LMFDB - Embedded newform 639.2.z.a.62.2

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			62.2
Character	$\chi$	$=$	639.62
Dual form			639.2.z.a.134.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54116 + 0.344223i) q^{2} +(4.41107 - 1.21738i) q^{4} +(-0.225573 - 0.310474i) q^{5} +(3.10021 + 2.96411i) q^{7} +(-6.07416 + 2.59622i) q^{8} +O(q^{10})$	\(q+(-2.54116 + 0.344223i) q^{2} +(4.41107 - 1.21738i) q^{4} +(-0.225573 - 0.310474i) q^{5} +(3.10021 + 2.96411i) q^{7} +(-6.07416 + 2.59622i) q^{8} +(0.680089 + 0.711317i) q^{10} +(5.26868 + 0.474189i) q^{11} +(0.0382469 + 0.424958i) q^{13} +(-8.89844 - 6.46510i) q^{14} +(6.68524 - 3.99424i) q^{16} +(0.912266 + 2.80767i) q^{17} +(-6.30234 + 2.36531i) q^{19} +(-1.37298 - 1.09492i) q^{20} +(-13.5518 + 0.608610i) q^{22} +(5.74426 + 2.76629i) q^{23} +(1.49957 - 4.61521i) q^{25} +(-0.243472 - 1.06672i) q^{26} +(17.2837 + 9.30075i) q^{28} +(-9.88943 - 0.444135i) q^{29} +(3.38158 - 5.65981i) q^{31} +(-5.28419 + 4.21400i) q^{32} +(-3.28468 - 6.82070i) q^{34} +(0.220955 - 1.63116i) q^{35} +(-0.0838498 + 0.0403799i) q^{37} +(15.2011 - 8.18004i) q^{38} +(2.17622 + 1.30023i) q^{40} +(-0.878501 + 3.84896i) q^{41} +(1.27632 - 2.37180i) q^{43} +(23.8178 - 4.32229i) q^{44} +(-15.5493 - 5.05227i) q^{46} +(0.643543 - 0.974926i) q^{47} +(0.511335 + 11.3858i) q^{49} +(-2.22199 + 12.2442i) q^{50} +(0.686044 + 1.82796i) q^{52} +(0.448914 + 0.123892i) q^{53} +(-1.04125 - 1.74275i) q^{55} +(-26.5267 - 9.95562i) q^{56} +(25.2835 - 2.27556i) q^{58} +(3.78392 + 3.30591i) q^{59} +(-5.10693 + 4.88273i) q^{61} +(-6.64489 + 15.5465i) q^{62} +(1.21399 - 1.26974i) q^{64} +(0.123311 - 0.107734i) q^{65} +(2.07359 + 7.51347i) q^{67} +(7.44206 + 11.2742i) q^{68} +4.22109i q^{70} +(1.22606 + 8.33647i) q^{71} +(1.25776 + 9.28514i) q^{73} +(0.199176 - 0.131475i) q^{74} +(-24.9206 + 18.1059i) q^{76} +(14.9285 + 17.0870i) q^{77} +(0.405151 + 0.947897i) q^{79} +(-2.74812 - 1.17460i) q^{80} +(0.907507 - 10.0832i) q^{82} +(3.50348 - 4.01005i) q^{83} +(0.665926 - 0.916569i) q^{85} +(-2.42690 + 6.46646i) q^{86} +(-33.2339 + 10.7983i) q^{88} +(4.40209 - 15.9506i) q^{89} +(-1.14105 + 1.43083i) q^{91} +(28.7060 + 5.20936i) q^{92} +(-1.29975 + 2.69896i) q^{94} +(2.15601 + 1.42317i) q^{95} +(1.53579 - 0.350535i) q^{97} +(-5.21863 - 28.7570i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{17}{70}\right)$	$-1$

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 $

$2$	−2.54116	+	0.344223i	−1.79687	+	0.243403i	−0.955069	−	0.296385i	$-0.904219\pi$
$2$	−2.54116	+	0.344223i	−1.79687	+	0.243403i	−0.841801	+	0.539787i	$0.818505\pi$
$3$		0			0
$3$		0			0
$4$	4.41107	−	1.21738i	2.20553	−	0.608689i
$5$	−0.225573	−	0.310474i	−0.100879	−	0.138848i	0.755593	−	0.655041i	$-0.227349\pi$
$5$	−0.225573	−	0.310474i	−0.100879	−	0.138848i	−0.856472	+	0.516193i	$0.827349\pi$
$6$		0			0
$7$	3.10021	+	2.96411i	1.17177	+	1.12033i	0.990588	+	0.136877i	$0.0437066\pi$
$7$	3.10021	+	2.96411i	1.17177	+	1.12033i	0.181182	+	0.983450i	$0.442008\pi$
$8$	−6.07416	+	2.59622i	−2.14754	+	0.917902i
$9$		0			0
$10$	0.680089	+	0.711317i	0.215063	+	0.224938i
$11$	5.26868	+	0.474189i	1.58857	+	0.142973i	0.848365	−	0.529412i	$-0.177587\pi$
$11$	5.26868	+	0.474189i	1.58857	+	0.142973i	0.740201	+	0.672386i	$0.234730\pi$
$12$		0			0
$13$	0.0382469	+	0.424958i	0.0106078	+	0.117862i	0.999533	−	0.0305512i	$-0.00972625\pi$
$13$	0.0382469	+	0.424958i	0.0106078	+	0.117862i	−0.988925	+	0.148413i	$0.952583\pi$
$14$	−8.89844	−	6.46510i	−2.37821	−	1.72787i
$15$		0			0
$16$	6.68524	−	3.99424i	1.67131	−	0.998561i
$17$	0.912266	+	2.80767i	0.221257	+	0.680959i	0.998650	+	0.0519439i	$0.0165417\pi$
$17$	0.912266	+	2.80767i	0.221257	+	0.680959i	−0.777393	+	0.629015i	$0.783458\pi$
$18$		0			0
$19$	−6.30234	+	2.36531i	−1.44586	+	0.542639i	−0.946199	−	0.323584i	$-0.895112\pi$
$19$	−6.30234	+	2.36531i	−1.44586	+	0.542639i	−0.499657	+	0.866223i	$0.666541\pi$
$20$	−1.37298	−	1.09492i	−0.307008	−	0.244831i
$21$		0			0
$22$	−13.5518	+	0.608610i	−2.88925	+	0.129756i
$23$	5.74426	+	2.76629i	1.19776	+	0.576812i	0.923037	−	0.384711i	$-0.125699\pi$
$23$	5.74426	+	2.76629i	1.19776	+	0.576812i	0.274725	+	0.961523i	$0.411413\pi$
$24$		0			0
$25$	1.49957	−	4.61521i	0.299915	−	0.923043i
$26$	−0.243472	−	1.06672i	−0.0477488	−	0.209201i
$27$		0			0
$28$	17.2837	+	9.30075i	3.26631	+	1.75768i
$29$	−9.88943	−	0.444135i	−1.83642	−	0.0824738i	−0.900537	−	0.434780i	$-0.856826\pi$
$29$	−9.88943	−	0.444135i	−1.83642	−	0.0824738i	−0.935885	+	0.352306i	$0.885398\pi$
$30$		0			0
$31$	3.38158	−	5.65981i	0.607349	−	1.01653i	−0.388135	−	0.921603i	$-0.626880\pi$
$31$	3.38158	−	5.65981i	0.607349	−	1.01653i	0.995484	−	0.0949289i	$-0.0302624\pi$
$32$	−5.28419	+	4.21400i	−0.934122	+	0.744937i
$33$		0			0
$34$	−3.28468	−	6.82070i	−0.563317	−	1.16974i
$35$	0.220955	−	1.63116i	0.0373483	−	0.275716i
$36$		0			0
$37$	−0.0838498	+	0.0403799i	−0.0137848	+	0.00663842i	−0.440763	−	0.897623i	$-0.645292\pi$
$37$	−0.0838498	+	0.0403799i	−0.0137848	+	0.00663842i	0.426979	+	0.904262i	$0.359578\pi$
$38$	15.2011	−	8.18004i	2.46594	−	1.32698i
$39$		0			0
$40$	2.17622	+	1.30023i	0.344091	+	0.205585i
$41$	−0.878501	+	3.84896i	−0.137199	+	0.601107i	0.858844	+	0.512237i	$0.171183\pi$
$41$	−0.878501	+	3.84896i	−0.137199	+	0.601107i	−0.996043	+	0.0888706i	$0.971674\pi$
$42$		0			0
$43$	1.27632	−	2.37180i	0.194637	−	0.361697i	−0.764506	−	0.644616i	$-0.777017\pi$
$43$	1.27632	−	2.37180i	0.194637	−	0.361697i	0.959144	+	0.282920i	$0.0913029\pi$
$44$	23.8178	−	4.32229i	3.59066	−	0.651609i
$45$		0			0
$46$	−15.5493	−	5.05227i	−2.29262	−	0.744917i
$47$	0.643543	−	0.974926i	0.0938704	−	0.142208i	−0.784604	−	0.619998i	$-0.787134\pi$
$47$	0.643543	−	0.974926i	0.0938704	−	0.142208i	0.878474	+	0.477790i	$0.158562\pi$
$48$		0			0
$49$	0.511335	+	11.3858i	0.0730479	+	1.62654i
$50$	−2.22199	+	12.2442i	−0.314237	+	1.73159i
$51$		0			0
$52$	0.686044	+	1.82796i	0.0951372	+	0.253492i
$53$	0.448914	+	0.123892i	0.0616630	+	0.0170179i	0.296732	−	0.954961i	$-0.404103\pi$
$53$	0.448914	+	0.123892i	0.0616630	+	0.0170179i	−0.235069	+	0.971979i	$0.575532\pi$
$54$		0			0
$55$	−1.04125	−	1.74275i	−0.140402	−	0.234993i
$56$	−26.5267	−	9.95562i	−3.54477	−	1.33038i
$57$		0			0
$58$	25.2835	−	2.27556i	3.31988	−	0.298795i
$59$	3.78392	+	3.30591i	0.492624	+	0.430393i	0.868063	−	0.496455i	$-0.165365\pi$
$59$	3.78392	+	3.30591i	0.492624	+	0.430393i	−0.375439	+	0.926847i	$0.622508\pi$
$60$		0			0
$61$	−5.10693	+	4.88273i	−0.653876	+	0.625169i	−0.943264	−	0.332042i	$-0.892262\pi$
$61$	−5.10693	+	4.88273i	−0.653876	+	0.625169i	0.289389	+	0.957212i	$0.406548\pi$
$62$	−6.64489	+	15.5465i	−0.843901	+	1.97441i
$63$		0			0
$64$	1.21399	−	1.26974i	0.151749	−	0.158717i
$65$	0.123311	−	0.107734i	0.0152949	−	0.0133627i
$66$		0			0
$67$	2.07359	+	7.51347i	0.253329	+	0.917916i	0.974356	+	0.225010i	$0.0722415\pi$
$67$	2.07359	+	7.51347i	0.253329	+	0.917916i	−0.721028	+	0.692906i	$0.756330\pi$
$68$	7.44206	+	11.2742i	0.902482	+	1.36720i
$69$		0			0
$70$			4.22109i			0.504517i
$71$	1.22606	+	8.33647i	0.145506	+	0.989357i
$71$	1.22606	+	8.33647i	0.145506	+	0.989357i
$72$		0			0
$73$	1.25776	+	9.28514i	0.147209	+	1.08674i	0.902296	+	0.431118i	$0.141881\pi$
$73$	1.25776	+	9.28514i	0.147209	+	1.08674i	−0.755086	+	0.655626i	$0.772405\pi$
$74$	0.199176	−	0.131475i	0.0231537	−	0.0152836i
$75$		0			0
$76$	−24.9206	+	18.1059i	−2.85859	+	2.07689i
$77$	14.9285	+	17.0870i	1.70126	+	1.94724i
$78$		0			0
$79$	0.405151	+	0.947897i	0.0455830	+	0.106647i	0.940772	−	0.339040i	$-0.110102\pi$
$79$	0.405151	+	0.947897i	0.0455830	+	0.106647i	−0.895189	+	0.445687i	$0.852959\pi$
$80$	−2.74812	−	1.17460i	−0.307249	−	0.131325i
$81$		0			0
$82$	0.907507	−	10.0832i	0.100217	−	1.11351i
$83$	3.50348	−	4.01005i	0.384556	−	0.440160i	−0.527917	−	0.849296i	$-0.677027\pi$
$83$	3.50348	−	4.01005i	0.384556	−	0.440160i	0.912474	+	0.409136i	$0.134170\pi$
$84$		0			0
$85$	0.665926	−	0.916569i	0.0722298	−	0.0994158i
$86$	−2.42690	+	6.46646i	−0.261700	+	0.697297i
$87$		0			0
$88$	−33.2339	+	10.7983i	−3.54274	+	1.15111i
$89$	4.40209	−	15.9506i	0.466620	−	1.69076i	−0.229893	−	0.973216i	$-0.573837\pi$
$89$	4.40209	−	15.9506i	0.466620	−	1.69076i	0.696513	−	0.717544i	$-0.254734\pi$
$90$		0			0
$91$	−1.14105	+	1.43083i	−0.119614	+	0.149992i
$92$	28.7060	+	5.20936i	2.99280	+	0.543114i
$93$		0			0
$94$	−1.29975	+	2.69896i	−0.134059	+	0.278377i
$95$	2.15601	+	1.42317i	0.221201	+	0.146014i
$96$		0			0
$97$	1.53579	−	0.350535i	0.155936	−	0.0355914i	−0.143840	−	0.989601i	$-0.545945\pi$
$97$	1.53579	−	0.350535i	0.155936	−	0.0355914i	0.299776	+	0.954010i	$0.403088\pi$
$98$	−5.21863	−	28.7570i	−0.527161	−	2.90490i
$99$		0			0
$100$	0.996265	−	22.1836i	0.0996265	−	2.21836i
$101$	1.71080	+	0.390480i	0.170231	+	0.0388542i	0.306787	−	0.951778i	$-0.400746\pi$
$101$	1.71080	+	0.390480i	0.170231	+	0.0388542i	−0.136556	+	0.990632i	$0.543603\pi$
$102$		0			0
$103$	12.4259	+	15.5816i	1.22436	+	1.53530i	0.760407	+	0.649447i	$0.224999\pi$
$103$	12.4259	+	15.5816i	1.22436	+	1.53530i	0.463957	+	0.885858i	$0.346429\pi$
$104$	−1.33560	−	2.48197i	−0.130967	−	0.243377i
$105$		0			0
$106$	−1.18341	−	0.160303i	−0.114943	−	0.0155700i
$107$	−7.37966	−	0.999642i	−0.713418	−	0.0966391i	−0.231474	−	0.972841i	$-0.574355\pi$
$107$	−7.37966	−	0.999642i	−0.713418	−	0.0966391i	−0.481944	+	0.876202i	$0.660069\pi$
$108$		0			0
$109$	−0.415241	−	0.771647i	−0.0397729	−	0.0739103i	0.859933	−	0.510406i	$-0.170505\pi$
$109$	−0.415241	−	0.771647i	−0.0397729	−	0.0739103i	−0.899706	+	0.436496i	$0.856219\pi$
$110$	3.24587	+	4.07019i	0.309481	+	0.388077i
$111$		0			0
$112$	32.5650	+	7.43275i	3.07711	+	0.702329i
$113$	0.209114	−	4.65628i	0.0196718	−	0.438026i	−0.964854	−	0.262787i	$-0.915358\pi$
$113$	0.209114	−	4.65628i	0.0196718	−	0.438026i	0.984526	−	0.175240i	$-0.0560701\pi$
$114$		0			0
$115$	−0.436887	−	2.40745i	−0.0407399	−	0.224496i
$116$	−44.1636	+	10.0801i	−4.10049	+	0.935910i
$117$		0			0
$118$	−10.7535	−	7.09832i	−0.989940	−	0.653453i
$119$	−5.49400	+	11.4084i	−0.503634	+	1.04581i
$120$		0			0
$121$	16.7109	+	3.03258i	1.51917	+	0.275689i
$122$	11.2968	−	14.1657i	1.02276	−	1.28250i
$123$		0			0
$124$	8.02625	−	29.0825i	0.720778	−	2.61168i
$125$	−3.59609	+	1.16844i	−0.321644	+	0.104509i
$126$		0			0
$127$	3.16613	−	8.43611i	0.280948	−	0.748584i	−0.717687	−	0.696365i	$-0.754799\pi$
$127$	3.16613	−	8.43611i	0.280948	−	0.748584i	0.998636	−	0.0522185i	$-0.0166292\pi$
$128$	5.29749	−	7.29137i	0.468237	−	0.644473i
$129$		0			0
$130$	−0.276269	+	0.316215i	−0.0242304	+	0.0277339i
$131$	1.30502	−	14.4999i	0.114020	−	1.26687i	−0.711578	−	0.702607i	$-0.752019\pi$
$131$	1.30502	−	14.4999i	0.114020	−	1.26687i	0.825598	−	0.564259i	$-0.190838\pi$
$132$		0			0
$133$	−26.5496	−	11.3479i	−2.30214	−	0.983984i
$134$	−7.85562	−	18.3791i	−0.678622	−	1.58772i
$135$		0			0
$136$	−12.8306	−	14.6858i	−1.10021	−	1.25929i
$137$	1.32377	−	0.961777i	0.113098	−	0.0821701i	−0.529799	−	0.848123i	$-0.677733\pi$
$137$	1.32377	−	0.961777i	0.113098	−	0.0821701i	0.642896	+	0.765953i	$0.277733\pi$
$138$		0			0
$139$	−17.3195	+	11.4325i	−1.46902	+	0.969693i	−0.472956	+	0.881086i	$0.656813\pi$
$139$	−17.3195	+	11.4325i	−1.46902	+	0.969693i	−0.996067	+	0.0886068i	$0.971759\pi$
$140$	−1.01109	−	7.46413i	−0.0854523	−	0.630835i
$141$		0			0
$142$	−5.98521	−	20.7623i	−0.502268	−	1.74233i
$143$			2.25710i			0.188748i
$144$		0			0
$145$	2.09289	+	3.17060i	0.173805	+	0.263304i
$146$	−6.39232	−	23.1621i	−0.529032	−	1.91691i
$147$		0			0
$148$	−0.320709	+	0.280195i	−0.0263621	+	0.0230319i
$149$	−8.01353	+	8.38150i	−0.656494	+	0.686639i	−0.964301	−	0.264810i	$-0.914691\pi$
$149$	−8.01353	+	8.38150i	−0.656494	+	0.686639i	0.307807	+	0.951449i	$0.400405\pi$
$150$		0			0
$151$	8.47717	−	19.8333i	0.689862	−	1.61401i	−0.0958323	−	0.995397i	$-0.530551\pi$
$151$	8.47717	−	19.8333i	0.689862	−	1.61401i	0.785694	−	0.618615i	$-0.212306\pi$
$152$	32.1406	−	30.7295i	2.60694	−	2.49249i
$153$		0			0
$154$	−43.8173	−	38.2821i	−3.53090	−	3.08486i
$155$	−2.52002	+	0.226806i	−0.202413	+	0.0182175i
$156$		0			0
$157$	17.4086	+	6.53354i	1.38935	+	0.521434i	0.930243	−	0.366945i	$-0.119596\pi$
$157$	17.4086	+	6.53354i	1.38935	+	0.521434i	0.459112	+	0.888378i	$0.348168\pi$
$158$	−1.35584	−	2.26929i	−0.107865	−	0.180535i
$159$		0			0
$160$	2.50031	+	0.690041i	0.197667	+	0.0545526i
$161$	9.60885	+	25.6027i	0.757284	+	2.01777i
$162$		0			0
$163$	0.0942744	−	0.519495i	0.00738414	−	0.0406900i	−0.980027	−	0.198864i	$-0.936275\pi$
$163$	0.0942744	−	0.519495i	0.00738414	−	0.0406900i	0.987411	+	0.158174i	$0.0505606\pi$
$164$	0.810515	+	18.0475i	0.0632906	+	1.40927i
$165$		0			0
$166$	−7.52253	+	11.3961i	−0.583862	+	0.884513i
$167$	−6.96206	−	2.26211i	−0.538740	−	0.175047i	0.0269929	−	0.999636i	$-0.491407\pi$
$167$	−6.96206	−	2.26211i	−0.538740	−	0.175047i	−0.565733	+	0.824588i	$0.691407\pi$
$168$		0			0
$169$	12.6120	−	2.28873i	0.970151	−	0.176056i
$170$	−1.37672	+	2.55837i	−0.105590	+	0.196218i
$171$		0			0
$172$	2.74256	−	12.0159i	0.209118	−	0.916207i
$173$	−15.1336	−	9.04189i	−1.15058	−	0.687442i	−0.194607	−	0.980881i	$-0.562343\pi$
$173$	−15.1336	−	9.04189i	−1.15058	−	0.687442i	−0.955978	+	0.293439i	$0.905200\pi$
$174$		0			0
$175$	18.3290	−	9.86324i	1.38554	−	0.745591i
$176$	37.1164	−	17.8743i	2.79775	−	1.34733i
$177$		0			0
$178$	−5.69583	+	42.0483i	−0.426920	+	3.15165i
$179$	8.55754	+	17.7699i	0.639621	+	1.32819i	0.928683	+	0.370876i	$0.120942\pi$
$179$	8.55754	+	17.7699i	0.639621	+	1.32819i	−0.289062	+	0.957310i	$0.593343\pi$
$180$		0			0
$181$	9.50195	−	7.57755i	0.706275	−	0.563235i	−0.203128	−	0.979152i	$-0.565111\pi$
$181$	9.50195	−	7.57755i	0.706275	−	0.563235i	0.909403	+	0.415917i	$0.136539\pi$
$182$	2.40706	−	4.02874i	0.178423	−	0.298630i
$183$		0			0
$184$	−42.0735	−	1.88952i	−3.10170	−	0.139297i
$185$	0.0314512	+	0.0169246i	0.00231233	+	0.00124432i
$186$		0			0
$187$	3.47507	+	15.2253i	0.254122	+	1.11338i
$188$	1.65186	−	5.08390i	0.120474	−	0.370781i
$189$		0			0
$190$	−5.96864	−	2.87434i	−0.433010	−	0.208527i
$191$	3.39536	−	0.152486i	0.245680	−	0.0110335i	0.0783155	−	0.996929i	$-0.475046\pi$
$191$	3.39536	−	0.152486i	0.245680	−	0.0110335i	0.167364	+	0.985895i	$0.446474\pi$
$192$		0			0
$193$	−6.45606	−	5.14853i	−0.464717	−	0.370600i	0.362959	−	0.931805i	$-0.381766\pi$
$193$	−6.45606	−	5.14853i	−0.464717	−	0.370600i	−0.827677	+	0.561205i	$0.810338\pi$
$194$	−3.78203	+	1.41942i	−0.271534	+	0.101908i
$195$		0			0
$196$	16.1163	+	49.6009i	1.15116	+	3.54292i
$197$	12.1011	−	7.23010i	0.862171	−	0.515123i	−0.0124545	−	0.999922i	$-0.503965\pi$
$197$	12.1011	−	7.23010i	0.862171	−	0.515123i	0.874625	+	0.484799i	$0.161107\pi$
$198$		0			0
$199$	−16.8558	−	12.2464i	−1.19487	−	0.868127i	−0.201104	−	0.979570i	$-0.564453\pi$
$199$	−16.8558	−	12.2464i	−1.19487	−	0.868127i	−0.993771	+	0.111442i	$0.964453\pi$
$200$	2.87346	+	31.9268i	0.203184	+	2.25756i
$201$		0			0
$202$	−4.48184	−	0.403373i	−0.315341	−	0.0283812i
$203$	−29.3429	−	30.6902i	−2.05947	−	2.15403i
$204$		0			0
$205$	1.39317	−	0.595470i	0.0973033	−	0.0415894i
$206$	−36.9398	−	35.3181i	−2.57372	−	2.46073i
$207$		0			0
$208$	1.95308	+	2.68818i	0.135422	+	0.186392i
$209$	−34.3266	+	9.47354i	−2.37442	+	0.655299i
$210$		0			0
$211$	−6.61532	+	0.896105i	−0.455417	+	0.0616904i	−0.358350	−	0.933587i	$-0.616660\pi$
$211$	−6.61532	+	0.896105i	−0.455417	+	0.0616904i	−0.0970673	+	0.995278i	$0.530946\pi$
$212$	2.13101			0.146359
$213$		0			0
$214$	19.0970			1.30544
$215$	−1.02429	+	0.138749i	−0.0698558	+	0.00946261i
$216$		0			0
$217$	27.2599	−	7.52325i	1.85052	−	0.510711i
$218$	1.32081	+	1.81794i	0.0894566	+	0.123126i
$219$		0			0
$220$	−6.71460	−	6.41981i	−0.452698	−	0.432824i
$221$	−1.15825	+	0.495060i	−0.0779123	+	0.0333013i
$222$		0			0
$223$	−14.9192	−	15.6043i	−0.999066	−	1.04494i	−0.998990	−	0.0449410i	$-0.985690\pi$
$223$	−14.9192	−	15.6043i	−0.999066	−	1.04494i	−7.61978e−5	−	1.00000i	$-0.500024\pi$
$224$	−28.8729	−	2.59860i	−1.92915	−	0.173627i
$225$		0			0
$226$	1.07141	+	11.9043i	0.0712691	+	0.791865i
$227$	4.23203	+	3.07475i	0.280890	+	0.204078i	0.719305	−	0.694694i	$-0.244460\pi$
$227$	4.23203	+	3.07475i	0.280890	+	0.204078i	−0.438416	+	0.898772i	$0.644460\pi$
$228$		0			0
$229$	15.0637	−	9.00013i	0.995436	−	0.594746i	0.0798245	−	0.996809i	$-0.474564\pi$
$229$	15.0637	−	9.00013i	0.995436	−	0.594746i	0.915612	+	0.402063i	$0.131707\pi$
$230$	1.93890	+	5.96731i	0.127847	+	0.393473i
$231$		0			0
$232$	61.2230	−	22.9774i	4.01949	−	1.50854i
$233$	15.3760	+	12.2620i	1.00732	+	0.803309i	0.980537	−	0.196332i	$-0.0629031\pi$
$233$	15.3760	+	12.2620i	1.00732	+	0.803309i	0.0267802	+	0.999641i	$0.491475\pi$
$234$		0			0
$235$	−0.447855	+	0.0201132i	−0.0292148	+	0.00131204i
$236$	20.7156	+	9.97613i	1.34847	+	0.649391i
$237$		0			0
$238$	10.0341	−	30.8817i	0.650413	−	2.00177i
$239$	−4.08658	−	17.9045i	−0.264339	−	1.15815i	−0.916491	−	0.400056i	$-0.868991\pi$
$239$	−4.08658	−	17.9045i	−0.264339	−	1.15815i	0.652151	−	0.758089i	$-0.273867\pi$
$240$		0			0
$241$	−15.7606	−	8.48117i	−1.01523	−	0.546320i	−0.120402	−	0.992725i	$-0.538418\pi$
$241$	−15.7606	−	8.48117i	−1.01523	−	0.546320i	−0.894831	+	0.446405i	$0.852704\pi$
$242$	−43.5088	−	1.95398i	−2.79685	−	0.125607i
$243$		0			0
$244$	−16.5829	+	27.7551i	−1.06161	+	1.77684i
$245$	3.41964	−	2.72708i	0.218473	−	0.174226i
$246$		0			0
$247$	−1.24620	−	2.58777i	−0.0792940	−	0.164656i
$248$	−5.84613	+	43.1579i	−0.371230	+	2.74053i
$249$		0			0
$250$	8.73603	−	4.20705i	0.552515	−	0.266077i
$251$	−8.19791	+	4.41148i	−0.517447	+	0.278450i	−0.711678	−	0.702506i	$-0.752065\pi$
$251$	−8.19791	+	4.41148i	−0.517447	+	0.278450i	0.194231	+	0.980956i	$0.437779\pi$
$252$		0			0
$253$	28.9529	+	17.2986i	1.82025	+	1.08755i
$254$	−5.14172	+	22.5273i	−0.322620	+	1.41349i
$255$		0			0
$256$	−12.6168	+	23.4459i	−0.788550	+	1.46537i
$257$	−20.8533	+	3.78431i	−1.30079	+	0.236059i	−0.784380	−	0.620281i	$-0.787018\pi$
$257$	−20.8533	+	3.78431i	−1.30079	+	0.236059i	−0.516412	+	0.856340i	$0.672733\pi$
$258$		0			0
$259$	−0.379642	−	0.123353i	−0.0235898	−	0.00766480i
$260$	0.412781	−	0.625337i	0.0255996	−	0.0387817i
$261$		0			0
$262$	1.67496	+	37.2959i	0.103479	+	2.30415i
$263$	2.42974	−	13.3890i	0.149824	−	0.825600i	−0.818236	−	0.574883i	$-0.805048\pi$
$263$	2.42974	−	13.3890i	0.149824	−	0.825600i	0.968060	−	0.250718i	$-0.0806665\pi$
$264$		0			0
$265$	−0.0627973	−	0.167323i	−0.00385761	−	0.0102786i
$266$	71.3730	+	19.6977i	4.37616	+	1.20774i
$267$		0			0
$268$	18.2935	+	30.6181i	1.11745	+	1.87030i
$269$	2.08627	+	0.782991i	0.127202	+	0.0477398i	0.414164	−	0.910202i	$-0.364074\pi$
$269$	2.08627	+	0.782991i	0.127202	+	0.0477398i	−0.286962	+	0.957942i	$0.592645\pi$
$270$		0			0
$271$	−2.40779	+	0.216705i	−0.146263	+	0.0131639i	−0.162529	−	0.986704i	$-0.551965\pi$
$271$	−2.40779	+	0.216705i	−0.146263	+	0.0131639i	0.0162658	+	0.999868i	$0.494822\pi$
$272$	17.3132	+	15.1261i	1.04977	+	0.917155i
$273$		0			0
$274$	−3.03285	+	2.89970i	−0.183221	+	0.175177i
$275$	10.0893	−	23.6050i	0.608405	−	1.42343i
$276$		0			0
$277$	−12.0204	+	12.5723i	−0.722234	+	0.755398i	−0.977377	−	0.211506i	$-0.932163\pi$
$277$	−12.0204	+	12.5723i	−0.722234	+	0.755398i	0.255142	+	0.966903i	$0.417878\pi$
$278$	40.0763	−	35.0136i	2.40362	−	2.09998i
$279$		0			0
$280$	2.89273	+	10.4816i	0.172874	+	0.626393i
$281$	11.4047	+	17.2773i	0.680346	+	1.03068i	0.996631	+	0.0820155i	$0.0261357\pi$
$281$	11.4047	+	17.2773i	0.680346	+	1.03068i	−0.316285	+	0.948664i	$0.602436\pi$
$282$		0			0
$283$			18.1856i			1.08102i	0.841337	+	0.540512i	$0.181769\pi$
$283$			18.1856i			1.08102i	−0.841337	+	0.540512i	$0.818231\pi$
$284$	15.5569	+	35.2802i	0.923129	+	2.09349i
$285$		0			0
$286$	−0.776947	−	5.73566i	−0.0459419	−	0.339156i
$287$	−14.1323	+	9.32864i	−0.834202	+	0.550652i
$288$		0			0
$289$	6.70253	−	4.86967i	0.394266	−	0.286451i
$290$	−6.40977	−	7.33657i	−0.376395	−	0.430818i
$291$		0			0
$292$	16.8516	+	39.4262i	0.986164	+	2.30724i
$293$	3.90508	+	1.66911i	0.228137	+	0.0975104i	0.504058	−	0.863670i	$-0.331840\pi$
$293$	3.90508	+	1.66911i	0.228137	+	0.0975104i	−0.275921	+	0.961180i	$0.588983\pi$
$294$		0			0
$295$	0.172851	−	1.92053i	0.0100638	−	0.111818i
$296$	0.404482	−	0.462966i	0.0235100	−	0.0269094i
$297$		0			0
$298$	17.4785	−	24.0571i	1.01250	−	1.39359i
$299$	−0.955858	+	2.54687i	−0.0552787	+	0.147290i
$300$		0			0
$301$	10.9871	−	3.56994i	0.633288	−	0.205768i
$302$	−14.7147	+	53.3176i	−0.846738	+	3.06808i
$303$		0			0
$304$	−32.6850	+	40.9858i	−1.87462	+	2.35069i
$305$	2.66795	+	0.484161i	0.152766	+	0.0277230i
$306$		0			0
$307$	−8.73841	+	18.1455i	−0.498727	+	1.03562i	0.487942	+	0.872876i	$0.337748\pi$
$307$	−8.73841	+	18.1455i	−0.498727	+	1.03562i	−0.986669	+	0.162741i	$0.947966\pi$
$308$	86.6518	+	57.1984i	4.93745	+	3.25918i
$309$		0			0
$310$	6.32569	−	1.44380i	0.359275	−	0.0820022i
$311$	−0.440277	−	2.42612i	−0.0249658	−	0.137573i	0.969039	−	0.246906i	$-0.0794140\pi$
$311$	−0.440277	−	2.42612i	−0.0249658	−	0.137573i	−0.994005	+	0.109334i	$0.965128\pi$
$312$		0			0
$313$	−0.310057	+	6.90396i	−0.0175255	+	0.390235i	0.970990	+	0.239118i	$0.0768584\pi$
$313$	−0.310057	+	6.90396i	−0.0175255	+	0.390235i	−0.988516	+	0.151117i	$0.951713\pi$
$314$	−46.4869	−	10.6103i	−2.62341	−	0.598776i
$315$		0			0
$316$	2.94109	+	3.68802i	0.165450	+	0.207467i
$317$	8.82002	+	16.3903i	0.495382	+	0.920573i	0.998414	+	0.0563054i	$0.0179321\pi$
$317$	8.82002	+	16.3903i	0.495382	+	0.920573i	−0.503032	+	0.864268i	$0.667782\pi$
$318$		0			0
$319$	−51.8936	−	7.02947i	−2.90548	−	0.393575i
$320$	−0.668064	−	0.0904955i	−0.0373459	−	0.00505885i
$321$		0			0
$322$	−33.2307	−	61.7529i	−1.85187	−	3.44135i
$323$	−12.3904	−	15.5371i	−0.689421	−	0.864507i
$324$		0			0
$325$	2.01863	+	0.460738i	0.111973	+	0.0255572i
$326$	−0.0607440	+	1.35257i	−0.00336430	+	0.0749119i
$327$		0			0
$328$	−4.65660	−	25.6600i	−0.257118	−	1.41684i
$329$	4.88490	−	1.11495i	0.269313	−	0.0614690i
$330$		0			0
$331$	−16.0991	−	10.6270i	−0.884889	−	0.584110i	0.0246650	−	0.999696i	$-0.492148\pi$
$331$	−16.0991	−	10.6270i	−0.884889	−	0.584110i	−0.909554	+	0.415586i	$0.863577\pi$
$332$	10.5723	−	21.9537i	0.580232	−	1.20486i
$333$		0			0
$334$	18.4704	+	3.35188i	1.01065	+	0.183407i
$335$	1.86499	−	2.33863i	0.101896	−	0.127773i
$336$		0			0
$337$	4.92806	−	17.8564i	0.268448	−	0.972701i	−0.698054	−	0.716045i	$-0.745951\pi$
$337$	4.92806	−	17.8564i	0.268448	−	0.972701i	0.966503	−	0.256656i	$-0.0826208\pi$
$338$	−31.2611	+	10.1574i	−1.70038	+	0.552488i
$339$		0			0
$340$	1.82163	−	4.85373i	0.0987920	−	0.263230i
$341$	20.5003	−	28.2162i	1.11015	−	1.52799i
$342$		0			0
$343$	−12.4092	+	14.2034i	−0.670031	+	0.766913i
$344$	−1.59486	+	17.7203i	−0.0859889	+	0.955415i
$345$		0			0
$346$	41.5692	+	17.7675i	2.23478	+	0.955189i
$347$	−0.0786314	−	0.183967i	−0.00422115	−	0.00987588i	0.917404	−	0.397957i	$-0.130281\pi$
$347$	−0.0786314	−	0.183967i	−0.00422115	−	0.00987588i	−0.921625	+	0.388081i	$0.873138\pi$
$348$		0			0
$349$	7.32244	+	8.38120i	0.391961	+	0.448636i	0.914867	−	0.403755i	$-0.132295\pi$
$349$	7.32244	+	8.38120i	0.391961	+	0.448636i	−0.522906	+	0.852390i	$0.675152\pi$
$350$	−43.1817	+	31.3733i	−2.30816	+	1.67697i
$351$		0			0
$352$	−29.8389	+	19.6965i	−1.59042	+	1.04983i
$353$	−0.609890	−	4.50239i	−0.0324612	−	0.239638i	0.967449	−	0.253067i	$-0.0814394\pi$
$353$	−0.609890	−	4.50239i	−0.0324612	−	0.239638i	−0.999910	+	0.0134295i	$0.995725\pi$
$354$		0			0
$355$	2.31170	−	2.26114i	0.122692	−	0.120009i
$356$		−	75.7182i		−	4.01306i
$357$		0			0
$358$	−27.8629	−	42.2105i	−1.47260	−	2.23089i
$359$	−6.22335	−	22.5498i	−0.328456	−	1.19013i	−0.922595	−	0.385771i	$-0.873935\pi$
$359$	−6.22335	−	22.5498i	−0.328456	−	1.19013i	0.594138	−	0.804363i	$-0.297493\pi$
$360$		0			0
$361$	19.8165	−	17.3131i	1.04297	−	0.911218i
$362$	−21.5376	+	22.5266i	−1.13199	+	1.18397i
$363$		0			0
$364$	−3.29138	+	7.70057i	−0.172515	+	0.403619i
$365$	2.59908	−	2.48498i	0.136042	−	0.130070i
$366$		0			0
$367$	−22.8812	−	19.9907i	−1.19439	−	1.04351i	−0.998015	−	0.0629780i	$-0.979940\pi$
$367$	−22.8812	−	19.9907i	−1.19439	−	1.04351i	−0.196375	−	0.980529i	$-0.562917\pi$
$368$	49.4510	−	4.45067i	2.57781	−	0.232007i
$369$		0			0
$370$	−0.0857482	−	0.0321818i	−0.00445784	−	0.00167305i
$371$	1.02450	+	1.71472i	0.0531893	+	0.0890238i
$372$		0			0
$373$	6.34589	+	1.75135i	0.328578	+	0.0906817i	0.426434	−	0.904519i	$-0.359770\pi$
$373$	6.34589	+	1.75135i	0.328578	+	0.0906817i	−0.0978557	+	0.995201i	$0.531198\pi$
$374$	−14.0716	−	37.4936i	−0.727625	−	1.93875i
$375$		0			0
$376$	−1.37786	+	7.59263i	−0.0710577	+	0.391560i
$377$	−0.189502	−	4.21958i	−0.00975983	−	0.217320i
$378$		0			0
$379$	7.31602	−	11.0833i	0.375799	−	0.569311i	−0.596628	−	0.802518i	$-0.703493\pi$
$379$	7.31602	−	11.0833i	0.375799	−	0.569311i	0.972427	+	0.233207i	$0.0749219\pi$
$380$	11.2428	+	3.65301i	0.576744	+	0.187396i
$381$		0			0
$382$	−8.57566	+	1.55625i	−0.438769	+	0.0796248i
$383$	−17.3695	+	32.2780i	−0.887540	+	1.64933i	−0.134935	+	0.990854i	$0.543083\pi$
$383$	−17.3695	+	32.2780i	−0.887540	+	1.64933i	−0.752605	+	0.658472i	$0.771203\pi$
$384$		0			0
$385$	1.93762	−	8.48927i	0.0987503	−	0.432653i
$386$	18.1781	+	10.8609i	0.925241	+	0.552806i
$387$		0			0
$388$	6.34775	−	3.41587i	0.322258	−	0.173415i
$389$	−18.9788	+	9.13971i	−0.962263	+	0.463401i	−0.847969	−	0.530046i	$-0.822175\pi$
$389$	−18.9788	+	9.13971i	−0.962263	+	0.463401i	−0.114294	+	0.993447i	$0.536461\pi$
$390$		0			0
$391$	−2.52653	+	18.6516i	−0.127772	+	0.943250i
$392$	−32.6659	−	67.8314i	−1.64988	−	3.42600i
$393$		0			0
$394$	−28.2622	+	22.5383i	−1.42383	+	1.13546i
$395$	0.202907	−	0.339609i	0.0102093	−	0.0170876i
$396$		0			0
$397$	−19.4252	−	0.872389i	−0.974925	−	0.0437839i	−0.448302	−	0.893882i	$-0.647971\pi$
$397$	−19.4252	−	0.872389i	−0.974925	−	0.0437839i	−0.526624	+	0.850098i	$0.676542\pi$
$398$	47.0487	+	25.3180i	2.35834	+	1.26908i
$399$		0			0
$400$	−8.40928	−	36.8435i	−0.420464	−	1.84217i
$401$	4.68455	−	14.4176i	0.233935	−	0.719979i	−0.763325	−	0.646014i	$-0.776435\pi$
$401$	4.68455	−	14.4176i	0.233935	−	0.719979i	0.997261	−	0.0739649i	$-0.0235653\pi$
$402$		0			0
$403$	2.53452	+	1.22056i	0.126253	+	0.0608004i
$404$	8.02184	−	0.360261i	0.399101	−	0.0179237i
$405$		0			0
$406$	85.1292	+	67.8882i	4.22489	+	3.36924i
$407$	−0.460925	+	0.172988i	−0.0228472	+	0.00857470i
$408$		0			0
$409$	−4.04834	−	12.4595i	−0.200178	−	0.616084i	−0.999877	−	0.0156829i	$-0.995008\pi$
$409$	−4.04834	−	12.4595i	−0.200178	−	0.616084i	0.799699	−	0.600401i	$-0.204992\pi$
$410$	−3.33529	+	1.99274i	−0.164718	+	0.0984146i
$411$		0			0
$412$	73.7804	+	53.6046i	3.63490	+	2.64091i
$413$	1.93188	+	21.4649i	0.0950616	+	1.05622i
$414$		0			0
$415$	−2.03531	−	0.183181i	−0.0999093	−	0.00899200i
$416$	−1.99288	−	2.08439i	−0.0977089	−	0.102196i
$417$		0			0
$418$	83.9683	−	35.8898i	4.10702	−	1.75543i
$419$	−3.41360	−	3.26374i	−0.166766	−	0.159444i	0.603066	−	0.797691i	$-0.293946\pi$
$419$	−3.41360	−	3.26374i	−0.166766	−	0.159444i	−0.769832	+	0.638247i	$0.779660\pi$
$420$		0			0
$421$	−12.0268	−	16.5535i	−0.586151	−	0.806768i	0.408202	−	0.912892i	$-0.366156\pi$
$421$	−12.0268	−	16.5535i	−0.586151	−	0.806768i	−0.994353	+	0.106124i	$0.966156\pi$
$422$	16.5021	−	4.55429i	0.803310	−	0.221699i
$423$		0			0
$424$	−3.04842	+	0.412937i	−0.148045	+	0.0200540i
$425$	14.3260			0.694913
$426$		0			0
$427$	−30.3055			−1.46659
$428$	−33.7691	+	4.57434i	−1.63229	+	0.221109i
$429$		0			0
$430$	2.55512	−	0.705167i	0.123219	−	0.0340062i
$431$	−19.2682	−	26.5204i	−0.928117	−	1.27744i	−0.960590	−	0.277971i	$-0.910338\pi$
$431$	−19.2682	−	26.5204i	−0.928117	−	1.27744i	0.0324728	−	0.999473i	$-0.489662\pi$
$432$		0			0
$433$	12.3375	+	11.7959i	0.592904	+	0.566874i	0.926715	−	0.375766i	$-0.122620\pi$
$433$	12.3375	+	11.7959i	0.592904	+	0.566874i	−0.333811	+	0.942640i	$0.608335\pi$
$434$	−66.6820	+	28.5012i	−3.20084	+	1.36810i
$435$		0			0
$436$	−2.77104	−	2.89828i	−0.132709	−	0.138802i
$437$	−42.7454	−	3.84716i	−2.04479	−	0.184035i
$438$		0			0
$439$	−1.27423	−	14.1579i	−0.0608157	−	0.675717i	−0.967326	−	0.253534i	$-0.918407\pi$
$439$	−1.27423	−	14.1579i	−0.0608157	−	0.675717i	0.906511	−	0.422183i	$-0.138736\pi$
$440$	10.8493	+	7.88245i	0.517218	+	0.375781i
$441$		0			0
$442$	2.77288	−	1.65672i	0.131893	−	0.0788022i
$443$	−0.377610	−	1.16216i	−0.0179408	−	0.0552161i	0.941685	−	0.336495i	$-0.109241\pi$
$443$	−0.377610	−	1.16216i	−0.0179408	−	0.0552161i	−0.959626	+	0.281279i	$0.909241\pi$
$444$		0			0
$445$	−5.94524	+	2.23129i	−0.281832	+	0.105773i
$446$	43.2835	+	34.5174i	2.04953	+	1.63445i
$447$		0			0
$448$	7.52727	−	0.338050i	0.355630	−	0.0159714i
$449$	−0.776739	−	0.374058i	−0.0366566	−	0.0176529i	0.415466	−	0.909609i	$-0.363619\pi$
$449$	−0.776739	−	0.374058i	−0.0366566	−	0.0176529i	−0.452122	+	0.891956i	$0.649333\pi$
$450$		0			0
$451$	−6.45368	+	19.8624i	−0.303892	+	0.935283i
$452$	−4.74604	−	20.7938i	−0.223235	−	0.978056i
$453$		0			0
$454$	−11.8127	−	6.35666i	−0.554395	−	0.298333i
$455$	0.701625	+	0.0315100i	0.0328927	+	0.00147721i
$456$		0			0
$457$	15.3056	−	25.6172i	0.715964	−	1.19832i	−0.256787	−	0.966468i	$-0.582664\pi$
$457$	15.3056	−	25.6172i	0.715964	−	1.19832i	0.972751	−	0.231853i	$-0.0744789\pi$
$458$	−35.1811	+	28.0560i	−1.64391	+	1.31097i
$459$		0			0
$460$	−4.85791	−	10.0876i	−0.226501	−	0.470335i
$461$	4.22084	−	31.1595i	0.196584	−	1.45124i	−0.576582	−	0.817039i	$-0.695614\pi$
$461$	4.22084	−	31.1595i	0.196584	−	1.45124i	0.773166	−	0.634203i	$-0.218672\pi$
$462$		0			0
$463$	35.1393	−	16.9222i	1.63306	−	0.786440i	0.633136	−	0.774040i	$-0.281767\pi$
$463$	35.1393	−	16.9222i	1.63306	−	0.786440i	0.999923	−	0.0123998i	$-0.00394707\pi$
$464$	−67.8872	+	36.5317i	−3.15158	+	1.69594i
$465$		0			0
$466$	−43.2938	−	25.8668i	−2.00555	−	1.19826i
$467$	6.83934	−	29.9651i	0.316487	−	1.38662i	−0.527180	−	0.849754i	$-0.676751\pi$
$467$	6.83934	−	29.9651i	0.316487	−	1.38662i	0.843667	−	0.536867i	$-0.180392\pi$
$468$		0			0
$469$	−15.8422	+	29.4397i	−0.731523	+	1.35940i
$470$	1.13115	−	0.205273i	0.0521759	−	0.00946854i
$471$		0			0
$472$	−31.5670	−	10.2567i	−1.45299	−	0.472104i
$473$	7.84921	−	11.8910i	0.360907	−	0.546751i
$474$		0			0
$475$	1.46558	+	32.6336i	0.0672453	+	1.49733i
$476$	−10.3461	+	57.0116i	−0.474212	+	2.61312i
$477$		0			0
$478$	16.5478	+	44.0914i	0.756878	+	2.01670i
$479$	22.2934	+	6.15260i	1.01861	+	0.281119i	0.735180	−	0.677872i	$-0.237098\pi$
$479$	22.2934	+	6.15260i	1.01861	+	0.281119i	0.283434	+	0.958992i	$0.408526\pi$
$480$		0			0
$481$	−0.0203668	−	0.0340882i	−0.000928645	−	0.00155429i
$482$	42.9697	+	16.1268i	1.95722	+	0.734556i
$483$		0			0
$484$	77.4046	−	6.96654i	3.51839	−	0.316661i
$485$	−0.455265	−	0.397753i	−0.0206725	−	0.0180610i
$486$		0			0
$487$	−4.01178	+	3.83565i	−0.181791	+	0.173810i	−0.776472	−	0.630152i	$-0.782993\pi$
$487$	−4.01178	+	3.83565i	−0.181791	+	0.173810i	0.594681	+	0.803962i	$0.297278\pi$
$488$	18.3437	−	42.9172i	0.830380	−	1.94277i
$489$		0			0
$490$	−7.75113	+	8.10705i	−0.350161	+	0.366239i
$491$	5.16881	−	4.51585i	0.233265	−	0.203798i	−0.533367	−	0.845884i	$-0.679074\pi$
$491$	5.16881	−	4.51585i	0.233265	−	0.203798i	0.766633	+	0.642086i	$0.221931\pi$
$492$		0			0
$493$	−7.77481	−	28.1714i	−0.350160	−	1.26878i
$494$	4.05757	+	6.14695i	0.182559	+	0.276564i
$495$		0			0
$496$		−	51.3440i		−	2.30541i
$497$	−20.9092	+	29.4790i	−0.937904	+	1.32231i
$498$		0			0
$499$	−1.88243	−	13.8967i	−0.0842691	−	0.622100i	−0.983001	−	0.183601i	$-0.941225\pi$
$499$	−1.88243	−	13.8967i	−0.0842691	−	0.622100i	0.898732	−	0.438499i	$-0.144490\pi$
$500$	−14.4402	+	9.53187i	−0.645784	+	0.426278i
$501$		0			0
$502$	19.3136	−	14.0322i	0.862010	−	0.626287i
$503$	5.28050	+	6.04402i	0.235446	+	0.269489i	0.858642	−	0.512576i	$-0.171309\pi$
$503$	5.28050	+	6.04402i	0.235446	+	0.269489i	−0.623196	+	0.782066i	$0.714166\pi$
$504$		0			0
$505$	−0.264677	−	0.619243i	−0.0117780	−	0.0275559i
$506$	−79.5285	−	33.9921i	−3.53547	−	1.51113i
$507$		0			0
$508$	3.69606	−	41.0666i	0.163986	−	1.82204i
$509$	−7.01834	+	8.03314i	−0.311083	+	0.356063i	−0.887266	−	0.461258i	$-0.847398\pi$
$509$	−7.01834	+	8.03314i	−0.311083	+	0.356063i	0.576184	+	0.817320i	$0.304541\pi$
$510$		0			0
$511$	−23.6228	+	32.5140i	−1.04501	+	1.43834i
$512$	17.6570	−	47.0470i	0.780337	−	2.07920i
$513$		0			0
$514$	51.6888	−	16.7947i	2.27990	−	0.740783i
$515$	2.03474	−	7.37273i	0.0896615	−	0.324881i
$516$		0			0
$517$	3.85292	−	4.83141i	0.169451	−	0.212485i
$518$	1.00719	+	0.182778i	0.0442535	+	0.00803082i
$519$		0			0
$520$	−0.469311	+	0.974535i	−0.0205807	+	0.0427362i
$521$	11.5888	+	7.64968i	0.507713	+	0.335138i	0.778650	−	0.627459i	$-0.215905\pi$
$521$	11.5888	+	7.64968i	0.507713	+	0.335138i	−0.270937	+	0.962597i	$0.587333\pi$
$522$		0			0
$523$	28.6462	−	6.53831i	1.25261	−	0.285900i	0.455775	−	0.890095i	$-0.349362\pi$
$523$	28.6462	−	6.53831i	1.25261	−	0.285900i	0.796837	+	0.604195i	$0.206505\pi$
$524$	−11.8954	−	65.5489i	−0.519652	−	2.86352i
$525$		0			0
$526$	−1.56556	+	34.8599i	−0.0682616	+	1.51996i
$527$	18.9758	+	4.33109i	0.826597	+	0.188665i
$528$		0			0
$529$	11.0039	+	13.7985i	0.478431	+	0.599934i
$530$	0.217174	+	0.403578i	0.00943345	+	0.0175303i
$531$		0			0
$532$	−130.927	−	17.7352i	−5.67640	−	0.768920i
$533$	−1.66925	−	0.226115i	−0.0723032	−	0.00979413i
$534$		0			0
$535$	1.35429	+	2.51669i	0.0585509	+	0.108806i
$536$	−32.1019	−	40.2545i	−1.38659	−	1.73873i
$537$		0			0
$538$	−5.57107	−	1.27156i	−0.240186	−	0.0548208i
$539$	−2.70495	+	60.2304i	−0.116510	+	2.59431i
$540$		0			0
$541$	0.276854	+	1.52559i	0.0119029	+	0.0655902i	0.989334	−	0.145663i	$-0.0465314\pi$
$541$	0.276854	+	1.52559i	0.0119029	+	0.0655902i	−0.977431	+	0.211253i	$0.932246\pi$
$542$	6.04399	−	1.37950i	0.259612	−	0.0592546i
$543$		0			0
$544$	−16.6521	−	10.9920i	−0.713953	−	0.471276i
$545$	−0.145909	+	0.302984i	−0.00625007	+	0.0129784i
$546$		0			0
$547$	31.0431	+	5.63349i	1.32731	+	0.240871i	0.795478	−	0.605982i	$-0.207220\pi$
$547$	31.0431	+	5.63349i	1.32731	+	0.240871i	0.531828	+	0.846852i	$0.321505\pi$
$548$	4.66840	−	5.85399i	0.199424	−	0.250070i
$549$		0			0
$550$	−17.5130	+	63.4569i	−0.746757	+	2.70581i
$551$	63.3771	−	20.5925i	2.69996	−	0.877269i
$552$		0			0
$553$	−1.55361	+	4.13959i	−0.0660664	+	0.176033i
$554$	26.2180	−	36.0860i	1.11390	−	1.53315i
$555$		0			0
$556$	−62.4799	+	71.5140i	−2.64974	+	3.03287i
$557$	−1.54463	+	17.1623i	−0.0654483	+	0.727190i	0.894510	+	0.447048i	$0.147525\pi$
$557$	−1.54463	+	17.1623i	−0.0654483	+	0.727190i	−0.959958	+	0.280142i	$0.909618\pi$
$558$		0			0
$559$	1.05673	+	0.451669i	0.0446950	+	0.0191036i
$560$	−5.03810	−	11.7872i	−0.212899	−	0.498101i
$561$		0			0
$562$	−34.9283	−	39.9787i	−1.47336	−	1.68640i
$563$	4.90391	−	3.56290i	0.206675	−	0.150158i	−0.479633	−	0.877469i	$-0.659230\pi$
$563$	4.90391	−	3.56290i	0.206675	−	0.150158i	0.686308	+	0.727311i	$0.259230\pi$
$564$		0			0
$565$	−1.49283	+	0.985407i	−0.0628037	+	0.0414564i
$566$	−6.25992	−	46.2125i	−0.263124	−	1.94246i
$567$		0			0
$568$	−29.0906	−	47.4539i	−1.22061	−	1.99112i
$569$			27.9822i			1.17307i	0.809922	+	0.586537i	$0.199509\pi$
$569$			27.9822i			1.17307i	−0.809922	+	0.586537i	$0.800491\pi$
$570$		0			0
$571$	12.8539	+	19.4728i	0.537919	+	0.814913i	0.997308	−	0.0733223i	$-0.0233602\pi$
$571$	12.8539	+	19.4728i	0.537919	+	0.814913i	−0.459389	+	0.888235i	$0.651932\pi$
$572$	2.74775	+	9.95624i	0.114889	+	0.416291i
$573$		0			0
$574$	32.7012	−	28.5702i	1.36492	−	1.19250i
$575$	21.3810	−	22.3627i	0.891648	−	0.932591i
$576$		0			0
$577$	9.02787	−	21.1218i	0.375835	−	0.879310i	−0.619693	−	0.784844i	$-0.712743\pi$
$577$	9.02787	−	21.1218i	0.375835	−	0.879310i	0.995528	−	0.0944657i	$-0.0301143\pi$
$578$	−15.3559	+	14.6818i	−0.638722	+	0.610681i
$579$		0			0
$580$	13.0917	+	11.4379i	0.543604	+	0.474932i
$581$	22.7477	−	2.04733i	0.943735	−	0.0849377i
$582$		0			0
$583$	2.30643	+	0.865619i	0.0955227	+	0.0358503i
$584$	−31.7461	−	53.1340i	−1.31366	−	2.19870i
$585$		0			0
$586$	−10.4980	−	2.89725i	−0.433667	−	0.119684i
$587$	1.90195	+	5.06773i	0.0785019	+	0.209167i	0.969626	−	0.244592i	$-0.0786540\pi$
$587$	1.90195	+	5.06773i	0.0785019	+	0.209167i	−0.891124	+	0.453759i	$0.850083\pi$
$588$		0			0
$589$	−7.92467	+	43.6685i	−0.326530	+	1.79933i
$590$	0.221850	+	4.93987i	0.00913342	+	0.203371i
$591$		0			0
$592$	−0.399268	+	0.604866i	−0.0164098	+	0.0248598i
$593$	−16.4157	−	5.33380i	−0.674114	−	0.219033i	−0.0480972	−	0.998843i	$-0.515316\pi$
$593$	−16.4157	−	5.33380i	−0.674114	−	0.219033i	−0.626016	+	0.779810i	$0.715316\pi$
$594$		0			0
$595$	4.78132	−	0.867681i	0.196015	−	0.0355715i
$596$	−25.1448	+	46.7268i	−1.02997	+	1.91401i
$597$		0			0
$598$	1.55229	−	6.80104i	0.0634780	−	0.278115i
$599$	−16.6547	−	9.95073i	−0.680493	−	0.406576i	0.130646	−	0.991429i	$-0.458295\pi$
$599$	−16.6547	−	9.95073i	−0.680493	−	0.406576i	−0.811139	+	0.584853i	$0.801152\pi$
$600$		0			0
$601$	−6.42028	+	3.45490i	−0.261889	+	0.140928i	−0.599545	−	0.800341i	$-0.704652\pi$
$601$	−6.42028	+	3.45490i	−0.261889	+	0.140928i	0.337656	+	0.941270i	$0.390366\pi$
$602$	−26.6912	+	12.8538i	−1.08785	+	0.523882i
$603$		0			0
$604$	13.2487	−	97.8060i	0.539083	−	3.97967i
$605$	−2.82798	−	5.87236i	−0.114974	−	0.238745i
$606$		0			0
$607$	11.7982	−	9.40875i	0.478874	−	0.381889i	−0.354095	−	0.935210i	$-0.615211\pi$
$607$	11.7982	−	9.40875i	0.478874	−	0.381889i	0.832968	+	0.553320i	$0.186639\pi$
$608$	23.3354	−	39.0568i	0.946374	−	1.58396i
$609$		0			0
$610$	−6.94633	−	0.311960i	−0.281249	−	0.0126309i
$611$	0.438916	+	0.236191i	0.0177566	+	0.00955526i
$612$		0			0
$613$	−7.57967	−	33.2087i	−0.306140	−	1.34129i	−0.860687	−	0.509135i	$-0.829965\pi$
$613$	−7.57967	−	33.2087i	−0.306140	−	1.34129i	0.554547	−	0.832153i	$-0.312892\pi$
$614$	15.9596	−	49.1185i	0.644076	−	1.98226i
$615$		0			0
$616$	−135.039	−	65.0316i	−5.44090	−	2.62020i
$617$	32.2727	−	1.44937i	1.29925	−	0.0583494i	0.615541	−	0.788105i	$-0.288937\pi$
$617$	32.2727	−	1.44937i	1.29925	−	0.0583494i	0.683709	+	0.729755i	$0.260366\pi$
$618$		0			0
$619$	−27.1192	−	21.6268i	−1.09001	−	0.869255i	−0.0979723	−	0.995189i	$-0.531236\pi$
$619$	−27.1192	−	21.6268i	−1.09001	−	0.869255i	−0.992039	+	0.125935i	$0.959807\pi$
$620$	−10.8399	+	4.06827i	−0.435339	+	0.163386i
$621$		0			0
$622$	1.95394	+	6.01361i	0.0783459	+	0.241124i
$623$	60.9267	−	36.4020i	2.44098	−	1.45842i
$624$		0			0
$625$	−18.4557	−	13.4089i	−0.738229	−	0.536355i
$626$	−1.58860	−	17.6508i	−0.0634932	−	0.705467i
$627$		0			0
$628$	84.7441	+	7.62711i	3.38166	+	0.304355i
$629$	−0.189867	−	0.198585i	−0.00757048	−	0.00791810i
$630$		0			0
$631$	−30.8821	+	13.1996i	−1.22940	+	0.525470i	−0.906998	−	0.421134i	$-0.861632\pi$
$631$	−30.8821	+	13.1996i	−1.22940	+	0.525470i	−0.322399	+	0.946604i	$0.604489\pi$
$632$	−4.92190	−	4.70582i	−0.195783	−	0.187187i
$633$		0			0
$634$	−28.0550	−	38.6144i	−1.11421	−	1.53357i
$635$	−3.33339	+	0.919957i	−0.132281	+	0.0365074i
$636$		0			0
$637$	−4.81892	+	0.652767i	−0.190932	+	0.0258636i
$638$	134.290			5.31657
$639$		0			0
$640$	−3.45876			−0.136719
$641$	−5.91957	+	0.801861i	−0.233809	+	0.0316716i	−0.250200	−	0.968194i	$-0.580497\pi$
$641$	−5.91957	+	0.801861i	−0.233809	+	0.0316716i	0.0163914	+	0.999866i	$0.494782\pi$
$642$		0			0
$643$	−35.9351	+	9.91747i	−1.41714	+	0.391107i	−0.888945	−	0.458014i	$-0.848561\pi$
$643$	−35.9351	+	9.91747i	−1.41714	+	0.391107i	−0.528199	+	0.849121i	$0.677132\pi$
$644$	73.5534	+	101.238i	2.89841	+	3.98932i
$645$		0			0
$646$	36.8342	+	35.2171i	1.44922	+	1.38560i
$647$	−30.5382	+	13.0526i	−1.20058	+	0.513152i	−0.898010	−	0.439975i	$-0.854987\pi$
$647$	−30.5382	+	13.0526i	−1.20058	+	0.513152i	−0.302570	+	0.953127i	$0.597844\pi$
$648$		0			0
$649$	18.3686	+	19.2121i	0.721031	+	0.754139i
$650$	−5.28825	−	0.475951i	−0.207422	−	0.0186683i
$651$		0			0
$652$	−0.216570	−	2.40629i	−0.00848155	−	0.0942378i
$653$	−4.19085	−	3.04483i	−0.164001	−	0.119153i	0.502758	−	0.864427i	$-0.332319\pi$
$653$	−4.19085	−	3.04483i	−0.164001	−	0.119153i	−0.666759	+	0.745274i	$0.732319\pi$
$654$		0			0
$655$	−4.79624	+	2.86562i	−0.187404	+	0.111969i
$656$	9.50072	+	29.2402i	0.370941	+	1.14164i
$657$		0			0
$658$	−12.0295	+	4.51475i	−0.468959	+	0.176003i
$659$	−17.1816	−	13.7018i	−0.669299	−	0.533748i	0.228838	−	0.973465i	$-0.426507\pi$
$659$	−17.1816	−	13.7018i	−0.669299	−	0.533748i	−0.898137	+	0.439717i	$0.855079\pi$
$660$		0			0
$661$	−6.55759	+	0.294502i	−0.255061	+	0.0114548i	−0.172028	−	0.985092i	$-0.555032\pi$
$661$	−6.55759	+	0.294502i	−0.255061	+	0.0114548i	−0.0830326	+	0.996547i	$0.526461\pi$
$662$	44.5685	+	21.4631i	1.73220	+	0.834186i
$663$		0			0
$664$	−10.8697	+	33.4535i	−0.421826	+	1.29825i
$665$	2.46566	+	10.8027i	0.0956140	+	0.418913i
$666$		0			0
$667$	−55.5789	−	29.9083i	−2.15202	−	1.15805i
$668$	−33.4640	−	1.50287i	−1.29476	−	0.0581477i
$669$		0			0
$670$	−3.93424	+	6.58480i	−0.151993	+	0.254393i
$671$	−29.2221	+	23.3039i	−1.12811	+	0.899635i
$672$		0			0
$673$	5.86837	+	12.1858i	0.226209	+	0.469728i	0.982923	−	0.184019i	$-0.0589107\pi$
$673$	5.86837	+	12.1858i	0.226209	+	0.469728i	−0.756714	+	0.653746i	$0.773196\pi$
$674$	−6.37638	+	47.0723i	−0.245609	+	1.81316i
$675$		0			0
$676$	52.8459	−	25.4493i	2.03254	−	0.978818i
$677$	3.26550	−	1.75724i	0.125503	−	0.0675363i	−0.409912	−	0.912125i	$-0.634441\pi$
$677$	3.26550	−	1.75724i	0.125503	−	0.0675363i	0.535416	+	0.844589i	$0.320155\pi$
$678$		0			0
$679$	5.80031	+	3.46552i	0.222595	+	0.132995i
$680$	−1.66533	+	7.29627i	−0.0638624	+	0.279799i
$681$		0			0
$682$	−42.3817	+	78.7585i	−1.62288	+	3.01582i
$683$	21.6551	−	3.92982i	0.828609	−	0.150370i	0.252349	−	0.967636i	$-0.418797\pi$
$683$	21.6551	−	3.92982i	0.828609	−	0.150370i	0.576261	+	0.817266i	$0.304511\pi$
$684$		0			0
$685$	−0.597214	−	0.194047i	−0.0228184	−	0.00741414i
$686$	26.6445	−	40.3646i	1.01729	−	1.54113i
$687$		0			0
$688$	−0.941046	−	20.9540i	−0.0358770	−	0.798864i
$689$	−0.0354795	+	0.195508i	−0.00135166	+	0.00744826i
$690$		0			0
$691$	−7.30418	−	19.4619i	−0.277864	−	0.740367i	−0.998874	−	0.0474417i	$-0.984893\pi$
$691$	−7.30418	−	19.4619i	−0.277864	−	0.740367i	0.721010	−	0.692925i	$-0.243678\pi$
$692$	−77.7626	−	21.4611i	−2.95609	−	0.815829i
$693$		0			0
$694$	0.263141	+	0.440423i	0.00998868	+	0.0167182i
$695$	7.45631	+	2.79840i	0.282834	+	0.106149i
$696$		0			0
$697$	−11.6080	+	1.04474i	−0.439686	+	0.0395724i
$698$	−21.4925	−	18.7774i	−0.813502	−	0.710735i
$699$		0			0
$700$	68.8431	−	65.8207i	2.60202	−	2.48779i
$701$	15.4523	−	36.1525i	0.583626	−	1.36546i	−0.324150	−	0.946006i	$-0.605078\pi$
$701$	15.4523	−	36.1525i	0.583626	−	1.36546i	0.907776	−	0.419455i	$-0.137779\pi$
$702$		0			0
$703$	0.432939	−	0.452819i	0.0163286	−	0.0170784i
$704$	6.99823	−	6.11417i	0.263756	−	0.230436i
$705$		0			0
$706$	3.09965	+	11.2313i	0.116657	+	0.422697i
$707$	4.14643	+	6.28158i	0.155943	+	0.236243i
$708$		0			0
$709$		−	31.8074i		−	1.19455i	−0.802036	−	0.597275i	$-0.796250\pi$
$709$		−	31.8074i		−	1.19455i	0.802036	−	0.597275i	$-0.203750\pi$
$710$	−5.09605	+	6.54166i	−0.191251	+	0.245504i
$711$		0			0
$712$	14.6723	+	108.315i	0.549868	+	4.05929i
$713$	35.0813	−	23.1570i	1.31381	−	0.867236i
$714$		0			0
$715$	0.700773	−	0.509141i	0.0262074	−	0.0190408i
$716$	59.3806	+	67.9666i	2.21916	+	2.54003i
$717$		0			0
$718$	23.5767	+	55.1604i	0.879875	+	2.05857i
$719$	27.6596	+	11.8223i	1.03153	+	0.440897i	0.841143	−	0.540812i	$-0.181883\pi$
$719$	27.6596	+	11.8223i	1.03153	+	0.440897i	0.190386	+	0.981709i	$0.439026\pi$
$720$		0			0
$721$	−7.66258	+	85.1382i	−0.285369	+	3.17071i
$722$	−44.3972	+	50.8167i	−1.65229	+	1.89120i
$723$		0			0
$724$	32.6890	−	44.9926i	1.21488	−	1.67214i
$725$	−16.8797	+	44.9758i	−0.626897	+	1.67036i
$726$		0			0
$727$	−39.6765	+	12.8917i	−1.47152	+	0.478126i	−0.931567	−	0.363569i	$-0.881558\pi$
$727$	−39.6765	+	12.8917i	−1.47152	+	0.478126i	−0.539954	+	0.841695i	$0.681558\pi$
$728$	3.21616	−	11.6535i	0.119199	−	0.431907i
$729$		0			0
$730$	−5.74929	+	7.20938i	−0.212791	+	0.266831i
$731$	7.82358	+	1.41977i	0.289365	+	0.0525121i
$732$		0			0
$733$	−15.0697	+	31.2925i	−0.556612	+	1.15582i	0.412901	+	0.910776i	$0.364516\pi$
$733$	−15.0697	+	31.2925i	−0.556612	+	1.15582i	−0.969513	+	0.245041i	$0.921199\pi$
$734$	65.0260	+	42.9233i	2.40016	+	1.58433i
$735$		0			0
$736$	−42.0109	+	9.58872i	−1.54854	+	0.353445i
$737$	7.36224	+	40.5693i	0.271192	+	1.49439i
$738$		0			0
$739$	1.00161	−	22.3025i	0.0368447	−	0.820410i	−0.892467	−	0.451113i	$-0.851027\pi$
$739$	1.00161	−	22.3025i	0.0368447	−	0.820410i	0.929311	−	0.369297i	$-0.120402\pi$
$740$	0.159337	+	0.0363676i	0.00585734	+	0.00133690i
$741$		0			0
$742$	−3.19366	−	4.00472i	−0.117243	−	0.147018i
$743$	3.25720	+	6.05290i	0.119495	+	0.222059i	0.933316	−	0.359057i	$-0.116902\pi$
$743$	3.25720	+	6.05290i	0.119495	+	0.222059i	−0.813820	+	0.581117i	$0.802616\pi$
$744$		0			0
$745$	4.40987	+	0.597358i	0.161565	+	0.0218855i
$746$	−16.7288	−	2.26607i	−0.612484	−	0.0829666i
$747$		0			0
$748$	33.8637	+	62.9292i	1.23818	+	2.30092i
$749$	−19.9155	−	24.9732i	−0.727695	−	0.912500i
$750$		0			0
$751$	52.7907	+	12.0491i	1.92636	+	0.439679i	0.997620	+	0.0689500i	$0.0219649\pi$
$751$	52.7907	+	12.0491i	1.92636	+	0.439679i	0.928741	+	0.370729i	$0.120892\pi$
$752$	0.408146	−	9.08808i	0.0148836	−	0.331408i
$753$		0			0
$754$	1.93403	+	10.6574i	0.0704333	+	0.388119i
$755$	−8.06995	+	1.84191i	−0.293696	+	0.0670341i
$756$		0			0
$757$	−7.58982	−	5.00999i	−0.275857	−	0.182091i	0.405393	−	0.914142i	$-0.367135\pi$
$757$	−7.58982	−	5.00999i	−0.275857	−	0.182091i	−0.681250	+	0.732051i	$0.738563\pi$
$758$	−14.7760	+	30.6828i	−0.536690	+	1.11445i
$759$		0			0
$760$	−16.7908	−	3.04708i	−0.609065	−	0.110529i
$761$	−5.18625	+	6.50335i	−0.188001	+	0.235746i	−0.866895	−	0.498490i	$-0.833888\pi$
$761$	−5.18625	+	6.50335i	−0.188001	+	0.235746i	0.678894	+	0.734236i	$0.262459\pi$
$762$		0			0
$763$	0.999908	−	3.62309i	0.0361991	−	0.131165i
$764$	14.7915	−	4.80606i	0.535139	−	0.173877i
$765$		0			0
$766$	33.0278	−	88.0024i	1.19334	−	3.17965i
$767$	−1.26015	+	1.73445i	−0.0455014	+	0.0626273i
$768$		0			0
$769$	−30.7018	+	35.1410i	−1.10713	+	1.26722i	−0.146557	+	0.989202i	$0.546819\pi$
$769$	−30.7018	+	35.1410i	−1.10713	+	1.26722i	−0.960577	+	0.278015i	$0.910324\pi$
$770$	−2.00160	+	22.2395i	−0.0721325	+	0.801458i
$771$		0			0
$772$	−34.7458	−	14.8511i	−1.25053	−	0.534502i
$773$	14.3766	+	33.6357i	0.517090	+	1.20979i	0.951100	+	0.308884i	$0.0999556\pi$
$773$	14.3766	+	33.6357i	0.517090	+	1.20979i	−0.434009	+	0.900908i	$0.642902\pi$
$774$		0			0
$775$	−21.0503	−	24.0940i	−0.756149	−	0.865482i
$776$	−8.41858	+	6.11646i	−0.302210	+	0.219568i
$777$		0			0
$778$	45.0820	−	29.7584i	1.61627	−	1.06689i
$779$	−3.56738	−	26.3354i	−0.127814	−	0.943564i
$780$		0			0
$781$	2.50663	+	44.5036i	0.0896942	+	1.59246i
$782$		−	48.2663i		−	1.72600i
$783$		0			0
$784$	48.8959	+	74.0742i	1.74628	+	2.64551i
$785$	−1.89840	−	6.87870i	−0.0677568	−	0.245511i
$786$		0			0
$787$	8.55438	−	7.47374i	0.304931	−	0.266410i	−0.491848	−	0.870681i	$-0.663678\pi$
$787$	8.55438	−	7.47374i	0.304931	−	0.266410i	0.796779	+	0.604271i	$0.206536\pi$
$788$	44.5772	−	46.6241i	1.58800	−	1.66092i
$789$		0			0
$790$	−0.398717	+	0.932844i	−0.0141857	+	0.0331891i
$791$	14.4500	−	13.8156i	0.513784	−	0.491227i
$792$		0			0
$793$	−2.27028	−	1.98348i	−0.0806200	−	0.0704356i
$794$	49.6629	−	4.46974i	1.76247	−	0.158625i
$795$		0			0
$796$	−89.2606	−	33.5000i	−3.16376	−	1.18738i
$797$	−24.6263	−	41.2176i	−0.872310	−	1.46000i	−0.887856	−	0.460122i	$-0.847806\pi$
$797$	−24.6263	−	41.2176i	−0.872310	−	1.46000i	0.0155460	−	0.999879i	$-0.495051\pi$
$798$		0			0
$799$	3.32435	+	0.917462i	0.117607	+	0.0324575i
$800$	11.5245	+	30.7069i	0.407452	+	1.08565i
$801$		0			0
$802$	−6.94132	+	38.2498i	−0.245107	+	1.35065i
$803$	2.22380	+	49.5168i	0.0784763	+	1.74741i
$804$		0			0
$805$	5.78148	−	8.75857i	0.203771	−	0.308699i
$806$	−6.86075	−	2.22919i	−0.241660	−	0.0785200i
$807$		0			0
$808$	−11.4055	+	2.06979i	−0.401243	+	0.0728149i
$809$	2.68399	−	4.98768i	0.0943640	−	0.175358i	−0.829038	−	0.559193i	$-0.811111\pi$
$809$	2.68399	−	4.98768i	0.0943640	−	0.175358i	0.923402	+	0.383835i	$0.125397\pi$
$810$		0			0
$811$	11.3579	−	49.7620i	0.398828	−	1.74738i	−0.233194	−	0.972430i	$-0.574918\pi$
$811$	11.3579	−	49.7620i	0.398828	−	1.74738i	0.632022	−	0.774950i	$-0.282225\pi$
$812$	−166.795	−	99.6554i	−5.85336	−	3.49722i
$813$		0			0
$814$	1.11174	−	0.598251i	0.0389663	−	0.0209687i
$815$	−0.182556	+	0.0879141i	−0.00639464	+	0.00307950i
$816$		0			0
$817$	−2.43377	+	17.9668i	−0.0851468	+	0.628579i
$818$	14.5763	+	30.2681i	0.509650	+	1.05830i
$819$		0			0
$820$	5.42046	−	4.32267i	0.189291	−	0.150954i
$821$	8.60273	−	14.3985i	0.300237	−	0.502513i	−0.670737	−	0.741695i	$-0.734022\pi$
$821$	8.60273	−	14.3985i	0.300237	−	0.502513i	0.970975	+	0.239182i	$0.0768794\pi$
$822$		0			0
$823$	−3.72599	−	0.167334i	−0.129880	−	0.00583291i	−0.0201699	−	0.999797i	$-0.506421\pi$
$823$	−3.72599	−	0.167334i	−0.129880	−	0.00583291i	−0.109710	+	0.993964i	$0.534992\pi$
$824$	−115.930	−	62.3849i	−4.03863	−	2.17328i
$825$		0			0
$826$	−12.2979	−	53.8808i	−0.427900	−	1.87475i
$827$	10.3283	−	31.7872i	0.359149	−	1.10535i	−0.594415	−	0.804158i	$-0.702616\pi$
$827$	10.3283	−	31.7872i	0.359149	−	1.10535i	0.953564	−	0.301190i	$-0.0973837\pi$
$828$		0			0
$829$	5.60437	+	2.69892i	0.194648	+	0.0937374i	0.528669	−	0.848828i	$-0.322691\pi$
$829$	5.60437	+	2.69892i	0.194648	+	0.0937374i	−0.334021	+	0.942566i	$0.608406\pi$
$830$	5.23509	−	0.235108i	0.181713	−	0.00816072i
$831$		0			0
$832$	0.586017	+	0.467333i	0.0203165	+	0.0162018i
$833$	−31.5010	+	11.8225i	−1.09144	+	0.409626i
$834$		0			0
$835$	0.868124	+	2.67181i	0.0300427	+	0.0924619i
$836$	−139.884	+	83.5769i	−4.83799	+	2.89057i
$837$		0			0
$838$	9.79796	+	7.11864i	0.338465	+	0.245909i
$839$	−1.29783	−	14.4201i	−0.0448060	−	0.497836i	−0.986771	−	0.162123i	$-0.948166\pi$
$839$	−1.29783	−	14.4201i	−0.0448060	−	0.497836i	0.941965	−	0.335712i	$-0.108977\pi$
$840$		0			0
$841$	68.7204	+	6.18494i	2.36967	+	0.213274i
$842$	36.2601	+	37.9251i	1.24961	+	1.30699i
$843$		0			0
$844$	−28.0897	+	12.0061i	−0.966888	+	0.413268i
$845$	−3.55551	−	3.39941i	−0.122313	−	0.116943i
$846$		0			0
$847$	42.8184	+	58.9344i	1.47126	+	2.02501i
$848$	3.49595	−	0.964821i	0.120051	−	0.0331321i
$849$		0			0
$850$	−36.4046	+	4.93134i	−1.24867	+	0.169144i
$851$	−0.593358			−0.0203400
$852$		0			0
$853$	−15.2702			−0.522840			−0.261420	−	0.965225i	$-0.584191\pi$
$853$	−15.2702			−0.522840			−0.261420	+	0.965225i	$0.584191\pi$
$854$	77.0111	−	10.4319i	2.63526	−	0.356971i
$855$		0			0
$856$	47.4205	−	13.0872i	1.62080	−	0.447312i
$857$	15.5561	+	21.4111i	0.531386	+	0.731390i	0.987341	−	0.158613i	$-0.0507022\pi$
$857$	15.5561	+	21.4111i	0.531386	+	0.731390i	−0.455955	+	0.890003i	$0.650702\pi$
$858$		0			0
$859$	4.65827	+	4.45376i	0.158938	+	0.151960i	0.766342	−	0.642433i	$-0.222075\pi$
$859$	4.65827	+	4.45376i	0.158938	+	0.151960i	−0.607404	+	0.794393i	$0.707789\pi$
$860$	−4.34929	+	1.85898i	−0.148310	+	0.0633906i
$861$		0			0
$862$	58.0925	+	60.7600i	1.97864	+	2.06949i
$863$	−51.8575	−	4.66726i	−1.76525	−	0.158875i	−0.841093	−	0.540891i	$-0.818087\pi$
$863$	−51.8575	−	4.66726i	−1.76525	−	0.158875i	−0.924156	+	0.382016i	$0.875230\pi$
$864$		0			0
$865$	0.606448	+	6.73819i	0.0206199	+	0.229105i
$866$	−35.4120	−	25.7284i	−1.20335	−	0.874285i
$867$		0			0
$868$	111.087	−	66.3711i	3.77052	−	2.25278i
$869$	1.68512	+	5.18628i	0.0571639	+	0.175932i
$870$		0			0
$871$	−3.11360	+	1.16855i	−0.105500	+	0.0395950i
$872$	4.52560	+	3.60905i	0.153256	+	0.122218i
$873$		0			0
$874$	109.947	−	4.93773i	3.71902	−	0.167021i
$875$	−14.6120	−	7.03678i	−0.493977	−	0.237887i
$876$		0			0
$877$	−0.966093	+	2.97333i	−0.0326226	+	0.100402i	−0.966042	−	0.258385i	$-0.916810\pi$
$877$	−0.966093	+	2.97333i	−0.0326226	+	0.100402i	0.933419	+	0.358787i	$0.116810\pi$
$878$	8.11148	+	35.5387i	0.273749	+	1.19937i
$879$		0			0
$880$	−13.9220	−	7.49173i	−0.469309	−	0.252546i
$881$	17.5145	+	0.786577i	0.590079	+	0.0265005i	0.337903	−	0.941181i	$-0.390282\pi$
$881$	17.5145	+	0.786577i	0.590079	+	0.0265005i	0.252176	+	0.967681i	$0.418854\pi$
$882$		0			0
$883$	−27.9980	+	46.8608i	−0.942208	+	1.57699i	−0.131680	+	0.991292i	$0.542037\pi$
$883$	−27.9980	+	46.8608i	−0.942208	+	1.57699i	−0.810529	+	0.585699i	$0.800820\pi$
$884$	−4.50644	+	3.59377i	−0.151568	+	0.120872i
$885$		0			0
$886$	1.35961	+	2.82326i	0.0456770	+	0.0948492i
$887$	−0.399875	+	2.95200i	−0.0134265	+	0.0991183i	−0.996423	−	0.0845061i	$-0.973069\pi$
$887$	−0.399875	+	2.95200i	−0.0134265	+	0.0991183i	0.982996	+	0.183624i	$0.0587830\pi$
$888$		0			0
$889$	34.8212	−	16.7690i	1.16787	−	0.562414i
$890$	14.3397	−	7.71654i	0.480669	−	0.258659i
$891$		0			0
$892$	−84.8061	−	50.6693i	−2.83952	−	1.69653i
$893$	−1.74983	+	7.66649i	−0.0585557	+	0.256549i
$894$		0			0
$895$	3.58675	−	6.66531i	0.119892	−	0.222797i
$896$	38.0358	−	6.90247i	1.27069	−	0.230595i
$897$		0			0
$898$	2.10258	+	0.683168i	0.0701639	+	0.0227976i
$899$	−35.9556	+	54.4704i	−1.19919	+	1.81669i
$900$		0			0
$901$	0.0616805	+	1.37342i	0.00205488	+	0.0457553i
$902$	9.56272	−	52.6949i	0.318404	−	1.75455i
$903$		0			0
$904$	10.8185	+	28.8259i	0.359819	+	0.958736i
$905$	−4.49602	−	1.24082i	−0.149453	−	0.0412463i
$906$		0			0
$907$	−26.4743	−	44.3105i	−0.879064	−	1.47131i	−0.881968	−	0.471310i	$-0.843781\pi$
$907$	−26.4743	−	44.3105i	−0.879064	−	1.47131i	0.00290319	−	0.999996i	$-0.499076\pi$
$908$	22.4109	+	8.41095i	0.743732	+	0.279127i
$909$		0			0
$910$	−1.79379	+	0.161444i	−0.0594634	+	0.00535181i
$911$	−32.9377	−	28.7768i	−1.09127	−	0.953417i	−0.0921702	−	0.995743i	$-0.529380\pi$
$911$	−32.9377	−	28.7768i	−1.09127	−	0.953417i	−0.999104	+	0.0423258i	$0.986523\pi$
$912$		0			0
$913$	20.3602	−	19.4663i	0.673824	−	0.644242i
$914$	−30.0758	+	70.3658i	−0.994819	+	2.32749i
$915$		0			0
$916$	55.4904	−	58.0384i	1.83345	−	1.91764i
$917$	47.0252	−	41.0847i	1.55291	−	1.35674i
$918$		0			0
$919$	5.26207	+	19.0667i	0.173580	+	0.628952i	0.998014	+	0.0629939i	$0.0200649\pi$
$919$	5.26207	+	19.0667i	0.173580	+	0.628952i	−0.824434	+	0.565958i	$0.808507\pi$
$920$	8.90398	+	13.4890i	0.293556	+	0.444718i
$921$		0			0
$922$			80.6341i			2.65554i
$923$	−3.49576	+	0.839867i	−0.115064	+	0.0276446i
$924$		0			0
$925$	0.0606230	+	0.447537i	0.00199327	+	0.0147149i
$926$	−83.4694	+	55.0977i	−2.74297	+	1.81062i
$927$		0			0
$928$	54.1292	−	39.3272i	1.77688	−	1.29098i
$929$	0.249795	+	0.285913i	0.00819551	+	0.00938052i	0.757155	−	0.653236i	$-0.226589\pi$
$929$	0.249795	+	0.285913i	0.00819551	+	0.00938052i	−0.748959	+	0.662616i	$0.769446\pi$
$930$		0			0
$931$	−30.1535	−	70.5475i	−0.988240	−	2.31210i
$932$	82.7522	+	35.3700i	2.71064	+	1.15858i
$933$		0			0
$934$	−7.06516	+	78.5004i	−0.231179	+	2.56861i
$935$	3.94318	−	4.51333i	0.128956	−	0.147602i
$936$		0			0
$937$	23.3727	−	32.1697i	0.763551	−	1.05094i	−0.233359	−	0.972391i	$-0.574972\pi$
$937$	23.3727	−	32.1697i	0.763551	−	1.05094i	0.996910	−	0.0785477i	$-0.0250283\pi$
$938$	30.1236	−	80.2641i	0.983571	−	2.62072i
$939$		0			0
$940$	−1.95103	+	0.633929i	−0.0636357	+	0.0206765i
$941$	8.20857	−	29.7431i	0.267592	−	0.969597i	−0.699388	−	0.714742i	$-0.746544\pi$
$941$	8.20857	−	29.7431i	0.267592	−	0.969597i	0.966979	−	0.254854i	$-0.0820275\pi$
$942$		0			0
$943$	−15.6937	+	19.6793i	−0.511057	+	0.640845i
$944$	38.5010	+	6.98690i	1.25310	+	0.227404i
$945$		0			0
$946$	−15.8529	+	32.9189i	−0.515422	+	1.07029i
$947$	−2.38472	−	1.57414i	−0.0774930	−	0.0511527i	0.511556	−	0.859250i	$-0.329069\pi$
$947$	−2.38472	−	1.57414i	−0.0774930	−	0.0511527i	−0.589049	+	0.808097i	$0.700498\pi$
$948$		0			0
$949$	−3.89769	+	0.889623i	−0.126524	+	0.0288784i
$950$	−14.9575	−	82.4227i	−0.485286	−	2.67414i
$951$		0			0
$952$	3.75269	−	83.5602i	0.121625	−	2.70820i
$953$	25.1035	+	5.72971i	0.813183	+	0.185604i	0.608837	−	0.793295i	$-0.291636\pi$
$953$	25.1035	+	5.72971i	0.813183	+	0.185604i	0.204345	+	0.978899i	$0.434493\pi$
$954$		0			0
$955$	−0.813244	−	1.01978i	−0.0263160	−	0.0329992i
$956$	−39.8227	−	74.0030i	−1.28796	−	2.39343i
$957$		0			0
$958$	−58.7690	−	7.96080i	−1.89874	−	0.257202i
$959$	6.95478	+	0.942090i	0.224582	+	0.0304217i
$960$		0			0
$961$	−5.90843	−	10.9797i	−0.190594	−	0.354184i
$962$	0.0634891	+	0.0796129i	0.00204697	+	0.00256682i
$963$		0			0
$964$	−79.8461	−	18.2243i	−2.57167	−	0.586967i
$965$	−0.142177	+	3.16581i	−0.00457683	+	0.101911i
$966$		0			0
$967$	0.953485	+	5.25413i	0.0306620	+	0.168962i	0.995627	−	0.0934167i	$-0.0297789\pi$
$967$	0.953485	+	5.25413i	0.0306620	+	0.168962i	−0.964965	+	0.262378i	$0.915493\pi$
$968$	−109.378	+	24.9647i	−3.51553	+	0.802397i
$969$		0			0
$970$	1.29382	+	0.854041i	0.0415419	+	0.0274216i
$971$	−0.357013	+	0.741346i	−0.0114571	+	0.0237909i	−0.906619	−	0.421950i	$-0.861346\pi$
$971$	−0.357013	+	0.741346i	−0.0114571	+	0.0237909i	0.895162	+	0.445741i	$0.147060\pi$
$972$		0			0
$973$	−87.5814	−	15.8937i	−2.80773	−	0.509528i
$974$	8.87424	−	11.1279i	0.284349	−	0.356562i
$975$		0			0
$976$	−14.6383	+	53.0405i	−0.468559	+	1.69779i
$977$	−1.98117	+	0.643721i	−0.0633832	+	0.0205945i	−0.340537	−	0.940231i	$-0.610609\pi$
$977$	−1.98117	+	0.643721i	−0.0633832	+	0.0205945i	0.277154	+	0.960826i	$0.410609\pi$
$978$		0			0
$979$	30.7568	−	81.9511i	0.982991	−	2.61917i
$980$	11.7644	−	16.1923i	0.375800	−	0.517244i
$981$		0			0
$982$	−11.5803	+	13.2547i	−0.369542	+	0.422975i
$983$	−0.745348	+	8.28150i	−0.0237729	+	0.264139i	0.975293	+	0.220917i	$0.0709050\pi$
$983$	−0.745348	+	8.28150i	−0.0237729	+	0.264139i	−0.999066	+	0.0432217i	$0.986238\pi$
$984$		0			0
$985$	−4.97445	−	2.12618i	−0.158499	−	0.0677458i
$986$	29.4543	+	68.9117i	0.938015	+	2.19460i
$987$		0			0
$988$	−8.64737	−	9.89772i	−0.275110	−	0.314888i
$989$	13.8926	−	10.0936i	0.441760	−	0.320957i
$990$		0			0
$991$	35.6156	−	23.5097i	1.13137	−	0.746809i	0.160644	−	0.987012i	$-0.448643\pi$
$991$	35.6156	−	23.5097i	1.13137	−	0.746809i	0.970723	+	0.240204i	$0.0772142\pi$
$992$	5.98154	+	44.1575i	0.189914	+	1.40200i
$993$		0			0
$994$	42.9861	−	82.1082i	1.36344	−	2.60431i
$995$			7.99575i			0.253482i
$996$		0			0
$997$	−0.858895	−	1.30117i	−0.0272015	−	0.0412085i	0.820718	−	0.571333i	$-0.193574\pi$
$997$	−0.858895	−	1.30117i	−0.0272015	−	0.0412085i	−0.847920	+	0.530125i	$0.822145\pi$
$998$	9.56710	+	34.6656i	0.302841	+	1.09732i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.62.2	✓	576
3.2	odd	2	inner	639.2.z.a.62.23	yes	576
71.63	odd	70	inner	639.2.z.a.134.23	yes	576
213.134	even	70	inner	639.2.z.a.134.2	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.62.2	✓	576	1.1	even	1	trivial
639.2.z.a.62.23	yes	576	3.2	odd	2	inner
639.2.z.a.134.2	yes	576	213.134	even	70	inner
639.2.z.a.134.23	yes	576	71.63	odd	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)

\(f(q)\)	\(=\)	\(q+(-2.54116 + 0.344223i) q^{2} +(4.41107 - 1.21738i) q^{4} +(-0.225573 - 0.310474i) q^{5} +(3.10021 + 2.96411i) q^{7} +(-6.07416 + 2.59622i) q^{8} +O(q^{10})\)	\(q+(-2.54116 + 0.344223i) q^{2} +(4.41107 - 1.21738i) q^{4} +(-0.225573 - 0.310474i) q^{5} +(3.10021 + 2.96411i) q^{7} +(-6.07416 + 2.59622i) q^{8} +(0.680089 + 0.711317i) q^{10} +(5.26868 + 0.474189i) q^{11} +(0.0382469 + 0.424958i) q^{13} +(-8.89844 - 6.46510i) q^{14} +(6.68524 - 3.99424i) q^{16} +(0.912266 + 2.80767i) q^{17} +(-6.30234 + 2.36531i) q^{19} +(-1.37298 - 1.09492i) q^{20} +(-13.5518 + 0.608610i) q^{22} +(5.74426 + 2.76629i) q^{23} +(1.49957 - 4.61521i) q^{25} +(-0.243472 - 1.06672i) q^{26} +(17.2837 + 9.30075i) q^{28} +(-9.88943 - 0.444135i) q^{29} +(3.38158 - 5.65981i) q^{31} +(-5.28419 + 4.21400i) q^{32} +(-3.28468 - 6.82070i) q^{34} +(0.220955 - 1.63116i) q^{35} +(-0.0838498 + 0.0403799i) q^{37} +(15.2011 - 8.18004i) q^{38} +(2.17622 + 1.30023i) q^{40} +(-0.878501 + 3.84896i) q^{41} +(1.27632 - 2.37180i) q^{43} +(23.8178 - 4.32229i) q^{44} +(-15.5493 - 5.05227i) q^{46} +(0.643543 - 0.974926i) q^{47} +(0.511335 + 11.3858i) q^{49} +(-2.22199 + 12.2442i) q^{50} +(0.686044 + 1.82796i) q^{52} +(0.448914 + 0.123892i) q^{53} +(-1.04125 - 1.74275i) q^{55} +(-26.5267 - 9.95562i) q^{56} +(25.2835 - 2.27556i) q^{58} +(3.78392 + 3.30591i) q^{59} +(-5.10693 + 4.88273i) q^{61} +(-6.64489 + 15.5465i) q^{62} +(1.21399 - 1.26974i) q^{64} +(0.123311 - 0.107734i) q^{65} +(2.07359 + 7.51347i) q^{67} +(7.44206 + 11.2742i) q^{68} +4.22109i q^{70} +(1.22606 + 8.33647i) q^{71} +(1.25776 + 9.28514i) q^{73} +(0.199176 - 0.131475i) q^{74} +(-24.9206 + 18.1059i) q^{76} +(14.9285 + 17.0870i) q^{77} +(0.405151 + 0.947897i) q^{79} +(-2.74812 - 1.17460i) q^{80} +(0.907507 - 10.0832i) q^{82} +(3.50348 - 4.01005i) q^{83} +(0.665926 - 0.916569i) q^{85} +(-2.42690 + 6.46646i) q^{86} +(-33.2339 + 10.7983i) q^{88} +(4.40209 - 15.9506i) q^{89} +(-1.14105 + 1.43083i) q^{91} +(28.7060 + 5.20936i) q^{92} +(-1.29975 + 2.69896i) q^{94} +(2.15601 + 1.42317i) q^{95} +(1.53579 - 0.350535i) q^{97} +(-5.21863 - 28.7570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 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

Related objects

Downloads

Learn more