LMFDB - Embedded newform 405.3.h.k.134.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.24
Character	$\chi$	$=$	405.134
Dual form			405.3.h.k.269.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.78706 + 3.09527i) q^{2} +(-4.38714 + 7.59875i) q^{4} +(1.88580 + 4.63074i) q^{5} +(5.21507 - 3.01092i) q^{7} -17.0638 q^{8} +(-10.9634 + 14.1125i) q^{10} +(-13.1642 + 7.60038i) q^{11} +(9.54973 + 5.51354i) q^{13} +(18.6393 + 10.7614i) q^{14} +(-12.9455 - 22.4222i) q^{16} -26.8426 q^{17} +15.8915 q^{19} +(-43.4611 - 5.98598i) q^{20} +(-47.0505 - 27.1646i) q^{22} +(-5.76711 + 9.98892i) q^{23} +(-17.8875 + 17.4653i) q^{25} +39.4120i q^{26} +52.8374i q^{28} +(47.1448 - 27.2191i) q^{29} +(15.7861 - 27.3423i) q^{31} +(12.1409 - 21.0287i) q^{32} +(-47.9692 - 83.0851i) q^{34} +(23.7774 + 18.4716i) q^{35} -38.1480i q^{37} +(28.3990 + 49.1885i) q^{38} +(-32.1790 - 79.0182i) q^{40} +(32.6176 + 18.8318i) q^{41} +(-3.93082 + 2.26946i) q^{43} -133.376i q^{44} -41.2246 q^{46} +(-1.85906 - 3.21998i) q^{47} +(-6.36869 + 11.0309i) q^{49} +(-86.0259 - 24.1552i) q^{50} +(-83.7921 + 48.3774i) q^{52} -56.1230 q^{53} +(-60.0205 - 46.6274i) q^{55} +(-88.9891 + 51.3779i) q^{56} +(168.501 + 97.2841i) q^{58} +(43.3384 + 25.0214i) q^{59} +(24.2209 + 41.9518i) q^{61} +112.842 q^{62} -16.7778 q^{64} +(-7.52288 + 54.6198i) q^{65} +(60.0763 + 34.6851i) q^{67} +(117.762 - 203.970i) q^{68} +(-14.6832 + 106.607i) q^{70} -38.5522i q^{71} -27.2700i q^{73} +(118.078 - 68.1726i) q^{74} +(-69.7183 + 120.756i) q^{76} +(-45.7683 + 79.2730i) q^{77} +(39.4493 + 68.3281i) q^{79} +(79.4189 - 102.231i) q^{80} +134.614i q^{82} +(75.3011 + 130.425i) q^{83} +(-50.6198 - 124.301i) q^{85} +(-14.0492 - 8.11131i) q^{86} +(224.633 - 129.692i) q^{88} +3.50521i q^{89} +66.4034 q^{91} +(-50.6022 - 87.6456i) q^{92} +(6.64448 - 11.5086i) q^{94} +(29.9682 + 73.5894i) q^{95} +(-23.9496 + 13.8273i) q^{97} -45.5248 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) $ 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.78706	+	3.09527i	0.893528	+	1.54764i	0.835616	+	0.549315i	$0.185111\pi$
$2$	1.78706	+	3.09527i	0.893528	+	1.54764i	0.0579128	+	0.998322i	$0.481555\pi$
$3$		0			0
$3$		0			0
$4$	−4.38714	+	7.59875i	−1.09679	+	1.89969i
$5$	1.88580	+	4.63074i	0.377160	+	0.926148i
$5$	1.88580	+	4.63074i	0.377160	+	0.926148i
$6$		0			0
$7$	5.21507	−	3.01092i	0.745010	−	0.430132i	−0.0788780	−	0.996884i	$-0.525134\pi$
$7$	5.21507	−	3.01092i	0.745010	−	0.430132i	0.823888	+	0.566752i	$0.191800\pi$
$8$	−17.0638			−2.13298
$9$		0			0
$10$	−10.9634	+	14.1125i	−1.09634	+	1.41125i
$11$	−13.1642	+	7.60038i	−1.19675	+	0.690944i	−0.959829	−	0.280585i	$-0.909471\pi$
$11$	−13.1642	+	7.60038i	−1.19675	+	0.690944i	−0.236920	+	0.971529i	$0.576138\pi$
$12$		0			0
$13$	9.54973	+	5.51354i	0.734595	+	0.424119i	0.820101	−	0.572219i	$-0.193917\pi$
$13$	9.54973	+	5.51354i	0.734595	+	0.424119i	−0.0855059	+	0.996338i	$0.527251\pi$
$14$	18.6393	+	10.7614i	1.33138	+	0.768670i
$15$		0			0
$16$	−12.9455	−	22.4222i	−0.809092	−	1.40139i
$17$	−26.8426			−1.57898			−0.789488	−	0.613767i	$-0.789654\pi$
$17$	−26.8426			−1.57898			−0.789488	+	0.613767i	$0.789654\pi$
$18$		0			0
$19$	15.8915			0.836395			0.418197	−	0.908356i	$-0.362662\pi$
$19$	15.8915			0.836395			0.418197	+	0.908356i	$0.362662\pi$
$20$	−43.4611	−	5.98598i	−2.17306	−	0.299299i
$21$		0			0
$22$	−47.0505	−	27.1646i	−2.13866	−	1.23476i
$23$	−5.76711	+	9.98892i	−0.250744	+	0.434301i	−0.963731	−	0.266876i	$-0.914008\pi$
$23$	−5.76711	+	9.98892i	−0.250744	+	0.434301i	0.712987	+	0.701177i	$0.247342\pi$
$24$		0			0
$25$	−17.8875	+	17.4653i	−0.715500	+	0.698612i
$26$			39.4120i			1.51585i
$27$		0			0
$28$			52.8374i			1.88705i
$29$	47.1448	−	27.2191i	1.62568	−	0.938589i	0.640324	−	0.768105i	$-0.278800\pi$
$29$	47.1448	−	27.2191i	1.62568	−	0.938589i	0.985360	−	0.170484i	$-0.0545331\pi$
$30$		0			0
$31$	15.7861	−	27.3423i	0.509228	−	0.882009i	−0.490715	−	0.871320i	$-0.663264\pi$
$31$	15.7861	−	27.3423i	0.509228	−	0.882009i	0.999943	−	0.0106889i	$-0.00340244\pi$
$32$	12.1409	−	21.0287i	0.379403	−	0.657146i
$33$		0			0
$34$	−47.9692	−	83.0851i	−1.41086	−	2.44368i
$35$	23.7774	+	18.4716i	0.679354	+	0.527761i
$36$		0			0
$37$		−	38.1480i		−	1.03103i	−0.856881	−	0.515514i	$-0.827601\pi$
$37$		−	38.1480i		−	1.03103i	0.856881	−	0.515514i	$-0.172399\pi$
$38$	28.3990	+	49.1885i	0.747342	+	1.29443i
$39$		0			0
$40$	−32.1790	−	79.0182i	−0.804475	−	1.97545i
$41$	32.6176	+	18.8318i	0.795552	+	0.459312i	0.841914	−	0.539612i	$-0.181429\pi$
$41$	32.6176	+	18.8318i	0.795552	+	0.459312i	−0.0463612	+	0.998925i	$0.514763\pi$
$42$		0			0
$43$	−3.93082	+	2.26946i	−0.0914145	+	0.0527782i	−0.545010	−	0.838429i	$-0.683474\pi$
$43$	−3.93082	+	2.26946i	−0.0914145	+	0.0527782i	0.453596	+	0.891207i	$0.350141\pi$
$44$		−	133.376i		−	3.03127i
$45$		0			0
$46$	−41.2246			−0.896187
$47$	−1.85906	−	3.21998i	−0.0395544	−	0.0685102i	0.845570	−	0.533864i	$-0.179261\pi$
$47$	−1.85906	−	3.21998i	−0.0395544	−	0.0685102i	−0.885125	+	0.465354i	$0.845927\pi$
$48$		0			0
$49$	−6.36869	+	11.0309i	−0.129973	+	0.225120i
$50$	−86.0259	−	24.1552i	−1.72052	−	0.483104i
$51$		0			0
$52$	−83.7921	+	48.3774i	−1.61139	+	0.930334i
$53$	−56.1230			−1.05892			−0.529462	−	0.848333i	$-0.677606\pi$
$53$	−56.1230			−1.05892			−0.529462	+	0.848333i	$0.677606\pi$
$54$		0			0
$55$	−60.0205	−	46.6274i	−1.09128	−	0.847771i
$56$	−88.9891	+	51.3779i	−1.58909	+	0.917462i
$57$		0			0
$58$	168.501	+	97.2841i	2.90519	+	1.67731i
$59$	43.3384	+	25.0214i	0.734549	+	0.424092i	0.820084	−	0.572243i	$-0.193927\pi$
$59$	43.3384	+	25.0214i	0.734549	+	0.424092i	−0.0855353	+	0.996335i	$0.527260\pi$
$60$		0			0
$61$	24.2209	+	41.9518i	0.397063	+	0.687734i	0.993362	−	0.115029i	$-0.0366960\pi$
$61$	24.2209	+	41.9518i	0.397063	+	0.687734i	−0.596299	+	0.802762i	$0.703363\pi$
$62$	112.842			1.82004
$63$		0			0
$64$	−16.7778			−0.262153
$65$	−7.52288	+	54.6198i	−0.115737	+	0.840304i
$66$		0			0
$67$	60.0763	+	34.6851i	0.896662	+	0.517688i	0.876116	−	0.482101i	$-0.160126\pi$
$67$	60.0763	+	34.6851i	0.896662	+	0.517688i	0.0205460	+	0.999789i	$0.493460\pi$
$68$	117.762	−	203.970i	1.73180	−	2.99956i
$69$		0			0
$70$	−14.6832	+	106.607i	−0.209760	+	1.52296i
$71$		−	38.5522i		−	0.542989i	−0.962440	−	0.271494i	$-0.912482\pi$
$71$		−	38.5522i		−	0.542989i	0.962440	−	0.271494i	$-0.0875179\pi$
$72$		0			0
$73$		−	27.2700i		−	0.373561i	−0.982402	−	0.186781i	$-0.940195\pi$
$73$		−	27.2700i		−	0.373561i	0.982402	−	0.186781i	$-0.0598054\pi$
$74$	118.078	−	68.1726i	1.59566	−	0.921252i
$75$		0			0
$76$	−69.7183	+	120.756i	−0.917346	+	1.58889i
$77$	−45.7683	+	79.2730i	−0.594394	+	1.02952i
$78$		0			0
$79$	39.4493	+	68.3281i	0.499358	+	0.864913i	1.00000		0.000741320i	$-0.000235969\pi$
$79$	39.4493	+	68.3281i	0.499358	+	0.864913i	−0.500642	+	0.865655i	$0.666903\pi$
$80$	79.4189	−	102.231i	0.992736	−	1.27789i
$81$		0			0
$82$			134.614i			1.64163i
$83$	75.3011	+	130.425i	0.907242	+	1.57139i	0.817879	+	0.575390i	$0.195150\pi$
$83$	75.3011	+	130.425i	0.907242	+	1.57139i	0.0893625	+	0.995999i	$0.471517\pi$
$84$		0			0
$85$	−50.6198	−	124.301i	−0.595527	−	1.46236i
$86$	−14.0492	−	8.11131i	−0.163363	−	0.0943176i
$87$		0			0
$88$	224.633	−	129.692i	2.55264	−	1.47377i
$89$			3.50521i			0.0393843i	0.999806	+	0.0196922i	$0.00626862\pi$
$89$			3.50521i			0.0393843i	−0.999806	+	0.0196922i	$0.993731\pi$
$90$		0			0
$91$	66.4034			0.729708
$92$	−50.6022	−	87.6456i	−0.550024	−	0.952670i
$93$		0			0
$94$	6.64448	−	11.5086i	0.0706859	−	0.122432i
$95$	29.9682	+	73.5894i	0.315455	+	0.774625i
$96$		0			0
$97$	−23.9496	+	13.8273i	−0.246903	+	0.142550i	−0.618345	−	0.785906i	$-0.712197\pi$
$97$	−23.9496	+	13.8273i	−0.246903	+	0.142550i	0.371442	+	0.928456i	$0.378863\pi$
$98$	−45.5248			−0.464539
$99$		0			0
$100$	−54.2396	−	212.546i	−0.542396	−	2.12546i
$101$	31.2554	−	18.0453i	0.309460	−	0.178667i	−0.337225	−	0.941424i	$-0.609488\pi$
$101$	31.2554	−	18.0453i	0.309460	−	0.178667i	0.646685	+	0.762757i	$0.276155\pi$
$102$		0			0
$103$	24.3017	+	14.0306i	0.235939	+	0.136219i	0.613309	−	0.789843i	$-0.289838\pi$
$103$	24.3017	+	14.0306i	0.235939	+	0.136219i	−0.377370	+	0.926063i	$0.623171\pi$
$104$	−162.955	−	94.0822i	−1.56688	−	0.904636i
$105$		0			0
$106$	−100.295	−	173.716i	−0.946179	−	1.63883i
$107$	91.8455			0.858369			0.429184	−	0.903217i	$-0.358801\pi$
$107$	91.8455			0.858369			0.429184	+	0.903217i	$0.358801\pi$
$108$		0			0
$109$	78.1779			0.717228			0.358614	−	0.933486i	$-0.383249\pi$
$109$	78.1779			0.717228			0.358614	+	0.933486i	$0.383249\pi$
$110$	37.0644	−	269.106i	0.336949	−	2.44642i
$111$		0			0
$112$	−135.023	−	77.9556i	−1.20556	−	0.696032i
$113$	−3.28363	+	5.68742i	−0.0290587	+	0.0503311i	−0.880189	−	0.474623i	$-0.842584\pi$
$113$	−3.28363	+	5.68742i	−0.0290587	+	0.0503311i	0.851130	+	0.524954i	$0.175918\pi$
$114$		0			0
$115$	−57.1317	−	7.86885i	−0.496798	−	0.0684248i
$116$			477.656i			4.11772i
$117$		0			0
$118$			178.859i			1.51575i
$119$	−139.986	+	80.8209i	−1.17635	+	0.679167i
$120$		0			0
$121$	55.0316	−	95.3175i	0.454806	−	0.787748i
$122$	−86.5681	+	149.940i	−0.709574	+	1.22902i
$123$		0			0
$124$	138.512	+	239.909i	1.11703	+	1.93475i
$125$	−114.610	−	49.8963i	−0.916877	−	0.399170i
$126$		0			0
$127$		−	247.486i		−	1.94871i	−0.225023	−	0.974353i	$-0.572246\pi$
$127$		−	247.486i		−	1.94871i	0.225023	−	0.974353i	$-0.427754\pi$
$128$	−78.5465	−	136.047i	−0.613645	−	1.06286i
$129$		0			0
$130$	−182.507	+	74.3233i	−1.40390	+	0.571718i
$131$	123.126	+	71.0869i	0.939894	+	0.542648i	0.889927	−	0.456103i	$-0.150755\pi$
$131$	123.126	+	71.0869i	0.939894	+	0.542648i	0.0499669	+	0.998751i	$0.484088\pi$
$132$		0			0
$133$	82.8753	−	47.8481i	0.623122	−	0.359760i
$134$			247.937i			1.85027i
$135$		0			0
$136$	458.037			3.36792
$137$	−36.4450	−	63.1246i	−0.266022	−	0.460763i	0.701809	−	0.712365i	$-0.252376\pi$
$137$	−36.4450	−	63.1246i	−0.266022	−	0.460763i	−0.967831	+	0.251602i	$0.919043\pi$
$138$		0			0
$139$	33.4995	−	58.0228i	0.241003	−	0.417430i	−0.719997	−	0.693977i	$-0.755857\pi$
$139$	33.4995	−	58.0228i	0.241003	−	0.417430i	0.961000	+	0.276547i	$0.0891902\pi$
$140$	−244.676	+	99.6408i	−1.74769	+	0.711720i
$141$		0			0
$142$	119.330	−	68.8950i	0.840350	−	0.485176i
$143$	−167.620			−1.17217
$144$		0			0
$145$	214.950	+	166.986i	1.48242	+	1.15163i
$146$	84.4080	−	48.7330i	0.578137	−	0.333788i
$147$		0			0
$148$	289.877	+	167.361i	1.95863	+	1.13082i
$149$	−66.3088	−	38.2834i	−0.445025	−	0.256936i	0.260702	−	0.965419i	$-0.416046\pi$
$149$	−66.3088	−	38.2834i	−0.445025	−	0.256936i	−0.705727	+	0.708484i	$0.749379\pi$
$150$		0			0
$151$	19.9525	+	34.5588i	0.132136	+	0.228866i	0.924500	−	0.381183i	$-0.124483\pi$
$151$	19.9525	+	34.5588i	0.132136	+	0.228866i	−0.792364	+	0.610049i	$0.791150\pi$
$152$	−271.170			−1.78401
$153$		0			0
$154$	−327.162			−2.12443
$155$	156.384	+	21.5391i	1.00893	+	0.138962i
$156$		0			0
$157$	−117.412	−	67.7877i	−0.747846	−	0.431769i	0.0770693	−	0.997026i	$-0.475444\pi$
$157$	−117.412	−	67.7877i	−0.747846	−	0.431769i	−0.824915	+	0.565257i	$0.808777\pi$
$158$	−140.996	+	244.213i	−0.892381	+	1.54565i
$159$		0			0
$160$	120.274	+	16.5655i	0.751710	+	0.103534i
$161$			69.4572i			0.431411i
$162$		0			0
$163$			85.9303i			0.527180i	0.964635	+	0.263590i	$0.0849066\pi$
$163$			85.9303i			0.527180i	−0.964635	+	0.263590i	$0.915093\pi$
$164$	−286.197	+	165.236i	−1.74510	+	1.00753i
$165$		0			0
$166$	−269.135	+	466.155i	−1.62129	+	2.80816i
$167$	55.8590	−	96.7506i	0.334485	−	0.579345i	−0.648901	−	0.760873i	$-0.724771\pi$
$167$	55.8590	−	96.7506i	0.334485	−	0.579345i	0.983386	+	0.181528i	$0.0581044\pi$
$168$		0			0
$169$	−23.7017	−	41.0526i	−0.140247	−	0.242915i
$170$	294.285	−	378.815i	1.73109	−	2.22832i
$171$		0			0
$172$		−	39.8258i		−	0.231545i
$173$	4.34493	+	7.52564i	0.0251152	+	0.0435008i	0.878310	−	0.478092i	$-0.158671\pi$
$173$	4.34493	+	7.52564i	0.0251152	+	0.0435008i	−0.853195	+	0.521593i	$0.825338\pi$
$174$		0			0
$175$	−40.6979	+	144.941i	−0.232560	+	0.828233i
$176$	340.835	+	196.781i	1.93656	+	1.11807i
$177$		0			0
$178$	−10.8496	+	6.26400i	−0.0609526	+	0.0351910i
$179$		−	57.4651i		−	0.321034i	−0.987033	−	0.160517i	$-0.948684\pi$
$179$		−	57.4651i		−	0.321034i	0.987033	−	0.160517i	$-0.0513162\pi$
$180$		0			0
$181$	−139.711			−0.771884			−0.385942	−	0.922523i	$-0.626124\pi$
$181$	−139.711			−0.771884			−0.385942	+	0.922523i	$0.626124\pi$
$182$	118.667	+	205.537i	0.652014	+	1.12932i
$183$		0			0
$184$	98.4090	−	170.449i	0.534831	−	0.926355i
$185$	176.653	−	71.9395i	0.954884	−	0.388862i
$186$		0			0
$187$	353.362	−	204.014i	1.88964	−	1.09098i
$188$	32.6238			0.173531
$189$		0			0
$190$	−174.224	+	224.268i	−0.916970	+	1.18036i
$191$	−27.2590	+	15.7380i	−0.142718	+	0.0823980i	−0.569659	−	0.821881i	$-0.692925\pi$
$191$	−27.2590	+	15.7380i	−0.142718	+	0.0823980i	0.426941	+	0.904279i	$0.359591\pi$
$192$		0			0
$193$	−43.3664	−	25.0376i	−0.224696	−	0.129729i	0.383427	−	0.923571i	$-0.374744\pi$
$193$	−43.3664	−	25.0376i	−0.224696	−	0.129729i	−0.608123	+	0.793843i	$0.708077\pi$
$194$	−85.5986	−	49.4204i	−0.441230	−	0.254744i
$195$		0			0
$196$	−55.8807	−	96.7882i	−0.285106	−	0.493817i
$197$	−37.4908			−0.190308			−0.0951542	−	0.995463i	$-0.530334\pi$
$197$	−37.4908			−0.190308			−0.0951542	+	0.995463i	$0.530334\pi$
$198$		0			0
$199$	40.5173			0.203604			0.101802	−	0.994805i	$-0.467539\pi$
$199$	40.5173			0.203604			0.101802	+	0.994805i	$0.467539\pi$
$200$	305.230	−	298.025i	1.52615	−	1.49013i
$201$		0			0
$202$	111.710	+	64.4961i	0.553022	+	0.319287i
$203$	163.909	−	283.899i	0.807434	−	1.39852i
$204$		0			0
$205$	−25.6948	+	186.557i	−0.125341	+	0.910034i
$206$			100.294i			0.486864i
$207$		0			0
$208$		−	285.502i		−	1.37260i
$209$	−209.200	+	120.781i	−1.00095	+	0.577902i
$210$		0			0
$211$	−86.2363	+	149.366i	−0.408703	+	0.707894i	−0.994745	−	0.102387i	$-0.967352\pi$
$211$	−86.2363	+	149.366i	−0.408703	+	0.707894i	0.586042	+	0.810281i	$0.300685\pi$
$212$	246.220	−	426.465i	1.16141	−	2.01163i
$213$		0			0
$214$	164.133	+	284.287i	0.766977	+	1.32844i
$215$	−17.9220	−	13.9229i	−0.0833583	−	0.0647575i
$216$		0			0
$217$		−	190.123i		−	0.876141i
$218$	139.708	+	241.982i	0.640864	+	1.11001i
$219$		0			0
$220$	617.629	−	251.520i	2.80740	−	1.14327i
$221$	−256.339	−	147.998i	−1.15991	−	0.669673i
$222$		0			0
$223$	−259.250	+	149.678i	−1.16255	+	0.671201i	−0.951915	−	0.306363i	$-0.900888\pi$
$223$	−259.250	+	149.678i	−1.16255	+	0.671201i	−0.210639	+	0.977564i	$0.567555\pi$
$224$		−	146.221i		−	0.652774i
$225$		0			0
$226$	−23.4721			−0.103859
$227$	−149.358	−	258.696i	−0.657965	−	1.13963i	−0.981142	−	0.193290i	$-0.938084\pi$
$227$	−149.358	−	258.696i	−0.657965	−	1.13963i	0.323177	−	0.946338i	$-0.395249\pi$
$228$		0			0
$229$	101.655	−	176.072i	0.443908	−	0.768871i	−0.554067	−	0.832472i	$-0.686925\pi$
$229$	101.655	−	176.072i	0.443908	−	0.768871i	0.997975	+	0.0636005i	$0.0202584\pi$
$230$	−77.7414	−	190.900i	−0.338006	−	0.830001i
$231$		0			0
$232$	−804.472	+	464.462i	−3.46755	+	2.00199i
$233$	436.398			1.87295			0.936476	−	0.350733i	$-0.114067\pi$
$233$	436.398			1.87295			0.936476	+	0.350733i	$0.114067\pi$
$234$		0			0
$235$	11.4051	−	14.6810i	0.0485322	−	0.0624725i
$236$	−380.263	+	219.545i	−1.61128	+	0.930276i
$237$		0			0
$238$	−500.326	−	288.863i	−2.10221	−	1.21371i
$239$	−207.584	−	119.848i	−0.868551	−	0.501458i	−0.00168434	−	0.999999i	$-0.500536\pi$
$239$	−207.584	−	119.848i	−0.868551	−	0.501458i	−0.866866	+	0.498541i	$0.833869\pi$
$240$		0			0
$241$	−102.674	−	177.837i	−0.426034	−	0.737912i	0.570483	−	0.821310i	$-0.306756\pi$
$241$	−102.674	−	177.837i	−0.426034	−	0.737912i	−0.996516	+	0.0833977i	$0.973423\pi$
$242$	393.378			1.62553
$243$		0			0
$244$	−425.041			−1.74197
$245$	−63.0913	−	8.68967i	−0.257515	−	0.0354681i
$246$		0			0
$247$	151.760	+	87.6184i	0.614411	+	0.354731i
$248$	−269.371	+	466.564i	−1.08617	+	1.88131i
$249$		0			0
$250$	−50.3712	−	443.915i	−0.201485	−	1.77566i
$251$		−	357.277i		−	1.42341i	−0.702477	−	0.711707i	$-0.747923\pi$
$251$		−	357.277i		−	1.42341i	0.702477	−	0.711707i	$-0.252077\pi$
$252$		0			0
$253$		−	175.329i		−	0.692999i
$254$	766.036	−	442.271i	3.01589	−	1.74122i
$255$		0			0
$256$	247.179	−	428.126i	0.965541	−	1.67237i
$257$	−140.257	+	242.932i	−0.545746	+	0.945260i	0.452814	+	0.891605i	$0.350420\pi$
$257$	−140.257	+	242.932i	−0.545746	+	0.945260i	−0.998560	+	0.0536544i	$0.982913\pi$
$258$		0			0
$259$	−114.861	−	198.945i	−0.443478	−	0.768126i
$260$	−382.038	−	296.789i	−1.46938	−	1.14150i
$261$		0			0
$262$			508.145i			1.93949i
$263$	−60.2472	−	104.351i	−0.229077	−	0.396772i	0.728458	−	0.685090i	$-0.240237\pi$
$263$	−60.2472	−	104.351i	−0.229077	−	0.396772i	−0.957535	+	0.288318i	$0.906904\pi$
$264$		0			0
$265$	−105.837	−	259.891i	−0.399384	−	0.980721i
$266$	296.206	+	171.014i	1.11356	+	0.642911i
$267$		0			0
$268$	−527.127	+	304.337i	−1.96689	+	1.13559i
$269$		−	308.065i		−	1.14522i	−0.819827	−	0.572612i	$-0.805930\pi$
$269$		−	308.065i		−	1.14522i	0.819827	−	0.572612i	$-0.194070\pi$
$270$		0			0
$271$	354.684			1.30880			0.654399	−	0.756149i	$-0.272922\pi$
$271$	354.684			1.30880			0.654399	+	0.756149i	$0.272922\pi$
$272$	347.490	+	601.870i	1.27754	+	2.21276i
$273$		0			0
$274$	130.259	−	225.614i	0.475396	−	0.823410i
$275$	102.733	−	365.869i	0.373573	−	1.33043i
$276$		0			0
$277$	415.957	−	240.153i	1.50165	−	0.866978i	0.501652	−	0.865070i	$-0.332726\pi$
$277$	415.957	−	240.153i	1.50165	−	0.866978i	0.999998	−	0.00190830i	$-0.000607433\pi$
$278$	239.462			0.861373
$279$		0			0
$280$	−405.733	−	315.197i	−1.44905	−	1.12570i
$281$	109.335	−	63.1249i	0.389094	−	0.224644i	−0.292673	−	0.956212i	$-0.594545\pi$
$281$	109.335	−	63.1249i	0.389094	−	0.224644i	0.681768	+	0.731569i	$0.261212\pi$
$282$		0			0
$283$	−316.137	−	182.522i	−1.11709	−	0.644954i	−0.176436	−	0.984312i	$-0.556457\pi$
$283$	−316.137	−	182.522i	−1.11709	−	0.644954i	−0.940657	+	0.339358i	$0.889790\pi$
$284$	292.949	+	169.134i	1.03151	+	0.595543i
$285$		0			0
$286$	−299.547	−	518.830i	−1.04737	−	1.81409i
$287$	226.804			0.790259
$288$		0			0
$289$	431.524			1.49316
$290$	−132.738	+	963.743i	−0.457717	+	3.32325i
$291$		0			0
$292$	207.218	+	119.637i	0.709650	+	0.409717i
$293$	97.0846	−	168.155i	0.331347	−	0.573909i	−0.651429	−	0.758709i	$-0.725830\pi$
$293$	97.0846	−	168.155i	0.331347	−	0.573909i	0.982776	+	0.184800i	$0.0591637\pi$
$294$		0			0
$295$	−34.1401	+	247.874i	−0.115729	+	0.840251i
$296$			650.951i			2.19916i
$297$		0			0
$298$		−	273.658i		−	0.918317i
$299$	−110.149	+	63.5944i	−0.368390	+	0.212690i
$300$		0			0
$301$	−13.6663	+	23.6708i	−0.0454031	+	0.0786405i
$302$	−71.3126	+	123.517i	−0.236134	+	0.408997i
$303$		0			0
$304$	−205.723	−	356.323i	−0.676720	−	1.17211i
$305$	−148.592	+	191.273i	−0.487187	+	0.627125i
$306$		0			0
$307$			492.555i			1.60441i	0.597046	+	0.802207i	$0.296341\pi$
$307$			492.555i			1.60441i	−0.597046	+	0.802207i	$0.703659\pi$
$308$	−401.584	−	695.564i	−1.30384	−	2.25833i
$309$		0			0
$310$	212.798	+	522.544i	0.686447	+	1.68563i
$311$	161.394	+	93.1810i	0.518953	+	0.299617i	0.736506	−	0.676431i	$-0.236474\pi$
$311$	161.394	+	93.1810i	0.518953	+	0.299617i	−0.217553	+	0.976048i	$0.569808\pi$
$312$		0			0
$313$	−189.353	+	109.323i	−0.604961	+	0.349274i	−0.770991	−	0.636847i	$-0.780238\pi$
$313$	−189.353	+	109.323i	−0.604961	+	0.349274i	0.166030	+	0.986121i	$0.446905\pi$
$314$		−	484.562i		−	1.54319i
$315$		0			0
$316$	−692.278			−2.19075
$317$	−102.301	−	177.191i	−0.322718	−	0.558963i	0.658330	−	0.752729i	$-0.271263\pi$
$317$	−102.301	−	177.191i	−0.322718	−	0.558963i	−0.981048	+	0.193766i	$0.937930\pi$
$318$		0			0
$319$	−413.751	+	716.637i	−1.29702	+	2.24651i
$320$	−31.6396	−	77.6937i	−0.0988738	−	0.242793i
$321$		0			0
$322$	−214.989	+	124.124i	−0.667668	+	0.385478i
$323$	−426.569			−1.32065
$324$		0			0
$325$	−267.117	+	68.1656i	−0.821897	+	0.209740i
$326$	−265.978	+	153.562i	−0.815883	+	0.471050i
$327$		0			0
$328$	−556.582	−	321.343i	−1.69690	−	0.979704i
$329$	−19.3902	−	11.1949i	−0.0589368	−	0.0340272i
$330$		0			0
$331$	298.305	+	516.680i	0.901224	+	1.56097i	0.825907	+	0.563807i	$0.190664\pi$
$331$	298.305	+	516.680i	0.901224	+	1.56097i	0.0753174	+	0.997160i	$0.476003\pi$
$332$	−1321.43			−3.98020
$333$		0			0
$334$	399.293			1.19549
$335$	−47.3256	+	343.607i	−0.141270	+	1.02569i
$336$		0			0
$337$	288.036	+	166.298i	0.854707	+	0.493466i	0.862236	−	0.506506i	$-0.169063\pi$
$337$	288.036	+	166.298i	0.854707	+	0.493466i	−0.00752898	+	0.999972i	$0.502397\pi$
$338$	84.7126	−	146.727i	0.250629	−	0.434102i
$339$		0			0
$340$	1166.61	+	160.679i	3.43120	+	0.472585i
$341$			479.921i			1.40739i
$342$		0			0
$343$			371.773i			1.08389i
$344$	67.0749	−	38.7257i	0.194985	−	0.112575i
$345$		0			0
$346$	−15.5293	+	26.8975i	−0.0448823	+	0.0777384i
$347$	34.6029	−	59.9339i	0.0997201	−	0.172720i	−0.811849	−	0.583868i	$-0.801539\pi$
$347$	34.6029	−	59.9339i	0.0997201	−	0.172720i	0.911569	+	0.411148i	$0.134872\pi$
$348$		0			0
$349$	−277.425	−	480.515i	−0.794915	−	1.37683i	−0.922893	−	0.385056i	$-0.874182\pi$
$349$	−277.425	−	480.515i	−0.794915	−	1.37683i	0.127978	−	0.991777i	$-0.459151\pi$
$350$	−521.361	+	133.046i	−1.48960	+	0.380132i
$351$		0			0
$352$			369.102i			1.04859i
$353$	−88.1341	−	152.653i	−0.249672	−	0.432444i	0.713763	−	0.700387i	$-0.246989\pi$
$353$	−88.1341	−	152.653i	−0.249672	−	0.432444i	−0.963435	+	0.267943i	$0.913656\pi$
$354$		0			0
$355$	178.525	−	72.7018i	0.502888	−	0.204794i
$356$	−26.6352	−	15.3778i	−0.0748180	−	0.0431962i
$357$		0			0
$358$	177.870	−	102.693i	0.496844	−	0.286853i
$359$		−	122.033i		−	0.339924i	−0.985451	−	0.169962i	$-0.945636\pi$
$359$		−	122.033i		−	0.339924i	0.985451	−	0.169962i	$-0.0543645\pi$
$360$		0			0
$361$	−108.460			−0.300444
$362$	−249.672	−	432.444i	−0.689700	−	1.19460i
$363$		0			0
$364$	−291.321	+	504.583i	−0.800333	+	1.38622i
$365$	126.280	−	51.4258i	0.345973	−	0.140892i
$366$		0			0
$367$	582.310	−	336.197i	1.58667	−	0.916067i	0.592825	−	0.805332i	$-0.298013\pi$
$367$	582.310	−	336.197i	1.58667	−	0.916067i	0.993850	−	0.110736i	$-0.0353207\pi$
$368$	298.632			0.811499
$369$		0			0
$370$	538.362	+	418.231i	1.45503	+	1.13035i
$371$	−292.685	+	168.982i	−0.788910	+	0.455477i
$372$		0			0
$373$	−444.978	−	256.908i	−1.19297	−	0.688762i	−0.233991	−	0.972239i	$-0.575179\pi$
$373$	−444.978	−	256.908i	−1.19297	−	0.688762i	−0.958979	+	0.283477i	$0.908512\pi$
$374$	1262.96	+	729.168i	3.37689	+	1.94965i
$375$		0			0
$376$	31.7226	+	54.9452i	0.0843687	+	0.146131i
$377$	600.294			1.59229
$378$		0			0
$379$	−496.340			−1.30960			−0.654802	−	0.755800i	$-0.727248\pi$
$379$	−496.340			−1.30960			−0.654802	+	0.755800i	$0.727248\pi$
$380$	−690.663	−	95.1262i	−1.81753	−	0.250332i
$381$		0			0
$382$	−97.4269	−	56.2495i	−0.255044	−	0.147250i
$383$	−297.962	+	516.085i	−0.777968	+	1.34748i	0.155143	+	0.987892i	$0.450416\pi$
$383$	−297.962	+	516.085i	−0.777968	+	1.34748i	−0.933111	+	0.359588i	$0.882917\pi$
$384$		0			0
$385$	−453.403	−	62.4480i	−1.17767	−	0.162202i
$386$		−	178.974i		−	0.463664i
$387$		0			0
$388$		−	242.650i		−	0.625385i
$389$	380.432	−	219.642i	0.977974	−	0.564633i	0.0763158	−	0.997084i	$-0.475684\pi$
$389$	380.432	−	219.642i	0.977974	−	0.564633i	0.901658	+	0.432450i	$0.142351\pi$
$390$		0			0
$391$	154.804	−	268.128i	0.395918	−	0.685750i
$392$	108.674	−	188.229i	0.277230	−	0.480177i
$393$		0			0
$394$	−66.9981	−	116.044i	−0.170046	−	0.294528i
$395$	−242.016	+	311.533i	−0.612700	+	0.788690i
$396$		0			0
$397$		−	405.932i		−	1.02250i	−0.859432	−	0.511250i	$-0.829183\pi$
$397$		−	405.932i		−	1.02250i	0.859432	−	0.511250i	$-0.170817\pi$
$398$	72.4067	+	125.412i	0.181926	+	0.315106i
$399$		0			0
$400$	623.173	+	174.981i	1.55793	+	0.437452i
$401$	−284.442	−	164.223i	−0.709332	−	0.409533i	0.101481	−	0.994837i	$-0.467642\pi$
$401$	−284.442	−	164.223i	−0.709332	−	0.409533i	−0.810814	+	0.585304i	$0.800975\pi$
$402$		0			0
$403$	301.506	−	174.074i	0.748153	−	0.431946i
$404$			316.670i			0.783836i
$405$		0			0
$406$	1171.66			2.88586
$407$	289.939	+	502.190i	0.712382	+	1.23388i
$408$		0			0
$409$	8.15681	−	14.1280i	0.0199433	−	0.0345428i	−0.855882	−	0.517172i	$-0.826985\pi$
$409$	8.15681	−	14.1280i	0.0199433	−	0.0345428i	0.875825	+	0.482629i	$0.160318\pi$
$410$	−623.363	+	253.855i	−1.52040	+	0.619159i
$411$		0			0
$412$	−213.230	+	123.109i	−0.517549	+	0.298807i
$413$	301.350			0.729662
$414$		0			0
$415$	−461.963	+	594.656i	−1.11316	+	1.43291i
$416$	231.885	−	133.879i	0.557416	−	0.321824i
$417$		0			0
$418$	−747.703	−	431.686i	−1.78876	−	1.03274i
$419$	−330.431	−	190.774i	−0.788618	−	0.455309i	0.0508576	−	0.998706i	$-0.483805\pi$
$419$	−330.431	−	190.774i	−0.788618	−	0.455309i	−0.839476	+	0.543397i	$0.817138\pi$
$420$		0			0
$421$	−211.669	−	366.621i	−0.502776	−	0.870834i	−0.999995	−	0.00320894i	$-0.998979\pi$
$421$	−211.669	−	366.621i	−0.502776	−	0.870834i	0.497218	−	0.867625i	$-0.334355\pi$
$422$	−616.436			−1.46075
$423$		0			0
$424$	957.674			2.25866
$425$	480.147	−	468.814i	1.12976	−	1.10309i
$426$		0			0
$427$	252.627	+	145.854i	0.591632	+	0.341579i
$428$	−402.939	+	697.911i	−0.941447	+	1.63063i
$429$		0			0
$430$	11.0674	−	80.3545i	0.0257381	−	0.186871i
$431$			48.3081i			0.112084i	0.998428	+	0.0560419i	$0.0178480\pi$
$431$			48.3081i			0.112084i	−0.998428	+	0.0560419i	$0.982152\pi$
$432$		0			0
$433$		−	36.0601i		−	0.0832797i	−0.999133	−	0.0416399i	$-0.986742\pi$
$433$		−	36.0601i		−	0.0832797i	0.999133	−	0.0416399i	$-0.0132582\pi$
$434$	588.481	−	339.760i	1.35595	−	0.782857i
$435$		0			0
$436$	−342.978	+	594.055i	−0.786646	+	1.36251i
$437$	−91.6480	+	158.739i	−0.209721	+	0.363247i
$438$		0			0
$439$	130.043	+	225.242i	0.296226	+	0.513079i	0.975269	−	0.221020i	$-0.0709385\pi$
$439$	130.043	+	225.242i	0.296226	+	0.513079i	−0.679043	+	0.734098i	$0.737605\pi$
$440$	1024.18	+	795.642i	2.32768	+	1.80828i
$441$		0			0
$442$		−	1057.92i		−	2.39349i
$443$	11.2647	+	19.5110i	0.0254282	+	0.0440430i	0.878459	−	0.477817i	$-0.158572\pi$
$443$	11.2647	+	19.5110i	0.0254282	+	0.0440430i	−0.853031	+	0.521860i	$0.825238\pi$
$444$		0			0
$445$	−16.2317	+	6.61012i	−0.0364757	+	0.0148542i
$446$	−926.587	−	534.965i	−2.07755	−	1.19947i
$447$		0			0
$448$	−87.4975	+	50.5167i	−0.195307	+	0.112761i
$449$			275.640i			0.613898i	0.951726	+	0.306949i	$0.0993080\pi$
$449$			275.640i			0.613898i	−0.951726	+	0.306949i	$0.900692\pi$
$450$		0			0
$451$	−572.516			−1.26944
$452$	−28.8115	−	49.9030i	−0.0637423	−	0.110405i
$453$		0			0
$454$	533.822	−	924.607i	1.17582	−	2.03658i
$455$	125.224	+	307.497i	0.275217	+	0.675817i
$456$		0			0
$457$	103.410	−	59.7038i	0.226280	−	0.130643i	−0.382575	−	0.923925i	$-0.624963\pi$
$457$	103.410	−	59.7038i	0.226280	−	0.130643i	0.608855	+	0.793282i	$0.291629\pi$
$458$	726.653			1.58658
$459$		0			0
$460$	310.438	−	399.608i	0.674866	−	0.868713i
$461$	78.2511	−	45.1783i	0.169742	−	0.0980007i	−0.412722	−	0.910857i	$-0.635422\pi$
$461$	78.2511	−	45.1783i	0.169742	−	0.0980007i	0.582464	+	0.812856i	$0.302089\pi$
$462$		0			0
$463$	528.653	+	305.218i	1.14180	+	0.659219i	0.946876	−	0.321600i	$-0.104221\pi$
$463$	528.653	+	305.218i	1.14180	+	0.659219i	0.194924	+	0.980818i	$0.437554\pi$
$464$	−1220.62	−	704.728i	−2.63066	−	1.51881i
$465$		0			0
$466$	779.867	+	1350.77i	1.67354	+	2.89865i
$467$	65.6533			0.140585			0.0702926	−	0.997526i	$-0.477607\pi$
$467$	65.6533			0.140585			0.0702926	+	0.997526i	$0.477607\pi$
$468$		0			0
$469$	417.736			0.890696
$470$	65.8234	+	9.06597i	0.140050	+	0.0192893i
$471$		0			0
$472$	−739.519	−	426.961i	−1.56678	−	0.904579i
$473$	34.4975	−	59.7515i	0.0729335	−	0.126324i
$474$		0			0
$475$	−284.259	+	277.550i	−0.598441	+	0.584316i
$476$		−	1418.29i		−	2.97960i
$477$		0			0
$478$		−	856.704i		−	1.79227i
$479$	81.3901	−	46.9906i	0.169917	−	0.0981015i	−0.412630	−	0.910899i	$-0.635390\pi$
$479$	81.3901	−	46.9906i	0.169917	−	0.0981015i	0.582547	+	0.812797i	$0.302056\pi$
$480$		0			0
$481$	210.331	−	364.303i	0.437278	−	0.757387i
$482$	366.969	−	635.609i	0.761346	−	1.31869i
$483$		0			0
$484$	482.863	+	836.343i	0.997650	+	1.72798i
$485$	−109.195	−	84.8288i	−0.225144	−	0.174905i
$486$		0			0
$487$		−	805.464i		−	1.65393i	−0.562253	−	0.826965i	$-0.690065\pi$
$487$		−	805.464i		−	1.65393i	0.562253	−	0.826965i	$-0.309935\pi$
$488$	−413.301	−	715.858i	−0.846928	−	1.46692i
$489$		0			0
$490$	−85.8508	−	210.814i	−0.175206	−	0.430232i
$491$	814.742	+	470.391i	1.65935	+	0.958027i	0.973015	+	0.230743i	$0.0741157\pi$
$491$	814.742	+	470.391i	1.65935	+	0.958027i	0.686337	+	0.727284i	$0.259218\pi$
$492$		0			0
$493$	−1265.49	+	730.630i	−2.56691	+	1.48201i
$494$			626.316i			1.26785i
$495$		0			0
$496$	−817.433			−1.64805
$497$	−116.078	−	201.053i	−0.233557	−	0.404532i
$498$		0			0
$499$	−189.964	+	329.028i	−0.380690	+	0.659375i	−0.991161	−	0.132664i	$-0.957647\pi$
$499$	−189.964	+	329.028i	−0.380690	+	0.659375i	0.610471	+	0.792039i	$0.290980\pi$
$500$	881.958	−	651.988i	1.76392	−	1.30398i
$501$		0			0
$502$	1105.87	−	638.474i	2.20293	−	1.27186i
$503$	−637.608			−1.26761			−0.633805	−	0.773493i	$-0.718508\pi$
$503$	−637.608			−1.26761			−0.633805	+	0.773493i	$0.718508\pi$
$504$		0			0
$505$	142.505	+	110.706i	0.282188	+	0.219220i
$506$	542.690	−	313.323i	1.07251	−	0.619214i
$507$		0			0
$508$	1880.58	+	1085.76i	3.70194	+	2.13731i
$509$	−834.081	−	481.557i	−1.63867	−	0.946084i	−0.981294	−	0.192517i	$-0.938335\pi$
$509$	−834.081	−	481.557i	−1.63867	−	0.946084i	−0.657372	−	0.753567i	$-0.728332\pi$
$510$		0			0
$511$	−82.1078	−	142.215i	−0.160681	−	0.278307i
$512$	1138.52			2.22366
$513$		0			0
$514$	−1002.59			−1.95056
$515$	−19.1439	+	138.994i	−0.0371726	+	0.269891i
$516$		0			0
$517$	48.9461	+	28.2591i	0.0946734	+	0.0546597i
$518$	410.525	−	711.050i	0.792519	−	1.37268i
$519$		0			0
$520$	128.369	−	932.023i	0.246864	−	1.79235i
$521$			36.7876i			0.0706095i	0.999377	+	0.0353048i	$0.0112402\pi$
$521$			36.7876i			0.0706095i	−0.999377	+	0.0353048i	$0.988760\pi$
$522$		0			0
$523$			441.292i			0.843770i	0.906649	+	0.421885i	$0.138631\pi$
$523$			441.292i			0.843770i	−0.906649	+	0.421885i	$0.861369\pi$
$524$	−1080.34	+	623.737i	−2.06172	+	1.19034i
$525$		0			0
$526$	215.330	−	372.963i	0.409373	−	0.709055i
$527$	−423.739	+	733.937i	−0.804059	+	1.39267i
$528$		0			0
$529$	197.981	+	342.913i	0.374255	+	0.648229i
$530$	615.297	−	792.034i	1.16094	−	1.49440i
$531$		0			0
$532$			839.665i			1.57832i
$533$	207.660	+	359.677i	0.389606	+	0.674817i
$534$		0			0
$535$	173.202	+	425.312i	0.323743	+	0.794977i
$536$	−1025.13	−	591.861i	−1.91256	−	1.10422i
$537$		0			0
$538$	953.546	−	550.530i	1.77239	−	1.02329i
$539$		−	193.618i		−	0.359217i
$540$		0			0
$541$	−426.631			−0.788598			−0.394299	−	0.918982i	$-0.629013\pi$
$541$	−426.631			−0.788598			−0.394299	+	0.918982i	$0.629013\pi$
$542$	633.841	+	1097.84i	1.16945	+	2.02554i
$543$		0			0
$544$	−325.893	+	564.464i	−0.599068	+	1.03762i
$545$	147.428	+	362.021i	0.270510	+	0.664260i
$546$		0			0
$547$	−522.151	+	301.464i	−0.954572	+	0.551122i	−0.894498	−	0.447072i	$-0.852467\pi$
$547$	−522.151	+	301.464i	−0.954572	+	0.551122i	−0.0600738	+	0.998194i	$0.519134\pi$
$548$	639.558			1.16708
$549$		0			0
$550$	1316.05	−	335.844i	2.39283	−	0.610626i
$551$	749.202	−	432.552i	1.35971	−	0.785031i
$552$		0			0
$553$	411.461	+	237.557i	0.744053	+	0.429579i
$554$	1486.68	+	858.334i	2.68353	+	1.54934i
$555$		0			0
$556$	293.934	+	509.108i	0.528658	+	0.915663i
$557$	527.490			0.947020			0.473510	−	0.880788i	$-0.342987\pi$
$557$	527.490			0.947020			0.473510	+	0.880788i	$0.342987\pi$
$558$		0			0
$559$	−50.0511			−0.0895368
$560$	106.366	−	772.266i	0.189938	−	1.37905i
$561$		0			0
$562$	390.777	+	225.615i	0.695333	+	0.401451i
$563$	−7.14026	+	12.3673i	−0.0126825	+	0.0219668i	−0.872297	−	0.488976i	$-0.837370\pi$
$563$	−7.14026	+	12.3673i	−0.0126825	+	0.0219668i	0.859614	+	0.510943i	$0.170704\pi$
$564$		0			0
$565$	−32.5292	−	4.48031i	−0.0575738	−	0.00792974i
$566$		−	1304.71i		−	2.30514i
$567$		0			0
$568$			657.849i			1.15818i
$569$	−582.646	+	336.391i	−1.02398	+	0.591197i	−0.915255	−	0.402875i	$-0.868011\pi$
$569$	−582.646	+	336.391i	−1.02398	+	0.591197i	−0.108728	+	0.994072i	$0.534678\pi$
$570$		0			0
$571$	−428.832	+	742.759i	−0.751020	+	1.30080i	0.196309	+	0.980542i	$0.437104\pi$
$571$	−428.832	+	742.759i	−0.751020	+	1.30080i	−0.947329	+	0.320262i	$0.896229\pi$
$572$	735.373	−	1273.70i	1.28562	−	2.22675i
$573$		0			0
$574$	405.312	+	702.022i	0.706119	+	1.22303i
$575$	−71.3005	−	279.401i	−0.124001	−	0.485915i
$576$		0			0
$577$			134.308i			0.232769i	0.993204	+	0.116385i	$0.0371305\pi$
$577$			134.308i			0.232769i	−0.993204	+	0.116385i	$0.962869\pi$
$578$	771.158	+	1335.68i	1.33418	+	2.31087i
$579$		0			0
$580$	−2211.90	+	900.764i	−3.81362	+	1.55304i
$581$	785.401	+	453.451i	1.35181	+	0.780467i
$582$		0			0
$583$	738.817	−	426.556i	1.26727	−	0.731657i
$584$			465.330i			0.796799i
$585$		0			0
$586$	693.983			1.18427
$587$	−450.137	−	779.660i	−0.766843	−	1.32821i	−0.939267	−	0.343188i	$-0.888493\pi$
$587$	−450.137	−	779.660i	−0.766843	−	1.32821i	0.172423	−	0.985023i	$-0.444840\pi$
$588$		0			0
$589$	250.864	−	434.510i	0.425916	−	0.737708i
$590$	−828.248	+	337.292i	−1.40381	+	0.571681i
$591$		0			0
$592$	−855.363	+	493.844i	−1.44487	+	0.834196i
$593$	−282.338			−0.476118			−0.238059	−	0.971251i	$-0.576511\pi$
$593$	−282.338			−0.476118			−0.238059	+	0.971251i	$0.576511\pi$
$594$		0			0
$595$	−638.246	−	495.826i	−1.07268	−	0.833322i
$596$	581.812	−	335.909i	0.976195	−	0.563607i
$597$		0			0
$598$	−393.684	−	227.293i	−0.658334	−	0.380089i
$599$	−83.3908	−	48.1457i	−0.139217	−	0.0803768i	0.428774	−	0.903412i	$-0.358946\pi$
$599$	−83.3908	−	48.1457i	−0.139217	−	0.0803768i	−0.567991	+	0.823035i	$0.692279\pi$
$600$		0			0
$601$	268.904	+	465.756i	0.447428	+	0.774969i	0.998218	−	0.0596755i	$-0.0190066\pi$
$601$	268.904	+	465.756i	0.447428	+	0.774969i	−0.550789	+	0.834644i	$0.685673\pi$
$602$	−97.6901			−0.162276
$603$		0			0
$604$	−350.138			−0.579699
$605$	545.169	+	75.0871i	0.901106	+	0.124111i
$606$		0			0
$607$	409.860	+	236.633i	0.675222	+	0.389839i	0.798052	−	0.602588i	$-0.205864\pi$
$607$	409.860	+	236.633i	0.675222	+	0.389839i	−0.122831	+	0.992428i	$0.539197\pi$
$608$	192.937	−	334.177i	0.317331	−	0.549633i
$609$		0			0
$610$	−857.585	−	118.117i	−1.40588	−	0.193634i
$611$		−	40.9999i		−	0.0671030i
$612$		0			0
$613$			109.517i			0.178658i	0.996002	+	0.0893288i	$0.0284722\pi$
$613$			109.517i			0.178658i	−0.996002	+	0.0893288i	$0.971528\pi$
$614$	−1524.59	+	880.224i	−2.48305	+	1.43359i
$615$		0			0
$616$	780.983	−	1352.70i	1.26783	−	2.19595i
$617$	−566.446	+	981.113i	−0.918064	+	1.59013i	−0.115712	+	0.993283i	$0.536915\pi$
$617$	−566.446	+	981.113i	−0.918064	+	1.59013i	−0.802352	+	0.596851i	$0.796418\pi$
$618$		0			0
$619$	−76.7644	−	132.960i	−0.124014	−	0.214798i	0.797333	−	0.603539i	$-0.206243\pi$
$619$	−76.7644	−	132.960i	−0.124014	−	0.214798i	−0.921347	+	0.388741i	$0.872910\pi$
$620$	−849.751	+	1093.83i	−1.37057	+	1.76424i
$621$		0			0
$622$			666.079i			1.07087i
$623$	10.5539	+	18.2799i	0.0169405	+	0.0293417i
$624$		0			0
$625$	14.9258	−	624.822i	0.0238814	−	0.999715i
$626$	−676.768	−	390.732i	−1.08110	−	0.624173i
$627$		0			0
$628$	1030.20	−	594.789i	1.64045	−	0.947116i
$629$			1023.99i			1.62797i
$630$		0			0
$631$	−289.486			−0.458774			−0.229387	−	0.973335i	$-0.573672\pi$
$631$	−289.486			−0.458774			−0.229387	+	0.973335i	$0.573672\pi$
$632$	−673.156	−	1165.94i	−1.06512	−	1.84484i
$633$		0			0
$634$	365.637	−	633.302i	0.576715	−	0.998899i
$635$	1146.04	−	466.709i	1.80479	−	0.734975i
$636$		0			0
$637$	−121.639	+	70.2281i	−0.190955	+	0.110248i
$638$	−2957.58			−4.63571
$639$		0			0
$640$	481.873	−	620.285i	0.752927	−	0.969196i
$641$	673.293	−	388.726i	1.05038	−	0.606436i	0.127623	−	0.991823i	$-0.459265\pi$
$641$	673.293	−	388.726i	1.05038	−	0.606436i	0.922755	+	0.385386i	$0.125932\pi$
$642$		0			0
$643$	253.513	+	146.366i	0.394265	+	0.227629i	0.684007	−	0.729476i	$-0.260236\pi$
$643$	253.513	+	146.366i	0.394265	+	0.227629i	−0.289741	+	0.957105i	$0.593569\pi$
$644$	−527.789	−	304.719i	−0.819547	−	0.473166i
$645$		0			0
$646$	−762.302	−	1320.35i	−1.18003	−	2.04388i
$647$	−504.594			−0.779899			−0.389949	−	0.920836i	$-0.627507\pi$
$647$	−504.594			−0.779899			−0.389949	+	0.920836i	$0.627507\pi$
$648$		0			0
$649$	−760.689			−1.17209
$650$	−688.344	−	704.983i	−1.05899	−	1.08459i
$651$		0			0
$652$	−652.963	−	376.989i	−1.00148	−	0.578203i
$653$	−110.675	+	191.695i	−0.169487	+	0.293560i	−0.938240	−	0.345986i	$-0.887544\pi$
$653$	−110.675	+	191.695i	−0.169487	+	0.293560i	0.768753	+	0.639546i	$0.220878\pi$
$654$		0			0
$655$	−96.9936	+	704.221i	−0.148082	+	1.07515i
$656$		−	975.146i		−	1.48650i
$657$		0			0
$658$		−	80.0240i		−	0.121617i
$659$	−665.570	+	384.267i	−1.00997	+	0.583106i	−0.911183	−	0.412002i	$-0.864830\pi$
$659$	−665.570	+	384.267i	−1.00997	+	0.583106i	−0.0987870	+	0.995109i	$0.531496\pi$
$660$		0			0
$661$	191.918	−	332.411i	0.290345	−	0.502891i	−0.683547	−	0.729907i	$-0.739563\pi$
$661$	191.918	−	332.411i	0.290345	−	0.502891i	0.973891	+	0.227015i	$0.0728968\pi$
$662$	−1066.18	+	1846.67i	−1.61054	+	2.78953i
$663$		0			0
$664$	−1284.93	−	2225.56i	−1.93513	−	3.35174i
$665$	377.858	+	293.542i	0.568208	+	0.441416i
$666$		0			0
$667$			627.901i			0.941381i
$668$	490.123	+	848.917i	0.733716	+	1.27083i
$669$		0			0
$670$	−1148.13	+	467.560i	−1.71363	+	0.697850i
$671$	−637.699	−	368.175i	−0.950370	−	0.548697i
$672$		0			0
$673$	−341.950	+	197.425i	−0.508098	+	0.293351i	−0.732052	−	0.681249i	$-0.761437\pi$
$673$	−341.950	+	197.425i	−0.508098	+	0.293351i	0.223953	+	0.974600i	$0.428104\pi$
$674$			1188.73i			1.76370i
$675$		0			0
$676$	415.931			0.615283
$677$	−303.489	−	525.659i	−0.448285	−	0.776453i	0.549989	−	0.835172i	$-0.314632\pi$
$677$	−303.489	−	525.659i	−0.448285	−	0.776453i	−0.998275	+	0.0587187i	$0.981299\pi$
$678$		0			0
$679$	−83.2659	+	144.221i	−0.122630	+	0.212402i
$680$	863.767	+	2121.05i	1.27025	+	3.11919i
$681$		0			0
$682$	−1485.49	+	857.646i	−2.17813	+	1.25754i
$683$	711.162			1.04123			0.520616	−	0.853791i	$-0.325702\pi$
$683$	711.162			1.04123			0.520616	+	0.853791i	$0.325702\pi$
$684$		0			0
$685$	223.586	−	287.808i	0.326402	−	0.420157i
$686$	−1150.74	+	664.379i	−1.67746	+	0.968483i
$687$		0			0
$688$	101.773	+	58.7585i	0.147925	+	0.0854048i
$689$	−535.960	−	309.437i	−0.777881	−	0.449110i
$690$		0			0
$691$	−425.440	−	736.883i	−0.615687	−	1.06640i	−0.990264	−	0.139205i	$-0.955545\pi$
$691$	−425.440	−	736.883i	−0.615687	−	1.06640i	0.374577	−	0.927196i	$-0.377788\pi$
$692$	−76.2473			−0.110184
$693$		0			0
$694$	247.349			0.356411
$695$	331.862	+	45.7079i	0.477499	+	0.0657668i
$696$		0			0
$697$	−875.542	−	505.494i	−1.25616	−	0.725243i
$698$	991.550	−	1717.41i	1.42056	−	2.46048i
$699$		0			0
$700$	−922.821	−	945.129i	−1.31832	−	1.35018i
$701$			1073.69i			1.53166i	0.643043	+	0.765830i	$0.277672\pi$
$701$			1073.69i			1.53166i	−0.643043	+	0.765830i	$0.722328\pi$
$702$		0			0
$703$		−	606.229i		−	0.862345i
$704$	220.867	−	127.518i	0.313732	−	0.181133i
$705$		0			0
$706$	315.001	−	545.598i	0.446177	−	0.772802i
$707$	108.666	−	188.215i	0.153700	−	0.266217i
$708$		0			0
$709$	−416.804	−	721.926i	−0.587876	−	1.01823i	−0.994510	−	0.104640i	$-0.966631\pi$
$709$	−416.804	−	721.926i	−0.587876	−	1.01823i	0.406634	−	0.913591i	$-0.366702\pi$
$710$	544.067	+	422.662i	0.766291	+	0.595299i
$711$		0			0
$712$		−	59.8123i		−	0.0840060i
$713$	182.080	+	315.372i	0.255372	+	0.442317i
$714$		0			0
$715$	−316.098	−	776.205i	−0.442095	−	1.08560i
$716$	436.663	+	252.108i	0.609865	+	0.352106i
$717$		0			0
$718$	377.724	−	218.079i	0.526079	−	0.303732i
$719$		−	433.030i		−	0.602267i	−0.953582	−	0.301134i	$-0.902635\pi$
$719$		−	433.030i		−	0.602267i	0.953582	−	0.301134i	$-0.0973650\pi$
$720$		0			0
$721$	168.980			0.234369
$722$	−193.825	−	335.714i	−0.268455	−	0.464978i
$723$		0			0
$724$	612.932	−	1061.63i	0.846592	−	1.46634i
$725$	−367.914	+	1310.28i	−0.507467	+	1.80728i
$726$		0			0
$727$	587.649	−	339.280i	0.808321	−	0.466684i	−0.0380515	−	0.999276i	$-0.512115\pi$
$727$	587.649	−	339.280i	0.808321	−	0.466684i	0.846372	+	0.532591i	$0.178782\pi$
$728$	−1133.10			−1.55645
$729$		0			0
$730$	384.847	+	298.971i	0.527187	+	0.409549i
$731$	105.513	−	60.9182i	0.144341	−	0.0833354i
$732$		0			0
$733$	157.665	+	91.0280i	0.215096	+	0.124186i	0.603677	−	0.797229i	$-0.293702\pi$
$733$	157.665	+	91.0280i	0.215096	+	0.124186i	−0.388582	+	0.921414i	$0.627035\pi$
$734$	2081.24	+	1201.60i	2.83548	+	1.63706i
$735$		0			0
$736$	140.036	+	242.549i	0.190266	+	0.329550i
$737$	−1054.48			−1.43077
$738$		0			0
$739$	727.990			0.985101			0.492551	−	0.870284i	$-0.336065\pi$
$739$	727.990			0.985101			0.492551	+	0.870284i	$0.336065\pi$
$740$	−228.353	+	1657.96i	−0.308585	+	2.24048i
$741$		0			0
$742$	−1046.09	−	603.961i	−1.40983	−	0.813964i
$743$	197.141	−	341.459i	0.265331	−	0.459567i	−0.702319	−	0.711862i	$-0.747852\pi$
$743$	197.141	−	341.459i	0.265331	−	0.459567i	0.967650	+	0.252295i	$0.0811853\pi$
$744$		0			0
$745$	52.2353	−	379.254i	0.0701145	−	0.509065i
$746$		−	1836.44i		−	2.46171i
$747$		0			0
$748$			3580.15i			4.78630i
$749$	478.981	−	276.540i	0.639493	−	0.369212i
$750$		0			0
$751$	−669.591	+	1159.77i	−0.891600	+	1.54430i	−0.0536427	+	0.998560i	$0.517083\pi$
$751$	−669.591	+	1159.77i	−0.891600	+	1.54430i	−0.837957	+	0.545736i	$0.816250\pi$
$752$	−48.1327	+	83.3683i	−0.0640063	+	0.110862i
$753$		0			0
$754$	1072.76	+	1858.07i	1.42276	+	2.46429i
$755$	−122.406	+	157.566i	−0.162128	+	0.208697i
$756$		0			0
$757$			185.595i			0.245171i	0.992458	+	0.122586i	$0.0391186\pi$
$757$			185.595i			0.245171i	−0.992458	+	0.122586i	$0.960881\pi$
$758$	−886.988	−	1536.31i	−1.17017	−	2.02679i
$759$		0			0
$760$	−511.373	−	1255.72i	−0.672859	−	1.65226i
$761$	−808.635	−	466.866i	−1.06260	−	0.613490i	−0.136446	−	0.990647i	$-0.543568\pi$
$761$	−808.635	−	466.866i	−1.06260	−	0.613490i	−0.926149	+	0.377158i	$0.876902\pi$
$762$		0			0
$763$	407.703	−	235.388i	0.534342	−	0.308503i
$764$		−	276.180i		−	0.361492i
$765$		0			0
$766$	−2129.90			−2.78054
$767$	275.913	+	477.896i	0.359730	+	0.623071i
$768$		0			0
$769$	−529.465	+	917.060i	−0.688511	+	1.19254i	0.283809	+	0.958881i	$0.408402\pi$
$769$	−529.465	+	917.060i	−0.688511	+	1.19254i	−0.972320	+	0.233655i	$0.924931\pi$
$770$	−616.963	−	1515.00i	−0.801251	−	1.96754i
$771$		0			0
$772$	380.509	−	219.687i	0.492888	−	0.284569i
$773$	−79.0622			−0.102280			−0.0511399	−	0.998692i	$-0.516285\pi$
$773$	−79.0622			−0.102280			−0.0511399	+	0.998692i	$0.516285\pi$
$774$		0			0
$775$	195.168	+	764.794i	0.251830	+	0.986831i
$776$	408.672	−	235.947i	0.526639	−	0.304055i
$777$		0			0
$778$	1359.71	+	785.027i	1.74769	+	1.00903i
$779$	518.343	+	299.266i	0.665396	+	0.384166i
$780$		0			0
$781$	293.012	+	507.511i	0.375175	+	0.649822i
$782$	1106.57			1.41506
$783$		0			0
$784$	329.783			0.420641
$785$	92.4920	−	671.538i	0.117824	−	0.855462i
$786$		0			0
$787$	836.792	+	483.122i	1.06327	+	0.613878i	0.926335	−	0.376702i	$-0.122942\pi$
$787$	836.792	+	483.122i	1.06327	+	0.613878i	0.136934	+	0.990580i	$0.456275\pi$
$788$	164.477	−	284.883i	0.208728	−	0.361527i
$789$		0			0
$790$	−1396.78	−	192.380i	−1.76807	−	0.243519i
$791$			39.5470i			0.0499962i
$792$		0			0
$793$			534.171i			0.673608i
$794$	1256.47	−	725.424i	1.58246	−	0.913632i
$795$		0			0
$796$	−177.755	+	307.881i	−0.223310	+	0.386785i
$797$	637.906	−	1104.89i	0.800384	−	1.38630i	−0.118980	−	0.992897i	$-0.537963\pi$
$797$	637.906	−	1104.89i	0.800384	−	1.38630i	0.919364	−	0.393408i	$-0.128704\pi$
$798$		0			0
$799$	49.9019	+	86.4325i	0.0624554	+	0.108176i
$800$	150.102	+	588.195i	0.187627	+	0.735244i
$801$		0			0
$802$		−	1173.90i		−	1.46372i
$803$	207.262	+	358.989i	0.258110	+	0.447059i
$804$		0			0
$805$	−321.638	+	130.983i	−0.399551	+	0.162711i
$806$	1077.62	+	622.162i	1.33699	+	0.771913i
$807$		0			0
$808$	−533.338	+	307.923i	−0.660071	+	0.381092i
$809$		−	1533.89i		−	1.89603i	−0.318220	−	0.948017i	$-0.603085\pi$
$809$		−	1533.89i		−	1.89603i	0.318220	−	0.948017i	$-0.396915\pi$
$810$		0			0
$811$	−753.037			−0.928530			−0.464265	−	0.885696i	$-0.653681\pi$
$811$	−753.037			−0.928530			−0.464265	+	0.885696i	$0.653681\pi$
$812$	1438.19	+	2491.01i	1.77116	+	3.06775i
$813$		0			0
$814$	−1036.28	+	1794.88i	−1.27307	+	2.20502i
$815$	−397.921	+	162.047i	−0.488247	+	0.198831i
$816$		0			0
$817$	−62.4666	+	36.0651i	−0.0764586	+	0.0441434i
$818$	58.3067			0.0712796
$819$		0			0
$820$	−1304.87	−	1013.70i	−1.59131	−	1.23622i
$821$	−1336.50	+	771.628i	−1.62789	+	0.939863i	−0.643170	+	0.765723i	$0.722381\pi$
$821$	−1336.50	+	771.628i	−1.62789	+	0.939863i	−0.984721	+	0.174140i	$0.944285\pi$
$822$		0			0
$823$	1011.48	+	583.978i	1.22902	+	0.709573i	0.966824	−	0.255443i	$-0.0822213\pi$
$823$	1011.48	+	583.978i	1.22902	+	0.709573i	0.262192	+	0.965016i	$0.415555\pi$
$824$	−414.681	−	239.416i	−0.503253	−	0.290553i
$825$		0			0
$826$	538.530	+	932.761i	0.651973	+	1.12925i
$827$	432.942			0.523509			0.261755	−	0.965134i	$-0.415699\pi$
$827$	432.942			0.523509			0.261755	+	0.965134i	$0.415699\pi$
$828$		0			0
$829$	470.069			0.567031			0.283515	−	0.958968i	$-0.408499\pi$
$829$	470.069			0.567031			0.283515	+	0.958968i	$0.408499\pi$
$830$	−2666.18	−	367.217i	−3.21226	−	0.442430i
$831$		0			0
$832$	−160.224	−	92.5052i	−0.192577	−	0.111184i
$833$	170.952	−	296.098i	0.205225	−	0.355459i
$834$		0			0
$835$	553.366	+	76.2160i	0.662713	+	0.0912767i
$836$		−	2119.54i		−	2.53534i
$837$		0			0
$838$		−	1363.70i		−	1.62733i
$839$	−874.006	+	504.607i	−1.04172	+	0.601439i	−0.920321	−	0.391164i	$-0.872072\pi$
$839$	−874.006	+	504.607i	−1.04172	+	0.601439i	−0.121402	+	0.992603i	$0.538739\pi$
$840$		0			0
$841$	1061.26	−	1838.15i	1.26190	−	2.18567i
$842$	756.529	−	1310.35i	0.898490	−	1.55623i
$843$		0			0
$844$	−756.662	−	1310.58i	−0.896519	−	1.55282i
$845$	145.407	−	187.173i	0.172079	−	0.221507i
$846$		0			0
$847$		−	662.783i		−	0.782507i
$848$	726.539	+	1258.40i	0.856767	+	1.48396i
$849$		0			0
$850$	2309.16	+	648.388i	2.71665	+	0.762810i
$851$	381.057	+	220.004i	0.447776	+	0.258524i
$852$		0			0
$853$	780.076	−	450.377i	0.914509	−	0.527992i	0.0326300	−	0.999467i	$-0.489612\pi$
$853$	780.076	−	450.377i	0.914509	−	0.527992i	0.881879	+	0.471475i	$0.156278\pi$
$854$			1042.60i			1.22084i
$855$		0			0
$856$	−1567.24			−1.83088
$857$	55.9121	+	96.8427i	0.0652417	+	0.113002i	0.896801	−	0.442434i	$-0.145885\pi$
$857$	55.9121	+	96.8427i	0.0652417	+	0.113002i	−0.831559	+	0.555436i	$0.812551\pi$
$858$		0			0
$859$	−90.2278	+	156.279i	−0.105038	+	0.181931i	−0.913754	−	0.406268i	$-0.866830\pi$
$859$	−90.2278	+	156.279i	−0.105038	+	0.181931i	0.808716	+	0.588200i	$0.200163\pi$
$860$	184.423	−	75.1035i	0.214445	−	0.0873297i
$861$		0			0
$862$	−149.527	+	86.3293i	−0.173465	+	0.100150i
$863$	451.735			0.523447			0.261724	−	0.965143i	$-0.415709\pi$
$863$	451.735			0.523447			0.261724	+	0.965143i	$0.415709\pi$
$864$		0			0
$865$	−26.6556	+	34.3121i	−0.0308157	+	0.0396672i
$866$	111.616	−	64.4415i	0.128887	−	0.0744128i
$867$		0			0
$868$	1444.70	+	834.095i	1.66440	+	0.960939i
$869$	−1038.64	−	599.659i	−1.19521	−	0.690056i
$870$		0			0
$871$	382.475	+	662.467i	0.439122	+	0.760582i
$872$	−1334.01			−1.52983
$873$		0			0
$874$	−655.120			−0.749566
$875$	−747.931	+	84.8679i	−0.854778	+	0.0969919i
$876$		0			0
$877$	−637.590	−	368.112i	−0.727012	−	0.419741i	0.0903161	−	0.995913i	$-0.471212\pi$
$877$	−637.590	−	368.112i	−0.727012	−	0.419741i	−0.817328	+	0.576173i	$0.804546\pi$
$878$	−464.789	+	805.039i	−0.529373	+	0.916901i
$879$		0			0
$880$	−268.495	+	1949.41i	−0.305108	+	2.21523i
$881$		−	52.0576i		−	0.0590892i	−0.999563	−	0.0295446i	$-0.990594\pi$
$881$		−	52.0576i		−	0.0590892i	0.999563	−	0.0295446i	$-0.00940571\pi$
$882$		0			0
$883$			637.785i			0.722294i	0.932509	+	0.361147i	$0.117615\pi$
$883$			637.785i			0.722294i	−0.932509	+	0.361147i	$0.882385\pi$
$884$	2249.20	−	1298.57i	2.54434	−	1.46897i
$885$		0			0
$886$	−40.2613	+	69.7347i	−0.0454417	+	0.0787073i
$887$	673.271	−	1166.14i	0.759043	−	1.31470i	−0.184297	−	0.982871i	$-0.559001\pi$
$887$	673.271	−	1166.14i	0.759043	−	1.31470i	0.943339	−	0.331830i	$-0.107666\pi$
$888$		0			0
$889$	−745.160	−	1290.66i	−0.838201	−	1.45181i
$890$	−49.4671	−	38.4289i	−0.0555810	−	0.0431785i
$891$		0			0
$892$		−	2626.63i		−	2.94465i
$893$	−29.5432	−	51.1703i	−0.0330831	−	0.0573016i
$894$		0			0
$895$	266.106	−	108.368i	0.297325	−	0.121081i
$896$	−819.252	−	472.995i	−0.914343	−	0.527896i
$897$		0			0
$898$	−853.181	+	492.584i	−0.950090	+	0.548535i
$899$		−	1718.73i		−	1.91182i
$900$		0			0
$901$	1506.49			1.67202
$902$	−1023.12	−	1772.09i	−1.13428	−	1.96463i
$903$		0			0
$904$	56.0313	−	97.0491i	0.0619816	−	0.107355i
$905$	−263.467	−	646.966i	−0.291124	−	0.714879i
$906$		0			0
$907$	−929.536	+	536.668i	−1.02485	+	0.591696i	−0.915504	−	0.402308i	$-0.868208\pi$
$907$	−929.536	+	536.668i	−1.02485	+	0.591696i	−0.109343	+	0.994004i	$0.534875\pi$
$908$	2621.02			2.88658
$909$		0			0
$910$	−728.005	+	937.115i	−0.800005	+	1.02980i
$911$	72.5021	−	41.8591i	0.0795851	−	0.0459485i	−0.459679	−	0.888085i	$-0.652036\pi$
$911$	72.5021	−	41.8591i	0.0795851	−	0.0459485i	0.539264	+	0.842136i	$0.318702\pi$
$912$		0			0
$913$	−1982.56	−	1144.63i	−2.17148	−	1.25371i
$914$	369.599	+	213.388i	0.404375	+	0.233466i
$915$		0			0
$916$	891.949	+	1544.90i	0.973744	+	1.68657i
$917$	856.149			0.933641
$918$		0			0
$919$	1235.72			1.34463			0.672317	−	0.740264i	$-0.265299\pi$
$919$	1235.72			1.34463			0.672317	+	0.740264i	$0.265299\pi$
$920$	974.886	+	134.273i	1.05966	+	0.145949i
$921$		0			0
$922$	279.678	+	161.472i	0.303339	+	0.175133i
$923$	212.559	−	368.163i	0.230292	−	0.398877i
$924$		0			0
$925$	666.267	+	682.373i	0.720288	+	0.737700i
$926$			2181.77i			2.35612i
$927$		0			0
$928$		−	1321.86i		−	1.42442i
$929$	645.248	−	372.534i	0.694562	−	0.401006i	−0.110757	−	0.993848i	$-0.535327\pi$
$929$	645.248	−	372.534i	0.694562	−	0.401006i	0.805319	+	0.592842i	$0.201994\pi$
$930$		0			0
$931$	−101.208	+	175.297i	−0.108709	+	0.188289i
$932$	−1914.54	+	3316.08i	−2.05423	+	3.55802i
$933$		0			0
$934$	117.326	+	203.215i	0.125617	+	0.217575i
$935$	1611.11	+	1251.60i	1.72311	+	1.33861i
$936$		0			0
$937$		−	353.460i		−	0.377225i	−0.982052	−	0.188613i	$-0.939601\pi$
$937$		−	353.460i		−	0.377225i	0.982052	−	0.188613i	$-0.0603991\pi$
$938$	746.519	+	1293.01i	0.795862	+	1.37847i
$939$		0			0
$940$	61.5220	+	151.072i	0.0654489	+	0.160715i
$941$	219.779	+	126.889i	0.233559	+	0.134845i	0.612213	−	0.790693i	$-0.290280\pi$
$941$	219.779	+	126.889i	0.233559	+	0.134845i	−0.378654	+	0.925538i	$0.623613\pi$
$942$		0			0
$943$	−376.219	+	217.210i	−0.398960	+	0.230339i
$944$		−	1295.66i		−	1.37252i
$945$		0			0
$946$	246.596			0.260673
$947$	787.358	+	1363.74i	0.831424	+	1.44007i	0.896909	+	0.442215i	$0.145807\pi$
$947$	787.358	+	1363.74i	0.831424	+	1.44007i	−0.0654856	+	0.997854i	$0.520860\pi$
$948$		0			0
$949$	150.354	−	260.421i	0.158434	−	0.274416i
$950$	−1367.08	−	383.863i	−1.43903	−	0.404066i
$951$		0			0
$952$	2388.70	−	1379.11i	2.50914	−	1.44865i
$953$	137.098			0.143860			0.0719300	−	0.997410i	$-0.477084\pi$
$953$	137.098			0.143860			0.0719300	+	0.997410i	$0.477084\pi$
$954$		0			0
$955$	−124.284	−	96.5508i	−0.130140	−	0.101100i
$956$	1821.40	−	1051.58i	1.90523	−	1.09998i
$957$		0			0
$958$	290.898	+	167.950i	0.303651	+	0.175313i
$959$	−380.126	−	219.466i	−0.396378	−	0.228849i
$960$		0			0
$961$	−17.9004	−	31.0045i	−0.0186269	−	0.0322627i
$962$	1503.49			1.56288
$963$		0			0
$964$	1801.78			1.86907
$965$	34.1622	−	248.034i	0.0354013	−	0.257031i
$966$		0			0
$967$	−326.711	−	188.627i	−0.337860	−	0.195064i	0.321465	−	0.946921i	$-0.395825\pi$
$967$	−326.711	−	188.627i	−0.337860	−	0.195064i	−0.659325	+	0.751858i	$0.729158\pi$
$968$	−939.050	+	1626.48i	−0.970093	+	1.68025i
$969$		0			0
$970$	67.4310	−	489.582i	0.0695165	−	0.504724i
$971$		−	855.490i		−	0.881040i	−0.897743	−	0.440520i	$-0.854794\pi$
$971$		−	855.490i		−	0.881040i	0.897743	−	0.440520i	$-0.145206\pi$
$972$		0			0
$973$		−	403.457i		−	0.414653i
$974$	2493.13	−	1439.41i	2.55968	−	1.47783i
$975$		0			0
$976$	627.101	−	1086.17i	0.642521	−	1.11288i
$977$	537.354	−	930.724i	0.550004	−	0.952635i	−0.448270	−	0.893898i	$-0.647960\pi$
$977$	537.354	−	930.724i	0.550004	−	0.952635i	0.998274	−	0.0587364i	$-0.0187072\pi$
$978$		0			0
$979$	−26.6409	−	46.1434i	−0.0272124	−	0.0471332i
$980$	342.821	−	441.292i	0.349818	−	0.450298i
$981$		0			0
$982$			3362.46i			3.42410i
$983$	−580.777	−	1005.94i	−0.590821	−	1.02333i	−0.994122	−	0.108264i	$-0.965471\pi$
$983$	−580.777	−	1005.94i	−0.590821	−	1.02333i	0.403301	−	0.915067i	$-0.367863\pi$
$984$		0			0
$985$	−70.7001	−	173.610i	−0.0717768	−	0.176254i
$986$	−4523.00	−	2611.36i	−4.58722	−	2.64843i
$987$		0			0
$988$	−1331.58	+	768.789i	−1.34775	+	0.778127i
$989$		−	52.3529i		−	0.0529352i
$990$		0			0
$991$	463.882			0.468095			0.234047	−	0.972225i	$-0.424803\pi$
$991$	463.882			0.468095			0.234047	+	0.972225i	$0.424803\pi$
$992$	−383.315	−	663.920i	−0.386406	−	0.669275i
$993$		0			0
$994$	414.875	−	718.585i	0.417379	−	0.722922i
$995$	76.4075	+	187.625i	0.0767915	+	0.188568i
$996$		0			0
$997$	−161.504	+	93.2442i	−0.161990	+	0.0935248i	−0.578803	−	0.815467i	$-0.696480\pi$
$997$	−161.504	+	93.2442i	−0.161990	+	0.0935248i	0.416814	+	0.908992i	$0.363147\pi$
$998$	−1357.91			−1.36063
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.k.134.24		48
3.2	odd	2	inner	405.3.h.k.134.1		48
5.4	even	2	inner	405.3.h.k.134.2		48
9.2	odd	6	inner	405.3.h.k.269.2		48
9.4	even	3		405.3.d.b.404.1	✓	24
9.5	odd	6		405.3.d.b.404.24	yes	24
9.7	even	3	inner	405.3.h.k.269.23		48
15.14	odd	2	inner	405.3.h.k.134.23		48
45.4	even	6		405.3.d.b.404.23	yes	24
45.14	odd	6		405.3.d.b.404.2	yes	24
45.29	odd	6	inner	405.3.h.k.269.24		48
45.34	even	6	inner	405.3.h.k.269.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.1	✓	24	9.4	even	3
405.3.d.b.404.2	yes	24	45.14	odd	6
405.3.d.b.404.23	yes	24	45.4	even	6
405.3.d.b.404.24	yes	24	9.5	odd	6
405.3.h.k.134.1		48	3.2	odd	2	inner
405.3.h.k.134.2		48	5.4	even	2	inner
405.3.h.k.134.23		48	15.14	odd	2	inner
405.3.h.k.134.24		48	1.1	even	1	trivial
405.3.h.k.269.1		48	45.34	even	6	inner
405.3.h.k.269.2		48	9.2	odd	6	inner
405.3.h.k.269.23		48	9.7	even	3	inner
405.3.h.k.269.24		48	45.29	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.78706 + 3.09527i) q^{2} +(-4.38714 + 7.59875i) q^{4} +(1.88580 + 4.63074i) q^{5} +(5.21507 - 3.01092i) q^{7} -17.0638 q^{8} +(-10.9634 + 14.1125i) q^{10} +(-13.1642 + 7.60038i) q^{11} +(9.54973 + 5.51354i) q^{13} +(18.6393 + 10.7614i) q^{14} +(-12.9455 - 22.4222i) q^{16} -26.8426 q^{17} +15.8915 q^{19} +(-43.4611 - 5.98598i) q^{20} +(-47.0505 - 27.1646i) q^{22} +(-5.76711 + 9.98892i) q^{23} +(-17.8875 + 17.4653i) q^{25} +39.4120i q^{26} +52.8374i q^{28} +(47.1448 - 27.2191i) q^{29} +(15.7861 - 27.3423i) q^{31} +(12.1409 - 21.0287i) q^{32} +(-47.9692 - 83.0851i) q^{34} +(23.7774 + 18.4716i) q^{35} -38.1480i q^{37} +(28.3990 + 49.1885i) q^{38} +(-32.1790 - 79.0182i) q^{40} +(32.6176 + 18.8318i) q^{41} +(-3.93082 + 2.26946i) q^{43} -133.376i q^{44} -41.2246 q^{46} +(-1.85906 - 3.21998i) q^{47} +(-6.36869 + 11.0309i) q^{49} +(-86.0259 - 24.1552i) q^{50} +(-83.7921 + 48.3774i) q^{52} -56.1230 q^{53} +(-60.0205 - 46.6274i) q^{55} +(-88.9891 + 51.3779i) q^{56} +(168.501 + 97.2841i) q^{58} +(43.3384 + 25.0214i) q^{59} +(24.2209 + 41.9518i) q^{61} +112.842 q^{62} -16.7778 q^{64} +(-7.52288 + 54.6198i) q^{65} +(60.0763 + 34.6851i) q^{67} +(117.762 - 203.970i) q^{68} +(-14.6832 + 106.607i) q^{70} -38.5522i q^{71} -27.2700i q^{73} +(118.078 - 68.1726i) q^{74} +(-69.7183 + 120.756i) q^{76} +(-45.7683 + 79.2730i) q^{77} +(39.4493 + 68.3281i) q^{79} +(79.4189 - 102.231i) q^{80} +134.614i q^{82} +(75.3011 + 130.425i) q^{83} +(-50.6198 - 124.301i) q^{85} +(-14.0492 - 8.11131i) q^{86} +(224.633 - 129.692i) q^{88} +3.50521i q^{89} +66.4034 q^{91} +(-50.6022 - 87.6456i) q^{92} +(6.64448 - 11.5086i) q^{94} +(29.9682 + 73.5894i) q^{95} +(-23.9496 + 13.8273i) q^{97} -45.5248 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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