LMFDB - Embedded newform 405.3.h.k.134.2

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			134.2
Character	$\chi$	$=$	405.134
Dual form			405.3.h.k.269.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78706 - 3.09527i) q^{2} +(-4.38714 + 7.59875i) q^{4} +(4.95324 - 0.682218i) q^{5} +(-5.21507 + 3.01092i) q^{7} +17.0638 q^{8} +(-10.9634 - 14.1125i) q^{10} +(-13.1642 + 7.60038i) q^{11} +(-9.54973 - 5.51354i) q^{13} +(18.6393 + 10.7614i) q^{14} +(-12.9455 - 22.4222i) q^{16} +26.8426 q^{17} +15.8915 q^{19} +(-16.5466 + 40.6314i) q^{20} +(47.0505 + 27.1646i) q^{22} +(5.76711 - 9.98892i) q^{23} +(24.0692 - 6.75838i) q^{25} +39.4120i q^{26} -52.8374i q^{28} +(47.1448 - 27.2191i) q^{29} +(15.7861 - 27.3423i) q^{31} +(-12.1409 + 21.0287i) q^{32} +(-47.9692 - 83.0851i) q^{34} +(-23.7774 + 18.4716i) q^{35} +38.1480i q^{37} +(-28.3990 - 49.1885i) q^{38} +(84.5213 - 11.6413i) q^{40} +(32.6176 + 18.8318i) q^{41} +(3.93082 - 2.26946i) q^{43} -133.376i q^{44} -41.2246 q^{46} +(1.85906 + 3.21998i) q^{47} +(-6.36869 + 11.0309i) q^{49} +(-63.9320 - 62.4230i) q^{50} +(83.7921 - 48.3774i) q^{52} +56.1230 q^{53} +(-60.0205 + 46.6274i) q^{55} +(-88.9891 + 51.3779i) q^{56} +(-168.501 - 97.2841i) q^{58} +(43.3384 + 25.0214i) q^{59} +(24.2209 + 41.9518i) q^{61} -112.842 q^{62} -16.7778 q^{64} +(-51.0636 - 20.7949i) q^{65} +(-60.0763 - 34.6851i) q^{67} +(-117.762 + 203.970i) q^{68} +(99.6663 + 40.5876i) q^{70} -38.5522i q^{71} +27.2700i q^{73} +(118.078 - 68.1726i) q^{74} +(-69.7183 + 120.756i) q^{76} +(45.7683 - 79.2730i) q^{77} +(39.4493 + 68.3281i) q^{79} +(-79.4189 - 102.231i) q^{80} -134.614i q^{82} +(-75.3011 - 130.425i) q^{83} +(132.958 - 18.3125i) q^{85} +(-14.0492 - 8.11131i) q^{86} +(-224.633 + 129.692i) q^{88} +3.50521i q^{89} +66.4034 q^{91} +(50.6022 + 87.6456i) q^{92} +(6.64448 - 11.5086i) q^{94} +(78.7144 - 10.8415i) q^{95} +(23.9496 - 13.8273i) q^{97} +45.5248 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.814889\pi$
$2$	−1.78706	−	3.09527i	−0.893528	−	1.54764i	−0.0579128	−	0.998322i	$-0.518445\pi$
$3$		0			0
$3$		0			0
$4$	−4.38714	+	7.59875i	−1.09679	+	1.89969i
$5$	4.95324	−	0.682218i	0.990648	−	0.136444i
$5$	4.95324	−	0.682218i	0.990648	−	0.136444i
$6$		0			0
$7$	−5.21507	+	3.01092i	−0.745010	+	0.430132i	−0.823888	−	0.566752i	$-0.808200\pi$
$7$	−5.21507	+	3.01092i	−0.745010	+	0.430132i	0.0788780	+	0.996884i	$0.474866\pi$
$8$	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	0.0855059	−	0.996338i	$-0.472749\pi$
$13$	−9.54973	−	5.51354i	−0.734595	−	0.424119i	−0.820101	+	0.572219i	$0.806083\pi$
$14$	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	$-0.210346\pi$
$17$	26.8426			1.57898			0.789488	+	0.613767i	$0.210346\pi$
$18$		0			0
$19$	15.8915			0.836395			0.418197	−	0.908356i	$-0.362662\pi$
$19$	15.8915			0.836395			0.418197	+	0.908356i	$0.362662\pi$
$20$	−16.5466	+	40.6314i	−0.827328	+	2.03157i
$21$		0			0
$22$	47.0505	+	27.1646i	2.13866	+	1.23476i
$23$	5.76711	−	9.98892i	0.250744	−	0.434301i	−0.712987	−	0.701177i	$-0.752658\pi$
$23$	5.76711	−	9.98892i	0.250744	−	0.434301i	0.963731	+	0.266876i	$0.0859915\pi$
$24$		0			0
$25$	24.0692	−	6.75838i	0.962766	−	0.270335i
$26$			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	$0.172399\pi$
$37$			38.1480i			1.03103i	−0.856881	+	0.515514i	$0.827601\pi$
$38$	−28.3990	−	49.1885i	−0.747342	−	1.29443i
$39$		0			0
$40$	84.5213	−	11.6413i	2.11303	−	0.291032i
$41$	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	−0.453596	−	0.891207i	$-0.649859\pi$
$43$	3.93082	−	2.26946i	0.0914145	−	0.0527782i	0.545010	+	0.838429i	$0.316526\pi$
$44$		−	133.376i		−	3.03127i
$45$		0			0
$46$	−41.2246			−0.896187
$47$	1.85906	+	3.21998i	0.0395544	+	0.0685102i	0.885125	−	0.465354i	$-0.154073\pi$
$47$	1.85906	+	3.21998i	0.0395544	+	0.0685102i	−0.845570	+	0.533864i	$0.820739\pi$
$48$		0			0
$49$	−6.36869	+	11.0309i	−0.129973	+	0.225120i
$50$	−63.9320	−	62.4230i	−1.27864	−	1.24846i
$51$		0			0
$52$	83.7921	−	48.3774i	1.61139	−	0.930334i
$53$	56.1230			1.05892			0.529462	−	0.848333i	$-0.322394\pi$
$53$	56.1230			1.05892			0.529462	+	0.848333i	$0.322394\pi$
$54$		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
$65$	−51.0636	−	20.7949i	−0.785593	−	0.319921i
$66$		0			0
$67$	−60.0763	−	34.6851i	−0.896662	−	0.517688i	−0.0205460	−	0.999789i	$-0.506540\pi$
$67$	−60.0763	−	34.6851i	−0.896662	−	0.517688i	−0.876116	+	0.482101i	$0.839874\pi$
$68$	−117.762	+	203.970i	−1.73180	+	2.99956i
$69$		0			0
$70$	99.6663	+	40.5876i	1.42380	+	0.579823i
$71$		−	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	$0.0598054\pi$
$73$			27.2700i			0.373561i	−0.982402	+	0.186781i	$0.940195\pi$
$74$	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	$-0.804850\pi$
$83$	−75.3011	−	130.425i	−0.907242	−	1.57139i	−0.0893625	−	0.995999i	$-0.528483\pi$
$84$		0			0
$85$	132.958	−	18.3125i	1.56421	−	0.215441i
$86$	−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
$95$	78.7144	−	10.8415i	0.828573	−	0.114121i
$96$		0			0
$97$	23.9496	−	13.8273i	0.246903	−	0.142550i	−0.371442	−	0.928456i	$-0.621137\pi$
$97$	23.9496	−	13.8273i	0.246903	−	0.142550i	0.618345	+	0.785906i	$0.287803\pi$
$98$	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	0.377370	−	0.926063i	$-0.376829\pi$
$103$	−24.3017	−	14.0306i	−0.235939	−	0.136219i	−0.613309	+	0.789843i	$0.710162\pi$
$104$	−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	$-0.641199\pi$
$107$	−91.8455			−0.858369			−0.429184	+	0.903217i	$0.641199\pi$
$108$		0			0
$109$	78.1779			0.717228			0.358614	−	0.933486i	$-0.383249\pi$
$109$	78.1779			0.717228			0.358614	+	0.933486i	$0.383249\pi$
$110$	251.585	+	102.454i	2.28713	+	0.931401i
$111$		0			0
$112$	135.023	+	77.9556i	1.20556	+	0.696032i
$113$	3.28363	−	5.68742i	0.0290587	−	0.0503311i	−0.851130	−	0.524954i	$-0.824082\pi$
$113$	3.28363	−	5.68742i	0.0290587	−	0.0503311i	0.880189	+	0.474623i	$0.157416\pi$
$114$		0			0
$115$	21.7512	−	53.4119i	0.189141	−	0.464452i
$116$			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	$0.427754\pi$
$127$			247.486i			1.94871i	−0.225023	+	0.974353i	$0.572246\pi$
$128$	78.5465	+	136.047i	0.613645	+	1.06286i
$129$		0			0
$130$	26.8876	+	195.217i	0.206828	+	1.50167i
$131$	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	0.967831	−	0.251602i	$-0.0809573\pi$
$137$	36.4450	+	63.1246i	0.266022	+	0.460763i	−0.701809	+	0.712365i	$0.747624\pi$
$138$		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	$0.0891902\pi$
$140$	−36.0466	−	261.716i	−0.257476	−	1.86940i
$141$		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
$155$	59.5388	−	146.202i	0.384121	−	0.943242i
$156$		0			0
$157$	117.412	+	67.7877i	0.747846	+	0.431769i	0.824915	−	0.565257i	$-0.191223\pi$
$157$	117.412	+	67.7877i	0.747846	+	0.431769i	−0.0770693	+	0.997026i	$0.524556\pi$
$158$	140.996	−	244.213i	0.892381	−	1.54565i
$159$		0			0
$160$	−45.7907	+	112.443i	−0.286192	+	0.702767i
$161$			69.4572i			0.431411i
$162$		0			0
$163$		−	85.9303i		−	0.527180i	−0.964635	−	0.263590i	$-0.915093\pi$
$163$		−	85.9303i		−	0.527180i	0.964635	−	0.263590i	$-0.0849066\pi$
$164$	−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	−0.983386	−	0.181528i	$-0.941896\pi$
$167$	−55.8590	+	96.7506i	−0.334485	+	0.579345i	0.648901	+	0.760873i	$0.275229\pi$
$168$		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	0.853195	−	0.521593i	$-0.174662\pi$
$173$	−4.34493	−	7.52564i	−0.0251152	−	0.0435008i	−0.878310	+	0.478092i	$0.841329\pi$
$174$		0			0
$175$	−105.173	+	107.716i	−0.600991	+	0.615519i
$176$	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
$185$	26.0253	+	188.956i	0.140677	+	1.02138i
$186$		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	0.608123	−	0.793843i	$-0.291923\pi$
$193$	43.3664	+	25.0376i	0.224696	+	0.129729i	−0.383427	+	0.923571i	$0.625256\pi$
$194$	−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	$-0.469666\pi$
$197$	37.4908			0.190308			0.0951542	+	0.995463i	$0.469666\pi$
$198$		0			0
$199$	40.5173			0.203604			0.101802	−	0.994805i	$-0.467539\pi$
$199$	40.5173			0.203604			0.101802	+	0.994805i	$0.467539\pi$
$200$	410.712	−	115.324i	2.05356	−	0.576620i
$201$		0			0
$202$	−111.710	−	64.4961i	−0.553022	−	0.319287i
$203$	−163.909	+	283.899i	−0.807434	+	1.39852i
$204$		0			0
$205$	174.410	+	71.0261i	0.850782	+	0.346469i
$206$			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
$220$	−90.9914	−	660.642i	−0.413597	−	3.00292i
$221$	−256.339	−	147.998i	−1.15991	−	0.669673i
$222$		0			0
$223$	259.250	−	149.678i	1.16255	−	0.671201i	0.210639	−	0.977564i	$-0.432445\pi$
$223$	259.250	−	149.678i	1.16255	−	0.671201i	0.951915	+	0.306363i	$0.0991122\pi$
$224$		−	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	$0.0619157\pi$
$227$	149.358	+	258.696i	0.657965	+	1.13963i	−0.323177	+	0.946338i	$0.604751\pi$
$228$		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	$0.0202584\pi$
$230$	−204.195	+	28.1242i	−0.887805	+	0.122279i
$231$		0			0
$232$	804.472	−	464.462i	3.46755	−	2.00199i
$233$	−436.398			−1.87295			−0.936476	−	0.350733i	$-0.885933\pi$
$233$	−436.398			−1.87295			−0.936476	+	0.350733i	$0.885933\pi$
$234$		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
$245$	−24.0202	+	58.9835i	−0.0980415	+	0.240749i
$246$		0			0
$247$	−151.760	−	87.6184i	−0.614411	−	0.354731i
$248$	269.371	−	466.564i	1.08617	−	1.88131i
$249$		0			0
$250$	−359.256	−	265.580i	−1.43703	−	1.06232i
$251$		−	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	$-0.649580\pi$
$257$	140.257	−	242.932i	0.545746	−	0.945260i	0.998560	−	0.0536544i	$-0.0170869\pi$
$258$		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	0.957535	−	0.288318i	$-0.0930960\pi$
$263$	60.2472	+	104.351i	0.229077	+	0.396772i	−0.728458	+	0.685090i	$0.759763\pi$
$264$		0			0
$265$	277.991	−	38.2881i	1.04902	−	0.144484i
$266$	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
$275$	−265.486	+	271.904i	−0.965404	+	0.988741i
$276$		0			0
$277$	−415.957	+	240.153i	−1.50165	+	0.866978i	−0.501652	+	0.865070i	$0.667274\pi$
$277$	−415.957	+	240.153i	−1.50165	+	0.866978i	−0.999998	+	0.00190830i	$0.999393\pi$
$278$	−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	0.940657	−	0.339358i	$-0.110210\pi$
$283$	316.137	+	182.522i	1.11709	+	0.644954i	0.176436	+	0.984312i	$0.443543\pi$
$284$	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
$290$	−900.995	−	366.917i	−3.10688	−	1.26523i
$291$		0			0
$292$	−207.218	−	119.637i	−0.709650	−	0.409717i
$293$	−97.0846	+	168.155i	−0.331347	+	0.573909i	−0.982776	−	0.184800i	$-0.940836\pi$
$293$	−97.0846	+	168.155i	−0.331347	+	0.573909i	0.651429	+	0.758709i	$0.274170\pi$
$294$		0			0
$295$	231.735	+	94.3708i	0.785544	+	0.319901i
$296$			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	$-0.703659\pi$
$307$		−	492.555i		−	1.60441i	0.597046	−	0.802207i	$-0.296341\pi$
$308$	401.584	+	695.564i	1.30384	+	2.25833i
$309$		0			0
$310$	−558.936	+	76.9832i	−1.80302	+	0.248333i
$311$	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	−0.166030	−	0.986121i	$-0.553095\pi$
$313$	189.353	−	109.323i	0.604961	−	0.349274i	0.770991	+	0.636847i	$0.219762\pi$
$314$		−	484.562i		−	1.54319i
$315$		0			0
$316$	−692.278			−2.19075
$317$	102.301	+	177.191i	0.322718	+	0.558963i	0.981048	−	0.193766i	$-0.0620703\pi$
$317$	102.301	+	177.191i	0.322718	+	0.558963i	−0.658330	+	0.752729i	$0.728737\pi$
$318$		0			0
$319$	−413.751	+	716.637i	−1.29702	+	2.24651i
$320$	−83.1045	+	11.4461i	−0.259702	+	0.0357692i
$321$		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
$335$	−321.235	−	130.818i	−0.958911	−	0.390503i
$336$		0			0
$337$	−288.036	−	166.298i	−0.854707	−	0.493466i	0.00752898	−	0.999972i	$-0.497603\pi$
$337$	−288.036	−	166.298i	−0.854707	−	0.493466i	−0.862236	+	0.506506i	$0.830937\pi$
$338$	−84.7126	+	146.727i	−0.250629	+	0.434102i
$339$		0			0
$340$	−444.152	+	1090.65i	−1.30633	+	3.20780i
$341$			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	−0.911569	−	0.411148i	$-0.865128\pi$
$347$	−34.6029	+	59.9339i	−0.0997201	+	0.172720i	0.811849	+	0.583868i	$0.198461\pi$
$348$		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	0.963435	−	0.267943i	$-0.0863440\pi$
$353$	88.1341	+	152.653i	0.249672	+	0.432444i	−0.713763	+	0.700387i	$0.753011\pi$
$354$		0			0
$355$	−26.3010	−	190.958i	−0.0740874	−	0.537911i
$356$	−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
$365$	18.6041	+	135.075i	0.0509701	+	0.370068i
$366$		0			0
$367$	−582.310	+	336.197i	−1.58667	+	0.916067i	−0.592825	+	0.805332i	$0.701987\pi$
$367$	−582.310	+	336.197i	−1.58667	+	0.916067i	−0.993850	+	0.110736i	$0.964679\pi$
$368$	−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	0.958979	−	0.283477i	$-0.0914879\pi$
$373$	444.978	+	256.908i	1.19297	+	0.688762i	0.233991	+	0.972239i	$0.424821\pi$
$374$	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	$0.727248\pi$
$380$	−262.950	+	645.694i	−0.691973	+	1.69920i
$381$		0			0
$382$	97.4269	+	56.2495i	0.255044	+	0.147250i
$383$	297.962	−	516.085i	0.777968	−	1.34748i	−0.155143	−	0.987892i	$-0.549584\pi$
$383$	297.962	−	516.085i	0.777968	−	1.34748i	0.933111	−	0.359588i	$-0.117083\pi$
$384$		0			0
$385$	172.620	−	423.882i	0.448363	−	1.10099i
$386$		−	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	$0.170817\pi$
$397$			405.932i			1.02250i	−0.859432	+	0.511250i	$0.829183\pi$
$398$	−72.4067	−	125.412i	−0.181926	−	0.315106i
$399$		0			0
$400$	−463.124	−	452.193i	−1.15781	−	1.13048i
$401$	−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	$0.160318\pi$
$410$	−91.8361	−	666.775i	−0.223991	−	1.62628i
$411$		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
$425$	646.078	−	181.412i	1.52018	−	0.426853i
$426$		0			0
$427$	−252.627	−	145.854i	−0.591632	−	0.341579i
$428$	402.939	−	697.911i	0.941447	−	1.63063i
$429$		0			0
$430$	−75.1227	−	30.5926i	−0.174704	−	0.0711457i
$431$			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	$0.0132582\pi$
$433$			36.0601i			0.0832797i	−0.999133	+	0.0416399i	$0.986742\pi$
$434$	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	0.853031	−	0.521860i	$-0.174762\pi$
$443$	−11.2647	−	19.5110i	−0.0254282	−	0.0440430i	−0.878459	+	0.477817i	$0.841428\pi$
$444$		0			0
$445$	2.39132	+	17.3621i	0.00537374	+	0.0390160i
$446$	−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
$455$	328.912	−	45.3016i	0.722883	−	0.0995640i
$456$		0			0
$457$	−103.410	+	59.7038i	−0.226280	+	0.130643i	−0.608855	−	0.793282i	$-0.708371\pi$
$457$	−103.410	+	59.7038i	−0.226280	+	0.130643i	0.382575	+	0.923925i	$0.375037\pi$
$458$	−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	−0.194924	−	0.980818i	$-0.562446\pi$
$463$	−528.653	−	305.218i	−1.14180	−	0.659219i	−0.946876	+	0.321600i	$0.895779\pi$
$464$	−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	$-0.522393\pi$
$467$	−65.6533			−0.140585			−0.0702926	+	0.997526i	$0.522393\pi$
$468$		0			0
$469$	417.736			0.890696
$470$	25.0603	−	61.5377i	0.0533198	−	0.130931i
$471$		0			0
$472$	739.519	+	426.961i	1.56678	+	0.904579i
$473$	−34.4975	+	59.7515i	−0.0729335	+	0.126324i
$474$		0			0
$475$	382.495	−	107.401i	0.805253	−	0.226107i
$476$		−	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	$0.309935\pi$
$487$			805.464i			1.65393i	−0.562253	+	0.826965i	$0.690065\pi$
$488$	413.301	+	715.858i	0.846928	+	1.46692i
$489$		0			0
$490$	225.495	−	31.0579i	0.460195	−	0.0633834i
$491$	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	$0.290980\pi$
$500$	−123.659	+	1089.79i	−0.247318	+	2.17958i
$501$		0			0
$502$	−1105.87	+	638.474i	−2.20293	+	1.27186i
$503$	637.608			1.26761			0.633805	−	0.773493i	$-0.281492\pi$
$503$	637.608			1.26761			0.633805	+	0.773493i	$0.281492\pi$
$504$		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
$515$	−129.944	−	52.9179i	−0.252319	−	0.102753i
$516$		0			0
$517$	−48.9461	−	28.2591i	−0.0946734	−	0.0546597i
$518$	−410.525	+	711.050i	−0.792519	+	1.37268i
$519$		0			0
$520$	−871.340	−	354.841i	−1.67565	−	0.682386i
$521$			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	$-0.861369\pi$
$523$		−	441.292i		−	0.843770i	0.906649	−	0.421885i	$-0.138631\pi$
$524$	−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
$535$	−454.933	+	62.6587i	−0.850341	+	0.117119i
$536$	−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
$545$	387.234	−	53.3344i	0.710521	−	0.0978612i
$546$		0			0
$547$	522.151	−	301.464i	0.954572	−	0.551122i	0.0600738	−	0.998194i	$-0.480866\pi$
$547$	522.151	−	301.464i	0.954572	−	0.551122i	0.894498	+	0.447072i	$0.147533\pi$
$548$	−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	$-0.657013\pi$
$557$	−527.490			−0.947020			−0.473510	+	0.880788i	$0.657013\pi$
$558$		0			0
$559$	−50.0511			−0.0895368
$560$	721.984	+	294.018i	1.28926	+	0.525031i
$561$		0			0
$562$	−390.777	−	225.615i	−0.695333	−	0.401451i
$563$	7.14026	−	12.3673i	0.0126825	−	0.0219668i	−0.859614	−	0.510943i	$-0.829296\pi$
$563$	7.14026	−	12.3673i	0.0126825	−	0.0219668i	0.872297	+	0.488976i	$0.162630\pi$
$564$		0			0
$565$	12.3845	−	30.4113i	0.0219196	−	0.0538253i
$566$		−	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	$-0.962869\pi$
$577$		−	134.308i		−	0.232769i	0.993204	−	0.116385i	$-0.0371305\pi$
$578$	−771.158	−	1335.68i	−1.33418	−	2.31087i
$579$		0			0
$580$	325.866	+	2365.94i	0.561837	+	4.07921i
$581$	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	$0.111507\pi$
$587$	450.137	+	779.660i	0.766843	+	1.32821i	−0.172423	+	0.985023i	$0.555160\pi$
$588$		0			0
$589$	250.864	−	434.510i	0.425916	−	0.737708i
$590$	−122.021	−	885.930i	−0.206815	−	1.50158i
$591$		0			0
$592$	855.363	−	493.844i	1.44487	−	0.834196i
$593$	282.338			0.476118			0.238059	−	0.971251i	$-0.423489\pi$
$593$	282.338			0.476118			0.238059	+	0.971251i	$0.423489\pi$
$594$		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
$605$	207.557	−	509.674i	0.343070	−	0.842436i
$606$		0			0
$607$	−409.860	−	236.633i	−0.675222	−	0.389839i	0.122831	−	0.992428i	$-0.460803\pi$
$607$	−409.860	−	236.633i	−0.675222	−	0.389839i	−0.798052	+	0.602588i	$0.794136\pi$
$608$	−192.937	+	334.177i	−0.317331	+	0.549633i
$609$		0			0
$610$	326.500	−	801.749i	0.535247	−	1.31434i
$611$		−	40.9999i		−	0.0671030i
$612$		0			0
$613$		−	109.517i		−	0.178658i	−0.996002	−	0.0893288i	$-0.971528\pi$
$613$		−	109.517i		−	0.178658i	0.996002	−	0.0893288i	$-0.0284722\pi$
$614$	−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	$-0.463085\pi$
$617$	566.446	−	981.113i	0.918064	−	1.59013i	0.802352	−	0.596851i	$-0.203582\pi$
$618$		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
$625$	533.649	−	325.337i	0.853838	−	0.520539i
$626$	−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
$635$	168.839	+	1225.86i	0.265889	+	1.93048i
$636$		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	0.289741	−	0.957105i	$-0.406431\pi$
$643$	−253.513	−	146.366i	−0.394265	−	0.227629i	−0.684007	+	0.729476i	$0.739764\pi$
$644$	−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	$-0.372493\pi$
$647$	504.594			0.779899			0.389949	+	0.920836i	$0.372493\pi$
$648$		0			0
$649$	−760.689			−1.17209
$650$	266.362	+	948.615i	0.409787	+	1.45941i
$651$		0			0
$652$	652.963	+	376.989i	1.00148	+	0.578203i
$653$	110.675	−	191.695i	0.169487	−	0.293560i	−0.768753	−	0.639546i	$-0.779122\pi$
$653$	110.675	−	191.695i	0.169487	−	0.293560i	0.938240	+	0.345986i	$0.112456\pi$
$654$		0			0
$655$	658.370	+	268.112i	1.00514	+	0.409331i
$656$		−	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
$670$	169.147	+	1228.09i	0.252458	+	1.83297i
$671$	−637.699	−	368.175i	−0.950370	−	0.548697i
$672$		0			0
$673$	341.950	−	197.425i	0.508098	−	0.293351i	−0.223953	−	0.974600i	$-0.571896\pi$
$673$	341.950	−	197.425i	0.508098	−	0.293351i	0.732052	+	0.681249i	$0.238563\pi$
$674$			1188.73i			1.76370i
$675$		0			0
$676$	415.931			0.615283
$677$	303.489	+	525.659i	0.448285	+	0.776453i	0.998275	−	0.0587187i	$-0.0187015\pi$
$677$	303.489	+	525.659i	0.448285	+	0.776453i	−0.549989	+	0.835172i	$0.685368\pi$
$678$		0			0
$679$	−83.2659	+	144.221i	−0.122630	+	0.212402i
$680$	2268.77	−	312.481i	3.33642	−	0.459532i
$681$		0			0
$682$	1485.49	−	857.646i	2.17813	−	1.25754i
$683$	−711.162			−1.04123			−0.520616	−	0.853791i	$-0.674298\pi$
$683$	−711.162			−1.04123			−0.520616	+	0.853791i	$0.674298\pi$
$684$		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
$695$	126.347	−	310.255i	0.181794	−	0.446410i
$696$		0			0
$697$	875.542	+	505.494i	1.25616	+	0.725243i
$698$	−991.550	+	1717.41i	−1.42056	+	2.46048i
$699$		0			0
$700$	−357.095	−	1271.75i	−0.510136	−	1.81679i
$701$			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
$715$	830.262	−	114.353i	1.16121	−	0.159935i
$716$	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
$725$	950.780	−	973.763i	1.31142	−	1.34312i
$726$		0			0
$727$	−587.649	+	339.280i	−0.808321	+	0.466684i	−0.846372	−	0.532591i	$-0.821218\pi$
$727$	−587.649	+	339.280i	−0.808321	+	0.466684i	0.0380515	+	0.999276i	$0.487885\pi$
$728$	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	0.388582	−	0.921414i	$-0.372965\pi$
$733$	−157.665	−	91.0280i	−0.215096	−	0.124186i	−0.603677	+	0.797229i	$0.706298\pi$
$734$	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	$0.336065\pi$
$740$	−1550.01	−	631.218i	−2.09461	−	0.852997i
$741$		0			0
$742$	1046.09	+	603.961i	1.40983	+	0.813964i
$743$	−197.141	+	341.459i	−0.265331	+	0.459567i	−0.967650	−	0.252295i	$-0.918815\pi$
$743$	−197.141	+	341.459i	−0.265331	+	0.459567i	0.702319	+	0.711862i	$0.252148\pi$
$744$		0			0
$745$	−354.561	−	144.390i	−0.475921	−	0.193812i
$746$		−	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	$-0.960881\pi$
$757$		−	185.595i		−	0.245171i	0.992458	−	0.122586i	$-0.0391186\pi$
$758$	886.988	+	1536.31i	1.17017	+	2.02679i
$759$		0			0
$760$	1343.17	−	184.997i	1.76733	−	0.243417i
$761$	−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	$0.924931\pi$
$770$	−1620.51	+	223.196i	−2.10456	+	0.289865i
$771$		0			0
$772$	−380.509	+	219.687i	−0.492888	+	0.284569i
$773$	79.0622			0.102280			0.0511399	−	0.998692i	$-0.483715\pi$
$773$	79.0622			0.102280			0.0511399	+	0.998692i	$0.483715\pi$
$774$		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
$785$	627.815	+	255.668i	0.799764	+	0.325692i
$786$		0			0
$787$	−836.792	−	483.122i	−1.06327	−	0.613878i	−0.136934	−	0.990580i	$-0.543725\pi$
$787$	−836.792	−	483.122i	−1.06327	−	0.613878i	−0.926335	+	0.376702i	$0.877058\pi$
$788$	−164.477	+	284.883i	−0.208728	+	0.361527i
$789$		0			0
$790$	531.781	−	1305.83i	0.673141	−	1.65295i
$791$			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	$0.462037\pi$
$797$	−637.906	+	1104.89i	−0.800384	+	1.38630i	−0.919364	+	0.393408i	$0.871296\pi$
$798$		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
$805$	47.3850	+	344.038i	0.0588634	+	0.427377i
$806$	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
$815$	−58.6232	−	425.633i	−0.0719303	−	0.522250i
$816$		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	−0.262192	−	0.965016i	$-0.584445\pi$
$823$	−1011.48	−	583.978i	−1.22902	−	0.709573i	−0.966824	+	0.255443i	$0.917779\pi$
$824$	−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	$-0.584301\pi$
$827$	−432.942			−0.523509			−0.261755	+	0.965134i	$0.584301\pi$
$828$		0			0
$829$	470.069			0.567031			0.283515	−	0.958968i	$-0.408499\pi$
$829$	470.069			0.567031			0.283515	+	0.958968i	$0.408499\pi$
$830$	−1015.07	+	2492.58i	−1.22297	+	3.00311i
$831$		0			0
$832$	160.224	+	92.5052i	0.192577	+	0.111184i
$833$	−170.952	+	296.098i	−0.205225	+	0.355459i
$834$		0			0
$835$	−210.678	+	517.337i	−0.252309	+	0.619565i
$836$		−	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
$850$	−1716.10	−	1675.59i	−2.01894	−	1.97129i
$851$	381.057	+	220.004i	0.447776	+	0.258524i
$852$		0			0
$853$	−780.076	+	450.377i	−0.914509	+	0.527992i	−0.881879	−	0.471475i	$-0.843722\pi$
$853$	−780.076	+	450.377i	−0.914509	+	0.527992i	−0.0326300	+	0.999467i	$0.510388\pi$
$854$			1042.60i			1.22084i
$855$		0			0
$856$	−1567.24			−1.83088
$857$	−55.9121	−	96.8427i	−0.0652417	−	0.113002i	0.831559	−	0.555436i	$-0.187449\pi$
$857$	−55.9121	−	96.8427i	−0.0652417	−	0.113002i	−0.896801	+	0.442434i	$0.854115\pi$
$858$		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	$0.200163\pi$
$860$	27.1699	+	197.267i	0.0315929	+	0.229380i
$861$		0			0
$862$	149.527	−	86.3293i	0.173465	−	0.100150i
$863$	−451.735			−0.523447			−0.261724	−	0.965143i	$-0.584291\pi$
$863$	−451.735			−0.523447			−0.261724	+	0.965143i	$0.584291\pi$
$864$		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
$875$	−447.463	+	605.293i	−0.511387	+	0.691764i
$876$		0			0
$877$	637.590	+	368.112i	0.727012	+	0.419741i	0.817328	−	0.576173i	$-0.195454\pi$
$877$	637.590	+	368.112i	0.727012	+	0.419741i	−0.0903161	+	0.995913i	$0.528788\pi$
$878$	464.789	−	805.039i	0.529373	−	0.916901i
$879$		0			0
$880$	1822.48	+	742.180i	2.07100	+	0.843386i
$881$		−	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	$-0.882385\pi$
$883$		−	637.785i		−	0.722294i	0.932509	−	0.361147i	$-0.117615\pi$
$884$	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	$0.440999\pi$
$887$	−673.271	+	1166.14i	−0.759043	+	1.31470i	−0.943339	+	0.331830i	$0.892334\pi$
$888$		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
$895$	−39.2038	−	284.639i	−0.0438031	−	0.318032i
$896$	−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
$905$	−692.022	+	95.3134i	−0.764665	+	0.105319i
$906$		0			0
$907$	929.536	−	536.668i	1.02485	−	0.591696i	0.109343	−	0.994004i	$-0.465125\pi$
$907$	929.536	−	536.668i	1.02485	−	0.591696i	0.915504	+	0.402308i	$0.131792\pi$
$908$	−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	$0.265299\pi$
$920$	371.159	−	911.413i	0.403434	−	0.990666i
$921$		0			0
$922$	−279.678	−	161.472i	−0.303339	−	0.175133i
$923$	−212.559	+	368.163i	−0.230292	+	0.398877i
$924$		0			0
$925$	257.819	+	918.190i	0.278723	+	0.992638i
$926$			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	$0.0603991\pi$
$937$			353.460i			0.377225i	−0.982052	+	0.188613i	$0.939601\pi$
$938$	−746.519	−	1293.01i	−0.795862	−	1.37847i
$939$		0			0
$940$	−161.593	+	22.2565i	−0.171908	+	0.0236772i
$941$	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	$-0.854193\pi$
$947$	−787.358	−	1363.74i	−0.831424	−	1.44007i	0.0654856	−	0.997854i	$-0.479140\pi$
$948$		0			0
$949$	150.354	−	260.421i	0.158434	−	0.274416i
$950$	−1015.97	−	991.995i	−1.06945	−	1.04421i
$951$		0			0
$952$	−2388.70	+	1379.11i	−2.50914	+	1.44865i
$953$	−137.098			−0.143860			−0.0719300	−	0.997410i	$-0.522916\pi$
$953$	−137.098			−0.143860			−0.0719300	+	0.997410i	$0.522916\pi$
$954$		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
$965$	231.885	+	94.4319i	0.240296	+	0.0978569i
$966$		0			0
$967$	326.711	+	188.627i	0.337860	+	0.195064i	0.659325	−	0.751858i	$-0.270842\pi$
$967$	326.711	+	188.627i	0.337860	+	0.195064i	−0.321465	+	0.946921i	$0.604175\pi$
$968$	939.050	−	1626.48i	0.970093	−	1.68025i
$969$		0			0
$970$	−457.706	−	186.394i	−0.471862	−	0.192159i
$971$		−	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	$0.352040\pi$
$977$	−537.354	+	930.724i	−0.550004	+	0.952635i	−0.998274	+	0.0587364i	$0.981293\pi$
$978$		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	$0.0345293\pi$
$983$	580.777	+	1005.94i	0.590821	+	1.02333i	−0.403301	+	0.915067i	$0.632137\pi$
$984$		0			0
$985$	185.701	−	25.5769i	0.188529	−	0.0259664i
$986$	−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
$995$	200.692	−	27.6416i	0.201700	−	0.0277805i
$996$		0			0
$997$	161.504	−	93.2442i	0.161990	−	0.0935248i	−0.416814	−	0.908992i	$-0.636853\pi$
$997$	161.504	−	93.2442i	0.161990	−	0.0935248i	0.578803	+	0.815467i	$0.303520\pi$
$998$	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.134.2		48
3.2	odd	2	inner	405.3.h.k.134.23		48
5.4	even	2	inner	405.3.h.k.134.24		48
9.2	odd	6	inner	405.3.h.k.269.24		48
9.4	even	3		405.3.d.b.404.23	yes	24
9.5	odd	6		405.3.d.b.404.2	yes	24
9.7	even	3	inner	405.3.h.k.269.1		48
15.14	odd	2	inner	405.3.h.k.134.1		48
45.4	even	6		405.3.d.b.404.1	✓	24
45.14	odd	6		405.3.d.b.404.24	yes	24
45.29	odd	6	inner	405.3.h.k.269.2		48
45.34	even	6	inner	405.3.h.k.269.23		48

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

\(f(q)\)	\(=\)	\(q+(-1.78706 - 3.09527i) q^{2} +(-4.38714 + 7.59875i) q^{4} +(4.95324 - 0.682218i) q^{5} +(-5.21507 + 3.01092i) q^{7} +17.0638 q^{8} +(-10.9634 - 14.1125i) q^{10} +(-13.1642 + 7.60038i) q^{11} +(-9.54973 - 5.51354i) q^{13} +(18.6393 + 10.7614i) q^{14} +(-12.9455 - 22.4222i) q^{16} +26.8426 q^{17} +15.8915 q^{19} +(-16.5466 + 40.6314i) q^{20} +(47.0505 + 27.1646i) q^{22} +(5.76711 - 9.98892i) q^{23} +(24.0692 - 6.75838i) q^{25} +39.4120i q^{26} -52.8374i q^{28} +(47.1448 - 27.2191i) q^{29} +(15.7861 - 27.3423i) q^{31} +(-12.1409 + 21.0287i) q^{32} +(-47.9692 - 83.0851i) q^{34} +(-23.7774 + 18.4716i) q^{35} +38.1480i q^{37} +(-28.3990 - 49.1885i) q^{38} +(84.5213 - 11.6413i) q^{40} +(32.6176 + 18.8318i) q^{41} +(3.93082 - 2.26946i) q^{43} -133.376i q^{44} -41.2246 q^{46} +(1.85906 + 3.21998i) q^{47} +(-6.36869 + 11.0309i) q^{49} +(-63.9320 - 62.4230i) q^{50} +(83.7921 - 48.3774i) q^{52} +56.1230 q^{53} +(-60.0205 + 46.6274i) q^{55} +(-88.9891 + 51.3779i) q^{56} +(-168.501 - 97.2841i) q^{58} +(43.3384 + 25.0214i) q^{59} +(24.2209 + 41.9518i) q^{61} -112.842 q^{62} -16.7778 q^{64} +(-51.0636 - 20.7949i) q^{65} +(-60.0763 - 34.6851i) q^{67} +(-117.762 + 203.970i) q^{68} +(99.6663 + 40.5876i) q^{70} -38.5522i q^{71} +27.2700i q^{73} +(118.078 - 68.1726i) q^{74} +(-69.7183 + 120.756i) q^{76} +(45.7683 - 79.2730i) q^{77} +(39.4493 + 68.3281i) q^{79} +(-79.4189 - 102.231i) q^{80} -134.614i q^{82} +(-75.3011 - 130.425i) q^{83} +(132.958 - 18.3125i) q^{85} +(-14.0492 - 8.11131i) q^{86} +(-224.633 + 129.692i) q^{88} +3.50521i q^{89} +66.4034 q^{91} +(50.6022 + 87.6456i) q^{92} +(6.64448 - 11.5086i) q^{94} +(78.7144 - 10.8415i) q^{95} +(23.9496 - 13.8273i) q^{97} +45.5248 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 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

Related objects

Downloads

Learn more