LMFDB - Embedded newform 351.2.r.b.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(10,351)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			10.1
Character	$\chi$	$=$	351.10
Dual form			351.2.r.b.316.1

$q$-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 $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.985919	−	0.167222i	$-0.946520\pi$
$2$	−2.29626	−	1.32574i	−1.62370	−	0.937442i	−0.637778	−	0.770220i	$-0.720146\pi$
$3$		0			0
$3$		0			0
$4$	2.51519	+	4.35644i	1.25760	+	2.17822i
$5$	2.43120	+	1.40366i	1.08727	+	0.627734i	0.932848	−	0.360271i	$-0.117316\pi$
$5$	2.43120	+	1.40366i	1.08727	+	0.627734i	0.154420	+	0.988005i	$0.450649\pi$
$6$		0			0
$7$			0.261179i			0.0987162i	0.998781	+	0.0493581i	$0.0157176\pi$
$7$			0.261179i			0.0987162i	−0.998781	+	0.0493581i	$0.984282\pi$
$8$		−	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	0.689504	−	0.724281i	$-0.257828\pi$
$11$	1.34990	+	0.779366i	0.407011	+	0.234988i	−0.282494	+	0.959269i	$0.591162\pi$
$12$		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	−0.0421777	+	0.999110i	$0.513430\pi$
$17$	−3.65449	+	6.32976i	−0.886344	+	1.53519i	−0.844166	+	0.536082i	$0.819904\pi$
$18$		0			0
$19$	0.447398	+	0.258305i	0.102640	+	0.0592593i	0.550441	−	0.834874i	$-0.314459\pi$
$19$	0.447398	+	0.258305i	0.102640	+	0.0592593i	−0.447801	+	0.894133i	$0.647793\pi$
$20$			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	−0.651612	−	0.758552i	$-0.725907\pi$
$29$	1.78313	−	3.08847i	0.331119	−	0.573515i	0.982732	+	0.185037i	$0.0592405\pi$
$30$		0			0
$31$	3.17297	+	1.83191i	0.569882	+	0.329021i	0.757102	−	0.653297i	$-0.226615\pi$
$31$	3.17297	+	1.83191i	0.569882	+	0.329021i	−0.187221	+	0.982318i	$0.559948\pi$
$32$	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	−0.334895	−	0.942256i	$-0.608701\pi$
$37$	1.90801	−	1.10159i	0.313675	−	0.181100i	0.648570	+	0.761155i	$0.275367\pi$
$38$	−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	$0.196850\pi$
$41$			7.42443i			1.15950i	−0.814794	+	0.579751i	$0.803150\pi$
$42$		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	0.117901	−	0.993025i	$-0.462383\pi$
$47$	7.10819	−	4.10392i	1.03684	−	0.598618i	0.918936	+	0.394407i	$0.129050\pi$
$48$		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	0.283864	−	0.958865i	$-0.408384\pi$
$59$	9.64903	−	5.57087i	1.25620	−	0.725265i	0.972333	+	0.233599i	$0.0750504\pi$
$60$		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	$0.167294\pi$
$67$			8.21327i			1.00341i	−0.865038	+	0.501706i	$0.832706\pi$
$68$	−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	0.785150	−	0.619306i	$-0.212586\pi$
$71$	5.40445	+	3.12026i	0.641390	+	0.370307i	−0.143760	+	0.989613i	$0.545919\pi$
$72$		0			0
$73$			3.76021i			0.440099i	0.975489	+	0.220050i	$0.0706220\pi$
$73$			3.76021i			0.440099i	−0.975489	+	0.220050i	$0.929378\pi$
$74$	−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	0.778916	−	0.627128i	$-0.215770\pi$
$79$	−1.36567	−	2.36542i	−0.153650	−	0.266130i	−0.932567	+	0.360998i	$0.882436\pi$
$80$	−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	−0.0511680	−	0.998690i	$-0.516294\pi$
$83$	7.18029	−	4.14554i	0.788139	−	0.455032i	0.839307	+	0.543658i	$0.182961\pi$
$84$		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	−0.435861	−	0.900014i	$-0.643556\pi$
$89$	1.18531	−	0.684339i	0.125643	−	0.0725398i	0.561504	+	0.827474i	$0.310223\pi$
$90$		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	$-0.758696\pi$
$97$		−	13.5427i		−	1.37506i	0.726158	−	0.687528i	$-0.241304\pi$
$98$	−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	0.172715	+	0.984972i	$0.444746\pi$
$101$	−7.70477	+	13.3451i	−0.766653	+	1.32788i	−0.939368	+	0.342911i	$0.888587\pi$
$102$		0			0
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	−0.457307	−	0.889309i	$-0.651186\pi$
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	0.998818	−	0.0486148i	$-0.0154807\pi$
$104$	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	0.893384	−	0.449294i	$-0.148325\pi$
$107$	0.595733	+	1.03184i	0.0575917	+	0.0997518i	−0.835792	+	0.549046i	$0.814991\pi$
$108$		0			0
$109$			1.56215i			0.149627i	0.997198	+	0.0748135i	$0.0238362\pi$
$109$			1.56215i			0.149627i	−0.997198	+	0.0748135i	$0.976164\pi$
$110$		−	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	0.737586	−	0.675254i	$-0.235966\pi$
$113$	−2.29605	−	3.97687i	−0.215994	−	0.374112i	−0.953580	+	0.301141i	$0.902632\pi$
$114$		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	0.999999	−	0.00116769i	$-0.000371687\pi$
$127$	5.62331	+	9.73987i	0.498988	+	0.864273i	−0.501011	+	0.865441i	$0.667038\pi$
$128$	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	−0.769302	−	0.638886i	$-0.779396\pi$
$131$	1.93018	−	3.34317i	0.168640	−	0.292094i	0.937942	+	0.346792i	$0.112729\pi$
$132$		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	$0.0303811\pi$
$137$			2.23092i			0.190600i	−0.995449	+	0.0953002i	$0.969619\pi$
$138$		0			0
$139$	−8.12287	−	14.0692i	−0.688973	−	1.19334i	−0.972170	−	0.234275i	$-0.924729\pi$
$139$	−8.12287	−	14.0692i	−0.688973	−	1.19334i	0.283197	−	0.959062i	$-0.408605\pi$
$140$	−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	−0.745802	−	0.666167i	$-0.767934\pi$
$149$	−6.61334	+	3.81821i	−0.541786	+	0.312800i	0.204017	+	0.978967i	$0.434600\pi$
$150$		0			0
$151$	10.8516	−	6.26520i	0.883095	−	0.509855i	0.0114171	−	0.999935i	$-0.496366\pi$
$151$	10.8516	−	6.26520i	0.883095	−	0.509855i	0.871677	+	0.490080i	$0.163032\pi$
$152$	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	−0.994017	−	0.109224i	$-0.965164\pi$
$157$	−5.04228	+	8.73349i	−0.402418	+	0.697009i	0.591599	+	0.806232i	$0.298497\pi$
$158$			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	0.0124407	−	0.999923i	$-0.496040\pi$
$163$	−10.8176	−	6.24553i	−0.847297	−	0.489187i	−0.859738	+	0.510735i	$0.829373\pi$
$164$	−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	$-0.609710\pi$
$167$		−	24.3257i		−	1.88238i	0.337882	−	0.941189i	$-0.390290\pi$
$168$		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	0.702612	−	0.711573i	$-0.252017\pi$
$179$	−3.54457	−	6.13938i	−0.264934	−	0.458879i	−0.967546	+	0.252694i	$0.918683\pi$
$180$		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	$0.0894774\pi$
$193$			7.70792i			0.554828i	−0.960750	+	0.277414i	$0.910523\pi$
$194$	−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	−0.371287	−	0.928518i	$-0.621083\pi$
$197$	3.46949	−	2.00311i	0.247191	−	0.142716i	0.618477	+	0.785803i	$0.287750\pi$
$198$		0			0
$199$	−6.44292	+	11.1595i	−0.456726	+	0.791073i	−0.998786	−	0.0492670i	$-0.984311\pi$
$199$	−6.44292	+	11.1595i	−0.456726	+	0.791073i	0.542059	+	0.840340i	$0.317645\pi$
$200$	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	0.747961	−	0.663743i	$-0.231033\pi$
$223$	8.17028	+	4.71711i	0.547122	+	0.315881i	−0.200838	+	0.979624i	$0.564367\pi$
$224$	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	$-0.791482\pi$
$227$		−	18.3577i		−	1.21844i	0.793001	−	0.609220i	$-0.208518\pi$
$228$		0			0
$229$	−11.3476	−	6.55153i	−0.749870	−	0.432937i	0.0757771	−	0.997125i	$-0.475856\pi$
$229$	−11.3476	−	6.55153i	−0.749870	−	0.432937i	−0.825647	+	0.564187i	$0.809190\pi$
$230$	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	−0.0119822	−	0.999928i	$-0.503814\pi$
$239$	−13.6653	−	7.88968i	−0.883936	−	0.510341i	−0.871954	+	0.489587i	$0.837147\pi$
$240$		0			0
$241$		−	16.2866i		−	1.04911i	−0.851375	−	0.524557i	$-0.824231\pi$
$241$		−	16.2866i		−	1.04911i	0.851375	−	0.524557i	$-0.175769\pi$
$242$			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	−0.00198652	+	0.999998i	$0.500632\pi$
$251$	−13.7361	+	23.7917i	−0.867017	+	1.50172i	−0.865030	+	0.501719i	$0.832701\pi$
$252$		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	−0.251941	−	0.967743i	$-0.581069\pi$
$263$	11.5486	−	20.0028i	0.712119	−	1.23343i	0.964060	−	0.265684i	$-0.0855977\pi$
$264$		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	−0.321008	−	0.947076i	$-0.604022\pi$
$269$	10.8197	−	18.7403i	0.659688	−	1.14261i	0.980696	−	0.195537i	$-0.0626450\pi$
$270$		0			0
$271$	−23.0990	+	13.3362i	−1.40316	+	0.810116i	−0.994716	−	0.102666i	$-0.967263\pi$
$271$	−23.0990	+	13.3362i	−1.40316	+	0.810116i	−0.408447	+	0.912782i	$0.633929\pi$
$272$	−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	−0.463035	−	0.886340i	$-0.653240\pi$
$281$	1.22438	−	0.706894i	0.0730402	−	0.0421698i	0.536075	+	0.844170i	$0.319906\pi$
$282$		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	−0.412265	−	0.911064i	$-0.635262\pi$
$293$	2.92034	−	1.68606i	0.170608	−	0.0985005i	0.582872	+	0.812564i	$0.301929\pi$
$294$		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	$-0.798830\pi$
$307$		−	20.7017i		−	1.18151i	0.806851	−	0.590756i	$-0.201170\pi$
$308$	−2.04791			−0.116690
$309$		0			0
$310$		−	27.2719i		−	1.54894i
$311$	−4.13884	+	7.16868i	−0.234692	+	0.406499i	−0.959183	−	0.282786i	$-0.908742\pi$
$311$	−4.13884	+	7.16868i	−0.234692	+	0.406499i	0.724491	+	0.689284i	$0.242075\pi$
$312$		0			0
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	0.986232	−	0.165369i	$-0.0528814\pi$
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	−0.636329	+	0.771417i	$0.719548\pi$
$314$	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	−0.606006	+	0.795460i	$0.707229\pi$
$317$	−28.4498	+	16.4255i	−1.59790	+	0.922547i	−0.991892	+	0.127087i	$0.959437\pi$
$318$		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	$0.124579\pi$
$331$			13.8802i			0.762922i	−0.924385	+	0.381461i	$0.875421\pi$
$332$	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	0.301706	+	0.953401i	$0.402444\pi$
$337$	−12.3880	+	21.4566i	−0.674816	+	1.16882i	−0.976522	+	0.215415i	$0.930889\pi$
$338$	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	0.999911	+	0.0133374i	$0.00424556\pi$
$347$	9.52830	+	16.5035i	0.511506	+	0.885955i	−0.488405	+	0.872617i	$0.662421\pi$
$348$		0			0
$349$	20.5588	+	11.8696i	1.10049	+	0.635367i	0.936349	−	0.351070i	$-0.114182\pi$
$349$	20.5588	+	11.8696i	1.10049	+	0.635367i	0.164139	+	0.986437i	$0.447516\pi$
$350$	1.99513			0.106644
$351$		0			0
$352$	21.4221			1.14180
$353$	1.89779	+	1.09569i	0.101009	+	0.0583176i	0.549654	−	0.835393i	$-0.314760\pi$
$353$	1.89779	+	1.09569i	0.101009	+	0.0583176i	−0.448644	+	0.893710i	$0.648093\pi$
$354$		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	$-0.952922\pi$
$359$		−	5.58420i		−	0.294723i	0.989083	−	0.147361i	$-0.0470780\pi$
$360$		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	−0.636952	−	0.770903i	$-0.719805\pi$
$367$	6.68867	−	11.5851i	0.349146	−	0.604738i	0.986098	+	0.166165i	$0.0531384\pi$
$368$	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	0.746866	−	0.664974i	$-0.231558\pi$
$373$	−3.90999	−	6.77230i	−0.202451	−	0.350656i	−0.949318	+	0.314318i	$0.898224\pi$
$374$	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	0.744561	−	0.667554i	$-0.232659\pi$
$379$	32.9974	−	19.0510i	1.69496	−	0.978586i	0.950399	−	0.311032i	$-0.100675\pi$
$380$	−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	−0.0515506	−	0.998670i	$-0.516416\pi$
$383$	15.4126	−	8.89848i	0.787548	−	0.454691i	0.839099	+	0.543979i	$0.183083\pi$
$384$		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	0.856644	+	0.515909i	$0.172546\pi$
$389$	17.2599	+	29.8950i	0.875112	+	1.51574i	0.0184682	+	0.999829i	$0.494121\pi$
$390$		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	0.297233	−	0.954805i	$-0.403936\pi$
$397$	−7.59209	−	4.38329i	−0.381036	−	0.219991i	−0.678269	+	0.734814i	$0.737270\pi$
$398$	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	$0.180325\pi$
$401$			21.4944i			1.07338i	−0.843780	+	0.536690i	$0.819675\pi$
$402$		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	0.519770	−	0.854306i	$-0.326018\pi$
$409$	30.7301	−	17.7420i	1.51951	−	0.877287i	0.999736	−	0.0229809i	$-0.00731570\pi$
$410$	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	−0.0755111	−	0.997145i	$-0.524059\pi$
$421$	15.3946	−	8.88807i	0.750286	−	0.433178i	0.825797	+	0.563967i	$0.190725\pi$
$422$	−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	−0.457761	−	0.889075i	$-0.651348\pi$
$431$	1.72978	−	0.998690i	0.0833206	−	0.0481052i	0.541081	+	0.840970i	$0.318015\pi$
$432$		0			0
$433$	−12.2465	+	21.2116i	−0.588532	+	1.01937i	0.405893	+	0.913920i	$0.366960\pi$
$433$	−12.2465	+	21.2116i	−0.588532	+	1.01937i	−0.994425	+	0.105446i	$0.966373\pi$
$434$	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	−0.988910	−	0.148513i	$-0.952551\pi$
$439$	−7.66518	+	13.2765i	−0.365839	+	0.633652i	0.623071	+	0.782165i	$0.285885\pi$
$440$	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	0.731421	−	0.681926i	$-0.238857\pi$
$443$	−4.73265	−	8.19718i	−0.224855	−	0.389460i	−0.956276	+	0.292466i	$0.905524\pi$
$444$		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	0.794846	−	0.606811i	$-0.207552\pi$
$449$	14.1283	+	8.15697i	0.666755	+	0.384951i	−0.128091	+	0.991762i	$0.540885\pi$
$450$		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	0.455579	−	0.890195i	$-0.349432\pi$
$457$	−1.87187	−	1.08073i	−0.0875626	−	0.0505543i	−0.543142	+	0.839641i	$0.682765\pi$
$458$	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	$-0.977254\pi$
$461$		−	3.06596i		−	0.142796i	0.997448	−	0.0713980i	$-0.0227460\pi$
$462$		0			0
$463$	13.8184	+	7.97807i	0.642197	+	0.370772i	0.785460	−	0.618912i	$-0.212426\pi$
$463$	13.8184	+	7.97807i	0.642197	+	0.370772i	−0.143264	+	0.989685i	$0.545760\pi$
$464$	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	0.683543	−	0.729910i	$-0.260438\pi$
$479$	8.60548	+	4.96837i	0.393194	+	0.227011i	−0.290349	+	0.956921i	$0.593771\pi$
$480$		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	−0.0278074	−	0.999613i	$-0.508853\pi$
$487$	−20.0246	−	11.5612i	−0.907402	−	0.523889i	−0.879594	+	0.475725i	$0.842186\pi$
$488$			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	−0.455907	−	0.890027i	$-0.650685\pi$
$499$	−32.4943	−	18.7606i	−1.45465	−	0.839841i	−0.998740	+	0.0501867i	$0.984018\pi$
$500$	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	0.336891	+	0.941544i	$0.390625\pi$
$503$	−14.5097	+	25.1315i	−0.646956	+	1.12056i	−0.983846	+	0.179016i	$0.942709\pi$
$504$		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	$0.0584651\pi$
$509$			8.24121i			0.365285i	−0.983179	+	0.182643i	$0.941535\pi$
$510$		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	0.830528	−	0.556977i	$-0.188039\pi$
$523$	−1.53435	−	2.65756i	−0.0670922	−	0.116207i	−0.897620	+	0.440770i	$0.854706\pi$
$524$	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	$-0.950120\pi$
$541$		−	7.25981i		−	0.312124i	0.987747	−	0.156062i	$-0.0498799\pi$
$542$	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	−0.998394	−	0.0566482i	$-0.981959\pi$
$547$	−12.8226	−	22.2094i	−0.548256	−	0.949607i	0.450138	−	0.892959i	$-0.351375\pi$
$548$	−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	−0.332744	−	0.943017i	$-0.607975\pi$
$557$	7.49468	−	4.32706i	0.317560	−	0.183343i	0.650304	+	0.759674i	$0.274641\pi$
$558$		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	−0.690493	−	0.723339i	$-0.742606\pi$
$563$	−23.0556	−	39.9334i	−0.971677	−	1.68299i	−0.281184	−	0.959654i	$-0.590727\pi$
$564$		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	−0.626966	−	0.779047i	$-0.715704\pi$
$569$	8.61575	−	14.9229i	0.361191	−	0.625601i	0.988157	+	0.153445i	$0.0490369\pi$
$570$		0			0
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	−0.547692	−	0.836680i	$-0.684493\pi$
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	0.998432	+	0.0559746i	$0.0178266\pi$
$572$	−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	$0.136228\pi$
$577$			19.9386i			0.830056i	−0.909809	+	0.415028i	$0.863772\pi$
$578$			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	0.766261	−	0.642529i	$-0.222115\pi$
$587$	14.3659	+	8.29416i	0.592945	+	0.342337i	−0.173316	+	0.984866i	$0.555448\pi$
$588$		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	$-0.896966\pi$
$593$		−	15.4909i		−	0.636137i	0.948068	−	0.318068i	$-0.103034\pi$
$594$		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	−0.248913	−	0.968526i	$-0.580073\pi$
$599$	17.4824	−	30.2804i	0.714312	−	1.23722i	0.963224	−	0.268698i	$-0.0865934\pi$
$600$		0			0
$601$	−14.3337	+	24.8266i	−0.584682	+	1.01270i	0.410233	+	0.911981i	$0.365447\pi$
$601$	−14.3337	+	24.8266i	−0.584682	+	1.01270i	−0.994915	+	0.100718i	$0.967886\pi$
$602$	−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	0.652303	−	0.757958i	$-0.273803\pi$
$607$	−8.13672	−	14.0932i	−0.330259	−	0.572026i	−0.982563	+	0.185932i	$0.940470\pi$
$608$	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	−0.818179	−	0.574964i	$-0.805016\pi$
$613$	−18.0575	+	10.4255i	−0.729336	+	0.421082i	0.0888435	+	0.996046i	$0.471683\pi$
$614$	−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	−0.152837	−	0.988251i	$-0.548841\pi$
$617$	15.5643	−	8.98605i	0.626595	−	0.361765i	0.779432	+	0.626487i	$0.215508\pi$
$618$		0			0
$619$	−6.56515	+	3.79039i	−0.263876	+	0.152349i	−0.626101	−	0.779742i	$-0.715350\pi$
$619$	−6.56515	+	3.79039i	−0.263876	+	0.152349i	0.362226	+	0.932090i	$0.382017\pi$
$620$	−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	0.718758	−	0.695260i	$-0.244711\pi$
$631$	11.9576	+	6.90373i	0.476025	+	0.274833i	−0.242734	+	0.970093i	$0.578044\pi$
$632$	−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	−0.645991	−	0.763345i	$-0.723556\pi$
$643$	−7.80782	+	4.50785i	−0.307910	+	0.177772i	0.338081	+	0.941117i	$0.390222\pi$
$644$	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	0.820714	−	0.571339i	$-0.193576\pi$
$647$	−2.14777	−	3.72004i	−0.0844374	−	0.146250i	−0.905151	+	0.425089i	$0.860243\pi$
$648$		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	$0.225979\pi$
$661$			33.5146i			1.30357i	−0.758405	+	0.651783i	$0.774021\pi$
$662$	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	−0.998134	−	0.0610643i	$-0.980551\pi$
$673$	−11.5750	+	20.0485i	−0.446184	+	0.772813i	0.551950	+	0.833877i	$0.313884\pi$
$674$	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	0.981434	−	0.191803i	$-0.0614333\pi$
$677$	8.44612	+	14.6291i	0.324611	+	0.562243i	−0.656823	+	0.754045i	$0.728100\pi$
$678$		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	0.823047	−	0.567973i	$-0.192272\pi$
$683$	19.4097	+	11.2062i	0.742692	+	0.428793i	−0.0803552	+	0.996766i	$0.525605\pi$
$684$		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	0.00149829	−	0.999999i	$-0.499523\pi$
$691$	−22.7060	−	13.1093i	−0.863777	−	0.498702i	−0.865275	+	0.501297i	$0.832856\pi$
$692$	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	$-0.817274\pi$
$709$		−	28.9190i		−	1.08608i	0.839708	−	0.543038i	$-0.182726\pi$
$710$		−	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	−0.750429	−	0.660951i	$-0.770153\pi$
$719$	5.28737	−	9.15800i	0.197186	−	0.341536i	0.947615	+	0.319415i	$0.103486\pi$
$720$		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	0.760290	−	0.649584i	$-0.225057\pi$
$727$	−4.91833	−	8.51880i	−0.182411	−	0.315945i	−0.942701	+	0.333639i	$0.891723\pi$
$728$	−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	0.995515	+	0.0946033i	$0.0301583\pi$
$733$	42.6470	+	24.6222i	1.57520	+	0.909443i	0.579686	+	0.814840i	$0.303175\pi$
$734$	−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	−0.358530	−	0.933518i	$-0.616722\pi$
$739$	7.35764	−	4.24793i	0.270655	−	0.156263i	0.629185	+	0.777255i	$0.283389\pi$
$740$	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	$0.167220\pi$
$743$			27.3401i			1.00301i	−0.865154	+	0.501506i	$0.832780\pi$
$744$		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	0.974698	+	0.223525i	$0.0717566\pi$
$757$	18.7348	+	32.4496i	0.680928	+	1.17940i	−0.293770	+	0.955876i	$0.594910\pi$
$758$	−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	−0.763792	−	0.645462i	$-0.776665\pi$
$761$	−16.1849	+	9.34435i	−0.586702	+	0.338732i	0.177091	+	0.984195i	$0.443331\pi$
$762$		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	$-0.699590\pi$
$769$		−	44.9114i		−	1.61955i	0.586744	−	0.809773i	$-0.300410\pi$
$770$	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	0.449335	−	0.893363i	$-0.351661\pi$
$773$	−2.77119	−	1.59995i	−0.0996728	−	0.0575461i	−0.549008	+	0.835817i	$0.684994\pi$
$774$		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	−0.888003	−	0.459837i	$-0.847908\pi$
$787$	−26.1957	+	15.1241i	−0.933775	+	0.539115i	−0.0457713	+	0.998952i	$0.514575\pi$
$788$	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	0.995048	+	0.0993945i	$0.0316906\pi$
$797$	16.4758	+	28.5369i	0.583602	+	1.01083i	−0.411446	+	0.911434i	$0.634976\pi$
$798$		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	−0.825308	−	0.564683i	$-0.808998\pi$
$809$	−25.6465	−	44.4211i	−0.901684	−	1.56176i	−0.0763761	−	0.997079i	$-0.524335\pi$
$810$		0			0
$811$			51.3422i			1.80287i	0.432915	+	0.901435i	$0.357485\pi$
$811$			51.3422i			1.80287i	−0.432915	+	0.901435i	$0.642515\pi$
$812$			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	0.557131	−	0.830425i	$-0.311902\pi$
$821$	3.33889	+	1.92771i	0.116528	+	0.0672774i	−0.440603	+	0.897702i	$0.645235\pi$
$822$		0			0
$823$	20.9364	+	36.2628i	0.729796	+	1.26404i	0.956969	+	0.290189i	$0.0937181\pi$
$823$	20.9364	+	36.2628i	0.729796	+	1.26404i	−0.227174	+	0.973854i	$0.572949\pi$
$824$	−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	$0.196085\pi$
$827$			33.2317i			1.15558i	−0.816185	+	0.577790i	$0.803915\pi$
$828$		0			0
$829$	−23.8687	−	41.3417i	−0.828993	−	1.43586i	−0.898829	−	0.438299i	$-0.855581\pi$
$829$	−23.8687	−	41.3417i	−0.828993	−	1.43586i	0.0698363	−	0.997558i	$-0.477752\pi$
$830$	−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	$0.0883855\pi$
$839$			15.8799i			0.548234i	−0.961696	+	0.274117i	$0.911615\pi$
$840$		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	0.264040	−	0.964512i	$-0.414945\pi$
$853$	35.9630	−	20.7633i	1.23135	−	0.710921i	0.967312	+	0.253591i	$0.0816117\pi$
$854$	−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	−0.968559	−	0.248783i	$-0.919969\pi$
$857$	−20.4844	−	35.4799i	−0.699732	−	1.21197i	0.268827	−	0.963188i	$-0.413364\pi$
$858$		0			0
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	−0.999856	−	0.0169889i	$-0.994592\pi$
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	0.514641	+	0.857406i	$0.327925\pi$
$860$		−	49.3868i		−	1.68408i
$861$		0			0
$862$	−5.29603			−0.180383
$863$		−	24.5762i		−	0.836584i	−0.908313	−	0.418292i	$-0.862629\pi$
$863$		−	24.5762i		−	0.836584i	0.908313	−	0.418292i	$-0.137371\pi$
$864$		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	−0.270893	−	0.962610i	$-0.587319\pi$
$877$	12.6543	−	7.30596i	0.427305	−	0.246705i	0.698198	+	0.715905i	$0.253986\pi$
$878$	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	0.845128	−	0.534564i	$-0.179524\pi$
$881$	−1.19861	−	2.07605i	−0.0403820	−	0.0699438i	−0.885510	+	0.464620i	$0.846191\pi$
$882$		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	0.220226	+	0.975449i	$0.429321\pi$
$907$	−22.1251	+	38.3217i	−0.734651	+	1.27245i	−0.954876	+	0.297004i	$0.904013\pi$
$908$	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	0.954588	−	0.297930i	$-0.0962962\pi$
$911$	6.61845	+	11.4635i	0.219279	+	0.379802i	−0.735309	+	0.677732i	$0.762963\pi$
$912$		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	0.255767	+	0.966739i	$0.417672\pi$
$919$	−21.5036	+	37.2452i	−0.709337	+	1.22861i	−0.965103	+	0.261869i	$0.915661\pi$
$920$	−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	$-0.966596\pi$
$929$		−	6.38535i		−	0.209497i	0.994499	−	0.104748i	$-0.0334037\pi$
$930$		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	0.999966	+	0.00829925i	$0.00264176\pi$
$941$	46.2325	+	26.6923i	1.50714	+	0.870145i	0.507170	+	0.861846i	$0.330692\pi$
$942$		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	0.446426	−	0.894821i	$-0.352697\pi$
$947$	−3.24038	−	1.87083i	−0.105298	−	0.0607940i	−0.551724	+	0.834027i	$0.686030\pi$
$948$		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	−0.988793	−	0.149291i	$-0.952301\pi$
$953$	−11.2711	+	19.5221i	−0.365107	+	0.632384i	0.623686	+	0.781675i	$0.285634\pi$
$954$		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	0.522002	−	0.852944i	$-0.325185\pi$
$967$	1.37859	+	0.795929i	0.0443325	+	0.0255954i	−0.477670	+	0.878539i	$0.658519\pi$
$968$	−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	−0.824018	−	0.566564i	$-0.808272\pi$
$971$	2.45081	−	4.24492i	0.0786501	−	0.136226i	0.902668	+	0.430338i	$0.141606\pi$
$972$		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	$-0.980296\pi$
$977$		−	3.86735i		−	0.123727i	0.998085	−	0.0618637i	$-0.0197044\pi$
$978$		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	−0.997604	−	0.0691791i	$-0.977962\pi$
$983$	−45.0382	+	26.0028i	−1.43650	+	0.829361i	−0.438891	+	0.898540i	$0.644629\pi$
$984$		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	0.923624	−	0.383299i	$-0.125212\pi$
$991$	4.08818	+	7.08094i	0.129865	+	0.224933i	−0.793759	+	0.608233i	$0.791879\pi$
$992$	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.10.1		22
3.2	odd	2		117.2.r.b.49.11	yes	22
9.2	odd	6		117.2.l.b.88.1	yes	22
9.7	even	3		351.2.l.b.127.11		22
13.4	even	6		351.2.l.b.199.1		22
39.17	odd	6		117.2.l.b.4.11	✓	22
117.43	even	6	inner	351.2.r.b.316.1		22
117.56	odd	6		117.2.r.b.43.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.11	✓	22	39.17	odd	6
117.2.l.b.88.1	yes	22	9.2	odd	6
117.2.r.b.43.11	yes	22	117.56	odd	6
117.2.r.b.49.11	yes	22	3.2	odd	2
351.2.l.b.127.11		22	9.7	even	3
351.2.l.b.199.1		22	13.4	even	6
351.2.r.b.10.1		22	1.1	even	1	trivial
351.2.r.b.316.1		22	117.43	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
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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