LMFDB - Embedded newform 567.2.g.f.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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, 4]))

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

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

chi := DirichletCharacter("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.f.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +(2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(5.00000 + 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} -1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-5.00000 + 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{50} +2.00000 q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +8.00000 q^{58} +(-6.00000 - 10.3923i) q^{59} +(-5.00000 + 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.50000 + 4.33013i) q^{67} +(10.0000 + 3.46410i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} -6.00000 q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.00000 + 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} +(3.00000 + 5.19615i) q^{83} -10.0000 q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(3.00000 + 5.19615i) q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + q^{7}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + q^7	$ 2 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + q^{7} + 4 q^{10} + 4 q^{11} - q^{13} + 10 q^{14} + 4 q^{16} - q^{19} - 4 q^{20} + 4 q^{22} - 2 q^{25} + 2 q^{26} + 8 q^{28} + 4 q^{29} - 9 q^{31} - 8 q^{32} + 2 q^{35} - 3 q^{37} - 4 q^{38} - 10 q^{41} - 5 q^{43} - 4 q^{44} - 6 q^{47} - 13 q^{49} - 2 q^{50} + 4 q^{52} + 12 q^{53} + 8 q^{55} + 16 q^{58} - 12 q^{59} - 10 q^{61} - 36 q^{62} - 16 q^{64} - 2 q^{65} + 5 q^{67} + 20 q^{70} + 12 q^{71} + 3 q^{73} - 12 q^{74} - 2 q^{76} + 2 q^{77} + q^{79} + 8 q^{80} + 20 q^{82} + 6 q^{83} - 20 q^{86} + 16 q^{89} - 5 q^{91} + 12 q^{94} - 2 q^{95} + 6 q^{97} - 4 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + q^7 + 4 * q^10 + 4 * q^11 - q^13 + 10 * q^14 + 4 * q^16 - q^19 - 4 * q^20 + 4 * q^22 - 2 * q^25 + 2 * q^26 + 8 * q^28 + 4 * q^29 - 9 * q^31 - 8 * q^32 + 2 * q^35 - 3 * q^37 - 4 * q^38 - 10 * q^41 - 5 * q^43 - 4 * q^44 - 6 * q^47 - 13 * q^49 - 2 * q^50 + 4 * q^52 + 12 * q^53 + 8 * q^55 + 16 * q^58 - 12 * q^59 - 10 * q^61 - 36 * q^62 - 16 * q^64 - 2 * q^65 + 5 * q^67 + 20 * q^70 + 12 * q^71 + 3 * q^73 - 12 * q^74 - 2 * q^76 + 2 * q^77 + q^79 + 8 * q^80 + 20 * q^82 + 6 * q^83 - 20 * q^86 + 16 * q^89 - 5 * q^91 + 12 * q^94 - 2 * q^95 + 6 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$		0			0
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		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	$0.210951\pi$
$14$	5.00000	+	1.73205i	1.33631	+	0.462910i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	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	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$		0			0
$31$	−4.50000	−	7.79423i	−0.808224	−	1.39988i	−0.914093	−	0.405505i	$-0.867096\pi$
$31$	−4.50000	−	7.79423i	−0.808224	−	1.39988i	0.105869	−	0.994380i	$-0.466238\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$		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	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$		0			0
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$		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
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−1.00000	+	1.73205i	−0.141421	+	0.244949i
$51$		0			0
$52$	2.00000			0.277350
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	8.00000			1.05045
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	−18.0000			−2.28600
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$		0			0
$70$	10.0000	+	3.46410i	1.19523	+	0.414039i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	−6.00000			−0.697486
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	1.00000	+	5.19615i	0.113961	+	0.592157i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	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	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$		0			0
$85$		0			0
$86$	−10.0000			−1.07833
$87$		0			0
$88$		0			0
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	0.882992	+	0.469389i	$0.155526\pi$
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	−0.0349934	+	0.999388i	$0.511141\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$		0			0
$93$		0			0
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$		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
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		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	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$		0			0
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$	4.00000	−	6.92820i	0.381385	−	0.660578i
$111$		0			0
$112$	10.0000	+	3.46410i	0.944911	+	0.327327i
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	−0.529065	−	0.848581i	$-0.677457\pi$
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	0.999425	+	0.0338931i	$0.0107906\pi$
$114$		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
$121$	−7.00000			−0.636364
$122$	10.0000	+	17.3205i	0.905357	+	1.56813i
$123$		0			0
$124$	−9.00000	+	15.5885i	−0.808224	+	1.39988i
$125$	−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
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	14.0000			1.22319			0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000			1.22319			0.611593	+	0.791173i	$0.290529\pi$
$132$		0			0
$133$	2.00000	−	1.73205i	0.173422	−	0.150188i
$134$	10.0000			0.863868
$135$		0			0
$136$		0			0
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		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	$0.126059\pi$
$140$	8.00000	−	6.92820i	0.676123	−	0.585540i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−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
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		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
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$		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	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	20.0000			1.56174
$165$		0			0
$166$	12.0000			0.931381
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	0.457132	+	0.889399i	$0.348877\pi$
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	−0.998808	+	0.0488118i	$0.984457\pi$
$168$		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
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	−0.672949	−	0.739689i	$-0.734973\pi$
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	0.977064	+	0.212947i	$0.0683062\pi$
$174$		0			0
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$		0			0
$178$	32.0000			2.39850
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−4.00000	+	3.46410i	−0.296500	+	0.256776i
$183$		0			0
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$	−4.00000			−0.290191
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	−0.626468	−	0.779447i	$-0.715500\pi$
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	0.988255	+	0.152813i	$0.0488333\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	12.0000			0.861550
$195$		0			0
$196$	11.0000	+	8.66025i	0.785714	+	0.618590i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$		0			0
$202$	−2.00000	+	3.46410i	−0.140720	+	0.243733i
$203$	−8.00000	+	6.92820i	−0.561490	+	0.486265i
$204$		0			0
$205$	−10.0000	+	17.3205i	−0.698430	+	1.20972i
$206$	−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	$0.210633\pi$
$212$	−24.0000			−1.64833
$213$		0			0
$214$	−16.0000			−1.09374
$215$	−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
$220$	−4.00000	−	6.92820i	−0.269680	−	0.467099i
$221$		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
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$		0			0
$229$	−19.0000			−1.25556			−0.627778	−	0.778393i	$-0.716035\pi$
$229$	−19.0000			−1.25556			−0.627778	+	0.778393i	$0.716035\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	−12.0000	+	20.7846i	−0.781133	+	1.35296i
$237$		0			0
$238$		0			0
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$	20.0000			1.28037
$245$	−13.0000	+	5.19615i	−0.830540	+	0.331970i
$246$		0			0
$247$	1.00000			0.0636285
$248$		0			0
$249$		0			0
$250$	−12.0000	+	20.7846i	−0.758947	+	1.31453i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$		0			0
$254$	−15.0000	+	25.9808i	−0.941184	+	1.63018i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−26.0000			−1.62184			−0.810918	−	0.585160i	$-0.801032\pi$
$257$	−26.0000			−1.62184			−0.810918	+	0.585160i	$0.801032\pi$
$258$		0			0
$259$	6.00000	−	5.19615i	0.372822	−	0.322873i
$260$	4.00000			0.248069
$261$		0			0
$262$	14.0000	−	24.2487i	0.864923	−	1.49809i
$263$	−4.00000			−0.246651			−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000			−0.246651			−0.123325	+	0.992366i	$0.539356\pi$
$264$		0			0
$265$	12.0000	−	20.7846i	0.737154	−	1.27679i
$266$	−1.00000	−	5.19615i	−0.0613139	−	0.318597i
$267$		0			0
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$		0			0
$274$	12.0000	−	20.7846i	0.724947	−	1.25564i
$275$	−2.00000			−0.120605
$276$		0			0
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$		0			0
$280$		0			0
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	0.800184	−	0.599754i	$-0.204735\pi$
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	−0.919494	+	0.393103i	$0.871402\pi$
$282$		0			0
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	0.981903	−	0.189383i	$-0.0606488\pi$
$283$	5.50000	+	9.52628i	0.326941	+	0.566279i	−0.654962	+	0.755662i	$0.727315\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		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
$290$	16.0000			0.939552
$291$		0			0
$292$	−6.00000			−0.351123
$293$	4.00000	−	6.92820i	0.233682	−	0.404750i	−0.725206	−	0.688531i	$-0.758256\pi$
$293$	4.00000	−	6.92820i	0.233682	−	0.404750i	0.958889	+	0.283782i	$0.0915890\pi$
$294$		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
$301$	10.0000	−	8.66025i	0.576390	−	0.499169i
$302$	−16.0000	+	27.7128i	−0.920697	+	1.59469i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	−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	$0.661224\pi$
$308$	8.00000	−	6.92820i	0.455842	−	0.394771i
$309$		0			0
$310$	−36.0000			−2.04466
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	28.0000			1.58013
$315$		0			0
$316$	−2.00000			−0.112509
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−16.0000			−0.894427
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$	−8.00000			−0.443079
$327$		0			0
$328$		0			0
$329$	−15.0000	−	5.19615i	−0.826977	−	0.286473i
$330$		0			0
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	−0.285722	−	0.958313i	$-0.592233\pi$
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	0.972784	−	0.231714i	$-0.0744333\pi$
$332$	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	$0.281872\pi$
$338$	24.0000			1.30543
$339$		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
$346$	−8.00000	−	13.8564i	−0.430083	−	0.744925i
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	0.872955	+	0.487800i	$0.162201\pi$
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	−0.0140303	+	0.999902i	$0.504466\pi$
$348$		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
$353$	−34.0000			−1.80964			−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000			−1.80964			−0.904819	+	0.425797i	$0.859994\pi$
$354$		0			0
$355$	12.0000			0.636894
$356$	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	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	13.0000	−	22.5167i	0.683265	−	1.18345i
$363$		0			0
$364$	1.00000	+	5.19615i	0.0524142	+	0.272352i
$365$	3.00000	−	5.19615i	0.157027	−	0.271979i
$366$		0			0
$367$	−9.00000			−0.469796			−0.234898	−	0.972020i	$-0.575476\pi$
$367$	−9.00000			−0.469796			−0.234898	+	0.972020i	$0.575476\pi$
$368$		0			0
$369$		0			0
$370$	−12.0000			−0.623850
$371$	30.0000	+	10.3923i	1.55752	+	0.539542i
$372$		0			0
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$		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	$0.475450\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$		0			0
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	12.0000			0.613171			0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000			0.613171			0.306586	+	0.951843i	$0.400813\pi$
$384$		0			0
$385$	2.00000	+	10.3923i	0.101929	+	0.529641i
$386$	−22.0000			−1.11977
$387$		0			0
$388$	6.00000	−	10.3923i	0.304604	−	0.527589i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−16.0000	+	27.7128i	−0.806068	+	1.39615i
$395$	1.00000	−	1.73205i	0.0503155	−	0.0871489i
$396$		0			0
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	0.956574	−	0.291491i	$-0.0941512\pi$
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	−0.730725	+	0.682672i	$0.760818\pi$
$398$		0			0
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	36.0000			1.79775			0.898877	−	0.438201i	$-0.144384\pi$
$401$	36.0000			1.79775			0.898877	+	0.438201i	$0.144384\pi$
$402$		0			0
$403$	9.00000			0.448322
$404$	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
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	20.0000	+	34.6410i	0.987730	+	1.71080i
$411$		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
$416$	8.00000			0.392232
$417$		0			0
$418$	−4.00000			−0.195646
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	−0.222885	−	0.974845i	$-0.571547\pi$
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	0.955683	−	0.294398i	$-0.0951193\pi$
$420$		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
$427$	−25.0000	−	8.66025i	−1.20983	−	0.419099i
$428$	−8.00000	+	13.8564i	−0.386695	+	0.669775i
$429$		0			0
$430$	−20.0000			−0.964486
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$		0			0
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$	−9.00000	−	46.7654i	−0.432014	−	2.24481i
$435$		0			0
$436$	18.0000			0.862044
$437$		0			0
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$		0			0
$445$	16.0000	+	27.7128i	0.758473	+	1.31371i
$446$	−32.0000			−1.51524
$447$		0			0
$448$	−4.00000	−	20.7846i	−0.188982	−	0.981981i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−10.0000	+	17.3205i	−0.470882	+	0.815591i
$452$	−20.0000			−0.940721
$453$		0			0
$454$	−18.0000	+	31.1769i	−0.844782	+	1.46321i
$455$	−5.00000	−	1.73205i	−0.234404	−	0.0811998i
$456$		0			0
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	−0.708233	−	0.705979i	$-0.750507\pi$
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	0.965512	+	0.260358i	$0.0838407\pi$
$458$	−19.0000	+	32.9090i	−0.887812	+	1.53773i
$459$		0			0
$460$		0			0
$461$	10.0000	+	17.3205i	0.465746	+	0.806696i	0.999235	−	0.0391109i	$-0.0124526\pi$
$461$	10.0000	+	17.3205i	0.465746	+	0.806696i	−0.533488	+	0.845807i	$0.679119\pi$
$462$		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	$0.0374014\pi$
$464$	16.0000			0.742781
$465$		0			0
$466$	12.0000			0.555889
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	0.927052	−	0.374934i	$-0.122335\pi$
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	−0.788228	+	0.615383i	$0.789001\pi$
$468$		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
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		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
$479$	28.0000			1.27935			0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000			1.27935			0.639676	+	0.768644i	$0.279068\pi$
$480$		0			0
$481$	3.00000			0.136788
$482$	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	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$		0			0
$489$		0			0
$490$	−4.00000	+	27.7128i	−0.180702	+	1.25194i
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	0.355370	+	0.934726i	$0.384355\pi$
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	−0.987181	+	0.159603i	$0.948978\pi$
$492$		0			0
$493$		0			0
$494$	1.00000	−	1.73205i	0.0449921	−	0.0779287i
$495$		0			0
$496$	−36.0000			−1.61645
$497$	3.00000	+	15.5885i	0.134568	+	0.699238i
$498$		0			0
$499$	37.0000			1.65635			0.828174	−	0.560471i	$-0.189380\pi$
$499$	37.0000			1.65635			0.828174	+	0.560471i	$0.189380\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$	8.00000	−	13.8564i	0.357057	−	0.618442i
$503$	42.0000			1.87269			0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000			1.87269			0.936344	+	0.351085i	$0.114187\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$		0			0
$508$	15.0000	+	25.9808i	0.665517	+	1.15271i
$509$	−2.00000			−0.0886484			−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000			−0.0886484			−0.0443242	+	0.999017i	$0.514113\pi$
$510$		0			0
$511$	7.50000	+	2.59808i	0.331780	+	0.114932i
$512$	−32.0000			−1.41421
$513$		0			0
$514$	−26.0000	+	45.0333i	−1.14681	+	1.98633i
$515$	−14.0000			−0.616914
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−3.00000	−	15.5885i	−0.131812	−	0.684917i
$519$		0			0
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	−0.975652	−	0.219326i	$-0.929614\pi$
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	0.297884	−	0.954602i	$-0.403719\pi$
$524$	−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
$529$	−23.0000			−1.00000
$530$	−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
$535$	−8.00000	−	13.8564i	−0.345870	−	0.599065i
$536$		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	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	−32.0000			−1.37452
$543$		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
$551$	2.00000	−	3.46410i	0.0852029	−	0.147576i
$552$		0			0
$553$	2.50000	+	0.866025i	0.106311	+	0.0368271i
$554$	13.0000	−	22.5167i	0.552317	−	0.956641i
$555$		0			0
$556$	−6.00000			−0.254457
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	20.0000	+	6.92820i	0.845154	+	0.292770i
$561$		0			0
$562$	−8.00000			−0.337460
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	−0.998419	−	0.0562051i	$-0.982100\pi$
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	0.450535	−	0.892759i	$-0.351233\pi$
$564$		0			0
$565$	10.0000	−	17.3205i	0.420703	−	0.728679i
$566$	22.0000			0.924729
$567$		0			0
$568$		0			0
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	0.453619	+	0.891196i	$0.350133\pi$
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	−0.998608	+	0.0527519i	$0.983201\pi$
$570$		0			0
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365228\pi$
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$572$	4.00000			0.167248
$573$		0			0
$574$	−40.0000	+	34.6410i	−1.66957	+	1.44589i
$575$		0			0
$576$		0			0
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$	34.0000			1.41421
$579$		0			0
$580$	8.00000	−	13.8564i	0.332182	−	0.575356i
$581$	−12.0000	+	10.3923i	−0.497844	+	0.431145i
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$		0			0
$586$	−8.00000	−	13.8564i	−0.330477	−	0.572403i
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	0.982550	−	0.185999i	$-0.0595520\pi$
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	−0.652355	+	0.757914i	$0.726219\pi$
$588$		0			0
$589$	−4.50000	+	7.79423i	−0.185419	+	0.321156i
$590$	−48.0000			−1.97613
$591$		0			0
$592$	−12.0000			−0.493197
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$		0			0
$596$	−12.0000	−	20.7846i	−0.491539	−	0.851371i
$597$		0			0
$598$		0			0
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		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
$605$	−14.0000			−0.569181
$606$		0			0
$607$	23.0000			0.933541			0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000			0.933541			0.466771	+	0.884378i	$0.345417\pi$
$608$	−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	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	−17.0000	+	29.4449i	−0.686064	+	1.18830i
$615$		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
$619$	−29.0000			−1.16561			−0.582804	−	0.812613i	$-0.698045\pi$
$619$	−29.0000			−1.16561			−0.582804	+	0.812613i	$0.698045\pi$
$620$	−18.0000	+	31.1769i	−0.722897	+	1.25210i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−32.0000	+	27.7128i	−1.28205	+	1.11029i
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−1.00000	−	1.73205i	−0.0399680	−	0.0692267i
$627$		0			0
$628$	14.0000	−	24.2487i	0.558661	−	0.967629i
$629$		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
$634$	−24.0000	−	41.5692i	−0.953162	−	1.65092i
$635$	−30.0000			−1.19051
$636$		0			0
$637$	1.00000	−	6.92820i	0.0396214	−	0.274505i
$638$	16.0000			0.633446
$639$		0			0
$640$		0			0
$641$		0			0			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$		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	$-0.820816\pi$
$647$	1.00000	−	1.73205i	0.0393141	−	0.0680939i	0.885013	+	0.465566i	$0.154149\pi$
$648$		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
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$		0			0
$655$	28.0000			1.09405
$656$	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	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$	−25.0000	−	43.3013i	−0.971653	−	1.68295i
$663$		0			0
$664$		0			0
$665$	4.00000	−	3.46410i	0.155113	−	0.134332i
$666$		0			0
$667$		0			0
$668$	28.0000			1.08335
$669$		0			0
$670$	20.0000			0.772667
$671$	−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
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$		0			0
$679$	−12.0000	+	10.3923i	−0.460518	+	0.398820i
$680$		0			0
$681$		0			0
$682$	−36.0000			−1.37851
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$	−37.0000	+	1.73205i	−1.41267	+	0.0661300i
$687$		0			0
$688$	−20.0000			−0.762493
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	18.5000	−	32.0429i	0.703773	−	1.21897i	−0.263359	−	0.964698i	$-0.584830\pi$
$691$	18.5000	−	32.0429i	0.703773	−	1.21897i	0.967132	−	0.254273i	$-0.0818362\pi$
$692$	−16.0000			−0.608229
$693$		0			0
$694$	64.0000			2.42941
$695$	3.00000	−	5.19615i	0.113796	−	0.197101i
$696$		0			0
$697$		0			0
$698$	28.0000			1.05982
$699$		0			0
$700$	−4.00000	+	3.46410i	−0.151186	+	0.130931i
$701$		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
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−34.0000	+	58.8897i	−1.27961	+	2.21634i
$707$	−1.00000	−	5.19615i	−0.0376089	−	0.195421i
$708$		0			0
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	0.433865	+	0.900978i	$0.357149\pi$
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	−0.997202	+	0.0747503i	$0.976184\pi$
$710$	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
$716$	−4.00000			−0.149487
$717$		0			0
$718$	40.0000			1.49279
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$	−18.0000	−	31.1769i	−0.669891	−	1.16028i
$723$		0			0
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$		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
$733$	−15.0000			−0.554038			−0.277019	−	0.960864i	$-0.589346\pi$
$733$	−15.0000			−0.554038			−0.277019	+	0.960864i	$0.589346\pi$
$734$	−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	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$		0			0
$742$	48.0000	−	41.5692i	1.76214	−	1.52605i
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	−0.166920	−	0.985970i	$-0.553382\pi$
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	0.937336	−	0.348428i	$-0.113284\pi$
$744$		0			0
$745$	24.0000			0.879292
$746$	23.0000	−	39.8372i	0.842090	−	1.45854i
$747$		0			0
$748$		0			0
$749$	16.0000	−	13.8564i	0.584627	−	0.506302i
$750$		0			0
$751$	13.0000			0.474377			0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000			0.474377			0.237188	+	0.971464i	$0.423774\pi$
$752$	12.0000	+	20.7846i	0.437595	+	0.757937i
$753$		0			0
$754$	−4.00000	+	6.92820i	−0.145671	+	0.252310i
$755$	−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	$0.630921\pi$
$758$	3.00000	−	5.19615i	0.108965	−	0.188733i
$759$		0			0
$760$		0			0
$761$	48.0000			1.74000			0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000			1.74000			0.869999	+	0.493053i	$0.164119\pi$
$762$		0			0
$763$	−22.5000	−	7.79423i	−0.814555	−	0.282170i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	12.0000			0.433295
$768$		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	$-0.178148\pi$
$770$	20.0000	+	6.92820i	0.720750	+	0.249675i
$771$		0			0
$772$	−11.0000	+	19.0526i	−0.395899	+	0.685717i
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	0.379549	+	0.925172i	$0.376079\pi$
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	−0.990997	+	0.133887i	$0.957254\pi$
$774$		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
$779$	10.0000			0.358287
$780$		0			0
$781$	12.0000			0.429394
$782$		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
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	0.250832	−	0.968031i	$-0.419296\pi$
$788$	16.0000	+	27.7128i	0.569976	+	0.987228i
$789$		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
$794$	18.0000			0.638796
$795$		0			0
$796$		0			0
$797$	−4.00000	+	6.92820i	−0.141687	+	0.245410i	−0.928132	−	0.372251i	$-0.878586\pi$
$797$	−4.00000	+	6.92820i	−0.141687	+	0.245410i	0.786445	+	0.617661i	$0.211919\pi$
$798$		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
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		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	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	20.0000	+	6.92820i	0.701862	+	0.243132i
$813$		0			0
$814$	−12.0000			−0.420600
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	40.0000			1.39686
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	−0.848048	−	0.529920i	$-0.822222\pi$
$821$	1.00000	−	1.73205i	0.0349002	−	0.0604490i	0.882948	+	0.469471i	$0.155555\pi$
$822$		0			0
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		0			0
$826$	−12.0000	−	62.3538i	−0.417533	−	2.16957i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	24.0000			0.833052
$831$		0			0
$832$	4.00000	−	6.92820i	0.138675	−	0.240192i
$833$		0			0
$834$		0			0
$835$	−14.0000	+	24.2487i	−0.484490	+	0.839161i
$836$	−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	$-0.892098\pi$
$839$	−22.0000	−	38.1051i	−0.759524	−	1.31553i	0.183569	−	0.983007i	$-0.441235\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	14.0000			0.482472
$843$		0			0
$844$	8.00000			0.275371
$845$	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
$857$	32.0000			1.09310			0.546550	−	0.837427i	$-0.315941\pi$
$857$	32.0000			1.09310			0.546550	+	0.837427i	$0.315941\pi$
$858$		0			0
$859$	−40.0000			−1.36478			−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000			−1.36478			−0.682391	+	0.730987i	$0.739060\pi$
$860$	−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	−0.800799	−	0.598933i	$-0.795592\pi$
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.118291	−	0.992979i	$-0.537742\pi$
$864$		0			0
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$	31.0000	−	53.6936i	1.05342	−	1.82458i
$867$		0			0
$868$	−45.0000	−	15.5885i	−1.52740	−	0.529107i
$869$	1.00000	−	1.73205i	0.0339227	−	0.0587558i
$870$		0			0
$871$	−5.00000			−0.169419
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	−	31.1769i	−0.202837	−	1.05397i
$876$		0			0
$877$	−38.0000			−1.28317			−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000			−1.28317			−0.641584	+	0.767052i	$0.721723\pi$
$878$		0			0
$879$		0			0
$880$	8.00000	−	13.8564i	0.269680	−	0.467099i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		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
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	34.0000			1.14161			0.570804	−	0.821086i	$-0.306632\pi$
$887$	34.0000			1.14161			0.570804	+	0.821086i	$0.306632\pi$
$888$		0			0
$889$	−7.50000	−	38.9711i	−0.251542	−	1.30705i
$890$	64.0000			2.14528
$891$		0			0
$892$	−16.0000	+	27.7128i	−0.535720	+	0.927894i
$893$	6.00000			0.200782
$894$		0			0
$895$	2.00000	−	3.46410i	0.0668526	−	0.115792i
$896$		0			0
$897$		0			0
$898$	18.0000	−	31.1769i	0.600668	−	1.04039i
$899$	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
$905$	26.0000			0.864269
$906$		0			0
$907$	−37.0000			−1.22856			−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000			−1.22856			−0.614282	+	0.789086i	$0.710554\pi$
$908$	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	0.595849	−	0.803097i	$-0.296816\pi$
$911$	−12.0000	−	20.7846i	−0.397578	−	0.688625i	−0.993426	+	0.114472i	$0.963482\pi$
$912$		0			0
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		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	0.611618	−	0.791153i	$-0.290519\pi$
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	−0.990968	+	0.134100i	$0.957186\pi$
$920$		0			0
$921$		0			0
$922$	40.0000			1.31733
$923$	−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
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$	5.50000	+	4.33013i	0.180255	+	0.141914i
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$		0			0
$934$	12.0000			0.392652
$935$		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	$0.421207\pi$
$938$	5.00000	+	25.9808i	0.163256	+	0.848302i
$939$		0			0
$940$	24.0000			0.782794
$941$	−2.00000	−	3.46410i	−0.0651981	−	0.112926i	0.831584	−	0.555399i	$-0.187435\pi$
$941$	−2.00000	−	3.46410i	−0.0651981	−	0.112926i	−0.896782	+	0.442473i	$0.854101\pi$
$942$		0			0
$943$		0			0
$944$	−48.0000			−1.56227
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	−0.935757	−	0.352646i	$-0.885282\pi$
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	0.773279	+	0.634066i	$0.218615\pi$
$948$		0			0
$949$	1.50000	+	2.59808i	0.0486921	+	0.0843371i
$950$	2.00000			0.0648886
$951$		0			0
$952$		0			0
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	10.0000	−	17.3205i	0.323592	−	0.560478i
$956$	−12.0000			−0.388108
$957$		0			0
$958$	28.0000	−	48.4974i	0.904639	−	1.56688i
$959$	6.00000	+	31.1769i	0.193750	+	1.00676i
$960$		0			0
$961$	−25.0000	+	43.3013i	−0.806452	+	1.39682i
$962$	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
$970$	24.0000			0.770594
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$	7.50000	+	2.59808i	0.240439	+	0.0832905i
$974$	31.0000	+	53.6936i	0.993304	+	1.72045i
$975$		0			0
$976$	20.0000	+	34.6410i	0.640184	+	1.10883i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		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
$983$	−36.0000			−1.14822			−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000			−1.14822			−0.574111	+	0.818778i	$0.694652\pi$
$984$		0			0
$985$	−32.0000			−1.01960
$986$		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	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	0.698853	+	0.715265i	$0.253694\pi$
$992$	−36.0000	+	62.3538i	−1.14300	+	1.97974i
$993$		0			0
$994$	30.0000	+	10.3923i	0.951542	+	0.329624i
$995$		0			0
$996$		0			0
$997$	19.0000			0.601736			0.300868	−	0.953666i	$-0.402724\pi$
$997$	19.0000			0.601736			0.300868	+	0.953666i	$0.402724\pi$
$998$	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.g.f.109.1		2
3.2	odd	2		567.2.g.a.109.1		2
7.2	even	3		567.2.h.a.352.1		2
9.2	odd	6		567.2.h.f.298.1		2
9.4	even	3		63.2.e.b.46.1		2
9.5	odd	6		21.2.e.a.4.1	✓	2
9.7	even	3		567.2.h.a.298.1		2
21.2	odd	6		567.2.h.f.352.1		2
36.23	even	6		336.2.q.f.193.1		2
36.31	odd	6		1008.2.s.d.865.1		2
45.14	odd	6		525.2.i.e.151.1		2
45.23	even	12		525.2.r.e.424.1		4
45.32	even	12		525.2.r.e.424.2		4
63.2	odd	6		567.2.g.a.541.1		2
63.4	even	3		441.2.a.b.1.1		1
63.5	even	6		147.2.e.a.79.1		2
63.13	odd	6		441.2.e.e.361.1		2
63.16	even	3	inner	567.2.g.f.541.1		2
63.23	odd	6		21.2.e.a.16.1	yes	2
63.31	odd	6		441.2.a.a.1.1		1
63.32	odd	6		147.2.a.c.1.1		1
63.40	odd	6		441.2.e.e.226.1		2
63.41	even	6		147.2.e.a.67.1		2
63.58	even	3		63.2.e.b.37.1		2
63.59	even	6		147.2.a.b.1.1		1
72.5	odd	6		1344.2.q.m.193.1		2
72.59	even	6		1344.2.q.c.193.1		2
252.23	even	6		336.2.q.f.289.1		2
252.31	even	6		7056.2.a.m.1.1		1
252.59	odd	6		2352.2.a.w.1.1		1
252.67	odd	6		7056.2.a.bp.1.1		1
252.95	even	6		2352.2.a.d.1.1		1
252.131	odd	6		2352.2.q.c.961.1		2
252.167	odd	6		2352.2.q.c.1537.1		2
252.247	odd	6		1008.2.s.d.289.1		2
315.23	even	12		525.2.r.e.499.2		4
315.59	even	6		3675.2.a.c.1.1		1
315.149	odd	6		525.2.i.e.226.1		2
315.212	even	12		525.2.r.e.499.1		4
315.284	odd	6		3675.2.a.a.1.1		1
504.59	odd	6		9408.2.a.k.1.1		1
504.149	odd	6		1344.2.q.m.961.1		2
504.221	odd	6		9408.2.a.bg.1.1		1
504.275	even	6		1344.2.q.c.961.1		2
504.347	even	6		9408.2.a.cv.1.1		1
504.437	even	6		9408.2.a.bz.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	9.5	odd	6
21.2.e.a.16.1	yes	2	63.23	odd	6
63.2.e.b.37.1		2	63.58	even	3
63.2.e.b.46.1		2	9.4	even	3
147.2.a.b.1.1		1	63.59	even	6
147.2.a.c.1.1		1	63.32	odd	6
147.2.e.a.67.1		2	63.41	even	6
147.2.e.a.79.1		2	63.5	even	6
336.2.q.f.193.1		2	36.23	even	6
336.2.q.f.289.1		2	252.23	even	6
441.2.a.a.1.1		1	63.31	odd	6
441.2.a.b.1.1		1	63.4	even	3
441.2.e.e.226.1		2	63.40	odd	6
441.2.e.e.361.1		2	63.13	odd	6
525.2.i.e.151.1		2	45.14	odd	6
525.2.i.e.226.1		2	315.149	odd	6
525.2.r.e.424.1		4	45.23	even	12
525.2.r.e.424.2		4	45.32	even	12
525.2.r.e.499.1		4	315.212	even	12
525.2.r.e.499.2		4	315.23	even	12
567.2.g.a.109.1		2	3.2	odd	2
567.2.g.a.541.1		2	63.2	odd	6
567.2.g.f.109.1		2	1.1	even	1	trivial
567.2.g.f.541.1		2	63.16	even	3	inner
567.2.h.a.298.1		2	9.7	even	3
567.2.h.a.352.1		2	7.2	even	3
567.2.h.f.298.1		2	9.2	odd	6
567.2.h.f.352.1		2	21.2	odd	6
1008.2.s.d.289.1		2	252.247	odd	6
1008.2.s.d.865.1		2	36.31	odd	6
1344.2.q.c.193.1		2	72.59	even	6
1344.2.q.c.961.1		2	504.275	even	6
1344.2.q.m.193.1		2	72.5	odd	6
1344.2.q.m.961.1		2	504.149	odd	6
2352.2.a.d.1.1		1	252.95	even	6
2352.2.a.w.1.1		1	252.59	odd	6
2352.2.q.c.961.1		2	252.131	odd	6
2352.2.q.c.1537.1		2	252.167	odd	6
3675.2.a.a.1.1		1	315.284	odd	6
3675.2.a.c.1.1		1	315.59	even	6
7056.2.a.m.1.1		1	252.31	even	6
7056.2.a.bp.1.1		1	252.67	odd	6
9408.2.a.k.1.1		1	504.59	odd	6
9408.2.a.bg.1.1		1	504.221	odd	6
9408.2.a.bz.1.1		1	504.437	even	6
9408.2.a.cv.1.1		1	504.347	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +(2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(5.00000 + 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} -1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-5.00000 + 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{50} +2.00000 q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +8.00000 q^{58} +(-6.00000 - 10.3923i) q^{59} +(-5.00000 + 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.50000 + 4.33013i) q^{67} +(10.0000 + 3.46410i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} -6.00000 q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.00000 + 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} +(3.00000 + 5.19615i) q^{83} -10.0000 q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(3.00000 + 5.19615i) q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + q^{7}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + q^7	\( 2 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + q^{7} + 4 q^{10} + 4 q^{11} - q^{13} + 10 q^{14} + 4 q^{16} - q^{19} - 4 q^{20} + 4 q^{22} - 2 q^{25} + 2 q^{26} + 8 q^{28} + 4 q^{29} - 9 q^{31} - 8 q^{32} + 2 q^{35} - 3 q^{37} - 4 q^{38} - 10 q^{41} - 5 q^{43} - 4 q^{44} - 6 q^{47} - 13 q^{49} - 2 q^{50} + 4 q^{52} + 12 q^{53} + 8 q^{55} + 16 q^{58} - 12 q^{59} - 10 q^{61} - 36 q^{62} - 16 q^{64} - 2 q^{65} + 5 q^{67} + 20 q^{70} + 12 q^{71} + 3 q^{73} - 12 q^{74} - 2 q^{76} + 2 q^{77} + q^{79} + 8 q^{80} + 20 q^{82} + 6 q^{83} - 20 q^{86} + 16 q^{89} - 5 q^{91} + 12 q^{94} - 2 q^{95} + 6 q^{97} - 4 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + q^7 + 4 * q^10 + 4 * q^11 - q^13 + 10 * q^14 + 4 * q^16 - q^19 - 4 * q^20 + 4 * q^22 - 2 * q^25 + 2 * q^26 + 8 * q^28 + 4 * q^29 - 9 * q^31 - 8 * q^32 + 2 * q^35 - 3 * q^37 - 4 * q^38 - 10 * q^41 - 5 * q^43 - 4 * q^44 - 6 * q^47 - 13 * q^49 - 2 * q^50 + 4 * q^52 + 12 * q^53 + 8 * q^55 + 16 * q^58 - 12 * q^59 - 10 * q^61 - 36 * q^62 - 16 * q^64 - 2 * q^65 + 5 * q^67 + 20 * q^70 + 12 * q^71 + 3 * q^73 - 12 * q^74 - 2 * q^76 + 2 * q^77 + q^79 + 8 * q^80 + 20 * q^82 + 6 * q^83 - 20 * q^86 + 16 * q^89 - 5 * q^91 + 12 * q^94 - 2 * q^95 + 6 * q^97 - 4 * q^98

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