LMFDB - Embedded newform 567.2.f.b.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:	no (minimal twist has level 21)
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.b.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(2.00000 - 3.46410i) q^{11} +(1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(2.00000 + 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} -2.00000 q^{26} +1.00000 q^{28} +(-1.00000 + 1.73205i) q^{29} +(-2.50000 - 4.33013i) q^{32} +(-3.00000 + 5.19615i) q^{34} -2.00000 q^{35} +6.00000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} -6.00000 q^{53} -8.00000 q^{55} +(-1.50000 + 2.59808i) q^{56} +(-1.00000 - 1.73205i) q^{58} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.00000 - 1.73205i) q^{70} -6.00000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-2.00000 - 3.46410i) q^{77} +(8.00000 - 13.8564i) q^{79} -2.00000 q^{80} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(2.00000 + 3.46410i) q^{86} +(-6.00000 + 10.3923i) q^{88} +14.0000 q^{89} +2.00000 q^{91} +(-4.00000 - 6.92820i) q^{95} +(-9.00000 + 15.5885i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) $ 2 * q - q^2 + q^4 - 2 * q^5 + q^7 - 6 * q^8	$ 2 q - q^{2} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 4 q^{10} + 4 q^{11} + 2 q^{13} + q^{14} + q^{16} + 12 q^{17} + 8 q^{19} + 2 q^{20} + 4 q^{22} + q^{25} - 4 q^{26} + 2 q^{28} - 2 q^{29} - 5 q^{32} - 6 q^{34} - 4 q^{35} + 12 q^{37} - 4 q^{38} + 6 q^{40} + 2 q^{41} + 4 q^{43} + 8 q^{44} - q^{49} + q^{50} - 2 q^{52} - 12 q^{53} - 16 q^{55} - 3 q^{56} - 2 q^{58} + 12 q^{59} + 2 q^{61} + 14 q^{64} + 4 q^{65} - 4 q^{67} + 6 q^{68} + 2 q^{70} - 12 q^{73} - 6 q^{74} + 4 q^{76} - 4 q^{77} + 16 q^{79} - 4 q^{80} - 4 q^{82} - 12 q^{83} - 12 q^{85} + 4 q^{86} - 12 q^{88} + 28 q^{89} + 4 q^{91} - 8 q^{95} - 18 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 4 * q^10 + 4 * q^11 + 2 * q^13 + q^14 + q^16 + 12 * q^17 + 8 * q^19 + 2 * q^20 + 4 * q^22 + q^25 - 4 * q^26 + 2 * q^28 - 2 * q^29 - 5 * q^32 - 6 * q^34 - 4 * q^35 + 12 * q^37 - 4 * q^38 + 6 * q^40 + 2 * q^41 + 4 * q^43 + 8 * q^44 - q^49 + q^50 - 2 * q^52 - 12 * q^53 - 16 * q^55 - 3 * q^56 - 2 * q^58 + 12 * q^59 + 2 * q^61 + 14 * q^64 + 4 * q^65 - 4 * q^67 + 6 * q^68 + 2 * q^70 - 12 * q^73 - 6 * q^74 + 4 * q^76 - 4 * q^77 + 16 * q^79 - 4 * q^80 - 4 * q^82 - 12 * q^83 - 12 * q^85 + 4 * q^86 - 12 * q^88 + 28 * q^89 + 4 * q^91 - 8 * q^95 - 18 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		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
$10$	2.00000			0.632456
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	1.00000			0.188982
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	−2.00000			−0.338062
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	3.00000	+	5.19615i	0.474342	+	0.821584i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$		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	$0.0680112\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−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
$55$	−8.00000			−1.07872
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$	1.00000	−	1.73205i	0.119523	−	0.207020i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−2.00000	−	3.46410i	−0.227921	−	0.394771i
$78$		0			0
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	−2.00000			−0.223607
$81$		0			0
$82$	−2.00000			−0.220863
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	−6.00000	+	10.3923i	−0.639602	+	1.10782i
$89$	14.0000			1.48400			0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000			1.48400			0.741999	+	0.670402i	$0.233878\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−9.00000	+	15.5885i	−0.913812	+	1.58277i	−0.105180	+	0.994453i	$0.533542\pi$
$97$	−9.00000	+	15.5885i	−0.913812	+	1.58277i	−0.808632	+	0.588315i	$0.799792\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	1.00000			0.100000
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$		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	$0.962288\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$	−18.0000			−1.72409			−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000			−1.72409			−0.862044	+	0.506834i	$0.830816\pi$
$110$	4.00000	−	6.92820i	0.381385	−	0.660578i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$		0			0
$115$		0			0
$116$	−2.00000			−0.185695
$117$		0			0
$118$	−12.0000			−1.10469
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$		0			0
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	4.00000			0.345547
$135$		0			0
$136$	−18.0000			−1.54349
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$		0			0
$142$		0			0
$143$	8.00000			0.668994
$144$		0			0
$145$	4.00000			0.332182
$146$	3.00000	−	5.19615i	0.248282	−	0.430037i
$147$		0			0
$148$	3.00000	+	5.19615i	0.246598	+	0.427121i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−12.0000			−0.973329
$153$		0			0
$154$	4.00000			0.322329
$155$		0			0
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$		0			0
$160$	−5.00000	+	8.66025i	−0.395285	+	0.684653i
$161$		0			0
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	12.0000			0.920358
$171$		0			0
$172$	4.00000			0.304997
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$	4.00000			0.298974			0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000			0.298974			0.149487	+	0.988764i	$0.452238\pi$
$180$		0			0
$181$	−26.0000			−1.93256			−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000			−1.93256			−0.966282	+	0.257485i	$0.917106\pi$
$182$	−1.00000	+	1.73205i	−0.0741249	+	0.128388i
$183$		0			0
$184$		0			0
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$		0			0
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$		0			0
$189$		0			0
$190$	8.00000			0.580381
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−9.00000	−	15.5885i	−0.646162	−	1.11919i
$195$		0			0
$196$	0.500000	−	0.866025i	0.0357143	−	0.0618590i
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	1.00000	+	1.73205i	0.0701862	+	0.121566i
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	8.00000			0.557386
$207$		0			0
$208$	2.00000			0.138675
$209$	8.00000	−	13.8564i	0.553372	−	0.958468i
$210$		0			0
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$	9.00000	−	15.5885i	0.609557	−	1.05578i
$219$		0			0
$220$	−4.00000	−	6.92820i	−0.269680	−	0.467099i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		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	$0.986707\pi$
$224$	−5.00000			−0.334077
$225$		0			0
$226$	14.0000			0.931266
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$		0			0
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	2.00000			0.128037
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$		0			0
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	0.912222	+	0.409695i	$0.134365\pi$
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	−0.101305	+	0.994855i	$0.532302\pi$
$258$		0			0
$259$	3.00000	−	5.19615i	0.186411	−	0.322873i
$260$	4.00000			0.248069
$261$		0			0
$262$	−4.00000			−0.247121
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	6.00000	+	10.3923i	0.368577	+	0.638394i
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$		0			0
$274$	−3.00000	−	5.19615i	−0.181237	−	0.313911i
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	12.0000			0.719712
$279$		0			0
$280$	6.00000			0.358569
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	0.993626	+	0.112728i	$0.0359589\pi$
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	−0.399188	+	0.916869i	$0.630708\pi$
$284$		0			0
$285$		0			0
$286$	−4.00000	+	6.92820i	−0.236525	+	0.409673i
$287$	2.00000			0.118056
$288$		0			0
$289$	19.0000			1.11765
$290$	−2.00000	+	3.46410i	−0.117444	+	0.203419i
$291$		0			0
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	7.00000	+	12.1244i	0.408944	+	0.708312i	0.994772	−	0.102123i	$-0.0325637\pi$
$293$	7.00000	+	12.1244i	0.408944	+	0.708312i	−0.585827	+	0.810436i	$0.699230\pi$
$294$		0			0
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	−18.0000			−1.04623
$297$		0			0
$298$	−6.00000			−0.347571
$299$		0			0
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	−4.00000	−	6.92820i	−0.230174	−	0.398673i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−4.00000			−0.229039
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	0.220006	+	0.975499i	$0.429392\pi$
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	−0.954810	+	0.297218i	$0.903941\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	16.0000			0.900070
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−7.00000	−	12.1244i	−0.391312	−	0.677772i
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	2.00000			0.110940
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$		0			0
$330$		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	$0.131604\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	8.00000			0.437741
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	7.00000	+	12.1244i	0.381314	+	0.660456i	0.991250	−	0.131995i	$-0.0421382\pi$
$337$	7.00000	+	12.1244i	0.381314	+	0.660456i	−0.609936	+	0.792451i	$0.708805\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$		0			0
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−6.00000	+	10.3923i	−0.323498	+	0.560316i
$345$		0			0
$346$	−5.00000	−	8.66025i	−0.268802	−	0.465578i
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	−20.0000			−1.06600
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	−0.701734	−	0.712439i	$-0.747591\pi$
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	0.967857	+	0.251500i	$0.0809239\pi$
$354$		0			0
$355$		0			0
$356$	7.00000	+	12.1244i	0.370999	+	0.642590i
$357$		0			0
$358$	−2.00000	+	3.46410i	−0.105703	+	0.183083i
$359$	−32.0000			−1.68890			−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000			−1.68890			−0.844448	+	0.535638i	$0.820071\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	13.0000	−	22.5167i	0.683265	−	1.18345i
$363$		0			0
$364$	1.00000	+	1.73205i	0.0524142	+	0.0907841i
$365$	6.00000	+	10.3923i	0.314054	+	0.543958i
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$		0			0
$369$		0			0
$370$	12.0000			0.623850
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	12.0000	+	20.7846i	0.620505	+	1.07475i
$375$		0			0
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	−4.00000	+	6.92820i	−0.203859	+	0.353094i
$386$	2.00000			0.101797
$387$		0			0
$388$	−18.0000			−0.913812
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$		0			0
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$		0			0
$394$	11.0000	−	19.0526i	0.554172	−	0.959854i
$395$	−32.0000			−1.61009
$396$		0			0
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$	−12.0000	+	20.7846i	−0.601506	+	1.04184i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$		0			0
$403$		0			0
$404$	14.0000			0.696526
$405$		0			0
$406$	−2.00000			−0.0992583
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	2.00000	+	3.46410i	0.0987730	+	0.171080i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	12.0000			0.590481
$414$		0			0
$415$	24.0000			1.17811
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$		0			0
$418$	8.00000	+	13.8564i	0.391293	+	0.677739i
$419$	−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
$421$	−19.0000	+	32.9090i	−0.926003	+	1.60388i	−0.136064	+	0.990700i	$0.543445\pi$
$421$	−19.0000	+	32.9090i	−0.926003	+	1.60388i	−0.789940	+	0.613185i	$0.789888\pi$
$422$	4.00000			0.194717
$423$		0			0
$424$	18.0000			0.874157
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$		0			0
$427$	−1.00000	−	1.73205i	−0.0483934	−	0.0838198i
$428$	−2.00000	−	3.46410i	−0.0966736	−	0.167444i
$429$		0			0
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$		0			0
$438$		0			0
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$	24.0000			1.14416
$441$		0			0
$442$	−12.0000			−0.570782
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	3.50000	−	6.06218i	0.165359	−	0.286411i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	8.00000			0.376705
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	−2.00000	−	3.46410i	−0.0937614	−	0.162400i
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−10.0000			−0.467269
$459$		0			0
$460$		0			0
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	−0.958652	−	0.284579i	$-0.908146\pi$
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	0.725779	+	0.687928i	$0.241479\pi$
$462$		0			0
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	0.618050	−	0.786139i	$-0.287923\pi$
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$		0			0
$472$	−18.0000	−	31.1769i	−0.828517	−	1.43503i
$473$	−8.00000	−	13.8564i	−0.367840	−	0.637118i
$474$		0			0
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	6.00000			0.275010
$477$		0			0
$478$	−24.0000			−1.09773
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	−1.00000	−	1.73205i	−0.0455488	−	0.0788928i
$483$		0			0
$484$	2.50000	−	4.33013i	0.113636	−	0.196824i
$485$	36.0000			1.63468
$486$		0			0
$487$	−8.00000			−0.362515			−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000			−0.362515			−0.181257	+	0.983436i	$0.558017\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$		0			0
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$		0			0
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	−8.00000			−0.359937
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	−10.0000	+	17.3205i	−0.446322	+	0.773052i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	−28.0000			−1.24598
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	−26.0000			−1.14681
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$		0			0
$518$	3.00000	+	5.19615i	0.131812	+	0.228306i
$519$		0			0
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$		0			0
$526$	8.00000	+	13.8564i	0.348817	+	0.604168i
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−12.0000			−0.521247
$531$		0			0
$532$	4.00000			0.173422
$533$	−2.00000	+	3.46410i	−0.0866296	+	0.150047i
$534$		0			0
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		0			0
$538$	3.00000	−	5.19615i	0.129339	−	0.224022i
$539$	−4.00000			−0.172292
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	−15.0000	−	25.9808i	−0.643120	−	1.11392i
$545$	18.0000	+	31.1769i	0.771035	+	1.33547i
$546$		0			0
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	−0.905610	−	0.424111i	$-0.860587\pi$
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	0.820096	+	0.572226i	$0.193920\pi$
$548$	−6.00000			−0.256307
$549$		0			0
$550$	4.00000			0.170561
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$		0			0
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	−11.0000	−	19.0526i	−0.467345	−	0.809466i
$555$		0			0
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	2.00000			0.0847427			0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000			0.0847427			0.0423714	+	0.999102i	$0.486509\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	−1.00000	+	1.73205i	−0.0422577	+	0.0731925i
$561$		0			0
$562$	−11.0000	−	19.0526i	−0.464007	−	0.803684i
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$		0			0
$565$	−14.0000	+	24.2487i	−0.588984	+	1.02015i
$566$	−20.0000			−0.840663
$567$		0			0
$568$		0			0
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$		0			0
$576$		0			0
$577$	34.0000			1.41544			0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$	2.00000	+	3.46410i	0.0830455	+	0.143839i
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$		0			0
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$	18.0000			0.744845
$585$		0			0
$586$	−14.0000			−0.578335
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	−0.417885	−	0.908500i	$-0.637228\pi$
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	0.995726	−	0.0923513i	$-0.0294383\pi$
$588$		0			0
$589$		0			0
$590$	12.0000	+	20.7846i	0.494032	+	0.855689i
$591$		0			0
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$		0			0
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.660006	+	0.751260i	$0.270554\pi$
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.320607	+	0.947212i	$0.396113\pi$
$600$		0			0
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	−0.798330	−	0.602220i	$-0.794283\pi$
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	0.920703	+	0.390264i	$0.127616\pi$
$602$	4.00000			0.163028
$603$		0			0
$604$	−8.00000			−0.325515
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	−10.0000	−	17.3205i	−0.405554	−	0.702439i
$609$		0			0
$610$	2.00000	−	3.46410i	0.0809776	−	0.140257i
$611$		0			0
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$		0			0
$616$	6.00000	+	10.3923i	0.241747	+	0.418718i
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$		0			0
$622$	24.0000			0.962312
$623$	7.00000	−	12.1244i	0.280449	−	0.485752i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−13.0000	−	22.5167i	−0.519584	−	0.899947i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	36.0000			1.43541
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−24.0000	+	41.5692i	−0.954669	+	1.65353i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$		0			0
$637$	1.00000	−	1.73205i	0.0396214	−	0.0686264i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−6.00000			−0.237171
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$		0			0
$643$	−10.0000	−	17.3205i	−0.394362	−	0.683054i	0.598658	−	0.801005i	$-0.295701\pi$
$643$	−10.0000	−	17.3205i	−0.394362	−	0.683054i	−0.993019	+	0.117951i	$0.962368\pi$
$644$		0			0
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	40.0000			1.57256			0.786281	−	0.617869i	$-0.212004\pi$
$647$	40.0000			1.57256			0.786281	+	0.617869i	$0.212004\pi$
$648$		0			0
$649$	48.0000			1.88416
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$	2.00000			0.0780869
$657$		0			0
$658$		0			0
$659$	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
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		0			0
$664$	18.0000	−	31.1769i	0.698535	−	1.20990i
$665$	−8.00000			−0.310227
$666$		0			0
$667$		0			0
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	−4.00000	−	6.92820i	−0.154418	−	0.267460i
$672$		0			0
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	0.326516	+	0.945192i	$0.394125\pi$
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	−0.981818	+	0.189824i	$0.939208\pi$
$674$	−14.0000			−0.539260
$675$		0			0
$676$	9.00000			0.346154
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	9.00000	+	15.5885i	0.345388	+	0.598230i
$680$	18.0000	+	31.1769i	0.690268	+	1.19558i
$681$		0			0
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	−10.0000			−0.380143
$693$		0			0
$694$	28.0000			1.06287
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	1.00000	+	1.73205i	0.0378506	+	0.0655591i
$699$		0			0
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	24.0000			0.905177
$704$	14.0000	−	24.2487i	0.527645	−	0.913908i
$705$		0			0
$706$	5.00000	+	8.66025i	0.188177	+	0.325933i
$707$	−7.00000	−	12.1244i	−0.263262	−	0.455983i
$708$		0			0
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$		0			0
$711$		0			0
$712$	−42.0000			−1.57402
$713$		0			0
$714$		0			0
$715$	−8.00000	−	13.8564i	−0.299183	−	0.518200i
$716$	2.00000	+	3.46410i	0.0747435	+	0.129460i
$717$		0			0
$718$	16.0000	−	27.7128i	0.597115	−	1.03423i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		0			0
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	−0.209935	−	0.977715i	$-0.567325\pi$
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	0.951694	−	0.307049i	$-0.0993415\pi$
$728$	−6.00000			−0.222375
$729$		0			0
$730$	−12.0000			−0.444140
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	0.982986	−	0.183679i	$-0.0588007\pi$
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	−0.650564	+	0.759452i	$0.725467\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.0000			−0.589368
$738$		0			0
$739$	36.0000			1.32428			0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000			1.32428			0.662141	+	0.749380i	$0.269648\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$		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
$745$	6.00000	−	10.3923i	0.219823	−	0.380745i
$746$	−10.0000			−0.366126
$747$		0			0
$748$	24.0000			0.877527
$749$	−2.00000	+	3.46410i	−0.0730784	+	0.126576i
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$		0			0
$753$		0			0
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$	16.0000			0.582300
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$		0			0
$760$	12.0000	+	20.7846i	0.435286	+	0.753937i
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$		0			0
$763$	−9.00000	+	15.5885i	−0.325822	+	0.564340i
$764$	−8.00000			−0.289430
$765$		0			0
$766$		0			0
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$		0			0
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$	−4.00000	−	6.92820i	−0.144150	−	0.249675i
$771$		0			0
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	−14.0000			−0.503545			−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000			−0.503545			−0.251773	+	0.967786i	$0.581013\pi$
$774$		0			0
$775$		0			0
$776$	27.0000	−	46.7654i	0.969244	−	1.67878i
$777$		0			0
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	4.00000	+	6.92820i	0.143315	+	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	2.00000	−	3.46410i	0.0713831	−	0.123639i
$786$		0			0
$787$	22.0000	+	38.1051i	0.784215	+	1.35830i	0.929467	+	0.368906i	$0.120268\pi$
$787$	22.0000	+	38.1051i	0.784215	+	1.35830i	−0.145251	+	0.989395i	$0.546399\pi$
$788$	−11.0000	−	19.0526i	−0.391859	−	0.678719i
$789$		0			0
$790$	16.0000	−	27.7128i	0.569254	−	0.985978i
$791$	−14.0000			−0.497783
$792$		0			0
$793$	4.00000			0.142044
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		0			0
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	0.538501	−	0.842625i	$-0.318991\pi$
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	−0.998985	+	0.0450436i	$0.985657\pi$
$798$		0			0
$799$		0			0
$800$	−5.00000			−0.176777
$801$		0			0
$802$	30.0000			1.05934
$803$	−12.0000	+	20.7846i	−0.423471	+	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−21.0000	+	36.3731i	−0.738777	+	1.27960i
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$	−1.00000	+	1.73205i	−0.0350931	+	0.0607831i
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	−22.0000			−0.769212
$819$		0			0
$820$	4.00000			0.139686
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	12.0000	+	20.7846i	0.418040	+	0.724066i
$825$		0			0
$826$	−6.00000	+	10.3923i	−0.208767	+	0.361595i
$827$	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
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	−12.0000	+	20.7846i	−0.416526	+	0.721444i
$831$		0			0
$832$	7.00000	+	12.1244i	0.242681	+	0.420336i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	16.0000			0.553372
$837$		0			0
$838$	12.0000			0.414533
$839$	−4.00000	+	6.92820i	−0.138095	+	0.239188i	−0.926776	−	0.375615i	$-0.877431\pi$
$839$	−4.00000	+	6.92820i	−0.138095	+	0.239188i	0.788680	+	0.614804i	$0.210765\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−19.0000	−	32.9090i	−0.654783	−	1.13412i
$843$		0			0
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	−18.0000			−0.619219
$846$		0			0
$847$	−5.00000			−0.171802
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$		0			0
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$		0			0
$852$		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	$0.111903\pi$
$854$	2.00000			0.0684386
$855$		0			0
$856$	12.0000			0.410152
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	−0.960461	−	0.278416i	$-0.910191\pi$
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	0.721345	+	0.692576i	$0.243524\pi$
$858$		0			0
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	−0.947518	−	0.319704i	$-0.896417\pi$
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	0.196887	−	0.980426i	$-0.436917\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$		0			0
$862$	−12.0000	+	20.7846i	−0.408722	+	0.707927i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	20.0000			0.680020
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$		0			0
$868$		0			0
$869$	−32.0000	−	55.4256i	−1.08553	−	1.88019i
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	54.0000			1.82867
$873$		0			0
$874$		0			0
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	−0.933860	−	0.357640i	$-0.883582\pi$
$877$	−23.0000	−	39.8372i	−0.776655	−	1.34521i	0.157205	−	0.987566i	$-0.449752\pi$
$878$	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	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$		0			0
$889$		0			0
$890$	28.0000			0.938562
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$		0			0
$895$	−4.00000	−	6.92820i	−0.133705	−	0.231584i
$896$	−1.50000	−	2.59808i	−0.0501115	−	0.0867956i
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$		0			0
$900$		0			0
$901$	−36.0000			−1.19933
$902$	−4.00000	+	6.92820i	−0.133185	+	0.230684i
$903$		0			0
$904$	21.0000	+	36.3731i	0.698450	+	1.20975i
$905$	26.0000	+	45.0333i	0.864269	+	1.49696i
$906$		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	$0.145512\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	4.00000			0.132599
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	−0.993426	−	0.114472i	$-0.963482\pi$
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	0.595849	+	0.803097i	$0.296816\pi$
$912$		0			0
$913$	24.0000	+	41.5692i	0.794284	+	1.37574i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	4.00000			0.132092
$918$		0			0
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$		0			0
$921$		0			0
$922$	−5.00000	−	8.66025i	−0.164666	−	0.285210i
$923$		0			0
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	16.0000			0.525793
$927$		0			0
$928$	10.0000			0.328266
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	−0.570045	−	0.821614i	$-0.693074\pi$
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	0.996561	+	0.0828661i	$0.0264074\pi$
$930$		0			0
$931$	−2.00000	−	3.46410i	−0.0655474	−	0.113531i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$		0			0
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$	−48.0000			−1.56977
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$	2.00000	−	3.46410i	0.0653023	−	0.113107i
$939$		0			0
$940$		0			0
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	0.989599	+	0.143856i	$0.0459502\pi$
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	−0.370216	+	0.928946i	$0.620716\pi$
$942$		0			0
$943$		0			0
$944$	12.0000			0.390567
$945$		0			0
$946$	16.0000			0.520205
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	−0.248093	−	0.968736i	$-0.579804\pi$
$947$	22.0000	−	38.1051i	0.714904	−	1.23825i	0.962997	−	0.269514i	$-0.0868629\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$		0			0
$952$	−9.00000	+	15.5885i	−0.291692	+	0.505225i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	16.0000			0.517748
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−8.00000	−	13.8564i	−0.258468	−	0.447680i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−12.0000			−0.386896
$963$		0			0
$964$	−2.00000			−0.0644157
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−20.0000	−	34.6410i	−0.643157	−	1.11398i	−0.984724	−	0.174123i	$-0.944291\pi$
$967$	−20.0000	−	34.6410i	−0.643157	−	1.11398i	0.341567	−	0.939857i	$-0.389042\pi$
$968$	7.50000	+	12.9904i	0.241059	+	0.417527i
$969$		0			0
$970$	−18.0000	+	31.1769i	−0.577945	+	1.00103i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	−12.0000			−0.384702
$974$	4.00000	−	6.92820i	0.128168	−	0.221994i
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$		0			0
$979$	28.0000	−	48.4974i	0.894884	−	1.54998i
$980$	−2.00000			−0.0638877
$981$		0			0
$982$	−20.0000			−0.638226
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		0			0
$985$	22.0000	+	38.1051i	0.700978	+	1.21413i
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$	−4.00000	+	6.92820i	−0.127257	+	0.220416i
$989$		0			0
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−24.0000	−	41.5692i	−0.760851	−	1.31783i
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$	4.00000			0.126618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.b.379.1		2
3.2	odd	2		567.2.f.g.379.1		2
9.2	odd	6		21.2.a.a.1.1	✓	1
9.4	even	3	inner	567.2.f.b.190.1		2
9.5	odd	6		567.2.f.g.190.1		2
9.7	even	3		63.2.a.a.1.1		1
36.7	odd	6		1008.2.a.l.1.1		1
36.11	even	6		336.2.a.a.1.1		1
45.2	even	12		525.2.d.a.274.1		2
45.7	odd	12		1575.2.d.a.1324.2		2
45.29	odd	6		525.2.a.d.1.1		1
45.34	even	6		1575.2.a.c.1.1		1
45.38	even	12		525.2.d.a.274.2		2
45.43	odd	12		1575.2.d.a.1324.1		2
63.2	odd	6		147.2.e.b.67.1		2
63.11	odd	6		147.2.e.b.79.1		2
63.16	even	3		441.2.e.a.361.1		2
63.20	even	6		147.2.a.a.1.1		1
63.25	even	3		441.2.e.a.226.1		2
63.34	odd	6		441.2.a.f.1.1		1
63.38	even	6		147.2.e.c.79.1		2
63.47	even	6		147.2.e.c.67.1		2
63.52	odd	6		441.2.e.b.226.1		2
63.61	odd	6		441.2.e.b.361.1		2
72.11	even	6		1344.2.a.s.1.1		1
72.29	odd	6		1344.2.a.g.1.1		1
72.43	odd	6		4032.2.a.k.1.1		1
72.61	even	6		4032.2.a.h.1.1		1
99.43	odd	6		7623.2.a.g.1.1		1
99.65	even	6		2541.2.a.j.1.1		1
117.38	odd	6		3549.2.a.c.1.1		1
144.11	even	12		5376.2.c.l.2689.2		2
144.29	odd	12		5376.2.c.r.2689.2		2
144.83	even	12		5376.2.c.l.2689.1		2
144.101	odd	12		5376.2.c.r.2689.1		2
153.101	odd	6		6069.2.a.b.1.1		1
171.56	even	6		7581.2.a.d.1.1		1
180.119	even	6		8400.2.a.bn.1.1		1
252.11	even	6		2352.2.q.x.961.1		2
252.47	odd	6		2352.2.q.e.1537.1		2
252.83	odd	6		2352.2.a.v.1.1		1
252.191	even	6		2352.2.q.x.1537.1		2
252.223	even	6		7056.2.a.p.1.1		1
252.227	odd	6		2352.2.q.e.961.1		2
315.209	even	6		3675.2.a.n.1.1		1
504.83	odd	6		9408.2.a.m.1.1		1
504.461	even	6		9408.2.a.bv.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.a.a.1.1	✓	1	9.2	odd	6
63.2.a.a.1.1		1	9.7	even	3
147.2.a.a.1.1		1	63.20	even	6
147.2.e.b.67.1		2	63.2	odd	6
147.2.e.b.79.1		2	63.11	odd	6
147.2.e.c.67.1		2	63.47	even	6
147.2.e.c.79.1		2	63.38	even	6
336.2.a.a.1.1		1	36.11	even	6
441.2.a.f.1.1		1	63.34	odd	6
441.2.e.a.226.1		2	63.25	even	3
441.2.e.a.361.1		2	63.16	even	3
441.2.e.b.226.1		2	63.52	odd	6
441.2.e.b.361.1		2	63.61	odd	6
525.2.a.d.1.1		1	45.29	odd	6
525.2.d.a.274.1		2	45.2	even	12
525.2.d.a.274.2		2	45.38	even	12
567.2.f.b.190.1		2	9.4	even	3	inner
567.2.f.b.379.1		2	1.1	even	1	trivial
567.2.f.g.190.1		2	9.5	odd	6
567.2.f.g.379.1		2	3.2	odd	2
1008.2.a.l.1.1		1	36.7	odd	6
1344.2.a.g.1.1		1	72.29	odd	6
1344.2.a.s.1.1		1	72.11	even	6
1575.2.a.c.1.1		1	45.34	even	6
1575.2.d.a.1324.1		2	45.43	odd	12
1575.2.d.a.1324.2		2	45.7	odd	12
2352.2.a.v.1.1		1	252.83	odd	6
2352.2.q.e.961.1		2	252.227	odd	6
2352.2.q.e.1537.1		2	252.47	odd	6
2352.2.q.x.961.1		2	252.11	even	6
2352.2.q.x.1537.1		2	252.191	even	6
2541.2.a.j.1.1		1	99.65	even	6
3549.2.a.c.1.1		1	117.38	odd	6
3675.2.a.n.1.1		1	315.209	even	6
4032.2.a.h.1.1		1	72.61	even	6
4032.2.a.k.1.1		1	72.43	odd	6
5376.2.c.l.2689.1		2	144.83	even	12
5376.2.c.l.2689.2		2	144.11	even	12
5376.2.c.r.2689.1		2	144.101	odd	12
5376.2.c.r.2689.2		2	144.29	odd	12
6069.2.a.b.1.1		1	153.101	odd	6
7056.2.a.p.1.1		1	252.223	even	6
7581.2.a.d.1.1		1	171.56	even	6
7623.2.a.g.1.1		1	99.43	odd	6
8400.2.a.bn.1.1		1	180.119	even	6
9408.2.a.m.1.1		1	504.83	odd	6
9408.2.a.bv.1.1		1	504.461	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(2.00000 - 3.46410i) q^{11} +(1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(2.00000 + 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} -2.00000 q^{26} +1.00000 q^{28} +(-1.00000 + 1.73205i) q^{29} +(-2.50000 - 4.33013i) q^{32} +(-3.00000 + 5.19615i) q^{34} -2.00000 q^{35} +6.00000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} -6.00000 q^{53} -8.00000 q^{55} +(-1.50000 + 2.59808i) q^{56} +(-1.00000 - 1.73205i) q^{58} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.00000 - 1.73205i) q^{70} -6.00000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-2.00000 - 3.46410i) q^{77} +(8.00000 - 13.8564i) q^{79} -2.00000 q^{80} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(2.00000 + 3.46410i) q^{86} +(-6.00000 + 10.3923i) q^{88} +14.0000 q^{89} +2.00000 q^{91} +(-4.00000 - 6.92820i) q^{95} +(-9.00000 + 15.5885i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) \) 2 * q - q^2 + q^4 - 2 * q^5 + q^7 - 6 * q^8	\( 2 q - q^{2} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 4 q^{10} + 4 q^{11} + 2 q^{13} + q^{14} + q^{16} + 12 q^{17} + 8 q^{19} + 2 q^{20} + 4 q^{22} + q^{25} - 4 q^{26} + 2 q^{28} - 2 q^{29} - 5 q^{32} - 6 q^{34} - 4 q^{35} + 12 q^{37} - 4 q^{38} + 6 q^{40} + 2 q^{41} + 4 q^{43} + 8 q^{44} - q^{49} + q^{50} - 2 q^{52} - 12 q^{53} - 16 q^{55} - 3 q^{56} - 2 q^{58} + 12 q^{59} + 2 q^{61} + 14 q^{64} + 4 q^{65} - 4 q^{67} + 6 q^{68} + 2 q^{70} - 12 q^{73} - 6 q^{74} + 4 q^{76} - 4 q^{77} + 16 q^{79} - 4 q^{80} - 4 q^{82} - 12 q^{83} - 12 q^{85} + 4 q^{86} - 12 q^{88} + 28 q^{89} + 4 q^{91} - 8 q^{95} - 18 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 4 * q^10 + 4 * q^11 + 2 * q^13 + q^14 + q^16 + 12 * q^17 + 8 * q^19 + 2 * q^20 + 4 * q^22 + q^25 - 4 * q^26 + 2 * q^28 - 2 * q^29 - 5 * q^32 - 6 * q^34 - 4 * q^35 + 12 * q^37 - 4 * q^38 + 6 * q^40 + 2 * q^41 + 4 * q^43 + 8 * q^44 - q^49 + q^50 - 2 * q^52 - 12 * q^53 - 16 * q^55 - 3 * q^56 - 2 * q^58 + 12 * q^59 + 2 * q^61 + 14 * q^64 + 4 * q^65 - 4 * q^67 + 6 * q^68 + 2 * q^70 - 12 * q^73 - 6 * q^74 + 4 * q^76 - 4 * q^77 + 16 * q^79 - 4 * q^80 - 4 * q^82 - 12 * q^83 - 12 * q^85 + 4 * q^86 - 12 * q^88 + 28 * q^89 + 4 * q^91 - 8 * q^95 - 18 * q^97 + 2 * q^98

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