LMFDB - Embedded newform 882.2.m.c.293.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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			293.5
Character	$\chi$	$=$	882.293
Dual form			882.2.m.c.587.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.414495 + 1.68172i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.712984 - 1.23492i) q^{5} +(-0.481898 - 1.66366i) q^{6} +1.00000i q^{8} +(-2.65639 - 1.39413i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.414495 + 1.68172i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.712984 - 1.23492i) q^{5} +(-0.481898 - 1.66366i) q^{6} +1.00000i q^{8} +(-2.65639 - 1.39413i) q^{9} +1.42597i q^{10} +(-2.12170 + 1.22496i) q^{11} +(1.24917 + 1.19983i) q^{12} +(-1.61819 - 0.934264i) q^{13} +(1.78127 + 1.71091i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.98625 q^{17} +(2.99757 - 0.120839i) q^{18} -5.90920i q^{19} +(-0.712984 - 1.23492i) q^{20} +(1.22496 - 2.12170i) q^{22} +(-5.65337 - 3.26397i) q^{23} +(-1.68172 - 0.414495i) q^{24} +(1.48331 + 2.56917i) q^{25} +1.86853 q^{26} +(3.44561 - 3.88945i) q^{27} +(-5.51198 + 3.18234i) q^{29} +(-2.39808 - 0.591057i) q^{30} +(-4.15157 - 2.39691i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.18062 - 4.07585i) q^{33} +(-1.72014 + 0.993125i) q^{34} +(-2.53555 + 1.60343i) q^{36} -1.83032 q^{37} +(2.95460 + 5.11752i) q^{38} +(2.24191 - 2.33410i) q^{39} +(1.23492 + 0.712984i) q^{40} +(-2.32289 + 4.02337i) q^{41} +(-5.07994 - 8.79872i) q^{43} +2.44993i q^{44} +(-3.61561 + 2.28644i) q^{45} +6.52794 q^{46} +(-6.47952 - 11.2229i) q^{47} +(1.66366 - 0.481898i) q^{48} +(-2.56917 - 1.48331i) q^{50} +(-0.823292 + 3.34032i) q^{51} +(-1.61819 + 0.934264i) q^{52} +11.8930i q^{53} +(-1.03926 + 5.09116i) q^{54} +3.49352i q^{55} +(9.93764 + 2.44934i) q^{57} +(3.18234 - 5.51198i) q^{58} +(2.88911 - 5.00408i) q^{59} +(2.37233 - 0.687171i) q^{60} +(8.38524 - 4.84122i) q^{61} +4.79382 q^{62} -1.00000 q^{64} +(-2.30749 + 1.33223i) q^{65} +(3.06037 + 2.93949i) q^{66} +(7.60449 - 13.1714i) q^{67} +(0.993125 - 1.72014i) q^{68} +(7.83239 - 8.15450i) q^{69} +0.594087i q^{71} +(1.39413 - 2.65639i) q^{72} -13.5874i q^{73} +(1.58511 - 0.915162i) q^{74} +(-4.93545 + 1.42961i) q^{75} +(-5.11752 - 2.95460i) q^{76} +(-0.774496 + 3.14235i) q^{78} +(4.87348 + 8.44111i) q^{79} -1.42597 q^{80} +(5.11278 + 7.40672i) q^{81} -4.64578i q^{82} +(-1.60586 - 2.78143i) q^{83} +(1.41616 - 2.45287i) q^{85} +(8.79872 + 5.07994i) q^{86} +(-3.06713 - 10.5887i) q^{87} +(-1.22496 - 2.12170i) q^{88} -0.144657 q^{89} +(1.98799 - 3.78792i) q^{90} +(-5.65337 + 3.26397i) q^{92} +(5.75174 - 5.98828i) q^{93} +(11.2229 + 6.47952i) q^{94} +(-7.29742 - 4.21317i) q^{95} +(-1.19983 + 1.24917i) q^{96} +(-2.32972 + 1.34506i) q^{97} +(7.34382 - 0.296046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 32 * q^9	$ 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.414495	+	1.68172i	−0.239309	+	0.970943i
$3$	−0.414495	+	1.68172i	−0.239309	+	0.970943i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.712984	−	1.23492i	0.318856	−	0.552275i	−0.661394	−	0.750039i	$-0.730035\pi$
$5$	0.712984	−	1.23492i	0.318856	−	0.552275i	0.980250	+	0.197764i	$0.0633680\pi$
$6$	−0.481898	−	1.66366i	−0.196734	−	0.679188i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.65639	−	1.39413i	−0.885462	−	0.464711i
$10$			1.42597i			0.450931i
$11$	−2.12170	+	1.22496i	−0.639717	+	0.369341i	−0.784505	−	0.620122i	$-0.787083\pi$
$11$	−2.12170	+	1.22496i	−0.639717	+	0.369341i	0.144789	+	0.989463i	$0.453750\pi$
$12$	1.24917	+	1.19983i	0.360604	+	0.346360i
$13$	−1.61819	−	0.934264i	−0.448806	−	0.259118i	0.258520	−	0.966006i	$-0.416765\pi$
$13$	−1.61819	−	0.934264i	−0.448806	−	0.259118i	−0.707326	+	0.706888i	$0.750099\pi$
$14$		0			0
$15$	1.78127	+	1.71091i	0.459923	+	0.441756i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.98625			0.481737			0.240868	−	0.970558i	$-0.422568\pi$
$17$	1.98625			0.481737			0.240868	+	0.970558i	$0.422568\pi$
$18$	2.99757	−	0.120839i	0.706533	−	0.0284819i
$19$		−	5.90920i		−	1.35566i	−0.735217	−	0.677832i	$-0.762920\pi$
$19$		−	5.90920i		−	1.35566i	0.735217	−	0.677832i	$-0.237080\pi$
$20$	−0.712984	−	1.23492i	−0.159428	−	0.276137i
$21$		0			0
$22$	1.22496	−	2.12170i	0.261163	−	0.452348i
$23$	−5.65337	−	3.26397i	−1.17881	−	0.680585i	−0.223070	−	0.974802i	$-0.571608\pi$
$23$	−5.65337	−	3.26397i	−1.17881	−	0.680585i	−0.955739	+	0.294217i	$0.904941\pi$
$24$	−1.68172	−	0.414495i	−0.343280	−	0.0846085i
$25$	1.48331	+	2.56917i	0.296662	+	0.513833i
$26$	1.86853			0.366448
$27$	3.44561	−	3.88945i	0.663107	−	0.748524i
$28$		0			0
$29$	−5.51198	+	3.18234i	−1.02355	+	0.590946i	−0.915130	−	0.403159i	$-0.867912\pi$
$29$	−5.51198	+	3.18234i	−1.02355	+	0.590946i	−0.108419	+	0.994105i	$0.534579\pi$
$30$	−2.39808	−	0.591057i	−0.437828	−	0.107912i
$31$	−4.15157	−	2.39691i	−0.745644	−	0.430498i	0.0784741	−	0.996916i	$-0.474995\pi$
$31$	−4.15157	−	2.39691i	−0.745644	−	0.430498i	−0.824118	+	0.566419i	$0.808329\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.18062	−	4.07585i	−0.205519	−	0.709515i
$34$	−1.72014	+	0.993125i	−0.295002	+	0.170320i
$35$		0			0
$36$	−2.53555	+	1.60343i	−0.422591	+	0.267239i
$37$	−1.83032			−0.300903			−0.150452	−	0.988617i	$-0.548073\pi$
$37$	−1.83032			−0.300903			−0.150452	+	0.988617i	$0.548073\pi$
$38$	2.95460	+	5.11752i	0.479300	+	0.830171i
$39$	2.24191	−	2.33410i	0.358992	−	0.373756i
$40$	1.23492	+	0.712984i	0.195259	+	0.112733i
$41$	−2.32289	+	4.02337i	−0.362775	+	0.628344i	−0.988416	−	0.151766i	$-0.951504\pi$
$41$	−2.32289	+	4.02337i	−0.362775	+	0.628344i	0.625642	+	0.780111i	$0.284837\pi$
$42$		0			0
$43$	−5.07994	−	8.79872i	−0.774684	−	1.34179i	−0.934972	−	0.354722i	$-0.884575\pi$
$43$	−5.07994	−	8.79872i	−0.774684	−	1.34179i	0.160288	−	0.987070i	$-0.448758\pi$
$44$			2.44993i			0.369341i
$45$	−3.61561	+	2.28644i	−0.538983	+	0.340843i
$46$	6.52794			0.962493
$47$	−6.47952	−	11.2229i	−0.945135	−	1.63702i	−0.755481	−	0.655170i	$-0.772597\pi$
$47$	−6.47952	−	11.2229i	−0.945135	−	1.63702i	−0.189654	−	0.981851i	$-0.560737\pi$
$48$	1.66366	−	0.481898i	0.240129	−	0.0695560i
$49$		0			0
$50$	−2.56917	−	1.48331i	−0.363335	−	0.209771i
$51$	−0.823292	+	3.34032i	−0.115284	+	0.467739i
$52$	−1.61819	+	0.934264i	−0.224403	+	0.129559i
$53$			11.8930i			1.63363i	0.576897	+	0.816817i	$0.304264\pi$
$53$			11.8930i			1.63363i	−0.576897	+	0.816817i	$0.695736\pi$
$54$	−1.03926	+	5.09116i	−0.141425	+	0.692819i
$55$			3.49352i			0.471066i
$56$		0			0
$57$	9.93764	+	2.44934i	1.31627	+	0.324423i
$58$	3.18234	−	5.51198i	0.417862	−	0.723759i
$59$	2.88911	−	5.00408i	0.376130	−	0.651475i	−0.614366	−	0.789021i	$-0.710588\pi$
$59$	2.88911	−	5.00408i	0.376130	−	0.651475i	0.990495	+	0.137546i	$0.0439214\pi$
$60$	2.37233	−	0.687171i	0.306266	−	0.0887134i
$61$	8.38524	−	4.84122i	1.07362	−	0.619855i	0.144452	−	0.989512i	$-0.453858\pi$
$61$	8.38524	−	4.84122i	1.07362	−	0.619855i	0.929168	+	0.369657i	$0.120525\pi$
$62$	4.79382			0.608815
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.30749	+	1.33223i	−0.286209	+	0.165243i
$66$	3.06037	+	2.93949i	0.376706	+	0.361826i
$67$	7.60449	−	13.1714i	0.929036	−	1.60914i	0.144098	−	0.989563i	$-0.453972\pi$
$67$	7.60449	−	13.1714i	0.929036	−	1.60914i	0.784938	−	0.619574i	$-0.212695\pi$
$68$	0.993125	−	1.72014i	0.120434	−	0.208598i
$69$	7.83239	−	8.15450i	0.942909	−	0.981686i
$70$		0			0
$71$			0.594087i			0.0705051i	0.999378	+	0.0352526i	$0.0112236\pi$
$71$			0.594087i			0.0705051i	−0.999378	+	0.0352526i	$0.988776\pi$
$72$	1.39413	−	2.65639i	0.164300	−	0.313058i
$73$		−	13.5874i		−	1.59029i	−0.606422	−	0.795143i	$-0.707396\pi$
$73$		−	13.5874i		−	1.59029i	0.606422	−	0.795143i	$-0.292604\pi$
$74$	1.58511	−	0.915162i	0.184265	−	0.106385i
$75$	−4.93545	+	1.42961i	−0.569897	+	0.165077i
$76$	−5.11752	−	2.95460i	−0.587020	−	0.338916i
$77$		0			0
$78$	−0.774496	+	3.14235i	−0.0876944	+	0.355801i
$79$	4.87348	+	8.44111i	0.548309	+	0.949699i	0.998391	+	0.0567119i	$0.0180616\pi$
$79$	4.87348	+	8.44111i	0.548309	+	0.949699i	−0.450081	+	0.892988i	$0.648605\pi$
$80$	−1.42597			−0.159428
$81$	5.11278	+	7.40672i	0.568087	+	0.822968i
$82$		−	4.64578i		−	0.513041i
$83$	−1.60586	−	2.78143i	−0.176266	−	0.305302i	0.764333	−	0.644822i	$-0.223069\pi$
$83$	−1.60586	−	2.78143i	−0.176266	−	0.305302i	−0.940599	+	0.339520i	$0.889735\pi$
$84$		0			0
$85$	1.41616	−	2.45287i	0.153605	−	0.266051i
$86$	8.79872	+	5.07994i	0.948791	+	0.547784i
$87$	−3.06713	−	10.5887i	−0.328831	−	1.13523i
$88$	−1.22496	−	2.12170i	−0.130582	−	0.226174i
$89$	−0.144657			−0.0153336			−0.00766680	−	0.999971i	$-0.502440\pi$
$89$	−0.144657			−0.0153336			−0.00766680	+	0.999971i	$0.502440\pi$
$90$	1.98799	−	3.78792i	0.209552	−	0.399282i
$91$		0			0
$92$	−5.65337	+	3.26397i	−0.589404	+	0.340293i
$93$	5.75174	−	5.98828i	0.596428	−	0.620956i
$94$	11.2229	+	6.47952i	1.15755	+	0.668311i
$95$	−7.29742	−	4.21317i	−0.748699	−	0.432262i
$96$	−1.19983	+	1.24917i	−0.122457	+	0.127493i
$97$	−2.32972	+	1.34506i	−0.236547	+	0.136571i	−0.613589	−	0.789626i	$-0.710275\pi$
$97$	−2.32972	+	1.34506i	−0.236547	+	0.136571i	0.377042	+	0.926196i	$0.376941\pi$
$98$		0			0
$99$	7.34382	−	0.296046i	0.738082	−	0.0297537i
$100$	2.96662			0.296662
$101$	1.84869	+	3.20202i	0.183951	+	0.318613i	0.943223	−	0.332161i	$-0.107778\pi$
$101$	1.84869	+	3.20202i	0.183951	+	0.318613i	−0.759271	+	0.650774i	$0.774444\pi$
$102$	−0.957170	−	3.30445i	−0.0947740	−	0.327189i
$103$	13.9648	+	8.06260i	1.37600	+	0.794431i	0.991675	−	0.128768i	$-0.0411024\pi$
$103$	13.9648	+	8.06260i	1.37600	+	0.794431i	0.384321	+	0.923200i	$0.374436\pi$
$104$	0.934264	−	1.61819i	0.0916121	−	0.158677i
$105$		0			0
$106$	−5.94652	−	10.2997i	−0.577577	−	1.00039i
$107$		−	0.545248i		−	0.0527111i	−0.999653	−	0.0263556i	$-0.991610\pi$
$107$		−	0.545248i		−	0.0527111i	0.999653	−	0.0263556i	$-0.00839020\pi$
$108$	−1.64556	−	4.92871i	−0.158344	−	0.474265i
$109$	−6.33018			−0.606321			−0.303161	−	0.952939i	$-0.598042\pi$
$109$	−6.33018			−0.606321			−0.303161	+	0.952939i	$0.598042\pi$
$110$	−1.74676	−	3.02547i	−0.166547	−	0.288468i
$111$	0.758661	−	3.07810i	0.0720089	−	0.292160i
$112$		0			0
$113$	−9.21222	−	5.31868i	−0.866612	−	0.500339i	−0.000391395	−	1.00000i	$-0.500125\pi$
$113$	−9.21222	−	5.31868i	−0.866612	−	0.500339i	−0.866221	+	0.499661i	$0.833458\pi$
$114$	−9.83092	+	2.84763i	−0.920750	+	0.266705i
$115$	−8.06152	+	4.65432i	−0.751740	+	0.434017i
$116$			6.36469i			0.590946i
$117$	2.99606	+	4.73774i	0.276986	+	0.438004i
$118$			5.77821i			0.531927i
$119$		0			0
$120$	−1.71091	+	1.78127i	−0.156184	+	0.162607i
$121$	−2.49893	+	4.32827i	−0.227175	+	0.393479i
$122$	−4.84122	+	8.38524i	−0.438304	+	0.759164i
$123$	−5.80336	−	5.57413i	−0.523271	−	0.502602i
$124$	−4.15157	+	2.39691i	−0.372822	+	0.215249i
$125$	11.3601			1.01608
$126$		0			0
$127$	5.92432			0.525698			0.262849	−	0.964837i	$-0.415338\pi$
$127$	5.92432			0.525698			0.262849	+	0.964837i	$0.415338\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	16.9026	−	4.89603i	1.48819	−	0.431071i
$130$	1.33223	−	2.30749i	0.116844	−	0.202380i
$131$	−6.81751	+	11.8083i	−0.595649	+	1.03169i	0.397806	+	0.917469i	$0.369772\pi$
$131$	−6.81751	+	11.8083i	−0.595649	+	1.03169i	−0.993455	+	0.114224i	$0.963562\pi$
$132$	−4.12010	−	1.01548i	−0.358609	−	0.0883865i
$133$		0			0
$134$			15.2090i			1.31386i
$135$	−2.34651	−	7.02818i	−0.201955	−	0.604889i
$136$			1.98625i			0.170320i
$137$	−15.5598	+	8.98348i	−1.32937	+	0.767510i	−0.985202	−	0.171399i	$-0.945171\pi$
$137$	−15.5598	+	8.98348i	−1.32937	+	0.767510i	−0.344165	+	0.938909i	$0.611838\pi$
$138$	−2.70580	+	10.9782i	−0.230333	+	0.934526i
$139$	−8.22479	−	4.74858i	−0.697617	−	0.402769i	0.108842	−	0.994059i	$-0.465286\pi$
$139$	−8.22479	−	4.74858i	−0.697617	−	0.402769i	−0.806459	+	0.591290i	$0.798619\pi$
$140$		0			0
$141$	21.5595	−	6.24493i	1.81563	−	0.525918i
$142$	−0.297043	−	0.514494i	−0.0249273	−	0.0431754i
$143$	4.57776			0.382811
$144$	0.120839	+	2.99757i	0.0100699	+	0.249797i
$145$			9.07584i			0.753707i
$146$	6.79371	+	11.7670i	0.562251	+	0.973847i
$147$		0			0
$148$	−0.915162	+	1.58511i	−0.0752258	+	0.130295i
$149$	4.61041	+	2.66182i	0.377699	+	0.218065i	0.676817	−	0.736151i	$-0.263359\pi$
$149$	4.61041	+	2.66182i	0.377699	+	0.218065i	−0.299117	+	0.954216i	$0.596692\pi$
$150$	3.55942	−	3.70580i	0.290626	−	0.302577i
$151$	−6.97282	−	12.0773i	−0.567440	−	0.982834i	−0.996818	−	0.0797096i	$-0.974601\pi$
$151$	−6.97282	−	12.0773i	−0.567440	−	0.982834i	0.429378	−	0.903125i	$-0.358733\pi$
$152$	5.90920			0.479300
$153$	−5.27625	−	2.76910i	−0.426560	−	0.223868i
$154$		0			0
$155$	−5.92000	+	3.41791i	−0.475506	+	0.274533i
$156$	−0.900440	−	3.10860i	−0.0720929	−	0.248887i
$157$	−4.55518	−	2.62993i	−0.363543	−	0.209891i	0.307091	−	0.951680i	$-0.400644\pi$
$157$	−4.55518	−	2.62993i	−0.363543	−	0.209891i	−0.670634	+	0.741789i	$0.733978\pi$
$158$	−8.44111	−	4.87348i	−0.671539	−	0.387713i
$159$	−20.0008	−	4.92961i	−1.58617	−	0.390943i
$160$	1.23492	−	0.712984i	0.0976293	−	0.0563663i
$161$		0			0
$162$	−8.13116	−	3.85801i	−0.638844	−	0.303114i
$163$	−9.87851			−0.773745			−0.386872	−	0.922133i	$-0.626445\pi$
$163$	−9.87851			−0.773745			−0.386872	+	0.922133i	$0.626445\pi$
$164$	2.32289	+	4.02337i	0.181387	+	0.314172i
$165$	−5.87513	−	1.44805i	−0.457378	−	0.112730i
$166$	2.78143	+	1.60586i	0.215881	+	0.124639i
$167$	−8.86749	+	15.3589i	−0.686187	+	1.18851i	0.286876	+	0.957968i	$0.407383\pi$
$167$	−8.86749	+	15.3589i	−0.686187	+	1.18851i	−0.973062	+	0.230542i	$0.925950\pi$
$168$		0			0
$169$	−4.75430	−	8.23469i	−0.365716	−	0.633438i
$170$			2.83233i			0.217230i
$171$	−8.23822	+	15.6971i	−0.629992	+	1.20039i
$172$	−10.1599			−0.774684
$173$	−4.20045	−	7.27539i	−0.319354	−	0.553137i	0.660999	−	0.750386i	$-0.270133\pi$
$173$	−4.20045	−	7.27539i	−0.319354	−	0.553137i	−0.980353	+	0.197249i	$0.936799\pi$
$174$	7.95056	+	7.63651i	0.602731	+	0.578923i
$175$		0			0
$176$	2.12170	+	1.22496i	0.159929	+	0.0923351i
$177$	7.21795	+	6.93284i	0.542535	+	0.521104i
$178$	0.125277	−	0.0723285i	0.00938988	−	0.00542125i
$179$		−	3.02300i		−	0.225950i	−0.993598	−	0.112975i	$-0.963962\pi$
$179$		−	3.02300i		−	0.225950i	0.993598	−	0.112975i	$-0.0360380\pi$
$180$	0.172312	+	4.27443i	0.0128434	+	0.318597i
$181$			4.94729i			0.367729i	0.982952	+	0.183865i	$0.0588608\pi$
$181$			4.94729i			0.367729i	−0.982952	+	0.183865i	$0.941139\pi$
$182$		0			0
$183$	4.66595	+	16.1083i	0.344917	+	1.19076i
$184$	3.26397	−	5.65337i	0.240623	−	0.416772i
$185$	−1.30499	+	2.26031i	−0.0959449	+	0.166181i
$186$	−1.98702	+	8.06188i	−0.145695	+	0.591125i
$187$	−4.21423	+	2.43309i	−0.308175	+	0.177925i
$188$	−12.9590			−0.945135
$189$		0			0
$190$	8.42633			0.611310
$191$	4.42179	−	2.55292i	0.319949	−	0.184723i	−0.331421	−	0.943483i	$-0.607528\pi$
$191$	4.42179	−	2.55292i	0.319949	−	0.184723i	0.651370	+	0.758760i	$0.274195\pi$
$192$	0.414495	−	1.68172i	0.0299136	−	0.121368i
$193$	−0.527061	+	0.912897i	−0.0379387	+	0.0657118i	−0.884371	−	0.466784i	$-0.845413\pi$
$193$	−0.527061	+	0.912897i	−0.0379387	+	0.0657118i	0.846433	+	0.532496i	$0.178746\pi$
$194$	1.34506	−	2.32972i	0.0965700	−	0.167264i
$195$	−1.28400	−	4.43276i	−0.0919490	−	0.317437i
$196$		0			0
$197$		−	4.97775i		−	0.354650i	−0.984152	−	0.177325i	$-0.943256\pi$
$197$		−	4.97775i		−	0.354650i	0.984152	−	0.177325i	$-0.0567444\pi$
$198$	−6.21191	+	3.92829i	−0.441461	+	0.279172i
$199$		−	1.15120i		−	0.0816064i	−0.999167	−	0.0408032i	$-0.987008\pi$
$199$		−	1.15120i		−	0.0816064i	0.999167	−	0.0408032i	$-0.0129917\pi$
$200$	−2.56917	+	1.48331i	−0.181667	+	0.104886i
$201$	18.9986	+	18.2481i	1.34005	+	1.28712i
$202$	−3.20202	−	1.84869i	−0.225294	−	0.130073i
$203$		0			0
$204$	2.48116	+	2.38315i	0.173716	+	0.166854i
$205$	3.31237	+	5.73719i	0.231346	+	0.400703i
$206$	−16.1252			−1.12350
$207$	10.4671	+	16.5519i	0.727515	+	1.15044i
$208$			1.86853i			0.129559i
$209$	7.23856	+	12.5376i	0.500702	+	0.867241i
$210$		0			0
$211$	−7.03245	+	12.1806i	−0.484134	+	0.838545i	−0.999834	−	0.0182244i	$-0.994199\pi$
$211$	−7.03245	+	12.1806i	−0.484134	+	0.838545i	0.515700	+	0.856769i	$0.327532\pi$
$212$	10.2997	+	5.94652i	0.707384	+	0.408409i
$213$	−0.999089	−	0.246246i	−0.0684565	−	0.0168725i
$214$	0.272624	+	0.472199i	0.0186362	+	0.0322788i
$215$	−14.4877			−0.988051
$216$	3.88945	+	3.44561i	0.264643	+	0.234444i
$217$		0			0
$218$	5.48210	−	3.16509i	0.371294	−	0.214367i
$219$	22.8503	+	5.63192i	1.54408	+	0.380570i
$220$	3.02547	+	1.74676i	0.203977	+	0.117766i
$221$	−3.21414	−	1.85568i	−0.216206	−	0.124827i
$222$	0.882030	+	3.04504i	0.0591980	+	0.204370i
$223$	−17.3777	+	10.0330i	−1.16370	+	0.671860i	−0.952187	−	0.305516i	$-0.901171\pi$
$223$	−17.3777	+	10.0330i	−1.16370	+	0.671860i	−0.211509	+	0.977376i	$0.567838\pi$
$224$		0			0
$225$	−0.358482	−	8.89263i	−0.0238988	−	0.592842i
$226$	10.6374			0.707586
$227$	−3.01495	−	5.22205i	−0.200109	−	0.346600i	0.748454	−	0.663187i	$-0.230796\pi$
$227$	−3.01495	−	5.22205i	−0.200109	−	0.346600i	−0.948563	+	0.316587i	$0.897463\pi$
$228$	7.09001	−	7.38158i	0.469547	−	0.488857i
$229$	19.8379	+	11.4534i	1.31092	+	0.756862i	0.982249	−	0.187581i	$-0.0600648\pi$
$229$	19.8379	+	11.4534i	1.31092	+	0.756862i	0.328674	+	0.944443i	$0.393398\pi$
$230$	4.65432	−	8.06152i	0.306897	−	0.531561i
$231$		0			0
$232$	−3.18234	−	5.51198i	−0.208931	−	0.361879i
$233$		−	29.7780i		−	1.95082i	−0.220395	−	0.975411i	$-0.570735\pi$
$233$		−	29.7780i		−	1.95082i	0.220395	−	0.975411i	$-0.429265\pi$
$234$	−4.96353	−	2.60498i	−0.324476	−	0.170293i
$235$	−18.4792			−1.20545
$236$	−2.88911	−	5.00408i	−0.188065	−	0.325738i
$237$	−16.2157	+	4.69704i	−1.05332	+	0.305106i
$238$		0			0
$239$	10.5976	+	6.11850i	0.685499	+	0.395773i	0.801924	−	0.597427i	$-0.203810\pi$
$239$	10.5976	+	6.11850i	0.685499	+	0.395773i	−0.116425	+	0.993200i	$0.537143\pi$
$240$	0.591057	−	2.39808i	0.0381526	−	0.154796i
$241$	−21.0423	+	12.1488i	−1.35545	+	0.782571i	−0.989007	−	0.147869i	$-0.952759\pi$
$241$	−21.0423	+	12.1488i	−1.35545	+	0.782571i	−0.366445	+	0.930440i	$0.619425\pi$
$242$		−	4.99785i		−	0.321274i
$243$	−14.5753	+	5.52824i	−0.935004	+	0.354637i
$244$		−	9.68245i		−	0.619855i
$245$		0			0
$246$	7.81292	+	1.92566i	0.498134	+	0.122775i
$247$	−5.52075	+	9.56223i	−0.351277	+	0.608430i
$248$	2.39691	−	4.15157i	0.152204	−	0.263625i
$249$	5.34322	−	1.54772i	0.338613	−	0.0980829i
$250$	−9.83817	+	5.68007i	−0.622220	+	0.359239i
$251$	13.0834			0.825815			0.412908	−	0.910773i	$-0.364513\pi$
$251$	13.0834			0.825815			0.412908	+	0.910773i	$0.364513\pi$
$252$		0			0
$253$	15.9930			1.00547
$254$	−5.13061	+	2.96216i	−0.321923	+	0.185862i
$255$	3.53805	+	3.39830i	0.221561	+	0.212810i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.24569	+	5.62170i	−0.202461	+	0.350672i	−0.949321	−	0.314309i	$-0.898227\pi$
$257$	−3.24569	+	5.62170i	−0.202461	+	0.350672i	0.746860	+	0.664981i	$0.231561\pi$
$258$	−12.1901	+	12.6914i	−0.758922	+	0.790132i
$259$		0			0
$260$			2.66446i			0.165243i
$261$	19.0786	−	0.769100i	1.18093	−	0.0476061i
$262$		−	13.6350i		−	0.842375i
$263$	23.2937	−	13.4486i	1.43635	−	0.829276i	0.438755	−	0.898607i	$-0.355420\pi$
$263$	23.2937	−	13.4486i	1.43635	−	0.829276i	0.997594	+	0.0693309i	$0.0220864\pi$
$264$	4.07585	−	1.18062i	0.250851	−	0.0726619i
$265$	14.6870	+	8.47954i	0.902215	+	0.520894i
$266$		0			0
$267$	0.0599597	−	0.243273i	0.00366947	−	0.0148881i
$268$	−7.60449	−	13.1714i	−0.464518	−	0.804569i
$269$	15.3040			0.933099			0.466550	−	0.884495i	$-0.345497\pi$
$269$	15.3040			0.933099			0.466550	+	0.884495i	$0.345497\pi$
$270$	5.54622	+	4.91332i	0.337532	+	0.299015i
$271$		−	9.36077i		−	0.568626i	−0.958731	−	0.284313i	$-0.908234\pi$
$271$		−	9.36077i		−	0.568626i	0.958731	−	0.284313i	$-0.0917656\pi$
$272$	−0.993125	−	1.72014i	−0.0602171	−	0.104299i
$273$		0			0
$274$	8.98348	−	15.5598i	0.542712	−	0.940004i
$275$	−6.29427	−	3.63400i	−0.379559	−	0.219138i
$276$	−3.14580	−	10.8603i	−0.189355	−	0.653713i
$277$	13.5195	+	23.4164i	0.812307	+	1.40696i	0.911246	+	0.411863i	$0.135122\pi$
$277$	13.5195	+	23.4164i	0.812307	+	1.40696i	−0.0989390	+	0.995093i	$0.531545\pi$
$278$	9.49716			0.569602
$279$	7.68656	+	12.1550i	0.460182	+	0.727698i
$280$		0			0
$281$	−16.4502	+	9.49754i	−0.981338	+	0.566576i	−0.902674	−	0.430325i	$-0.858399\pi$
$281$	−16.4502	+	9.49754i	−0.981338	+	0.566576i	−0.0786642	+	0.996901i	$0.525065\pi$
$282$	−15.5486	+	16.1880i	−0.925904	+	0.963982i
$283$	15.6354	+	9.02710i	0.929428	+	0.536606i	0.886631	−	0.462478i	$-0.153040\pi$
$283$	15.6354	+	9.02710i	0.929428	+	0.536606i	0.0427975	+	0.999084i	$0.486373\pi$
$284$	0.514494	+	0.297043i	0.0305296	+	0.0176263i
$285$	10.1101	−	10.5259i	0.598872	−	0.623500i
$286$	−3.96445	+	2.28888i	−0.234423	+	0.135344i
$287$		0			0
$288$	−1.60343	−	2.53555i	−0.0944831	−	0.149409i
$289$	−13.0548			−0.767930
$290$	−4.53792	−	7.85991i	−0.266476	−	0.461550i
$291$	−1.29637	−	4.47547i	−0.0759945	−	0.262357i
$292$	−11.7670	−	6.79371i	−0.688614	−	0.397572i
$293$	−9.99970	+	17.3200i	−0.584189	+	1.01184i	0.410788	+	0.911731i	$0.365254\pi$
$293$	−9.99970	+	17.3200i	−0.584189	+	1.01184i	−0.994976	+	0.100113i	$0.968080\pi$
$294$		0			0
$295$	−4.11977	−	7.13565i	−0.239862	−	0.415454i
$296$		−	1.83032i		−	0.106385i
$297$	−2.54611	+	12.4730i	−0.147740	+	0.723756i
$298$	−5.32364			−0.308390
$299$	6.09882	+	10.5635i	0.352704	+	0.610901i
$300$	−1.22965	+	4.98903i	−0.0709938	+	0.288042i
$301$		0			0
$302$	12.0773	+	6.97282i	0.694969	+	0.401240i
$303$	−6.15119	+	1.78176i	−0.353377	+	0.102359i
$304$	−5.11752	+	2.95460i	−0.293510	+	0.169458i
$305$		−	13.8069i		−	0.790578i
$306$	5.95392	−	0.240016i	0.340363	−	0.0137208i
$307$		−	2.13374i		−	0.121779i	−0.998145	−	0.0608896i	$-0.980606\pi$
$307$		−	2.13374i		−	0.121779i	0.998145	−	0.0608896i	$-0.0193937\pi$
$308$		0			0
$309$	−19.3474	+	20.1431i	−1.10064	+	1.14590i
$310$	3.41791	−	5.92000i	0.194124	−	0.336233i
$311$	4.56419	−	7.90541i	0.258812	−	0.448275i	−0.707112	−	0.707101i	$-0.750002\pi$
$311$	4.56419	−	7.90541i	0.258812	−	0.448275i	0.965924	+	0.258827i	$0.0833358\pi$
$312$	2.33410	+	2.24191i	0.132143	+	0.126923i
$313$	−12.9579	+	7.48122i	−0.732421	+	0.422864i	−0.819307	−	0.573355i	$-0.805642\pi$
$313$	−12.9579	+	7.48122i	−0.732421	+	0.422864i	0.0868859	+	0.996218i	$0.472308\pi$
$314$	5.25986			0.296831
$315$		0			0
$316$	9.74696			0.548309
$317$	1.83555	−	1.05976i	0.103095	−	0.0595219i	−0.447566	−	0.894251i	$-0.647709\pi$
$317$	1.83555	−	1.05976i	0.103095	−	0.0595219i	0.550661	+	0.834729i	$0.314376\pi$
$318$	19.7860	−	5.73123i	1.10954	−	0.321392i
$319$	7.79651	−	13.5040i	0.436521	−	0.756076i
$320$	−0.712984	+	1.23492i	−0.0398570	+	0.0690344i
$321$	0.916956	+	0.226003i	0.0511795	+	0.0126142i
$322$		0			0
$323$		−	11.7372i		−	0.653073i
$324$	8.97080	−	0.724443i	0.498378	−	0.0402468i
$325$		−	5.54321i		−	0.307482i
$326$	8.55504	−	4.93926i	0.473820	−	0.273560i
$327$	2.62383	−	10.6456i	0.145098	−	0.588704i
$328$	−4.02337	−	2.32289i	−0.222153	−	0.128260i
$329$		0			0
$330$	5.81204	−	1.68352i	0.319942	−	0.0926747i
$331$	6.21840	+	10.7706i	0.341794	+	0.592005i	0.984766	−	0.173885i	$-0.0556322\pi$
$331$	6.21840	+	10.7706i	0.341794	+	0.592005i	−0.642972	+	0.765890i	$0.722299\pi$
$332$	−3.21172			−0.176266
$333$	4.86205	+	2.55172i	0.266439	+	0.139833i
$334$		−	17.7350i		−	0.970414i
$335$	−10.8438	−	18.7819i	−0.592457	−	1.02617i
$336$		0			0
$337$	−9.57144	+	16.5782i	−0.521389	+	0.903073i	0.478301	+	0.878196i	$0.341253\pi$
$337$	−9.57144	+	16.5782i	−0.521389	+	0.903073i	−0.999691	+	0.0248771i	$0.992081\pi$
$338$	8.23469	+	4.75430i	0.447908	+	0.258600i
$339$	12.7630	−	13.2878i	0.693189	−	0.721696i
$340$	−1.41616	−	2.45287i	−0.0768023	−	0.133025i
$341$	11.7445			0.636001
$342$	−0.714060	−	17.7132i	−0.0386119	−	0.957821i
$343$		0			0
$344$	8.79872	−	5.07994i	0.474395	−	0.273892i
$345$	−4.48581	−	15.4864i	−0.241508	−	0.833762i
$346$	7.27539	+	4.20045i	0.391127	+	0.225817i
$347$	3.85149	+	2.22366i	0.206759	+	0.119372i	0.599804	−	0.800147i	$-0.295245\pi$
$347$	3.85149	+	2.22366i	0.206759	+	0.119372i	−0.393045	+	0.919519i	$0.628578\pi$
$348$	−10.7036	−	2.63813i	−0.573776	−	0.141419i
$349$	25.0865	−	14.4837i	1.34285	−	0.775294i	0.355624	−	0.934629i	$-0.384268\pi$
$349$	25.0865	−	14.4837i	1.34285	−	0.775294i	0.987225	+	0.159335i	$0.0509349\pi$
$350$		0			0
$351$	−9.20942	+	3.07477i	−0.491563	+	0.164119i
$352$	−2.44993			−0.130582
$353$	−10.7060	−	18.5433i	−0.569822	−	0.986961i	−0.996583	−	0.0825966i	$-0.973679\pi$
$353$	−10.7060	−	18.5433i	−0.569822	−	0.986961i	0.426761	−	0.904365i	$-0.359655\pi$
$354$	−9.71735	−	2.39504i	−0.516471	−	0.127295i
$355$	0.733652	+	0.423574i	0.0389382	+	0.0224810i
$356$	−0.0723285	+	0.125277i	−0.00383340	+	0.00663965i
$357$		0			0
$358$	1.51150	+	2.61800i	0.0798853	+	0.138365i
$359$			11.4103i			0.602214i	0.953590	+	0.301107i	$0.0973561\pi$
$359$			11.4103i			0.602214i	−0.953590	+	0.301107i	$0.902644\pi$
$360$	−2.28644	−	3.61561i	−0.120506	−	0.190559i
$361$	−15.9187			−0.837825
$362$	−2.47364	−	4.28448i	−0.130012	−	0.225187i
$363$	−6.24316	−	5.99655i	−0.327681	−	0.314737i
$364$		0			0
$365$	−16.7794	−	9.68760i	−0.878275	−	0.507072i
$366$	−12.0950	−	11.6172i	−0.632216	−	0.607243i
$367$	−13.4460	+	7.76303i	−0.701873	+	0.405227i	−0.808045	−	0.589121i	$-0.799474\pi$
$367$	−13.4460	+	7.76303i	−0.701873	+	0.405227i	0.106171	+	0.994348i	$0.466141\pi$
$368$			6.52794i			0.340293i
$369$	11.7796	−	7.44920i	0.613222	−	0.387790i
$370$		−	2.60998i		−	0.135687i
$371$		0			0
$372$	−2.31013	−	7.97530i	−0.119775	−	0.413500i
$373$	9.04807	−	15.6717i	0.468491	−	0.811451i	−0.530860	−	0.847459i	$-0.678131\pi$
$373$	9.04807	−	15.6717i	0.468491	−	0.811451i	0.999351	+	0.0360087i	$0.0114644\pi$
$374$	2.43309	−	4.21423i	0.125812	−	0.217913i
$375$	−4.70872	+	19.1046i	−0.243158	+	0.986558i
$376$	11.2229	−	6.47952i	0.578774	−	0.334156i
$377$	11.8926			0.612500
$378$		0			0
$379$	−24.2482			−1.24555			−0.622774	−	0.782402i	$-0.713994\pi$
$379$	−24.2482			−1.24555			−0.622774	+	0.782402i	$0.713994\pi$
$380$	−7.29742	+	4.21317i	−0.374350	+	0.216131i
$381$	−2.45560	+	9.96307i	−0.125804	+	0.510423i
$382$	−2.55292	+	4.42179i	−0.130619	+	0.226238i
$383$	−3.05053	+	5.28368i	−0.155875	+	0.269983i	−0.933377	−	0.358897i	$-0.883153\pi$
$383$	−3.05053	+	5.28368i	−0.155875	+	0.269983i	0.777502	+	0.628880i	$0.216486\pi$
$384$	0.481898	+	1.66366i	0.0245918	+	0.0848984i
$385$		0			0
$386$		−	1.05412i		−	0.0536534i
$387$	1.22771	+	30.4549i	0.0624078	+	1.54811i
$388$			2.69013i			0.136571i
$389$	8.39221	−	4.84524i	0.425502	−	0.245664i	−0.271927	−	0.962318i	$-0.587661\pi$
$389$	8.39221	−	4.84524i	0.425502	−	0.245664i	0.697429	+	0.716654i	$0.254327\pi$
$390$	3.32836	+	3.19689i	0.168538	+	0.161881i
$391$	−11.2290	−	6.48307i	−0.567875	−	0.327863i
$392$		0			0
$393$	−17.0324	−	16.3596i	−0.859172	−	0.825235i
$394$	2.48888	+	4.31086i	0.125388	+	0.217178i
$395$	13.8988			0.699327
$396$	3.41553	−	6.50796i	0.171637	−	0.327037i
$397$		−	14.4928i		−	0.727373i	−0.931521	−	0.363687i	$-0.881518\pi$
$397$		−	14.4928i		−	0.727373i	0.931521	−	0.363687i	$-0.118482\pi$
$398$	0.575600	+	0.996968i	0.0288522	+	0.0499735i
$399$		0			0
$400$	1.48331	−	2.56917i	0.0741654	−	0.128458i
$401$	−21.6413	−	12.4946i	−1.08072	−	0.623952i	−0.149627	−	0.988742i	$-0.547807\pi$
$401$	−21.6413	−	12.4946i	−1.08072	−	0.623952i	−0.931090	+	0.364790i	$0.881141\pi$
$402$	−25.5773	−	6.30405i	−1.27568	−	0.314417i
$403$	4.47869	+	7.75732i	0.223099	+	0.386420i
$404$	3.69738			0.183951
$405$	12.7921	−	1.03303i	0.635643	−	0.0513318i
$406$		0			0
$407$	3.88340	−	2.24208i	0.192493	−	0.111136i
$408$	−3.34032	−	0.823292i	−0.165371	−	0.0407590i
$409$	32.2174	+	18.6007i	1.59305	+	0.919746i	0.992781	+	0.119945i	$0.0382718\pi$
$409$	32.2174	+	18.6007i	1.59305	+	0.919746i	0.600266	+	0.799801i	$0.295061\pi$
$410$	−5.73719	−	3.31237i	−0.283340	−	0.163586i
$411$	−8.65824	−	29.8909i	−0.427079	−	1.47441i
$412$	13.9648	−	8.06260i	0.687998	−	0.397216i
$413$		0			0
$414$	−17.3407	−	9.10083i	−0.852251	−	0.447281i
$415$	−4.57981			−0.224814
$416$	−0.934264	−	1.61819i	−0.0458061	−	0.0793384i
$417$	11.3949	−	11.8635i	0.558012	−	0.580960i
$418$	−12.5376	−	7.23856i	−0.613232	−	0.354050i
$419$	17.7624	−	30.7654i	0.867750	−	1.50299i	0.00345977	−	0.999994i	$-0.498899\pi$
$419$	17.7624	−	30.7654i	0.867750	−	1.50299i	0.864290	−	0.502993i	$-0.167768\pi$
$420$		0			0
$421$	16.8698	+	29.2193i	0.822181	+	1.42406i	0.904055	+	0.427417i	$0.140576\pi$
$421$	16.8698	+	29.2193i	0.822181	+	1.42406i	−0.0818731	+	0.996643i	$0.526090\pi$
$422$		−	14.0649i		−	0.684669i
$423$	1.56595	+	38.8456i	0.0761392	+	1.88874i
$424$	−11.8930			−0.577577
$425$	2.94622	+	5.10301i	0.142913	+	0.247532i
$426$	0.988360	−	0.286289i	0.0478862	−	0.0138708i
$427$		0			0
$428$	−0.472199	−	0.272624i	−0.0228246	−	0.0131778i
$429$	−1.89746	+	7.69852i	−0.0916102	+	0.371688i
$430$	12.5467	−	7.24384i	0.605055	−	0.349329i
$431$			3.13857i			0.151180i	0.997139	+	0.0755899i	$0.0240840\pi$
$431$			3.13857i			0.151180i	−0.997139	+	0.0755899i	$0.975916\pi$
$432$	−5.09116	−	1.03926i	−0.244949	−	0.0500014i
$433$		−	36.1258i		−	1.73609i	−0.496482	−	0.868047i	$-0.665375\pi$
$433$		−	36.1258i		−	1.73609i	0.496482	−	0.868047i	$-0.334625\pi$
$434$		0			0
$435$	−15.2631	−	3.76189i	−0.731807	−	0.180369i
$436$	−3.16509	+	5.48210i	−0.151580	+	0.262545i
$437$	−19.2875	+	33.4069i	−0.922645	+	1.59807i
$438$	−22.6049	+	6.54775i	−1.08010	+	0.312863i
$439$	−12.5331	+	7.23602i	−0.598175	+	0.345356i	−0.768323	−	0.640062i	$-0.778909\pi$
$439$	−12.5331	+	7.23602i	−0.598175	+	0.345356i	0.170149	+	0.985418i	$0.445575\pi$
$440$	−3.49352			−0.166547
$441$		0			0
$442$	3.71136			0.176532
$443$	−9.50209	+	5.48604i	−0.451458	+	0.260649i	−0.708446	−	0.705765i	$-0.750603\pi$
$443$	−9.50209	+	5.48604i	−0.451458	+	0.260649i	0.256988	+	0.966415i	$0.417270\pi$
$444$	−2.28638	−	2.19607i	−0.108507	−	0.104221i
$445$	−0.103138	+	0.178640i	−0.00488921	+	0.00846837i
$446$	10.0330	−	17.3777i	0.475077	−	0.822857i
$447$	−6.38744	+	6.65012i	−0.302115	+	0.314540i
$448$		0			0
$449$		−	29.7298i		−	1.40304i	−0.712652	−	0.701518i	$-0.752506\pi$
$449$		−	29.7298i		−	1.40304i	0.712652	−	0.701518i	$-0.247494\pi$
$450$	4.75677	+	7.52200i	0.224236	+	0.354590i
$451$		−	11.3818i		−	0.535949i
$452$	−9.21222	+	5.31868i	−0.433306	+	0.250169i
$453$	23.2008	−	6.72037i	1.09007	−	0.315751i
$454$	5.22205	+	3.01495i	0.245083	+	0.141499i
$455$		0			0
$456$	−2.44934	+	9.93764i	−0.114701	+	0.465373i
$457$	−5.07662	−	8.79296i	−0.237474	−	0.411317i	0.722515	−	0.691356i	$-0.242986\pi$
$457$	−5.07662	−	8.79296i	−0.237474	−	0.411317i	−0.959989	+	0.280038i	$0.909653\pi$
$458$	−22.9068			−1.07036
$459$	6.84384	−	7.72542i	0.319443	−	0.360592i
$460$			9.30864i			0.434017i
$461$	−13.9677	−	24.1927i	−0.650539	−	1.12677i	−0.982992	−	0.183647i	$-0.941210\pi$
$461$	−13.9677	−	24.1927i	−0.650539	−	1.12677i	0.332454	−	0.943120i	$-0.392124\pi$
$462$		0			0
$463$	−11.4477	+	19.8280i	−0.532019	+	0.921485i	0.467282	+	0.884108i	$0.345233\pi$
$463$	−11.4477	+	19.8280i	−0.532019	+	0.921485i	−0.999301	+	0.0373763i	$0.988100\pi$
$464$	5.51198	+	3.18234i	0.255887	+	0.147737i
$465$	−3.29417	−	11.3725i	−0.152764	−	0.527388i
$466$	14.8890	+	25.7885i	0.689719	+	1.19463i
$467$	−14.8691			−0.688059			−0.344029	−	0.938959i	$-0.611792\pi$
$467$	−14.8691			−0.688059			−0.344029	+	0.938959i	$0.611792\pi$
$468$	5.60103	−	0.225790i	0.258908	−	0.0104372i
$469$		0			0
$470$	16.0034	−	9.23958i	0.738183	−	0.426190i
$471$	6.31092	−	6.57045i	0.290792	−	0.302750i
$472$	5.00408	+	2.88911i	0.230331	+	0.132982i
$473$	21.5562	+	12.4455i	0.991157	+	0.572245i
$474$	11.6946	−	12.1756i	0.537153	−	0.559243i
$475$	15.1817	−	8.76517i	0.696585	−	0.402174i
$476$		0			0
$477$	16.5805	−	31.5925i	0.759168	−	1.44652i
$478$	−12.2370			−0.559707
$479$	3.82550	+	6.62595i	0.174791	+	0.302748i	0.940089	−	0.340929i	$-0.110742\pi$
$479$	3.82550	+	6.62595i	0.174791	+	0.302748i	−0.765298	+	0.643677i	$0.777408\pi$
$480$	0.687171	+	2.37233i	0.0313649	+	0.108282i
$481$	2.96182	+	1.71001i	0.135047	+	0.0779695i
$482$	12.1488	−	21.0423i	0.553361	−	0.958449i
$483$		0			0
$484$	2.49893	+	4.32827i	0.113588	+	0.196739i
$485$			3.83604i			0.174186i
$486$	9.85844	−	12.0752i	0.447188	−	0.547744i
$487$	22.0497			0.999168			0.499584	−	0.866265i	$-0.333486\pi$
$487$	22.0497			0.999168			0.499584	+	0.866265i	$0.333486\pi$
$488$	4.84122	+	8.38524i	0.219152	+	0.379582i
$489$	4.09460	−	16.6129i	0.185164	−	0.751262i
$490$		0			0
$491$	26.3385	+	15.2065i	1.18864	+	0.686261i	0.957997	−	0.286778i	$-0.0925843\pi$
$491$	26.3385	+	15.2065i	1.18864	+	0.686261i	0.230641	+	0.973039i	$0.425918\pi$
$492$	−7.72902	+	2.23879i	−0.348451	+	0.100933i
$493$	−10.9482	+	6.32093i	−0.493081	+	0.284681i
$494$		−	11.0415i		−	0.496781i
$495$	4.87043	−	9.28013i	0.218910	−	0.417111i
$496$			4.79382i			0.215249i
$497$		0			0
$498$	−3.85351	+	4.01198i	−0.172680	+	0.179781i
$499$	−12.6832	+	21.9680i	−0.567778	+	0.983421i	0.429007	+	0.903301i	$0.358864\pi$
$499$	−12.6832	+	21.9680i	−0.567778	+	0.983421i	−0.996785	+	0.0801195i	$0.974470\pi$
$500$	5.68007	−	9.83817i	0.254020	−	0.439976i
$501$	−22.1539	−	21.2789i	−0.989765	−	0.950670i
$502$	−11.3305	+	6.54169i	−0.505706	+	0.291970i
$503$	−29.1075			−1.29784			−0.648919	−	0.760858i	$-0.724778\pi$
$503$	−29.1075			−1.29784			−0.648919	+	0.760858i	$0.724778\pi$
$504$		0			0
$505$	5.27234			0.234616
$506$	−13.8503	+	7.99650i	−0.615723	+	0.355488i
$507$	15.8191	−	4.58218i	0.702551	−	0.203502i
$508$	2.96216	−	5.13061i	0.131425	−	0.227634i
$509$	5.80749	−	10.0589i	0.257412	−	0.445851i	−0.708136	−	0.706076i	$-0.750463\pi$
$509$	5.80749	−	10.0589i	0.257412	−	0.445851i	0.965548	+	0.260225i	$0.0837968\pi$
$510$	−4.76319	−	1.17399i	−0.210918	−	0.0519850i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−22.9835	−	20.3608i	−1.01475	−	0.898951i
$514$		−	6.49138i		−	0.286323i
$515$	19.9134	−	11.4970i	0.877489	−	0.506618i
$516$	4.21123	−	17.0861i	0.185389	−	0.752175i
$517$	27.4952	+	15.8744i	1.20924	+	0.698153i
$518$		0			0
$519$	13.9763	−	4.04837i	0.613489	−	0.177704i
$520$	−1.33223	−	2.30749i	−0.0584221	−	0.101190i
$521$	1.41619			0.0620443			0.0310221	−	0.999519i	$-0.490124\pi$
$521$	1.41619			0.0620443			0.0310221	+	0.999519i	$0.490124\pi$
$522$	−16.1380	+	10.2053i	−0.706340	+	0.446676i
$523$		−	8.91703i		−	0.389915i	−0.980812	−	0.194957i	$-0.937543\pi$
$523$		−	8.91703i		−	0.389915i	0.980812	−	0.194957i	$-0.0624568\pi$
$524$	6.81751	+	11.8083i	0.297824	+	0.515847i
$525$		0			0
$526$	−13.4486	+	23.2937i	−0.586387	+	1.01565i
$527$	−8.24605	−	4.76086i	−0.359204	−	0.207386i
$528$	−2.93949	+	3.06037i	−0.127925	+	0.133186i
$529$	9.80703	+	16.9863i	0.426393	+	0.738534i
$530$	−16.9591			−0.736656
$531$	−14.6509	+	9.26497i	−0.635796	+	0.402065i
$532$		0			0
$533$	7.51777	−	4.34039i	0.325631	−	0.188003i
$534$	0.0697099	+	0.240660i	0.00301664	+	0.0104144i
$535$	−0.673340	−	0.388753i	−0.0291110	−	0.0168073i
$536$	13.1714	+	7.60449i	0.568916	+	0.328464i
$537$	5.08385	+	1.25302i	0.219384	+	0.0540718i
$538$	−13.2536	+	7.65198i	−0.571404	+	0.329900i
$539$		0			0
$540$	−7.25983	−	1.48195i	−0.312413	−	0.0637730i
$541$	8.74127			0.375817			0.187908	−	0.982187i	$-0.439829\pi$
$541$	8.74127			0.375817			0.187908	+	0.982187i	$0.439829\pi$
$542$	4.68039	+	8.10667i	0.201040	+	0.348211i
$543$	−8.31997	−	2.05063i	−0.357044	−	0.0880009i
$544$	1.72014	+	0.993125i	0.0737505	+	0.0425799i
$545$	−4.51332	+	7.81729i	−0.193329	+	0.334856i
$546$		0			0
$547$	−12.4767	−	21.6103i	−0.533466	−	0.923990i	−0.999236	−	0.0390840i	$-0.987556\pi$
$547$	−12.4767	−	21.6103i	−0.533466	−	0.923990i	0.465770	−	0.884906i	$-0.345777\pi$
$548$			17.9670i			0.767510i
$549$	−29.0238	+	1.17001i	−1.23870	+	0.0499349i
$550$	7.26800			0.309908
$551$	18.8051	+	32.5714i	0.801125	+	1.38759i
$552$	8.15450	+	7.83239i	0.347078	+	0.333369i
$553$		0			0
$554$	−23.4164	−	13.5195i	−0.994869	−	0.574388i
$555$	−3.26031	−	3.13152i	−0.138392	−	0.132926i
$556$	−8.22479	+	4.74858i	−0.348809	+	0.201385i
$557$			0.0493284i			0.00209011i	0.999999	+	0.00104506i	$0.000332652\pi$
$557$			0.0493284i			0.00209011i	−0.999999	+	0.00104506i	$0.999667\pi$
$558$	−12.7342	−	6.68322i	−0.539083	−	0.282923i
$559$			18.9840i			0.802939i
$560$		0			0
$561$	−2.34500	−	8.09567i	−0.0990059	−	0.341799i
$562$	9.49754	−	16.4502i	0.400630	−	0.693911i
$563$	3.24507	−	5.62062i	0.136763	−	0.236881i	−0.789506	−	0.613742i	$-0.789663\pi$
$563$	3.24507	−	5.62062i	0.136763	−	0.236881i	0.926270	+	0.376861i	$0.122997\pi$
$564$	5.37146	−	21.7935i	0.226179	−	0.917672i
$565$	−13.1363	+	7.58426i	−0.552649	+	0.319072i
$566$	−18.0542			−0.758875
$567$		0			0
$568$	−0.594087			−0.0249273
$569$	33.5802	−	19.3876i	1.40776	−	0.812768i	0.412585	−	0.910919i	$-0.364626\pi$
$569$	33.5802	−	19.3876i	1.40776	−	0.812768i	0.995172	+	0.0981509i	$0.0312928\pi$
$570$	−3.49268	+	14.1708i	−0.146292	+	0.593548i
$571$	−0.128832	+	0.223143i	−0.00539143	+	0.00933824i	−0.868709	−	0.495324i	$-0.835049\pi$
$571$	−0.128832	+	0.223143i	−0.00539143	+	0.00933824i	0.863317	+	0.504662i	$0.168383\pi$
$572$	2.28888	−	3.96445i	0.0957028	−	0.165762i
$573$	2.46049	+	8.49439i	0.102789	+	0.354858i
$574$		0			0
$575$		−	19.3659i		−	0.807614i
$576$	2.65639	+	1.39413i	0.110683	+	0.0580889i
$577$		−	33.5074i		−	1.39493i	−0.716618	−	0.697465i	$-0.754311\pi$
$577$		−	33.5074i		−	1.39493i	0.716618	−	0.697465i	$-0.245689\pi$
$578$	11.3058	−	6.52740i	0.470259	−	0.271504i
$579$	−1.31678	−	1.26476i	−0.0547233	−	0.0525618i
$580$	7.85991	+	4.53792i	0.326365	+	0.188427i
$581$		0			0
$582$	3.36042	+	3.22769i	0.139294	+	0.133792i
$583$	−14.5685	−	25.2335i	−0.603367	−	1.04506i
$584$	13.5874			0.562251
$585$	7.98689	−	0.321970i	0.330217	−	0.0133118i
$586$		−	19.9994i		−	0.826167i
$587$	−22.4541	−	38.8916i	−0.926779	−	1.60523i	−0.788675	−	0.614811i	$-0.789232\pi$
$587$	−22.4541	−	38.8916i	−0.926779	−	1.60523i	−0.138104	−	0.990418i	$-0.544101\pi$
$588$		0			0
$589$	−14.1638	+	24.5325i	−0.583610	+	1.01084i
$590$	7.13565	+	4.11977i	0.293770	+	0.169608i
$591$	8.37120	+	2.06326i	0.344345	+	0.0848710i
$592$	0.915162	+	1.58511i	0.0376129	+	0.0651475i
$593$	21.2653			0.873260			0.436630	−	0.899641i	$-0.356172\pi$
$593$	21.2653			0.873260			0.436630	+	0.899641i	$0.356172\pi$
$594$	−4.03149	−	12.0750i	−0.165414	−	0.495442i
$595$		0			0
$596$	4.61041	−	2.66182i	0.188850	−	0.109032i
$597$	1.93600	+	0.477167i	0.0792352	+	0.0195291i
$598$	−10.5635	−	6.09882i	−0.431972	−	0.249399i
$599$	22.1002	+	12.7596i	0.902990	+	0.521341i	0.878169	−	0.478351i	$-0.158765\pi$
$599$	22.1002	+	12.7596i	0.902990	+	0.521341i	0.0248208	+	0.999692i	$0.492098\pi$
$600$	−1.42961	−	4.93545i	−0.0583635	−	0.201489i
$601$	14.4139	−	8.32184i	0.587953	−	0.339455i	−0.176335	−	0.984330i	$-0.556424\pi$
$601$	14.4139	−	8.32184i	0.587953	−	0.339455i	0.764288	+	0.644875i	$0.223091\pi$
$602$		0			0
$603$	−38.5631	+	24.3866i	−1.57041	+	0.993097i
$604$	−13.9456			−0.567440
$605$	3.56339	+	6.17197i	0.144872	+	0.250926i
$606$	4.43621	−	4.61864i	0.180209	−	0.187620i
$607$	−4.89357	−	2.82531i	−0.198624	−	0.114676i	0.397389	−	0.917650i	$-0.369916\pi$
$607$	−4.89357	−	2.82531i	−0.198624	−	0.114676i	−0.596014	+	0.802974i	$0.703250\pi$
$608$	2.95460	−	5.11752i	0.119825	−	0.207543i
$609$		0			0
$610$	6.90343	+	11.9571i	0.279512	+	0.484128i
$611$			24.2143i			0.979606i
$612$	−5.03623	+	3.18482i	−0.203578	+	0.128739i
$613$	39.8457			1.60935			0.804676	−	0.593714i	$-0.202339\pi$
$613$	39.8457			1.60935			0.804676	+	0.593714i	$0.202339\pi$
$614$	1.06687	+	1.84788i	0.0430554	+	0.0745742i
$615$	−11.0213	+	3.19245i	−0.444423	+	0.128732i
$616$		0			0
$617$	13.6398	+	7.87493i	0.549117	+	0.317033i	0.748766	−	0.662835i	$-0.230647\pi$
$617$	13.6398	+	7.87493i	0.549117	+	0.317033i	−0.199649	+	0.979868i	$0.563980\pi$
$618$	6.68382	−	27.1181i	0.268863	−	1.09085i
$619$	23.3655	−	13.4901i	0.939140	−	0.542213i	0.0494494	−	0.998777i	$-0.484253\pi$
$619$	23.3655	−	13.4901i	0.939140	−	0.542213i	0.889691	+	0.456564i	$0.150920\pi$
$620$			6.83583i			0.274533i
$621$	−32.1743	+	10.7421i	−1.29111	+	0.431066i
$622$			9.12838i			0.366015i
$623$		0			0
$624$	−3.14235	−	0.774496i	−0.125795	−	0.0310047i
$625$	0.683051	−	1.18308i	0.0273220	−	0.0473232i
$626$	7.48122	−	12.9579i	0.299010	−	0.517900i
$627$	−24.0850	+	6.97650i	−0.961864	+	0.278614i
$628$	−4.55518	+	2.62993i	−0.181771	+	0.104946i
$629$	−3.63548			−0.144956
$630$		0			0
$631$	22.1618			0.882246			0.441123	−	0.897447i	$-0.354580\pi$
$631$	22.1618			0.882246			0.441123	+	0.897447i	$0.354580\pi$
$632$	−8.44111	+	4.87348i	−0.335769	+	0.193857i
$633$	−17.5694	−	16.8754i	−0.698322	−	0.670738i
$634$	−1.05976	+	1.83555i	−0.0420883	+	0.0728992i
$635$	4.22394	−	7.31609i	0.167622	−	0.290330i
$636$	−14.2696	+	14.8564i	−0.565825	+	0.589094i
$637$		0			0
$638$			15.5930i			0.617334i
$639$	0.828236	−	1.57812i	0.0327645	−	0.0624296i
$640$		−	1.42597i		−	0.0563663i
$641$	−21.1748	+	12.2253i	−0.836356	+	0.482870i	−0.856024	−	0.516936i	$-0.827072\pi$
$641$	−21.1748	+	12.2253i	−0.836356	+	0.482870i	0.0196680	+	0.999807i	$0.493739\pi$
$642$	−0.907109	+	0.262754i	−0.0358007	+	0.0103701i
$643$	5.38012	+	3.10621i	0.212171	+	0.122497i	0.602320	−	0.798255i	$-0.294243\pi$
$643$	5.38012	+	3.10621i	0.212171	+	0.122497i	−0.390149	+	0.920752i	$0.627576\pi$
$644$		0			0
$645$	6.00507	−	24.3643i	0.236450	−	0.959342i
$646$	5.86858	+	10.1647i	0.230896	+	0.399924i
$647$	−34.2800			−1.34769			−0.673844	−	0.738874i	$-0.735358\pi$
$647$	−34.2800			−1.34769			−0.673844	+	0.738874i	$0.735358\pi$
$648$	−7.40672	+	5.11278i	−0.290963	+	0.200849i
$649$			14.1562i			0.555679i
$650$	2.77160	+	4.80056i	0.108711	+	0.188293i
$651$		0			0
$652$	−4.93926	+	8.55504i	−0.193436	+	0.335041i
$653$	−7.85846	−	4.53709i	−0.307525	−	0.177550i	0.338293	−	0.941041i	$-0.390150\pi$
$653$	−7.85846	−	4.53709i	−0.307525	−	0.177550i	−0.645819	+	0.763491i	$0.723484\pi$
$654$	3.05050	+	10.5313i	0.119284	+	0.411806i
$655$	9.72155	+	16.8382i	0.379852	+	0.657924i
$656$	4.64578			0.181387
$657$	−18.9427	+	36.0934i	−0.739024	+	1.40814i
$658$		0			0
$659$	42.1898	−	24.3583i	1.64348	−	0.948865i	0.663900	−	0.747821i	$-0.268900\pi$
$659$	42.1898	−	24.3583i	1.64348	−	0.948865i	0.979582	−	0.201043i	$-0.0644332\pi$
$660$	−4.19161	+	4.36399i	−0.163158	+	0.169868i
$661$	9.43876	+	5.44947i	0.367125	+	0.211960i	0.672202	−	0.740368i	$-0.265349\pi$
$661$	9.43876	+	5.44947i	0.367125	+	0.211960i	−0.305077	+	0.952328i	$0.598682\pi$
$662$	−10.7706	−	6.21840i	−0.418610	−	0.241685i
$663$	4.45299	−	4.63612i	0.172940	−	0.180052i
$664$	2.78143	−	1.60586i	0.107941	−	0.0623195i
$665$		0			0
$666$	−5.48652	+	0.221174i	−0.212598	+	0.00857031i
$667$	41.5483			1.60876
$668$	8.86749	+	15.3589i	0.343093	+	0.594255i
$669$	−9.66978	−	33.3831i	−0.373855	−	1.29066i
$670$	18.7819	+	10.8438i	0.725609	+	0.418931i
$671$	−11.8606	+	20.5432i	−0.457875	+	0.793063i
$672$		0			0
$673$	23.6565	+	40.9743i	0.911893	+	1.57944i	0.811388	+	0.584508i	$0.198712\pi$
$673$	23.6565	+	40.9743i	0.911893	+	1.57944i	0.100505	+	0.994937i	$0.467954\pi$
$674$		−	19.1429i		−	0.737356i
$675$	15.1035	+	3.08309i	0.581335	+	0.118668i
$676$	−9.50860			−0.365716
$677$	−2.46212	−	4.26452i	−0.0946270	−	0.163899i	0.814826	−	0.579706i	$-0.196833\pi$
$677$	−2.46212	−	4.26452i	−0.0946270	−	0.163899i	−0.909453	+	0.415807i	$0.863499\pi$
$678$	−4.40913	+	17.8891i	−0.169332	+	0.687026i
$679$		0			0
$680$	2.45287	+	1.41616i	0.0940632	+	0.0543074i
$681$	10.0317	−	2.90580i	0.384417	−	0.111350i
$682$	−10.1710	+	5.87225i	−0.389469	+	0.224860i
$683$		−	11.2280i		−	0.429629i	−0.976655	−	0.214814i	$-0.931085\pi$
$683$		−	11.2280i		−	0.429629i	0.976655	−	0.214814i	$-0.0689147\pi$
$684$	9.47500	+	14.9831i	0.362286	+	0.572892i
$685$			25.6203i			0.978901i
$686$		0			0
$687$	−27.4842	+	28.6144i	−1.04859	+	1.09171i
$688$	−5.07994	+	8.79872i	−0.193671	+	0.335448i
$689$	11.1112	−	19.2452i	0.423304	−	0.733185i
$690$	11.6280	+	11.1687i	0.442672	+	0.425187i
$691$	12.0725	−	6.97005i	0.459259	−	0.265153i	−0.252474	−	0.967604i	$-0.581244\pi$
$691$	12.0725	−	6.97005i	0.459259	−	0.265153i	0.711732	+	0.702451i	$0.247911\pi$
$692$	−8.40089			−0.319354
$693$		0			0
$694$	−4.44732			−0.168818
$695$	−11.7283	+	6.77132i	−0.444879	+	0.256851i
$696$	10.5887	−	3.06713i	0.401363	−	0.116259i
$697$	−4.61384	+	7.99141i	−0.174762	+	0.302696i
$698$	−14.4837	+	25.0865i	−0.548216	+	0.949538i
$699$	50.0783	+	12.3428i	1.89414	+	0.466849i
$700$		0			0
$701$			33.1186i			1.25087i	0.780276	+	0.625435i	$0.215079\pi$
$701$			33.1186i			1.25087i	−0.780276	+	0.625435i	$0.784921\pi$
$702$	6.43821	−	7.26754i	0.242995	−	0.274296i
$703$			10.8158i			0.407924i
$704$	2.12170	−	1.22496i	0.0799646	−	0.0461676i
$705$	7.65953	−	31.0768i	0.288475	−	1.17042i
$706$	18.5433	+	10.7060i	0.697887	+	0.402925i
$707$		0			0
$708$	9.61300	−	2.78451i	0.361278	−	0.104648i
$709$	9.06989	+	15.7095i	0.340627	+	0.589983i	0.984549	−	0.175108i	$-0.0560274\pi$
$709$	9.06989	+	15.7095i	0.340627	+	0.589983i	−0.643922	+	0.765091i	$0.722694\pi$
$710$	−0.847148			−0.0317929
$711$	−1.17781	−	29.2171i	−0.0441713	−	1.09573i
$712$		−	0.144657i		−	0.00542125i
$713$	15.6469	+	27.1012i	0.585981	+	1.01495i
$714$		0			0
$715$	3.26387	−	5.65318i	0.122062	−	0.211417i
$716$	−2.61800	−	1.51150i	−0.0978391	−	0.0564874i
$717$	−14.6823	+	15.2861i	−0.548319	+	0.570869i
$718$	−5.70516	−	9.88163i	−0.212915	−	0.368779i
$719$	25.0164			0.932953			0.466476	−	0.884534i	$-0.345523\pi$
$719$	25.0164			0.932953			0.466476	+	0.884534i	$0.345523\pi$
$720$	3.78792	+	1.98799i	0.141168	+	0.0740880i
$721$		0			0
$722$	13.7860	−	7.95934i	0.513061	−	0.296216i
$723$	−11.7089	−	40.4229i	−0.435460	−	1.50334i
$724$	4.28448	+	2.47364i	0.159231	+	0.0919323i
$725$	−16.3519	−	9.44080i	−0.607296	−	0.350622i
$726$	8.40501	+	2.07159i	0.311939	+	0.0768838i
$727$	−32.3382	+	18.6705i	−1.19936	+	0.692450i	−0.960412	−	0.278583i	$-0.910135\pi$
$727$	−32.3382	+	18.6705i	−1.19936	+	0.692450i	−0.238946	+	0.971033i	$0.576802\pi$
$728$		0			0
$729$	−3.25558	−	26.8030i	−0.120577	−	0.992704i
$730$	19.3752			0.717109
$731$	−10.0900	−	17.4765i	−0.373194	−	0.646390i
$732$	16.2832	+	4.01333i	0.601844	+	0.148337i
$733$	−34.3841	−	19.8516i	−1.27000	−	0.733237i	−0.295016	−	0.955492i	$-0.595325\pi$
$733$	−34.3841	−	19.8516i	−1.27000	−	0.733237i	−0.974989	+	0.222255i	$0.928658\pi$
$734$	7.76303	−	13.4460i	0.286539	−	0.496299i
$735$		0			0
$736$	−3.26397	−	5.65337i	−0.120312	−	0.208386i
$737$			37.2609i			1.37252i
$738$	−6.47684	+	12.3410i	−0.238416	+	0.454278i
$739$	−39.8006			−1.46409			−0.732044	−	0.681257i	$-0.761433\pi$
$739$	−39.8006			−1.46409			−0.732044	+	0.681257i	$0.761433\pi$
$740$	1.30499	+	2.26031i	0.0479724	+	0.0830907i
$741$	−13.7927	−	13.2479i	−0.506687	−	0.486673i
$742$		0			0
$743$	34.6622	+	20.0123i	1.27163	+	0.734178i	0.975295	−	0.220905i	$-0.0709009\pi$
$743$	34.6622	+	20.0123i	1.27163	+	0.734178i	0.296339	+	0.955083i	$0.404234\pi$
$744$	5.98828	+	5.75174i	0.219541	+	0.210869i
$745$	6.57429	−	3.79567i	0.240863	−	0.139063i
$746$			18.0961i			0.662547i
$747$	0.388100	+	9.62735i	0.0141998	+	0.352246i
$748$			4.86617i			0.177925i
$749$		0			0
$750$	−5.47443	−	18.8994i	−0.199898	−	0.690110i
$751$	5.98284	−	10.3626i	0.218317	−	0.378136i	−0.735977	−	0.677007i	$-0.763277\pi$
$751$	5.98284	−	10.3626i	0.218317	−	0.378136i	0.954294	+	0.298871i	$0.0966100\pi$
$752$	−6.47952	+	11.2229i	−0.236284	+	0.409255i
$753$	−5.42300	+	22.0026i	−0.197625	+	0.801820i
$754$	−10.2993	+	5.94630i	−0.375078	+	0.216551i
$755$	−19.8860			−0.723726
$756$		0			0
$757$	−0.372779			−0.0135489			−0.00677443	−	0.999977i	$-0.502156\pi$
$757$	−0.372779			−0.0135489			−0.00677443	+	0.999977i	$0.502156\pi$
$758$	20.9996	−	12.1241i	0.762739	−	0.440368i
$759$	−6.62902	+	26.8958i	−0.240618	+	0.976255i
$760$	4.21317	−	7.29742i	0.152828	−	0.264705i
$761$	−3.82232	+	6.62046i	−0.138559	+	0.239991i	−0.926951	−	0.375181i	$-0.877580\pi$
$761$	−3.82232	+	6.62046i	−0.138559	+	0.239991i	0.788392	+	0.615173i	$0.210914\pi$
$762$	−2.85492	−	9.85607i	−0.103423	−	0.357048i
$763$		0			0
$764$		−	5.10584i		−	0.184723i
$765$	−7.18151	+	4.54145i	−0.259648	+	0.164196i
$766$		−	6.10106i		−	0.220440i
$767$	−9.35026	+	5.39837i	−0.337618	+	0.194924i
$768$	−1.24917	−	1.19983i	−0.0450754	−	0.0432950i
$769$	−7.18496	−	4.14824i	−0.259096	−	0.149589i	0.364826	−	0.931076i	$-0.381128\pi$
$769$	−7.18496	−	4.14824i	−0.259096	−	0.149589i	−0.623922	+	0.781486i	$0.714462\pi$
$770$		0			0
$771$	−8.10883	−	7.78853i	−0.292032	−	0.280497i
$772$	0.527061	+	0.912897i	0.0189694	+	0.0328559i
$773$	16.8724			0.606856			0.303428	−	0.952854i	$-0.401869\pi$
$773$	16.8724			0.606856			0.303428	+	0.952854i	$0.401869\pi$
$774$	−16.2907	−	25.7609i	−0.585557	−	0.925956i
$775$		−	14.2214i		−	0.510848i
$776$	−1.34506	−	2.32972i	−0.0482850	−	0.0836321i
$777$		0			0
$778$	−4.84524	+	8.39221i	−0.173710	+	0.300875i
$779$	23.7749	+	13.7264i	0.851823	+	0.491801i
$780$	−4.48088	−	1.10441i	−0.160441	−	0.0395441i
$781$	−0.727735	−	1.26047i	−0.0260404	−	0.0451033i
$782$	12.9661			0.463668
$783$	−6.61457	+	32.4037i	−0.236385	+	1.15801i
$784$		0			0
$785$	−6.49553	+	3.75020i	−0.231835	+	0.133850i
$786$	22.9303	+	5.65166i	0.817898	+	0.201588i
$787$	−28.6503	−	16.5413i	−1.02127	−	0.589633i	−0.106802	−	0.994280i	$-0.534061\pi$
$787$	−28.6503	−	16.5413i	−1.02127	−	0.589633i	−0.914473	+	0.404647i	$0.867394\pi$
$788$	−4.31086	−	2.48888i	−0.153568	−	0.0886625i
$789$	12.9617	+	44.7479i	0.461449	+	1.59307i
$790$	−12.0368	+	6.94942i	−0.428248	+	0.247249i
$791$		0			0
$792$	0.296046	+	7.34382i	0.0105195	+	0.260951i
$793$	−18.0919			−0.642463
$794$	7.24641	+	12.5511i	0.257165	+	0.445423i
$795$	−20.3479	+	21.1847i	−0.721667	+	0.751345i
$796$	−0.996968	−	0.575600i	−0.0353366	−	0.0204016i
$797$	8.51205	−	14.7433i	0.301512	−	0.522234i	−0.674967	−	0.737848i	$-0.735842\pi$
$797$	8.51205	−	14.7433i	0.301512	−	0.522234i	0.976479	+	0.215614i	$0.0691753\pi$
$798$		0			0
$799$	−12.8699	−	22.2914i	−0.455306	−	0.788613i
$800$			2.96662i			0.104886i
$801$	0.384265	+	0.201671i	0.0135773	+	0.00712570i
$802$	24.9893			0.882402
$803$	16.6441	+	28.8284i	0.587357	+	1.01733i
$804$	25.3026	−	7.32918i	0.892354	−	0.258480i
$805$		0			0
$806$	−7.75732	−	4.47869i	−0.273240	−	0.157755i
$807$	−6.34342	+	25.7370i	−0.223299	+	0.905986i
$808$	−3.20202	+	1.84869i	−0.112647	+	0.0650366i
$809$		−	31.2639i		−	1.09918i	−0.835435	−	0.549590i	$-0.814784\pi$
$809$		−	31.2639i		−	1.09918i	0.835435	−	0.549590i	$-0.185216\pi$
$810$	−10.5617	+	7.29066i	−0.371102	+	0.256168i
$811$			14.9333i			0.524380i	0.965016	+	0.262190i	$0.0844448\pi$
$811$			14.9333i			0.524380i	−0.965016	+	0.262190i	$0.915555\pi$
$812$		0			0
$813$	15.7422	+	3.88000i	0.552104	+	0.136077i
$814$	−2.24208	+	3.88340i	−0.0785849	+	0.136113i
$815$	−7.04322	+	12.1992i	−0.246713	+	0.427320i
$816$	3.30445	−	0.957170i	0.115679	−	0.0335077i
$817$	−51.9934	+	30.0184i	−1.81902	+	1.05021i
$818$	−37.2014			−1.30072
$819$		0			0
$820$	6.62473			0.231346
$821$	−6.23049	+	3.59718i	−0.217446	+	0.125542i	−0.604767	−	0.796402i	$-0.706734\pi$
$821$	−6.23049	+	3.59718i	−0.217446	+	0.125542i	0.387321	+	0.921945i	$0.373400\pi$
$822$	22.4437	+	21.5572i	0.782815	+	0.751894i
$823$	−13.6761	+	23.6877i	−0.476719	+	0.825701i	−0.999644	−	0.0266772i	$-0.991507\pi$
$823$	−13.6761	+	23.6877i	−0.476719	+	0.825701i	0.522925	+	0.852379i	$0.324841\pi$
$824$	−8.06260	+	13.9648i	−0.280874	+	0.486488i
$825$	8.72033	−	9.07894i	0.303603	−	0.316088i
$826$		0			0
$827$		−	18.1171i		−	0.629994i	−0.949093	−	0.314997i	$-0.897996\pi$
$827$		−	18.1171i		−	0.629994i	0.949093	−	0.314997i	$-0.102004\pi$
$828$	19.5679	−	0.788828i	0.680033	−	0.0274137i
$829$		−	22.3227i		−	0.775301i	−0.921807	−	0.387650i	$-0.873287\pi$
$829$		−	22.3227i		−	0.775301i	0.921807	−	0.387650i	$-0.126713\pi$
$830$	3.96623	−	2.28991i	0.137670	−	0.0794838i
$831$	−44.9837	+	13.0300i	−1.56047	+	0.452006i
$832$	1.61819	+	0.934264i	0.0561007	+	0.0323898i
$833$		0			0
$834$	−3.93653	+	15.9716i	−0.136311	+	0.553051i
$835$	12.6447	+	21.9013i	0.437589	+	0.757927i
$836$	14.4771			0.500702
$837$	−23.6273	+	7.88849i	−0.816680	+	0.272666i
$838$			35.5248i			1.22718i
$839$	−5.47947	−	9.49072i	−0.189172	−	0.327656i	0.755802	−	0.654800i	$-0.227247\pi$
$839$	−5.47947	−	9.49072i	−0.189172	−	0.327656i	−0.944975	+	0.327144i	$0.893914\pi$
$840$		0			0
$841$	5.75463	−	9.96731i	0.198435	−	0.343700i
$842$	−29.2193	−	16.8698i	−1.00696	−	0.581370i
$843$	−9.15369	−	31.6014i	−0.315270	−	1.08841i
$844$	7.03245	+	12.1806i	0.242067	+	0.419272i
$845$	−13.5590			−0.466442
$846$	−20.7789	−	32.8583i	−0.714394	−	1.12969i
$847$		0			0
$848$	10.2997	−	5.94652i	0.353692	−	0.204204i
$849$	−21.6619	+	22.5527i	−0.743434	+	0.774008i
$850$	−5.10301	−	2.94622i	−0.175032	−	0.101055i
$851$	10.3475	+	5.97413i	0.354707	+	0.204790i
$852$	−0.712800	+	0.742114i	−0.0244201	+	0.0254244i
$853$	23.6890	−	13.6768i	0.811095	−	0.468286i	−0.0362411	−	0.999343i	$-0.511538\pi$
$853$	23.6890	−	13.6768i	0.811095	−	0.468286i	0.847336	+	0.531057i	$0.178205\pi$
$854$		0			0
$855$	13.5110	+	21.3654i	0.462068	+	0.730680i
$856$	0.545248			0.0186362
$857$	−4.14390	−	7.17745i	−0.141553	−	0.245177i	0.786529	−	0.617554i	$-0.211876\pi$
$857$	−4.14390	−	7.17745i	−0.141553	−	0.245177i	−0.928082	+	0.372377i	$0.878543\pi$
$858$	−2.20601	−	7.61585i	−0.0753120	−	0.260001i
$859$	−9.29234	−	5.36494i	−0.317051	−	0.183049i	0.333027	−	0.942917i	$-0.391930\pi$
$859$	−9.29234	−	5.36494i	−0.317051	−	0.183049i	−0.650077	+	0.759868i	$0.725263\pi$
$860$	−7.24384	+	12.5467i	−0.247013	+	0.427839i
$861$		0			0
$862$	−1.56929	−	2.71808i	−0.0534501	−	0.0925783i
$863$		−	5.16864i		−	0.175942i	−0.996123	−	0.0879712i	$-0.971962\pi$
$863$		−	5.16864i		−	0.175942i	0.996123	−	0.0879712i	$-0.0280384\pi$
$864$	4.92871	−	1.64556i	0.167678	−	0.0559829i
$865$	−11.9794			−0.407312
$866$	18.0629	+	31.2858i	0.613802	+	1.06314i
$867$	5.41116	−	21.9546i	0.183773	−	0.745616i
$868$		0			0
$869$	−20.6801	−	11.9397i	−0.701525	−	0.405026i
$870$	15.0991	−	4.37363i	0.511909	−	0.148280i
$871$	−24.6110	+	14.2092i	−0.833914	+	0.481460i
$872$		−	6.33018i		−	0.214367i
$873$	8.06384	−	0.325072i	0.272920	−	0.0110020i
$874$		−	38.5749i		−	1.30482i
$875$		0			0
$876$	16.3025	−	16.9730i	0.550811	−	0.573463i
$877$	26.7198	−	46.2800i	0.902263	−	1.56276i	0.0777127	−	0.996976i	$-0.475238\pi$
$877$	26.7198	−	46.2800i	0.902263	−	1.56276i	0.824550	−	0.565789i	$-0.191428\pi$
$878$	7.23602	−	12.5331i	0.244204	−	0.422973i
$879$	−24.9826	−	23.9958i	−0.842642	−	0.809357i
$880$	3.02547	−	1.74676i	0.101989	−	0.0588832i
$881$	21.7352			0.732277			0.366139	−	0.930560i	$-0.380680\pi$
$881$	21.7352			0.732277			0.366139	+	0.930560i	$0.380680\pi$
$882$		0			0
$883$	20.2657			0.681996			0.340998	−	0.940064i	$-0.389235\pi$
$883$	20.2657			0.681996			0.340998	+	0.940064i	$0.389235\pi$
$884$	−3.21414	+	1.85568i	−0.108103	+	0.0624133i
$885$	13.7078	−	3.97062i	0.460783	−	0.133471i
$886$	5.48604	−	9.50209i	0.184307	−	0.319229i
$887$	−4.61858	+	7.99962i	−0.155077	+	0.268601i	−0.933087	−	0.359651i	$-0.882896\pi$
$887$	−4.61858	+	7.99962i	−0.155077	+	0.268601i	0.778010	+	0.628252i	$0.216229\pi$
$888$	3.07810	+	0.758661i	0.103294	+	0.0254590i
$889$		0			0
$890$		−	0.206276i		−	0.00691439i
$891$	−19.9208	−	9.45185i	−0.667370	−	0.316649i
$892$			20.0660i			0.671860i
$893$	−66.3181	+	38.2888i	−2.21925	+	1.28129i
$894$	2.20662	−	8.95289i	0.0738006	−	0.299429i
$895$	−3.73318	−	2.15535i	−0.124786	−	0.0720454i
$896$		0			0
$897$	−20.2928	+	5.87802i	−0.677556	+	0.196261i
$898$	14.8649	+	25.7468i	0.496048	+	0.859181i
$899$	30.5112			1.01760
$900$	−7.88048	−	4.13586i	−0.262683	−	0.137862i
$901$			23.6226i			0.786981i
$902$	5.69092	+	9.85695i	0.189487	+	0.328201i
$903$		0			0
$904$	5.31868	−	9.21222i	0.176897	−	0.306394i
$905$	6.10953	+	3.52734i	0.203088	+	0.117253i
$906$	−16.7323	+	17.4204i	−0.555894	+	0.578755i
$907$	−19.0122	−	32.9300i	−0.631289	−	1.09342i	−0.987289	−	0.158938i	$-0.949193\pi$
$907$	−19.0122	−	32.9300i	−0.631289	−	1.09342i	0.356000	−	0.934486i	$-0.384140\pi$
$908$	−6.02990			−0.200109
$909$	−0.446786	−	11.0831i	−0.0148190	−	0.367604i
$910$		0			0
$911$	−7.06404	+	4.07842i	−0.234042	+	0.135124i	−0.612435	−	0.790521i	$-0.709810\pi$
$911$	−7.06404	+	4.07842i	−0.234042	+	0.135124i	0.378393	+	0.925645i	$0.376477\pi$
$912$	−2.84763	−	9.83092i	−0.0942946	−	0.325534i
$913$	6.81431	+	3.93424i	0.225521	+	0.130204i
$914$	8.79296	+	5.07662i	0.290845	+	0.167920i
$915$	23.2193	+	5.72288i	0.767607	+	0.189192i
$916$	19.8379	−	11.4534i	0.655462	−	0.378431i
$917$		0			0
$918$	−2.06423	+	10.1123i	−0.0681298	+	0.333756i
$919$	−9.50580			−0.313567			−0.156784	−	0.987633i	$-0.550113\pi$
$919$	−9.50580			−0.313567			−0.156784	+	0.987633i	$0.550113\pi$
$920$	−4.65432	−	8.06152i	−0.153448	−	0.265780i
$921$	3.58837	+	0.884427i	0.118241	+	0.0291429i
$922$	24.1927	+	13.9677i	0.796744	+	0.460000i
$923$	0.555034	−	0.961346i	0.0182692	−	0.0316431i
$924$		0			0
$925$	−2.71493	−	4.70240i	−0.0892665	−	0.154614i
$926$		−	22.8954i		−	0.752389i
$927$	−25.8557	−	40.8862i	−0.849211	−	1.34288i
$928$	−6.36469			−0.208931
$929$	−15.0501	−	26.0675i	−0.493776	−	0.855246i	0.506198	−	0.862417i	$-0.331051\pi$
$929$	−15.0501	−	26.0675i	−0.493776	−	0.855246i	−0.999974	+	0.00717155i	$0.997717\pi$
$930$	8.53909	+	8.20180i	0.280008	+	0.268948i
$931$		0			0
$932$	−25.7885	−	14.8890i	−0.844730	−	0.487705i
$933$	11.4029	+	10.9525i	0.373313	+	0.358568i
$934$	12.8770	−	7.43454i	0.421348	−	0.243265i
$935$			6.93900i			0.226930i
$936$	−4.73774	+	2.99606i	−0.154858	+	0.0979292i
$937$			17.4421i			0.569807i	0.958556	+	0.284904i	$0.0919616\pi$
$937$			17.4421i			0.569807i	−0.958556	+	0.284904i	$0.908038\pi$
$938$		0			0
$939$	−7.21037	−	24.8925i	−0.235302	−	0.812335i
$940$	−9.23958	+	16.0034i	−0.301362	+	0.521974i
$941$	−3.40279	+	5.89380i	−0.110928	+	0.192132i	−0.916145	−	0.400848i	$-0.868716\pi$
$941$	−3.40279	+	5.89380i	−0.110928	+	0.192132i	0.805217	+	0.592980i	$0.202049\pi$
$942$	−2.18019	+	8.84564i	−0.0710344	+	0.288206i
$943$	26.2643	−	15.1637i	0.855284	−	0.493798i
$944$	−5.77821			−0.188065
$945$		0			0
$946$	−24.8910			−0.809276
$947$	47.8503	−	27.6264i	1.55493	−	0.897736i	0.557196	−	0.830381i	$-0.311877\pi$
$947$	47.8503	−	27.6264i	1.55493	−	0.897736i	0.997729	−	0.0673554i	$-0.0214561\pi$
$948$	−4.04007	+	16.3917i	−0.131215	+	0.532377i
$949$	−12.6942	+	21.9870i	−0.412072	+	0.713730i
$950$	−8.76517	+	15.1817i	−0.284380	+	0.492560i
$951$	1.02139	+	3.52616i	0.0331208	+	0.114344i
$952$		0			0
$953$			17.8094i			0.576904i	0.957494	+	0.288452i	$0.0931405\pi$
$953$			17.8094i			0.576904i	−0.957494	+	0.288452i	$0.906859\pi$
$954$	1.43714	+	35.6502i	0.0465291	+	1.15422i
$955$		−	7.28076i		−	0.235600i
$956$	10.5976	−	6.11850i	0.342749	−	0.197886i
$957$	19.4783	+	18.7089i	0.629644	+	0.604773i
$958$	−6.62595	−	3.82550i	−0.214075	−	0.123596i
$959$		0			0
$960$	−1.78127	−	1.71091i	−0.0574903	−	0.0552194i
$961$	−4.00966	−	6.94493i	−0.129344	−	0.224030i
$962$	−3.42001			−0.110266
$963$	−0.760148	+	1.44839i	−0.0244954	+	0.0466737i
$964$			24.2975i			0.782571i
$965$	0.751573	+	1.30176i	0.0241940	+	0.0419052i
$966$		0			0
$967$	19.4677	−	33.7190i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$967$	19.4677	−	33.7190i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$968$	−4.32827	−	2.49893i	−0.139116	−	0.0803185i
$969$	19.7387	+	4.86500i	0.634097	+	0.156286i
$970$	−1.91802	−	3.32211i	−0.0615839	−	0.106666i
$971$	−50.4684			−1.61961			−0.809804	−	0.586700i	$-0.800427\pi$
$971$	−50.4684			−1.61961			−0.809804	+	0.586700i	$0.800427\pi$
$972$	−2.50004	+	15.3867i	−0.0801889	+	0.493528i
$973$		0			0
$974$	−19.0956	+	11.0249i	−0.611863	+	0.353259i
$975$	9.32214	+	2.29763i	0.298547	+	0.0735832i
$976$	−8.38524	−	4.84122i	−0.268405	−	0.154964i
$977$	−30.3086	−	17.4987i	−0.969658	−	0.559832i	−0.0705259	−	0.997510i	$-0.522468\pi$
$977$	−30.3086	−	17.4987i	−0.969658	−	0.559832i	−0.899132	+	0.437678i	$0.855801\pi$
$978$	4.76044	+	16.4345i	0.152222	+	0.525518i
$979$	0.306919	−	0.177200i	0.00980916	−	0.00566332i
$980$		0			0
$981$	16.8154	+	8.82512i	0.536875	+	0.281764i
$982$	−30.4130			−0.970519
$983$	3.48888	+	6.04291i	0.111278	+	0.192739i	0.916286	−	0.400525i	$-0.131172\pi$
$983$	3.48888	+	6.04291i	0.111278	+	0.192739i	−0.805008	+	0.593264i	$0.797839\pi$
$984$	5.57413	−	5.80336i	0.177697	−	0.185004i
$985$	−6.14714	−	3.54906i	−0.195864	−	0.113082i
$986$	6.32093	−	10.9482i	0.201300	−	0.348661i
$987$		0			0
$988$	5.52075	+	9.56223i	0.175639	+	0.304215i
$989$			66.3232i			2.10895i
$990$	0.422152	+	10.4720i	0.0134169	+	0.332824i
$991$	−31.3465			−0.995754			−0.497877	−	0.867248i	$-0.665887\pi$
$991$	−31.3465			−0.995754			−0.497877	+	0.867248i	$0.665887\pi$
$992$	−2.39691	−	4.15157i	−0.0761019	−	0.131812i
$993$	−20.6906	+	5.99327i	−0.656597	+	0.190191i
$994$		0			0
$995$	−1.42164	−	0.820786i	−0.0450691	−	0.0260207i
$996$	1.33124	−	5.40123i	0.0421821	−	0.171144i
$997$	43.1945	−	24.9384i	1.36798	−	0.789806i	0.377313	−	0.926086i	$-0.376848\pi$
$997$	43.1945	−	24.9384i	1.36798	−	0.789806i	0.990670	+	0.136280i	$0.0435148\pi$
$998$		−	25.3664i		−	0.802960i
$999$	−6.30658	+	7.11895i	−0.199531	+	0.225233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.c.293.5	✓	48
3.2	odd	2		2646.2.m.c.881.19		48
7.2	even	3		882.2.t.c.815.15		48
7.3	odd	6		882.2.l.c.509.2		48
7.4	even	3		882.2.l.c.509.11		48
7.5	odd	6		882.2.t.c.815.22		48
7.6	odd	2	inner	882.2.m.c.293.8	yes	48
9.2	odd	6	inner	882.2.m.c.587.8	yes	48
9.7	even	3		2646.2.m.c.1763.20		48
21.2	odd	6		2646.2.t.c.2285.4		48
21.5	even	6		2646.2.t.c.2285.3		48
21.11	odd	6		2646.2.l.c.1097.11		48
21.17	even	6		2646.2.l.c.1097.12		48
21.20	even	2		2646.2.m.c.881.20		48
63.2	odd	6		882.2.l.c.227.14		48
63.11	odd	6		882.2.t.c.803.22		48
63.16	even	3		2646.2.l.c.521.12		48
63.20	even	6	inner	882.2.m.c.587.5	yes	48
63.25	even	3		2646.2.t.c.1979.3		48
63.34	odd	6		2646.2.m.c.1763.19		48
63.38	even	6		882.2.t.c.803.15		48
63.47	even	6		882.2.l.c.227.23		48
63.52	odd	6		2646.2.t.c.1979.4		48
63.61	odd	6		2646.2.l.c.521.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.14		48	63.2	odd	6
882.2.l.c.227.23		48	63.47	even	6
882.2.l.c.509.2		48	7.3	odd	6
882.2.l.c.509.11		48	7.4	even	3
882.2.m.c.293.5	✓	48	1.1	even	1	trivial
882.2.m.c.293.8	yes	48	7.6	odd	2	inner
882.2.m.c.587.5	yes	48	63.20	even	6	inner
882.2.m.c.587.8	yes	48	9.2	odd	6	inner
882.2.t.c.803.15		48	63.38	even	6
882.2.t.c.803.22		48	63.11	odd	6
882.2.t.c.815.15		48	7.2	even	3
882.2.t.c.815.22		48	7.5	odd	6
2646.2.l.c.521.11		48	63.61	odd	6
2646.2.l.c.521.12		48	63.16	even	3
2646.2.l.c.1097.11		48	21.11	odd	6
2646.2.l.c.1097.12		48	21.17	even	6
2646.2.m.c.881.19		48	3.2	odd	2
2646.2.m.c.881.20		48	21.20	even	2
2646.2.m.c.1763.19		48	63.34	odd	6
2646.2.m.c.1763.20		48	9.7	even	3
2646.2.t.c.1979.3		48	63.25	even	3
2646.2.t.c.1979.4		48	63.52	odd	6
2646.2.t.c.2285.3		48	21.5	even	6
2646.2.t.c.2285.4		48	21.2	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.414495 + 1.68172i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.712984 - 1.23492i) q^{5} +(-0.481898 - 1.66366i) q^{6} +1.00000i q^{8} +(-2.65639 - 1.39413i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.414495 + 1.68172i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.712984 - 1.23492i) q^{5} +(-0.481898 - 1.66366i) q^{6} +1.00000i q^{8} +(-2.65639 - 1.39413i) q^{9} +1.42597i q^{10} +(-2.12170 + 1.22496i) q^{11} +(1.24917 + 1.19983i) q^{12} +(-1.61819 - 0.934264i) q^{13} +(1.78127 + 1.71091i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.98625 q^{17} +(2.99757 - 0.120839i) q^{18} -5.90920i q^{19} +(-0.712984 - 1.23492i) q^{20} +(1.22496 - 2.12170i) q^{22} +(-5.65337 - 3.26397i) q^{23} +(-1.68172 - 0.414495i) q^{24} +(1.48331 + 2.56917i) q^{25} +1.86853 q^{26} +(3.44561 - 3.88945i) q^{27} +(-5.51198 + 3.18234i) q^{29} +(-2.39808 - 0.591057i) q^{30} +(-4.15157 - 2.39691i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.18062 - 4.07585i) q^{33} +(-1.72014 + 0.993125i) q^{34} +(-2.53555 + 1.60343i) q^{36} -1.83032 q^{37} +(2.95460 + 5.11752i) q^{38} +(2.24191 - 2.33410i) q^{39} +(1.23492 + 0.712984i) q^{40} +(-2.32289 + 4.02337i) q^{41} +(-5.07994 - 8.79872i) q^{43} +2.44993i q^{44} +(-3.61561 + 2.28644i) q^{45} +6.52794 q^{46} +(-6.47952 - 11.2229i) q^{47} +(1.66366 - 0.481898i) q^{48} +(-2.56917 - 1.48331i) q^{50} +(-0.823292 + 3.34032i) q^{51} +(-1.61819 + 0.934264i) q^{52} +11.8930i q^{53} +(-1.03926 + 5.09116i) q^{54} +3.49352i q^{55} +(9.93764 + 2.44934i) q^{57} +(3.18234 - 5.51198i) q^{58} +(2.88911 - 5.00408i) q^{59} +(2.37233 - 0.687171i) q^{60} +(8.38524 - 4.84122i) q^{61} +4.79382 q^{62} -1.00000 q^{64} +(-2.30749 + 1.33223i) q^{65} +(3.06037 + 2.93949i) q^{66} +(7.60449 - 13.1714i) q^{67} +(0.993125 - 1.72014i) q^{68} +(7.83239 - 8.15450i) q^{69} +0.594087i q^{71} +(1.39413 - 2.65639i) q^{72} -13.5874i q^{73} +(1.58511 - 0.915162i) q^{74} +(-4.93545 + 1.42961i) q^{75} +(-5.11752 - 2.95460i) q^{76} +(-0.774496 + 3.14235i) q^{78} +(4.87348 + 8.44111i) q^{79} -1.42597 q^{80} +(5.11278 + 7.40672i) q^{81} -4.64578i q^{82} +(-1.60586 - 2.78143i) q^{83} +(1.41616 - 2.45287i) q^{85} +(8.79872 + 5.07994i) q^{86} +(-3.06713 - 10.5887i) q^{87} +(-1.22496 - 2.12170i) q^{88} -0.144657 q^{89} +(1.98799 - 3.78792i) q^{90} +(-5.65337 + 3.26397i) q^{92} +(5.75174 - 5.98828i) q^{93} +(11.2229 + 6.47952i) q^{94} +(-7.29742 - 4.21317i) q^{95} +(-1.19983 + 1.24917i) q^{96} +(-2.32972 + 1.34506i) q^{97} +(7.34382 - 0.296046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 32 * q^9	\( 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 32 * q^9 + 48 * q^11 + 48 * q^15 - 24 * q^16 + 16 * q^18 + 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 - 64 * q^39 - 48 * q^50 - 80 * q^57 - 48 * q^64 + 32 * q^72 + 32 * q^78 + 48 * q^79 + 48 * q^85 + 96 * q^86 + 48 * q^92 + 96 * q^93 - 192 * q^95 + 104 * q^99

Introduction

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