LMFDB - Embedded newform 819.2.et.c.145.9

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			145.9
Character	$\chi$	$=$	819.145
Dual form			819.2.et.c.514.9

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.272248	−	0.962227i	$-0.412233\pi$
$2$	1.74581	−	1.74581i	1.23447	−	1.23447i	0.962227	−	0.272248i	$-0.0877670\pi$
$3$		0			0
$3$		0			0
$4$		−	4.09571i		−	2.04786i
$5$	2.78539	−	0.746344i	1.24567	−	0.333775i	0.425005	−	0.905191i	$-0.360272\pi$
$5$	2.78539	−	0.746344i	1.24567	−	0.333775i	0.820661	+	0.571416i	$0.193606\pi$
$6$		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	−0.0489388	−	0.998802i	$-0.515584\pi$
$11$	1.35345	−	0.362655i	0.408080	−	0.109345i	0.457019	+	0.889457i	$0.348917\pi$
$12$		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	−0.383106	−	0.923704i	$-0.625146\pi$
$19$	1.78944	−	6.67828i	0.410526	−	1.53210i	0.793632	−	0.608399i	$-0.208188\pi$
$20$	−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	$-0.923670\pi$
$23$		−	2.27807i		−	0.475010i	0.971386	−	0.237505i	$-0.0763296\pi$
$24$		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	0.969652	+	0.244487i	$0.0786197\pi$
$29$	3.75108	+	6.49707i	0.696559	+	1.20647i	−0.273094	+	0.961987i	$0.588047\pi$
$30$		0			0
$31$	−1.39265	+	5.19745i	−0.250128	+	0.933490i	0.720608	+	0.693342i	$0.243863\pi$
$31$	−1.39265	+	5.19745i	−0.250128	+	0.933490i	−0.970736	+	0.240148i	$0.922804\pi$
$32$	−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	0.827430	−	0.561569i	$-0.189802\pi$
$37$	1.61717	+	1.61717i	0.265862	+	0.265862i	−0.561569	+	0.827430i	$0.689802\pi$
$38$	−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	0.483948	+	0.875097i	$0.339203\pi$
$41$	−2.38652	+	8.90661i	−0.372712	+	1.39098i	−0.856659	+	0.515882i	$0.827464\pi$
$42$		0			0
$43$	3.04772	+	1.75960i	0.464773	+	0.268337i	0.714049	−	0.700096i	$-0.246859\pi$
$43$	3.04772	+	1.75960i	0.464773	+	0.268337i	−0.249276	+	0.968432i	$0.580193\pi$
$44$	−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	0.980301	−	0.197510i	$-0.0632854\pi$
$47$	0.223361	+	0.833593i	0.0325805	+	0.121592i	−0.947720	+	0.319102i	$0.896619\pi$
$48$		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	0.920457	−	0.390844i	$-0.127817\pi$
$53$	0.886338	+	1.53518i	0.121748	+	0.210873i	−0.798709	+	0.601717i	$0.794483\pi$
$54$		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	−0.910045	−	0.414509i	$-0.863953\pi$
$59$	−3.80628	+	3.80628i	−0.495536	+	0.495536i	0.414509	+	0.910045i	$0.363953\pi$
$60$		0			0
$61$	−3.62667	+	2.09386i	−0.464347	+	0.268091i	−0.713870	−	0.700278i	$-0.753059\pi$
$61$	−3.62667	+	2.09386i	−0.464347	+	0.268091i	0.249523	+	0.968369i	$0.419726\pi$
$62$	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	−0.996358	−	0.0852636i	$-0.972827\pi$
$67$	−1.44159	−	5.38010i	−0.176119	−	0.657283i	0.820240	−	0.572020i	$-0.193840\pi$
$68$			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	0.988491	+	0.151279i	$0.0483391\pi$
$71$	1.75325	+	6.54321i	0.208072	+	0.776536i	−0.780419	+	0.625257i	$0.784994\pi$
$72$		0			0
$73$	8.10009	+	2.17041i	0.948043	+	0.254027i	0.699532	−	0.714601i	$-0.253392\pi$
$73$	8.10009	+	2.17041i	0.948043	+	0.254027i	0.248512	+	0.968629i	$0.420059\pi$
$74$	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	−0.841922	−	0.539600i	$-0.818576\pi$
$79$	0.411935	−	0.713493i	0.0463463	−	0.0802742i	0.888268	+	0.459326i	$0.151909\pi$
$80$	−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	0.578952	−	0.815362i	$-0.303462\pi$
$83$	−2.15380	−	2.15380i	−0.236410	−	0.236410i	−0.815362	+	0.578952i	$0.803462\pi$
$84$		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	−0.796948	−	0.604047i	$-0.793554\pi$
$89$	−1.81982	+	1.81982i	−0.192901	+	0.192901i	0.604047	+	0.796948i	$0.293554\pi$
$90$		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	0.216896	−	0.976195i	$-0.430407\pi$
$97$	8.79336	−	2.35617i	0.892830	−	0.239233i	0.675934	+	0.736962i	$0.263740\pi$
$98$	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	−0.0571540	+	0.998365i	$0.518203\pi$
$101$	−8.97642	+	15.5476i	−0.893187	+	1.54704i	−0.836033	+	0.548679i	$0.815131\pi$
$102$		0			0
$103$	3.06226	−	5.30399i	0.301734	−	0.522618i	−0.674795	−	0.738005i	$-0.735768\pi$
$103$	3.06226	−	5.30399i	0.301734	−	0.522618i	0.976529	+	0.215387i	$0.0691014\pi$
$104$	−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	0.954162	−	0.299291i	$-0.0967502\pi$
$109$	17.0265	+	4.56224i	1.63084	+	0.436983i	0.676683	+	0.736275i	$0.263417\pi$
$110$	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	−0.338380	−	0.941010i	$-0.609879\pi$
$113$	6.86440	−	11.8895i	0.645748	−	1.11847i	0.984128	−	0.177459i	$-0.0567879\pi$
$114$		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	−0.854128	−	0.520063i	$-0.825908\pi$
$127$	−9.36268	+	5.40554i	−0.830803	+	0.479665i	0.0233243	+	0.999728i	$0.492575\pi$
$128$	−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	−0.384635	−	0.923069i	$-0.625673\pi$
$131$	−15.7531	−	9.09505i	−1.37635	−	0.794638i	−0.991719	+	0.128431i	$0.959006\pi$
$132$		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	0.937191	−	0.348815i	$-0.113416\pi$
$137$	6.88676	+	6.88676i	0.588376	+	0.588376i	−0.348815	+	0.937191i	$0.613416\pi$
$138$		0			0
$139$	−13.6153	−	7.86079i	−1.15483	−	0.666744i	−0.204773	−	0.978809i	$-0.565646\pi$
$139$	−13.6153	−	7.86079i	−1.15483	−	0.666744i	−0.950060	+	0.312066i	$0.898979\pi$
$140$	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	−0.289567	−	0.957158i	$-0.593511\pi$
$149$	−12.4375	−	3.33261i	−1.01892	−	0.273018i	−0.729351	+	0.684140i	$0.760178\pi$
$150$		0			0
$151$	0.904012	−	3.37382i	0.0735674	−	0.274557i	−0.919337	−	0.393471i	$-0.871274\pi$
$151$	0.904012	−	3.37382i	0.0735674	−	0.274557i	0.992905	+	0.118913i	$0.0379410\pi$
$152$	−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	−0.490131	−	0.871649i	$-0.663051\pi$
$157$	0.246511	−	0.142323i	0.0196737	−	0.0113586i	0.509805	+	0.860290i	$0.329718\pi$
$158$	−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	−0.675982	−	0.736918i	$-0.736280\pi$
$163$	3.54792	−	13.2410i	0.277895	−	1.03712i	0.953877	−	0.300199i	$-0.0970531\pi$
$164$	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	0.570776	−	0.821106i	$-0.306642\pi$
$167$	8.45838	+	2.26642i	0.654529	+	0.175381i	0.0837535	+	0.996487i	$0.473309\pi$
$168$		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	0.995127	−	0.0986015i	$-0.0314369\pi$
$173$	5.42128	+	9.38993i	0.412172	+	0.713903i	−0.582955	+	0.812504i	$0.698104\pi$
$174$		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	0.740624	−	0.671920i	$-0.234530\pi$
$179$	7.07802	+	4.08650i	0.529036	+	0.305439i	−0.211588	+	0.977359i	$0.567863\pi$
$180$		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	0.774954	−	0.632017i	$-0.217773\pi$
$191$	−2.20939	−	3.82678i	−0.159866	−	0.276896i	−0.934820	+	0.355121i	$0.884440\pi$
$192$		0			0
$193$	10.8992	−	2.92042i	0.784538	−	0.210216i	0.155754	−	0.987796i	$-0.450219\pi$
$193$	10.8992	−	2.92042i	0.784538	−	0.210216i	0.628785	+	0.777580i	$0.283553\pi$
$194$	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	0.0888723	−	0.996043i	$-0.471674\pi$
$197$	−4.66242	−	1.24929i	−0.332183	−	0.0890083i	−0.421056	+	0.907035i	$0.638340\pi$
$198$		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	0.790317	−	0.612699i	$-0.209916\pi$
$211$	−1.96759	−	3.40797i	−0.135454	−	0.234614i	−0.925771	+	0.378085i	$0.876583\pi$
$212$	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	−0.838724	−	0.544556i	$-0.816698\pi$
$223$	2.38797	−	8.91203i	0.159910	−	0.596794i	0.998635	−	0.0522375i	$-0.0166353\pi$
$224$	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	0.555553	−	0.831481i	$-0.312507\pi$
$227$	−4.15727	−	4.15727i	−0.275928	−	0.275928i	−0.831481	+	0.555553i	$0.812507\pi$
$228$		0			0
$229$	0.564755	+	2.10769i	0.0373201	+	0.139280i	0.982072	−	0.188505i	$-0.0603643\pi$
$229$	0.564755	+	2.10769i	0.0373201	+	0.139280i	−0.944752	+	0.327786i	$0.893698\pi$
$230$	−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	0.805004	−	0.593269i	$-0.202163\pi$
$233$	10.5892	+	6.11367i	0.693720	+	0.400520i	−0.111284	+	0.993789i	$0.535496\pi$
$234$		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	−0.916340	−	0.400402i	$-0.868870\pi$
$239$	−7.97620	+	7.97620i	−0.515938	+	0.515938i	0.400402	+	0.916340i	$0.368870\pi$
$240$		0			0
$241$	−9.09005	+	9.09005i	−0.585542	+	0.585542i	−0.936421	−	0.350879i	$-0.885883\pi$
$241$	−9.09005	+	9.09005i	−0.585542	+	0.585542i	0.350879	+	0.936421i	$0.385883\pi$
$242$	−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	0.0726757	+	0.997356i	$0.476846\pi$
$251$	−13.1084	+	22.7045i	−0.827397	+	1.43309i	−0.900073	+	0.435739i	$0.856487\pi$
$252$		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	−0.536255	−	0.844056i	$-0.680162\pi$
$263$	7.50610	−	13.0010i	0.462846	−	0.801673i	0.999101	+	0.0423827i	$0.0134949\pi$
$264$		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	$-0.763784\pi$
$269$		−	22.1690i		−	1.35167i	0.737054	−	0.675834i	$-0.236216\pi$
$270$		0			0
$271$	−14.9017	+	14.9017i	−0.905214	+	0.905214i	−0.995881	−	0.0906673i	$-0.971100\pi$
$271$	−14.9017	+	14.9017i	−0.905214	+	0.905214i	0.0906673	+	0.995881i	$0.471100\pi$
$272$	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	$0.0958061\pi$
$277$			9.86815i			0.592920i	−0.955045	+	0.296460i	$0.904194\pi$
$278$	−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	−0.942768	−	0.333449i	$-0.891788\pi$
$281$	−21.3933	−	21.3933i	−1.27622	−	1.27622i	−0.333449	−	0.942768i	$-0.608212\pi$
$282$		0			0
$283$	10.7440	−	18.6092i	0.638666	−	1.10620i	−0.347060	−	0.937843i	$-0.612820\pi$
$283$	10.7440	−	18.6092i	0.638666	−	1.10620i	0.985726	−	0.168359i	$-0.0538466\pi$
$284$	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	0.973102	−	0.230375i	$-0.0739952\pi$
$293$	0.259901	+	0.969962i	0.0151836	+	0.0566658i	−0.957918	+	0.287041i	$0.907329\pi$
$294$		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	−0.832095	−	0.554634i	$-0.812858\pi$
$307$	−4.86151	+	4.86151i	−0.277461	+	0.277461i	0.554634	+	0.832095i	$0.312858\pi$
$308$	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	0.603498	−	0.797364i	$-0.293773\pi$
$311$	−6.85636	−	11.8756i	−0.388789	−	0.673402i	−0.992287	+	0.123963i	$0.960440\pi$
$312$		0			0
$313$	−29.5010	−	17.0324i	−1.66750	−	0.962730i	−0.968981	−	0.247137i	$-0.920510\pi$
$313$	−29.5010	−	17.0324i	−1.66750	−	0.962730i	−0.698517	−	0.715593i	$-0.746156\pi$
$314$	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	0.999880	+	0.0154772i	$0.00492673\pi$
$317$	2.52285	+	9.41539i	0.141697	+	0.528821i	−0.858183	+	0.513344i	$0.828407\pi$
$318$		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	−0.337223	−	0.941425i	$-0.609488\pi$
$331$	−20.0124	−	5.36230i	−1.09998	−	0.294739i	−0.762756	+	0.646686i	$0.776154\pi$
$332$	−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	$0.261399\pi$
$337$			26.8744i			1.46394i	−0.681336	+	0.731971i	$0.738601\pi$
$338$	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	−0.346896	−	0.937904i	$-0.612764\pi$
$349$	−20.8536	−	5.58771i	−1.11627	−	0.299103i	−0.769372	+	0.638801i	$0.779431\pi$
$350$	−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	−0.582677	−	0.812704i	$-0.697995\pi$
$353$	−12.7937	+	3.42805i	−0.680938	+	0.182457i	−0.0982609	+	0.995161i	$0.531328\pi$
$354$		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	−0.382473	−	0.923967i	$-0.624927\pi$
$359$	−4.76941	+	1.27796i	−0.251720	+	0.0674482i	0.130753	+	0.991415i	$0.458261\pi$
$360$		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	0.885688	−	0.464281i	$-0.153687\pi$
$367$	17.7483	+	10.2470i	0.926453	+	0.534888i	0.0407648	+	0.999169i	$0.487021\pi$
$368$			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	−0.992558	−	0.121770i	$-0.961143\pi$
$373$	−11.6214	−	20.1289i	−0.601735	−	1.04224i	0.390823	−	0.920466i	$-0.372190\pi$
$374$	−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	−0.314007	−	0.949421i	$-0.601671\pi$
$379$	−20.6487	−	5.53282i	−1.06066	−	0.284202i	−0.746648	+	0.665219i	$0.768338\pi$
$380$	−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	0.859480	+	0.511169i	$0.170787\pi$
$383$	−2.74839	+	10.2571i	−0.140436	+	0.524114i	−0.999916	+	0.0129453i	$0.995879\pi$
$384$		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	−0.817274	−	0.576250i	$-0.804516\pi$
$389$	−14.3360	+	8.27689i	−0.726864	+	0.419655i	0.0904098	+	0.995905i	$0.471182\pi$
$390$		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	−0.543632	−	0.839323i	$-0.682951\pi$
$397$	−28.5741	−	7.65641i	−1.43409	−	0.384264i	−0.890461	+	0.455059i	$0.849618\pi$
$398$	−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	0.505123	−	0.863047i	$-0.331447\pi$
$401$	−7.16742	−	7.16742i	−0.357924	−	0.357924i	−0.863047	+	0.505123i	$0.831447\pi$
$402$		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	0.654284	−	0.756249i	$-0.272970\pi$
$409$	−2.06212	−	2.06212i	−0.101965	−	0.101965i	−0.756249	+	0.654284i	$0.772970\pi$
$410$	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	−0.703076	−	0.711115i	$-0.748191\pi$
$419$	−8.98142	+	5.18542i	−0.438771	+	0.253325i	0.264305	+	0.964439i	$0.414857\pi$
$420$		0			0
$421$	26.7368	−	26.7368i	1.30307	−	1.30307i	0.376762	−	0.926310i	$-0.377038\pi$
$421$	26.7368	−	26.7368i	1.30307	−	1.30307i	0.926310	−	0.376762i	$-0.122962\pi$
$422$	−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	0.932966	+	0.359964i	$0.117211\pi$
$431$	6.33146	+	23.6293i	0.304976	+	1.13818i	−0.627991	+	0.778221i	$0.716122\pi$
$432$		0			0
$433$	8.76052	−	15.1737i	0.421004	−	0.729200i	−0.575034	−	0.818129i	$-0.695011\pi$
$433$	8.76052	−	15.1737i	0.421004	−	0.729200i	0.996038	+	0.0889293i	$0.0283445\pi$
$434$	−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	−0.988828	−	0.149059i	$-0.952376\pi$
$443$	−7.68921	+	13.3181i	−0.365325	+	0.632762i	0.623503	+	0.781821i	$0.285709\pi$
$444$		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	−0.177966	−	0.984037i	$-0.556952\pi$
$449$	3.38883	−	0.908034i	0.159929	−	0.0428528i	0.337895	+	0.941184i	$0.390285\pi$
$450$		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	−0.00885742	+	0.999961i	$0.502819\pi$
$457$	−21.5661	+	21.5661i	−1.00882	+	1.00882i	−0.999961	+	0.00885742i	$0.997181\pi$
$458$	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	0.230882	−	0.972982i	$-0.425839\pi$
$461$	19.6958	−	5.27746i	0.917323	−	0.245796i	0.686441	+	0.727186i	$0.259172\pi$
$462$		0			0
$463$	7.72370	+	7.72370i	0.358951	+	0.358951i	0.863426	−	0.504475i	$-0.168314\pi$
$463$	7.72370	+	7.72370i	0.358951	+	0.358951i	−0.504475	+	0.863426i	$0.668314\pi$
$464$	−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	0.136147	+	0.990689i	$0.456528\pi$
$467$	−17.0696	+	29.5655i	−0.789888	+	1.36813i	−0.926035	+	0.377438i	$0.876805\pi$
$468$		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	−0.989319	−	0.145769i	$-0.953434\pi$
$479$	−4.49601	−	16.7793i	−0.205428	−	0.766668i	0.783891	−	0.620899i	$-0.213232\pi$
$480$		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	−0.472644	−	0.881254i	$-0.656700\pi$
$487$	9.01723	−	9.01723i	0.408610	−	0.408610i	0.881254	+	0.472644i	$0.156700\pi$
$488$	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	−0.0929498	−	0.995671i	$-0.529630\pi$
$491$	16.0173	−	9.24760i	0.722851	−	0.417339i	0.815801	+	0.578332i	$0.196296\pi$
$492$		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	0.747622	+	0.664124i	$0.231195\pi$
$499$	9.65516	+	36.0336i	0.432224	+	1.61308i	−0.315398	+	0.948960i	$0.602138\pi$
$500$	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	0.191900	−	0.981415i	$-0.438535\pi$
$503$	−12.6061	−	7.27816i	−0.562080	−	0.324517i	−0.753980	+	0.656897i	$0.771868\pi$
$504$		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	0.698601	−	0.715512i	$-0.253806\pi$
$509$	−0.381529	−	0.381529i	−0.0169110	−	0.0169110i	−0.715512	+	0.698601i	$0.753806\pi$
$510$		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	0.340499	−	0.940245i	$-0.389404\pi$
$521$	30.2442	−	17.4615i	1.32502	−	0.765003i	0.984525	+	0.175242i	$0.0560707\pi$
$522$		0			0
$523$		−	21.0562i		−	0.920725i	−0.887731	−	0.460362i	$-0.847719\pi$
$523$		−	21.0562i		−	0.920725i	0.887731	−	0.460362i	$-0.152281\pi$
$524$	−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	−0.853627	−	0.520884i	$-0.825602\pi$
$541$	−30.9919	+	8.30427i	−1.33245	+	0.357028i	−0.478821	+	0.877913i	$0.658936\pi$
$542$			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	0.451354	−	0.892345i	$-0.350941\pi$
$557$	30.4076	−	8.14769i	1.28841	−	0.345229i	0.837057	+	0.547116i	$0.184274\pi$
$558$		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	$0.206040\pi$
$569$			28.7690i			1.20606i	−0.797718	+	0.603030i	$0.793960\pi$
$570$		0			0
$571$	38.1385	−	22.0193i	1.59605	−	0.921478i	0.603808	−	0.797130i	$-0.293649\pi$
$571$	38.1385	−	22.0193i	1.59605	−	0.921478i	0.992239	−	0.124348i	$-0.0396839\pi$
$572$	−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	−0.758950	−	0.651149i	$-0.774287\pi$
$577$	5.37814	−	20.0715i	0.223895	−	0.835587i	0.982844	−	0.184437i	$-0.0590462\pi$
$578$	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	−0.215049	−	0.976603i	$-0.568991\pi$
$587$	11.1326	−	41.5473i	0.459491	−	1.71484i	0.674540	−	0.738239i	$-0.264342\pi$
$588$		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	0.974737	−	0.223354i	$-0.0717006\pi$
$593$	0.460561	+	1.71884i	0.0189130	+	0.0705842i	−0.955824	+	0.293938i	$0.905034\pi$
$594$		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	0.639052	−	0.769164i	$-0.279327\pi$
$599$	−8.48260	−	14.6923i	−0.346590	−	0.600311i	−0.985641	+	0.168853i	$0.945994\pi$
$600$		0			0
$601$	30.5871	−	17.6595i	1.24767	−	0.720345i	0.277029	−	0.960862i	$-0.410650\pi$
$601$	30.5871	−	17.6595i	1.24767	−	0.720345i	0.970645	+	0.240517i	$0.0773170\pi$
$602$	−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	−0.812164	−	0.583430i	$-0.801710\pi$
$607$	−17.5660	+	10.1417i	−0.712980	+	0.411639i	0.0991833	+	0.995069i	$0.468377\pi$
$608$	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	−0.965498	−	0.260410i	$-0.916142\pi$
$613$	−6.42633	−	23.9834i	−0.259557	−	0.968680i	0.705941	−	0.708270i	$-0.250524\pi$
$614$			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	−0.924575	−	0.380999i	$-0.875580\pi$
$617$	−7.80877	−	29.1427i	−0.314369	−	1.17324i	0.610206	−	0.792243i	$-0.291087\pi$
$618$		0			0
$619$	−38.9926	−	10.4480i	−1.56724	−	0.419942i	−0.632296	−	0.774727i	$-0.717887\pi$
$619$	−38.9926	−	10.4480i	−1.56724	−	0.419942i	−0.934948	+	0.354785i	$0.884554\pi$
$620$	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	−0.0144963	−	0.999895i	$-0.504614\pi$
$631$	11.8790	−	3.18298i	0.472897	−	0.126712i	0.487393	+	0.873183i	$0.337948\pi$
$632$	−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	$0.0696200\pi$
$641$			10.9869i			0.433956i	−0.976176	+	0.216978i	$0.930380\pi$
$642$		0			0
$643$	−5.20127	+	1.39368i	−0.205118	+	0.0549612i	−0.359915	−	0.932985i	$-0.617194\pi$
$643$	−5.20127	+	1.39368i	−0.205118	+	0.0549612i	0.154797	+	0.987946i	$0.450528\pi$
$644$	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	−0.192866	−	0.981225i	$-0.561778\pi$
$647$	19.1619	−	33.1894i	0.753333	−	1.30481i	0.946199	−	0.323586i	$-0.104888\pi$
$648$		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	−0.895435	−	0.445193i	$-0.853135\pi$
$659$	−1.59593	+	2.76423i	−0.0621686	+	0.107679i	0.833266	+	0.552872i	$0.186468\pi$
$660$		0			0
$661$	1.11096	+	4.14615i	0.0432113	+	0.161267i	0.984160	−	0.177282i	$-0.0567306\pi$
$661$	1.11096	+	4.14615i	0.0432113	+	0.161267i	−0.940949	+	0.338549i	$0.890064\pi$
$662$	−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	−0.258908	−	0.965902i	$-0.583362\pi$
$673$	11.6256	−	6.71205i	0.448134	−	0.258731i	0.707042	+	0.707172i	$0.250029\pi$
$674$	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	0.823097	−	0.567901i	$-0.192244\pi$
$677$	19.3278	+	11.1589i	0.742830	+	0.428873i	−0.0802677	+	0.996773i	$0.525578\pi$
$678$		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	0.798843	−	0.601539i	$-0.205446\pi$
$683$	5.15641	+	5.15641i	0.197304	+	0.197304i	−0.601539	+	0.798843i	$0.705446\pi$
$684$		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	0.842539	−	0.538635i	$-0.181060\pi$
$691$	7.98871	+	7.98871i	0.303905	+	0.303905i	−0.538635	+	0.842539i	$0.681060\pi$
$692$	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	$0.00467590\pi$
$701$			0.777837i			0.0293785i	−0.999892	+	0.0146892i	$0.995324\pi$
$702$		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	−0.954356	−	0.298672i	$-0.903456\pi$
$709$	0.571859	−	2.13421i	0.0214766	−	0.0801518i	0.975832	+	0.218520i	$0.0701230\pi$
$710$	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	0.957653	−	0.287926i	$-0.0929656\pi$
$719$	6.15320	+	10.6577i	0.229476	+	0.397463i	−0.728177	+	0.685389i	$0.759632\pi$
$720$		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	0.0500300	−	0.998748i	$-0.484068\pi$
$733$	16.0476	−	4.29994i	0.592731	−	0.158822i	0.542701	+	0.839926i	$0.317402\pi$
$734$	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	−0.320988	−	0.947083i	$-0.604015\pi$
$739$	−3.40979	+	0.913649i	−0.125431	+	0.0336091i	0.195557	+	0.980692i	$0.437348\pi$
$740$	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	−0.639073	−	0.769146i	$-0.720682\pi$
$743$	−42.9886	−	11.5188i	−1.57710	−	0.422583i	−0.938027	+	0.346563i	$0.887349\pi$
$744$		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	$-0.600654\pi$
$751$		−	52.0913i		−	1.90084i	0.310970	−	0.950420i	$-0.399346\pi$
$752$	−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	0.875083	+	0.483973i	$0.160807\pi$
$757$	23.5702	+	40.8248i	0.856674	+	1.48380i	−0.0184085	+	0.999831i	$0.505860\pi$
$758$	−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	−0.312723	−	0.949844i	$-0.601241\pi$
$761$	−29.1992	−	7.82391i	−1.05847	−	0.283616i	−0.745748	+	0.666228i	$0.767908\pi$
$762$		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	−0.941551	−	0.336871i	$-0.890631\pi$
$769$	1.17278	−	4.37689i	0.0422916	−	0.157835i	0.983842	+	0.179037i	$0.0572980\pi$
$770$	−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	0.734979	−	0.678090i	$-0.237192\pi$
$773$	1.58168	+	1.58168i	0.0568893	+	0.0568893i	−0.678090	+	0.734979i	$0.737192\pi$
$774$		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	−0.999970	−	0.00768427i	$-0.997554\pi$
$787$	−27.8371	+	27.8371i	−0.992286	+	0.992286i	0.00768427	+	0.999970i	$0.497554\pi$
$788$	−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	−0.667658	−	0.744468i	$-0.732703\pi$
$797$	8.77705	−	15.2023i	0.310899	−	0.538493i	0.978557	+	0.205975i	$0.0660366\pi$
$798$		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	−0.792293	−	0.610141i	$-0.791113\pi$
$809$	3.76160	−	6.51528i	0.132251	−	0.229065i	0.924544	+	0.381076i	$0.124446\pi$
$810$		0			0
$811$	39.4597	+	39.4597i	1.38562	+	1.38562i	0.834289	+	0.551327i	$0.185878\pi$
$811$	39.4597	+	39.4597i	1.38562	+	1.38562i	0.551327	+	0.834289i	$0.314122\pi$
$812$	−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	−0.864162	−	0.503214i	$-0.832151\pi$
$821$	−10.3423	+	10.3423i	−0.360948	+	0.360948i	0.503214	+	0.864162i	$0.332151\pi$
$822$		0			0
$823$			6.19008i			0.215773i	0.994163	+	0.107886i	$0.0344082\pi$
$823$			6.19008i			0.215773i	−0.994163	+	0.107886i	$0.965592\pi$
$824$	−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	0.938910	−	0.344162i	$-0.111837\pi$
$827$	17.1035	+	17.1035i	0.594748	+	0.594748i	−0.344162	+	0.938910i	$0.611837\pi$
$828$		0			0
$829$	14.8485	−	25.7183i	0.515710	−	0.893235i	−0.484124	−	0.874999i	$-0.660862\pi$
$829$	14.8485	−	25.7183i	0.515710	−	0.893235i	0.999834	−	0.0182358i	$-0.00580496\pi$
$830$	−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	0.883797	+	0.467870i	$0.154978\pi$
$839$	10.2057	+	38.0883i	0.352341	+	1.31496i	−0.531456	+	0.847086i	$0.678355\pi$
$840$		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	−0.912161	−	0.409832i	$-0.865587\pi$
$853$	−14.6711	+	14.6711i	−0.502329	+	0.502329i	0.409832	+	0.912161i	$0.365587\pi$
$854$	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	0.780034	−	0.625737i	$-0.215202\pi$
$857$	−4.44642	−	7.70143i	−0.151887	−	0.263076i	−0.931921	+	0.362661i	$0.881868\pi$
$858$		0			0
$859$	−17.8913	−	10.3296i	−0.610445	−	0.352440i	0.162695	−	0.986676i	$-0.447981\pi$
$859$	−17.8913	−	10.3296i	−0.610445	−	0.352440i	−0.773139	+	0.634236i	$0.781315\pi$
$860$	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	0.891797	−	0.452435i	$-0.149445\pi$
$863$	−3.13567	−	11.7025i	−0.106740	−	0.398358i	−0.998537	+	0.0540779i	$0.982778\pi$
$864$		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	0.195462	−	0.980711i	$-0.437379\pi$
$877$	−3.72011	−	0.996801i	−0.125619	−	0.0336596i	−0.321081	+	0.947052i	$0.604046\pi$
$878$	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	0.993299	−	0.115574i	$-0.0368707\pi$
$881$	11.7705	+	20.3872i	0.396559	+	0.686861i	−0.596739	+	0.802435i	$0.703537\pi$
$882$		0			0
$883$			27.7063i			0.932390i	0.884682	+	0.466195i	$0.154375\pi$
$883$			27.7063i			0.932390i	−0.884682	+	0.466195i	$0.845625\pi$
$884$	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	$-0.846133\pi$
$887$		−	27.6847i		−	0.929561i	0.885426	−	0.464780i	$-0.153867\pi$
$888$		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	0.665441	−	0.746451i	$-0.268244\pi$
$907$	10.5924	+	6.11555i	0.351716	+	0.203063i	−0.313725	+	0.949514i	$0.601577\pi$
$908$	−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	0.953677	+	0.300833i	$0.0972648\pi$
$919$	22.3533	+	38.7171i	0.737368	+	1.27716i	−0.216309	+	0.976325i	$0.569402\pi$
$920$	−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	0.843057	+	0.537825i	$0.180754\pi$
$929$	−4.75371	+	17.7411i	−0.155964	+	0.582066i	−0.999021	+	0.0442414i	$0.985913\pi$
$930$		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	$0.204435\pi$
$937$			36.6713i			1.19800i	−0.800749	+	0.598999i	$0.795565\pi$
$938$	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	−0.956146	−	0.292891i	$-0.905383\pi$
$941$	0.562780	−	2.10032i	0.0183461	−	0.0684686i	0.974492	+	0.224422i	$0.0720495\pi$
$942$		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	0.208487	−	0.978025i	$-0.433146\pi$
$947$	−23.6813	−	23.6813i	−0.769539	−	0.769539i	−0.978025	+	0.208487i	$0.933146\pi$
$948$		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	0.833901	−	0.551914i	$-0.186102\pi$
$953$	23.8594	+	13.7752i	0.772881	+	0.446223i	−0.0610206	+	0.998137i	$0.519436\pi$
$954$		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	−0.913613	−	0.406584i	$-0.866720\pi$
$967$	−15.7669	+	15.7669i	−0.507030	+	0.507030i	0.406584	+	0.913613i	$0.366720\pi$
$968$	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	−0.253932	−	0.967222i	$-0.581724\pi$
$971$	14.2324	−	8.21711i	0.456741	−	0.263700i	0.710673	+	0.703523i	$0.248391\pi$
$972$		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	−0.927477	−	0.373880i	$-0.878027\pi$
$977$	−9.72713	−	36.3022i	−0.311199	−	1.16141i	0.616278	−	0.787528i	$-0.288640\pi$
$978$		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	0.835409	−	0.549629i	$-0.185231\pi$
$983$	40.2595	+	10.7875i	1.28408	+	0.344068i	0.448671	+	0.893697i	$0.351898\pi$
$984$		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	−0.963901	−	0.266260i	$-0.914212\pi$
$991$	−7.91295	+	13.7056i	−0.251363	+	0.435374i	0.712538	+	0.701633i	$0.247545\pi$
$992$	−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	$0.0557957\pi$
$997$			11.0129i			0.348782i	−0.984676	+	0.174391i	$0.944204\pi$
$998$	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.145.9		36
3.2	odd	2		273.2.bt.a.145.1	✓	36
7.3	odd	6		819.2.gh.c.262.9		36
13.7	odd	12		819.2.gh.c.397.9		36
21.17	even	6		273.2.cg.a.262.1	yes	36
39.20	even	12		273.2.cg.a.124.1	yes	36
91.59	even	12	inner	819.2.et.c.514.9		36
273.59	odd	12		273.2.bt.a.241.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.1	✓	36	3.2	odd	2
273.2.bt.a.241.1	yes	36	273.59	odd	12
273.2.cg.a.124.1	yes	36	39.20	even	12
273.2.cg.a.262.1	yes	36	21.17	even	6
819.2.et.c.145.9		36	1.1	even	1	trivial
819.2.et.c.514.9		36	91.59	even	12	inner
819.2.gh.c.262.9		36	7.3	odd	6
819.2.gh.c.397.9		36	13.7	odd	12

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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