LMFDB - Embedded newform 585.2.j.f.406.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.3
Root			$0.500000 - 0.385124i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.f.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30084 + 2.25312i) q^{2} +(-2.38437 + 4.12985i) q^{4} -1.00000 q^{5} +(-1.80084 + 3.11915i) q^{7} -7.20336 q^{8} +O(q^{10})$	\(q+(1.30084 + 2.25312i) q^{2} +(-2.38437 + 4.12985i) q^{4} -1.00000 q^{5} +(-1.80084 + 3.11915i) q^{7} -7.20336 q^{8} +(-1.30084 - 2.25312i) q^{10} +(-2.60168 - 4.50624i) q^{11} +(3.01815 - 1.97250i) q^{13} -9.37041 q^{14} +(-4.60168 - 7.97034i) q^{16} +(-1.46789 + 2.54247i) q^{17} +(-3.38437 + 5.86190i) q^{19} +(2.38437 - 4.12985i) q^{20} +(6.76873 - 11.7238i) q^{22} +(2.76873 + 4.79559i) q^{23} +1.00000 q^{25} +(8.37041 + 4.23435i) q^{26} +(-8.58773 - 14.8744i) q^{28} +(0.916472 + 1.58738i) q^{29} +4.10284 q^{31} +(4.76873 - 8.25969i) q^{32} -7.63798 q^{34} +(1.80084 - 3.11915i) q^{35} +(1.76873 + 3.06354i) q^{37} -17.6101 q^{38} +7.20336 q^{40} +(-2.68521 - 4.65091i) q^{41} +(-1.58353 + 2.74275i) q^{43} +24.8134 q^{44} +(-7.20336 + 12.4766i) q^{46} -3.80504 q^{47} +(-2.98605 - 5.17198i) q^{49} +(1.30084 + 2.25312i) q^{50} +(0.949743 + 17.1677i) q^{52} +5.20336 q^{53} +(2.60168 + 4.50624i) q^{55} +(12.9721 - 22.4683i) q^{56} +(-2.38437 + 4.12985i) q^{58} +(-3.68521 + 6.38297i) q^{59} +(1.71731 - 2.97447i) q^{61} +(5.33714 + 9.24420i) q^{62} +6.40672 q^{64} +(-3.01815 + 1.97250i) q^{65} +(-1.75058 - 3.03210i) q^{67} +(-7.00000 - 12.1244i) q^{68} +9.37041 q^{70} +(-4.85226 + 8.40436i) q^{71} -0.805037 q^{73} +(-4.60168 + 7.97034i) q^{74} +(-16.1391 - 27.9538i) q^{76} +18.7408 q^{77} -4.10284 q^{79} +(4.60168 + 7.97034i) q^{80} +(6.98605 - 12.1002i) q^{82} +11.5375 q^{83} +(1.46789 - 2.54247i) q^{85} -8.23966 q^{86} +(18.7408 + 32.4601i) q^{88} +(4.91647 + 8.51558i) q^{89} +(0.717312 + 12.9662i) q^{91} -26.4067 q^{92} +(-4.94974 - 8.57321i) q^{94} +(3.38437 - 5.86190i) q^{95} +(2.78689 - 4.82703i) q^{97} +(7.76873 - 13.4558i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.30084	+	2.25312i	0.919832	+	1.59320i	0.799668	+	0.600443i	$0.205009\pi$
$2$	1.30084	+	2.25312i	0.919832	+	1.59320i	0.120165	+	0.992754i	$0.461658\pi$
$3$		0			0
$3$		0			0
$4$	−2.38437	+	4.12985i	−1.19218	+	2.06492i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.80084	+	3.11915i	−0.680653	+	1.17893i	0.294128	+	0.955766i	$0.404971\pi$
$7$	−1.80084	+	3.11915i	−0.680653	+	1.17893i	−0.974782	+	0.223160i	$0.928363\pi$
$8$	−7.20336			−2.54677
$9$		0			0
$10$	−1.30084	−	2.25312i	−0.411362	−	0.712499i
$11$	−2.60168	−	4.50624i	−0.784436	−	1.35868i	−0.929336	−	0.369236i	$-0.879619\pi$
$11$	−2.60168	−	4.50624i	−0.784436	−	1.35868i	0.144900	−	0.989446i	$-0.453714\pi$
$12$		0			0
$13$	3.01815	−	1.97250i	0.837085	−	0.547073i
$13$	3.01815	−	1.97250i	0.837085	−	0.547073i
$14$	−9.37041			−2.50435
$15$		0			0
$16$	−4.60168	−	7.97034i	−1.15042	−	1.99259i
$17$	−1.46789	+	2.54247i	−0.356017	+	0.616639i	−0.987291	−	0.158920i	$-0.949199\pi$
$17$	−1.46789	+	2.54247i	−0.356017	+	0.616639i	0.631275	+	0.775559i	$0.282532\pi$
$18$		0			0
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	0.157562	+	0.987509i	$0.449637\pi$
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	−0.933989	+	0.357302i	$0.883697\pi$
$20$	2.38437	−	4.12985i	0.533161	−	0.923461i
$21$		0			0
$22$	6.76873	−	11.7238i	1.44310	−	2.49952i
$23$	2.76873	+	4.79559i	0.577321	+	0.999949i	0.995785	+	0.0917160i	$0.0292352\pi$
$23$	2.76873	+	4.79559i	0.577321	+	0.999949i	−0.418464	+	0.908233i	$0.637431\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	8.37041	+	4.23435i	1.64157	+	0.830424i
$27$		0			0
$28$	−8.58773	−	14.8744i	−1.62293	−	2.81099i
$29$	0.916472	+	1.58738i	0.170185	+	0.294768i	0.938484	−	0.345322i	$-0.112230\pi$
$29$	0.916472	+	1.58738i	0.170185	+	0.294768i	−0.768300	+	0.640090i	$0.778897\pi$
$30$		0			0
$31$	4.10284			0.736893			0.368446	−	0.929649i	$-0.379890\pi$
$31$	4.10284			0.736893			0.368446	+	0.929649i	$0.379890\pi$
$32$	4.76873	−	8.25969i	0.843001	−	1.46012i
$33$		0			0
$34$	−7.63798			−1.30990
$35$	1.80084	−	3.11915i	0.304397	−	0.527232i
$36$		0			0
$37$	1.76873	+	3.06354i	0.290778	+	0.503642i	0.973994	−	0.226574i	$-0.0727525\pi$
$37$	1.76873	+	3.06354i	0.290778	+	0.503642i	−0.683216	+	0.730217i	$0.739419\pi$
$38$	−17.6101			−2.85673
$39$		0			0
$40$	7.20336			1.13895
$41$	−2.68521	−	4.65091i	−0.419359	−	0.726351i	0.576516	−	0.817086i	$-0.304412\pi$
$41$	−2.68521	−	4.65091i	−0.419359	−	0.726351i	−0.995875	+	0.0907349i	$0.971078\pi$
$42$		0			0
$43$	−1.58353	+	2.74275i	−0.241486	+	0.418265i	−0.961138	−	0.276069i	$-0.910968\pi$
$43$	−1.58353	+	2.74275i	−0.241486	+	0.418265i	0.719652	+	0.694335i	$0.244301\pi$
$44$	24.8134			3.74077
$45$		0			0
$46$	−7.20336	+	12.4766i	−1.06208	+	1.83957i
$47$	−3.80504			−0.555022			−0.277511	−	0.960722i	$-0.589509\pi$
$47$	−3.80504			−0.555022			−0.277511	+	0.960722i	$0.589509\pi$
$48$		0			0
$49$	−2.98605	−	5.17198i	−0.426578	−	0.738855i
$50$	1.30084	+	2.25312i	0.183966	+	0.318639i
$51$		0			0
$52$	0.949743	+	17.1677i	0.131706	+	2.38073i
$53$	5.20336			0.714736			0.357368	−	0.933964i	$-0.383674\pi$
$53$	5.20336			0.714736			0.357368	+	0.933964i	$0.383674\pi$
$54$		0			0
$55$	2.60168	+	4.50624i	0.350810	+	0.607621i
$56$	12.9721	−	22.4683i	1.73347	−	3.00246i
$57$		0			0
$58$	−2.38437	+	4.12985i	−0.313083	+	0.542275i
$59$	−3.68521	+	6.38297i	−0.479773	+	0.830991i	−0.999731	−	0.0232007i	$-0.992614\pi$
$59$	−3.68521	+	6.38297i	−0.479773	+	0.830991i	0.519958	+	0.854192i	$0.325948\pi$
$60$		0			0
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	−0.734892	−	0.678185i	$-0.762767\pi$
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	0.954771	+	0.297343i	$0.0961003\pi$
$62$	5.33714	+	9.24420i	0.677818	+	1.17401i
$63$		0			0
$64$	6.40672			0.800840
$65$	−3.01815	+	1.97250i	−0.374356	+	0.244659i
$66$		0			0
$67$	−1.75058	−	3.03210i	−0.213868	−	0.370430i	0.739054	−	0.673646i	$-0.235273\pi$
$67$	−1.75058	−	3.03210i	−0.213868	−	0.370430i	−0.952922	+	0.303216i	$0.901939\pi$
$68$	−7.00000	−	12.1244i	−0.848875	−	1.47029i
$69$		0			0
$70$	9.37041			1.11998
$71$	−4.85226	+	8.40436i	−0.575858	+	0.997415i	0.420090	+	0.907482i	$0.361998\pi$
$71$	−4.85226	+	8.40436i	−0.575858	+	0.997415i	−0.995948	+	0.0899322i	$0.971335\pi$
$72$		0			0
$73$	−0.805037			−0.0942225			−0.0471113	−	0.998890i	$-0.515002\pi$
$73$	−0.805037			−0.0942225			−0.0471113	+	0.998890i	$0.515002\pi$
$74$	−4.60168	+	7.97034i	−0.534934	+	0.926533i
$75$		0			0
$76$	−16.1391	−	27.9538i	−1.85129	−	3.20652i
$77$	18.7408			2.13572
$78$		0			0
$79$	−4.10284			−0.461606			−0.230803	−	0.973000i	$-0.574135\pi$
$79$	−4.10284			−0.461606			−0.230803	+	0.973000i	$0.574135\pi$
$80$	4.60168	+	7.97034i	0.514483	+	0.891111i
$81$		0			0
$82$	6.98605	−	12.1002i	0.771480	−	1.33624i
$83$	11.5375			1.26640			0.633201	−	0.773988i	$-0.281741\pi$
$83$	11.5375			1.26640			0.633201	+	0.773988i	$0.281741\pi$
$84$		0			0
$85$	1.46789	−	2.54247i	0.159216	−	0.275769i
$86$	−8.23966			−0.888506
$87$		0			0
$88$	18.7408	+	32.4601i	1.99778	+	3.46025i
$89$	4.91647	+	8.51558i	0.521145	+	0.902650i	0.999698	+	0.0245908i	$0.00782827\pi$
$89$	4.91647	+	8.51558i	0.521145	+	0.902650i	−0.478553	+	0.878059i	$0.658838\pi$
$90$		0			0
$91$	0.717312	+	12.9662i	0.0751947	+	1.35923i
$92$	−26.4067			−2.75309
$93$		0			0
$94$	−4.94974	−	8.57321i	−0.510527	−	0.884259i
$95$	3.38437	−	5.86190i	0.347229	−	0.601418i
$96$		0			0
$97$	2.78689	−	4.82703i	0.282965	−	0.490110i	−0.689148	−	0.724620i	$-0.742015\pi$
$97$	2.78689	−	4.82703i	0.282965	−	0.490110i	0.972114	+	0.234510i	$0.0753485\pi$
$98$	7.76873	−	13.4558i	0.784761	−	1.35925i
$99$		0			0
$100$	−2.38437	+	4.12985i	−0.238437	+	0.412985i
$101$	1.20336	+	2.08428i	0.119739	+	0.207393i	0.919664	−	0.392706i	$-0.128461\pi$
$101$	1.20336	+	2.08428i	0.119739	+	0.207393i	−0.799925	+	0.600099i	$0.795128\pi$
$102$		0			0
$103$	18.4430			1.81724			0.908622	−	0.417619i	$-0.137135\pi$
$103$	18.4430			1.81724			0.908622	+	0.417619i	$0.137135\pi$
$104$	−21.7408	+	14.2086i	−2.13186	+	1.39327i
$105$		0			0
$106$	6.76873	+	11.7238i	0.657438	+	1.13872i
$107$	5.46789	+	9.47067i	0.528601	+	0.915564i	0.999444	+	0.0333471i	$0.0106167\pi$
$107$	5.46789	+	9.47067i	0.528601	+	0.915564i	−0.470842	+	0.882217i	$0.656050\pi$
$108$		0			0
$109$	13.8692			1.32843			0.664217	−	0.747540i	$-0.268765\pi$
$109$	13.8692			1.32843			0.664217	+	0.747540i	$0.268765\pi$
$110$	−6.76873	+	11.7238i	−0.645373	+	1.11782i
$111$		0			0
$112$	33.1475			3.13215
$113$	−5.60168	+	9.70239i	−0.526962	+	0.912724i	0.472545	+	0.881307i	$0.343336\pi$
$113$	−5.60168	+	9.70239i	−0.526962	+	0.912724i	−0.999506	+	0.0314176i	$0.989998\pi$
$114$		0			0
$115$	−2.76873	−	4.79559i	−0.258186	−	0.447191i
$116$	−8.74083			−0.811565
$117$		0			0
$118$	−19.1755			−1.76524
$119$	−5.28689	−	9.15715i	−0.484648	−	0.839435i
$120$		0			0
$121$	−8.03747	+	13.9213i	−0.730679	+	1.26557i
$122$	8.93579			0.809008
$123$		0			0
$124$	−9.78269	+	16.9441i	−0.878511	+	1.52163i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	1.59748	+	2.76692i	0.141754	+	0.245524i	0.928157	−	0.372189i	$-0.121393\pi$
$127$	1.59748	+	2.76692i	0.141754	+	0.245524i	−0.786403	+	0.617713i	$0.788059\pi$
$128$	−1.20336	−	2.08428i	−0.106363	−	0.184226i
$129$		0			0
$130$	−8.37041	−	4.23435i	−0.734134	−	0.371377i
$131$	4.57377			0.399612			0.199806	−	0.979835i	$-0.435969\pi$
$131$	4.57377			0.399612			0.199806	+	0.979835i	$0.435969\pi$
$132$		0			0
$133$	−12.1894	−	21.1127i	−1.05696	−	1.83070i
$134$	4.55445	−	7.88855i	0.393445	−	0.681467i
$135$		0			0
$136$	10.5738	−	18.3143i	0.906693	−	1.57044i
$137$	5.33714	−	9.24420i	0.455983	−	0.789785i	−0.542761	−	0.839887i	$-0.682621\pi$
$137$	5.33714	−	9.24420i	0.455983	−	0.789785i	0.998744	+	0.0501015i	$0.0159545\pi$
$138$		0			0
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	0.973497	−	0.228700i	$-0.0734474\pi$
$140$	8.58773	+	14.8744i	0.725795	+	1.25711i
$141$		0			0
$142$	−25.2481			−2.11877
$143$	−16.7408	−	8.46870i	−1.39994	−	0.708188i
$144$		0			0
$145$	−0.916472	−	1.58738i	−0.0761089	−	0.131824i
$146$	−1.04722	−	1.81385i	−0.0866689	−	0.150115i
$147$		0			0
$148$	−16.8692			−1.38664
$149$	−4.83294	+	8.37091i	−0.395930	+	0.685771i	−0.993219	−	0.116255i	$-0.962911\pi$
$149$	−4.83294	+	8.37091i	−0.395930	+	0.685771i	0.597289	+	0.802026i	$0.296244\pi$
$150$		0			0
$151$	−18.7129			−1.52284			−0.761418	−	0.648261i	$-0.775496\pi$
$151$	−18.7129			−1.52284			−0.761418	+	0.648261i	$0.775496\pi$
$152$	24.3788	−	42.2253i	1.97738	−	3.42493i
$153$		0			0
$154$	24.3788	+	42.2253i	1.96450	+	3.40261i
$155$	−4.10284			−0.329548
$156$		0			0
$157$	−10.3704			−0.827649			−0.413825	−	0.910357i	$-0.635807\pi$
$157$	−10.3704			−0.827649			−0.413825	+	0.910357i	$0.635807\pi$
$158$	−5.33714	−	9.24420i	−0.424600	−	0.735429i
$159$		0			0
$160$	−4.76873	+	8.25969i	−0.377002	+	0.652986i
$161$	−19.9442			−1.57182
$162$		0			0
$163$	5.73663	−	9.93613i	0.449327	−	0.778258i	−0.549015	−	0.835813i	$-0.684997\pi$
$163$	5.73663	−	9.93613i	0.449327	−	0.778258i	0.998342	+	0.0575546i	$0.0183303\pi$
$164$	25.6101			1.99981
$165$		0			0
$166$	15.0084	+	25.9953i	1.16488	+	2.01763i
$167$	−1.56538	−	2.71131i	−0.121132	−	0.209808i	0.799082	−	0.601222i	$-0.205319\pi$
$167$	−1.56538	−	2.71131i	−0.121132	−	0.209808i	−0.920215	+	0.391414i	$0.871986\pi$
$168$		0			0
$169$	5.21848	−	11.9066i	0.401421	−	0.915893i
$170$	7.63798			0.585806
$171$		0			0
$172$	−7.55142	−	13.0794i	−0.575791	−	0.997298i
$173$	4.13378	−	7.15992i	0.314286	−	0.544359i	−0.665000	−	0.746844i	$-0.731568\pi$
$173$	4.13378	−	7.15992i	0.314286	−	0.544359i	0.979285	+	0.202485i	$0.0649016\pi$
$174$		0			0
$175$	−1.80084	+	3.11915i	−0.136131	+	0.235785i
$176$	−23.9442	+	41.4725i	−1.80486	+	3.12611i
$177$		0			0
$178$	−12.7911	+	22.1548i	−0.958732	+	1.66057i
$179$	−9.22268	−	15.9741i	−0.689335	−	1.19396i	−0.972053	−	0.234760i	$-0.924569\pi$
$179$	−9.22268	−	15.9741i	−0.689335	−	1.19396i	0.282718	−	0.959203i	$-0.408764\pi$
$180$		0			0
$181$	21.1028			1.56856			0.784281	−	0.620406i	$-0.213032\pi$
$181$	21.1028			1.56856			0.784281	+	0.620406i	$0.213032\pi$
$182$	−28.2813	+	18.4832i	−2.09635	+	1.37006i
$183$		0			0
$184$	−19.9442	−	34.5443i	−1.47030	−	2.54664i
$185$	−1.76873	−	3.06354i	−0.130040	−	0.225236i
$186$		0			0
$187$	15.2760			1.11709
$188$	9.07261	−	15.7142i	0.661688	−	1.14608i
$189$		0			0
$190$	17.6101			1.27757
$191$	−4.35110	+	7.53632i	−0.314834	+	0.545309i	−0.979402	−	0.201919i	$-0.935282\pi$
$191$	−4.35110	+	7.53632i	−0.314834	+	0.545309i	0.664568	+	0.747228i	$0.268616\pi$
$192$		0			0
$193$	−9.63378	−	16.6862i	−0.693455	−	1.20110i	−0.970699	−	0.240300i	$-0.922754\pi$
$193$	−9.63378	−	16.6862i	−0.693455	−	1.20110i	0.277244	−	0.960800i	$-0.410579\pi$
$194$	14.5012			1.04112
$195$		0			0
$196$	28.4793			2.03424
$197$	−7.57377	−	13.1182i	−0.539609	−	0.934630i	−0.998925	−	0.0463571i	$-0.985239\pi$
$197$	−7.57377	−	13.1182i	−0.539609	−	0.934630i	0.459316	−	0.888273i	$-0.348095\pi$
$198$		0			0
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	−0.774339	−	0.632771i	$-0.781917\pi$
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	0.935165	+	0.354212i	$0.115251\pi$
$200$	−7.20336			−0.509354
$201$		0			0
$202$	−3.13075	+	5.42262i	−0.220279	+	0.381534i
$203$	−6.60168			−0.463347
$204$		0			0
$205$	2.68521	+	4.65091i	0.187543	+	0.324834i
$206$	23.9914	+	41.5543i	1.67156	+	2.89523i
$207$		0			0
$208$	−29.6101	−	14.9789i	−2.05309	−	1.03860i
$209$	35.2201			2.43623
$210$		0			0
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	0.941636	+	0.336632i	$0.109288\pi$
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	−0.179286	+	0.983797i	$0.557379\pi$
$212$	−12.4067	+	21.4891i	−0.852097	+	1.47587i
$213$		0			0
$214$	−14.2257	+	24.6396i	−0.972449	+	1.68433i
$215$	1.58353	−	2.74275i	0.107996	−	0.187054i
$216$		0			0
$217$	−7.38856	+	12.7974i	−0.501568	+	0.868742i
$218$	18.0417	+	31.2491i	1.22194	+	2.11645i
$219$		0			0
$220$	−24.8134			−1.67292
$221$	0.584693	+	10.5690i	0.0393307	+	0.710946i
$222$		0			0
$223$	3.80504	+	6.59052i	0.254804	+	0.441334i	0.964842	−	0.262829i	$-0.0846557\pi$
$223$	3.80504	+	6.59052i	0.254804	+	0.441334i	−0.710038	+	0.704163i	$0.751322\pi$
$224$	17.1755	+	29.7488i	1.14758	+	1.98767i
$225$		0			0
$226$	−29.1475			−1.93887
$227$	11.6713	−	20.2152i	0.774648	−	1.34173i	−0.160344	−	0.987061i	$-0.551260\pi$
$227$	11.6713	−	20.2152i	0.774648	−	1.34173i	0.934992	−	0.354669i	$-0.115406\pi$
$228$		0			0
$229$	0.824549			0.0544877			0.0272439	−	0.999629i	$-0.491327\pi$
$229$	0.824549			0.0544877			0.0272439	+	0.999629i	$0.491327\pi$
$230$	7.20336	−	12.4766i	0.474975	−	0.822681i
$231$		0			0
$232$	−6.60168	−	11.4344i	−0.433421	−	0.750708i
$233$	13.4044			0.878150			0.439075	−	0.898450i	$-0.355306\pi$
$233$	13.4044			0.878150			0.439075	+	0.898450i	$0.355306\pi$
$234$		0			0
$235$	3.80504			0.248213
$236$	−17.5738	−	30.4387i	−1.14396	−	1.98139i
$237$		0			0
$238$	13.7548	−	23.8240i	0.891590	−	1.54428i
$239$	−12.7966			−0.827746			−0.413873	−	0.910335i	$-0.635824\pi$
$239$	−12.7966			−0.827746			−0.413873	+	0.910335i	$0.635824\pi$
$240$		0			0
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	−0.995027	−	0.0996048i	$-0.968242\pi$
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	0.583774	+	0.811916i	$0.301575\pi$
$242$	−41.8218			−2.68841
$243$		0			0
$244$	8.18940	+	14.1845i	0.524273	+	0.908067i
$245$	2.98605	+	5.17198i	0.190771	+	0.330426i
$246$		0			0
$247$	1.34806	+	24.3678i	0.0857753	+	1.55048i
$248$	−29.5543			−1.87670
$249$		0			0
$250$	−1.30084	−	2.25312i	−0.0822723	−	0.142500i
$251$	−4.20336	+	7.28043i	−0.265314	+	0.459537i	−0.967646	−	0.252313i	$-0.918809\pi$
$251$	−4.20336	+	7.28043i	−0.265314	+	0.459537i	0.702332	+	0.711849i	$0.252142\pi$
$252$		0			0
$253$	14.4067	−	24.9532i	0.905743	−	1.56879i
$254$	−4.15613	+	7.19863i	−0.260779	+	0.451683i
$255$		0			0
$256$	9.53747	−	16.5194i	0.596092	−	1.03246i
$257$	3.06957	+	5.31666i	0.191475	+	0.331644i	0.945739	−	0.324927i	$-0.105340\pi$
$257$	3.06957	+	5.31666i	0.191475	+	0.331644i	−0.754264	+	0.656571i	$0.772006\pi$
$258$		0			0
$259$	−12.7408			−0.791676
$260$	−0.949743	−	17.1677i	−0.0589006	−	1.06469i
$261$		0			0
$262$	5.94974	+	10.3053i	0.367576	+	0.636661i
$263$	−2.36505	−	4.09639i	−0.145835	−	0.252594i	0.783849	−	0.620951i	$-0.213254\pi$
$263$	−2.36505	−	4.09639i	−0.145835	−	0.252594i	−0.929684	+	0.368357i	$0.879920\pi$
$264$		0			0
$265$	−5.20336			−0.319640
$266$	31.7129	−	54.9284i	1.94444	−	3.36788i
$267$		0			0
$268$	16.6961			1.01988
$269$	−2.72151	+	4.71379i	−0.165933	+	0.287405i	−0.936986	−	0.349366i	$-0.886397\pi$
$269$	−2.72151	+	4.71379i	−0.165933	+	0.287405i	0.771053	+	0.636771i	$0.219730\pi$
$270$		0			0
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	−0.935422	−	0.353533i	$-0.884980\pi$
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	0.161543	−	0.986866i	$-0.448353\pi$
$272$	27.0191			1.63827
$273$		0			0
$274$	27.7711			1.67771
$275$	−2.60168	−	4.50624i	−0.156887	−	0.271737i
$276$		0			0
$277$	11.4067	−	19.7570i	0.685363	−	1.18708i	−0.287959	−	0.957643i	$-0.592977\pi$
$277$	11.4067	−	19.7570i	0.685363	−	1.18708i	0.973323	−	0.229441i	$-0.0736899\pi$
$278$	42.0107			2.51964
$279$		0			0
$280$	−12.9721	+	22.4683i	−0.775231	+	1.34274i
$281$	2.16706			0.129276			0.0646378	−	0.997909i	$-0.479411\pi$
$281$	2.16706			0.129276			0.0646378	+	0.997909i	$0.479411\pi$
$282$		0			0
$283$	14.8734	+	25.7616i	0.884135	+	1.53137i	0.846702	+	0.532067i	$0.178584\pi$
$283$	14.8734	+	25.7616i	0.884135	+	1.53137i	0.0374322	+	0.999299i	$0.488082\pi$
$284$	−23.1391	−	40.0782i	−1.37306	−	2.37820i
$285$		0			0
$286$	−2.69613	−	48.7355i	−0.159425	−	2.88179i
$287$	19.3425			1.14175
$288$		0			0
$289$	4.19057	+	7.25828i	0.246504	+	0.426958i
$290$	2.38437	−	4.12985i	0.140015	−	0.242513i
$291$		0			0
$292$	1.91950	−	3.32468i	0.112331	−	0.194562i
$293$	16.5428	−	28.6530i	0.966443	−	1.67393i	0.260754	−	0.965405i	$-0.416029\pi$
$293$	16.5428	−	28.6530i	0.966443	−	1.67393i	0.705688	−	0.708522i	$-0.250638\pi$
$294$		0			0
$295$	3.68521	−	6.38297i	0.214561	−	0.371631i
$296$	−12.7408	−	22.0678i	−0.740546	−	1.28266i
$297$		0			0
$298$	−25.1475			−1.45676
$299$	17.8158	+	9.01248i	1.03031	+	0.521205i
$300$		0			0
$301$	−5.70336	−	9.87851i	−0.328736	−	0.569388i
$302$	−24.3425	−	42.1625i	−1.40075	−	2.42618i
$303$		0			0
$304$	62.2951			3.57287
$305$	−1.71731	+	2.97447i	−0.0983330	+	0.170318i
$306$		0			0
$307$	−14.3704			−0.820163			−0.410081	−	0.912049i	$-0.634500\pi$
$307$	−14.3704			−0.820163			−0.410081	+	0.912049i	$0.634500\pi$
$308$	−44.6850	+	77.3967i	−2.54616	+	4.41009i
$309$		0			0
$310$	−5.33714	−	9.24420i	−0.303129	−	0.525035i
$311$	8.70685			0.493720			0.246860	−	0.969051i	$-0.420601\pi$
$311$	8.70685			0.493720			0.246860	+	0.969051i	$0.420601\pi$
$312$		0			0
$313$	−8.16472			−0.461497			−0.230749	−	0.973013i	$-0.574118\pi$
$313$	−8.16472			−0.461497			−0.230749	+	0.973013i	$0.574118\pi$
$314$	−13.4902	−	23.3658i	−0.761299	−	1.31861i
$315$		0			0
$316$	9.78269	−	16.9441i	0.550319	−	0.953181i
$317$	−13.4090			−0.753127			−0.376564	−	0.926391i	$-0.622894\pi$
$317$	−13.4090			−0.753127			−0.376564	+	0.926391i	$0.622894\pi$
$318$		0			0
$319$	4.76873	−	8.25969i	0.266998	−	0.462454i
$320$	−6.40672			−0.358146
$321$		0			0
$322$	−25.9442	−	44.9366i	−1.44581	−	2.50422i
$323$	−9.93579	−	17.2093i	−0.552842	−	0.957551i
$324$		0			0
$325$	3.01815	−	1.97250i	0.167417	−	0.109415i
$326$	29.8497			1.65322
$327$		0			0
$328$	19.3425	+	33.5022i	1.06801	+	1.84985i
$329$	6.85226	−	11.8685i	0.377777	−	0.654330i
$330$		0			0
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	0.403886	+	0.914809i	$0.367659\pi$
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	−0.994191	+	0.107629i	$0.965674\pi$
$332$	−27.5096	+	47.6480i	−1.50978	+	2.61502i
$333$		0			0
$334$	4.07261	−	7.05396i	0.222843	−	0.385976i
$335$	1.75058	+	3.03210i	0.0956446	+	0.165661i
$336$		0			0
$337$	−7.44535			−0.405574			−0.202787	−	0.979223i	$-0.565000\pi$
$337$	−7.44535			−0.405574			−0.202787	+	0.979223i	$0.565000\pi$
$338$	33.6154	−	3.73074i	1.82844	−	0.202925i
$339$		0			0
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	−10.6743	−	18.4884i	−0.578045	−	1.00120i
$342$		0			0
$343$	−3.70219			−0.199900
$344$	11.4067	−	19.7570i	0.615009	−	1.06523i
$345$		0			0
$346$	21.5096			1.15636
$347$	−12.4733	+	21.6043i	−0.669600	+	1.15978i	0.308417	+	0.951251i	$0.400201\pi$
$347$	−12.4733	+	21.6043i	−0.669600	+	1.15978i	−0.978016	+	0.208529i	$0.933132\pi$
$348$		0			0
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	0.836512	−	0.547949i	$-0.184591\pi$
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	−0.892793	+	0.450466i	$0.851258\pi$
$350$	−9.37041			−0.500870
$351$		0			0
$352$	−49.6269			−2.64512
$353$	9.26990	+	16.0559i	0.493387	+	0.854571i	0.999971	−	0.00761929i	$-0.00242532\pi$
$353$	9.26990	+	16.0559i	0.493387	+	0.854571i	−0.506584	+	0.862191i	$0.669092\pi$
$354$		0			0
$355$	4.85226	−	8.40436i	0.257531	−	0.446057i
$356$	−46.8907			−2.48520
$357$		0			0
$358$	23.9944	−	41.5596i	1.26815	−	2.19649i
$359$	4.75801			0.251118			0.125559	−	0.992086i	$-0.459928\pi$
$359$	4.75801			0.251118			0.125559	+	0.992086i	$0.459928\pi$
$360$		0			0
$361$	−13.4079	−	23.2231i	−0.705678	−	1.22227i
$362$	27.4514	+	47.5472i	1.44281	+	2.49903i
$363$		0			0
$364$	−55.2588	−	27.9538i	−2.89635	−	1.46518i
$365$	0.805037			0.0421376
$366$		0			0
$367$	5.12100	+	8.86983i	0.267314	+	0.463001i	0.968167	−	0.250304i	$-0.0805306\pi$
$367$	5.12100	+	8.86983i	0.267314	+	0.463001i	−0.700853	+	0.713305i	$0.747197\pi$
$368$	25.4817	−	44.1355i	1.32832	−	2.30072i
$369$		0			0
$370$	4.60168	−	7.97034i	0.239230	−	0.414358i
$371$	−9.37041	+	16.2300i	−0.486488	+	0.842621i
$372$		0			0
$373$	11.6701	−	20.2132i	0.604254	−	1.04660i	−0.387915	−	0.921695i	$-0.626804\pi$
$373$	11.6701	−	20.2132i	0.604254	−	1.04660i	0.992169	−	0.124904i	$-0.0398622\pi$
$374$	19.8716	+	34.4186i	1.02753	+	1.77974i
$375$		0			0
$376$	27.4090			1.41351
$377$	5.89716	+	2.98320i	0.303719	+	0.153643i
$378$		0			0
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.805739	+	0.592271i	$0.201769\pi$
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.110052	+	0.993926i	$0.464898\pi$
$380$	16.1391	+	27.9538i	0.827921	+	1.43400i
$381$		0			0
$382$	−22.6403			−1.15838
$383$	−15.3092	+	26.5164i	−0.782265	+	1.35492i	0.148354	+	0.988934i	$0.452603\pi$
$383$	−15.3092	+	26.5164i	−0.782265	+	1.35492i	−0.930619	+	0.365989i	$0.880731\pi$
$384$		0			0
$385$	−18.7408			−0.955121
$386$	25.0640	−	43.4121i	1.27572	−	2.20962i
$387$		0			0
$388$	13.2899	+	23.0188i	0.674693	+	1.16860i
$389$	−25.0191			−1.26852			−0.634260	−	0.773120i	$-0.718695\pi$
$389$	−25.0191			−1.26852			−0.634260	+	0.773120i	$0.718695\pi$
$390$		0			0
$391$	−16.2568			−0.822144
$392$	21.5096	+	37.2557i	1.08640	+	1.88169i
$393$		0			0
$394$	19.7045	−	34.1292i	0.992700	−	1.71941i
$395$	4.10284			0.206437
$396$		0			0
$397$	−5.41647	+	9.38161i	−0.271845	+	0.470849i	−0.969334	−	0.245746i	$-0.920967\pi$
$397$	−5.41647	+	9.38161i	−0.271845	+	0.470849i	0.697489	+	0.716595i	$0.254300\pi$
$398$	11.8050			0.591733
$399$		0			0
$400$	−4.60168	−	7.97034i	−0.230084	−	0.398517i
$401$	−12.2397	−	21.1997i	−0.611220	−	1.05866i	−0.991035	−	0.133601i	$-0.957346\pi$
$401$	−12.2397	−	21.1997i	−0.611220	−	1.05866i	0.379816	−	0.925062i	$-0.375987\pi$
$402$		0			0
$403$	12.3830	−	8.09287i	0.616842	−	0.403134i
$404$	−11.4770			−0.571002
$405$		0			0
$406$	−8.58773	−	14.8744i	−0.426202	−	0.738203i
$407$	9.20336	−	15.9407i	0.456194	−	0.790150i
$408$		0			0
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	0.320140	+	0.947370i	$0.396270\pi$
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	−0.980517	+	0.196436i	$0.937063\pi$
$410$	−6.98605	+	12.1002i	−0.345016	+	0.597586i
$411$		0			0
$412$	−43.9749	+	76.1668i	−2.16649	+	3.75247i
$413$	−13.2729	−	22.9894i	−0.653118	−	1.13123i
$414$		0			0
$415$	−11.5375			−0.566352
$416$	−1.89949	−	34.3353i	−0.0931300	−	1.68343i
$417$		0			0
$418$	45.8158	+	79.3552i	2.24092	+	3.88139i
$419$	7.51815	+	13.0218i	0.367286	+	0.636158i	0.989140	−	0.146975i	$-0.0469538\pi$
$419$	7.51815	+	13.0218i	0.367286	+	0.636158i	−0.621854	+	0.783133i	$0.713620\pi$
$420$		0			0
$421$	−5.90182			−0.287637			−0.143818	−	0.989604i	$-0.545938\pi$
$421$	−5.90182			−0.287637			−0.143818	+	0.989604i	$0.545938\pi$
$422$	−28.8104	+	49.9011i	−1.40247	+	2.42915i
$423$		0			0
$424$	−37.4817			−1.82027
$425$	−1.46789	+	2.54247i	−0.0712034	+	0.123328i
$426$		0			0
$427$	6.18521	+	10.7131i	0.299323	+	0.518443i
$428$	−52.1499			−2.52076
$429$		0			0
$430$	8.23966			0.397352
$431$	19.6743	+	34.0769i	0.947677	+	1.64142i	0.750301	+	0.661097i	$0.229909\pi$
$431$	19.6743	+	34.0769i	0.947677	+	1.64142i	0.197376	+	0.980328i	$0.436758\pi$
$432$		0			0
$433$	−6.20756	+	10.7518i	−0.298316	+	0.516699i	−0.975751	−	0.218884i	$-0.929758\pi$
$433$	−6.20756	+	10.7518i	−0.298316	+	0.516699i	0.677435	+	0.735583i	$0.263092\pi$
$434$	−38.4454			−1.84544
$435$		0			0
$436$	−33.0694	+	57.2778i	−1.58374	+	2.74311i
$437$	−37.4817			−1.79299
$438$		0			0
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	−0.942926	−	0.333003i	$-0.891938\pi$
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	0.183074	−	0.983099i	$-0.441395\pi$
$440$	−18.7408	−	32.4601i	−0.893434	−	1.54747i
$441$		0			0
$442$	−23.0526	+	15.0659i	−1.09650	+	0.716613i
$443$	1.06421			0.0505622			0.0252811	−	0.999680i	$-0.491952\pi$
$443$	1.06421			0.0505622			0.0252811	+	0.999680i	$0.491952\pi$
$444$		0			0
$445$	−4.91647	−	8.51558i	−0.233063	−	0.403677i
$446$	−9.89949	+	17.1464i	−0.468754	+	0.811906i
$447$		0			0
$448$	−11.5375	+	19.9835i	−0.545094	+	0.944131i
$449$	7.70219	−	13.3406i	0.363489	−	0.629581i	−0.625044	−	0.780590i	$-0.714919\pi$
$449$	7.70219	−	13.3406i	0.363489	−	0.629581i	0.988532	+	0.151009i	$0.0482521\pi$
$450$		0			0
$451$	−13.9721	+	24.2004i	−0.657920	+	1.13955i
$452$	−26.7129	−	46.2681i	−1.25647	−	2.17627i
$453$		0			0
$454$	60.7297			2.85019
$455$	−0.717312	−	12.9662i	−0.0336281	−	0.607865i
$456$		0			0
$457$	4.78689	+	8.29113i	0.223921	+	0.387843i	0.955995	−	0.293382i	$-0.0947809\pi$
$457$	4.78689	+	8.29113i	0.223921	+	0.387843i	−0.732074	+	0.681225i	$0.761448\pi$
$458$	1.07261	+	1.85781i	0.0501196	+	0.0868097i
$459$		0			0
$460$	26.4067			1.23122
$461$	8.18637	−	14.1792i	0.381277	−	0.660392i	−0.609968	−	0.792426i	$-0.708818\pi$
$461$	8.18637	−	14.1792i	0.381277	−	0.660392i	0.991245	+	0.132034i	$0.0421510\pi$
$462$		0			0
$463$	−24.6487			−1.14552			−0.572761	−	0.819722i	$-0.694128\pi$
$463$	−24.6487			−1.14552			−0.572761	+	0.819722i	$0.694128\pi$
$464$	8.43462	−	14.6092i	0.391568	−	0.678215i
$465$		0			0
$466$	17.4370	+	30.2017i	0.807751	+	1.39907i
$467$	20.3402			0.941231			0.470616	−	0.882338i	$-0.344032\pi$
$467$	20.3402			0.941231			0.470616	+	0.882338i	$0.344032\pi$
$468$		0			0
$469$	12.6101			0.582279
$470$	4.94974	+	8.57321i	0.228315	+	0.395453i
$471$		0			0
$472$	26.5459	−	45.9788i	1.22187	−	2.11635i
$473$	16.4793			0.757720
$474$		0			0
$475$	−3.38437	+	5.86190i	−0.155285	+	0.268962i
$476$	50.4235			2.31116
$477$		0			0
$478$	−16.6464	−	28.8324i	−0.761388	−	1.31876i
$479$	−0.0811965	−	0.140637i	−0.00370996	−	0.00642585i	0.864164	−	0.503209i	$-0.167848\pi$
$479$	−0.0811965	−	0.140637i	−0.00370996	−	0.00642585i	−0.867874	+	0.496784i	$0.834514\pi$
$480$		0			0
$481$	11.3811	+	5.75739i	0.518935	+	0.262514i
$482$	−33.2201			−1.51314
$483$		0			0
$484$	−38.3286	−	66.3870i	−1.74221	−	3.01759i
$485$	−2.78689	+	4.82703i	−0.126546	+	0.219184i
$486$		0			0
$487$	−1.28152	+	2.21966i	−0.0580713	+	0.100582i	−0.893600	−	0.448865i	$-0.851828\pi$
$487$	−1.28152	+	2.21966i	−0.0580713	+	0.100582i	0.835528	+	0.549447i	$0.185162\pi$
$488$	−12.3704	+	21.4262i	−0.559982	+	0.969918i
$489$		0			0
$490$	−7.76873	+	13.4558i	−0.350956	+	0.607873i
$491$	14.2203	+	24.6304i	0.641755	+	1.11155i	0.985041	+	0.172321i	$0.0551268\pi$
$491$	14.2203	+	24.6304i	0.641755	+	1.11155i	−0.343286	+	0.939231i	$0.611540\pi$
$492$		0			0
$493$	−5.38114			−0.242354
$494$	−53.1499	+	34.7359i	−2.39133	+	1.56284i
$495$		0			0
$496$	−18.8800	−	32.7011i	−0.847736	−	1.46832i
$497$	−17.4763	−	30.2698i	−0.783919	−	1.35779i
$498$		0			0
$499$	−27.8605			−1.24721			−0.623603	−	0.781741i	$-0.714332\pi$
$499$	−27.8605			−1.24721			−0.623603	+	0.781741i	$0.714332\pi$
$500$	2.38437	−	4.12985i	0.106632	−	0.184692i
$501$		0			0
$502$	−21.8716			−0.976176
$503$	15.7129	−	27.2156i	0.700604	−	1.21348i	−0.267650	−	0.963516i	$-0.586247\pi$
$503$	15.7129	−	27.2156i	0.700604	−	1.21348i	0.968255	−	0.249966i	$-0.0804196\pi$
$504$		0			0
$505$	−1.20336	−	2.08428i	−0.0535487	−	0.0927491i
$506$	74.9633			3.33253
$507$		0			0
$508$	−15.2359			−0.675985
$509$	8.11124	+	14.0491i	0.359524	+	0.622715i	0.987881	−	0.155211i	$-0.0496056\pi$
$509$	8.11124	+	14.0491i	0.359524	+	0.622715i	−0.628357	+	0.777925i	$0.716272\pi$
$510$		0			0
$511$	1.44974	−	2.51103i	0.0641329	−	0.111081i
$512$	44.8134			1.98049
$513$		0			0
$514$	−7.98605	+	13.8322i	−0.352249	+	0.610114i
$515$	−18.4430			−0.812697
$516$		0			0
$517$	9.89949	+	17.1464i	0.435379	+	0.754098i
$518$	−16.5738	−	28.7066i	−0.728210	−	1.26130i
$519$		0			0
$520$	21.7408	−	14.2086i	0.953398	−	0.623090i
$521$	20.0386			0.877909			0.438954	−	0.898509i	$-0.355349\pi$
$521$	20.0386			0.877909			0.438954	+	0.898509i	$0.355349\pi$
$522$		0			0
$523$	6.62959	+	11.4828i	0.289892	+	0.502107i	0.973784	−	0.227476i	$-0.0730474\pi$
$523$	6.62959	+	11.4828i	0.289892	+	0.502107i	−0.683892	+	0.729583i	$0.739714\pi$
$524$	−10.9056	+	18.8890i	−0.476411	+	0.825168i
$525$		0			0
$526$	6.15310	−	10.6575i	0.268288	−	0.464688i
$527$	−6.02254	+	10.4314i	−0.262346	+	0.454397i
$528$		0			0
$529$	−3.83178	+	6.63684i	−0.166599	+	0.288558i
$530$	−6.76873	−	11.7238i	−0.294015	−	0.509249i
$531$		0			0
$532$	116.256			5.04034
$533$	−17.2783	−	8.74059i	−0.748406	−	0.378597i
$534$		0			0
$535$	−5.46789	−	9.47067i	−0.236398	−	0.409453i
$536$	12.6101	+	21.8413i	0.544672	+	0.943400i
$537$		0			0
$538$	−14.1610			−0.610524
$539$	−15.5375	+	26.9117i	−0.669246	+	1.15917i
$540$		0			0
$541$	35.6850			1.53422			0.767109	−	0.641516i	$-0.221694\pi$
$541$	35.6850			1.53422			0.767109	+	0.641516i	$0.221694\pi$
$542$	33.1445	−	57.4080i	1.42368	−	2.46588i
$543$		0			0
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	−13.8692			−0.594093
$546$		0			0
$547$	−0.627256			−0.0268195			−0.0134098	−	0.999910i	$-0.504269\pi$
$547$	−0.627256			−0.0268195			−0.0134098	+	0.999910i	$0.504269\pi$
$548$	25.4514	+	44.0831i	1.08723	+	1.88314i
$549$		0			0
$550$	6.76873	−	11.7238i	0.288620	−	0.499904i
$551$	−12.4067			−0.528544
$552$		0			0
$553$	7.38856	−	12.7974i	0.314194	−	0.544200i
$554$	59.3532			2.52168
$555$		0			0
$556$	38.5017	+	66.6869i	1.63283	+	2.82815i
$557$	4.60401	+	7.97438i	0.195078	+	0.337885i	0.946926	−	0.321451i	$-0.104171\pi$
$557$	4.60401	+	7.97438i	0.195078	+	0.337885i	−0.751848	+	0.659337i	$0.770837\pi$
$558$		0			0
$559$	0.630752	+	11.4015i	0.0266780	+	0.482234i
$560$	−33.1475			−1.40074
$561$		0			0
$562$	2.81899	+	4.88264i	0.118912	+	0.205962i
$563$	1.33411	−	2.31075i	0.0562260	−	0.0973864i	−0.836542	−	0.547902i	$-0.815427\pi$
$563$	1.33411	−	2.31075i	0.0562260	−	0.0973864i	0.892768	+	0.450516i	$0.148760\pi$
$564$		0			0
$565$	5.60168	−	9.70239i	0.235664	−	0.408183i
$566$	−38.6959	+	67.0233i	−1.62651	+	2.81720i
$567$		0			0
$568$	34.9526	−	60.5396i	1.46658	−	2.54019i
$569$	−13.0919	−	22.6759i	−0.548842	−	0.950622i	−0.998354	−	0.0573480i	$-0.981736\pi$
$569$	−13.0919	−	22.6759i	−0.548842	−	0.950622i	0.449512	−	0.893274i	$-0.351598\pi$
$570$		0			0
$571$	−19.2481			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$571$	−19.2481			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$572$	74.8907	−	48.9445i	3.13134	−	2.04647i
$573$		0			0
$574$	25.1615	+	43.5810i	1.05022	+	1.81904i
$575$	2.76873	+	4.79559i	0.115464	+	0.199990i
$576$		0			0
$577$	23.8716			0.993787			0.496893	−	0.867812i	$-0.334474\pi$
$577$	23.8716			0.993787			0.496893	+	0.867812i	$0.334474\pi$
$578$	−10.9025	+	18.8837i	−0.453485	+	0.785459i
$579$		0			0
$580$	8.74083			0.362943
$581$	−20.7771	+	35.9870i	−0.861981	+	1.49299i
$582$		0			0
$583$	−13.5375	−	23.4476i	−0.560665	−	0.971100i
$584$	5.79897			0.239963
$585$		0			0
$586$	86.0783			3.55586
$587$	14.4377	+	25.0068i	0.595906	+	1.03214i	0.993418	+	0.114542i	$0.0365402\pi$
$587$	14.4377	+	25.0068i	0.595906	+	1.03214i	−0.397513	+	0.917597i	$0.630126\pi$
$588$		0			0
$589$	−13.8855	+	24.0504i	−0.572143	+	0.990981i
$590$	19.1755			0.789441
$591$		0			0
$592$	16.2783	−	28.1948i	0.669034	−	1.15880i
$593$	8.74083			0.358943			0.179471	−	0.983763i	$-0.442561\pi$
$593$	8.74083			0.358943			0.179471	+	0.983763i	$0.442561\pi$
$594$		0			0
$595$	5.28689	+	9.15715i	0.216741	+	0.375407i
$596$	−23.0470	−	39.9186i	−0.944043	−	1.63513i
$597$		0			0
$598$	2.86925	+	51.8649i	0.117332	+	2.12091i
$599$	−21.5929			−0.882262			−0.441131	−	0.897443i	$-0.645423\pi$
$599$	−21.5929			−0.882262			−0.441131	+	0.897443i	$0.645423\pi$
$600$		0			0
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	−0.990036	−	0.140818i	$-0.955027\pi$
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	0.373066	−	0.927805i	$-0.378306\pi$
$602$	14.8383	−	25.7007i	0.604764	−	1.04748i
$603$		0			0
$604$	44.6185	−	77.2815i	1.81550	−	3.14454i
$605$	8.03747	−	13.9213i	0.326770	−	0.565981i
$606$		0			0
$607$	11.2536	−	19.4918i	0.456770	−	0.791149i	−0.542018	−	0.840367i	$-0.682340\pi$
$607$	11.2536	−	19.4918i	0.456770	−	0.791149i	0.998788	+	0.0492178i	$0.0156729\pi$
$608$	32.2783	+	55.9076i	1.30906	+	2.26735i
$609$		0			0
$610$	−8.93579			−0.361800
$611$	−11.4842	+	7.50544i	−0.464600	+	0.303638i
$612$		0			0
$613$	−9.38856	−	16.2615i	−0.379201	−	0.656795i	0.611746	−	0.791055i	$-0.290468\pi$
$613$	−9.38856	−	16.2615i	−0.379201	−	0.656795i	−0.990946	+	0.134260i	$0.957134\pi$
$614$	−18.6936	−	32.3783i	−0.754412	−	1.30668i
$615$		0			0
$616$	−134.997			−5.43918
$617$	−1.80504	+	3.12642i	−0.0726681	+	0.125865i	−0.900070	−	0.435746i	$-0.856485\pi$
$617$	−1.80504	+	3.12642i	−0.0726681	+	0.125865i	0.827402	+	0.561610i	$0.189818\pi$
$618$		0			0
$619$	2.87158			0.115419			0.0577093	−	0.998333i	$-0.481620\pi$
$619$	2.87158			0.115419			0.0577093	+	0.998333i	$0.481620\pi$
$620$	9.78269	−	16.9441i	0.392882	−	0.680492i
$621$		0			0
$622$	11.3262	+	19.6176i	0.454140	+	0.786594i
$623$	−35.4151			−1.41888
$624$		0			0
$625$	1.00000			0.0400000
$626$	−10.6210	−	18.3961i	−0.424500	−	0.735256i
$627$		0			0
$628$	24.7269	−	42.8282i	0.986710	−	1.70903i
$629$	−10.3853			−0.414088
$630$		0			0
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	−0.984086	−	0.177691i	$-0.943137\pi$
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	0.645928	+	0.763398i	$0.276471\pi$
$632$	29.5543			1.17561
$633$		0			0
$634$	−17.4430	−	30.2122i	−0.692751	−	1.19988i
$635$	−1.59748	−	2.76692i	−0.0633941	−	0.109802i
$636$		0			0
$637$	−19.2141	−	9.71985i	−0.761290	−	0.385115i
$638$	24.8134			0.982373
$639$		0			0
$640$	1.20336	+	2.08428i	0.0475669	+	0.0823883i
$641$	−8.30620	+	14.3868i	−0.328075	+	0.568243i	−0.982130	−	0.188204i	$-0.939733\pi$
$641$	−8.30620	+	14.3868i	−0.328075	+	0.568243i	0.654055	+	0.756447i	$0.273067\pi$
$642$		0			0
$643$	−22.6701	+	39.2657i	−0.894021	+	1.54849i	−0.0590094	+	0.998257i	$0.518794\pi$
$643$	−22.6701	+	39.2657i	−0.894021	+	1.54849i	−0.835012	+	0.550232i	$0.814539\pi$
$644$	47.5543	−	82.3664i	1.87390	−	3.24569i
$645$		0			0
$646$	25.8497	−	44.7731i	1.01704	−	1.76157i
$647$	2.43462	+	4.21689i	0.0957149	+	0.165783i	0.909907	−	0.414813i	$-0.136153\pi$
$647$	2.43462	+	4.21689i	0.0957149	+	0.165783i	−0.814192	+	0.580596i	$0.802820\pi$
$648$		0			0
$649$	38.3509			1.50540
$650$	8.37041	+	4.23435i	0.328315	+	0.166085i
$651$		0			0
$652$	27.3565	+	47.3828i	1.07136	+	1.85565i
$653$	9.63495	+	16.6882i	0.377045	+	0.653061i	0.990631	−	0.136567i	$-0.0436070\pi$
$653$	9.63495	+	16.6882i	0.377045	+	0.653061i	−0.613586	+	0.789628i	$0.710274\pi$
$654$		0			0
$655$	−4.57377			−0.178712
$656$	−24.7129	+	42.8040i	−0.964877	+	1.67122i
$657$		0			0
$658$	35.6548			1.38997
$659$	0.167055	−	0.289348i	0.00650755	−	0.0112714i	−0.862753	−	0.505625i	$-0.831262\pi$
$659$	0.167055	−	0.289348i	0.00650755	−	0.0112714i	0.869261	+	0.494354i	$0.164595\pi$
$660$		0			0
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	0.967777	−	0.251808i	$-0.0810253\pi$
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	−0.701961	+	0.712215i	$0.747692\pi$
$662$	−55.8823			−2.17193
$663$		0			0
$664$	−83.1085			−3.22524
$665$	12.1894	+	21.1127i	0.472685	+	0.818714i
$666$		0			0
$667$	−5.07494	+	8.79005i	−0.196502	+	0.340352i
$668$	14.9297			0.577648
$669$		0			0
$670$	−4.55445	+	7.88855i	−0.175954	+	0.304761i
$671$	−17.8716			−0.689925
$672$		0			0
$673$	10.9400	+	18.9486i	0.421706	+	0.730415i	0.996106	−	0.0881587i	$-0.0280983\pi$
$673$	10.9400	+	18.9486i	0.421706	+	0.730415i	−0.574401	+	0.818574i	$0.694765\pi$
$674$	−9.68521	−	16.7753i	−0.373060	−	0.646159i
$675$		0			0
$676$	36.7297	+	49.9412i	1.41268	+	1.92082i
$677$	17.0749			0.656243			0.328122	−	0.944636i	$-0.393584\pi$
$677$	17.0749			0.656243			0.328122	+	0.944636i	$0.393584\pi$
$678$		0			0
$679$	10.0375	+	17.3854i	0.385203	+	0.667191i
$680$	−10.5738	+	18.3143i	−0.405486	+	0.702322i
$681$		0			0
$682$	27.7711	−	48.1009i	1.06341	−	1.84188i
$683$	−13.3651	+	23.1489i	−0.511399	+	0.885770i	0.488513	+	0.872556i	$0.337539\pi$
$683$	−13.3651	+	23.1489i	−0.511399	+	0.885770i	−0.999913	+	0.0132133i	$0.995794\pi$
$684$		0			0
$685$	−5.33714	+	9.24420i	−0.203922	+	0.353203i
$686$	−4.81596	−	8.34149i	−0.183874	−	0.318479i
$687$		0			0
$688$	29.1475			1.11124
$689$	15.7045	−	10.2636i	0.598295	−	0.391013i
$690$		0			0
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.788955	−	0.614451i	$-0.789378\pi$
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.137653	−	0.990481i	$-0.543956\pi$
$692$	19.7129	+	34.1438i	0.749373	+	1.29795i
$693$		0			0
$694$	−64.9028			−2.46368
$695$	−8.07377	+	13.9842i	−0.306256	+	0.530450i
$696$		0			0
$697$	15.7664			0.597195
$698$	2.73546	−	4.73796i	0.103539	−	0.179334i
$699$		0			0
$700$	−8.58773	−	14.8744i	−0.324586	−	0.562199i
$701$	−22.9419			−0.866502			−0.433251	−	0.901273i	$-0.642634\pi$
$701$	−22.9419			−0.866502			−0.433251	+	0.901273i	$0.642634\pi$
$702$		0			0
$703$	−23.9442			−0.903072
$704$	−16.6682	−	28.8702i	−0.628207	−	1.08809i
$705$		0			0
$706$	−24.1173	+	41.7724i	−0.907667	+	1.57212i
$707$	−8.66822			−0.326002
$708$		0			0
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	−0.791109	−	0.611675i	$-0.790496\pi$
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	0.925281	+	0.379283i	$0.123829\pi$
$710$	25.2481			0.947543
$711$		0			0
$712$	−35.4151	−	61.3408i	−1.32724	−	2.29884i
$713$	11.3597	+	19.6756i	0.425424	+	0.736855i
$714$		0			0
$715$	16.7408	+	8.46870i	0.626071	+	0.316711i
$716$	87.9610			3.28726
$717$		0			0
$718$	6.18940	+	10.7204i	0.230987	+	0.400080i
$719$	20.9891	−	36.3542i	0.782761	−	1.35578i	−0.147567	−	0.989052i	$-0.547144\pi$
$719$	20.9891	−	36.3542i	0.782761	−	1.35578i	0.930328	−	0.366729i	$-0.119522\pi$
$720$		0			0
$721$	−33.2129	+	57.5265i	−1.23691	+	2.14240i
$722$	34.8830	−	60.4191i	1.29821	−	2.24857i
$723$		0			0
$724$	−50.3169	+	87.1515i	−1.87001	+	3.23896i
$725$	0.916472	+	1.58738i	0.0340369	+	0.0589537i
$726$		0			0
$727$	−11.4965			−0.426382			−0.213191	−	0.977011i	$-0.568386\pi$
$727$	−11.4965			−0.426382			−0.213191	+	0.977011i	$0.568386\pi$
$728$	−5.16706	−	93.4003i	−0.191504	−	3.46164i
$729$		0			0
$730$	1.04722	+	1.81385i	0.0387595	+	0.0671335i
$731$	−4.64890	−	8.05214i	−0.171946	−	0.297819i
$732$		0			0
$733$	46.1136			1.70324			0.851622	−	0.524157i	$-0.175619\pi$
$733$	46.1136			1.70324			0.851622	+	0.524157i	$0.175619\pi$
$734$	−13.3232	+	23.0764i	−0.491768	+	0.851767i
$735$		0			0
$736$	52.8134			1.94673
$737$	−9.10891	+	15.7771i	−0.335531	+	0.581157i
$738$		0			0
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	0.952820	−	0.303534i	$-0.0981667\pi$
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	−0.739279	+	0.673400i	$0.764833\pi$
$740$	16.8692			0.620126
$741$		0			0
$742$	−48.7576			−1.78995
$743$	6.70756	+	11.6178i	0.246076	+	0.426217i	0.962434	−	0.271517i	$-0.0875253\pi$
$743$	6.70756	+	11.6178i	0.246076	+	0.426217i	−0.716357	+	0.697734i	$0.754192\pi$
$744$		0			0
$745$	4.83294	−	8.37091i	0.177065	−	0.306686i
$746$	60.7236			2.22325
$747$		0			0
$748$	−36.4235	+	63.0874i	−1.33178	+	2.30670i
$749$	−39.3872			−1.43918
$750$		0			0
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	−0.915648	−	0.401981i	$-0.868322\pi$
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	0.109698	−	0.993965i	$-0.465012\pi$
$752$	17.5096	+	30.3274i	0.638508	+	1.10593i
$753$		0			0
$754$	0.949743	+	17.1677i	0.0345876	+	0.625210i
$755$	18.7129			0.681033
$756$		0			0
$757$	−3.98605	−	6.90403i	−0.144875	−	0.250931i	0.784451	−	0.620191i	$-0.212945\pi$
$757$	−3.98605	−	6.90403i	−0.144875	−	0.250931i	−0.929326	+	0.369259i	$0.879611\pi$
$758$	−46.3842	+	80.3397i	−1.68475	+	2.91807i
$759$		0			0
$760$	−24.3788	+	42.2253i	−0.884312	+	1.53167i
$761$	6.83294	−	11.8350i	0.247694	−	0.429019i	−0.715192	−	0.698928i	$-0.753661\pi$
$761$	6.83294	−	11.8350i	0.247694	−	0.429019i	0.962886	+	0.269910i	$0.0869939\pi$
$762$		0			0
$763$	−24.9763	+	43.2602i	−0.904202	+	1.56612i
$764$	−20.7492	−	35.9387i	−0.750681	−	1.30022i
$765$		0			0
$766$	−79.6594			−2.87821
$767$	1.46789	+	26.5338i	0.0530026	+	0.958081i
$768$		0			0
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	0.678194	−	0.734883i	$-0.262763\pi$
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	−0.975524	+	0.219892i	$0.929430\pi$
$770$	−24.3788	−	42.2253i	−0.878551	−	1.52170i
$771$		0			0
$772$	91.8819			3.30690
$773$	−22.8521	+	39.5809i	−0.821932	+	1.42363i	0.0823101	+	0.996607i	$0.473770\pi$
$773$	−22.8521	+	39.5809i	−0.821932	+	1.42363i	−0.904242	+	0.427021i	$0.859563\pi$
$774$		0			0
$775$	4.10284			0.147379
$776$	−20.0749	+	34.7708i	−0.720648	+	1.24820i
$777$		0			0
$778$	−32.5459	−	56.3711i	−1.16683	−	2.02100i
$779$	36.3509			1.30241
$780$		0			0
$781$	50.4961			1.80689
$782$	−21.1475	−	36.6286i	−0.756235	−	1.30984i
$783$		0			0
$784$	−27.4817	+	47.5996i	−0.981488	+	1.69999i
$785$	10.3704			0.370136
$786$		0			0
$787$	24.4109	−	42.2809i	0.870155	−	1.50715i	0.00831938	−	0.999965i	$-0.497352\pi$
$787$	24.4109	−	42.2809i	0.870155	−	1.50715i	0.861836	−	0.507187i	$-0.169315\pi$
$788$	72.2346			2.57325
$789$		0			0
$790$	5.33714	+	9.24420i	0.189887	+	0.328894i
$791$	−20.1755	−	34.9449i	−0.717356	−	1.24250i
$792$		0			0
$793$	−0.684041	−	12.3648i	−0.0242910	−	0.439087i
$794$	−28.1838			−1.00021
$795$		0			0
$796$	10.8190	+	18.7390i	0.383469	+	0.664188i
$797$	6.87461	−	11.9072i	0.243511	−	0.421774i	−0.718201	−	0.695836i	$-0.755034\pi$
$797$	6.87461	−	11.9072i	0.243511	−	0.421774i	0.961712	+	0.274062i	$0.0883674\pi$
$798$		0			0
$799$	5.58539	−	9.67419i	0.197597	−	0.342248i
$800$	4.76873	−	8.25969i	0.168600	−	0.292024i
$801$		0			0
$802$	31.8437	−	55.1549i	1.12444	−	1.94759i
$803$	2.09445	+	3.62769i	0.0739115	+	0.128018i
$804$		0			0
$805$	19.9442			0.702940
$806$	34.3425	+	17.3729i	1.20966	+	0.611934i
$807$		0			0
$808$	−8.66822	−	15.0138i	−0.304947	−	0.528184i
$809$	10.1671	+	17.6099i	0.357455	+	0.619130i	0.987535	−	0.157400i	$-0.0503113\pi$
$809$	10.1671	+	17.6099i	0.357455	+	0.619130i	−0.630080	+	0.776530i	$0.716978\pi$
$810$		0			0
$811$	22.4817			0.789438			0.394719	−	0.918802i	$-0.370842\pi$
$811$	22.4817			0.789438			0.394719	+	0.918802i	$0.370842\pi$
$812$	15.7408	−	27.2639i	0.552395	−	0.956776i
$813$		0			0
$814$	47.8884			1.67849
$815$	−5.73663	+	9.93613i	−0.200945	+	0.348048i
$816$		0			0
$817$	−10.7185	−	18.5649i	−0.374992	−	0.649505i
$818$	−69.4924			−2.42974
$819$		0			0
$820$	−25.6101			−0.894343
$821$	−16.3039	−	28.2391i	−0.569009	−	0.985553i	−0.996664	−	0.0816107i	$-0.973994\pi$
$821$	−16.3039	−	28.2391i	−0.569009	−	0.985553i	0.427655	−	0.903942i	$-0.359340\pi$
$822$		0			0
$823$	−16.7408	+	28.9960i	−0.583549	+	1.01074i	0.411506	+	0.911407i	$0.365003\pi$
$823$	−16.7408	+	28.9960i	−0.583549	+	1.01074i	−0.995055	+	0.0993287i	$0.968330\pi$
$824$	−132.852			−4.62811
$825$		0			0
$826$	34.5319	−	59.8110i	1.20152	−	2.08109i
$827$	51.0298			1.77448			0.887241	−	0.461306i	$-0.152619\pi$
$827$	51.0298			1.77448			0.887241	+	0.461306i	$0.152619\pi$
$828$		0			0
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	0.621203	−	0.783650i	$-0.286644\pi$
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	−0.989262	+	0.146153i	$0.953311\pi$
$830$	−15.0084	−	25.9953i	−0.520949	−	0.902310i
$831$		0			0
$832$	19.3364	−	12.6373i	0.670370	−	0.438118i
$833$	17.5328			0.607476
$834$		0			0
$835$	1.56538	+	2.71131i	0.0541721	+	0.0938288i
$836$	−83.9778	+	145.454i	−2.90443	+	5.03062i
$837$		0			0
$838$	−19.5598	+	33.8786i	−0.675683	+	1.17032i
$839$	26.9419	−	46.6647i	0.930136	−	1.61104i	0.147051	−	0.989129i	$-0.453022\pi$
$839$	26.9419	−	46.6647i	0.930136	−	1.61104i	0.783086	−	0.621914i	$-0.213645\pi$
$840$		0			0
$841$	12.8202	−	22.2052i	0.442074	−	0.765695i
$842$	−7.67732	−	13.2975i	−0.264578	−	0.458262i
$843$		0			0
$844$	−105.616			−3.63544
$845$	−5.21848	+	11.9066i	−0.179521	+	0.409600i
$846$		0			0
$847$	−28.9484	−	50.1401i	−0.994678	−	1.72283i
$848$	−23.9442	−	41.4725i	−0.822247	−	1.42417i
$849$		0			0
$850$	−7.63798			−0.261981
$851$	−9.79431	+	16.9642i	−0.335745	+	0.581527i
$852$		0			0
$853$	−4.06421			−0.139156			−0.0695780	−	0.997577i	$-0.522165\pi$
$853$	−4.06421			−0.139156			−0.0695780	+	0.997577i	$0.522165\pi$
$854$	−16.0919	+	27.8720i	−0.550654	+	0.953761i
$855$		0			0
$856$	−39.3872	−	68.2206i	−1.34623	−	2.33173i
$857$	39.2141			1.33953			0.669764	−	0.742574i	$-0.266395\pi$
$857$	39.2141			1.33953			0.669764	+	0.742574i	$0.266395\pi$
$858$		0			0
$859$	−5.64031			−0.192445			−0.0962225	−	0.995360i	$-0.530676\pi$
$859$	−5.64031			−0.192445			−0.0962225	+	0.995360i	$0.530676\pi$
$860$	7.55142	+	13.0794i	0.257501	+	0.446005i
$861$		0			0
$862$	−51.1862	+	88.6571i	−1.74341	+	3.01967i
$863$	9.66589			0.329031			0.164515	−	0.986375i	$-0.447394\pi$
$863$	9.66589			0.329031			0.164515	+	0.986375i	$0.447394\pi$
$864$		0			0
$865$	−4.13378	+	7.15992i	−0.140553	+	0.243445i
$866$	−32.3001			−1.09760
$867$		0			0
$868$	−35.2341	−	61.0273i	−1.19592	−	2.07140i
$869$	10.6743	+	18.4884i	0.362100	+	0.627176i
$870$		0			0
$871$	−11.2643	−	5.69831i	−0.381678	−	0.193080i
$872$	−99.9052			−3.38322
$873$		0			0
$874$	−48.7576	−	84.4507i	−1.64925	−	2.85659i
$875$	1.80084	−	3.11915i	0.0608795	−	0.105446i
$876$		0			0
$877$	−7.93579	+	13.7452i	−0.267973	+	0.464142i	−0.968338	−	0.249642i	$-0.919687\pi$
$877$	−7.93579	+	13.7452i	−0.267973	+	0.464142i	0.700366	+	0.713784i	$0.253020\pi$
$878$	41.4205	−	71.7424i	1.39787	−	2.42119i
$879$		0			0
$880$	23.9442	−	41.4725i	0.807158	−	1.39804i
$881$	−14.6017	−	25.2909i	−0.491943	−	0.852070i	0.508014	−	0.861349i	$-0.330380\pi$
$881$	−14.6017	−	25.2909i	−0.491943	−	0.852070i	−0.999957	+	0.00927849i	$0.997047\pi$
$882$		0			0
$883$	30.4598			1.02505			0.512527	−	0.858671i	$-0.328709\pi$
$883$	30.4598			1.02505			0.512527	+	0.858671i	$0.328709\pi$
$884$	−45.0424	−	22.7856i	−1.51494	−	0.766364i
$885$		0			0
$886$	1.38437	+	2.39779i	0.0465087	+	0.0805555i
$887$	5.79967	+	10.0453i	0.194734	+	0.337289i	0.946813	−	0.321783i	$-0.104282\pi$
$887$	5.79967	+	10.0453i	0.194734	+	0.337289i	−0.752079	+	0.659073i	$0.770949\pi$
$888$		0			0
$889$	−11.5072			−0.385940
$890$	12.7911	−	22.1548i	0.428758	−	0.742631i
$891$		0			0
$892$	−36.2904			−1.21509
$893$	12.8776	−	22.3047i	0.430934	−	0.746399i
$894$		0			0
$895$	9.22268	+	15.9741i	0.308280	+	0.533957i
$896$	8.66822			0.289585
$897$		0			0
$898$	40.0773			1.33740
$899$	3.76014	+	6.51276i	0.125408	+	0.217213i
$900$		0			0
$901$	−7.63798	+	13.2294i	−0.254458	+	0.440734i
$902$	−72.7018			−2.42071
$903$		0			0
$904$	40.3509	−	69.8898i	1.34205	−	2.32450i
$905$	−21.1028			−0.701482
$906$		0			0
$907$	−21.4593	−	37.1686i	−0.712545	−	1.23416i	−0.963899	−	0.266268i	$-0.914209\pi$
$907$	−21.4593	−	37.1686i	−0.712545	−	1.23416i	0.251354	−	0.967895i	$-0.419124\pi$
$908$	55.6571	+	96.4009i	1.84705	+	3.19918i
$909$		0			0
$910$	28.2813	−	18.4832i	0.937517	−	0.612711i
$911$	−42.0726			−1.39393			−0.696964	−	0.717106i	$-0.745466\pi$
$911$	−42.0726			−1.39393			−0.696964	+	0.717106i	$0.745466\pi$
$912$		0			0
$913$	−30.0168	−	51.9906i	−0.993411	−	1.72064i
$914$	−12.4539	+	21.5709i	−0.411940	+	0.713501i
$915$		0			0
$916$	−1.96603	+	3.40526i	−0.0649594	+	0.112513i
$917$	−8.23663	+	14.2663i	−0.271997	+	0.471113i
$918$		0			0
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	0.339127	+	0.940741i	$0.389868\pi$
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	−0.984269	+	0.176678i	$0.943465\pi$
$920$	19.9442	+	34.5443i	0.657540	+	1.13889i
$921$		0			0
$922$	42.5966			1.40285
$923$	1.93276	+	34.9367i	0.0636175	+	1.14996i
$924$		0			0
$925$	1.76873	+	3.06354i	0.0581556	+	0.100728i
$926$	−32.0640	−	55.5365i	−1.05369	−	1.82504i
$927$		0			0
$928$	17.4817			0.573863
$929$	5.23127	−	9.06082i	0.171632	−	0.297276i	−0.767358	−	0.641218i	$-0.778429\pi$
$929$	5.23127	−	9.06082i	0.171632	−	0.297276i	0.938991	+	0.343943i	$0.111763\pi$
$930$		0			0
$931$	40.4235			1.32483
$932$	−31.9610	+	55.3580i	−1.04692	+	1.81331i
$933$		0			0
$934$	26.4593	+	45.8289i	0.865775	+	1.49957i
$935$	−15.2760			−0.499577
$936$		0			0
$937$	39.6269			1.29455			0.647277	−	0.762255i	$-0.275908\pi$
$937$	39.6269			1.29455			0.647277	+	0.762255i	$0.275908\pi$
$938$	16.4037	+	28.4120i	0.535599	+	0.927685i
$939$		0			0
$940$	−9.07261	+	15.7142i	−0.295916	+	0.512541i
$941$	−15.3146			−0.499242			−0.249621	−	0.968344i	$-0.580306\pi$
$941$	−15.3146			−0.499242			−0.249621	+	0.968344i	$0.580306\pi$
$942$		0			0
$943$	14.8692	−	25.7543i	0.484209	−	0.838675i
$944$	67.8326			2.20776
$945$		0			0
$946$	21.4370	+	37.1299i	0.696976	+	1.20720i
$947$	−16.6433	−	28.8271i	−0.540836	−	0.936756i	−0.998856	−	0.0478138i	$-0.984775\pi$
$947$	−16.6433	−	28.8271i	−0.540836	−	0.936756i	0.458020	−	0.888942i	$-0.348559\pi$
$948$		0			0
$949$	−2.42972	+	1.58794i	−0.0788722	+	0.0515466i
$950$	−17.6101			−0.571346
$951$		0			0
$952$	38.0833	+	65.9623i	1.23429	+	2.13785i
$953$	11.7045	−	20.2728i	0.379147	−	0.656701i	−0.611792	−	0.791019i	$-0.709551\pi$
$953$	11.7045	−	20.2728i	0.379147	−	0.656701i	0.990938	+	0.134318i	$0.0428842\pi$
$954$		0			0
$955$	4.35110	−	7.53632i	0.140798	−	0.243870i
$956$	30.5119	−	52.8481i	0.986825	−	1.70923i
$957$		0			0
$958$	0.211247	−	0.365891i	0.00682509	−	0.0118214i
$959$	19.2227	+	33.2947i	0.620733	+	1.07514i
$960$		0			0
$961$	−14.1667			−0.456989
$962$	1.83294	+	33.1325i	0.0590965	+	1.06824i
$963$		0			0
$964$	−30.4454	−	52.7329i	−0.980579	−	1.69841i
$965$	9.63378	+	16.6862i	0.310122	+	0.537148i
$966$		0			0
$967$	27.8669			0.896140			0.448070	−	0.893999i	$-0.352112\pi$
$967$	27.8669			0.896140			0.448070	+	0.893999i	$0.352112\pi$
$968$	57.8968	−	100.280i	1.86087	−	3.22313i
$969$		0			0
$970$	−14.5012			−0.465604
$971$	−2.25917	+	3.91300i	−0.0725003	+	0.125574i	−0.899997	−	0.435897i	$-0.856431\pi$
$971$	−2.25917	+	3.91300i	−0.0725003	+	0.125574i	0.827496	+	0.561471i	$0.189764\pi$
$972$		0			0
$973$	29.0791	+	50.3665i	0.932234	+	1.61468i
$974$	−6.66822			−0.213664
$975$		0			0
$976$	−31.6101			−1.01181
$977$	−21.2420	−	36.7922i	−0.679592	−	1.17709i	−0.975104	−	0.221748i	$-0.928824\pi$
$977$	−21.2420	−	36.7922i	−0.679592	−	1.17709i	0.295512	−	0.955339i	$-0.404510\pi$
$978$		0			0
$979$	25.5822	−	44.3096i	0.817610	−	1.41614i
$980$	−28.4793			−0.909739
$981$		0			0
$982$	−36.9968	+	64.0803i	−1.18061	+	2.04488i
$983$	−9.87158			−0.314854			−0.157427	−	0.987531i	$-0.550320\pi$
$983$	−9.87158			−0.314854			−0.157427	+	0.987531i	$0.550320\pi$
$984$		0			0
$985$	7.57377	+	13.1182i	0.241320	+	0.417979i
$986$	−7.00000	−	12.1244i	−0.222925	−	0.386118i
$987$		0			0
$988$	−103.849	−	52.5344i	−3.30389	−	1.67134i
$989$	−17.5375			−0.557659
$990$		0			0
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	0.648126	−	0.761533i	$-0.275553\pi$
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	−0.983570	+	0.180527i	$0.942220\pi$
$992$	19.5654	−	33.8882i	0.621201	−	1.07595i
$993$		0			0
$994$	45.4677	−	78.7524i	1.44215	−	2.49787i
$995$	−2.26873	+	3.92956i	−0.0719237	+	0.124576i
$996$		0			0
$997$	−8.54167	+	14.7946i	−0.270517	+	0.468550i	−0.968994	−	0.247083i	$-0.920528\pi$
$997$	−8.54167	+	14.7946i	−0.270517	+	0.468550i	0.698477	+	0.715632i	$0.253861\pi$
$998$	−36.2420	−	62.7730i	−1.14722	−	1.98704i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.f.406.3		6
3.2	odd	2		195.2.i.d.16.1	✓	6
13.3	even	3		7605.2.a.bv.1.1		3
13.9	even	3	inner	585.2.j.f.451.3		6
13.10	even	6		7605.2.a.bw.1.3		3
15.2	even	4		975.2.bb.k.874.6		12
15.8	even	4		975.2.bb.k.874.1		12
15.14	odd	2		975.2.i.l.601.3		6
39.23	odd	6		2535.2.a.ba.1.1		3
39.29	odd	6		2535.2.a.bb.1.3		3
39.35	odd	6		195.2.i.d.61.1	yes	6
195.74	odd	6		975.2.i.l.451.3		6
195.113	even	12		975.2.bb.k.724.6		12
195.152	even	12		975.2.bb.k.724.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.1	✓	6	3.2	odd	2
195.2.i.d.61.1	yes	6	39.35	odd	6
585.2.j.f.406.3		6	1.1	even	1	trivial
585.2.j.f.451.3		6	13.9	even	3	inner
975.2.i.l.451.3		6	195.74	odd	6
975.2.i.l.601.3		6	15.14	odd	2
975.2.bb.k.724.1		12	195.152	even	12
975.2.bb.k.724.6		12	195.113	even	12
975.2.bb.k.874.1		12	15.8	even	4
975.2.bb.k.874.6		12	15.2	even	4
2535.2.a.ba.1.1		3	39.23	odd	6
2535.2.a.bb.1.3		3	39.29	odd	6
7605.2.a.bv.1.1		3	13.3	even	3
7605.2.a.bw.1.3		3	13.10	even	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30084 + 2.25312i) q^{2} +(-2.38437 + 4.12985i) q^{4} -1.00000 q^{5} +(-1.80084 + 3.11915i) q^{7} -7.20336 q^{8} +O(q^{10})\)	\(q+(1.30084 + 2.25312i) q^{2} +(-2.38437 + 4.12985i) q^{4} -1.00000 q^{5} +(-1.80084 + 3.11915i) q^{7} -7.20336 q^{8} +(-1.30084 - 2.25312i) q^{10} +(-2.60168 - 4.50624i) q^{11} +(3.01815 - 1.97250i) q^{13} -9.37041 q^{14} +(-4.60168 - 7.97034i) q^{16} +(-1.46789 + 2.54247i) q^{17} +(-3.38437 + 5.86190i) q^{19} +(2.38437 - 4.12985i) q^{20} +(6.76873 - 11.7238i) q^{22} +(2.76873 + 4.79559i) q^{23} +1.00000 q^{25} +(8.37041 + 4.23435i) q^{26} +(-8.58773 - 14.8744i) q^{28} +(0.916472 + 1.58738i) q^{29} +4.10284 q^{31} +(4.76873 - 8.25969i) q^{32} -7.63798 q^{34} +(1.80084 - 3.11915i) q^{35} +(1.76873 + 3.06354i) q^{37} -17.6101 q^{38} +7.20336 q^{40} +(-2.68521 - 4.65091i) q^{41} +(-1.58353 + 2.74275i) q^{43} +24.8134 q^{44} +(-7.20336 + 12.4766i) q^{46} -3.80504 q^{47} +(-2.98605 - 5.17198i) q^{49} +(1.30084 + 2.25312i) q^{50} +(0.949743 + 17.1677i) q^{52} +5.20336 q^{53} +(2.60168 + 4.50624i) q^{55} +(12.9721 - 22.4683i) q^{56} +(-2.38437 + 4.12985i) q^{58} +(-3.68521 + 6.38297i) q^{59} +(1.71731 - 2.97447i) q^{61} +(5.33714 + 9.24420i) q^{62} +6.40672 q^{64} +(-3.01815 + 1.97250i) q^{65} +(-1.75058 - 3.03210i) q^{67} +(-7.00000 - 12.1244i) q^{68} +9.37041 q^{70} +(-4.85226 + 8.40436i) q^{71} -0.805037 q^{73} +(-4.60168 + 7.97034i) q^{74} +(-16.1391 - 27.9538i) q^{76} +18.7408 q^{77} -4.10284 q^{79} +(4.60168 + 7.97034i) q^{80} +(6.98605 - 12.1002i) q^{82} +11.5375 q^{83} +(1.46789 - 2.54247i) q^{85} -8.23966 q^{86} +(18.7408 + 32.4601i) q^{88} +(4.91647 + 8.51558i) q^{89} +(0.717312 + 12.9662i) q^{91} -26.4067 q^{92} +(-4.94974 - 8.57321i) q^{94} +(3.38437 - 5.86190i) q^{95} +(2.78689 - 4.82703i) q^{97} +(7.76873 - 13.4558i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

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