LMFDB - Embedded newform 504.2.bk.c.451.4

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			451.4
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09919 - 0.889821i) q^{2} +(0.416438 + 1.95616i) q^{4} +(0.225540 + 0.390646i) q^{5} +(0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +O(q^{10})$	\(q+(-1.09919 - 0.889821i) q^{2} +(0.416438 + 1.95616i) q^{4} +(0.225540 + 0.390646i) q^{5} +(0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +(0.0996941 - 0.630084i) q^{10} +(0.360048 - 0.623622i) q^{11} -3.48975 q^{13} +(-2.82232 + 2.45653i) q^{14} +(-3.65316 + 1.62924i) q^{16} +(3.55796 + 2.05419i) q^{17} +(3.97736 - 2.29633i) q^{19} +(-0.670245 + 0.603872i) q^{20} +(-0.950673 + 0.365101i) q^{22} +(0.0459022 - 0.0265016i) q^{23} +(2.39826 - 4.15391i) q^{25} +(3.83590 + 3.10526i) q^{26} +(5.28813 - 0.188836i) q^{28} -7.85260i q^{29} +(4.58331 - 7.93852i) q^{31} +(5.46525 + 1.45981i) q^{32} +(-2.08301 - 5.42389i) q^{34} +(1.12128 - 0.408713i) q^{35} +(-7.51467 + 4.33860i) q^{37} +(-6.41519 - 1.01503i) q^{38} +(1.27406 - 0.0673729i) q^{40} -3.94348i q^{41} +5.17408 q^{43} +(1.36984 + 0.444614i) q^{44} +(-0.0740369 - 0.0117144i) q^{46} +(0.460124 + 0.796959i) q^{47} +(-6.58011 - 2.38791i) q^{49} +(-6.33239 + 2.43192i) q^{50} +(-1.45327 - 6.82653i) q^{52} +(-2.71489 - 1.56744i) q^{53} +0.324821 q^{55} +(-5.98069 - 4.49792i) q^{56} +(-6.98741 + 8.63151i) q^{58} +(4.86409 + 2.80828i) q^{59} +(2.54813 + 4.41348i) q^{61} +(-12.1018 + 4.64762i) q^{62} +(-4.70838 - 6.46770i) q^{64} +(-0.787078 - 1.36326i) q^{65} +(-4.93346 + 8.54500i) q^{67} +(-2.53666 + 7.81539i) q^{68} +(-1.59618 - 0.548482i) q^{70} -11.1608i q^{71} +(-3.33103 - 1.92317i) q^{73} +(12.1206 + 1.91777i) q^{74} +(6.14832 + 6.82409i) q^{76} +(-1.46004 - 1.22395i) q^{77} +(8.40929 - 4.85511i) q^{79} +(-1.46039 - 1.05963i) q^{80} +(-3.50899 + 4.33463i) q^{82} -9.53613i q^{83} +1.85320i q^{85} +(-5.68729 - 4.60400i) q^{86} +(-1.11009 - 1.70763i) q^{88} +(12.6107 - 7.28081i) q^{89} +(-1.59899 + 9.09351i) q^{91} +(0.0709569 + 0.0787559i) q^{92} +(0.203386 - 1.28544i) q^{94} +(1.79410 + 1.03583i) q^{95} +5.14572i q^{97} +(5.10798 + 8.47989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.09919	−	0.889821i	−0.777245	−	0.629198i
$2$	−1.09919	−	0.889821i	−0.777245	−	0.629198i
$3$		0			0
$3$		0			0
$4$	0.416438	+	1.95616i	0.208219	+	0.978082i
$5$	0.225540	+	0.390646i	0.100864	+	0.174702i	0.912041	−	0.410099i	$-0.134506\pi$
$5$	0.225540	+	0.390646i	0.100864	+	0.174702i	−0.811177	+	0.584801i	$0.801173\pi$
$6$		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
$10$	0.0996941	−	0.630084i	0.0315260	−	0.199250i
$11$	0.360048	−	0.623622i	0.108559	−	0.188029i	−0.806628	−	0.591060i	$-0.798710\pi$
$11$	0.360048	−	0.623622i	0.108559	−	0.188029i	0.915187	+	0.403030i	$0.132043\pi$
$12$		0			0
$13$	−3.48975			−0.967884			−0.483942	−	0.875100i	$-0.660795\pi$
$13$	−3.48975			−0.967884			−0.483942	+	0.875100i	$0.660795\pi$
$14$	−2.82232	+	2.45653i	−0.754296	+	0.656535i
$15$		0			0
$16$	−3.65316	+	1.62924i	−0.913290	+	0.407310i
$17$	3.55796	+	2.05419i	0.862931	+	0.498214i	0.864993	−	0.501784i	$-0.167323\pi$
$17$	3.55796	+	2.05419i	0.862931	+	0.498214i	−0.00206160	+	0.999998i	$0.500656\pi$
$18$		0			0
$19$	3.97736	−	2.29633i	0.912468	−	0.526814i	0.0312438	−	0.999512i	$-0.490053\pi$
$19$	3.97736	−	2.29633i	0.912468	−	0.526814i	0.881225	+	0.472698i	$0.156720\pi$
$20$	−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	$-0.664908\pi$
$23$	0.0459022	−	0.0265016i	0.00957126	−	0.00552597i	0.504778	+	0.863249i	$0.331574\pi$
$24$		0			0
$25$	2.39826	−	4.15391i	0.479653	−	0.830783i
$26$	3.83590	+	3.10526i	0.752283	+	0.608991i
$27$		0			0
$28$	5.28813	−	0.188836i	0.999363	−	0.0356866i
$29$		−	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	−0.0801113	−	0.996786i	$-0.525528\pi$
$31$	4.58331	−	7.93852i	0.823186	−	1.42580i	0.903298	−	0.429015i	$-0.141139\pi$
$32$	5.46525	+	1.45981i	0.966129	+	0.258060i
$33$		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	$-0.919449\pi$
$37$	−7.51467	+	4.33860i	−1.23540	+	0.713261i	−0.267253	+	0.963626i	$0.586116\pi$
$38$	−6.41519	−	1.01503i	−1.04068	−	0.164660i
$39$		0			0
$40$	1.27406	−	0.0673729i	0.201447	−	0.0106526i
$41$		−	3.94348i		−	0.615868i	−0.951408	−	0.307934i	$-0.900362\pi$
$41$		−	3.94348i		−	0.615868i	0.951408	−	0.307934i	$-0.0996375\pi$
$42$		0			0
$43$	5.17408			0.789039			0.394520	−	0.918888i	$-0.370911\pi$
$43$	5.17408			0.789039			0.394520	+	0.918888i	$0.370911\pi$
$44$	1.36984	+	0.444614i	0.206512	+	0.0670281i
$45$		0			0
$46$	−0.0740369	−	0.0117144i	−0.0109161	−	0.00172719i
$47$	0.460124	+	0.796959i	0.0671160	+	0.116248i	0.897631	−	0.440748i	$-0.145287\pi$
$47$	0.460124	+	0.796959i	0.0671160	+	0.116248i	−0.830515	+	0.556997i	$0.811954\pi$
$48$		0			0
$49$	−6.58011	−	2.38791i	−0.940016	−	0.341130i
$50$	−6.33239	+	2.43192i	−0.895535	+	0.343925i
$51$		0			0
$52$	−1.45327	−	6.82653i	−0.201532	−	0.946670i
$53$	−2.71489	−	1.56744i	−0.372919	−	0.215305i	0.301814	−	0.953367i	$-0.402408\pi$
$53$	−2.71489	−	1.56744i	−0.372919	−	0.215305i	−0.674733	+	0.738062i	$0.735741\pi$
$54$		0			0
$55$	0.324821			0.0437988
$56$	−5.98069	−	4.49792i	−0.799204	−	0.601060i
$57$		0			0
$58$	−6.98741	+	8.63151i	−0.917492	+	1.13337i
$59$	4.86409	+	2.80828i	0.633250	+	0.365607i	0.782010	−	0.623266i	$-0.214195\pi$
$59$	4.86409	+	2.80828i	0.633250	+	0.365607i	−0.148759	+	0.988873i	$0.547528\pi$
$60$		0			0
$61$	2.54813	+	4.41348i	0.326254	+	0.565089i	0.981765	−	0.190097i	$-0.0608802\pi$
$61$	2.54813	+	4.41348i	0.326254	+	0.565089i	−0.655511	+	0.755185i	$0.727547\pi$
$62$	−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	0.389690	+	0.920946i	$0.372582\pi$
$67$	−4.93346	+	8.54500i	−0.602718	+	1.04394i	−0.992408	+	0.122992i	$0.960751\pi$
$68$	−2.53666	+	7.81539i	−0.307615	+	0.947755i
$69$		0			0
$70$	−1.59618	−	0.548482i	−0.190780	−	0.0655562i
$71$		−	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	0.292235	−	0.956346i	$-0.405601\pi$
$73$	−3.33103	−	1.92317i	−0.389867	−	0.225090i	−0.682103	+	0.731256i	$0.738934\pi$
$74$	12.1206	+	1.91777i	1.40899	+	0.222936i
$75$		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	$-0.482724\pi$
$79$	8.40929	−	4.85511i	0.946119	−	0.546242i	0.891873	+	0.452285i	$0.149391\pi$
$80$	−1.46039	−	1.05963i	−0.163276	−	0.118471i
$81$		0			0
$82$	−3.50899	+	4.33463i	−0.387503	+	0.478680i
$83$		−	9.53613i		−	1.04673i	−0.852110	−	0.523363i	$-0.824677\pi$
$83$		−	9.53613i		−	1.04673i	0.852110	−	0.523363i	$-0.175323\pi$
$84$		0			0
$85$			1.85320i			0.201008i
$86$	−5.68729	−	4.60400i	−0.613277	−	0.496462i
$87$		0			0
$88$	−1.11009	−	1.70763i	−0.118336	−	0.182034i
$89$	12.6107	−	7.28081i	1.33673	−	0.771764i	0.350413	−	0.936595i	$-0.386041\pi$
$89$	12.6107	−	7.28081i	1.33673	−	0.771764i	0.986322	+	0.164831i	$0.0527078\pi$
$90$		0			0
$91$	−1.59899	+	9.09351i	−0.167620	+	0.953259i
$92$	0.0709569	+	0.0787559i	0.00739777	+	0.00821087i
$93$		0			0
$94$	0.203386	−	1.28544i	0.0209777	−	0.132583i
$95$	1.79410	+	1.03583i	0.184071	+	0.106273i
$96$		0			0
$97$			5.14572i			0.522469i	0.965275	+	0.261235i	$0.0841296\pi$
$97$			5.14572i			0.522469i	−0.965275	+	0.261235i	$0.915870\pi$
$98$	5.10798	+	8.47989i	0.515984	+	0.856598i
$99$		0			0
$100$	9.12447	+	2.96155i	0.912447	+	0.296155i
$101$	−7.14490	+	12.3753i	−0.710944	+	1.23139i	0.253559	+	0.967320i	$0.418399\pi$
$101$	−7.14490	+	12.3753i	−0.710944	+	1.23139i	−0.964503	+	0.264072i	$0.914934\pi$
$102$		0			0
$103$	7.46214	+	12.9248i	0.735267	+	1.27352i	0.954606	+	0.297871i	$0.0962764\pi$
$103$	7.46214	+	12.9248i	0.735267	+	1.27352i	−0.219339	+	0.975649i	$0.570390\pi$
$104$	−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	0.940520	+	0.339738i	$0.110338\pi$
$107$	7.90786	+	13.6968i	0.764482	+	1.32412i	−0.176039	+	0.984383i	$0.556328\pi$
$108$		0			0
$109$	−0.208805	−	0.120553i	−0.0199999	−	0.0115469i	0.489967	−	0.871741i	$-0.337009\pi$
$109$	−0.208805	−	0.120553i	−0.0199999	−	0.0115469i	−0.509967	+	0.860194i	$0.670342\pi$
$110$	−0.357040	−	0.289032i	−0.0340424	−	0.0275581i
$111$		0			0
$112$	2.57157	+	10.2658i	0.242991	+	0.970029i
$113$	−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
$116$	15.3610	−	3.27012i	1.42623	−	0.303623i
$117$		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
$122$	1.12633	−	7.11863i	0.101974	−	0.644491i
$123$		0			0
$124$	17.4377	+	5.65980i	1.56595	+	0.508265i
$125$	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	$0.992692\pi$
$128$	−0.579692	+	11.2988i	−0.0512380	+	0.998686i
$129$		0			0
$130$	−0.347908	+	2.19884i	−0.0305135	+	0.192851i
$131$	−11.6665	+	6.73566i	−1.01931	+	0.588497i	−0.913903	−	0.405932i	$-0.866947\pi$
$131$	−11.6665	+	6.73566i	−1.01931	+	0.588497i	−0.105404	+	0.994429i	$0.533614\pi$
$132$		0			0
$133$	−4.16130	−	11.4163i	−0.360831	−	0.989915i
$134$	13.0263	−	5.00269i	1.12530	−	0.432166i
$135$		0			0
$136$	9.74257	−	6.33343i	0.835418	−	0.543087i
$137$	−11.2294	+	19.4498i	−0.959389	+	1.66171i	−0.235399	+	0.971899i	$0.575640\pi$
$137$	−11.2294	+	19.4498i	−0.959389	+	1.66171i	−0.723989	+	0.689811i	$0.757694\pi$
$138$		0			0
$139$		−	1.05090i		−	0.0891361i	−0.999006	−	0.0445681i	$-0.985809\pi$
$139$		−	1.05090i		−	0.0891361i	0.999006	−	0.0445681i	$-0.0141912\pi$
$140$	1.26645	+	2.02320i	0.107035	+	0.170991i
$141$		0			0
$142$	−9.93108	+	12.2678i	−0.833398	+	1.02949i
$143$	−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	$-0.839661\pi$
$149$	−10.9331	+	6.31222i	−0.895673	+	0.517117i	−0.0198791	+	0.999802i	$0.506328\pi$
$150$		0			0
$151$	−2.86647	−	1.65496i	−0.233270	−	0.134679i	0.378810	−	0.925475i	$-0.376334\pi$
$151$	−2.86647	−	1.65496i	−0.233270	−	0.134679i	−0.612080	+	0.790796i	$0.709667\pi$
$152$	−0.685956	−	12.9719i	−0.0556384	−	1.05216i
$153$		0			0
$154$	0.515775	+	2.64453i	0.0415623	+	0.213102i
$155$	4.13487			0.332121
$156$		0			0
$157$	−1.75915	+	3.04694i	−0.140396	+	0.243172i	−0.927646	−	0.373462i	$-0.878171\pi$
$157$	−1.75915	+	3.04694i	−0.140396	+	0.243172i	0.787250	+	0.616634i	$0.211504\pi$
$158$	−13.5636	−	2.14608i	−1.07906	−	0.170733i
$159$		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	−0.955819	−	0.293957i	$-0.905028\pi$
$163$	−9.35173	−	16.1977i	−0.732484	−	1.26870i	0.223335	−	0.974742i	$-0.428306\pi$
$164$	7.71409	−	1.64221i	0.602369	−	0.128235i
$165$		0			0
$166$	−8.48545	+	10.4820i	−0.658599	+	0.813563i
$167$	23.5845			1.82502			0.912510	−	0.409054i	$-0.134141\pi$
$167$	23.5845			1.82502			0.912510	+	0.409054i	$0.134141\pi$
$168$		0			0
$169$	−0.821615			−0.0632012
$170$	1.64902	−	2.03702i	0.126474	−	0.156232i
$171$		0			0
$172$	2.15468	+	10.1213i	0.164293	+	0.771745i
$173$	12.4108	+	21.4961i	0.943572	+	1.63432i	0.758585	+	0.651575i	$0.225891\pi$
$173$	12.4108	+	21.4961i	0.943572	+	1.63432i	0.184988	+	0.982741i	$0.440775\pi$
$174$		0			0
$175$	−9.72529	−	8.15264i	−0.735163	−	0.616282i
$176$	−0.299283	+	2.86480i	−0.0225593	+	0.215942i
$177$		0			0
$178$	−20.3402	−	3.21830i	−1.52456	−	0.241222i
$179$	−0.498970	+	0.864242i	−0.0372948	+	0.0645965i	−0.884070	−	0.467354i	$-0.845207\pi$
$179$	−0.498970	+	0.864242i	−0.0372948	+	0.0645965i	0.846776	+	0.531950i	$0.178541\pi$
$180$		0			0
$181$	−5.81455			−0.432192			−0.216096	−	0.976372i	$-0.569332\pi$
$181$	−5.81455			−0.432192			−0.216096	+	0.976372i	$0.569332\pi$
$182$	9.84919	−	8.57268i	0.730071	−	0.635449i
$183$		0			0
$184$	−0.00791653	−	0.149707i	−0.000583614	−	0.0110365i
$185$	−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	$-0.828370\pi$
$191$	−11.6440	+	6.72270i	−0.842534	+	0.486437i	0.0155908	+	0.999878i	$0.495037\pi$
$192$		0			0
$193$	3.70703	−	6.42076i	0.266838	−	0.462176i	−0.701206	−	0.712959i	$-0.747355\pi$
$193$	3.70703	−	6.42076i	0.266838	−	0.462176i	0.968043	+	0.250783i	$0.0806879\pi$
$194$	4.57877	−	5.65613i	0.328737	−	0.406086i
$195$		0			0
$196$	1.93094	−	13.8662i	0.137924	−	0.990443i
$197$			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	$-0.958270\pi$
$199$	−5.39583	+	9.34584i	−0.382500	+	0.662509i	0.608919	+	0.793232i	$0.291603\pi$
$200$	−7.39428	−	11.3744i	−0.522854	−	0.804295i
$201$		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
$206$	3.29845	−	20.8468i	0.229814	−	1.45246i
$207$		0			0
$208$	12.7486	−	5.68565i	0.883958	−	0.394229i
$209$		−	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	$0.442962\pi$
$212$	1.93559	−	5.96352i	0.132937	−	0.409576i
$213$		0			0
$214$	3.49547	−	22.0920i	0.238945	−	1.51018i
$215$	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
$220$	0.135268	+	0.635402i	0.00911974	+	0.0428388i
$221$	−12.4164	−	7.16861i	−0.835217	−	0.482213i
$222$		0			0
$223$	19.0791			1.27763			0.638815	−	0.769361i	$-0.279425\pi$
$223$	19.0791			1.27763			0.638815	+	0.769361i	$0.279425\pi$
$224$	6.30809	−	13.5723i	0.421477	−	0.906839i
$225$		0			0
$226$	14.6551	+	11.8637i	0.974845	+	0.789160i
$227$	2.06649	+	1.19309i	0.137158	+	0.0791879i	0.567009	−	0.823712i	$-0.308101\pi$
$227$	2.06649	+	1.19309i	0.137158	+	0.0791879i	−0.429851	+	0.902900i	$0.641434\pi$
$228$		0			0
$229$	5.11149	+	8.85335i	0.337776	+	0.585046i	0.984014	−	0.178090i	$-0.0569919\pi$
$229$	5.11149	+	8.85335i	0.337776	+	0.585046i	−0.646238	+	0.763136i	$0.723659\pi$
$230$	−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	−0.997553	−	0.0699194i	$-0.977726\pi$
$233$	−8.53778	−	14.7879i	−0.559328	−	0.968785i	0.438224	−	0.898866i	$-0.355608\pi$
$234$		0			0
$235$	−0.207553	+	0.359492i	−0.0135392	+	0.0234506i
$236$	−3.46787	+	10.6844i	−0.225739	+	0.695497i
$237$		0			0
$238$	−15.0878	+	2.94265i	−0.978000	+	0.190744i
$239$			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	0.889762	−	0.456424i	$-0.150870\pi$
$241$	14.5829	+	8.41946i	0.939369	+	0.542345i	0.0496064	+	0.998769i	$0.484203\pi$
$242$	2.31653	−	14.6409i	0.148912	−	0.941152i
$243$		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
$248$	−14.1312	−	21.7376i	−0.897329	−	1.38034i
$249$		0			0
$250$	−4.85733	−	3.93213i	−0.307205	−	0.248690i
$251$		−	23.1292i		−	1.45990i	−0.683500	−	0.729951i	$-0.739543\pi$
$251$		−	23.1292i		−	1.45990i	0.683500	−	0.729951i	$-0.260457\pi$
$252$		0			0
$253$		−	0.0381674i		−	0.00239957i
$254$	0.460390	−	0.568716i	0.0288874	−	0.0356844i
$255$		0			0
$256$	10.6911	−	11.9038i	0.668196	−	0.743985i
$257$	10.4388	−	6.02683i	0.651153	−	0.375943i	−0.137745	−	0.990468i	$-0.543985\pi$
$257$	10.4388	−	6.02683i	0.651153	−	0.375943i	0.788898	+	0.614524i	$0.210652\pi$
$258$		0			0
$259$	7.86221	+	21.5695i	0.488534	+	1.34026i
$260$	2.33899	−	2.10737i	0.145058	−	0.130693i
$261$		0			0
$262$	18.8172	+	2.97733i	1.16253	+	0.183940i
$263$	−20.2875	−	11.7130i	−1.25098	−	0.722254i	−0.279677	−	0.960094i	$-0.590227\pi$
$263$	−20.2875	−	11.7130i	−1.25098	−	0.722254i	−0.971304	+	0.237840i	$0.923561\pi$
$264$		0			0
$265$		−	1.41408i		−	0.0868664i
$266$	−5.58437	+	16.2515i	−0.342399	+	0.996441i
$267$		0			0
$268$	−18.7699	−	6.09220i	−1.14655	−	0.372140i
$269$	5.98880	−	10.3729i	0.365144	−	0.632447i	−0.623655	−	0.781699i	$-0.714353\pi$
$269$	5.98880	−	10.3729i	0.365144	−	0.632447i	0.988799	+	0.149252i	$0.0476865\pi$
$270$		0			0
$271$	−3.99591	−	6.92112i	−0.242734	−	0.420428i	0.718758	−	0.695260i	$-0.244711\pi$
$271$	−3.99591	−	6.92112i	−0.242734	−	0.420428i	−0.961492	+	0.274832i	$0.911378\pi$
$272$	−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	$-0.249057\pi$
$277$	7.54343	+	4.35520i	0.453241	+	0.261679i	−0.255957	+	0.966688i	$0.582391\pi$
$278$	−0.935112	+	1.15514i	−0.0560843	+	0.0692806i
$279$		0			0
$280$	0.408213	−	3.35079i	0.0243954	−	0.200248i
$281$	−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	0.0606110	−	0.998161i	$-0.480695\pi$
$283$	−13.0126	−	7.51281i	−0.773517	−	0.446590i	−0.834128	+	0.551571i	$0.814028\pi$
$284$	21.8323	−	4.64777i	1.29551	−	0.275794i
$285$		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
$290$	−4.94780	−	0.782858i	−0.290545	−	0.0459710i
$291$		0			0
$292$	2.37487	−	7.31692i	0.138979	−	0.428190i
$293$	−2.77974			−0.162394			−0.0811971	−	0.996698i	$-0.525874\pi$
$293$	−2.77974			−0.162394			−0.0811971	+	0.996698i	$0.525874\pi$
$294$		0			0
$295$			2.53352i			0.147507i
$296$	1.29602	+	24.5086i	0.0753296	+	1.42453i
$297$		0			0
$298$	17.6343	+	2.79016i	1.02153	+	0.161629i
$299$	−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
$304$	−10.7886	+	14.8689i	−0.618771	+	0.852792i
$305$	−1.14941	+	1.99083i	−0.0658148	+	0.113995i
$306$		0			0
$307$		−	24.7943i		−	1.41508i	−0.706672	−	0.707542i	$-0.749804\pi$
$307$		−	24.7943i		−	1.41508i	0.706672	−	0.707542i	$-0.250196\pi$
$308$	1.78622	−	3.36578i	0.101779	−	0.191783i
$309$		0			0
$310$	−4.54501	−	3.67929i	−0.258139	−	0.208970i
$311$	−1.29417	+	2.24157i	−0.0733858	+	0.127108i	−0.900383	−	0.435098i	$-0.856714\pi$
$311$	−1.29417	+	2.24157i	−0.0733858	+	0.127108i	0.826997	+	0.562206i	$0.190047\pi$
$312$		0			0
$313$	−2.50486	+	1.44618i	−0.141583	+	0.0817431i	−0.569118	−	0.822256i	$-0.692715\pi$
$313$	−2.50486	+	1.44618i	−0.141583	+	0.0817431i	0.427535	+	0.903999i	$0.359382\pi$
$314$	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	0.680098	−	0.733121i	$-0.261937\pi$
$317$	29.4673	−	17.0130i	1.65505	−	0.955543i	0.974951	−	0.222421i	$-0.0713960\pi$
$318$		0			0
$319$	−4.89706	−	2.82732i	−0.274182	−	0.158299i
$320$	1.46466	−	3.29803i	0.0818768	−	0.184366i
$321$		0			0
$322$	−0.0644484	+	0.187556i	−0.00359157	+	0.0104521i
$323$	18.8684			1.04986
$324$		0			0
$325$	−8.36935	+	14.4961i	−0.464248	+	0.804101i
$326$	−4.13369	+	26.1257i	−0.228944	+	1.44697i
$327$		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	0.897670	−	0.440669i	$-0.145259\pi$
$331$	1.22267	+	2.11772i	0.0672040	+	0.116401i	−0.830466	+	0.557070i	$0.811926\pi$
$332$	18.6542	−	3.97121i	1.02378	−	0.217948i
$333$		0			0
$334$	−25.9238	−	20.9859i	−1.41849	−	1.14830i
$335$	−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	$0.777309\pi$
$338$	0.903112	+	0.731091i	0.0491228	+	0.0397661i
$339$		0			0
$340$	−3.62517	+	0.771743i	−0.196602	+	0.0418537i
$341$	−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
$346$	5.48586	−	34.6716i	0.294922	−	1.86396i
$347$	−8.51021	+	14.7401i	−0.456852	+	0.791291i	−0.998793	−	0.0491260i	$-0.984356\pi$
$347$	−8.51021	+	14.7401i	−0.456852	+	0.791291i	0.541941	+	0.840417i	$0.317690\pi$
$348$		0			0
$349$	28.1655			1.50766			0.753831	−	0.657068i	$-0.228204\pi$
$349$	28.1655			1.50766			0.753831	+	0.657068i	$0.228204\pi$
$350$	3.43555	+	17.6151i	0.183638	+	0.941565i
$351$		0			0
$352$	2.87812	−	2.88265i	0.153404	−	0.153646i
$353$	17.9835	+	10.3828i	0.957164	+	0.552619i	0.895299	−	0.445466i	$-0.146962\pi$
$353$	17.9835	+	10.3828i	0.957164	+	0.552619i	0.0618651	+	0.998085i	$0.480295\pi$
$354$		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	$-0.672095\pi$
$359$	−0.559584	+	0.323076i	−0.0295337	+	0.0170513i	0.485160	+	0.874425i	$0.338761\pi$
$360$		0			0
$361$	1.04625	−	1.81215i	0.0550656	−	0.0953764i
$362$	6.39129	+	5.17390i	0.335919	+	0.271934i
$363$		0			0
$364$	−18.4543	+	0.658990i	−0.967267	+	0.0345405i
$365$		−	1.73500i		−	0.0908143i
$366$		0			0
$367$	3.69198	−	6.39470i	0.192720	−	0.333801i	−0.753431	−	0.657527i	$-0.771602\pi$
$367$	3.69198	−	6.39470i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$368$	−0.124510	+	0.171600i	−0.00649055	+	0.00894529i
$369$		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	$-0.755602\pi$
$373$	−9.22518	+	5.32616i	−0.477662	+	0.275778i	0.241780	+	0.970331i	$0.422269\pi$
$374$	−4.13244	−	0.653849i	−0.213683	−	0.0338097i
$375$		0			0
$376$	2.59923	−	0.137448i	0.134045	−	0.00708832i
$377$			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	$0.484013\pi$
$380$	−1.27911	+	3.94092i	−0.0656171	+	0.202165i
$381$		0			0
$382$	18.7810	+	2.97160i	0.960921	+	0.152040i
$383$	2.21292	+	3.83290i	0.113075	+	0.195852i	0.917009	−	0.398867i	$-0.130597\pi$
$383$	2.21292	+	3.83290i	0.113075	+	0.195852i	−0.803934	+	0.594719i	$0.797263\pi$
$384$		0			0
$385$	0.148832	−	0.846409i	0.00758516	−	0.0431370i
$386$	−9.78805	+	3.75905i	−0.498199	+	0.191330i
$387$		0			0
$388$	−10.0659	+	2.14287i	−0.511018	+	0.108788i
$389$	−9.07706	−	5.24065i	−0.460225	−	0.265711i	0.251914	−	0.967750i	$-0.418940\pi$
$389$	−9.07706	−	5.24065i	−0.460225	−	0.265711i	−0.712139	+	0.702038i	$0.752273\pi$
$390$		0			0
$391$	0.217757			0.0110125
$392$	−14.4609	+	13.5234i	−0.730386	+	0.683035i
$393$		0			0
$394$	5.89777	−	7.28548i	0.297125	−	0.367037i
$395$	3.79326	+	2.19004i	0.190859	+	0.110193i
$396$		0			0
$397$	−6.09656	−	10.5596i	−0.305978	−	0.529969i	0.671501	−	0.741004i	$-0.265650\pi$
$397$	−6.09656	−	10.5596i	−0.305978	−	0.529969i	−0.977478	+	0.211035i	$0.932317\pi$
$398$	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	0.921751	−	0.387782i	$-0.126759\pi$
$401$	2.50405	+	4.33714i	0.125046	+	0.216586i	−0.796705	+	0.604369i	$0.793425\pi$
$402$		0			0
$403$	−15.9946	+	27.7035i	−0.796749	+	1.38001i
$404$	−27.1836	−	8.82305i	−1.35243	−	0.438963i
$405$		0			0
$406$	19.2901	+	22.1625i	0.957354	+	1.09991i
$407$			6.24842i			0.309722i
$408$		0			0
$409$	26.3361	+	15.2051i	1.30223	+	0.751845i	0.980787	−	0.195082i	$-0.0624974\pi$
$409$	26.3361	+	15.2051i	1.30223	+	0.751845i	0.321447	+	0.946928i	$0.395831\pi$
$410$	−2.48472	−	0.393141i	−0.122712	−	0.0194159i
$411$		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
$416$	−19.0724	−	5.09438i	−0.935100	−	0.249772i
$417$		0			0
$418$	−2.94278	+	3.63519i	−0.143936	+	0.177803i
$419$		−	1.70610i		−	0.0833485i	−0.999131	−	0.0416743i	$-0.986731\pi$
$419$		−	1.70610i		−	0.0833485i	0.999131	−	0.0416743i	$-0.0132692\pi$
$420$		0			0
$421$		−	13.0483i		−	0.635937i	−0.948101	−	0.317969i	$-0.896999\pi$
$421$		−	13.0483i		−	0.635937i	0.948101	−	0.317969i	$-0.103001\pi$
$422$	−5.69155	−	4.60745i	−0.277060	−	0.224287i
$423$		0			0
$424$	−7.43405	+	4.83271i	−0.361029	+	0.234697i
$425$	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
$430$	0.515825	−	3.26010i	0.0248753	−	0.157216i
$431$	−1.95335	−	1.12777i	−0.0940894	−	0.0543226i	0.452217	−	0.891908i	$-0.350633\pi$
$431$	−1.95335	−	1.12777i	−0.0940894	−	0.0543226i	−0.546306	+	0.837585i	$0.683967\pi$
$432$		0			0
$433$			7.41221i			0.356208i	0.984012	+	0.178104i	$0.0569963\pi$
$433$			7.41221i			0.356208i	−0.984012	+	0.178104i	$0.943004\pi$
$434$	6.56566	+	33.6640i	0.315162	+	1.61593i
$435$		0			0
$436$	0.148868	−	0.458659i	0.00712949	−	0.0219658i
$437$	0.121713	−	0.210813i	0.00582231	−	0.0100845i
$438$		0			0
$439$	−5.12867	−	8.88312i	−0.244778	−	0.423968i	0.717291	−	0.696774i	$-0.245382\pi$
$439$	−5.12867	−	8.88312i	−0.244778	−	0.423968i	−0.962069	+	0.272806i	$0.912048\pi$
$440$	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	−0.999981	−	0.00610446i	$-0.998057\pi$
$443$	−10.6349	−	18.4201i	−0.505277	−	0.875166i	0.494704	−	0.869061i	$-0.335276\pi$
$444$		0			0
$445$	5.68844	+	3.28422i	0.269658	+	0.155687i
$446$	−20.9715	−	16.9770i	−0.993031	−	0.803882i
$447$		0			0
$448$	−19.0107	+	9.30549i	−0.898172	+	0.439643i
$449$	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
$452$	−5.55222	−	26.0809i	−0.261155	−	1.22674i
$453$		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	0.886494	+	0.462739i	$0.153133\pi$
$457$	18.0425	+	31.2505i	0.843991	+	1.46184i	−0.0425032	+	0.999096i	$0.513533\pi$
$458$	2.25940	−	14.2798i	0.105575	−	0.667252i
$459$		0			0
$460$	−0.0147621	+	0.0454816i	−0.000688285	+	0.00212059i
$461$	30.9944			1.44355			0.721776	−	0.692127i	$-0.243326\pi$
$461$	30.9944			1.44355			0.721776	+	0.692127i	$0.243326\pi$
$462$		0			0
$463$			4.76599i			0.221494i	0.993849	+	0.110747i	$0.0353244\pi$
$463$			4.76599i			0.221494i	−0.993849	+	0.110747i	$0.964676\pi$
$464$	12.7938	+	28.6868i	0.593937	+	1.33175i
$465$		0			0
$466$	−3.77391	+	23.8518i	−0.174823	+	1.10491i
$467$	−0.964225	+	0.556695i	−0.0446190	+	0.0257608i	−0.522144	−	0.852858i	$-0.674867\pi$
$467$	−0.964225	+	0.556695i	−0.0446190	+	0.0257608i	0.477525	+	0.878618i	$0.341534\pi$
$468$		0			0
$469$	20.0059	+	16.7708i	0.923784	+	0.774402i
$470$	0.548023	−	0.210465i	0.0252784	−	0.00970803i
$471$		0			0
$472$	13.3191	−	8.65844i	0.613060	−	0.398537i
$473$	1.86292	−	3.22667i	0.0856570	−	0.148362i
$474$		0			0
$475$		−	22.0288i		−	1.01075i
$476$	19.2028	+	10.1909i	0.880161	+	0.467101i
$477$		0			0
$478$	26.6177	−	32.8807i	1.21747	−	1.50393i
$479$	−13.3498	+	23.1224i	−0.609966	+	1.05649i	0.381280	+	0.924460i	$0.375483\pi$
$479$	−13.3498	+	23.1224i	−0.609966	+	1.05649i	−0.991245	+	0.132032i	$0.957850\pi$
$480$		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	$-0.502235\pi$
$487$	−19.3435	−	11.1680i	−0.876536	−	0.506068i	−0.869515	+	0.493907i	$0.835568\pi$
$488$	14.3943	−	0.761172i	0.651598	−	0.0344567i
$489$		0			0
$490$	−2.16058	+	3.90796i	−0.0976052	+	0.176544i
$491$	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
$494$	22.3874	+	3.54222i	1.00726	+	0.159372i
$495$		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	0.788196	−	0.615424i	$-0.211015\pi$
$499$	−3.10223	−	5.37322i	−0.138875	−	0.240538i	−0.927071	+	0.374886i	$0.877682\pi$
$500$	1.84024	+	8.64431i	0.0822982	+	0.386585i
$501$		0			0
$502$	−20.5808	+	25.4234i	−0.918568	+	1.13470i
$503$	−5.86342			−0.261437			−0.130718	−	0.991420i	$-0.541728\pi$
$503$	−5.86342			−0.261437			−0.130718	+	0.991420i	$0.541728\pi$
$504$		0			0
$505$	−6.44583			−0.286836
$506$	−0.0339622	+	0.0419533i	−0.00150980	+	0.00186505i
$507$		0			0
$508$	−1.01211	+	0.215463i	−0.0449052	+	0.00955963i
$509$	−17.5030	−	30.3161i	−0.775808	−	1.34374i	−0.934339	−	0.356386i	$-0.884009\pi$
$509$	−17.5030	−	30.3161i	−0.775808	−	1.34374i	0.158530	−	0.987354i	$-0.449324\pi$
$510$		0			0
$511$	−6.53761	+	7.79872i	−0.289207	+	0.344995i
$512$	−22.3438	+	3.57129i	−0.987466	+	0.157830i
$513$		0			0
$514$	−16.8370	−	2.66401i	−0.742648	−	0.117504i
$515$	−3.36602	+	5.83011i	−0.148324	+	0.256905i
$516$		0			0
$517$	0.662668			0.0291441
$518$	10.5509	−	30.7049i	0.463579	−	1.34910i
$519$		0			0
$520$	−4.44617	+	0.235115i	−0.194978	+	0.0103105i
$521$	6.98875	+	4.03495i	0.306182	+	0.176775i	0.645217	−	0.763999i	$-0.276767\pi$
$521$	6.98875	+	4.03495i	0.306182	+	0.176775i	−0.339034	+	0.940774i	$0.610100\pi$
$522$		0			0
$523$	−26.9826	+	15.5784i	−1.17987	+	0.681196i	−0.955984	−	0.293420i	$-0.905206\pi$
$523$	−26.9826	+	15.5784i	−1.17987	+	0.681196i	−0.223882	+	0.974616i	$0.571873\pi$
$524$	−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
$530$	−1.25828	+	1.55435i	−0.0546562	+	0.0675164i
$531$		0			0
$532$	20.5992	−	12.8944i	0.893087	−	0.559041i
$533$			13.7618i			0.596088i
$534$		0			0
$535$	−3.56707	+	6.17835i	−0.154218	+	0.267113i
$536$	15.2107	+	23.3983i	0.657004	+	1.01065i
$537$		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	$-0.489813\pi$
$541$	21.2493	−	12.2683i	0.913581	−	0.527456i	0.881581	+	0.472032i	$0.156479\pi$
$542$	−1.76629	+	11.1633i	−0.0758687	+	0.479504i
$543$		0			0
$544$	16.4464	+	16.4206i	0.705133	+	0.704027i
$545$		−	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	$0.270977\pi$
$548$	−42.7234	−	13.8668i	−1.82505	−	0.592362i
$549$		0			0
$550$	−0.763368	+	4.82462i	−0.0325501	+	0.205723i
$551$	−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
$556$	2.05573	−	0.437634i	0.0871824	−	0.0185598i
$557$	33.2404	+	19.1914i	1.40844	+	0.813164i	0.995238	−	0.0974752i	$-0.0310767\pi$
$557$	33.2404	+	19.1914i	1.40844	+	0.813164i	0.413203	+	0.910639i	$0.364410\pi$
$558$		0			0
$559$	−18.0563			−0.763698
$560$	−3.43031	+	3.31992i	−0.144957	+	0.140292i
$561$		0			0
$562$	7.49869	+	6.07037i	0.316313	+	0.256063i
$563$	0.879959	+	0.508045i	0.0370859	+	0.0214115i	0.518428	−	0.855121i	$-0.326517\pi$
$563$	0.879959	+	0.508045i	0.0370859	+	0.0214115i	−0.481342	+	0.876533i	$0.659851\pi$
$564$		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	0.829001	−	0.559247i	$-0.188910\pi$
$569$	−1.66552	−	2.88476i	−0.0698220	−	0.120935i	−0.898823	+	0.438312i	$0.855576\pi$
$570$		0			0
$571$	3.34133	−	5.78735i	0.139830	−	0.242193i	−0.787602	−	0.616184i	$-0.788678\pi$
$571$	3.34133	−	5.78735i	0.139830	−	0.242193i	0.927432	+	0.373991i	$0.122011\pi$
$572$	−4.78042	−	1.55159i	−0.199879	−	0.0648754i
$573$		0			0
$574$	9.68726	+	11.1297i	0.404339	+	0.464546i
$575$		−	0.254232i		−	0.0106022i
$576$		0			0
$577$	−0.561113	−	0.323959i	−0.0233595	−	0.0134866i	0.488275	−	0.872690i	$-0.337626\pi$
$577$	−0.561113	−	0.323959i	−0.0233595	−	0.0134866i	−0.511634	+	0.859203i	$0.670960\pi$
$578$	−0.0268004	+	0.169384i	−0.00111475	+	0.00704543i
$579$		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
$584$	−9.12118	+	5.92948i	−0.377437	+	0.245364i
$585$		0			0
$586$	3.05546	+	2.47347i	0.126220	+	0.102178i
$587$		−	4.35212i		−	0.179631i	−0.995958	−	0.0898157i	$-0.971372\pi$
$587$		−	4.35212i		−	0.179631i	0.995958	−	0.0898157i	$-0.0286278\pi$
$588$		0			0
$589$		−	42.0991i		−	1.73466i
$590$	2.25437	−	2.78482i	0.0928111	−	0.114649i
$591$		0			0
$592$	20.3837	−	28.0928i	0.837763	−	1.15461i
$593$	−21.7338	+	12.5480i	−0.892502	+	0.515286i	−0.874760	−	0.484556i	$-0.838981\pi$
$593$	−21.7338	+	12.5480i	−0.892502	+	0.515286i	−0.0177420	+	0.999843i	$0.505648\pi$
$594$		0			0
$595$	4.82902	+	0.849130i	0.197971	+	0.0348109i
$596$	−16.9007	−	18.7583i	−0.692279	−	0.768368i
$597$		0			0
$598$	0.258371	+	0.0408803i	0.0105656	+	0.00167172i
$599$	20.4978	+	11.8344i	0.837519	+	0.483542i	0.856420	−	0.516279i	$-0.172683\pi$
$599$	20.4978	+	11.8344i	0.837519	+	0.483542i	−0.0189009	+	0.999821i	$0.506017\pi$
$600$		0			0
$601$			14.8295i			0.604907i	0.953164	+	0.302453i	$0.0978057\pi$
$601$			14.8295i			0.604907i	−0.953164	+	0.302453i	$0.902194\pi$
$602$	−14.6029	+	12.7103i	−0.595169	+	0.518032i
$603$		0			0
$604$	2.04366	−	6.29647i	0.0831554	−	0.256200i
$605$	−2.36398	+	4.09454i	−0.0961096	+	0.166467i
$606$		0			0
$607$	−0.527187	−	0.913114i	−0.0213979	−	0.0370622i	0.855128	−	0.518417i	$-0.173478\pi$
$607$	−0.527187	−	0.913114i	−0.0213979	−	0.0370622i	−0.876526	+	0.481354i	$0.840145\pi$
$608$	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	$-0.608405\pi$
$613$	−32.6152	−	18.8304i	−1.31731	−	0.760552i	−0.983296	+	0.182015i	$0.941738\pi$
$614$	−22.0624	+	27.2536i	−0.890368	+	1.09987i
$615$		0			0
$616$	−4.95834	+	2.11022i	−0.199777	+	0.0850232i
$617$	−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	0.589597	−	0.807697i	$-0.299287\pi$
$619$	4.60049	+	2.65609i	0.184909	+	0.106757i	−0.404688	+	0.914455i	$0.632620\pi$
$620$	1.72192	+	8.08848i	0.0691538	+	0.324841i
$621$		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
$626$	4.04017	+	0.639249i	0.161477	+	0.0255495i
$627$		0			0
$628$	−6.69289	−	2.17233i	−0.267075	−	0.0866853i
$629$	−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	$0.731868\pi$
$632$	−1.45031	−	27.4263i	−0.0576903	−	1.09096i
$633$		0			0
$634$	−47.5286	−	7.52015i	−1.88760	−	0.298663i
$635$	−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
$640$	−4.54459	+	2.32188i	−0.179641	+	0.0917805i
$641$	11.0865	−	19.2023i	0.437889	−	0.758445i	−0.559638	−	0.828737i	$-0.689060\pi$
$641$	11.0865	−	19.2023i	0.437889	−	0.758445i	0.997526	+	0.0702920i	$0.0223931\pi$
$642$		0			0
$643$		−	29.4039i		−	1.15958i	−0.814767	−	0.579788i	$-0.803135\pi$
$643$		−	29.4039i		−	1.15958i	0.814767	−	0.579788i	$-0.196865\pi$
$644$	0.237732	−	0.148812i	0.00936796	−	0.00586402i
$645$		0			0
$646$	−20.7399	−	16.7895i	−0.816001	−	0.660572i
$647$	10.3938	−	18.0026i	0.408623	−	0.707755i	−0.586113	−	0.810229i	$-0.699343\pi$
$647$	10.3938	−	18.0026i	0.408623	−	0.707755i	0.994736	+	0.102474i	$0.0326758\pi$
$648$		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	$-0.642475\pi$
$653$	3.36065	−	1.94027i	0.131512	−	0.0759287i	0.564313	+	0.825561i	$0.309141\pi$
$654$		0			0
$655$	−5.26252	−	3.03832i	−0.205624	−	0.118717i
$656$	6.42488	+	14.4061i	0.250849	+	0.562466i
$657$		0			0
$658$	−3.25637	−	1.11896i	−0.126946	−	0.0436217i
$659$	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	$-0.867690\pi$
$661$	−2.76963	+	4.79715i	−0.107726	+	0.186587i	0.807122	+	0.590384i	$0.201024\pi$
$662$	0.540450	−	3.41574i	0.0210052	−	0.132756i
$663$		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
$668$	9.82146	+	46.1351i	0.380004	+	1.78502i
$669$		0			0
$670$	4.89223	+	3.96038i	0.189003	+	0.153003i
$671$	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	$0.538547\pi$
$674$	30.8769	+	24.9956i	1.18934	+	0.962795i
$675$		0			0
$676$	−0.342152	−	1.60721i	−0.0131597	−	0.0618160i
$677$	22.2551	+	38.5470i	0.855333	+	1.48148i	0.876335	+	0.481701i	$0.159981\pi$
$677$	22.2551	+	38.5470i	0.855333	+	1.48148i	−0.0210020	+	0.999779i	$0.506686\pi$
$678$		0			0
$679$	13.4086	+	2.35775i	0.514575	+	0.0904822i
$680$	4.67146	+	2.37746i	0.179142	+	0.0911713i
$681$		0			0
$682$	−1.45887	+	9.22031i	−0.0558630	+	0.353064i
$683$	8.00201	−	13.8599i	0.306189	−	0.530334i	−0.671337	−	0.741153i	$-0.734280\pi$
$683$	8.00201	−	13.8599i	0.306189	−	0.530334i	0.977525	+	0.210818i	$0.0676129\pi$
$684$		0			0
$685$	−10.1307			−0.387073
$686$	24.4371	−	9.42479i	0.933014	−	0.359840i
$687$		0			0
$688$	−18.9017	+	8.42982i	−0.720621	+	0.321384i
$689$	9.47431	+	5.46999i	0.360942	+	0.208390i
$690$		0			0
$691$	−32.1161	+	18.5422i	−1.22175	+	0.705380i	−0.965292	−	0.261175i	$-0.915890\pi$
$691$	−32.1161	+	18.5422i	−1.22175	+	0.705380i	−0.256462	+	0.966554i	$0.582557\pi$
$692$	−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
$698$	−30.9592	−	25.0622i	−1.17182	−	0.948618i
$699$		0			0
$700$	11.8979	−	22.4193i	0.449699	−	0.847371i
$701$		−	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
$704$	−5.72864	+	0.607563i	−0.215906	+	0.0228984i
$705$		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	$-0.550423\pi$
$709$	16.4705	−	9.50925i	0.618563	−	0.357127i	0.776309	+	0.630352i	$0.217090\pi$
$710$	−7.03222	−	1.11266i	−0.263915	−	0.0417575i
$711$		0			0
$712$	−2.17491	−	41.1290i	−0.0815083	−	1.54138i
$713$		−	0.485860i		−	0.0181956i
$714$		0			0
$715$	−1.13354			−0.0423921
$716$	−1.89839	−	0.616165i	−0.0709462	−	0.0230272i
$717$		0			0
$718$	0.902569	+	0.142808i	0.0336836	+	0.00532953i
$719$	1.02572	+	1.77660i	0.0382529	+	0.0662559i	0.884518	−	0.466506i	$-0.154487\pi$
$719$	1.02572	+	1.77660i	0.0382529	+	0.0662559i	−0.846265	+	0.532762i	$0.821154\pi$
$720$		0			0
$721$	37.0983	−	13.5226i	1.38161	−	0.503606i
$722$	−2.76251	+	1.06093i	−0.102810	+	0.0394837i
$723$		0			0
$724$	−2.42140	−	11.3742i	−0.0899905	−	0.422719i
$725$	−32.6191	−	18.8326i	−1.21144	−	0.699426i
$726$		0			0
$727$	29.6614			1.10008			0.550039	−	0.835139i	$-0.314613\pi$
$727$	29.6614			1.10008			0.550039	+	0.835139i	$0.314613\pi$
$728$	20.8711	+	15.6966i	0.773536	+	0.581756i
$729$		0			0
$730$	−1.54384	+	1.90710i	−0.0571402	+	0.0705849i
$731$	18.4091	+	10.6285i	0.680886	+	0.393110i
$732$		0			0
$733$	13.8269	+	23.9490i	0.510710	+	0.884575i	0.999923	+	0.0124107i	$0.00395056\pi$
$733$	13.8269	+	23.9490i	0.510710	+	0.884575i	−0.489213	+	0.872164i	$0.662716\pi$
$734$	−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	−0.838467	−	0.544952i	$-0.816548\pi$
$739$	1.43287	−	2.48180i	0.0527090	−	0.0912946i	0.891176	+	0.453658i	$0.149881\pi$
$740$	2.41671	−	7.44582i	0.0888400	−	0.273714i
$741$		0			0
$742$	11.5128	−	2.24539i	0.422646	−	0.0824307i
$743$		−	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
$746$	14.8796	+	2.35430i	0.544779	+	0.0861969i
$747$		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	$-0.669643\pi$
$751$	−0.443784	+	0.256219i	−0.0161939	+	0.00934956i	0.491881	+	0.870662i	$0.336309\pi$
$752$	−2.97935	−	2.16176i	−0.108646	−	0.0788314i
$753$		0			0
$754$	24.3843	−	30.1218i	0.888026	−	1.09697i
$755$		−	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	$0.893502\pi$
$758$	−2.14857	−	1.73932i	−0.0780395	−	0.0631748i
$759$		0			0
$760$	4.91270	−	3.19364i	0.178202	−	0.115845i
$761$	34.4739	−	19.9035i	1.24968	−	0.721501i	0.278632	−	0.960398i	$-0.410119\pi$
$761$	34.4739	−	19.9035i	1.24968	−	0.721501i	0.971045	+	0.238897i	$0.0767858\pi$
$762$		0			0
$763$	−0.409808	+	0.488860i	−0.0148361	+	0.0176979i
$764$	−17.9997	−	19.9781i	−0.651207	−	0.722782i
$765$		0			0
$766$	0.978167	−	6.18219i	0.0353426	−	0.223372i
$767$	−16.9745	−	9.80022i	−0.612913	−	0.353865i
$768$		0			0
$769$			45.5560i			1.64279i	0.570358	+	0.821396i	$0.306805\pi$
$769$			45.5560i			1.64279i	−0.570358	+	0.821396i	$0.693195\pi$
$770$	−0.916746	+	0.797931i	−0.0330372	+	0.0287554i
$771$		0			0
$772$	14.1038	+	4.57771i	0.507607	+	0.164755i
$773$	−20.8182	+	36.0581i	−0.748777	+	1.29692i	0.199632	+	0.979871i	$0.436025\pi$
$773$	−20.8182	+	36.0581i	−0.748777	+	1.29692i	−0.948409	+	0.317049i	$0.897308\pi$
$774$		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
$782$	−0.239357	−	0.193765i	−0.00855937	−	0.00692902i
$783$		0			0
$784$	27.9287	−	1.99718i	0.997453	−	0.0713277i
$785$	−1.58703			−0.0566436
$786$		0			0
$787$	14.5316	+	8.38984i	0.517997	+	0.299065i	0.736115	−	0.676857i	$-0.236658\pi$
$787$	14.5316	+	8.38984i	0.517997	+	0.299065i	−0.218118	+	0.975922i	$0.569992\pi$
$788$	−12.9655	+	2.76017i	−0.461878	+	0.0983269i
$789$		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
$794$	−2.69483	+	17.0318i	−0.0956359	+	0.604436i
$795$		0			0
$796$	−20.5290	−	6.66316i	−0.727632	−	0.236169i
$797$	−22.4555			−0.795415			−0.397707	−	0.917512i	$-0.630194\pi$
$797$	−22.4555			−0.795415			−0.397707	+	0.917512i	$0.630194\pi$
$798$		0			0
$799$			3.78073i			0.133752i
$800$	19.1710	−	19.2012i	0.677799	−	0.678864i
$801$		0			0
$802$	1.10685	−	6.99549i	0.0390843	−	0.247019i
$803$	−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
$808$	22.0290	+	33.8867i	0.774978	+	1.19213i
$809$	−7.04864	+	12.2086i	−0.247817	+	0.429232i	−0.962920	−	0.269788i	$-0.913047\pi$
$809$	−7.04864	+	12.2086i	−0.247817	+	0.429232i	0.715103	+	0.699019i	$0.246380\pi$
$810$		0			0
$811$		−	14.2766i		−	0.501320i	−0.968075	−	0.250660i	$-0.919352\pi$
$811$		−	14.2766i		−	0.501320i	0.968075	−	0.250660i	$-0.0806477\pi$
$812$	−1.48285	−	41.5256i	−0.0520379	−	1.45726i
$813$		0			0
$814$	5.55997	−	6.86820i	0.194877	−	0.240730i
$815$	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	$-0.739243\pi$
$821$	−11.2178	+	6.47658i	−0.391503	+	0.226034i	0.291308	+	0.956629i	$0.405909\pi$
$822$		0			0
$823$	8.69701	+	5.02122i	0.303159	+	0.175029i	0.643861	−	0.765143i	$-0.277332\pi$
$823$	8.69701	+	5.02122i	0.303159	+	0.175029i	−0.340702	+	0.940171i	$0.610665\pi$
$824$	42.1534	−	2.22908i	1.46848	−	0.0776537i
$825$		0			0
$826$	−20.6266	+	4.02291i	−0.717692	+	0.139975i
$827$	−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	0.219202	+	0.975679i	$0.429655\pi$
$829$	−21.1728	+	36.6724i	−0.735362	+	1.27368i	−0.954564	+	0.298005i	$0.903679\pi$
$830$	−6.00857	−	0.950696i	−0.208560	−	0.0329991i
$831$		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
$836$	6.46934	−	1.37722i	0.223747	−	0.0476323i
$837$		0			0
$838$	−1.51812	+	1.87533i	−0.0524427	+	0.0647822i
$839$	−7.15440			−0.246997			−0.123499	−	0.992345i	$-0.539411\pi$
$839$	−7.15440			−0.246997			−0.123499	+	0.992345i	$0.539411\pi$
$840$		0			0
$841$	−32.6634			−1.12632
$842$	−11.6107	+	14.3426i	−0.400131	+	0.494279i
$843$		0			0
$844$	2.15629	+	10.1289i	0.0742227	+	0.348652i
$845$	−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
$850$	−27.5260	−	4.35525i	−0.944133	−	0.149384i
$851$	−0.229960	+	0.398302i	−0.00788292	+	0.0136536i
$852$		0			0
$853$	−43.0151			−1.47281			−0.736405	−	0.676541i	$-0.763478\pi$
$853$	−43.0151			−1.47281			−0.736405	+	0.676541i	$0.763478\pi$
$854$	−18.0335	−	6.19670i	−0.617092	−	0.212047i
$855$		0			0
$856$	44.6712	−	2.36222i	1.52683	−	0.0807392i
$857$	2.28337	+	1.31831i	0.0779985	+	0.0450325i	0.538492	−	0.842631i	$-0.318994\pi$
$857$	2.28337	+	1.31831i	0.0779985	+	0.0450325i	−0.460493	+	0.887663i	$0.652328\pi$
$858$		0			0
$859$	−13.8594	+	8.00171i	−0.472875	+	0.273015i	−0.717443	−	0.696618i	$-0.754687\pi$
$859$	−13.8594	+	8.00171i	−0.472875	+	0.273015i	0.244567	+	0.969632i	$0.421354\pi$
$860$	−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	$-0.659532\pi$
$863$	1.14047	−	0.658448i	0.0388219	−	0.0224138i	0.519285	+	0.854601i	$0.326198\pi$
$864$		0			0
$865$	−5.59823	+	9.69643i	−0.190346	+	0.329688i
$866$	6.59554	−	8.14743i	0.224125	−	0.276861i
$867$		0			0
$868$	22.7381	−	42.8454i	0.771780	−	1.45427i
$869$		−	6.99229i		−	0.237197i
$870$		0			0
$871$	17.2166	−	29.8200i	0.583361	−	1.01041i
$872$	−0.571759	+	0.371688i	−0.0193622	+	0.0125869i
$873$		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	$-0.800052\pi$
$877$	−20.8705	+	12.0496i	−0.704748	+	0.406886i	0.104366	+	0.994539i	$0.466719\pi$
$878$	−2.26700	+	14.3278i	−0.0765075	+	0.483541i
$879$		0			0
$880$	−1.18662	+	0.529211i	−0.0400010	+	0.0178397i
$881$			1.71827i			0.0578899i	0.999581	+	0.0289449i	$0.00921474\pi$
$881$			1.71827i			0.0578899i	−0.999581	+	0.0289449i	$0.990785\pi$
$882$		0			0
$883$	31.5753			1.06259			0.531297	−	0.847185i	$-0.321705\pi$
$883$	31.5753			1.06259			0.531297	+	0.847185i	$0.321705\pi$
$884$	8.85232	−	27.2738i	0.297736	−	0.917317i
$885$		0			0
$886$	−4.70087	+	29.7103i	−0.157929	+	0.998138i
$887$	25.0131	+	43.3240i	0.839859	+	1.45468i	0.890012	+	0.455937i	$0.150696\pi$
$887$	25.0131	+	43.3240i	0.839859	+	1.45468i	−0.0501528	+	0.998742i	$0.515971\pi$
$888$		0			0
$889$	1.34822	+	0.237069i	0.0452177	+	0.00795103i
$890$	−3.33031	−	8.67168i	−0.111632	−	0.290675i
$891$		0			0
$892$	7.94525	+	37.3218i	0.266027	+	1.24963i
$893$	3.66016	+	2.11319i	0.122483	+	0.0707153i
$894$		0			0
$895$	−0.450150			−0.0150469
$896$	29.1766	+	6.68764i	0.974723	+	0.223418i
$897$		0			0
$898$	−16.9400	−	13.7134i	−0.565296	−	0.457621i
$899$	−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	−0.792838	−	0.609432i	$-0.791398\pi$
$907$	3.95622	−	6.85238i	0.131364	−	0.227530i	0.924203	+	0.381902i	$0.124731\pi$
$908$	−1.47331	+	4.53923i	−0.0488935	+	0.150640i
$909$		0			0
$910$	5.57027	+	1.91407i	0.184652	+	0.0634507i
$911$		−	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
$914$	7.97522	−	50.4048i	0.263797	−	1.66724i
$915$		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	$-0.373748\pi$
$919$	41.7821	−	24.1229i	1.37827	−	0.795742i	0.991951	+	0.126625i	$0.0404146\pi$
$920$	0.0566968	−	0.0368573i	0.00186924	−	0.00121515i
$921$		0			0
$922$	−34.0687	−	27.5794i	−1.12199	−	0.908280i
$923$			38.9483i			1.28200i
$924$		0			0
$925$			41.6204i			1.36847i
$926$	4.24088	−	5.23873i	0.139364	−	0.172155i
$927$		0			0
$928$	11.4633	−	42.9164i	0.376302	−	1.40880i
$929$	−44.9765	+	25.9672i	−1.47563	+	0.851956i	−0.999622	−	0.0274853i	$-0.991250\pi$
$929$	−44.9765	+	25.9672i	−1.47563	+	0.851956i	−0.476008	+	0.879441i	$0.657917\pi$
$930$		0			0
$931$	−31.6549	+	5.61252i	−1.03745	+	0.183943i
$932$	25.3720	−	22.8595i	0.831089	−	0.748788i
$933$		0			0
$934$	1.55523	+	0.246073i	0.0508885	+	0.00805176i
$935$	1.15570	+	0.667242i	0.0377953	+	0.0218212i
$936$		0			0
$937$			10.7775i			0.352087i	0.984382	+	0.176044i	$0.0563300\pi$
$937$			10.7775i			0.352087i	−0.984382	+	0.176044i	$0.943670\pi$
$938$	−7.06726	−	36.2359i	−0.230754	−	1.18314i
$939$		0			0
$940$	−0.789657	−	0.256301i	−0.0257558	−	0.00835962i
$941$	8.56040	−	14.8270i	0.279061	−	0.483348i	−0.692091	−	0.721811i	$-0.743310\pi$
$941$	8.56040	−	14.8270i	0.279061	−	0.483348i	0.971152	+	0.238463i	$0.0766435\pi$
$942$		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	0.814776	−	0.579776i	$-0.196860\pi$
$947$	−2.91463	−	5.04828i	−0.0947126	−	0.164047i	−0.909489	+	0.415729i	$0.863527\pi$
$948$		0			0
$949$	11.6245	+	6.71139i	0.377346	+	0.217861i
$950$	−19.6017	+	24.2138i	−0.635963	+	0.785601i
$951$		0			0
$952$	−12.0395	−	28.2889i	−0.390201	−	0.916848i
$953$	−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
$956$	−58.5159	+	12.4572i	−1.89254	+	0.402893i
$957$		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
$962$	−42.2980	−	6.69254i	−1.36374	−	0.215776i
$963$		0			0
$964$	−10.3970	+	32.0328i	−0.334863	+	1.03171i
$965$	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	$-0.308342\pi$
$968$	29.6047	−	1.56550i	0.951531	−	0.0503172i
$969$		0			0
$970$	3.24224	+	0.512998i	0.104102	+	0.0164714i
$971$	11.0630	−	6.38720i	0.355027	−	0.204975i	−0.311870	−	0.950125i	$-0.600955\pi$
$971$	11.0630	−	6.38720i	0.355027	−	0.204975i	0.666897	+	0.745150i	$0.267622\pi$
$972$		0			0
$973$	−2.73841	−	0.481518i	−0.0877892	−	0.0154368i
$974$	11.3247	+	29.4879i	0.362866	+	0.944854i
$975$		0			0
$976$	−16.4993	−	11.9716i	−0.528131	−	0.383203i
$977$	15.9469	−	27.6208i	0.510186	−	0.883668i	−0.489744	−	0.871866i	$-0.662910\pi$
$977$	15.9469	−	27.6208i	0.510186	−	0.883668i	0.999930	−	0.0118021i	$-0.00375682\pi$
$978$		0			0
$979$		−	10.4858i		−	0.335127i
$980$	5.85228	−	2.37306i	0.186944	−	0.0758047i
$981$		0			0
$982$	−19.6090	−	15.8739i	−0.625747	−	0.506558i
$983$	−25.6278	+	44.3886i	−0.817399	+	1.41578i	0.0901941	+	0.995924i	$0.471251\pi$
$983$	−25.6278	+	44.3886i	−0.817399	+	1.41578i	−0.907593	+	0.419852i	$0.862082\pi$
$984$		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	$-0.213639\pi$
$991$	20.0234	+	11.5605i	0.636064	+	0.367232i	−0.147033	+	0.989132i	$0.546972\pi$
$992$	36.6377	−	36.6952i	1.16325	−	1.16508i
$993$		0			0
$994$	27.4167	+	31.4992i	0.869606	+	0.999094i
$995$	−4.86789			−0.154322
$996$		0			0
$997$	−21.7369	+	37.6494i	−0.688413	+	1.19237i	0.283938	+	0.958843i	$0.408359\pi$
$997$	−21.7369	+	37.6494i	−0.688413	+	1.19237i	−0.972351	+	0.233524i	$0.924974\pi$
$998$	−1.37126	+	8.66662i	−0.0434066	+	0.274337i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.10	✓	32	21.5	even	6
168.2.t.a.19.13	yes	32	168.131	odd	6
168.2.t.a.115.10	yes	32	24.11	even	2
168.2.t.a.115.13	yes	32	3.2	odd	2
504.2.bk.c.19.4		32	56.19	even	6	inner
504.2.bk.c.19.7		32	7.5	odd	6	inner
504.2.bk.c.451.4		32	1.1	even	1	trivial
504.2.bk.c.451.7		32	8.3	odd	2	inner
672.2.bb.a.271.3		32	168.5	even	6
672.2.bb.a.271.6		32	84.47	odd	6
672.2.bb.a.367.3		32	12.11	even	2
672.2.bb.a.367.6		32	24.5	odd	2
1176.2.p.a.979.1		32	168.59	odd	6
1176.2.p.a.979.2		32	168.11	even	6
1176.2.p.a.979.3		32	21.11	odd	6
1176.2.p.a.979.4		32	21.17	even	6
2016.2.bs.c.271.6		32	28.19	even	6
2016.2.bs.c.271.11		32	56.5	odd	6
2016.2.bs.c.1711.6		32	8.5	even	2
2016.2.bs.c.1711.11		32	4.3	odd	2
4704.2.p.a.3919.7		32	168.101	even	6
4704.2.p.a.3919.8		32	84.11	even	6
4704.2.p.a.3919.11		32	84.59	odd	6
4704.2.p.a.3919.12		32	168.53	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09919 - 0.889821i) q^{2} +(0.416438 + 1.95616i) q^{4} +(0.225540 + 0.390646i) q^{5} +(0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +O(q^{10})\)	\(q+(-1.09919 - 0.889821i) q^{2} +(0.416438 + 1.95616i) q^{4} +(0.225540 + 0.390646i) q^{5} +(0.458196 - 2.60577i) q^{7} +(1.28289 - 2.52075i) q^{8} +(0.0996941 - 0.630084i) q^{10} +(0.360048 - 0.623622i) q^{11} -3.48975 q^{13} +(-2.82232 + 2.45653i) q^{14} +(-3.65316 + 1.62924i) q^{16} +(3.55796 + 2.05419i) q^{17} +(3.97736 - 2.29633i) q^{19} +(-0.670245 + 0.603872i) q^{20} +(-0.950673 + 0.365101i) q^{22} +(0.0459022 - 0.0265016i) q^{23} +(2.39826 - 4.15391i) q^{25} +(3.83590 + 3.10526i) q^{26} +(5.28813 - 0.188836i) q^{28} -7.85260i q^{29} +(4.58331 - 7.93852i) q^{31} +(5.46525 + 1.45981i) q^{32} +(-2.08301 - 5.42389i) q^{34} +(1.12128 - 0.408713i) q^{35} +(-7.51467 + 4.33860i) q^{37} +(-6.41519 - 1.01503i) q^{38} +(1.27406 - 0.0673729i) q^{40} -3.94348i q^{41} +5.17408 q^{43} +(1.36984 + 0.444614i) q^{44} +(-0.0740369 - 0.0117144i) q^{46} +(0.460124 + 0.796959i) q^{47} +(-6.58011 - 2.38791i) q^{49} +(-6.33239 + 2.43192i) q^{50} +(-1.45327 - 6.82653i) q^{52} +(-2.71489 - 1.56744i) q^{53} +0.324821 q^{55} +(-5.98069 - 4.49792i) q^{56} +(-6.98741 + 8.63151i) q^{58} +(4.86409 + 2.80828i) q^{59} +(2.54813 + 4.41348i) q^{61} +(-12.1018 + 4.64762i) q^{62} +(-4.70838 - 6.46770i) q^{64} +(-0.787078 - 1.36326i) q^{65} +(-4.93346 + 8.54500i) q^{67} +(-2.53666 + 7.81539i) q^{68} +(-1.59618 - 0.548482i) q^{70} -11.1608i q^{71} +(-3.33103 - 1.92317i) q^{73} +(12.1206 + 1.91777i) q^{74} +(6.14832 + 6.82409i) q^{76} +(-1.46004 - 1.22395i) q^{77} +(8.40929 - 4.85511i) q^{79} +(-1.46039 - 1.05963i) q^{80} +(-3.50899 + 4.33463i) q^{82} -9.53613i q^{83} +1.85320i q^{85} +(-5.68729 - 4.60400i) q^{86} +(-1.11009 - 1.70763i) q^{88} +(12.6107 - 7.28081i) q^{89} +(-1.59899 + 9.09351i) q^{91} +(0.0709569 + 0.0787559i) q^{92} +(0.203386 - 1.28544i) q^{94} +(1.79410 + 1.03583i) q^{95} +5.14572i q^{97} +(5.10798 + 8.47989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 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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