LMFDB - Embedded newform 567.2.f.f.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("567.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.f.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -1.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +3.00000 q^{17} -2.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{26} +1.00000 q^{28} +(2.50000 - 4.33013i) q^{29} +(3.00000 + 5.19615i) q^{31} +(2.50000 + 4.33013i) q^{32} +(1.50000 - 2.59808i) q^{34} -1.00000 q^{35} -3.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(5.00000 + 8.66025i) q^{41} +(2.00000 - 3.46410i) q^{43} +2.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-2.50000 + 4.33013i) q^{52} -6.00000 q^{53} -2.00000 q^{55} +(1.50000 - 2.59808i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.50000 + 6.06218i) q^{61} +6.00000 q^{62} +7.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(1.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-0.500000 + 0.866025i) q^{70} -12.0000 q^{71} -15.0000 q^{73} +(-1.50000 + 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +10.0000 q^{82} +(-9.00000 + 15.5885i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{88} -5.00000 q^{89} +5.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(9.00000 - 15.5885i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} - q^{5} + q^{7} + 6 q^{8} - 2 q^{10} + 2 q^{11} + 5 q^{13} - q^{14} + q^{16} + 6 q^{17} - 4 q^{19} + q^{20} - 2 q^{22} - 6 q^{23} + 4 q^{25} + 10 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 - q^5 + q^7 + 6 * q^8 - 2 * q^10 + 2 * q^11 + 5 * q^13 - q^14 + q^16 + 6 * q^17 - 4 * q^19 + q^20 - 2 * q^22 - 6 * q^23 + 4 * q^25 + 10 * q^26 + 2 * q^28 + 5 * q^29 + 6 * q^31 + 5 * q^32 + 3 * q^34 - 2 * q^35 - 6 * q^37 - 2 * q^38 - 3 * q^40 + 10 * q^41 + 4 * q^43 + 4 * q^44 - 12 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 5 * q^52 - 12 * q^53 - 4 * q^55 + 3 * q^56 - 5 * q^58 - 6 * q^59 - 7 * q^61 + 12 * q^62 + 14 * q^64 + 5 * q^65 + 2 * q^67 + 3 * q^68 - q^70 - 24 * q^71 - 30 * q^73 - 3 * q^74 - 2 * q^76 - 2 * q^77 - 14 * q^79 - 2 * q^80 + 20 * q^82 - 18 * q^83 - 3 * q^85 - 4 * q^86 + 6 * q^88 - 10 * q^89 + 10 * q^91 + 6 * q^92 - 6 * q^94 + 2 * q^95 + 18 * q^97 - 2 * q^98

Character values

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

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

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	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	3.00000			1.06066
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	5.00000			0.980581
$27$		0			0
$28$	1.00000			0.188982
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		0			0
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	0.931436	+	0.363905i	$0.118557\pi$
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	−0.150567	+	0.988600i	$0.548110\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	−6.00000			−0.884652
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−2.50000	−	4.33013i	−0.328266	−	0.568574i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	7.00000			0.875000
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−15.0000			−1.75562			−0.877809	−	0.479012i	$-0.840995\pi$
$73$	−15.0000			−1.75562			−0.877809	+	0.479012i	$0.840995\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−1.00000	−	1.73205i	−0.113961	−	0.197386i
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	10.0000			1.10432
$83$	−9.00000	+	15.5885i	−0.987878	+	1.71106i	−0.359506	+	0.933143i	$0.617055\pi$
$83$	−9.00000	+	15.5885i	−0.987878	+	1.71106i	−0.628372	+	0.777913i	$0.716279\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	−5.00000			−0.529999			−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000			−0.529999			−0.264999	+	0.964249i	$0.585372\pi$
$90$		0			0
$91$	5.00000			0.524142
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	9.00000	−	15.5885i	0.913812	−	1.58277i	0.105180	−	0.994453i	$-0.466458\pi$
$97$	9.00000	−	15.5885i	0.913812	−	1.58277i	0.808632	−	0.588315i	$-0.200208\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	4.00000			0.400000
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	7.50000	+	12.9904i	0.735436	+	1.27381i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$		0			0
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	0.841549	−	0.540181i	$-0.181644\pi$
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	−0.888585	+	0.458712i	$0.848311\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	5.00000			0.464238
$117$		0			0
$118$	−6.00000			−0.552345
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	3.50000	+	6.06218i	0.316875	+	0.548844i
$123$		0			0
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$		0			0
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	−0.968826	−	0.247741i	$-0.920312\pi$
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	0.269863	−	0.962899i	$-0.413022\pi$
$132$		0			0
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	2.00000			0.172774
$135$		0			0
$136$	9.00000			0.771744
$137$	−10.5000	+	18.1865i	−0.897076	+	1.55378i	−0.0658609	+	0.997829i	$0.520979\pi$
$137$	−10.5000	+	18.1865i	−0.897076	+	1.55378i	−0.831215	+	0.555952i	$0.812354\pi$
$138$		0			0
$139$	3.00000	+	5.19615i	0.254457	+	0.440732i	0.964748	−	0.263176i	$-0.0847700\pi$
$139$	3.00000	+	5.19615i	0.254457	+	0.440732i	−0.710291	+	0.703908i	$0.751437\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$		0			0
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	10.0000			0.836242
$144$		0			0
$145$	−5.00000			−0.415227
$146$	−7.50000	+	12.9904i	−0.620704	+	1.07509i
$147$		0			0
$148$	−1.50000	−	2.59808i	−0.123299	−	0.213561i
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−6.00000			−0.486664
$153$		0			0
$154$	−2.00000			−0.161165
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$	7.00000	+	12.1244i	0.556890	+	0.964562i
$159$		0			0
$160$	2.50000	−	4.33013i	0.197642	−	0.342327i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$		0			0
$166$	9.00000	+	15.5885i	0.698535	+	1.20990i
$167$	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
$170$	−3.00000			−0.230089
$171$		0			0
$172$	4.00000			0.304997
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	−0.945274	−	0.326278i	$-0.894205\pi$
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	0.755202	+	0.655492i	$0.227539\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	−2.50000	+	4.33013i	−0.187383	+	0.324557i
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	2.50000	−	4.33013i	0.185312	−	0.320970i
$183$		0			0
$184$	−9.00000	−	15.5885i	−0.663489	−	1.14920i
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	6.00000			0.437595
$189$		0			0
$190$	2.00000			0.145095
$191$	7.00000	−	12.1244i	0.506502	−	0.877288i	−0.493469	−	0.869763i	$-0.664272\pi$
$191$	7.00000	−	12.1244i	0.506502	−	0.877288i	0.999972	−	0.00752447i	$-0.00239513\pi$
$192$		0			0
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$	−9.00000	−	15.5885i	−0.646162	−	1.11919i
$195$		0			0
$196$	0.500000	−	0.866025i	0.0357143	−	0.0618590i
$197$	−5.00000			−0.356235			−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000			−0.356235			−0.178118	+	0.984009i	$0.557001\pi$
$198$		0			0
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	6.00000	−	10.3923i	0.424264	−	0.734847i
$201$		0			0
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	−2.50000	−	4.33013i	−0.175466	−	0.303915i
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$	−8.00000			−0.557386
$207$		0			0
$208$	5.00000			0.346688
$209$	−2.00000	+	3.46410i	−0.138343	+	0.239617i
$210$		0			0
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	−0.944237	−	0.329266i	$-0.893199\pi$
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	0.186966	−	0.982366i	$-0.440135\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	−4.00000			−0.272798
$216$		0			0
$217$	6.00000			0.407307
$218$	4.50000	−	7.79423i	0.304778	−	0.527892i
$219$		0			0
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$		0			0
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	5.00000			0.334077
$225$		0			0
$226$	−1.00000			−0.0665190
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	−0.125435	−	0.992102i	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$		0			0
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$		0			0
$232$	7.50000	−	12.9904i	0.492399	−	0.852860i
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$		0			0
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−15.0000	−	25.9808i	−0.970269	−	1.68056i	−0.694737	−	0.719264i	$-0.744479\pi$
$239$	−15.0000	−	25.9808i	−0.970269	−	1.68056i	−0.275533	−	0.961292i	$-0.588854\pi$
$240$		0			0
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	−7.00000			−0.448129
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	9.00000	+	15.5885i	0.571501	+	0.989868i
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	0.994375	−	0.105919i	$-0.0337784\pi$
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	−0.588916	+	0.808194i	$0.700445\pi$
$258$		0			0
$259$	−1.50000	+	2.59808i	−0.0932055	+	0.161437i
$260$	5.00000			0.310087
$261$		0			0
$262$	−16.0000			−0.988483
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	−0.977993	−	0.208635i	$-0.933098\pi$
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	0.669680	+	0.742650i	$0.266431\pi$
$264$		0			0
$265$	3.00000	+	5.19615i	0.184289	+	0.319197i
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$		0			0
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	9.00000			0.548740			0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000			0.548740			0.274370	+	0.961624i	$0.411531\pi$
$270$		0			0
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	10.5000	+	18.1865i	0.634328	+	1.09869i
$275$	−4.00000	−	6.92820i	−0.241209	−	0.417786i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	6.00000			0.359856
$279$		0			0
$280$	−3.00000			−0.179284
$281$	−2.50000	+	4.33013i	−0.149137	+	0.258314i	−0.930909	−	0.365251i	$-0.880983\pi$
$281$	−2.50000	+	4.33013i	−0.149137	+	0.258314i	0.781771	+	0.623565i	$0.214316\pi$
$282$		0			0
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	0.960076	−	0.279741i	$-0.0902485\pi$
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	−0.722300	+	0.691580i	$0.756915\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	5.00000	−	8.66025i	0.295656	−	0.512092i
$287$	10.0000			0.590281
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−2.50000	+	4.33013i	−0.146805	+	0.254274i
$291$		0			0
$292$	−7.50000	−	12.9904i	−0.438904	−	0.760205i
$293$	15.5000	+	26.8468i	0.905520	+	1.56841i	0.820218	+	0.572051i	$0.193852\pi$
$293$	15.5000	+	26.8468i	0.905520	+	1.56841i	0.0853015	+	0.996355i	$0.472815\pi$
$294$		0			0
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	−9.00000			−0.523114
$297$		0			0
$298$	−15.0000			−0.868927
$299$	15.0000	−	25.9808i	0.867472	−	1.50251i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	7.00000			0.400819
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	−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
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	5.00000			0.282166
$315$		0			0
$316$	−14.0000			−0.787562
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$		0			0
$319$	−5.00000	−	8.66025i	−0.279946	−	0.484881i
$320$	−3.50000	−	6.06218i	−0.195656	−	0.338886i
$321$		0			0
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	−6.00000			−0.333849
$324$		0			0
$325$	20.0000			1.10940
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	15.0000	+	25.9808i	0.828236	+	1.43455i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−18.0000			−0.987878
$333$		0			0
$334$	14.0000			0.766046
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	1.00000	+	1.73205i	0.0544735	+	0.0943508i	0.891976	−	0.452082i	$-0.149319\pi$
$337$	1.00000	+	1.73205i	0.0544735	+	0.0943508i	−0.837503	+	0.546433i	$0.815985\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	12.0000			0.649836
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	6.00000	−	10.3923i	0.323498	−	0.560316i
$345$		0			0
$346$	2.50000	+	4.33013i	0.134401	+	0.232789i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	10.0000			0.533002
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	−0.617388	−	0.786659i	$-0.711809\pi$
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	0.989960	+	0.141344i	$0.0451425\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$	−2.50000	−	4.33013i	−0.132500	−	0.229496i
$357$		0			0
$358$	1.00000	−	1.73205i	0.0528516	−	0.0915417i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		0			0
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$	7.50000	+	12.9904i	0.392568	+	0.679948i
$366$		0			0
$367$	15.0000	−	25.9808i	0.782994	−	1.35618i	−0.147197	−	0.989107i	$-0.547025\pi$
$367$	15.0000	−	25.9808i	0.782994	−	1.35618i	0.930190	−	0.367078i	$-0.119642\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	3.00000			0.155963
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	9.00000	−	15.5885i	0.464140	−	0.803913i
$377$	25.0000			1.28757
$378$		0			0
$379$	6.00000			0.308199			0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000			0.308199			0.154100	+	0.988055i	$0.450752\pi$
$380$	−1.00000	+	1.73205i	−0.0512989	+	0.0888523i
$381$		0			0
$382$	−7.00000	−	12.1244i	−0.358151	−	0.620336i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$	13.0000			0.661683
$387$		0			0
$388$	18.0000			0.913812
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$		0			0
$394$	−2.50000	+	4.33013i	−0.125948	+	0.218149i
$395$	14.0000			0.704416
$396$		0			0
$397$	15.0000			0.752828			0.376414	−	0.926451i	$-0.377157\pi$
$397$	15.0000			0.752828			0.376414	+	0.926451i	$0.377157\pi$
$398$	−3.00000	+	5.19615i	−0.150376	+	0.260460i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−15.0000	+	25.9808i	−0.747203	+	1.29419i
$404$	−14.0000			−0.696526
$405$		0			0
$406$	−5.00000			−0.248146
$407$	−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	$0.872783\pi$
$410$	−5.00000	−	8.66025i	−0.246932	−	0.427699i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	−6.00000			−0.295241
$414$		0			0
$415$	18.0000			0.883585
$416$	−12.5000	+	21.6506i	−0.612863	+	1.06151i
$417$		0			0
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$		0			0
$421$	−14.5000	+	25.1147i	−0.706687	+	1.22402i	0.259393	+	0.965772i	$0.416478\pi$
$421$	−14.5000	+	25.1147i	−0.706687	+	1.22402i	−0.966079	+	0.258245i	$0.916856\pi$
$422$	−22.0000			−1.07094
$423$		0			0
$424$	−18.0000			−0.874157
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	3.50000	+	6.06218i	0.169377	+	0.293369i
$428$	−4.00000	−	6.92820i	−0.193347	−	0.334887i
$429$		0			0
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	1.00000			0.0480569			0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000			0.0480569			0.0240285	+	0.999711i	$0.492351\pi$
$434$	3.00000	−	5.19615i	0.144005	−	0.249423i
$435$		0			0
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		0			0
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	0.0137020	+	0.999906i	$0.495638\pi$
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	−0.872795	+	0.488087i	$0.837695\pi$
$440$	−6.00000			−0.286039
$441$		0			0
$442$	15.0000			0.713477
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$		0			0
$445$	2.50000	+	4.33013i	0.118511	+	0.205268i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$		0			0
$448$	3.50000	−	6.06218i	0.165359	−	0.286411i
$449$	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
$451$	20.0000			0.941763
$452$	0.500000	−	0.866025i	0.0235180	−	0.0407344i
$453$		0			0
$454$	−12.0000	−	20.7846i	−0.563188	−	0.975470i
$455$	−2.50000	−	4.33013i	−0.117202	−	0.202999i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$	−11.0000			−0.513996
$459$		0			0
$460$	−6.00000			−0.279751
$461$	−19.0000	+	32.9090i	−0.884918	+	1.53272i	−0.0391109	+	0.999235i	$0.512453\pi$
$461$	−19.0000	+	32.9090i	−0.884918	+	1.53272i	−0.845807	+	0.533488i	$0.820881\pi$
$462$		0			0
$463$	1.00000	+	1.73205i	0.0464739	+	0.0804952i	0.888327	−	0.459212i	$-0.151868\pi$
$463$	1.00000	+	1.73205i	0.0464739	+	0.0804952i	−0.841853	+	0.539707i	$0.818535\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$	−3.00000	+	5.19615i	−0.138380	+	0.239681i
$471$		0			0
$472$	−9.00000	−	15.5885i	−0.414259	−	0.717517i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	3.00000			0.137505
$477$		0			0
$478$	−30.0000			−1.37217
$479$	17.0000	−	29.4449i	0.776750	−	1.34537i	−0.157056	−	0.987590i	$-0.550200\pi$
$479$	17.0000	−	29.4449i	0.776750	−	1.34537i	0.933806	−	0.357780i	$-0.116466\pi$
$480$		0			0
$481$	−7.50000	−	12.9904i	−0.341971	−	0.592310i
$482$	−9.50000	−	16.4545i	−0.432713	−	0.749481i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−18.0000			−0.817338
$486$		0			0
$487$	34.0000			1.54069			0.770344	−	0.637629i	$-0.220085\pi$
$487$	34.0000			1.54069			0.770344	+	0.637629i	$0.220085\pi$
$488$	−10.5000	+	18.1865i	−0.475313	+	0.823266i
$489$		0			0
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	0.987181	+	0.159603i	$0.0510215\pi$
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	−0.355370	+	0.934726i	$0.615645\pi$
$492$		0			0
$493$	7.50000	−	12.9904i	0.337783	−	0.585057i
$494$	−10.0000			−0.449921
$495$		0			0
$496$	6.00000			0.269408
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	−1.00000	+	1.73205i	−0.0446322	+	0.0773052i
$503$	−18.0000			−0.802580			−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000			−0.802580			−0.401290	+	0.915951i	$0.631438\pi$
$504$		0			0
$505$	14.0000			0.622992
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$		0			0
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$		0			0
$511$	−7.50000	+	12.9904i	−0.331780	+	0.574661i
$512$	11.0000			0.486136
$513$		0			0
$514$	13.0000			0.573405
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	1.50000	+	2.59808i	0.0659062	+	0.114153i
$519$		0			0
$520$	7.50000	−	12.9904i	0.328897	−	0.569666i
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	8.00000	−	13.8564i	0.349482	−	0.605320i
$525$		0			0
$526$	5.00000	+	8.66025i	0.218010	+	0.377605i
$527$	9.00000	+	15.5885i	0.392046	+	0.679044i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	6.00000			0.260623
$531$		0			0
$532$	−2.00000			−0.0867110
$533$	−25.0000	+	43.3013i	−1.08287	+	1.87559i
$534$		0			0
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	3.00000	+	5.19615i	0.129580	+	0.224440i
$537$		0			0
$538$	4.50000	−	7.79423i	0.194009	−	0.336033i
$539$	−2.00000			−0.0861461
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$		0			0
$544$	7.50000	+	12.9904i	0.321560	+	0.556958i
$545$	−4.50000	−	7.79423i	−0.192759	−	0.333868i
$546$		0			0
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	−0.999424	−	0.0339321i	$-0.989197\pi$
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	0.529098	+	0.848561i	$0.322530\pi$
$548$	−21.0000			−0.897076
$549$		0			0
$550$	−8.00000			−0.341121
$551$	−5.00000	+	8.66025i	−0.213007	+	0.368939i
$552$		0			0
$553$	7.00000	+	12.1244i	0.297670	+	0.515580i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	−3.00000	+	5.19615i	−0.127228	+	0.220366i
$557$	−29.0000			−1.22877			−0.614385	−	0.789007i	$-0.710596\pi$
$557$	−29.0000			−1.22877			−0.614385	+	0.789007i	$0.710596\pi$
$558$		0			0
$559$	20.0000			0.845910
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$		0			0
$562$	2.50000	+	4.33013i	0.105456	+	0.182655i
$563$	16.0000	+	27.7128i	0.674320	+	1.16796i	0.976667	+	0.214758i	$0.0688963\pi$
$563$	16.0000	+	27.7128i	0.674320	+	1.16796i	−0.302348	+	0.953198i	$0.597770\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	8.00000			0.336265
$567$		0			0
$568$	−36.0000			−1.51053
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	−0.727405	−	0.686209i	$-0.759274\pi$
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	0.957977	+	0.286846i	$0.0926069\pi$
$570$		0			0
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	−0.922760	−	0.385376i	$-0.874072\pi$
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	0.127634	−	0.991821i	$-0.459262\pi$
$572$	5.00000	+	8.66025i	0.209061	+	0.362103i
$573$		0			0
$574$	5.00000	−	8.66025i	0.208696	−	0.361472i
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−23.0000			−0.957503			−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000			−0.957503			−0.478751	+	0.877951i	$0.658910\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		0			0
$580$	−2.50000	−	4.33013i	−0.103807	−	0.179799i
$581$	9.00000	+	15.5885i	0.373383	+	0.646718i
$582$		0			0
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−45.0000			−1.86211
$585$		0			0
$586$	31.0000			1.28060
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	−0.462518	−	0.886610i	$-0.653054\pi$
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	0.999086	−	0.0427523i	$-0.0136126\pi$
$588$		0			0
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$	3.00000	+	5.19615i	0.123508	+	0.213922i
$591$		0			0
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$		0			0
$595$	−3.00000			−0.122988
$596$	7.50000	−	12.9904i	0.307212	−	0.532107i
$597$		0			0
$598$	−15.0000	−	25.9808i	−0.613396	−	1.06243i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	−16.5000	+	28.5788i	−0.673049	+	1.16576i	0.303986	+	0.952676i	$0.401682\pi$
$601$	−16.5000	+	28.5788i	−0.673049	+	1.16576i	−0.977035	+	0.213079i	$0.931651\pi$
$602$	−4.00000			−0.163028
$603$		0			0
$604$	10.0000			0.406894
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	−5.00000	−	8.66025i	−0.202777	−	0.351220i
$609$		0			0
$610$	3.50000	−	6.06218i	0.141711	−	0.245450i
$611$	30.0000			1.21367
$612$		0			0
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$	−3.00000	−	5.19615i	−0.120873	−	0.209359i
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	0.976575	−	0.215177i	$-0.0690329\pi$
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	−0.674636	+	0.738150i	$0.735700\pi$
$618$		0			0
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$	6.00000			0.240966
$621$		0			0
$622$	−6.00000			−0.240578
$623$	−2.50000	+	4.33013i	−0.100160	+	0.173483i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−9.50000	−	16.4545i	−0.379696	−	0.657653i
$627$		0			0
$628$	−2.50000	+	4.33013i	−0.0997609	+	0.172791i
$629$	−9.00000			−0.358854
$630$		0			0
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$	−21.0000	+	36.3731i	−0.835335	+	1.44684i
$633$		0			0
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$		0			0
$637$	2.50000	−	4.33013i	0.0990536	−	0.171566i
$638$	−10.0000			−0.395904
$639$		0			0
$640$	3.00000			0.118585
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$		0			0
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$		0			0
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	10.0000	−	17.3205i	0.392232	−	0.679366i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$		0			0
$655$	−8.00000	+	13.8564i	−0.312586	+	0.541415i
$656$	10.0000			0.390434
$657$		0			0
$658$	−6.00000			−0.233904
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		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	$0.539564\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	−27.0000	+	46.7654i	−1.04780	+	1.81485i
$665$	2.00000			0.0775567
$666$		0			0
$667$	−30.0000			−1.16160
$668$	−7.00000	+	12.1244i	−0.270838	+	0.469105i
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	7.00000	+	12.1244i	0.270232	+	0.468056i
$672$		0			0
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	−0.135615	−	0.990762i	$-0.543301\pi$
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	0.925832	−	0.377934i	$-0.123365\pi$
$674$	2.00000			0.0770371
$675$		0			0
$676$	−12.0000			−0.461538
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$	−9.00000	−	15.5885i	−0.345388	−	0.598230i
$680$	−4.50000	−	7.79423i	−0.172567	−	0.298895i
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	21.0000			0.802369
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−15.0000	−	25.9808i	−0.571454	−	0.989788i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	−5.00000			−0.190071
$693$		0			0
$694$	4.00000			0.151838
$695$	3.00000	−	5.19615i	0.113796	−	0.197101i
$696$		0			0
$697$	15.0000	+	25.9808i	0.568166	+	0.984092i
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$		0			0
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	−9.00000			−0.339925			−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000			−0.339925			−0.169963	+	0.985451i	$0.554365\pi$
$702$		0			0
$703$	6.00000			0.226294
$704$	7.00000	−	12.1244i	0.263822	−	0.456954i
$705$		0			0
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$	7.00000	+	12.1244i	0.263262	+	0.455983i
$708$		0			0
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	−0.223544	−	0.974694i	$-0.571763\pi$
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	0.955882	−	0.293752i	$-0.0949041\pi$
$710$	12.0000			0.450352
$711$		0			0
$712$	−15.0000			−0.562149
$713$	18.0000	−	31.1769i	0.674105	−	1.16758i
$714$		0			0
$715$	−5.00000	−	8.66025i	−0.186989	−	0.323875i
$716$	1.00000	+	1.73205i	0.0373718	+	0.0647298i
$717$		0			0
$718$	4.00000	−	6.92820i	0.149279	−	0.258558i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$		0			0
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$		0			0
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	15.0000			0.555937
$729$		0			0
$730$	15.0000			0.555175
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	−15.0000	−	25.9808i	−0.553660	−	0.958967i
$735$		0			0
$736$	15.0000	−	25.9808i	0.552907	−	0.957664i
$737$	4.00000			0.147342
$738$		0			0
$739$	54.0000			1.98642			0.993211	−	0.116326i	$-0.0371118\pi$
$739$	54.0000			1.98642			0.993211	+	0.116326i	$0.0371118\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$		0			0
$742$	3.00000	+	5.19615i	0.110133	+	0.190757i
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	−7.50000	+	12.9904i	−0.274779	+	0.475931i
$746$	22.0000			0.805477
$747$		0			0
$748$	6.00000			0.219382
$749$	−4.00000	+	6.92820i	−0.146157	+	0.253151i
$750$		0			0
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	0.917772	+	0.397108i	$0.129986\pi$
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	−0.114981	+	0.993368i	$0.536681\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$		0			0
$754$	12.5000	−	21.6506i	0.455223	−	0.788470i
$755$	−10.0000			−0.363937
$756$		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
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	0.993098	+	0.117289i	$0.0374205\pi$
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	−0.394973	+	0.918693i	$0.629246\pi$
$762$		0			0
$763$	4.50000	−	7.79423i	0.162911	−	0.282170i
$764$	14.0000			0.506502
$765$		0			0
$766$		0			0
$767$	15.0000	−	25.9808i	0.541619	−	0.938111i
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$	1.00000	+	1.73205i	0.0360375	+	0.0624188i
$771$		0			0
$772$	−6.50000	+	11.2583i	−0.233940	+	0.405196i
$773$	29.0000			1.04306			0.521529	−	0.853234i	$-0.325362\pi$
$773$	29.0000			1.04306			0.521529	+	0.853234i	$0.325362\pi$
$774$		0			0
$775$	24.0000			0.862105
$776$	27.0000	−	46.7654i	0.969244	−	1.67878i
$777$		0			0
$778$	9.00000	+	15.5885i	0.322666	+	0.558873i
$779$	−10.0000	−	17.3205i	−0.358287	−	0.620572i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$	−18.0000			−0.643679
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	2.50000	−	4.33013i	0.0892288	−	0.154549i
$786$		0			0
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	0.687481	−	0.726202i	$-0.258716\pi$
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	−0.972650	+	0.232275i	$0.925383\pi$
$788$	−2.50000	−	4.33013i	−0.0890588	−	0.154254i
$789$		0			0
$790$	7.00000	−	12.1244i	0.249049	−	0.431365i
$791$	−1.00000			−0.0355559
$792$		0			0
$793$	−35.0000			−1.24289
$794$	7.50000	−	12.9904i	0.266165	−	0.461011i
$795$		0			0
$796$	−3.00000	−	5.19615i	−0.106332	−	0.184173i
$797$	−18.5000	−	32.0429i	−0.655304	−	1.13502i	−0.981818	−	0.189827i	$-0.939207\pi$
$797$	−18.5000	−	32.0429i	−0.655304	−	1.13502i	0.326514	−	0.945192i	$-0.394126\pi$
$798$		0			0
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$	20.0000			0.707107
$801$		0			0
$802$	3.00000			0.105934
$803$	−15.0000	+	25.9808i	−0.529339	+	0.916841i
$804$		0			0
$805$	3.00000	+	5.19615i	0.105736	+	0.183140i
$806$	15.0000	+	25.9808i	0.528352	+	0.915133i
$807$		0			0
$808$	−21.0000	+	36.3731i	−0.738777	+	1.27960i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$	2.50000	−	4.33013i	0.0877328	−	0.151958i
$813$		0			0
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$	−5.00000			−0.174821
$819$		0			0
$820$	10.0000			0.349215
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	0.0854103	+	0.996346i	$0.472780\pi$
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	−0.905566	+	0.424205i	$0.860553\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	−12.0000	−	20.7846i	−0.418040	−	0.724066i
$825$		0			0
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	9.00000	−	15.5885i	0.312395	−	0.541083i
$831$		0			0
$832$	17.5000	+	30.3109i	0.606703	+	1.05084i
$833$	−1.50000	−	2.59808i	−0.0519719	−	0.0900180i
$834$		0			0
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$	−4.00000			−0.138343
$837$		0			0
$838$	−36.0000			−1.24360
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	−0.788680	−	0.614804i	$-0.789235\pi$
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	0.926776	+	0.375615i	$0.122569\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	14.5000	+	25.1147i	0.499703	+	0.865511i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	12.0000			0.412813
$846$		0			0
$847$	7.00000			0.240523
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	9.00000	+	15.5885i	0.308516	+	0.534365i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	−24.0000			−0.820303
$857$	20.5000	−	35.5070i	0.700267	−	1.21290i	−0.268106	−	0.963389i	$-0.586398\pi$
$857$	20.5000	−	35.5070i	0.700267	−	1.21290i	0.968373	−	0.249508i	$-0.0802689\pi$
$858$		0			0
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.843278	+	0.537478i	$0.180623\pi$
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.0438309	+	0.999039i	$0.486044\pi$
$860$	−2.00000	−	3.46410i	−0.0681994	−	0.118125i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	54.0000			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$864$		0			0
$865$	5.00000			0.170005
$866$	0.500000	−	0.866025i	0.0169907	−	0.0294287i
$867$		0			0
$868$	3.00000	+	5.19615i	0.101827	+	0.176369i
$869$	14.0000	+	24.2487i	0.474917	+	0.822581i
$870$		0			0
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	27.0000			0.914335
$873$		0			0
$874$	12.0000			0.405906
$875$	−4.50000	+	7.79423i	−0.152128	+	0.263493i
$876$		0			0
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	0.943820	−	0.330461i	$-0.107204\pi$
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	−0.758098	+	0.652141i	$0.773871\pi$
$878$	18.0000	+	31.1769i	0.607471	+	1.05217i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$	−7.50000	+	12.9904i	−0.252252	+	0.436914i
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	−0.985880	−	0.167452i	$-0.946446\pi$
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	0.347923	−	0.937523i	$-0.386887\pi$
$888$		0			0
$889$	6.00000	−	10.3923i	0.201234	−	0.348547i
$890$	5.00000			0.167600
$891$		0			0
$892$	−4.00000			−0.133930
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	−1.00000	−	1.73205i	−0.0334263	−	0.0578961i
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$		0			0
$898$	9.00000	−	15.5885i	0.300334	−	0.520194i
$899$	30.0000			1.00056
$900$		0			0
$901$	−18.0000			−0.599667
$902$	10.0000	−	17.3205i	0.332964	−	0.576710i
$903$		0			0
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$	7.00000	+	12.1244i	0.232688	+	0.403027i
$906$		0			0
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	−0.830909	−	0.556408i	$-0.812179\pi$
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	0.897318	+	0.441384i	$0.145512\pi$
$908$	24.0000			0.796468
$909$		0			0
$910$	−5.00000			−0.165748
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	−0.948136	−	0.317865i	$-0.897034\pi$
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	0.749347	+	0.662177i	$0.230367\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−8.50000	−	14.7224i	−0.281155	−	0.486975i
$915$		0			0
$916$	5.50000	−	9.52628i	0.181725	−	0.314757i
$917$	−16.0000			−0.528367
$918$		0			0
$919$	−34.0000			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$		0			0
$922$	19.0000	+	32.9090i	0.625732	+	1.08380i
$923$	−30.0000	−	51.9615i	−0.987462	−	1.71033i
$924$		0			0
$925$	−6.00000	+	10.3923i	−0.197279	+	0.341697i
$926$	2.00000			0.0657241
$927$		0			0
$928$	25.0000			0.820665
$929$	18.5000	−	32.0429i	0.606965	−	1.05129i	−0.384772	−	0.923012i	$-0.625720\pi$
$929$	18.5000	−	32.0429i	0.606965	−	1.05129i	0.991738	−	0.128283i	$-0.0409467\pi$
$930$		0			0
$931$	1.00000	+	1.73205i	0.0327737	+	0.0567657i
$932$	10.5000	+	18.1865i	0.343939	+	0.595720i
$933$		0			0
$934$	−9.00000	+	15.5885i	−0.294489	+	0.510070i
$935$	−6.00000			−0.196221
$936$		0			0
$937$	33.0000			1.07806			0.539032	−	0.842286i	$-0.318790\pi$
$937$	33.0000			1.07806			0.539032	+	0.842286i	$0.318790\pi$
$938$	1.00000	−	1.73205i	0.0326512	−	0.0565535i
$939$		0			0
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−20.5000	−	35.5070i	−0.668281	−	1.15750i	−0.978385	−	0.206794i	$-0.933697\pi$
$941$	−20.5000	−	35.5070i	−0.668281	−	1.15750i	0.310104	−	0.950703i	$-0.399636\pi$
$942$		0			0
$943$	30.0000	−	51.9615i	0.976934	−	1.69210i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−8.00000			−0.260102
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		0			0
$949$	−37.5000	−	64.9519i	−1.21730	−	2.10843i
$950$	4.00000	+	6.92820i	0.129777	+	0.224781i
$951$		0			0
$952$	4.50000	−	7.79423i	0.145846	−	0.252612i
$953$	5.00000			0.161966			0.0809829	−	0.996715i	$-0.474194\pi$
$953$	5.00000			0.161966			0.0809829	+	0.996715i	$0.474194\pi$
$954$		0			0
$955$	−14.0000			−0.453029
$956$	15.0000	−	25.9808i	0.485135	−	0.840278i
$957$		0			0
$958$	−17.0000	−	29.4449i	−0.549245	−	0.951320i
$959$	10.5000	+	18.1865i	0.339063	+	0.587274i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−15.0000			−0.483619
$963$		0			0
$964$	19.0000			0.611949
$965$	6.50000	−	11.2583i	0.209242	−	0.362418i
$966$		0			0
$967$	13.0000	+	22.5167i	0.418052	+	0.724087i	0.995743	−	0.0921681i	$-0.0293797\pi$
$967$	13.0000	+	22.5167i	0.418052	+	0.724087i	−0.577692	+	0.816255i	$0.696046\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$		0			0
$970$	−9.00000	+	15.5885i	−0.288973	+	0.500515i
$971$	−54.0000			−1.73294			−0.866471	−	0.499227i	$-0.833617\pi$
$971$	−54.0000			−1.73294			−0.866471	+	0.499227i	$0.833617\pi$
$972$		0			0
$973$	6.00000			0.192351
$974$	17.0000	−	29.4449i	0.544715	−	0.943474i
$975$		0			0
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	−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
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	−1.00000			−0.0319438
$981$		0			0
$982$	28.0000			0.893516
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$		0			0
$985$	2.50000	+	4.33013i	0.0796566	+	0.137969i
$986$	−7.50000	−	12.9904i	−0.238849	−	0.413698i
$987$		0			0
$988$	5.00000	−	8.66025i	0.159071	−	0.275519i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−15.0000	+	25.9808i	−0.476250	+	0.824890i
$993$		0			0
$994$	6.00000	+	10.3923i	0.190308	+	0.329624i
$995$	3.00000	+	5.19615i	0.0951064	+	0.164729i
$996$		0			0
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	−0.916112	−	0.400923i	$-0.868689\pi$
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	0.805266	+	0.592914i	$0.202023\pi$
$998$	−10.0000			−0.316544
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.f.379.1		2
3.2	odd	2		567.2.f.c.379.1		2
9.2	odd	6		567.2.a.b.1.1	yes	1
9.4	even	3	inner	567.2.f.f.190.1		2
9.5	odd	6		567.2.f.c.190.1		2
9.7	even	3		567.2.a.a.1.1	✓	1
36.7	odd	6		9072.2.a.q.1.1		1
36.11	even	6		9072.2.a.j.1.1		1
63.20	even	6		3969.2.a.e.1.1		1
63.34	odd	6		3969.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.a.a.1.1	✓	1	9.7	even	3
567.2.a.b.1.1	yes	1	9.2	odd	6
567.2.f.c.190.1		2	9.5	odd	6
567.2.f.c.379.1		2	3.2	odd	2
567.2.f.f.190.1		2	9.4	even	3	inner
567.2.f.f.379.1		2	1.1	even	1	trivial
3969.2.a.b.1.1		1	63.34	odd	6
3969.2.a.e.1.1		1	63.20	even	6
9072.2.a.j.1.1		1	36.11	even	6
9072.2.a.q.1.1		1	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -1.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +3.00000 q^{17} -2.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{26} +1.00000 q^{28} +(2.50000 - 4.33013i) q^{29} +(3.00000 + 5.19615i) q^{31} +(2.50000 + 4.33013i) q^{32} +(1.50000 - 2.59808i) q^{34} -1.00000 q^{35} -3.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(5.00000 + 8.66025i) q^{41} +(2.00000 - 3.46410i) q^{43} +2.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-2.50000 + 4.33013i) q^{52} -6.00000 q^{53} -2.00000 q^{55} +(1.50000 - 2.59808i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.50000 + 6.06218i) q^{61} +6.00000 q^{62} +7.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(1.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-0.500000 + 0.866025i) q^{70} -12.0000 q^{71} -15.0000 q^{73} +(-1.50000 + 2.59808i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +10.0000 q^{82} +(-9.00000 + 15.5885i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{88} -5.00000 q^{89} +5.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(9.00000 - 15.5885i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} - q^{5} + q^{7} + 6 q^{8} - 2 q^{10} + 2 q^{11} + 5 q^{13} - q^{14} + q^{16} + 6 q^{17} - 4 q^{19} + q^{20} - 2 q^{22} - 6 q^{23} + 4 q^{25} + 10 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 - q^5 + q^7 + 6 * q^8 - 2 * q^10 + 2 * q^11 + 5 * q^13 - q^14 + q^16 + 6 * q^17 - 4 * q^19 + q^20 - 2 * q^22 - 6 * q^23 + 4 * q^25 + 10 * q^26 + 2 * q^28 + 5 * q^29 + 6 * q^31 + 5 * q^32 + 3 * q^34 - 2 * q^35 - 6 * q^37 - 2 * q^38 - 3 * q^40 + 10 * q^41 + 4 * q^43 + 4 * q^44 - 12 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 5 * q^52 - 12 * q^53 - 4 * q^55 + 3 * q^56 - 5 * q^58 - 6 * q^59 - 7 * q^61 + 12 * q^62 + 14 * q^64 + 5 * q^65 + 2 * q^67 + 3 * q^68 - q^70 - 24 * q^71 - 30 * q^73 - 3 * q^74 - 2 * q^76 - 2 * q^77 - 14 * q^79 - 2 * q^80 + 20 * q^82 - 18 * q^83 - 3 * q^85 - 4 * q^86 + 6 * q^88 - 10 * q^89 + 10 * q^91 + 6 * q^92 - 6 * q^94 + 2 * q^95 + 18 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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