LMFDB - Embedded newform 819.2.et.c.514.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			514.9
Character	$\chi$	$=$	819.514
Dual form			819.2.et.c.145.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74581 + 1.74581i) q^{2} +4.09571i q^{4} +(2.78539 + 0.746344i) q^{5} +(-2.58285 - 0.573466i) q^{7} +(-3.65872 + 3.65872i) q^{8} +O(q^{10})$	\(q+(1.74581 + 1.74581i) q^{2} +4.09571i q^{4} +(2.78539 + 0.746344i) q^{5} +(-2.58285 - 0.573466i) q^{7} +(-3.65872 + 3.65872i) q^{8} +(3.55979 + 6.16574i) q^{10} +(1.35345 + 0.362655i) q^{11} +(3.49837 + 0.872572i) q^{13} +(-3.50801 - 5.51034i) q^{14} -4.58344 q^{16} -7.55665 q^{17} +(1.78944 + 6.67828i) q^{19} +(-3.05681 + 11.4082i) q^{20} +(1.72974 + 2.99599i) q^{22} +2.27807i q^{23} +(2.87125 + 1.65772i) q^{25} +(4.58415 + 7.63085i) q^{26} +(2.34875 - 10.5786i) q^{28} +(3.75108 - 6.49707i) q^{29} +(-1.39265 - 5.19745i) q^{31} +(-0.684379 - 0.684379i) q^{32} +(-13.1925 - 13.1925i) q^{34} +(-6.76626 - 3.52502i) q^{35} +(1.61717 - 1.61717i) q^{37} +(-8.53499 + 14.7830i) q^{38} +(-12.9216 + 7.46031i) q^{40} +(-2.38652 - 8.90661i) q^{41} +(3.04772 - 1.75960i) q^{43} +(-1.48533 + 5.54333i) q^{44} +(-3.97708 + 3.97708i) q^{46} +(0.223361 - 0.833593i) q^{47} +(6.34227 + 2.96236i) q^{49} +(2.11860 + 7.90673i) q^{50} +(-3.57380 + 14.3283i) q^{52} +(0.886338 - 1.53518i) q^{53} +(3.49922 + 2.02027i) q^{55} +(11.5481 - 7.35179i) q^{56} +(17.8913 - 4.79397i) q^{58} +(-3.80628 - 3.80628i) q^{59} +(-3.62667 - 2.09386i) q^{61} +(6.64246 - 11.5051i) q^{62} +6.77728i q^{64} +(9.09310 + 5.04144i) q^{65} +(-1.44159 + 5.38010i) q^{67} -30.9499i q^{68} +(-5.65859 - 17.9666i) q^{70} +(1.75325 - 6.54321i) q^{71} +(8.10009 - 2.17041i) q^{73} +5.64656 q^{74} +(-27.3523 + 7.32903i) q^{76} +(-3.28779 - 1.71284i) q^{77} +(0.411935 + 0.713493i) q^{79} +(-12.7667 - 3.42082i) q^{80} +(11.3829 - 19.7157i) q^{82} +(-2.15380 + 2.15380i) q^{83} +(-21.0482 - 5.63986i) q^{85} +(8.39268 + 2.24881i) q^{86} +(-6.27874 + 3.62503i) q^{88} +(-1.81982 - 1.81982i) q^{89} +(-8.53540 - 4.25992i) q^{91} -9.33031 q^{92} +(1.84524 - 1.06535i) q^{94} +19.9372i q^{95} +(8.79336 + 2.35617i) q^{97} +(5.90070 + 16.2441i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.74581	+	1.74581i	1.23447	+	1.23447i	0.962227	+	0.272248i	$0.0877670\pi$
$2$	1.74581	+	1.74581i	1.23447	+	1.23447i	0.272248	+	0.962227i	$0.412233\pi$
$3$		0			0
$3$		0			0
$4$			4.09571i			2.04786i
$5$	2.78539	+	0.746344i	1.24567	+	0.333775i	0.820661	−	0.571416i	$-0.193606\pi$
$5$	2.78539	+	0.746344i	1.24567	+	0.333775i	0.425005	+	0.905191i	$0.360272\pi$
$6$		0			0
$7$	−2.58285	−	0.573466i	−0.976227	−	0.216750i
$7$	−2.58285	−	0.573466i	−0.976227	−	0.216750i
$8$	−3.65872	+	3.65872i	−1.29355	+	1.29355i
$9$		0			0
$10$	3.55979	+	6.16574i	1.12571	+	1.94978i
$11$	1.35345	+	0.362655i	0.408080	+	0.109345i	0.457019	−	0.889457i	$-0.348917\pi$
$11$	1.35345	+	0.362655i	0.408080	+	0.109345i	−0.0489388	+	0.998802i	$0.515584\pi$
$12$		0			0
$13$	3.49837	+	0.872572i	0.970274	+	0.242008i
$13$	3.49837	+	0.872572i	0.970274	+	0.242008i
$14$	−3.50801	−	5.51034i	−0.937556	−	1.47270i
$15$		0			0
$16$	−4.58344			−1.14586
$17$	−7.55665			−1.83276			−0.916379	−	0.400312i	$-0.868902\pi$
$17$	−7.55665			−1.83276			−0.916379	+	0.400312i	$0.868902\pi$
$18$		0			0
$19$	1.78944	+	6.67828i	0.410526	+	1.53210i	0.793632	+	0.608399i	$0.208188\pi$
$19$	1.78944	+	6.67828i	0.410526	+	1.53210i	−0.383106	+	0.923704i	$0.625146\pi$
$20$	−3.05681	+	11.4082i	−0.683523	+	2.55094i
$21$		0			0
$22$	1.72974	+	2.99599i	0.368781	+	0.638747i
$23$			2.27807i			0.475010i	0.971386	+	0.237505i	$0.0763296\pi$
$23$			2.27807i			0.475010i	−0.971386	+	0.237505i	$0.923670\pi$
$24$		0			0
$25$	2.87125	+	1.65772i	0.574251	+	0.331544i
$26$	4.58415	+	7.63085i	0.899027	+	1.49653i
$27$		0			0
$28$	2.34875	−	10.5786i	0.443872	−	1.99917i
$29$	3.75108	−	6.49707i	0.696559	−	1.20647i	−0.273094	−	0.961987i	$-0.588047\pi$
$29$	3.75108	−	6.49707i	0.696559	−	1.20647i	0.969652	−	0.244487i	$-0.0786197\pi$
$30$		0			0
$31$	−1.39265	−	5.19745i	−0.250128	−	0.933490i	−0.970736	−	0.240148i	$-0.922804\pi$
$31$	−1.39265	−	5.19745i	−0.250128	−	0.933490i	0.720608	−	0.693342i	$-0.243863\pi$
$32$	−0.684379	−	0.684379i	−0.120982	−	0.120982i
$33$		0			0
$34$	−13.1925	−	13.1925i	−2.26249	−	2.26249i
$35$	−6.76626	−	3.52502i	−1.14371	−	0.595838i
$36$		0			0
$37$	1.61717	−	1.61717i	0.265862	−	0.265862i	−0.561569	−	0.827430i	$-0.689802\pi$
$37$	1.61717	−	1.61717i	0.265862	−	0.265862i	0.827430	+	0.561569i	$0.189802\pi$
$38$	−8.53499	+	14.7830i	−1.38456	+	2.39813i
$39$		0			0
$40$	−12.9216	+	7.46031i	−2.04309	+	1.17958i
$41$	−2.38652	−	8.90661i	−0.372712	−	1.39098i	−0.856659	−	0.515882i	$-0.827464\pi$
$41$	−2.38652	−	8.90661i	−0.372712	−	1.39098i	0.483948	−	0.875097i	$-0.339203\pi$
$42$		0			0
$43$	3.04772	−	1.75960i	0.464773	−	0.268337i	−0.249276	−	0.968432i	$-0.580193\pi$
$43$	3.04772	−	1.75960i	0.464773	−	0.268337i	0.714049	+	0.700096i	$0.246859\pi$
$44$	−1.48533	+	5.54333i	−0.223922	+	0.835689i
$45$		0			0
$46$	−3.97708	+	3.97708i	−0.586388	+	0.586388i
$47$	0.223361	−	0.833593i	0.0325805	−	0.121592i	−0.947720	−	0.319102i	$-0.896619\pi$
$47$	0.223361	−	0.833593i	0.0325805	−	0.121592i	0.980301	+	0.197510i	$0.0632854\pi$
$48$		0			0
$49$	6.34227	+	2.96236i	0.906039	+	0.423194i
$50$	2.11860	+	7.90673i	0.299616	+	1.11818i
$51$		0			0
$52$	−3.57380	+	14.3283i	−0.495597	+	1.98698i
$53$	0.886338	−	1.53518i	0.121748	−	0.210873i	−0.798709	−	0.601717i	$-0.794483\pi$
$53$	0.886338	−	1.53518i	0.121748	−	0.210873i	0.920457	+	0.390844i	$0.127817\pi$
$54$		0			0
$55$	3.49922	+	2.02027i	0.471834	+	0.272414i
$56$	11.5481	−	7.35179i	1.54318	−	0.982424i
$57$		0			0
$58$	17.8913	−	4.79397i	2.34925	−	0.629479i
$59$	−3.80628	−	3.80628i	−0.495536	−	0.495536i	0.414509	−	0.910045i	$-0.363953\pi$
$59$	−3.80628	−	3.80628i	−0.495536	−	0.495536i	−0.910045	+	0.414509i	$0.863953\pi$
$60$		0			0
$61$	−3.62667	−	2.09386i	−0.464347	−	0.268091i	0.249523	−	0.968369i	$-0.419726\pi$
$61$	−3.62667	−	2.09386i	−0.464347	−	0.268091i	−0.713870	+	0.700278i	$0.753059\pi$
$62$	6.64246	−	11.5051i	0.843594	−	1.46115i
$63$		0			0
$64$			6.77728i			0.847160i
$65$	9.09310	+	5.04144i	1.12786	+	0.625314i
$66$		0			0
$67$	−1.44159	+	5.38010i	−0.176119	+	0.657283i	0.820240	+	0.572020i	$0.193840\pi$
$67$	−1.44159	+	5.38010i	−0.176119	+	0.657283i	−0.996358	+	0.0852636i	$0.972827\pi$
$68$		−	30.9499i		−	3.75322i
$69$		0			0
$70$	−5.65859	−	17.9666i	−0.676330	−	2.14742i
$71$	1.75325	−	6.54321i	0.208072	−	0.776536i	−0.780419	−	0.625257i	$-0.784994\pi$
$71$	1.75325	−	6.54321i	0.208072	−	0.776536i	0.988491	−	0.151279i	$-0.0483391\pi$
$72$		0			0
$73$	8.10009	−	2.17041i	0.948043	−	0.254027i	0.248512	−	0.968629i	$-0.420059\pi$
$73$	8.10009	−	2.17041i	0.948043	−	0.254027i	0.699532	+	0.714601i	$0.253392\pi$
$74$	5.64656			0.656399
$75$		0			0
$76$	−27.3523	+	7.32903i	−3.13753	+	0.840698i
$77$	−3.28779	−	1.71284i	−0.374678	−	0.195196i
$78$		0			0
$79$	0.411935	+	0.713493i	0.0463463	+	0.0802742i	0.888268	−	0.459326i	$-0.151909\pi$
$79$	0.411935	+	0.713493i	0.0463463	+	0.0802742i	−0.841922	+	0.539600i	$0.818576\pi$
$80$	−12.7667	−	3.42082i	−1.42736	−	0.382459i
$81$		0			0
$82$	11.3829	−	19.7157i	1.25703	−	2.17723i
$83$	−2.15380	+	2.15380i	−0.236410	+	0.236410i	−0.815362	−	0.578952i	$-0.803462\pi$
$83$	−2.15380	+	2.15380i	−0.236410	+	0.236410i	0.578952	+	0.815362i	$0.303462\pi$
$84$		0			0
$85$	−21.0482	−	5.63986i	−2.28300	−	0.611729i
$86$	8.39268	+	2.24881i	0.905006	+	0.242496i
$87$		0			0
$88$	−6.27874	+	3.62503i	−0.669316	+	0.386430i
$89$	−1.81982	−	1.81982i	−0.192901	−	0.192901i	0.604047	−	0.796948i	$-0.293554\pi$
$89$	−1.81982	−	1.81982i	−0.192901	−	0.192901i	−0.796948	+	0.604047i	$0.793554\pi$
$90$		0			0
$91$	−8.53540	−	4.25992i	−0.894753	−	0.446561i
$92$	−9.33031			−0.972752
$93$		0			0
$94$	1.84524	−	1.06535i	0.190322	−	0.109883i
$95$			19.9372i			2.04551i
$96$		0			0
$97$	8.79336	+	2.35617i	0.892830	+	0.239233i	0.675934	−	0.736962i	$-0.263740\pi$
$97$	8.79336	+	2.35617i	0.892830	+	0.239233i	0.216896	+	0.976195i	$0.430407\pi$
$98$	5.90070	+	16.2441i	0.596060	+	1.64090i
$99$		0			0
$100$	−6.78954	+	11.7598i	−0.678954	+	1.17598i
$101$	−8.97642	−	15.5476i	−0.893187	−	1.54704i	−0.836033	−	0.548679i	$-0.815131\pi$
$101$	−8.97642	−	15.5476i	−0.893187	−	1.54704i	−0.0571540	−	0.998365i	$-0.518203\pi$
$102$		0			0
$103$	3.06226	+	5.30399i	0.301734	+	0.522618i	0.976529	−	0.215387i	$-0.0691014\pi$
$103$	3.06226	+	5.30399i	0.301734	+	0.522618i	−0.674795	+	0.738005i	$0.735768\pi$
$104$	−15.9921	+	9.60707i	−1.56815	+	0.942051i
$105$		0			0
$106$	4.22752	−	1.13276i	0.410613	−	0.110023i
$107$	4.73397			0.457650			0.228825	−	0.973468i	$-0.426512\pi$
$107$	4.73397			0.457650			0.228825	+	0.973468i	$0.426512\pi$
$108$		0			0
$109$	17.0265	−	4.56224i	1.63084	−	0.436983i	0.676683	−	0.736275i	$-0.263417\pi$
$109$	17.0265	−	4.56224i	1.63084	−	0.436983i	0.954162	+	0.299291i	$0.0967502\pi$
$110$	2.58196	+	9.63599i	0.246180	+	0.918755i
$111$		0			0
$112$	11.8384	+	2.62844i	1.11862	+	0.248365i
$113$	6.86440	+	11.8895i	0.645748	+	1.11847i	0.984128	+	0.177459i	$0.0567879\pi$
$113$	6.86440	+	11.8895i	0.645748	+	1.11847i	−0.338380	+	0.941010i	$0.609879\pi$
$114$		0			0
$115$	−1.70022	+	6.34531i	−0.158546	+	0.591703i
$116$	26.6101	+	15.3634i	2.47069	+	1.42645i
$117$		0			0
$118$		−	13.2901i		−	1.22345i
$119$	19.5177	+	4.33348i	1.78919	+	0.397250i
$120$		0			0
$121$	−7.82598	−	4.51833i	−0.711453	−	0.410757i
$122$	−2.67600	−	9.98695i	−0.242273	−	0.904176i
$123$		0			0
$124$	21.2873	−	5.70391i	1.91165	−	0.512226i
$125$	−3.43490	−	3.43490i	−0.307227	−	0.307227i
$126$		0			0
$127$	−9.36268	−	5.40554i	−0.830803	−	0.479665i	0.0233243	−	0.999728i	$-0.492575\pi$
$127$	−9.36268	−	5.40554i	−0.830803	−	0.479665i	−0.854128	+	0.520063i	$0.825908\pi$
$128$	−13.2006	+	13.2006i	−1.16678	+	1.16678i
$129$		0			0
$130$	7.07344	+	24.6763i	0.620381	+	2.16425i
$131$	−15.7531	+	9.09505i	−1.37635	+	0.794638i	−0.991719	−	0.128431i	$-0.959006\pi$
$131$	−15.7531	+	9.09505i	−1.37635	+	0.794638i	−0.384635	+	0.923069i	$0.625673\pi$
$132$		0			0
$133$	−0.792097	−	18.2752i	−0.0686835	−	1.58466i
$134$	−11.9094	+	6.87588i	−1.02881	+	0.593986i
$135$		0			0
$136$	27.6477	−	27.6477i	2.37077	−	2.37077i
$137$	6.88676	−	6.88676i	0.588376	−	0.588376i	−0.348815	−	0.937191i	$-0.613416\pi$
$137$	6.88676	−	6.88676i	0.588376	−	0.588376i	0.937191	+	0.348815i	$0.113416\pi$
$138$		0			0
$139$	−13.6153	+	7.86079i	−1.15483	+	0.666744i	−0.950060	−	0.312066i	$-0.898979\pi$
$139$	−13.6153	+	7.86079i	−1.15483	+	0.666744i	−0.204773	+	0.978809i	$0.565646\pi$
$140$	14.4375	−	27.7127i	1.22019	−	2.34215i
$141$		0			0
$142$	14.4840	−	8.36236i	1.21547	−	0.701754i
$143$	4.41842	+	2.44968i	0.369487	+	0.204853i
$144$		0			0
$145$	15.2973	−	15.2973i	1.27037	−	1.27037i
$146$	17.9303	+	10.3521i	1.48393	+	0.856745i
$147$		0			0
$148$	6.62347	+	6.62347i	0.544446	+	0.544446i
$149$	−12.4375	+	3.33261i	−1.01892	+	0.273018i	−0.729351	−	0.684140i	$-0.760178\pi$
$149$	−12.4375	+	3.33261i	−1.01892	+	0.273018i	−0.289567	+	0.957158i	$0.593511\pi$
$150$		0			0
$151$	0.904012	+	3.37382i	0.0735674	+	0.274557i	0.992905	−	0.118913i	$-0.0379410\pi$
$151$	0.904012	+	3.37382i	0.0735674	+	0.274557i	−0.919337	+	0.393471i	$0.871274\pi$
$152$	−30.9810	−	17.8869i	−2.51289	−	1.45082i
$153$		0			0
$154$	−2.74956	−	8.73015i	−0.221566	−	0.703496i
$155$		−	15.5163i		−	1.24630i
$156$		0			0
$157$	0.246511	+	0.142323i	0.0196737	+	0.0113586i	0.509805	−	0.860290i	$-0.329718\pi$
$157$	0.246511	+	0.142323i	0.0196737	+	0.0113586i	−0.490131	+	0.871649i	$0.663051\pi$
$158$	−0.526462	+	1.96478i	−0.0418831	+	0.156310i
$159$		0			0
$160$	−1.39548	−	2.41705i	−0.110323	−	0.191084i
$161$	1.30639	−	5.88392i	0.102958	−	0.463718i
$162$		0			0
$163$	3.54792	+	13.2410i	0.277895	+	1.03712i	0.953877	+	0.300199i	$0.0970531\pi$
$163$	3.54792	+	13.2410i	0.277895	+	1.03712i	−0.675982	+	0.736918i	$0.736280\pi$
$164$	36.4789	−	9.77450i	2.84853	−	0.763260i
$165$		0			0
$166$	−7.52025			−0.583684
$167$	8.45838	−	2.26642i	0.654529	−	0.175381i	0.0837535	−	0.996487i	$-0.473309\pi$
$167$	8.45838	−	2.26642i	0.654529	−	0.175381i	0.570776	+	0.821106i	$0.306642\pi$
$168$		0			0
$169$	11.4772	+	6.10516i	0.882864	+	0.469628i
$170$	−26.9001	−	46.5924i	−2.06315	−	3.57347i
$171$		0			0
$172$	7.20683	+	12.4826i	0.549515	+	0.951789i
$173$	5.42128	−	9.38993i	0.412172	−	0.713903i	−0.582955	−	0.812504i	$-0.698104\pi$
$173$	5.42128	−	9.38993i	0.412172	−	0.713903i	0.995127	+	0.0986015i	$0.0314369\pi$
$174$		0			0
$175$	−6.46539	−	5.92821i	−0.488737	−	0.448131i
$176$	−6.20344	−	1.66221i	−0.467602	−	0.125294i
$177$		0			0
$178$		−	6.35414i		−	0.476263i
$179$	7.07802	−	4.08650i	0.529036	−	0.305439i	−0.211588	−	0.977359i	$-0.567863\pi$
$179$	7.07802	−	4.08650i	0.529036	−	0.305439i	0.740624	+	0.671920i	$0.234530\pi$
$180$		0			0
$181$	4.10394			0.305043			0.152522	−	0.988300i	$-0.451261\pi$
$181$	4.10394			0.305043			0.152522	+	0.988300i	$0.451261\pi$
$182$	−7.46417	−	22.3382i	−0.553281	−	1.65582i
$183$		0			0
$184$	−8.33481	−	8.33481i	−0.614450	−	0.614450i
$185$	5.71143	−	3.29749i	0.419912	−	0.242437i
$186$		0			0
$187$	−10.2275	−	2.74046i	−0.747911	−	0.200402i
$188$	3.41416	+	0.914821i	0.249003	+	0.0667201i
$189$		0			0
$190$	−34.8065	+	34.8065i	−2.52513	+	2.52513i
$191$	−2.20939	+	3.82678i	−0.159866	+	0.276896i	−0.934820	−	0.355121i	$-0.884440\pi$
$191$	−2.20939	+	3.82678i	−0.159866	+	0.276896i	0.774954	+	0.632017i	$0.217773\pi$
$192$		0			0
$193$	10.8992	+	2.92042i	0.784538	+	0.210216i	0.628785	−	0.777580i	$-0.283553\pi$
$193$	10.8992	+	2.92042i	0.784538	+	0.210216i	0.155754	+	0.987796i	$0.450219\pi$
$194$	11.2381	+	19.4650i	0.806849	+	1.39750i
$195$		0			0
$196$	−12.1330	+	25.9761i	−0.866640	+	1.85544i
$197$	−4.66242	+	1.24929i	−0.332183	+	0.0890083i	−0.421056	−	0.907035i	$-0.638340\pi$
$197$	−4.66242	+	1.24929i	−0.332183	+	0.0890083i	0.0888723	+	0.996043i	$0.471674\pi$
$198$		0			0
$199$	−11.5108			−0.815981			−0.407991	−	0.912986i	$-0.633770\pi$
$199$	−11.5108			−0.815981			−0.407991	+	0.912986i	$0.633770\pi$
$200$	−16.5702	+	4.43998i	−1.17169	+	0.313954i
$201$		0			0
$202$	11.4721	−	42.8143i	0.807171	−	3.01240i
$203$	−13.4143	+	14.6299i	−0.941503	+	1.02681i
$204$		0			0
$205$		−	26.5896i		−	1.85710i
$206$	−3.91364	+	14.6059i	−0.272676	+	1.01764i
$207$		0			0
$208$	−16.0346	−	3.99938i	−1.11180	−	0.277307i
$209$			9.68766i			0.670109i
$210$		0			0
$211$	−1.96759	+	3.40797i	−0.135454	+	0.234614i	−0.925771	−	0.378085i	$-0.876583\pi$
$211$	−1.96759	+	3.40797i	−0.135454	+	0.234614i	0.790317	+	0.612699i	$0.209916\pi$
$212$	6.28766	+	3.63018i	0.431839	+	0.249322i
$213$		0			0
$214$	8.26461	+	8.26461i	0.564957	+	0.564957i
$215$	9.80237	−	2.62654i	0.668516	−	0.179128i
$216$		0			0
$217$	0.616459	+	14.2229i	0.0418480	+	0.965514i
$218$	37.6899	+	21.7603i	2.55268	+	1.47379i
$219$		0			0
$220$	−8.27446	+	14.3318i	−0.557864	+	0.966249i
$221$	−26.4360	−	6.59372i	−1.77828	−	0.443542i
$222$		0			0
$223$	2.38797	+	8.91203i	0.159910	+	0.596794i	0.998635	+	0.0522375i	$0.0166353\pi$
$223$	2.38797	+	8.91203i	0.159910	+	0.596794i	−0.838724	+	0.544556i	$0.816698\pi$
$224$	1.37518	+	2.16012i	0.0918833	+	0.144329i
$225$		0			0
$226$	−8.77286	+	32.7408i	−0.583562	+	2.17788i
$227$	−4.15727	+	4.15727i	−0.275928	+	0.275928i	−0.831481	−	0.555553i	$-0.812507\pi$
$227$	−4.15727	+	4.15727i	−0.275928	+	0.275928i	0.555553	+	0.831481i	$0.312507\pi$
$228$		0			0
$229$	0.564755	−	2.10769i	0.0373201	−	0.139280i	−0.944752	−	0.327786i	$-0.893698\pi$
$229$	0.564755	−	2.10769i	0.0373201	−	0.139280i	0.982072	+	0.188505i	$0.0603643\pi$
$230$	−14.0460	+	8.10945i	−0.926164	+	0.534721i
$231$		0			0
$232$	10.0468	+	37.4951i	0.659603	+	2.46167i
$233$	10.5892	−	6.11367i	0.693720	−	0.400520i	−0.111284	−	0.993789i	$-0.535496\pi$
$233$	10.5892	−	6.11367i	0.693720	−	0.400520i	0.805004	+	0.593269i	$0.202163\pi$
$234$		0			0
$235$	1.24429	−	2.15518i	0.0811688	−	0.140588i
$236$	15.5894	−	15.5894i	1.01479	−	1.01479i
$237$		0			0
$238$	26.5088	+	41.6397i	1.71831	+	2.69910i
$239$	−7.97620	−	7.97620i	−0.515938	−	0.515938i	0.400402	−	0.916340i	$-0.368870\pi$
$239$	−7.97620	−	7.97620i	−0.515938	−	0.515938i	−0.916340	+	0.400402i	$0.868870\pi$
$240$		0			0
$241$	−9.09005	−	9.09005i	−0.585542	−	0.585542i	0.350879	−	0.936421i	$-0.385883\pi$
$241$	−9.09005	−	9.09005i	−0.585542	−	0.585542i	−0.936421	+	0.350879i	$0.885883\pi$
$242$	−5.77453	−	21.5508i	−0.371201	−	1.38534i
$243$		0			0
$244$	8.57584	−	14.8538i	0.549012	−	0.950916i
$245$	15.4548	+	12.9848i	0.987370	+	0.829571i
$246$		0			0
$247$	0.432850	+	24.9245i	0.0275416	+	1.58591i
$248$	24.1114	+	13.9207i	1.53107	+	0.883965i
$249$		0			0
$250$		−	11.9934i		−	0.758528i
$251$	−13.1084	−	22.7045i	−0.827397	−	1.43309i	−0.900073	−	0.435739i	$-0.856487\pi$
$251$	−13.1084	−	22.7045i	−0.827397	−	1.43309i	0.0726757	−	0.997356i	$-0.476846\pi$
$252$		0			0
$253$	−0.826153	+	3.08324i	−0.0519398	+	0.193842i
$254$	−6.90841	−	25.7825i	−0.433472	−	1.61774i
$255$		0			0
$256$	−32.5370			−2.03356
$257$	−6.43364			−0.401319			−0.200660	−	0.979661i	$-0.564309\pi$
$257$	−6.43364			−0.401319			−0.200660	+	0.979661i	$0.564309\pi$
$258$		0			0
$259$	−5.10431	+	3.24953i	−0.317167	+	0.201916i
$260$	−20.6483	+	37.2427i	−1.28055	+	2.30970i
$261$		0			0
$262$	−43.3802	−	11.6237i	−2.68003	−	0.718113i
$263$	7.50610	+	13.0010i	0.462846	+	0.801673i	0.999101	−	0.0423827i	$-0.0134949\pi$
$263$	7.50610	+	13.0010i	0.462846	+	0.801673i	−0.536255	+	0.844056i	$0.680162\pi$
$264$		0			0
$265$	3.61457	−	3.61457i	0.222041	−	0.222041i
$266$	30.5222	−	33.2879i	1.87144	−	2.04101i
$267$		0			0
$268$	−22.0353	−	5.90435i	−1.34602	−	0.360665i
$269$			22.1690i			1.35167i	0.737054	+	0.675834i	$0.236216\pi$
$269$			22.1690i			1.35167i	−0.737054	+	0.675834i	$0.763784\pi$
$270$		0			0
$271$	−14.9017	−	14.9017i	−0.905214	−	0.905214i	0.0906673	−	0.995881i	$-0.471100\pi$
$271$	−14.9017	−	14.9017i	−0.905214	−	0.905214i	−0.995881	+	0.0906673i	$0.971100\pi$
$272$	34.6354			2.10008
$273$		0			0
$274$	24.0460			1.45267
$275$	3.28491	+	3.28491i	0.198088	+	0.198088i
$276$		0			0
$277$		−	9.86815i		−	0.592920i	−0.955045	−	0.296460i	$-0.904194\pi$
$277$		−	9.86815i		−	0.592920i	0.955045	−	0.296460i	$-0.0958061\pi$
$278$	−37.4932	−	10.0463i	−2.24869	−	0.602535i
$279$		0			0
$280$	37.6529	−	11.8588i	2.25019	−	0.708697i
$281$	−21.3933	+	21.3933i	−1.27622	+	1.27622i	−0.333449	+	0.942768i	$0.608212\pi$
$281$	−21.3933	+	21.3933i	−1.27622	+	1.27622i	−0.942768	+	0.333449i	$0.891788\pi$
$282$		0			0
$283$	10.7440	+	18.6092i	0.638666	+	1.10620i	0.985726	+	0.168359i	$0.0538466\pi$
$283$	10.7440	+	18.6092i	0.638666	+	1.10620i	−0.347060	+	0.937843i	$0.612820\pi$
$284$	26.7991	+	7.18080i	1.59023	+	0.426102i
$285$		0			0
$286$	3.43705	+	11.9904i	0.203237	+	0.709008i
$287$	1.05639	+	24.3731i	0.0623570	+	1.43870i
$288$		0			0
$289$	40.1030			2.35900
$290$	53.4123			3.13648
$291$		0			0
$292$	8.88938	+	33.1756i	0.520212	+	1.94146i
$293$	0.259901	−	0.969962i	0.0151836	−	0.0566658i	−0.957918	−	0.287041i	$-0.907329\pi$
$293$	0.259901	−	0.969962i	0.0151836	−	0.0566658i	0.973102	+	0.230375i	$0.0739952\pi$
$294$		0			0
$295$	−7.76120	−	13.4428i	−0.451874	−	0.782670i
$296$			11.8336i			0.687812i
$297$		0			0
$298$	−27.5316	−	15.8954i	−1.59486	−	0.920795i
$299$	−1.98778	+	7.96953i	−0.114956	+	0.460890i
$300$		0			0
$301$	−8.88089	+	2.79703i	−0.511886	+	0.161218i
$302$	−4.31182	+	7.46828i	−0.248117	+	0.429751i
$303$		0			0
$304$	−8.20179	−	30.6095i	−0.470405	−	1.75557i
$305$	−8.53895	−	8.53895i	−0.488939	−	0.488939i
$306$		0			0
$307$	−4.86151	−	4.86151i	−0.277461	−	0.277461i	0.554634	−	0.832095i	$-0.312858\pi$
$307$	−4.86151	−	4.86151i	−0.277461	−	0.277461i	−0.832095	+	0.554634i	$0.812858\pi$
$308$	7.01531	−	13.4658i	0.399734	−	0.767287i
$309$		0			0
$310$	27.0886	−	27.0886i	1.53853	−	1.53853i
$311$	−6.85636	+	11.8756i	−0.388789	+	0.673402i	−0.992287	−	0.123963i	$-0.960440\pi$
$311$	−6.85636	+	11.8756i	−0.388789	+	0.673402i	0.603498	+	0.797364i	$0.293773\pi$
$312$		0			0
$313$	−29.5010	+	17.0324i	−1.66750	+	0.962730i	−0.698517	+	0.715593i	$0.746156\pi$
$313$	−29.5010	+	17.0324i	−1.66750	+	0.962730i	−0.968981	+	0.247137i	$0.920510\pi$
$314$	0.181892	+	0.678830i	0.0102648	+	0.0383086i
$315$		0			0
$316$	−2.92226	+	1.68717i	−0.164390	+	0.0949106i
$317$	2.52285	−	9.41539i	0.141697	−	0.528821i	−0.858183	−	0.513344i	$-0.828407\pi$
$317$	2.52285	−	9.41539i	0.141697	−	0.528821i	0.999880	−	0.0154772i	$-0.00492673\pi$
$318$		0			0
$319$	7.43309	−	7.43309i	0.416173	−	0.416173i
$320$	−5.05818	+	18.8774i	−0.282761	+	1.05528i
$321$		0			0
$322$	12.5529	−	7.99149i	0.699547	−	0.445348i
$323$	−13.5222	−	50.4655i	−0.752394	−	2.80797i
$324$		0			0
$325$	8.59824	+	8.30470i	0.476945	+	0.460662i
$326$	−16.9223	+	29.3103i	−0.937241	+	1.62335i
$327$		0			0
$328$	41.3184	+	23.8552i	2.28143	+	1.31718i
$329$	−1.05494	+	2.02496i	−0.0581610	+	0.111640i
$330$		0			0
$331$	−20.0124	+	5.36230i	−1.09998	+	0.294739i	−0.762756	−	0.646686i	$-0.776154\pi$
$331$	−20.0124	+	5.36230i	−1.09998	+	0.294739i	−0.337223	+	0.941425i	$0.609488\pi$
$332$	−8.82134	−	8.82134i	−0.484134	−	0.484134i
$333$		0			0
$334$	18.7235	+	10.8100i	1.02450	+	0.591497i
$335$	−8.03080	+	13.9098i	−0.438769	+	0.759971i
$336$		0			0
$337$		−	26.8744i		−	1.46394i	−0.681336	−	0.731971i	$-0.738601\pi$
$337$		−	26.8744i		−	1.46394i	0.681336	−	0.731971i	$-0.261399\pi$
$338$	9.37862	+	30.6956i	0.510130	+	1.66962i
$339$		0			0
$340$	23.0992	−	86.2076i	1.25273	−	4.67526i
$341$		−	7.53954i		−	0.408289i
$342$		0			0
$343$	−14.6824	−	11.2884i	−0.792773	−	0.609517i
$344$	−4.71286	+	17.5886i	−0.254101	+	0.948316i
$345$		0			0
$346$	25.8576	−	6.92851i	1.39011	−	0.372479i
$347$	6.16871			0.331154			0.165577	−	0.986197i	$-0.447051\pi$
$347$	6.16871			0.331154			0.165577	+	0.986197i	$0.447051\pi$
$348$		0			0
$349$	−20.8536	+	5.58771i	−1.11627	+	0.299103i	−0.769372	−	0.638801i	$-0.779431\pi$
$349$	−20.8536	+	5.58771i	−1.11627	+	0.299103i	−0.346896	+	0.937904i	$0.612764\pi$
$350$	−0.937801	−	21.6369i	−0.0501276	−	1.15654i
$351$		0			0
$352$	−0.678077	−	1.17446i	−0.0361416	−	0.0625992i
$353$	−12.7937	−	3.42805i	−0.680938	−	0.182457i	−0.0982609	−	0.995161i	$-0.531328\pi$
$353$	−12.7937	−	3.42805i	−0.680938	−	0.182457i	−0.582677	+	0.812704i	$0.697995\pi$
$354$		0			0
$355$	9.76696	−	16.9169i	0.518376	−	0.897854i
$356$	7.45348	−	7.45348i	0.395034	−	0.395034i
$357$		0			0
$358$	19.4911	+	5.22264i	1.03014	+	0.276025i
$359$	−4.76941	−	1.27796i	−0.251720	−	0.0674482i	0.130753	−	0.991415i	$-0.458261\pi$
$359$	−4.76941	−	1.27796i	−0.251720	−	0.0674482i	−0.382473	+	0.923967i	$0.624927\pi$
$360$		0			0
$361$	−24.9429	+	14.4008i	−1.31278	+	0.757936i
$362$	7.16470	+	7.16470i	0.376568	+	0.376568i
$363$		0			0
$364$	17.4474	−	34.9585i	0.914494	−	1.83233i
$365$	24.1818			1.26573
$366$		0			0
$367$	17.7483	−	10.2470i	0.926453	−	0.534888i	0.0407648	−	0.999169i	$-0.487021\pi$
$367$	17.7483	−	10.2470i	0.926453	−	0.534888i	0.885688	+	0.464281i	$0.153687\pi$
$368$		−	10.4414i		−	0.544295i
$369$		0			0
$370$	15.7279	+	4.21427i	0.817653	+	0.219090i
$371$	−3.16966	+	3.45687i	−0.164560	+	0.179472i
$372$		0			0
$373$	−11.6214	+	20.1289i	−0.601735	+	1.04224i	0.390823	+	0.920466i	$0.372190\pi$
$373$	−11.6214	+	20.1289i	−0.601735	+	1.04224i	−0.992558	+	0.121770i	$0.961143\pi$
$374$	−13.0710	−	22.6397i	−0.675886	−	1.17067i
$375$		0			0
$376$	2.23267	+	3.86710i	0.115141	+	0.199430i
$377$	18.7918	−	19.4561i	0.967829	−	1.00204i
$378$		0			0
$379$	−20.6487	+	5.53282i	−1.06066	+	0.284202i	−0.746648	−	0.665219i	$-0.768338\pi$
$379$	−20.6487	+	5.53282i	−1.06066	+	0.284202i	−0.314007	+	0.949421i	$0.601671\pi$
$380$	−81.6569			−4.18891
$381$		0			0
$382$	−10.5380	+	2.82365i	−0.539171	+	0.144471i
$383$	−2.74839	−	10.2571i	−0.140436	−	0.524114i	−0.999916	−	0.0129453i	$-0.995879\pi$
$383$	−2.74839	−	10.2571i	−0.140436	−	0.524114i	0.859480	−	0.511169i	$-0.170787\pi$
$384$		0			0
$385$	−7.87941	−	7.22476i	−0.401572	−	0.368208i
$386$	13.9294	+	24.1264i	0.708986	+	1.22800i
$387$		0			0
$388$	−9.65021	+	36.0151i	−0.489915	+	1.82839i
$389$	−14.3360	−	8.27689i	−0.726864	−	0.419655i	0.0904098	−	0.995905i	$-0.471182\pi$
$389$	−14.3360	−	8.27689i	−0.726864	−	0.419655i	−0.817274	+	0.576250i	$0.804516\pi$
$390$		0			0
$391$		−	17.2146i		−	0.870578i
$392$	−34.0430	+	12.3662i	−1.71943	+	0.624586i
$393$		0			0
$394$	−10.3207	−	5.95867i	−0.519951	−	0.300194i
$395$	0.614890	+	2.29480i	0.0309385	+	0.115464i
$396$		0			0
$397$	−28.5741	+	7.65641i	−1.43409	+	0.384264i	−0.890461	−	0.455059i	$-0.849618\pi$
$397$	−28.5741	+	7.65641i	−1.43409	+	0.384264i	−0.543632	+	0.839323i	$0.682951\pi$
$398$	−20.0957	−	20.0957i	−1.00731	−	1.00731i
$399$		0			0
$400$	−13.1602	−	7.59805i	−0.658011	−	0.379903i
$401$	−7.16742	+	7.16742i	−0.357924	+	0.357924i	−0.863047	−	0.505123i	$-0.831447\pi$
$401$	−7.16742	+	7.16742i	−0.357924	+	0.357924i	0.505123	+	0.863047i	$0.331447\pi$
$402$		0			0
$403$	−0.336871	−	19.3978i	−0.0167807	−	0.966275i
$404$	63.6785	−	36.7648i	3.16813	−	1.82912i
$405$		0			0
$406$	−48.9599	+	2.12205i	−2.42984	+	0.105316i
$407$	2.77523	−	1.60228i	0.137563	−	0.0794222i
$408$		0			0
$409$	−2.06212	+	2.06212i	−0.101965	+	0.101965i	−0.756249	−	0.654284i	$-0.772970\pi$
$409$	−2.06212	+	2.06212i	−0.101965	+	0.101965i	0.654284	+	0.756249i	$0.272970\pi$
$410$	46.4204	−	46.4204i	2.29254	−	2.29254i
$411$		0			0
$412$	−21.7236	+	12.5421i	−1.07025	+	0.617907i
$413$	7.64830	+	12.0139i	0.376348	+	0.591163i
$414$		0			0
$415$	−7.60664	+	4.39170i	−0.373395	+	0.215580i
$416$	−1.79704	−	2.99138i	−0.0881073	−	0.146665i
$417$		0			0
$418$	−16.9128	+	16.9128i	−0.827233	+	0.827233i
$419$	−8.98142	−	5.18542i	−0.438771	−	0.253325i	0.264305	−	0.964439i	$-0.414857\pi$
$419$	−8.98142	−	5.18542i	−0.438771	−	0.253325i	−0.703076	+	0.711115i	$0.748191\pi$
$420$		0			0
$421$	26.7368	+	26.7368i	1.30307	+	1.30307i	0.926310	+	0.376762i	$0.122962\pi$
$421$	26.7368	+	26.7368i	1.30307	+	1.30307i	0.376762	+	0.926310i	$0.377038\pi$
$422$	−9.38470	+	2.51462i	−0.456840	+	0.122410i
$423$		0			0
$424$	2.37394	+	8.85966i	0.115289	+	0.430263i
$425$	−21.6971	−	12.5268i	−1.05246	−	0.607640i
$426$		0			0
$427$	8.16640	+	7.48790i	0.395200	+	0.362365i
$428$			19.3890i			0.937201i
$429$		0			0
$430$	21.6985	+	12.5276i	1.04640	+	0.604137i
$431$	6.33146	−	23.6293i	0.304976	−	1.13818i	−0.627991	−	0.778221i	$-0.716122\pi$
$431$	6.33146	−	23.6293i	0.304976	−	1.13818i	0.932966	−	0.359964i	$-0.117211\pi$
$432$		0			0
$433$	8.76052	+	15.1737i	0.421004	+	0.729200i	0.996038	−	0.0889293i	$-0.0283445\pi$
$433$	8.76052	+	15.1737i	0.421004	+	0.729200i	−0.575034	+	0.818129i	$0.695011\pi$
$434$	−23.7543	+	25.9067i	−1.14024	+	1.24356i
$435$		0			0
$436$	18.6856	+	69.7357i	0.894879	+	3.33974i
$437$	−15.2136	+	4.07647i	−0.727764	+	0.195004i
$438$		0			0
$439$	19.8929			0.949437			0.474719	−	0.880138i	$-0.342550\pi$
$439$	19.8929			0.949437			0.474719	+	0.880138i	$0.342550\pi$
$440$	−20.1943	+	5.41104i	−0.962724	+	0.257961i
$441$		0			0
$442$	−34.6409	−	57.6636i	−1.64770	−	2.74278i
$443$	−7.68921	−	13.3181i	−0.365325	−	0.632762i	0.623503	−	0.781821i	$-0.285709\pi$
$443$	−7.68921	−	13.3181i	−0.365325	−	0.632762i	−0.988828	+	0.149059i	$0.952376\pi$
$444$		0			0
$445$	−3.71071	−	6.42714i	−0.175905	−	0.304676i
$446$	−11.3898	+	19.7277i	−0.539322	+	0.934132i
$447$		0			0
$448$	3.88654	−	17.5047i	0.183622	−	0.827021i
$449$	3.38883	+	0.908034i	0.159929	+	0.0428528i	0.337895	−	0.941184i	$-0.390285\pi$
$449$	3.38883	+	0.908034i	0.159929	+	0.0428528i	−0.177966	+	0.984037i	$0.556952\pi$
$450$		0			0
$451$		−	12.9201i		−	0.608385i
$452$	−48.6959	+	28.1146i	−2.29046	+	1.32240i
$453$		0			0
$454$	−14.5156			−0.681252
$455$	−20.5951	−	18.2359i	−0.965512	−	0.854912i
$456$		0			0
$457$	−21.5661	−	21.5661i	−1.00882	−	1.00882i	−0.999961	−	0.00885742i	$-0.997181\pi$
$457$	−21.5661	−	21.5661i	−1.00882	−	1.00882i	−0.00885742	−	0.999961i	$-0.502819\pi$
$458$	4.66559	−	2.69368i	0.218009	−	0.125867i
$459$		0			0
$460$	−25.9886	−	6.96362i	−1.21172	−	0.324680i
$461$	19.6958	+	5.27746i	0.917323	+	0.245796i	0.686441	−	0.727186i	$-0.259172\pi$
$461$	19.6958	+	5.27746i	0.917323	+	0.245796i	0.230882	+	0.972982i	$0.425839\pi$
$462$		0			0
$463$	7.72370	−	7.72370i	0.358951	−	0.358951i	−0.504475	−	0.863426i	$-0.668314\pi$
$463$	7.72370	−	7.72370i	0.358951	−	0.358951i	0.863426	+	0.504475i	$0.168314\pi$
$464$	−17.1929	+	29.7789i	−0.798158	+	1.38245i
$465$		0			0
$466$	29.1600	+	7.81340i	1.35081	+	0.361949i
$467$	−17.0696	−	29.5655i	−0.789888	−	1.36813i	−0.926035	−	0.377438i	$-0.876805\pi$
$467$	−17.0696	−	29.5655i	−0.789888	−	1.36813i	0.136147	−	0.990689i	$-0.456528\pi$
$468$		0			0
$469$	6.80872	−	13.0693i	0.314398	−	0.603484i
$470$	5.93484	−	1.59023i	0.273754	−	0.0733521i
$471$		0			0
$472$	27.8522			1.28200
$473$	4.76306	−	1.27626i	0.219006	−	0.0586824i
$474$		0			0
$475$	−5.93278	+	22.1414i	−0.272215	+	1.01592i
$476$	−17.7487	+	79.9390i	−0.813510	+	3.66400i
$477$		0			0
$478$		−	27.8499i		−	1.27382i
$479$	−4.49601	+	16.7793i	−0.205428	+	0.766668i	0.783891	+	0.620899i	$0.213232\pi$
$479$	−4.49601	+	16.7793i	−0.205428	+	0.766668i	−0.989319	+	0.145769i	$0.953434\pi$
$480$		0			0
$481$	7.06857	−	4.24638i	0.322299	−	0.193618i
$482$		−	31.7390i		−	1.44567i
$483$		0			0
$484$	18.5058	−	32.0530i	0.841172	−	1.45695i
$485$	22.7344	+	13.1257i	1.03232	+	0.596009i
$486$		0			0
$487$	9.01723	+	9.01723i	0.408610	+	0.408610i	0.881254	−	0.472644i	$-0.156700\pi$
$487$	9.01723	+	9.01723i	0.408610	+	0.408610i	−0.472644	+	0.881254i	$0.656700\pi$
$488$	20.9298	−	5.60812i	0.947447	−	0.253868i
$489$		0			0
$490$	4.31205	+	49.6502i	0.194799	+	2.24297i
$491$	16.0173	+	9.24760i	0.722851	+	0.417339i	0.815801	−	0.578332i	$-0.196296\pi$
$491$	16.0173	+	9.24760i	0.722851	+	0.417339i	−0.0929498	+	0.995671i	$0.529630\pi$
$492$		0			0
$493$	−28.3456	+	49.0961i	−1.27662	+	2.21118i
$494$	−42.7579	+	44.2692i	−1.92377	+	1.99177i
$495$		0			0
$496$	6.38314	+	23.8222i	0.286612	+	1.06965i
$497$	−8.28069	+	15.8947i	−0.371440	+	0.712976i
$498$		0			0
$499$	9.65516	−	36.0336i	0.432224	−	1.61308i	−0.315398	−	0.948960i	$-0.602138\pi$
$499$	9.65516	−	36.0336i	0.432224	−	1.61308i	0.747622	−	0.664124i	$-0.231195\pi$
$500$	14.0684	−	14.0684i	0.629157	−	0.629157i
$501$		0			0
$502$	16.7529	−	62.5226i	0.747718	−	2.79052i
$503$	−12.6061	+	7.27816i	−0.562080	+	0.324517i	−0.753980	−	0.656897i	$-0.771868\pi$
$503$	−12.6061	+	7.27816i	−0.562080	+	0.324517i	0.191900	+	0.981415i	$0.438535\pi$
$504$		0			0
$505$	−13.3990	−	50.0057i	−0.596247	−	2.22522i
$506$	−6.82507	+	3.94046i	−0.303411	+	0.175175i
$507$		0			0
$508$	22.1396	−	38.3468i	0.982284	−	1.70137i
$509$	−0.381529	+	0.381529i	−0.0169110	+	0.0169110i	−0.715512	−	0.698601i	$-0.753806\pi$
$509$	−0.381529	+	0.381529i	−0.0169110	+	0.0169110i	0.698601	+	0.715512i	$0.253806\pi$
$510$		0			0
$511$	−22.1660	+	0.960734i	−0.980566	+	0.0425004i
$512$	−30.4022	−	30.4022i	−1.34360	−	1.34360i
$513$		0			0
$514$	−11.2319	−	11.2319i	−0.495419	−	0.495419i
$515$	4.57100	+	17.0592i	0.201422	+	0.751718i
$516$		0			0
$517$	0.604614	−	1.04722i	0.0265909	−	0.0460567i
$518$	−14.5842	−	3.23811i	−0.640794	−	0.142274i
$519$		0			0
$520$	−51.7143	+	14.8239i	−2.26782	+	0.650070i
$521$	30.2442	+	17.4615i	1.32502	+	0.765003i	0.984525	−	0.175242i	$-0.0560707\pi$
$521$	30.2442	+	17.4615i	1.32502	+	0.765003i	0.340499	+	0.940245i	$0.389404\pi$
$522$		0			0
$523$			21.0562i			0.920725i	0.887731	+	0.460362i	$0.152281\pi$
$523$			21.0562i			0.920725i	−0.887731	+	0.460362i	$0.847719\pi$
$524$	−37.2507	−	64.5201i	−1.62730	−	2.81857i
$525$		0			0
$526$	−9.59297	+	35.8014i	−0.418273	+	1.56102i
$527$	10.5238	+	39.2754i	0.458424	+	1.71086i
$528$		0			0
$529$	17.8104			0.774366
$530$	12.6207			0.548209
$531$		0			0
$532$	74.8500	−	3.24420i	3.24516	−	0.140654i
$533$	−0.577279	−	33.2411i	−0.0250047	−	1.43983i
$534$		0			0
$535$	13.1860	+	3.53317i	0.570078	+	0.152752i
$536$	−14.4099	−	24.9586i	−0.622412	−	1.07805i
$537$		0			0
$538$	−38.7029	+	38.7029i	−1.66860	+	1.66860i
$539$	7.50962	+	6.30945i	0.323462	+	0.271767i
$540$		0			0
$541$	−30.9919	−	8.30427i	−1.33245	−	0.357028i	−0.478821	−	0.877913i	$-0.658936\pi$
$541$	−30.9919	−	8.30427i	−1.33245	−	0.357028i	−0.853627	+	0.520884i	$0.825602\pi$
$542$		−	52.0311i		−	2.23493i
$543$		0			0
$544$	5.17161	+	5.17161i	0.221731	+	0.221731i
$545$	50.8305			2.17734
$546$		0			0
$547$	12.5039			0.534630			0.267315	−	0.963609i	$-0.413864\pi$
$547$	12.5039			0.534630			0.267315	+	0.963609i	$0.413864\pi$
$548$	28.2062	+	28.2062i	1.20491	+	1.20491i
$549$		0			0
$550$			11.4697i			0.489068i
$551$	50.1016	+	13.4247i	2.13440	+	0.571911i
$552$		0			0
$553$	−0.654805	−	2.07908i	−0.0278451	−	0.0884114i
$554$	17.2279	−	17.2279i	0.731944	−	0.731944i
$555$		0			0
$556$	−32.1955	−	55.7643i	−1.36540	−	2.36493i
$557$	30.4076	+	8.14769i	1.28841	+	0.345229i	0.837057	−	0.547116i	$-0.184274\pi$
$557$	30.4076	+	8.14769i	1.28841	+	0.345229i	0.451354	+	0.892345i	$0.350941\pi$
$558$		0			0
$559$	12.1974	−	3.49639i	0.515897	−	0.147882i
$560$	31.0127	+	16.1567i	1.31053	+	0.682746i
$561$		0			0
$562$	−74.6973			−3.15092
$563$	−3.71449			−0.156547			−0.0782736	−	0.996932i	$-0.524941\pi$
$563$	−3.71449			−0.156547			−0.0782736	+	0.996932i	$0.524941\pi$
$564$		0			0
$565$	10.2464	+	38.2401i	0.431069	+	1.60877i
$566$	−13.7311	+	51.2452i	−0.577161	+	2.15399i
$567$		0			0
$568$	17.5251	+	30.3544i	0.735337	+	1.27364i
$569$		−	28.7690i		−	1.20606i	−0.797718	−	0.603030i	$-0.793960\pi$
$569$		−	28.7690i		−	1.20606i	0.797718	−	0.603030i	$-0.206040\pi$
$570$		0			0
$571$	38.1385	+	22.0193i	1.59605	+	0.921478i	0.992239	+	0.124348i	$0.0396839\pi$
$571$	38.1385	+	22.0193i	1.59605	+	0.921478i	0.603808	+	0.797130i	$0.293649\pi$
$572$	−10.0332	+	18.0966i	−0.419509	+	0.756656i
$573$		0			0
$574$	−40.7065	+	44.3951i	−1.69906	+	1.85301i
$575$	−3.77640	+	6.54091i	−0.157487	+	0.272775i
$576$		0			0
$577$	5.37814	+	20.0715i	0.223895	+	0.835587i	0.982844	+	0.184437i	$0.0590462\pi$
$577$	5.37814	+	20.0715i	0.223895	+	0.835587i	−0.758950	+	0.651149i	$0.774287\pi$
$578$	70.0123	+	70.0123i	2.91213	+	2.91213i
$579$		0			0
$580$	62.6533	+	62.6533i	2.60154	+	2.60154i
$581$	6.79808	−	4.32782i	0.282032	−	0.179548i
$582$		0			0
$583$	1.75635	−	1.75635i	0.0727407	−	0.0727407i
$584$	−21.6950	+	37.5769i	−0.897746	+	1.55494i
$585$		0			0
$586$	2.14711	−	1.23963i	0.0886962	−	0.0512088i
$587$	11.1326	+	41.5473i	0.459491	+	1.71484i	0.674540	+	0.738239i	$0.264342\pi$
$587$	11.1326	+	41.5473i	0.459491	+	1.71484i	−0.215049	+	0.976603i	$0.568991\pi$
$588$		0			0
$589$	32.2180	−	18.6011i	1.32752	−	0.766444i
$590$	9.91899	−	37.0182i	0.408358	−	1.52401i
$591$		0			0
$592$	−7.41221	+	7.41221i	−0.304640	+	0.304640i
$593$	0.460561	−	1.71884i	0.0189130	−	0.0705842i	−0.955824	−	0.293938i	$-0.905034\pi$
$593$	0.460561	−	1.71884i	0.0189130	−	0.0705842i	0.974737	+	0.223354i	$0.0717006\pi$
$594$		0			0
$595$	51.1303	+	26.6374i	2.09614	+	1.09203i
$596$	−13.6494	−	50.9403i	−0.559102	−	2.08660i
$597$		0			0
$598$	−17.3836	+	10.4430i	−0.710867	+	0.427047i
$599$	−8.48260	+	14.6923i	−0.346590	+	0.600311i	−0.985641	−	0.168853i	$-0.945994\pi$
$599$	−8.48260	+	14.6923i	−0.346590	+	0.600311i	0.639052	+	0.769164i	$0.279327\pi$
$600$		0			0
$601$	30.5871	+	17.6595i	1.24767	+	0.720345i	0.970645	−	0.240517i	$-0.0773170\pi$
$601$	30.5871	+	17.6595i	1.24767	+	0.720345i	0.277029	+	0.960862i	$0.410650\pi$
$602$	−20.3875	−	10.6213i	−0.830931	−	0.432891i
$603$		0			0
$604$	−13.8182	+	3.70257i	−0.562254	+	0.150656i
$605$	−18.4262	−	18.4262i	−0.749131	−	0.749131i
$606$		0			0
$607$	−17.5660	−	10.1417i	−0.712980	−	0.411639i	0.0991833	−	0.995069i	$-0.468377\pi$
$607$	−17.5660	−	10.1417i	−0.712980	−	0.411639i	−0.812164	+	0.583430i	$0.801710\pi$
$608$	3.34582	−	5.79513i	0.135691	−	0.235024i
$609$		0			0
$610$		−	29.8148i		−	1.20717i
$611$	1.50877	−	2.72132i	0.0610382	−	0.110093i
$612$		0			0
$613$	−6.42633	+	23.9834i	−0.259557	+	0.968680i	0.705941	+	0.708270i	$0.250524\pi$
$613$	−6.42633	+	23.9834i	−0.259557	+	0.968680i	−0.965498	+	0.260410i	$0.916142\pi$
$614$		−	16.9745i		−	0.685037i
$615$		0			0
$616$	18.2959	−	5.76228i	0.737163	−	0.232169i
$617$	−7.80877	+	29.1427i	−0.314369	+	1.17324i	0.610206	+	0.792243i	$0.291087\pi$
$617$	−7.80877	+	29.1427i	−0.314369	+	1.17324i	−0.924575	+	0.380999i	$0.875580\pi$
$618$		0			0
$619$	−38.9926	+	10.4480i	−1.56724	+	0.419942i	−0.934948	−	0.354785i	$-0.884554\pi$
$619$	−38.9926	+	10.4480i	−1.56724	+	0.419942i	−0.632296	+	0.774727i	$0.717887\pi$
$620$	63.5505			2.55225
$621$		0			0
$622$	−32.7024	+	8.76259i	−1.31125	+	0.351348i
$623$	3.65674	+	5.74395i	0.146504	+	0.230127i
$624$		0			0
$625$	−15.2925	−	26.4874i	−0.611701	−	1.05950i
$626$	−81.2387	−	21.7678i	−3.24695	−	0.870018i
$627$		0			0
$628$	−0.582914	+	1.00964i	−0.0232608	+	0.0402889i
$629$	−12.2204	+	12.2204i	−0.487260	+	0.487260i
$630$		0			0
$631$	11.8790	+	3.18298i	0.472897	+	0.126712i	0.487393	−	0.873183i	$-0.337948\pi$
$631$	11.8790	+	3.18298i	0.472897	+	0.126712i	−0.0144963	+	0.999895i	$0.504614\pi$
$632$	−4.11762	−	1.10331i	−0.163790	−	0.0438875i
$633$		0			0
$634$	20.8419	−	12.0331i	0.827738	−	0.477895i
$635$	−22.0443	−	22.0443i	−0.874803	−	0.874803i
$636$		0			0
$637$	19.6028	+	15.8975i	0.776690	+	0.629883i
$638$	25.9535			1.02751
$639$		0			0
$640$	−46.6211	+	26.9167i	−1.84286	+	1.06398i
$641$		−	10.9869i		−	0.433956i	−0.976176	−	0.216978i	$-0.930380\pi$
$641$		−	10.9869i		−	0.433956i	0.976176	−	0.216978i	$-0.0696200\pi$
$642$		0			0
$643$	−5.20127	−	1.39368i	−0.205118	−	0.0549612i	0.154797	−	0.987946i	$-0.450528\pi$
$643$	−5.20127	−	1.39368i	−0.205118	−	0.0549612i	−0.359915	+	0.932985i	$0.617194\pi$
$644$	24.0988	+	5.35061i	0.949627	+	0.210844i
$645$		0			0
$646$	64.4960	−	111.710i	2.53756	−	4.39518i
$647$	19.1619	+	33.1894i	0.753333	+	1.30481i	0.946199	+	0.323586i	$0.104888\pi$
$647$	19.1619	+	33.1894i	0.753333	+	1.30481i	−0.192866	+	0.981225i	$0.561778\pi$
$648$		0			0
$649$	−3.77124	−	6.53198i	−0.148034	−	0.256402i
$650$	0.512472	+	29.5093i	0.0201008	+	1.15745i
$651$		0			0
$652$	−54.2315	+	14.5313i	−2.12387	+	0.569089i
$653$	−7.74794			−0.303200			−0.151600	−	0.988442i	$-0.548443\pi$
$653$	−7.74794			−0.303200			−0.151600	+	0.988442i	$0.548443\pi$
$654$		0			0
$655$	−50.6666	+	13.5761i	−1.97971	+	0.530461i
$656$	10.9385	+	40.8229i	0.427075	+	1.59387i
$657$		0			0
$658$	−5.37693	+	1.69346i	−0.209615	+	0.0660180i
$659$	−1.59593	−	2.76423i	−0.0621686	−	0.107679i	0.833266	−	0.552872i	$-0.186468\pi$
$659$	−1.59593	−	2.76423i	−0.0621686	−	0.107679i	−0.895435	+	0.445193i	$0.853135\pi$
$660$		0			0
$661$	1.11096	−	4.14615i	0.0432113	−	0.161267i	−0.940949	−	0.338549i	$-0.890064\pi$
$661$	1.11096	−	4.14615i	0.0432113	−	0.161267i	0.984160	+	0.177282i	$0.0567306\pi$
$662$	−44.2994	−	25.5763i	−1.72174	−	0.994049i
$663$		0			0
$664$		−	15.7603i		−	0.611617i
$665$	11.4333	−	51.4948i	0.443364	−	1.99688i
$666$		0			0
$667$	14.8008	+	8.54522i	0.573087	+	0.330872i
$668$	9.28259	+	34.6431i	0.359154	+	1.34038i
$669$		0			0
$670$	−38.3041	+	10.2635i	−1.47982	+	0.396515i
$671$	−4.14915	−	4.14915i	−0.160176	−	0.160176i
$672$		0			0
$673$	11.6256	+	6.71205i	0.448134	+	0.258731i	0.707042	−	0.707172i	$-0.250029\pi$
$673$	11.6256	+	6.71205i	0.448134	+	0.258731i	−0.258908	+	0.965902i	$0.583362\pi$
$674$	46.9176	−	46.9176i	1.80720	−	1.80720i
$675$		0			0
$676$	−25.0050	+	47.0075i	−0.961731	+	1.80798i
$677$	19.3278	−	11.1589i	0.742830	−	0.428873i	−0.0802677	−	0.996773i	$-0.525578\pi$
$677$	19.3278	−	11.1589i	0.742830	−	0.428873i	0.823097	+	0.567901i	$0.192244\pi$
$678$		0			0
$679$	−21.3608	−	11.1283i	−0.819751	−	0.427067i
$680$	97.6443	−	56.3749i	3.74449	−	2.16188i
$681$		0			0
$682$	13.1626	−	13.1626i	0.504022	−	0.504022i
$683$	5.15641	−	5.15641i	0.197304	−	0.197304i	−0.601539	−	0.798843i	$-0.705446\pi$
$683$	5.15641	−	5.15641i	0.197304	−	0.197304i	0.798843	+	0.601539i	$0.205446\pi$
$684$		0			0
$685$	24.3222	−	14.0424i	0.929305	−	0.536534i
$686$	−5.92518	−	45.3401i	−0.226225	−	1.73109i
$687$		0			0
$688$	−13.9690	+	8.06503i	−0.532565	+	0.307476i
$689$	4.44030	−	4.59725i	0.169162	−	0.175141i
$690$		0			0
$691$	7.98871	−	7.98871i	0.303905	−	0.303905i	−0.538635	−	0.842539i	$-0.681060\pi$
$691$	7.98871	−	7.98871i	0.303905	−	0.303905i	0.842539	+	0.538635i	$0.181060\pi$
$692$	38.4584	+	22.2040i	1.46197	+	0.844069i
$693$		0			0
$694$	10.7694	+	10.7694i	0.408801	+	0.408801i
$695$	−43.7908	+	11.7337i	−1.66108	+	0.445085i
$696$		0			0
$697$	18.0341	+	67.3042i	0.683090	+	2.54933i
$698$	−46.1615	−	26.6514i	−1.74724	−	1.00877i
$699$		0			0
$700$	24.2803	−	26.4804i	0.917708	−	1.00086i
$701$		−	0.777837i		−	0.0293785i	−0.999892	−	0.0146892i	$-0.995324\pi$
$701$		−	0.777837i		−	0.0293785i	0.999892	−	0.0146892i	$-0.00467590\pi$
$702$		0			0
$703$	13.6938	+	7.90610i	0.516470	+	0.298184i
$704$	−2.45782	+	9.17270i	−0.0926325	+	0.345709i
$705$		0			0
$706$	−16.3506	−	28.3200i	−0.615362	−	1.06584i
$707$	14.2688	+	45.3049i	0.536632	+	1.70387i
$708$		0			0
$709$	0.571859	+	2.13421i	0.0214766	+	0.0801518i	0.975832	−	0.218520i	$-0.0701230\pi$
$709$	0.571859	+	2.13421i	0.0214766	+	0.0801518i	−0.954356	+	0.298672i	$0.903456\pi$
$710$	46.5849	−	12.4824i	1.74830	−	0.468456i
$711$		0			0
$712$	13.3165			0.499055
$713$	11.8402	−	3.17256i	0.443417	−	0.118813i
$714$		0			0
$715$	10.4787	+	10.1210i	0.391882	+	0.378504i
$716$	16.7371	+	28.9896i	0.625496	+	1.08339i
$717$		0			0
$718$	−6.09542	−	10.5576i	−0.227479	−	0.394005i
$719$	6.15320	−	10.6577i	0.229476	−	0.397463i	−0.728177	−	0.685389i	$-0.759632\pi$
$719$	6.15320	−	10.6577i	0.229476	−	0.397463i	0.957653	+	0.287926i	$0.0929656\pi$
$720$		0			0
$721$	−4.86772	−	15.4555i	−0.181283	−	0.575594i
$722$	−68.6866	−	18.4045i	−2.55625	−	0.684945i
$723$		0			0
$724$			16.8086i			0.624685i
$725$	21.5406	−	12.4365i	0.799999	−	0.461880i
$726$		0			0
$727$	46.3414			1.71871			0.859353	−	0.511383i	$-0.170867\pi$
$727$	46.3414			1.71871			0.859353	+	0.511383i	$0.170867\pi$
$728$	46.8145	−	15.6428i	1.73506	−	0.579759i
$729$		0			0
$730$	42.2168	+	42.2168i	1.56252	+	1.56252i
$731$	−23.0306	+	13.2967i	−0.851817	+	0.491797i
$732$		0			0
$733$	16.0476	+	4.29994i	0.592731	+	0.158822i	0.542701	−	0.839926i	$-0.317402\pi$
$733$	16.0476	+	4.29994i	0.592731	+	0.158822i	0.0500300	+	0.998748i	$0.484068\pi$
$734$	48.8744	+	13.0959i	1.80399	+	0.483377i
$735$		0			0
$736$	1.55906	−	1.55906i	0.0574678	−	0.0574678i
$737$	−3.90224	+	6.75888i	−0.143741	+	0.248966i
$738$		0			0
$739$	−3.40979	−	0.913649i	−0.125431	−	0.0336091i	0.195557	−	0.980692i	$-0.437348\pi$
$739$	−3.40979	−	0.913649i	−0.125431	−	0.0336091i	−0.320988	+	0.947083i	$0.604015\pi$
$740$	13.5056	+	23.3924i	0.496475	+	0.859920i
$741$		0			0
$742$	−11.5687	+	0.501417i	−0.424699	+	0.0184076i
$743$	−42.9886	+	11.5188i	−1.57710	+	0.422583i	−0.938027	−	0.346563i	$-0.887349\pi$
$743$	−42.9886	+	11.5188i	−1.57710	+	0.422583i	−0.639073	+	0.769146i	$0.720682\pi$
$744$		0			0
$745$	−37.1305			−1.36036
$746$	−55.4301	+	14.8525i	−2.02944	+	0.543787i
$747$		0			0
$748$	11.2241	−	41.8890i	0.410395	−	1.53161i
$749$	−12.2271	−	2.71477i	−0.446770	−	0.0991955i
$750$		0			0
$751$			52.0913i			1.90084i	0.310970	+	0.950420i	$0.399346\pi$
$751$			52.0913i			1.90084i	−0.310970	+	0.950420i	$0.600654\pi$
$752$	−1.02376	+	3.82072i	−0.0373327	+	0.139327i
$753$		0			0
$754$	66.7736	−	1.15962i	2.43175	−	0.0422309i
$755$			10.0721i			0.366562i
$756$		0			0
$757$	23.5702	−	40.8248i	0.856674	−	1.48380i	−0.0184085	−	0.999831i	$-0.505860\pi$
$757$	23.5702	−	40.8248i	0.856674	−	1.48380i	0.875083	−	0.483973i	$-0.160807\pi$
$758$	−45.7081	−	26.3896i	−1.66019	−	0.958512i
$759$		0			0
$760$	−72.9445	−	72.9445i	−2.64598	−	2.64598i
$761$	−29.1992	+	7.82391i	−1.05847	+	0.283616i	−0.745748	−	0.666228i	$-0.767908\pi$
$761$	−29.1992	+	7.82391i	−1.05847	+	0.283616i	−0.312723	+	0.949844i	$0.601241\pi$
$762$		0			0
$763$	−46.5933	+	2.01948i	−1.68679	+	0.0731101i
$764$	−15.6734	−	9.04903i	−0.567043	−	0.327382i
$765$		0			0
$766$	13.1088	−	22.7052i	0.473641	−	0.820371i
$767$	−9.99455	−	16.6371i	−0.360882	−	0.600729i
$768$		0			0
$769$	1.17278	+	4.37689i	0.0422916	+	0.157835i	0.983842	−	0.179037i	$-0.0572980\pi$
$769$	1.17278	+	4.37689i	0.0422916	+	0.157835i	−0.941551	+	0.336871i	$0.890631\pi$
$770$	−1.14290	−	26.3690i	−0.0411874	−	0.950273i
$771$		0			0
$772$	−11.9612	+	44.6398i	−0.430493	+	1.60662i
$773$	1.58168	−	1.58168i	0.0568893	−	0.0568893i	−0.678090	−	0.734979i	$-0.737192\pi$
$773$	1.58168	−	1.58168i	0.0568893	−	0.0568893i	0.734979	+	0.678090i	$0.237192\pi$
$774$		0			0
$775$	4.61726	−	17.2318i	0.165857	−	0.618986i
$776$	−40.7930	+	23.5518i	−1.46438	+	0.845462i
$777$		0			0
$778$	−10.5781	−	39.4778i	−0.379242	−	1.41535i
$779$	55.2104	−	31.8757i	1.97812	−	1.14207i
$780$		0			0
$781$	4.74586	−	8.22006i	0.169820	−	0.294137i
$782$	30.0534	−	30.0534i	1.07471	−	1.07471i
$783$		0			0
$784$	−29.0694	−	13.5778i	−1.03819	−	0.484921i
$785$	0.580407	+	0.580407i	0.0207156	+	0.0207156i
$786$		0			0
$787$	−27.8371	−	27.8371i	−0.992286	−	0.992286i	0.00768427	−	0.999970i	$-0.497554\pi$
$787$	−27.8371	−	27.8371i	−0.992286	−	0.992286i	−0.999970	+	0.00768427i	$0.997554\pi$
$788$	−5.11674	−	19.0959i	−0.182276	−	0.680264i
$789$		0			0
$790$	−2.93281	+	5.07977i	−0.104345	+	0.180730i
$791$	−10.9115	−	34.6453i	−0.387969	−	1.23185i
$792$		0			0
$793$	−10.8604	−	10.4896i	−0.385664	−	0.372497i
$794$	−63.2516	−	36.5184i	−2.24472	−	1.29599i
$795$		0			0
$796$		−	47.1451i		−	1.67101i
$797$	8.77705	+	15.2023i	0.310899	+	0.538493i	0.978557	−	0.205975i	$-0.0660366\pi$
$797$	8.77705	+	15.2023i	0.310899	+	0.538493i	−0.667658	+	0.744468i	$0.732703\pi$
$798$		0			0
$799$	−1.68786	+	6.29917i	−0.0597121	+	0.222849i
$800$	−0.830518	−	3.09953i	−0.0293632	−	0.109585i
$801$		0			0
$802$	−25.0259			−0.883696
$803$	11.7502			0.414654
$804$		0			0
$805$	8.03024	−	15.4140i	0.283029	−	0.543272i
$806$	33.2768	−	34.4531i	1.17213	−	1.21356i
$807$		0			0
$808$	89.7265	+	24.0421i	3.15657	+	0.845800i
$809$	3.76160	+	6.51528i	0.132251	+	0.229065i	0.924544	−	0.381076i	$-0.124446\pi$
$809$	3.76160	+	6.51528i	0.132251	+	0.229065i	−0.792293	+	0.610141i	$0.791113\pi$
$810$		0			0
$811$	39.4597	−	39.4597i	1.38562	−	1.38562i	0.551327	−	0.834289i	$-0.314122\pi$
$811$	39.4597	−	39.4597i	1.38562	−	1.38562i	0.834289	−	0.551327i	$-0.185878\pi$
$812$	−59.9197	−	54.9413i	−2.10277	−	1.92806i
$813$		0			0
$814$	7.64232	+	2.04775i	0.267863	+	0.0717737i
$815$			39.5294i			1.38466i
$816$		0			0
$817$	17.2048	+	17.2048i	0.601921	+	0.601921i
$818$	−7.20013			−0.251747
$819$		0			0
$820$	108.903			3.80307
$821$	−10.3423	−	10.3423i	−0.360948	−	0.360948i	0.503214	−	0.864162i	$-0.332151\pi$
$821$	−10.3423	−	10.3423i	−0.360948	−	0.360948i	−0.864162	+	0.503214i	$0.832151\pi$
$822$		0			0
$823$		−	6.19008i		−	0.215773i	−0.994163	−	0.107886i	$-0.965592\pi$
$823$		−	6.19008i		−	0.215773i	0.994163	−	0.107886i	$-0.0344082\pi$
$824$	−30.6098	−	8.20186i	−1.06634	−	0.285725i
$825$		0			0
$826$	−7.62142	+	34.3264i	−0.265183	+	1.19437i
$827$	17.1035	−	17.1035i	0.594748	−	0.594748i	−0.344162	−	0.938910i	$-0.611837\pi$
$827$	17.1035	−	17.1035i	0.594748	−	0.594748i	0.938910	+	0.344162i	$0.111837\pi$
$828$		0			0
$829$	14.8485	+	25.7183i	0.515710	+	0.893235i	0.999834	+	0.0182358i	$0.00580496\pi$
$829$	14.8485	+	25.7183i	0.515710	+	0.893235i	−0.484124	+	0.874999i	$0.660862\pi$
$830$	−20.9468	−	5.61269i	−0.727075	−	0.194819i
$831$		0			0
$832$	−5.91367	+	23.7095i	−0.205019	+	0.821978i
$833$	−47.9264	−	22.3855i	−1.66055	−	0.775612i
$834$		0			0
$835$	25.2514			0.873862
$836$	−39.6779			−1.37229
$837$		0			0
$838$	−6.62709	−	24.7326i	−0.228929	−	0.854375i
$839$	10.2057	−	38.0883i	0.352341	−	1.31496i	−0.531456	−	0.847086i	$-0.678355\pi$
$839$	10.2057	−	38.0883i	0.352341	−	1.31496i	0.883797	−	0.467870i	$-0.154978\pi$
$840$		0			0
$841$	−13.6412	−	23.6273i	−0.470388	−	0.814735i
$842$			93.3548i			3.21722i
$843$		0			0
$844$	−13.9580	−	8.05868i	−0.480456	−	0.277391i
$845$	27.4121	+	25.5712i	0.943003	+	0.879677i
$846$		0			0
$847$	17.6223	+	16.1581i	0.605508	+	0.555200i
$848$	−4.06247	+	7.03641i	−0.139506	+	0.241631i
$849$		0			0
$850$	−16.0095	−	59.7484i	−0.549123	−	2.04935i
$851$	3.68403	+	3.68403i	0.126287	+	0.126287i
$852$		0			0
$853$	−14.6711	−	14.6711i	−0.502329	−	0.502329i	0.409832	−	0.912161i	$-0.365587\pi$
$853$	−14.6711	−	14.6711i	−0.502329	−	0.502329i	−0.912161	+	0.409832i	$0.865587\pi$
$854$	1.18453	+	27.3294i	0.0405338	+	0.935194i
$855$		0			0
$856$	−17.3203	+	17.3203i	−0.591994	+	0.591994i
$857$	−4.44642	+	7.70143i	−0.151887	+	0.263076i	−0.931921	−	0.362661i	$-0.881868\pi$
$857$	−4.44642	+	7.70143i	−0.151887	+	0.263076i	0.780034	+	0.625737i	$0.215202\pi$
$858$		0			0
$859$	−17.8913	+	10.3296i	−0.610445	+	0.352440i	−0.773139	−	0.634236i	$-0.781315\pi$
$859$	−17.8913	+	10.3296i	−0.610445	+	0.352440i	0.162695	+	0.986676i	$0.447981\pi$
$860$	10.7575	+	40.1477i	0.366829	+	1.36902i
$861$		0			0
$862$	52.3059	−	30.1988i	1.78154	−	1.02858i
$863$	−3.13567	+	11.7025i	−0.106740	+	0.398358i	−0.998537	−	0.0540779i	$-0.982778\pi$
$863$	−3.13567	+	11.7025i	−0.106740	+	0.398358i	0.891797	+	0.452435i	$0.149445\pi$
$864$		0			0
$865$	22.1085	−	22.1085i	0.751711	−	0.751711i
$866$	−11.1961	+	41.7846i	−0.380461	+	1.41990i
$867$		0			0
$868$	−58.2529	+	2.52484i	−1.97723	+	0.0856986i
$869$	0.298781	+	1.11507i	0.0101354	+	0.0378260i
$870$		0			0
$871$	−9.73775	+	17.5637i	−0.329951	+	0.595123i
$872$	−45.6033	+	78.9872i	−1.54432	+	2.67484i
$873$		0			0
$874$	−33.6768	−	19.4433i	−1.13913	−	0.657679i
$875$	6.90205	+	10.8416i	0.233332	+	0.366515i
$876$		0			0
$877$	−3.72011	+	0.996801i	−0.125619	+	0.0336596i	−0.321081	−	0.947052i	$-0.604046\pi$
$877$	−3.72011	+	0.996801i	−0.125619	+	0.0336596i	0.195462	+	0.980711i	$0.437379\pi$
$878$	34.7293	+	34.7293i	1.17206	+	1.17206i
$879$		0			0
$880$	−16.0384	−	9.25980i	−0.540656	−	0.312148i
$881$	11.7705	−	20.3872i	0.396559	−	0.686861i	−0.596739	−	0.802435i	$-0.703537\pi$
$881$	11.7705	−	20.3872i	0.396559	−	0.686861i	0.993299	+	0.115574i	$0.0368707\pi$
$882$		0			0
$883$		−	27.7063i		−	0.932390i	−0.884682	−	0.466195i	$-0.845625\pi$
$883$		−	27.7063i		−	0.932390i	0.884682	−	0.466195i	$-0.154375\pi$
$884$	27.0060	−	108.274i	0.908310	−	3.64166i
$885$		0			0
$886$	9.82698	−	36.6748i	0.330144	−	1.23211i
$887$			27.6847i			0.929561i	0.885426	+	0.464780i	$0.153867\pi$
$887$			27.6847i			0.929561i	−0.885426	+	0.464780i	$0.846133\pi$
$888$		0			0
$889$	21.0825	+	19.3309i	0.707086	+	0.648338i
$890$	4.74237	−	17.6988i	0.158965	−	0.593264i
$891$		0			0
$892$	−36.5011	+	9.78045i	−1.22215	+	0.327474i
$893$	5.96666			0.199667
$894$		0			0
$895$	22.7650	−	6.09987i	0.760950	−	0.203896i
$896$	41.6654	−	26.5252i	1.39194	−	0.886143i
$897$		0			0
$898$	4.33100	+	7.50151i	0.144527	+	0.250329i
$899$	−38.9922	−	10.4479i	−1.30046	−	0.348458i
$900$		0			0
$901$	−6.69775	+	11.6008i	−0.223134	+	0.386480i
$902$	22.5561	−	22.5561i	0.751036	−	0.751036i
$903$		0			0
$904$	−68.6152	−	18.3854i	−2.28211	−	0.611489i
$905$	11.4311	+	3.06295i	0.379982	+	0.101816i
$906$		0			0
$907$	10.5924	−	6.11555i	0.351716	−	0.203063i	−0.313725	−	0.949514i	$-0.601577\pi$
$907$	10.5924	−	6.11555i	0.351716	−	0.203063i	0.665441	+	0.746451i	$0.268244\pi$
$908$	−17.0270	−	17.0270i	−0.565061	−	0.565061i
$909$		0			0
$910$	−4.11867	−	67.7915i	−0.136532	−	2.24727i
$911$	−1.08514			−0.0359525			−0.0179762	−	0.999838i	$-0.505722\pi$
$911$	−1.08514			−0.0359525			−0.0179762	+	0.999838i	$0.505722\pi$
$912$		0			0
$913$	−3.69614	+	2.13397i	−0.122324	+	0.0706240i
$914$		−	75.3006i		−	2.49072i
$915$		0			0
$916$	8.63251	+	2.31307i	0.285226	+	0.0764261i
$917$	45.9036	−	14.4573i	1.51587	−	0.477423i
$918$		0			0
$919$	22.3533	−	38.7171i	0.737368	−	1.27716i	−0.216309	−	0.976325i	$-0.569402\pi$
$919$	22.3533	−	38.7171i	0.737368	−	1.27716i	0.953677	−	0.300833i	$-0.0972648\pi$
$920$	−16.9951	−	29.4363i	−0.560311	−	0.970487i
$921$		0			0
$922$	25.1716	+	43.5985i	0.828983	+	1.43584i
$923$	11.8429	−	21.3607i	0.389815	−	0.703098i
$924$		0			0
$925$	7.32413	−	1.96250i	0.240816	−	0.0645265i
$926$	26.9682			0.886231
$927$		0			0
$928$	−7.01362	+	1.87929i	−0.230233	+	0.0616908i
$929$	−4.75371	−	17.7411i	−0.155964	−	0.582066i	−0.999021	−	0.0442414i	$-0.985913\pi$
$929$	−4.75371	−	17.7411i	−0.155964	−	0.582066i	0.843057	−	0.537825i	$-0.180754\pi$
$930$		0			0
$931$	−8.43434	+	47.6565i	−0.276424	+	1.56188i
$932$	25.0398	+	43.3703i	0.820207	+	1.42064i
$933$		0			0
$934$	21.8154	−	81.4160i	0.713820	−	2.66401i
$935$	−26.4424	−	15.2665i	−0.864758	−	0.499268i
$936$		0			0
$937$		−	36.6713i		−	1.19800i	−0.800749	−	0.598999i	$-0.795565\pi$
$937$		−	36.6713i		−	1.19800i	0.800749	−	0.598999i	$-0.204435\pi$
$938$	34.7033	−	10.9298i	1.13310	−	0.356870i
$939$		0			0
$940$	8.82700	+	5.09627i	0.287905	+	0.166222i
$941$	0.562780	+	2.10032i	0.0183461	+	0.0684686i	0.974492	−	0.224422i	$-0.0720495\pi$
$941$	0.562780	+	2.10032i	0.0183461	+	0.0684686i	−0.956146	+	0.292891i	$0.905383\pi$
$942$		0			0
$943$	20.2899	−	5.43665i	0.660729	−	0.177042i
$944$	17.4459	+	17.4459i	0.567815	+	0.567815i
$945$		0			0
$946$	10.5435	+	6.08730i	0.342799	+	0.197915i
$947$	−23.6813	+	23.6813i	−0.769539	+	0.769539i	−0.978025	−	0.208487i	$-0.933146\pi$
$947$	−23.6813	+	23.6813i	−0.769539	+	0.769539i	0.208487	+	0.978025i	$0.433146\pi$
$948$		0			0
$949$	30.2310	−	0.525004i	0.981339	−	0.0170424i
$950$	−49.0123	+	28.2973i	−1.59017	+	0.918084i
$951$		0			0
$952$	−87.2649	+	55.5549i	−2.82827	+	1.80054i
$953$	23.8594	−	13.7752i	0.772881	−	0.446223i	−0.0610206	−	0.998137i	$-0.519436\pi$
$953$	23.8594	−	13.7752i	0.772881	−	0.446223i	0.833901	+	0.551914i	$0.186102\pi$
$954$		0			0
$955$	−9.01011	+	9.01011i	−0.291560	+	0.291560i
$956$	32.6682	−	32.6682i	1.05657	−	1.05657i
$957$		0			0
$958$	−37.1427	+	21.4444i	−1.20003	+	0.692836i
$959$	−21.7368	+	13.8382i	−0.701919	+	0.446858i
$960$		0			0
$961$	1.77273	−	1.02349i	0.0571850	−	0.0330158i
$962$	19.7538	+	4.92703i	0.636887	+	0.158854i
$963$		0			0
$964$	37.2303	−	37.2303i	1.19911	−	1.19911i
$965$	28.1788	+	16.2690i	0.907107	+	0.523718i
$966$		0			0
$967$	−15.7669	−	15.7669i	−0.507030	−	0.507030i	0.406584	−	0.913613i	$-0.366720\pi$
$967$	−15.7669	−	15.7669i	−0.507030	−	0.507030i	−0.913613	+	0.406584i	$0.866720\pi$
$968$	45.1643	−	12.1018i	1.45164	−	0.388965i
$969$		0			0
$970$	16.7750	+	62.6051i	0.538612	+	2.01013i
$971$	14.2324	+	8.21711i	0.456741	+	0.263700i	0.710673	−	0.703523i	$-0.248391\pi$
$971$	14.2324	+	8.21711i	0.456741	+	0.263700i	−0.253932	+	0.967222i	$0.581724\pi$
$972$		0			0
$973$	39.6742	−	12.4954i	1.27190	−	0.400583i
$974$			31.4848i			1.00884i
$975$		0			0
$976$	16.6226	+	9.59706i	0.532076	+	0.307194i
$977$	−9.72713	+	36.3022i	−0.311199	+	1.16141i	0.616278	+	0.787528i	$0.288640\pi$
$977$	−9.72713	+	36.3022i	−0.311199	+	1.16141i	−0.927477	+	0.373880i	$0.878027\pi$
$978$		0			0
$979$	−1.80307	−	3.12301i	−0.0576263	−	0.0998117i
$980$	−53.1822	+	63.2984i	−1.69884	+	2.02199i
$981$		0			0
$982$	11.8186	+	44.1078i	0.377148	+	1.40754i
$983$	40.2595	−	10.7875i	1.28408	−	0.344068i	0.448671	−	0.893697i	$-0.351898\pi$
$983$	40.2595	−	10.7875i	1.28408	−	0.344068i	0.835409	+	0.549629i	$0.185231\pi$
$984$		0			0
$985$	−13.9191			−0.443498
$986$	−135.199	+	36.2264i	−4.30560	+	1.15368i
$987$		0			0
$988$	−102.084	+	1.77283i	−3.24772	+	0.0564013i
$989$	4.00849	+	6.94292i	0.127463	+	0.220772i
$990$		0			0
$991$	−7.91295	−	13.7056i	−0.251363	−	0.435374i	0.712538	−	0.701633i	$-0.247545\pi$
$991$	−7.91295	−	13.7056i	−0.251363	−	0.435374i	−0.963901	+	0.266260i	$0.914212\pi$
$992$	−2.60393	+	4.51013i	−0.0826747	+	0.143197i
$993$		0			0
$994$	−42.2057	+	13.2927i	−1.33868	+	0.421618i
$995$	−32.0622	−	8.59104i	−1.01644	−	0.272354i
$996$		0			0
$997$		−	11.0129i		−	0.348782i	−0.984676	−	0.174391i	$-0.944204\pi$
$997$		−	11.0129i		−	0.348782i	0.984676	−	0.174391i	$-0.0557957\pi$
$998$	79.7639	−	46.0517i	2.52488	−	1.45774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.514.9		36
3.2	odd	2		273.2.bt.a.241.1	yes	36
7.5	odd	6		819.2.gh.c.397.9		36
13.2	odd	12		819.2.gh.c.262.9		36
21.5	even	6		273.2.cg.a.124.1	yes	36
39.2	even	12		273.2.cg.a.262.1	yes	36
91.54	even	12	inner	819.2.et.c.145.9		36
273.236	odd	12		273.2.bt.a.145.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.1	✓	36	273.236	odd	12
273.2.bt.a.241.1	yes	36	3.2	odd	2
273.2.cg.a.124.1	yes	36	21.5	even	6
273.2.cg.a.262.1	yes	36	39.2	even	12
819.2.et.c.145.9		36	91.54	even	12	inner
819.2.et.c.514.9		36	1.1	even	1	trivial
819.2.gh.c.262.9		36	13.2	odd	12
819.2.gh.c.397.9		36	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74581 + 1.74581i) q^{2} +4.09571i q^{4} +(2.78539 + 0.746344i) q^{5} +(-2.58285 - 0.573466i) q^{7} +(-3.65872 + 3.65872i) q^{8} +O(q^{10})\)	\(q+(1.74581 + 1.74581i) q^{2} +4.09571i q^{4} +(2.78539 + 0.746344i) q^{5} +(-2.58285 - 0.573466i) q^{7} +(-3.65872 + 3.65872i) q^{8} +(3.55979 + 6.16574i) q^{10} +(1.35345 + 0.362655i) q^{11} +(3.49837 + 0.872572i) q^{13} +(-3.50801 - 5.51034i) q^{14} -4.58344 q^{16} -7.55665 q^{17} +(1.78944 + 6.67828i) q^{19} +(-3.05681 + 11.4082i) q^{20} +(1.72974 + 2.99599i) q^{22} +2.27807i q^{23} +(2.87125 + 1.65772i) q^{25} +(4.58415 + 7.63085i) q^{26} +(2.34875 - 10.5786i) q^{28} +(3.75108 - 6.49707i) q^{29} +(-1.39265 - 5.19745i) q^{31} +(-0.684379 - 0.684379i) q^{32} +(-13.1925 - 13.1925i) q^{34} +(-6.76626 - 3.52502i) q^{35} +(1.61717 - 1.61717i) q^{37} +(-8.53499 + 14.7830i) q^{38} +(-12.9216 + 7.46031i) q^{40} +(-2.38652 - 8.90661i) q^{41} +(3.04772 - 1.75960i) q^{43} +(-1.48533 + 5.54333i) q^{44} +(-3.97708 + 3.97708i) q^{46} +(0.223361 - 0.833593i) q^{47} +(6.34227 + 2.96236i) q^{49} +(2.11860 + 7.90673i) q^{50} +(-3.57380 + 14.3283i) q^{52} +(0.886338 - 1.53518i) q^{53} +(3.49922 + 2.02027i) q^{55} +(11.5481 - 7.35179i) q^{56} +(17.8913 - 4.79397i) q^{58} +(-3.80628 - 3.80628i) q^{59} +(-3.62667 - 2.09386i) q^{61} +(6.64246 - 11.5051i) q^{62} +6.77728i q^{64} +(9.09310 + 5.04144i) q^{65} +(-1.44159 + 5.38010i) q^{67} -30.9499i q^{68} +(-5.65859 - 17.9666i) q^{70} +(1.75325 - 6.54321i) q^{71} +(8.10009 - 2.17041i) q^{73} +5.64656 q^{74} +(-27.3523 + 7.32903i) q^{76} +(-3.28779 - 1.71284i) q^{77} +(0.411935 + 0.713493i) q^{79} +(-12.7667 - 3.42082i) q^{80} +(11.3829 - 19.7157i) q^{82} +(-2.15380 + 2.15380i) q^{83} +(-21.0482 - 5.63986i) q^{85} +(8.39268 + 2.24881i) q^{86} +(-6.27874 + 3.62503i) q^{88} +(-1.81982 - 1.81982i) q^{89} +(-8.53540 - 4.25992i) q^{91} -9.33031 q^{92} +(1.84524 - 1.06535i) q^{94} +19.9372i q^{95} +(8.79336 + 2.35617i) q^{97} +(5.90070 + 16.2441i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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