LMFDB - Embedded newform 504.2.cj.e.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (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			37.4
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06853 + 0.926418i) q^{2} +(0.283500 - 1.97980i) q^{4} +(-1.23074 - 0.710569i) q^{5} +(1.39545 - 2.24783i) q^{7} +(1.53120 + 2.37811i) q^{8} +O(q^{10})$	\(q+(-1.06853 + 0.926418i) q^{2} +(0.283500 - 1.97980i) q^{4} +(-1.23074 - 0.710569i) q^{5} +(1.39545 - 2.24783i) q^{7} +(1.53120 + 2.37811i) q^{8} +(1.97336 - 0.380919i) q^{10} +(-0.832525 + 0.480658i) q^{11} +3.57192i q^{13} +(0.591351 + 3.69463i) q^{14} +(-3.83926 - 1.12255i) q^{16} +(-2.43064 - 4.21000i) q^{17} +(-6.28094 - 3.62630i) q^{19} +(-1.75570 + 2.23518i) q^{20} +(0.444285 - 1.28486i) q^{22} +(2.72132 - 4.71346i) q^{23} +(-1.49018 - 2.58107i) q^{25} +(-3.30909 - 3.81670i) q^{26} +(-4.05465 - 3.39998i) q^{28} -6.78641i q^{29} +(3.67285 + 6.36156i) q^{31} +(5.14230 - 2.35728i) q^{32} +(6.49742 + 2.24670i) q^{34} +(-3.31467 + 1.77493i) q^{35} +(-2.21085 - 1.27644i) q^{37} +(10.0708 - 1.94397i) q^{38} +(-0.194696 - 4.01487i) q^{40} -2.20216 q^{41} -4.45897i q^{43} +(0.715589 + 1.78450i) q^{44} +(1.45883 + 7.55754i) q^{46} +(-0.211793 + 0.366836i) q^{47} +(-3.10544 - 6.27345i) q^{49} +(3.98345 + 1.37741i) q^{50} +(7.07171 + 1.01264i) q^{52} +(-8.41117 + 4.85619i) q^{53} +1.36616 q^{55} +(7.48230 - 0.123332i) q^{56} +(6.28705 + 7.25146i) q^{58} +(6.43952 - 3.71786i) q^{59} +(-1.67889 - 0.969306i) q^{61} +(-9.81800 - 3.39491i) q^{62} +(-3.31086 + 7.28273i) q^{64} +(2.53810 - 4.39612i) q^{65} +(9.13752 - 5.27555i) q^{67} +(-9.02406 + 3.61867i) q^{68} +(1.89749 - 4.96733i) q^{70} +8.12089 q^{71} +(-4.99925 - 8.65896i) q^{73} +(3.54487 - 0.684267i) q^{74} +(-8.96001 + 11.4070i) q^{76} +(-0.0813093 + 2.54211i) q^{77} +(0.139607 - 0.241807i) q^{79} +(3.92748 + 4.10963i) q^{80} +(2.35307 - 2.04012i) q^{82} +6.69361i q^{83} +6.90856i q^{85} +(4.13087 + 4.76453i) q^{86} +(-2.41782 - 1.24386i) q^{88} +(1.07402 - 1.86026i) q^{89} +(8.02906 + 4.98444i) q^{91} +(-8.56024 - 6.72394i) q^{92} +(-0.113537 - 0.588183i) q^{94} +(5.15348 + 8.92608i) q^{95} -9.44983 q^{97} +(9.13009 + 3.82642i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.06853	+	0.926418i	−0.755563	+	0.655076i
$2$	−1.06853	+	0.926418i	−0.755563	+	0.655076i
$3$		0			0
$3$		0			0
$4$	0.283500	−	1.97980i	0.141750	−	0.989902i
$5$	−1.23074	−	0.710569i	−0.550405	−	0.317776i	0.198881	−	0.980024i	$-0.436269\pi$
$5$	−1.23074	−	0.710569i	−0.550405	−	0.317776i	−0.749285	+	0.662248i	$0.769603\pi$
$6$		0			0
$7$	1.39545	−	2.24783i	0.527430	−	0.849598i
$7$	1.39545	−	2.24783i	0.527430	−	0.849598i
$8$	1.53120	+	2.37811i	0.541361	+	0.840790i
$9$		0			0
$10$	1.97336	−	0.380919i	0.624033	−	0.120457i
$11$	−0.832525	+	0.480658i	−0.251016	+	0.144924i	−0.620229	−	0.784421i	$-0.712960\pi$
$11$	−0.832525	+	0.480658i	−0.251016	+	0.144924i	0.369214	+	0.929345i	$0.379627\pi$
$12$		0			0
$13$			3.57192i			0.990673i	0.868701	+	0.495337i	$0.164955\pi$
$13$			3.57192i			0.990673i	−0.868701	+	0.495337i	$0.835045\pi$
$14$	0.591351	+	3.69463i	0.158045	+	0.987432i
$15$		0			0
$16$	−3.83926	−	1.12255i	−0.959814	−	0.280637i
$17$	−2.43064	−	4.21000i	−0.589518	−	1.02107i	−0.994296	−	0.106659i	$-0.965985\pi$
$17$	−2.43064	−	4.21000i	−0.589518	−	1.02107i	0.404778	−	0.914415i	$-0.367349\pi$
$18$		0			0
$19$	−6.28094	−	3.62630i	−1.44095	−	0.831931i	−0.443033	−	0.896505i	$-0.646098\pi$
$19$	−6.28094	−	3.62630i	−1.44095	−	0.831931i	−0.997913	+	0.0645747i	$0.979431\pi$
$20$	−1.75570	+	2.23518i	−0.392587	+	0.499802i
$21$		0			0
$22$	0.444285	−	1.28486i	0.0947218	−	0.273934i
$23$	2.72132	−	4.71346i	0.567434	−	0.982824i	−0.429385	−	0.903122i	$-0.641270\pi$
$23$	2.72132	−	4.71346i	0.567434	−	0.982824i	0.996819	−	0.0797027i	$-0.0253971\pi$
$24$		0			0
$25$	−1.49018	−	2.58107i	−0.298037	−	0.516214i
$26$	−3.30909	−	3.81670i	−0.648967	−	0.748516i
$27$		0			0
$28$	−4.05465	−	3.39998i	−0.766256	−	0.642535i
$29$		−	6.78641i		−	1.26020i	−0.776512	−	0.630102i	$-0.783013\pi$
$29$		−	6.78641i		−	1.26020i	0.776512	−	0.630102i	$-0.216987\pi$
$30$		0			0
$31$	3.67285	+	6.36156i	0.659663	+	1.14257i	0.980703	+	0.195504i	$0.0626343\pi$
$31$	3.67285	+	6.36156i	0.659663	+	1.14257i	−0.321040	+	0.947066i	$0.604032\pi$
$32$	5.14230	−	2.35728i	0.909038	−	0.416712i
$33$		0			0
$34$	6.49742	+	2.24670i	1.11430	+	0.385307i
$35$	−3.31467	+	1.77493i	−0.560282	+	0.300018i
$36$		0			0
$37$	−2.21085	−	1.27644i	−0.363462	−	0.209845i	0.307136	−	0.951666i	$-0.400629\pi$
$37$	−2.21085	−	1.27644i	−0.363462	−	0.209845i	−0.670598	+	0.741821i	$0.733963\pi$
$38$	10.0708	−	1.94397i	1.63370	−	0.315354i
$39$		0			0
$40$	−0.194696	−	4.01487i	−0.0307842	−	0.634806i
$41$	−2.20216			−0.343920			−0.171960	−	0.985104i	$-0.555010\pi$
$41$	−2.20216			−0.343920			−0.171960	+	0.985104i	$0.555010\pi$
$42$		0			0
$43$		−	4.45897i		−	0.679986i	−0.940428	−	0.339993i	$-0.889575\pi$
$43$		−	4.45897i		−	0.679986i	0.940428	−	0.339993i	$-0.110425\pi$
$44$	0.715589	+	1.78450i	0.107879	+	0.269024i
$45$		0			0
$46$	1.45883	+	7.55754i	0.215093	+	1.11430i
$47$	−0.211793	+	0.366836i	−0.0308932	+	0.0535086i	−0.881059	−	0.473007i	$-0.843169\pi$
$47$	−0.211793	+	0.366836i	−0.0308932	+	0.0535086i	0.850165	+	0.526516i	$0.176502\pi$
$48$		0			0
$49$	−3.10544	−	6.27345i	−0.443635	−	0.896208i
$50$	3.98345	+	1.37741i	0.563345	+	0.194796i
$51$		0			0
$52$	7.07171	+	1.01264i	0.980670	+	0.140428i
$53$	−8.41117	+	4.85619i	−1.15536	+	0.667049i	−0.950188	−	0.311676i	$-0.899110\pi$
$53$	−8.41117	+	4.85619i	−1.15536	+	0.667049i	−0.205175	+	0.978725i	$0.565776\pi$
$54$		0			0
$55$	1.36616			0.184214
$56$	7.48230	−	0.123332i	0.999864	−	0.0164810i
$57$		0			0
$58$	6.28705	+	7.25146i	0.825530	+	0.952163i
$59$	6.43952	−	3.71786i	0.838354	−	0.484024i	−0.0183503	−	0.999832i	$-0.505841\pi$
$59$	6.43952	−	3.71786i	0.838354	−	0.484024i	0.856704	+	0.515808i	$0.172508\pi$
$60$		0			0
$61$	−1.67889	−	0.969306i	−0.214960	−	0.124107i	0.388655	−	0.921384i	$-0.372940\pi$
$61$	−1.67889	−	0.969306i	−0.214960	−	0.124107i	−0.603614	+	0.797277i	$0.706273\pi$
$62$	−9.81800	−	3.39491i	−1.24689	−	0.431153i
$63$		0			0
$64$	−3.31086	+	7.28273i	−0.413857	+	0.910342i
$65$	2.53810	−	4.39612i	0.314812	−	0.545271i
$66$		0			0
$67$	9.13752	−	5.27555i	1.11633	−	0.644511i	0.175866	−	0.984414i	$-0.443728\pi$
$67$	9.13752	−	5.27555i	1.11633	−	0.644511i	0.940460	+	0.339903i	$0.110394\pi$
$68$	−9.02406	+	3.61867i	−1.09433	+	0.438828i
$69$		0			0
$70$	1.89749	−	4.96733i	0.226794	−	0.593710i
$71$	8.12089			0.963772			0.481886	−	0.876234i	$-0.339952\pi$
$71$	8.12089			0.963772			0.481886	+	0.876234i	$0.339952\pi$
$72$		0			0
$73$	−4.99925	−	8.65896i	−0.585118	−	1.01345i	−0.994861	−	0.101253i	$-0.967715\pi$
$73$	−4.99925	−	8.65896i	−0.585118	−	1.01345i	0.409743	−	0.912201i	$-0.365619\pi$
$74$	3.54487	−	0.684267i	0.412083	−	0.0795444i
$75$		0			0
$76$	−8.96001	+	11.4070i	−1.02778	+	1.30847i
$77$	−0.0813093	+	2.54211i	−0.00926606	+	0.289700i
$78$		0			0
$79$	0.139607	−	0.241807i	0.0157071	−	0.0272054i	−0.858065	−	0.513541i	$-0.828333\pi$
$79$	0.139607	−	0.241807i	0.0157071	−	0.0272054i	0.873772	+	0.486336i	$0.161667\pi$
$80$	3.92748	+	4.10963i	0.439106	+	0.459470i
$81$		0			0
$82$	2.35307	−	2.04012i	0.259853	−	0.225294i
$83$			6.69361i			0.734719i	0.930079	+	0.367359i	$0.119738\pi$
$83$			6.69361i			0.734719i	−0.930079	+	0.367359i	$0.880262\pi$
$84$		0			0
$85$			6.90856i			0.749339i
$86$	4.13087	+	4.76453i	0.445443	+	0.513772i
$87$		0			0
$88$	−2.41782	−	1.24386i	−0.257741	−	0.132595i
$89$	1.07402	−	1.86026i	0.113846	−	0.197187i	−0.803472	−	0.595343i	$-0.797016\pi$
$89$	1.07402	−	1.86026i	0.113846	−	0.197187i	0.917318	+	0.398155i	$0.130350\pi$
$90$		0			0
$91$	8.02906	+	4.98444i	0.841674	+	0.522511i
$92$	−8.56024	−	6.72394i	−0.892467	−	0.701020i
$93$		0			0
$94$	−0.113537	−	0.588183i	−0.0117105	−	0.0606665i
$95$	5.15348	+	8.92608i	0.528735	+	0.915797i
$96$		0			0
$97$	−9.44983			−0.959485			−0.479742	−	0.877409i	$-0.659270\pi$
$97$	−9.44983			−0.959485			−0.479742	+	0.877409i	$0.659270\pi$
$98$	9.13009	+	3.82642i	0.922278	+	0.386526i
$99$		0			0
$100$	−5.53249	+	2.21854i	−0.553249	+	0.221854i
$101$	−3.08218	+	1.77950i	−0.306689	+	0.177067i	−0.645444	−	0.763808i	$-0.723328\pi$
$101$	−3.08218	+	1.77950i	−0.306689	+	0.177067i	0.338755	+	0.940875i	$0.389994\pi$
$102$		0			0
$103$	−0.618710	+	1.07164i	−0.0609633	+	0.105591i	−0.894896	−	0.446274i	$-0.852751\pi$
$103$	−0.618710	+	1.07164i	−0.0609633	+	0.105591i	0.833933	+	0.551866i	$0.186084\pi$
$104$	−8.49444	+	5.46933i	−0.832949	+	0.536312i
$105$		0			0
$106$	4.48870	−	12.9812i	0.435981	−	1.26085i
$107$	−14.4424	−	8.33834i	−1.39620	−	0.806098i	−0.402210	−	0.915548i	$-0.631758\pi$
$107$	−14.4424	−	8.33834i	−1.39620	−	0.806098i	−0.993992	+	0.109450i	$0.965091\pi$
$108$		0			0
$109$	8.84714	−	5.10790i	0.847403	−	0.489248i	−0.0123709	−	0.999923i	$-0.503938\pi$
$109$	8.84714	−	5.10790i	0.847403	−	0.489248i	0.859774	+	0.510675i	$0.170605\pi$
$110$	−1.45978	+	1.26564i	−0.139185	+	0.120674i
$111$		0			0
$112$	−7.88078	+	7.06352i	−0.744664	+	0.667440i
$113$	−12.4039			−1.16686			−0.583432	−	0.812162i	$-0.698291\pi$
$113$	−12.4039			−1.16686			−0.583432	+	0.812162i	$0.698291\pi$
$114$		0			0
$115$	−6.69848	+	3.86737i	−0.624636	+	0.360634i
$116$	−13.4358	−	1.92395i	−1.24748	−	0.178634i
$117$		0			0
$118$	−3.43651	+	9.93832i	−0.316356	+	0.914896i
$119$	−12.8552	−	0.411173i	−1.17843	−	0.0376922i
$120$		0			0
$121$	−5.03793	+	8.72596i	−0.457994	+	0.793269i
$122$	2.69192	−	0.519622i	0.243715	−	0.0470443i
$123$		0			0
$124$	13.6359	−	5.46802i	1.22454	−	0.491043i
$125$			11.3412i			1.01439i
$126$		0			0
$127$	17.3710			1.54142			0.770712	−	0.637184i	$-0.219901\pi$
$127$	17.3710			1.54142			0.770712	+	0.637184i	$0.219901\pi$
$128$	−3.20911	−	10.8490i	−0.283648	−	0.958928i
$129$		0			0
$130$	1.36061	+	7.04871i	0.119334	+	0.618213i
$131$	12.8469	+	7.41718i	1.12244	+	0.648042i	0.942023	−	0.335548i	$-0.108921\pi$
$131$	12.8469	+	7.41718i	1.12244	+	0.648042i	0.180418	+	0.983590i	$0.442255\pi$
$132$		0			0
$133$	−16.9160	+	9.05814i	−1.46681	+	0.785440i
$134$	−4.87632	+	14.1022i	−0.421250	+	1.21825i
$135$		0			0
$136$	6.29006	−	12.2267i	0.539368	−	1.04843i
$137$	6.93006	+	12.0032i	0.592075	+	1.02550i	0.993953	+	0.109810i	$0.0350244\pi$
$137$	6.93006	+	12.0032i	0.592075	+	1.02550i	−0.401878	+	0.915693i	$0.631642\pi$
$138$		0			0
$139$			20.8746i			1.77056i	0.465055	+	0.885282i	$0.346035\pi$
$139$			20.8746i			1.77056i	−0.465055	+	0.885282i	$0.653965\pi$
$140$	2.57431	+	7.06560i	0.217569	+	0.597152i
$141$		0			0
$142$	−8.67739	+	7.52333i	−0.728190	+	0.631344i
$143$	−1.71687	−	2.97371i	−0.143572	−	0.248675i
$144$		0			0
$145$	−4.82221	+	8.35232i	−0.400463	+	0.693622i
$146$	13.3636	+	4.62093i	1.10598	+	0.382431i
$147$		0			0
$148$	−3.15387	+	4.01519i	−0.259247	+	0.330047i
$149$	17.9443	+	10.3601i	1.47005	+	0.848736i	0.999435	−	0.0336002i	$-0.0106973\pi$
$149$	17.9443	+	10.3601i	1.47005	+	0.848736i	0.470619	+	0.882337i	$0.344031\pi$
$150$		0			0
$151$	1.23596	+	2.14074i	0.100581	+	0.174211i	0.911924	−	0.410359i	$-0.134597\pi$
$151$	1.23596	+	2.14074i	0.100581	+	0.174211i	−0.811343	+	0.584570i	$0.801263\pi$
$152$	−0.993608	−	20.4894i	−0.0805923	−	1.66191i
$153$		0			0
$154$	−2.26817	−	2.79163i	−0.182774	−	0.224956i
$155$		−	10.4392i		−	0.838501i
$156$		0			0
$157$	2.59394	−	1.49761i	0.207019	−	0.119522i	−0.392906	−	0.919578i	$-0.628530\pi$
$157$	2.59394	−	1.49761i	0.207019	−	0.119522i	0.599925	+	0.800056i	$0.295197\pi$
$158$	0.0748402	+	0.387712i	0.00595396	+	0.0308447i
$159$		0			0
$160$	−8.00385	−	0.752754i	−0.632760	−	0.0595105i
$161$	−6.79758	−	12.6944i	−0.535724	−	1.00046i
$162$		0			0
$163$	1.95349	+	1.12785i	0.153009	+	0.0883400i	0.574550	−	0.818470i	$-0.305177\pi$
$163$	1.95349	+	1.12785i	0.153009	+	0.0883400i	−0.421541	+	0.906810i	$0.638510\pi$
$164$	−0.624313	+	4.35985i	−0.0487507	+	0.340447i
$165$		0			0
$166$	−6.20108	−	7.15230i	−0.481297	−	0.555126i
$167$	2.45671			0.190106			0.0950529	−	0.995472i	$-0.469698\pi$
$167$	2.45671			0.190106			0.0950529	+	0.995472i	$0.469698\pi$
$168$		0			0
$169$	0.241366			0.0185666
$170$	−6.40021	−	7.38198i	−0.490874	−	0.566172i
$171$		0			0
$172$	−8.82788	−	1.26412i	−0.673120	−	0.0963880i
$173$	7.62911	+	4.40467i	0.580031	+	0.334881i	0.761146	−	0.648581i	$-0.224637\pi$
$173$	7.62911	+	4.40467i	0.580031	+	0.334881i	−0.181115	+	0.983462i	$0.557971\pi$
$174$		0			0
$175$	−7.88128	−	0.252083i	−0.595768	−	0.0190557i
$176$	3.73584	−	0.910820i	0.281599	−	0.0686557i
$177$		0			0
$178$	0.575758	+	2.98273i	0.0431549	+	0.223565i
$179$	12.0819	−	6.97551i	0.903046	−	0.521374i	0.0248589	−	0.999691i	$-0.492086\pi$
$179$	12.0819	−	6.97551i	0.903046	−	0.521374i	0.878187	+	0.478317i	$0.158753\pi$
$180$		0			0
$181$		−	15.7546i		−	1.17103i	−0.810661	−	0.585515i	$-0.800892\pi$
$181$		−	15.7546i		−	1.17103i	0.810661	−	0.585515i	$-0.199108\pi$
$182$	−13.1969	+	2.11226i	−0.978222	+	0.156571i
$183$		0			0
$184$	15.3760	−	0.745642i	1.13354	−	0.0549695i
$185$	1.81399	+	3.14193i	0.133367	+	0.230999i
$186$		0			0
$187$	4.04714	+	2.33662i	0.295956	+	0.170870i
$188$	0.666221	+	0.523307i	0.0485892	+	0.0381661i
$189$		0			0
$190$	−13.7759	−	4.76349i	−0.999410	−	0.345580i
$191$	−6.21677	+	10.7678i	−0.449830	+	0.779128i	−0.998375	−	0.0569933i	$-0.981849\pi$
$191$	−6.21677	+	10.7678i	−0.449830	+	0.779128i	0.548545	+	0.836121i	$0.315182\pi$
$192$		0			0
$193$	2.92875	+	5.07274i	0.210816	+	0.365144i	0.951970	−	0.306191i	$-0.0990546\pi$
$193$	2.92875	+	5.07274i	0.210816	+	0.365144i	−0.741154	+	0.671335i	$0.765721\pi$
$194$	10.0974	−	8.75449i	0.724951	−	0.628536i
$195$		0			0
$196$	−13.3006	+	4.36965i	−0.950043	+	0.312118i
$197$		−	27.5019i		−	1.95943i	−0.200404	−	0.979713i	$-0.564226\pi$
$197$		−	27.5019i		−	1.95943i	0.200404	−	0.979713i	$-0.435774\pi$
$198$		0			0
$199$	11.9106	+	20.6297i	0.844318	+	1.46240i	0.886212	+	0.463280i	$0.153328\pi$
$199$	11.9106	+	20.6297i	0.844318	+	1.46240i	−0.0418939	+	0.999122i	$0.513339\pi$
$200$	3.85632	−	7.49596i	0.272683	−	0.530045i
$201$		0			0
$202$	1.64484	−	4.75683i	0.115730	−	0.334689i
$203$	−15.2547	−	9.47008i	−1.07067	−	0.664670i
$204$		0			0
$205$	2.71029	+	1.56479i	0.189295	+	0.109290i
$206$	−0.331675	−	1.71826i	−0.0231089	−	0.119717i
$207$		0			0
$208$	4.00966	−	13.7135i	0.278020	−	0.950862i
$209$	6.97205			0.482267
$210$		0			0
$211$		−	26.3273i		−	1.81245i	−0.422800	−	0.906223i	$-0.638953\pi$
$211$		−	26.3273i		−	1.81245i	0.422800	−	0.906223i	$-0.361047\pi$
$212$	7.22975	+	18.0292i	0.496541	+	1.23825i
$213$		0			0
$214$	23.1569	−	4.46998i	1.58297	−	0.305562i
$215$	−3.16840	+	5.48784i	−0.216083	+	0.374267i
$216$		0			0
$217$	19.4249	+	0.621308i	1.31865	+	0.0421771i
$218$	−4.72136	+	13.6541i	−0.319771	+	0.924771i
$219$		0			0
$220$	0.387308	−	2.70474i	0.0261123	−	0.182353i
$221$	15.0378	−	8.68207i	1.01155	−	0.584019i
$222$		0			0
$223$	−15.5052			−1.03831			−0.519153	−	0.854681i	$-0.673753\pi$
$223$	−15.5052			−1.03831			−0.519153	+	0.854681i	$0.673753\pi$
$224$	1.87706	−	14.8485i	0.125416	−	0.992104i
$225$		0			0
$226$	13.2539	−	11.4912i	0.881639	−	0.764385i
$227$	1.11618	−	0.644429i	0.0740837	−	0.0427722i	−0.462501	−	0.886619i	$-0.653048\pi$
$227$	1.11618	−	0.644429i	0.0740837	−	0.0427722i	0.536584	+	0.843847i	$0.319714\pi$
$228$		0			0
$229$	2.71834	+	1.56943i	0.179633	+	0.103711i	0.587120	−	0.809500i	$-0.300262\pi$
$229$	2.71834	+	1.56943i	0.179633	+	0.103711i	−0.407487	+	0.913211i	$0.633595\pi$
$230$	3.57471	−	10.3380i	0.235709	−	0.681666i
$231$		0			0
$232$	16.1389	−	10.3913i	1.05957	−	0.682225i
$233$	−2.33320	+	4.04121i	−0.152853	+	0.264749i	−0.932275	−	0.361750i	$-0.882179\pi$
$233$	−2.33320	+	4.04121i	−0.152853	+	0.264749i	0.779422	+	0.626499i	$0.215513\pi$
$234$		0			0
$235$	0.521325	−	0.300987i	0.0340075	−	0.0196342i
$236$	−5.53503	−	13.8030i	−0.360300	−	0.898499i
$237$		0			0
$238$	14.1170	−	11.4699i	0.915071	−	0.743484i
$239$	18.2659			1.18152			0.590762	−	0.806846i	$-0.298827\pi$
$239$	18.2659			1.18152			0.590762	+	0.806846i	$0.298827\pi$
$240$		0			0
$241$	−11.6727	−	20.2178i	−0.751908	−	1.30234i	−0.946897	−	0.321537i	$-0.895801\pi$
$241$	−11.6727	−	20.2178i	−0.751908	−	1.30234i	0.194989	−	0.980805i	$-0.437533\pi$
$242$	−2.70071	−	13.9912i	−0.173609	−	0.899386i
$243$		0			0
$244$	−2.39500	+	3.04907i	−0.153324	+	0.195197i
$245$	−0.635722	+	9.92763i	−0.0406148	+	0.634253i
$246$		0			0
$247$	12.9529	−	22.4350i	0.824171	−	1.42751i
$248$	−9.50465	+	18.4753i	−0.603546	+	1.17318i
$249$		0			0
$250$	−10.5067	−	12.1184i	−0.664502	−	0.766434i
$251$		−	0.893668i		−	0.0564078i	−0.999602	−	0.0282039i	$-0.991021\pi$
$251$		−	0.893668i		−	0.0564078i	0.999602	−	0.0282039i	$-0.00897877\pi$
$252$		0			0
$253$			5.23210i			0.328939i
$254$	−18.5613	+	16.0928i	−1.16464	+	1.00975i
$255$		0			0
$256$	13.4798	+	8.61951i	0.842485	+	0.538719i
$257$	−14.9284	+	25.8568i	−0.931209	+	1.61290i	−0.149952	+	0.988693i	$0.547912\pi$
$257$	−14.9284	+	25.8568i	−0.931209	+	1.61290i	−0.781258	+	0.624209i	$0.785421\pi$
$258$		0			0
$259$	−5.95434	+	3.18841i	−0.369985	+	0.198118i
$260$	−7.98390	−	6.27124i	−0.495140	−	0.388926i
$261$		0			0
$262$	−20.5987	+	3.97617i	−1.27259	+	0.245649i
$263$	0.498465	+	0.863366i	0.0307367	+	0.0532375i	0.880985	−	0.473145i	$-0.156881\pi$
$263$	0.498465	+	0.863366i	0.0307367	+	0.0532375i	−0.850248	+	0.526382i	$0.823548\pi$
$264$		0			0
$265$	13.8026			0.847890
$266$	9.68361	−	25.3502i	0.593740	−	1.55432i
$267$		0			0
$268$	−7.85407	−	19.5861i	−0.479764	−	1.19641i
$269$	−14.3936	+	8.31015i	−0.877593	+	0.506679i	−0.869864	−	0.493291i	$-0.835794\pi$
$269$	−14.3936	+	8.31015i	−0.877593	+	0.506679i	−0.00772927	+	0.999970i	$0.502460\pi$
$270$		0			0
$271$	−3.96742	+	6.87177i	−0.241004	+	0.417430i	−0.961000	−	0.276547i	$-0.910810\pi$
$271$	−3.96742	+	6.87177i	−0.241004	+	0.417430i	0.719997	+	0.693977i	$0.244143\pi$
$272$	4.60593	+	18.8918i	0.279276	+	1.14548i
$273$		0			0
$274$	−18.5249	−	6.40563i	−1.11913	−	0.386978i
$275$	2.48123	+	1.43254i	0.149624	+	0.0863853i
$276$		0			0
$277$	12.3878	−	7.15213i	0.744313	−	0.429730i	−0.0793221	−	0.996849i	$-0.525276\pi$
$277$	12.3878	−	7.15213i	0.744313	−	0.429730i	0.823636	+	0.567119i	$0.191942\pi$
$278$	−19.3386	−	22.3051i	−1.15985	−	1.33777i
$279$		0			0
$280$	−9.29641	−	5.16490i	−0.555567	−	0.308662i
$281$	30.9343			1.84539			0.922694	−	0.385534i	$-0.125983\pi$
$281$	30.9343			1.84539			0.922694	+	0.385534i	$0.125983\pi$
$282$		0			0
$283$	0.109033	−	0.0629502i	0.00648134	−	0.00374200i	−0.496756	−	0.867890i	$-0.665476\pi$
$283$	0.109033	−	0.0629502i	0.00648134	−	0.00374200i	0.503237	+	0.864148i	$0.332142\pi$
$284$	2.30227	−	16.0778i	0.136615	−	0.954040i
$285$		0			0
$286$	4.58943	+	1.58695i	0.271379	+	0.0938384i
$287$	−3.07301	+	4.95008i	−0.181394	+	0.292194i
$288$		0			0
$289$	−3.31605	+	5.74357i	−0.195062	+	0.337857i
$290$	−2.58507	−	13.3921i	−0.151801	−	0.786409i
$291$		0			0
$292$	−18.5603	+	7.44273i	−1.08616	+	0.435553i
$293$		−	11.5096i		−	0.672397i	−0.941791	−	0.336198i	$-0.890859\pi$
$293$		−	11.5096i		−	0.672397i	0.941791	−	0.336198i	$-0.109141\pi$
$294$		0			0
$295$	−10.5672			−0.615245
$296$	−0.349744	−	7.21214i	−0.0203285	−	0.419197i
$297$		0			0
$298$	−28.7718	+	5.55382i	−1.66671	+	0.321724i
$299$	16.8361	+	9.72034i	0.973658	+	0.562142i
$300$		0			0
$301$	−10.0230	−	6.22226i	−0.577715	−	0.358645i
$302$	−3.30387	−	1.14243i	−0.190116	−	0.0657392i
$303$		0			0
$304$	20.0434	+	20.9730i	1.14957	+	1.20288i
$305$	1.37752	+	2.38593i	0.0788765	+	0.136618i
$306$		0			0
$307$		−	18.0146i		−	1.02815i	−0.857745	−	0.514075i	$-0.828135\pi$
$307$		−	18.0146i		−	1.02815i	0.857745	−	0.514075i	$-0.171865\pi$
$308$	5.00982	+	0.881663i	0.285461	+	0.0502374i
$309$		0			0
$310$	9.67111	+	11.1546i	0.549282	+	0.633540i
$311$	1.55812	+	2.69875i	0.0883532	+	0.153032i	0.906815	−	0.421529i	$-0.138506\pi$
$311$	1.55812	+	2.69875i	0.0883532	+	0.153032i	−0.818462	+	0.574561i	$0.805173\pi$
$312$		0			0
$313$	0.726624	−	1.25855i	0.0410712	−	0.0711375i	−0.844759	−	0.535147i	$-0.820256\pi$
$313$	0.726624	−	1.25855i	0.0410712	−	0.0711375i	0.885830	+	0.464009i	$0.153590\pi$
$314$	−1.38428	+	4.00330i	−0.0781193	+	0.225919i
$315$		0			0
$316$	−0.439152	−	0.344948i	−0.0247043	−	0.0194048i
$317$	−15.5731	−	8.99111i	−0.874671	−	0.504991i	−0.00577305	−	0.999983i	$-0.501838\pi$
$317$	−15.5731	−	8.99111i	−0.874671	−	0.504991i	−0.868897	+	0.494992i	$0.835171\pi$
$318$		0			0
$319$	3.26194	+	5.64985i	0.182634	+	0.316331i
$320$	9.24970	−	6.61057i	0.517074	−	0.369542i
$321$		0			0
$322$	19.0238	+	7.26696i	1.06015	+	0.404972i
$323$			35.2570i			1.96175i
$324$		0			0
$325$	9.21939	−	5.32282i	0.511400	−	0.295257i
$326$	−3.13222	+	0.604613i	−0.173478	+	0.0334864i
$327$		0			0
$328$	−3.37195	−	5.23700i	−0.186185	−	0.289165i
$329$	0.529038	+	0.987975i	0.0291668	+	0.0544688i
$330$		0			0
$331$	7.56479	+	4.36753i	0.415798	+	0.240061i	0.693278	−	0.720670i	$-0.256166\pi$
$331$	7.56479	+	4.36753i	0.415798	+	0.240061i	−0.277480	+	0.960731i	$0.589499\pi$
$332$	13.2520	+	1.89764i	0.727300	+	0.104146i
$333$		0			0
$334$	−2.62506	+	2.27594i	−0.143637	+	0.124534i
$335$	−14.9946			−0.819241
$336$		0			0
$337$	7.28406			0.396788			0.198394	−	0.980122i	$-0.436427\pi$
$337$	7.28406			0.396788			0.198394	+	0.980122i	$0.436427\pi$
$338$	−0.257906	+	0.223605i	−0.0140282	+	0.0121625i
$339$		0			0
$340$	13.6776	+	1.95858i	0.741772	+	0.106219i
$341$	−6.11547	−	3.53077i	−0.331171	−	0.191202i
$342$		0			0
$343$	−18.4351	−	1.77378i	−0.995403	−	0.0957754i
$344$	10.6039	−	6.82757i	0.571726	−	0.368118i
$345$		0			0
$346$	−12.2325	+	2.36124i	−0.657622	+	0.126941i
$347$	−0.264838	+	0.152905i	−0.0142173	+	0.00820835i	−0.507092	−	0.861892i	$-0.669279\pi$
$347$	−0.264838	+	0.152905i	−0.0142173	+	0.00820835i	0.492875	+	0.870100i	$0.335946\pi$
$348$		0			0
$349$			6.94160i			0.371575i	0.982590	+	0.185788i	$0.0594837\pi$
$349$			6.94160i			0.371575i	−0.982590	+	0.185788i	$0.940516\pi$
$350$	8.65489	−	7.03200i	0.462623	−	0.375876i
$351$		0			0
$352$	−3.14804	+	4.43418i	−0.167791	+	0.236343i
$353$	−17.9762	−	31.1356i	−0.956775	−	1.65718i	−0.730253	−	0.683176i	$-0.760598\pi$
$353$	−17.9762	−	31.1356i	−0.956775	−	1.65718i	−0.226521	−	0.974006i	$-0.572735\pi$
$354$		0			0
$355$	−9.99472	−	5.77045i	−0.530464	−	0.306264i
$356$	−3.37847	−	2.65374i	−0.179059	−	0.140648i
$357$		0			0
$358$	−6.44764	+	18.6464i	−0.340768	+	0.985495i
$359$	5.85386	−	10.1392i	0.308955	−	0.535126i	−0.669179	−	0.743101i	$-0.733354\pi$
$359$	5.85386	−	10.1392i	0.308955	−	0.535126i	0.978134	+	0.207975i	$0.0666874\pi$
$360$		0			0
$361$	16.8001	+	29.0987i	0.884217	+	1.53151i
$362$	14.5953	+	16.8342i	0.767114	+	0.884787i
$363$		0			0
$364$	12.1445	−	14.4829i	0.636542	−	0.759110i
$365$			14.2093i			0.743747i
$366$		0			0
$367$	−14.9631	−	25.9169i	−0.781068	−	1.35285i	−0.931320	−	0.364202i	$-0.881342\pi$
$367$	−14.9631	−	25.9169i	−0.781068	−	1.35285i	0.150252	−	0.988648i	$-0.451992\pi$
$368$	−15.7389	+	15.0414i	−0.820448	+	0.784085i
$369$		0			0
$370$	−4.84904	−	1.67672i	−0.252090	−	0.0871685i
$371$	−0.821485	+	25.6834i	−0.0426494	+	1.33342i
$372$		0			0
$373$	0.0152179	+	0.00878607i	0.000787954	+	0.000454926i	0.500394	−	0.865798i	$-0.333189\pi$
$373$	0.0152179	+	0.00878607i	0.000787954	+	0.000454926i	−0.499606	+	0.866253i	$0.666522\pi$
$374$	−6.48916	+	1.25260i	−0.335547	+	0.0647706i
$375$		0			0
$376$	−1.19668	+	0.0580314i	−0.0617139	+	0.00299274i
$377$	24.2405			1.24845
$378$		0			0
$379$		−	3.37530i		−	0.173377i	−0.996235	−	0.0866887i	$-0.972371\pi$
$379$		−	3.37530i		−	0.173377i	0.996235	−	0.0866887i	$-0.0276286\pi$
$380$	19.1329	−	7.67233i	0.981498	−	0.393582i
$381$		0			0
$382$	−3.33266	−	17.2650i	−0.170514	−	0.883353i
$383$	5.19747	−	9.00228i	0.265578	−	0.459995i	−0.702137	−	0.712042i	$-0.747770\pi$
$383$	5.19747	−	9.00228i	0.265578	−	0.459995i	0.967715	+	0.252047i	$0.0811038\pi$
$384$		0			0
$385$	1.90641	−	3.07090i	0.0971598	−	0.156508i
$386$	−7.82892	−	2.70712i	−0.398482	−	0.137789i
$387$		0			0
$388$	−2.67903	+	18.7088i	−0.136007	+	0.949797i
$389$	11.8164	−	6.82217i	0.599113	−	0.345898i	−0.169580	−	0.985516i	$-0.554241\pi$
$389$	11.8164	−	6.82217i	0.599113	−	0.345898i	0.768692	+	0.639619i	$0.220908\pi$
$390$		0			0
$391$	−26.4582			−1.33805
$392$	10.1639	−	16.9910i	0.513356	−	0.858176i
$393$		0			0
$394$	25.4782	+	29.3865i	1.28357	+	1.48047i
$395$	−0.343641	+	0.198402i	−0.0172905	+	0.00998266i
$396$		0			0
$397$	18.0104	+	10.3983i	0.903917	+	0.521876i	0.878469	−	0.477800i	$-0.158566\pi$
$397$	18.0104	+	10.3983i	0.903917	+	0.521876i	0.0254477	+	0.999676i	$0.491899\pi$
$398$	−31.8385	−	11.0092i	−1.59592	−	0.551843i
$399$		0			0
$400$	2.82381	+	11.5822i	0.141191	+	0.579110i
$401$	−9.16853	+	15.8804i	−0.457855	+	0.793028i	−0.998847	−	0.0479997i	$-0.984715\pi$
$401$	−9.16853	+	15.8804i	−0.457855	+	0.793028i	0.540993	+	0.841027i	$0.318049\pi$
$402$		0			0
$403$	−22.7230	+	13.1191i	−1.13191	+	0.653510i
$404$	2.64926	+	6.60661i	0.131806	+	0.328691i
$405$		0			0
$406$	25.0733	−	4.01315i	1.24437	−	0.199169i
$407$	2.45412			0.121646
$408$		0			0
$409$	0.0404092	+	0.0699908i	0.00199811	+	0.00346082i	0.867023	−	0.498269i	$-0.166031\pi$
$409$	0.0404092	+	0.0699908i	0.00199811	+	0.00346082i	−0.865025	+	0.501729i	$0.832697\pi$
$410$	−4.34567	+	0.838846i	−0.214617	+	0.0414276i
$411$		0			0
$412$	1.94623	+	1.52873i	0.0958837	+	0.0753153i
$413$	0.628922	−	19.6630i	0.0309472	−	0.967553i
$414$		0			0
$415$	4.75627	−	8.23810i	0.233476	−	0.404392i
$416$	8.42003	+	18.3679i	0.412826	+	0.900560i
$417$		0			0
$418$	−7.44982	+	6.45903i	−0.364383	+	0.315922i
$419$		−	22.5177i		−	1.10006i	−0.835144	−	0.550031i	$-0.814616\pi$
$419$		−	22.5177i		−	1.10006i	0.835144	−	0.550031i	$-0.185384\pi$
$420$		0			0
$421$			24.4058i			1.18947i	0.803923	+	0.594733i	$0.202742\pi$
$421$			24.4058i			1.18947i	−0.803923	+	0.594733i	$0.797258\pi$
$422$	24.3901	+	28.1314i	1.18729	+	1.36942i
$423$		0			0
$424$	−24.4278	−	12.5669i	−1.18632	−	0.610304i
$425$	−7.24421	+	12.5473i	−0.351396	+	0.608635i
$426$		0			0
$427$	−4.52163	+	2.42123i	−0.218817	+	0.117172i
$428$	−20.6027	+	26.2293i	−0.995870	+	1.26784i
$429$		0			0
$430$	−1.69850	−	8.79917i	−0.0819092	−	0.424333i
$431$	−16.8626	−	29.2068i	−0.812241	−	1.40684i	−0.911292	−	0.411760i	$-0.864914\pi$
$431$	−16.8626	−	29.2068i	−0.812241	−	1.40684i	0.0990516	−	0.995082i	$-0.468419\pi$
$432$		0			0
$433$	24.9475			1.19890			0.599449	−	0.800413i	$-0.295386\pi$
$433$	24.9475			1.19890			0.599449	+	0.800413i	$0.295386\pi$
$434$	−21.3317	+	17.3317i	−1.02395	+	0.831950i
$435$		0			0
$436$	−7.60448	−	18.9637i	−0.364189	−	0.908197i
$437$	−34.1849	+	19.7366i	−1.63528	+	0.944131i
$438$		0			0
$439$	1.69821	−	2.94139i	0.0810513	−	0.140385i	−0.822650	−	0.568547i	$-0.807506\pi$
$439$	1.69821	−	2.94139i	0.0810513	−	0.140385i	0.903702	+	0.428162i	$0.140839\pi$
$440$	2.09187	+	3.24890i	0.0997260	+	0.154885i
$441$		0			0
$442$	−8.02506	+	23.2083i	−0.381713	+	1.10391i
$443$	−3.89785	−	2.25043i	−0.185193	−	0.106921i	0.404537	−	0.914521i	$-0.367433\pi$
$443$	−3.89785	−	2.25043i	−0.185193	−	0.106921i	−0.589730	+	0.807600i	$0.700766\pi$
$444$		0			0
$445$	−2.64369	+	1.52634i	−0.125323	+	0.0723552i
$446$	16.5678	−	14.3643i	0.784506	−	0.680170i
$447$		0			0
$448$	11.7502	+	17.6049i	0.555144	+	0.831754i
$449$	−1.45841			−0.0688264			−0.0344132	−	0.999408i	$-0.510956\pi$
$449$	−1.45841			−0.0688264			−0.0344132	+	0.999408i	$0.510956\pi$
$450$		0			0
$451$	1.83336	−	1.05849i	0.0863294	−	0.0498423i
$452$	−3.51651	+	24.5574i	−0.165403	+	1.15508i
$453$		0			0
$454$	−0.595662	+	1.72264i	−0.0279558	+	0.0808476i
$455$	−6.33992	−	11.8398i	−0.297220	−	0.555056i
$456$		0			0
$457$	−13.8539	+	23.9957i	−0.648058	+	1.12247i	0.335528	+	0.942030i	$0.391085\pi$
$457$	−13.8539	+	23.9957i	−0.648058	+	1.12247i	−0.983586	+	0.180439i	$0.942248\pi$
$458$	−4.35857	+	0.841336i	−0.203663	+	0.0393131i
$459$		0			0
$460$	5.75762	+	14.3581i	0.268450	+	0.669449i
$461$		−	16.9591i		−	0.789865i	−0.918710	−	0.394933i	$-0.870768\pi$
$461$		−	16.9591i		−	0.789865i	0.918710	−	0.394933i	$-0.129232\pi$
$462$		0			0
$463$	8.12386			0.377548			0.188774	−	0.982021i	$-0.439549\pi$
$463$	8.12386			0.377548			0.188774	+	0.982021i	$0.439549\pi$
$464$	−7.61808	+	26.0548i	−0.353660	+	1.20956i
$465$		0			0
$466$	−1.25077	−	6.47966i	−0.0579408	−	0.300164i
$467$	−19.8375	−	11.4532i	−0.917972	−	0.529991i	−0.0349845	−	0.999388i	$-0.511138\pi$
$467$	−19.8375	−	11.4532i	−0.917972	−	0.529991i	−0.882988	+	0.469396i	$0.844472\pi$
$468$		0			0
$469$	0.892425	−	27.9013i	0.0412084	−	1.28836i
$470$	−0.278210	+	0.804578i	−0.0128329	+	0.0371124i
$471$		0			0
$472$	18.7017	+	9.62113i	0.860815	+	0.442849i
$473$	2.14324	+	3.71220i	0.0985463	+	0.170687i
$474$		0			0
$475$			21.6154i			0.991783i
$476$	−4.45849	+	25.3342i	−0.204354	+	1.16119i
$477$		0			0
$478$	−19.5176	+	16.9219i	−0.892715	+	0.773988i
$479$	−2.85974	−	4.95322i	−0.130665	−	0.226318i	0.793268	−	0.608872i	$-0.208378\pi$
$479$	−2.85974	−	4.95322i	−0.130665	−	0.226318i	−0.923933	+	0.382554i	$0.875045\pi$
$480$		0			0
$481$	4.55933	−	7.89700i	0.207888	−	0.360072i
$482$	31.2028	+	10.7894i	1.42125	+	0.491444i
$483$		0			0
$484$	15.8474	+	12.4479i	0.720338	+	0.565815i
$485$	11.6303	+	6.71476i	0.528105	+	0.304901i
$486$		0			0
$487$	−11.3841	−	19.7178i	−0.515862	−	0.893499i	−0.999830	−	0.0184136i	$-0.994138\pi$
$487$	−11.3841	−	19.7178i	−0.515862	−	0.893499i	0.483969	−	0.875085i	$-0.339195\pi$
$488$	−0.265590	−	5.47679i	−0.0120227	−	0.247923i
$489$		0			0
$490$	−8.51785	−	11.1969i	−0.384797	−	0.505824i
$491$		−	8.65619i		−	0.390649i	−0.980739	−	0.195324i	$-0.937424\pi$
$491$		−	8.65619i		−	0.390649i	0.980739	−	0.195324i	$-0.0625759\pi$
$492$		0			0
$493$	−28.5708	+	16.4953i	−1.28676	+	0.742912i
$494$	6.94372	+	35.9722i	0.312413	+	1.61847i
$495$		0			0
$496$	−6.95984	−	28.5466i	−0.312506	−	1.28178i
$497$	11.3323	−	18.2543i	0.508322	−	0.818819i
$498$		0			0
$499$	−3.20914	−	1.85280i	−0.143661	−	0.0829426i	0.426447	−	0.904513i	$-0.359765\pi$
$499$	−3.20914	−	1.85280i	−0.143661	−	0.0829426i	−0.570108	+	0.821570i	$0.693098\pi$
$500$	22.4534	+	3.21523i	1.00415	+	0.143789i
$501$		0			0
$502$	0.827910	+	0.954908i	0.0369514	+	0.0426196i
$503$	−10.6986			−0.477028			−0.238514	−	0.971139i	$-0.576660\pi$
$503$	−10.6986			−0.477028			−0.238514	+	0.971139i	$0.576660\pi$
$504$		0			0
$505$	5.05783			0.225070
$506$	−4.84711	−	5.59064i	−0.215480	−	0.248534i
$507$		0			0
$508$	4.92467	−	34.3911i	0.218497	−	1.52586i
$509$	8.03974	+	4.64175i	0.356355	+	0.205742i	0.667481	−	0.744627i	$-0.267373\pi$
$509$	8.03974	+	4.64175i	0.356355	+	0.205742i	−0.311125	+	0.950369i	$0.600706\pi$
$510$		0			0
$511$	−26.4400	−	0.845685i	−1.16964	−	0.0374109i
$512$	−22.3888	+	3.27772i	−0.989453	+	0.144856i
$513$		0			0
$514$	−8.00277	−	41.4586i	−0.352987	−	1.82866i
$515$	1.52294	−	0.879272i	0.0671089	−	0.0387454i
$516$		0			0
$517$		−	0.407200i		−	0.0179087i
$518$	3.40857	−	8.92311i	0.149764	−	0.392059i
$519$		0			0
$520$	14.3408	−	0.695440i	0.628886	−	0.0304971i
$521$	6.29844	+	10.9092i	0.275940	+	0.477942i	0.970372	−	0.241617i	$-0.0776776\pi$
$521$	6.29844	+	10.9092i	0.275940	+	0.477942i	−0.694432	+	0.719558i	$0.744344\pi$
$522$		0			0
$523$	20.1037	+	11.6069i	0.879074	+	0.507534i	0.870353	−	0.492428i	$-0.163891\pi$
$523$	20.1037	+	11.6069i	0.879074	+	0.507534i	0.00872093	+	0.999962i	$0.497224\pi$
$524$	18.3267	−	23.3316i	0.800604	−	1.01925i
$525$		0			0
$526$	−1.33246	−	0.460744i	−0.0580981	−	0.0200894i
$527$	17.8548	−	30.9254i	0.777766	−	1.34713i
$528$		0			0
$529$	−3.31114	−	5.73506i	−0.143963	−	0.249350i
$530$	−14.7485	+	12.7870i	−0.640634	+	0.555432i
$531$		0			0
$532$	13.1377	+	36.0584i	0.569590	+	1.56333i
$533$		−	7.86596i		−	0.340712i
$534$		0			0
$535$	11.8499	+	20.5247i	0.512317	+	0.887359i
$536$	26.5372	+	13.6522i	1.14623	+	0.589683i
$537$		0			0
$538$	7.68128	−	22.2141i	0.331164	−	0.957718i
$539$	5.60075	+	3.73015i	0.241241	+	0.160669i
$540$		0			0
$541$	−0.0793579	−	0.0458173i	−0.00341186	−	0.00196984i	0.498293	−	0.867009i	$-0.333960\pi$
$541$	−0.0793579	−	0.0458173i	−0.00341186	−	0.00196984i	−0.501705	+	0.865039i	$0.667294\pi$
$542$	−2.12684	−	11.0182i	−0.0913555	−	0.473271i
$543$		0			0
$544$	−22.4232	−	15.9194i	−0.961388	−	0.682537i
$545$	−14.5181			−0.621886
$546$		0			0
$547$			17.7752i			0.760015i	0.924983	+	0.380007i	$0.124079\pi$
$547$			17.7752i			0.760015i	−0.924983	+	0.380007i	$0.875921\pi$
$548$	25.7287	−	10.3173i	1.09908	−	0.440731i
$549$		0			0
$550$	−3.97839	+	0.767949i	−0.169639	+	0.0327454i
$551$	−24.6096	+	42.6250i	−1.04840	+	1.81589i
$552$		0			0
$553$	−0.348725	−	0.651243i	−0.0148293	−	0.0276937i
$554$	−6.61089	+	19.1186i	−0.280870	+	0.812270i
$555$		0			0
$556$	41.3277	+	5.91796i	1.75269	+	0.250977i
$557$	4.26326	−	2.46139i	0.180640	−	0.104293i	−0.406953	−	0.913449i	$-0.633409\pi$
$557$	4.26326	−	2.46139i	0.180640	−	0.104293i	0.587593	+	0.809156i	$0.300075\pi$
$558$		0			0
$559$	15.9271			0.673644
$560$	14.7183	−	3.09353i	0.621963	−	0.130725i
$561$		0			0
$562$	−33.0542	+	28.6581i	−1.39431	+	1.20887i
$563$	−14.6661	+	8.46747i	−0.618102	+	0.356862i	−0.776130	−	0.630573i	$-0.782820\pi$
$563$	−14.6661	+	8.46747i	−0.618102	+	0.356862i	0.158028	+	0.987435i	$0.449487\pi$
$564$		0			0
$565$	15.2660	+	8.81385i	0.642247	+	0.370802i
$566$	−0.0581865	+	0.168274i	−0.00244576	+	0.00707309i
$567$		0			0
$568$	12.4347	+	19.3124i	0.521748	+	0.810330i
$569$	10.2382	−	17.7331i	0.429208	−	0.743411i	−0.567595	−	0.823308i	$-0.692126\pi$
$569$	10.2382	−	17.7331i	0.429208	−	0.743411i	0.996803	+	0.0798973i	$0.0254592\pi$
$570$		0			0
$571$	−4.92200	+	2.84172i	−0.205979	+	0.118922i	−0.599441	−	0.800419i	$-0.704611\pi$
$571$	−4.92200	+	2.84172i	−0.205979	+	0.118922i	0.393462	+	0.919341i	$0.371277\pi$
$572$	−6.37411	+	2.55603i	−0.266515	+	0.106873i
$573$		0			0
$574$	−1.30225	−	8.13618i	−0.0543550	−	0.339598i
$575$	−16.2210			−0.676464
$576$		0			0
$577$	−9.12362	−	15.8026i	−0.379821	−	0.657870i	0.611215	−	0.791465i	$-0.290681\pi$
$577$	−9.12362	−	15.8026i	−0.379821	−	0.657870i	−0.991036	+	0.133595i	$0.957348\pi$
$578$	−1.77765	−	9.20920i	−0.0739407	−	0.383052i
$579$		0			0
$580$	15.1689	+	11.9149i	0.629853	+	0.494740i
$581$	15.0461	+	9.34059i	0.624216	+	0.387513i
$582$		0			0
$583$	4.66834	−	8.08580i	0.193343	−	0.334880i
$584$	12.9371	−	25.1474i	0.535343	−	1.04061i
$585$		0			0
$586$	10.6627	+	12.2983i	0.440471	+	0.508038i
$587$		−	3.25244i		−	0.134243i	−0.997745	−	0.0671213i	$-0.978619\pi$
$587$		−	3.25244i		−	0.134243i	0.997745	−	0.0671213i	$-0.0213815\pi$
$588$		0			0
$589$		−	53.2754i		−	2.19517i
$590$	11.2913	−	9.78963i	0.464856	−	0.403033i
$591$		0			0
$592$	7.05517	+	7.38236i	0.289966	+	0.303413i
$593$	10.6829	−	18.5034i	0.438696	−	0.759843i	−0.558894	−	0.829239i	$-0.688774\pi$
$593$	10.6829	−	18.5034i	0.438696	−	0.759843i	0.997589	+	0.0693963i	$0.0221073\pi$
$594$		0			0
$595$	15.5292	+	9.64054i	0.636637	+	0.395224i
$596$	25.5983	−	32.5891i	1.04855	−	1.33490i
$597$		0			0
$598$	−26.9949	+	5.21084i	−1.10391	+	0.213087i
$599$	0.572755	+	0.992041i	0.0234021	+	0.0405337i	0.877489	−	0.479596i	$-0.159217\pi$
$599$	0.572755	+	0.992041i	0.0234021	+	0.0405337i	−0.854087	+	0.520130i	$0.825884\pi$
$600$		0			0
$601$	38.8738			1.58570			0.792848	−	0.609419i	$-0.208597\pi$
$601$	38.8738			1.58570			0.792848	+	0.609419i	$0.208597\pi$
$602$	16.4742	−	2.63682i	0.671440	−	0.107469i
$603$		0			0
$604$	4.58864	−	1.84005i	0.186709	−	0.0748707i
$605$	12.4008	−	7.15960i	0.504164	−	0.291079i
$606$		0			0
$607$	2.80705	−	4.86195i	0.113935	−	0.197341i	−0.803419	−	0.595414i	$-0.796988\pi$
$607$	2.80705	−	4.86195i	0.113935	−	0.197341i	0.917353	+	0.398074i	$0.130321\pi$
$608$	−40.8467	−	3.84159i	−1.65655	−	0.155797i
$609$		0			0
$610$	−3.68228	−	1.27327i	−0.149091	−	0.0515534i
$611$	−1.31031	−	0.756508i	−0.0530095	−	0.0306051i
$612$		0			0
$613$	−34.5018	+	19.9196i	−1.39351	+	0.804545i	−0.993702	−	0.112053i	$-0.964257\pi$
$613$	−34.5018	+	19.9196i	−1.39351	+	0.804545i	−0.399810	+	0.916598i	$0.630924\pi$
$614$	16.6891	+	19.2491i	0.673517	+	0.776832i
$615$		0			0
$616$	−6.16992	+	3.69911i	−0.248593	+	0.149041i
$617$	−8.53231			−0.343498			−0.171749	−	0.985141i	$-0.554942\pi$
$617$	−8.53231			−0.343498			−0.171749	+	0.985141i	$0.554942\pi$
$618$		0			0
$619$	−6.85011	+	3.95491i	−0.275329	+	0.158961i	−0.631307	−	0.775533i	$-0.717481\pi$
$619$	−6.85011	+	3.95491i	−0.275329	+	0.158961i	0.355978	+	0.934494i	$0.384148\pi$
$620$	−20.6677	−	2.95953i	−0.830034	−	0.118857i
$621$		0			0
$622$	−4.16507	−	1.44021i	−0.167004	−	0.0577473i
$623$	−2.68280	−	5.01012i	−0.107484	−	0.200726i
$624$		0			0
$625$	0.607795	−	1.05273i	0.0243118	−	0.0421093i
$626$	0.389526	+	2.01795i	0.0155686	+	0.0806536i
$627$		0			0
$628$	−2.22959	−	5.56006i	−0.0889705	−	0.221870i
$629$			12.4103i			0.494829i
$630$		0			0
$631$	0.418675			0.0166672			0.00833360	−	0.999965i	$-0.497347\pi$
$631$	0.418675			0.0166672			0.00833360	+	0.999965i	$0.497347\pi$
$632$	0.788812	−	0.0382525i	0.0313773	−	0.00152160i
$633$		0			0
$634$	24.9698	−	4.81992i	0.991676	−	0.191423i
$635$	−21.3792	−	12.3433i	−0.848407	−	0.489828i
$636$		0			0
$637$	22.4083	−	11.0924i	0.887849	−	0.439497i
$638$	−8.71960	−	3.01510i	−0.345212	−	0.119369i
$639$		0			0
$640$	−3.75940	+	15.6327i	−0.148603	+	0.617935i
$641$	−8.64934	−	14.9811i	−0.341629	−	0.591718i	0.643107	−	0.765777i	$-0.277645\pi$
$641$	−8.64934	−	14.9811i	−0.341629	−	0.591718i	−0.984735	+	0.174059i	$0.944312\pi$
$642$		0			0
$643$			3.36919i			0.132868i	0.997791	+	0.0664340i	$0.0211622\pi$
$643$			3.36919i			0.132868i	−0.997791	+	0.0664340i	$0.978838\pi$
$644$	−27.0596	+	9.85901i	−1.06630	+	0.388499i
$645$		0			0
$646$	−32.6627	−	37.6730i	−1.28510	−	1.48223i
$647$	7.44102	+	12.8882i	0.292537	+	0.506688i	0.974409	−	0.224783i	$-0.0721673\pi$
$647$	7.44102	+	12.8882i	0.292537	+	0.506688i	−0.681872	+	0.731471i	$0.738834\pi$
$648$		0			0
$649$	−3.57404	+	6.19042i	−0.140293	+	0.242995i
$650$	−4.92002	+	14.2286i	−0.192979	+	0.558091i
$651$		0			0
$652$	2.78674	−	3.54779i	0.109137	−	0.138942i
$653$	−6.62437	−	3.82458i	−0.259232	−	0.149668i	0.364752	−	0.931105i	$-0.381154\pi$
$653$	−6.62437	−	3.82458i	−0.259232	−	0.149668i	−0.623984	+	0.781437i	$0.714487\pi$
$654$		0			0
$655$	−10.5408	−	18.2573i	−0.411865	−	0.713370i
$656$	8.45467	+	2.47204i	0.330099	+	0.0965168i
$657$		0			0
$658$	−1.48057	−	0.565568i	−0.0577186	−	0.0220481i
$659$		−	39.2806i		−	1.53015i	−0.643939	−	0.765077i	$-0.722701\pi$
$659$		−	39.2806i		−	1.53015i	0.643939	−	0.765077i	$-0.277299\pi$
$660$		0			0
$661$	16.6484	−	9.61194i	0.647547	−	0.373861i	−0.139969	−	0.990156i	$-0.544700\pi$
$661$	16.6484	−	9.61194i	0.647547	−	0.373861i	0.787516	+	0.616295i	$0.211367\pi$
$662$	−12.1293	+	2.34133i	−0.471420	+	0.0909983i
$663$		0			0
$664$	−15.9182	+	10.2492i	−0.617744	+	0.397748i
$665$	27.2557	+	0.871774i	1.05693	+	0.0338060i
$666$		0			0
$667$	−31.9875	−	18.4680i	−1.23856	−	0.715083i
$668$	0.696477	−	4.86380i	0.0269475	−	0.188186i
$669$		0			0
$670$	16.0221	−	13.8912i	0.618988	−	0.536665i
$671$	1.86362			0.0719443
$672$		0			0
$673$	−37.7330			−1.45450			−0.727250	−	0.686373i	$-0.759202\pi$
$673$	−37.7330			−1.45450			−0.727250	+	0.686373i	$0.759202\pi$
$674$	−7.78321	+	6.74808i	−0.299798	+	0.259926i
$675$		0			0
$676$	0.0684272	−	0.477857i	0.00263181	−	0.0183791i
$677$	10.7109	+	6.18392i	0.411652	+	0.237667i	0.691499	−	0.722377i	$-0.256951\pi$
$677$	10.7109	+	6.18392i	0.411652	+	0.237667i	−0.279847	+	0.960044i	$0.590284\pi$
$678$		0			0
$679$	−13.1868	+	21.2416i	−0.506061	+	0.815177i
$680$	−16.4293	+	10.5784i	−0.630037	+	0.405662i
$681$		0			0
$682$	9.80552	−	1.89276i	0.375473	−	0.0724775i
$683$	−7.14537	+	4.12538i	−0.273410	+	0.157853i	−0.630436	−	0.776241i	$-0.717124\pi$
$683$	−7.14537	+	4.12538i	−0.273410	+	0.157853i	0.357026	+	0.934094i	$0.383791\pi$
$684$		0			0
$685$		−	19.6971i		−	0.752589i
$686$	21.3417	−	15.1833i	0.814830	−	0.579701i
$687$		0			0
$688$	−5.00541	+	17.1191i	−0.190829	+	0.652660i
$689$	−17.3459	−	30.0441i	−0.660828	−	1.14459i
$690$		0			0
$691$	13.2717	+	7.66244i	0.504880	+	0.291493i	0.730727	−	0.682670i	$-0.239181\pi$
$691$	13.2717	+	7.66244i	0.504880	+	0.291493i	−0.225846	+	0.974163i	$0.572515\pi$
$692$	10.8832	−	13.8554i	0.413719	−	0.526705i
$693$		0			0
$694$	0.141334	−	0.408734i	0.00536495	−	0.0155153i
$695$	14.8329	−	25.6913i	0.562643	−	0.974526i
$696$		0			0
$697$	5.35267	+	9.27110i	0.202747	+	0.351168i
$698$	−6.43082	−	7.41729i	−0.243410	−	0.280749i
$699$		0			0
$700$	−2.73342	+	15.5319i	−0.103313	+	0.587052i
$701$			41.2674i			1.55865i	0.626622	+	0.779324i	$0.284437\pi$
$701$			41.2674i			1.55865i	−0.626622	+	0.779324i	$0.715563\pi$
$702$		0			0
$703$	9.25749	+	16.0344i	0.349153	+	0.604751i
$704$	−0.744137	−	7.65445i	−0.0280457	−	0.288488i
$705$		0			0
$706$	48.0526	+	16.6158i	1.80848	+	0.625345i
$707$	−0.301024	+	9.41141i	−0.0113212	+	0.353952i
$708$		0			0
$709$	−6.38237	−	3.68486i	−0.239695	−	0.138388i	0.375342	−	0.926887i	$-0.377525\pi$
$709$	−6.38237	−	3.68486i	−0.239695	−	0.138388i	−0.615037	+	0.788499i	$0.710859\pi$
$710$	16.0255	−	3.09340i	0.601425	−	0.116093i
$711$		0			0
$712$	6.06846	−	0.294283i	0.227425	−	0.0110287i
$713$	39.9799			1.49726
$714$		0			0
$715$			4.87983i			0.182495i
$716$	−10.3849	−	25.8974i	−0.388103	−	0.967832i
$717$		0			0
$718$	3.13811	+	16.2571i	0.117113	+	0.606710i
$719$	0.151601	−	0.262580i	0.00565375	−	0.00979259i	−0.863185	−	0.504888i	$-0.831534\pi$
$719$	0.151601	−	0.262580i	0.00565375	−	0.00979259i	0.868838	+	0.495096i	$0.164867\pi$
$720$		0			0
$721$	1.54547	+	2.88617i	0.0575565	+	0.107486i
$722$	−44.9089	−	15.5288i	−1.67134	−	0.577921i
$723$		0			0
$724$	−31.1910	−	4.46643i	−1.15921	−	0.165994i
$725$	−17.5162	+	10.1130i	−0.650536	+	0.375587i
$726$		0			0
$727$	9.78796			0.363015			0.181508	−	0.983390i	$-0.441902\pi$
$727$	9.78796			0.363015			0.181508	+	0.983390i	$0.441902\pi$
$728$	0.440533	+	26.7262i	0.0163273	+	0.990539i
$729$		0			0
$730$	−13.1637	−	15.1830i	−0.487211	−	0.561947i
$731$	−18.7722	+	10.8382i	−0.694316	+	0.400864i
$732$		0			0
$733$	−23.6363	−	13.6464i	−0.873026	−	0.504042i	−0.00467329	−	0.999989i	$-0.501488\pi$
$733$	−23.6363	−	13.6464i	−0.873026	−	0.504042i	−0.868353	+	0.495947i	$0.834821\pi$
$734$	39.9983	+	13.8308i	1.47637	+	0.510503i
$735$		0			0
$736$	2.88288	−	30.6529i	0.106264	−	1.12988i
$737$	−5.07148	+	8.78405i	−0.186810	+	0.323565i
$738$		0			0
$739$	−1.81086	+	1.04550i	−0.0666134	+	0.0384593i	−0.532937	−	0.846155i	$-0.678912\pi$
$739$	−1.81086	+	1.04550i	−0.0666134	+	0.0384593i	0.466323	+	0.884614i	$0.345578\pi$
$740$	6.73467	−	2.70062i	0.247572	−	0.0992767i
$741$		0			0
$742$	−22.9158	−	28.2045i	−0.841265	−	1.03542i
$743$	47.9593			1.75945			0.879727	−	0.475479i	$-0.157725\pi$
$743$	47.9593			1.75945			0.879727	+	0.475479i	$0.157725\pi$
$744$		0			0
$745$	−14.7232	−	25.5013i	−0.539416	−	0.934297i
$746$	−0.0244003	+	0.00471000i	−0.000893360	+	0.000172445i
$747$		0			0
$748$	5.77341	−	7.35012i	0.211097	−	0.268747i
$749$	−38.8968	+	20.8283i	−1.42126	+	0.761051i
$750$		0			0
$751$	13.6435	−	23.6313i	0.497859	−	0.862317i	−0.502138	−	0.864788i	$-0.667453\pi$
$751$	13.6435	−	23.6313i	0.497859	−	0.862317i	0.999997	+	0.00247029i	$0.000786318\pi$
$752$	1.22492	−	1.17063i	0.0446682	−	0.0426885i
$753$		0			0
$754$	−25.9017	+	22.4569i	−0.943283	+	0.817830i
$755$		−	3.51293i		−	0.127849i
$756$		0			0
$757$		−	11.9222i		−	0.433320i	−0.976247	−	0.216660i	$-0.930484\pi$
$757$		−	11.9222i		−	0.433320i	0.976247	−	0.216660i	$-0.0695163\pi$
$758$	3.12694	+	3.60660i	0.113575	+	0.130998i
$759$		0			0
$760$	−13.3362	+	25.9232i	−0.483756	+	0.940332i
$761$	−12.9315	+	22.3980i	−0.468767	+	0.811928i	−0.999363	−	0.0356967i	$-0.988635\pi$
$761$	−12.9315	+	22.3980i	−0.468767	+	0.811928i	0.530596	+	0.847625i	$0.321968\pi$
$762$		0			0
$763$	0.864065	−	27.0147i	0.0312812	−	0.977996i
$764$	19.5556	+	15.3607i	0.707497	+	0.555729i
$765$		0			0
$766$	2.78624	+	14.4342i	0.100671	+	0.521529i
$767$	13.2799	+	23.0015i	0.479510	+	0.830535i
$768$		0			0
$769$	1.72326			0.0621423			0.0310712	−	0.999517i	$-0.490108\pi$
$769$	1.72326			0.0621423			0.0310712	+	0.999517i	$0.490108\pi$
$770$	0.807883	+	5.04747i	0.0291141	+	0.181898i
$771$		0			0
$772$	10.8733	−	4.36023i	0.391340	−	0.156928i
$773$	22.4410	−	12.9563i	0.807145	−	0.466005i	−0.0388184	−	0.999246i	$-0.512359\pi$
$773$	22.4410	−	12.9563i	0.807145	−	0.466005i	0.845963	+	0.533241i	$0.179026\pi$
$774$		0			0
$775$	10.9464	−	18.9598i	0.393207	−	0.681055i
$776$	−14.4696	−	22.4728i	−0.519427	−	0.806726i
$777$		0			0
$778$	−6.30591	+	18.2366i	−0.226078	+	0.653812i
$779$	13.8317	+	7.98571i	0.495570	+	0.286118i
$780$		0			0
$781$	−6.76084	+	3.90337i	−0.241922	+	0.139674i
$782$	28.2713	−	24.5114i	1.01098	−	0.876524i
$783$		0			0
$784$	4.88033	+	27.5714i	0.174298	+	0.984693i
$785$	−4.25662			−0.151925
$786$		0			0
$787$	34.3131	−	19.8107i	1.22313	−	0.706174i	0.257546	−	0.966266i	$-0.417086\pi$
$787$	34.3131	−	19.8107i	1.22313	−	0.706174i	0.965584	+	0.260092i	$0.0837529\pi$
$788$	−54.4483	−	7.79678i	−1.93964	−	0.277749i
$789$		0			0
$790$	0.183388	−	0.530353i	0.00652464	−	0.0188691i
$791$	−17.3091	+	27.8819i	−0.615439	+	0.991366i
$792$		0			0
$793$	3.46229	−	5.99686i	0.122949	−	0.212955i
$794$	−28.8778	+	5.57428i	−1.02483	+	0.197824i
$795$		0			0
$796$	44.2195	−	17.7321i	1.56732	−	0.628497i
$797$		−	15.7107i		−	0.556502i	−0.960508	−	0.278251i	$-0.910245\pi$
$797$		−	15.7107i		−	0.556502i	0.960508	−	0.278251i	$-0.0897547\pi$
$798$		0			0
$799$	2.05917			0.0728483
$800$	−13.7473	−	9.75986i	−0.486040	−	0.345063i
$801$		0			0
$802$	−4.91503	−	25.4625i	−0.173556	−	0.899112i
$803$	8.32400	+	4.80587i	0.293748	+	0.169595i
$804$		0			0
$805$	−0.654213	+	20.4537i	−0.0230580	+	0.720899i
$806$	12.1263	−	35.0691i	0.427132	−	1.23526i
$807$		0			0
$808$	−8.95129	−	4.60501i	−0.314905	−	0.162004i
$809$	16.4434	+	28.4809i	0.578121	+	1.00133i	0.995695	+	0.0926918i	$0.0295471\pi$
$809$	16.4434	+	28.4809i	0.578121	+	1.00133i	−0.417574	+	0.908643i	$0.637120\pi$
$810$		0			0
$811$		−	43.5139i		−	1.52798i	−0.645227	−	0.763991i	$-0.723237\pi$
$811$		−	43.5139i		−	1.52798i	0.645227	−	0.763991i	$-0.276763\pi$
$812$	−23.0736	+	27.5165i	−0.809725	+	0.965639i
$813$		0			0
$814$	−2.62229	+	2.27354i	−0.0919114	+	0.0796876i
$815$	−1.60283	−	2.77618i	−0.0561447	−	0.0972455i
$816$		0			0
$817$	−16.1696	+	28.0065i	−0.565701	+	0.979823i
$818$	−0.108019	−	0.0373512i	−0.00377680	−	0.00130596i
$819$		0			0
$820$	3.86635	−	4.92224i	0.135019	−	0.171892i
$821$	−29.4342	−	16.9938i	−1.02726	−	0.593089i	−0.111062	−	0.993814i	$-0.535425\pi$
$821$	−29.4342	−	16.9938i	−1.02726	−	0.593089i	−0.916199	+	0.400725i	$0.868758\pi$
$822$		0			0
$823$	−5.27792	−	9.14163i	−0.183977	−	0.318657i	0.759254	−	0.650794i	$-0.225564\pi$
$823$	−5.27792	−	9.14163i	−0.183977	−	0.318657i	−0.943231	+	0.332137i	$0.892230\pi$
$824$	−3.49584	+	0.169527i	−0.121783	+	0.00590574i
$825$		0			0
$826$	17.5441	+	21.5931i	0.610439	+	0.751320i
$827$		−	7.79584i		−	0.271088i	−0.990771	−	0.135544i	$-0.956722\pi$
$827$		−	7.79584i		−	0.271088i	0.990771	−	0.135544i	$-0.0432782\pi$
$828$		0			0
$829$	−46.7154	+	26.9712i	−1.62249	+	0.936747i	−0.636244	+	0.771488i	$0.719513\pi$
$829$	−46.7154	+	26.9712i	−1.62249	+	0.936747i	−0.986250	+	0.165260i	$0.947154\pi$
$830$	2.54972	+	13.2089i	0.0885021	+	0.458489i
$831$		0			0
$832$	−26.0134	−	11.8261i	−0.901851	−	0.409997i
$833$	−18.8630	+	28.3224i	−0.653564	+	0.981314i
$834$		0			0
$835$	−3.02357	−	1.74566i	−0.104635	−	0.0604111i
$836$	1.97658	−	13.8033i	0.0683613	−	0.477397i
$837$		0			0
$838$	20.8608	+	24.0608i	0.720625	+	0.831167i
$839$	−32.7564			−1.13088			−0.565439	−	0.824790i	$-0.691293\pi$
$839$	−32.7564			−1.13088			−0.565439	+	0.824790i	$0.691293\pi$
$840$		0			0
$841$	−17.0553			−0.588115
$842$	−22.6100	−	26.0783i	−0.779191	−	0.898716i
$843$		0			0
$844$	−52.1229	−	7.46379i	−1.79415	−	0.256914i
$845$	−0.297059	−	0.171507i	−0.0102191	−	0.00590002i
$846$		0			0
$847$	12.5843	+	23.5010i	0.432400	+	0.807505i
$848$	37.7440	−	9.20221i	1.29613	−	0.316005i
$849$		0			0
$850$	−3.88344	−	20.1183i	−0.133201	−	0.690053i
$851$	−12.0329	+	6.94718i	−0.412481	+	0.238146i
$852$		0			0
$853$		−	29.5726i		−	1.01255i	−0.862373	−	0.506274i	$-0.831022\pi$
$853$		−	29.5726i		−	1.01255i	0.862373	−	0.506274i	$-0.168978\pi$
$854$	2.58842	−	6.77607i	0.0885738	−	0.231872i
$855$		0			0
$856$	−2.28471	−	47.1134i	−0.0780897	−	1.61030i
$857$	13.3754	+	23.1669i	0.456895	+	0.791366i	0.998795	−	0.0490772i	$-0.0156281\pi$
$857$	13.3754	+	23.1669i	0.456895	+	0.791366i	−0.541900	+	0.840443i	$0.682295\pi$
$858$		0			0
$859$	1.51398	+	0.874100i	0.0516565	+	0.0298239i	0.525606	−	0.850728i	$-0.323839\pi$
$859$	1.51398	+	0.874100i	0.0516565	+	0.0298239i	−0.473949	+	0.880552i	$0.657172\pi$
$860$	9.96660	+	7.82862i	0.339858	+	0.266954i
$861$		0			0
$862$	45.0758	+	15.5865i	1.53529	+	0.530878i
$863$	−24.1071	+	41.7548i	−0.820617	+	1.42135i	0.0846071	+	0.996414i	$0.473036\pi$
$863$	−24.1071	+	41.7548i	−0.820617	+	1.42135i	−0.905224	+	0.424935i	$0.860297\pi$
$864$		0			0
$865$	−6.25965	−	10.8420i	−0.212834	−	0.368640i
$866$	−26.6570	+	23.1118i	−0.905843	+	0.785370i
$867$		0			0
$868$	6.73704	−	38.2815i	0.228670	−	1.29936i
$869$			0.268414i			0.00910532i
$870$		0			0
$871$	18.8439	+	32.6385i	0.638500	+	1.10591i
$872$	25.6939	+	13.2183i	0.870106	+	0.447628i
$873$		0			0
$874$	18.2431	−	52.7586i	0.617081	−	1.78459i
$875$	25.4931	+	15.8261i	0.861823	+	0.535019i
$876$		0			0
$877$	29.8088	+	17.2101i	1.00657	+	0.581144i	0.910186	−	0.414201i	$-0.135939\pi$
$877$	29.8088	+	17.2101i	1.00657	+	0.581144i	0.0963845	+	0.995344i	$0.469272\pi$
$878$	0.910371	+	4.71621i	0.0307235	+	0.159164i
$879$		0			0
$880$	−5.24505	−	1.53359i	−0.176811	−	0.0516972i
$881$	−53.0365			−1.78685			−0.893423	−	0.449216i	$-0.851703\pi$
$881$	−53.0365			−1.78685			−0.893423	+	0.449216i	$0.851703\pi$
$882$		0			0
$883$			1.90861i			0.0642300i	0.999484	+	0.0321150i	$0.0102243\pi$
$883$			1.90861i			0.0642300i	−0.999484	+	0.0321150i	$0.989776\pi$
$884$	−12.9256	−	32.2332i	−0.434735	−	1.08412i
$885$		0			0
$886$	6.24980	−	1.20640i	0.209966	−	0.0405298i
$887$	28.0441	−	48.5738i	0.941629	−	1.63095i	0.179265	−	0.983801i	$-0.442628\pi$
$887$	28.0441	−	48.5738i	0.941629	−	1.63095i	0.762364	−	0.647148i	$-0.224039\pi$
$888$		0			0
$889$	24.2403	−	39.0469i	0.812993	−	1.30959i
$890$	1.41083	−	4.08009i	0.0472911	−	0.136765i
$891$		0			0
$892$	−4.39573	+	30.6973i	−0.147180	+	1.02782i
$893$	2.66052	−	1.53605i	0.0890308	−	0.0514020i
$894$		0			0
$895$	−19.8263			−0.662721
$896$	−28.8649	−	7.92574i	−0.964309	−	0.264781i
$897$		0			0
$898$	1.55835	−	1.35109i	0.0520027	−	0.0450866i
$899$	43.1721	−	24.9254i	1.43987	−	0.831310i
$900$		0			0
$901$	40.8891	+	23.6073i	1.36221	+	0.786474i
$902$	−0.978388	+	2.82948i	−0.0325767	+	0.0942113i
$903$		0			0
$904$	−18.9929	−	29.4980i	−0.631694	−	0.981088i
$905$	−11.1947	+	19.3899i	−0.372126	+	0.644541i
$906$		0			0
$907$	0.681646	−	0.393549i	0.0226337	−	0.0130676i	−0.488640	−	0.872485i	$-0.662507\pi$
$907$	0.681646	−	0.393549i	0.0226337	−	0.0130676i	0.511274	+	0.859418i	$0.329174\pi$
$908$	−0.959405	−	2.39252i	−0.0318390	−	0.0793986i
$909$		0			0
$910$	17.7429	+	6.77769i	0.588173	+	0.224678i
$911$	−25.5097			−0.845175			−0.422587	−	0.906322i	$-0.638878\pi$
$911$	−25.5097			−0.845175			−0.422587	+	0.906322i	$0.638878\pi$
$912$		0			0
$913$	−3.21734	−	5.57259i	−0.106478	−	0.184426i
$914$	−7.42674	−	38.4745i	−0.245655	−	1.27262i
$915$		0			0
$916$	3.87782	−	4.93685i	0.128127	−	0.163118i
$917$	34.5998	−	18.5274i	1.14258	−	0.611828i
$918$		0			0
$919$	−0.0790741	+	0.136960i	−0.00260841	+	0.00451790i	−0.867327	−	0.497739i	$-0.834164\pi$
$919$	−0.0790741	+	0.136960i	−0.00260841	+	0.00451790i	0.864718	+	0.502257i	$0.167497\pi$
$920$	−19.4538	−	10.0080i	−0.641371	−	0.329955i
$921$		0			0
$922$	15.7112	+	18.1213i	0.517422	+	0.596793i
$923$			29.0072i			0.954783i
$924$		0			0
$925$			7.60850i			0.250166i
$926$	−8.68056	+	7.52609i	−0.285261	+	0.247323i
$927$		0			0
$928$	−15.9975	−	34.8977i	−0.525143	−	1.14557i
$929$	10.9079	−	18.8931i	0.357878	−	0.619862i	−0.629728	−	0.776815i	$-0.716834\pi$
$929$	10.9079	−	18.8931i	0.357878	−	0.619862i	0.987606	+	0.156953i	$0.0501672\pi$
$930$		0			0
$931$	−3.24433	+	50.6644i	−0.106329	+	1.66046i
$932$	7.33935	+	5.76496i	0.240409	+	0.188837i
$933$		0			0
$934$	31.8074	−	6.13979i	1.04077	−	0.200900i
$935$	−3.32066	−	5.75155i	−0.108597	−	0.188096i
$936$		0			0
$937$	21.9184			0.716044			0.358022	−	0.933713i	$-0.383451\pi$
$937$	21.9184			0.716044			0.358022	+	0.933713i	$0.383451\pi$
$938$	24.8947	+	30.6401i	0.812841	+	1.00043i
$939$		0			0
$940$	−0.448100	−	1.11745i	−0.0146154	−	0.0364473i
$941$	46.0309	−	26.5760i	1.50056	−	0.866351i	0.500565	−	0.865699i	$-0.333126\pi$
$941$	46.0309	−	26.5760i	1.50056	−	0.866351i	1.00000		0.000652139i	$-0.000207582\pi$
$942$		0			0
$943$	−5.99279	+	10.3798i	−0.195152	+	0.338013i
$944$	−28.8964	+	7.04513i	−0.940499	+	0.229299i
$945$		0			0
$946$	−5.72916	−	1.98105i	−0.186271	−	0.0644095i
$947$	8.42390	+	4.86354i	0.273740	+	0.158044i	0.630586	−	0.776119i	$-0.282815\pi$
$947$	8.42390	+	4.86354i	0.273740	+	0.158044i	−0.356846	+	0.934163i	$0.616148\pi$
$948$		0			0
$949$	30.9291	−	17.8569i	1.00400	−	0.579661i
$950$	−20.0249	−	23.0966i	−0.649694	−	0.749354i
$951$		0			0
$952$	−18.7060	−	31.2007i	−0.606266	−	1.01122i
$953$	−5.09514			−0.165048			−0.0825239	−	0.996589i	$-0.526298\pi$
$953$	−5.09514			−0.165048			−0.0825239	+	0.996589i	$0.526298\pi$
$954$		0			0
$955$	15.3025	−	8.83489i	0.495177	−	0.285890i
$956$	5.17839	−	36.1629i	0.167481	−	1.16959i
$957$		0			0
$958$	7.64446	+	2.64333i	0.246981	+	0.0854022i
$959$	36.6517	+	1.17231i	1.18354	+	0.0378557i
$960$		0			0
$961$	−11.4796	+	19.8833i	−0.370310	+	0.641396i
$962$	2.44415	+	12.6620i	0.0788025	+	0.408239i
$963$		0			0
$964$	−43.3365	+	17.3780i	−1.39577	+	0.559708i
$965$		−	8.32431i		−	0.267969i
$966$		0			0
$967$	38.9910			1.25387			0.626933	−	0.779073i	$-0.284310\pi$
$967$	38.9910			1.25387			0.626933	+	0.779073i	$0.284310\pi$
$968$	−28.4654	+	1.38040i	−0.914913	+	0.0443676i
$969$		0			0
$970$	−18.6480	+	3.59962i	−0.598750	+	0.115577i
$971$	34.4205	+	19.8727i	1.10461	+	0.637746i	0.937427	−	0.348181i	$-0.113200\pi$
$971$	34.4205	+	19.8727i	1.10461	+	0.637746i	0.167181	+	0.985926i	$0.446534\pi$
$972$		0			0
$973$	46.9226	+	29.1295i	1.50427	+	0.933849i
$974$	30.4311	+	10.5226i	0.975076	+	0.337166i
$975$		0			0
$976$	5.35758	+	5.60605i	0.171492	+	0.179445i
$977$	−21.7445	−	37.6625i	−0.695667	−	1.20493i	−0.969955	−	0.243284i	$-0.921775\pi$
$977$	−21.7445	−	37.6625i	−0.695667	−	1.20493i	0.274288	−	0.961648i	$-0.411558\pi$
$978$		0			0
$979$			2.06495i			0.0659962i
$980$	19.4746	+	4.07309i	0.622092	+	0.130110i
$981$		0			0
$982$	8.01925	+	9.24938i	0.255905	+	0.295159i
$983$	17.3291	+	30.0149i	0.552713	+	0.957327i	0.998078	+	0.0619779i	$0.0197408\pi$
$983$	17.3291	+	30.0149i	0.552713	+	0.957327i	−0.445364	+	0.895349i	$0.646926\pi$
$984$		0			0
$985$	−19.5420	+	33.8477i	−0.622659	+	1.07848i
$986$	15.2471	−	44.0942i	0.485565	−	1.40424i
$987$		0			0
$988$	−40.7448	−	32.0045i	−1.29627	−	1.01820i
$989$	−21.0172	−	12.1343i	−0.668307	−	0.385847i
$990$		0			0
$991$	15.4425	+	26.7473i	0.490548	+	0.849655i	0.999941	−	0.0108797i	$-0.00346317\pi$
$991$	15.4425	+	26.7473i	0.490548	+	0.849655i	−0.509392	+	0.860534i	$0.670130\pi$
$992$	33.8829	+	24.0551i	1.07578	+	0.763750i
$993$		0			0
$994$	4.80230	+	30.0037i	0.152320	+	0.951659i
$995$		−	33.8531i		−	1.07322i
$996$		0			0
$997$	−29.4376	+	16.9958i	−0.932297	+	0.538262i	−0.887537	−	0.460736i	$-0.847586\pi$
$997$	−29.4376	+	16.9958i	−0.932297	+	0.538262i	−0.0447599	+	0.998998i	$0.514252\pi$
$998$	5.14551	−	0.993239i	0.162878	−	0.0314404i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.4		32
3.2	odd	2		168.2.bc.a.37.13	yes	32
4.3	odd	2		2016.2.cr.e.1297.6		32
7.4	even	3	inner	504.2.cj.e.109.8		32
8.3	odd	2		2016.2.cr.e.1297.11		32
8.5	even	2	inner	504.2.cj.e.37.8		32
12.11	even	2		672.2.bk.a.625.14		32
21.2	odd	6		1176.2.c.e.589.3		16
21.5	even	6		1176.2.c.f.589.3		16
21.11	odd	6		168.2.bc.a.109.9	yes	32
24.5	odd	2		168.2.bc.a.37.9	✓	32
24.11	even	2		672.2.bk.a.625.3		32
28.11	odd	6		2016.2.cr.e.1873.11		32
56.11	odd	6		2016.2.cr.e.1873.6		32
56.53	even	6	inner	504.2.cj.e.109.4		32
84.11	even	6		672.2.bk.a.529.3		32
84.23	even	6		4704.2.c.e.2353.11		16
84.47	odd	6		4704.2.c.f.2353.6		16
168.5	even	6		1176.2.c.f.589.4		16
168.11	even	6		672.2.bk.a.529.14		32
168.53	odd	6		168.2.bc.a.109.13	yes	32
168.107	even	6		4704.2.c.e.2353.6		16
168.131	odd	6		4704.2.c.f.2353.11		16
168.149	odd	6		1176.2.c.e.589.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.9	✓	32	24.5	odd	2
168.2.bc.a.37.13	yes	32	3.2	odd	2
168.2.bc.a.109.9	yes	32	21.11	odd	6
168.2.bc.a.109.13	yes	32	168.53	odd	6
504.2.cj.e.37.4		32	1.1	even	1	trivial
504.2.cj.e.37.8		32	8.5	even	2	inner
504.2.cj.e.109.4		32	56.53	even	6	inner
504.2.cj.e.109.8		32	7.4	even	3	inner
672.2.bk.a.529.3		32	84.11	even	6
672.2.bk.a.529.14		32	168.11	even	6
672.2.bk.a.625.3		32	24.11	even	2
672.2.bk.a.625.14		32	12.11	even	2
1176.2.c.e.589.3		16	21.2	odd	6
1176.2.c.e.589.4		16	168.149	odd	6
1176.2.c.f.589.3		16	21.5	even	6
1176.2.c.f.589.4		16	168.5	even	6
2016.2.cr.e.1297.6		32	4.3	odd	2
2016.2.cr.e.1297.11		32	8.3	odd	2
2016.2.cr.e.1873.6		32	56.11	odd	6
2016.2.cr.e.1873.11		32	28.11	odd	6
4704.2.c.e.2353.6		16	168.107	even	6
4704.2.c.e.2353.11		16	84.23	even	6
4704.2.c.f.2353.6		16	84.47	odd	6
4704.2.c.f.2353.11		16	168.131	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.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06853 + 0.926418i) q^{2} +(0.283500 - 1.97980i) q^{4} +(-1.23074 - 0.710569i) q^{5} +(1.39545 - 2.24783i) q^{7} +(1.53120 + 2.37811i) q^{8} +O(q^{10})\)	\(q+(-1.06853 + 0.926418i) q^{2} +(0.283500 - 1.97980i) q^{4} +(-1.23074 - 0.710569i) q^{5} +(1.39545 - 2.24783i) q^{7} +(1.53120 + 2.37811i) q^{8} +(1.97336 - 0.380919i) q^{10} +(-0.832525 + 0.480658i) q^{11} +3.57192i q^{13} +(0.591351 + 3.69463i) q^{14} +(-3.83926 - 1.12255i) q^{16} +(-2.43064 - 4.21000i) q^{17} +(-6.28094 - 3.62630i) q^{19} +(-1.75570 + 2.23518i) q^{20} +(0.444285 - 1.28486i) q^{22} +(2.72132 - 4.71346i) q^{23} +(-1.49018 - 2.58107i) q^{25} +(-3.30909 - 3.81670i) q^{26} +(-4.05465 - 3.39998i) q^{28} -6.78641i q^{29} +(3.67285 + 6.36156i) q^{31} +(5.14230 - 2.35728i) q^{32} +(6.49742 + 2.24670i) q^{34} +(-3.31467 + 1.77493i) q^{35} +(-2.21085 - 1.27644i) q^{37} +(10.0708 - 1.94397i) q^{38} +(-0.194696 - 4.01487i) q^{40} -2.20216 q^{41} -4.45897i q^{43} +(0.715589 + 1.78450i) q^{44} +(1.45883 + 7.55754i) q^{46} +(-0.211793 + 0.366836i) q^{47} +(-3.10544 - 6.27345i) q^{49} +(3.98345 + 1.37741i) q^{50} +(7.07171 + 1.01264i) q^{52} +(-8.41117 + 4.85619i) q^{53} +1.36616 q^{55} +(7.48230 - 0.123332i) q^{56} +(6.28705 + 7.25146i) q^{58} +(6.43952 - 3.71786i) q^{59} +(-1.67889 - 0.969306i) q^{61} +(-9.81800 - 3.39491i) q^{62} +(-3.31086 + 7.28273i) q^{64} +(2.53810 - 4.39612i) q^{65} +(9.13752 - 5.27555i) q^{67} +(-9.02406 + 3.61867i) q^{68} +(1.89749 - 4.96733i) q^{70} +8.12089 q^{71} +(-4.99925 - 8.65896i) q^{73} +(3.54487 - 0.684267i) q^{74} +(-8.96001 + 11.4070i) q^{76} +(-0.0813093 + 2.54211i) q^{77} +(0.139607 - 0.241807i) q^{79} +(3.92748 + 4.10963i) q^{80} +(2.35307 - 2.04012i) q^{82} +6.69361i q^{83} +6.90856i q^{85} +(4.13087 + 4.76453i) q^{86} +(-2.41782 - 1.24386i) q^{88} +(1.07402 - 1.86026i) q^{89} +(8.02906 + 4.98444i) q^{91} +(-8.56024 - 6.72394i) q^{92} +(-0.113537 - 0.588183i) q^{94} +(5.15348 + 8.92608i) q^{95} -9.44983 q^{97} +(9.13009 + 3.82642i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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