LMFDB - Embedded newform 567.2.h.f.352.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (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:	$0$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.f.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})$	\(q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(4.00000 + 3.46410i) q^{14} -4.00000 q^{16} +(-0.500000 + 0.866025i) q^{19} +(2.00000 + 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 + 3.46410i) q^{28} +(-2.00000 - 3.46410i) q^{29} +9.00000 q^{31} -8.00000 q^{32} +(-1.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(5.00000 - 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(2.00000 - 3.46410i) q^{44} -6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.00000 - 1.73205i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} -12.0000 q^{59} +10.0000 q^{61} +18.0000 q^{62} -8.00000 q^{64} -2.00000 q^{65} -5.00000 q^{67} +(-2.00000 + 10.3923i) q^{70} -6.00000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(5.00000 - 1.73205i) q^{77} -1.00000 q^{79} +(-4.00000 - 6.92820i) q^{80} +(10.0000 - 17.3205i) q^{82} +(-3.00000 - 5.19615i) q^{83} +(-5.00000 - 8.66025i) q^{86} +(-8.00000 + 13.8564i) q^{89} +(-2.50000 + 0.866025i) q^{91} -12.0000 q^{94} -2.00000 q^{95} +(3.00000 + 5.19615i) q^{97} +(2.00000 + 13.8564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 2 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^7	$ 2 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{7} + 4 q^{10} + 2 q^{11} - q^{13} + 8 q^{14} - 8 q^{16} - q^{19} + 4 q^{20} + 4 q^{22} + q^{25} - 2 q^{26} + 8 q^{28} - 4 q^{29} + 18 q^{31} - 16 q^{32} - 2 q^{35} - 3 q^{37} - 2 q^{38} + 10 q^{41} - 5 q^{43} + 4 q^{44} - 12 q^{47} + 2 q^{49} + 2 q^{50} - 2 q^{52} - 12 q^{53} + 8 q^{55} - 8 q^{58} - 24 q^{59} + 20 q^{61} + 36 q^{62} - 16 q^{64} - 4 q^{65} - 10 q^{67} - 4 q^{70} - 12 q^{71} + 3 q^{73} - 6 q^{74} - 2 q^{76} + 10 q^{77} - 2 q^{79} - 8 q^{80} + 20 q^{82} - 6 q^{83} - 10 q^{86} - 16 q^{89} - 5 q^{91} - 24 q^{94} - 4 q^{95} + 6 q^{97} + 4 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^7 + 4 * q^10 + 2 * q^11 - q^13 + 8 * q^14 - 8 * q^16 - q^19 + 4 * q^20 + 4 * q^22 + q^25 - 2 * q^26 + 8 * q^28 - 4 * q^29 + 18 * q^31 - 16 * q^32 - 2 * q^35 - 3 * q^37 - 2 * q^38 + 10 * q^41 - 5 * q^43 + 4 * q^44 - 12 * q^47 + 2 * q^49 + 2 * q^50 - 2 * q^52 - 12 * q^53 + 8 * q^55 - 8 * q^58 - 24 * q^59 + 20 * q^61 + 36 * q^62 - 16 * q^64 - 4 * q^65 - 10 * q^67 - 4 * q^70 - 12 * q^71 + 3 * q^73 - 6 * q^74 - 2 * q^76 + 10 * q^77 - 2 * q^79 - 8 * q^80 + 20 * q^82 - 6 * q^83 - 10 * q^86 - 16 * q^89 - 5 * q^91 - 24 * q^94 - 4 * q^95 + 6 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.00000			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$3$		0			0
$3$		0			0
$4$	2.00000			1.00000
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	4.00000	+	3.46410i	1.06904	+	0.925820i
$15$		0			0
$16$	−4.00000			−1.00000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	2.00000	+	3.46410i	0.447214	+	0.774597i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	−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
$31$	9.00000			1.61645			0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000			1.61645			0.808224	+	0.588875i	$0.200429\pi$
$32$	−8.00000			−1.41421
$33$		0			0
$34$		0			0
$35$	−1.00000	+	5.19615i	−0.169031	+	0.878310i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$		0			0
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$		0			0
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	0.609994	−	0.792406i	$-0.291172\pi$
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	1.00000	−	1.73205i	0.141421	−	0.244949i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	18.0000			2.28600
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.00000			−0.248069
$66$		0			0
$67$	−5.00000			−0.610847			−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000			−0.610847			−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$		0			0
$70$	−2.00000	+	10.3923i	−0.239046	+	1.24212i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	5.00000	−	1.73205i	0.569803	−	0.197386i
$78$		0			0
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$	−4.00000	−	6.92820i	−0.447214	−	0.774597i
$81$		0			0
$82$	10.0000	−	17.3205i	1.10432	−	1.91273i
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$		0			0
$88$		0			0
$89$	−8.00000	+	13.8564i	−0.847998	+	1.46878i	0.0349934	+	0.999388i	$0.488859\pi$
$89$	−8.00000	+	13.8564i	−0.847998	+	1.46878i	−0.882992	+	0.469389i	$0.844474\pi$
$90$		0			0
$91$	−2.50000	+	0.866025i	−0.262071	+	0.0907841i
$92$		0			0
$93$		0			0
$94$	−12.0000			−1.23771
$95$	−2.00000			−0.205196
$96$		0			0
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	0.977173	−	0.212445i	$-0.0681426\pi$
$97$	3.00000	+	5.19615i	0.304604	+	0.527589i	−0.672569	+	0.740034i	$0.734809\pi$
$98$	2.00000	+	13.8564i	0.202031	+	1.39971i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$	−12.0000	−	20.7846i	−1.16554	−	2.01878i
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	−0.605308	−	0.795991i	$-0.706950\pi$
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	0.992003	+	0.126217i	$0.0402834\pi$
$108$		0			0
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$	8.00000			0.762770
$111$		0			0
$112$	−8.00000	−	6.92820i	−0.755929	−	0.654654i
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	−0.999425	−	0.0338931i	$-0.989209\pi$
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	0.529065	+	0.848581i	$0.322543\pi$
$114$		0			0
$115$		0			0
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$		0			0
$118$	−24.0000			−2.20938
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	20.0000			1.81071
$123$		0			0
$124$	18.0000			1.61645
$125$	12.0000			1.07331
$126$		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
$130$	−4.00000			−0.350823
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$		0			0
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$	−2.00000	+	10.3923i	−0.169031	+	0.878310i
$141$		0			0
$142$	−12.0000			−1.00702
$143$	1.00000	+	1.73205i	0.0836242	+	0.144841i
$144$		0			0
$145$	4.00000	−	6.92820i	0.332182	−	0.575356i
$146$	3.00000	+	5.19615i	0.248282	+	0.430037i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$		0			0
$154$	10.0000	−	3.46410i	0.805823	−	0.279145i
$155$	9.00000	+	15.5885i	0.722897	+	1.25210i
$156$		0			0
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−2.00000			−0.159111
$159$		0			0
$160$	−8.00000	−	13.8564i	−0.632456	−	1.09545i
$161$		0			0
$162$		0			0
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	10.0000	−	17.3205i	0.780869	−	1.35250i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	−0.457132	−	0.889399i	$-0.651123\pi$
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	0.998808	−	0.0488118i	$-0.0155435\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	8.00000			0.608229			0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000			0.608229			0.304114	+	0.952636i	$0.401639\pi$
$174$		0			0
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	−4.00000	+	6.92820i	−0.301511	+	0.522233i
$177$		0			0
$178$	−16.0000	+	27.7128i	−1.19925	+	2.07716i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−5.00000	+	1.73205i	−0.370625	+	0.128388i
$183$		0			0
$184$		0			0
$185$	−6.00000			−0.441129
$186$		0			0
$187$		0			0
$188$	−12.0000			−0.875190
$189$		0			0
$190$	−4.00000			−0.290191
$191$	10.0000			0.723575			0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000			0.723575			0.361787	+	0.932261i	$0.382167\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	6.00000	+	10.3923i	0.430775	+	0.746124i
$195$		0			0
$196$	2.00000	+	13.8564i	0.142857	+	0.989743i
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$		0			0
$202$	−2.00000	+	3.46410i	−0.140720	+	0.243733i
$203$	2.00000	−	10.3923i	0.140372	−	0.729397i
$204$		0			0
$205$	20.0000			1.39686
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	1.00000	+	1.73205i	0.0691714	+	0.119808i
$210$		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	$0.210633\pi$
$212$	−12.0000	−	20.7846i	−0.824163	−	1.42749i
$213$		0			0
$214$	8.00000	−	13.8564i	0.546869	−	0.947204i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	18.0000	+	15.5885i	1.22192	+	1.05821i
$218$	−9.00000	−	15.5885i	−0.609557	−	1.05578i
$219$		0			0
$220$	8.00000			0.539360
$221$		0			0
$222$		0			0
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	−16.0000	−	13.8564i	−1.06904	−	0.925820i
$225$		0			0
$226$	−10.0000	+	17.3205i	−0.665190	+	1.15214i
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$		0			0
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	−6.00000	−	10.3923i	−0.391397	−	0.677919i
$236$	−24.0000			−1.56227
$237$		0			0
$238$		0			0
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$		0			0
$244$	20.0000			1.28037
$245$	−11.0000	+	8.66025i	−0.702764	+	0.553283i
$246$		0			0
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$		0			0
$249$		0			0
$250$	24.0000			1.51789
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		0			0
$253$		0			0
$254$	−30.0000			−1.88237
$255$		0			0
$256$	16.0000			1.00000
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	−0.912222	−	0.409695i	$-0.865635\pi$
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	0.101305	−	0.994855i	$-0.467698\pi$
$258$		0			0
$259$	−7.50000	+	2.59808i	−0.466027	+	0.161437i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	14.0000	+	24.2487i	0.864923	+	1.49809i
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$		0			0
$265$	12.0000	−	20.7846i	0.737154	−	1.27679i
$266$	−5.00000	+	1.73205i	−0.306570	+	0.106199i
$267$		0			0
$268$	−10.0000			−0.610847
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$		0			0
$273$		0			0
$274$	12.0000	−	20.7846i	0.724947	−	1.25564i
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	3.00000	−	5.19615i	0.179928	−	0.311645i
$279$		0			0
$280$		0			0
$281$	2.00000	+	3.46410i	0.119310	+	0.206651i	0.919494	−	0.393103i	$-0.128598\pi$
$281$	2.00000	+	3.46410i	0.119310	+	0.206651i	−0.800184	+	0.599754i	$0.795265\pi$
$282$		0			0
$283$	−11.0000			−0.653882			−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000			−0.653882			−0.326941	+	0.945045i	$0.606018\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$	2.00000	+	3.46410i	0.118262	+	0.204837i
$287$	25.0000	−	8.66025i	1.47570	−	0.511199i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	8.00000	−	13.8564i	0.469776	−	0.813676i
$291$		0			0
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−4.00000	+	6.92820i	−0.233682	+	0.404750i	−0.958889	−	0.283782i	$-0.908411\pi$
$293$	−4.00000	+	6.92820i	−0.233682	+	0.404750i	0.725206	+	0.688531i	$0.241744\pi$
$294$		0			0
$295$	−12.0000	−	20.7846i	−0.698667	−	1.21013i
$296$		0			0
$297$		0			0
$298$	12.0000	+	20.7846i	0.695141	+	1.20402i
$299$		0			0
$300$		0			0
$301$	2.50000	−	12.9904i	0.144098	−	0.748753i
$302$	16.0000	−	27.7128i	0.920697	−	1.59469i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	10.0000	+	17.3205i	0.572598	+	0.991769i
$306$		0			0
$307$	−17.0000			−0.970241			−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000			−0.970241			−0.485121	+	0.874447i	$0.661224\pi$
$308$	10.0000	−	3.46410i	0.569803	−	0.197386i
$309$		0			0
$310$	18.0000	+	31.1769i	1.02233	+	1.77073i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	−28.0000			−1.58013
$315$		0			0
$316$	−2.00000			−0.112509
$317$	24.0000			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$318$		0			0
$319$	−8.00000			−0.447914
$320$	−8.00000	−	13.8564i	−0.447214	−	0.774597i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	14.0000	−	24.2487i	0.766046	−	1.32683i
$335$	−5.00000	−	8.66025i	−0.273179	−	0.473160i
$336$		0			0
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	12.0000	+	20.7846i	0.652714	+	1.13053i
$339$		0			0
$340$		0			0
$341$	9.00000	−	15.5885i	0.487377	−	0.844162i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$	16.0000			0.860165
$347$	32.0000			1.71785			0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000			1.71785			0.858925	+	0.512101i	$0.171133\pi$
$348$		0			0
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$	5.00000	−	1.73205i	0.267261	−	0.0925820i
$351$		0			0
$352$	−8.00000	+	13.8564i	−0.426401	+	0.738549i
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.0836583	+	0.996495i	$0.526660\pi$
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.821160	+	0.570697i	$0.806673\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	−16.0000	+	27.7128i	−0.847998	+	1.46878i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	26.0000			1.36653
$363$		0			0
$364$	−5.00000	+	1.73205i	−0.262071	+	0.0907841i
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$		0			0
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$		0			0
$369$		0			0
$370$	−12.0000			−0.623850
$371$	6.00000	−	31.1769i	0.311504	−	1.61862i
$372$		0			0
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.00000			0.206010
$378$		0			0
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$	−4.00000			−0.205196
$381$		0			0
$382$	20.0000			1.02329
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$	8.00000	+	6.92820i	0.407718	+	0.353094i
$386$	22.0000			1.11977
$387$		0			0
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	32.0000			1.61214
$395$	−1.00000	−	1.73205i	−0.0503155	−	0.0871489i
$396$		0			0
$397$	4.50000	−	7.79423i	0.225849	−	0.391181i	−0.730725	−	0.682672i	$-0.760818\pi$
$397$	4.50000	−	7.79423i	0.225849	−	0.391181i	0.956574	+	0.291491i	$0.0941512\pi$
$398$		0			0
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.828932	+	0.559350i	$0.188949\pi$
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.0699455	+	0.997551i	$0.477717\pi$
$402$		0			0
$403$	−4.50000	+	7.79423i	−0.224161	+	0.388258i
$404$	−2.00000	+	3.46410i	−0.0995037	+	0.172345i
$405$		0			0
$406$	4.00000	−	20.7846i	0.198517	−	1.03152i
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	5.00000			0.247234			0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000			0.247234			0.123617	+	0.992330i	$0.460551\pi$
$410$	40.0000			1.97546
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$	−24.0000	−	20.7846i	−1.18096	−	1.02274i
$414$		0			0
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$		0			0
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	0.222885	+	0.974845i	$0.428453\pi$
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	−0.955683	+	0.294398i	$0.904881\pi$
$420$		0			0
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	0.938623	−	0.344946i	$-0.112103\pi$
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	−0.768043	+	0.640398i	$0.778769\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	20.0000	+	17.3205i	0.967868	+	0.838198i
$428$	8.00000	−	13.8564i	0.386695	−	0.669775i
$429$		0			0
$430$	10.0000	−	17.3205i	0.482243	−	0.835269i
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$	36.0000	+	31.1769i	1.72806	+	1.49654i
$435$		0			0
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	−32.0000			−1.51695
$446$	−16.0000	−	27.7128i	−0.757622	−	1.31224i
$447$		0			0
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−10.0000	−	17.3205i	−0.470882	−	0.815591i
$452$	−10.0000	+	17.3205i	−0.470360	+	0.814688i
$453$		0			0
$454$	−18.0000	+	31.1769i	−0.844782	+	1.46321i
$455$	−4.00000	−	3.46410i	−0.187523	−	0.162400i
$456$		0			0
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	19.0000	+	32.9090i	0.887812	+	1.53773i
$459$		0			0
$460$		0			0
$461$	−10.0000	−	17.3205i	−0.465746	−	0.806696i	0.533488	−	0.845807i	$-0.320881\pi$
$461$	−10.0000	−	17.3205i	−0.465746	−	0.806696i	−0.999235	+	0.0391109i	$0.987547\pi$
$462$		0			0
$463$	8.50000	−	14.7224i	0.395029	−	0.684209i	−0.598076	−	0.801439i	$-0.704068\pi$
$463$	8.50000	−	14.7224i	0.395029	−	0.684209i	0.993105	+	0.117230i	$0.0374014\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$		0			0
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$468$		0			0
$469$	−10.0000	−	8.66025i	−0.461757	−	0.399893i
$470$	−12.0000	−	20.7846i	−0.553519	−	0.958723i
$471$		0			0
$472$		0			0
$473$	−10.0000			−0.459800
$474$		0			0
$475$	0.500000	+	0.866025i	0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$	−14.0000	+	24.2487i	−0.637683	+	1.10450i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$		0			0
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	−0.967632	−	0.252367i	$-0.918791\pi$
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	0.265260	−	0.964177i	$-0.414542\pi$
$488$		0			0
$489$		0			0
$490$	−22.0000	+	17.3205i	−0.993859	+	0.782461i
$491$	14.0000	−	24.2487i	0.631811	−	1.09433i	−0.355370	−	0.934726i	$-0.615645\pi$
$491$	14.0000	−	24.2487i	0.631811	−	1.09433i	0.987181	−	0.159603i	$-0.0510215\pi$
$492$		0			0
$493$		0			0
$494$	−1.00000	−	1.73205i	−0.0449921	−	0.0779287i
$495$		0			0
$496$	−36.0000			−1.61645
$497$	−12.0000	−	10.3923i	−0.538274	−	0.466159i
$498$		0			0
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	−0.899469	−	0.436984i	$-0.856047\pi$
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	0.0712957	−	0.997455i	$-0.477287\pi$
$500$	24.0000			1.07331
$501$		0			0
$502$	−16.0000			−0.714115
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$		0			0
$508$	−30.0000			−1.33103
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$		0			0
$511$	−1.50000	+	7.79423i	−0.0663561	+	0.344796i
$512$	32.0000			1.41421
$513$		0			0
$514$	−26.0000	−	45.0333i	−1.14681	−	1.98633i
$515$	−7.00000	+	12.1244i	−0.308457	+	0.534263i
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−15.0000	+	5.19615i	−0.659062	+	0.228306i
$519$		0			0
$520$		0			0
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	0.704137	−	0.710064i	$-0.251334\pi$
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	−0.967002	+	0.254769i	$0.918001\pi$
$522$		0			0
$523$	−15.5000	+	26.8468i	−0.677768	+	1.17393i	0.297884	+	0.954602i	$0.403719\pi$
$523$	−15.5000	+	26.8468i	−0.677768	+	1.17393i	−0.975652	+	0.219326i	$0.929614\pi$
$524$	14.0000	+	24.2487i	0.611593	+	1.05931i
$525$		0			0
$526$	−4.00000	+	6.92820i	−0.174408	+	0.302084i
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	24.0000	−	41.5692i	1.04249	−	1.80565i
$531$		0			0
$532$	−5.00000	+	1.73205i	−0.216777	+	0.0750939i
$533$	5.00000	+	8.66025i	0.216574	+	0.375117i
$534$		0			0
$535$	16.0000			0.691740
$536$		0			0
$537$		0			0
$538$	−6.00000	−	10.3923i	−0.258678	−	0.448044i
$539$	13.0000	+	5.19615i	0.559950	+	0.223814i
$540$		0			0
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$	−16.0000	+	27.7128i	−0.687259	+	1.19037i
$543$		0			0
$544$		0			0
$545$	9.00000	−	15.5885i	0.385518	−	0.667736i
$546$		0			0
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	−0.993028	−	0.117875i	$-0.962392\pi$
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	0.394432	−	0.918925i	$-0.370941\pi$
$548$	12.0000	−	20.7846i	0.512615	−	0.887875i
$549$		0			0
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	4.00000			0.170406
$552$		0			0
$553$	−2.00000	−	1.73205i	−0.0850487	−	0.0736543i
$554$	−13.0000	+	22.5167i	−0.552317	+	0.956641i
$555$		0			0
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	4.00000	−	20.7846i	0.169031	−	0.878310i
$561$		0			0
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	−26.0000			−1.09577			−0.547885	−	0.836554i	$-0.684567\pi$
$563$	−26.0000			−1.09577			−0.547885	+	0.836554i	$0.684567\pi$
$564$		0			0
$565$	−20.0000			−0.841406
$566$	−22.0000			−0.924729
$567$		0			0
$568$		0			0
$569$	−26.0000			−1.08998			−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000			−1.08998			−0.544988	+	0.838444i	$0.683466\pi$
$570$		0			0
$571$	−19.0000			−0.795125			−0.397563	−	0.917575i	$-0.630144\pi$
$571$	−19.0000			−0.795125			−0.397563	+	0.917575i	$0.630144\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$	50.0000	−	17.3205i	2.08696	−	0.722944i
$575$		0			0
$576$		0			0
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	0.986922	−	0.161198i	$-0.0515357\pi$
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	−0.633062	+	0.774101i	$0.718202\pi$
$578$	17.0000	−	29.4449i	0.707107	−	1.22474i
$579$		0			0
$580$	8.00000	−	13.8564i	0.332182	−	0.575356i
$581$	3.00000	−	15.5885i	0.124461	−	0.646718i
$582$		0			0
$583$	−24.0000			−0.993978
$584$		0			0
$585$		0			0
$586$	−8.00000	+	13.8564i	−0.330477	+	0.572403i
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	0.652355	−	0.757914i	$-0.273781\pi$
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	−0.982550	+	0.185999i	$0.940448\pi$
$588$		0			0
$589$	−4.50000	+	7.79423i	−0.185419	+	0.321156i
$590$	−24.0000	−	41.5692i	−0.988064	−	1.71138i
$591$		0			0
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$	12.0000	+	20.7846i	0.491539	+	0.851371i
$597$		0			0
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	0.943090	−	0.332538i	$-0.107905\pi$
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	−0.759531	+	0.650471i	$0.774572\pi$
$602$	5.00000	−	25.9808i	0.203785	−	1.05890i
$603$		0			0
$604$	16.0000	−	27.7128i	0.651031	−	1.12762i
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	4.00000	−	6.92820i	0.162221	−	0.280976i
$609$		0			0
$610$	20.0000	+	34.6410i	0.809776	+	1.40257i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$	−34.0000			−1.37213
$615$		0			0
$616$		0			0
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$		0			0
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$	18.0000	+	31.1769i	0.722897	+	1.25210i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−40.0000	+	13.8564i	−1.60257	+	0.555145i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−2.00000			−0.0799361
$627$		0			0
$628$	−28.0000			−1.11732
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$		0			0
$634$	48.0000			1.90632
$635$	−15.0000	−	25.9808i	−0.595257	−	1.03102i
$636$		0			0
$637$	−6.50000	−	2.59808i	−0.257539	−	0.102940i
$638$	−16.0000			−0.633446
$639$		0			0
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.00000	−	1.73205i	−0.0393141	−	0.0680939i	0.845699	−	0.533660i	$-0.179184\pi$
$647$	−1.00000	−	1.73205i	−0.0393141	−	0.0680939i	−0.885013	+	0.465566i	$0.845851\pi$
$648$		0			0
$649$	−12.0000	+	20.7846i	−0.471041	+	0.815867i
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$		0			0
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	−14.0000	+	24.2487i	−0.547025	+	0.947476i
$656$	−20.0000	+	34.6410i	−0.780869	+	1.35250i
$657$		0			0
$658$	−24.0000	−	20.7846i	−0.935617	−	0.810268i
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	−41.0000			−1.59472			−0.797358	−	0.603507i	$-0.793769\pi$
$661$	−41.0000			−1.59472			−0.797358	+	0.603507i	$0.793769\pi$
$662$	−50.0000			−1.94331
$663$		0			0
$664$		0			0
$665$	−4.00000	−	3.46410i	−0.155113	−	0.134332i
$666$		0			0
$667$		0			0
$668$	14.0000	−	24.2487i	0.541676	−	0.938211i
$669$		0			0
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$	10.0000	−	17.3205i	0.386046	−	0.668651i
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$	−13.0000	+	22.5167i	−0.500741	+	0.867309i
$675$		0			0
$676$	12.0000	+	20.7846i	0.461538	+	0.799408i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$	−3.00000	+	15.5885i	−0.115129	+	0.598230i
$680$		0			0
$681$		0			0
$682$	18.0000	−	31.1769i	0.689256	−	1.19383i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$	−20.0000	+	31.1769i	−0.763604	+	1.19034i
$687$		0			0
$688$	10.0000	+	17.3205i	0.381246	+	0.660338i
$689$	12.0000			0.457164
$690$		0			0
$691$	−37.0000			−1.40755			−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000			−1.40755			−0.703773	+	0.710425i	$0.748503\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$	64.0000			2.42941
$695$	6.00000			0.227593
$696$		0			0
$697$		0			0
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$		0			0
$700$	5.00000	−	1.73205i	0.188982	−	0.0654654i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−1.50000	−	2.59808i	−0.0565736	−	0.0979883i
$704$	−8.00000	+	13.8564i	−0.301511	+	0.522233i
$705$		0			0
$706$	−34.0000	+	58.8897i	−1.27961	+	2.21634i
$707$	−5.00000	+	1.73205i	−0.188044	+	0.0651405i
$708$		0			0
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$	−12.0000	−	20.7846i	−0.450352	−	0.780033i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$		0			0
$718$	−20.0000	+	34.6410i	−0.746393	+	1.29279i
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$		0			0
$721$	−3.50000	+	18.1865i	−0.130347	+	0.677302i
$722$	18.0000	+	31.1769i	0.669891	+	1.16028i
$723$		0			0
$724$	26.0000			0.966282
$725$	−4.00000			−0.148556
$726$		0			0
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	0.961020	−	0.276479i	$-0.0891678\pi$
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	−0.719948	+	0.694028i	$0.755834\pi$
$728$		0			0
$729$		0			0
$730$	−6.00000	+	10.3923i	−0.222070	+	0.384636i
$731$		0			0
$732$		0			0
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	0.970642	−	0.240527i	$-0.0773202\pi$
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	−0.693624	+	0.720338i	$0.743987\pi$
$734$	9.00000	−	15.5885i	0.332196	−	0.575380i
$735$		0			0
$736$		0			0
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$		0			0
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	0.970360	−	0.241665i	$-0.0776935\pi$
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	−0.694468	+	0.719524i	$0.744360\pi$
$740$	−12.0000			−0.441129
$741$		0			0
$742$	12.0000	−	62.3538i	0.440534	−	2.28908i
$743$	−21.0000	+	36.3731i	−0.770415	+	1.33440i	0.166920	+	0.985970i	$0.446618\pi$
$743$	−21.0000	+	36.3731i	−0.770415	+	1.33440i	−0.937336	+	0.348428i	$0.886716\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$	−23.0000	−	39.8372i	−0.842090	−	1.45854i
$747$		0			0
$748$		0			0
$749$	20.0000	−	6.92820i	0.730784	−	0.253151i
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$	24.0000			0.875190
$753$		0			0
$754$	8.00000			0.291343
$755$	32.0000			1.16460
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	6.00000			0.217930
$759$		0			0
$760$		0			0
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$		0			0
$763$	4.50000	−	23.3827i	0.162911	−	0.846510i
$764$	20.0000			0.723575
$765$		0			0
$766$	12.0000	+	20.7846i	0.433578	+	0.750978i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		0			0
$769$	24.5000	−	42.4352i	0.883493	−	1.53025i	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	24.5000	−	42.4352i	0.883493	−	1.53025i	0.847432	−	0.530904i	$-0.178148\pi$
$770$	16.0000	+	13.8564i	0.576600	+	0.499350i
$771$		0			0
$772$	22.0000			0.791797
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	0.990997	+	0.133887i	$0.0427458\pi$
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	−0.379549	+	0.925172i	$0.623921\pi$
$774$		0			0
$775$	4.50000	−	7.79423i	0.161645	−	0.279977i
$776$		0			0
$777$		0			0
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	5.00000	+	8.66025i	0.179144	+	0.310286i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$		0			0
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$	−14.0000	−	24.2487i	−0.499681	−	0.865474i
$786$		0			0
$787$	40.0000			1.42585			0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000			1.42585			0.712923	+	0.701242i	$0.247371\pi$
$788$	32.0000			1.13995
$789$		0			0
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	−25.0000	+	8.66025i	−0.888898	+	0.307923i
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		0			0
$796$		0			0
$797$	4.00000	−	6.92820i	0.141687	−	0.245410i	−0.786445	−	0.617661i	$-0.788081\pi$
$797$	4.00000	−	6.92820i	0.141687	−	0.245410i	0.928132	+	0.372251i	$0.121414\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000	+	6.92820i	−0.141421	+	0.244949i
$801$		0			0
$802$	36.0000	+	62.3538i	1.27120	+	2.20179i
$803$	6.00000			0.211735
$804$		0			0
$805$		0			0
$806$	−9.00000	+	15.5885i	−0.317011	+	0.549080i
$807$		0			0
$808$		0			0
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	4.00000	−	20.7846i	0.140372	−	0.729397i
$813$		0			0
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	−8.00000			−0.280228
$816$		0			0
$817$	5.00000			0.174928
$818$	10.0000			0.349642
$819$		0			0
$820$	40.0000			1.39686
$821$	2.00000			0.0698005			0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000			0.0698005			0.0349002	+	0.999391i	$0.488889\pi$
$822$		0			0
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$		0			0
$825$		0			0
$826$	−48.0000	−	41.5692i	−1.67013	−	1.44638i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	−0.964107	−	0.265513i	$-0.914459\pi$
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	0.252113	−	0.967698i	$-0.418875\pi$
$830$	12.0000	−	20.7846i	0.416526	−	0.721444i
$831$		0			0
$832$	4.00000	−	6.92820i	0.138675	−	0.240192i
$833$		0			0
$834$		0			0
$835$	28.0000			0.968980
$836$	2.00000	+	3.46410i	0.0691714	+	0.119808i
$837$		0			0
$838$	−30.0000	+	51.9615i	−1.03633	+	1.79498i
$839$	22.0000	+	38.1051i	0.759524	+	1.31553i	0.943093	+	0.332528i	$0.107902\pi$
$839$	22.0000	+	38.1051i	0.759524	+	1.31553i	−0.183569	+	0.983007i	$0.558765\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	7.00000	+	12.1244i	0.241236	+	0.417833i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−12.0000	+	20.7846i	−0.412813	+	0.715012i
$846$		0			0
$847$	−3.50000	+	18.1865i	−0.120261	+	0.624897i
$848$	24.0000	+	41.5692i	0.824163	+	1.42749i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	0.393753	−	0.919216i	$-0.371177\pi$
$854$	40.0000	+	34.6410i	1.36877	+	1.18539i
$855$		0			0
$856$		0			0
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	−0.451958	−	0.892039i	$-0.649274\pi$
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	0.998508	−	0.0546125i	$-0.0173923\pi$
$858$		0			0
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$	10.0000	−	17.3205i	0.340997	−	0.590624i
$861$		0			0
$862$	18.0000	+	31.1769i	0.613082	+	1.06189i
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.118291	−	0.992979i	$-0.462258\pi$
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.800799	−	0.598933i	$-0.204408\pi$
$864$		0			0
$865$	8.00000	+	13.8564i	0.272008	+	0.471132i
$866$	62.0000			2.10685
$867$		0			0
$868$	36.0000	+	31.1769i	1.22192	+	1.05821i
$869$	−1.00000	+	1.73205i	−0.0339227	+	0.0587558i
$870$		0			0
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.0000	+	20.7846i	0.811348	+	0.702648i
$876$		0			0
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$		0			0
$880$	−16.0000			−0.539360
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$		0			0
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$		0			0
$885$		0			0
$886$	24.0000			0.806296
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	0.996484	+	0.0837878i	$0.0267018\pi$
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	−0.425679	+	0.904874i	$0.639965\pi$
$888$		0			0
$889$	−30.0000	−	25.9808i	−1.00617	−	0.871367i
$890$	−64.0000			−2.14528
$891$		0			0
$892$	−16.0000	−	27.7128i	−0.535720	−	0.927894i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$	2.00000	−	3.46410i	0.0668526	−	0.115792i
$896$		0			0
$897$		0			0
$898$	−36.0000			−1.20134
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$		0			0
$901$		0			0
$902$	−20.0000	−	34.6410i	−0.665927	−	1.15342i
$903$		0			0
$904$		0			0
$905$	13.0000	+	22.5167i	0.432135	+	0.748479i
$906$		0			0
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	−18.0000	+	31.1769i	−0.597351	+	1.03464i
$909$		0			0
$910$	−8.00000	−	6.92820i	−0.265197	−	0.229668i
$911$	12.0000	+	20.7846i	0.397578	+	0.688625i	0.993426	−	0.114472i	$-0.0365176\pi$
$911$	12.0000	+	20.7846i	0.397578	+	0.688625i	−0.595849	+	0.803097i	$0.703184\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$	−22.0000			−0.727695
$915$		0			0
$916$	19.0000	+	32.9090i	0.627778	+	1.08734i
$917$	−7.00000	+	36.3731i	−0.231160	+	1.20114i
$918$		0			0
$919$	−11.5000	+	19.9186i	−0.379350	+	0.657053i	−0.990968	−	0.134100i	$-0.957186\pi$
$919$	−11.5000	+	19.9186i	−0.379350	+	0.657053i	0.611618	+	0.791153i	$0.290519\pi$
$920$		0			0
$921$		0			0
$922$	−20.0000	−	34.6410i	−0.658665	−	1.14084i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$		0			0
$928$	16.0000	+	27.7128i	0.525226	+	0.909718i
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$	−6.50000	−	2.59808i	−0.213029	−	0.0851485i
$932$	−6.00000	+	10.3923i	−0.196537	+	0.340411i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	15.0000			0.490029			0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000			0.490029			0.245014	+	0.969519i	$0.421207\pi$
$938$	−20.0000	−	17.3205i	−0.653023	−	0.565535i
$939$		0			0
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	−4.00000			−0.130396			−0.0651981	−	0.997872i	$-0.520768\pi$
$941$	−4.00000			−0.130396			−0.0651981	+	0.997872i	$0.520768\pi$
$942$		0			0
$943$		0			0
$944$	48.0000			1.56227
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$		0			0
$949$	−3.00000			−0.0973841
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$		0			0
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$		0			0
$955$	10.0000	+	17.3205i	0.323592	+	0.560478i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	28.0000	−	48.4974i	0.904639	−	1.56688i
$959$	30.0000	−	10.3923i	0.968751	−	0.335585i
$960$		0			0
$961$	50.0000			1.61290
$962$	−3.00000	−	5.19615i	−0.0967239	−	0.167531i
$963$		0			0
$964$	−14.0000	+	24.2487i	−0.450910	+	0.780998i
$965$	11.0000	+	19.0526i	0.354103	+	0.613324i
$966$		0			0
$967$	−9.50000	+	16.4545i	−0.305499	+	0.529140i	−0.977372	−	0.211526i	$-0.932157\pi$
$967$	−9.50000	+	16.4545i	−0.305499	+	0.529140i	0.671873	+	0.740666i	$0.265490\pi$
$968$		0			0
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$		0			0
$973$	7.50000	−	2.59808i	0.240439	−	0.0832905i
$974$	−31.0000	−	53.6936i	−0.993304	−	1.72045i
$975$		0			0
$976$	−40.0000			−1.28037
$977$	−18.0000			−0.575871			−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000			−0.575871			−0.287936	+	0.957650i	$0.592969\pi$
$978$		0			0
$979$	16.0000	+	27.7128i	0.511362	+	0.885705i
$980$	−22.0000	+	17.3205i	−0.702764	+	0.553283i
$981$		0			0
$982$	28.0000	−	48.4974i	0.893516	−	1.54761i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$		0			0
$987$		0			0
$988$	−1.00000	−	1.73205i	−0.0318142	−	0.0551039i
$989$		0			0
$990$		0			0
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	−72.0000			−2.28600
$993$		0			0
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$		0			0
$996$		0			0
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	−0.976333	−	0.216274i	$-0.930610\pi$
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	0.675465	+	0.737392i	$0.263943\pi$
$998$	−37.0000	−	64.0859i	−1.17121	−	2.02860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.f.352.1		2
3.2	odd	2		567.2.h.a.352.1		2
7.4	even	3		567.2.g.a.109.1		2
9.2	odd	6		567.2.g.f.541.1		2
9.4	even	3		21.2.e.a.16.1	yes	2
9.5	odd	6		63.2.e.b.37.1		2
9.7	even	3		567.2.g.a.541.1		2
21.11	odd	6		567.2.g.f.109.1		2
36.23	even	6		1008.2.s.d.289.1		2
36.31	odd	6		336.2.q.f.289.1		2
45.4	even	6		525.2.i.e.226.1		2
45.13	odd	12		525.2.r.e.499.2		4
45.22	odd	12		525.2.r.e.499.1		4
63.4	even	3		21.2.e.a.4.1	✓	2
63.5	even	6		441.2.a.a.1.1		1
63.11	odd	6		567.2.h.a.298.1		2
63.13	odd	6		147.2.e.a.79.1		2
63.23	odd	6		441.2.a.b.1.1		1
63.25	even	3	inner	567.2.h.f.298.1		2
63.31	odd	6		147.2.e.a.67.1		2
63.32	odd	6		63.2.e.b.46.1		2
63.40	odd	6		147.2.a.b.1.1		1
63.41	even	6		441.2.e.e.226.1		2
63.58	even	3		147.2.a.c.1.1		1
63.59	even	6		441.2.e.e.361.1		2
72.13	even	6		1344.2.q.m.961.1		2
72.67	odd	6		1344.2.q.c.961.1		2
252.23	even	6		7056.2.a.bp.1.1		1
252.31	even	6		2352.2.q.c.1537.1		2
252.67	odd	6		336.2.q.f.193.1		2
252.95	even	6		1008.2.s.d.865.1		2
252.103	even	6		2352.2.a.w.1.1		1
252.131	odd	6		7056.2.a.m.1.1		1
252.139	even	6		2352.2.q.c.961.1		2
252.247	odd	6		2352.2.a.d.1.1		1
315.4	even	6		525.2.i.e.151.1		2
315.67	odd	12		525.2.r.e.424.2		4
315.184	even	6		3675.2.a.a.1.1		1
315.193	odd	12		525.2.r.e.424.1		4
315.229	odd	6		3675.2.a.c.1.1		1
504.67	odd	6		1344.2.q.c.193.1		2
504.229	odd	6		9408.2.a.bz.1.1		1
504.355	even	6		9408.2.a.k.1.1		1
504.373	even	6		9408.2.a.bg.1.1		1
504.445	even	6		1344.2.q.m.193.1		2
504.499	odd	6		9408.2.a.cv.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	63.4	even	3
21.2.e.a.16.1	yes	2	9.4	even	3
63.2.e.b.37.1		2	9.5	odd	6
63.2.e.b.46.1		2	63.32	odd	6
147.2.a.b.1.1		1	63.40	odd	6
147.2.a.c.1.1		1	63.58	even	3
147.2.e.a.67.1		2	63.31	odd	6
147.2.e.a.79.1		2	63.13	odd	6
336.2.q.f.193.1		2	252.67	odd	6
336.2.q.f.289.1		2	36.31	odd	6
441.2.a.a.1.1		1	63.5	even	6
441.2.a.b.1.1		1	63.23	odd	6
441.2.e.e.226.1		2	63.41	even	6
441.2.e.e.361.1		2	63.59	even	6
525.2.i.e.151.1		2	315.4	even	6
525.2.i.e.226.1		2	45.4	even	6
525.2.r.e.424.1		4	315.193	odd	12
525.2.r.e.424.2		4	315.67	odd	12
525.2.r.e.499.1		4	45.22	odd	12
525.2.r.e.499.2		4	45.13	odd	12
567.2.g.a.109.1		2	7.4	even	3
567.2.g.a.541.1		2	9.7	even	3
567.2.g.f.109.1		2	21.11	odd	6
567.2.g.f.541.1		2	9.2	odd	6
567.2.h.a.298.1		2	63.11	odd	6
567.2.h.a.352.1		2	3.2	odd	2
567.2.h.f.298.1		2	63.25	even	3	inner
567.2.h.f.352.1		2	1.1	even	1	trivial
1008.2.s.d.289.1		2	36.23	even	6
1008.2.s.d.865.1		2	252.95	even	6
1344.2.q.c.193.1		2	504.67	odd	6
1344.2.q.c.961.1		2	72.67	odd	6
1344.2.q.m.193.1		2	504.445	even	6
1344.2.q.m.961.1		2	72.13	even	6
2352.2.a.d.1.1		1	252.247	odd	6
2352.2.a.w.1.1		1	252.103	even	6
2352.2.q.c.961.1		2	252.139	even	6
2352.2.q.c.1537.1		2	252.31	even	6
3675.2.a.a.1.1		1	315.184	even	6
3675.2.a.c.1.1		1	315.229	odd	6
7056.2.a.m.1.1		1	252.131	odd	6
7056.2.a.bp.1.1		1	252.23	even	6
9408.2.a.k.1.1		1	504.355	even	6
9408.2.a.bg.1.1		1	504.373	even	6
9408.2.a.bz.1.1		1	504.229	odd	6
9408.2.a.cv.1.1		1	504.499	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(4.00000 + 3.46410i) q^{14} -4.00000 q^{16} +(-0.500000 + 0.866025i) q^{19} +(2.00000 + 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 + 3.46410i) q^{28} +(-2.00000 - 3.46410i) q^{29} +9.00000 q^{31} -8.00000 q^{32} +(-1.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(5.00000 - 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(2.00000 - 3.46410i) q^{44} -6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.00000 - 1.73205i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} -12.0000 q^{59} +10.0000 q^{61} +18.0000 q^{62} -8.00000 q^{64} -2.00000 q^{65} -5.00000 q^{67} +(-2.00000 + 10.3923i) q^{70} -6.00000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(5.00000 - 1.73205i) q^{77} -1.00000 q^{79} +(-4.00000 - 6.92820i) q^{80} +(10.0000 - 17.3205i) q^{82} +(-3.00000 - 5.19615i) q^{83} +(-5.00000 - 8.66025i) q^{86} +(-8.00000 + 13.8564i) q^{89} +(-2.50000 + 0.866025i) q^{91} -12.0000 q^{94} -2.00000 q^{95} +(3.00000 + 5.19615i) q^{97} +(2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 2 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^7	\( 2 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{7} + 4 q^{10} + 2 q^{11} - q^{13} + 8 q^{14} - 8 q^{16} - q^{19} + 4 q^{20} + 4 q^{22} + q^{25} - 2 q^{26} + 8 q^{28} - 4 q^{29} + 18 q^{31} - 16 q^{32} - 2 q^{35} - 3 q^{37} - 2 q^{38} + 10 q^{41} - 5 q^{43} + 4 q^{44} - 12 q^{47} + 2 q^{49} + 2 q^{50} - 2 q^{52} - 12 q^{53} + 8 q^{55} - 8 q^{58} - 24 q^{59} + 20 q^{61} + 36 q^{62} - 16 q^{64} - 4 q^{65} - 10 q^{67} - 4 q^{70} - 12 q^{71} + 3 q^{73} - 6 q^{74} - 2 q^{76} + 10 q^{77} - 2 q^{79} - 8 q^{80} + 20 q^{82} - 6 q^{83} - 10 q^{86} - 16 q^{89} - 5 q^{91} - 24 q^{94} - 4 q^{95} + 6 q^{97} + 4 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^7 + 4 * q^10 + 2 * q^11 - q^13 + 8 * q^14 - 8 * q^16 - q^19 + 4 * q^20 + 4 * q^22 + q^25 - 2 * q^26 + 8 * q^28 - 4 * q^29 + 18 * q^31 - 16 * q^32 - 2 * q^35 - 3 * q^37 - 2 * q^38 + 10 * q^41 - 5 * q^43 + 4 * q^44 - 12 * q^47 + 2 * q^49 + 2 * q^50 - 2 * q^52 - 12 * q^53 + 8 * q^55 - 8 * q^58 - 24 * q^59 + 20 * q^61 + 36 * q^62 - 16 * q^64 - 4 * q^65 - 10 * q^67 - 4 * q^70 - 12 * q^71 + 3 * q^73 - 6 * q^74 - 2 * q^76 + 10 * q^77 - 2 * q^79 - 8 * q^80 + 20 * q^82 - 6 * q^83 - 10 * q^86 - 16 * q^89 - 5 * q^91 - 24 * q^94 - 4 * q^95 + 6 * q^97 + 4 * q^98

Introduction

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