$	−4.93169	+	2.84731i	−0.180683	+	0.104317i
$746$	−9.47866	+	11.7089i	−0.347038	+	0.428694i
$747$		0			0
$748$	−3.96053	−	4.39583i	−0.144811	−	0.160728i
$749$	−39.3141	−	14.3303i	−1.43651	−	0.523616i
$750$		0			0
$751$	0.443784	+	0.256219i	0.0161939	+	0.00934956i	0.508075	−	0.861313i	$-0.330357\pi$
$751$	0.443784	+	0.256219i	0.0161939	+	0.00934956i	−0.491881	+	0.870662i	$0.663691\pi$
$752$	−3.36182	+	1.49931i	−0.122593	+	0.0546741i
$753$		0			0
$754$	38.2784	+	6.05655i	1.39402	+	0.220566i
$755$			1.49303i			0.0543371i
$756$		0			0
$757$			18.0691i			0.656732i	0.944551	+	0.328366i	$0.106498\pi$
$757$			18.0691i			0.656732i	−0.944551	+	0.328366i	$0.893502\pi$
$758$	−0.432009	+	2.73037i	−0.0156913	+	0.0991716i
$759$		0			0
$760$	0.309420	+	5.85134i	0.0112239	+	0.212250i
$761$	34.4739	+	19.9035i	1.24968	+	0.721501i	0.971045	−	0.238897i	$-0.0767858\pi$
$761$	34.4739	+	19.9035i	1.24968	+	0.721501i	0.278632	+	0.960398i	$0.410119\pi$
$762$		0			0
$763$	−0.409808	−	0.488860i	−0.0148361	−	0.0176979i
$764$	−17.9997	−	19.9781i	−0.651207	−	0.722782i
$765$		0			0
$766$	−4.86485	−	3.93821i	−0.175774	−	0.142293i
$767$	16.9745	−	9.80022i	0.612913	−	0.353865i
$768$		0			0
$769$		−	45.5560i		−	1.64279i	−0.570358	−	0.821396i	$-0.693195\pi$
$769$		−	45.5560i		−	1.64279i	0.570358	−	0.821396i	$-0.306805\pi$
$770$	−1.21519	+	0.0208266i	−0.0437924	+	0.000750538i
$771$		0			0
$772$	−3.08749	−	14.5031i	−0.111121	−	0.521978i
$773$	20.8182	+	36.0581i	0.748777	+	1.29692i	0.948409	+	0.317049i	$0.102692\pi$
$773$	20.8182	+	36.0581i	0.748777	+	1.29692i	−0.199632	+	0.979871i	$0.563975\pi$
$774$		0			0
$775$	21.9840	−	38.0773i	0.789687	−	1.36778i
$776$	−12.9711	−	6.60141i	−0.465635	−	0.236977i
$777$		0			0
$778$	5.31418	+	13.8374i	0.190523	+	0.496096i
$779$	−9.05552	+	15.6846i	−0.324448	+	0.561960i
$780$		0			0
$781$	6.96010	−	4.01841i	0.249052	−	0.143790i
$782$	0.0481270	−	0.304171i	0.00172102	−	0.0108771i
$783$		0			0
$784$	−26.9129	−	7.72642i	−0.961174	−	0.275944i
$785$	−1.58703			−0.0566436
$786$		0			0
$787$	14.5316	−	8.38984i	0.517997	−	0.299065i	−0.218118	−	0.975922i	$-0.569992\pi$
$787$	14.5316	−	8.38984i	0.517997	−	0.299065i	0.736115	+	0.676857i	$0.236658\pi$
$788$	4.09239	−	12.6086i	0.145786	−	0.449162i
$789$		0			0
$790$	2.22077	+	5.78259i	0.0790114	+	0.205735i
$791$	6.10897	+	34.7419i	0.217210	+	1.23528i
$792$		0			0
$793$	−8.89233	+	15.4020i	−0.315776	+	0.546940i
$794$	13.4026	+	10.8497i	0.475639	+	0.385041i
$795$		0			0
$796$	−4.49405	−	21.1102i	−0.159287	−	0.748233i
$797$	22.4555			0.795415			0.397707	−	0.917512i	$-0.369806\pi$
$797$	22.4555			0.795415			0.397707	+	0.917512i	$0.369806\pi$
$798$		0			0
$799$			3.78073i			0.133752i
$800$	−26.2142	−	7.00202i	−0.926813	−	0.247559i
$801$		0			0
$802$	5.50485	+	4.45631i	0.194383	+	0.157358i
$803$	−2.39866	−	1.38487i	−0.0846469	−	0.0488709i
$804$		0			0
$805$	−0.0406375	−	0.0484764i	−0.00143228	−	0.00170857i
$806$	42.2323	−	16.2191i	1.48757	−	0.571292i
$807$		0			0
$808$	40.3613	−	2.13431i	1.41990	−	0.0750849i
$809$	−7.04864	−	12.2086i	−0.247817	−	0.429232i	0.715103	−	0.699019i	$-0.246380\pi$
$809$	−7.04864	−	12.2086i	−0.247817	−	0.429232i	−0.962920	+	0.269788i	$0.913047\pi$
$810$		0			0
$811$			14.2766i			0.501320i	0.968075	+	0.250660i	$0.0806477\pi$
$811$			14.2766i			0.501320i	−0.968075	+	0.250660i	$0.919352\pi$
$812$	41.1468	+	5.78949i	1.44397	+	0.203171i
$813$		0			0
$814$	−8.72802	−	1.38098i	−0.305917	−	0.0484032i
$815$	−4.21837	−	7.30643i	−0.147763	−	0.255933i
$816$		0			0
$817$	20.5791	+	11.8814i	0.719973	+	0.415677i
$818$	15.4185	+	40.1477i	0.539095	+	1.40373i
$819$		0			0
$820$	2.38136	+	2.64309i	0.0831606	+	0.0923009i
$821$	11.2178	+	6.47658i	0.391503	+	0.226034i	0.682811	−	0.730595i	$-0.260757\pi$
$821$	11.2178	+	6.47658i	0.391503	+	0.226034i	−0.291308	+	0.956629i	$0.594091\pi$
$822$		0			0
$823$	−8.69701	+	5.02122i	−0.303159	+	0.175029i	−0.643861	−	0.765143i	$-0.722668\pi$
$823$	−8.69701	+	5.02122i	−0.303159	+	0.175029i	0.340702	+	0.940171i	$0.389335\pi$
$824$	23.0071	+	35.3913i	0.801491	+	1.23292i
$825$		0			0
$826$	18.0170	−	10.8180i	0.626892	−	0.376405i
$827$	−45.1481			−1.56995			−0.784976	−	0.619526i	$-0.787325\pi$
$827$	−45.1481			−1.56995			−0.784976	+	0.619526i	$0.787325\pi$
$828$		0			0
$829$	21.1728	+	36.6724i	0.735362	+	1.27368i	0.954564	+	0.298005i	$0.0963212\pi$
$829$	21.1728	+	36.6724i	0.735362	+	1.27368i	−0.219202	+	0.975679i	$0.570345\pi$
$830$	3.82761	−	4.72822i	0.132858	−	0.164119i
$831$		0			0
$832$	−16.4311	−	22.5707i	−0.569645	−	0.782498i
$833$	−18.5065	+	22.0129i	−0.641214	+	0.762701i
$834$		0			0
$835$	5.31923	−	9.21318i	0.184080	−	0.318835i
$836$	2.04196	−	6.29123i	0.0706226	−	0.217587i
$837$		0			0
$838$	−2.38315	−	0.377070i	−0.0823244	−	0.0130257i
$839$	7.15440			0.246997			0.123499	−	0.992345i	$-0.460589\pi$
$839$	7.15440			0.246997			0.123499	+	0.992345i	$0.460589\pi$
$840$		0			0
$841$	−32.6634			−1.12632
$842$	18.2264	+	2.88385i	0.628124	+	0.0993839i
$843$		0			0
$844$	−9.85005	−	3.19706i	−0.339053	−	0.110047i
$845$	0.185307	−	0.320961i	0.00637475	−	0.0110414i
$846$		0			0
$847$	−26.0544	−	9.49701i	−0.895241	−	0.326321i
$848$	12.4717	+	1.30291i	0.428279	+	0.0447419i
$849$		0			0
$850$	−17.5347	+	21.6606i	−0.601437	+	0.742951i
$851$	−0.229960	−	0.398302i	−0.00788292	−	0.0136536i
$852$		0			0
$853$	43.0151			1.47281			0.736405	−	0.676541i	$-0.236522\pi$
$853$	43.0151			1.47281			0.736405	+	0.676541i	$0.236522\pi$
$854$	−9.24983	+	16.6747i	−0.316523	+	0.570596i
$855$		0			0
$856$	−24.3813	−	37.5053i	−0.833337	−	1.28190i
$857$	2.28337	−	1.31831i	0.0779985	−	0.0450325i	−0.460493	−	0.887663i	$-0.652328\pi$
$857$	2.28337	−	1.31831i	0.0779985	−	0.0450325i	0.538492	+	0.842631i	$0.318994\pi$
$858$		0			0
$859$	−13.8594	−	8.00171i	−0.472875	−	0.273015i	0.244567	−	0.969632i	$-0.421354\pi$
$859$	−13.8594	−	8.00171i	−0.472875	−	0.273015i	−0.717443	+	0.696618i	$0.754687\pi$
$860$	3.46790	−	3.12448i	0.118254	−	0.106544i
$861$		0			0
$862$	1.14359	+	2.97776i	0.0389509	+	0.101423i
$863$	−1.14047	−	0.658448i	−0.0388219	−	0.0224138i	0.480463	−	0.877015i	$-0.340468\pi$
$863$	−1.14047	−	0.658448i	−0.0388219	−	0.0224138i	−0.519285	+	0.854601i	$0.673802\pi$
$864$		0			0
$865$	−5.59823	−	9.69643i	−0.190346	−	0.329688i
$866$	10.3536	+	1.63819i	0.351831	+	0.0556679i
$867$		0			0
$868$	44.9761	−	18.1632i	1.52659	−	0.616499i
$869$		−	6.99229i		−	0.237197i
$870$		0			0
$871$	−17.2166	−	29.8200i	−0.583361	−	1.01041i
$872$	−0.0360115	−	0.681002i	−0.00121950	−	0.0230616i
$873$		0			0
$874$	0.321371	−	0.123421i	0.0108705	−	0.00417477i
$875$	2.02477	+	11.5149i	0.0684498	+	0.389276i
$876$		0			0
$877$	20.8705	+	12.0496i	0.704748	+	0.406886i	0.809113	−	0.587653i	$-0.199948\pi$
$877$	20.8705	+	12.0496i	0.704748	+	0.406886i	−0.104366	+	0.994539i	$0.533281\pi$
$878$	11.2748	+	9.12719i	0.380505	+	0.308028i
$879$		0			0
$880$	−1.05162	−	0.763038i	−0.0354501	−	0.0257220i
$881$		−	1.71827i		−	0.0578899i	−0.999581	−	0.0289449i	$-0.990785\pi$
$881$		−	1.71827i		−	0.0578899i	0.999581	−	0.0289449i	$-0.00921474\pi$
$882$		0			0
$883$	31.5753			1.06259			0.531297	−	0.847185i	$-0.321705\pi$
$883$	31.5753			1.06259			0.531297	+	0.847185i	$0.321705\pi$
$884$	−28.0460	+	5.97056i	−0.943287	+	0.200812i
$885$		0			0
$886$	−23.3795	−	18.9262i	−0.785448	−	0.635839i
$887$	−25.0131	+	43.3240i	−0.839859	+	1.45468i	0.0501528	+	0.998742i	$0.484029\pi$
$887$	−25.0131	+	43.3240i	−0.839859	+	1.45468i	−0.890012	+	0.455937i	$0.849304\pi$
$888$		0			0
$889$	1.34822	−	0.237069i	0.0452177	−	0.00795103i
$890$	−3.33031	−	8.67168i	−0.111632	−	0.290675i
$891$		0			0
$892$	36.2943	+	11.7801i	1.21522	+	0.394428i
$893$	−3.66016	+	2.11319i	−0.122483	+	0.0707153i
$894$		0			0
$895$	0.450150			0.0150469
$896$	−18.0292	−	23.8945i	−0.602315	−	0.798259i
$897$		0			0
$898$	−3.40610	+	21.5272i	−0.113663	+	0.718371i
$899$	−62.3381	+	35.9909i	−2.07909	+	1.20036i
$900$		0			0
$901$	6.43964	−	11.1538i	0.214536	−	0.371587i
$902$	−1.43977	−	3.74896i	−0.0479390	−	0.124827i
$903$		0			0
$904$	−17.1044	+	33.6083i	−0.568882	+	1.11780i
$905$	−1.31141	+	2.27143i	−0.0435928	+	0.0755049i
$906$		0			0
$907$	3.95622	+	6.85238i	0.131364	+	0.227530i	0.924203	−	0.381902i	$-0.124731\pi$
$907$	3.95622	+	6.85238i	0.131364	+	0.227530i	−0.792838	+	0.609432i	$0.791398\pi$
$908$	−4.66775	+	0.993693i	−0.154905	+	0.0329769i
$909$		0			0
$910$	−2.85713	+	5.15056i	−0.0947131	+	0.170739i
$911$		−	28.5805i		−	0.946914i	−0.880817	−	0.473457i	$-0.843006\pi$
$911$		−	28.5805i		−	0.946914i	0.880817	−	0.473457i	$-0.156994\pi$
$912$		0			0
$913$	−5.94694	+	3.43347i	−0.196815	+	0.113631i
$914$	39.6642	+	32.1091i	1.31198	+	1.06208i
$915$		0			0
$916$	15.1900	−	13.6858i	0.501892	−	0.452191i
$917$	−12.2061	+	33.4865i	−0.403080	+	1.10582i
$918$		0			0
$919$	−41.7821	−	24.1229i	−1.37827	−	0.795742i	−0.386314	−	0.922367i	$-0.626252\pi$
$919$	−41.7821	−	24.1229i	−1.37827	−	0.795742i	−0.991951	+	0.126625i	$0.959585\pi$
$920$	−0.00357098	−	0.0675295i	−0.000117732	−	0.00222638i
$921$		0			0
$922$	6.85014	−	43.2941i	0.225597	−	1.42581i
$923$		−	38.9483i		−	1.28200i
$924$		0			0
$925$			41.6204i			1.36847i
$926$	−6.65731	−	1.05334i	−0.218773	−	0.0346150i
$927$		0			0
$928$	31.4351	+	31.3857i	1.03191	+	1.03029i
$929$	−44.9765	−	25.9672i	−1.47563	−	0.851956i	−0.476008	−	0.879441i	$-0.657917\pi$
$929$	−44.9765	−	25.9672i	−1.47563	−	0.851956i	−0.999622	+	0.0274853i	$0.991250\pi$
$930$		0			0
$931$	−31.6549	−	5.61252i	−1.03745	−	0.183943i
$932$	25.3720	−	22.8595i	0.831089	−	0.748788i
$933$		0			0
$934$	0.990718	−	1.22383i	0.0324173	−	0.0400449i
$935$	−1.15570	+	0.667242i	−0.0377953	+	0.0218212i
$936$		0			0
$937$		−	10.7775i		−	0.352087i	−0.984382	−	0.176044i	$-0.943670\pi$
$937$		−	10.7775i		−	0.352087i	0.984382	−	0.176044i	$-0.0563300\pi$
$938$	−19.0045	−	31.6515i	−0.620519	−	1.03346i
$939$		0			0
$940$	0.172865	+	0.812014i	0.00563825	+	0.0264850i
$941$	−8.56040	−	14.8270i	−0.279061	−	0.483348i	0.692091	−	0.721811i	$-0.256690\pi$
$941$	−8.56040	−	14.8270i	−0.279061	−	0.483348i	−0.971152	+	0.238463i	$0.923356\pi$
$942$		0			0
$943$	0.104509	−	0.181014i	0.00340327	−	0.00589463i
$944$	22.3447	+	2.33433i	0.727257	+	0.0759759i
$945$		0			0
$946$	−4.91885	+	1.88906i	−0.159926	+	0.0614186i
$947$	−2.91463	+	5.04828i	−0.0947126	+	0.164047i	−0.909489	−	0.415729i	$-0.863527\pi$
$947$	−2.91463	+	5.04828i	−0.0947126	+	0.164047i	0.814776	+	0.579776i	$0.196860\pi$
$948$		0			0
$949$	−11.6245	+	6.71139i	−0.377346	+	0.217861i
$950$	−30.7706	−	4.86864i	−0.998332	−	0.157959i
$951$		0			0
$952$	−29.9563	+	6.91588i	−0.970889	+	0.224145i
$953$	−45.9790			−1.48941			−0.744703	−	0.667396i	$-0.767409\pi$
$953$	−45.9790			−1.48941			−0.744703	+	0.667396i	$0.767409\pi$
$954$		0			0
$955$	−5.25239	+	3.03247i	−0.169963	+	0.0981284i
$956$	18.4697	−	56.9048i	0.597354	−	1.84043i
$957$		0			0
$958$	−35.2487	+	13.5371i	−1.13884	+	0.437363i
$959$	−45.5366	+	38.1730i	−1.47045	+	1.23267i
$960$		0			0
$961$	−26.5134	+	45.9226i	−0.855271	+	1.48137i
$962$	−26.9449	+	33.2849i	−0.868739	+	1.07315i
$963$		0			0
$964$	−32.9397	+	7.01236i	−1.06092	+	0.225853i
$965$	−3.34433			−0.107658
$966$		0			0
$967$		−	51.2560i		−	1.64828i	−0.566384	−	0.824141i	$-0.691658\pi$
$967$		−	51.2560i		−	1.64828i	0.566384	−	0.824141i	$-0.308342\pi$
$968$	−16.1581	−	24.8557i	−0.519341	−	0.798891i
$969$		0			0
$970$	−2.06539	+	2.55136i	−0.0663156	+	0.0819193i
$971$	11.0630	+	6.38720i	0.355027	+	0.204975i	0.666897	−	0.745150i	$-0.267622\pi$
$971$	11.0630	+	6.38720i	0.355027	+	0.204975i	−0.311870	+	0.950125i	$0.600955\pi$
$972$		0			0
$973$	2.73841	−	0.481518i	0.0877892	−	0.0154368i
$974$	11.3247	+	29.4879i	0.362866	+	0.944854i
$975$		0			0
$976$	−18.6174	+	8.30303i	−0.595929	+	0.265773i
$977$	15.9469	+	27.6208i	0.510186	+	0.883668i	0.999930	+	0.0118021i	$0.00375682\pi$
$977$	15.9469	+	27.6208i	0.510186	+	0.883668i	−0.489744	+	0.871866i	$0.662910\pi$
$978$		0			0
$979$			10.4858i			0.335127i
$980$	−2.96829	+	5.57403i	−0.0948186	+	0.178056i
$981$		0			0
$982$	−3.94274	+	24.9188i	−0.125818	+	0.795192i
$983$	25.6278	+	44.3886i	0.817399	+	1.41578i	0.907593	+	0.419852i	$0.137918\pi$
$983$	25.6278	+	44.3886i	0.817399	+	1.41578i	−0.0901941	+	0.995924i	$0.528749\pi$
$984$		0			0
$985$	−2.58922	−	1.49489i	−0.0824993	−	0.0476310i
$986$	42.5916	−	16.3571i	1.35639	−	0.520915i
$987$		0			0
$988$	−21.4561	−	23.8144i	−0.682610	−	0.757637i
$989$	−0.237501	−	0.137121i	−0.00755210	−	0.00436021i
$990$		0			0
$991$	−20.0234	+	11.5605i	−0.636064	+	0.367232i	−0.783097	−	0.621900i	$-0.786361\pi$
$991$	−20.0234	+	11.5605i	−0.636064	+	0.367232i	0.147033	+	0.989132i	$0.453028\pi$
$992$	50.0978	+	13.3815i	1.59061	+	0.424864i
$993$		0			0
$994$	−0.715597	−	41.7536i	−0.0226974	−	1.32434i
$995$	−4.86789			−0.154322
$996$		0			0
$997$	21.7369	+	37.6494i	0.688413	+	1.19237i	0.972351	+	0.233524i	$0.0750258\pi$
$997$	21.7369	+	37.6494i	0.688413	+	1.19237i	−0.283938	+	0.958843i	$0.591641\pi$
$998$	−6.81988	−	5.52086i	−0.215880	−	0.174760i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.7		32
3.2	odd	2		168.2.t.a.19.10	✓	32
4.3	odd	2		2016.2.bs.c.271.6		32
7.3	odd	6	inner	504.2.bk.c.451.4		32
8.3	odd	2	inner	504.2.bk.c.19.4		32
8.5	even	2		2016.2.bs.c.271.11		32
12.11	even	2		672.2.bb.a.271.6		32
21.2	odd	6		1176.2.p.a.979.4		32
21.5	even	6		1176.2.p.a.979.3		32
21.17	even	6		168.2.t.a.115.13	yes	32
24.5	odd	2		672.2.bb.a.271.3		32
24.11	even	2		168.2.t.a.19.13	yes	32
28.3	even	6		2016.2.bs.c.1711.11		32
56.3	even	6	inner	504.2.bk.c.451.7		32
56.45	odd	6		2016.2.bs.c.1711.6		32
84.23	even	6		4704.2.p.a.3919.11		32
84.47	odd	6		4704.2.p.a.3919.8		32
84.59	odd	6		672.2.bb.a.367.3		32
168.5	even	6		4704.2.p.a.3919.12		32
168.59	odd	6		168.2.t.a.115.10	yes	32
168.101	even	6		672.2.bb.a.367.6		32
168.107	even	6		1176.2.p.a.979.1		32
168.131	odd	6		1176.2.p.a.979.2		32
168.149	odd	6		4704.2.p.a.3919.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.10	✓	32	3.2	odd	2
168.2.t.a.19.13	yes	32	24.11	even	2
168.2.t.a.115.10	yes	32	168.59	odd	6
168.2.t.a.115.13	yes	32	21.17	even	6
504.2.bk.c.19.4		32	8.3	odd	2	inner
504.2.bk.c.19.7		32	1.1	even	1	trivial
504.2.bk.c.451.4		32	7.3	odd	6	inner
504.2.bk.c.451.7		32	56.3	even	6	inner
672.2.bb.a.271.3		32	24.5	odd	2
672.2.bb.a.271.6		32	12.11	even	2
672.2.bb.a.367.3		32	84.59	odd	6
672.2.bb.a.367.6		32	168.101	even	6
1176.2.p.a.979.1		32	168.107	even	6
1176.2.p.a.979.2		32	168.131	odd	6
1176.2.p.a.979.3		32	21.5	even	6
1176.2.p.a.979.4		32	21.2	odd	6
2016.2.bs.c.271.6		32	4.3	odd	2
2016.2.bs.c.271.11		32	8.5	even	2
2016.2.bs.c.1711.6		32	56.45	odd	6
2016.2.bs.c.1711.11		32	28.3	even	6
4704.2.p.a.3919.7		32	168.149	odd	6
4704.2.p.a.3919.8		32	84.47	odd	6
4704.2.p.a.3919.11		32	84.23	even	6
4704.2.p.a.3919.12		32	168.5	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.221012 + 1.39684i) q^{2} +(-1.90231 - 0.617436i) q^{4} +(-0.225540 + 0.390646i) q^{5} +(-0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +O(q^{10})\)	\(q+(-0.221012 + 1.39684i) q^{2} +(-1.90231 - 0.617436i) q^{4} +(-0.225540 + 0.390646i) q^{5} +(-0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +(-0.495822 - 0.401380i) q^{10} +(0.360048 + 0.623622i) q^{11} +3.48975 q^{13} +(3.74111 - 0.0641172i) q^{14} +(3.23754 + 2.34911i) q^{16} +(3.55796 - 2.05419i) q^{17} +(3.97736 + 2.29633i) q^{19} +(0.670245 - 0.603872i) q^{20} +(-0.950673 + 0.365101i) q^{22} +(-0.0459022 - 0.0265016i) q^{23} +(2.39826 + 4.15391i) q^{25} +(-0.771279 + 4.87462i) q^{26} +(-0.737270 + 5.23989i) q^{28} -7.85260i q^{29} +(-4.58331 - 7.93852i) q^{31} +(-3.99686 + 4.00314i) q^{32} +(2.08301 + 5.42389i) q^{34} +(1.12128 + 0.408713i) q^{35} +(7.51467 + 4.33860i) q^{37} +(-4.08664 + 5.04820i) q^{38} +(0.695379 + 1.06969i) q^{40} +3.94348i q^{41} +5.17408 q^{43} +(-0.299875 - 1.40863i) q^{44} +(0.0471634 - 0.0582606i) q^{46} +(-0.460124 + 0.796959i) q^{47} +(-6.58011 + 2.38791i) q^{49} +(-6.33239 + 2.43192i) q^{50} +(-6.63858 - 2.15470i) q^{52} +(2.71489 - 1.56744i) q^{53} -0.324821 q^{55} +(-7.15632 - 2.18793i) q^{56} +(10.9688 + 1.73552i) q^{58} +(4.86409 - 2.80828i) q^{59} +(-2.54813 + 4.41348i) q^{61} +(12.1018 - 4.64762i) q^{62} +(-4.70838 - 6.46770i) q^{64} +(-0.787078 + 1.36326i) q^{65} +(-4.93346 - 8.54500i) q^{67} +(-8.03666 + 1.71088i) q^{68} +(-0.818721 + 1.47591i) q^{70} -11.1608i q^{71} +(-3.33103 + 1.92317i) q^{73} +(-7.72115 + 9.53788i) q^{74} +(-6.14832 - 6.82409i) q^{76} +(1.46004 - 1.22395i) q^{77} +(-8.40929 - 4.85511i) q^{79} +(-1.64786 + 0.734917i) q^{80} +(-5.50839 - 0.871557i) q^{82} +9.53613i q^{83} +1.85320i q^{85} +(-1.14353 + 7.22734i) q^{86} +(2.03390 - 0.107553i) q^{88} +(12.6107 + 7.28081i) q^{89} +(-1.59899 - 9.09351i) q^{91} +(0.0709569 + 0.0787559i) q^{92} +(-1.01153 - 0.818857i) q^{94} +(-1.79410 + 1.03583i) q^{95} -5.14572i q^{97} +(-1.88124 - 9.71910i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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