LMFDB - Embedded newform 405.3.h.k.134.18

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			134.18
Character	$\chi$	$=$	405.134
Dual form			405.3.h.k.269.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06375 + 1.84247i) q^{2} +(-0.263128 + 0.455750i) q^{4} +(0.323905 + 4.98950i) q^{5} +(1.01789 - 0.587680i) q^{7} +7.39039 q^{8} +(-8.84844 + 5.90436i) q^{10} +(16.6268 - 9.59948i) q^{11} +(6.82763 + 3.94194i) q^{13} +(2.16556 + 1.25029i) q^{14} +(8.91404 + 15.4396i) q^{16} +2.17700 q^{17} -19.9576 q^{19} +(-2.35919 - 1.16525i) q^{20} +(35.3735 + 20.4229i) q^{22} +(-16.6281 + 28.8008i) q^{23} +(-24.7902 + 3.23224i) q^{25} +16.7729i q^{26} +0.618539i q^{28} +(14.6152 - 8.43812i) q^{29} +(-2.27644 + 3.94291i) q^{31} +(-4.18383 + 7.24661i) q^{32} +(2.31579 + 4.01106i) q^{34} +(3.26193 + 4.88841i) q^{35} +50.3038i q^{37} +(-21.2299 - 36.7713i) q^{38} +(2.39378 + 36.8743i) q^{40} +(16.3362 + 9.43171i) q^{41} +(43.8953 - 25.3430i) q^{43} +10.1036i q^{44} -70.7527 q^{46} +(-5.42949 - 9.40415i) q^{47} +(-23.8093 + 41.2389i) q^{49} +(-32.3258 - 42.2368i) q^{50} +(-3.59308 + 2.07446i) q^{52} +86.1924 q^{53} +(53.2821 + 79.8500i) q^{55} +(7.52261 - 4.34318i) q^{56} +(31.0939 + 17.9521i) q^{58} +(-83.5848 - 48.2577i) q^{59} +(-20.8160 - 36.0544i) q^{61} -9.68626 q^{62} +53.5101 q^{64} +(-17.4568 + 35.3433i) q^{65} +(-58.6786 - 33.8781i) q^{67} +(-0.572829 + 0.992169i) q^{68} +(-5.53687 + 11.2100i) q^{70} -49.6797i q^{71} -106.022i q^{73} +(-92.6832 + 53.5107i) q^{74} +(5.25140 - 9.09570i) q^{76} +(11.2828 - 19.5425i) q^{77} +(-22.0052 - 38.1142i) q^{79} +(-74.1484 + 49.4775i) q^{80} +40.1319i q^{82} +(-44.5432 - 77.1510i) q^{83} +(0.705141 + 10.8621i) q^{85} +(93.3872 + 53.9171i) q^{86} +(122.878 - 70.9439i) q^{88} +19.9472i q^{89} +9.26638 q^{91} +(-8.75065 - 15.1566i) q^{92} +(11.5512 - 20.0073i) q^{94} +(-6.46437 - 99.5786i) q^{95} +(-133.934 + 77.3270i) q^{97} -101.308 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.06375	+	1.84247i	0.531875	+	0.921234i	0.999308	+	0.0372057i	$0.0118457\pi$
$2$	1.06375	+	1.84247i	0.531875	+	0.921234i	−0.467433	+	0.884029i	$0.654821\pi$
$3$		0			0
$3$		0			0
$4$	−0.263128	+	0.455750i	−0.0657819	+	0.113938i
$5$	0.323905	+	4.98950i	0.0647809	+	0.997900i
$5$	0.323905	+	4.98950i	0.0647809	+	0.997900i
$6$		0			0
$7$	1.01789	−	0.587680i	0.145413	−	0.0839542i	−0.425528	−	0.904945i	$-0.639912\pi$
$7$	1.01789	−	0.587680i	0.145413	−	0.0839542i	0.570941	+	0.820991i	$0.306578\pi$
$8$	7.39039			0.923799
$9$		0			0
$10$	−8.84844	+	5.90436i	−0.884844	+	0.590436i
$11$	16.6268	−	9.59948i	1.51153	−	0.872680i	0.511617	−	0.859214i	$-0.329047\pi$
$11$	16.6268	−	9.59948i	1.51153	−	0.872680i	0.999909	−	0.0134667i	$-0.00428672\pi$
$12$		0			0
$13$	6.82763	+	3.94194i	0.525203	+	0.303226i	0.739061	−	0.673639i	$-0.235270\pi$
$13$	6.82763	+	3.94194i	0.525203	+	0.303226i	−0.213858	+	0.976865i	$0.568603\pi$
$14$	2.16556	+	1.25029i	0.154683	+	0.0893063i
$15$		0			0
$16$	8.91404	+	15.4396i	0.557127	+	0.964973i
$17$	2.17700			0.128059			0.0640295	−	0.997948i	$-0.479605\pi$
$17$	2.17700			0.128059			0.0640295	+	0.997948i	$0.479605\pi$
$18$		0			0
$19$	−19.9576			−1.05040			−0.525201	−	0.850978i	$-0.676010\pi$
$19$	−19.9576			−1.05040			−0.525201	+	0.850978i	$0.676010\pi$
$20$	−2.35919	−	1.16525i	−0.117960	−	0.0582627i
$21$		0			0
$22$	35.3735	+	20.4229i	1.60789	+	0.928313i
$23$	−16.6281	+	28.8008i	−0.722963	+	1.25221i	0.236844	+	0.971548i	$0.423887\pi$
$23$	−16.6281	+	28.8008i	−0.722963	+	1.25221i	−0.959807	+	0.280661i	$0.909446\pi$
$24$		0			0
$25$	−24.7902	+	3.23224i	−0.991607	+	0.129290i
$26$			16.7729i			0.645113i
$27$		0			0
$28$			0.618539i			0.0220907i
$29$	14.6152	−	8.43812i	0.503974	−	0.290969i	−0.226379	−	0.974039i	$-0.572689\pi$
$29$	14.6152	−	8.43812i	0.503974	−	0.290969i	0.730353	+	0.683070i	$0.239356\pi$
$30$		0			0
$31$	−2.27644	+	3.94291i	−0.0734336	+	0.127191i	−0.900404	−	0.435055i	$-0.856729\pi$
$31$	−2.27644	+	3.94291i	−0.0734336	+	0.127191i	0.826970	+	0.562245i	$0.190062\pi$
$32$	−4.18383	+	7.24661i	−0.130745	+	0.226456i
$33$		0			0
$34$	2.31579	+	4.01106i	0.0681113	+	0.117972i
$35$	3.26193	+	4.88841i	0.0931979	+	0.139669i
$36$		0			0
$37$			50.3038i			1.35956i	0.733415	+	0.679781i	$0.237925\pi$
$37$			50.3038i			1.35956i	−0.733415	+	0.679781i	$0.762075\pi$
$38$	−21.2299	−	36.7713i	−0.558682	−	0.967666i
$39$		0			0
$40$	2.39378	+	36.8743i	0.0598445	+	0.921858i
$41$	16.3362	+	9.43171i	0.398444	+	0.230042i	0.685812	−	0.727778i	$-0.259447\pi$
$41$	16.3362	+	9.43171i	0.398444	+	0.230042i	−0.287368	+	0.957820i	$0.592780\pi$
$42$		0			0
$43$	43.8953	−	25.3430i	1.02082	−	0.589371i	0.106479	−	0.994315i	$-0.466042\pi$
$43$	43.8953	−	25.3430i	1.02082	−	0.589371i	0.914342	+	0.404944i	$0.132709\pi$
$44$			10.1036i			0.229626i
$45$		0			0
$46$	−70.7527			−1.53810
$47$	−5.42949	−	9.40415i	−0.115521	−	0.200088i	0.802467	−	0.596697i	$-0.203520\pi$
$47$	−5.42949	−	9.40415i	−0.115521	−	0.200088i	−0.917988	+	0.396608i	$0.870187\pi$
$48$		0			0
$49$	−23.8093	+	41.2389i	−0.485903	+	0.841609i
$50$	−32.3258	−	42.2368i	−0.646517	−	0.844736i
$51$		0			0
$52$	−3.59308	+	2.07446i	−0.0690976	+	0.0398935i
$53$	86.1924			1.62627			0.813136	−	0.582073i	$-0.197758\pi$
$53$	86.1924			1.62627			0.813136	+	0.582073i	$0.197758\pi$
$54$		0			0
$55$	53.2821	+	79.8500i	0.968765	+	1.45182i
$56$	7.52261	−	4.34318i	0.134332	−	0.0775568i
$57$		0			0
$58$	31.0939	+	17.9521i	0.536102	+	0.309519i
$59$	−83.5848	−	48.2577i	−1.41669	−	0.817927i	−0.420685	−	0.907207i	$-0.638210\pi$
$59$	−83.5848	−	48.2577i	−1.41669	−	0.817927i	−0.996007	+	0.0892792i	$0.971544\pi$
$60$		0			0
$61$	−20.8160	−	36.0544i	−0.341246	−	0.591056i	0.643418	−	0.765515i	$-0.277516\pi$
$61$	−20.8160	−	36.0544i	−0.341246	−	0.591056i	−0.984664	+	0.174459i	$0.944182\pi$
$62$	−9.68626			−0.156230
$63$		0			0
$64$	53.5101			0.836095
$65$	−17.4568	+	35.3433i	−0.268566	+	0.543743i
$66$		0			0
$67$	−58.6786	−	33.8781i	−0.875800	−	0.505643i	−0.00652877	−	0.999979i	$-0.502078\pi$
$67$	−58.6786	−	33.8781i	−0.875800	−	0.505643i	−0.869271	+	0.494335i	$0.835412\pi$
$68$	−0.572829	+	0.992169i	−0.00842396	+	0.0145907i
$69$		0			0
$70$	−5.53687	+	11.2100i	−0.0790982	+	0.160144i
$71$		−	49.6797i		−	0.699714i	−0.936803	−	0.349857i	$-0.886230\pi$
$71$		−	49.6797i		−	0.699714i	0.936803	−	0.349857i	$-0.113770\pi$
$72$		0			0
$73$		−	106.022i		−	1.45235i	−0.687510	−	0.726175i	$-0.741296\pi$
$73$		−	106.022i		−	1.45235i	0.687510	−	0.726175i	$-0.258704\pi$
$74$	−92.6832	+	53.5107i	−1.25248	+	0.723117i
$75$		0			0
$76$	5.25140	−	9.09570i	0.0690974	−	0.119680i
$77$	11.2828	−	19.5425i	0.146530	−	0.253798i
$78$		0			0
$79$	−22.0052	−	38.1142i	−0.278547	−	0.482458i	0.692477	−	0.721440i	$-0.256520\pi$
$79$	−22.0052	−	38.1142i	−0.278547	−	0.482458i	−0.971024	+	0.238982i	$0.923186\pi$
$80$	−74.1484	+	49.4775i	−0.926855	+	0.618469i
$81$		0			0
$82$			40.1319i			0.489414i
$83$	−44.5432	−	77.1510i	−0.536665	−	0.929530i	−0.999081	−	0.0428674i	$-0.986351\pi$
$83$	−44.5432	−	77.1510i	−0.536665	−	0.929530i	0.462416	−	0.886663i	$-0.346983\pi$
$84$		0			0
$85$	0.705141	+	10.8621i	0.00829578	+	0.127790i
$86$	93.3872	+	53.9171i	1.08590	+	0.626943i
$87$		0			0
$88$	122.878	−	70.9439i	1.39635	−	0.806181i
$89$			19.9472i			0.224125i	0.993701	+	0.112063i	$0.0357457\pi$
$89$			19.9472i			0.224125i	−0.993701	+	0.112063i	$0.964254\pi$
$90$		0			0
$91$	9.26638			0.101828
$92$	−8.75065	−	15.1566i	−0.0951157	−	0.164745i
$93$		0			0
$94$	11.5512	−	20.0073i	0.122885	−	0.212844i
$95$	−6.46437	−	99.5786i	−0.0680460	−	1.04820i
$96$		0			0
$97$	−133.934	+	77.3270i	−1.38077	+	0.797185i	−0.992250	−	0.124257i	$-0.960345\pi$
$97$	−133.934	+	77.3270i	−1.38077	+	0.797185i	−0.388515	+	0.921442i	$0.627012\pi$
$98$	−101.308			−1.03376
$99$		0			0
$100$	5.04988	−	12.1486i	0.0504988	−	0.121486i
$101$	156.087	−	90.1170i	1.54542	−	0.892248i	0.546936	−	0.837174i	$-0.315794\pi$
$101$	156.087	−	90.1170i	1.54542	−	0.892248i	0.998482	−	0.0550733i	$-0.0175393\pi$
$102$		0			0
$103$	−108.983	−	62.9212i	−1.05808	−	0.610885i	−0.133183	−	0.991092i	$-0.542520\pi$
$103$	−108.983	−	62.9212i	−1.05808	−	0.610885i	−0.924902	+	0.380206i	$0.875853\pi$
$104$	50.4589	+	29.1324i	0.485182	+	0.280120i
$105$		0			0
$106$	91.6872	+	158.807i	0.864974	+	1.49818i
$107$	4.04617			0.0378147			0.0189074	−	0.999821i	$-0.493981\pi$
$107$	4.04617			0.0378147			0.0189074	+	0.999821i	$0.493981\pi$
$108$		0			0
$109$	13.9374			0.127866			0.0639332	−	0.997954i	$-0.479636\pi$
$109$	13.9374			0.127866			0.0639332	+	0.997954i	$0.479636\pi$
$110$	−90.4424	+	183.111i	−0.822203	+	1.66465i
$111$		0			0
$112$	18.1470	+	10.4772i	0.162027	+	0.0935464i
$113$	−56.3045	+	97.5222i	−0.498270	+	0.863029i	−0.999998	−	0.00199662i	$-0.999364\pi$
$113$	−56.3045	+	97.5222i	−0.498270	+	0.863029i	0.501728	+	0.865025i	$0.332698\pi$
$114$		0			0
$115$	−149.087	−	73.6374i	−1.29641	−	0.640325i
$116$			8.88120i			0.0765621i
$117$		0			0
$118$		−	205.337i		−	1.74014i
$119$	2.21595	−	1.27938i	0.0186214	−	0.0107511i
$120$		0			0
$121$	123.800	−	214.428i	1.02314	−	1.77213i
$122$	44.2861	−	76.7057i	0.363001	−	0.628736i
$123$		0			0
$124$	−1.19799	−	2.07498i	−0.00966121	−	0.0167337i
$125$	−24.1569	−	122.644i	−0.193255	−	0.981148i
$126$		0			0
$127$		−	141.781i		−	1.11638i	−0.829712	−	0.558191i	$-0.811495\pi$
$127$		−	141.781i		−	1.11638i	0.829712	−	0.558191i	$-0.188505\pi$
$128$	73.6567	+	127.577i	0.575443	+	0.996696i
$129$		0			0
$130$	−83.6885	+	5.43283i	−0.643758	+	0.0417910i
$131$	135.223	+	78.0713i	1.03224	+	0.595964i	0.917625	−	0.397446i	$-0.130103\pi$
$131$	135.223	+	78.0713i	1.03224	+	0.595964i	0.114614	+	0.993410i	$0.463437\pi$
$132$		0			0
$133$	−20.3147	+	11.7287i	−0.152742	+	0.0881857i
$134$		−	144.151i		−	1.07576i
$135$		0			0
$136$	16.0889			0.118301
$137$	120.913	+	209.428i	0.882580	+	1.52867i	0.848462	+	0.529256i	$0.177529\pi$
$137$	120.913	+	209.428i	0.882580	+	1.52867i	0.0341175	+	0.999418i	$0.489138\pi$
$138$		0			0
$139$	53.2807	−	92.2849i	0.383314	−	0.663920i	−0.608219	−	0.793769i	$-0.708116\pi$
$139$	53.2807	−	92.2849i	0.383314	−	0.663920i	0.991534	+	0.129849i	$0.0414493\pi$
$140$	−3.08620	+	0.200348i	−0.0220443	+	0.00143105i
$141$		0			0
$142$	91.5333	−	52.8468i	0.644601	−	0.372160i
$143$	151.362			1.05848
$144$		0			0
$145$	46.8359	+	70.1896i	0.323006	+	0.484066i
$146$	195.341	−	112.780i	1.33796	−	0.772469i
$147$		0			0
$148$	−22.9260	−	13.2363i	−0.154905	−	0.0894346i
$149$	90.9819	+	52.5284i	0.610617	+	0.352540i	0.773207	−	0.634154i	$-0.218651\pi$
$149$	90.9819	+	52.5284i	0.610617	+	0.352540i	−0.162590	+	0.986694i	$0.551985\pi$
$150$		0			0
$151$	96.4725	+	167.095i	0.638890	+	1.10659i	0.985677	+	0.168647i	$0.0539396\pi$
$151$	96.4725	+	167.095i	0.638890	+	1.10659i	−0.346786	+	0.937944i	$0.612727\pi$
$152$	−147.495			−0.970360
$153$		0			0
$154$	48.0085			0.311743
$155$	−20.4105	−	10.0812i	−0.131681	−	0.0650398i
$156$		0			0
$157$	−172.043	−	99.3293i	−1.09582	−	0.632671i	−0.160698	−	0.987004i	$-0.551375\pi$
$157$	−172.043	−	99.3293i	−1.09582	−	0.632671i	−0.935119	+	0.354333i	$0.884708\pi$
$158$	46.8161	−	81.0879i	0.296305	−	0.513215i
$159$		0			0
$160$	−37.5121	−	18.5280i	−0.234451	−	0.115800i
$161$			39.0881i			0.242783i
$162$		0			0
$163$		−	76.4333i		−	0.468916i	−0.972126	−	0.234458i	$-0.924668\pi$
$163$		−	76.4333i		−	0.468916i	0.972126	−	0.234458i	$-0.0753316\pi$
$164$	−8.59701	+	4.96348i	−0.0524208	+	0.0302651i
$165$		0			0
$166$	94.7656	−	164.139i	0.570877	−	0.988788i
$167$	−5.22654	+	9.05264i	−0.0312967	+	0.0542074i	−0.881250	−	0.472651i	$-0.843297\pi$
$167$	−5.22654	+	9.05264i	−0.0312967	+	0.0542074i	0.849953	+	0.526859i	$0.176630\pi$
$168$		0			0
$169$	−53.4223	−	92.5301i	−0.316108	−	0.547515i
$170$	−19.2631	+	12.8538i	−0.113312	+	0.0756106i
$171$		0			0
$172$			26.6737i			0.155080i
$173$	−55.6646	−	96.4140i	−0.321761	−	0.557306i	0.659091	−	0.752064i	$-0.270941\pi$
$173$	−55.6646	−	96.4140i	−0.321761	−	0.557306i	−0.980851	+	0.194757i	$0.937608\pi$
$174$		0			0
$175$	−23.3342	+	17.8588i	−0.133338	+	0.102050i
$176$	296.424	+	171.140i	1.68423	+	0.972388i
$177$		0			0
$178$	−36.7520	+	21.2188i	−0.206472	+	0.119207i
$179$			167.070i			0.933355i	0.884428	+	0.466677i	$0.154549\pi$
$179$			167.070i			0.933355i	−0.884428	+	0.466677i	$0.845451\pi$
$180$		0			0
$181$	−259.240			−1.43226			−0.716131	−	0.697966i	$-0.754089\pi$
$181$	−259.240			−1.43226			−0.716131	+	0.697966i	$0.754089\pi$
$182$	9.85711	+	17.0730i	0.0541600	+	0.0938078i
$183$		0			0
$184$	−122.888	+	212.849i	−0.667872	+	1.15679i
$185$	−250.991	+	16.2936i	−1.35671	+	0.0880737i
$186$		0			0
$187$	36.1966	−	20.8981i	0.193564	−	0.111754i
$188$	5.71459			0.0303968
$189$		0			0
$190$	176.594	−	117.837i	0.929442	−	0.620195i
$191$	95.6109	−	55.2010i	0.500581	−	0.289010i	−0.228373	−	0.973574i	$-0.573340\pi$
$191$	95.6109	−	55.2010i	0.500581	−	0.289010i	0.728953	+	0.684563i	$0.240007\pi$
$192$		0			0
$193$	−9.66216	−	5.57845i	−0.0500630	−	0.0289039i	0.474760	−	0.880116i	$-0.342535\pi$
$193$	−9.66216	−	5.57845i	−0.0500630	−	0.0289039i	−0.524823	+	0.851212i	$0.675868\pi$
$194$	−284.945	−	164.513i	−1.46879	−	0.848006i
$195$		0			0
$196$	−12.5297	−	21.7022i	−0.0639273	−	0.110725i
$197$	−155.209			−0.787863			−0.393932	−	0.919140i	$-0.628885\pi$
$197$	−155.209			−0.787863			−0.393932	+	0.919140i	$0.628885\pi$
$198$		0			0
$199$	166.552			0.836945			0.418472	−	0.908230i	$-0.362566\pi$
$199$	166.552			0.836945			0.418472	+	0.908230i	$0.362566\pi$
$200$	−183.209	+	23.8875i	−0.916045	+	0.119438i
$201$		0			0
$202$	332.076	+	191.724i	1.64394	+	0.949128i
$203$	9.91782	−	17.1782i	0.0488562	−	0.0846215i
$204$		0			0
$205$	−41.7681	+	84.5644i	−0.203747	+	0.412509i
$206$		−	267.730i		−	1.29966i
$207$		0			0
$208$			140.554i			0.675742i
$209$	−331.831	+	191.583i	−1.58771	+	0.916665i
$210$		0			0
$211$	−56.2297	+	97.3928i	−0.266492	+	0.461577i	−0.967953	−	0.251130i	$-0.919198\pi$
$211$	−56.2297	+	97.3928i	−0.266492	+	0.461577i	0.701462	+	0.712707i	$0.252531\pi$
$212$	−22.6796	+	39.2822i	−0.106979	+	0.185294i
$213$		0			0
$214$	4.30412	+	7.45495i	0.0201127	+	0.0348362i
$215$	140.667	+	210.807i	0.654263	+	0.980497i
$216$		0			0
$217$			5.35128i			0.0246603i
$218$	14.8259	+	25.6793i	0.0680089	+	0.117795i
$219$		0			0
$220$	−50.4117	+	3.27259i	−0.229144	+	0.0148754i
$221$	14.8638	+	8.58160i	0.0672569	+	0.0388308i
$222$		0			0
$223$	−60.4661	+	34.9101i	−0.271148	+	0.156548i	−0.629409	−	0.777074i	$-0.716703\pi$
$223$	−60.4661	+	34.9101i	−0.271148	+	0.156548i	0.358261	+	0.933621i	$0.383370\pi$
$224$			9.83501i			0.0439063i
$225$		0			0
$226$	−239.576			−1.06007
$227$	−220.219	−	381.431i	−0.970128	−	1.68031i	−0.695156	−	0.718859i	$-0.744665\pi$
$227$	−220.219	−	381.431i	−0.970128	−	1.68031i	−0.274973	−	0.961452i	$-0.588669\pi$
$228$		0			0
$229$	56.3756	−	97.6454i	0.246182	−	0.426399i	−0.716281	−	0.697811i	$-0.754157\pi$
$229$	56.3756	−	97.6454i	0.246182	−	0.426399i	0.962463	+	0.271412i	$0.0874907\pi$
$230$	−22.9171	−	353.021i	−0.0996397	−	1.53487i
$231$		0			0
$232$	108.012	−	62.3610i	0.465571	−	0.268797i
$233$	−290.682			−1.24756			−0.623781	−	0.781599i	$-0.714404\pi$
$233$	−290.682			−1.24756			−0.623781	+	0.781599i	$0.714404\pi$
$234$		0			0
$235$	45.1633	−	30.1365i	0.192184	−	0.128240i
$236$	43.9869	−	25.3959i	0.186385	−	0.107610i
$237$		0			0
$238$	4.71443	+	2.72188i	0.0198085	+	0.0114365i
$239$	−128.930	−	74.4376i	−0.539455	−	0.311454i	0.205403	−	0.978677i	$-0.434149\pi$
$239$	−128.930	−	74.4376i	−0.539455	−	0.311454i	−0.744858	+	0.667223i	$0.767483\pi$
$240$		0			0
$241$	−130.295	−	225.677i	−0.540643	−	0.936421i	−0.998867	−	0.0475841i	$-0.984848\pi$
$241$	−130.295	−	225.677i	−0.540643	−	0.936421i	0.458225	−	0.888836i	$-0.348486\pi$
$242$	526.769			2.17673
$243$		0			0
$244$	21.9091			0.0897913
$245$	−213.473	−	105.439i	−0.871319	−	0.430363i
$246$		0			0
$247$	−136.263	−	78.6717i	−0.551674	−	0.318509i
$248$	−16.8238	+	29.1397i	−0.0678379	+	0.117499i
$249$		0			0
$250$	200.270	−	174.970i	0.801080	−	0.699882i
$251$			46.8742i			0.186750i	0.995631	+	0.0933748i	$0.0297655\pi$
$251$			46.8742i			0.186750i	−0.995631	+	0.0933748i	$0.970235\pi$
$252$		0			0
$253$			638.486i			2.52366i
$254$	261.226	−	150.819i	1.02845	−	0.593776i
$255$		0			0
$256$	−49.6844	+	86.0559i	−0.194080	+	0.336156i
$257$	31.7894	−	55.0608i	0.123694	−	0.214244i	−0.797528	−	0.603282i	$-0.793859\pi$
$257$	31.7894	−	55.0608i	0.123694	−	0.214244i	0.921222	+	0.389038i	$0.127193\pi$
$258$		0			0
$259$	29.5625	+	51.2038i	0.114141	+	0.197698i
$260$	−11.5143	−	17.2557i	−0.0442859	−	0.0663681i
$261$		0			0
$262$			332.193i			1.26791i
$263$	20.7920	+	36.0128i	0.0790571	+	0.136931i	0.902843	−	0.429970i	$-0.141476\pi$
$263$	20.7920	+	36.0128i	0.0790571	+	0.136931i	−0.823786	+	0.566901i	$0.808142\pi$
$264$		0			0
$265$	27.9181	+	430.057i	0.105351	+	1.62286i
$266$	−43.2195	−	24.9528i	−0.162479	−	0.0938075i
$267$		0			0
$268$	30.8799	−	17.8285i	0.115224	−	0.0665244i
$269$			206.293i			0.766890i	0.923564	+	0.383445i	$0.125262\pi$
$269$			206.293i			0.766890i	−0.923564	+	0.383445i	$0.874738\pi$
$270$		0			0
$271$	−17.1983			−0.0634625			−0.0317312	−	0.999496i	$-0.510102\pi$
$271$	−17.1983			−0.0634625			−0.0317312	+	0.999496i	$0.510102\pi$
$272$	19.4059	+	33.6120i	0.0713451	+	0.123573i
$273$		0			0
$274$	−257.243	+	445.559i	−0.938844	+	1.62613i
$275$	−381.153	+	291.715i	−1.38601	+	1.06078i
$276$		0			0
$277$	−85.3215	+	49.2604i	−0.308020	+	0.177835i	−0.646040	−	0.763304i	$-0.723576\pi$
$277$	−85.3215	+	49.2604i	−0.308020	+	0.177835i	0.338020	+	0.941139i	$0.390243\pi$
$278$	226.709			0.815501
$279$		0			0
$280$	24.1069	+	36.1273i	0.0860961	+	0.129026i
$281$	269.989	−	155.878i	0.960813	−	0.554726i	0.0643900	−	0.997925i	$-0.479490\pi$
$281$	269.989	−	155.878i	0.960813	−	0.554726i	0.896423	+	0.443199i	$0.146157\pi$
$282$		0			0
$283$	362.495	+	209.287i	1.28090	+	0.739529i	0.977013	−	0.213178i	$-0.0683815\pi$
$283$	362.495	+	209.287i	1.28090	+	0.739529i	0.303889	+	0.952708i	$0.401715\pi$
$284$	22.6415	+	13.0721i	0.0797237	+	0.0460285i
$285$		0			0
$286$	161.011	+	278.880i	0.562977	+	0.975105i
$287$	22.1713			0.0772519
$288$		0			0
$289$	−284.261			−0.983601
$290$	−79.5004	+	160.958i	−0.274139	+	0.555027i
$291$		0			0
$292$	48.3194	+	27.8972i	0.165477	+	0.0955384i
$293$	97.2504	−	168.443i	0.331913	−	0.574889i	−0.650974	−	0.759100i	$-0.725639\pi$
$293$	97.2504	−	168.443i	0.331913	−	0.574889i	0.982887	+	0.184210i	$0.0589728\pi$
$294$		0			0
$295$	213.708	−	432.677i	0.724435	−	1.46670i
$296$			371.765i			1.25596i
$297$		0			0
$298$			223.508i			0.750028i
$299$	−227.062	+	131.094i	−0.759404	+	0.438442i
$300$		0			0
$301$	29.7871	−	51.5927i	0.0989604	−	0.171404i
$302$	−205.245	+	355.495i	−0.679620	+	1.17714i
$303$		0			0
$304$	−177.903	−	308.137i	−0.585208	−	1.01361i
$305$	173.151	−	115.540i	0.567708	−	0.378819i
$306$		0			0
$307$		−	425.006i		−	1.38438i	−0.721714	−	0.692191i	$-0.756645\pi$
$307$		−	425.006i		−	1.38438i	0.721714	−	0.692191i	$-0.243355\pi$
$308$	5.93765	+	10.2843i	0.0192781	+	0.0333906i
$309$		0			0
$310$	−3.13743	−	48.3296i	−0.0101207	−	0.155902i
$311$	67.5564	+	39.0037i	0.217223	+	0.125414i	0.604664	−	0.796481i	$-0.293307\pi$
$311$	67.5564	+	39.0037i	0.217223	+	0.125414i	−0.387441	+	0.921895i	$0.626641\pi$
$312$		0			0
$313$	−418.180	+	241.437i	−1.33604	+	0.771363i	−0.986218	−	0.165453i	$-0.947091\pi$
$313$	−418.180	+	241.437i	−1.33604	+	0.771363i	−0.349822	+	0.936816i	$0.613758\pi$
$314$		−	422.646i		−	1.34601i
$315$		0			0
$316$	23.1607			0.0732935
$317$	5.10864	+	8.84842i	0.0161156	+	0.0279130i	0.873971	−	0.485979i	$-0.161537\pi$
$317$	5.10864	+	8.84842i	0.0161156	+	0.0279130i	−0.857855	+	0.513892i	$0.828203\pi$
$318$		0			0
$319$	162.003	−	280.598i	0.507847	−	0.879616i
$320$	17.3322	+	266.989i	0.0541630	+	0.834339i
$321$		0			0
$322$	−72.0186	+	41.5800i	−0.223660	+	0.129130i
$323$	−43.4478			−0.134513
$324$		0			0
$325$	−181.999	−	75.6527i	−0.559998	−	0.232778i
$326$	140.826	−	81.3059i	0.431982	−	0.249405i
$327$		0			0
$328$	120.731	+	69.7040i	0.368082	+	0.212512i
$329$	−11.0533	−	6.38160i	−0.0335965	−	0.0193970i
$330$		0			0
$331$	316.714	+	548.566i	0.956841	+	1.65730i	0.730097	+	0.683343i	$0.239475\pi$
$331$	316.714	+	548.566i	0.956841	+	1.65730i	0.226744	+	0.973954i	$0.427192\pi$
$332$	46.8821			0.141211
$333$		0			0
$334$	−22.2389			−0.0665836
$335$	150.028	−	303.750i	0.447846	−	0.906717i
$336$		0			0
$337$	−31.6872	−	18.2946i	−0.0940273	−	0.0542867i	0.452249	−	0.891892i	$-0.350622\pi$
$337$	−31.6872	−	18.2946i	−0.0940273	−	0.0542867i	−0.546276	+	0.837605i	$0.683955\pi$
$338$	113.656	−	196.858i	0.336260	−	0.582420i
$339$		0			0
$340$	−5.13597	−	2.53676i	−0.0151058	−	0.00746106i
$341$			87.4107i			0.256336i
$342$		0			0
$343$			113.561i			0.331083i
$344$	324.403	−	187.294i	0.943033	−	0.544460i
$345$		0			0
$346$	118.426	−	205.121i	0.342273	−	0.592834i
$347$	−31.6633	+	54.8425i	−0.0912488	+	0.158048i	−0.908037	−	0.418890i	$-0.862419\pi$
$347$	−31.6633	+	54.8425i	−0.0912488	+	0.158048i	0.816788	+	0.576938i	$0.195753\pi$
$348$		0			0
$349$	230.082	+	398.514i	0.659261	+	1.14187i	0.980807	+	0.194980i	$0.0624641\pi$
$349$	230.082	+	398.514i	0.659261	+	1.14187i	−0.321546	+	0.946894i	$0.604203\pi$
$350$	−57.7259	−	23.9952i	−0.164931	−	0.0685578i
$351$		0			0
$352$			160.650i			0.456393i
$353$	138.101	+	239.199i	0.391222	+	0.677617i	0.992611	−	0.121340i	$-0.0387190\pi$
$353$	138.101	+	239.199i	0.391222	+	0.677617i	−0.601389	+	0.798957i	$0.705386\pi$
$354$		0			0
$355$	247.877	−	16.0915i	0.698244	−	0.0453281i
$356$	−9.09092	−	5.24865i	−0.0255363	−	0.0147434i
$357$		0			0
$358$	−307.822	+	177.721i	−0.859838	+	0.496428i
$359$			226.125i			0.629874i	0.949113	+	0.314937i	$0.101983\pi$
$359$			226.125i			0.629874i	−0.949113	+	0.314937i	$0.898017\pi$
$360$		0			0
$361$	37.3073			0.103344
$362$	−275.766	−	477.641i	−0.761785	−	1.31945i
$363$		0			0
$364$	−2.43824	+	4.22316i	−0.00669846	+	0.0116021i
$365$	528.994	−	34.3409i	1.44930	−	0.0940846i
$366$		0			0
$367$	207.053	−	119.542i	0.564177	−	0.325728i	−0.190643	−	0.981659i	$-0.561057\pi$
$367$	207.053	−	119.542i	0.564177	−	0.325728i	0.754820	+	0.655931i	$0.227724\pi$
$368$	−592.896			−1.61113
$369$		0			0
$370$	−297.012	−	445.110i	−0.802735	−	1.20300i
$371$	87.7345	−	50.6535i	0.236481	−	0.136532i
$372$		0			0
$373$	168.280	+	97.1563i	0.451152	+	0.260473i	0.708317	−	0.705895i	$-0.249455\pi$
$373$	168.280	+	97.1563i	0.451152	+	0.260473i	−0.257165	+	0.966368i	$0.582788\pi$
$374$	77.0082	+	44.4607i	0.205904	+	0.118879i
$375$		0			0
$376$	−40.1260	−	69.5003i	−0.106718	−	0.184841i
$377$	133.050			0.352918
$378$		0			0
$379$	−322.695			−0.851439			−0.425720	−	0.904855i	$-0.639979\pi$
$379$	−322.695			−0.851439			−0.425720	+	0.904855i	$0.639979\pi$
$380$	47.0839	+	23.2557i	0.123905	+	0.0611993i
$381$		0			0
$382$	203.412	+	117.440i	0.532493	+	0.307435i
$383$	−140.110	+	242.678i	−0.365824	+	0.633625i	−0.988908	−	0.148530i	$-0.952546\pi$
$383$	−140.110	+	242.678i	−0.365824	+	0.633625i	0.623084	+	0.782155i	$0.285879\pi$
$384$		0			0
$385$	101.162	+	49.9658i	0.262757	+	0.129781i
$386$		−	23.7363i		−	0.0614930i
$387$		0			0
$388$		−	81.3874i		−	0.209761i
$389$	−103.944	+	60.0122i	−0.267209	+	0.154273i	−0.627618	−	0.778521i	$-0.715970\pi$
$389$	−103.944	+	60.0122i	−0.267209	+	0.154273i	0.360410	+	0.932794i	$0.382637\pi$
$390$		0			0
$391$	−36.1995	+	62.6994i	−0.0925818	+	0.160356i
$392$	−175.960	+	304.771i	−0.448877	+	0.777478i
$393$		0			0
$394$	−165.104	−	285.968i	−0.419045	−	0.725807i
$395$	183.043	−	122.140i	0.463400	−	0.309216i
$396$		0			0
$397$		−	335.458i		−	0.844983i	−0.906367	−	0.422492i	$-0.861156\pi$
$397$		−	335.458i		−	0.844983i	0.906367	−	0.422492i	$-0.138844\pi$
$398$	177.170	+	306.867i	0.445150	+	0.771022i
$399$		0			0
$400$	−270.885	−	353.937i	−0.677212	−	0.884843i
$401$	205.718	+	118.771i	0.513013	+	0.296188i	0.734071	−	0.679072i	$-0.237618\pi$
$401$	205.718	+	118.771i	0.513013	+	0.296188i	−0.221058	+	0.975261i	$0.570951\pi$
$402$		0			0
$403$	−31.0854	+	17.9472i	−0.0771351	+	0.0445339i
$404$			94.8491i			0.234775i
$405$		0			0
$406$	42.2003			0.103942
$407$	482.890	+	836.391i	1.18646	+	2.05501i
$408$		0			0
$409$	−50.2635	+	87.0590i	−0.122894	+	0.212858i	−0.920908	−	0.389781i	$-0.872551\pi$
$409$	−50.2635	+	87.0590i	−0.122894	+	0.212858i	0.798014	+	0.602639i	$0.205884\pi$
$410$	−200.238	+	12.9989i	−0.488386	+	0.0317047i
$411$		0			0
$412$	57.3527	−	33.1126i	0.139206	−	0.0803704i
$413$	−113.440			−0.274674
$414$		0			0
$415$	370.517	−	247.238i	0.892812	−	0.595753i
$416$	−57.1313	+	32.9848i	−0.137335	+	0.0792903i
$417$		0			0
$418$	−705.971	−	407.593i	−1.68893	−	0.975102i
$419$	133.287	+	76.9534i	0.318108	+	0.183660i	0.650549	−	0.759464i	$-0.274539\pi$
$419$	133.287	+	76.9534i	0.318108	+	0.183660i	−0.332441	+	0.943124i	$0.607872\pi$
$420$		0			0
$421$	−379.328	−	657.016i	−0.901018	−	1.56061i	−0.826175	−	0.563413i	$-0.809488\pi$
$421$	−379.328	−	657.016i	−0.901018	−	1.56061i	−0.0748425	−	0.997195i	$-0.523845\pi$
$422$	−239.258			−0.566961
$423$		0			0
$424$	636.996			1.50235
$425$	−53.9682	+	7.03660i	−0.126984	+	0.0165567i
$426$		0			0
$427$	−42.3769	−	24.4663i	−0.0992433	−	0.0572981i
$428$	−1.06466	+	1.84404i	−0.00248752	+	0.00430852i
$429$		0			0
$430$	−238.771	+	483.419i	−0.555281	+	1.12423i
$431$		−	682.009i		−	1.58239i	−0.611566	−	0.791194i	$-0.709460\pi$
$431$		−	682.009i		−	1.58239i	0.611566	−	0.791194i	$-0.290540\pi$
$432$		0			0
$433$			295.078i			0.681473i	0.940159	+	0.340737i	$0.110676\pi$
$433$			295.078i			0.681473i	−0.940159	+	0.340737i	$0.889324\pi$
$434$	−9.85956	+	5.69242i	−0.0227179	+	0.0131162i
$435$		0			0
$436$	−3.66732	+	6.35199i	−0.00841129	+	0.0145688i
$437$	331.858	−	574.796i	0.759402	−	1.31532i
$438$		0			0
$439$	239.973	+	415.646i	0.546636	+	0.946802i	0.998502	+	0.0547159i	$0.0174253\pi$
$439$	239.973	+	415.646i	0.546636	+	0.946802i	−0.451866	+	0.892086i	$0.649241\pi$
$440$	393.775	+	590.123i	0.894944	+	1.34119i
$441$		0			0
$442$			36.5147i			0.0826125i
$443$	29.6451	+	51.3468i	0.0669189	+	0.115907i	0.897544	−	0.440926i	$-0.145350\pi$
$443$	29.6451	+	51.3468i	0.0669189	+	0.115907i	−0.830625	+	0.556833i	$0.812016\pi$
$444$		0			0
$445$	−99.5263	+	6.46098i	−0.223655	+	0.0145190i
$446$	−128.642	−	74.2713i	−0.288434	−	0.166528i
$447$		0			0
$448$	54.4675	−	31.4468i	0.121579	−	0.0701938i
$449$		−	306.745i		−	0.683173i	−0.939850	−	0.341587i	$-0.889036\pi$
$449$		−	306.745i		−	0.683173i	0.939850	−	0.341587i	$-0.110964\pi$
$450$		0			0
$451$	362.158			0.803011
$452$	−29.6305	−	51.3216i	−0.0655543	−	0.113543i
$453$		0			0
$454$	468.516	−	811.494i	1.03197	−	1.78743i
$455$	3.00142	+	46.2346i	0.00659654	+	0.101614i
$456$		0			0
$457$	301.330	−	173.973i	0.659365	−	0.380685i	−0.132670	−	0.991160i	$-0.542355\pi$
$457$	301.330	−	173.973i	0.659365	−	0.380685i	0.792035	+	0.610476i	$0.209022\pi$
$458$	239.878			0.523752
$459$		0			0
$460$	72.7893	−	48.5706i	0.158238	−	0.105588i
$461$	−683.228	+	394.462i	−1.48206	+	0.855665i	−0.999793	−	0.0203616i	$-0.993518\pi$
$461$	−683.228	+	394.462i	−1.48206	+	0.855665i	−0.482263	+	0.876027i	$0.660185\pi$
$462$		0			0
$463$	−232.472	−	134.218i	−0.502100	−	0.289887i	0.227481	−	0.973783i	$-0.426951\pi$
$463$	−232.472	−	134.218i	−0.502100	−	0.289887i	−0.729580	+	0.683895i	$0.760285\pi$
$464$	260.562	+	150.435i	0.561555	+	0.324214i
$465$		0			0
$466$	−309.213	−	535.573i	−0.663547	−	1.14930i
$467$	−630.007			−1.34905			−0.674525	−	0.738252i	$-0.735652\pi$
$467$	−630.007			−1.34905			−0.674525	+	0.738252i	$0.735652\pi$
$468$		0			0
$469$	−79.6379			−0.169804
$470$	103.568	+	51.1544i	0.220357	+	0.108839i
$471$		0			0
$472$	−617.725	−	356.643i	−1.30874	−	0.755600i
$473$	486.559	−	842.744i	1.02867	−	1.78170i
$474$		0			0
$475$	494.753	−	64.5079i	1.04159	−	0.135806i
$476$			1.34656i			0.00282891i
$477$		0			0
$478$		−	316.732i		−	0.662619i
$479$	137.022	−	79.1097i	0.286059	−	0.165156i	−0.350104	−	0.936711i	$-0.613854\pi$
$479$	137.022	−	79.1097i	0.286059	−	0.165156i	0.636163	+	0.771555i	$0.280521\pi$
$480$		0			0
$481$	−198.294	+	343.456i	−0.412254	+	0.714045i
$482$	277.202	−	480.129i	0.575109	−	0.996117i
$483$		0			0
$484$	65.1504	+	112.844i	0.134608	+	0.233149i
$485$	−429.205	−	643.218i	−0.884958	−	1.32622i
$486$		0			0
$487$		−	652.722i		−	1.34029i	−0.742230	−	0.670145i	$-0.766232\pi$
$487$		−	652.722i		−	1.34029i	0.742230	−	0.670145i	$-0.233768\pi$
$488$	−153.839	−	266.456i	−0.315243	−	0.546017i
$489$		0			0
$490$	−32.8143	−	505.478i	−0.0669679	−	1.03159i
$491$	−539.030	−	311.209i	−1.09782	−	0.633827i	−0.162173	−	0.986762i	$-0.551850\pi$
$491$	−539.030	−	311.209i	−1.09782	−	0.633827i	−0.935648	+	0.352935i	$0.885184\pi$
$492$		0			0
$493$	31.8174	−	18.3698i	0.0645384	−	0.0372612i
$494$		−	334.748i		−	0.677628i
$495$		0			0
$496$	−81.1692			−0.163648
$497$	−29.1958	−	50.5685i	−0.0587440	−	0.101748i
$498$		0			0
$499$	−187.305	+	324.421i	−0.375360	+	0.650142i	−0.990381	−	0.138369i	$-0.955814\pi$
$499$	−187.305	+	324.421i	−0.375360	+	0.650142i	0.615021	+	0.788511i	$0.289148\pi$
$500$	62.2512	+	21.2614i	0.124502	+	0.0425228i
$501$		0			0
$502$	−86.3642	+	49.8624i	−0.172040	+	0.0993275i
$503$	166.821			0.331653			0.165826	−	0.986155i	$-0.446971\pi$
$503$	166.821			0.331653			0.165826	+	0.986155i	$0.446971\pi$
$504$		0			0
$505$	500.196	+	749.608i	0.990487	+	1.48437i
$506$	−1176.39	+	679.190i	−2.32488	+	1.34227i
$507$		0			0
$508$	64.6166	+	37.3064i	0.127198	+	0.0734378i
$509$	−130.690	−	75.4542i	−0.256759	−	0.148240i	0.366096	−	0.930577i	$-0.380694\pi$
$509$	−130.690	−	75.4542i	−0.256759	−	0.148240i	−0.622855	+	0.782337i	$0.714027\pi$
$510$		0			0
$511$	−62.3067	−	107.918i	−0.121931	−	0.211191i
$512$	377.847			0.737982
$513$		0			0
$514$	135.264			0.263159
$515$	278.645	−	564.149i	0.541058	−	1.09544i
$516$		0			0
$517$	−180.550	−	104.241i	−0.349226	−	0.201626i
$518$	−62.8943	+	108.936i	−0.121417	+	0.210301i
$519$		0			0
$520$	−129.012	+	261.201i	−0.248101	+	0.502309i
$521$		−	62.5200i		−	0.120000i	−0.998198	−	0.0600000i	$-0.980890\pi$
$521$		−	62.5200i		−	0.120000i	0.998198	−	0.0600000i	$-0.0191101\pi$
$522$		0			0
$523$		−	641.422i		−	1.22643i	−0.789917	−	0.613214i	$-0.789876\pi$
$523$		−	641.422i		−	1.22643i	0.789917	−	0.613214i	$-0.210124\pi$
$524$	−71.1620	+	41.0854i	−0.135805	+	0.0784073i
$525$		0			0
$526$	−44.2350	+	76.6173i	−0.0840970	+	0.145660i
$527$	−4.95582	+	8.58373i	−0.00940383	+	0.0162879i
$528$		0			0
$529$	−288.490	−	499.680i	−0.545350	−	0.944575i
$530$	−762.669	+	508.911i	−1.43900	+	0.960210i
$531$		0			0
$532$		−	12.3446i		−	0.0232041i
$533$	74.3584	+	128.792i	0.139509	+	0.241637i
$534$		0			0
$535$	1.31057	+	20.1884i	0.00244967	+	0.0377353i
$536$	−433.658	−	250.372i	−0.809063	−	0.467113i
$537$		0			0
$538$	−380.089	+	219.445i	−0.706486	+	0.407890i
$539$			914.227i			1.69615i
$540$		0			0
$541$	586.258			1.08366			0.541828	−	0.840489i	$-0.317732\pi$
$541$	586.258			1.08366			0.541828	+	0.840489i	$0.317732\pi$
$542$	−18.2947	−	31.6874i	−0.0337541	−	0.0584638i
$543$		0			0
$544$	−9.10821	+	15.7759i	−0.0167430	+	0.0289998i
$545$	4.51440	+	69.5408i	0.00828330	+	0.127598i
$546$		0			0
$547$	86.7828	−	50.1041i	0.158652	−	0.0915980i	−0.418572	−	0.908184i	$-0.637469\pi$
$547$	86.7828	−	50.1041i	0.158652	−	0.0915980i	0.577224	+	0.816586i	$0.304136\pi$
$548$	−127.263			−0.232231
$549$		0			0
$550$	−942.927	−	391.951i	−1.71441	−	0.712639i
$551$	−291.686	+	168.405i	−0.529375	+	0.305635i
$552$		0			0
$553$	−44.7979	−	25.8641i	−0.0810088	−	0.0467705i
$554$	−181.521	−	104.801i	−0.327656	−	0.189172i
$555$		0			0
$556$	28.0392	+	48.5654i	0.0504303	+	0.0873478i
$557$	−455.918			−0.818523			−0.409262	−	0.912417i	$-0.634214\pi$
$557$	−455.918			−0.818523			−0.409262	+	0.912417i	$0.634214\pi$
$558$		0			0
$559$	399.601			0.714850
$560$	−46.3980	+	93.9382i	−0.0828536	+	0.167747i
$561$		0			0
$562$	574.400	+	331.630i	1.02206	+	0.590089i
$563$	−359.308	+	622.340i	−0.638203	+	1.10540i	0.347624	+	0.937634i	$0.386988\pi$
$563$	−359.308	+	622.340i	−0.638203	+	1.10540i	−0.985827	+	0.167765i	$0.946345\pi$
$564$		0			0
$565$	−504.824	−	249.343i	−0.893494	−	0.441315i
$566$			890.515i			1.57335i
$567$		0			0
$568$		−	367.152i		−	0.646395i
$569$	−447.135	+	258.153i	−0.785825	+	0.453696i	−0.838491	−	0.544916i	$-0.816562\pi$
$569$	−447.135	+	258.153i	−0.785825	+	0.453696i	0.0526655	+	0.998612i	$0.483228\pi$
$570$		0			0
$571$	−61.2417	+	106.074i	−0.107253	+	0.185768i	−0.914657	−	0.404232i	$-0.867539\pi$
$571$	−61.2417	+	106.074i	−0.107253	+	0.185768i	0.807403	+	0.590000i	$0.200872\pi$
$572$	−39.8276	+	68.9833i	−0.0696286	+	0.120600i
$573$		0			0
$574$	23.5847	+	40.8499i	0.0410883	+	0.0711671i
$575$	319.123	−	767.723i	0.554997	−	1.33517i
$576$		0			0
$577$			738.985i			1.28074i	0.768068	+	0.640369i	$0.221218\pi$
$577$			738.985i			1.28074i	−0.768068	+	0.640369i	$0.778782\pi$
$578$	−302.382	−	523.741i	−0.523153	−	0.906127i
$579$		0			0
$580$	−44.3127	+	2.87666i	−0.0764013	+	0.00495976i
$581$	−90.6802	−	52.3542i	−0.156076	−	0.0901105i
$582$		0			0
$583$	1433.10	−	827.403i	2.45815	−	1.41922i
$584$		−	783.541i		−	1.34168i
$585$		0			0
$586$	413.800			0.706144
$587$	−109.084	−	188.939i	−0.185833	−	0.321872i	0.758024	−	0.652227i	$-0.226165\pi$
$587$	−109.084	−	188.939i	−0.185833	−	0.321872i	−0.943857	+	0.330354i	$0.892832\pi$
$588$		0			0
$589$	45.4324	−	78.6912i	0.0771348	−	0.133601i
$590$	1024.53	−	66.5095i	1.73649	−	0.112728i
$591$		0			0
$592$	−776.669	+	448.410i	−1.31194	+	0.757449i
$593$	−273.286			−0.460854			−0.230427	−	0.973090i	$-0.574012\pi$
$593$	−273.286			−0.460854			−0.230427	+	0.973090i	$0.574012\pi$
$594$		0			0
$595$	7.10122	+	10.6421i	0.0119348	+	0.0178859i
$596$	−47.8797	+	27.6433i	−0.0803350	+	0.0463815i
$597$		0			0
$598$	−483.074	−	278.903i	−0.807816	−	0.466393i
$599$	656.605	+	379.091i	1.09617	+	0.632873i	0.935212	−	0.354088i	$-0.115209\pi$
$599$	656.605	+	379.091i	1.09617	+	0.632873i	0.160957	+	0.986961i	$0.448542\pi$
$600$		0			0
$601$	124.480	+	215.606i	0.207122	+	0.358745i	0.950807	−	0.309785i	$-0.100257\pi$
$601$	124.480	+	215.606i	0.207122	+	0.358745i	−0.743685	+	0.668530i	$0.766924\pi$
$602$	126.744			0.210538
$603$		0			0
$604$	−101.538			−0.168110
$605$	1109.99	+	548.246i	1.83469	+	0.906192i
$606$		0			0
$607$	−212.354	−	122.603i	−0.349842	−	0.201981i	0.314774	−	0.949167i	$-0.398071\pi$
$607$	−212.354	−	122.603i	−0.349842	−	0.201981i	−0.664616	+	0.747185i	$0.731405\pi$
$608$	83.4994	−	144.625i	0.137334	−	0.237870i
$609$		0			0
$610$	397.068	+	196.120i	0.650930	+	0.321508i
$611$		−	85.6108i		−	0.140116i
$612$		0			0
$613$			140.396i			0.229031i	0.993421	+	0.114515i	$0.0365315\pi$
$613$			140.396i			0.229031i	−0.993421	+	0.114515i	$0.963468\pi$
$614$	783.060	−	452.100i	1.27534	−	0.736319i
$615$		0			0
$616$	83.3846	−	144.426i	0.135365	−	0.234458i
$617$	101.735	−	176.211i	0.164887	−	0.285593i	−0.771728	−	0.635953i	$-0.780607\pi$
$617$	101.735	−	176.211i	0.164887	−	0.285593i	0.936615	+	0.350360i	$0.113941\pi$
$618$		0			0
$619$	287.187	+	497.422i	0.463953	+	0.803590i	0.999154	−	0.0411351i	$-0.0130974\pi$
$619$	287.187	+	497.422i	0.463953	+	0.803590i	−0.535201	+	0.844725i	$0.679764\pi$
$620$	9.96507	−	6.64946i	0.0160727	−	0.0107249i
$621$		0			0
$622$			165.961i			0.266818i
$623$	11.7225	+	20.3040i	0.0188163	+	0.0325907i
$624$		0			0
$625$	604.105	−	160.256i	0.966568	−	0.256409i
$626$	−889.679	−	513.656i	−1.42121	−	0.820537i
$627$		0			0
$628$	90.5387	−	52.2725i	0.144170	−	0.0832365i
$629$			109.511i			0.174104i
$630$		0			0
$631$	624.155			0.989152			0.494576	−	0.869134i	$-0.335323\pi$
$631$	624.155			0.989152			0.494576	+	0.869134i	$0.335323\pi$
$632$	−162.627	−	281.679i	−0.257322	−	0.445694i
$633$		0			0
$634$	−10.8686	+	18.8250i	−0.0171429	+	0.0296924i
$635$	707.414	−	45.9234i	1.11404	−	0.0723203i
$636$		0			0
$637$	−325.122	+	187.709i	−0.510395	+	0.294677i
$638$	689.323			1.08044
$639$		0			0
$640$	−612.688	+	408.833i	−0.957325	+	0.638801i
$641$	373.039	−	215.374i	0.581964	−	0.335997i	−0.179950	−	0.983676i	$-0.557593\pi$
$641$	373.039	−	215.374i	0.581964	−	0.335997i	0.761913	+	0.647679i	$0.224260\pi$
$642$		0			0
$643$	561.630	+	324.257i	0.873453	+	0.504288i	0.868494	−	0.495699i	$-0.165088\pi$
$643$	561.630	+	324.257i	0.873453	+	0.504288i	0.00495885	+	0.999988i	$0.498422\pi$
$644$	−17.8144	−	10.2852i	−0.0276621	−	0.0159707i
$645$		0			0
$646$	−46.2176	−	80.0512i	−0.0715443	−	0.123918i
$647$	1048.10			1.61994			0.809969	−	0.586472i	$-0.199484\pi$
$647$	1048.10			1.61994			0.809969	+	0.586472i	$0.199484\pi$
$648$		0			0
$649$	−1853.00			−2.85516
$650$	−54.2142	−	415.804i	−0.0834064	−	0.639698i
$651$		0			0
$652$	34.8345	+	20.1117i	0.0534272	+	0.0308462i
$653$	−402.556	+	697.248i	−0.616472	+	1.06776i	0.373652	+	0.927569i	$0.378105\pi$
$653$	−402.556	+	697.248i	−0.616472	+	1.06776i	−0.990124	+	0.140193i	$0.955228\pi$
$654$		0			0
$655$	−345.737	+	699.984i	−0.527843	+	1.06868i
$656$			336.298i			0.512650i
$657$		0			0
$658$		−	27.1537i		−	0.0412670i
$659$	293.226	−	169.294i	0.444955	−	0.256895i	−0.260742	−	0.965409i	$-0.583967\pi$
$659$	293.226	−	169.294i	0.444955	−	0.256895i	0.705697	+	0.708513i	$0.250634\pi$
$660$		0			0
$661$	−514.079	+	890.411i	−0.777729	+	1.34707i	0.155519	+	0.987833i	$0.450295\pi$
$661$	−514.079	+	890.411i	−0.777729	+	1.34707i	−0.933248	+	0.359233i	$0.883038\pi$
$662$	−673.810	+	1167.07i	−1.01784	+	1.76295i
$663$		0			0
$664$	−329.191	−	570.176i	−0.495770	−	0.858699i
$665$	−65.1003	−	97.5612i	−0.0978952	−	0.146709i
$666$		0			0
$667$			561.241i			0.841440i
$668$	−2.75049	−	4.76400i	−0.00411751	−	0.00713173i
$669$		0			0
$670$	719.243	−	46.6913i	1.07350	−	0.0696885i
$671$	−692.207	−	399.646i	−1.03161	−	0.595598i
$672$		0			0
$673$	561.170	−	323.992i	0.833834	−	0.481414i	−0.0213295	−	0.999772i	$-0.506790\pi$
$673$	561.170	−	323.992i	0.833834	−	0.481414i	0.855164	+	0.518358i	$0.173457\pi$
$674$		−	77.8436i		−	0.115495i
$675$		0			0
$676$	56.2275			0.0831768
$677$	474.397	+	821.679i	0.700734	+	1.21371i	0.968209	+	0.250142i	$0.0804772\pi$
$677$	474.397	+	821.679i	0.700734	+	1.21371i	−0.267476	+	0.963565i	$0.586189\pi$
$678$		0			0
$679$	−90.8870	+	157.421i	−0.133854	+	0.231842i
$680$	5.21127	+	80.2755i	0.00766363	+	0.118052i
$681$		0			0
$682$	−161.051	+	92.9831i	−0.236146	+	0.136339i
$683$	883.438			1.29347			0.646733	−	0.762716i	$-0.276135\pi$
$683$	883.438			1.29347			0.646733	+	0.762716i	$0.276135\pi$
$684$		0			0
$685$	−1005.78	+	671.132i	−1.46829	+	0.979755i
$686$	−209.234	+	120.801i	−0.305005	+	0.176095i
$687$		0			0
$688$	782.569	+	451.816i	1.13745	+	0.656710i
$689$	588.490	+	339.765i	0.854122	+	0.493128i
$690$		0			0
$691$	−142.267	−	246.413i	−0.205885	−	0.356603i	0.744529	−	0.667590i	$-0.232674\pi$
$691$	−142.267	−	246.413i	−0.205885	−	0.356603i	−0.950414	+	0.310986i	$0.899341\pi$
$692$	58.5876			0.0846641
$693$		0			0
$694$	−134.728			−0.194132
$695$	477.713	+	235.952i	0.687357	+	0.339500i
$696$		0			0
$697$	35.5639	+	20.5328i	0.0510243	+	0.0294589i
$698$	−489.500	+	847.838i	−0.701289	+	1.21467i
$699$		0			0
$700$	−1.99927	−	15.3337i	−0.00285610	−	0.0219053i
$701$		−	760.111i		−	1.08432i	−0.840274	−	0.542162i	$-0.817606\pi$
$701$		−	760.111i		−	1.08432i	0.840274	−	0.542162i	$-0.182394\pi$
$702$		0			0
$703$		−	1003.94i		−	1.42809i
$704$	889.701	−	513.669i	1.26378	−	0.729644i
$705$		0			0
$706$	−293.811	+	508.895i	−0.416163	+	0.720815i
$707$	105.920	−	183.459i	0.149816	−	0.259489i
$708$		0			0
$709$	560.505	+	970.823i	0.790557	+	1.36928i	0.925623	+	0.378448i	$0.123542\pi$
$709$	560.505	+	970.823i	0.790557	+	1.36928i	−0.135066	+	0.990837i	$0.543125\pi$
$710$	293.327	+	439.588i	0.413137	+	0.619138i
$711$		0			0
$712$			147.417i			0.207047i
$713$	−75.7060	−	131.127i	−0.106180	−	0.183908i
$714$		0			0
$715$	49.0269	+	755.221i	0.0685691	+	1.05625i
$716$	−76.1424	−	43.9608i	−0.106344	−	0.0613978i
$717$		0			0
$718$	−416.628	+	240.540i	−0.580261	+	0.335014i
$719$			721.362i			1.00328i	0.865075	+	0.501642i	$0.167271\pi$
$719$			721.362i			1.00328i	−0.865075	+	0.501642i	$0.832729\pi$
$720$		0			0
$721$	−147.910			−0.205146
$722$	39.6856	+	68.7375i	0.0549662	+	0.0952042i
$723$		0			0
$724$	68.2131	−	118.148i	0.0942169	−	0.163189i
$725$	−335.040	+	256.422i	−0.462125	+	0.353686i
$726$		0			0
$727$	338.923	−	195.677i	0.466194	−	0.269157i	−0.248451	−	0.968644i	$-0.579922\pi$
$727$	338.923	−	195.677i	0.466194	−	0.269157i	0.714645	+	0.699487i	$0.246588\pi$
$728$	68.4822			0.0940689
$729$		0			0
$730$	625.990	+	938.126i	0.857520	+	1.28510i
$731$	95.5601	−	55.1717i	0.130725	−	0.0754742i
$732$		0			0
$733$	770.166	+	444.656i	1.05070	+	0.606625i	0.922846	−	0.385168i	$-0.125856\pi$
$733$	770.166	+	444.656i	1.05070	+	0.606625i	0.127858	+	0.991792i	$0.459190\pi$
$734$	440.505	+	254.326i	0.600144	+	0.346493i
$735$		0			0
$736$	−139.139	−	240.995i	−0.189047	−	0.327439i
$737$	−1300.85			−1.76506
$738$		0			0
$739$	533.497			0.721917			0.360958	−	0.932582i	$-0.382450\pi$
$739$	533.497			0.721917			0.360958	+	0.932582i	$0.382450\pi$
$740$	58.6167	−	118.676i	0.0792118	−	0.160373i
$741$		0			0
$742$	186.655	+	107.765i	0.251557	+	0.145236i
$743$	133.366	−	230.996i	0.179496	−	0.310897i	−0.762212	−	0.647328i	$-0.775887\pi$
$743$	133.366	−	230.996i	0.179496	−	0.310897i	0.941708	+	0.336431i	$0.109220\pi$
$744$		0			0
$745$	−232.621	+	470.968i	−0.312243	+	0.632172i
$746$			413.400i			0.554156i
$747$		0			0
$748$			21.9955i			0.0294057i
$749$	4.11856	−	2.37785i	0.00549875	−	0.00317470i
$750$		0			0
$751$	−124.309	+	215.309i	−0.165525	+	0.286697i	−0.936841	−	0.349754i	$-0.886265\pi$
$751$	−124.309	+	215.309i	−0.165525	+	0.286697i	0.771317	+	0.636451i	$0.219598\pi$
$752$	96.7973	−	167.658i	0.128720	−	0.222949i
$753$		0			0
$754$	141.532	+	245.141i	0.187708	+	0.325120i
$755$	−802.473	+	535.472i	−1.06288	+	0.709234i
$756$		0			0
$757$			440.978i			0.582534i	0.956642	+	0.291267i	$0.0940768\pi$
$757$			440.978i			0.582534i	−0.956642	+	0.291267i	$0.905923\pi$
$758$	−343.267	−	594.556i	−0.452859	−	0.784375i
$759$		0			0
$760$	−47.7742	−	735.925i	−0.0628608	−	0.968322i
$761$	394.571	+	227.806i	0.518490	+	0.299350i	0.736317	−	0.676637i	$-0.236563\pi$
$761$	394.571	+	227.806i	0.518490	+	0.299350i	−0.217826	+	0.975988i	$0.569897\pi$
$762$		0			0
$763$	14.1868	−	8.19074i	0.0185934	−	0.0107349i
$764$			58.0996i			0.0760466i
$765$		0			0
$766$	−596.170			−0.778289
$767$	−380.458	−	658.972i	−0.496033	−	0.859155i
$768$		0			0
$769$	628.535	−	1088.65i	0.817341	−	1.41568i	−0.0902939	−	0.995915i	$-0.528781\pi$
$769$	628.535	−	1088.65i	0.817341	−	1.41568i	0.907635	−	0.419761i	$-0.137886\pi$
$770$	15.5502	+	239.538i	0.0201950	+	0.311089i
$771$		0			0
$772$	5.08476	−	2.93569i	0.00658648	−	0.00380270i
$773$	842.543			1.08997			0.544983	−	0.838447i	$-0.316536\pi$
$773$	842.543			1.08997			0.544983	+	0.838447i	$0.316536\pi$
$774$		0			0
$775$	43.6889	−	105.104i	0.0563728	−	0.135617i
$776$	−989.826	+	571.476i	−1.27555	+	0.736439i
$777$		0			0
$778$	−221.141	−	127.676i	−0.284243	−	0.164108i
$779$	−326.032	−	188.235i	−0.418526	−	0.241636i
$780$		0			0
$781$	−476.899	−	826.014i	−0.610627	−	1.05764i
$782$	−154.029			−0.196968
$783$		0			0
$784$	−848.947			−1.08284
$785$	439.878	−	890.583i	0.560354	−	1.13450i
$786$		0			0
$787$	775.001	+	447.447i	0.984753	+	0.568547i	0.903702	−	0.428162i	$-0.140839\pi$
$787$	775.001	+	447.447i	0.984753	+	0.568547i	0.0810513	+	0.996710i	$0.474172\pi$
$788$	40.8398	−	70.7366i	0.0518271	−	0.0897672i
$789$		0			0
$790$	419.752	+	207.324i	0.531332	+	0.262436i
$791$			132.356i			0.167327i
$792$		0			0
$793$		−	328.222i		−	0.413899i
$794$	618.072	−	356.844i	0.778428	−	0.449425i
$795$		0			0
$796$	−43.8244	+	75.9061i	−0.0550558	+	0.0953594i
$797$	−356.728	+	617.871i	−0.447588	+	0.775246i	−0.998228	−	0.0594970i	$-0.981050\pi$
$797$	−356.728	+	617.871i	−0.447588	+	0.775246i	0.550640	+	0.834743i	$0.314384\pi$
$798$		0			0
$799$	−11.8200	−	20.4729i	−0.0147935	−	0.0256231i
$800$	80.2951	−	193.168i	0.100369	−	0.241460i
$801$		0			0
$802$			505.373i			0.630140i
$803$	−1017.75	−	1762.80i	−1.26744	−	2.19527i
$804$		0			0
$805$	−195.030	+	12.6608i	−0.242273	+	0.0157277i
$806$	−66.1342	−	38.1826i	−0.0820524	−	0.0473730i
$807$		0			0
$808$	1153.55	−	666.000i	1.42766	−	0.824257i
$809$		−	148.086i		−	0.183049i	−0.995803	−	0.0915243i	$-0.970826\pi$
$809$		−	148.086i		−	0.183049i	0.995803	−	0.0915243i	$-0.0291739\pi$
$810$		0			0
$811$	−515.062			−0.635095			−0.317548	−	0.948242i	$-0.602859\pi$
$811$	−515.062			−0.635095			−0.317548	+	0.948242i	$0.602859\pi$
$812$	5.21930	+	9.04010i	0.00642771	+	0.0111331i
$813$		0			0
$814$	−1027.35	+	1779.42i	−1.26210	+	2.18602i
$815$	381.364	−	24.7571i	0.467931	−	0.0303768i
$816$		0			0
$817$	−876.046	+	505.786i	−1.07227	+	0.619077i
$818$	−213.871			−0.261456
$819$		0			0
$820$	−27.5499	−	41.2871i	−0.0335974	−	0.0503501i
$821$	−1176.46	+	679.230i	−1.43296	+	0.827320i	−0.997346	−	0.0728135i	$-0.976802\pi$
$821$	−1176.46	+	679.230i	−1.43296	+	0.827320i	−0.435614	+	0.900133i	$0.643469\pi$
$822$		0			0
$823$	−673.793	−	389.014i	−0.818703	−	0.472678i	0.0312660	−	0.999511i	$-0.490046\pi$
$823$	−673.793	−	389.014i	−0.818703	−	0.472678i	−0.849969	+	0.526833i	$0.823379\pi$
$824$	−805.425	−	465.012i	−0.977457	−	0.564335i
$825$		0			0
$826$	−120.672	−	209.010i	−0.146092	−	0.253039i
$827$	1018.93			1.23208			0.616038	−	0.787716i	$-0.288737\pi$
$827$	1018.93			1.23208			0.616038	+	0.787716i	$0.288737\pi$
$828$		0			0
$829$	667.620			0.805332			0.402666	−	0.915347i	$-0.368084\pi$
$829$	667.620			0.805332			0.402666	+	0.915347i	$0.368084\pi$
$830$	849.665	+	419.667i	1.02369	+	0.505623i
$831$		0			0
$832$	365.347	+	210.933i	0.439119	+	0.253526i
$833$	−51.8328	+	89.7771i	−0.0622243	+	0.107776i
$834$		0			0
$835$	−46.8610	−	23.1456i	−0.0561210	−	0.0277193i
$836$		−	201.643i		−	0.241200i
$837$		0			0
$838$			327.437i			0.390736i
$839$	−982.041	+	566.982i	−1.17049	+	0.675783i	−0.953795	−	0.300457i	$-0.902861\pi$
$839$	−982.041	+	566.982i	−1.17049	+	0.675783i	−0.216694	+	0.976240i	$0.569527\pi$
$840$		0			0
$841$	−278.096	+	481.677i	−0.330674	+	0.572743i
$842$	807.021	−	1397.80i	0.958458	−	1.66010i
$843$		0			0
$844$	−29.5912	−	51.2534i	−0.0350606	−	0.0607268i
$845$	444.375	−	296.521i	0.525888	−	0.350913i
$846$		0			0
$847$		−	291.019i		−	0.343588i
$848$	768.323	+	1330.77i	0.906041	+	1.56931i
$849$		0			0
$850$	−70.3734	−	91.9496i	−0.0827923	−	0.108176i
$851$	−1448.79	−	836.459i	−1.70245	−	0.982913i
$852$		0			0
$853$	−642.450	+	370.919i	−0.753165	+	0.434840i	−0.826836	−	0.562443i	$-0.809862\pi$
$853$	−642.450	+	370.919i	−0.753165	+	0.434840i	0.0736714	+	0.997283i	$0.476528\pi$
$854$		−	104.104i		−	0.121902i
$855$		0			0
$856$	29.9028			0.0349332
$857$	−65.1670	−	112.872i	−0.0760408	−	0.131707i	0.825498	−	0.564406i	$-0.190895\pi$
$857$	−65.1670	−	112.872i	−0.0760408	−	0.131707i	−0.901538	+	0.432699i	$0.857561\pi$
$858$		0			0
$859$	462.273	−	800.681i	0.538153	−	0.932108i	−0.460850	−	0.887478i	$-0.652456\pi$
$859$	462.273	−	800.681i	0.538153	−	0.932108i	0.999004	−	0.0446307i	$-0.0142111\pi$
$860$	−133.088	+	8.63974i	−0.154754	+	0.0100462i
$861$		0			0
$862$	1256.58	−	725.487i	1.45775	−	0.841632i
$863$	−829.441			−0.961113			−0.480557	−	0.876964i	$-0.659565\pi$
$863$	−829.441			−0.961113			−0.480557	+	0.876964i	$0.659565\pi$
$864$		0			0
$865$	463.027	−	308.967i	0.535292	−	0.357188i
$866$	−543.672	+	313.889i	−0.627796	+	0.362458i
$867$		0			0
$868$	−2.43885	−	1.40807i	−0.00280973	−	0.00162220i
$869$	−731.753	−	422.478i	−0.842063	−	0.486166i
$870$		0			0
$871$	−267.091	−	462.615i	−0.306648	−	0.531130i
$872$	103.003			0.118123
$873$		0			0
$874$	1412.06			1.61563
$875$	−96.6642	−	110.641i	−0.110473	−	0.126447i
$876$		0			0
$877$	924.311	+	533.651i	1.05395	+	0.608496i	0.923751	−	0.382992i	$-0.125106\pi$
$877$	924.311	+	533.651i	1.05395	+	0.608496i	0.130195	+	0.991488i	$0.458440\pi$
$878$	−510.543	+	884.287i	−0.581484	+	1.00716i
$879$		0			0
$880$	−757.891	+	1534.44i	−0.861240	+	1.74368i
$881$			675.790i			0.767072i	0.923526	+	0.383536i	$0.125294\pi$
$881$			675.790i			0.767072i	−0.923526	+	0.383536i	$0.874706\pi$
$882$		0			0
$883$			305.799i			0.346319i	0.984894	+	0.173159i	$0.0553975\pi$
$883$			305.799i			0.346319i	−0.984894	+	0.173159i	$0.944602\pi$
$884$	−7.82213	+	4.51611i	−0.00884857	+	0.00510872i
$885$		0			0
$886$	−63.0699	+	109.240i	−0.0711850	+	0.123296i
$887$	246.512	−	426.971i	0.277916	−	0.481365i	−0.692951	−	0.720985i	$-0.743690\pi$
$887$	246.512	−	426.971i	0.277916	−	0.481365i	0.970867	+	0.239620i	$0.0770229\pi$
$888$		0			0
$889$	−83.3216	−	144.317i	−0.0937251	−	0.162337i
$890$	−117.775	−	176.501i	−0.132332	−	0.198316i
$891$		0			0
$892$		−	36.7433i		−	0.0411920i
$893$	108.360	+	187.685i	0.121344	+	0.210173i
$894$		0			0
$895$	−833.598	+	54.1149i	−0.931394	+	0.0604636i
$896$	149.949	+	86.5731i	0.167354	+	0.0966217i
$897$		0			0
$898$	565.168	−	326.300i	0.629363	−	0.363363i
$899$			76.8355i			0.0854678i
$900$		0			0
$901$	187.641			0.208259
$902$	385.246	+	667.265i	0.427102	+	0.739762i
$903$		0			0
$904$	−416.112	+	720.728i	−0.460301	+	0.797265i
$905$	−83.9689	−	1293.48i	−0.0927833	−	1.42925i
$906$		0			0
$907$	772.842	−	446.201i	0.852086	−	0.491952i	−0.00926798	−	0.999957i	$-0.502950\pi$
$907$	772.842	−	446.201i	0.852086	−	0.491952i	0.861354	+	0.508005i	$0.169617\pi$
$908$	231.783			0.255267
$909$		0			0
$910$	−81.9930	+	54.7121i	−0.0901022	+	0.0601232i
$911$	536.628	−	309.823i	0.589054	−	0.340091i	−0.175669	−	0.984449i	$-0.556209\pi$
$911$	536.628	−	309.823i	0.589054	−	0.340091i	0.764723	+	0.644359i	$0.222876\pi$
$912$		0			0
$913$	−1481.22	−	855.183i	−1.62237	−	0.936673i
$914$	641.079	+	370.127i	0.701400	+	0.404953i
$915$		0			0
$916$	29.6680	+	51.3864i	0.0323886	+	0.0560987i
$917$	183.524			0.200135
$918$		0			0
$919$	−858.908			−0.934612			−0.467306	−	0.884096i	$-0.654775\pi$
$919$	−858.908			−0.934612			−0.467306	+	0.884096i	$0.654775\pi$
$920$	−1101.81	−	544.209i	−1.19762	−	0.591532i
$921$		0			0
$922$	−1453.57	−	839.217i	−1.57654	−	0.910214i
$923$	195.834	−	339.195i	0.212171	−	0.367492i
$924$		0			0
$925$	−162.594	−	1247.04i	−0.175777	−	1.34815i
$926$		−	571.097i		−	0.616735i
$927$		0			0
$928$			141.215i			0.152171i
$929$	−1211.81	+	699.640i	−1.30443	+	0.753110i	−0.981160	−	0.193198i	$-0.938114\pi$
$929$	−1211.81	+	699.640i	−1.30443	+	0.753110i	−0.323266	+	0.946308i	$0.604781\pi$
$930$		0			0
$931$	475.177	−	823.030i	0.510394	−	0.884028i
$932$	76.4865	−	132.478i	0.0820670	−	0.142144i
$933$		0			0
$934$	−670.169	−	1160.77i	−0.717526	−	1.24279i
$935$	115.995	+	173.834i	0.124059	+	0.185918i
$936$		0			0
$937$		−	193.997i		−	0.207040i	−0.994627	−	0.103520i	$-0.966989\pi$
$937$		−	193.997i		−	0.207040i	0.994627	−	0.103520i	$-0.0330106\pi$
$938$	−84.7148	−	146.730i	−0.0903143	−	0.156429i
$939$		0			0
$940$	1.85098	+	28.5129i	0.00196913	+	0.0303329i
$941$	801.683	+	462.852i	0.851948	+	0.491873i	0.861308	−	0.508084i	$-0.169646\pi$
$941$	801.683	+	462.852i	0.851948	+	0.491873i	−0.00935936	+	0.999956i	$0.502979\pi$
$942$		0			0
$943$	−543.281	+	313.664i	−0.576120	+	0.332623i
$944$		−	1720.68i		−	1.82276i
$945$		0			0
$946$	2070.31			2.18848
$947$	−45.6148	−	79.0071i	−0.0481677	−	0.0834289i	0.840936	−	0.541134i	$-0.182005\pi$
$947$	−45.6148	−	79.0071i	−0.0481677	−	0.0834289i	−0.889104	+	0.457705i	$0.848672\pi$
$948$		0			0
$949$	417.930	−	723.876i	0.440390	−	0.762778i
$950$	645.148	+	842.947i	0.679103	+	0.887313i
$951$		0			0
$952$	16.3767	−	9.45512i	0.0172025	−	0.00993185i
$953$	−88.9452			−0.0933318			−0.0466659	−	0.998911i	$-0.514860\pi$
$953$	−88.9452			−0.0933318			−0.0466659	+	0.998911i	$0.514860\pi$
$954$		0			0
$955$	306.394	+	459.171i	0.320831	+	0.480807i
$956$	67.8499	−	39.1732i	0.0709727	−	0.0409761i
$957$		0			0
$958$	291.514	+	168.306i	0.304295	+	0.175685i
$959$	246.153	+	142.117i	0.256677	+	0.148193i
$960$		0			0
$961$	470.136	+	814.299i	0.489215	+	0.847345i
$962$	−843.742			−0.877071
$963$		0			0
$964$	137.137			0.142258
$965$	24.7041	−	50.0162i	0.0256001	−	0.0518303i
$966$		0			0
$967$	−1352.97	−	781.135i	−1.39914	−	0.807792i	−0.404835	−	0.914390i	$-0.632671\pi$
$967$	−1352.97	−	781.135i	−1.39914	−	0.807792i	−0.994302	+	0.106598i	$0.966004\pi$
$968$	914.931	−	1584.71i	0.945177	−	1.63709i
$969$		0			0
$970$	728.543	−	1475.02i	0.751075	−	1.52064i
$971$			442.765i			0.455989i	0.973662	+	0.227994i	$0.0732168\pi$
$971$			442.765i			0.455989i	−0.973662	+	0.227994i	$0.926783\pi$
$972$		0			0
$973$		−	125.248i		−	0.128723i
$974$	1202.62	−	694.332i	1.23472	−	0.712867i
$975$		0			0
$976$	371.110	−	642.781i	0.380235	−	0.658587i
$977$	89.9999	−	155.884i	0.0921187	−	0.159554i	−0.816284	−	0.577651i	$-0.803969\pi$
$977$	89.9999	−	155.884i	0.0921187	−	0.159554i	0.908402	+	0.418097i	$0.137303\pi$
$978$		0			0
$979$	191.482	+	331.657i	0.195590	+	0.338771i
$980$	104.224	−	69.5466i	0.106351	−	0.0709659i
$981$		0			0
$982$		−	1324.19i		−	1.34847i
$983$	515.624	+	893.088i	0.524542	+	0.908533i	0.999592	+	0.0285740i	$0.00909662\pi$
$983$	515.624	+	893.088i	0.524542	+	0.908533i	−0.475050	+	0.879959i	$0.657570\pi$
$984$		0			0
$985$	−50.2729	−	774.415i	−0.0510385	−	0.786208i
$986$	67.6915	+	39.0817i	0.0686527	+	0.0396366i
$987$		0			0
$988$	71.7093	−	41.4014i	0.0725803	−	0.0419042i
$989$			1685.63i			1.70437i
$990$		0			0
$991$	549.520			0.554511			0.277256	−	0.960796i	$-0.410575\pi$
$991$	549.520			0.554511			0.277256	+	0.960796i	$0.410575\pi$
$992$	−19.0485	−	32.9930i	−0.0192021	−	0.0332590i
$993$		0			0
$994$	62.1140	−	107.585i	0.0624889	−	0.108234i
$995$	53.9470	+	831.011i	0.0542181	+	0.835187i
$996$		0			0
$997$	−1447.89	+	835.941i	−1.45225	+	0.838457i	−0.998609	−	0.0527282i	$-0.983208\pi$
$997$	−1447.89	+	835.941i	−1.45225	+	0.838457i	−0.453640	+	0.891185i	$0.649875\pi$
$998$	−796.981			−0.798578
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.k.134.18		48
3.2	odd	2	inner	405.3.h.k.134.7		48
5.4	even	2	inner	405.3.h.k.134.8		48
9.2	odd	6	inner	405.3.h.k.269.8		48
9.4	even	3		405.3.d.b.404.7	✓	24
9.5	odd	6		405.3.d.b.404.18	yes	24
9.7	even	3	inner	405.3.h.k.269.17		48
15.14	odd	2	inner	405.3.h.k.134.17		48
45.4	even	6		405.3.d.b.404.17	yes	24
45.14	odd	6		405.3.d.b.404.8	yes	24
45.29	odd	6	inner	405.3.h.k.269.18		48
45.34	even	6	inner	405.3.h.k.269.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.7	✓	24	9.4	even	3
405.3.d.b.404.8	yes	24	45.14	odd	6
405.3.d.b.404.17	yes	24	45.4	even	6
405.3.d.b.404.18	yes	24	9.5	odd	6
405.3.h.k.134.7		48	3.2	odd	2	inner
405.3.h.k.134.8		48	5.4	even	2	inner
405.3.h.k.134.17		48	15.14	odd	2	inner
405.3.h.k.134.18		48	1.1	even	1	trivial
405.3.h.k.269.7		48	45.34	even	6	inner
405.3.h.k.269.8		48	9.2	odd	6	inner
405.3.h.k.269.17		48	9.7	even	3	inner
405.3.h.k.269.18		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)

\(f(q)\)	\(=\)	\(q+(1.06375 + 1.84247i) q^{2} +(-0.263128 + 0.455750i) q^{4} +(0.323905 + 4.98950i) q^{5} +(1.01789 - 0.587680i) q^{7} +7.39039 q^{8} +(-8.84844 + 5.90436i) q^{10} +(16.6268 - 9.59948i) q^{11} +(6.82763 + 3.94194i) q^{13} +(2.16556 + 1.25029i) q^{14} +(8.91404 + 15.4396i) q^{16} +2.17700 q^{17} -19.9576 q^{19} +(-2.35919 - 1.16525i) q^{20} +(35.3735 + 20.4229i) q^{22} +(-16.6281 + 28.8008i) q^{23} +(-24.7902 + 3.23224i) q^{25} +16.7729i q^{26} +0.618539i q^{28} +(14.6152 - 8.43812i) q^{29} +(-2.27644 + 3.94291i) q^{31} +(-4.18383 + 7.24661i) q^{32} +(2.31579 + 4.01106i) q^{34} +(3.26193 + 4.88841i) q^{35} +50.3038i q^{37} +(-21.2299 - 36.7713i) q^{38} +(2.39378 + 36.8743i) q^{40} +(16.3362 + 9.43171i) q^{41} +(43.8953 - 25.3430i) q^{43} +10.1036i q^{44} -70.7527 q^{46} +(-5.42949 - 9.40415i) q^{47} +(-23.8093 + 41.2389i) q^{49} +(-32.3258 - 42.2368i) q^{50} +(-3.59308 + 2.07446i) q^{52} +86.1924 q^{53} +(53.2821 + 79.8500i) q^{55} +(7.52261 - 4.34318i) q^{56} +(31.0939 + 17.9521i) q^{58} +(-83.5848 - 48.2577i) q^{59} +(-20.8160 - 36.0544i) q^{61} -9.68626 q^{62} +53.5101 q^{64} +(-17.4568 + 35.3433i) q^{65} +(-58.6786 - 33.8781i) q^{67} +(-0.572829 + 0.992169i) q^{68} +(-5.53687 + 11.2100i) q^{70} -49.6797i q^{71} -106.022i q^{73} +(-92.6832 + 53.5107i) q^{74} +(5.25140 - 9.09570i) q^{76} +(11.2828 - 19.5425i) q^{77} +(-22.0052 - 38.1142i) q^{79} +(-74.1484 + 49.4775i) q^{80} +40.1319i q^{82} +(-44.5432 - 77.1510i) q^{83} +(0.705141 + 10.8621i) q^{85} +(93.3872 + 53.9171i) q^{86} +(122.878 - 70.9439i) q^{88} +19.9472i q^{89} +9.26638 q^{91} +(-8.75065 - 15.1566i) q^{92} +(11.5512 - 20.0073i) q^{94} +(-6.46437 - 99.5786i) q^{95} +(-133.934 + 77.3270i) q^{97} -101.308 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 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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