LMFDB - Embedded newform 639.2.z.a.269.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			269.22
Character	$\chi$	$=$	639.269
Dual form			639.2.z.a.620.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16212 + 0.924133i) q^{2} +(2.43861 + 2.55058i) q^{4} +(2.31285 + 0.751492i) q^{5} +(-0.903009 - 1.03358i) q^{7} +(1.26307 + 3.36545i) q^{8} +O(q^{10})$	\(q+(2.16212 + 0.924133i) q^{2} +(2.43861 + 2.55058i) q^{4} +(2.31285 + 0.751492i) q^{5} +(-0.903009 - 1.03358i) q^{7} +(1.26307 + 3.36545i) q^{8} +(4.30618 + 3.76220i) q^{10} +(0.807261 - 0.222790i) q^{11} +(-0.838870 + 3.03958i) q^{13} +(-0.997248 - 3.06921i) q^{14} +(-0.0625732 + 1.39330i) q^{16} +(0.263640 - 0.191546i) q^{17} +(-0.510487 - 0.948645i) q^{19} +(3.72340 + 7.73171i) q^{20} +(1.95128 + 0.264319i) q^{22} +(0.341423 - 1.49587i) q^{23} +(0.739466 + 0.537253i) q^{25} +(-4.62271 + 5.79669i) q^{26} +(0.434139 - 4.82368i) q^{28} +(-6.01748 + 0.815123i) q^{29} +(-1.18117 + 0.0530465i) q^{31} +(1.69644 - 3.52270i) q^{32} +(0.747035 - 0.170506i) q^{34} +(-1.31180 - 3.06911i) q^{35} +(1.50650 + 6.60042i) q^{37} +(-0.227060 - 2.52284i) q^{38} +(0.392199 + 8.73298i) q^{40} +(-5.40826 - 6.78174i) q^{41} +(5.56991 + 0.501301i) q^{43} +(2.53683 + 1.51569i) q^{44} +(2.12058 - 2.91873i) q^{46} +(2.55873 - 0.464340i) q^{47} +(0.686777 - 5.06999i) q^{49} +(1.10232 + 1.84497i) q^{50} +(-9.79836 + 5.27272i) q^{52} +(-7.47931 + 7.82275i) q^{53} +(2.03450 + 0.0913695i) q^{55} +(2.33788 - 4.34451i) q^{56} +(-13.7638 - 3.79856i) q^{58} +(-5.77672 - 8.75135i) q^{59} +(1.54659 - 1.77021i) q^{61} +(-2.60285 - 0.976868i) q^{62} +(9.02399 - 7.88402i) q^{64} +(-4.22440 + 6.39969i) q^{65} +(-0.181537 + 0.173567i) q^{67} +(1.13147 + 0.205331i) q^{68} -7.84807i q^{70} +(-8.40781 + 0.555642i) q^{71} +(-1.91457 + 4.47935i) q^{73} +(-2.84243 + 15.6631i) q^{74} +(1.17472 - 3.61541i) q^{76} +(-0.959234 - 0.633185i) q^{77} +(16.2379 - 6.09419i) q^{79} +(-1.19178 + 3.17548i) q^{80} +(-5.42605 - 19.6609i) q^{82} +(-2.31270 + 1.52660i) q^{83} +(0.753706 - 0.244894i) q^{85} +(11.5795 + 6.23121i) q^{86} +(1.76942 + 2.43539i) q^{88} +(2.87840 + 2.75203i) q^{89} +(3.89914 - 1.87773i) q^{91} +(4.64793 - 2.77701i) q^{92} +(5.96138 + 1.36065i) q^{94} +(-0.467784 - 2.57770i) q^{95} +(2.13474 + 1.70240i) q^{97} +(6.17024 - 10.3272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{19}{70}\right)$	$-1$

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 $

$2$	2.16212	+	0.924133i	1.52885	+	0.653461i	0.982864	−	0.184334i	$-0.0590129\pi$
$2$	2.16212	+	0.924133i	1.52885	+	0.653461i	0.545984	+	0.837795i	$0.316156\pi$
$3$		0			0
$3$		0			0
$4$	2.43861	+	2.55058i	1.21930	+	1.27529i
$5$	2.31285	+	0.751492i	1.03434	+	0.336077i	0.776504	−	0.630112i	$-0.216991\pi$
$5$	2.31285	+	0.751492i	1.03434	+	0.336077i	0.257835	+	0.966189i	$0.416991\pi$
$6$		0			0
$7$	−0.903009	−	1.03358i	−0.341305	−	0.390655i	0.556646	−	0.830750i	$-0.312088\pi$
$7$	−0.903009	−	1.03358i	−0.341305	−	0.390655i	−0.897952	+	0.440094i	$0.854945\pi$
$8$	1.26307	+	3.36545i	0.446564	+	1.18987i
$9$		0			0
$10$	4.30618	+	3.76220i	1.36173	+	1.18971i
$11$	0.807261	−	0.222790i	0.243398	−	0.0671736i	−0.142209	−	0.989837i	$-0.545421\pi$
$11$	0.807261	−	0.222790i	0.243398	−	0.0671736i	0.385607	+	0.922663i	$0.373992\pi$
$12$		0			0
$13$	−0.838870	+	3.03958i	−0.232661	+	0.843027i	0.750590	+	0.660768i	$0.229769\pi$
$13$	−0.838870	+	3.03958i	−0.232661	+	0.843027i	−0.983251	+	0.182259i	$0.941659\pi$
$14$	−0.997248	−	3.06921i	−0.266526	−	0.820282i
$15$		0			0
$16$	−0.0625732	+	1.39330i	−0.0156433	+	0.348325i
$17$	0.263640	−	0.191546i	0.0639421	−	0.0464567i	−0.555355	−	0.831613i	$-0.687418\pi$
$17$	0.263640	−	0.191546i	0.0639421	−	0.0464567i	0.619297	+	0.785157i	$0.287418\pi$
$18$		0			0
$19$	−0.510487	−	0.948645i	−0.117114	−	0.217634i	0.815289	−	0.579054i	$-0.196578\pi$
$19$	−0.510487	−	0.948645i	−0.117114	−	0.217634i	−0.932403	+	0.361420i	$0.882292\pi$
$20$	3.72340	+	7.73171i	0.832577	+	1.72886i
$21$		0			0
$22$	1.95128	+	0.264319i	0.416014	+	0.0563530i
$23$	0.341423	−	1.49587i	0.0711915	−	0.311910i	−0.926778	−	0.375611i	$-0.877433\pi$
$23$	0.341423	−	1.49587i	0.0711915	−	0.311910i	0.997969	+	0.0637002i	$0.0202901\pi$
$24$		0			0
$25$	0.739466	+	0.537253i	0.147893	+	0.107451i
$26$	−4.62271	+	5.79669i	−0.906588	+	1.13683i
$27$		0			0
$28$	0.434139	−	4.82368i	0.0820446	−	0.911590i
$29$	−6.01748	+	0.815123i	−1.11742	+	0.151365i	−0.669573	−	0.742747i	$-0.733523\pi$
$29$	−6.01748	+	0.815123i	−1.11742	+	0.151365i	−0.447845	+	0.894111i	$0.647808\pi$
$30$		0			0
$31$	−1.18117	+	0.0530465i	−0.212145	+	0.00952743i	−0.150684	−	0.988582i	$-0.548147\pi$
$31$	−1.18117	+	0.0530465i	−0.212145	+	0.00952743i	−0.0614612	+	0.998109i	$0.519576\pi$
$32$	1.69644	−	3.52270i	0.299892	−	0.622732i
$33$		0			0
$34$	0.747035	−	0.170506i	0.128115	−	0.0292415i
$35$	−1.31180	−	3.06911i	−0.221735	−	0.518775i
$36$		0			0
$37$	1.50650	+	6.60042i	0.247668	+	1.08510i	0.933848	+	0.357671i	$0.116429\pi$
$37$	1.50650	+	6.60042i	0.247668	+	1.08510i	−0.686180	+	0.727432i	$0.740714\pi$
$38$	−0.227060	−	2.52284i	−0.0368339	−	0.409259i
$39$		0			0
$40$	0.392199	+	8.73298i	0.0620120	+	1.38081i
$41$	−5.40826	−	6.78174i	−0.844628	−	1.05913i	−0.997485	−	0.0708812i	$-0.977419\pi$
$41$	−5.40826	−	6.78174i	−0.844628	−	1.05913i	0.152857	−	0.988248i	$-0.451153\pi$
$42$		0			0
$43$	5.56991	+	0.501301i	0.849403	+	0.0764477i	0.505783	−	0.862661i	$-0.331204\pi$
$43$	5.56991	+	0.501301i	0.849403	+	0.0764477i	0.343621	+	0.939109i	$0.388347\pi$
$44$	2.53683	+	1.51569i	0.382442	+	0.228498i
$45$		0			0
$46$	2.12058	−	2.91873i	0.312662	−	0.430343i
$47$	2.55873	−	0.464340i	0.373229	−	0.0677310i	0.0112983	−	0.999936i	$-0.496404\pi$
$47$	2.55873	−	0.464340i	0.373229	−	0.0677310i	0.361930	+	0.932205i	$0.382118\pi$
$48$		0			0
$49$	0.686777	−	5.06999i	0.0981110	−	0.724284i
$50$	1.10232	+	1.84497i	0.155891	+	0.260918i
$51$		0			0
$52$	−9.79836	+	5.27272i	−1.35879	+	0.731195i
$53$	−7.47931	+	7.82275i	−1.02736	+	1.07454i	−0.0301784	+	0.999545i	$0.509608\pi$
$53$	−7.47931	+	7.82275i	−1.02736	+	1.07454i	−0.997184	+	0.0749924i	$0.976107\pi$
$54$		0			0
$55$	2.03450	+	0.0913695i	0.274332	+	0.0123203i
$56$	2.33788	−	4.34451i	0.312413	−	0.580560i
$57$		0			0
$58$	−13.7638	−	3.79856i	−1.80727	−	0.498776i
$59$	−5.77672	−	8.75135i	−0.752065	−	1.13933i	−0.985946	−	0.167064i	$-0.946571\pi$
$59$	−5.77672	−	8.75135i	−0.752065	−	1.13933i	0.233881	−	0.972265i	$-0.424857\pi$
$60$		0			0
$61$	1.54659	−	1.77021i	0.198020	−	0.226652i	−0.645486	−	0.763772i	$-0.723345\pi$
$61$	1.54659	−	1.77021i	0.198020	−	0.226652i	0.843506	+	0.537120i	$0.180488\pi$
$62$	−2.60285	−	0.976868i	−0.330563	−	0.124062i
$63$		0			0
$64$	9.02399	−	7.88402i	1.12800	−	0.985503i
$65$	−4.22440	+	6.39969i	−0.523972	+	0.793784i
$66$		0			0
$67$	−0.181537	+	0.173567i	−0.0221783	+	0.0212046i	−0.702070	−	0.712107i	$-0.747741\pi$
$67$	−0.181537	+	0.173567i	−0.0221783	+	0.0212046i	0.679892	+	0.733312i	$0.262027\pi$
$68$	1.13147	+	0.205331i	0.137211	+	0.0249000i
$69$		0			0
$70$		−	7.84807i		−	0.938023i
$71$	−8.40781	+	0.555642i	−0.997823	+	0.0659426i
$71$	−8.40781	+	0.555642i	−0.997823	+	0.0659426i
$72$		0			0
$73$	−1.91457	+	4.47935i	−0.224083	+	0.524269i	−0.993414	−	0.114582i	$-0.963447\pi$
$73$	−1.91457	+	4.47935i	−0.224083	+	0.524269i	0.769331	+	0.638851i	$0.220590\pi$
$74$	−2.84243	+	15.6631i	−0.330426	+	1.82080i
$75$		0			0
$76$	1.17472	−	3.61541i	0.134749	−	0.414716i
$77$	−0.959234	−	0.633185i	−0.109315	−	0.0721581i
$78$		0			0
$79$	16.2379	−	6.09419i	1.82691	−	0.685650i	0.836413	−	0.548099i	$-0.184648\pi$
$79$	16.2379	−	6.09419i	1.82691	−	0.685650i	0.990495	−	0.137551i	$-0.0439231\pi$
$80$	−1.19178	+	3.17548i	−0.133245	+	0.355029i
$81$		0			0
$82$	−5.42605	−	19.6609i	−0.599207	−	2.17118i
$83$	−2.31270	+	1.52660i	−0.253852	+	0.167566i	−0.671415	−	0.741082i	$-0.734313\pi$
$83$	−2.31270	+	1.52660i	−0.253852	+	0.167566i	0.417562	+	0.908648i	$0.362884\pi$
$84$		0			0
$85$	0.753706	−	0.244894i	0.0817509	−	0.0265625i
$86$	11.5795	+	6.23121i	1.24865	+	0.671929i
$87$		0			0
$88$	1.76942	+	2.43539i	0.188621	+	0.259614i
$89$	2.87840	+	2.75203i	0.305109	+	0.291714i	0.828049	−	0.560655i	$-0.189451\pi$
$89$	2.87840	+	2.75203i	0.305109	+	0.291714i	−0.522940	+	0.852369i	$0.675165\pi$
$90$		0			0
$91$	3.89914	−	1.87773i	0.408741	−	0.196839i
$92$	4.64793	−	2.77701i	0.484580	−	0.289523i
$93$		0			0
$94$	5.96138	+	1.36065i	0.614869	+	0.140340i
$95$	−0.467784	−	2.57770i	−0.0479936	−	0.264467i
$96$		0			0
$97$	2.13474	+	1.70240i	0.216750	+	0.172852i	0.725846	−	0.687858i	$-0.241449\pi$
$97$	2.13474	+	1.70240i	0.216750	+	0.172852i	−0.509096	+	0.860710i	$0.670020\pi$
$98$	6.17024	−	10.3272i	0.623288	−	1.04321i
$99$		0			0
$100$	0.432957	+	3.19621i	0.0432957	+	0.319621i
$101$	−6.85335	+	5.46536i	−0.681934	+	0.543824i	−0.902040	−	0.431652i	$-0.857931\pi$
$101$	−6.85335	+	5.46536i	−0.681934	+	0.543824i	0.220107	+	0.975476i	$0.429359\pi$
$102$		0			0
$103$	7.45849	+	3.59182i	0.734907	+	0.353913i	0.763612	−	0.645675i	$-0.223424\pi$
$103$	7.45849	+	3.59182i	0.734907	+	0.353913i	−0.0287049	+	0.999588i	$0.509138\pi$
$104$	−11.2891	+	1.01604i	−1.10699	+	0.0996306i
$105$		0			0
$106$	−23.4004	+	10.0018i	−2.27285	+	0.971462i
$107$	11.0702	−	4.73163i	1.07020	−	0.457424i	0.215474	−	0.976510i	$-0.430870\pi$
$107$	11.0702	−	4.73163i	1.07020	−	0.457424i	0.854722	+	0.519086i	$0.173728\pi$
$108$		0			0
$109$	5.95552	−	0.536006i	0.570435	−	0.0513401i	0.199333	−	0.979932i	$-0.436123\pi$
$109$	5.95552	−	0.536006i	0.570435	−	0.0513401i	0.371103	+	0.928592i	$0.378980\pi$
$110$	4.31439	+	2.07770i	0.411361	+	0.198101i
$111$		0			0
$112$	1.49659	−	1.19349i	0.141414	−	0.112774i
$113$	−1.41868	−	10.4731i	−0.133459	−	0.985231i	−0.926561	−	0.376143i	$-0.877250\pi$
$113$	−1.41868	−	10.4731i	−0.133459	−	0.985231i	0.793103	−	0.609088i	$-0.208464\pi$
$114$		0			0
$115$	1.91379	−	3.20315i	0.178462	−	0.298695i
$116$	−16.7533	−	13.3603i	−1.55550	−	1.24047i
$117$		0			0
$118$	−4.40253	−	24.2599i	−0.405285	−	2.23331i
$119$	−0.436047	−	0.0995248i	−0.0399723	−	0.00912342i
$120$		0			0
$121$	−8.84090	+	5.28219i	−0.803718	+	0.480199i
$122$	4.97981	−	2.39815i	0.450851	−	0.217118i
$123$		0			0
$124$	−3.01571	−	2.88332i	−0.270819	−	0.258929i
$125$	−5.84058	−	8.03886i	−0.522397	−	0.719018i
$126$		0			0
$127$	−9.71860	−	5.22980i	−0.862386	−	0.464070i	−0.0180209	−	0.999838i	$-0.505737\pi$
$127$	−9.71860	−	5.22980i	−0.862386	−	0.464070i	−0.844365	+	0.535768i	$0.820022\pi$
$128$	19.3597	−	6.29036i	1.71117	−	0.555994i
$129$		0			0
$130$	−15.0478	+	9.93298i	−1.31978	+	0.871180i
$131$	2.31617	+	8.39244i	0.202364	+	0.733251i	0.992703	+	0.120581i	$0.0384758\pi$
$131$	2.31617	+	8.39244i	0.202364	+	0.733251i	−0.790339	+	0.612670i	$0.790096\pi$
$132$		0			0
$133$	−0.519522	+	1.38426i	−0.0450483	+	0.120031i
$134$	−0.552904	+	0.207508i	−0.0477637	+	0.0179260i
$135$		0			0
$136$	0.977635	+	0.645331i	0.0838315	+	0.0553367i
$137$	6.26568	−	19.2838i	0.535313	−	1.64753i	−0.207658	−	0.978202i	$-0.566584\pi$
$137$	6.26568	−	19.2838i	0.535313	−	1.64753i	0.742971	−	0.669324i	$-0.233416\pi$
$138$		0			0
$139$	−3.51281	+	19.3572i	−0.297953	+	1.64185i	0.393422	+	0.919358i	$0.371291\pi$
$139$	−3.51281	+	19.3572i	−0.297953	+	1.64185i	−0.691375	+	0.722496i	$0.742995\pi$
$140$	4.62906	−	10.8302i	0.391227	−	0.915320i
$141$		0			0
$142$	−18.6922	−	6.56858i	−1.56861	−	0.551223i
$143$			2.64062i			0.220820i
$144$		0			0
$145$	−14.5301	−	2.63683i	−1.20666	−	0.218976i
$146$	−8.27904	+	7.91557i	−0.685178	+	0.655098i
$147$		0			0
$148$	−13.1611	+	19.9383i	−1.08184	+	1.63892i
$149$	−3.36798	+	2.94252i	−0.275916	+	0.241060i	−0.784762	−	0.619797i	$-0.787215\pi$
$149$	−3.36798	+	2.94252i	−0.275916	+	0.241060i	0.508847	+	0.860857i	$0.330072\pi$
$150$		0			0
$151$	1.39503	+	0.523563i	0.113526	+	0.0426069i	0.407491	−	0.913209i	$-0.366404\pi$
$151$	1.39503	+	0.523563i	0.113526	+	0.0426069i	−0.293966	+	0.955816i	$0.594975\pi$
$152$	2.54783	−	2.91623i	0.206656	−	0.236537i
$153$		0			0
$154$	−1.48883	−	2.25548i	−0.119973	−	0.181752i
$155$	−2.77174	−	0.764952i	−0.222632	−	0.0614424i
$156$		0			0
$157$	−8.75068	+	16.2615i	−0.698380	+	1.29781i	0.246101	+	0.969244i	$0.420850\pi$
$157$	−8.75068	+	16.2615i	−0.698380	+	1.29781i	−0.944482	+	0.328564i	$0.893435\pi$
$158$	40.7401	+	1.82964i	3.24111	+	0.145558i
$159$		0			0
$160$	6.57091	−	6.87263i	0.519476	−	0.543329i
$161$	−1.85440	+	0.997897i	−0.146147	+	0.0786453i
$162$		0			0
$163$	−10.2834	−	17.2115i	−0.805460	−	1.34811i	−0.934315	−	0.356449i	$-0.883987\pi$
$163$	−10.2834	−	17.2115i	−0.805460	−	1.34811i	0.128855	−	0.991663i	$-0.458870\pi$
$164$	4.10877	−	30.3322i	0.320841	−	2.36854i
$165$		0			0
$166$	−6.41112	+	1.16345i	−0.497600	+	0.0903010i
$167$	7.33290	−	10.0929i	0.567437	−	0.781010i	−0.424811	−	0.905282i	$-0.639660\pi$
$167$	7.33290	−	10.0929i	0.567437	−	0.781010i	0.992248	+	0.124272i	$0.0396595\pi$
$168$		0			0
$169$	2.62451	+	1.56807i	0.201886	+	0.120621i
$170$	1.85592	+	0.167035i	0.142342	+	0.0128110i
$171$		0			0
$172$	12.3042	+	15.4290i	0.938187	+	1.17645i
$173$	0.522110	+	11.6257i	0.0396953	+	0.883883i	0.915769	+	0.401706i	$0.131583\pi$
$173$	0.522110	+	11.6257i	0.0396953	+	0.883883i	−0.876073	+	0.482178i	$0.839846\pi$
$174$		0			0
$175$	−0.112452	−	1.24944i	−0.00850053	−	0.0944487i
$176$	0.259900	+	1.13870i	0.0195907	+	0.0858326i
$177$		0			0
$178$	3.68019	+	8.61023i	0.275842	+	0.645364i
$179$	−14.1412	+	3.22764i	−1.05696	+	0.241245i	−0.715473	−	0.698641i	$-0.753789\pi$
$179$	−14.1412	+	3.22764i	−1.05696	+	0.241245i	−0.341490	+	0.939885i	$0.610931\pi$
$180$		0			0
$181$	−4.84553	+	10.0618i	−0.360165	+	0.747891i	−0.999784	−	0.0208016i	$-0.993378\pi$
$181$	−4.84553	+	10.0618i	−0.360165	+	0.747891i	0.639618	+	0.768693i	$0.279092\pi$
$182$	10.1657	−	0.456541i	0.753530	−	0.0338411i
$183$		0			0
$184$	5.46552	−	0.740354i	0.402923	−	0.0545797i
$185$	−1.47584	+	16.3979i	−0.108506	+	1.20560i
$186$		0			0
$187$	0.170152	−	0.213364i	0.0124427	−	0.0156027i
$188$	7.42406	+	5.39390i	0.541455	+	0.393390i
$189$		0			0
$190$	1.37074	−	6.00559i	0.0994437	−	0.435691i
$191$	19.8021	+	2.68238i	1.43283	+	0.194090i	0.809156	−	0.587594i	$-0.199925\pi$
$191$	19.8021	+	2.68238i	1.43283	+	0.194090i	0.623675	+	0.781684i	$0.285639\pi$
$192$		0			0
$193$	5.65970	+	11.7525i	0.407394	+	0.845962i	0.999204	+	0.0398850i	$0.0126992\pi$
$193$	5.65970	+	11.7525i	0.407394	+	0.845962i	−0.591810	+	0.806077i	$0.701587\pi$
$194$	3.04232	+	5.65357i	0.218426	+	0.405903i
$195$		0			0
$196$	14.6062	−	10.6120i	1.04330	−	0.758002i
$197$	0.0396220	−	0.882251i	0.00282295	−	0.0628578i	−0.997087	−	0.0762715i	$-0.975698\pi$
$197$	0.0396220	−	0.882251i	0.00282295	−	0.0628578i	0.999910	+	0.0134137i	$0.00426985\pi$
$198$		0			0
$199$	1.43385	+	4.41292i	0.101643	+	0.312824i	0.988928	−	0.148397i	$-0.0474115\pi$
$199$	1.43385	+	4.41292i	0.101643	+	0.312824i	−0.887285	+	0.461221i	$0.847411\pi$
$200$	−0.874098	+	3.16722i	−0.0618081	+	0.223957i
$201$		0			0
$202$	−19.8685	+	5.48335i	−1.39794	+	0.385807i
$203$	6.27633	+	5.48346i	0.440512	+	0.384864i
$204$		0			0
$205$	−7.41208	−	19.7494i	−0.517682	−	1.37936i
$206$	12.8068	+	14.6586i	0.892293	+	1.02131i
$207$		0			0
$208$	−4.18256	−	1.35899i	−0.290008	−	0.0942293i
$209$	−0.623445	−	0.652072i	−0.0431246	−	0.0451048i
$210$		0			0
$211$	11.6488	+	4.97894i	0.801937	+	0.342764i	0.754659	−	0.656118i	$-0.227802\pi$
$211$	11.6488	+	4.97894i	0.801937	+	0.342764i	0.0472780	+	0.998882i	$0.484945\pi$
$212$	−38.1916			−2.62301
$213$		0			0
$214$	28.3077			1.93508
$215$	12.5057	+	5.34518i	0.852879	+	0.364538i
$216$		0			0
$217$	1.12144	+	1.17293i	0.0761280	+	0.0796237i
$218$	13.3719	+	4.34479i	0.905658	+	0.294266i
$219$		0			0
$220$	4.72830	+	5.41197i	0.318782	+	0.364875i
$221$	0.361058	+	0.962036i	0.0242874	+	0.0647136i
$222$		0			0
$223$	13.4323	+	11.7354i	0.899493	+	0.785863i	0.977466	−	0.211092i	$-0.0677021\pi$
$223$	13.4323	+	11.7354i	0.899493	+	0.785863i	−0.0779735	+	0.996955i	$0.524845\pi$
$224$	−5.17289	+	1.42763i	−0.345628	+	0.0953873i
$225$		0			0
$226$	6.61122	−	23.9552i	0.439772	−	1.59348i
$227$	0.258040	+	0.794164i	0.0171267	+	0.0527105i	0.959255	−	0.282543i	$-0.0911780\pi$
$227$	0.258040	+	0.794164i	0.0171267	+	0.0527105i	−0.942128	+	0.335254i	$0.891178\pi$
$228$		0			0
$229$	−0.122752	+	2.73328i	−0.00811167	+	0.180620i	0.990847	+	0.134991i	$0.0431006\pi$
$229$	−0.122752	+	2.73328i	−0.00811167	+	0.180620i	−0.998958	+	0.0456290i	$0.985471\pi$
$230$	7.09799	−	5.15699i	0.468027	−	0.340042i
$231$		0			0
$232$	−10.3438	−	19.2220i	−0.679102	−	1.26198i
$233$	2.53479	+	5.26354i	0.166059	+	0.344826i	0.967348	−	0.253452i	$-0.0815661\pi$
$233$	2.53479	+	5.26354i	0.166059	+	0.344826i	−0.801288	+	0.598278i	$0.795852\pi$
$234$		0			0
$235$	6.26691	+	0.848910i	0.408808	+	0.0553768i
$236$	8.23390	−	36.0751i	0.535981	−	2.34829i
$237$		0			0
$238$	−0.850810	−	0.618150i	−0.0551498	−	0.0400687i
$239$	−3.31243	+	4.15366i	−0.214263	+	0.268678i	−0.877335	−	0.479878i	$-0.840681\pi$
$239$	−3.31243	+	4.15366i	−0.214263	+	0.268678i	0.663072	+	0.748556i	$0.269252\pi$
$240$		0			0
$241$	−2.52715	+	28.0789i	−0.162788	+	1.80872i	0.335856	+	0.941913i	$0.390974\pi$
$241$	−2.52715	+	28.0789i	−0.162788	+	1.80872i	−0.498644	+	0.866807i	$0.666168\pi$
$242$	−23.9965	+	3.25055i	−1.54255	+	0.208953i
$243$		0			0
$244$	8.28658	−	0.372151i	0.530494	−	0.0238245i
$245$	5.39847	−	11.2100i	0.344896	−	0.716183i
$246$		0			0
$247$	3.31171	−	0.755876i	0.210719	−	0.0480953i
$248$	−1.67043	−	3.90817i	−0.106073	−	0.248169i
$249$		0			0
$250$	−5.19903	−	22.7784i	−0.328816	−	1.44063i
$251$	2.39821	+	26.6462i	0.151373	+	1.68190i	0.609326	+	0.792920i	$0.291440\pi$
$251$	2.39821	+	26.6462i	0.151373	+	1.68190i	−0.457953	+	0.888977i	$0.651417\pi$
$252$		0			0
$253$	−0.0576475	−	1.28362i	−0.00362427	−	0.0807006i
$254$	−16.1797	−	20.2887i	−1.01521	−	1.27303i
$255$		0			0
$256$	23.8018	+	2.14220i	1.48761	+	0.133888i
$257$	1.91726	+	1.14551i	0.119595	+	0.0714549i	0.571451	−	0.820636i	$-0.306381\pi$
$257$	1.91726	+	1.14551i	0.119595	+	0.0714549i	−0.451856	+	0.892091i	$0.649238\pi$
$258$		0			0
$259$	5.46166	−	7.51733i	0.339371	−	0.467104i
$260$	−26.6246	+	4.83165i	−1.65119	+	0.299646i
$261$		0			0
$262$	−2.74791	+	20.2859i	−0.169766	+	1.25327i
$263$	−1.57309	−	2.63291i	−0.0970010	−	0.162352i	0.806102	−	0.591777i	$-0.201573\pi$
$263$	−1.57309	−	2.63291i	−0.0970010	−	0.162352i	−0.903103	+	0.429425i	$0.858716\pi$
$264$		0			0
$265$	−23.1773	+	12.4722i	−1.42377	+	0.766163i
$266$	−2.40251	+	2.51283i	−0.147307	+	0.154071i
$267$		0			0
$268$	−0.885395	−	0.0397632i	−0.0540841	−	0.00242892i
$269$	1.72993	−	3.21475i	0.105476	−	0.196007i	−0.822387	−	0.568928i	$-0.807358\pi$
$269$	1.72993	−	3.21475i	0.105476	−	0.196007i	0.927863	+	0.372921i	$0.121644\pi$
$270$		0			0
$271$	−8.84935	−	2.44227i	−0.537560	−	0.148357i	−0.0132938	−	0.999912i	$-0.504232\pi$
$271$	−8.84935	−	2.44227i	−0.537560	−	0.148357i	−0.524266	+	0.851555i	$0.675660\pi$
$272$	0.250384	+	0.379316i	0.0151818	+	0.0229994i
$273$		0			0
$274$	31.3679	−	35.9035i	1.89501	−	2.16901i
$275$	0.716636	+	0.268958i	0.0432148	+	0.0162188i
$276$		0			0
$277$	18.4771	−	16.1429i	1.11018	−	0.969935i	0.110467	−	0.993880i	$-0.464765\pi$
$277$	18.4771	−	16.1429i	1.11018	−	0.969935i	0.999713	+	0.0239444i	$0.00762247\pi$
$278$	−25.4837	+	38.6062i	−1.52841	+	2.31545i
$279$		0			0
$280$	8.67204	−	8.29132i	0.518254	−	0.495501i
$281$	12.5786	+	2.28268i	0.750376	+	0.136173i	0.540254	−	0.841502i	$-0.318328\pi$
$281$	12.5786	+	2.28268i	0.750376	+	0.136173i	0.210122	+	0.977675i	$0.432614\pi$
$282$		0			0
$283$		−	17.0994i		−	1.01645i	−0.861223	−	0.508227i	$-0.830301\pi$
$283$		−	17.0994i		−	1.01645i	0.861223	−	0.508227i	$-0.169699\pi$
$284$	−21.9205	−	20.0898i	−1.30074	−	1.19211i
$285$		0			0
$286$	−2.44029	+	5.70933i	−0.144297	+	0.337600i
$287$	−2.12574	+	11.7138i	−0.125479	+	0.691445i
$288$		0			0
$289$	−5.22047	+	16.0670i	−0.307087	+	0.945115i
$290$	−28.9790	−	19.1289i	−1.70171	−	1.12329i
$291$		0			0
$292$	−16.0938	+	6.04011i	−0.941820	+	0.353471i
$293$	−9.41542	+	25.0873i	−0.550055	+	1.46562i	0.307663	+	0.951495i	$0.400453\pi$
$293$	−9.41542	+	25.0873i	−0.550055	+	1.46562i	−0.857718	+	0.514120i	$0.828119\pi$
$294$		0			0
$295$	−6.78413	−	24.5818i	−0.394987	−	1.43120i
$296$	−20.3106	+	13.4069i	−1.18053	+	0.779260i
$297$		0			0
$298$	−10.0012	+	3.24960i	−0.579357	+	0.188244i
$299$	4.26040	+	2.29262i	0.246385	+	0.132586i
$300$		0			0
$301$	−4.51154	−	6.20961i	−0.260041	−	0.357916i
$302$	2.53237	+	2.42120i	0.145722	+	0.139324i
$303$		0			0
$304$	1.35369	−	0.651903i	0.0776395	−	0.0373892i
$305$	4.90732	−	2.93199i	0.280993	−	0.167885i
$306$		0			0
$307$	5.95428	+	1.35903i	0.339829	+	0.0775637i	0.389030	−	0.921225i	$-0.372810\pi$
$307$	5.95428	+	1.35903i	0.339829	+	0.0775637i	−0.0492009	+	0.998789i	$0.515667\pi$
$308$	−0.724203	−	3.99069i	−0.0412653	−	0.227391i
$309$		0			0
$310$	−5.28591	−	4.21538i	−0.300220	−	0.239417i
$311$	−12.7443	+	21.3304i	−0.722663	+	1.20953i	0.247923	+	0.968780i	$0.420252\pi$
$311$	−12.7443	+	21.3304i	−0.722663	+	1.20953i	−0.970586	+	0.240755i	$0.922605\pi$
$312$		0			0
$313$	1.13692	+	8.39306i	0.0642623	+	0.474404i	0.994273	+	0.106871i	$0.0340831\pi$
$313$	1.13692	+	8.39306i	0.0642623	+	0.474404i	−0.930011	+	0.367533i	$0.880203\pi$
$314$	−33.9478	+	27.0725i	−1.91578	+	1.52779i
$315$		0			0
$316$	55.1416	+	26.5548i	3.10196	+	1.49382i
$317$	−17.5946	+	1.58354i	−0.988210	+	0.0889405i	−0.571936	−	0.820298i	$-0.693807\pi$
$317$	−17.5946	+	1.58354i	−0.988210	+	0.0889405i	−0.416275	+	0.909239i	$0.636664\pi$
$318$		0			0
$319$	−4.67607	+	1.99865i	−0.261810	+	0.111903i
$320$	26.7959	−	11.4531i	1.49794	−	0.640250i
$321$		0			0
$322$	−4.93163	+	0.443855i	−0.274829	+	0.0247351i
$323$	−0.316294	−	0.152319i	−0.0175991	−	0.00847526i
$324$		0			0
$325$	−2.25334	+	1.79698i	−0.124993	+	0.0996783i
$326$	−6.32820	−	46.7166i	−0.350487	−	2.58740i
$327$		0			0
$328$	15.9926	−	26.7670i	0.883042	−	1.47796i
$329$	−2.79048	−	2.22534i	−0.153844	−	0.122687i
$330$		0			0
$331$	4.51322	+	24.8699i	0.248069	+	1.36697i	0.831822	+	0.555042i	$0.187298\pi$
$331$	4.51322	+	24.8699i	0.248069	+	1.36697i	−0.583754	+	0.811931i	$0.698417\pi$
$332$	−9.53350	−	2.17596i	−0.523219	−	0.119421i
$333$		0			0
$334$	25.1818	−	15.0454i	1.37788	−	0.823248i
$335$	−0.550303	+	0.265012i	−0.0300663	+	0.0144792i
$336$		0			0
$337$	−19.9051	−	19.0312i	−1.08430	−	1.03670i	−0.999187	−	0.0403267i	$-0.987160\pi$
$337$	−19.9051	−	19.0312i	−1.08430	−	1.03670i	−0.0851144	−	0.996371i	$-0.527126\pi$
$338$	4.22540	+	5.81576i	0.229831	+	0.316336i
$339$		0			0
$340$	2.46261	+	1.32519i	0.133554	+	0.0718685i
$341$	−0.941695	+	0.305975i	−0.0509957	+	0.0165695i
$342$		0			0
$343$	−13.8784	+	9.16108i	−0.749366	+	0.494652i
$344$	5.34811	+	19.3784i	0.288351	+	1.04481i
$345$		0			0
$346$	−9.61481	+	25.6186i	−0.516895	+	1.37726i
$347$	−5.48932	+	2.06017i	−0.294682	+	0.110596i	−0.494337	−	0.869270i	$-0.664589\pi$
$347$	−5.48932	+	2.06017i	−0.294682	+	0.110596i	0.199655	+	0.979866i	$0.436018\pi$
$348$		0			0
$349$	8.27867	+	5.46470i	0.443147	+	0.292519i	0.752700	−	0.658363i	$-0.228751\pi$
$349$	8.27867	+	5.46470i	0.443147	+	0.292519i	−0.309553	+	0.950882i	$0.600180\pi$
$350$	0.911515	−	2.80535i	0.0487225	−	0.149952i
$351$		0			0
$352$	0.584651	−	3.22169i	0.0311620	−	0.171717i
$353$	12.4129	−	29.0413i	0.660670	−	1.54572i	−0.167884	−	0.985807i	$-0.553693\pi$
$353$	12.4129	−	29.0413i	0.660670	−	1.54572i	0.828555	−	0.559908i	$-0.189164\pi$
$354$		0			0
$355$	−19.8636	−	5.03328i	−1.05425	−	0.267139i
$356$			14.0527i			0.744791i
$357$		0			0
$358$	−33.5577	−	6.08982i	−1.77358	−	0.321857i
$359$	10.2672	−	9.81649i	0.541884	−	0.518095i	−0.369731	−	0.929139i	$-0.620550\pi$
$359$	10.2672	−	9.81649i	0.541884	−	0.518095i	0.911615	+	0.411044i	$0.134836\pi$
$360$		0			0
$361$	9.82771	−	14.8883i	0.517248	−	0.783597i
$362$	−19.7751	+	17.2770i	−1.03936	+	0.908058i
$363$		0			0
$364$	14.2978	+	5.36604i	0.749406	+	0.281257i
$365$	−7.79431	+	8.92131i	−0.407973	+	0.466962i
$366$		0			0
$367$	−7.96482	−	12.0662i	−0.415760	−	0.629850i	0.564994	−	0.825095i	$-0.308878\pi$
$367$	−7.96482	−	12.0662i	−0.415760	−	0.629850i	−0.980754	+	0.195245i	$0.937450\pi$
$368$	2.06283	+	0.569306i	0.107533	+	0.0296771i
$369$		0			0
$370$	−18.3448	+	34.0904i	−0.953702	+	1.77228i
$371$	14.8393	+	0.666433i	0.770418	+	0.0345995i
$372$		0			0
$373$	4.03850	−	4.22394i	0.209106	−	0.218707i	−0.609922	−	0.792462i	$-0.708799\pi$
$373$	4.03850	−	4.22394i	0.209106	−	0.218707i	0.819028	+	0.573754i	$0.194513\pi$
$374$	0.565065	−	0.304074i	0.0292188	−	0.0157233i
$375$		0			0
$376$	4.79457	+	8.02477i	0.247261	+	0.413846i
$377$	2.57025	−	18.9744i	0.132375	−	0.977230i
$378$		0			0
$379$	−11.5146	+	2.08959i	−0.591464	+	0.107335i	−0.466033	−	0.884767i	$-0.654317\pi$
$379$	−11.5146	+	2.08959i	−0.591464	+	0.107335i	−0.125431	+	0.992102i	$0.540031\pi$
$380$	5.43390	−	7.47912i	0.278753	−	0.383671i
$381$		0			0
$382$	40.3356	+	24.0994i	2.06375	+	1.23303i
$383$	16.0095	+	1.44088i	0.818047	+	0.0736255i	0.490755	−	0.871298i	$-0.336721\pi$
$383$	16.0095	+	1.44088i	0.818047	+	0.0736255i	0.327292	+	0.944923i	$0.393864\pi$
$384$		0			0
$385$	−1.74273	−	2.18532i	−0.0888179	−	0.111374i
$386$	1.37607	+	30.6406i	0.0700401	+	1.55956i
$387$		0			0
$388$	0.863683	+	9.59631i	0.0438469	+	0.487179i
$389$	−4.43111	−	19.4139i	−0.224666	−	0.984326i	−0.953915	−	0.300078i	$-0.902987\pi$
$389$	−4.43111	−	19.4139i	−0.224666	−	0.984326i	0.729249	−	0.684249i	$-0.239870\pi$
$390$		0			0
$391$	−0.196515	−	0.459769i	−0.00993819	−	0.0232515i
$392$	17.9302	−	4.09246i	0.905614	−	0.206701i
$393$		0			0
$394$	0.900985	−	1.87092i	0.0453910	−	0.0942554i
$395$	42.1356	−	1.89231i	2.12007	−	0.0952127i
$396$		0			0
$397$	−18.5302	+	2.51008i	−0.930003	+	0.125977i	−0.583538	−	0.812086i	$-0.698332\pi$
$397$	−18.5302	+	2.51008i	−0.930003	+	0.125977i	−0.346464	+	0.938063i	$0.612618\pi$
$398$	−0.977987	+	10.8663i	−0.0490221	+	0.544680i
$399$		0			0
$400$	−0.794826	+	0.996681i	−0.0397413	+	0.0498340i
$401$	−8.95558	−	6.50661i	−0.447220	−	0.324924i	0.341277	−	0.939963i	$-0.389141\pi$
$401$	−8.95558	−	6.50661i	−0.447220	−	0.324924i	−0.788497	+	0.615038i	$0.789141\pi$
$402$		0			0
$403$	0.829611	−	3.63476i	0.0413258	−	0.181060i
$404$	−30.6525	−	4.15216i	−1.52502	−	0.206578i
$405$		0			0
$406$	8.50271	+	17.6561i	0.421982	+	0.876255i
$407$	2.68665	+	4.99263i	0.133172	+	0.247475i
$408$		0			0
$409$	2.96143	−	2.15160i	0.146433	−	0.106390i	−0.512157	−	0.858892i	$-0.671153\pi$
$409$	2.96143	−	2.15160i	0.146433	−	0.106390i	0.658590	+	0.752502i	$0.271153\pi$
$410$	2.22531	−	49.5503i	0.109900	−	2.44712i
$411$		0			0
$412$	9.02709	+	27.7825i	0.444733	+	1.36875i
$413$	−3.82877	+	13.8732i	−0.188401	+	0.682657i
$414$		0			0
$415$	−6.49617	+	1.79283i	−0.318885	+	0.0880066i
$416$	9.28443	+	8.11156i	0.455207	+	0.397702i
$417$		0			0
$418$	−0.745359	−	1.98600i	−0.0364567	−	0.0971386i
$419$	−26.1204	−	29.8972i	−1.27607	−	1.46057i	−0.821872	−	0.569672i	$-0.807070\pi$
$419$	−26.1204	−	29.8972i	−1.27607	−	1.46057i	−0.454194	−	0.890903i	$-0.650073\pi$
$420$		0			0
$421$	2.31664	+	0.752721i	0.112906	+	0.0366854i	0.364925	−	0.931037i	$-0.381095\pi$
$421$	2.31664	+	0.752721i	0.112906	+	0.0366854i	−0.252019	+	0.967722i	$0.581095\pi$
$422$	20.5849	+	21.5301i	1.00206	+	1.04807i
$423$		0			0
$424$	−35.7740	−	15.2905i	−1.73734	−	0.742574i
$425$	0.297861			0.0144484
$426$		0			0
$427$	−3.22623			−0.156128
$428$	39.0642	+	16.6968i	1.88824	+	0.807073i
$429$		0			0
$430$	22.0991	+	23.1138i	1.06571	+	1.11465i
$431$	21.2256	+	6.89661i	1.02240	+	0.332198i	0.771782	−	0.635888i	$-0.219366\pi$
$431$	21.2256	+	6.89661i	1.02240	+	0.332198i	0.250619	+	0.968086i	$0.419366\pi$
$432$		0			0
$433$	25.2649	+	28.9180i	1.21415	+	1.38971i	0.897410	+	0.441198i	$0.145446\pi$
$433$	25.2649	+	28.9180i	1.21415	+	1.38971i	0.316743	+	0.948511i	$0.397411\pi$
$434$	1.34073	+	3.57237i	0.0643572	+	0.171479i
$435$		0			0
$436$	15.8903	+	13.8829i	0.761007	+	0.664872i
$437$	−1.59334	+	0.439734i	−0.0762198	+	0.0210353i
$438$		0			0
$439$	8.76255	−	31.7504i	0.418214	−	1.51536i	−0.386832	−	0.922150i	$-0.626431\pi$
$439$	8.76255	−	31.7504i	0.418214	−	1.51536i	0.805046	−	0.593213i	$-0.202141\pi$
$440$	2.26222	+	6.96241i	0.107847	+	0.331920i
$441$		0			0
$442$	−0.108399	+	2.41370i	−0.00515604	+	0.114808i
$443$	−2.58341	+	1.87696i	−0.122742	+	0.0891770i	−0.647462	−	0.762097i	$-0.724170\pi$
$443$	−2.58341	+	1.87696i	−0.122742	+	0.0891770i	0.524721	+	0.851274i	$0.324170\pi$
$444$		0			0
$445$	4.58918	+	8.52813i	0.217548	+	0.404272i
$446$	18.1971	+	37.7866i	0.861657	+	1.78925i
$447$		0			0
$448$	−16.2975	−	2.20764i	−0.769983	−	0.104301i
$449$	2.35042	−	10.2979i	0.110923	−	0.485987i	−0.888699	−	0.458492i	$-0.848390\pi$
$449$	2.35042	−	10.2979i	0.110923	−	0.485987i	0.999622	−	0.0274952i	$-0.00875309\pi$
$450$		0			0
$451$	−5.87677	−	4.26973i	−0.276726	−	0.201054i
$452$	23.2530	−	29.1583i	1.09373	−	1.37149i
$453$		0			0
$454$	−0.176002	+	1.95554i	−0.00826017	+	0.0917780i
$455$	10.4292	−	1.41274i	0.488930	−	0.0662301i
$456$		0			0
$457$	33.5508	−	1.50677i	1.56944	−	0.0704836i	0.756955	−	0.653467i	$-0.226686\pi$
$457$	33.5508	−	1.50677i	1.56944	−	0.0704836i	0.812484	+	0.582983i	$0.198115\pi$
$458$	−2.79132	+	5.79624i	−0.130430	+	0.270840i
$459$		0			0
$460$	12.8369	−	2.92993i	0.598523	−	0.136609i
$461$	1.72176	+	4.02826i	0.0801904	+	0.187615i	0.954826	−	0.297167i	$-0.0960418\pi$
$461$	1.72176	+	4.02826i	0.0801904	+	0.187615i	−0.874635	+	0.484782i	$0.838899\pi$
$462$		0			0
$463$	−1.50570	−	6.59689i	−0.0699757	−	0.306584i	0.927813	−	0.373045i	$-0.121686\pi$
$463$	−1.50570	−	6.59689i	−0.0699757	−	0.306584i	−0.997789	+	0.0664613i	$0.978829\pi$
$464$	−0.759179	−	8.43517i	−0.0352440	−	0.391593i
$465$		0			0
$466$	0.616295	+	13.7229i	0.0285493	+	0.635700i
$467$	−8.43093	−	10.5721i	−0.390137	−	0.489216i	0.547513	−	0.836797i	$-0.315575\pi$
$467$	−8.43093	−	10.5721i	−0.390137	−	0.489216i	−0.937650	+	0.347581i	$0.887003\pi$
$468$		0			0
$469$	0.343325	+	0.0308998i	0.0158533	+	0.00142682i
$470$	12.7653	+	7.62690i	0.588819	+	0.351803i
$471$		0			0
$472$	22.1558	−	30.4949i	1.01980	−	1.40364i
$473$	4.60805	−	0.836238i	0.211879	−	0.0384503i
$474$		0			0
$475$	0.132174	−	0.975751i	0.00606458	−	0.0447705i
$476$	−0.809499	−	1.35487i	−0.0371033	−	0.0621005i
$477$		0			0
$478$	−11.0004	+	5.91957i	−0.503147	+	0.270755i
$479$	−19.8161	+	20.7260i	−0.905419	+	0.946994i	−0.998817	−	0.0486352i	$-0.984513\pi$
$479$	−19.8161	+	20.7260i	−0.905419	+	0.946994i	0.0933980	+	0.995629i	$0.470227\pi$
$480$		0			0
$481$	−21.3263	−	0.957763i	−0.972393	−	0.0436702i
$482$	−31.4126	+	58.3744i	−1.43081	+	2.65888i
$483$		0			0
$484$	−35.0321	−	9.66825i	−1.59237	−	0.439466i
$485$	3.65800	+	5.54164i	0.166101	+	0.251633i
$486$		0			0
$487$	24.8704	−	28.4665i	1.12698	−	1.28994i	0.174736	−	0.984615i	$-0.444093\pi$
$487$	24.8704	−	28.4665i	1.12698	−	1.28994i	0.952249	−	0.305323i	$-0.0987643\pi$
$488$	7.91100	+	2.96905i	0.358114	+	0.134403i
$489$		0			0
$490$	22.0317	−	19.2485i	0.995291	−	0.869559i
$491$	−15.8443	+	24.0030i	−0.715042	+	1.08324i	0.277427	+	0.960747i	$0.410518\pi$
$491$	−15.8443	+	24.0030i	−0.715042	+	1.08324i	−0.992469	+	0.122495i	$0.960910\pi$
$492$		0			0
$493$	−1.43032	+	1.36752i	−0.0644182	+	0.0615901i
$494$	7.85884	+	1.42617i	0.353586	+	0.0641664i
$495$		0			0
$496$		−	1.64905i		−	0.0740444i
$497$	8.16662	+	8.18837i	0.366323	+	0.367298i
$498$		0			0
$499$	11.8317	−	27.6816i	0.529659	−	1.23920i	−0.414602	−	0.910003i	$-0.636079\pi$
$499$	11.8317	−	27.6816i	0.529659	−	1.23920i	0.944261	−	0.329197i	$-0.106778\pi$
$500$	6.26091	−	34.5005i	0.279997	−	1.54291i
$501$		0			0
$502$	−19.4395	+	59.8286i	−0.867627	+	2.67028i
$503$	−0.239149	−	0.157861i	−0.0106631	−	0.00703866i	0.545554	−	0.838076i	$-0.316319\pi$
$503$	−0.239149	−	0.157861i	−0.0106631	−	0.00703866i	−0.556217	+	0.831037i	$0.687748\pi$
$504$		0			0
$505$	−19.9580	+	7.49035i	−0.888118	+	0.333316i
$506$	1.06160	−	2.82862i	0.0471938	−	0.125747i
$507$		0			0
$508$	−10.3608	−	37.5415i	−0.459686	−	1.66563i
$509$	−7.37285	+	4.86677i	−0.326796	+	0.215716i	−0.703633	−	0.710563i	$-0.748440\pi$
$509$	−7.37285	+	4.86677i	−0.326796	+	0.215716i	0.376837	+	0.926279i	$0.377012\pi$
$510$		0			0
$511$	6.35863	−	2.06604i	0.281289	−	0.0913964i
$512$	13.6318	+	7.33557i	0.602445	+	0.324189i
$513$		0			0
$514$	3.08674	+	4.24853i	0.136150	+	0.187395i
$515$	14.5512	+	13.9123i	0.641201	+	0.613051i
$516$		0			0
$517$	1.96211	−	0.944902i	0.0862934	−	0.0415567i
$518$	18.7558	−	11.2060i	0.824081	−	0.492365i
$519$		0			0
$520$	−26.8736	−	6.13371i	−1.17848	−	0.268981i
$521$	−7.66554	−	42.2406i	−0.335834	−	1.85060i	−0.502493	−	0.864581i	$-0.667584\pi$
$521$	−7.66554	−	42.2406i	−0.335834	−	1.85060i	0.166660	−	0.986014i	$-0.446702\pi$
$522$		0			0
$523$	−8.53417	−	6.80577i	−0.373173	−	0.297596i	0.418887	−	0.908038i	$-0.362420\pi$
$523$	−8.53417	−	6.80577i	−0.373173	−	0.297596i	−0.792061	+	0.610443i	$0.790992\pi$
$524$	−15.7574	+	26.3734i	−0.688364	+	1.15213i
$525$		0			0
$526$	−0.968048	−	7.14641i	−0.0422089	−	0.311598i
$527$	−0.301244	+	0.240234i	−0.0131224	+	0.0104647i
$528$		0			0
$529$	18.6012	+	8.95788i	0.808749	+	0.389473i
$530$	−61.6380	+	5.54752i	−2.67738	+	0.240969i
$531$		0			0
$532$	−4.79758	+	2.05059i	−0.208002	+	0.0889041i
$533$	25.1504	−	10.7498i	1.08939	−	0.465626i
$534$		0			0
$535$	29.1595	−	2.62440i	1.26068	−	0.113463i
$536$	−0.813427	−	0.391726i	−0.0351347	−	0.0169200i
$537$		0			0
$538$	6.71118	−	5.35199i	0.289339	−	0.230741i
$539$	−0.575134	−	4.24581i	−0.0247728	−	0.182880i
$540$		0			0
$541$	−7.84747	+	13.1344i	−0.337389	+	0.564694i	−0.979382	−	0.202016i	$-0.935251\pi$
$541$	−7.84747	+	13.1344i	−0.337389	+	0.564694i	0.641993	+	0.766710i	$0.278108\pi$
$542$	−16.8764	−	13.4584i	−0.724902	−	0.578090i
$543$		0			0
$544$	−0.227508	−	1.25367i	−0.00975433	−	0.0537508i
$545$	14.1770	+	3.23582i	0.607278	+	0.138607i
$546$		0			0
$547$	10.1865	−	6.08613i	0.435542	−	0.260224i	−0.278351	−	0.960480i	$-0.589788\pi$
$547$	10.1865	−	6.08613i	0.435542	−	0.260224i	0.713892	+	0.700256i	$0.246931\pi$
$548$	64.4644	−	31.0444i	2.75378	−	1.32615i
$549$		0			0
$550$	1.30090	+	1.24379i	0.0554705	+	0.0530352i
$551$	3.84511	+	5.29234i	0.163807	+	0.225461i
$552$		0			0
$553$	−20.9618	−	11.2800i	−0.891386	−	0.479675i
$554$	54.8679	−	17.8276i	2.33111	−	0.757424i
$555$		0			0
$556$	−57.9384	+	38.2448i	−2.45714	+	1.62194i
$557$	−1.72307	−	6.24340i	−0.0730087	−	0.264541i	0.918341	−	0.395791i	$-0.129530\pi$
$557$	−1.72307	−	6.24340i	−0.0730087	−	0.264541i	−0.991349	+	0.131250i	$0.958101\pi$
$558$		0			0
$559$	−6.19617	+	16.5096i	−0.262070	+	0.698283i
$560$	4.35829	−	1.63569i	0.184171	−	0.0691206i
$561$		0			0
$562$	25.0869	+	16.5597i	1.05823	+	0.698530i
$563$	8.71922	−	26.8350i	0.367471	−	1.13096i	−0.580948	−	0.813941i	$-0.697318\pi$
$563$	8.71922	−	26.8350i	0.367471	−	1.13096i	0.948419	−	0.317019i	$-0.102682\pi$
$564$		0			0
$565$	4.58927	−	25.2890i	0.193072	−	1.06392i
$566$	15.8021	−	36.9709i	0.664213	−	1.55400i
$567$		0			0
$568$	−12.4897	−	27.5942i	−0.524055	−	1.15783i
$569$		−	38.2948i		−	1.60540i	−0.596381	−	0.802702i	$-0.703395\pi$
$569$		−	38.2948i		−	1.60540i	0.596381	−	0.802702i	$-0.296605\pi$
$570$		0			0
$571$	−4.78904	−	0.869083i	−0.200415	−	0.0363700i	0.0774208	−	0.996999i	$-0.475331\pi$
$571$	−4.78904	−	0.869083i	−0.200415	−	0.0363700i	−0.277836	+	0.960628i	$0.589617\pi$
$572$	−6.73512	+	6.43943i	−0.281609	+	0.269246i
$573$		0			0
$574$	−15.4212	+	23.3622i	−0.643670	+	0.975118i
$575$	1.05613	−	0.922714i	0.0440437	−	0.0384798i
$576$		0			0
$577$	7.46867	+	2.80304i	0.310925	+	0.116692i	0.501959	−	0.864891i	$-0.332613\pi$
$577$	7.46867	+	2.80304i	0.310925	+	0.116692i	−0.191034	+	0.981583i	$0.561184\pi$
$578$	−26.1353	+	29.9143i	−1.08708	+	1.24427i
$579$		0			0
$580$	−28.7078	−	43.4904i	−1.19202	−	1.80584i
$581$	3.66625	+	1.01182i	0.152102	+	0.0419774i
$582$		0			0
$583$	−4.29493	+	7.98131i	−0.177878	+	0.330552i
$584$	−17.4933	−	0.785624i	−0.723877	−	0.0325094i
$585$		0			0
$586$	−43.5413	+	45.5406i	−1.79867	+	1.88126i
$587$	4.51615	−	2.43024i	0.186401	−	0.100307i	−0.378006	−	0.925803i	$-0.623390\pi$
$587$	4.51615	−	2.43024i	0.186401	−	0.100307i	0.564408	+	0.825496i	$0.309105\pi$
$588$		0			0
$589$	0.653296	+	1.09343i	0.0269186	+	0.0450541i
$590$	8.04873	−	59.4181i	0.331361	−	2.44620i
$591$		0			0
$592$	−9.29065	+	1.68600i	−0.381843	+	0.0692943i
$593$	5.43586	−	7.48183i	0.223224	−	0.307242i	−0.682686	−	0.730712i	$-0.739188\pi$
$593$	5.43586	−	7.48183i	0.223224	−	0.307242i	0.905910	+	0.423470i	$0.139188\pi$
$594$		0			0
$595$	−0.933720	−	0.557872i	−0.0382788	−	0.0228705i
$596$	−15.7183	−	1.41467i	−0.643847	−	0.0579472i
$597$		0			0
$598$	7.09280	+	8.89409i	0.290046	+	0.363707i
$599$	0.440980	+	9.81918i	0.0180180	+	0.401201i	0.987654	+	0.156649i	$0.0500693\pi$
$599$	0.440980	+	9.81918i	0.0180180	+	0.401201i	−0.969636	+	0.244551i	$0.921359\pi$
$600$		0			0
$601$	2.80970	+	31.2183i	0.114610	+	1.27342i	0.823180	+	0.567781i	$0.192198\pi$
$601$	2.80970	+	31.2183i	0.114610	+	1.27342i	−0.708570	+	0.705641i	$0.750659\pi$
$602$	−4.01598	−	17.5952i	−0.163679	−	0.717126i
$603$		0			0
$604$	2.06653	+	4.83489i	0.0840860	+	0.196729i
$605$	−24.4172	+	5.57307i	−0.992702	+	0.226578i
$606$		0			0
$607$	7.45668	−	15.4840i	0.302657	−	0.628475i	−0.693064	−	0.720876i	$-0.743740\pi$
$607$	7.45668	−	15.4840i	0.302657	−	0.628475i	0.995722	+	0.0924010i	$0.0294542\pi$
$608$	−4.20781	+	0.188973i	−0.170649	+	0.00766386i
$609$		0			0
$610$	13.3198	−	1.80428i	0.539301	−	0.0730533i
$611$	−0.735040	+	8.16696i	−0.0297365	+	0.330400i
$612$		0			0
$613$	−4.25858	+	5.34009i	−0.172002	+	0.215684i	−0.860359	−	0.509688i	$-0.829761\pi$
$613$	−4.25858	+	5.34009i	−0.172002	+	0.215684i	0.688357	+	0.725372i	$0.258332\pi$
$614$	11.6179	+	8.44093i	0.468862	+	0.340648i
$615$		0			0
$616$	0.919367	−	4.02801i	0.0370424	−	0.162293i
$617$	−40.0915	−	5.43077i	−1.61403	−	0.218635i	−0.729113	−	0.684393i	$-0.760067\pi$
$617$	−40.0915	−	5.43077i	−1.61403	−	0.218635i	−0.884912	+	0.465759i	$0.845782\pi$
$618$		0			0
$619$	−9.86303	−	20.4808i	−0.396429	−	0.823192i	−0.999671	−	0.0256348i	$-0.991839\pi$
$619$	−9.86303	−	20.4808i	−0.396429	−	0.823192i	0.603243	−	0.797558i	$-0.293875\pi$
$620$	−4.80811	−	8.93497i	−0.193098	−	0.358837i
$621$		0			0
$622$	−47.2668	+	34.3413i	−1.89523	+	1.37696i
$623$	0.245216	−	5.46015i	0.00982435	−	0.218756i
$624$		0			0
$625$	−8.87951	−	27.3283i	−0.355180	−	1.09313i
$626$	−5.29816	+	19.1974i	−0.211757	+	0.767284i
$627$		0			0
$628$	−62.8157	+	17.3360i	−2.50662	+	0.691783i
$629$	1.66146	+	1.45157i	0.0662467	+	0.0578780i
$630$		0			0
$631$	−17.2091	−	45.8535i	−0.685084	−	1.82540i	−0.551144	−	0.834410i	$-0.685808\pi$
$631$	−17.2091	−	45.8535i	−0.685084	−	1.82540i	−0.133940	−	0.990989i	$-0.542763\pi$
$632$	41.0194	+	46.9505i	1.63166	+	1.86759i
$633$		0			0
$634$	−39.5050	−	12.8359i	−1.56894	−	0.509780i
$635$	−18.5475	−	19.3992i	−0.736037	−	0.769834i
$636$		0			0
$637$	14.8345	+	6.34057i	0.587765	+	0.251223i
$638$	−11.9572			−0.473392
$639$		0			0
$640$	49.5034			1.95679
$641$	2.45809	+	1.05064i	0.0970887	+	0.0414977i	0.441021	−	0.897497i	$-0.354616\pi$
$641$	2.45809	+	1.05064i	0.0970887	+	0.0414977i	−0.343933	+	0.938994i	$0.611759\pi$
$642$		0			0
$643$	4.08335	+	4.27085i	0.161032	+	0.168426i	0.798388	−	0.602143i	$-0.205686\pi$
$643$	4.08335	+	4.27085i	0.161032	+	0.168426i	−0.637356	+	0.770569i	$0.719972\pi$
$644$	−7.06737	−	2.29633i	−0.278494	−	0.0904881i
$645$		0			0
$646$	−0.543101	−	0.621630i	−0.0213680	−	0.0244577i
$647$	−15.2642	−	40.6714i	−0.600098	−	1.59896i	−0.787256	−	0.616627i	$-0.788499\pi$
$647$	−15.2642	−	40.6714i	−0.600098	−	1.59896i	0.187157	−	0.982330i	$-0.440073\pi$
$648$		0			0
$649$	−6.61303	−	5.77763i	−0.259584	−	0.226792i
$650$	−6.53263	+	1.80289i	−0.256231	+	0.0707152i
$651$		0			0
$652$	18.8222	−	68.2009i	0.737136	−	2.67095i
$653$	−11.8230	−	36.3874i	−0.462669	−	1.42395i	−0.861891	−	0.507094i	$-0.830720\pi$
$653$	−11.8230	−	36.3874i	−0.462669	−	1.42395i	0.399222	−	0.916854i	$-0.369280\pi$
$654$		0			0
$655$	−0.949895	+	21.1511i	−0.0371155	+	0.826440i
$656$	9.78742	−	7.11098i	0.382134	−	0.277637i
$657$		0			0
$658$	−3.97685	−	7.39022i	−0.155034	−	0.288101i
$659$	6.75505	+	14.0270i	0.263139	+	0.546414i	0.990117	−	0.140247i	$-0.0447897\pi$
$659$	6.75505	+	14.0270i	0.263139	+	0.546414i	−0.726977	+	0.686662i	$0.759075\pi$
$660$		0			0
$661$	8.03484	+	1.08839i	0.312519	+	0.0423336i	0.288813	−	0.957385i	$-0.406739\pi$
$661$	8.03484	+	1.08839i	0.312519	+	0.0423336i	0.0237056	+	0.999719i	$0.492454\pi$
$662$	−13.2250	+	57.9424i	−0.514004	+	2.25200i
$663$		0			0
$664$	−8.05882	−	5.85508i	−0.312743	−	0.227221i
$665$	−2.24184	+	2.81118i	−0.0869348	+	0.109013i
$666$		0			0
$667$	−0.835185	+	9.27967i	−0.0323385	+	0.359310i
$668$	43.6247	−	5.90937i	1.68789	−	0.228641i
$669$		0			0
$670$	−1.43473	+	0.0644337i	−0.0554284	+	0.00248929i
$671$	0.854113	−	1.77358i	0.0329727	−	0.0684685i
$672$		0			0
$673$	−25.8445	+	5.89884i	−0.996232	+	0.227383i	−0.689400	−	0.724380i	$-0.742126\pi$
$673$	−25.8445	+	5.89884i	−0.996232	+	0.227383i	−0.306831	+	0.951764i	$0.599269\pi$
$674$	−25.4498	−	59.5428i	−0.980290	−	2.29350i
$675$		0			0
$676$	2.40065	+	10.5179i	0.0923328	+	0.404536i
$677$	1.53668	+	17.0739i	0.0590595	+	0.656205i	0.969909	+	0.243467i	$0.0782847\pi$
$677$	1.53668	+	17.0739i	0.0590595	+	0.656205i	−0.910850	+	0.412738i	$0.864572\pi$
$678$		0			0
$679$	−0.168130	−	3.74370i	−0.00645223	−	0.143670i
$680$	1.77616	+	2.22724i	0.0681128	+	0.0854108i
$681$		0			0
$682$	−2.31882	−	0.208697i	−0.0887921	−	0.00799144i
$683$	14.8142	+	8.85108i	0.566850	+	0.338677i	0.767564	−	0.640973i	$-0.221469\pi$
$683$	14.8142	+	8.85108i	0.566850	+	0.338677i	−0.200714	+	0.979650i	$0.564326\pi$
$684$		0			0
$685$	28.9832	−	39.8920i	1.10739	−	1.52419i
$686$	−38.4729	+	6.98180i	−1.46890	+	0.266566i
$687$		0			0
$688$	−1.04699	+	7.72920i	−0.0399162	+	0.294673i
$689$	−17.5037	−	29.2962i	−0.666837	−	1.11610i
$690$		0			0
$691$	15.2366	−	8.19915i	0.579626	−	0.311910i	−0.157657	−	0.987494i	$-0.550394\pi$
$691$	15.2366	−	8.19915i	0.579626	−	0.311910i	0.737283	+	0.675584i	$0.236108\pi$
$692$	−28.3790	+	29.6821i	−1.07881	+	1.12834i
$693$		0			0
$694$	−13.7724	−	0.618520i	−0.522794	−	0.0234787i
$695$	−22.6714	+	42.1305i	−0.859974	+	1.59810i
$696$		0			0
$697$	−2.72485	−	0.752010i	−0.103211	−	0.0284844i
$698$	12.8493	+	19.4659i	0.486355	+	0.736796i
$699$		0			0
$700$	2.91257	−	3.33370i	0.110085	−	0.126002i
$701$	21.8353	+	8.19493i	0.824708	+	0.309518i	0.727812	−	0.685776i	$-0.240537\pi$
$701$	21.8353	+	8.19493i	0.824708	+	0.309518i	0.0968960	+	0.995295i	$0.469109\pi$
$702$		0			0
$703$	5.49241	−	4.79857i	0.207150	−	0.180982i
$704$	5.52823	−	8.37491i	0.208353	−	0.315641i
$705$		0			0
$706$	53.6762	−	51.3197i	2.02013	−	1.93144i
$707$	11.8375	+	2.14819i	0.445195	+	0.0807910i
$708$		0			0
$709$		−	34.9395i		−	1.31218i	−0.754683	−	0.656090i	$-0.772209\pi$
$709$		−	34.9395i		−	1.31218i	0.754683	−	0.656090i	$-0.227791\pi$
$710$	−38.2960	−	29.2392i	−1.43722	−	1.09733i
$711$		0			0
$712$	−5.62618	+	13.1631i	−0.210850	+	0.493308i
$713$	−0.323928	+	1.78499i	−0.0121312	+	0.0668484i
$714$		0			0
$715$	−1.98440	+	6.10737i	−0.0742125	+	0.228403i
$716$	−42.7171	−	28.1973i	−1.59641	−	1.05378i
$717$		0			0
$718$	31.2707	−	11.7361i	1.16701	−	0.437988i
$719$	4.32516	−	11.5243i	0.161301	−	0.429785i	−0.830589	−	0.556886i	$-0.811996\pi$
$719$	4.32516	−	11.5243i	0.161301	−	0.429785i	0.991890	+	0.127101i	$0.0405673\pi$
$720$		0			0
$721$	−3.02266	−	10.9524i	−0.112570	−	0.407888i
$722$	35.0075	−	23.1082i	1.30284	−	0.860000i
$723$		0			0
$724$	−37.4799	+	12.1780i	−1.39293	+	0.452590i
$725$	−4.88765	−	2.63015i	−0.181523	−	0.0976815i
$726$		0			0
$727$	−6.81510	−	9.38018i	−0.252758	−	0.347892i	0.663717	−	0.747984i	$-0.268978\pi$
$727$	−6.81510	−	9.38018i	−0.252758	−	0.347892i	−0.916475	+	0.400092i	$0.868978\pi$
$728$	11.2443	+	10.7507i	0.416742	+	0.398446i
$729$		0			0
$730$	−25.0967	+	12.0859i	−0.928870	+	0.447320i
$731$	1.56447	−	0.934730i	0.0578642	−	0.0345722i
$732$		0			0
$733$	−14.4350	−	3.29469i	−0.533168	−	0.121692i	−0.0525437	−	0.998619i	$-0.516733\pi$
$733$	−14.4350	−	3.29469i	−0.533168	−	0.121692i	−0.480625	+	0.876926i	$0.659590\pi$
$734$	−6.07011	−	33.4491i	−0.224052	−	1.23463i
$735$		0			0
$736$	−4.69030	−	3.74039i	−0.172887	−	0.137873i
$737$	−0.107879	+	0.180559i	−0.00397377	+	0.00665097i
$738$		0			0
$739$	−3.43527	−	25.3602i	−0.126368	−	0.932890i	−0.937490	−	0.348012i	$-0.886857\pi$
$739$	−3.43527	−	25.3602i	−0.126368	−	0.932890i	0.811122	−	0.584878i	$-0.198857\pi$
$740$	−45.4233	+	36.2238i	−1.66979	+	1.33161i
$741$		0			0
$742$	31.4684	+	15.1544i	1.15524	+	0.556335i
$743$	−6.40498	+	0.576458i	−0.234976	+	0.0211482i	−0.206501	−	0.978446i	$-0.566208\pi$
$743$	−6.40498	+	0.576458i	−0.234976	+	0.0211482i	−0.0284745	+	0.999595i	$0.509065\pi$
$744$		0			0
$745$	−10.0009	+	4.27460i	−0.366405	+	0.156609i
$746$	12.6352	−	5.40055i	0.462608	−	0.197728i
$747$		0			0
$748$	0.959135	−	0.0863237i	0.0350694	−	0.00315631i
$749$	−14.8870	−	7.16919i	−0.543958	−	0.261957i
$750$		0			0
$751$	−16.3423	+	13.0325i	−0.596338	+	0.475563i	−0.874536	−	0.484960i	$-0.838834\pi$
$751$	−16.3423	+	13.0325i	−0.596338	+	0.475563i	0.278199	+	0.960524i	$0.410263\pi$
$752$	0.486858	+	3.59413i	0.0177539	+	0.131065i
$753$		0			0
$754$	23.0920	−	38.6496i	0.840962	−	1.40753i
$755$	2.83304	+	2.25928i	0.103105	+	0.0822234i
$756$		0			0
$757$	3.47339	+	19.1399i	0.126242	+	0.695653i	0.983520	+	0.180799i	$0.0578683\pi$
$757$	3.47339	+	19.1399i	0.126242	+	0.695653i	−0.857278	+	0.514854i	$0.827846\pi$
$758$	−26.8269	−	6.12307i	−0.974397	−	0.222400i
$759$		0			0
$760$	8.08428	−	4.83013i	0.293248	−	0.175207i
$761$	−33.1033	+	15.9417i	−1.19999	+	0.577886i	−0.923673	−	0.383180i	$-0.874829\pi$
$761$	−33.1033	+	15.9417i	−1.19999	+	0.577886i	−0.276318	+	0.961066i	$0.589114\pi$
$762$		0			0
$763$	−5.93189	−	5.67147i	−0.214749	−	0.205321i
$764$	41.4479	+	57.0482i	1.49953	+	2.06393i
$765$		0			0
$766$	33.2828	+	17.9103i	1.20256	+	0.647124i
$767$	31.4463	−	10.2175i	1.13546	−	0.368934i
$768$		0			0
$769$	−34.7221	+	22.9198i	−1.25211	+	0.826510i	−0.990345	−	0.138621i	$-0.955733\pi$
$769$	−34.7221	+	22.9198i	−1.25211	+	0.826510i	−0.261764	+	0.965132i	$0.584304\pi$
$770$	−1.74847	−	6.33543i	−0.0630104	−	0.228313i
$771$		0			0
$772$	−16.1739	+	43.0952i	−0.582111	+	1.55103i
$773$	−42.8511	+	16.0823i	−1.54125	+	0.578440i	−0.970164	−	0.242451i	$-0.922049\pi$
$773$	−42.8511	+	16.0823i	−1.54125	+	0.578440i	−0.571084	+	0.820891i	$0.693477\pi$
$774$		0			0
$775$	−0.901935	−	0.595362i	−0.0323985	−	0.0213860i
$776$	−3.03300	+	9.33462i	−0.108878	+	0.335093i
$777$		0			0
$778$	8.36050	−	46.0702i	0.299739	−	1.65170i
$779$	−3.67261	+	8.59251i	−0.131585	+	0.307858i
$780$		0			0
$781$	−6.66350	+	2.32172i	−0.238439	+	0.0830777i
$782$		−	1.17568i		−	0.0420423i
$783$		0			0
$784$	7.02105	+	1.27413i	0.250752	+	0.0455048i
$785$	−32.4594	+	31.0344i	−1.15853	+	1.10766i
$786$		0			0
$787$	25.0357	−	37.9275i	0.892427	−	1.35197i	−0.0432331	−	0.999065i	$-0.513766\pi$
$787$	25.0357	−	37.9275i	0.892427	−	1.35197i	0.935660	−	0.352904i	$-0.114806\pi$
$788$	2.34688	−	2.05040i	0.0836040	−	0.0730426i
$789$		0			0
$790$	92.8510	+	34.8476i	3.30349	+	1.23982i
$791$	−9.54372	+	10.9237i	−0.339336	+	0.388401i
$792$		0			0
$793$	4.08330	+	6.18594i	0.145002	+	0.219669i
$794$	−42.3841	−	11.6973i	−1.50415	−	0.415120i
$795$		0			0
$796$	−7.75893	+	14.4185i	−0.275008	+	0.511051i
$797$	27.8228	+	1.24953i	0.985535	+	0.0442605i	0.531795	−	0.846873i	$-0.321518\pi$
$797$	27.8228	+	1.24953i	0.985535	+	0.0442605i	0.453741	+	0.891134i	$0.350089\pi$
$798$		0			0
$799$	0.585641	−	0.612532i	0.0207185	−	0.0216698i
$800$	3.14705	−	1.69350i	0.111265	−	0.0598742i
$801$		0			0
$802$	−13.3500	−	22.3442i	−0.471406	−	0.789001i
$803$	−0.547601	+	4.04255i	−0.0193244	+	0.142659i
$804$		0			0
$805$	−5.03887	+	0.914421i	−0.177597	+	0.0322291i
$806$	5.15272	−	7.09211i	0.181497	−	0.249809i
$807$		0			0
$808$	−27.0497	−	16.1614i	−0.951605	−	0.568557i
$809$	40.6876	+	3.66195i	1.43050	+	0.128747i	0.777629	−	0.628723i	$-0.216422\pi$
$809$	40.6876	+	3.66195i	1.43050	+	0.128747i	0.652869	+	0.757470i	$0.273565\pi$
$810$		0			0
$811$	10.8267	+	13.5763i	0.380178	+	0.476728i	0.934698	−	0.355442i	$-0.115670\pi$
$811$	10.8267	+	13.5763i	0.380178	+	0.476728i	−0.554520	+	0.832170i	$0.687098\pi$
$812$	1.31947	+	29.3803i	0.0463043	+	1.03105i
$813$		0			0
$814$	1.19499	+	13.2775i	0.0418845	+	0.465375i
$815$	−10.8497	−	47.5357i	−0.380049	−	1.66510i
$816$		0			0
$817$	−2.36781	−	5.53977i	−0.0828393	−	0.193812i
$818$	8.39132	−	1.91526i	0.293396	−	0.0669657i
$819$		0			0
$820$	32.2974	−	67.0662i	1.12787	−	2.34205i
$821$	6.21791	−	0.279247i	0.217007	−	0.00974578i	0.0639039	−	0.997956i	$-0.479645\pi$
$821$	6.21791	−	0.279247i	0.217007	−	0.00974578i	0.153103	+	0.988210i	$0.451073\pi$
$822$		0			0
$823$	44.9937	−	6.09481i	1.56838	−	0.212452i	0.702126	−	0.712053i	$-0.252234\pi$
$823$	44.9937	−	6.09481i	1.56838	−	0.212452i	0.866256	+	0.499601i	$0.166520\pi$
$824$	−2.66746	+	29.6379i	−0.0929254	+	1.03249i
$825$		0			0
$826$	−21.0990	+	26.4573i	−0.734127	+	0.920566i
$827$	19.2944	+	14.0182i	0.670931	+	0.487460i	0.870337	−	0.492457i	$-0.163901\pi$
$827$	19.2944	+	14.0182i	0.670931	+	0.487460i	−0.199406	+	0.979917i	$0.563901\pi$
$828$		0			0
$829$	−0.237884	+	1.04224i	−0.00826205	+	0.0361984i	−0.978891	−	0.204383i	$-0.934481\pi$
$829$	−0.237884	+	1.04224i	−0.00826205	+	0.0361984i	0.970629	+	0.240582i	$0.0773382\pi$
$830$	−15.7023	−	2.12702i	−0.545035	−	0.0738300i
$831$		0			0
$832$	16.3941	+	34.0428i	0.568364	+	1.18022i
$833$	−0.790074	−	1.46820i	−0.0273744	−	0.0508702i
$834$		0			0
$835$	24.5446	−	17.8327i	0.849402	−	0.617127i
$836$	0.142827	−	3.18029i	0.00493978	−	0.109993i
$837$		0			0
$838$	−28.8464	−	88.7801i	−0.996482	−	3.06686i
$839$	12.5020	−	45.2999i	0.431616	−	1.56393i	−0.347892	−	0.937534i	$-0.613103\pi$
$839$	12.5020	−	45.2999i	0.431616	−	1.56393i	0.779509	−	0.626392i	$-0.215469\pi$
$840$		0			0
$841$	7.59071	−	2.09490i	0.261749	−	0.0722381i
$842$	4.31323	+	3.76835i	0.148644	+	0.129866i
$843$		0			0
$844$	15.7076	+	41.8529i	0.540680	+	1.44064i
$845$	4.89172	+	5.59902i	0.168280	+	0.192612i
$846$		0			0
$847$	13.4430	+	4.36788i	0.461906	+	0.150082i
$848$	−10.4314	−	10.9104i	−0.358217	−	0.374666i
$849$		0			0
$850$	0.644011	+	0.275264i	0.0220894	+	0.00944147i
$851$	10.3877			0.356087
$852$		0			0
$853$	7.81343			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$853$	7.81343			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$854$	−6.97548	−	2.98147i	−0.238696	−	0.102024i
$855$		0			0
$856$	29.9065	+	31.2798i	1.02218	+	1.06912i
$857$	6.27128	+	2.03766i	0.214223	+	0.0696053i	0.414162	−	0.910203i	$-0.364075\pi$
$857$	6.27128	+	2.03766i	0.214223	+	0.0696053i	−0.199939	+	0.979808i	$0.564075\pi$
$858$		0			0
$859$	33.2497	+	38.0573i	1.13446	+	1.29850i	0.948797	+	0.315887i	$0.102302\pi$
$859$	33.2497	+	38.0573i	1.13446	+	1.29850i	0.185668	+	0.982612i	$0.440555\pi$
$860$	16.8631	+	44.9315i	0.575026	+	1.53215i
$861$		0			0
$862$	39.5188	+	34.5266i	1.34602	+	1.17598i
$863$	44.9400	−	12.4027i	1.52978	−	0.422191i	0.602980	−	0.797756i	$-0.293980\pi$
$863$	44.9400	−	12.4027i	1.52978	−	0.422191i	0.926796	+	0.375565i	$0.122551\pi$
$864$		0			0
$865$	−7.52903	+	27.2808i	−0.255995	+	0.927576i
$866$	27.9016	+	85.8722i	0.948134	+	2.91806i
$867$		0			0
$868$	−0.256914	+	5.72063i	−0.00872022	+	0.194171i
$869$	11.7505	−	8.53724i	0.398609	−	0.289606i
$870$		0			0
$871$	−0.375285	−	0.697397i	−0.0127161	−	0.0236304i
$872$	9.32617	+	19.3660i	0.315824	+	0.655815i
$873$		0			0
$874$	−3.85136	−	0.521703i	−0.130274	−	0.0176469i
$875$	−3.03469	+	13.2958i	−0.102591	+	0.449482i
$876$		0			0
$877$	32.8073	+	23.8359i	1.10782	+	0.804882i	0.982320	−	0.187211i	$-0.0599449\pi$
$877$	32.8073	+	23.8359i	1.10782	+	0.804882i	0.125505	+	0.992093i	$0.459945\pi$
$878$	48.2872	−	60.5503i	1.62962	−	2.04347i
$879$		0			0
$880$	−0.254611	+	2.82895i	−0.00858292	+	0.0953640i
$881$	10.8282	−	1.46678i	0.364811	−	0.0494170i	0.0504658	−	0.998726i	$-0.483929\pi$
$881$	10.8282	−	1.46678i	0.364811	−	0.0494170i	0.314345	+	0.949309i	$0.398215\pi$
$882$		0			0
$883$	−46.9265	+	2.10747i	−1.57920	+	0.0709221i	−0.817085	−	0.576517i	$-0.804412\pi$
$883$	−46.9265	+	2.10747i	−1.57920	+	0.0709221i	−0.762117	+	0.647439i	$0.775840\pi$
$884$	−1.57327	+	3.26694i	−0.0529149	+	0.109879i
$885$		0			0
$886$	−7.32021	+	1.67079i	−0.245927	+	0.0561313i
$887$	8.16995	+	19.1146i	0.274320	+	0.641804i	0.998875	−	0.0474129i	$-0.0150977\pi$
$887$	8.16995	+	19.1146i	0.274320	+	0.641804i	−0.724555	+	0.689217i	$0.757955\pi$
$888$		0			0
$889$	3.37058	+	14.7675i	0.113046	+	0.495285i
$890$	2.04122	+	22.6798i	0.0684219	+	0.760230i
$891$		0			0
$892$	2.82386	+	62.8782i	0.0945500	+	2.10532i
$893$	−1.74669	−	2.19028i	−0.0584508	−	0.0732950i
$894$		0			0
$895$	−35.1320	−	3.16194i	−1.17433	−	0.105692i
$896$	−23.9836	−	14.3295i	−0.801235	−	0.478715i
$897$		0			0
$898$	14.5985	−	20.0931i	0.487159	−	0.670516i
$899$	7.06444	−	1.28201i	0.235612	−	0.0427573i
$900$		0			0
$901$	−0.473433	+	3.49502i	−0.0157723	+	0.116436i
$902$	−8.76048	−	14.6626i	−0.291692	−	0.488210i
$903$		0			0
$904$	33.4549	−	18.0029i	1.11270	−	0.598767i
$905$	−18.7684	+	19.6302i	−0.623882	+	0.652530i
$906$		0			0
$907$	−7.39544	−	0.332130i	−0.245562	−	0.0110282i	−0.0782561	−	0.996933i	$-0.524935\pi$
$907$	−7.39544	−	0.332130i	−0.245562	−	0.0110282i	−0.167305	+	0.985905i	$0.553507\pi$
$908$	−1.39632	+	2.59480i	−0.0463386	+	0.0861116i
$909$		0			0
$910$	23.8548	+	6.58351i	0.790779	+	0.218241i
$911$	−5.73240	−	8.68421i	−0.189923	−	0.287721i	0.727119	−	0.686511i	$-0.240859\pi$
$911$	−5.73240	−	8.68421i	−0.189923	−	0.287721i	−0.917042	+	0.398790i	$0.869430\pi$
$912$		0			0
$913$	−1.52684	+	1.74761i	−0.0505311	+	0.0578375i
$914$	73.9332	+	27.7476i	2.44549	+	0.917809i
$915$		0			0
$916$	−7.27080	+	6.35231i	−0.240234	+	0.209886i
$917$	6.58271	−	9.97238i	0.217380	−	0.329317i
$918$		0			0
$919$	6.14788	−	5.87798i	0.202800	−	0.193897i	−0.582828	−	0.812595i	$-0.698054\pi$
$919$	6.14788	−	5.87798i	0.202800	−	0.193897i	0.785628	+	0.618699i	$0.212340\pi$
$920$	13.1973	+	2.39496i	0.435102	+	0.0789594i
$921$		0			0
$922$			10.3007i			0.339236i
$923$	5.36414	−	26.0223i	0.176563	−	0.856534i
$924$		0			0
$925$	−2.43209	+	5.69016i	−0.0799667	+	0.187091i
$926$	2.84091	−	15.6547i	0.0933582	−	0.514446i
$927$		0			0
$928$	−7.33688	+	22.5806i	−0.240845	+	0.741245i
$929$	−3.32853	−	2.19714i	−0.109205	−	0.0720859i	0.495114	−	0.868828i	$-0.335126\pi$
$929$	−3.32853	−	2.19714i	−0.109205	−	0.0720859i	−0.604319	+	0.796742i	$0.706555\pi$
$930$		0			0
$931$	−5.16021	+	1.93666i	−0.169119	+	0.0634715i
$932$	−7.24374	+	19.3009i	−0.237277	+	0.632221i
$933$		0			0
$934$	−8.45868	−	30.6493i	−0.276776	−	1.00288i
$935$	0.553877	−	0.365611i	0.0181137	−	0.0119568i
$936$		0			0
$937$	−18.2301	+	5.92332i	−0.595551	+	0.193506i	−0.591255	−	0.806484i	$-0.701367\pi$
$937$	−18.2301	+	5.92332i	−0.595551	+	0.193506i	−0.00429590	+	0.999991i	$0.501367\pi$
$938$	0.713753	+	0.384087i	0.0233049	+	0.0125409i
$939$		0			0
$940$	13.1173	+	18.0544i	0.427839	+	0.588870i
$941$	33.8968	+	32.4086i	1.10500	+	1.05649i	0.998062	+	0.0622251i	$0.0198197\pi$
$941$	33.8968	+	32.4086i	1.10500	+	1.05649i	0.106940	+	0.994265i	$0.465895\pi$
$942$		0			0
$943$	−11.9911	+	5.77461i	−0.390484	+	0.188047i
$944$	12.5547	−	7.50111i	0.408622	−	0.244140i
$945$		0			0
$946$	10.7360	+	2.45041i	0.349056	+	0.0796697i
$947$	−4.61779	−	25.4461i	−0.150058	−	0.826888i	−0.967879	−	0.251416i	$-0.919104\pi$
$947$	−4.61779	−	25.4461i	−0.150058	−	0.826888i	0.817821	−	0.575473i	$-0.195182\pi$
$948$		0			0
$949$	−12.0093	−	9.57707i	−0.389837	−	0.310885i
$950$	1.18750	−	1.98754i	0.0385276	−	0.0644844i
$951$		0			0
$952$	−0.215814	−	1.59320i	−0.00699456	−	0.0516359i
$953$	−36.2747	+	28.9281i	−1.17505	+	0.937073i	−0.998881	−	0.0472870i	$-0.984942\pi$
$953$	−36.2747	+	28.9281i	−1.17505	+	0.937073i	−0.176171	+	0.984360i	$0.556371\pi$
$954$		0			0
$955$	43.7836	+	21.0851i	1.41680	+	0.682297i
$956$	−18.6720	+	1.68051i	−0.603894	+	0.0543515i
$957$		0			0
$958$	−61.9982	+	26.4993i	−2.00307	+	0.856154i
$959$	−25.5892	+	10.9374i	−0.826320	+	0.353186i
$960$		0			0
$961$	−29.4828	+	2.65350i	−0.951060	+	0.0855969i
$962$	−45.2248	−	21.7791i	−1.45811	−	0.702186i
$963$		0			0
$964$	−77.7802	+	62.0276i	−2.50513	+	1.99778i
$965$	4.25816	+	31.4350i	0.137075	+	1.01193i
$966$		0			0
$967$	3.19707	−	5.35099i	0.102811	−	0.172076i	−0.802721	−	0.596355i	$-0.796615\pi$
$967$	3.19707	−	5.35099i	0.102811	−	0.172076i	0.905532	+	0.424279i	$0.139472\pi$
$968$	−28.9437	−	23.0818i	−0.930285	−	0.741877i
$969$		0			0
$970$	2.78782	+	15.3622i	0.0895115	+	0.493249i
$971$	−38.1151	−	8.69953i	−1.22317	−	0.279181i	−0.438295	−	0.898831i	$-0.644417\pi$
$971$	−38.1151	−	8.69953i	−1.22317	−	0.279181i	−0.784878	+	0.619650i	$0.787274\pi$
$972$		0			0
$973$	23.1792	−	13.8489i	0.743092	−	0.443977i
$974$	80.0795	−	38.5643i	2.56591	−	1.23568i
$975$		0			0
$976$	2.36966	+	2.26563i	0.0758510	+	0.0725210i
$977$	−5.46579	−	7.52302i	−0.174866	−	0.240683i	0.712583	−	0.701587i	$-0.247525\pi$
$977$	−5.46579	−	7.52302i	−0.174866	−	0.240683i	−0.887450	+	0.460905i	$0.847525\pi$
$978$		0			0
$979$	2.93674	+	1.58033i	0.0938586	+	0.0505075i
$980$	41.7568	−	13.5676i	1.33387	−	0.433402i
$981$		0			0
$982$	−56.4392	+	37.2552i	−1.80105	+	1.18886i
$983$	11.9191	+	43.1880i	0.380161	+	1.37748i	0.864514	+	0.502609i	$0.167627\pi$
$983$	11.9191	+	43.1880i	0.380161	+	1.37748i	−0.484353	+	0.874873i	$0.660945\pi$
$984$		0			0
$985$	0.754644	−	2.01074i	0.0240450	−	0.0640676i
$986$	−4.35628	+	1.63494i	−0.138732	+	0.0520671i
$987$		0			0
$988$	10.0039	+	6.60350i	0.318266	+	0.210085i
$989$	2.65157	−	8.16071i	0.0843151	−	0.259495i
$990$		0			0
$991$	−1.30237	+	7.17664i	−0.0413711	+	0.227974i	−0.997990	−	0.0633678i	$-0.979816\pi$
$991$	−1.30237	+	7.17664i	−0.0413711	+	0.227974i	0.956619	+	0.291341i	$0.0941016\pi$
$992$	−1.81693	+	4.25091i	−0.0576874	+	0.134966i
$993$		0			0
$994$	10.0901	+	25.2513i	0.320037	+	0.800921i
$995$			11.2840i			0.357726i
$996$		0			0
$997$	39.4687	+	7.16252i	1.24999	+	0.226839i	0.762902	−	0.646515i	$-0.223774\pi$
$997$	39.4687	+	7.16252i	1.24999	+	0.226839i	0.487086	+	0.873354i	$0.338060\pi$
$998$	51.1630	−	48.9169i	1.61954	−	1.54844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.269.22	yes	576
3.2	odd	2	inner	639.2.z.a.269.3	✓	576
71.52	odd	70	inner	639.2.z.a.620.3	yes	576
213.194	even	70	inner	639.2.z.a.620.22	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.269.3	✓	576	3.2	odd	2	inner
639.2.z.a.269.22	yes	576	1.1	even	1	trivial
639.2.z.a.620.3	yes	576	71.52	odd	70	inner
639.2.z.a.620.22	yes	576	213.194	even	70	inner

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16212 + 0.924133i) q^{2} +(2.43861 + 2.55058i) q^{4} +(2.31285 + 0.751492i) q^{5} +(-0.903009 - 1.03358i) q^{7} +(1.26307 + 3.36545i) q^{8} +O(q^{10})\)	\(q+(2.16212 + 0.924133i) q^{2} +(2.43861 + 2.55058i) q^{4} +(2.31285 + 0.751492i) q^{5} +(-0.903009 - 1.03358i) q^{7} +(1.26307 + 3.36545i) q^{8} +(4.30618 + 3.76220i) q^{10} +(0.807261 - 0.222790i) q^{11} +(-0.838870 + 3.03958i) q^{13} +(-0.997248 - 3.06921i) q^{14} +(-0.0625732 + 1.39330i) q^{16} +(0.263640 - 0.191546i) q^{17} +(-0.510487 - 0.948645i) q^{19} +(3.72340 + 7.73171i) q^{20} +(1.95128 + 0.264319i) q^{22} +(0.341423 - 1.49587i) q^{23} +(0.739466 + 0.537253i) q^{25} +(-4.62271 + 5.79669i) q^{26} +(0.434139 - 4.82368i) q^{28} +(-6.01748 + 0.815123i) q^{29} +(-1.18117 + 0.0530465i) q^{31} +(1.69644 - 3.52270i) q^{32} +(0.747035 - 0.170506i) q^{34} +(-1.31180 - 3.06911i) q^{35} +(1.50650 + 6.60042i) q^{37} +(-0.227060 - 2.52284i) q^{38} +(0.392199 + 8.73298i) q^{40} +(-5.40826 - 6.78174i) q^{41} +(5.56991 + 0.501301i) q^{43} +(2.53683 + 1.51569i) q^{44} +(2.12058 - 2.91873i) q^{46} +(2.55873 - 0.464340i) q^{47} +(0.686777 - 5.06999i) q^{49} +(1.10232 + 1.84497i) q^{50} +(-9.79836 + 5.27272i) q^{52} +(-7.47931 + 7.82275i) q^{53} +(2.03450 + 0.0913695i) q^{55} +(2.33788 - 4.34451i) q^{56} +(-13.7638 - 3.79856i) q^{58} +(-5.77672 - 8.75135i) q^{59} +(1.54659 - 1.77021i) q^{61} +(-2.60285 - 0.976868i) q^{62} +(9.02399 - 7.88402i) q^{64} +(-4.22440 + 6.39969i) q^{65} +(-0.181537 + 0.173567i) q^{67} +(1.13147 + 0.205331i) q^{68} -7.84807i q^{70} +(-8.40781 + 0.555642i) q^{71} +(-1.91457 + 4.47935i) q^{73} +(-2.84243 + 15.6631i) q^{74} +(1.17472 - 3.61541i) q^{76} +(-0.959234 - 0.633185i) q^{77} +(16.2379 - 6.09419i) q^{79} +(-1.19178 + 3.17548i) q^{80} +(-5.42605 - 19.6609i) q^{82} +(-2.31270 + 1.52660i) q^{83} +(0.753706 - 0.244894i) q^{85} +(11.5795 + 6.23121i) q^{86} +(1.76942 + 2.43539i) q^{88} +(2.87840 + 2.75203i) q^{89} +(3.89914 - 1.87773i) q^{91} +(4.64793 - 2.77701i) q^{92} +(5.96138 + 1.36065i) q^{94} +(-0.467784 - 2.57770i) q^{95} +(2.13474 + 1.70240i) q^{97} +(6.17024 - 10.3272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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