LMFDB - Embedded newform 567.2.g.e.541.1

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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.e.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(2.00000 + 3.46410i) q^{10} -2.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{20} +(-1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +11.0000 q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} +(1.00000 - 1.73205i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{32} +(3.00000 - 5.19615i) q^{34} +(2.00000 + 10.3923i) q^{35} +(-1.50000 + 2.59808i) q^{37} -4.00000 q^{38} +12.0000 q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(5.50000 + 9.52628i) q^{50} -1.00000 q^{52} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(1.50000 + 7.79423i) q^{56} +2.00000 q^{58} +(3.00000 - 5.19615i) q^{59} +(2.50000 + 4.33013i) q^{61} -3.00000 q^{62} +7.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-3.50000 + 6.06218i) q^{67} -6.00000 q^{68} +(-8.00000 + 6.92820i) q^{70} +(3.00000 + 5.19615i) q^{73} -3.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-1.00000 - 5.19615i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(2.00000 + 3.46410i) q^{80} +(1.00000 - 1.73205i) q^{82} +(3.00000 - 5.19615i) q^{83} +(-12.0000 - 20.7846i) q^{85} +1.00000 q^{86} -6.00000 q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.73205i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 8 q^{5} + q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + 4 q^{20} - 2 q^{22} - 12 q^{23} + 22 q^{25} + q^{26} + 5 q^{28} + 2 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 8 * q^5 + q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - q^13 - 4 * q^14 + q^16 - 6 * q^17 - 4 * q^19 + 4 * q^20 - 2 * q^22 - 12 * q^23 + 22 * q^25 + q^26 + 5 * q^28 + 2 * q^29 - 3 * q^31 + 5 * q^32 + 6 * q^34 + 4 * q^35 - 3 * q^37 - 8 * q^38 + 24 * q^40 - 2 * q^41 + q^43 - 2 * q^44 - 6 * q^46 + 6 * q^47 - 13 * q^49 + 11 * q^50 - 2 * q^52 - 6 * q^53 - 16 * q^55 + 3 * q^56 + 4 * q^58 + 6 * q^59 + 5 * q^61 - 6 * q^62 + 14 * q^64 - 4 * q^65 - 7 * q^67 - 12 * q^68 - 16 * q^70 + 6 * q^73 - 6 * q^74 + 4 * q^76 - 2 * q^77 - 11 * q^79 + 4 * q^80 + 2 * q^82 + 6 * q^83 - 24 * q^85 + 2 * q^86 - 12 * q^88 - 4 * q^89 + 4 * q^91 - 6 * q^92 - 6 * q^94 - 16 * q^95 - 9 * q^97 - 11 * q^98

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	4.00000			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	3.00000			1.06066
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	2.00000	−	3.46410i	0.447214	−	0.774597i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$	11.0000			2.20000
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	2.00000	+	10.3923i	0.338062	+	1.75662i
$36$		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	$0.245980\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	12.0000			1.89737
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$		0			0
$52$	−1.00000			−0.138675
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−8.00000			−1.07872
$56$	1.50000	+	7.79423i	0.200446	+	1.04155i
$57$		0			0
$58$	2.00000			0.262613
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	−3.00000			−0.381000
$63$		0			0
$64$	7.00000			0.875000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$	−8.00000	+	6.92820i	−0.956183	+	0.828079i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$	−3.00000			−0.348743
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−1.00000	−	5.19615i	−0.113961	−	0.592157i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$		0			0
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	−0.653079	−	0.757290i	$-0.726523\pi$
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	0.982372	+	0.186938i	$0.0598564\pi$
$84$		0			0
$85$	−12.0000	−	20.7846i	−1.30158	−	2.25441i
$86$	1.00000			0.107833
$87$		0			0
$88$	−6.00000			−0.639602
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−8.00000	+	13.8564i	−0.820783	+	1.42164i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	5.50000	−	9.52628i	0.550000	−	0.952628i
$101$	8.00000			0.796030			0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000			0.796030			0.398015	+	0.917379i	$0.369699\pi$
$102$		0			0
$103$	17.0000			1.67506			0.837530	−	0.546392i	$-0.183999\pi$
$103$	17.0000			1.67506			0.837530	+	0.546392i	$0.183999\pi$
$104$	−1.50000	−	2.59808i	−0.147087	−	0.254762i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		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	$0.975180\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−8.00000	−	13.8564i	−0.752577	−	1.30350i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−8.00000	−	13.8564i	−0.752577	−	1.30350i	0.193993	−	0.981003i	$-0.437856\pi$
$114$		0			0
$115$	−24.0000			−2.23801
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$		0			0
$118$	6.00000			0.552345
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−2.50000	+	4.33013i	−0.226339	+	0.392031i
$123$		0			0
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$	24.0000			2.14663
$126$		0			0
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	−10.0000	−	3.46410i	−0.867110	−	0.300376i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	−9.00000	−	15.5885i	−0.771744	−	1.33670i
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$		0			0
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$	10.0000	+	3.46410i	0.845154	+	0.292770i
$141$		0			0
$142$		0			0
$143$	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
$148$	1.50000	+	2.59808i	0.123299	+	0.213561i
$149$	24.0000			1.96616			0.983078	−	0.183186i	$-0.0586410\pi$
$149$	24.0000			1.96616			0.983078	+	0.183186i	$0.0586410\pi$
$150$		0			0
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$		0			0
$154$	4.00000	−	3.46410i	0.322329	−	0.279145i
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$		0			0
$160$	10.0000	−	17.3205i	0.790569	−	1.36931i
$161$	−3.00000	−	15.5885i	−0.236433	−	1.22854i
$162$		0			0
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	0.206518	+	0.978443i	$0.433787\pi$
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	−0.950615	+	0.310372i	$0.899546\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	6.00000			0.465690
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	0.998808	+	0.0488118i	$0.0155435\pi$
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	−0.457132	+	0.889399i	$0.651123\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	12.0000	−	20.7846i	0.920358	−	1.59411i
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	0.991532	+	0.129861i	$0.0414530\pi$
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	−0.383304	+	0.923622i	$0.625214\pi$
$174$		0			0
$175$	5.50000	+	28.5788i	0.415761	+	2.16036i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	−4.00000			−0.299813
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	2.50000	+	0.866025i	0.185312	+	0.0641941i
$183$		0			0
$184$	−18.0000			−1.32698
$185$	−6.00000	+	10.3923i	−0.441129	+	0.764057i
$186$		0			0
$187$	6.00000	+	10.3923i	0.438763	+	0.759961i
$188$	6.00000			0.437595
$189$		0			0
$190$	−16.0000			−1.16076
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	−9.00000			−0.646162
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	−20.0000			−1.42494			−0.712470	−	0.701702i	$-0.752424\pi$
$197$	−20.0000			−1.42494			−0.712470	+	0.701702i	$0.752424\pi$
$198$		0			0
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	0.980279	−	0.197619i	$-0.0633208\pi$
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	−0.661282	+	0.750137i	$0.729987\pi$
$200$	33.0000			2.33345
$201$		0			0
$202$	4.00000	+	6.92820i	0.281439	+	0.487467i
$203$	5.00000	+	1.73205i	0.350931	+	0.121566i
$204$		0			0
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$	8.50000	+	14.7224i	0.592223	+	1.02576i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	4.00000	−	6.92820i	0.276686	−	0.479234i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	2.00000			0.136717
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$		0			0
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	4.50000	−	7.79423i	0.304778	−	0.527892i
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	12.5000	+	4.33013i	0.835191	+	0.289319i
$225$		0			0
$226$	8.00000	−	13.8564i	0.532152	−	0.921714i
$227$	−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
$229$	−7.00000			−0.462573			−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000			−0.462573			−0.231287	+	0.972886i	$0.574293\pi$
$230$	−12.0000	−	20.7846i	−0.791257	−	1.37050i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$		0			0
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$		0			0
$238$	15.0000	+	5.19615i	0.972306	+	0.336817i
$239$	−6.00000	−	10.3923i	−0.388108	−	0.672222i	0.604087	−	0.796918i	$-0.293538\pi$
$239$	−6.00000	−	10.3923i	−0.388108	−	0.672222i	−0.992195	+	0.124696i	$0.960204\pi$
$240$		0			0
$241$	17.0000			1.09507			0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000			1.09507			0.547533	+	0.836784i	$0.315567\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	5.00000			0.320092
$245$	−26.0000	+	10.3923i	−1.66108	+	0.663940i
$246$		0			0
$247$	4.00000			0.254514
$248$	−4.50000	+	7.79423i	−0.285750	+	0.494934i
$249$		0			0
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	−26.0000			−1.64111			−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000			−1.64111			−0.820553	+	0.571571i	$0.806334\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	−4.50000	−	7.79423i	−0.282355	−	0.489053i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−10.0000			−0.623783			−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000			−0.623783			−0.311891	+	0.950118i	$0.600963\pi$
$258$		0			0
$259$	−7.50000	−	2.59808i	−0.466027	−	0.161437i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	−2.00000			−0.123325			−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000			−0.123325			−0.0616626	+	0.998097i	$0.519640\pi$
$264$		0			0
$265$	−12.0000	−	20.7846i	−0.737154	−	1.27679i
$266$	−2.00000	−	10.3923i	−0.122628	−	0.637193i
$267$		0			0
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$		0			0
$274$	−9.00000	−	15.5885i	−0.543710	−	0.941733i
$275$	−22.0000			−1.32665
$276$		0			0
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$	4.50000	−	7.79423i	0.269892	−	0.467467i
$279$		0			0
$280$	6.00000	+	31.1769i	0.358569	+	1.86318i
$281$	8.00000	−	13.8564i	0.477240	−	0.826604i	−0.522420	−	0.852688i	$-0.674971\pi$
$281$	8.00000	−	13.8564i	0.477240	−	0.826604i	0.999660	+	0.0260845i	$0.00830391\pi$
$282$		0			0
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$		0			0
$285$		0			0
$286$	−1.00000	+	1.73205i	−0.0591312	+	0.102418i
$287$	4.00000	−	3.46410i	0.236113	−	0.204479i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	8.00000			0.469776
$291$		0			0
$292$	6.00000			0.351123
$293$	11.0000	+	19.0526i	0.642627	+	1.11306i	0.984844	+	0.173442i	$0.0554888\pi$
$293$	11.0000	+	19.0526i	0.642627	+	1.11306i	−0.342217	+	0.939621i	$0.611178\pi$
$294$		0			0
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$	12.0000	+	20.7846i	0.695141	+	1.20402i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	2.50000	+	0.866025i	0.144098	+	0.0499169i
$302$	2.50000	+	4.33013i	0.143859	+	0.249171i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	10.0000	+	17.3205i	0.572598	+	0.991769i
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$	−5.00000	−	1.73205i	−0.284901	−	0.0986928i
$309$		0			0
$310$	−12.0000			−0.681554
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	0.989158	+	0.146852i	$0.0469141\pi$
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	−0.367402	+	0.930062i	$0.619753\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−11.0000			−0.618798
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		0			0
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$	28.0000			1.56525
$321$		0			0
$322$	12.0000	−	10.3923i	0.668734	−	0.579141i
$323$	24.0000			1.33540
$324$		0			0
$325$	−5.50000	−	9.52628i	−0.305085	−	0.528423i
$326$	−19.0000			−1.05231
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$		0			0
$334$	−7.00000	+	12.1244i	−0.383023	+	0.663415i
$335$	−14.0000	+	24.2487i	−0.764902	+	1.32485i
$336$		0			0
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$	12.0000			0.652714
$339$		0			0
$340$	−24.0000			−1.30158
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	1.50000	−	2.59808i	0.0808746	−	0.140079i
$345$		0			0
$346$	−8.00000	+	13.8564i	−0.430083	+	0.744925i
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$		0			0
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$	−22.0000	+	19.0526i	−1.17595	+	1.01840i
$351$		0			0
$352$	−5.00000	+	8.66025i	−0.266501	+	0.461593i
$353$	28.0000			1.49029			0.745145	−	0.666903i	$-0.232380\pi$
$353$	28.0000			1.49029			0.745145	+	0.666903i	$0.232380\pi$
$354$		0			0
$355$		0			0
$356$	2.00000	+	3.46410i	0.106000	+	0.183597i
$357$		0			0
$358$	−2.00000	+	3.46410i	−0.105703	+	0.183083i
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	−0.414855	−	0.909887i	$-0.636168\pi$
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	0.995413	−	0.0956683i	$-0.0304988\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$		0			0
$364$	−0.500000	−	2.59808i	−0.0262071	−	0.136176i
$365$	12.0000	+	20.7846i	0.628109	+	1.08792i
$366$		0			0
$367$	12.0000			0.626395			0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000			0.626395			0.313197	+	0.949688i	$0.398600\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$		0			0
$370$	−12.0000			−0.623850
$371$	12.0000	−	10.3923i	0.623009	−	0.539542i
$372$		0			0
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$		0			0
$376$	9.00000	+	15.5885i	0.464140	+	0.803913i
$377$	−2.00000			−0.103005
$378$		0			0
$379$	−9.00000			−0.462299			−0.231149	−	0.972918i	$-0.574249\pi$
$379$	−9.00000			−0.462299			−0.231149	+	0.972918i	$0.574249\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	18.0000			0.919757			0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000			0.919757			0.459879	+	0.887982i	$0.347893\pi$
$384$		0			0
$385$	−4.00000	−	20.7846i	−0.203859	−	1.05928i
$386$	25.0000			1.27247
$387$		0			0
$388$	4.50000	+	7.79423i	0.228453	+	0.395692i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	−19.5000	+	7.79423i	−0.984899	+	0.393668i
$393$		0			0
$394$	−10.0000	−	17.3205i	−0.503793	−	0.872595i
$395$	−22.0000	−	38.1051i	−1.10694	−	1.91728i
$396$		0			0
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	−0.0714068	−	0.997447i	$-0.522749\pi$
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	0.899518	−	0.436884i	$-0.143918\pi$
$398$	−4.50000	+	7.79423i	−0.225565	+	0.390689i
$399$		0			0
$400$	5.50000	+	9.52628i	0.275000	+	0.476314i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$	3.00000			0.149441
$404$	4.00000	−	6.92820i	0.199007	−	0.344691i
$405$		0			0
$406$	1.00000	+	5.19615i	0.0496292	+	0.257881i
$407$	3.00000	−	5.19615i	0.148704	−	0.257564i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	4.00000	−	6.92820i	0.197546	−	0.342160i
$411$		0			0
$412$	8.50000	−	14.7224i	0.418765	−	0.725322i
$413$	15.0000	+	5.19615i	0.738102	+	0.255686i
$414$		0			0
$415$	12.0000	−	20.7846i	0.589057	−	1.02028i
$416$	−5.00000			−0.245145
$417$		0			0
$418$	8.00000			0.391293
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$		0			0
$424$	−9.00000	−	15.5885i	−0.437079	−	0.757042i
$425$	−33.0000	−	57.1577i	−1.60074	−	2.77255i
$426$		0			0
$427$	−10.0000	+	8.66025i	−0.483934	+	0.419099i
$428$	−1.00000	−	1.73205i	−0.0483368	−	0.0837218i
$429$		0			0
$430$	4.00000			0.192897
$431$	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
$433$	−17.0000			−0.816968			−0.408484	−	0.912766i	$-0.633942\pi$
$433$	−17.0000			−0.816968			−0.408484	+	0.912766i	$0.633942\pi$
$434$	−1.50000	−	7.79423i	−0.0720023	−	0.374135i
$435$		0			0
$436$	−9.00000			−0.431022
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$	−24.0000			−1.14416
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	−8.00000	+	13.8564i	−0.379236	+	0.656857i
$446$	−16.0000			−0.757622
$447$		0			0
$448$	3.50000	+	18.1865i	0.165359	+	0.859233i
$449$	36.0000			1.69895			0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000			1.69895			0.849473	+	0.527633i	$0.176920\pi$
$450$		0			0
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	−16.0000			−0.752577
$453$		0			0
$454$	−9.00000	−	15.5885i	−0.422391	−	0.731603i
$455$	8.00000	−	6.92820i	0.375046	−	0.324799i
$456$		0			0
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	0.672994	−	0.739648i	$-0.265008\pi$
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	−0.977051	+	0.213006i	$0.931675\pi$
$458$	−3.50000	−	6.06218i	−0.163544	−	0.283267i
$459$		0			0
$460$	−12.0000	+	20.7846i	−0.559503	+	0.969087i
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	−0.888373	−	0.459123i	$-0.848164\pi$
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	0.841798	+	0.539792i	$0.181497\pi$
$462$		0			0
$463$	16.0000	+	27.7128i	0.743583	+	1.28792i	0.950854	+	0.309640i	$0.100209\pi$
$463$	16.0000	+	27.7128i	0.743583	+	1.28792i	−0.207271	+	0.978284i	$0.566458\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	−24.0000			−1.11178
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$	−17.5000	−	6.06218i	−0.808075	−	0.279925i
$470$	−12.0000	+	20.7846i	−0.553519	+	0.958723i
$471$		0			0
$472$	9.00000	−	15.5885i	0.414259	−	0.717517i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$		0			0
$475$	−22.0000	+	38.1051i	−1.00943	+	1.74838i
$476$	−3.00000	−	15.5885i	−0.137505	−	0.714496i
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−16.0000			−0.731059			−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000			−0.731059			−0.365529	+	0.930800i	$0.619112\pi$
$480$		0			0
$481$	3.00000			0.136788
$482$	8.50000	+	14.7224i	0.387164	+	0.670588i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−18.0000	+	31.1769i	−0.817338	+	1.41567i
$486$		0			0
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	7.50000	+	12.9904i	0.339509	+	0.588047i
$489$		0			0
$490$	−22.0000	−	17.3205i	−0.993859	−	0.782461i
$491$	17.0000	+	29.4449i	0.767199	+	1.32883i	0.939076	+	0.343710i	$0.111684\pi$
$491$	17.0000	+	29.4449i	0.767199	+	1.32883i	−0.171877	+	0.985118i	$0.554983\pi$
$492$		0			0
$493$	−12.0000			−0.540453
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$		0			0
$496$	−3.00000			−0.134704
$497$		0			0
$498$		0			0
$499$	−17.0000			−0.761025			−0.380512	−	0.924776i	$-0.624252\pi$
$499$	−17.0000			−0.761025			−0.380512	+	0.924776i	$0.624252\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$		0			0
$502$	−13.0000	−	22.5167i	−0.580218	−	1.00497i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	32.0000			1.42398
$506$	6.00000	+	10.3923i	0.266733	+	0.461994i
$507$		0			0
$508$	−4.50000	+	7.79423i	−0.199655	+	0.345813i
$509$	−22.0000			−0.975133			−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000			−0.975133			−0.487566	+	0.873086i	$0.662115\pi$
$510$		0			0
$511$	−12.0000	+	10.3923i	−0.530849	+	0.459728i
$512$	11.0000			0.486136
$513$		0			0
$514$	−5.00000	−	8.66025i	−0.220541	−	0.381987i
$515$	68.0000			2.99644
$516$		0			0
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	−1.50000	−	7.79423i	−0.0659062	−	0.342459i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	8.50000	−	14.7224i	0.371679	−	0.643767i	−0.618145	−	0.786064i	$-0.712116\pi$
$523$	8.50000	−	14.7224i	0.371679	−	0.643767i	0.989824	+	0.142297i	$0.0454489\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	−1.00000	−	1.73205i	−0.0436021	−	0.0755210i
$527$	18.0000			0.784092
$528$		0			0
$529$	13.0000			0.565217
$530$	12.0000	−	20.7846i	0.521247	−	0.902826i
$531$		0			0
$532$	−8.00000	+	6.92820i	−0.346844	+	0.300376i
$533$	−1.00000	+	1.73205i	−0.0433148	+	0.0750234i
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$		0			0
$538$		0			0
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	11.0000			0.472490
$543$		0			0
$544$	−30.0000			−1.28624
$545$	−18.0000	−	31.1769i	−0.771035	−	1.33547i
$546$		0			0
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.118753	+	0.992924i	$0.537890\pi$
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.800521	+	0.599305i	$0.795444\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$		0			0
$550$	−11.0000	−	19.0526i	−0.469042	−	0.812404i
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$		0			0
$553$	22.0000	−	19.0526i	0.935535	−	0.810197i
$554$	6.50000	+	11.2583i	0.276159	+	0.478321i
$555$		0			0
$556$	−9.00000			−0.381685
$557$	−14.0000	−	24.2487i	−0.593199	−	1.02745i	−0.993798	−	0.111198i	$-0.964531\pi$
$557$	−14.0000	−	24.2487i	−0.593199	−	1.02745i	0.400599	−	0.916253i	$-0.368802\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$	−8.00000	+	6.92820i	−0.338062	+	0.292770i
$561$		0			0
$562$	16.0000			0.674919
$563$	−5.00000	+	8.66025i	−0.210725	+	0.364986i	−0.951942	−	0.306280i	$-0.900916\pi$
$563$	−5.00000	+	8.66025i	−0.210725	+	0.364986i	0.741217	+	0.671266i	$0.234249\pi$
$564$		0			0
$565$	−32.0000	−	55.4256i	−1.34625	−	2.33177i
$566$	5.00000			0.210166
$567$		0			0
$568$		0			0
$569$	16.0000	+	27.7128i	0.670755	+	1.16178i	0.977690	+	0.210051i	$0.0673631\pi$
$569$	16.0000	+	27.7128i	0.670755	+	1.16178i	−0.306935	+	0.951730i	$0.599304\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	2.00000			0.0836242
$573$		0			0
$574$	5.00000	+	1.73205i	0.208696	+	0.0722944i
$575$	−66.0000			−2.75239
$576$		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	$0.718202\pi$
$578$	−19.0000			−0.790296
$579$		0			0
$580$	−4.00000	−	6.92820i	−0.166091	−	0.287678i
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$	9.00000	+	15.5885i	0.372423	+	0.645055i
$585$		0			0
$586$	−11.0000	+	19.0526i	−0.454406	+	0.787054i
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	0.417885	+	0.908500i	$0.362772\pi$
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	−0.995726	+	0.0923513i	$0.970562\pi$
$588$		0			0
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$	24.0000			0.988064
$591$		0			0
$592$	−3.00000			−0.123299
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$	48.0000	−	41.5692i	1.96781	−	1.70417i
$596$	12.0000	−	20.7846i	0.491539	−	0.851371i
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	−0.303986	−	0.952676i	$-0.598318\pi$
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	0.977035	−	0.213079i	$-0.0683491\pi$
$602$	0.500000	+	2.59808i	0.0203785	+	0.105890i
$603$		0			0
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	−28.0000			−1.13836
$606$		0			0
$607$	−16.0000			−0.649420			−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000			−0.649420			−0.324710	+	0.945814i	$0.605267\pi$
$608$	10.0000	+	17.3205i	0.405554	+	0.702439i
$609$		0			0
$610$	−10.0000	+	17.3205i	−0.404888	+	0.701287i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−3.50000	−	6.06218i	−0.141364	−	0.244849i	0.786647	−	0.617403i	$-0.211815\pi$
$613$	−3.50000	−	6.06218i	−0.141364	−	0.244849i	−0.928010	+	0.372554i	$0.878482\pi$
$614$	12.5000	+	21.6506i	0.504459	+	0.873749i
$615$		0			0
$616$	−3.00000	−	15.5885i	−0.120873	−	0.628077i
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$		0			0
$619$	−41.0000			−1.64793			−0.823965	−	0.566641i	$-0.808243\pi$
$619$	−41.0000			−1.64793			−0.823965	+	0.566641i	$0.808243\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$		0			0
$622$	24.0000			0.962312
$623$	−10.0000	−	3.46410i	−0.400642	−	0.138786i
$624$		0			0
$625$	41.0000			1.64000
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$		0			0
$628$	5.00000	+	8.66025i	0.199522	+	0.345582i
$629$	18.0000			0.717707
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$	−16.5000	−	28.5788i	−0.656335	−	1.13681i
$633$		0			0
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	−36.0000			−1.42862
$636$		0			0
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−6.00000	−	10.3923i	−0.237171	−	0.410792i
$641$	−6.00000			−0.236986			−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000			−0.236986			−0.118493	+	0.992955i	$0.537806\pi$
$642$		0			0
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$	−15.0000	−	5.19615i	−0.591083	−	0.204757i
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	0.998246	+	0.0592060i	$0.0188569\pi$
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	−0.447849	+	0.894109i	$0.647810\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	5.50000	−	9.52628i	0.215728	−	0.373651i
$651$		0			0
$652$	9.50000	+	16.4545i	0.372049	+	0.644407i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		0			0
$655$	16.0000			0.625172
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$		0			0
$658$	−15.0000	−	5.19615i	−0.584761	−	0.202567i
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−14.0000	+	24.2487i	−0.544125	+	0.942453i
$663$		0			0
$664$	9.00000	−	15.5885i	0.349268	−	0.604949i
$665$	−40.0000	−	13.8564i	−1.55113	−	0.537328i
$666$		0			0
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	14.0000			0.541676
$669$		0			0
$670$	−28.0000			−1.08173
$671$	−5.00000	−	8.66025i	−0.193023	−	0.334325i
$672$		0			0
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	−0.996328	−	0.0856156i	$-0.972714\pi$
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	0.572309	+	0.820038i	$0.306048\pi$
$674$	5.00000	−	8.66025i	0.192593	−	0.333581i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$		0			0
$679$	−22.5000	−	7.79423i	−0.863471	−	0.299115i
$680$	−36.0000	−	62.3538i	−1.38054	−	2.39116i
$681$		0			0
$682$	6.00000			0.229752
$683$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$683$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$	−72.0000			−2.75098
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	1.00000			0.0381246
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	0.152167	−	0.988355i	$-0.451375\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$	16.0000			0.607352
$695$	−18.0000	−	31.1769i	−0.682779	−	1.18261i
$696$		0			0
$697$	−6.00000	+	10.3923i	−0.227266	+	0.393637i
$698$	5.00000			0.189253
$699$		0			0
$700$	27.5000	+	9.52628i	1.03940	+	0.360060i
$701$	−24.0000			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$702$		0			0
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$	−14.0000			−0.527645
$705$		0			0
$706$	14.0000	+	24.2487i	0.526897	+	0.912612i
$707$	4.00000	+	20.7846i	0.150435	+	0.781686i
$708$		0			0
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	0.598680	−	0.800988i	$-0.295692\pi$
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	−0.993016	+	0.117978i	$0.962359\pi$
$710$		0			0
$711$		0			0
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	9.00000	−	15.5885i	0.337053	−	0.583792i
$714$		0			0
$715$	4.00000	+	6.92820i	0.149592	+	0.259100i
$716$	4.00000			0.149487
$717$		0			0
$718$	22.0000			0.821033
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$	8.50000	+	44.1673i	0.316557	+	1.64488i
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	11.0000	−	19.0526i	0.408530	−	0.707594i
$726$		0			0
$727$	−20.5000	+	35.5070i	−0.760303	+	1.31688i	0.182392	+	0.983226i	$0.441616\pi$
$727$	−20.5000	+	35.5070i	−0.760303	+	1.31688i	−0.942694	+	0.333657i	$0.891717\pi$
$728$	6.00000	−	5.19615i	0.222375	−	0.192582i
$729$		0			0
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	−6.00000			−0.221918
$732$		0			0
$733$	21.0000			0.775653			0.387826	−	0.921732i	$-0.373226\pi$
$733$	21.0000			0.775653			0.387826	+	0.921732i	$0.373226\pi$
$734$	6.00000	+	10.3923i	0.221464	+	0.383587i
$735$		0			0
$736$	−15.0000	+	25.9808i	−0.552907	+	0.957664i
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$		0			0
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$	6.00000	+	10.3923i	0.220564	+	0.382029i
$741$		0			0
$742$	15.0000	+	5.19615i	0.550667	+	0.190757i
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	−0.937336	−	0.348428i	$-0.886716\pi$
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	0.166920	−	0.985970i	$-0.446618\pi$
$744$		0			0
$745$	96.0000			3.51717
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$	12.0000			0.438763
$749$	5.00000	+	1.73205i	0.182696	+	0.0632878i
$750$		0			0
$751$	−8.00000			−0.291924			−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000			−0.291924			−0.145962	+	0.989290i	$0.546628\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−1.00000	−	1.73205i	−0.0364179	−	0.0630776i
$755$	20.0000			0.727875
$756$		0			0
$757$	17.0000			0.617876			0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000			0.617876			0.308938	+	0.951082i	$0.400027\pi$
$758$	−4.50000	−	7.79423i	−0.163447	−	0.283099i
$759$		0			0
$760$	−24.0000	+	41.5692i	−0.870572	+	1.50787i
$761$	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
$763$	18.0000	−	15.5885i	0.651644	−	0.564340i
$764$	−4.00000			−0.144715
$765$		0			0
$766$	9.00000	+	15.5885i	0.325183	+	0.563234i
$767$	−6.00000			−0.216647
$768$		0			0
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$	16.0000	−	13.8564i	0.576600	−	0.499350i
$771$		0			0
$772$	−12.5000	−	21.6506i	−0.449885	−	0.779223i
$773$	8.00000	+	13.8564i	0.287740	+	0.498380i	0.973270	−	0.229664i	$-0.0737628\pi$
$773$	8.00000	+	13.8564i	0.287740	+	0.498380i	−0.685530	+	0.728044i	$0.740429\pi$
$774$		0			0
$775$	−16.5000	+	28.5788i	−0.592697	+	1.02658i
$776$	−13.5000	+	23.3827i	−0.484622	+	0.839390i
$777$		0			0
$778$	6.00000	+	10.3923i	0.215110	+	0.372582i
$779$	8.00000			0.286630
$780$		0			0
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$		0			0
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$	−20.0000	+	34.6410i	−0.713831	+	1.23639i
$786$		0			0
$787$	23.5000	−	40.7032i	0.837685	−	1.45091i	−0.0541413	−	0.998533i	$-0.517242\pi$
$787$	23.5000	−	40.7032i	0.837685	−	1.45091i	0.891826	−	0.452379i	$-0.149425\pi$
$788$	−10.0000	+	17.3205i	−0.356235	+	0.617018i
$789$		0			0
$790$	22.0000	−	38.1051i	0.782725	−	1.35572i
$791$	32.0000	−	27.7128i	1.13779	−	0.985354i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$	33.0000			1.17113
$795$		0			0
$796$	9.00000			0.318997
$797$	7.00000	+	12.1244i	0.247953	+	0.429467i	0.962958	−	0.269653i	$-0.0869089\pi$
$797$	7.00000	+	12.1244i	0.247953	+	0.429467i	−0.715005	+	0.699119i	$0.753576\pi$
$798$		0			0
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$	27.5000	−	47.6314i	0.972272	−	1.68402i
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	−12.0000	−	62.3538i	−0.422944	−	2.19768i
$806$	1.50000	+	2.59808i	0.0528352	+	0.0915133i
$807$		0			0
$808$	24.0000			0.844317
$809$	−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	−	3.46410i	0.140372	−	0.121566i
$813$		0			0
$814$	6.00000			0.210300
$815$	−38.0000	+	65.8179i	−1.33108	+	2.30550i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	−5.00000			−0.174821
$819$		0			0
$820$	−8.00000			−0.279372
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$		0			0
$823$	−22.5000	+	38.9711i	−0.784301	+	1.35845i	0.145115	+	0.989415i	$0.453645\pi$
$823$	−22.5000	+	38.9711i	−0.784301	+	1.35845i	−0.929416	+	0.369034i	$0.879689\pi$
$824$	51.0000			1.77667
$825$		0			0
$826$	3.00000	+	15.5885i	0.104383	+	0.542392i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$	24.0000			0.833052
$831$		0			0
$832$	−3.50000	−	6.06218i	−0.121341	−	0.210168i
$833$	33.0000	+	25.9808i	1.14338	+	0.900180i
$834$		0			0
$835$	28.0000	+	48.4974i	0.968980	+	1.67832i
$836$	−4.00000	−	6.92820i	−0.138343	−	0.239617i
$837$		0			0
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	13.0000	−	22.5167i	0.448810	−	0.777361i	−0.549499	−	0.835494i	$-0.685181\pi$
$839$	13.0000	−	22.5167i	0.448810	−	0.777361i	0.998309	+	0.0581329i	$0.0185147\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	10.0000			0.344623
$843$		0			0
$844$	5.00000			0.172107
$845$	24.0000	−	41.5692i	0.825625	−	1.43002i
$846$		0			0
$847$	−3.50000	−	18.1865i	−0.120261	−	0.624897i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	33.0000	−	57.1577i	1.13189	−	1.96049i
$851$	9.00000	−	15.5885i	0.308516	−	0.534365i
$852$		0			0
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$	−12.5000	−	4.33013i	−0.427741	−	0.148174i
$855$		0			0
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	16.0000			0.546550			0.273275	−	0.961936i	$-0.411893\pi$
$857$	16.0000			0.546550			0.273275	+	0.961936i	$0.411893\pi$
$858$		0			0
$859$	−25.0000			−0.852989			−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000			−0.852989			−0.426494	+	0.904490i	$0.640252\pi$
$860$	−2.00000	−	3.46410i	−0.0681994	−	0.118125i
$861$		0			0
$862$	−9.00000	+	15.5885i	−0.306541	+	0.530945i
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	−0.378052	−	0.925785i	$-0.623406\pi$
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	0.990779	−	0.135490i	$-0.0432609\pi$
$864$		0			0
$865$	32.0000	+	55.4256i	1.08803	+	1.88453i
$866$	−8.50000	−	14.7224i	−0.288842	−	0.500289i
$867$		0			0
$868$	−6.00000	+	5.19615i	−0.203653	+	0.176369i
$869$	11.0000	+	19.0526i	0.373149	+	0.646314i
$870$		0			0
$871$	7.00000			0.237186
$872$	−13.5000	−	23.3827i	−0.457168	−	0.791838i
$873$		0			0
$874$	24.0000			0.811812
$875$	12.0000	+	62.3538i	0.405674	+	2.10794i
$876$		0			0
$877$	7.00000			0.236373			0.118187	−	0.992991i	$-0.462292\pi$
$877$	7.00000			0.236373			0.118187	+	0.992991i	$0.462292\pi$
$878$	12.0000	−	20.7846i	0.404980	−	0.701447i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	−22.0000			−0.738688			−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000			−0.738688			−0.369344	+	0.929293i	$0.620418\pi$
$888$		0			0
$889$	−4.50000	−	23.3827i	−0.150925	−	0.784230i
$890$	−16.0000			−0.536321
$891$		0			0
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$	−24.0000			−0.803129
$894$		0			0
$895$	8.00000	+	13.8564i	0.267411	+	0.463169i
$896$	6.00000	−	5.19615i	0.200446	−	0.173591i
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−2.00000	+	3.46410i	−0.0665927	+	0.115342i
$903$		0			0
$904$	−24.0000	−	41.5692i	−0.798228	−	1.38257i
$905$	−8.00000			−0.265929
$906$		0			0
$907$	−13.0000			−0.431658			−0.215829	−	0.976431i	$-0.569245\pi$
$907$	−13.0000			−0.431658			−0.215829	+	0.976431i	$0.569245\pi$
$908$	−9.00000	+	15.5885i	−0.298675	+	0.517321i
$909$		0			0
$910$	10.0000	+	3.46410i	0.331497	+	0.114834i
$911$	−9.00000	+	15.5885i	−0.298183	+	0.516469i	−0.975720	−	0.219020i	$-0.929714\pi$
$911$	−9.00000	+	15.5885i	−0.298183	+	0.516469i	0.677537	+	0.735489i	$0.263047\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	6.50000	−	11.2583i	0.215001	−	0.372392i
$915$		0			0
$916$	−3.50000	+	6.06218i	−0.115643	+	0.200300i
$917$	2.00000	+	10.3923i	0.0660458	+	0.343184i
$918$		0			0
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$	−72.0000			−2.37377
$921$		0			0
$922$	−2.00000			−0.0658665
$923$		0			0
$924$		0			0
$925$	−16.5000	+	28.5788i	−0.542517	+	0.939666i
$926$	−16.0000	+	27.7128i	−0.525793	+	0.910700i
$927$		0			0
$928$	−5.00000	−	8.66025i	−0.164133	−	0.284287i
$929$	2.00000	+	3.46410i	0.0656179	+	0.113653i	0.896968	−	0.442096i	$-0.145765\pi$
$929$	2.00000	+	3.46410i	0.0656179	+	0.113653i	−0.831350	+	0.555749i	$0.812431\pi$
$930$		0			0
$931$	4.00000	−	27.7128i	0.131095	−	0.908251i
$932$	12.0000	+	20.7846i	0.393073	+	0.680823i
$933$		0			0
$934$		0			0
$935$	24.0000	+	41.5692i	0.784884	+	1.35946i
$936$		0			0
$937$	−21.0000			−0.686040			−0.343020	−	0.939328i	$-0.611450\pi$
$937$	−21.0000			−0.686040			−0.343020	+	0.939328i	$0.611450\pi$
$938$	−3.50000	−	18.1865i	−0.114279	−	0.593811i
$939$		0			0
$940$	24.0000			0.782794
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	−0.198150	−	0.980172i	$-0.563493\pi$
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	0.947929	−	0.318483i	$-0.103173\pi$
$942$		0			0
$943$	6.00000	+	10.3923i	0.195387	+	0.338420i
$944$	6.00000			0.195283
$945$		0			0
$946$	−2.00000			−0.0650256
$947$	−13.0000	−	22.5167i	−0.422443	−	0.731693i	0.573735	−	0.819041i	$-0.305494\pi$
$947$	−13.0000	−	22.5167i	−0.422443	−	0.731693i	−0.996178	+	0.0873481i	$0.972161\pi$
$948$		0			0
$949$	3.00000	−	5.19615i	0.0973841	−	0.168674i
$950$	−44.0000			−1.42755
$951$		0			0
$952$	36.0000	−	31.1769i	1.16677	−	1.01045i
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$		0			0
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$	−12.0000			−0.388108
$957$		0			0
$958$	−8.00000	−	13.8564i	−0.258468	−	0.447680i
$959$	−9.00000	−	46.7654i	−0.290625	−	1.51013i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	1.50000	+	2.59808i	0.0483619	+	0.0837653i
$963$		0			0
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	50.0000	−	86.6025i	1.60956	−	2.78783i
$966$		0			0
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	0.969715	−	0.244238i	$-0.0785377\pi$
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	−0.696374	+	0.717679i	$0.745204\pi$
$968$	−21.0000			−0.674966
$969$		0			0
$970$	−36.0000			−1.15589
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$	18.0000	−	15.5885i	0.577054	−	0.499743i
$974$	8.00000	−	13.8564i	0.256337	−	0.443988i
$975$		0			0
$976$	−2.50000	+	4.33013i	−0.0800230	+	0.138604i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	4.00000	−	6.92820i	0.127841	−	0.221426i
$980$	−4.00000	+	27.7128i	−0.127775	+	0.885253i
$981$		0			0
$982$	−17.0000	+	29.4449i	−0.542492	+	0.939623i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	−80.0000			−2.54901
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$	2.00000	−	3.46410i	0.0636285	−	0.110208i
$989$	−3.00000	+	5.19615i	−0.0953945	+	0.165228i
$990$		0			0
$991$	27.5000	+	47.6314i	0.873566	+	1.51306i	0.858282	+	0.513178i	$0.171532\pi$
$991$	27.5000	+	47.6314i	0.873566	+	1.51306i	0.0152841	+	0.999883i	$0.495135\pi$
$992$	7.50000	+	12.9904i	0.238125	+	0.412445i
$993$		0			0
$994$		0			0
$995$	18.0000	+	31.1769i	0.570638	+	0.988375i
$996$		0			0
$997$	−29.0000			−0.918439			−0.459220	−	0.888323i	$-0.651871\pi$
$997$	−29.0000			−0.918439			−0.459220	+	0.888323i	$0.651871\pi$
$998$	−8.50000	−	14.7224i	−0.269063	−	0.466030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.e.541.1		2
3.2	odd	2		567.2.g.b.541.1		2
7.4	even	3		567.2.h.b.298.1		2
9.2	odd	6		189.2.e.a.163.1	yes	2
9.4	even	3		567.2.h.b.352.1		2
9.5	odd	6		567.2.h.e.352.1		2
9.7	even	3		189.2.e.c.163.1	yes	2
21.11	odd	6		567.2.h.e.298.1		2
63.2	odd	6		1323.2.a.m.1.1		1
63.4	even	3	inner	567.2.g.e.109.1		2
63.11	odd	6		189.2.e.a.109.1	✓	2
63.16	even	3		1323.2.a.g.1.1		1
63.25	even	3		189.2.e.c.109.1	yes	2
63.32	odd	6		567.2.g.b.109.1		2
63.47	even	6		1323.2.a.p.1.1		1
63.61	odd	6		1323.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.a.109.1	✓	2	63.11	odd	6
189.2.e.a.163.1	yes	2	9.2	odd	6
189.2.e.c.109.1	yes	2	63.25	even	3
189.2.e.c.163.1	yes	2	9.7	even	3
567.2.g.b.109.1		2	63.32	odd	6
567.2.g.b.541.1		2	3.2	odd	2
567.2.g.e.109.1		2	63.4	even	3	inner
567.2.g.e.541.1		2	1.1	even	1	trivial
567.2.h.b.298.1		2	7.4	even	3
567.2.h.b.352.1		2	9.4	even	3
567.2.h.e.298.1		2	21.11	odd	6
567.2.h.e.352.1		2	9.5	odd	6
1323.2.a.d.1.1		1	63.61	odd	6
1323.2.a.g.1.1		1	63.16	even	3
1323.2.a.m.1.1		1	63.2	odd	6
1323.2.a.p.1.1		1	63.47	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(2.00000 + 3.46410i) q^{10} -2.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{20} +(-1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +11.0000 q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} +(1.00000 - 1.73205i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{32} +(3.00000 - 5.19615i) q^{34} +(2.00000 + 10.3923i) q^{35} +(-1.50000 + 2.59808i) q^{37} -4.00000 q^{38} +12.0000 q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(5.50000 + 9.52628i) q^{50} -1.00000 q^{52} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(1.50000 + 7.79423i) q^{56} +2.00000 q^{58} +(3.00000 - 5.19615i) q^{59} +(2.50000 + 4.33013i) q^{61} -3.00000 q^{62} +7.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-3.50000 + 6.06218i) q^{67} -6.00000 q^{68} +(-8.00000 + 6.92820i) q^{70} +(3.00000 + 5.19615i) q^{73} -3.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-1.00000 - 5.19615i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(2.00000 + 3.46410i) q^{80} +(1.00000 - 1.73205i) q^{82} +(3.00000 - 5.19615i) q^{83} +(-12.0000 - 20.7846i) q^{85} +1.00000 q^{86} -6.00000 q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.73205i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 8 q^{5} + q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + 4 q^{20} - 2 q^{22} - 12 q^{23} + 22 q^{25} + q^{26} + 5 q^{28} + 2 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 8 * q^5 + q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - q^13 - 4 * q^14 + q^16 - 6 * q^17 - 4 * q^19 + 4 * q^20 - 2 * q^22 - 12 * q^23 + 22 * q^25 + q^26 + 5 * q^28 + 2 * q^29 - 3 * q^31 + 5 * q^32 + 6 * q^34 + 4 * q^35 - 3 * q^37 - 8 * q^38 + 24 * q^40 - 2 * q^41 + q^43 - 2 * q^44 - 6 * q^46 + 6 * q^47 - 13 * q^49 + 11 * q^50 - 2 * q^52 - 6 * q^53 - 16 * q^55 + 3 * q^56 + 4 * q^58 + 6 * q^59 + 5 * q^61 - 6 * q^62 + 14 * q^64 - 4 * q^65 - 7 * q^67 - 12 * q^68 - 16 * q^70 + 6 * q^73 - 6 * q^74 + 4 * q^76 - 2 * q^77 - 11 * q^79 + 4 * q^80 + 2 * q^82 + 6 * q^83 - 24 * q^85 + 2 * q^86 - 12 * q^88 - 4 * q^89 + 4 * q^91 - 6 * q^92 - 6 * q^94 - 16 * q^95 - 9 * q^97 - 11 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more