LMFDB - Embedded newform 504.2.bk.c.19.4

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			19.4
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.4

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	−0.811177	−	0.584801i	$-0.801173\pi$
$5$	0.225540	−	0.390646i	0.100864	−	0.174702i	0.912041	+	0.410099i	$0.134506\pi$
$6$		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	0.915187	−	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	$-0.660795\pi$
$13$	−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	−0.00206160	−	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	0.504778	−	0.863249i	$-0.331574\pi$
$23$	0.0459022	+	0.0265016i	0.00957126	+	0.00552597i	−0.495207	+	0.868775i	$0.664908\pi$
$24$		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	$0.260059\pi$
$29$			7.85260i			1.45819i	−0.684411	+	0.729096i	$0.739941\pi$
$30$		0			0
$31$	4.58331	+	7.93852i	0.823186	+	1.42580i	0.903298	+	0.429015i	$0.141139\pi$
$31$	4.58331	+	7.93852i	0.823186	+	1.42580i	−0.0801113	+	0.996786i	$0.525528\pi$
$32$	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	−0.267253	−	0.963626i	$-0.586116\pi$
$37$	−7.51467	−	4.33860i	−1.23540	−	0.713261i	−0.968151	+	0.250366i	$0.919449\pi$
$38$	−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	$0.0996375\pi$
$41$			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	$0.370911\pi$
$44$	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	−0.830515	−	0.556997i	$-0.811954\pi$
$47$	0.460124	−	0.796959i	0.0671160	−	0.116248i	0.897631	+	0.440748i	$0.145287\pi$
$48$		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	−0.674733	−	0.738062i	$-0.735741\pi$
$53$	−2.71489	+	1.56744i	−0.372919	+	0.215305i	0.301814	+	0.953367i	$0.402408\pi$
$54$		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	−0.148759	−	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	−0.655511	−	0.755185i	$-0.727547\pi$
$61$	2.54813	−	4.41348i	0.326254	−	0.565089i	0.981765	+	0.190097i	$0.0608802\pi$
$62$	−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	$-0.372582\pi$
$68$	−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	$0.230407\pi$
$71$			11.1608i			1.32454i	−0.749266	+	0.662270i	$0.769593\pi$
$72$		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	$0.405601\pi$
$74$	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	0.891873	−	0.452285i	$-0.149391\pi$
$79$	8.40929	+	4.85511i	0.946119	+	0.546242i	0.0542460	+	0.998528i	$0.482724\pi$
$80$	−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	$0.175323\pi$
$83$			9.53613i			1.04673i	−0.852110	+	0.523363i	$0.824677\pi$
$84$		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	0.986322	−	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
$94$	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	$-0.915870\pi$
$97$		−	5.14572i		−	0.522469i	0.965275	−	0.261235i	$-0.0841296\pi$
$98$	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	−0.964503	−	0.264072i	$-0.914934\pi$
$101$	−7.14490	−	12.3753i	−0.710944	−	1.23139i	0.253559	−	0.967320i	$-0.418399\pi$
$102$		0			0
$103$	7.46214	−	12.9248i	0.735267	−	1.27352i	−0.219339	−	0.975649i	$-0.570390\pi$
$103$	7.46214	−	12.9248i	0.735267	−	1.27352i	0.954606	−	0.297871i	$-0.0962764\pi$
$104$	−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	−0.509967	−	0.860194i	$-0.670342\pi$
$109$	−0.208805	+	0.120553i	−0.0199999	+	0.0115469i	0.489967	+	0.871741i	$0.337009\pi$
$110$	−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	$-0.992692\pi$
$127$		−	0.517396i		−	0.0459115i	0.999736	−	0.0229557i	$-0.00730768\pi$
$128$	−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	−0.105404	−	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
$136$	9.74257	+	6.33343i	0.835418	+	0.543087i
$137$	−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	$0.985809\pi$
$140$	1.26645	−	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	−0.0198791	−	0.999802i	$-0.506328\pi$
$149$	−10.9331	−	6.31222i	−0.895673	−	0.517117i	−0.875794	+	0.482685i	$0.839661\pi$
$150$		0			0
$151$	−2.86647	+	1.65496i	−0.233270	+	0.134679i	−0.612080	−	0.790796i	$-0.709667\pi$
$151$	−2.86647	+	1.65496i	−0.233270	+	0.134679i	0.378810	+	0.925475i	$0.376334\pi$
$152$	−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	0.787250	−	0.616634i	$-0.211504\pi$
$157$	−1.75915	−	3.04694i	−0.140396	−	0.243172i	−0.927646	+	0.373462i	$0.878171\pi$
$158$	−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	0.223335	+	0.974742i	$0.428306\pi$
$163$	−9.35173	+	16.1977i	−0.732484	+	1.26870i	−0.955819	+	0.293957i	$0.905028\pi$
$164$	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	0.184988	−	0.982741i	$-0.440775\pi$
$173$	12.4108	−	21.4961i	0.943572	−	1.63432i	0.758585	−	0.651575i	$-0.225891\pi$
$174$		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	0.846776	−	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	$-0.569332\pi$
$181$	−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	0.0155908	−	0.999878i	$-0.495037\pi$
$191$	−11.6440	−	6.72270i	−0.842534	−	0.486437i	−0.858125	+	0.513441i	$0.828370\pi$
$192$		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	$0.747355\pi$
$194$	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	$-0.924126\pi$
$197$		−	6.62804i		−	0.472228i	0.971725	−	0.236114i	$-0.0758739\pi$
$198$		0			0
$199$	−5.39583	−	9.34584i	−0.382500	−	0.662509i	0.608919	−	0.793232i	$-0.291603\pi$
$199$	−5.39583	−	9.34584i	−0.382500	−	0.662509i	−0.991419	+	0.130723i	$0.958270\pi$
$200$	−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	−0.429851	−	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	−0.646238	−	0.763136i	$-0.723659\pi$
$229$	5.11149	−	8.85335i	0.337776	−	0.585046i	0.984014	+	0.178090i	$0.0569919\pi$
$230$	−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
$236$	−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	$-0.581407\pi$
$239$		−	29.9136i		−	1.93495i	0.252968	−	0.967475i	$-0.418593\pi$
$240$		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	$0.150870\pi$
$242$	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	$0.260457\pi$
$251$			23.1292i			1.45990i	−0.683500	+	0.729951i	$0.739543\pi$
$252$		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	0.788898	−	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
$262$	18.8172	−	2.97733i	1.16253	−	0.183940i
$263$	−20.2875	+	11.7130i	−1.25098	+	0.722254i	−0.971304	−	0.237840i	$-0.923561\pi$
$263$	−20.2875	+	11.7130i	−1.25098	+	0.722254i	−0.279677	+	0.960094i	$0.590227\pi$
$264$		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	0.988799	−	0.149252i	$-0.0476865\pi$
$269$	5.98880	+	10.3729i	0.365144	+	0.632447i	−0.623655	+	0.781699i	$0.714353\pi$
$270$		0			0
$271$	−3.99591	+	6.92112i	−0.242734	+	0.420428i	−0.961492	−	0.274832i	$-0.911378\pi$
$271$	−3.99591	+	6.92112i	−0.242734	+	0.420428i	0.718758	+	0.695260i	$0.244711\pi$
$272$	−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	−0.255957	−	0.966688i	$-0.582391\pi$
$277$	7.54343	−	4.35520i	0.453241	−	0.261679i	0.709198	+	0.705009i	$0.249057\pi$
$278$	−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	−0.834128	−	0.551571i	$-0.814028\pi$
$283$	−13.0126	+	7.51281i	−0.773517	+	0.446590i	0.0606110	+	0.998161i	$0.480695\pi$
$284$	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	$0.250196\pi$
$307$			24.7943i			1.41508i	−0.706672	+	0.707542i	$0.749804\pi$
$308$	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	0.826997	−	0.562206i	$-0.190047\pi$
$311$	−1.29417	−	2.24157i	−0.0733858	−	0.127108i	−0.900383	+	0.435098i	$0.856714\pi$
$312$		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	$0.0713960\pi$
$317$	29.4673	+	17.0130i	1.65505	+	0.955543i	0.680098	+	0.733121i	$0.261937\pi$
$318$		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	−0.830466	−	0.557070i	$-0.811926\pi$
$331$	1.22267	−	2.11772i	0.0672040	−	0.116401i	0.897670	+	0.440669i	$0.145259\pi$
$332$	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	0.541941	−	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	$-0.228204\pi$
$349$	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	0.0618651	−	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	0.485160	−	0.874425i	$-0.338761\pi$
$359$	−0.559584	−	0.323076i	−0.0295337	−	0.0170513i	−0.514694	+	0.857374i	$0.672095\pi$
$360$		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	0.946151	−	0.323726i	$-0.104936\pi$
$367$	3.69198	+	6.39470i	0.192720	+	0.333801i	−0.753431	+	0.657527i	$0.771602\pi$
$368$	−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	0.241780	−	0.970331i	$-0.422269\pi$
$373$	−9.22518	−	5.32616i	−0.477662	−	0.275778i	−0.719442	+	0.694553i	$0.755602\pi$
$374$	−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	−0.803934	−	0.594719i	$-0.797263\pi$
$383$	2.21292	−	3.83290i	0.113075	−	0.195852i	0.917009	+	0.398867i	$0.130597\pi$
$384$		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	−0.712139	−	0.702038i	$-0.752273\pi$
$389$	−9.07706	+	5.24065i	−0.460225	+	0.265711i	0.251914	+	0.967750i	$0.418940\pi$
$390$		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	−0.977478	−	0.211035i	$-0.932317\pi$
$397$	−6.09656	+	10.5596i	−0.305978	+	0.529969i	0.671501	+	0.741004i	$0.265650\pi$
$398$	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
$404$	−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	0.321447	−	0.946928i	$-0.395831\pi$
$409$	26.3361	−	15.2051i	1.30223	−	0.751845i	0.980787	+	0.195082i	$0.0624974\pi$
$410$	−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	$0.0132692\pi$
$419$			1.70610i			0.0833485i	−0.999131	+	0.0416743i	$0.986731\pi$
$420$		0			0
$421$			13.0483i			0.635937i	0.948101	+	0.317969i	$0.103001\pi$
$421$			13.0483i			0.635937i	−0.948101	+	0.317969i	$0.896999\pi$
$422$	−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	−0.546306	−	0.837585i	$-0.683967\pi$
$431$	−1.95335	+	1.12777i	−0.0940894	+	0.0543226i	0.452217	+	0.891908i	$0.350633\pi$
$432$		0			0
$433$		−	7.41221i		−	0.356208i	−0.984012	−	0.178104i	$-0.943004\pi$
$433$		−	7.41221i		−	0.356208i	0.984012	−	0.178104i	$-0.0569963\pi$
$434$	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	−0.962069	−	0.272806i	$-0.912048\pi$
$439$	−5.12867	+	8.88312i	−0.244778	+	0.423968i	0.717291	+	0.696774i	$0.245382\pi$
$440$	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
$446$	−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	−0.0425032	−	0.999096i	$-0.513533\pi$
$457$	18.0425	−	31.2505i	0.843991	−	1.46184i	0.886494	−	0.462739i	$-0.153133\pi$
$458$	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	$-0.964676\pi$
$463$		−	4.76599i		−	0.221494i	0.993849	−	0.110747i	$-0.0353244\pi$
$464$	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	0.477525	−	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
$472$	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	−0.991245	−	0.132032i	$-0.957850\pi$
$479$	−13.3498	−	23.1224i	−0.609966	−	1.05649i	0.381280	−	0.924460i	$-0.375483\pi$
$480$		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	−0.869515	−	0.493907i	$-0.835568\pi$
$487$	−19.3435	+	11.1680i	−0.876536	+	0.506068i	−0.00702114	+	0.999975i	$0.502235\pi$
$488$	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	−0.927071	−	0.374886i	$-0.877682\pi$
$499$	−3.10223	+	5.37322i	−0.138875	+	0.240538i	0.788196	+	0.615424i	$0.211015\pi$
$500$	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	0.158530	+	0.987354i	$0.449324\pi$
$509$	−17.5030	+	30.3161i	−0.775808	+	1.34374i	−0.934339	+	0.356386i	$0.884009\pi$
$510$		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	−0.339034	−	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
$530$	−1.25828	−	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	0.881581	−	0.472032i	$-0.156479\pi$
$541$	21.2493	+	12.2683i	0.913581	+	0.527456i	0.0319992	+	0.999488i	$0.489813\pi$
$542$	−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	0.413203	−	0.910639i	$-0.364410\pi$
$557$	33.2404	−	19.1914i	1.40844	−	0.813164i	0.995238	+	0.0974752i	$0.0310767\pi$
$558$		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	−0.481342	−	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	$0.788678\pi$
$572$	−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	−0.511634	−	0.859203i	$-0.670960\pi$
$577$	−0.561113	+	0.323959i	−0.0233595	+	0.0134866i	0.488275	+	0.872690i	$0.337626\pi$
$578$	−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	$0.0286278\pi$
$587$			4.35212i			0.179631i	−0.995958	+	0.0898157i	$0.971372\pi$
$588$		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	−0.0177420	−	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
$598$	0.258371	−	0.0408803i	0.0105656	−	0.00167172i
$599$	20.4978	−	11.8344i	0.837519	−	0.483542i	−0.0189009	−	0.999821i	$-0.506017\pi$
$599$	20.4978	−	11.8344i	0.837519	−	0.483542i	0.856420	+	0.516279i	$0.172683\pi$
$600$		0			0
$601$		−	14.8295i		−	0.604907i	−0.953164	−	0.302453i	$-0.902194\pi$
$601$		−	14.8295i		−	0.604907i	0.953164	−	0.302453i	$-0.0978057\pi$
$602$	−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	−0.876526	−	0.481354i	$-0.840145\pi$
$607$	−0.527187	+	0.913114i	−0.0213979	+	0.0370622i	0.855128	+	0.518417i	$0.173478\pi$
$608$	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	−0.983296	−	0.182015i	$-0.941738\pi$
$613$	−32.6152	+	18.8304i	−1.31731	+	0.760552i	−0.334019	+	0.942566i	$0.608405\pi$
$614$	−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	−0.404688	−	0.914455i	$-0.632620\pi$
$619$	4.60049	−	2.65609i	0.184909	−	0.106757i	0.589597	+	0.807697i	$0.299287\pi$
$620$	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	$-0.731868\pi$
$631$		−	37.4896i		−	1.49244i	0.665702	−	0.746218i	$-0.268132\pi$
$632$	−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	0.997526	−	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	$0.803135\pi$
$644$	0.237732	+	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	0.994736	−	0.102474i	$-0.0326758\pi$
$647$	10.3938	+	18.0026i	0.408623	+	0.707755i	−0.586113	+	0.810229i	$0.699343\pi$
$648$		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	0.564313	−	0.825561i	$-0.309141\pi$
$653$	3.36065	+	1.94027i	0.131512	+	0.0759287i	−0.432800	+	0.901490i	$0.642475\pi$
$654$		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	0.807122	−	0.590384i	$-0.201024\pi$
$661$	−2.76963	−	4.79715i	−0.107726	−	0.186587i	−0.914849	+	0.403797i	$0.867690\pi$
$662$	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	−0.0210020	−	0.999779i	$-0.506686\pi$
$677$	22.2551	−	38.5470i	0.855333	−	1.48148i	0.876335	−	0.481701i	$-0.159981\pi$
$678$		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	0.977525	−	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
$686$	24.4371	+	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	−0.256462	−	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
$698$	−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	$0.130279\pi$
$701$			21.0727i			0.795906i	−0.917406	+	0.397953i	$0.869721\pi$
$702$		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	0.776309	−	0.630352i	$-0.217090\pi$
$709$	16.4705	+	9.50925i	0.618563	+	0.357127i	−0.157746	+	0.987480i	$0.550423\pi$
$710$	−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	−0.846265	−	0.532762i	$-0.821154\pi$
$719$	1.02572	−	1.77660i	0.0382529	−	0.0662559i	0.884518	+	0.466506i	$0.154487\pi$
$720$		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	−0.489213	−	0.872164i	$-0.662716\pi$
$733$	13.8269	−	23.9490i	0.510710	−	0.884575i	0.999923	−	0.0124107i	$-0.00395056\pi$
$734$	−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	$0.816548\pi$
$740$	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	$0.0231163\pi$
$743$			3.95558i			0.145116i	−0.997364	+	0.0725581i	$0.976884\pi$
$744$		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	0.491881	−	0.870662i	$-0.336309\pi$
$751$	−0.443784	−	0.256219i	−0.0161939	−	0.00934956i	−0.508075	+	0.861313i	$0.669643\pi$
$752$	−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	$-0.893502\pi$
$757$		−	18.0691i		−	0.656732i	0.944551	−	0.328366i	$-0.106498\pi$
$758$	−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	0.971045	−	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
$766$	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	$-0.693195\pi$
$769$		−	45.5560i		−	1.64279i	0.570358	−	0.821396i	$-0.306805\pi$
$770$	−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	−0.948409	−	0.317049i	$-0.897308\pi$
$773$	−20.8182	−	36.0581i	−0.748777	−	1.29692i	0.199632	−	0.979871i	$-0.436025\pi$
$774$		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	−0.218118	−	0.975922i	$-0.569992\pi$
$787$	14.5316	−	8.38984i	0.517997	−	0.299065i	0.736115	+	0.676857i	$0.236658\pi$
$788$	−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	0.715103	−	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	$0.919352\pi$
$812$	−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	0.291308	−	0.956629i	$-0.405909\pi$
$821$	−11.2178	−	6.47658i	−0.391503	−	0.226034i	−0.682811	+	0.730595i	$0.739243\pi$
$822$		0			0
$823$	8.69701	−	5.02122i	0.303159	−	0.175029i	−0.340702	−	0.940171i	$-0.610665\pi$
$823$	8.69701	−	5.02122i	0.303159	−	0.175029i	0.643861	+	0.765143i	$0.277332\pi$
$824$	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	−0.954564	−	0.298005i	$-0.903679\pi$
$829$	−21.1728	−	36.6724i	−0.735362	−	1.27368i	0.219202	−	0.975679i	$-0.429655\pi$
$830$	−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	−0.460493	−	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	0.519285	−	0.854601i	$-0.326198\pi$
$863$	1.14047	+	0.658448i	0.0388219	+	0.0224138i	−0.480463	+	0.877015i	$0.659532\pi$
$864$		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	0.104366	−	0.994539i	$-0.466719\pi$
$877$	−20.8705	−	12.0496i	−0.704748	−	0.406886i	−0.809113	+	0.587653i	$0.800052\pi$
$878$	−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	$-0.990785\pi$
$881$		−	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	$0.321705\pi$
$884$	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	−0.0501528	−	0.998742i	$-0.515971\pi$
$887$	25.0131	−	43.3240i	0.839859	−	1.45468i	0.890012	−	0.455937i	$-0.150696\pi$
$888$		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	0.924203	−	0.381902i	$-0.124731\pi$
$907$	3.95622	+	6.85238i	0.131364	+	0.227530i	−0.792838	+	0.609432i	$0.791398\pi$
$908$	−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	$0.156994\pi$
$911$			28.5805i			0.946914i	−0.880817	+	0.473457i	$0.843006\pi$
$912$		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	0.991951	−	0.126625i	$-0.0404146\pi$
$919$	41.7821	+	24.1229i	1.37827	+	0.795742i	0.386314	+	0.922367i	$0.373748\pi$
$920$	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	−0.476008	−	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
$934$	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	$-0.943670\pi$
$937$		−	10.7775i		−	0.352087i	0.984382	−	0.176044i	$-0.0563300\pi$
$938$	−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	0.971152	−	0.238463i	$-0.0766435\pi$
$941$	8.56040	+	14.8270i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$942$		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
$950$	−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	$0.308342\pi$
$967$			51.2560i			1.64828i	−0.566384	+	0.824141i	$0.691658\pi$
$968$	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	0.666897	−	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
$976$	−16.4993	+	11.9716i	−0.528131	+	0.383203i
$977$	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
$980$	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	−0.907593	−	0.419852i	$-0.862082\pi$
$983$	−25.6278	−	44.3886i	−0.817399	−	1.41578i	0.0901941	−	0.995924i	$-0.471251\pi$
$984$		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	−0.147033	−	0.989132i	$-0.546972\pi$
$991$	20.0234	−	11.5605i	0.636064	−	0.367232i	0.783097	+	0.621900i	$0.213639\pi$
$992$	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	−0.972351	−	0.233524i	$-0.924974\pi$
$997$	−21.7369	−	37.6494i	−0.688413	−	1.19237i	0.283938	−	0.958843i	$-0.408359\pi$
$998$	−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.19.4		32
3.2	odd	2		168.2.t.a.19.13	yes	32
4.3	odd	2		2016.2.bs.c.271.11		32
7.3	odd	6	inner	504.2.bk.c.451.7		32
8.3	odd	2	inner	504.2.bk.c.19.7		32
8.5	even	2		2016.2.bs.c.271.6		32
12.11	even	2		672.2.bb.a.271.3		32
21.2	odd	6		1176.2.p.a.979.1		32
21.5	even	6		1176.2.p.a.979.2		32
21.17	even	6		168.2.t.a.115.10	yes	32
24.5	odd	2		672.2.bb.a.271.6		32
24.11	even	2		168.2.t.a.19.10	✓	32
28.3	even	6		2016.2.bs.c.1711.6		32
56.3	even	6	inner	504.2.bk.c.451.4		32
56.45	odd	6		2016.2.bs.c.1711.11		32
84.23	even	6		4704.2.p.a.3919.7		32
84.47	odd	6		4704.2.p.a.3919.12		32
84.59	odd	6		672.2.bb.a.367.6		32
168.5	even	6		4704.2.p.a.3919.8		32
168.59	odd	6		168.2.t.a.115.13	yes	32
168.101	even	6		672.2.bb.a.367.3		32
168.107	even	6		1176.2.p.a.979.4		32
168.131	odd	6		1176.2.p.a.979.3		32
168.149	odd	6		4704.2.p.a.3919.11		32

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