LMFDB - Embedded newform 567.2.f.a.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(190,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not 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:	$4.52751779461$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			190.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.a.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} +2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} +(1.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.00000 q^{17} -8.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(-4.00000 + 6.92820i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(2.00000 + 3.46410i) q^{25} -4.00000 q^{26} -2.00000 q^{28} +(-2.00000 - 3.46410i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(4.00000 - 6.92820i) q^{32} +(3.00000 + 5.19615i) q^{34} -1.00000 q^{35} -3.00000 q^{37} +(8.00000 + 13.8564i) q^{38} +(0.500000 - 0.866025i) q^{41} +(-5.50000 - 9.52628i) q^{43} +8.00000 q^{44} +12.0000 q^{46} +(4.50000 + 7.79423i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(4.00000 - 6.92820i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{53} +4.00000 q^{55} +(-4.00000 + 6.92820i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-2.00000 - 3.46410i) q^{61} +12.0000 q^{62} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} +12.0000 q^{71} +6.00000 q^{73} +(3.00000 + 5.19615i) q^{74} +(8.00000 - 13.8564i) q^{76} +(2.00000 - 3.46410i) q^{77} +(0.500000 + 0.866025i) q^{79} -4.00000 q^{80} -2.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-11.0000 + 19.0526i) q^{86} -2.00000 q^{89} +2.00000 q^{91} +(-6.00000 - 10.3923i) q^{92} +(9.00000 - 15.5885i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-6.00000 - 10.3923i) q^{97} +2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 4 q^{10} - 4 q^{11} + 2 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} - 16 q^{19} - 2 q^{20} - 8 q^{22} - 6 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{29} - 6 q^{31}+ \cdots + 4 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 - q^5 + q^7 + 4 * q^10 - 4 * q^11 + 2 * q^13 + 2 * q^14 + 4 * q^16 - 6 * q^17 - 16 * q^19 - 2 * q^20 - 8 * q^22 - 6 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^29 - 6 * q^31 + 8 * q^32 + 6 * q^34 - 2 * q^35 - 6 * q^37 + 16 * q^38 + q^41 - 11 * q^43 + 16 * q^44 + 24 * q^46 + 9 * q^47 - q^49 + 8 * q^50 + 4 * q^52 - 12 * q^53 + 8 * q^55 - 8 * q^58 - 15 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 2 * q^65 + 8 * q^67 + 6 * q^68 + 2 * q^70 + 24 * q^71 + 12 * q^73 + 6 * q^74 + 16 * q^76 + 4 * q^77 + q^79 - 8 * q^80 - 4 * q^82 - 9 * q^83 + 3 * q^85 - 22 * q^86 - 4 * q^89 + 4 * q^91 - 12 * q^92 + 18 * q^94 + 8 * q^95 - 12 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$		0			0
$10$	2.00000			0.632456
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	−4.00000	+	6.92820i	−0.852803	+	1.47710i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−4.00000			−0.784465
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$	8.00000	+	13.8564i	1.29777	+	2.24781i
$39$		0			0
$40$		0			0
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	−0.824338	−	0.566099i	$-0.808452\pi$
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	0.902424	+	0.430848i	$0.141786\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	8.00000			1.20605
$45$		0			0
$46$	12.0000			1.76930
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	4.00000	−	6.92820i	0.565685	−	0.979796i
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	12.0000			1.52400
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$	1.00000	+	1.73205i	0.119523	+	0.207020i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$		0			0
$76$	8.00000	−	13.8564i	0.917663	−	1.58944i
$77$	2.00000	−	3.46410i	0.227921	−	0.394771i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−4.00000			−0.447214
$81$		0			0
$82$	−2.00000			−0.220863
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−11.0000	+	19.0526i	−1.18616	+	2.05449i
$87$		0			0
$88$		0			0
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	−6.00000	−	10.3923i	−0.625543	−	1.08347i
$93$		0			0
$94$	9.00000	−	15.5885i	0.928279	−	1.60783i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	−0.991371	−	0.131084i	$-0.958154\pi$
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	0.382164	−	0.924095i	$-0.375179\pi$
$98$	2.00000			0.202031
$99$		0			0
$100$	−8.00000			−0.800000
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		0			0
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	−0.911078	−	0.412235i	$-0.864748\pi$
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	0.812545	+	0.582899i	$0.198082\pi$
$104$		0			0
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	−2.00000			−0.193347			−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000			−0.193347			−0.0966736	+	0.995316i	$0.530820\pi$
$108$		0			0
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	1.00000	−	1.73205i	0.0940721	−	0.162938i	−0.815149	−	0.579252i	$-0.803345\pi$
$113$	1.00000	−	1.73205i	0.0940721	−	0.162938i	0.909221	+	0.416314i	$0.136678\pi$
$114$		0			0
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	8.00000			0.742781
$117$		0			0
$118$	30.0000			2.76172
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$		0			0
$124$	−6.00000	−	10.3923i	−0.538816	−	0.933257i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$		0			0
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$		0			0
$133$	−4.00000	−	6.92820i	−0.346844	−	0.600751i
$134$	−16.0000			−1.38219
$135$		0			0
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−12.0000	−	20.7846i	−1.00702	−	1.74421i
$143$	−8.00000			−0.668994
$144$		0			0
$145$	4.00000			0.332182
$146$	−6.00000	−	10.3923i	−0.496564	−	0.860073i
$147$		0			0
$148$	3.00000	−	5.19615i	0.246598	−	0.427121i
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	−0.508413	−	0.861113i	$-0.669768\pi$
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	0.999953	+	0.00974235i	$0.00310113\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$		0			0
$153$		0			0
$154$	−8.00000			−0.644658
$155$	−3.00000	−	5.19615i	−0.240966	−	0.417365i
$156$		0			0
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$		0			0
$160$	4.00000	+	6.92820i	0.316228	+	0.547723i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$		0			0
$166$	−9.00000	+	15.5885i	−0.698535	+	1.20990i
$167$	8.50000	−	14.7224i	0.657750	−	1.13926i	−0.323447	−	0.946246i	$-0.604842\pi$
$167$	8.50000	−	14.7224i	0.657750	−	1.13926i	0.981197	−	0.193010i	$-0.0618249\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−6.00000			−0.460179
$171$		0			0
$172$	22.0000			1.67748
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	0.892956	+	0.450145i	$0.148628\pi$
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	−0.0566411	+	0.998395i	$0.518039\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	8.00000	−	13.8564i	0.603023	−	1.04447i
$177$		0			0
$178$	2.00000	+	3.46410i	0.149906	+	0.259645i
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	−2.00000	−	3.46410i	−0.148250	−	0.256776i
$183$		0			0
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	6.00000	+	10.3923i	0.438763	+	0.759961i
$188$	−18.0000			−1.31278
$189$		0			0
$190$	−16.0000			−1.16076
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	0.899934	−	0.436026i	$-0.143614\pi$
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	−0.827577	+	0.561353i	$0.810281\pi$
$192$		0			0
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	−12.0000	+	20.7846i	−0.861550	+	1.49225i
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$		0			0
$199$	−12.0000			−0.850657			−0.425329	−	0.905039i	$-0.639842\pi$
$199$	−12.0000			−0.850657			−0.425329	+	0.905039i	$0.639842\pi$
$200$		0			0
$201$		0			0
$202$	10.0000	−	17.3205i	0.703598	−	1.21867i
$203$	2.00000	−	3.46410i	0.140372	−	0.243132i
$204$		0			0
$205$	0.500000	+	0.866025i	0.0349215	+	0.0604858i
$206$	4.00000			0.278693
$207$		0			0
$208$	8.00000			0.554700
$209$	16.0000	+	27.7128i	1.10674	+	1.91694i
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	11.0000			0.750194
$216$		0			0
$217$	−6.00000			−0.407307
$218$	9.00000	+	15.5885i	0.609557	+	1.05578i
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	8.00000			0.534522
$225$		0			0
$226$	−4.00000			−0.266076
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$	−6.00000	+	10.3923i	−0.395628	+	0.685248i
$231$		0			0
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	−15.0000	−	25.9808i	−0.976417	−	1.69120i
$237$		0			0
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	0.413061	+	0.910703i	$0.364460\pi$
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	−0.995223	+	0.0976302i	$0.968874\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	10.0000			0.642824
$243$		0			0
$244$	8.00000			0.512148
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$		0			0
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$		0			0
$249$		0			0
$250$	9.00000	+	15.5885i	0.569210	+	0.985901i
$251$	25.0000			1.57799			0.788993	−	0.614402i	$-0.210603\pi$
$251$	25.0000			1.57799			0.788993	+	0.614402i	$0.210603\pi$
$252$		0			0
$253$	24.0000			1.50887
$254$	15.0000	+	25.9808i	0.941184	+	1.63018i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	−0.666880	−	0.745165i	$-0.732371\pi$
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	0.978772	+	0.204953i	$0.0657041\pi$
$258$		0			0
$259$	−1.50000	−	2.59808i	−0.0932055	−	0.161437i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	8.00000			0.494242
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	0.997015	−	0.0772134i	$-0.0246023\pi$
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	−0.565376	+	0.824833i	$0.691269\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	−8.00000	+	13.8564i	−0.490511	+	0.849591i
$267$		0			0
$268$	8.00000	+	13.8564i	0.488678	+	0.846415i
$269$	21.0000			1.28039			0.640196	−	0.768211i	$-0.278853\pi$
$269$	21.0000			1.28039			0.640196	+	0.768211i	$0.278853\pi$
$270$		0			0
$271$	−2.00000			−0.121491			−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000			−0.121491			−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−6.00000	−	10.3923i	−0.363803	−	0.630126i
$273$		0			0
$274$	−18.0000	+	31.1769i	−1.08742	+	1.88347i
$275$	8.00000	−	13.8564i	0.482418	−	0.835573i
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.00000	+	8.66025i	0.298275	+	0.516627i	0.975741	−	0.218926i	$-0.0702554\pi$
$281$	5.00000	+	8.66025i	0.298275	+	0.516627i	−0.677466	+	0.735554i	$0.736922\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	−12.0000	+	20.7846i	−0.712069	+	1.23334i
$285$		0			0
$286$	8.00000	+	13.8564i	0.473050	+	0.819346i
$287$	1.00000			0.0590281
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−4.00000	−	6.92820i	−0.234888	−	0.406838i
$291$		0			0
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	−0.851051	−	0.525084i	$-0.824034\pi$
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	0.880261	+	0.474490i	$0.157367\pi$
$294$		0			0
$295$	−7.50000	−	12.9904i	−0.436667	−	0.756329i
$296$		0			0
$297$		0			0
$298$	−24.0000			−1.39028
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	5.50000	−	9.52628i	0.317015	−	0.549086i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$	−16.0000	−	27.7128i	−0.917663	−	1.58944i
$305$	4.00000			0.229039
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	4.00000	+	6.92820i	0.227921	+	0.394771i
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$		0			0
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	−2.00000			−0.112509
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$	4.00000	−	6.92820i	0.223607	−	0.387298i
$321$		0			0
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$	24.0000			1.33540
$324$		0			0
$325$	8.00000			0.443760
$326$	11.0000	+	19.0526i	0.609234	+	1.05522i
$327$		0			0
$328$		0			0
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	18.0000			0.987878
$333$		0			0
$334$	−34.0000			−1.86040
$335$	4.00000	+	6.92820i	0.218543	+	0.378528i
$336$		0			0
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	−0.945468	−	0.325714i	$-0.894395\pi$
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	0.754811	+	0.655942i	$0.227729\pi$
$338$	9.00000	−	15.5885i	0.489535	−	0.847900i
$339$		0			0
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	24.0000			1.29967
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$	22.0000	−	38.1051i	1.18273	−	2.04854i
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$		0			0
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	0.999149	+	0.0412379i	$0.0131301\pi$
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	−0.463862	+	0.885908i	$0.653537\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$	−32.0000			−1.70561
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	−0.979202	−	0.202889i	$-0.934967\pi$
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	0.313894	−	0.949458i	$-0.398366\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$	2.00000	−	3.46410i	0.106000	−	0.183597i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	−34.0000			−1.79445			−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000			−1.79445			−0.897226	+	0.441572i	$0.854421\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$	−16.0000	−	27.7128i	−0.840941	−	1.45655i
$363$		0			0
$364$	−2.00000	+	3.46410i	−0.104828	+	0.181568i
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$		0			0
$367$	15.0000	+	25.9808i	0.782994	+	1.35618i	0.930190	+	0.367078i	$0.119642\pi$
$367$	15.0000	+	25.9808i	0.782994	+	1.35618i	−0.147197	+	0.989107i	$0.547025\pi$
$368$	−24.0000			−1.25109
$369$		0			0
$370$	−6.00000			−0.311925
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	12.0000	−	20.7846i	0.620505	−	1.07475i
$375$		0			0
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	−3.00000			−0.154100			−0.0770498	−	0.997027i	$-0.524550\pi$
$379$	−3.00000			−0.154100			−0.0770498	+	0.997027i	$0.524550\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$		0			0
$385$	2.00000	+	3.46410i	0.101929	+	0.176547i
$386$	−50.0000			−2.54493
$387$		0			0
$388$	24.0000			1.21842
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	−0.991500	−	0.130105i	$-0.958469\pi$
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	0.383076	−	0.923717i	$-0.374865\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$	−1.00000			−0.0503155
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	12.0000	+	20.7846i	0.601506	+	1.04184i
$399$		0			0
$400$	−8.00000	+	13.8564i	−0.400000	+	0.692820i
$401$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$401$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$402$		0			0
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	−20.0000			−0.995037
$405$		0			0
$406$	−8.00000			−0.397033
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$		0			0
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$		0			0
$412$	−2.00000	−	3.46410i	−0.0985329	−	0.170664i
$413$	−15.0000			−0.738102
$414$		0			0
$415$	9.00000			0.441793
$416$	−8.00000	−	13.8564i	−0.392232	−	0.679366i
$417$		0			0
$418$	32.0000	−	55.4256i	1.56517	−	2.71096i
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	0.109483	+	0.993989i	$0.465080\pi$
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	−0.915561	+	0.402179i	$0.868253\pi$
$420$		0			0
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	0.643489	−	0.765455i	$-0.277486\pi$
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	−0.984648	+	0.174550i	$0.944153\pi$
$422$	8.00000			0.389434
$423$		0			0
$424$		0			0
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	2.00000	−	3.46410i	0.0967868	−	0.167640i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$		0			0
$430$	−11.0000	−	19.0526i	−0.530467	−	0.918796i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	6.00000	+	10.3923i	0.288009	+	0.498847i
$435$		0			0
$436$	9.00000	−	15.5885i	0.431022	−	0.746552i
$437$	24.0000	−	41.5692i	1.14808	−	1.98853i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		0			0
$448$	−4.00000	−	6.92820i	−0.188982	−	0.327327i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−4.00000			−0.188353
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$		0			0
$454$	−24.0000	+	41.5692i	−1.12638	+	1.95094i
$455$	−1.00000	+	1.73205i	−0.0468807	+	0.0811998i
$456$		0			0
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	0.982004	−	0.188858i	$-0.0604787\pi$
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	−0.654558	+	0.756012i	$0.727145\pi$
$458$	−8.00000			−0.373815
$459$		0			0
$460$	12.0000			0.559503
$461$	0.500000	+	0.866025i	0.0232873	+	0.0403348i	0.877434	−	0.479697i	$-0.159253\pi$
$461$	0.500000	+	0.866025i	0.0232873	+	0.0403348i	−0.854147	+	0.520032i	$0.825920\pi$
$462$		0			0
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	0.999190	−	0.0402476i	$-0.0128147\pi$
$464$	8.00000	−	13.8564i	0.371391	−	0.643268i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$		0			0
$472$		0			0
$473$	−22.0000	+	38.1051i	−1.01156	+	1.75208i
$474$		0			0
$475$	−16.0000	−	27.7128i	−0.734130	−	1.27155i
$476$	6.00000			0.275010
$477$		0			0
$478$	36.0000			1.64660
$479$	−8.50000	−	14.7224i	−0.388375	−	0.672685i	0.603856	−	0.797093i	$-0.293630\pi$
$479$	−8.50000	−	14.7224i	−0.388375	−	0.672685i	−0.992231	+	0.124408i	$0.960297\pi$
$480$		0			0
$481$	−3.00000	+	5.19615i	−0.136788	+	0.236924i
$482$	10.0000	−	17.3205i	0.455488	−	0.788928i
$483$		0			0
$484$	−5.00000	−	8.66025i	−0.227273	−	0.393648i
$485$	12.0000			0.544892
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$		0			0
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	−13.0000	+	22.5167i	−0.586682	+	1.01616i	0.407982	+	0.912990i	$0.366233\pi$
$491$	−13.0000	+	22.5167i	−0.586682	+	1.01616i	−0.994663	+	0.103173i	$0.967101\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$	32.0000			1.43975
$495$		0			0
$496$	−24.0000			−1.07763
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$		0			0
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	−0.974042	−	0.226369i	$-0.927315\pi$
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	0.683062	+	0.730361i	$0.260648\pi$
$500$	9.00000	−	15.5885i	0.402492	−	0.697137i
$501$		0			0
$502$	−25.0000	−	43.3013i	−1.11580	−	1.93263i
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	−24.0000	−	41.5692i	−1.06693	−	1.84798i
$507$		0			0
$508$	15.0000	−	25.9808i	0.665517	−	1.15271i
$509$	−20.5000	+	35.5070i	−0.908647	+	1.57382i	−0.0927004	+	0.995694i	$0.529550\pi$
$509$	−20.5000	+	35.5070i	−0.908647	+	1.57382i	−0.815946	+	0.578128i	$0.803783\pi$
$510$		0			0
$511$	3.00000	+	5.19615i	0.132712	+	0.229864i
$512$	32.0000			1.41421
$513$		0			0
$514$	−20.0000			−0.882162
$515$	−1.00000	−	1.73205i	−0.0440653	−	0.0763233i
$516$		0			0
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$	−3.00000	+	5.19615i	−0.131812	+	0.228306i
$519$		0			0
$520$		0			0
$521$	−15.0000			−0.657162			−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000			−0.657162			−0.328581	+	0.944476i	$0.606570\pi$
$522$		0			0
$523$	−26.0000			−1.13690			−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000			−1.13690			−0.568450	+	0.822718i	$0.692457\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$		0			0
$526$	14.0000	−	24.2487i	0.610429	−	1.05729i
$527$	9.00000	−	15.5885i	0.392046	−	0.679044i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−12.0000			−0.521247
$531$		0			0
$532$	16.0000			0.693688
$533$	−1.00000	−	1.73205i	−0.0433148	−	0.0750234i
$534$		0			0
$535$	1.00000	−	1.73205i	0.0432338	−	0.0748831i
$536$		0			0
$537$		0			0
$538$	−21.0000	−	36.3731i	−0.905374	−	1.56815i
$539$	4.00000			0.172292
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$		0			0
$544$	−12.0000	+	20.7846i	−0.514496	+	0.891133i
$545$	4.50000	−	7.79423i	0.192759	−	0.333868i
$546$		0			0
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	36.0000			1.53784
$549$		0			0
$550$	−32.0000			−1.36448
$551$	16.0000	+	27.7128i	0.681623	+	1.18061i
$552$		0			0
$553$	−0.500000	+	0.866025i	−0.0212622	+	0.0368271i
$554$	−13.0000	+	22.5167i	−0.552317	+	0.956641i
$555$		0			0
$556$		0			0
$557$	4.00000			0.169485			0.0847427	−	0.996403i	$-0.472993\pi$
$557$	4.00000			0.169485			0.0847427	+	0.996403i	$0.472993\pi$
$558$		0			0
$559$	−22.0000			−0.930501
$560$	−2.00000	−	3.46410i	−0.0845154	−	0.146385i
$561$		0			0
$562$	10.0000	−	17.3205i	0.421825	−	0.730622i
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$		0			0
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$	56.0000			2.35386
$567$		0			0
$568$		0			0
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	0.886225	−	0.463255i	$-0.153319\pi$
$569$	1.00000	+	1.73205i	0.0419222	+	0.0726113i	−0.844303	+	0.535866i	$0.819985\pi$
$570$		0			0
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	−0.957857	−	0.287244i	$-0.907261\pi$
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	0.727690	+	0.685907i	$0.240594\pi$
$572$	8.00000	−	13.8564i	0.334497	−	0.579365i
$573$		0			0
$574$	−1.00000	−	1.73205i	−0.0417392	−	0.0722944i
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−20.0000			−0.832611			−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000			−0.832611			−0.416305	+	0.909225i	$0.636675\pi$
$578$	8.00000	+	13.8564i	0.332756	+	0.576351i
$579$		0			0
$580$	−4.00000	+	6.92820i	−0.166091	+	0.287678i
$581$	4.50000	−	7.79423i	0.186691	−	0.323359i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$	−2.00000			−0.0826192
$587$	10.0000	+	17.3205i	0.412744	+	0.714894i	0.995189	−	0.0979766i	$-0.0312370\pi$
$587$	10.0000	+	17.3205i	0.412744	+	0.714894i	−0.582445	+	0.812870i	$0.697904\pi$
$588$		0			0
$589$	24.0000	−	41.5692i	0.988903	−	1.71283i
$590$	−15.0000	+	25.9808i	−0.617540	+	1.06961i
$591$		0			0
$592$	−6.00000	−	10.3923i	−0.246598	−	0.427121i
$593$	33.0000			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$594$		0			0
$595$	3.00000			0.122988
$596$	12.0000	+	20.7846i	0.491539	+	0.851371i
$597$		0			0
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$		0			0
$601$	9.00000	+	15.5885i	0.367118	+	0.635866i	0.989114	−	0.147154i	$-0.0470113\pi$
$601$	9.00000	+	15.5885i	0.367118	+	0.635866i	−0.621996	+	0.783020i	$0.713678\pi$
$602$	−22.0000			−0.896653
$603$		0			0
$604$	10.0000			0.406894
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	−32.0000	+	55.4256i	−1.29777	+	2.24781i
$609$		0			0
$610$	−4.00000	−	6.92820i	−0.161955	−	0.280515i
$611$	18.0000			0.728202
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	2.00000	+	3.46410i	0.0807134	+	0.139800i
$615$		0			0
$616$		0			0
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$	12.0000			0.481932
$621$		0			0
$622$	6.00000			0.240578
$623$	−1.00000	−	1.73205i	−0.0400642	−	0.0693932i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	16.0000	−	27.7128i	0.639489	−	1.10763i
$627$		0			0
$628$	8.00000	+	13.8564i	0.319235	+	0.552931i
$629$	9.00000			0.358854
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$		0			0
$633$		0			0
$634$	−18.0000	+	31.1769i	−0.714871	+	1.23819i
$635$	7.50000	−	12.9904i	0.297628	−	0.515508i
$636$		0			0
$637$	1.00000	+	1.73205i	0.0396214	+	0.0686264i
$638$	32.0000			1.26689
$639$		0			0
$640$		0			0
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	0.959848	−	0.280521i	$-0.0905072\pi$
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	−0.722862	+	0.690992i	$0.757174\pi$
$642$		0			0
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	0.487222	+	0.873278i	$0.338010\pi$
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	−0.999892	+	0.0146923i	$0.995323\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$	−24.0000	−	41.5692i	−0.944267	−	1.63552i
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		0			0
$649$	60.0000			2.35521
$650$	−8.00000	−	13.8564i	−0.313786	−	0.543493i
$651$		0			0
$652$	11.0000	−	19.0526i	0.430793	−	0.746156i
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	0.0825519	+	0.996587i	$0.473693\pi$
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	−0.904345	+	0.426801i	$0.859640\pi$
$654$		0			0
$655$	−2.00000	−	3.46410i	−0.0781465	−	0.135354i
$656$	4.00000			0.156174
$657$		0			0
$658$	18.0000			0.701713
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	1.00000	−	1.73205i	0.0388661	−	0.0673181i
$663$		0			0
$664$		0			0
$665$	8.00000			0.310227
$666$		0			0
$667$	24.0000			0.929284
$668$	17.0000	+	29.4449i	0.657750	+	1.13926i
$669$		0			0
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$	−8.00000	+	13.8564i	−0.308837	+	0.534921i
$672$		0			0
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	0.884655	−	0.466246i	$-0.154394\pi$
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	−0.846108	+	0.533011i	$0.821060\pi$
$674$	14.0000			0.539260
$675$		0			0
$676$	−18.0000			−0.692308
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$		0			0
$679$	6.00000	−	10.3923i	0.230259	−	0.398820i
$680$		0			0
$681$		0			0
$682$	−24.0000	−	41.5692i	−0.919007	−	1.59177i
$683$	−42.0000			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	1.00000	+	1.73205i	0.0381802	+	0.0661300i
$687$		0			0
$688$	22.0000	−	38.1051i	0.838742	−	1.45274i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$	−44.0000			−1.67263
$693$		0			0
$694$	4.00000			0.151838
$695$		0			0
$696$		0			0
$697$	−1.50000	+	2.59808i	−0.0568166	+	0.0984092i
$698$	20.0000	−	34.6410i	0.757011	−	1.31118i
$699$		0			0
$700$	−4.00000	−	6.92820i	−0.151186	−	0.261861i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	24.0000			0.905177
$704$	16.0000	+	27.7128i	0.603023	+	1.04447i
$705$		0			0
$706$	−25.0000	+	43.3013i	−0.940887	+	1.62966i
$707$	−5.00000	+	8.66025i	−0.188044	+	0.325702i
$708$		0			0
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	0.690127	−	0.723688i	$-0.257554\pi$
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	−0.971796	+	0.235824i	$0.924221\pi$
$710$	24.0000			0.900704
$711$		0			0
$712$		0			0
$713$	−18.0000	−	31.1769i	−0.674105	−	1.16758i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$		0			0
$718$	34.0000	+	58.8897i	1.26887	+	2.19775i
$719$	−33.0000			−1.23069			−0.615346	−	0.788257i	$-0.710984\pi$
$719$	−33.0000			−1.23069			−0.615346	+	0.788257i	$0.710984\pi$
$720$		0			0
$721$	−2.00000			−0.0744839
$722$	−45.0000	−	77.9423i	−1.67473	−	2.90071i
$723$		0			0
$724$	−16.0000	+	27.7128i	−0.594635	+	1.02994i
$725$	8.00000	−	13.8564i	0.297113	−	0.514614i
$726$		0			0
$727$	2.00000	+	3.46410i	0.0741759	+	0.128476i	0.900728	−	0.434384i	$-0.143034\pi$
$727$	2.00000	+	3.46410i	0.0741759	+	0.128476i	−0.826552	+	0.562861i	$0.809701\pi$
$728$		0			0
$729$		0			0
$730$	12.0000			0.444140
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$733$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$734$	30.0000	−	51.9615i	1.10732	−	1.91793i
$735$		0			0
$736$	24.0000	+	41.5692i	0.884652	+	1.53226i
$737$	−32.0000			−1.17874
$738$		0			0
$739$	12.0000			0.441427			0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000			0.441427			0.220714	+	0.975339i	$0.429161\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$		0			0
$742$	−6.00000	+	10.3923i	−0.220267	+	0.381514i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	−26.0000			−0.951928
$747$		0			0
$748$	−24.0000			−0.877527
$749$	−1.00000	−	1.73205i	−0.0365392	−	0.0632878i
$750$		0			0
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	−0.974265	−	0.225407i	$-0.927629\pi$
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	0.682341	+	0.731034i	$0.260962\pi$
$752$	−18.0000	+	31.1769i	−0.656392	+	1.13691i
$753$		0			0
$754$	8.00000	+	13.8564i	0.291343	+	0.504621i
$755$	5.00000			0.181969
$756$		0			0
$757$	23.0000			0.835949			0.417975	−	0.908459i	$-0.362740\pi$
$757$	23.0000			0.835949			0.417975	+	0.908459i	$0.362740\pi$
$758$	3.00000	+	5.19615i	0.108965	+	0.188733i
$759$		0			0
$760$		0			0
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		0			0
$763$	−4.50000	−	7.79423i	−0.162911	−	0.282170i
$764$	−4.00000			−0.144715
$765$		0			0
$766$	−42.0000			−1.51752
$767$	15.0000	+	25.9808i	0.541619	+	0.938111i
$768$		0			0
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	0.130547	+	0.991442i	$0.458327\pi$
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	−0.923888	+	0.382664i	$0.875007\pi$
$770$	4.00000	−	6.92820i	0.144150	−	0.249675i
$771$		0			0
$772$	25.0000	+	43.3013i	0.899770	+	1.55845i
$773$	−49.0000			−1.76241			−0.881204	−	0.472737i	$-0.843266\pi$
$773$	−49.0000			−1.76241			−0.881204	+	0.472737i	$0.843266\pi$
$774$		0			0
$775$	−24.0000			−0.862105
$776$		0			0
$777$		0			0
$778$	−24.0000	+	41.5692i	−0.860442	+	1.49033i
$779$	−4.00000	+	6.92820i	−0.143315	+	0.248229i
$780$		0			0
$781$	−24.0000	−	41.5692i	−0.858788	−	1.48746i
$782$	−36.0000			−1.28736
$783$		0			0
$784$	−4.00000			−0.142857
$785$	4.00000	+	6.92820i	0.142766	+	0.247278i
$786$		0			0
$787$	1.00000	−	1.73205i	0.0356462	−	0.0617409i	−0.847652	−	0.530553i	$-0.821984\pi$
$787$	1.00000	−	1.73205i	0.0356462	−	0.0617409i	0.883298	+	0.468812i	$0.155318\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$		0			0
$790$	1.00000	+	1.73205i	0.0355784	+	0.0616236i
$791$	2.00000			0.0711118
$792$		0			0
$793$	−8.00000			−0.284088
$794$	−6.00000	−	10.3923i	−0.212932	−	0.368809i
$795$		0			0
$796$	12.0000	−	20.7846i	0.425329	−	0.736691i
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$		0			0
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$	32.0000			1.13137
$801$		0			0
$802$		0			0
$803$	−12.0000	−	20.7846i	−0.423471	−	0.733473i
$804$		0			0
$805$	3.00000	−	5.19615i	0.105736	−	0.183140i
$806$	12.0000	−	20.7846i	0.422682	−	0.732107i
$807$		0			0
$808$		0			0
$809$	42.0000			1.47664			0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000			1.47664			0.738321	+	0.674450i	$0.235619\pi$
$810$		0			0
$811$	−46.0000			−1.61528			−0.807639	−	0.589677i	$-0.799255\pi$
$811$	−46.0000			−1.61528			−0.807639	+	0.589677i	$0.799255\pi$
$812$	4.00000	+	6.92820i	0.140372	+	0.243132i
$813$		0			0
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	5.50000	−	9.52628i	0.192657	−	0.333691i
$816$		0			0
$817$	44.0000	+	76.2102i	1.53937	+	2.66626i
$818$	64.0000			2.23771
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	−4.00000	−	6.92820i	−0.139601	−	0.241796i	0.787745	−	0.616002i	$-0.211249\pi$
$821$	−4.00000	−	6.92820i	−0.139601	−	0.241796i	−0.927346	+	0.374206i	$0.877915\pi$
$822$		0			0
$823$	1.50000	−	2.59808i	0.0522867	−	0.0905632i	−0.838697	−	0.544598i	$-0.816682\pi$
$823$	1.50000	−	2.59808i	0.0522867	−	0.0905632i	0.890984	+	0.454034i	$0.150016\pi$
$824$		0			0
$825$		0			0
$826$	15.0000	+	25.9808i	0.521917	+	0.903986i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$		0			0
$829$	−16.0000			−0.555703			−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000			−0.555703			−0.277851	+	0.960624i	$0.589622\pi$
$830$	−9.00000	−	15.5885i	−0.312395	−	0.541083i
$831$		0			0
$832$	−8.00000	+	13.8564i	−0.277350	+	0.480384i
$833$	1.50000	−	2.59808i	0.0519719	−	0.0900180i
$834$		0			0
$835$	8.50000	+	14.7224i	0.294155	+	0.509491i
$836$	−64.0000			−2.21349
$837$		0			0
$838$	66.0000			2.27993
$839$	−27.5000	−	47.6314i	−0.949405	−	1.64442i	−0.746681	−	0.665183i	$-0.768354\pi$
$839$	−27.5000	−	47.6314i	−0.949405	−	1.64442i	−0.202725	−	0.979236i	$-0.564980\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−14.0000	+	24.2487i	−0.482472	+	0.835666i
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−9.00000			−0.309609
$846$		0			0
$847$	−5.00000			−0.171802
$848$	−12.0000	−	20.7846i	−0.412082	−	0.713746i
$849$		0			0
$850$	−12.0000	+	20.7846i	−0.411597	+	0.712906i
$851$	9.00000	−	15.5885i	0.308516	−	0.534365i
$852$		0			0
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$854$	−8.00000			−0.273754
$855$		0			0
$856$		0			0
$857$	8.50000	+	14.7224i	0.290354	+	0.502909i	0.973894	−	0.227005i	$-0.0728935\pi$
$857$	8.50000	+	14.7224i	0.290354	+	0.502909i	−0.683539	+	0.729914i	$0.739560\pi$
$858$		0			0
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	−0.882581	−	0.470160i	$-0.844196\pi$
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	0.848461	+	0.529257i	$0.177529\pi$
$860$	−11.0000	+	19.0526i	−0.375097	+	0.649687i
$861$		0			0
$862$	24.0000	+	41.5692i	0.817443	+	1.41585i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$		0			0
$865$	−22.0000			−0.748022
$866$	2.00000	+	3.46410i	0.0679628	+	0.117715i
$867$		0			0
$868$	6.00000	−	10.3923i	0.203653	−	0.352738i
$869$	2.00000	−	3.46410i	0.0678454	−	0.117512i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$		0			0
$873$		0			0
$874$	−96.0000			−3.24725
$875$	−4.50000	−	7.79423i	−0.152128	−	0.263493i
$876$		0			0
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	0.363898	+	0.931439i	$0.381446\pi$
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	−0.988599	+	0.150574i	$0.951888\pi$
$878$	−24.0000	+	41.5692i	−0.809961	+	1.40289i
$879$		0			0
$880$	8.00000	+	13.8564i	0.269680	+	0.467099i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	41.0000			1.37976			0.689880	−	0.723924i	$-0.257663\pi$
$883$	41.0000			1.37976			0.689880	+	0.723924i	$0.257663\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	−24.0000	+	41.5692i	−0.806296	+	1.39655i
$887$	6.50000	−	11.2583i	0.218249	−	0.378018i	−0.736024	−	0.676955i	$-0.763299\pi$
$887$	6.50000	−	11.2583i	0.218249	−	0.378018i	0.954273	+	0.298938i	$0.0966323\pi$
$888$		0			0
$889$	−7.50000	−	12.9904i	−0.251542	−	0.435683i
$890$	−4.00000			−0.134080
$891$		0			0
$892$	−4.00000			−0.133930
$893$	−36.0000	−	62.3538i	−1.20469	−	2.08659i
$894$		0			0
$895$	−1.00000	+	1.73205i	−0.0334263	+	0.0578961i
$896$		0			0
$897$		0			0
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$	24.0000			0.800445
$900$		0			0
$901$	18.0000			0.599667
$902$	4.00000	+	6.92820i	0.133185	+	0.230684i
$903$		0			0
$904$		0			0
$905$	−8.00000	+	13.8564i	−0.265929	+	0.460603i
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	48.0000			1.59294
$909$		0			0
$910$	4.00000			0.132599
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$	14.0000	−	24.2487i	0.463079	−	0.802076i
$915$		0			0
$916$	4.00000	+	6.92820i	0.132164	+	0.228914i
$917$	−4.00000			−0.132092
$918$		0			0
$919$	−43.0000			−1.41844			−0.709220	−	0.704988i	$-0.750953\pi$
$919$	−43.0000			−1.41844			−0.709220	+	0.704988i	$0.750953\pi$
$920$		0			0
$921$		0			0
$922$	1.00000	−	1.73205i	0.0329332	−	0.0570421i
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	−6.00000	−	10.3923i	−0.197279	−	0.341697i
$926$	−46.0000			−1.51165
$927$		0			0
$928$	−32.0000			−1.05045
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	−0.996133	−	0.0878612i	$-0.971997\pi$
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	0.421976	−	0.906607i	$-0.361337\pi$
$930$		0			0
$931$	4.00000	−	6.92820i	0.131095	−	0.227063i
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$		0			0
$934$	12.0000	+	20.7846i	0.392652	+	0.680093i
$935$	−12.0000			−0.392442
$936$		0			0
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$	−8.00000	−	13.8564i	−0.261209	−	0.452428i
$939$		0			0
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	−0.970661	−	0.240453i	$-0.922704\pi$
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	0.693569	+	0.720390i	$0.256037\pi$
$942$		0			0
$943$	3.00000	+	5.19615i	0.0976934	+	0.169210i
$944$	−60.0000			−1.95283
$945$		0			0
$946$	88.0000			2.86113
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	0.998685	−	0.0512727i	$-0.0163278\pi$
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	−0.543746	+	0.839250i	$0.682994\pi$
$948$		0			0
$949$	6.00000	−	10.3923i	0.194768	−	0.337348i
$950$	−32.0000	+	55.4256i	−1.03822	+	1.79824i
$951$		0			0
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	−2.00000			−0.0647185
$956$	−18.0000	−	31.1769i	−0.582162	−	1.00833i
$957$		0			0
$958$	−17.0000	+	29.4449i	−0.549245	+	0.951320i
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	12.0000			0.386896
$963$		0			0
$964$	−20.0000			−0.644157
$965$	12.5000	+	21.6506i	0.402389	+	0.696959i
$966$		0			0
$967$	−20.0000	+	34.6410i	−0.643157	+	1.11398i	0.341567	+	0.939857i	$0.389042\pi$
$967$	−20.0000	+	34.6410i	−0.643157	+	1.11398i	−0.984724	+	0.174123i	$0.944291\pi$
$968$		0			0
$969$		0			0
$970$	−12.0000	−	20.7846i	−0.385297	−	0.667354i
$971$	45.0000			1.44412			0.722059	−	0.691831i	$-0.243196\pi$
$971$	45.0000			1.44412			0.722059	+	0.691831i	$0.243196\pi$
$972$		0			0
$973$		0			0
$974$	−16.0000	−	27.7128i	−0.512673	−	0.887976i
$975$		0			0
$976$	8.00000	−	13.8564i	0.256074	−	0.443533i
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	4.00000	+	6.92820i	0.127841	+	0.221426i
$980$	2.00000			0.0638877
$981$		0			0
$982$	52.0000			1.65939
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.0637253	+	0.110375i
$986$	12.0000	−	20.7846i	0.382158	−	0.661917i
$987$		0			0
$988$	−16.0000	−	27.7128i	−0.509028	−	0.881662i
$989$	66.0000			2.09868
$990$		0			0
$991$	11.0000			0.349427			0.174713	−	0.984619i	$-0.444100\pi$
$991$	11.0000			0.349427			0.174713	+	0.984619i	$0.444100\pi$
$992$	24.0000	+	41.5692i	0.762001	+	1.31982i
$993$		0			0
$994$	12.0000	−	20.7846i	0.380617	−	0.659248i
$995$	6.00000	−	10.3923i	0.190213	−	0.329458i
$996$		0			0
$997$	−20.0000	−	34.6410i	−0.633406	−	1.09709i	−0.986850	−	0.161636i	$-0.948323\pi$
$997$	−20.0000	−	34.6410i	−0.633406	−	1.09709i	0.353444	−	0.935456i	$-0.385010\pi$
$998$	26.0000			0.823016
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.a.190.1		2
3.2	odd	2		567.2.f.h.190.1		2
9.2	odd	6		567.2.f.h.379.1		2
9.4	even	3		189.2.a.d.1.1	yes	1
9.5	odd	6		189.2.a.a.1.1	✓	1
9.7	even	3	inner	567.2.f.a.379.1		2
36.23	even	6		3024.2.a.l.1.1		1
36.31	odd	6		3024.2.a.u.1.1		1
45.4	even	6		4725.2.a.c.1.1		1
45.14	odd	6		4725.2.a.s.1.1		1
63.13	odd	6		1323.2.a.r.1.1		1
63.41	even	6		1323.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.a.a.1.1	✓	1	9.5	odd	6
189.2.a.d.1.1	yes	1	9.4	even	3
567.2.f.a.190.1		2	1.1	even	1	trivial
567.2.f.a.379.1		2	9.7	even	3	inner
567.2.f.h.190.1		2	3.2	odd	2
567.2.f.h.379.1		2	9.2	odd	6
1323.2.a.b.1.1		1	63.41	even	6
1323.2.a.r.1.1		1	63.13	odd	6
3024.2.a.l.1.1		1	36.23	even	6
3024.2.a.u.1.1		1	36.31	odd	6
4725.2.a.c.1.1		1	45.4	even	6
4725.2.a.s.1.1		1	45.14	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} +2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} +(1.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.00000 q^{17} -8.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(-4.00000 + 6.92820i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(2.00000 + 3.46410i) q^{25} -4.00000 q^{26} -2.00000 q^{28} +(-2.00000 - 3.46410i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(4.00000 - 6.92820i) q^{32} +(3.00000 + 5.19615i) q^{34} -1.00000 q^{35} -3.00000 q^{37} +(8.00000 + 13.8564i) q^{38} +(0.500000 - 0.866025i) q^{41} +(-5.50000 - 9.52628i) q^{43} +8.00000 q^{44} +12.0000 q^{46} +(4.50000 + 7.79423i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(4.00000 - 6.92820i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{53} +4.00000 q^{55} +(-4.00000 + 6.92820i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-2.00000 - 3.46410i) q^{61} +12.0000 q^{62} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} +12.0000 q^{71} +6.00000 q^{73} +(3.00000 + 5.19615i) q^{74} +(8.00000 - 13.8564i) q^{76} +(2.00000 - 3.46410i) q^{77} +(0.500000 + 0.866025i) q^{79} -4.00000 q^{80} -2.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-11.0000 + 19.0526i) q^{86} -2.00000 q^{89} +2.00000 q^{91} +(-6.00000 - 10.3923i) q^{92} +(9.00000 - 15.5885i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-6.00000 - 10.3923i) q^{97} +2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 4 q^{10} - 4 q^{11} + 2 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} - 16 q^{19} - 2 q^{20} - 8 q^{22} - 6 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{29} - 6 q^{31}+ \cdots + 4 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 - q^5 + q^7 + 4 * q^10 - 4 * q^11 + 2 * q^13 + 2 * q^14 + 4 * q^16 - 6 * q^17 - 16 * q^19 - 2 * q^20 - 8 * q^22 - 6 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^29 - 6 * q^31 + 8 * q^32 + 6 * q^34 - 2 * q^35 - 6 * q^37 + 16 * q^38 + q^41 - 11 * q^43 + 16 * q^44 + 24 * q^46 + 9 * q^47 - q^49 + 8 * q^50 + 4 * q^52 - 12 * q^53 + 8 * q^55 - 8 * q^58 - 15 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 2 * q^65 + 8 * q^67 + 6 * q^68 + 2 * q^70 + 24 * q^71 + 12 * q^73 + 6 * q^74 + 16 * q^76 + 4 * q^77 + q^79 - 8 * q^80 - 4 * q^82 - 9 * q^83 + 3 * q^85 - 22 * q^86 - 4 * q^89 + 4 * q^91 - 12 * q^92 + 18 * q^94 + 8 * q^95 - 12 * q^97 + 4 * q^98

Introduction

L-functions

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