LMFDB - Embedded newform 405.3.h.k.269.17

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)

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);

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")

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			269.17
Character	$\chi$	$=$	405.269
Dual form			405.3.h.k.134.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06375 - 1.84247i) q^{2} +(-0.263128 - 0.455750i) q^{4} +(-4.48298 - 2.21424i) q^{5} +(-1.01789 - 0.587680i) q^{7} +7.39039 q^{8} +(-8.84844 + 5.90436i) q^{10} +(-16.6268 - 9.59948i) q^{11} +(-6.82763 + 3.94194i) q^{13} +(-2.16556 + 1.25029i) q^{14} +(8.91404 - 15.4396i) q^{16} +2.17700 q^{17} -19.9576 q^{19} +(0.170456 + 2.62575i) q^{20} +(-35.3735 + 20.4229i) q^{22} +(-16.6281 - 28.8008i) q^{23} +(15.1943 + 19.8528i) q^{25} +16.7729i q^{26} +0.618539i q^{28} +(-14.6152 - 8.43812i) q^{29} +(-2.27644 - 3.94291i) q^{31} +(-4.18383 - 7.24661i) q^{32} +(2.31579 - 4.01106i) q^{34} +(3.26193 + 4.88841i) q^{35} +50.3038i q^{37} +(-21.2299 + 36.7713i) q^{38} +(-33.1310 - 16.3641i) q^{40} +(-16.3362 + 9.43171i) q^{41} +(-43.8953 - 25.3430i) q^{43} +10.1036i q^{44} -70.7527 q^{46} +(-5.42949 + 9.40415i) q^{47} +(-23.8093 - 41.2389i) q^{49} +(52.7411 - 6.87660i) q^{50} +(3.59308 + 2.07446i) q^{52} +86.1924 q^{53} +(53.2821 + 79.8500i) q^{55} +(-7.52261 - 4.34318i) q^{56} +(-31.0939 + 17.9521i) q^{58} +(83.5848 - 48.2577i) q^{59} +(-20.8160 + 36.0544i) q^{61} -9.68626 q^{62} +53.5101 q^{64} +(39.3366 - 2.55362i) q^{65} +(58.6786 - 33.8781i) q^{67} +(-0.572829 - 0.992169i) q^{68} +(12.4766 - 0.809948i) q^{70} -49.6797i q^{71} -106.022i q^{73} +(92.6832 + 53.5107i) q^{74} +(5.25140 + 9.09570i) q^{76} +(11.2828 + 19.5425i) q^{77} +(-22.0052 + 38.1142i) q^{79} +(-74.1484 + 49.4775i) q^{80} +40.1319i q^{82} +(-44.5432 + 77.1510i) q^{83} +(-9.75946 - 4.82040i) q^{85} +(-93.3872 + 53.9171i) q^{86} +(-122.878 - 70.9439i) q^{88} +19.9472i q^{89} +9.26638 q^{91} +(-8.75065 + 15.1566i) q^{92} +(11.5512 + 20.0073i) q^{94} +(89.4698 + 44.1910i) q^{95} +(133.934 + 77.3270i) q^{97} -101.308 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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	−0.467433	−	0.884029i	$-0.654821\pi$
$2$	1.06375	−	1.84247i	0.531875	−	0.921234i	0.999308	−	0.0372057i	$-0.0118457\pi$
$3$		0			0
$3$		0			0
$4$	−0.263128	−	0.455750i	−0.0657819	−	0.113938i
$5$	−4.48298	−	2.21424i	−0.896597	−	0.442848i
$5$	−4.48298	−	2.21424i	−0.896597	−	0.442848i
$6$		0			0
$7$	−1.01789	−	0.587680i	−0.145413	−	0.0839542i	0.425528	−	0.904945i	$-0.360088\pi$
$7$	−1.01789	−	0.587680i	−0.145413	−	0.0839542i	−0.570941	+	0.820991i	$0.693422\pi$
$8$	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	−0.999909	−	0.0134667i	$-0.995713\pi$
$11$	−16.6268	−	9.59948i	−1.51153	−	0.872680i	−0.511617	−	0.859214i	$-0.670953\pi$
$12$		0			0
$13$	−6.82763	+	3.94194i	−0.525203	+	0.303226i	−0.739061	−	0.673639i	$-0.764730\pi$
$13$	−6.82763	+	3.94194i	−0.525203	+	0.303226i	0.213858	+	0.976865i	$0.431397\pi$
$14$	−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	$0.676010\pi$
$20$	0.170456	+	2.62575i	0.00852282	+	0.131287i
$21$		0			0
$22$	−35.3735	+	20.4229i	−1.60789	+	0.928313i
$23$	−16.6281	−	28.8008i	−0.722963	−	1.25221i	−0.959807	−	0.280661i	$-0.909446\pi$
$23$	−16.6281	−	28.8008i	−0.722963	−	1.25221i	0.236844	−	0.971548i	$-0.423887\pi$
$24$		0			0
$25$	15.1943	+	19.8528i	0.607772	+	0.794112i
$26$			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	$-0.427311\pi$
$29$	−14.6152	−	8.43812i	−0.503974	−	0.290969i	−0.730353	+	0.683070i	$0.760644\pi$
$30$		0			0
$31$	−2.27644	−	3.94291i	−0.0734336	−	0.127191i	0.826970	−	0.562245i	$-0.190062\pi$
$31$	−2.27644	−	3.94291i	−0.0734336	−	0.127191i	−0.900404	+	0.435055i	$0.856729\pi$
$32$	−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
$40$	−33.1310	−	16.3641i	−0.828275	−	0.409102i
$41$	−16.3362	+	9.43171i	−0.398444	+	0.230042i	−0.685812	−	0.727778i	$-0.740553\pi$
$41$	−16.3362	+	9.43171i	−0.398444	+	0.230042i	0.287368	+	0.957820i	$0.407220\pi$
$42$		0			0
$43$	−43.8953	−	25.3430i	−1.02082	−	0.589371i	−0.106479	−	0.994315i	$-0.533958\pi$
$43$	−43.8953	−	25.3430i	−1.02082	−	0.589371i	−0.914342	+	0.404944i	$0.867291\pi$
$44$			10.1036i			0.229626i
$45$		0			0
$46$	−70.7527			−1.53810
$47$	−5.42949	+	9.40415i	−0.115521	+	0.200088i	−0.917988	−	0.396608i	$-0.870187\pi$
$47$	−5.42949	+	9.40415i	−0.115521	+	0.200088i	0.802467	+	0.596697i	$0.203520\pi$
$48$		0			0
$49$	−23.8093	−	41.2389i	−0.485903	−	0.841609i
$50$	52.7411	−	6.87660i	1.05482	−	0.137532i
$51$		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	$-0.361790\pi$
$59$	83.5848	−	48.2577i	1.41669	−	0.817927i	0.996007	+	0.0892792i	$0.0284564\pi$
$60$		0			0
$61$	−20.8160	+	36.0544i	−0.341246	+	0.591056i	−0.984664	−	0.174459i	$-0.944182\pi$
$61$	−20.8160	+	36.0544i	−0.341246	+	0.591056i	0.643418	+	0.765515i	$0.277516\pi$
$62$	−9.68626			−0.156230
$63$		0			0
$64$	53.5101			0.836095
$65$	39.3366	−	2.55362i	0.605178	−	0.0392865i
$66$		0			0
$67$	58.6786	−	33.8781i	0.875800	−	0.505643i	0.00652877	−	0.999979i	$-0.497922\pi$
$67$	58.6786	−	33.8781i	0.875800	−	0.505643i	0.869271	+	0.494335i	$0.164588\pi$
$68$	−0.572829	−	0.992169i	−0.00842396	−	0.0145907i
$69$		0			0
$70$	12.4766	−	0.809948i	0.178237	−	0.0115707i
$71$		−	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	−0.971024	−	0.238982i	$-0.923186\pi$
$79$	−22.0052	+	38.1142i	−0.278547	+	0.482458i	0.692477	+	0.721440i	$0.256520\pi$
$80$	−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	0.462416	+	0.886663i	$0.346983\pi$
$83$	−44.5432	+	77.1510i	−0.536665	+	0.929530i	−0.999081	+	0.0428674i	$0.986351\pi$
$84$		0			0
$85$	−9.75946	−	4.82040i	−0.114817	−	0.0567106i
$86$	−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
$95$	89.4698	+	44.1910i	0.941787	+	0.465168i
$96$		0			0
$97$	133.934	+	77.3270i	1.38077	+	0.797185i	0.992250	−	0.124257i	$-0.0396548\pi$
$97$	133.934	+	77.3270i	1.38077	+	0.797185i	0.388515	+	0.921442i	$0.372988\pi$
$98$	−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	−0.998482	−	0.0550733i	$-0.982461\pi$
$101$	−156.087	−	90.1170i	−1.54542	−	0.892248i	−0.546936	−	0.837174i	$-0.684206\pi$
$102$		0			0
$103$	108.983	−	62.9212i	1.05808	−	0.610885i	0.133183	−	0.991092i	$-0.457480\pi$
$103$	108.983	−	62.9212i	1.05808	−	0.610885i	0.924902	+	0.380206i	$0.124147\pi$
$104$	−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	$0.479636\pi$
$110$	203.800	−	13.2301i	1.85273	−	0.120274i
$111$		0			0
$112$	−18.1470	+	10.4772i	−0.162027	+	0.0935464i
$113$	−56.3045	−	97.5222i	−0.498270	−	0.863029i	0.501728	−	0.865025i	$-0.332698\pi$
$113$	−56.3045	−	97.5222i	−0.498270	−	0.863029i	−0.999998	+	0.00199662i	$0.999364\pi$
$114$		0			0
$115$	10.7719	+	165.932i	0.0936684	+	1.44289i
$116$			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
$130$	37.1393	−	75.1928i	0.285687	−	0.578406i
$131$	−135.223	+	78.0713i	−1.03224	+	0.595964i	−0.917625	−	0.397446i	$-0.869897\pi$
$131$	−135.223	+	78.0713i	−1.03224	+	0.595964i	−0.114614	+	0.993410i	$0.536563\pi$
$132$		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	0.0341175	−	0.999418i	$-0.489138\pi$
$137$	120.913	−	209.428i	0.882580	−	1.52867i	0.848462	−	0.529256i	$-0.177529\pi$
$138$		0			0
$139$	53.2807	+	92.2849i	0.383314	+	0.663920i	0.991534	−	0.129849i	$-0.0414493\pi$
$139$	53.2807	+	92.2849i	0.383314	+	0.663920i	−0.608219	+	0.793769i	$0.708116\pi$
$140$	1.36959	−	2.77290i	0.00978281	−	0.0198064i
$141$		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	$-0.781349\pi$
$149$	−90.9819	+	52.5284i	−0.610617	+	0.352540i	0.162590	+	0.986694i	$0.448015\pi$
$150$		0			0
$151$	96.4725	−	167.095i	0.638890	−	1.10659i	−0.346786	−	0.937944i	$-0.612727\pi$
$151$	96.4725	−	167.095i	0.638890	−	1.10659i	0.985677	−	0.168647i	$-0.0539396\pi$
$152$	−147.495			−0.970360
$153$		0			0
$154$	48.0085			0.311743
$155$	1.47470	+	22.7166i	0.00951420	+	0.146559i
$156$		0			0
$157$	172.043	−	99.3293i	1.09582	−	0.632671i	0.160698	−	0.987004i	$-0.448625\pi$
$157$	172.043	−	99.3293i	1.09582	−	0.632671i	0.935119	+	0.354333i	$0.115292\pi$
$158$	46.8161	+	81.0879i	0.296305	+	0.513215i
$159$		0			0
$160$	2.71032	+	41.7504i	0.0169395	+	0.260940i
$161$			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	0.849953	−	0.526859i	$-0.176630\pi$
$167$	−5.22654	−	9.05264i	−0.0312967	−	0.0542074i	−0.881250	+	0.472651i	$0.843297\pi$
$168$		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	−0.980851	−	0.194757i	$-0.937608\pi$
$173$	−55.6646	+	96.4140i	−0.321761	+	0.557306i	0.659091	+	0.752064i	$0.270941\pi$
$174$		0			0
$175$	−3.79905	−	29.1374i	−0.0217088	−	0.166499i
$176$	−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
$185$	111.385	−	225.511i	0.602079	−	1.21898i
$186$		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	$-0.426660\pi$
$191$	−95.6109	−	55.2010i	−0.500581	−	0.289010i	−0.728953	+	0.684563i	$0.759993\pi$
$192$		0			0
$193$	9.66216	−	5.57845i	0.0500630	−	0.0289039i	−0.474760	−	0.880116i	$-0.657465\pi$
$193$	9.66216	−	5.57845i	0.0500630	−	0.0289039i	0.524823	+	0.851212i	$0.324132\pi$
$194$	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	$0.362566\pi$
$200$	112.292	+	146.720i	0.561459	+	0.733600i
$201$		0			0
$202$	−332.076	+	191.724i	−1.64394	+	0.949128i
$203$	9.91782	+	17.1782i	0.0488562	+	0.0846215i
$204$		0			0
$205$	94.1190	−	6.10995i	0.459117	−	0.0298046i
$206$		−	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	0.701462	−	0.712707i	$-0.252531\pi$
$211$	−56.2297	−	97.3928i	−0.266492	−	0.461577i	−0.967953	+	0.251130i	$0.919198\pi$
$212$	−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
$220$	22.3717	−	45.2941i	0.101689	−	0.205882i
$221$	−14.8638	+	8.58160i	−0.0672569	+	0.0388308i
$222$		0			0
$223$	60.4661	+	34.9101i	0.271148	+	0.156548i	0.629409	−	0.777074i	$-0.283297\pi$
$223$	60.4661	+	34.9101i	0.271148	+	0.156548i	−0.358261	+	0.933621i	$0.616630\pi$
$224$			9.83501i			0.0439063i
$225$		0			0
$226$	−239.576			−1.06007
$227$	−220.219	+	381.431i	−0.970128	+	1.68031i	−0.274973	+	0.961452i	$0.588669\pi$
$227$	−220.219	+	381.431i	−0.970128	+	1.68031i	−0.695156	+	0.718859i	$0.744665\pi$
$228$		0			0
$229$	56.3756	+	97.6454i	0.246182	+	0.426399i	0.962463	−	0.271412i	$-0.0874907\pi$
$229$	56.3756	+	97.6454i	0.246182	+	0.426399i	−0.716281	+	0.697811i	$0.754157\pi$
$230$	317.183	+	156.663i	1.37906	+	0.681146i
$231$		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	$-0.565851\pi$
$239$	128.930	−	74.4376i	0.539455	−	0.311454i	0.744858	+	0.667223i	$0.232517\pi$
$240$		0			0
$241$	−130.295	+	225.677i	−0.540643	+	0.936421i	0.458225	+	0.888836i	$0.348486\pi$
$241$	−130.295	+	225.677i	−0.540643	+	0.936421i	−0.998867	+	0.0475841i	$0.984848\pi$
$242$	526.769			2.17673
$243$		0			0
$244$	21.9091			0.0897913
$245$	15.4239	+	237.593i	0.0629545	+	0.969765i
$246$		0			0
$247$	136.263	−	78.6717i	0.551674	−	0.318509i
$248$	−16.8238	−	29.1397i	−0.0678379	−	0.117499i
$249$		0			0
$250$	−251.664	−	85.9537i	−1.00666	−	0.343815i
$251$			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	0.921222	−	0.389038i	$-0.127193\pi$
$257$	31.7894	+	55.0608i	0.123694	+	0.214244i	−0.797528	+	0.603282i	$0.793859\pi$
$258$		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	−0.823786	−	0.566901i	$-0.808142\pi$
$263$	20.7920	−	36.0128i	0.0790571	−	0.136931i	0.902843	+	0.429970i	$0.141476\pi$
$264$		0			0
$265$	−386.399	−	190.851i	−1.45811	−	0.720191i
$266$	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
$275$	−62.0557	−	475.946i	−0.225657	−	1.73071i
$276$		0			0
$277$	85.3215	+	49.2604i	0.308020	+	0.177835i	0.646040	−	0.763304i	$-0.276424\pi$
$277$	85.3215	+	49.2604i	0.308020	+	0.177835i	−0.338020	+	0.941139i	$0.609757\pi$
$278$	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	$-0.520510\pi$
$281$	−269.989	−	155.878i	−0.960813	−	0.554726i	−0.896423	+	0.443199i	$0.853843\pi$
$282$		0			0
$283$	−362.495	+	209.287i	−1.28090	+	0.739529i	−0.977013	−	0.213178i	$-0.931618\pi$
$283$	−362.495	+	209.287i	−1.28090	+	0.739529i	−0.303889	+	0.952708i	$0.598285\pi$
$284$	−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
$290$	179.144	−	11.6295i	0.617737	−	0.0401018i
$291$		0			0
$292$	−48.3194	+	27.8972i	−0.165477	+	0.0955384i
$293$	97.2504	+	168.443i	0.331913	+	0.574889i	0.982887	−	0.184210i	$-0.0589728\pi$
$293$	97.2504	+	168.443i	0.331913	+	0.574889i	−0.650974	+	0.759100i	$0.725639\pi$
$294$		0			0
$295$	−481.564	+	31.2618i	−1.63242	+	0.105972i
$296$			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
$310$	43.4234	+	21.4477i	0.140075	+	0.0691861i
$311$	−67.5564	+	39.0037i	−0.217223	+	0.125414i	−0.604664	−	0.796481i	$-0.706693\pi$
$311$	−67.5564	+	39.0037i	−0.217223	+	0.125414i	0.387441	+	0.921895i	$0.373359\pi$
$312$		0			0
$313$	418.180	+	241.437i	1.33604	+	0.771363i	0.986218	−	0.165453i	$-0.0529086\pi$
$313$	418.180	+	241.437i	1.33604	+	0.771363i	0.349822	+	0.936816i	$0.386242\pi$
$314$		−	422.646i		−	1.34601i
$315$		0			0
$316$	23.1607			0.0732935
$317$	5.10864	−	8.84842i	0.0161156	−	0.0279130i	−0.857855	−	0.513892i	$-0.828203\pi$
$317$	5.10864	−	8.84842i	0.0161156	−	0.0279130i	0.873971	+	0.485979i	$0.161537\pi$
$318$		0			0
$319$	162.003	+	280.598i	0.507847	+	0.879616i
$320$	−239.885	−	118.484i	−0.749640	−	0.370263i
$321$		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	0.226744	−	0.973954i	$-0.427192\pi$
$331$	316.714	−	548.566i	0.956841	−	1.65730i	0.730097	−	0.683343i	$-0.239475\pi$
$332$	46.8821			0.141211
$333$		0			0
$334$	−22.2389			−0.0665836
$335$	−338.069	+	21.9466i	−1.00916	+	0.0655121i
$336$		0			0
$337$	31.6872	−	18.2946i	0.0940273	−	0.0542867i	−0.452249	−	0.891892i	$-0.649378\pi$
$337$	31.6872	−	18.2946i	0.0940273	−	0.0542867i	0.546276	+	0.837605i	$0.316045\pi$
$338$	113.656	+	196.858i	0.336260	+	0.582420i
$339$		0			0
$340$	0.371084	+	5.71626i	0.00109142	+	0.0168125i
$341$			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	0.816788	−	0.576938i	$-0.195753\pi$
$347$	−31.6633	−	54.8425i	−0.0912488	−	0.158048i	−0.908037	+	0.418890i	$0.862419\pi$
$348$		0			0
$349$	230.082	−	398.514i	0.659261	−	1.14187i	−0.321546	−	0.946894i	$-0.604203\pi$
$349$	230.082	−	398.514i	0.659261	−	1.14187i	0.980807	−	0.194980i	$-0.0624641\pi$
$350$	−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	−0.601389	−	0.798957i	$-0.705386\pi$
$353$	138.101	−	239.199i	0.391222	−	0.677617i	0.992611	+	0.121340i	$0.0387190\pi$
$354$		0			0
$355$	−110.003	+	222.713i	−0.309867	+	0.627361i
$356$	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
$365$	−234.757	+	475.293i	−0.643170	+	1.30217i
$366$		0			0
$367$	−207.053	−	119.542i	−0.564177	−	0.325728i	0.190643	−	0.981659i	$-0.438943\pi$
$367$	−207.053	−	119.542i	−0.564177	−	0.325728i	−0.754820	+	0.655931i	$0.772276\pi$
$368$	−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	$-0.750545\pi$
$373$	−168.280	+	97.1563i	−0.451152	+	0.260473i	0.257165	+	0.966368i	$0.417212\pi$
$374$	−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	$0.639979\pi$
$380$	−3.40191	−	52.4037i	−0.00895239	−	0.137905i
$381$		0			0
$382$	−203.412	+	117.440i	−0.532493	+	0.307435i
$383$	−140.110	−	242.678i	−0.365824	−	0.633625i	0.623084	−	0.782155i	$-0.285879\pi$
$383$	−140.110	−	242.678i	−0.365824	−	0.633625i	−0.988908	+	0.148530i	$0.952546\pi$
$384$		0			0
$385$	−7.30913	−	112.591i	−0.0189848	−	0.292445i
$386$		−	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	$-0.284030\pi$
$389$	103.944	+	60.0122i	0.267209	+	0.154273i	−0.360410	+	0.932794i	$0.617363\pi$
$390$		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
$400$	441.961	−	57.6247i	1.10490	−	0.144062i
$401$	−205.718	+	118.771i	−0.513013	+	0.296188i	−0.734071	−	0.679072i	$-0.762382\pi$
$401$	−205.718	+	118.771i	−0.513013	+	0.296188i	0.221058	+	0.975261i	$0.429049\pi$
$402$		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	0.798014	−	0.602639i	$-0.205884\pi$
$409$	−50.2635	−	87.0590i	−0.122894	−	0.212858i	−0.920908	+	0.389781i	$0.872551\pi$
$410$	88.8617	−	179.911i	0.216736	−	0.438807i
$411$		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	$-0.725461\pi$
$419$	−133.287	+	76.9534i	−0.318108	+	0.183660i	0.332441	+	0.943124i	$0.392128\pi$
$420$		0			0
$421$	−379.328	+	657.016i	−0.901018	+	1.56061i	−0.0748425	+	0.997195i	$0.523845\pi$
$421$	−379.328	+	657.016i	−0.901018	+	1.56061i	−0.826175	+	0.563413i	$0.809488\pi$
$422$	−239.258			−0.566961
$423$		0			0
$424$	636.996			1.50235
$425$	33.0780	+	43.2196i	0.0778306	+	0.101693i
$426$		0			0
$427$	42.3769	−	24.4663i	0.0992433	−	0.0572981i
$428$	−1.06466	−	1.84404i	−0.00248752	−	0.00430852i
$429$		0			0
$430$	538.039	−	34.9280i	1.25125	−	0.0812280i
$431$		−	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	−0.451866	−	0.892086i	$-0.649241\pi$
$439$	239.973	−	415.646i	0.546636	−	0.946802i	0.998502	−	0.0547159i	$-0.0174253\pi$
$440$	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	−0.830625	−	0.556833i	$-0.812016\pi$
$443$	29.6451	−	51.3468i	0.0669189	−	0.115907i	0.897544	+	0.440926i	$0.145350\pi$
$444$		0			0
$445$	44.1678	−	89.4228i	0.0992534	−	0.200950i
$446$	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
$455$	−41.5410	−	20.5180i	−0.0912990	−	0.0450945i
$456$		0			0
$457$	−301.330	−	173.973i	−0.659365	−	0.380685i	0.132670	−	0.991160i	$-0.457645\pi$
$457$	−301.330	−	173.973i	−0.659365	−	0.380685i	−0.792035	+	0.610476i	$0.790978\pi$
$458$	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	$-0.00648176\pi$
$461$	683.228	+	394.462i	1.48206	+	0.855665i	0.482263	+	0.876027i	$0.339815\pi$
$462$		0			0
$463$	232.472	−	134.218i	0.502100	−	0.289887i	−0.227481	−	0.973783i	$-0.573049\pi$
$463$	232.472	−	134.218i	0.502100	−	0.289887i	0.729580	+	0.683895i	$0.239715\pi$
$464$	−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
$470$	−7.48300	−	115.270i	−0.0159213	−	0.245255i
$471$		0			0
$472$	617.725	−	356.643i	1.30874	−	0.755600i
$473$	486.559	+	842.744i	1.02867	+	1.78170i
$474$		0			0
$475$	−303.242	−	396.215i	−0.638404	−	0.834137i
$476$			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	$-0.386146\pi$
$479$	−137.022	−	79.1097i	−0.286059	−	0.165156i	−0.636163	+	0.771555i	$0.719479\pi$
$480$		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
$490$	454.164	+	224.321i	0.926865	+	0.457798i
$491$	539.030	−	311.209i	1.09782	−	0.633827i	0.162173	−	0.986762i	$-0.448150\pi$
$491$	539.030	−	311.209i	1.09782	−	0.633827i	0.935648	+	0.352935i	$0.114816\pi$
$492$		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	0.615021	−	0.788511i	$-0.289148\pi$
$499$	−187.305	−	324.421i	−0.375360	−	0.650142i	−0.990381	+	0.138369i	$0.955814\pi$
$500$	−49.5385	+	43.2804i	−0.0990770	+	0.0865608i
$501$		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	$-0.619306\pi$
$509$	130.690	−	75.4542i	0.256759	−	0.148240i	0.622855	+	0.782337i	$0.285973\pi$
$510$		0			0
$511$	−62.3067	+	107.918i	−0.121931	+	0.211191i
$512$	377.847			0.737982
$513$		0			0
$514$	135.264			0.263159
$515$	−627.890	+	40.7609i	−1.21920	+	0.0791474i
$516$		0			0
$517$	180.550	−	104.241i	0.349226	−	0.201626i
$518$	−62.8943	−	108.936i	−0.121417	−	0.210301i
$519$		0			0
$520$	290.713	−	18.8723i	0.559063	−	0.0362928i
$521$		−	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
$535$	−18.1389	−	8.95920i	−0.0339045	−	0.0167462i
$536$	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
$545$	−62.4813	−	30.8608i	−0.114645	−	0.0566253i
$546$		0			0
$547$	−86.7828	−	50.1041i	−0.158652	−	0.0915980i	0.418572	−	0.908184i	$-0.362531\pi$
$547$	−86.7828	−	50.1041i	−0.158652	−	0.0915980i	−0.577224	+	0.816586i	$0.695864\pi$
$548$	−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
$560$	104.552	−	6.78723i	0.186700	−	0.0121200i
$561$		0			0
$562$	−574.400	+	331.630i	−1.02206	+	0.590089i
$563$	−359.308	−	622.340i	−0.638203	−	1.10540i	−0.985827	−	0.167765i	$-0.946345\pi$
$563$	−359.308	−	622.340i	−0.638203	−	1.10540i	0.347624	−	0.937634i	$-0.386988\pi$
$564$		0			0
$565$	36.4746	+	561.862i	0.0645568	+	0.994447i
$566$			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	$-0.183438\pi$
$569$	447.135	+	258.153i	0.785825	+	0.453696i	−0.0526655	+	0.998612i	$0.516772\pi$
$570$		0			0
$571$	−61.2417	−	106.074i	−0.107253	−	0.185768i	0.807403	−	0.590000i	$-0.200872\pi$
$571$	−61.2417	−	106.074i	−0.107253	−	0.185768i	−0.914657	+	0.404232i	$0.867539\pi$
$572$	−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
$580$	19.6651	−	39.8143i	0.0339054	−	0.0686453i
$581$	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	−0.943857	−	0.330354i	$-0.892832\pi$
$587$	−109.084	+	188.939i	−0.185833	+	0.321872i	0.758024	+	0.652227i	$0.226165\pi$
$588$		0			0
$589$	45.4324	+	78.6912i	0.0771348	+	0.133601i
$590$	−454.664	+	920.521i	−0.770617	+	1.56020i
$591$		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	$-0.884791\pi$
$599$	−656.605	+	379.091i	−1.09617	+	0.632873i	−0.160957	+	0.986961i	$0.551458\pi$
$600$		0			0
$601$	124.480	−	215.606i	0.207122	−	0.358745i	−0.743685	−	0.668530i	$-0.766924\pi$
$601$	124.480	−	215.606i	0.207122	−	0.358745i	0.950807	+	0.309785i	$0.100257\pi$
$602$	126.744			0.210538
$603$		0			0
$604$	−101.538			−0.168110
$605$	−80.1989	−	1235.40i	−0.132560	−	2.04198i
$606$		0			0
$607$	212.354	−	122.603i	0.349842	−	0.201981i	−0.314774	−	0.949167i	$-0.601929\pi$
$607$	212.354	−	122.603i	0.349842	−	0.201981i	0.664616	+	0.747185i	$0.268595\pi$
$608$	83.4994	+	144.625i	0.137334	+	0.237870i
$609$		0			0
$610$	−28.6889	−	441.931i	−0.0470310	−	0.724476i
$611$		−	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	0.936615	−	0.350360i	$-0.113941\pi$
$617$	101.735	+	176.211i	0.164887	+	0.285593i	−0.771728	+	0.635953i	$0.780607\pi$
$618$		0			0
$619$	287.187	−	497.422i	0.463953	−	0.803590i	−0.535201	−	0.844725i	$-0.679764\pi$
$619$	287.187	−	497.422i	0.463953	−	0.803590i	0.999154	+	0.0411351i	$0.0130974\pi$
$620$	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
$625$	−163.267	+	603.298i	−0.261227	+	0.965277i
$626$	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
$635$	−313.936	+	635.600i	−0.494388	+	1.00095i
$636$		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	$-0.442407\pi$
$641$	−373.039	−	215.374i	−0.581964	−	0.335997i	−0.761913	+	0.647679i	$0.775740\pi$
$642$		0			0
$643$	−561.630	+	324.257i	−0.873453	+	0.504288i	−0.868494	−	0.495699i	$-0.834912\pi$
$643$	−561.630	+	324.257i	−0.873453	+	0.504288i	−0.00495885	+	0.999988i	$0.501578\pi$
$644$	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
$650$	−332.990	+	254.853i	−0.512292	+	0.392081i
$651$		0			0
$652$	−34.8345	+	20.1117i	−0.0534272	+	0.0308462i
$653$	−402.556	−	697.248i	−0.616472	−	1.06776i	−0.990124	−	0.140193i	$-0.955228\pi$
$653$	−402.556	−	697.248i	−0.616472	−	1.06776i	0.373652	−	0.927569i	$-0.378105\pi$
$654$		0			0
$655$	779.073	−	50.5753i	1.18942	−	0.0772142i
$656$			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	$-0.416033\pi$
$659$	−293.226	−	169.294i	−0.444955	−	0.256895i	−0.705697	+	0.708513i	$0.749366\pi$
$660$		0			0
$661$	−514.079	−	890.411i	−0.777729	−	1.34707i	−0.933248	−	0.359233i	$-0.883038\pi$
$661$	−514.079	−	890.411i	−0.777729	−	1.34707i	0.155519	−	0.987833i	$-0.450295\pi$
$662$	−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
$670$	−319.186	+	646.228i	−0.476396	+	0.964520i
$671$	692.207	−	399.646i	1.03161	−	0.595598i
$672$		0			0
$673$	−561.170	−	323.992i	−0.833834	−	0.481414i	0.0213295	−	0.999772i	$-0.493210\pi$
$673$	−561.170	−	323.992i	−0.833834	−	0.481414i	−0.855164	+	0.518358i	$0.826543\pi$
$674$		−	77.8436i		−	0.115495i
$675$		0			0
$676$	56.2275			0.0831768
$677$	474.397	−	821.679i	0.700734	−	1.21371i	−0.267476	−	0.963565i	$-0.586189\pi$
$677$	474.397	−	821.679i	0.700734	−	1.21371i	0.968209	−	0.250142i	$-0.0804772\pi$
$678$		0			0
$679$	−90.8870	−	157.421i	−0.133854	−	0.231842i
$680$	−72.1263	−	35.6247i	−0.106068	−	0.0523892i
$681$		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	−0.950414	−	0.310986i	$-0.899341\pi$
$691$	−142.267	+	246.413i	−0.205885	+	0.356603i	0.744529	+	0.667590i	$0.232674\pi$
$692$	58.5876			0.0846641
$693$		0			0
$694$	−134.728			−0.194132
$695$	−34.5157	−	531.688i	−0.0496629	−	0.765018i
$696$		0			0
$697$	−35.5639	+	20.5328i	−0.0510243	+	0.0294589i
$698$	−489.500	−	847.838i	−0.701289	−	1.21467i
$699$		0			0
$700$	−12.2797	+	9.39826i	−0.0175425	+	0.0134261i
$701$		−	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	−0.135066	−	0.990837i	$-0.543125\pi$
$709$	560.505	−	970.823i	0.790557	−	1.36928i	0.925623	−	0.378448i	$-0.123542\pi$
$710$	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
$715$	−678.554	−	335.152i	−0.949027	−	0.468744i
$716$	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
$725$	−54.5481	−	418.365i	−0.0752387	−	0.577055i
$726$		0			0
$727$	−338.923	−	195.677i	−0.466194	−	0.269157i	0.248451	−	0.968644i	$-0.420078\pi$
$727$	−338.923	−	195.677i	−0.466194	−	0.269157i	−0.714645	+	0.699487i	$0.753412\pi$
$728$	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	$-0.874144\pi$
$733$	−770.166	+	444.656i	−1.05070	+	0.606625i	−0.127858	+	0.991792i	$0.540810\pi$
$734$	−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	$0.382450\pi$
$740$	−132.085	+	8.57461i	−0.178493	+	0.0115873i
$741$		0			0
$742$	−186.655	+	107.765i	−0.251557	+	0.145236i
$743$	133.366	+	230.996i	0.179496	+	0.310897i	0.941708	−	0.336431i	$-0.109220\pi$
$743$	133.366	+	230.996i	0.179496	+	0.310897i	−0.762212	+	0.647328i	$0.775887\pi$
$744$		0			0
$745$	524.181	−	34.0284i	0.703598	−	0.0456757i
$746$			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	0.771317	−	0.636451i	$-0.219598\pi$
$751$	−124.309	−	215.309i	−0.165525	−	0.286697i	−0.936841	+	0.349754i	$0.886265\pi$
$752$	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
$760$	661.217	+	326.589i	0.870022	+	0.429722i
$761$	−394.571	+	227.806i	−0.518490	+	0.299350i	−0.736317	−	0.676637i	$-0.763437\pi$
$761$	−394.571	+	227.806i	−0.518490	+	0.299350i	0.217826	+	0.975988i	$0.430103\pi$
$762$		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	0.907635	+	0.419761i	$0.137886\pi$
$769$	628.535	+	1088.65i	0.817341	+	1.41568i	−0.0902939	+	0.995915i	$0.528781\pi$
$770$	−215.221	−	106.302i	−0.279508	−	0.138055i
$771$		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
$785$	−991.207	+	64.3464i	−1.26268	+	0.0819700i
$786$		0			0
$787$	−775.001	+	447.447i	−0.984753	+	0.568547i	−0.903702	−	0.428162i	$-0.859161\pi$
$787$	−775.001	+	447.447i	−0.984753	+	0.568547i	−0.0810513	+	0.996710i	$0.525828\pi$
$788$	40.8398	+	70.7366i	0.0518271	+	0.0897672i
$789$		0			0
$790$	−30.3279	−	467.178i	−0.0383898	−	0.591365i
$791$			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	0.550640	−	0.834743i	$-0.314384\pi$
$797$	−356.728	−	617.871i	−0.447588	−	0.775246i	−0.998228	+	0.0594970i	$0.981050\pi$
$798$		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
$805$	86.5504	−	175.231i	0.107516	−	0.217679i
$806$	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
$815$	−169.242	+	342.649i	−0.207658	+	0.420429i
$816$		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	$-0.0231978\pi$
$821$	1176.46	+	679.230i	1.43296	+	0.827320i	0.435614	+	0.900133i	$0.356531\pi$
$822$		0			0
$823$	673.793	−	389.014i	0.818703	−	0.472678i	−0.0312660	−	0.999511i	$-0.509954\pi$
$823$	673.793	−	389.014i	0.818703	−	0.472678i	0.849969	+	0.526833i	$0.176621\pi$
$824$	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	$0.368084\pi$
$830$	−61.3900	−	945.665i	−0.0739639	−	1.13936i
$831$		0			0
$832$	−365.347	+	210.933i	−0.439119	+	0.253526i
$833$	−51.8328	−	89.7771i	−0.0622243	−	0.107776i
$834$		0			0
$835$	3.38580	+	52.1556i	0.00405485	+	0.0624618i
$836$		−	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	$-0.0971392\pi$
$839$	982.041	+	566.982i	1.17049	+	0.675783i	0.216694	+	0.976240i	$0.430473\pi$
$840$		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
$850$	114.817	−	14.9704i	0.135079	−	0.0176122i
$851$	1448.79	−	836.459i	1.70245	−	0.982913i
$852$		0			0
$853$	642.450	+	370.919i	0.753165	+	0.434840i	0.826836	−	0.562443i	$-0.190138\pi$
$853$	642.450	+	370.919i	0.753165	+	0.434840i	−0.0736714	+	0.997283i	$0.523472\pi$
$854$		−	104.104i		−	0.121902i
$855$		0			0
$856$	29.9028			0.0349332
$857$	−65.1670	+	112.872i	−0.0760408	+	0.131707i	−0.901538	−	0.432699i	$-0.857561\pi$
$857$	−65.1670	+	112.872i	−0.0760408	+	0.131707i	0.825498	+	0.564406i	$0.190895\pi$
$858$		0			0
$859$	462.273	+	800.681i	0.538153	+	0.932108i	0.999004	+	0.0446307i	$0.0142111\pi$
$859$	462.273	+	800.681i	0.538153	+	0.932108i	−0.460850	+	0.887478i	$0.652456\pi$
$860$	59.0620	−	119.578i	0.0686767	−	0.139044i
$861$		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
$875$	−47.4860	+	139.034i	−0.0542697	+	0.158896i
$876$		0			0
$877$	−924.311	+	533.651i	−1.05395	+	0.608496i	−0.923751	−	0.382992i	$-0.874894\pi$
$877$	−924.311	+	533.651i	−1.05395	+	0.608496i	−0.130195	+	0.991488i	$0.541560\pi$
$878$	−510.543	−	884.287i	−0.581484	−	1.00716i
$879$		0			0
$880$	1707.81	−	110.866i	1.94069	−	0.125984i
$881$			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	0.970867	−	0.239620i	$-0.0770229\pi$
$887$	246.512	+	426.971i	0.277916	+	0.481365i	−0.692951	+	0.720985i	$0.743690\pi$
$888$		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
$895$	369.934	−	748.974i	0.413334	−	0.836843i
$896$	−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
$905$	1162.17	+	574.018i	1.28416	+	0.634274i
$906$		0			0
$907$	−772.842	−	446.201i	−0.852086	−	0.491952i	0.00926798	−	0.999957i	$-0.497050\pi$
$907$	−772.842	−	446.201i	−0.852086	−	0.491952i	−0.861354	+	0.508005i	$0.830383\pi$
$908$	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	$-0.443791\pi$
$911$	−536.628	−	309.823i	−0.589054	−	0.340091i	−0.764723	+	0.644359i	$0.777124\pi$
$912$		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	$0.654775\pi$
$920$	79.6083	+	1226.30i	0.0865308	+	1.33294i
$921$		0			0
$922$	1453.57	−	839.217i	1.57654	−	0.910214i
$923$	195.834	+	339.195i	0.212171	+	0.367492i
$924$		0			0
$925$	−998.671	+	764.330i	−1.07964	+	0.826303i
$926$		−	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	$-0.0618859\pi$
$929$	1211.81	+	699.640i	1.30443	+	0.753110i	0.323266	+	0.946308i	$0.395219\pi$
$930$		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
$940$	−25.6184	−	12.6535i	−0.0272536	−	0.0134611i
$941$	−801.683	+	462.852i	−0.851948	+	0.491873i	−0.861308	−	0.508084i	$-0.830354\pi$
$941$	−801.683	+	462.852i	−0.851948	+	0.491873i	0.00935936	+	0.999956i	$0.497021\pi$
$942$		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	−0.889104	−	0.457705i	$-0.848672\pi$
$947$	−45.6148	+	79.0071i	−0.0481677	+	0.0834289i	0.840936	+	0.541134i	$0.182005\pi$
$948$		0			0
$949$	417.930	+	723.876i	0.440390	+	0.762778i
$950$	−1052.59	+	137.241i	−1.10799	+	0.144464i
$951$		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
$965$	−55.6673	+	3.61377i	−0.0576864	+	0.00374484i
$966$		0			0
$967$	1352.97	−	781.135i	1.39914	−	0.807792i	0.404835	−	0.914390i	$-0.367329\pi$
$967$	1352.97	−	781.135i	1.39914	−	0.807792i	0.994302	+	0.106598i	$0.0339958\pi$
$968$	914.931	+	1584.71i	0.945177	+	1.63709i
$969$		0			0
$970$	−1641.68	+	106.573i	−1.69245	+	0.109869i
$971$			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	0.908402	−	0.418097i	$-0.137303\pi$
$977$	89.9999	+	155.884i	0.0921187	+	0.159554i	−0.816284	+	0.577651i	$0.803969\pi$
$978$		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	−0.475050	−	0.879959i	$-0.657570\pi$
$983$	515.624	−	893.088i	0.524542	−	0.908533i	0.999592	−	0.0285740i	$-0.00909662\pi$
$984$		0			0
$985$	695.800	+	343.670i	0.706396	+	0.348904i
$986$	−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
$995$	−746.650	−	368.786i	−0.750402	−	0.370639i
$996$		0			0
$997$	1447.89	+	835.941i	1.45225	+	0.838457i	0.998609	−	0.0527282i	$-0.0167917\pi$
$997$	1447.89	+	835.941i	1.45225	+	0.838457i	0.453640	+	0.891185i	$0.350125\pi$
$998$	−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.269.17		48
3.2	odd	2	inner	405.3.h.k.269.8		48
5.4	even	2	inner	405.3.h.k.269.7		48
9.2	odd	6		405.3.d.b.404.18	yes	24
9.4	even	3	inner	405.3.h.k.134.18		48
9.5	odd	6	inner	405.3.h.k.134.7		48
9.7	even	3		405.3.d.b.404.7	✓	24
15.14	odd	2	inner	405.3.h.k.269.18		48
45.4	even	6	inner	405.3.h.k.134.8		48
45.14	odd	6	inner	405.3.h.k.134.17		48
45.29	odd	6		405.3.d.b.404.8	yes	24
45.34	even	6		405.3.d.b.404.17	yes	24

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

\(f(q)\)	\(=\)	\(q+(1.06375 - 1.84247i) q^{2} +(-0.263128 - 0.455750i) q^{4} +(-4.48298 - 2.21424i) q^{5} +(-1.01789 - 0.587680i) q^{7} +7.39039 q^{8} +(-8.84844 + 5.90436i) q^{10} +(-16.6268 - 9.59948i) q^{11} +(-6.82763 + 3.94194i) q^{13} +(-2.16556 + 1.25029i) q^{14} +(8.91404 - 15.4396i) q^{16} +2.17700 q^{17} -19.9576 q^{19} +(0.170456 + 2.62575i) q^{20} +(-35.3735 + 20.4229i) q^{22} +(-16.6281 - 28.8008i) q^{23} +(15.1943 + 19.8528i) q^{25} +16.7729i q^{26} +0.618539i q^{28} +(-14.6152 - 8.43812i) q^{29} +(-2.27644 - 3.94291i) q^{31} +(-4.18383 - 7.24661i) q^{32} +(2.31579 - 4.01106i) q^{34} +(3.26193 + 4.88841i) q^{35} +50.3038i q^{37} +(-21.2299 + 36.7713i) q^{38} +(-33.1310 - 16.3641i) q^{40} +(-16.3362 + 9.43171i) q^{41} +(-43.8953 - 25.3430i) q^{43} +10.1036i q^{44} -70.7527 q^{46} +(-5.42949 + 9.40415i) q^{47} +(-23.8093 - 41.2389i) q^{49} +(52.7411 - 6.87660i) q^{50} +(3.59308 + 2.07446i) q^{52} +86.1924 q^{53} +(53.2821 + 79.8500i) q^{55} +(-7.52261 - 4.34318i) q^{56} +(-31.0939 + 17.9521i) q^{58} +(83.5848 - 48.2577i) q^{59} +(-20.8160 + 36.0544i) q^{61} -9.68626 q^{62} +53.5101 q^{64} +(39.3366 - 2.55362i) q^{65} +(58.6786 - 33.8781i) q^{67} +(-0.572829 - 0.992169i) q^{68} +(12.4766 - 0.809948i) q^{70} -49.6797i q^{71} -106.022i q^{73} +(92.6832 + 53.5107i) q^{74} +(5.25140 + 9.09570i) q^{76} +(11.2828 + 19.5425i) q^{77} +(-22.0052 + 38.1142i) q^{79} +(-74.1484 + 49.4775i) q^{80} +40.1319i q^{82} +(-44.5432 + 77.1510i) q^{83} +(-9.75946 - 4.82040i) q^{85} +(-93.3872 + 53.9171i) q^{86} +(-122.878 - 70.9439i) q^{88} +19.9472i q^{89} +9.26638 q^{91} +(-8.75065 + 15.1566i) q^{92} +(11.5512 + 20.0073i) q^{94} +(89.4698 + 44.1910i) q^{95} +(133.934 + 77.3270i) q^{97} -101.308 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 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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