LMFDB - Embedded newform 351.2.r.b.316.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(10,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Character	$\chi$	$=$	351.316
Dual form			351.2.r.b.10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.29626 + 1.32574i) q^{2} +(2.51519 - 4.35644i) q^{4} +(2.43120 - 1.40366i) q^{5} -0.261179i q^{7} +8.03502i q^{8} +(-3.72178 + 6.44631i) q^{10} +(1.34990 - 0.779366i) q^{11} +(-1.29932 - 3.36330i) q^{13} +(0.346256 + 0.599733i) q^{14} +(-5.62200 - 9.73759i) q^{16} +(-3.65449 - 6.32976i) q^{17} +(0.447398 - 0.258305i) q^{19} -14.1219i q^{20} +(-2.06648 + 3.57925i) q^{22} -2.74949 q^{23} +(1.44050 - 2.49502i) q^{25} +(7.44243 + 6.00043i) q^{26} +(-1.13781 - 0.656914i) q^{28} +(1.78313 + 3.08847i) q^{29} +(3.17297 - 1.83191i) q^{31} +(11.9020 + 6.87163i) q^{32} +(16.7833 + 9.68983i) q^{34} +(-0.366605 - 0.634978i) q^{35} +(1.90801 + 1.10159i) q^{37} +(-0.684893 + 1.18627i) q^{38} +(11.2784 + 19.5348i) q^{40} -7.42443i q^{41} -3.49719 q^{43} -7.84102i q^{44} +(6.31353 - 3.64512i) q^{46} +(7.10819 + 4.10392i) q^{47} +6.93179 q^{49} +7.63895i q^{50} +(-17.9200 - 2.79895i) q^{52} -4.68042 q^{53} +(2.18792 - 3.78960i) q^{55} +2.09858 q^{56} +(-8.18905 - 4.72795i) q^{58} +(9.64903 + 5.57087i) q^{59} -3.61462 q^{61} +(-4.85729 + 8.41308i) q^{62} -13.9521 q^{64} +(-7.87982 - 6.35307i) q^{65} -8.21327i q^{67} -36.7670 q^{68} +(1.68364 + 0.972048i) q^{70} +(5.40445 - 3.12026i) q^{71} -3.76021i q^{73} -5.84171 q^{74} -2.59875i q^{76} +(-0.203554 - 0.352565i) q^{77} +(-1.36567 + 2.36542i) q^{79} +(-27.3365 - 15.7827i) q^{80} +(9.84289 + 17.0484i) q^{82} +(7.18029 + 4.14554i) q^{83} +(-17.7696 - 10.2593i) q^{85} +(8.03044 - 4.63638i) q^{86} +(6.26222 + 10.8465i) q^{88} +(1.18531 + 0.684339i) q^{89} +(-0.878421 + 0.339353i) q^{91} +(-6.91550 + 11.9780i) q^{92} -21.7630 q^{94} +(0.725143 - 1.25599i) q^{95} +13.5427i q^{97} +(-15.9171 + 9.18977i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) $ 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.29626	+	1.32574i	−1.62370	+	0.937442i	−0.637778	+	0.770220i	$0.720146\pi$
$2$	−2.29626	+	1.32574i	−1.62370	+	0.937442i	−0.985919	+	0.167222i	$0.946520\pi$
$3$		0			0
$3$		0			0
$4$	2.51519	−	4.35644i	1.25760	−	2.17822i
$5$	2.43120	−	1.40366i	1.08727	−	0.627734i	0.154420	−	0.988005i	$-0.450649\pi$
$5$	2.43120	−	1.40366i	1.08727	−	0.627734i	0.932848	+	0.360271i	$0.117316\pi$
$6$		0			0
$7$		−	0.261179i		−	0.0987162i	−0.998781	−	0.0493581i	$-0.984282\pi$
$7$		−	0.261179i		−	0.0987162i	0.998781	−	0.0493581i	$-0.0157176\pi$
$8$			8.03502i			2.84081i
$9$		0			0
$10$	−3.72178	+	6.44631i	−1.17693	+	2.03850i
$11$	1.34990	−	0.779366i	0.407011	−	0.234988i	−0.282494	−	0.959269i	$-0.591162\pi$
$11$	1.34990	−	0.779366i	0.407011	−	0.234988i	0.689504	+	0.724281i	$0.257828\pi$
$12$		0			0
$13$	−1.29932	−	3.36330i	−0.360365	−	0.932811i
$13$	−1.29932	−	3.36330i	−0.360365	−	0.932811i
$14$	0.346256	+	0.599733i	0.0925407	+	0.160285i
$15$		0			0
$16$	−5.62200	−	9.73759i	−1.40550	−	2.43440i
$17$	−3.65449	−	6.32976i	−0.886344	−	1.53519i	−0.844166	−	0.536082i	$-0.819904\pi$
$17$	−3.65449	−	6.32976i	−0.886344	−	1.53519i	−0.0421777	−	0.999110i	$-0.513430\pi$
$18$		0			0
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	−0.447801	−	0.894133i	$-0.647793\pi$
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	0.550441	+	0.834874i	$0.314459\pi$
$20$		−	14.1219i		−	3.15774i
$21$		0			0
$22$	−2.06648	+	3.57925i	−0.440575	+	0.763098i
$23$	−2.74949			−0.573308			−0.286654	−	0.958034i	$-0.592543\pi$
$23$	−2.74949			−0.573308			−0.286654	+	0.958034i	$0.592543\pi$
$24$		0			0
$25$	1.44050	−	2.49502i	0.288101	−	0.499005i
$26$	7.44243	+	6.00043i	1.45958	+	1.17678i
$27$		0			0
$28$	−1.13781	−	0.656914i	−0.215026	−	0.124145i
$29$	1.78313	+	3.08847i	0.331119	+	0.573515i	0.982732	−	0.185037i	$-0.0592405\pi$
$29$	1.78313	+	3.08847i	0.331119	+	0.573515i	−0.651612	+	0.758552i	$0.725907\pi$
$30$		0			0
$31$	3.17297	−	1.83191i	0.569882	−	0.329021i	−0.187221	−	0.982318i	$-0.559948\pi$
$31$	3.17297	−	1.83191i	0.569882	−	0.329021i	0.757102	+	0.653297i	$0.226615\pi$
$32$	11.9020	+	6.87163i	2.10400	+	1.21474i
$33$		0			0
$34$	16.7833	+	9.68983i	2.87831	+	1.66179i
$35$	−0.366605	−	0.634978i	−0.0619675	−	0.107331i
$36$		0			0
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	0.648570	−	0.761155i	$-0.275367\pi$
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	−0.334895	+	0.942256i	$0.608701\pi$
$38$	−0.684893	+	1.18627i	−0.111104	+	0.192438i
$39$		0			0
$40$	11.2784	+	19.5348i	1.78327	+	3.08872i
$41$		−	7.42443i		−	1.15950i	−0.814794	−	0.579751i	$-0.803150\pi$
$41$		−	7.42443i		−	1.15950i	0.814794	−	0.579751i	$-0.196850\pi$
$42$		0			0
$43$	−3.49719			−0.533316			−0.266658	−	0.963791i	$-0.585919\pi$
$43$	−3.49719			−0.533316			−0.266658	+	0.963791i	$0.585919\pi$
$44$		−	7.84102i		−	1.18208i
$45$		0			0
$46$	6.31353	−	3.64512i	0.930880	−	0.537444i
$47$	7.10819	+	4.10392i	1.03684	+	0.598618i	0.918936	−	0.394407i	$-0.129050\pi$
$47$	7.10819	+	4.10392i	1.03684	+	0.598618i	0.117901	+	0.993025i	$0.462383\pi$
$48$		0			0
$49$	6.93179			0.990255
$50$			7.63895i			1.08031i
$51$		0			0
$52$	−17.9200	−	2.79895i	−2.48506	−	0.388144i
$53$	−4.68042			−0.642905			−0.321452	−	0.946926i	$-0.604171\pi$
$53$	−4.68042			−0.642905			−0.321452	+	0.946926i	$0.604171\pi$
$54$		0			0
$55$	2.18792	−	3.78960i	0.295020	−	0.510989i
$56$	2.09858			0.280434
$57$		0			0
$58$	−8.18905	−	4.72795i	−1.07527	−	0.620810i
$59$	9.64903	+	5.57087i	1.25620	+	0.725265i	0.972333	−	0.233599i	$-0.0750504\pi$
$59$	9.64903	+	5.57087i	1.25620	+	0.725265i	0.283864	+	0.958865i	$0.408384\pi$
$60$		0			0
$61$	−3.61462			−0.462805			−0.231403	−	0.972858i	$-0.574331\pi$
$61$	−3.61462			−0.462805			−0.231403	+	0.972858i	$0.574331\pi$
$62$	−4.85729	+	8.41308i	−0.616877	+	1.06846i
$63$		0			0
$64$	−13.9521			−1.74401
$65$	−7.87982	−	6.35307i	−0.977371	−	0.788002i
$66$		0			0
$67$		−	8.21327i		−	1.00341i	−0.865038	−	0.501706i	$-0.832706\pi$
$67$		−	8.21327i		−	1.00341i	0.865038	−	0.501706i	$-0.167294\pi$
$68$	−36.7670			−4.45865
$69$		0			0
$70$	1.68364	+	0.972048i	0.201233	+	0.116182i
$71$	5.40445	−	3.12026i	0.641390	−	0.370307i	−0.143760	−	0.989613i	$-0.545919\pi$
$71$	5.40445	−	3.12026i	0.641390	−	0.370307i	0.785150	+	0.619306i	$0.212586\pi$
$72$		0			0
$73$		−	3.76021i		−	0.440099i	−0.975489	−	0.220050i	$-0.929378\pi$
$73$		−	3.76021i		−	0.440099i	0.975489	−	0.220050i	$-0.0706220\pi$
$74$	−5.84171			−0.679085
$75$		0			0
$76$		−	2.59875i		−	0.298097i
$77$	−0.203554	−	0.352565i	−0.0231971	−	0.0401785i
$78$		0			0
$79$	−1.36567	+	2.36542i	−0.153650	+	0.266130i	−0.932567	−	0.360998i	$-0.882436\pi$
$79$	−1.36567	+	2.36542i	−0.153650	+	0.266130i	0.778916	+	0.627128i	$0.215770\pi$
$80$	−27.3365	−	15.7827i	−3.05631	−	1.76456i
$81$		0			0
$82$	9.84289	+	17.0484i	1.08697	+	1.88268i
$83$	7.18029	+	4.14554i	0.788139	+	0.455032i	0.839307	−	0.543658i	$-0.182961\pi$
$83$	7.18029	+	4.14554i	0.788139	+	0.455032i	−0.0511680	+	0.998690i	$0.516294\pi$
$84$		0			0
$85$	−17.7696	−	10.2593i	−1.92739	−	1.11278i
$86$	8.03044	−	4.63638i	0.865944	−	0.499953i
$87$		0			0
$88$	6.26222	+	10.8465i	0.667555	+	1.15624i
$89$	1.18531	+	0.684339i	0.125643	+	0.0725398i	0.561504	−	0.827474i	$-0.310223\pi$
$89$	1.18531	+	0.684339i	0.125643	+	0.0725398i	−0.435861	+	0.900014i	$0.643556\pi$
$90$		0			0
$91$	−0.878421	+	0.339353i	−0.0920836	+	0.0355739i
$92$	−6.91550	+	11.9780i	−0.720990	+	1.24879i
$93$		0			0
$94$	−21.7630			−2.24468
$95$	0.725143	−	1.25599i	0.0743981	−	0.128861i
$96$		0			0
$97$			13.5427i			1.37506i	0.726158	+	0.687528i	$0.241304\pi$
$97$			13.5427i			1.37506i	−0.726158	+	0.687528i	$0.758696\pi$
$98$	−15.9171	+	9.18977i	−1.60787	+	0.928307i
$99$		0			0
$100$	−7.24628	−	12.5509i	−0.724628	−	1.25509i
$101$	−7.70477	−	13.3451i	−0.766653	−	1.32788i	−0.939368	−	0.342911i	$-0.888587\pi$
$101$	−7.70477	−	13.3451i	−0.766653	−	1.32788i	0.172715	−	0.984972i	$-0.444746\pi$
$102$		0			0
$103$	5.49573	+	9.51889i	0.541510	+	0.937924i	0.998818	+	0.0486148i	$0.0154807\pi$
$103$	5.49573	+	9.51889i	0.541510	+	0.937924i	−0.457307	+	0.889309i	$0.651186\pi$
$104$	27.0242	−	10.4400i	2.64994	−	1.02373i
$105$		0			0
$106$	10.7474	−	6.20503i	1.04388	−	0.602686i
$107$	0.595733	−	1.03184i	0.0575917	−	0.0997518i	−0.835792	−	0.549046i	$-0.814991\pi$
$107$	0.595733	−	1.03184i	0.0575917	−	0.0997518i	0.893384	+	0.449294i	$0.148325\pi$
$108$		0			0
$109$		−	1.56215i		−	0.149627i	−0.997198	−	0.0748135i	$-0.976164\pi$
$109$		−	1.56215i		−	0.149627i	0.997198	−	0.0748135i	$-0.0238362\pi$
$110$			11.6025i			1.10626i
$111$		0			0
$112$	−2.54325	+	1.46835i	−0.240314	+	0.138746i
$113$	−2.29605	+	3.97687i	−0.215994	+	0.374112i	−0.953580	−	0.301141i	$-0.902632\pi$
$113$	−2.29605	+	3.97687i	−0.215994	+	0.374112i	0.737586	+	0.675254i	$0.235966\pi$
$114$		0			0
$115$	−6.68457	+	3.85934i	−0.623340	+	0.359885i
$116$	17.9397			1.66566
$117$		0			0
$118$	−29.5422			−2.71958
$119$	−1.65320	+	0.954474i	−0.151548	+	0.0874965i
$120$		0			0
$121$	−4.28518	+	7.42214i	−0.389562	+	0.674740i
$122$	8.30010	−	4.79207i	0.751456	−	0.433853i
$123$		0			0
$124$		−	18.4304i		−	1.65510i
$125$			5.94868i			0.532066i
$126$		0			0
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	−0.501011	−	0.865441i	$-0.667038\pi$
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	0.999999	+	0.00116769i	$0.000371687\pi$
$128$	8.23353	−	4.75363i	0.727749	−	0.420166i
$129$		0			0
$130$	26.5166	+	4.14166i	2.32566	+	0.363247i
$131$	1.93018	+	3.34317i	0.168640	+	0.292094i	0.937942	−	0.346792i	$-0.112729\pi$
$131$	1.93018	+	3.34317i	0.168640	+	0.292094i	−0.769302	+	0.638886i	$0.779396\pi$
$132$		0			0
$133$	−0.0674638	−	0.116851i	−0.00584985	−	0.0101322i
$134$	10.8887	+	18.8598i	0.940640	+	1.62924i
$135$		0			0
$136$	50.8598	−	29.3639i	4.36119	−	2.51793i
$137$		−	2.23092i		−	0.190600i	−0.995449	−	0.0953002i	$-0.969619\pi$
$137$		−	2.23092i		−	0.190600i	0.995449	−	0.0953002i	$-0.0303811\pi$
$138$		0			0
$139$	−8.12287	+	14.0692i	−0.688973	+	1.19334i	0.283197	+	0.959062i	$0.408605\pi$
$139$	−8.12287	+	14.0692i	−0.688973	+	1.19334i	−0.972170	+	0.234275i	$0.924729\pi$
$140$	−3.68833			−0.311721
$141$		0			0
$142$	−8.27333	+	14.3298i	−0.694282	+	1.20253i
$143$	−4.37519	−	3.52748i	−0.365872	−	0.294983i
$144$		0			0
$145$	8.67031	+	5.00581i	0.720030	+	0.415710i
$146$	4.98508	+	8.63440i	0.412568	+	0.714588i
$147$		0			0
$148$	9.59803	−	5.54143i	0.788953	−	0.455502i
$149$	−6.61334	−	3.81821i	−0.541786	−	0.312800i	0.204017	−	0.978967i	$-0.434600\pi$
$149$	−6.61334	−	3.81821i	−0.541786	−	0.312800i	−0.745802	+	0.666167i	$0.767934\pi$
$150$		0			0
$151$	10.8516	+	6.26520i	0.883095	+	0.509855i	0.871677	−	0.490080i	$-0.163032\pi$
$151$	10.8516	+	6.26520i	0.883095	+	0.509855i	0.0114171	+	0.999935i	$0.496366\pi$
$152$	2.07549	+	3.59485i	0.168344	+	0.291581i
$153$		0			0
$154$	0.934822	+	0.539720i	0.0753301	+	0.0434919i
$155$	5.14275	−	8.90751i	0.413076	−	0.715468i
$156$		0			0
$157$	−5.04228	−	8.73349i	−0.402418	−	0.697009i	0.591599	−	0.806232i	$-0.298497\pi$
$157$	−5.04228	−	8.73349i	−0.402418	−	0.697009i	−0.994017	+	0.109224i	$0.965164\pi$
$158$		−	7.24214i		−	0.576153i
$159$		0			0
$160$	38.5816			3.05015
$161$			0.718108i			0.0565948i
$162$		0			0
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	−0.859738	−	0.510735i	$-0.829373\pi$
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	0.0124407	+	0.999923i	$0.496040\pi$
$164$	−32.3441	−	18.6739i	−2.52565	−	1.45818i
$165$		0			0
$166$	−21.9837			−1.70627
$167$			24.3257i			1.88238i	0.337882	+	0.941189i	$0.390290\pi$
$167$			24.3257i			1.88238i	−0.337882	+	0.941189i	$0.609710\pi$
$168$		0			0
$169$	−9.62356	+	8.73998i	−0.740274	+	0.672306i
$170$	54.4048			4.17265
$171$		0			0
$172$	−8.79610	+	15.2353i	−0.670696	+	1.16168i
$173$	10.5463			0.801822			0.400911	−	0.916117i	$-0.368694\pi$
$173$	10.5463			0.801822			0.400911	+	0.916117i	$0.368694\pi$
$174$		0			0
$175$	−0.651647	−	0.376228i	−0.0492599	−	0.0284402i
$176$	−15.1783	−	8.76319i	−1.14411	−	0.660550i
$177$		0			0
$178$	−3.62903			−0.272007
$179$	−3.54457	+	6.13938i	−0.264934	+	0.458879i	−0.967546	−	0.252694i	$-0.918683\pi$
$179$	−3.54457	+	6.13938i	−0.264934	+	0.458879i	0.702612	+	0.711573i	$0.252017\pi$
$180$		0			0
$181$	15.7315			1.16931			0.584656	−	0.811281i	$-0.301230\pi$
$181$	15.7315			1.16931			0.584656	+	0.811281i	$0.301230\pi$
$182$	1.56718	−	1.94380i	0.116167	−	0.144084i
$183$		0			0
$184$		−	22.0922i		−	1.62866i
$185$	6.18502			0.454732
$186$		0			0
$187$	−9.86640	−	5.69637i	−0.721502	−	0.416560i
$188$	35.7569	−	20.6443i	2.60784	−	1.50564i
$189$		0			0
$190$			3.84542i			0.278976i
$191$	−8.12183			−0.587675			−0.293837	−	0.955855i	$-0.594932\pi$
$191$	−8.12183			−0.587675			−0.293837	+	0.955855i	$0.594932\pi$
$192$		0			0
$193$		−	7.70792i		−	0.554828i	−0.960750	−	0.277414i	$-0.910523\pi$
$193$		−	7.70792i		−	0.554828i	0.960750	−	0.277414i	$-0.0894774\pi$
$194$	−17.9542	−	31.0976i	−1.28904	−	2.23268i
$195$		0			0
$196$	17.4348	−	30.1979i	1.24534	−	2.15699i
$197$	3.46949	+	2.00311i	0.247191	+	0.142716i	0.618477	−	0.785803i	$-0.287750\pi$
$197$	3.46949	+	2.00311i	0.247191	+	0.142716i	−0.371287	+	0.928518i	$0.621083\pi$
$198$		0			0
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	0.542059	−	0.840340i	$-0.317645\pi$
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	−0.998786	+	0.0492670i	$0.984311\pi$
$200$	20.0476	+	11.5745i	1.41758	+	0.818439i
$201$		0			0
$202$	35.3842	+	20.4291i	2.48963	+	1.43739i
$203$	0.806643	−	0.465716i	0.0566152	−	0.0326868i
$204$		0			0
$205$	−10.4214	−	18.0503i	−0.727859	−	1.26069i
$206$	−25.2392	−	14.5719i	−1.75850	−	1.01527i
$207$		0			0
$208$	−25.4457	+	31.5607i	−1.76434	+	2.18834i
$209$	0.402628	−	0.697373i	0.0278504	−	0.0482383i
$210$		0			0
$211$	17.2151			1.18513			0.592567	−	0.805521i	$-0.298114\pi$
$211$	17.2151			1.18513			0.592567	+	0.805521i	$0.298114\pi$
$212$	−11.7721	+	20.3900i	−0.808514	+	1.40039i
$213$		0			0
$214$			3.15916i			0.215956i
$215$	−8.50238	+	4.90885i	−0.579858	+	0.334781i
$216$		0			0
$217$	−0.478456	−	0.828711i	−0.0324797	−	0.0562565i
$218$	2.07101	+	3.58710i	0.140267	+	0.242949i
$219$		0			0
$220$	−11.0061	−	19.0631i	−0.742031	−	1.28524i
$221$	−16.5405	+	20.5155i	−1.11264	+	1.38002i
$222$		0			0
$223$	8.17028	−	4.71711i	0.547122	−	0.315881i	−0.200838	−	0.979624i	$-0.564367\pi$
$223$	8.17028	−	4.71711i	0.547122	−	0.315881i	0.747961	+	0.663743i	$0.231033\pi$
$224$	1.79472	−	3.10855i	0.119915	−	0.207699i
$225$		0			0
$226$		−	12.1759i		−	0.809927i
$227$			18.3577i			1.21844i	0.793001	+	0.609220i	$0.208518\pi$
$227$			18.3577i			1.21844i	−0.793001	+	0.609220i	$0.791482\pi$
$228$		0			0
$229$	−11.3476	+	6.55153i	−0.749870	+	0.432937i	−0.825647	−	0.564187i	$-0.809190\pi$
$229$	−11.3476	+	6.55153i	−0.749870	+	0.432937i	0.0757771	+	0.997125i	$0.475856\pi$
$230$	10.2330	−	17.7241i	0.674743	−	1.16869i
$231$		0			0
$232$	−24.8160	+	14.3275i	−1.62925	+	0.940647i
$233$	−4.84195			−0.317207			−0.158603	−	0.987342i	$-0.550699\pi$
$233$	−4.84195			−0.317207			−0.158603	+	0.987342i	$0.550699\pi$
$234$		0			0
$235$	23.0420			1.50309
$236$	48.5383	−	28.0236i	3.15958	−	1.82418i
$237$		0			0
$238$	2.53078	−	4.38343i	0.164046	−	0.284136i
$239$	−13.6653	+	7.88968i	−0.883936	+	0.510341i	−0.871954	−	0.489587i	$-0.837147\pi$
$239$	−13.6653	+	7.88968i	−0.883936	+	0.510341i	−0.0119822	+	0.999928i	$0.503814\pi$
$240$		0			0
$241$			16.2866i			1.04911i	0.851375	+	0.524557i	$0.175769\pi$
$241$			16.2866i			1.04911i	−0.851375	+	0.524557i	$0.824231\pi$
$242$		−	22.7242i		−	1.46077i
$243$		0			0
$244$	−9.09147	+	15.7469i	−0.582022	+	1.00809i
$245$	16.8526	−	9.72985i	1.07667	−	0.621617i
$246$		0			0
$247$	−1.45007	−	1.16911i	−0.0922656	−	0.0743888i
$248$	14.7195	+	25.4949i	0.934687	+	1.61893i
$249$		0			0
$250$	−7.88642	−	13.6597i	−0.498781	−	0.863914i
$251$	−13.7361	−	23.7917i	−0.867017	−	1.50172i	−0.865030	−	0.501719i	$-0.832701\pi$
$251$	−13.7361	−	23.7917i	−0.867017	−	1.50172i	−0.00198652	−	0.999998i	$-0.500632\pi$
$252$		0			0
$253$	−3.71154	+	2.14286i	−0.233343	+	0.134720i
$254$			29.8203i			1.87109i
$255$		0			0
$256$	1.34789	−	2.33462i	0.0842434	−	0.145914i
$257$	9.79971			0.611289			0.305644	−	0.952146i	$-0.401128\pi$
$257$	9.79971			0.611289			0.305644	+	0.952146i	$0.401128\pi$
$258$		0			0
$259$	0.287712	−	0.498332i	0.0178775	−	0.0309648i
$260$	−47.4960	+	18.3488i	−2.94558	+	1.13794i
$261$		0			0
$262$	−8.86436	−	5.11784i	−0.547642	−	0.316181i
$263$	11.5486	+	20.0028i	0.712119	+	1.23343i	0.964060	+	0.265684i	$0.0855977\pi$
$263$	11.5486	+	20.0028i	0.712119	+	1.23343i	−0.251941	+	0.967743i	$0.581069\pi$
$264$		0			0
$265$	−11.3790	+	6.56970i	−0.699009	+	0.403573i
$266$	0.309828	+	0.178879i	0.0189968	+	0.0109678i
$267$		0			0
$268$	−35.7806	−	20.6580i	−2.18565	−	1.26189i
$269$	10.8197	+	18.7403i	0.659688	+	1.14261i	0.980696	+	0.195537i	$0.0626450\pi$
$269$	10.8197	+	18.7403i	0.659688	+	1.14261i	−0.321008	+	0.947076i	$0.604022\pi$
$270$		0			0
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.408447	−	0.912782i	$-0.633929\pi$
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.994716	+	0.102666i	$0.967263\pi$
$272$	−41.0911	+	71.1718i	−2.49151	+	4.31542i
$273$		0			0
$274$	2.95763	+	5.12276i	0.178677	+	0.309478i
$275$		−	4.49072i		−	0.270800i
$276$		0			0
$277$	6.44278			0.387109			0.193554	−	0.981090i	$-0.437998\pi$
$277$	6.44278			0.387109			0.193554	+	0.981090i	$0.437998\pi$
$278$		−	43.0754i		−	2.58349i
$279$		0			0
$280$	5.10207	−	2.94568i	0.304907	−	0.176038i
$281$	1.22438	+	0.706894i	0.0730402	+	0.0421698i	0.536075	−	0.844170i	$-0.319906\pi$
$281$	1.22438	+	0.706894i	0.0730402	+	0.0421698i	−0.463035	+	0.886340i	$0.653240\pi$
$282$		0			0
$283$	19.9798			1.18767			0.593837	−	0.804585i	$-0.297612\pi$
$283$	19.9798			1.18767			0.593837	+	0.804585i	$0.297612\pi$
$284$		−	31.3922i		−	1.86278i
$285$		0			0
$286$	14.7231	+	2.29961i	0.870594	+	0.135979i
$287$	−1.93910			−0.114462
$288$		0			0
$289$	−18.2106	+	31.5416i	−1.07121	+	1.85539i
$290$	−26.5457			−1.55882
$291$		0			0
$292$	−16.3811	−	9.45765i	−0.958634	−	0.553467i
$293$	2.92034	+	1.68606i	0.170608	+	0.0985005i	0.582872	−	0.812564i	$-0.301929\pi$
$293$	2.92034	+	1.68606i	0.170608	+	0.0985005i	−0.412265	+	0.911064i	$0.635262\pi$
$294$		0			0
$295$	31.2783			1.82110
$296$	−8.85131	+	15.3309i	−0.514472	+	0.891092i
$297$		0			0
$298$	20.2479			1.17293
$299$	3.57246	+	9.24736i	0.206601	+	0.534789i
$300$		0			0
$301$			0.913391i			0.0526470i
$302$	−33.2242			−1.91184
$303$		0			0
$304$	−5.03054	−	2.90438i	−0.288521	−	0.166578i
$305$	−8.78789	+	5.07369i	−0.503193	+	0.290519i
$306$		0			0
$307$			20.7017i			1.18151i	0.806851	+	0.590756i	$0.201170\pi$
$307$			20.7017i			1.18151i	−0.806851	+	0.590756i	$0.798830\pi$
$308$	−2.04791			−0.116690
$309$		0			0
$310$			27.2719i			1.54894i
$311$	−4.13884	−	7.16868i	−0.234692	−	0.406499i	0.724491	−	0.689284i	$-0.242075\pi$
$311$	−4.13884	−	7.16868i	−0.234692	−	0.406499i	−0.959183	+	0.282786i	$0.908742\pi$
$312$		0			0
$313$	6.19041	−	10.7221i	0.349902	−	0.606049i	−0.636329	−	0.771417i	$-0.719548\pi$
$313$	6.19041	−	10.7221i	0.349902	−	0.606049i	0.986232	+	0.165369i	$0.0528814\pi$
$314$	23.1567	+	13.3696i	1.30681	+	0.754488i
$315$		0			0
$316$	6.86987	+	11.8990i	0.386460	+	0.669369i
$317$	−28.4498	−	16.4255i	−1.59790	−	0.922547i	−0.991892	−	0.127087i	$-0.959437\pi$
$317$	−28.4498	−	16.4255i	−1.59790	−	0.922547i	−0.606006	−	0.795460i	$-0.707229\pi$
$318$		0			0
$319$	4.81410	+	2.77942i	0.269538	+	0.155618i
$320$	−33.9204	+	19.5839i	−1.89621	+	1.09478i
$321$		0			0
$322$	−0.952027	−	1.64896i	−0.0530544	−	0.0918929i
$323$	−3.27002	−	1.88795i	−0.181949	−	0.105048i
$324$		0			0
$325$	−10.2632	−	1.60302i	−0.569299	−	0.0889194i
$326$	16.5599	−	28.6826i	0.917170	−	1.58858i
$327$		0			0
$328$	59.6555			3.29392
$329$	1.07186	−	1.85651i	0.0590933	−	0.102353i
$330$		0			0
$331$		−	13.8802i		−	0.762922i	−0.924385	−	0.381461i	$-0.875421\pi$
$331$		−	13.8802i		−	0.762922i	0.924385	−	0.381461i	$-0.124579\pi$
$332$	36.1196	−	20.8537i	1.98232	−	1.14449i
$333$		0			0
$334$	−32.2496	−	55.8580i	−1.76462	−	3.05641i
$335$	−11.5286	−	19.9681i	−0.629876	−	1.09098i
$336$		0			0
$337$	−12.3880	−	21.4566i	−0.674816	−	1.16882i	−0.976522	−	0.215415i	$-0.930889\pi$
$337$	−12.3880	−	21.4566i	−0.674816	−	1.16882i	0.301706	−	0.953401i	$-0.402444\pi$
$338$	10.5112	−	32.8276i	0.571733	−	1.78559i
$339$		0			0
$340$	−89.3880	+	51.6082i	−4.84774	+	2.79885i
$341$	2.85546	−	4.94580i	0.154632	−	0.267830i
$342$		0			0
$343$		−	3.63868i		−	0.196470i
$344$		−	28.1000i		−	1.51505i
$345$		0			0
$346$	−24.2170	+	13.9817i	−1.30192	+	0.751662i
$347$	9.52830	−	16.5035i	0.511506	−	0.885955i	−0.488405	−	0.872617i	$-0.662421\pi$
$347$	9.52830	−	16.5035i	0.511506	−	0.885955i	0.999911	−	0.0133374i	$-0.00424556\pi$
$348$		0			0
$349$	20.5588	−	11.8696i	1.10049	−	0.635367i	0.164139	−	0.986437i	$-0.447516\pi$
$349$	20.5588	−	11.8696i	1.10049	−	0.635367i	0.936349	+	0.351070i	$0.114182\pi$
$350$	1.99513			0.106644
$351$		0			0
$352$	21.4221			1.14180
$353$	1.89779	−	1.09569i	0.101009	−	0.0583176i	−0.448644	−	0.893710i	$-0.648093\pi$
$353$	1.89779	−	1.09569i	0.101009	−	0.0583176i	0.549654	+	0.835393i	$0.314760\pi$
$354$		0			0
$355$	8.75954	−	15.1720i	0.464908	−	0.805245i
$356$	5.96256	−	3.44249i	0.316015	−	0.182452i
$357$		0			0
$358$		−	18.7968i		−	0.993441i
$359$			5.58420i			0.294723i	0.989083	+	0.147361i	$0.0470780\pi$
$359$			5.58420i			0.294723i	−0.989083	+	0.147361i	$0.952922\pi$
$360$		0			0
$361$	−9.36656	+	16.2234i	−0.492977	+	0.853861i
$362$	−36.1235	+	20.8559i	−1.89861	+	1.09616i
$363$		0			0
$364$	−0.731025	+	4.68033i	−0.0383161	+	0.245316i
$365$	−5.27805	−	9.14184i	−0.276266	−	0.478506i
$366$		0			0
$367$	6.68867	+	11.5851i	0.349146	+	0.604738i	0.986098	−	0.166165i	$-0.0531384\pi$
$367$	6.68867	+	11.5851i	0.349146	+	0.604738i	−0.636952	+	0.770903i	$0.719805\pi$
$368$	15.4576	+	26.7734i	0.805785	+	1.39566i
$369$		0			0
$370$	−14.2024	+	8.19975i	−0.738347	+	0.426285i
$371$			1.22242i			0.0634651i
$372$		0			0
$373$	−3.90999	+	6.77230i	−0.202451	+	0.350656i	−0.949318	−	0.314318i	$-0.898224\pi$
$373$	−3.90999	+	6.77230i	−0.202451	+	0.350656i	0.746866	+	0.664974i	$0.231558\pi$
$374$	30.2077			1.56200
$375$		0			0
$376$	−32.9751	+	57.1145i	−1.70056	+	2.94546i
$377$	8.07061	−	10.0101i	0.415658	−	0.515547i
$378$		0			0
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.950399	+	0.311032i	$0.100675\pi$
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.744561	+	0.667554i	$0.232659\pi$
$380$	−3.64775	−	6.31809i	−0.187126	−	0.324111i
$381$		0			0
$382$	18.6498	−	10.7675i	0.954206	−	0.550911i
$383$	15.4126	+	8.89848i	0.787548	+	0.454691i	0.839099	−	0.543979i	$-0.183083\pi$
$383$	15.4126	+	8.89848i	0.787548	+	0.454691i	−0.0515506	+	0.998670i	$0.516416\pi$
$384$		0			0
$385$	−0.989761	−	0.571439i	−0.0504429	−	0.0291232i
$386$	10.2187	+	17.6994i	0.520120	+	0.900873i
$387$		0			0
$388$	58.9981	+	34.0626i	2.99518	+	1.72927i
$389$	17.2599	−	29.8950i	0.875112	−	1.51574i	0.0184682	−	0.999829i	$-0.494121\pi$
$389$	17.2599	−	29.8950i	0.875112	−	1.51574i	0.856644	−	0.515909i	$-0.172546\pi$
$390$		0			0
$391$	10.0480	+	17.4036i	0.508148	+	0.880139i
$392$			55.6971i			2.81313i
$393$		0			0
$394$	−10.6224			−0.535151
$395$			7.66775i			0.385806i
$396$		0			0
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	−0.678269	−	0.734814i	$-0.737270\pi$
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	0.297233	+	0.954805i	$0.403936\pi$
$398$	29.5892	+	17.0833i	1.48317	+	0.856309i
$399$		0			0
$400$	−32.3940			−1.61970
$401$		−	21.4944i		−	1.07338i	−0.843780	−	0.536690i	$-0.819675\pi$
$401$		−	21.4944i		−	1.07338i	0.843780	−	0.536690i	$-0.180325\pi$
$402$		0			0
$403$	−10.2840	−	8.29140i	−0.512280	−	0.413024i
$404$	−77.5159			−3.85656
$405$		0			0
$406$	−1.23484	+	2.13880i	−0.0612840	+	0.106147i
$407$	3.43417			0.170225
$408$		0			0
$409$	30.7301	+	17.7420i	1.51951	+	0.877287i	0.999736	+	0.0229809i	$0.00731570\pi$
$409$	30.7301	+	17.7420i	1.51951	+	0.877287i	0.519770	+	0.854306i	$0.326018\pi$
$410$	47.8602	+	27.6321i	2.36365	+	1.36465i
$411$		0			0
$412$	55.2913			2.72401
$413$	1.45499	−	2.52012i	0.0715954	−	0.124007i
$414$		0			0
$415$	23.2757			1.14256
$416$	7.64687	−	48.9585i	0.374919	−	2.40039i
$417$		0			0
$418$			2.13513i			0.104433i
$419$	20.0287			0.978464			0.489232	−	0.872154i	$-0.337277\pi$
$419$	20.0287			0.978464			0.489232	+	0.872154i	$0.337277\pi$
$420$		0			0
$421$	15.3946	+	8.88807i	0.750286	+	0.433178i	0.825797	−	0.563967i	$-0.190725\pi$
$421$	15.3946	+	8.88807i	0.750286	+	0.433178i	−0.0755111	+	0.997145i	$0.524059\pi$
$422$	−39.5302	+	22.8228i	−1.92430	+	1.11100i
$423$		0			0
$424$		−	37.6073i		−	1.82637i
$425$	−21.0572			−1.02142
$426$		0			0
$427$			0.944062i			0.0456864i
$428$	−2.99677	−	5.19055i	−0.144854	−	0.250895i
$429$		0			0
$430$	13.0158	−	22.5440i	0.627676	−	1.08717i
$431$	1.72978	+	0.998690i	0.0833206	+	0.0481052i	0.541081	−	0.840970i	$-0.318015\pi$
$431$	1.72978	+	0.998690i	0.0833206	+	0.0481052i	−0.457761	+	0.889075i	$0.651348\pi$
$432$		0			0
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	−0.994425	−	0.105446i	$-0.966373\pi$
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	0.405893	−	0.913920i	$-0.366960\pi$
$434$	2.19732	+	1.26862i	0.105475	+	0.0608957i
$435$		0			0
$436$	−6.80543	−	3.92911i	−0.325921	−	0.188170i
$437$	−1.23012	+	0.710208i	−0.0588444	+	0.0339738i
$438$		0			0
$439$	−7.66518	−	13.2765i	−0.365839	−	0.633652i	0.623071	−	0.782165i	$-0.285885\pi$
$439$	−7.66518	−	13.2765i	−0.365839	−	0.633652i	−0.988910	+	0.148513i	$0.952551\pi$
$440$	30.4495	+	17.5800i	1.45162	+	0.838095i
$441$		0			0
$442$	10.7830	−	69.0373i	0.512895	−	3.28377i
$443$	−4.73265	+	8.19718i	−0.224855	+	0.389460i	−0.956276	−	0.292466i	$-0.905524\pi$
$443$	−4.73265	+	8.19718i	−0.224855	+	0.389460i	0.731421	+	0.681926i	$0.238857\pi$
$444$		0			0
$445$	3.84231			0.182143
$446$	−12.5074	+	21.6634i	−0.592241	+	1.02579i
$447$		0			0
$448$			3.64399i			0.172162i
$449$	14.1283	−	8.15697i	0.666755	−	0.384951i	−0.128091	−	0.991762i	$-0.540885\pi$
$449$	14.1283	−	8.15697i	0.666755	−	0.384951i	0.794846	+	0.606811i	$0.207552\pi$
$450$		0			0
$451$	−5.78635	−	10.0223i	−0.272469	−	0.471929i
$452$	11.5500	+	20.0052i	0.543266	+	0.940964i
$453$		0			0
$454$	−24.3376	−	42.1539i	−1.14222	−	1.97838i
$455$	−1.65929	+	2.05804i	−0.0777885	+	0.0964824i
$456$		0			0
$457$	−1.87187	+	1.08073i	−0.0875626	+	0.0505543i	−0.543142	−	0.839641i	$-0.682765\pi$
$457$	−1.87187	+	1.08073i	−0.0875626	+	0.0505543i	0.455579	+	0.890195i	$0.349432\pi$
$458$	17.3713	−	30.0880i	0.811708	−	1.40592i
$459$		0			0
$460$			38.8279i			1.81036i
$461$			3.06596i			0.142796i	0.997448	+	0.0713980i	$0.0227460\pi$
$461$			3.06596i			0.142796i	−0.997448	+	0.0713980i	$0.977254\pi$
$462$		0			0
$463$	13.8184	−	7.97807i	0.642197	−	0.370772i	−0.143264	−	0.989685i	$-0.545760\pi$
$463$	13.8184	−	7.97807i	0.642197	−	0.370772i	0.785460	+	0.618912i	$0.212426\pi$
$464$	20.0495	−	34.7268i	0.930776	−	1.61215i
$465$		0			0
$466$	11.1184	−	6.41919i	0.515048	−	0.297363i
$467$	−3.15406			−0.145952			−0.0729762	−	0.997334i	$-0.523250\pi$
$467$	−3.15406			−0.145952			−0.0729762	+	0.997334i	$0.523250\pi$
$468$		0			0
$469$	−2.14513			−0.0990529
$470$	−52.9102	+	30.5477i	−2.44057	+	1.40906i
$471$		0			0
$472$	−44.7621	+	77.5302i	−2.06034	+	3.56862i
$473$	−4.72086	+	2.72559i	−0.217065	+	0.125323i
$474$		0			0
$475$		−	1.48836i		−	0.0682905i
$476$			9.60274i			0.440141i
$477$		0			0
$478$	20.9194	−	36.2334i	0.956830	−	1.65728i
$479$	8.60548	−	4.96837i	0.393194	−	0.227011i	−0.290349	−	0.956921i	$-0.593771\pi$
$479$	8.60548	−	4.96837i	0.393194	−	0.227011i	0.683543	+	0.729910i	$0.260438\pi$
$480$		0			0
$481$	1.22587	−	7.84853i	0.0558948	−	0.357862i
$482$	−21.5919	−	37.3983i	−0.983484	−	1.70344i
$483$		0			0
$484$	21.5561	+	37.3362i	0.979822	+	1.69710i
$485$	19.0093	+	32.9251i	0.863170	+	1.49505i
$486$		0			0
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.879594	−	0.475725i	$-0.842186\pi$
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.0278074	+	0.999613i	$0.508853\pi$
$488$		−	29.0436i		−	1.31474i
$489$		0			0
$490$	−25.7986	+	44.6844i	−1.16546	+	2.01864i
$491$	−29.7055			−1.34059			−0.670295	−	0.742095i	$-0.733832\pi$
$491$	−29.7055			−1.34059			−0.670295	+	0.742095i	$0.733832\pi$
$492$		0			0
$493$	13.0329	−	22.5736i	0.586971	−	1.01666i
$494$	4.87967	+	0.762161i	0.219547	+	0.0342912i
$495$		0			0
$496$	−35.6768	−	20.5980i	−1.60194	−	0.924878i
$497$	−0.814945	−	1.41153i	−0.0365553	−	0.0633156i
$498$		0			0
$499$	−32.4943	+	18.7606i	−1.45465	+	0.839841i	−0.998740	−	0.0501867i	$-0.984018\pi$
$499$	−32.4943	+	18.7606i	−1.45465	+	0.839841i	−0.455907	+	0.890027i	$0.650685\pi$
$500$	25.9151	+	14.9621i	1.15896	+	0.669124i
$501$		0			0
$502$	63.0833	+	36.4212i	2.81555	+	1.62556i
$503$	−14.5097	−	25.1315i	−0.646956	−	1.12056i	−0.983846	−	0.179016i	$-0.942709\pi$
$503$	−14.5097	−	25.1315i	−0.646956	−	1.12056i	0.336891	−	0.941544i	$-0.390625\pi$
$504$		0			0
$505$	−37.4637	−	21.6297i	−1.66711	−	0.962509i
$506$	5.68176	−	9.84110i	0.252585	−	0.437490i
$507$		0			0
$508$	−28.2874	−	48.9953i	−1.25505	−	2.17381i
$509$		−	8.24121i		−	0.365285i	−0.983179	−	0.182643i	$-0.941535\pi$
$509$		−	8.24121i		−	0.365285i	0.983179	−	0.182643i	$-0.0584651\pi$
$510$		0			0
$511$	−0.982086			−0.0434449
$512$			26.1624i			1.15622i
$513$		0			0
$514$	−22.5026	+	12.9919i	−0.992548	+	0.573048i
$515$	26.7225	+	15.4282i	1.17753	+	0.679849i
$516$		0			0
$517$	12.7938			0.562671
$518$			1.52573i			0.0670367i
$519$		0			0
$520$	51.0471	−	63.3145i	2.23856	−	2.77653i
$521$	−37.2716			−1.63290			−0.816449	−	0.577418i	$-0.804060\pi$
$521$	−37.2716			−1.63290			−0.816449	+	0.577418i	$0.804060\pi$
$522$		0			0
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	−0.897620	−	0.440770i	$-0.854706\pi$
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	0.830528	+	0.556977i	$0.188039\pi$
$524$	19.4191			0.848326
$525$		0			0
$526$	−53.0372	−	30.6210i	−2.31253	−	1.33514i
$527$	−23.1911	−	13.3894i	−1.01022	−	0.583252i
$528$		0			0
$529$	−15.4403			−0.671317
$530$	17.4195	−	30.1714i	0.756653	−	1.31056i
$531$		0			0
$532$	−0.678737			−0.0294270
$533$	−24.9706	+	9.64668i	−1.08160	+	0.417844i
$534$		0			0
$535$		−	3.34482i		−	0.144609i
$536$	65.9939			2.85050
$537$		0			0
$538$	−49.6896	−	28.6883i	−2.14227	−	1.23684i
$539$	9.35723	−	5.40240i	0.403044	−	0.232698i
$540$		0			0
$541$			7.25981i			0.312124i	0.987747	+	0.156062i	$0.0498799\pi$
$541$			7.25981i			0.312124i	−0.987747	+	0.156062i	$0.950120\pi$
$542$	70.7215			3.03775
$543$		0			0
$544$		−	100.449i		−	4.30672i
$545$	−2.19273	−	3.79791i	−0.0939261	−	0.162685i
$546$		0			0
$547$	−12.8226	+	22.2094i	−0.548256	+	0.949607i	0.450138	+	0.892959i	$0.351375\pi$
$547$	−12.8226	+	22.2094i	−0.548256	+	0.949607i	−0.998394	+	0.0566482i	$0.981959\pi$
$548$	−9.71888	−	5.61120i	−0.415170	−	0.239698i
$549$		0			0
$550$	5.95354	+	10.3118i	0.253860	+	0.439698i
$551$	1.59554	+	0.921184i	0.0679722	+	0.0392438i
$552$		0			0
$553$	0.617796	+	0.356685i	0.0262714	+	0.0151678i
$554$	−14.7943	+	8.54147i	−0.628548	+	0.362892i
$555$		0			0
$556$	40.8612	+	70.7736i	1.73290	+	3.00147i
$557$	7.49468	+	4.32706i	0.317560	+	0.183343i	0.650304	−	0.759674i	$-0.274641\pi$
$557$	7.49468	+	4.32706i	0.317560	+	0.183343i	−0.332744	+	0.943017i	$0.607975\pi$
$558$		0			0
$559$	4.54395	+	11.7621i	0.192189	+	0.497483i
$560$	−4.12210	+	7.13969i	−0.174191	+	0.301707i
$561$		0			0
$562$	−3.74864			−0.158127
$563$	−23.0556	+	39.9334i	−0.971677	+	1.68299i	−0.281184	+	0.959654i	$0.590727\pi$
$563$	−23.0556	+	39.9334i	−0.971677	+	1.68299i	−0.690493	+	0.723339i	$0.742606\pi$
$564$		0			0
$565$			12.8914i			0.542347i
$566$	−45.8786	+	26.4880i	−1.92842	+	1.11338i
$567$		0			0
$568$	25.0714	+	43.4249i	1.05197	+	1.82207i
$569$	8.61575	+	14.9229i	0.361191	+	0.625601i	0.988157	−	0.153445i	$-0.0490369\pi$
$569$	8.61575	+	14.9229i	0.361191	+	0.625601i	−0.626966	+	0.779047i	$0.715704\pi$
$570$		0			0
$571$	10.7707	+	18.6554i	0.450741	+	0.780706i	0.998432	−	0.0559746i	$-0.0178266\pi$
$571$	10.7707	+	18.6554i	0.450741	+	0.780706i	−0.547692	+	0.836680i	$0.684493\pi$
$572$	−26.3717	+	10.1880i	−1.10266	+	0.425980i
$573$		0			0
$574$	4.45267	−	2.57075i	0.185851	−	0.107301i
$575$	−3.96065	+	6.86005i	−0.165171	+	0.286084i
$576$		0			0
$577$		−	19.9386i		−	0.830056i	−0.909809	−	0.415028i	$-0.863772\pi$
$577$		−	19.9386i		−	0.830056i	0.909809	−	0.415028i	$-0.136228\pi$
$578$		−	96.5702i		−	4.01679i
$579$		0			0
$580$	43.6150	−	25.1811i	1.81101	−	1.04559i
$581$	1.08273	−	1.87534i	0.0449191	−	0.0778021i
$582$		0			0
$583$	−6.31810	+	3.64776i	−0.261669	+	0.151075i
$584$	30.2134			1.25024
$585$		0			0
$586$	−8.94111			−0.369354
$587$	14.3659	−	8.29416i	0.592945	−	0.342337i	−0.173316	−	0.984866i	$-0.555448\pi$
$587$	14.3659	−	8.29416i	0.592945	−	0.342337i	0.766261	+	0.642529i	$0.222115\pi$
$588$		0			0
$589$	0.946385	−	1.63919i	0.0389951	−	0.0675415i
$590$	−71.8231	+	41.4671i	−2.95691	+	1.70717i
$591$		0			0
$592$		−	24.7726i		−	1.01815i
$593$			15.4909i			0.636137i	0.948068	+	0.318068i	$0.103034\pi$
$593$			15.4909i			0.636137i	−0.948068	+	0.318068i	$0.896966\pi$
$594$		0			0
$595$	−2.67951	+	4.64104i	−0.109849	+	0.190264i
$596$	−33.2676	+	19.2071i	−1.36270	+	0.786752i
$597$		0			0
$598$	−20.4629	−	16.4981i	−0.836790	−	0.674659i
$599$	17.4824	+	30.2804i	0.714312	+	1.23722i	0.963224	+	0.268698i	$0.0865934\pi$
$599$	17.4824	+	30.2804i	0.714312	+	1.23722i	−0.248913	+	0.968526i	$0.580073\pi$
$600$		0			0
$601$	−14.3337	−	24.8266i	−0.584682	−	1.01270i	−0.994915	−	0.100718i	$-0.967886\pi$
$601$	−14.3337	−	24.8266i	−0.584682	−	1.01270i	0.410233	−	0.911981i	$-0.365447\pi$
$602$	−1.21092	−	2.09738i	−0.0493535	−	0.0854827i
$603$		0			0
$604$	54.5880	−	31.5164i	2.22115	−	1.28238i
$605$			24.0597i			0.978165i
$606$		0			0
$607$	−8.13672	+	14.0932i	−0.330259	+	0.572026i	−0.982563	−	0.185932i	$-0.940470\pi$
$607$	−8.13672	+	14.0932i	−0.330259	+	0.572026i	0.652303	+	0.757958i	$0.273803\pi$
$608$	7.09991			0.287939
$609$		0			0
$610$	13.4528	−	23.3010i	0.544689	−	0.943429i
$611$	4.56691	−	29.2393i	0.184757	−	1.18289i
$612$		0			0
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	0.0888435	−	0.996046i	$-0.471683\pi$
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	−0.818179	+	0.574964i	$0.805016\pi$
$614$	−27.4452	−	47.5365i	−1.10760	−	1.91842i
$615$		0			0
$616$	2.83287	−	1.63556i	0.114140	−	0.0658985i
$617$	15.5643	+	8.98605i	0.626595	+	0.361765i	0.779432	−	0.626487i	$-0.215508\pi$
$617$	15.5643	+	8.98605i	0.626595	+	0.361765i	−0.152837	+	0.988251i	$0.548841\pi$
$618$		0			0
$619$	−6.56515	−	3.79039i	−0.263876	−	0.152349i	0.362226	−	0.932090i	$-0.382017\pi$
$619$	−6.56515	−	3.79039i	−0.263876	−	0.152349i	−0.626101	+	0.779742i	$0.715350\pi$
$620$	−25.8700	−	44.8082i	−1.03897	−	1.79954i
$621$		0			0
$622$	19.0077	+	10.9741i	0.762138	+	0.440021i
$623$	0.178735	−	0.309578i	0.00716085	−	0.0124030i
$624$		0			0
$625$	15.5524	+	26.9376i	0.622097	+	1.07750i
$626$			32.8276i			1.31205i
$627$		0			0
$628$	−50.7293			−2.02432
$629$		−	16.1030i		−	0.642069i
$630$		0			0
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	−0.242734	−	0.970093i	$-0.578044\pi$
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	0.718758	+	0.695260i	$0.244711\pi$
$632$	−19.0062	−	10.9732i	−0.756026	−	0.436492i
$633$		0			0
$634$	87.1039			3.45934
$635$		−	31.5728i		−	1.25293i
$636$		0			0
$637$	−9.00658	−	23.3137i	−0.356854	−	0.923721i
$638$	−14.7392			−0.583531
$639$		0			0
$640$	13.3449	−	23.1141i	0.527505	−	0.913665i
$641$	−34.5348			−1.36404			−0.682022	−	0.731332i	$-0.738899\pi$
$641$	−34.5348			−1.36404			−0.682022	+	0.731332i	$0.738899\pi$
$642$		0			0
$643$	−7.80782	−	4.50785i	−0.307910	−	0.177772i	0.338081	−	0.941117i	$-0.390222\pi$
$643$	−7.80782	−	4.50785i	−0.307910	−	0.177772i	−0.645991	+	0.763345i	$0.723556\pi$
$644$	3.12839	+	1.80618i	0.123276	+	0.0711734i
$645$		0			0
$646$	10.0117			0.393906
$647$	−2.14777	+	3.72004i	−0.0844374	+	0.146250i	−0.905151	−	0.425089i	$-0.860243\pi$
$647$	−2.14777	+	3.72004i	−0.0844374	+	0.146250i	0.820714	+	0.571339i	$0.193576\pi$
$648$		0			0
$649$	17.3670			0.681714
$650$	25.6921	−	9.92541i	1.00773	−	0.389307i
$651$		0			0
$652$			62.8348i			2.46080i
$653$	37.1624			1.45428			0.727138	−	0.686491i	$-0.240850\pi$
$653$	37.1624			1.45428			0.727138	+	0.686491i	$0.240850\pi$
$654$		0			0
$655$	9.38531	+	5.41861i	0.366715	+	0.211723i
$656$	−72.2960	+	41.7401i	−2.82269	+	1.62968i
$657$		0			0
$658$			5.68402i			0.221586i
$659$	−1.31776			−0.0513325			−0.0256663	−	0.999671i	$-0.508171\pi$
$659$	−1.31776			−0.0513325			−0.0256663	+	0.999671i	$0.508171\pi$
$660$		0			0
$661$		−	33.5146i		−	1.30357i	−0.758405	−	0.651783i	$-0.774021\pi$
$661$		−	33.5146i		−	1.30357i	0.758405	−	0.651783i	$-0.225979\pi$
$662$	18.4015	+	31.8724i	0.715196	+	1.23875i
$663$		0			0
$664$	−33.3095	+	57.6938i	−1.29266	+	2.23895i
$665$	−0.328036	−	0.189392i	−0.0127207	−	0.00734430i
$666$		0			0
$667$	−4.90270	−	8.49173i	−0.189833	−	0.328801i
$668$	105.973	+	61.1837i	4.10023	+	2.36727i
$669$		0			0
$670$	52.9453	+	30.5680i	2.04545	+	1.18094i
$671$	−4.87939	+	2.81712i	−0.188367	+	0.108754i
$672$		0			0
$673$	−11.5750	−	20.0485i	−0.446184	−	0.772813i	0.551950	−	0.833877i	$-0.313884\pi$
$673$	−11.5750	−	20.0485i	−0.446184	−	0.772813i	−0.998134	+	0.0610643i	$0.980551\pi$
$674$	56.8919	+	32.8466i	2.19140	+	1.26520i
$675$		0			0
$676$	13.8701	+	63.9072i	0.533465	+	2.45797i
$677$	8.44612	−	14.6291i	0.324611	−	0.562243i	−0.656823	−	0.754045i	$-0.728100\pi$
$677$	8.44612	−	14.6291i	0.324611	−	0.562243i	0.981434	+	0.191803i	$0.0614333\pi$
$678$		0			0
$679$	3.53707			0.135740
$680$	82.4337	−	142.779i	3.16119	−	5.47534i
$681$		0			0
$682$			15.1424i			0.579834i
$683$	19.4097	−	11.2062i	0.742692	−	0.428793i	−0.0803552	−	0.996766i	$-0.525605\pi$
$683$	19.4097	−	11.2062i	0.742692	−	0.428793i	0.823047	+	0.567973i	$0.192272\pi$
$684$		0			0
$685$	−3.13145	−	5.42383i	−0.119646	−	0.207234i
$686$	4.82396	+	8.35535i	0.184180	+	0.319009i
$687$		0			0
$688$	19.6612	+	34.0542i	0.749576	+	1.29830i
$689$	6.08134	+	15.7416i	0.231681	+	0.599709i
$690$		0			0
$691$	−22.7060	+	13.1093i	−0.863777	+	0.498702i	−0.865275	−	0.501297i	$-0.832856\pi$
$691$	−22.7060	+	13.1093i	−0.863777	+	0.498702i	0.00149829	+	0.999999i	$0.499523\pi$
$692$	26.5260	−	45.9444i	1.00837	−	1.74654i
$693$		0			0
$694$			50.5283i			1.91803i
$695$			45.6069i			1.72997i
$696$		0			0
$697$	−46.9949	+	27.1325i	−1.78006	+	1.02772i
$698$	−31.4722	+	54.5114i	−1.19124	+	2.06329i
$699$		0			0
$700$	−3.27803	+	1.89257i	−0.123898	+	0.0715326i
$701$	49.5379			1.87102			0.935510	−	0.353300i	$-0.114941\pi$
$701$	49.5379			1.87102			0.935510	+	0.353300i	$0.114941\pi$
$702$		0			0
$703$	1.13819			0.0429275
$704$	−18.8339	+	10.8738i	−0.709831	+	0.409821i
$705$		0			0
$706$	−2.90520	+	5.03196i	−0.109339	+	0.189380i
$707$	−3.48544	+	2.01232i	−0.131084	+	0.0756811i
$708$		0			0
$709$			28.9190i			1.08608i	0.839708	+	0.543038i	$0.182726\pi$
$709$			28.9190i			1.08608i	−0.839708	+	0.543038i	$0.817274\pi$
$710$			46.4516i			1.74330i
$711$		0			0
$712$	−5.49868	+	9.52399i	−0.206072	+	0.356927i
$713$	−8.72404	+	5.03683i	−0.326718	+	0.188631i
$714$		0			0
$715$	−15.5883	−	2.43476i	−0.582971	−	0.0910549i
$716$	17.8306	+	30.8835i	0.666360	+	1.15417i
$717$		0			0
$718$	−7.40322	−	12.8227i	−0.276286	−	0.478541i
$719$	5.28737	+	9.15800i	0.197186	+	0.341536i	0.947615	−	0.319415i	$-0.103486\pi$
$719$	5.28737	+	9.15800i	0.197186	+	0.341536i	−0.750429	+	0.660951i	$0.770153\pi$
$720$		0			0
$721$	2.48613	−	1.43537i	0.0925883	−	0.0534559i
$722$		−	49.6706i		−	1.84855i
$723$		0			0
$724$	39.5677	−	68.5333i	1.47052	−	2.54702i
$725$	10.2744			0.381583
$726$		0			0
$727$	−4.91833	+	8.51880i	−0.182411	+	0.315945i	−0.942701	−	0.333639i	$-0.891723\pi$
$727$	−4.91833	+	8.51880i	−0.182411	+	0.315945i	0.760290	+	0.649584i	$0.225057\pi$
$728$	−2.72671	−	7.05814i	−0.101059	−	0.261592i
$729$		0			0
$730$	24.2395	+	13.9947i	0.897143	+	0.517966i
$731$	12.7804	+	22.1364i	0.472701	+	0.818743i
$732$		0			0
$733$	42.6470	−	24.6222i	1.57520	−	0.909443i	0.579686	−	0.814840i	$-0.303175\pi$
$733$	42.6470	−	24.6222i	1.57520	−	0.909443i	0.995515	−	0.0946033i	$-0.0301583\pi$
$734$	−30.7178	−	17.7349i	−1.13381	−	0.654608i
$735$		0			0
$736$	−32.7245	−	18.8935i	−1.20624	−	0.696423i
$737$	−6.40115	−	11.0871i	−0.235789	−	0.408399i
$738$		0			0
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	0.629185	−	0.777255i	$-0.283389\pi$
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	−0.358530	+	0.933518i	$0.616722\pi$
$740$	15.5565	−	26.9447i	0.571869	−	0.990506i
$741$		0			0
$742$	−1.62062	−	2.80700i	−0.0594949	−	0.103048i
$743$		−	27.3401i		−	1.00301i	−0.865154	−	0.501506i	$-0.832780\pi$
$743$		−	27.3401i		−	1.00301i	0.865154	−	0.501506i	$-0.167220\pi$
$744$		0			0
$745$	−21.4378			−0.785421
$746$		−	20.7346i		−	0.759146i
$747$		0			0
$748$	−49.6318	+	28.6549i	−1.81472	+	1.04773i
$749$	−0.269494	−	0.155593i	−0.00984711	−	0.00568523i
$750$		0			0
$751$	−32.4964			−1.18581			−0.592906	−	0.805272i	$-0.702019\pi$
$751$	−32.4964			−1.18581			−0.592906	+	0.805272i	$0.702019\pi$
$752$		−	92.2889i		−	3.36543i
$753$		0			0
$754$	−5.26134	+	33.6853i	−0.191607	+	1.22675i
$755$	35.1768			1.28021
$756$		0			0
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	−0.293770	−	0.955876i	$-0.594910\pi$
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	0.974698	−	0.223525i	$-0.0717566\pi$
$758$	−101.027			−3.66947
$759$		0			0
$760$	10.0919	+	5.82654i	0.366071	+	0.211351i
$761$	−16.1849	−	9.34435i	−0.586702	−	0.338732i	0.177091	−	0.984195i	$-0.443331\pi$
$761$	−16.1849	−	9.34435i	−0.586702	−	0.338732i	−0.763792	+	0.645462i	$0.776665\pi$
$762$		0			0
$763$	−0.408001			−0.0147706
$764$	−20.4280	+	35.3823i	−0.739058	+	1.28009i
$765$		0			0
$766$	−47.1884			−1.70499
$767$	6.19936	−	39.6909i	0.223846	−	1.43315i
$768$		0			0
$769$			44.9114i			1.61955i	0.586744	+	0.809773i	$0.300410\pi$
$769$			44.9114i			1.61955i	−0.586744	+	0.809773i	$0.699590\pi$
$770$	3.03033			0.109205
$771$		0			0
$772$	−33.5791	−	19.3869i	−1.20854	−	0.697750i
$773$	−2.77119	+	1.59995i	−0.0996728	+	0.0575461i	−0.549008	−	0.835817i	$-0.684994\pi$
$773$	−2.77119	+	1.59995i	−0.0996728	+	0.0575461i	0.449335	+	0.893363i	$0.351661\pi$
$774$		0			0
$775$		−	10.5555i		−	0.379165i
$776$	−108.816			−3.90627
$777$		0			0
$778$			91.5288i			3.28147i
$779$	−1.91777	−	3.32167i	−0.0687112	−	0.119011i
$780$		0			0
$781$	4.86365	−	8.42408i	0.174035	−	0.301437i
$782$	−46.1455	−	26.6421i	−1.65016	−	0.952719i
$783$		0			0
$784$	−38.9705	−	67.4989i	−1.39180	−	2.41067i
$785$	−24.5176	−	14.1553i	−0.875072	−	0.505223i
$786$		0			0
$787$	−26.1957	−	15.1241i	−0.933775	−	0.539115i	−0.0457713	−	0.998952i	$-0.514575\pi$
$787$	−26.1957	−	15.1241i	−0.933775	−	0.539115i	−0.888003	+	0.459837i	$0.847908\pi$
$788$	17.4528	−	10.0764i	0.621732	−	0.358957i
$789$		0			0
$790$	−10.1655	−	17.6071i	−0.361671	−	0.626433i
$791$	1.03867	+	0.599678i	0.0369309	+	0.0213221i
$792$		0			0
$793$	4.69654	+	12.1571i	0.166779	+	0.431710i
$794$	11.6223	−	20.1303i	0.412458	−	0.714399i
$795$		0			0
$796$	−64.8207			−2.29751
$797$	16.4758	−	28.5369i	0.583602	−	1.01083i	−0.411446	−	0.911434i	$-0.634976\pi$
$797$	16.4758	−	28.5369i	0.583602	−	1.01083i	0.995048	−	0.0993945i	$-0.0316906\pi$
$798$		0			0
$799$		−	59.9909i		−	2.12232i
$800$	34.2898	−	19.7972i	1.21233	−	0.699937i
$801$		0			0
$802$	28.4961	+	49.3567i	1.00623	+	1.74284i
$803$	−2.93058	−	5.07591i	−0.103418	−	0.179125i
$804$		0			0
$805$	1.00798	+	1.74587i	0.0355265	+	0.0615337i
$806$	34.6069	+	5.40528i	1.21897	+	0.190393i
$807$		0			0
$808$	107.228	−	61.9080i	3.77226	−	2.17792i
$809$	−25.6465	+	44.4211i	−0.901684	+	1.56176i	−0.0763761	+	0.997079i	$0.524335\pi$
$809$	−25.6465	+	44.4211i	−0.901684	+	1.56176i	−0.825308	+	0.564683i	$0.808998\pi$
$810$		0			0
$811$		−	51.3422i		−	1.80287i	−0.432915	−	0.901435i	$-0.642515\pi$
$811$		−	51.3422i		−	1.80287i	0.432915	−	0.901435i	$-0.357485\pi$
$812$		−	4.68546i		−	0.164427i
$813$		0			0
$814$	−7.88573	+	4.55283i	−0.276395	+	0.159577i
$815$	−17.5331	+	30.3683i	−0.614159	+	1.06376i
$816$		0			0
$817$	−1.56463	+	0.903342i	−0.0547396	+	0.0316039i
$818$	−94.0856			−3.28962
$819$		0			0
$820$	−104.847			−3.66141
$821$	3.33889	−	1.92771i	0.116528	−	0.0672774i	−0.440603	−	0.897702i	$-0.645235\pi$
$821$	3.33889	−	1.92771i	0.116528	−	0.0672774i	0.557131	+	0.830425i	$0.311902\pi$
$822$		0			0
$823$	20.9364	−	36.2628i	0.729796	−	1.26404i	−0.227174	−	0.973854i	$-0.572949\pi$
$823$	20.9364	−	36.2628i	0.729796	−	1.26404i	0.956969	−	0.290189i	$-0.0937181\pi$
$824$	−76.4845	+	44.1583i	−2.66446	+	1.53833i
$825$		0			0
$826$			7.71578i			0.268466i
$827$		−	33.2317i		−	1.15558i	−0.816185	−	0.577790i	$-0.803915\pi$
$827$		−	33.2317i		−	1.15558i	0.816185	−	0.577790i	$-0.196085\pi$
$828$		0			0
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	0.0698363	+	0.997558i	$0.477752\pi$
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	−0.898829	+	0.438299i	$0.855581\pi$
$830$	−53.4469	+	30.8576i	−1.85517	+	1.07108i
$831$		0			0
$832$	18.1282	+	46.9251i	0.628481	+	1.62683i
$833$	−25.3321	−	43.8765i	−0.877706	−	1.52023i
$834$		0			0
$835$	34.1449	+	59.1407i	1.18163	+	2.04665i
$836$	−2.02538	−	3.50805i	−0.0700491	−	0.121329i
$837$		0			0
$838$	−45.9909	+	26.5529i	−1.58873	+	0.917254i
$839$		−	15.8799i		−	0.548234i	−0.961696	−	0.274117i	$-0.911615\pi$
$839$		−	15.8799i		−	0.548234i	0.961696	−	0.274117i	$-0.0883855\pi$
$840$		0			0
$841$	8.14089	−	14.1004i	0.280720	−	0.486222i
$842$	−47.1332			−1.62432
$843$		0			0
$844$	43.2992	−	74.9965i	1.49042	−	2.58148i
$845$	−11.1289	+	34.7568i	−0.382846	+	1.19567i
$846$		0			0
$847$	1.93850	+	1.11920i	0.0666078	+	0.0384560i
$848$	26.3133	+	45.5760i	0.903602	+	1.56509i
$849$		0			0
$850$	48.3527	−	27.9165i	1.65848	−	0.957527i
$851$	−5.24606	−	3.02881i	−0.179833	−	0.103826i
$852$		0			0
$853$	35.9630	+	20.7633i	1.23135	+	0.710921i	0.967312	−	0.253591i	$-0.0816117\pi$
$853$	35.9630	+	20.7633i	1.23135	+	0.710921i	0.264040	+	0.964512i	$0.414945\pi$
$854$	−1.25158	−	2.16781i	−0.0428283	−	0.0741809i
$855$		0			0
$856$	8.29086	+	4.78673i	0.283376	+	0.163607i
$857$	−20.4844	+	35.4799i	−0.699732	+	1.21197i	0.268827	+	0.963188i	$0.413364\pi$
$857$	−20.4844	+	35.4799i	−0.699732	+	1.21197i	−0.968559	+	0.248783i	$0.919969\pi$
$858$		0			0
$859$	−14.2210	−	24.6315i	−0.485215	−	0.840417i	0.514641	−	0.857406i	$-0.327925\pi$
$859$	−14.2210	−	24.6315i	−0.485215	−	0.840417i	−0.999856	+	0.0169889i	$0.994592\pi$
$860$			49.3868i			1.68408i
$861$		0			0
$862$	−5.29603			−0.180383
$863$			24.5762i			0.836584i	0.908313	+	0.418292i	$0.137371\pi$
$863$			24.5762i			0.836584i	−0.908313	+	0.418292i	$0.862629\pi$
$864$		0			0
$865$	25.6403	−	14.8034i	0.871795	−	0.503331i
$866$	56.2424	+	32.4716i	1.91119	+	1.10343i
$867$		0			0
$868$	−4.81364			−0.163386
$869$			4.25744i			0.144424i
$870$		0			0
$871$	−27.6237	+	10.6716i	−0.935993	+	0.361595i
$872$	12.5519			0.425062
$873$		0			0
$874$	1.88311	−	3.26164i	0.0636970	−	0.110326i
$875$	1.55367			0.0525235
$876$		0			0
$877$	12.6543	+	7.30596i	0.427305	+	0.246705i	0.698198	−	0.715905i	$-0.253986\pi$
$877$	12.6543	+	7.30596i	0.427305	+	0.246705i	−0.270893	+	0.962610i	$0.587319\pi$
$878$	35.2024	+	20.3241i	1.18802	+	0.685906i
$879$		0			0
$880$	−49.2020			−1.65860
$881$	−1.19861	+	2.07605i	−0.0403820	+	0.0699438i	−0.885510	−	0.464620i	$-0.846191\pi$
$881$	−1.19861	+	2.07605i	−0.0403820	+	0.0699438i	0.845128	+	0.534564i	$0.179524\pi$
$882$		0			0
$883$	−5.90861			−0.198840			−0.0994202	−	0.995046i	$-0.531699\pi$
$883$	−5.90861			−0.198840			−0.0994202	+	0.995046i	$0.531699\pi$
$884$	47.7719	+	123.658i	1.60674	+	4.15908i
$885$		0			0
$886$		−	25.0971i		−	0.843153i
$887$	27.2603			0.915312			0.457656	−	0.889129i	$-0.348689\pi$
$887$	27.2603			0.915312			0.457656	+	0.889129i	$0.348689\pi$
$888$		0			0
$889$	−2.54384	−	1.46869i	−0.0853178	−	0.0492582i
$890$	−8.82292	+	5.09391i	−0.295745	+	0.170748i
$891$		0			0
$892$		−	47.4578i		−	1.58900i
$893$	4.24025			0.141895
$894$		0			0
$895$			19.9015i			0.665233i
$896$	−1.24155	−	2.15042i	−0.0414772	−	0.0718406i
$897$		0			0
$898$	−21.6281	+	37.4610i	−0.721739	+	1.25009i
$899$	11.3156	+	6.53308i	0.377397	+	0.217890i
$900$		0			0
$901$	17.1045	+	29.6259i	0.569834	+	0.986982i
$902$	26.5739	+	15.3424i	0.884813	+	0.510847i
$903$		0			0
$904$	−31.9542	−	18.4488i	−1.06278	−	0.613597i
$905$	38.2464	−	22.0816i	1.27135	−	0.734017i
$906$		0			0
$907$	−22.1251	−	38.3217i	−0.734651	−	1.27245i	−0.954876	−	0.297004i	$-0.904013\pi$
$907$	−22.1251	−	38.3217i	−0.734651	−	1.27245i	0.220226	−	0.975449i	$-0.429321\pi$
$908$	79.9741	+	46.1730i	2.65403	+	1.53231i
$909$		0			0
$910$	1.08171	−	6.92557i	0.0358584	−	0.229580i
$911$	6.61845	−	11.4635i	0.219279	−	0.379802i	−0.735309	−	0.677732i	$-0.762963\pi$
$911$	6.61845	−	11.4635i	0.219279	−	0.379802i	0.954588	+	0.297930i	$0.0962962\pi$
$912$		0			0
$913$	12.9236			0.427708
$914$	2.86553	−	4.96325i	0.0947834	−	0.164170i
$915$		0			0
$916$			65.9135i			2.17784i
$917$	0.873163	−	0.504121i	0.0288344	−	0.0166475i
$918$		0			0
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	−0.965103	−	0.261869i	$-0.915661\pi$
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	0.255767	−	0.966739i	$-0.417672\pi$
$920$	−31.0099	−	53.7107i	−1.02237	−	1.77079i
$921$		0			0
$922$	−4.06468	−	7.04023i	−0.133863	−	0.231858i
$923$	−17.5164	−	14.1226i	−0.576561	−	0.464850i
$924$		0			0
$925$	5.49699	−	3.17369i	0.180740	−	0.104350i
$926$	−21.1538	+	36.6394i	−0.695156	+	1.20404i
$927$		0			0
$928$			49.0121i			1.60890i
$929$			6.38535i			0.209497i	0.994499	+	0.104748i	$0.0334037\pi$
$929$			6.38535i			0.209497i	−0.994499	+	0.104748i	$0.966596\pi$
$930$		0			0
$931$	3.10126	−	1.79052i	0.101640	−	0.0586818i
$932$	−12.1784	+	21.0937i	−0.398918	+	0.690947i
$933$		0			0
$934$	7.24252	−	4.18147i	0.236983	−	0.136822i
$935$	−31.9830			−1.04596
$936$		0			0
$937$	58.7846			1.92041			0.960204	−	0.279298i	$-0.0901018\pi$
$937$	58.7846			1.92041			0.960204	+	0.279298i	$0.0901018\pi$
$938$	4.92577	−	2.84389i	0.160832	−	0.0928564i
$939$		0			0
$940$	57.9550	−	100.381i	1.89028	−	3.27407i
$941$	46.2325	−	26.6923i	1.50714	−	0.870145i	0.507170	−	0.861846i	$-0.330692\pi$
$941$	46.2325	−	26.6923i	1.50714	−	0.870145i	0.999966	−	0.00829925i	$-0.00264176\pi$
$942$		0			0
$943$			20.4134i			0.664752i
$944$		−	125.278i		−	4.07744i
$945$		0			0
$946$	7.22687	−	12.5173i	0.234966	−	0.406973i
$947$	−3.24038	+	1.87083i	−0.105298	+	0.0607940i	−0.551724	−	0.834027i	$-0.686030\pi$
$947$	−3.24038	+	1.87083i	−0.105298	+	0.0607940i	0.446426	+	0.894821i	$0.352697\pi$
$948$		0			0
$949$	−12.6467	+	4.88570i	−0.410530	+	0.158597i
$950$	1.97318	+	3.41765i	0.0640184	+	0.110883i
$951$		0			0
$952$	−7.66922	−	13.2835i	−0.248561	−	0.430520i
$953$	−11.2711	−	19.5221i	−0.365107	−	0.632384i	0.623686	−	0.781675i	$-0.285634\pi$
$953$	−11.2711	−	19.5221i	−0.365107	−	0.632384i	−0.988793	+	0.149291i	$0.952301\pi$
$954$		0			0
$955$	−19.7458	+	11.4003i	−0.638960	+	0.368904i
$956$			79.3762i			2.56721i
$957$		0			0
$958$	−13.1736	+	22.8173i	−0.425619	+	0.737194i
$959$	−0.582669			−0.0188154
$960$		0			0
$961$	−8.78819	+	15.2216i	−0.283490	+	0.491019i
$962$	7.59023	+	19.6474i	0.244719	+	0.633458i
$963$		0			0
$964$	70.9518	+	40.9640i	2.28520	+	1.31936i
$965$	−10.8193	−	18.7395i	−0.348285	−	0.603247i
$966$		0			0
$967$	1.37859	−	0.795929i	0.0443325	−	0.0255954i	−0.477670	−	0.878539i	$-0.658519\pi$
$967$	1.37859	−	0.795929i	0.0443325	−	0.0255954i	0.522002	+	0.852944i	$0.325185\pi$
$968$	−59.6371	−	34.4315i	−1.91681	−	1.10667i
$969$		0			0
$970$	−87.3006	−	50.4030i	−2.80305	−	1.61834i
$971$	2.45081	+	4.24492i	0.0786501	+	0.136226i	0.902668	−	0.430338i	$-0.141606\pi$
$971$	2.45081	+	4.24492i	0.0786501	+	0.136226i	−0.824018	+	0.566564i	$0.808272\pi$
$972$		0			0
$973$	3.67458	+	2.12152i	0.117802	+	0.0680128i
$974$	30.6544	−	53.0950i	0.982231	−	1.70127i
$975$		0			0
$976$	20.3214	+	35.1977i	0.650473	+	1.12665i
$977$			3.86735i			0.123727i	0.998085	+	0.0618637i	$0.0197044\pi$
$977$			3.86735i			0.123727i	−0.998085	+	0.0618637i	$0.980296\pi$
$978$		0			0
$979$	2.13340			0.0681838
$980$		−	97.8897i		−	3.12697i
$981$		0			0
$982$	68.2114	−	39.3819i	2.17671	−	1.25673i
$983$	−45.0382	−	26.0028i	−1.43650	−	0.829361i	−0.438891	−	0.898540i	$-0.644629\pi$
$983$	−45.0382	−	26.0028i	−1.43650	−	0.829361i	−0.997604	+	0.0691791i	$0.977962\pi$
$984$		0			0
$985$	11.2467			0.358350
$986$			69.1129i			2.20100i
$987$		0			0
$988$	−8.74037	+	3.37660i	−0.278068	+	0.107424i
$989$	9.61549			0.305755
$990$		0			0
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	−0.793759	−	0.608233i	$-0.791879\pi$
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	0.923624	+	0.383299i	$0.125212\pi$
$992$	50.3529			1.59871
$993$		0			0
$994$	3.74264	+	2.16081i	0.118709	+	0.0685369i
$995$	−31.3281	−	18.0873i	−0.993167	−	0.573406i
$996$		0			0
$997$	30.4678			0.964926			0.482463	−	0.875916i	$-0.339742\pi$
$997$	30.4678			0.964926			0.482463	+	0.875916i	$0.339742\pi$
$998$	49.7435	−	86.1583i	1.57460	−	2.72729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.r.b.316.1		22
3.2	odd	2		117.2.r.b.43.11	yes	22
9.4	even	3		351.2.l.b.199.1		22
9.5	odd	6		117.2.l.b.4.11	✓	22
13.10	even	6		351.2.l.b.127.11		22
39.23	odd	6		117.2.l.b.88.1	yes	22
117.23	odd	6		117.2.r.b.49.11	yes	22
117.49	even	6	inner	351.2.r.b.10.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.11	✓	22	9.5	odd	6
117.2.l.b.88.1	yes	22	39.23	odd	6
117.2.r.b.43.11	yes	22	3.2	odd	2
117.2.r.b.49.11	yes	22	117.23	odd	6
351.2.l.b.127.11		22	13.10	even	6
351.2.l.b.199.1		22	9.4	even	3
351.2.r.b.10.1		22	117.49	even	6	inner
351.2.r.b.316.1		22	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.29626 + 1.32574i) q^{2} +(2.51519 - 4.35644i) q^{4} +(2.43120 - 1.40366i) q^{5} -0.261179i q^{7} +8.03502i q^{8} +(-3.72178 + 6.44631i) q^{10} +(1.34990 - 0.779366i) q^{11} +(-1.29932 - 3.36330i) q^{13} +(0.346256 + 0.599733i) q^{14} +(-5.62200 - 9.73759i) q^{16} +(-3.65449 - 6.32976i) q^{17} +(0.447398 - 0.258305i) q^{19} -14.1219i q^{20} +(-2.06648 + 3.57925i) q^{22} -2.74949 q^{23} +(1.44050 - 2.49502i) q^{25} +(7.44243 + 6.00043i) q^{26} +(-1.13781 - 0.656914i) q^{28} +(1.78313 + 3.08847i) q^{29} +(3.17297 - 1.83191i) q^{31} +(11.9020 + 6.87163i) q^{32} +(16.7833 + 9.68983i) q^{34} +(-0.366605 - 0.634978i) q^{35} +(1.90801 + 1.10159i) q^{37} +(-0.684893 + 1.18627i) q^{38} +(11.2784 + 19.5348i) q^{40} -7.42443i q^{41} -3.49719 q^{43} -7.84102i q^{44} +(6.31353 - 3.64512i) q^{46} +(7.10819 + 4.10392i) q^{47} +6.93179 q^{49} +7.63895i q^{50} +(-17.9200 - 2.79895i) q^{52} -4.68042 q^{53} +(2.18792 - 3.78960i) q^{55} +2.09858 q^{56} +(-8.18905 - 4.72795i) q^{58} +(9.64903 + 5.57087i) q^{59} -3.61462 q^{61} +(-4.85729 + 8.41308i) q^{62} -13.9521 q^{64} +(-7.87982 - 6.35307i) q^{65} -8.21327i q^{67} -36.7670 q^{68} +(1.68364 + 0.972048i) q^{70} +(5.40445 - 3.12026i) q^{71} -3.76021i q^{73} -5.84171 q^{74} -2.59875i q^{76} +(-0.203554 - 0.352565i) q^{77} +(-1.36567 + 2.36542i) q^{79} +(-27.3365 - 15.7827i) q^{80} +(9.84289 + 17.0484i) q^{82} +(7.18029 + 4.14554i) q^{83} +(-17.7696 - 10.2593i) q^{85} +(8.03044 - 4.63638i) q^{86} +(6.26222 + 10.8465i) q^{88} +(1.18531 + 0.684339i) q^{89} +(-0.878421 + 0.339353i) q^{91} +(-6.91550 + 11.9780i) q^{92} -21.7630 q^{94} +(0.725143 - 1.25599i) q^{95} +13.5427i q^{97} +(-15.9171 + 9.18977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) \) 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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