LMFDB - Embedded newform 378.3.r.a.233.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(233,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.233"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			233.10
Character	$\chi$	$=$	378.233
Dual form			378.3.r.a.305.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} -2.00000 q^{4} +(-5.46142 + 3.15315i) q^{5} +(-3.23416 - 6.20807i) q^{7} -2.82843i q^{8} +(-4.45923 - 7.72361i) q^{10} +(4.22055 + 2.43674i) q^{11} +(-1.62436 + 2.81348i) q^{13} +(8.77954 - 4.57380i) q^{14} +4.00000 q^{16} +(17.6988 - 10.2184i) q^{17} +(14.7381 - 25.5272i) q^{19} +(10.9228 - 6.30630i) q^{20} +(-3.44607 + 5.96876i) q^{22} +(5.47592 - 3.16152i) q^{23} +(7.38470 - 12.7907i) q^{25} +(-3.97886 - 2.29720i) q^{26} +(6.46833 + 12.4161i) q^{28} +(-23.6013 + 13.6262i) q^{29} +46.9819 q^{31} +5.65685i q^{32} +(14.4510 + 25.0299i) q^{34} +(37.2381 + 23.7071i) q^{35} +(25.7193 - 44.5471i) q^{37} +(36.1009 + 20.8429i) q^{38} +(8.91845 + 15.4472i) q^{40} +(-29.7417 - 17.1714i) q^{41} +(-34.9190 - 60.4815i) q^{43} +(-8.44110 - 4.87347i) q^{44} +(4.47107 + 7.74412i) q^{46} +12.1442i q^{47} +(-28.0804 + 40.1559i) q^{49} +(18.0888 + 10.4435i) q^{50} +(3.24873 - 5.62696i) q^{52} +(-2.78077 + 1.60548i) q^{53} -30.7336 q^{55} +(-17.5591 + 9.14759i) q^{56} +(-19.2704 - 33.3773i) q^{58} -105.505i q^{59} +67.7403 q^{61} +66.4424i q^{62} -8.00000 q^{64} -20.4875i q^{65} +26.7086 q^{67} +(-35.3976 + 20.4368i) q^{68} +(-33.5269 + 52.6626i) q^{70} +59.5162i q^{71} +(17.7882 + 30.8100i) q^{73} +(62.9991 + 36.3725i) q^{74} +(-29.4763 + 51.0544i) q^{76} +(1.47749 - 34.0823i) q^{77} -72.2749 q^{79} +(-21.8457 + 12.6126i) q^{80} +(24.2840 - 42.0611i) q^{82} +(110.071 - 63.5495i) q^{83} +(-64.4403 + 111.614i) q^{85} +(85.5338 - 49.3830i) q^{86} +(6.89213 - 11.9375i) q^{88} +(-35.7487 - 20.6395i) q^{89} +(22.7198 + 0.984917i) q^{91} +(-10.9518 + 6.32305i) q^{92} -17.1745 q^{94} +185.886i q^{95} +(-73.4338 - 127.191i) q^{97} +(-56.7889 - 39.7117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) $ 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	−5.46142	+	3.15315i	−1.09228	+	0.630630i	−0.934183	−	0.356793i	$-0.883870\pi$
$5$	−5.46142	+	3.15315i	−1.09228	+	0.630630i	−0.158100	+	0.987423i	$0.550537\pi$
$6$		0			0
$7$	−3.23416	−	6.20807i	−0.462023	−	0.886868i
$7$	−3.23416	−	6.20807i	−0.462023	−	0.886868i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−4.45923	−	7.72361i	−0.445923	−	0.772361i
$11$	4.22055	+	2.43674i	0.383687	+	0.221522i	0.679421	−	0.733749i	$-0.262231\pi$
$11$	4.22055	+	2.43674i	0.383687	+	0.221522i	−0.295734	+	0.955270i	$0.595564\pi$
$12$		0			0
$13$	−1.62436	+	2.81348i	−0.124951	+	0.216422i	−0.921714	−	0.387871i	$-0.873211\pi$
$13$	−1.62436	+	2.81348i	−0.124951	+	0.216422i	0.796763	+	0.604292i	$0.206544\pi$
$14$	8.77954	−	4.57380i	0.627110	−	0.326700i
$15$		0			0
$16$	4.00000			0.250000
$17$	17.6988	−	10.2184i	1.04111	−	0.601083i	0.120959	−	0.992657i	$-0.461403\pi$
$17$	17.6988	−	10.2184i	1.04111	−	0.601083i	0.920146	+	0.391575i	$0.128070\pi$
$18$		0			0
$19$	14.7381	−	25.5272i	0.775691	−	1.34354i	−0.158714	−	0.987325i	$-0.550735\pi$
$19$	14.7381	−	25.5272i	0.775691	−	1.34354i	0.934405	−	0.356212i	$-0.115932\pi$
$20$	10.9228	−	6.30630i	0.546142	−	0.315315i
$21$		0			0
$22$	−3.44607	+	5.96876i	−0.156639	+	0.271307i
$23$	5.47592	−	3.16152i	0.238084	−	0.137458i	−0.376212	−	0.926534i	$-0.622774\pi$
$23$	5.47592	−	3.16152i	0.238084	−	0.137458i	0.614296	+	0.789076i	$0.289440\pi$
$24$		0			0
$25$	7.38470	−	12.7907i	0.295388	−	0.511627i
$26$	−3.97886	−	2.29720i	−0.153033	−	0.0883538i
$27$		0			0
$28$	6.46833	+	12.4161i	0.231012	+	0.443434i
$29$	−23.6013	+	13.6262i	−0.813838	+	0.469870i	−0.848287	−	0.529537i	$-0.822366\pi$
$29$	−23.6013	+	13.6262i	−0.813838	+	0.469870i	0.0344489	+	0.999406i	$0.489032\pi$
$30$		0			0
$31$	46.9819			1.51554			0.757772	−	0.652519i	$-0.226288\pi$
$31$	46.9819			1.51554			0.757772	+	0.652519i	$0.226288\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	14.4510	+	25.0299i	0.425030	+	0.736173i
$35$	37.2381	+	23.7071i	1.06395	+	0.677345i
$36$		0			0
$37$	25.7193	−	44.5471i	0.695115	−	1.20398i	−0.275026	−	0.961437i	$-0.588687\pi$
$37$	25.7193	−	44.5471i	0.695115	−	1.20398i	0.970142	−	0.242539i	$-0.0779801\pi$
$38$	36.1009	+	20.8429i	0.950024	+	0.548497i
$39$		0			0
$40$	8.91845	+	15.4472i	0.222961	+	0.386180i
$41$	−29.7417	−	17.1714i	−0.725408	−	0.418814i	0.0913320	−	0.995821i	$-0.470888\pi$
$41$	−29.7417	−	17.1714i	−0.725408	−	0.418814i	−0.816740	+	0.577006i	$0.804221\pi$
$42$		0			0
$43$	−34.9190	−	60.4815i	−0.812070	−	1.40655i	−0.911413	−	0.411494i	$-0.865007\pi$
$43$	−34.9190	−	60.4815i	−0.812070	−	1.40655i	0.0993422	−	0.995053i	$-0.468326\pi$
$44$	−8.44110	−	4.87347i	−0.191843	−	0.110761i
$45$		0			0
$46$	4.47107	+	7.74412i	0.0971972	+	0.168350i
$47$			12.1442i			0.258387i	0.991619	+	0.129194i	$0.0412388\pi$
$47$			12.1442i			0.258387i	−0.991619	+	0.129194i	$0.958761\pi$
$48$		0			0
$49$	−28.0804	+	40.1559i	−0.573069	+	0.819507i
$50$	18.0888	+	10.4435i	0.361775	+	0.208871i
$51$		0			0
$52$	3.24873	−	5.62696i	0.0624756	−	0.108211i
$53$	−2.78077	+	1.60548i	−0.0524674	+	0.0302921i	−0.526004	−	0.850482i	$-0.676310\pi$
$53$	−2.78077	+	1.60548i	−0.0524674	+	0.0302921i	0.473537	+	0.880774i	$0.342977\pi$
$54$		0			0
$55$	−30.7336			−0.558792
$56$	−17.5591	+	9.14759i	−0.313555	+	0.163350i
$57$		0			0
$58$	−19.2704	−	33.3773i	−0.332248	−	0.575470i
$59$		−	105.505i		−	1.78821i	−0.447854	−	0.894107i	$-0.647811\pi$
$59$		−	105.505i		−	1.78821i	0.447854	−	0.894107i	$-0.352189\pi$
$60$		0			0
$61$	67.7403			1.11050			0.555248	−	0.831685i	$-0.312623\pi$
$61$	67.7403			1.11050			0.555248	+	0.831685i	$0.312623\pi$
$62$			66.4424i			1.07165i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		−	20.4875i		−	0.315192i
$66$		0			0
$67$	26.7086			0.398636			0.199318	−	0.979935i	$-0.436127\pi$
$67$	26.7086			0.398636			0.199318	+	0.979935i	$0.436127\pi$
$68$	−35.3976	+	20.4368i	−0.520553	+	0.300541i
$69$		0			0
$70$	−33.5269	+	52.6626i	−0.478955	+	0.752323i
$71$			59.5162i			0.838257i	0.907927	+	0.419128i	$0.137664\pi$
$71$			59.5162i			0.838257i	−0.907927	+	0.419128i	$0.862336\pi$
$72$		0			0
$73$	17.7882	+	30.8100i	0.243674	+	0.422055i	0.961758	−	0.273901i	$-0.0883141\pi$
$73$	17.7882	+	30.8100i	0.243674	+	0.422055i	−0.718084	+	0.695956i	$0.754981\pi$
$74$	62.9991	+	36.3725i	0.851339	+	0.491521i
$75$		0			0
$76$	−29.4763	+	51.0544i	−0.387846	+	0.671768i
$77$	1.47749	−	34.0823i	0.0191882	−	0.442627i
$78$		0			0
$79$	−72.2749			−0.914872			−0.457436	−	0.889243i	$-0.651232\pi$
$79$	−72.2749			−0.914872			−0.457436	+	0.889243i	$0.651232\pi$
$80$	−21.8457	+	12.6126i	−0.273071	+	0.157657i
$81$		0			0
$82$	24.2840	−	42.0611i	0.296147	−	0.512941i
$83$	110.071	−	63.5495i	1.32616	−	0.765656i	0.341453	−	0.939899i	$-0.389081\pi$
$83$	110.071	−	63.5495i	1.32616	−	0.765656i	0.984703	+	0.174242i	$0.0557476\pi$
$84$		0			0
$85$	−64.4403	+	111.614i	−0.758121	+	1.31310i
$86$	85.5338	−	49.3830i	0.994579	−	0.574220i
$87$		0			0
$88$	6.89213	−	11.9375i	0.0783197	−	0.135654i
$89$	−35.7487	−	20.6395i	−0.401671	−	0.231905i	0.285534	−	0.958369i	$-0.407829\pi$
$89$	−35.7487	−	20.6395i	−0.401671	−	0.231905i	−0.687205	+	0.726464i	$0.741162\pi$
$90$		0			0
$91$	22.7198	+	0.984917i	0.249668	+	0.0108233i
$92$	−10.9518	+	6.32305i	−0.119042	+	0.0687288i
$93$		0			0
$94$	−17.1745			−0.182707
$95$			185.886i			1.95670i
$96$		0			0
$97$	−73.4338	−	127.191i	−0.757050	−	1.31125i	−0.944349	−	0.328945i	$-0.893307\pi$
$97$	−73.4338	−	127.191i	−0.757050	−	1.31125i	0.187299	−	0.982303i	$-0.440027\pi$
$98$	−56.7889	−	39.7117i	−0.579479	−	0.405221i
$99$		0			0
$100$	−14.7694	+	25.5814i	−0.147694	+	0.255814i
$101$	−17.0117	−	9.82170i	−0.168433	−	0.0972446i	0.413414	−	0.910543i	$-0.364336\pi$
$101$	−17.0117	−	9.82170i	−0.168433	−	0.0972446i	−0.581847	+	0.813299i	$0.697670\pi$
$102$		0			0
$103$	42.1011	+	72.9212i	0.408749	+	0.707973i	0.994750	−	0.102337i	$-0.0326320\pi$
$103$	42.1011	+	72.9212i	0.408749	+	0.707973i	−0.586001	+	0.810310i	$0.699299\pi$
$104$	7.95773	+	4.59440i	0.0765166	+	0.0441769i
$105$		0			0
$106$	−2.27049	−	3.93261i	−0.0214197	−	0.0371001i
$107$	−86.7767	−	50.1006i	−0.810997	−	0.468229i	0.0363048	−	0.999341i	$-0.488441\pi$
$107$	−86.7767	−	50.1006i	−0.810997	−	0.468229i	−0.847302	+	0.531111i	$0.821775\pi$
$108$		0			0
$109$	41.1176	+	71.2177i	0.377225	+	0.653373i	0.990657	−	0.136374i	$-0.0435449\pi$
$109$	41.1176	+	71.2177i	0.377225	+	0.653373i	−0.613432	+	0.789747i	$0.710212\pi$
$110$		−	43.4639i		−	0.395126i
$111$		0			0
$112$	−12.9367	−	24.8323i	−0.115506	−	0.221717i
$113$	−83.9806	−	48.4862i	−0.743191	−	0.429081i	0.0800375	−	0.996792i	$-0.474496\pi$
$113$	−83.9806	−	48.4862i	−0.743191	−	0.429081i	−0.823228	+	0.567710i	$0.807829\pi$
$114$		0			0
$115$	−19.9375	+	34.5328i	−0.173370	+	0.300285i
$116$	47.2026	−	27.2524i	0.406919	−	0.234935i
$117$		0			0
$118$	149.206			1.26446
$119$	−120.677	−	76.8274i	−1.01410	−	0.645609i
$120$		0			0
$121$	−48.6246	−	84.2203i	−0.401856	−	0.696036i
$122$			95.7992i			0.785240i
$123$		0			0
$124$	−93.9638			−0.757772
$125$		−	64.5172i		−	0.516137i
$126$		0			0
$127$	30.6055			0.240988			0.120494	−	0.992714i	$-0.461552\pi$
$127$	30.6055			0.240988			0.120494	+	0.992714i	$0.461552\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	28.9736			0.222874
$131$	−194.881	+	112.515i	−1.48764	+	0.858892i	−0.999901	−	0.0140952i	$-0.995513\pi$
$131$	−194.881	+	112.515i	−1.48764	+	0.858892i	−0.487744	+	0.872987i	$0.662180\pi$
$132$		0			0
$133$	−206.140	−	8.93632i	−1.54993	−	0.0671904i
$134$			37.7717i			0.281878i
$135$		0			0
$136$	−28.9020	−	50.0597i	−0.212515	−	0.368086i
$137$	−111.484	−	64.3655i	−0.813754	−	0.469821i	0.0345035	−	0.999405i	$-0.489015\pi$
$137$	−111.484	−	64.3655i	−0.813754	−	0.469821i	−0.848258	+	0.529583i	$0.822348\pi$
$138$		0			0
$139$	84.8478	−	146.961i	0.610416	−	1.05727i	−0.380755	−	0.924676i	$-0.624336\pi$
$139$	84.8478	−	146.961i	0.610416	−	1.05727i	0.991170	−	0.132595i	$-0.0423309\pi$
$140$	−74.4762	−	47.4141i	−0.531973	−	0.338672i
$141$		0			0
$142$	−84.1686			−0.592737
$143$	−13.7114	+	7.91630i	−0.0958841	+	0.0553587i
$144$		0			0
$145$	85.9310	−	148.837i	0.592628	−	1.02646i
$146$	−43.5720	+	25.1563i	−0.298438	+	0.172303i
$147$		0			0
$148$	−51.4385	+	89.0942i	−0.347558	+	0.601988i
$149$	188.801	−	109.004i	1.26712	−	0.731573i	0.292679	−	0.956211i	$-0.405453\pi$
$149$	188.801	−	109.004i	1.26712	−	0.731573i	0.974442	+	0.224637i	$0.0721198\pi$
$150$		0			0
$151$	−65.8810	+	114.109i	−0.436298	+	0.755690i	−0.997401	−	0.0720560i	$-0.977044\pi$
$151$	−65.8810	+	114.109i	−0.436298	+	0.755690i	0.561103	+	0.827746i	$0.310377\pi$
$152$	−72.2018	−	41.6857i	−0.475012	−	0.274248i
$153$		0			0
$154$	48.1997	+	2.08949i	0.312985	+	0.0135681i
$155$	−256.588	+	148.141i	−1.65540	+	0.955748i
$156$		0			0
$157$	113.010			0.719807			0.359904	−	0.932990i	$-0.382810\pi$
$157$	113.010			0.719807			0.359904	+	0.932990i	$0.382810\pi$
$158$		−	102.212i		−	0.646912i
$159$		0			0
$160$	−17.8369	−	30.8944i	−0.111481	−	0.193090i
$161$	−37.3370	−	23.7700i	−0.231907	−	0.147640i
$162$		0			0
$163$	−99.9004	+	173.032i	−0.612886	+	1.06155i	0.377866	+	0.925860i	$0.376658\pi$
$163$	−99.9004	+	173.032i	−0.612886	+	1.06155i	−0.990752	+	0.135689i	$0.956675\pi$
$164$	59.4834	+	34.3428i	0.362704	+	0.209407i
$165$		0			0
$166$	89.8725	+	155.664i	0.541401	+	0.937734i
$167$	78.9503	+	45.5820i	0.472756	+	0.272946i	0.717393	−	0.696669i	$-0.245335\pi$
$167$	78.9503	+	45.5820i	0.472756	+	0.272946i	−0.244637	+	0.969615i	$0.578669\pi$
$168$		0			0
$169$	79.2229	+	137.218i	0.468774	+	0.811941i
$170$	−157.846	−	91.1323i	−0.928505	−	0.536073i
$171$		0			0
$172$	69.8381	+	120.963i	0.406035	+	0.703274i
$173$		−	215.803i		−	1.24742i	−0.781656	−	0.623709i	$-0.785625\pi$
$173$		−	215.803i		−	1.24742i	0.781656	−	0.623709i	$-0.214375\pi$
$174$		0			0
$175$	−103.289	−	4.47764i	−0.590222	−	0.0255865i
$176$	16.8822	+	9.74695i	0.0959216	+	0.0553804i
$177$		0			0
$178$	29.1887	−	50.5563i	0.163981	−	0.284024i
$179$	275.249	−	158.915i	1.53770	−	0.887793i	0.538729	−	0.842479i	$-0.318905\pi$
$179$	275.249	−	158.915i	1.53770	−	0.887793i	0.998973	−	0.0453139i	$-0.0144288\pi$
$180$		0			0
$181$	112.737			0.622859			0.311429	−	0.950269i	$-0.399192\pi$
$181$	112.737			0.622859			0.311429	+	0.950269i	$0.399192\pi$
$182$	−1.39288	+	32.1306i	−0.00765320	+	0.176542i
$183$		0			0
$184$	−8.94214	−	15.4882i	−0.0485986	−	0.0841752i
$185$			324.387i			1.75344i
$186$		0			0
$187$	99.5982			0.532611
$188$		−	24.2884i		−	0.129194i
$189$		0			0
$190$	−262.883			−1.38359
$191$			112.048i			0.586639i	0.956014	+	0.293320i	$0.0947600\pi$
$191$			112.048i			0.586639i	−0.956014	+	0.293320i	$0.905240\pi$
$192$		0			0
$193$	−99.1203			−0.513577			−0.256788	−	0.966468i	$-0.582664\pi$
$193$	−99.1203			−0.513577			−0.256788	+	0.966468i	$0.582664\pi$
$194$	179.875	−	103.851i	0.927193	−	0.535315i
$195$		0			0
$196$	56.1608	−	80.3117i	0.286534	−	0.409754i
$197$			58.3155i			0.296018i	0.988986	+	0.148009i	$0.0472864\pi$
$197$			58.3155i			0.296018i	−0.988986	+	0.148009i	$0.952714\pi$
$198$		0			0
$199$	2.72114	+	4.71315i	0.0136741	+	0.0236842i	0.872781	−	0.488111i	$-0.162314\pi$
$199$	2.72114	+	4.71315i	0.0136741	+	0.0236842i	−0.859107	+	0.511795i	$0.828981\pi$
$200$	−36.1775	−	20.8871i	−0.180888	−	0.104435i
$201$		0			0
$202$	13.8900	−	24.0582i	0.0687623	−	0.119100i
$203$	160.923	+	102.449i	0.792724	+	0.504676i
$204$		0			0
$205$	216.576			1.05647
$206$	−103.126	+	59.5400i	−0.500613	+	0.289029i
$207$		0			0
$208$	−6.49746	+	11.2539i	−0.0312378	+	0.0541054i
$209$	124.406	−	71.8259i	0.595245	−	0.343665i
$210$		0			0
$211$	−142.592	+	246.976i	−0.675791	+	1.17050i	0.300447	+	0.953799i	$0.402864\pi$
$211$	−142.592	+	246.976i	−0.675791	+	1.17050i	−0.976237	+	0.216705i	$0.930469\pi$
$212$	5.56155	−	3.21096i	0.0262337	−	0.0151460i
$213$		0			0
$214$	70.8529	−	122.721i	0.331088	−	0.573462i
$215$	381.415	+	220.210i	1.77402	+	1.02423i
$216$		0			0
$217$	−151.947	−	291.667i	−0.700217	−	1.34409i
$218$	−100.717	+	58.1490i	−0.462005	+	0.266739i
$219$		0			0
$220$	61.4672			0.279396
$221$			66.3936i			0.300424i
$222$		0			0
$223$	51.3114	+	88.8739i	0.230096	+	0.398538i	0.957836	−	0.287315i	$-0.0927627\pi$
$223$	51.3114	+	88.8739i	0.230096	+	0.398538i	−0.727740	+	0.685853i	$0.759429\pi$
$224$	35.1182	−	18.2952i	0.156778	−	0.0816750i
$225$		0			0
$226$	68.5698	−	118.766i	0.303406	−	0.525515i
$227$	296.905	+	171.418i	1.30795	+	0.755146i	0.981754	−	0.190155i	$-0.0608992\pi$
$227$	296.905	+	171.418i	1.30795	+	0.755146i	0.326198	+	0.945302i	$0.394233\pi$
$228$		0			0
$229$	−57.3196	−	99.2805i	−0.250304	−	0.433539i	0.713305	−	0.700853i	$-0.247197\pi$
$229$	−57.3196	−	99.2805i	−0.250304	−	0.433539i	−0.963610	+	0.267314i	$0.913864\pi$
$230$	−48.8367	−	28.1959i	−0.212334	−	0.122591i
$231$		0			0
$232$	38.5408	+	66.7546i	0.166124	+	0.287735i
$233$	145.507	+	84.0086i	0.624494	+	0.360552i	0.778617	−	0.627500i	$-0.215922\pi$
$233$	145.507	+	84.0086i	0.624494	+	0.360552i	−0.154122	+	0.988052i	$0.549255\pi$
$234$		0			0
$235$	−38.2925	−	66.3245i	−0.162947	−	0.282232i
$236$			211.009i			0.894107i
$237$		0			0
$238$	108.650	−	170.664i	0.456514	−	0.717074i
$239$	−73.8958	−	42.6638i	−0.309187	−	0.178509i	0.337375	−	0.941370i	$-0.390461\pi$
$239$	−73.8958	−	42.6638i	−0.309187	−	0.178509i	−0.646563	+	0.762861i	$0.723794\pi$
$240$		0			0
$241$	112.846	−	195.455i	0.468240	−	0.811016i	−0.531101	−	0.847309i	$-0.678222\pi$
$241$	112.846	−	195.455i	0.468240	−	0.811016i	0.999341	+	0.0362927i	$0.0115549\pi$
$242$	119.106	−	68.7656i	0.492172	−	0.284155i
$243$		0			0
$244$	−135.481			−0.555248
$245$	26.7412	−	307.849i	0.109148	−	1.25653i
$246$		0			0
$247$	47.8802	+	82.9310i	0.193847	+	0.335753i
$248$		−	132.885i		−	0.535826i
$249$		0			0
$250$	91.2411			0.364964
$251$		−	125.182i		−	0.498731i	−0.968409	−	0.249366i	$-0.919778\pi$
$251$		−	125.182i		−	0.498731i	0.968409	−	0.249366i	$-0.0802221\pi$
$252$		0			0
$253$	30.8152			0.121799
$254$			43.2828i			0.170405i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−227.633	+	131.424i	−0.885732	+	0.511378i	−0.872544	−	0.488535i	$-0.837531\pi$
$257$	−227.633	+	131.424i	−0.885732	+	0.511378i	−0.0131879	+	0.999913i	$0.504198\pi$
$258$		0			0
$259$	−359.732	−	15.5946i	−1.38893	−	0.0602109i
$260$			40.9749i			0.157596i
$261$		0			0
$262$	−159.120	−	275.604i	−0.607328	−	1.05192i
$263$	301.267	+	173.936i	1.14550	+	0.661355i	0.947787	−	0.318904i	$-0.103315\pi$
$263$	301.267	+	173.936i	1.14550	+	0.661355i	0.197714	+	0.980260i	$0.436648\pi$
$264$		0			0
$265$	10.1246	−	17.5364i	0.0382062	−	0.0661751i
$266$	12.6379	−	291.526i	0.0475108	−	1.09596i
$267$		0			0
$268$	−53.4172			−0.199318
$269$	22.9715	−	13.2626i	0.0853960	−	0.0493034i	−0.456694	−	0.889624i	$-0.650967\pi$
$269$	22.9715	−	13.2626i	0.0853960	−	0.0493034i	0.542090	+	0.840320i	$0.317633\pi$
$270$		0			0
$271$	−207.625	+	359.618i	−0.766145	+	1.32700i	0.173494	+	0.984835i	$0.444494\pi$
$271$	−207.625	+	359.618i	−0.766145	+	1.32700i	−0.939639	+	0.342167i	$0.888839\pi$
$272$	70.7952	−	40.8736i	0.260276	−	0.150271i
$273$		0			0
$274$	91.0266	−	157.663i	0.332214	−	0.575411i
$275$	62.3350	−	35.9892i	0.226673	−	0.130870i
$276$		0			0
$277$	147.756	−	255.921i	0.533415	−	0.923902i	−0.465823	−	0.884878i	$-0.654242\pi$
$277$	147.756	−	255.921i	0.533415	−	0.923902i	0.999238	−	0.0390240i	$-0.0124249\pi$
$278$	207.834	+	119.993i	0.747603	+	0.431629i
$279$		0			0
$280$	67.0537	−	105.325i	0.239478	−	0.376162i
$281$	−253.233	+	146.204i	−0.901185	+	0.520300i	−0.877585	−	0.479422i	$-0.840846\pi$
$281$	−253.233	+	146.204i	−0.901185	+	0.520300i	−0.0236007	+	0.999721i	$0.507513\pi$
$282$		0			0
$283$	450.482			1.59181			0.795905	−	0.605422i	$-0.206996\pi$
$283$	450.482			1.59181			0.795905	+	0.605422i	$0.206996\pi$
$284$		−	119.032i		−	0.419128i
$285$		0			0
$286$	−11.1953	−	19.3909i	−0.0391445	−	0.0678003i
$287$	−10.4117	+	240.174i	−0.0362777	+	0.836843i
$288$		0			0
$289$	64.3315	−	111.425i	0.222600	−	0.385555i
$290$	210.487	+	121.525i	0.725818	+	0.419051i
$291$		0			0
$292$	−35.5764	−	61.6201i	−0.121837	−	0.211028i
$293$	53.2835	+	30.7632i	0.181855	+	0.104994i	0.588164	−	0.808742i	$-0.299851\pi$
$293$	53.2835	+	30.7632i	0.181855	+	0.104994i	−0.406309	+	0.913736i	$0.633184\pi$
$294$		0			0
$295$	332.672	+	576.204i	1.12770	+	1.95324i
$296$	−125.998	−	72.7451i	−0.425670	−	0.245760i
$297$		0			0
$298$	154.156	+	267.005i	0.517300	+	0.895990i
$299$			20.5419i			0.0687019i
$300$		0			0
$301$	−262.540	+	412.387i	−0.872226	+	1.37006i
$302$	−161.375	−	93.1698i	−0.534354	−	0.308509i
$303$		0			0
$304$	58.9525	−	102.109i	0.193923	−	0.335884i
$305$	−369.958	+	213.595i	−1.21298	+	0.700312i
$306$		0			0
$307$	202.030			0.658079			0.329040	−	0.944316i	$-0.393275\pi$
$307$	202.030			0.658079			0.329040	+	0.944316i	$0.393275\pi$
$308$	−2.95498	+	68.1646i	−0.00959409	+	0.221314i
$309$		0			0
$310$	−209.503	−	362.870i	−0.675816	−	1.17055i
$311$		−	246.199i		−	0.791635i	−0.918329	−	0.395818i	$-0.870461\pi$
$311$		−	246.199i		−	0.791635i	0.918329	−	0.395818i	$-0.129539\pi$
$312$		0			0
$313$	52.4657			0.167622			0.0838111	−	0.996482i	$-0.473291\pi$
$313$	52.4657			0.167622			0.0838111	+	0.996482i	$0.473291\pi$
$314$			159.820i			0.508980i
$315$		0			0
$316$	144.550			0.457436
$317$		−	439.574i		−	1.38667i	−0.720616	−	0.693334i	$-0.756141\pi$
$317$		−	439.574i		−	1.38667i	0.720616	−	0.693334i	$-0.243859\pi$
$318$		0			0
$319$	−132.814			−0.416345
$320$	43.6913	−	25.2252i	0.136535	−	0.0788287i
$321$		0			0
$322$	33.6159	−	52.8025i	0.104397	−	0.163983i
$323$		−	602.401i		−	1.86502i
$324$		0			0
$325$	23.9909	+	41.5535i	0.0738182	+	0.127857i
$326$	−244.705	−	141.280i	−0.750629	−	0.433376i
$327$		0			0
$328$	−48.5680	+	84.1223i	−0.148073	+	0.256470i
$329$	75.3921	−	39.2763i	0.229155	−	0.119381i
$330$		0			0
$331$	87.1114			0.263177			0.131588	−	0.991304i	$-0.457992\pi$
$331$	87.1114			0.263177			0.131588	+	0.991304i	$0.457992\pi$
$332$	−220.142	+	127.099i	−0.663078	+	0.382828i
$333$		0			0
$334$	−64.4626	+	111.653i	−0.193002	+	0.334289i
$335$	−145.867	+	84.2162i	−0.435423	+	0.251392i
$336$		0			0
$337$	196.987	−	341.192i	0.584531	−	1.01244i	−0.410402	−	0.911905i	$-0.634612\pi$
$337$	196.987	−	341.192i	0.584531	−	1.01244i	0.994934	−	0.100533i	$-0.0320549\pi$
$338$	−194.056	+	112.038i	−0.574129	+	0.331474i
$339$		0			0
$340$	128.881	−	223.228i	0.379061	−	0.656552i
$341$	198.289	+	114.482i	0.581494	+	0.335726i
$342$		0			0
$343$	340.107	+	44.4545i	0.991566	+	0.129605i
$344$	−171.068	+	98.7659i	−0.497290	+	0.287110i
$345$		0			0
$346$	305.192			0.882058
$347$			92.0389i			0.265242i	0.991167	+	0.132621i	$0.0423393\pi$
$347$			92.0389i			0.265242i	−0.991167	+	0.132621i	$0.957661\pi$
$348$		0			0
$349$	21.2427	+	36.7935i	0.0608674	+	0.105425i	0.894853	−	0.446360i	$-0.147280\pi$
$349$	21.2427	+	36.7935i	0.0608674	+	0.105425i	−0.833986	+	0.551786i	$0.813947\pi$
$350$	6.33234	−	146.072i	0.0180924	−	0.417350i
$351$		0			0
$352$	−13.7843	+	23.8750i	−0.0391598	+	0.0678268i
$353$	359.759	+	207.707i	1.01915	+	0.588404i	0.913857	−	0.406037i	$-0.133090\pi$
$353$	359.759	+	207.707i	1.01915	+	0.588404i	0.105290	+	0.994442i	$0.466423\pi$
$354$		0			0
$355$	−187.664	−	325.043i	−0.528630	−	0.915613i
$356$	71.4974	+	41.2790i	0.200835	+	0.115952i
$357$		0			0
$358$	224.740	+	389.260i	0.627764	+	1.08732i
$359$	−71.5463	−	41.3072i	−0.199293	−	0.115062i	0.397033	−	0.917805i	$-0.370040\pi$
$359$	−71.5463	−	41.3072i	−0.199293	−	0.115062i	−0.596326	+	0.802743i	$0.703373\pi$
$360$		0			0
$361$	−253.925	−	439.812i	−0.703394	−	1.21831i
$362$			159.435i			0.440428i
$363$		0			0
$364$	−45.4395	−	1.96983i	−0.124834	−	0.00541163i
$365$	−194.297	−	112.178i	−0.532321	−	0.307336i
$366$		0			0
$367$	14.1032	−	24.4275i	0.0384284	−	0.0665599i	−0.846172	−	0.532911i	$-0.821098\pi$
$367$	14.1032	−	24.4275i	0.0384284	−	0.0665599i	0.884600	+	0.466351i	$0.154432\pi$
$368$	21.9037	−	12.6461i	0.0595209	−	0.0343644i
$369$		0			0
$370$	−458.752			−1.23987
$371$	18.9604	+	12.0709i	0.0511063	+	0.0325360i
$372$		0			0
$373$	−349.936	−	606.107i	−0.938166	−	1.62495i	−0.768888	−	0.639383i	$-0.779190\pi$
$373$	−349.936	−	606.107i	−0.938166	−	1.62495i	−0.169278	−	0.985568i	$-0.554144\pi$
$374$			140.853i			0.376613i
$375$		0			0
$376$	34.3490			0.0913536
$377$		−	88.5358i		−	0.234843i
$378$		0			0
$379$	−278.543			−0.734942			−0.367471	−	0.930035i	$-0.619776\pi$
$379$	−278.543			−0.734942			−0.367471	+	0.930035i	$0.619776\pi$
$380$		−	371.772i		−	0.978348i
$381$		0			0
$382$	−158.460			−0.414817
$383$	113.186	−	65.3482i	0.295526	−	0.170622i	−0.344905	−	0.938637i	$-0.612089\pi$
$383$	113.186	−	65.3482i	0.295526	−	0.170622i	0.640431	+	0.768015i	$0.278756\pi$
$384$		0			0
$385$	99.3974	+	190.796i	0.258175	+	0.495575i
$386$		−	140.177i		−	0.363154i
$387$		0			0
$388$	146.868	+	254.382i	0.378525	+	0.655624i
$389$	−275.095	−	158.826i	−0.707186	−	0.408294i	0.102833	−	0.994699i	$-0.467209\pi$
$389$	−275.095	−	158.826i	−0.707186	−	0.408294i	−0.810018	+	0.586405i	$0.800543\pi$
$390$		0			0
$391$	64.6115	−	111.910i	0.165247	−	0.286216i
$392$	113.578	+	79.4233i	0.289740	+	0.202610i
$393$		0			0
$394$	−82.4705			−0.209316
$395$	394.723	−	227.893i	0.999299	−	0.576945i
$396$		0			0
$397$	−336.916	+	583.555i	−0.848654	+	1.46991i	0.0337554	+	0.999430i	$0.489253\pi$
$397$	−336.916	+	583.555i	−0.848654	+	1.46991i	−0.882410	+	0.470482i	$0.844080\pi$
$398$	−6.66540	+	3.84827i	−0.0167472	+	0.00966902i
$399$		0			0
$400$	29.5388	−	51.1627i	0.0738470	−	0.127907i
$401$	−228.933	+	132.174i	−0.570905	+	0.329612i	−0.757511	−	0.652823i	$-0.773585\pi$
$401$	−228.933	+	132.174i	−0.570905	+	0.329612i	0.186606	+	0.982435i	$0.440251\pi$
$402$		0			0
$403$	−76.3157	+	132.183i	−0.189369	+	0.327997i
$404$	34.0234	+	19.6434i	0.0842163	+	0.0486223i
$405$		0			0
$406$	−144.885	+	227.580i	−0.356860	+	0.560541i
$407$	217.099	−	125.342i	0.533413	−	0.307966i
$408$		0			0
$409$	336.832			0.823551			0.411775	−	0.911285i	$-0.364909\pi$
$409$	336.832			0.823551			0.411775	+	0.911285i	$0.364909\pi$
$410$			306.285i			0.747035i
$411$		0			0
$412$	−84.2022	−	145.842i	−0.204374	−	0.353987i
$413$	−654.980	+	341.219i	−1.58591	+	0.826196i
$414$		0			0
$415$	−400.762	+	694.140i	−0.965692	+	1.67263i
$416$	−15.9155	−	9.18879i	−0.0382583	−	0.0220884i
$417$		0			0
$418$	101.577	+	175.937i	0.243008	+	0.420902i
$419$	81.8382	+	47.2493i	0.195318	+	0.112767i	0.594470	−	0.804118i	$-0.297362\pi$
$419$	81.8382	+	47.2493i	0.195318	+	0.112767i	−0.399152	+	0.916885i	$0.630695\pi$
$420$		0			0
$421$	−125.288	−	217.004i	−0.297595	−	0.515450i	0.677990	−	0.735071i	$-0.262851\pi$
$421$	−125.288	−	217.004i	−0.297595	−	0.515450i	−0.975585	+	0.219621i	$0.929518\pi$
$422$	−349.277	−	201.655i	−0.827671	−	0.477856i
$423$		0			0
$424$	4.54099	+	7.86522i	0.0107099	+	0.0185500i
$425$		−	301.839i		−	0.710211i
$426$		0			0
$427$	−219.083	−	420.537i	−0.513075	−	0.984864i
$428$	173.553	+	100.201i	0.405499	+	0.234115i
$429$		0			0
$430$	−311.424	+	539.402i	−0.724241	+	1.25442i
$431$	−393.894	+	227.415i	−0.913908	+	0.527645i	−0.881686	−	0.471836i	$-0.843591\pi$
$431$	−393.894	+	227.415i	−0.913908	+	0.527645i	−0.0322213	+	0.999481i	$0.510258\pi$
$432$		0			0
$433$	8.44112			0.0194945			0.00974725	−	0.999952i	$-0.496897\pi$
$433$	8.44112			0.0194945			0.00974725	+	0.999952i	$0.496897\pi$
$434$	412.479	−	214.886i	0.950413	−	0.495128i
$435$		0			0
$436$	−82.2351	−	142.435i	−0.188613	−	0.326687i
$437$		−	186.380i		−	0.426499i
$438$		0			0
$439$	−394.400			−0.898406			−0.449203	−	0.893430i	$-0.648292\pi$
$439$	−394.400			−0.898406			−0.449203	+	0.893430i	$0.648292\pi$
$440$			86.9277i			0.197563i
$441$		0			0
$442$	−93.8948			−0.212432
$443$			477.093i			1.07696i	0.842638	+	0.538480i	$0.181001\pi$
$443$			477.093i			1.07696i	−0.842638	+	0.538480i	$0.818999\pi$
$444$		0			0
$445$	260.318			0.584984
$446$	−125.687	+	72.5653i	−0.281809	+	0.162702i
$447$		0			0
$448$	25.8733	+	49.6646i	0.0577529	+	0.110858i
$449$			346.215i			0.771081i	0.922691	+	0.385540i	$0.125985\pi$
$449$			346.215i			0.771081i	−0.922691	+	0.385540i	$0.874015\pi$
$450$		0			0
$451$	−83.6843	−	144.946i	−0.185553	−	0.321387i
$452$	167.961	+	96.9724i	0.371595	+	0.214541i
$453$		0			0
$454$	−242.422	+	419.887i	−0.533969	+	0.924861i
$455$	−127.188	+	66.2598i	−0.279533	+	0.145626i
$456$		0			0
$457$	595.267			1.30255			0.651277	−	0.758840i	$-0.274234\pi$
$457$	595.267			1.30255			0.651277	+	0.758840i	$0.274234\pi$
$458$	140.404	−	81.0622i	0.306559	−	0.176992i
$459$		0			0
$460$	39.8750	−	69.0656i	0.0866849	−	0.150143i
$461$	−506.009	+	292.145i	−1.09763	+	0.633719i	−0.935599	−	0.353066i	$-0.885139\pi$
$461$	−506.009	+	292.145i	−1.09763	+	0.633719i	−0.162035	+	0.986785i	$0.551806\pi$
$462$		0			0
$463$	−196.286	+	339.977i	−0.423943	+	0.734291i	−0.996321	−	0.0856990i	$-0.972688\pi$
$463$	−196.286	+	339.977i	−0.423943	+	0.734291i	0.572378	+	0.819990i	$0.306021\pi$
$464$	−94.4052	+	54.5049i	−0.203460	+	0.117467i
$465$		0			0
$466$	−118.806	+	205.778i	−0.254949	+	0.441584i
$467$	−637.126	−	367.845i	−1.36430	−	0.787677i	−0.374104	−	0.927387i	$-0.622050\pi$
$467$	−637.126	−	367.845i	−1.36430	−	0.787677i	−0.990192	+	0.139710i	$0.955383\pi$
$468$		0			0
$469$	−86.3800	−	165.809i	−0.184179	−	0.353537i
$470$	93.7970	−	54.1537i	0.199568	−	0.115221i
$471$		0			0
$472$	−298.412			−0.632229
$473$		−	340.354i		−	0.719564i
$474$		0			0
$475$	−217.674	−	377.022i	−0.458260	−	0.793730i
$476$	241.355	+	153.655i	0.507048	+	0.322804i
$477$		0			0
$478$	60.3357	−	104.504i	0.126225	−	0.218629i
$479$	−376.726	−	217.503i	−0.786485	−	0.454077i	0.0522388	−	0.998635i	$-0.483364\pi$
$479$	−376.726	−	217.503i	−0.786485	−	0.454077i	−0.838724	+	0.544557i	$0.816698\pi$
$480$		0			0
$481$	83.5549	+	144.721i	0.173711	+	0.300876i
$482$	276.415	+	159.588i	0.573475	+	0.331096i
$483$		0			0
$484$	97.2493	+	168.441i	0.200928	+	0.348018i
$485$	802.105	+	463.096i	1.65382	+	0.954836i
$486$		0			0
$487$	61.2233	+	106.042i	0.125715	+	0.217745i	0.922012	−	0.387161i	$-0.126544\pi$
$487$	61.2233	+	106.042i	0.125715	+	0.217745i	−0.796297	+	0.604906i	$0.793211\pi$
$488$		−	191.598i		−	0.392620i
$489$		0			0
$490$	435.365	+	37.8178i	0.888500	+	0.0771791i
$491$	269.718	+	155.722i	0.549324	+	0.317153i	0.748849	−	0.662740i	$-0.230607\pi$
$491$	269.718	+	155.722i	0.549324	+	0.317153i	−0.199525	+	0.979893i	$0.563940\pi$
$492$		0			0
$493$	−278.476	+	482.335i	−0.564861	+	0.978368i
$494$	−117.282	+	67.7129i	−0.237413	+	0.137071i
$495$		0			0
$496$	187.928			0.378886
$497$	369.481	−	192.485i	0.743423	−	0.387294i
$498$		0			0
$499$	6.65537	+	11.5274i	0.0133374	+	0.0231011i	0.872617	−	0.488405i	$-0.162421\pi$
$499$	6.65537	+	11.5274i	0.0133374	+	0.0231011i	−0.859280	+	0.511506i	$0.829088\pi$
$500$			129.034i			0.258069i
$501$		0			0
$502$	177.033			0.352656
$503$		−	386.747i		−	0.768881i	−0.923150	−	0.384440i	$-0.874394\pi$
$503$		−	386.747i		−	0.768881i	0.923150	−	0.384440i	$-0.125606\pi$
$504$		0			0
$505$	123.877			0.245301
$506$			43.5793i			0.0861251i
$507$		0			0
$508$	−61.2111			−0.120494
$509$	−522.282	+	301.540i	−1.02610	+	0.592416i	−0.915864	−	0.401490i	$-0.868493\pi$
$509$	−522.282	+	301.540i	−1.02610	+	0.592416i	−0.110232	+	0.993906i	$0.535159\pi$
$510$		0			0
$511$	133.741	−	210.075i	0.261724	−	0.411106i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−185.862	−	321.922i	−0.361599	−	0.626307i
$515$	−459.863	−	265.502i	−0.892938	−	0.515538i
$516$		0			0
$517$	−29.5922	+	51.2552i	−0.0572383	+	0.0991397i
$518$	22.0541	−	508.738i	0.0425755	−	0.982119i
$519$		0			0
$520$	−57.9473			−0.111437
$521$	−362.474	+	209.274i	−0.695727	+	0.401678i	−0.805754	−	0.592250i	$-0.798240\pi$
$521$	−362.474	+	209.274i	−0.695727	+	0.401678i	0.110027	+	0.993929i	$0.464906\pi$
$522$		0			0
$523$	230.619	−	399.444i	0.440955	−	0.763756i	−0.556806	−	0.830643i	$-0.687973\pi$
$523$	230.619	−	399.444i	0.440955	−	0.763756i	0.997761	+	0.0668867i	$0.0213066\pi$
$524$	389.763	−	225.030i	0.743822	−	0.429446i
$525$		0			0
$526$	−245.983	+	426.056i	−0.467649	+	0.809992i
$527$	831.522	−	480.080i	1.57784	−	0.910967i
$528$		0			0
$529$	−244.510	+	423.503i	−0.462211	+	0.800573i
$530$	24.8002	+	14.3184i	0.0467928	+	0.0270159i
$531$		0			0
$532$	412.281	+	17.8726i	0.774964	+	0.0335952i
$533$	96.6228	−	55.7852i	0.181281	−	0.104663i
$534$		0			0
$535$	631.898			1.18112
$536$		−	75.5433i		−	0.140939i
$537$		0			0
$538$	18.7562	+	32.4866i	0.0348628	+	0.0603841i
$539$	−216.364	+	101.055i	−0.401417	+	0.187487i
$540$		0			0
$541$	−420.654	+	728.594i	−0.777549	+	1.34675i	0.155801	+	0.987788i	$0.450204\pi$
$541$	−420.654	+	728.594i	−0.777549	+	1.34675i	−0.933351	+	0.358966i	$0.883129\pi$
$542$	−508.576	−	293.626i	−0.938332	−	0.541746i
$543$		0			0
$544$	57.8040	+	100.119i	0.106257	+	0.184043i
$545$	−449.120	−	259.300i	−0.824074	−	0.475779i
$546$		0			0
$547$	−183.875	−	318.481i	−0.336151	−	0.582231i	0.647554	−	0.762020i	$-0.275792\pi$
$547$	−183.875	−	318.481i	−0.336151	−	0.582231i	−0.983705	+	0.179788i	$0.942459\pi$
$548$	222.969	+	128.731i	0.406877	+	0.234911i
$549$		0			0
$550$	50.8964	+	88.1551i	0.0925388	+	0.160282i
$551$			803.300i			1.45790i
$552$		0			0
$553$	233.749	+	448.688i	0.422692	+	0.811370i
$554$	361.927	+	208.958i	0.653297	+	0.377181i
$555$		0			0
$556$	−169.696	+	293.921i	−0.305208	+	0.528635i
$557$	134.947	−	77.9118i	0.242275	−	0.139877i	−0.373947	−	0.927450i	$-0.621996\pi$
$557$	134.947	−	77.9118i	0.242275	−	0.139877i	0.616222	+	0.787573i	$0.288662\pi$
$558$		0			0
$559$	226.885			0.405876
$560$	148.952	+	94.8283i	0.265986	+	0.169336i
$561$		0			0
$562$	−206.764	−	358.126i	−0.367907	−	0.637234i
$563$			55.8041i			0.0991192i	0.998771	+	0.0495596i	$0.0157818\pi$
$563$			55.8041i			0.0991192i	−0.998771	+	0.0495596i	$0.984218\pi$
$564$		0			0
$565$	611.537			1.08237
$566$			637.078i			1.12558i
$567$		0			0
$568$	168.337			0.296368
$569$		−	650.955i		−	1.14403i	−0.820242	−	0.572017i	$-0.806161\pi$
$569$		−	650.955i		−	1.14403i	0.820242	−	0.572017i	$-0.193839\pi$
$570$		0			0
$571$	−392.937			−0.688156			−0.344078	−	0.938941i	$-0.611808\pi$
$571$	−392.937			−0.688156			−0.344078	+	0.938941i	$0.611808\pi$
$572$	27.4229	−	15.8326i	0.0479421	−	0.0276794i
$573$		0			0
$574$	−339.657	−	14.7244i	−0.591737	−	0.0256522i
$575$		−	93.3877i		−	0.162413i
$576$		0			0
$577$	−285.333	−	494.212i	−0.494512	−	0.856520i	0.505468	−	0.862845i	$-0.331320\pi$
$577$	−285.333	−	494.212i	−0.494512	−	0.856520i	−0.999980	+	0.00632539i	$0.997987\pi$
$578$	157.579	+	90.9785i	0.272629	+	0.157402i
$579$		0			0
$580$	−171.862	+	297.674i	−0.296314	+	0.513231i
$581$	−750.507	−	477.799i	−1.29175	−	0.822374i
$582$		0			0
$583$	−15.6485			−0.0268414
$584$	87.1439	−	50.3126i	0.149219	−	0.0861517i
$585$		0			0
$586$	−43.5058	+	75.3542i	−0.0742420	+	0.128591i
$587$	−561.273	+	324.051i	−0.956172	+	0.552046i	−0.894993	−	0.446081i	$-0.852819\pi$
$587$	−561.273	+	324.051i	−0.956172	+	0.552046i	−0.0611794	+	0.998127i	$0.519486\pi$
$588$		0			0
$589$	692.425	−	1199.32i	1.17559	−	2.03619i
$590$	−814.876	+	470.469i	−1.38115	+	0.797405i
$591$		0			0
$592$	102.877	−	178.188i	0.173779	−	0.300994i
$593$	130.961	+	75.6105i	0.220845	+	0.127505i	0.606342	−	0.795204i	$-0.292636\pi$
$593$	130.961	+	75.6105i	0.220845	+	0.127505i	−0.385496	+	0.922709i	$0.625970\pi$
$594$		0			0
$595$	901.318	+	39.0727i	1.51482	+	0.0656684i
$596$	−377.602	+	218.009i	−0.633561	+	0.365787i
$597$		0			0
$598$	−29.0506			−0.0485796
$599$		−	249.992i		−	0.417349i	−0.977985	−	0.208674i	$-0.933085\pi$
$599$		−	249.992i		−	0.417349i	0.977985	−	0.208674i	$-0.0669149\pi$
$600$		0			0
$601$	−251.801	−	436.133i	−0.418970	−	0.725678i	0.576866	−	0.816839i	$-0.304276\pi$
$601$	−251.801	−	436.133i	−0.418970	−	0.725678i	−0.995836	+	0.0911609i	$0.970942\pi$
$602$	−583.203	−	371.288i	−0.968776	−	0.616757i
$603$		0			0
$604$	131.762	−	228.218i	0.218149	−	0.377845i
$605$	531.119	+	306.641i	0.877882	+	0.506845i
$606$		0			0
$607$	−126.223	−	218.625i	−0.207946	−	0.360173i	0.743121	−	0.669157i	$-0.233344\pi$
$607$	−126.223	−	218.625i	−0.207946	−	0.360173i	−0.951067	+	0.308984i	$0.900011\pi$
$608$	144.404	+	83.3715i	0.237506	+	0.137124i
$609$		0			0
$610$	−302.069	−	523.199i	−0.495196	−	0.857704i
$611$	−34.1675	−	19.7266i	−0.0559206	−	0.0322858i
$612$		0			0
$613$	−130.589	−	226.186i	−0.213032	−	0.368982i	0.739630	−	0.673014i	$-0.235001\pi$
$613$	−130.589	−	226.186i	−0.213032	−	0.368982i	−0.952662	+	0.304032i	$0.901667\pi$
$614$			285.714i			0.465332i
$615$		0			0
$616$	−96.3993	−	4.17897i	−0.156492	−	0.00678405i
$617$	92.8353	+	53.5985i	0.150462	+	0.0868695i	0.573341	−	0.819317i	$-0.305647\pi$
$617$	92.8353	+	53.5985i	0.150462	+	0.0868695i	−0.422879	+	0.906186i	$0.638980\pi$
$618$		0			0
$619$	−122.170	+	211.605i	−0.197367	+	0.341850i	−0.947674	−	0.319240i	$-0.896572\pi$
$619$	−122.170	+	211.605i	−0.197367	+	0.341850i	0.750307	+	0.661090i	$0.229906\pi$
$620$	513.175	−	296.282i	0.827702	−	0.477874i
$621$		0			0
$622$	348.177			0.559771
$623$	−12.5146	+	288.682i	−0.0200876	+	0.463374i
$624$		0			0
$625$	388.050	+	672.122i	0.620880	+	1.07540i
$626$			74.1978i			0.118527i
$627$		0			0
$628$	−226.019			−0.359904
$629$		−	1051.24i		−	1.67129i
$630$		0			0
$631$	−593.344			−0.940323			−0.470161	−	0.882580i	$-0.655804\pi$
$631$	−593.344			−0.940323			−0.470161	+	0.882580i	$0.655804\pi$
$632$			204.424i			0.323456i
$633$		0			0
$634$	621.651			0.980522
$635$	−167.150	+	96.5038i	−0.263228	+	0.151975i
$636$		0			0
$637$	−67.3650	−	144.231i	−0.105754	−	0.226423i
$638$		−	187.827i		−	0.294400i
$639$		0			0
$640$	35.6738	+	61.7889i	0.0557403	+	0.0965451i
$641$	650.284	+	375.442i	1.01448	+	0.585713i	0.912502	−	0.409073i	$-0.134148\pi$
$641$	650.284	+	375.442i	1.01448	+	0.585713i	0.101983	+	0.994786i	$0.467481\pi$
$642$		0			0
$643$	142.353	−	246.563i	0.221390	−	0.383458i	−0.733841	−	0.679322i	$-0.762274\pi$
$643$	142.353	−	246.563i	0.221390	−	0.383458i	0.955230	+	0.295864i	$0.0956075\pi$
$644$	74.6740	+	47.5401i	0.115953	+	0.0738200i
$645$		0			0
$646$	851.924			1.31877
$647$	−15.0136	+	8.66810i	−0.0232049	+	0.0133974i	−0.511558	−	0.859249i	$-0.670931\pi$
$647$	−15.0136	+	8.66810i	−0.0232049	+	0.0133974i	0.488353	+	0.872646i	$0.337598\pi$
$648$		0			0
$649$	257.087	−	445.288i	0.396128	−	0.686114i
$650$	−58.7655	+	33.9283i	−0.0904084	+	0.0521973i
$651$		0			0
$652$	199.801	−	346.065i	0.306443	−	0.530775i
$653$	832.106	−	480.417i	1.27428	−	0.735707i	0.298491	−	0.954412i	$-0.403517\pi$
$653$	832.106	−	480.417i	1.27428	−	0.735707i	0.975791	+	0.218705i	$0.0701832\pi$
$654$		0			0
$655$	709.552	−	1228.98i	1.08329	−	1.87631i
$656$	−118.967	−	68.6856i	−0.181352	−	0.104704i
$657$		0			0
$658$	55.5451	+	106.620i	0.0844150	+	0.162037i
$659$	679.097	−	392.077i	1.03050	−	0.594957i	0.113369	−	0.993553i	$-0.463836\pi$
$659$	679.097	−	392.077i	1.03050	−	0.594957i	0.917127	+	0.398596i	$0.130502\pi$
$660$		0			0
$661$	−966.338			−1.46193			−0.730967	−	0.682413i	$-0.760931\pi$
$661$	−966.338			−1.46193			−0.730967	+	0.682413i	$0.760931\pi$
$662$			123.194i			0.186094i
$663$		0			0
$664$	−179.745	−	311.328i	−0.270700	−	0.468867i
$665$	1154.00	−	601.186i	1.73533	−	0.904040i
$666$		0			0
$667$	−86.1592	+	149.232i	−0.129174	+	0.223736i
$668$	−157.901	−	91.1639i	−0.236378	−	0.136473i
$669$		0			0
$670$	−119.100	−	206.287i	−0.177761	−	0.307891i
$671$	285.901	+	165.065i	0.426083	+	0.245999i
$672$		0			0
$673$	−142.389	−	246.625i	−0.211574	−	0.366457i	0.740633	−	0.671909i	$-0.234526\pi$
$673$	−142.389	−	246.625i	−0.211574	−	0.366457i	−0.952207	+	0.305453i	$0.901192\pi$
$674$	482.518	+	278.582i	0.715902	+	0.413326i
$675$		0			0
$676$	−158.446	−	274.436i	−0.234387	−	0.405971i
$677$		−	790.920i		−	1.16827i	−0.811656	−	0.584136i	$-0.801434\pi$
$677$		−	790.920i		−	1.16827i	0.811656	−	0.584136i	$-0.198566\pi$
$678$		0			0
$679$	−552.115	+	867.239i	−0.813129	+	1.27723i
$680$	315.692	+	182.265i	0.464253	+	0.268036i
$681$		0			0
$682$	−161.903	+	280.424i	−0.237394	+	0.411178i
$683$	−495.712	+	286.200i	−0.725787	+	0.419033i	−0.816879	−	0.576809i	$-0.804298\pi$
$683$	−495.712	+	286.200i	−0.725787	+	0.419033i	0.0910922	+	0.995842i	$0.470964\pi$
$684$		0			0
$685$	811.817			1.18513
$686$	−62.8682	+	480.984i	−0.0916446	+	0.701143i
$687$		0			0
$688$	−139.676	−	241.926i	−0.203018	−	0.351637i
$689$		−	10.4315i		−	0.0151401i
$690$		0			0
$691$	1017.46			1.47245			0.736223	−	0.676739i	$-0.236607\pi$
$691$	1017.46			1.47245			0.736223	+	0.676739i	$0.236607\pi$
$692$			431.607i			0.623709i
$693$		0			0
$694$	−130.163			−0.187554
$695$			1070.15i			1.53979i
$696$		0			0
$697$	−701.857			−1.00697
$698$	−52.0338	+	30.0417i	−0.0745470	+	0.0430398i
$699$		0			0
$700$	206.578	+	8.95528i	0.295111	+	0.0127933i
$701$			123.911i			0.176763i	0.996087	+	0.0883815i	$0.0281695\pi$
$701$			123.911i			0.176763i	−0.996087	+	0.0883815i	$0.971831\pi$
$702$		0			0
$703$	−758.108	−	1313.08i	−1.07839	−	1.86783i
$704$	−33.7644	−	19.4939i	−0.0479608	−	0.0276902i
$705$		0			0
$706$	−293.742	+	508.776i	−0.416065	+	0.720645i
$707$	−5.95529	+	137.375i	−0.00842332	+	0.194307i
$708$		0			0
$709$	117.698			0.166006			0.0830029	−	0.996549i	$-0.473549\pi$
$709$	117.698			0.166006			0.0830029	+	0.996549i	$0.473549\pi$
$710$	459.680	−	265.396i	0.647436	−	0.373798i
$711$		0			0
$712$	−58.3773	+	101.113i	−0.0819907	+	0.142012i
$713$	257.269	−	148.534i	0.360826	−	0.208323i
$714$		0			0
$715$	49.9225	−	86.4684i	0.0698217	−	0.120935i
$716$	−550.497	+	317.830i	−0.768851	+	0.443896i
$717$		0			0
$718$	58.4173	−	101.182i	0.0813611	−	0.140922i
$719$	622.294	+	359.281i	0.865499	+	0.499696i	0.865850	−	0.500304i	$-0.166778\pi$
$719$	622.294	+	359.281i	0.865499	+	0.499696i	−0.000350873		1.00000i	$0.500112\pi$
$720$		0			0
$721$	316.539	−	497.206i	0.439027	−	0.689606i
$722$	621.988	−	359.105i	0.861479	−	0.497375i
$723$		0			0
$724$	−225.475			−0.311429
$725$			402.502i			0.555176i
$726$		0			0
$727$	−264.639	−	458.367i	−0.364015	−	0.630492i	0.624603	−	0.780942i	$-0.285261\pi$
$727$	−264.639	−	458.367i	−0.364015	−	0.630492i	−0.988617	+	0.150451i	$0.951927\pi$
$728$	2.78577	−	64.2612i	0.00382660	−	0.0882709i
$729$		0			0
$730$	158.643	−	274.778i	0.217319	−	0.376408i
$731$	−1236.05	−	713.633i	−1.69090	−	0.976243i
$732$		0			0
$733$	215.715	+	373.630i	0.294291	+	0.509727i	0.974820	−	0.222995i	$-0.0715833\pi$
$733$	215.715	+	373.630i	0.294291	+	0.509727i	−0.680529	+	0.732721i	$0.738250\pi$
$734$	34.5457	+	19.9450i	0.0470650	+	0.0271730i
$735$		0			0
$736$	17.8843	+	30.9765i	0.0242993	+	0.0420876i
$737$	112.725	+	65.0818i	0.152951	+	0.0883064i
$738$		0			0
$739$	254.964	+	441.611i	0.345012	+	0.597579i	0.985356	−	0.170510i	$-0.0545414\pi$
$739$	254.964	+	441.611i	0.345012	+	0.597579i	−0.640344	+	0.768088i	$0.721208\pi$
$740$		−	648.774i		−	0.876721i
$741$		0			0
$742$	−17.0708	+	26.8141i	−0.0230064	+	0.0361376i
$743$	1168.43	+	674.592i	1.57258	+	0.907929i	0.995851	+	0.0909936i	$0.0290043\pi$
$743$	1168.43	+	674.592i	1.57258	+	0.907929i	0.576729	+	0.816936i	$0.304329\pi$
$744$		0			0
$745$	−687.414	+	1190.64i	−0.922704	+	1.59817i
$746$	857.165	−	494.884i	1.14901	−	0.663384i
$747$		0			0
$748$	−199.196			−0.266305
$749$	−30.3780	+	700.750i	−0.0405580	+	0.935580i
$750$		0			0
$751$	716.351	+	1240.76i	0.953863	+	1.65214i	0.736949	+	0.675948i	$0.236266\pi$
$751$	716.351	+	1240.76i	0.953863	+	1.65214i	0.216914	+	0.976191i	$0.430401\pi$
$752$			48.5768i			0.0645968i
$753$		0			0
$754$	125.209			0.166059
$755$		−	830.930i		−	1.10057i
$756$		0			0
$757$	−118.907			−0.157077			−0.0785386	−	0.996911i	$-0.525025\pi$
$757$	−118.907			−0.157077			−0.0785386	+	0.996911i	$0.525025\pi$
$758$		−	393.919i		−	0.519682i
$759$		0			0
$760$	525.766			0.691797
$761$	675.903	−	390.233i	0.888177	−	0.512789i	0.0148312	−	0.999890i	$-0.495279\pi$
$761$	675.903	−	390.233i	0.888177	−	0.512789i	0.873346	+	0.487101i	$0.161946\pi$
$762$		0			0
$763$	309.144	−	485.591i	0.405169	−	0.636423i
$764$		−	224.096i		−	0.293320i
$765$		0			0
$766$	92.4164	+	160.070i	0.120648	+	0.208968i
$767$	296.835	+	171.378i	0.387008	+	0.223439i
$768$		0			0
$769$	−293.677	+	508.663i	−0.381894	+	0.661460i	−0.991333	−	0.131373i	$-0.958061\pi$
$769$	−293.677	+	508.663i	−0.381894	+	0.661460i	0.609439	+	0.792833i	$0.291395\pi$
$770$	−269.827	+	140.569i	−0.350424	+	0.182557i
$771$		0			0
$772$	198.241			0.256788
$773$	148.903	−	85.9691i	0.192630	−	0.111215i	−0.400583	−	0.916260i	$-0.631192\pi$
$773$	148.903	−	85.9691i	0.192630	−	0.111215i	0.593213	+	0.805045i	$0.297859\pi$
$774$		0			0
$775$	346.947	−	600.930i	0.447674	−	0.775394i
$776$	−359.751	+	207.702i	−0.463596	+	0.267657i
$777$		0			0
$778$	224.614	−	389.043i	0.288707	−	0.500056i
$779$	−876.675	+	506.149i	−1.12539	+	0.649742i
$780$		0			0
$781$	−145.025	+	251.191i	−0.185692	+	0.321628i
$782$	158.265	+	91.3744i	0.202385	+	0.116847i
$783$		0			0
$784$	−112.322	+	160.623i	−0.143267	+	0.204877i
$785$	−617.193	+	356.336i	−0.786233	+	0.453932i
$786$		0			0
$787$	569.839			0.724065			0.362032	−	0.932165i	$-0.382083\pi$
$787$	569.839			0.724065			0.362032	+	0.932165i	$0.382083\pi$
$788$		−	116.631i		−	0.148009i
$789$		0			0
$790$	322.290	+	558.223i	0.407962	+	0.706611i
$791$	−29.3991	+	678.170i	−0.0371670	+	0.857358i
$792$		0			0
$793$	−110.035	+	190.586i	−0.138758	+	0.240336i
$794$	−825.272	−	476.471i	−1.03938	−	0.600089i
$795$		0			0
$796$	−5.44228	−	9.42630i	−0.00683703	−	0.0118421i
$797$	274.142	+	158.276i	0.343968	+	0.198590i	0.662025	−	0.749482i	$-0.269697\pi$
$797$	274.142	+	158.276i	0.343968	+	0.198590i	−0.318058	+	0.948071i	$0.603031\pi$
$798$		0			0
$799$	124.094	+	214.938i	0.155312	+	0.269008i
$800$	72.3550	+	41.7742i	0.0904438	+	0.0522177i
$801$		0			0
$802$	−186.923	−	323.760i	−0.233071	−	0.403691i
$803$			173.380i			0.215916i
$804$		0			0
$805$	278.863	+	12.0889i	0.346414	+	0.0150173i
$806$	−186.935	−	107.927i	−0.231929	−	0.133904i
$807$		0			0
$808$	−27.7800	+	48.1163i	−0.0343811	+	0.0595499i
$809$	−791.083	+	456.732i	−0.977853	+	0.564564i	−0.901621	−	0.432527i	$-0.857622\pi$
$809$	−791.083	+	456.732i	−0.977853	+	0.564564i	−0.0762316	+	0.997090i	$0.524289\pi$
$810$		0			0
$811$	954.927			1.17747			0.588734	−	0.808327i	$-0.299626\pi$
$811$	954.927			1.17747			0.588734	+	0.808327i	$0.299626\pi$
$812$	−321.846	−	204.898i	−0.396362	−	0.252338i
$813$		0			0
$814$	177.261	+	307.024i	0.217765	+	0.377180i
$815$		−	1260.00i		−	1.54602i
$816$		0			0
$817$	−2058.57			−2.51966
$818$			476.353i			0.582338i
$819$		0			0
$820$	−433.152			−0.528234
$821$			1228.87i			1.49679i	0.663252	+	0.748396i	$0.269176\pi$
$821$			1228.87i			1.49679i	−0.663252	+	0.748396i	$0.730824\pi$
$822$		0			0
$823$	−329.129			−0.399914			−0.199957	−	0.979805i	$-0.564080\pi$
$823$	−329.129			−0.399914			−0.199957	+	0.979805i	$0.564080\pi$
$824$	206.252	−	119.080i	0.250306	−	0.144514i
$825$		0			0
$826$	−482.557	−	926.282i	−0.584209	−	1.12141i
$827$		−	207.575i		−	0.250998i	−0.992094	−	0.125499i	$-0.959947\pi$
$827$		−	207.575i		−	0.250998i	0.992094	−	0.125499i	$-0.0400532\pi$
$828$		0			0
$829$	388.885	+	673.568i	0.469101	+	0.812507i	0.999376	−	0.0353187i	$-0.0112446\pi$
$829$	388.885	+	673.568i	0.469101	+	0.812507i	−0.530275	+	0.847826i	$0.677911\pi$
$830$	−981.662	−	566.763i	−1.18273	−	0.682847i
$831$		0			0
$832$	12.9949	−	22.5079i	0.0156189	−	0.0270527i
$833$	−86.6601	+	997.647i	−0.104034	+	1.19766i
$834$		0			0
$835$	−574.907			−0.688511
$836$	−248.812	+	143.652i	−0.297622	+	0.171832i
$837$		0			0
$838$	−66.8206	+	115.737i	−0.0797382	+	0.138111i
$839$	92.9798	−	53.6819i	0.110822	−	0.0639832i	−0.443564	−	0.896242i	$-0.646286\pi$
$839$	92.9798	−	53.6819i	0.110822	−	0.0639832i	0.554387	+	0.832259i	$0.312953\pi$
$840$		0			0
$841$	−49.1524	+	85.1344i	−0.0584451	+	0.101230i
$842$	306.891	−	177.183i	0.364478	−	0.210432i
$843$		0			0
$844$	285.184	−	493.953i	0.337895	−	0.585252i
$845$	−865.338	−	499.603i	−1.02407	−	0.591246i
$846$		0			0
$847$	−365.586	+	574.248i	−0.431625	+	0.677978i
$848$	−11.1231	+	6.42192i	−0.0131169	+	0.00757302i
$849$		0			0
$850$	426.865			0.502195
$851$		−	325.248i		−	0.382196i
$852$		0			0
$853$	53.8779	+	93.3192i	0.0631628	+	0.109401i	0.895878	−	0.444301i	$-0.146548\pi$
$853$	53.8779	+	93.3192i	0.0631628	+	0.109401i	−0.832715	+	0.553702i	$0.813215\pi$
$854$	594.729	−	309.830i	0.696404	−	0.362799i
$855$		0			0
$856$	−141.706	+	245.442i	−0.165544	+	0.286731i
$857$	858.932	+	495.904i	1.00225	+	0.578652i	0.908914	−	0.416983i	$-0.136912\pi$
$857$	858.932	+	495.904i	1.00225	+	0.578652i	0.0933395	+	0.995634i	$0.470246\pi$
$858$		0			0
$859$	−601.209	−	1041.32i	−0.699894	−	1.21225i	−0.968503	−	0.249002i	$-0.919897\pi$
$859$	−601.209	−	1041.32i	−0.699894	−	1.21225i	0.268609	−	0.963249i	$-0.413436\pi$
$860$	−762.829	−	440.420i	−0.887011	−	0.512116i
$861$		0			0
$862$	−321.613	−	557.051i	−0.373101	−	0.646230i
$863$	−1030.39	−	594.899i	−1.19397	−	0.689338i	−0.234764	−	0.972052i	$-0.575432\pi$
$863$	−1030.39	−	594.899i	−1.19397	−	0.689338i	−0.959204	+	0.282715i	$0.908765\pi$
$864$		0			0
$865$	680.461	+	1178.59i	0.786660	+	1.36253i
$866$			11.9375i			0.0137847i
$867$		0			0
$868$	303.894	+	583.334i	0.350108	+	0.672044i
$869$	−305.040	−	176.115i	−0.351024	−	0.202664i
$870$		0			0
$871$	−43.3845	+	75.1442i	−0.0498100	+	0.0862735i
$872$	201.434	−	116.298i	0.231002	−	0.133369i
$873$		0			0
$874$	263.581			0.301580
$875$	−400.528	+	208.659i	−0.457746	+	0.238468i
$876$		0			0
$877$	−5.78270	−	10.0159i	−0.00659373	−	0.0114207i	0.862710	−	0.505699i	$-0.168766\pi$
$877$	−5.78270	−	10.0159i	−0.00659373	−	0.0114207i	−0.869303	+	0.494279i	$0.835432\pi$
$878$		−	557.766i		−	0.635269i
$879$		0			0
$880$	−122.934			−0.139698
$881$			1307.45i			1.48405i	0.670372	+	0.742025i	$0.266135\pi$
$881$			1307.45i			1.48405i	−0.670372	+	0.742025i	$0.733865\pi$
$882$		0			0
$883$	1083.73			1.22733			0.613663	−	0.789568i	$-0.289695\pi$
$883$	1083.73			1.22733			0.613663	+	0.789568i	$0.289695\pi$
$884$		−	132.787i		−	0.150212i
$885$		0			0
$886$	−674.712			−0.761526
$887$	1087.25	−	627.725i	1.22576	−	0.707695i	0.259623	−	0.965710i	$-0.416402\pi$
$887$	1087.25	−	627.725i	1.22576	−	0.707695i	0.966141	+	0.258015i	$0.0830684\pi$
$888$		0			0
$889$	−98.9833	−	190.001i	−0.111342	−	0.213725i
$890$			368.145i			0.413646i
$891$		0			0
$892$	−102.623	−	177.748i	−0.115048	−	0.199269i
$893$	310.007	+	178.983i	0.347153	+	0.200429i
$894$		0			0
$895$	−1002.16	+	1735.80i	−1.11974	+	1.93944i
$896$	−70.2363	+	36.5904i	−0.0783888	+	0.0408375i
$897$		0			0
$898$	−489.622			−0.545237
$899$	−1108.83	+	640.185i	−1.23341	+	0.712108i
$900$		0			0
$901$	−32.8109	+	56.8301i	−0.0364161	+	0.0630745i
$902$	204.984	−	118.348i	0.227255	−	0.131206i
$903$		0			0
$904$	−137.140	+	237.533i	−0.151703	+	0.262758i
$905$	−615.706	+	355.478i	−0.680338	+	0.392793i
$906$		0			0
$907$	−765.770	+	1326.35i	−0.844289	+	1.46235i	0.0419479	+	0.999120i	$0.486644\pi$
$907$	−765.770	+	1326.35i	−0.844289	+	1.46235i	−0.886237	+	0.463232i	$0.846690\pi$
$908$	−593.810	−	342.836i	−0.653976	−	0.377573i
$909$		0			0
$910$	−93.7055	−	179.871i	−0.102973	−	0.197660i
$911$	1007.21	−	581.512i	1.10561	−	0.638323i	0.167920	−	0.985801i	$-0.446295\pi$
$911$	1007.21	−	581.512i	1.10561	−	0.638323i	0.937688	+	0.347478i	$0.112962\pi$
$912$		0			0
$913$	619.414			0.678438
$914$			841.835i			0.921044i
$915$		0			0
$916$	114.639	+	198.561i	0.125152	+	0.216770i
$917$	1328.78	+	845.947i	1.44905	+	0.922516i
$918$		0			0
$919$	477.282	−	826.676i	0.519349	−	0.899539i	−0.480398	−	0.877050i	$-0.659508\pi$
$919$	477.282	−	826.676i	0.519349	−	0.899539i	0.999747	−	0.0224882i	$-0.00715881\pi$
$920$	97.6735	+	56.3918i	0.106167	+	0.0612955i
$921$		0			0
$922$	−413.155	−	715.605i	−0.448107	−	0.776144i
$923$	−167.448	−	96.6760i	−0.181417	−	0.104741i
$924$		0			0
$925$	−379.858	−	657.934i	−0.410658	−	0.711280i
$926$	−480.800	−	277.590i	−0.519222	−	0.299773i
$927$		0			0
$928$	−77.0815	−	133.509i	−0.0830620	−	0.143868i
$929$		−	1083.28i		−	1.16607i	−0.812446	−	0.583037i	$-0.801864\pi$
$929$		−	1083.28i		−	1.16607i	0.812446	−	0.583037i	$-0.198136\pi$
$930$		0			0
$931$	611.214	+	1308.64i	0.656514	+	1.40562i
$932$	−291.014	−	168.017i	−0.312247	−	0.180276i
$933$		0			0
$934$	520.211	−	901.033i	0.556972	−	0.964703i
$935$	−543.947	+	314.048i	−0.581762	+	0.335880i
$936$		0			0
$937$	651.831			0.695657			0.347829	−	0.937558i	$-0.386919\pi$
$937$	651.831			0.695657			0.347829	+	0.937558i	$0.386919\pi$
$938$	234.489	−	122.160i	0.249989	−	0.130234i
$939$		0			0
$940$	76.5849	+	132.649i	0.0814733	+	0.141116i
$941$			571.094i			0.606902i	0.952847	+	0.303451i	$0.0981388\pi$
$941$			571.094i			0.606902i	−0.952847	+	0.303451i	$0.901861\pi$
$942$		0			0
$943$	−217.151			−0.230277
$944$		−	422.018i		−	0.447053i
$945$		0			0
$946$	481.333			0.508809
$947$		−	878.855i		−	0.928041i	−0.885824	−	0.464021i	$-0.846406\pi$
$947$		−	878.855i		−	0.928041i	0.885824	−	0.464021i	$-0.153594\pi$
$948$		0			0
$949$	−115.578			−0.121789
$950$	533.189	−	307.837i	0.561252	−	0.324039i
$951$		0			0
$952$	−217.301	+	341.327i	−0.228257	+	0.358537i
$953$		−	109.448i		−	0.114846i	−0.998350	−	0.0574231i	$-0.981712\pi$
$953$		−	109.448i		−	0.114846i	0.998350	−	0.0574231i	$-0.0182884\pi$
$954$		0			0
$955$	−353.304	−	611.941i	−0.369952	−	0.640776i
$956$	147.792	+	85.3275i	0.154594	+	0.0892547i
$957$		0			0
$958$	307.596	−	532.771i	0.321081	−	0.556129i
$959$	−39.0274	+	900.272i	−0.0406959	+	0.938761i
$960$		0			0
$961$	1246.30			1.29687
$962$	−204.667	+	118.165i	−0.212752	+	0.122832i
$963$		0			0
$964$	−225.692	+	390.910i	−0.234120	+	0.405508i
$965$	541.337	−	312.541i	0.560971	−	0.323877i
$966$		0			0
$967$	619.027	−	1072.19i	0.640152	−	1.10878i	−0.345247	−	0.938512i	$-0.612205\pi$
$967$	619.027	−	1072.19i	0.640152	−	1.10878i	0.985399	−	0.170264i	$-0.0544619\pi$
$968$	−238.211	+	137.531i	−0.246086	+	0.142078i
$969$		0			0
$970$	−654.916	+	1134.35i	−0.675171	+	1.16943i
$971$	−659.604	−	380.823i	−0.679304	−	0.392196i	0.120289	−	0.992739i	$-0.461618\pi$
$971$	−659.604	−	380.823i	−0.679304	−	0.392196i	−0.799593	+	0.600543i	$0.794951\pi$
$972$		0			0
$973$	−1186.75	−	51.4466i	−1.21969	−	0.0528742i
$974$	−149.966	+	86.5828i	−0.153969	+	0.0888941i
$975$		0			0
$976$	270.961			0.277624
$977$		−	1513.92i		−	1.54956i	−0.632234	−	0.774778i	$-0.717862\pi$
$977$		−	1513.92i		−	1.54956i	0.632234	−	0.774778i	$-0.282138\pi$
$978$		0			0
$979$	−100.586	−	174.220i	−0.102744	−	0.177957i
$980$	−53.4824	+	615.699i	−0.0545739	+	0.628264i
$981$		0			0
$982$	−220.224	+	381.439i	−0.224261	+	0.388431i
$983$	−341.837	−	197.360i	−0.347749	−	0.200773i	0.315944	−	0.948778i	$-0.397679\pi$
$983$	−341.837	−	197.360i	−0.347749	−	0.200773i	−0.663693	+	0.748005i	$0.731012\pi$
$984$		0			0
$985$	−183.877	−	318.485i	−0.186678	−	0.323335i
$986$	−682.125	−	393.825i	−0.691810	−	0.399417i
$987$		0			0
$988$	−95.7604	−	165.862i	−0.0969235	−	0.167876i
$989$	−382.428	−	220.795i	−0.386681	−	0.223250i
$990$		0			0
$991$	19.0104	+	32.9271i	0.0191831	+	0.0332261i	0.875458	−	0.483295i	$-0.160560\pi$
$991$	19.0104	+	32.9271i	0.0191831	+	0.0332261i	−0.856274	+	0.516521i	$0.827227\pi$
$992$			265.770i			0.267913i
$993$		0			0
$994$	272.215	+	522.525i	0.273858	+	0.525679i
$995$	−29.7225	−	17.1603i	−0.0298719	−	0.0172465i
$996$		0			0
$997$	−414.702	+	718.284i	−0.415949	+	0.720445i	−0.995528	−	0.0944712i	$-0.969884\pi$
$997$	−414.702	+	718.284i	−0.415949	+	0.720445i	0.579578	+	0.814917i	$0.303217\pi$
$998$	−16.3023	+	9.41212i	−0.0163349	+	0.00943098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.233.10		32
3.2	odd	2		126.3.r.a.23.3	yes	32
7.4	even	3		378.3.i.a.179.2		32
9.2	odd	6		378.3.i.a.359.7		32
9.7	even	3		126.3.i.a.65.11	✓	32
21.11	odd	6		126.3.i.a.95.11	yes	32
63.11	odd	6	inner	378.3.r.a.305.2		32
63.25	even	3		126.3.r.a.11.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.11	✓	32	9.7	even	3
126.3.i.a.95.11	yes	32	21.11	odd	6
126.3.r.a.11.11	yes	32	63.25	even	3
126.3.r.a.23.3	yes	32	3.2	odd	2
378.3.i.a.179.2		32	7.4	even	3
378.3.i.a.359.7		32	9.2	odd	6
378.3.r.a.233.10		32	1.1	even	1	trivial
378.3.r.a.305.2		32	63.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-5.46142 + 3.15315i) q^{5} +(-3.23416 - 6.20807i) q^{7} -2.82843i q^{8} +(-4.45923 - 7.72361i) q^{10} +(4.22055 + 2.43674i) q^{11} +(-1.62436 + 2.81348i) q^{13} +(8.77954 - 4.57380i) q^{14} +4.00000 q^{16} +(17.6988 - 10.2184i) q^{17} +(14.7381 - 25.5272i) q^{19} +(10.9228 - 6.30630i) q^{20} +(-3.44607 + 5.96876i) q^{22} +(5.47592 - 3.16152i) q^{23} +(7.38470 - 12.7907i) q^{25} +(-3.97886 - 2.29720i) q^{26} +(6.46833 + 12.4161i) q^{28} +(-23.6013 + 13.6262i) q^{29} +46.9819 q^{31} +5.65685i q^{32} +(14.4510 + 25.0299i) q^{34} +(37.2381 + 23.7071i) q^{35} +(25.7193 - 44.5471i) q^{37} +(36.1009 + 20.8429i) q^{38} +(8.91845 + 15.4472i) q^{40} +(-29.7417 - 17.1714i) q^{41} +(-34.9190 - 60.4815i) q^{43} +(-8.44110 - 4.87347i) q^{44} +(4.47107 + 7.74412i) q^{46} +12.1442i q^{47} +(-28.0804 + 40.1559i) q^{49} +(18.0888 + 10.4435i) q^{50} +(3.24873 - 5.62696i) q^{52} +(-2.78077 + 1.60548i) q^{53} -30.7336 q^{55} +(-17.5591 + 9.14759i) q^{56} +(-19.2704 - 33.3773i) q^{58} -105.505i q^{59} +67.7403 q^{61} +66.4424i q^{62} -8.00000 q^{64} -20.4875i q^{65} +26.7086 q^{67} +(-35.3976 + 20.4368i) q^{68} +(-33.5269 + 52.6626i) q^{70} +59.5162i q^{71} +(17.7882 + 30.8100i) q^{73} +(62.9991 + 36.3725i) q^{74} +(-29.4763 + 51.0544i) q^{76} +(1.47749 - 34.0823i) q^{77} -72.2749 q^{79} +(-21.8457 + 12.6126i) q^{80} +(24.2840 - 42.0611i) q^{82} +(110.071 - 63.5495i) q^{83} +(-64.4403 + 111.614i) q^{85} +(85.5338 - 49.3830i) q^{86} +(6.89213 - 11.9375i) q^{88} +(-35.7487 - 20.6395i) q^{89} +(22.7198 + 0.984917i) q^{91} +(-10.9518 + 6.32305i) q^{92} -17.1745 q^{94} +185.886i q^{95} +(-73.4338 - 127.191i) q^{97} +(-56.7889 - 39.7117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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