LMFDB - Embedded newform 1638.2.r.k.1387.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (of order $3$, degree $2$, 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:	$13.0794958511$
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 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.k.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(-3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-0.500000 + 0.866025i) q^{23} -1.00000 q^{25} +(2.50000 - 2.59808i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-1.00000 + 1.73205i) q^{29} -9.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} -7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{37} +2.00000 q^{38} +2.00000 q^{40} +(1.00000 - 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +4.00000 q^{44} +(-0.500000 - 0.866025i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.00000 + 3.46410i) q^{52} -3.00000 q^{53} +(-4.00000 + 6.92820i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-1.00000 - 1.73205i) q^{58} +(7.50000 + 12.9904i) q^{59} +(3.50000 + 6.06218i) q^{61} +(4.50000 - 7.79423i) q^{62} +1.00000 q^{64} +(-7.00000 - 1.73205i) q^{65} +(2.50000 - 4.33013i) q^{67} +(3.50000 - 6.06218i) q^{68} -2.00000 q^{70} +(0.500000 + 0.866025i) q^{71} +12.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(1.00000 + 1.73205i) q^{82} +1.00000 q^{83} +(7.00000 + 12.1244i) q^{85} -5.00000 q^{86} +(-2.00000 + 3.46410i) q^{88} +(1.50000 - 2.59808i) q^{89} +(-1.00000 - 3.46410i) q^{91} +1.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(8.00000 + 13.8564i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8} - 2 q^{10} - 4 q^{11} - 7 q^{13} - 2 q^{14} - q^{16} + 7 q^{17} - 2 q^{19} - 2 q^{20} - 4 q^{22} - q^{23} - 2 q^{25} + 5 q^{26} + q^{28} - 2 q^{29} - 18 q^{31} - q^{32} - 14 q^{34} + 2 q^{35} + 2 q^{37} + 4 q^{38} + 4 q^{40} + 2 q^{41} + 5 q^{43} + 8 q^{44} - q^{46} - 12 q^{47} - q^{49} + q^{50} + 2 q^{52} - 6 q^{53} - 8 q^{55} + q^{56} - 2 q^{58} + 15 q^{59} + 7 q^{61} + 9 q^{62} + 2 q^{64} - 14 q^{65} + 5 q^{67} + 7 q^{68} - 4 q^{70} + q^{71} + 24 q^{73} + 2 q^{74} - 2 q^{76} - 8 q^{77} - 8 q^{79} - 2 q^{80} + 2 q^{82} + 2 q^{83} + 14 q^{85} - 10 q^{86} - 4 q^{88} + 3 q^{89} - 2 q^{91} + 2 q^{92} + 6 q^{94} - 4 q^{95} + 16 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8 - 2 * q^10 - 4 * q^11 - 7 * q^13 - 2 * q^14 - q^16 + 7 * q^17 - 2 * q^19 - 2 * q^20 - 4 * q^22 - q^23 - 2 * q^25 + 5 * q^26 + q^28 - 2 * q^29 - 18 * q^31 - q^32 - 14 * q^34 + 2 * q^35 + 2 * q^37 + 4 * q^38 + 4 * q^40 + 2 * q^41 + 5 * q^43 + 8 * q^44 - q^46 - 12 * q^47 - q^49 + q^50 + 2 * q^52 - 6 * q^53 - 8 * q^55 + q^56 - 2 * q^58 + 15 * q^59 + 7 * q^61 + 9 * q^62 + 2 * q^64 - 14 * q^65 + 5 * q^67 + 7 * q^68 - 4 * q^70 + q^71 + 24 * q^73 + 2 * q^74 - 2 * q^76 - 8 * q^77 - 8 * q^79 - 2 * q^80 + 2 * q^82 + 2 * q^83 + 14 * q^85 - 10 * q^86 - 4 * q^88 + 3 * q^89 - 2 * q^91 + 2 * q^92 + 6 * q^94 - 4 * q^95 + 16 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−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
$31$	−9.00000			−1.61645			−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000			−1.61645			−0.808224	+	0.588875i	$0.799571\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−7.00000			−1.20049
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$		0			0
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	2.00000			0.316228
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	1.00000	+	3.46410i	0.138675	+	0.480384i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$	−4.00000	+	6.92820i	−0.539360	+	0.934199i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.675178	+	0.737655i	$0.264067\pi$
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.301239	+	0.953549i	$0.402600\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	4.50000	−	7.79423i	0.571501	−	0.989868i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.00000	−	1.73205i	−0.868243	−	0.214834i
$66$		0			0
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	3.50000	−	6.06218i	0.424437	−	0.735147i
$69$		0			0
$70$	−2.00000			−0.239046
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$72$		0			0
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−4.00000			−0.455842
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$		0			0
$82$	1.00000	+	1.73205i	0.110432	+	0.191273i
$83$	1.00000			0.109764			0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000			0.109764			0.0548821	+	0.998493i	$0.482522\pi$
$84$		0			0
$85$	7.00000	+	12.1244i	0.759257	+	1.31507i
$86$	−5.00000			−0.539164
$87$		0			0
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	1.00000			0.104257
$93$		0			0
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$		0			0
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	0.911267	+	0.411816i	$0.135106\pi$
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	−0.0989899	+	0.995088i	$0.531561\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−11.0000			−1.08386			−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000			−1.08386			−0.541931	+	0.840423i	$0.682307\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	0.614231	−	0.789127i	$-0.289466\pi$
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	−0.990519	+	0.137376i	$0.956133\pi$
$114$		0			0
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$	2.00000			0.185695
$117$		0			0
$118$	−15.0000			−1.38086
$119$	−3.50000	+	6.06218i	−0.320844	+	0.555719i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−7.00000			−0.633750
$123$		0			0
$124$	4.50000	+	7.79423i	0.404112	+	0.699942i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	0.255014	+	0.966937i	$0.417920\pi$
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	−0.964899	+	0.262620i	$0.915413\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	5.00000	−	5.19615i	0.438529	−	0.455733i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	1.00000	−	1.73205i	0.0867110	−	0.150188i
$134$	2.50000	+	4.33013i	0.215967	+	0.374066i
$135$		0			0
$136$	3.50000	+	6.06218i	0.300123	+	0.519827i
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−1.00000			−0.0839181
$143$	10.0000	−	10.3923i	0.836242	−	0.869048i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	0.871742	+	0.489966i	$0.162991\pi$
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	−0.0115483	+	0.999933i	$0.503676\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$	2.00000	−	3.46410i	0.161165	−	0.279145i
$155$	−18.0000			−1.44579
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$		0			0
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	−10.5000	−	18.1865i	−0.822423	−	1.42448i	−0.903873	−	0.427802i	$-0.859288\pi$
$163$	−10.5000	−	18.1865i	−0.822423	−	1.42448i	0.0814491	−	0.996678i	$-0.474045\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	−0.500000	+	0.866025i	−0.0388075	+	0.0672166i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−14.0000			−1.07375
$171$		0			0
$172$	2.50000	−	4.33013i	0.190623	−	0.330169i
$173$	−8.00000	−	13.8564i	−0.608229	−	1.05348i	−0.991532	−	0.129861i	$-0.958547\pi$
$173$	−8.00000	−	13.8564i	−0.608229	−	1.05348i	0.383304	−	0.923622i	$-0.374786\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	1.50000	+	2.59808i	0.112430	+	0.194734i
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	3.50000	+	0.866025i	0.259437	+	0.0641941i
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	−28.0000			−2.04756
$188$	3.00000	+	5.19615i	0.218797	+	0.378968i
$189$		0			0
$190$	4.00000			0.290191
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$	−16.0000			−1.14873
$195$		0			0
$196$	1.00000			0.0714286
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	−0.980614	−	0.195947i	$-0.937222\pi$
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	0.660003	+	0.751263i	$0.270555\pi$
$198$		0			0
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	0.940927	−	0.338608i	$-0.109956\pi$
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	−0.763707	+	0.645563i	$0.776623\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$		0			0
$203$	−2.00000			−0.140372
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	5.50000	−	9.52628i	0.383203	−	0.663727i
$207$		0			0
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	8.00000			0.553372
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		0			0
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	−4.50000	−	7.79423i	−0.305480	−	0.529107i
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$		0			0
$220$	8.00000			0.539360
$221$	−7.00000	−	24.2487i	−0.470871	−	1.63114i
$222$		0			0
$223$	−1.50000	+	2.59808i	−0.100447	+	0.173980i	−0.911869	−	0.410481i	$-0.865361\pi$
$223$	−1.50000	+	2.59808i	−0.100447	+	0.173980i	0.811422	+	0.584461i	$0.198694\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	8.00000			0.532152
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.784642	+	0.619949i	$0.212847\pi$
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.144571	+	0.989494i	$0.453820\pi$
$228$		0			0
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$		0			0
$232$	−1.00000	+	1.73205i	−0.0656532	+	0.113715i
$233$	16.0000			1.04819			0.524097	−	0.851658i	$-0.324403\pi$
$233$	16.0000			1.04819			0.524097	+	0.851658i	$0.324403\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	7.50000	−	12.9904i	0.488208	−	0.845602i
$237$		0			0
$238$	−3.50000	−	6.06218i	−0.226871	−	0.392953i
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	3.50000	−	6.06218i	0.224065	−	0.388091i
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	2.00000	+	6.92820i	0.127257	+	0.440831i
$248$	−9.00000			−0.571501
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	11.5000	+	19.9186i	0.725874	+	1.25725i	0.958613	+	0.284711i	$0.0918976\pi$
$251$	11.5000	+	19.9186i	0.725874	+	1.25725i	−0.232740	+	0.972539i	$0.574769\pi$
$252$		0			0
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	2.00000	+	6.92820i	0.124035	+	0.429669i
$261$		0			0
$262$	7.50000	−	12.9904i	0.463352	−	0.802548i
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$		0			0
$268$	−5.00000			−0.305424
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	−4.50000	+	7.79423i	−0.273356	+	0.473466i	−0.969719	−	0.244224i	$-0.921467\pi$
$271$	−4.50000	+	7.79423i	−0.273356	+	0.473466i	0.696363	+	0.717689i	$0.254800\pi$
$272$	−7.00000			−0.424437
$273$		0			0
$274$	−4.00000			−0.241649
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	0.960810	−	0.277207i	$-0.0894088\pi$
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	−0.720473	+	0.693482i	$0.756075\pi$
$278$	16.0000			0.959616
$279$		0			0
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$		0			0
$286$	4.00000	+	13.8564i	0.236525	+	0.819346i
$287$	2.00000			0.118056
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	−2.00000	−	3.46410i	−0.117444	−	0.203419i
$291$		0			0
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−8.00000	−	13.8564i	−0.467365	−	0.809500i	0.531940	−	0.846782i	$-0.321463\pi$
$293$	−8.00000	−	13.8564i	−0.467365	−	0.809500i	−0.999305	+	0.0372823i	$0.988130\pi$
$294$		0			0
$295$	15.0000	+	25.9808i	0.873334	+	1.51266i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	−21.0000			−1.21650
$299$	2.50000	−	2.59808i	0.144579	−	0.150251i
$300$		0			0
$301$	−2.50000	+	4.33013i	−0.144098	+	0.249584i
$302$	−10.0000	+	17.3205i	−0.575435	+	0.996683i
$303$		0			0
$304$	2.00000			0.114708
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$		0			0
$307$	30.0000			1.71219			0.856095	−	0.516818i	$-0.172884\pi$
$307$	30.0000			1.71219			0.856095	+	0.516818i	$0.172884\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$		0			0
$310$	9.00000	−	15.5885i	0.511166	−	0.885365i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	−5.00000	+	8.66025i	−0.282166	+	0.488726i
$315$		0			0
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	−23.0000			−1.29181			−0.645904	−	0.763418i	$-0.723520\pi$
$317$	−23.0000			−1.29181			−0.645904	+	0.763418i	$0.723520\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	2.00000			0.111803
$321$		0			0
$322$	0.500000	−	0.866025i	0.0278639	−	0.0482617i
$323$	7.00000	−	12.1244i	0.389490	−	0.674617i
$324$		0			0
$325$	3.50000	+	0.866025i	0.194145	+	0.0480384i
$326$	21.0000			1.16308
$327$		0			0
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−18.0000	−	31.1769i	−0.989369	−	1.71364i	−0.620625	−	0.784107i	$-0.713121\pi$
$331$	−18.0000	−	31.1769i	−0.989369	−	1.71364i	−0.368744	−	0.929531i	$-0.620212\pi$
$332$	−0.500000	−	0.866025i	−0.0274411	−	0.0475293i
$333$		0			0
$334$		0			0
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$		0			0
$340$	7.00000	−	12.1244i	0.379628	−	0.657536i
$341$	18.0000	−	31.1769i	0.974755	−	1.68832i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	2.50000	+	4.33013i	0.134791	+	0.233465i
$345$		0			0
$346$	16.0000			0.860165
$347$	5.00000	+	8.66025i	0.268414	+	0.464907i	0.968452	−	0.249198i	$-0.0801671\pi$
$347$	5.00000	+	8.66025i	0.268414	+	0.464907i	−0.700038	+	0.714105i	$0.746834\pi$
$348$		0			0
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	−0.309044	−	0.951048i	$-0.600009\pi$
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	0.978153	−	0.207884i	$-0.0666577\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	4.00000			0.213201
$353$	−17.5000	+	30.3109i	−0.931431	+	1.61329i	−0.150553	+	0.988602i	$0.548106\pi$
$353$	−17.5000	+	30.3109i	−0.931431	+	1.61329i	−0.780878	+	0.624684i	$0.785228\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$	−3.00000			−0.159000
$357$		0			0
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	1.00000	−	1.73205i	0.0525588	−	0.0910346i
$363$		0			0
$364$	−2.50000	+	2.59808i	−0.131036	+	0.136176i
$365$	24.0000			1.25622
$366$		0			0
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	−0.824217	−	0.566274i	$-0.808384\pi$
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	0.902516	+	0.430656i	$0.141718\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$		0			0
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	−1.50000	−	2.59808i	−0.0778761	−	0.134885i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	14.0000	−	24.2487i	0.723923	−	1.25387i
$375$		0			0
$376$	−6.00000			−0.309426
$377$	5.00000	−	5.19615i	0.257513	−	0.267615i
$378$		0			0
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$		0			0
$382$	−3.00000			−0.153493
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$	−8.00000			−0.407718
$386$	11.0000	+	19.0526i	0.559885	+	0.969750i
$387$		0			0
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	1.00000			0.0507020			0.0253510	−	0.999679i	$-0.491930\pi$
$389$	1.00000			0.0507020			0.0253510	+	0.999679i	$0.491930\pi$
$390$		0			0
$391$	−7.00000			−0.354005
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$		0			0
$394$	−4.50000	−	7.79423i	−0.226707	−	0.392668i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−5.00000			−0.250627
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	16.0000	−	27.7128i	0.799002	−	1.38391i	−0.121265	−	0.992620i	$-0.538695\pi$
$401$	16.0000	−	27.7128i	0.799002	−	1.38391i	0.920267	−	0.391292i	$-0.127972\pi$
$402$		0			0
$403$	31.5000	+	7.79423i	1.56913	+	0.388258i
$404$		0			0
$405$		0			0
$406$	1.00000	−	1.73205i	0.0496292	−	0.0859602i
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	2.00000	+	3.46410i	0.0987730	+	0.171080i
$411$		0			0
$412$	5.50000	+	9.52628i	0.270966	+	0.469326i
$413$	−7.50000	+	12.9904i	−0.369051	+	0.639215i
$414$		0			0
$415$	2.00000			0.0981761
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	−4.00000	+	6.92820i	−0.195646	+	0.338869i
$419$	−15.5000	+	26.8468i	−0.757225	+	1.31155i	0.187036	+	0.982353i	$0.440112\pi$
$419$	−15.5000	+	26.8468i	−0.757225	+	1.31155i	−0.944261	+	0.329198i	$0.893222\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$		0			0
$424$	−3.00000			−0.145693
$425$	−3.50000	−	6.06218i	−0.169775	−	0.294059i
$426$		0			0
$427$	−3.50000	+	6.06218i	−0.169377	+	0.293369i
$428$	6.00000			0.290021
$429$		0			0
$430$	−10.0000			−0.482243
$431$	−0.500000	+	0.866025i	−0.0240842	+	0.0417150i	−0.877816	−	0.478997i	$-0.841000\pi$
$431$	−0.500000	+	0.866025i	−0.0240842	+	0.0417150i	0.853732	+	0.520712i	$0.174334\pi$
$432$		0			0
$433$	−6.00000	−	10.3923i	−0.288342	−	0.499422i	0.685072	−	0.728475i	$-0.259771\pi$
$433$	−6.00000	−	10.3923i	−0.288342	−	0.499422i	−0.973414	+	0.229053i	$0.926437\pi$
$434$	9.00000			0.432014
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	2.00000			0.0956730
$438$		0			0
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$	−4.00000	+	6.92820i	−0.190693	+	0.330289i
$441$		0			0
$442$	24.5000	+	6.06218i	1.16535	+	0.288348i
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−1.50000	−	2.59808i	−0.0710271	−	0.123022i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	0.996396	−	0.0848262i	$-0.0270335\pi$
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	−0.571660	+	0.820491i	$0.693700\pi$
$450$		0			0
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	−4.00000	+	6.92820i	−0.188144	+	0.325875i
$453$		0			0
$454$	−28.0000			−1.31411
$455$	−2.00000	−	6.92820i	−0.0937614	−	0.324799i
$456$		0			0
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$	−6.50000	+	11.2583i	−0.303725	+	0.526067i
$459$		0			0
$460$	2.00000			0.0932505
$461$	−10.0000	−	17.3205i	−0.465746	−	0.806696i	0.533488	−	0.845807i	$-0.320881\pi$
$461$	−10.0000	−	17.3205i	−0.465746	−	0.806696i	−0.999235	+	0.0391109i	$0.987547\pi$
$462$		0			0
$463$	18.0000			0.836531			0.418265	−	0.908325i	$-0.362638\pi$
$463$	18.0000			0.836531			0.418265	+	0.908325i	$0.362638\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$		0			0
$466$	−8.00000	+	13.8564i	−0.370593	+	0.641886i
$467$	−37.0000			−1.71216			−0.856078	−	0.516847i	$-0.827106\pi$
$467$	−37.0000			−1.71216			−0.856078	+	0.516847i	$0.827106\pi$
$468$		0			0
$469$	5.00000			0.230879
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$		0			0
$472$	7.50000	+	12.9904i	0.345215	+	0.597931i
$473$	−20.0000			−0.919601
$474$		0			0
$475$	1.00000	+	1.73205i	0.0458831	+	0.0794719i
$476$	7.00000			0.320844
$477$		0			0
$478$	−4.50000	+	7.79423i	−0.205825	+	0.356500i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−5.00000	+	5.19615i	−0.227980	+	0.236924i
$482$	14.0000			0.637683
$483$		0			0
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	16.0000	+	27.7128i	0.726523	+	1.25837i
$486$		0			0
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	0.986642	+	0.162905i	$0.0520863\pi$
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	−0.352241	+	0.935909i	$0.614580\pi$
$488$	3.50000	+	6.06218i	0.158438	+	0.274422i
$489$		0			0
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$		0			0
$493$	−14.0000			−0.630528
$494$	−7.00000	−	1.73205i	−0.314945	−	0.0779287i
$495$		0			0
$496$	4.50000	−	7.79423i	0.202056	−	0.349971i
$497$	−0.500000	+	0.866025i	−0.0224281	+	0.0388465i
$498$		0			0
$499$	7.00000			0.313363			0.156682	−	0.987649i	$-0.449920\pi$
$499$	7.00000			0.313363			0.156682	+	0.987649i	$0.449920\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	−23.0000			−1.02654
$503$	−2.00000	−	3.46410i	−0.0891756	−	0.154457i	0.817987	−	0.575236i	$-0.195090\pi$
$503$	−2.00000	−	3.46410i	−0.0891756	−	0.154457i	−0.907163	+	0.420780i	$0.861757\pi$
$504$		0			0
$505$		0			0
$506$	4.00000			0.177822
$507$		0			0
$508$	16.0000			0.709885
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	−0.967811	−	0.251679i	$-0.919017\pi$
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	0.701866	+	0.712309i	$0.252351\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.5000	+	23.3827i	0.595459	+	1.03137i
$515$	−22.0000			−0.969436
$516$		0			0
$517$	12.0000	−	20.7846i	0.527759	−	0.914106i
$518$	−1.00000	+	1.73205i	−0.0439375	+	0.0761019i
$519$		0			0
$520$	−7.00000	−	1.73205i	−0.306970	−	0.0759555i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	−0.474862	−	0.880060i	$-0.657502\pi$
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	0.999586	−	0.0287874i	$-0.00916457\pi$
$524$	7.50000	+	12.9904i	0.327639	+	0.567487i
$525$		0			0
$526$	2.00000	+	3.46410i	0.0872041	+	0.151042i
$527$	−31.5000	−	54.5596i	−1.37216	−	2.37665i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$		0			0
$532$	−2.00000			−0.0867110
$533$	−5.00000	+	5.19615i	−0.216574	+	0.225070i
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−2.00000	−	3.46410i	−0.0861461	−	0.149209i
$540$		0			0
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$	−4.50000	−	7.79423i	−0.193292	−	0.334791i
$543$		0			0
$544$	3.50000	−	6.06218i	0.150061	−	0.259914i
$545$	−32.0000			−1.37073
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	2.00000	−	3.46410i	0.0854358	−	0.147979i
$549$		0			0
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	4.00000			0.170406
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	−8.00000			−0.339887
$555$		0			0
$556$	−8.00000	+	13.8564i	−0.339276	+	0.587643i
$557$	6.50000	−	11.2583i	0.275414	−	0.477031i	−0.694826	−	0.719178i	$-0.744518\pi$
$557$	6.50000	−	11.2583i	0.275414	−	0.477031i	0.970239	+	0.242147i	$0.0778518\pi$
$558$		0			0
$559$	−5.00000	−	17.3205i	−0.211477	−	0.732579i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−13.0000	+	22.5167i	−0.548372	+	0.949808i
$563$	−20.0000	−	34.6410i	−0.842900	−	1.45994i	−0.887433	−	0.460937i	$-0.847513\pi$
$563$	−20.0000	−	34.6410i	−0.842900	−	1.45994i	0.0445334	−	0.999008i	$-0.485820\pi$
$564$		0			0
$565$	−8.00000	−	13.8564i	−0.336563	−	0.582943i
$566$	−7.00000	−	12.1244i	−0.294232	−	0.509625i
$567$		0			0
$568$	0.500000	+	0.866025i	0.0209795	+	0.0363376i
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	−0.453619	−	0.891196i	$-0.649867\pi$
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	0.998608	−	0.0527519i	$-0.0167993\pi$
$570$		0			0
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$	−14.0000	−	3.46410i	−0.585369	−	0.144841i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	0.500000	−	0.866025i	0.0208514	−	0.0361158i
$576$		0			0
$577$	6.00000			0.249783			0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000			0.249783			0.124892	+	0.992170i	$0.460142\pi$
$578$	−16.0000	−	27.7128i	−0.665512	−	1.15270i
$579$		0			0
$580$	4.00000			0.166091
$581$	0.500000	+	0.866025i	0.0207435	+	0.0359288i
$582$		0			0
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$	12.0000			0.496564
$585$		0			0
$586$	16.0000			0.660954
$587$	22.5000	−	38.9711i	0.928674	−	1.60851i	0.143132	−	0.989704i	$-0.454283\pi$
$587$	22.5000	−	38.9711i	0.928674	−	1.60851i	0.785543	−	0.618808i	$-0.212384\pi$
$588$		0			0
$589$	9.00000	+	15.5885i	0.370839	+	0.642311i
$590$	−30.0000			−1.23508
$591$		0			0
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−29.0000			−1.19089			−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000			−1.19089			−0.595444	+	0.803397i	$0.703024\pi$
$594$		0			0
$595$	−7.00000	+	12.1244i	−0.286972	+	0.497050i
$596$	10.5000	−	18.1865i	0.430097	−	0.744949i
$597$		0			0
$598$	1.00000	+	3.46410i	0.0408930	+	0.141658i
$599$	−9.00000			−0.367730			−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000			−0.367730			−0.183865	+	0.982952i	$0.558861\pi$
$600$		0			0
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	0.159754	+	0.987157i	$0.448930\pi$
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	−0.934780	+	0.355228i	$0.884403\pi$
$602$	−2.50000	−	4.33013i	−0.101892	−	0.176483i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.737011	−	0.675881i	$-0.763763\pi$
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.216825	−	0.976210i	$-0.569570\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$		0			0
$610$	−14.0000			−0.566843
$611$	21.0000	+	5.19615i	0.849569	+	0.210214i
$612$		0			0
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	−0.972056	−	0.234751i	$-0.924572\pi$
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	0.689328	+	0.724449i	$0.257906\pi$
$614$	−15.0000	+	25.9808i	−0.605351	+	1.04850i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	0.591452	−	0.806340i	$-0.298555\pi$
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	−0.994037	+	0.109043i	$0.965221\pi$
$618$		0			0
$619$	−22.0000			−0.884255			−0.442127	−	0.896952i	$-0.645776\pi$
$619$	−22.0000			−0.884255			−0.442127	+	0.896952i	$0.645776\pi$
$620$	9.00000	+	15.5885i	0.361449	+	0.626048i
$621$		0			0
$622$	15.0000	−	25.9808i	0.601445	−	1.04173i
$623$	3.00000			0.120192
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$		0			0
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$	14.0000			0.558217
$630$		0			0
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	0.993491	−	0.113913i	$-0.0363385\pi$
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	−0.595397	+	0.803432i	$0.703005\pi$
$632$	−4.00000			−0.159111
$633$		0			0
$634$	11.5000	−	19.9186i	0.456723	−	0.791068i
$635$	−16.0000	+	27.7128i	−0.634941	+	1.09975i
$636$		0			0
$637$	2.50000	−	2.59808i	0.0990536	−	0.102940i
$638$	8.00000			0.316723
$639$		0			0
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	16.0000	+	27.7128i	0.631962	+	1.09459i	0.987150	+	0.159795i	$0.0510835\pi$
$641$	16.0000	+	27.7128i	0.631962	+	1.09459i	−0.355188	+	0.934795i	$0.615583\pi$
$642$		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	$0.922360\pi$
$644$	0.500000	+	0.866025i	0.0197028	+	0.0341262i
$645$		0			0
$646$	7.00000	+	12.1244i	0.275411	+	0.477026i
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	−0.918952	−	0.394369i	$-0.870963\pi$
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	0.801010	+	0.598651i	$0.204296\pi$
$648$		0			0
$649$	−60.0000			−2.35521
$650$	−2.50000	+	2.59808i	−0.0980581	+	0.101905i
$651$		0			0
$652$	−10.5000	+	18.1865i	−0.411212	+	0.712240i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	−30.0000			−1.17220
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$		0			0
$658$	6.00000			0.233904
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$		0			0
$661$	17.5000	−	30.3109i	0.680671	−	1.17896i	−0.294105	−	0.955773i	$-0.595022\pi$
$661$	17.5000	−	30.3109i	0.680671	−	1.17896i	0.974776	−	0.223184i	$-0.0716450\pi$
$662$	36.0000			1.39918
$663$		0			0
$664$	1.00000			0.0388075
$665$	2.00000	−	3.46410i	0.0775567	−	0.134332i
$666$		0			0
$667$	−1.00000	−	1.73205i	−0.0387202	−	0.0670653i
$668$		0			0
$669$		0			0
$670$	5.00000	+	8.66025i	0.193167	+	0.334575i
$671$	−28.0000			−1.08093
$672$		0			0
$673$	16.5000	−	28.5788i	0.636028	−	1.10163i	−0.350268	−	0.936650i	$-0.613909\pi$
$673$	16.5000	−	28.5788i	0.636028	−	1.10163i	0.986296	−	0.164984i	$-0.0527572\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		0			0
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	−28.0000			−1.07613			−0.538064	−	0.842904i	$-0.680844\pi$
$677$	−28.0000			−1.07613			−0.538064	+	0.842904i	$0.680844\pi$
$678$		0			0
$679$	−8.00000	+	13.8564i	−0.307012	+	0.531760i
$680$	7.00000	+	12.1244i	0.268438	+	0.464948i
$681$		0			0
$682$	18.0000	+	31.1769i	0.689256	+	1.19383i
$683$	11.0000	+	19.0526i	0.420903	+	0.729026i	0.996028	−	0.0890398i	$-0.0283798\pi$
$683$	11.0000	+	19.0526i	0.420903	+	0.729026i	−0.575125	+	0.818066i	$0.695047\pi$
$684$		0			0
$685$	4.00000	+	6.92820i	0.152832	+	0.264713i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	−5.00000			−0.190623
$689$	10.5000	+	2.59808i	0.400018	+	0.0989788i
$690$		0			0
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$	−8.00000	+	13.8564i	−0.304114	+	0.526742i
$693$		0			0
$694$	−10.0000			−0.379595
$695$	−16.0000	−	27.7128i	−0.606915	−	1.05121i
$696$		0			0
$697$	14.0000			0.530288
$698$	12.5000	+	21.6506i	0.473132	+	0.819489i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	−17.5000	−	30.3109i	−0.658621	−	1.14077i
$707$		0			0
$708$		0			0
$709$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$	−2.00000			−0.0750587
$711$		0			0
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$	4.50000	−	7.79423i	0.168526	−	0.291896i
$714$		0			0
$715$	20.0000	−	20.7846i	0.747958	−	0.777300i
$716$	−6.00000			−0.224231
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	10.0000	+	17.3205i	0.372937	+	0.645946i	0.990016	−	0.140955i	$-0.0450174\pi$
$719$	10.0000	+	17.3205i	0.372937	+	0.645946i	−0.617079	+	0.786901i	$0.711684\pi$
$720$		0			0
$721$	−5.50000	−	9.52628i	−0.204831	−	0.354777i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$		0			0
$727$	−21.0000			−0.778847			−0.389423	−	0.921059i	$-0.627326\pi$
$727$	−21.0000			−0.778847			−0.389423	+	0.921059i	$0.627326\pi$
$728$	−1.00000	−	3.46410i	−0.0370625	−	0.128388i
$729$		0			0
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	−17.5000	+	30.3109i	−0.647261	+	1.12109i
$732$		0			0
$733$	−21.0000			−0.775653			−0.387826	−	0.921732i	$-0.626774\pi$
$733$	−21.0000			−0.775653			−0.387826	+	0.921732i	$0.626774\pi$
$734$	1.50000	+	2.59808i	0.0553660	+	0.0958967i
$735$		0			0
$736$	1.00000			0.0368605
$737$	10.0000	+	17.3205i	0.368355	+	0.638009i
$738$		0			0
$739$	−24.5000	+	42.4352i	−0.901247	+	1.56101i	−0.0753699	+	0.997156i	$0.524014\pi$
$739$	−24.5000	+	42.4352i	−0.901247	+	1.56101i	−0.825877	+	0.563850i	$0.809320\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	3.00000			0.110133
$743$	−20.5000	+	35.5070i	−0.752072	+	1.30263i	0.194745	+	0.980854i	$0.437612\pi$
$743$	−20.5000	+	35.5070i	−0.752072	+	1.30263i	−0.946817	+	0.321773i	$0.895721\pi$
$744$		0			0
$745$	21.0000	+	36.3731i	0.769380	+	1.33261i
$746$	4.00000			0.146450
$747$		0			0
$748$	14.0000	+	24.2487i	0.511891	+	0.886621i
$749$	−6.00000			−0.219235
$750$		0			0
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	−0.525193	−	0.850983i	$-0.676007\pi$
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	0.999570	+	0.0293387i	$0.00934013\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	2.00000	+	6.92820i	0.0728357	+	0.252310i
$755$	40.0000			1.45575
$756$		0			0
$757$	−23.0000	+	39.8372i	−0.835949	+	1.44791i	0.0573060	+	0.998357i	$0.481749\pi$
$757$	−23.0000	+	39.8372i	−0.835949	+	1.44791i	−0.893255	+	0.449550i	$0.851584\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$		0			0
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	0.942306	−	0.334752i	$-0.108652\pi$
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	−0.761057	+	0.648686i	$0.775319\pi$
$762$		0			0
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$	1.50000	−	2.59808i	0.0542681	−	0.0939951i
$765$		0			0
$766$	−24.0000			−0.867155
$767$	−15.0000	−	51.9615i	−0.541619	−	1.87622i
$768$		0			0
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	−0.899831	−	0.436239i	$-0.856310\pi$
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	0.827709	+	0.561157i	$0.189644\pi$
$770$	4.00000	−	6.92820i	0.144150	−	0.249675i
$771$		0			0
$772$	−22.0000			−0.791797
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	0.761987	−	0.647592i	$-0.224224\pi$
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	−0.941825	+	0.336104i	$0.890891\pi$
$774$		0			0
$775$	9.00000			0.323290
$776$	8.00000	+	13.8564i	0.287183	+	0.497416i
$777$		0			0
$778$	−0.500000	+	0.866025i	−0.0179259	+	0.0310485i
$779$	−4.00000			−0.143315
$780$		0			0
$781$	−4.00000			−0.143131
$782$	3.50000	−	6.06218i	0.125160	−	0.216783i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	20.0000			0.713831
$786$		0			0
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	9.00000			0.320612
$789$		0			0
$790$	4.00000	−	6.92820i	0.142314	−	0.246494i
$791$	4.00000	−	6.92820i	0.142224	−	0.246339i
$792$		0			0
$793$	−7.00000	−	24.2487i	−0.248577	−	0.861097i
$794$	−1.00000			−0.0354887
$795$		0			0
$796$	2.50000	−	4.33013i	0.0886102	−	0.153477i
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$	−21.0000	−	36.3731i	−0.742927	−	1.28679i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	16.0000	+	27.7128i	0.564980	+	0.978573i
$803$	−24.0000	+	41.5692i	−0.846942	+	1.46695i
$804$		0			0
$805$	−2.00000			−0.0704907
$806$	−22.5000	+	23.3827i	−0.792529	+	0.823620i
$807$		0			0
$808$		0			0
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	1.00000	+	1.73205i	0.0350931	+	0.0607831i
$813$		0			0
$814$	−8.00000			−0.280400
$815$	−21.0000	−	36.3731i	−0.735598	−	1.27409i
$816$		0			0
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	14.0000			0.489499
$819$		0			0
$820$	−4.00000			−0.139686
$821$	21.5000	−	37.2391i	0.750355	−	1.29965i	−0.197295	−	0.980344i	$-0.563216\pi$
$821$	21.5000	−	37.2391i	0.750355	−	1.29965i	0.947651	−	0.319309i	$-0.103451\pi$
$822$		0			0
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	0.985997	−	0.166762i	$-0.0533313\pi$
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	−0.637419	+	0.770517i	$0.719998\pi$
$824$	−11.0000			−0.383203
$825$		0			0
$826$	−7.50000	−	12.9904i	−0.260958	−	0.451993i
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$		0			0
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	0.227794	+	0.973709i	$0.426849\pi$
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	−0.957154	+	0.289579i	$0.906485\pi$
$830$	−1.00000	+	1.73205i	−0.0347105	+	0.0601204i
$831$		0			0
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	−7.00000			−0.242536
$834$		0			0
$835$		0			0
$836$	−4.00000	−	6.92820i	−0.138343	−	0.239617i
$837$		0			0
$838$	−15.5000	−	26.8468i	−0.535439	−	0.927407i
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	0.978517	−	0.206165i	$-0.0660984\pi$
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	−0.667803	+	0.744338i	$0.732765\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$		0			0
$844$	4.00000			0.137686
$845$	23.0000	+	12.1244i	0.791224	+	0.417091i
$846$		0			0
$847$	2.50000	−	4.33013i	0.0859010	−	0.148785i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$		0			0
$850$	7.00000			0.240098
$851$	1.00000	+	1.73205i	0.0342796	+	0.0593739i
$852$		0			0
$853$	−29.0000			−0.992941			−0.496471	−	0.868054i	$-0.665371\pi$
$853$	−29.0000			−0.992941			−0.496471	+	0.868054i	$0.665371\pi$
$854$	−3.50000	−	6.06218i	−0.119768	−	0.207443i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	−0.500000	−	0.866025i	−0.0170301	−	0.0294969i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$		0			0
$865$	−16.0000	−	27.7128i	−0.544016	−	0.942264i
$866$	12.0000			0.407777
$867$		0			0
$868$	−4.50000	+	7.79423i	−0.152740	+	0.264553i
$869$	8.00000	−	13.8564i	0.271381	−	0.470046i
$870$		0			0
$871$	−12.5000	+	12.9904i	−0.423546	+	0.440162i
$872$	−16.0000			−0.541828
$873$		0			0
$874$	−1.00000	+	1.73205i	−0.0338255	+	0.0585875i
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$		0			0
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	0.558632	−	0.829416i	$-0.311326\pi$
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	−0.997611	+	0.0690819i	$0.977993\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−23.5000	+	40.7032i	−0.791735	+	1.37133i	0.133157	+	0.991095i	$0.457489\pi$
$881$	−23.5000	+	40.7032i	−0.791735	+	1.37133i	−0.924892	+	0.380230i	$0.875845\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	−17.5000	+	18.1865i	−0.588589	+	0.611679i
$885$		0			0
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	−0.848749	−	0.528796i	$-0.822644\pi$
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	0.882325	+	0.470640i	$0.155977\pi$
$888$		0			0
$889$	−16.0000			−0.536623
$890$	3.00000	+	5.19615i	0.100560	+	0.174175i
$891$		0			0
$892$	3.00000			0.100447
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−18.0000			−0.600668
$899$	9.00000	−	15.5885i	0.300167	−	0.519904i
$900$		0			0
$901$	−10.5000	−	18.1865i	−0.349806	−	0.605881i
$902$	−8.00000			−0.266371
$903$		0			0
$904$	−4.00000	−	6.92820i	−0.133038	−	0.230429i
$905$	−4.00000			−0.132964
$906$		0			0
$907$	−19.5000	+	33.7750i	−0.647487	+	1.12148i	0.336234	+	0.941778i	$0.390847\pi$
$907$	−19.5000	+	33.7750i	−0.647487	+	1.12148i	−0.983721	+	0.179702i	$0.942487\pi$
$908$	14.0000	−	24.2487i	0.464606	−	0.804722i
$909$		0			0
$910$	7.00000	+	1.73205i	0.232048	+	0.0574169i
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	−2.00000	+	3.46410i	−0.0661903	+	0.114645i
$914$	4.50000	+	7.79423i	0.148847	+	0.257810i
$915$		0			0
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	−7.50000	−	12.9904i	−0.247672	−	0.428980i
$918$		0			0
$919$	23.0000	+	39.8372i	0.758700	+	1.31411i	0.943514	+	0.331333i	$0.107498\pi$
$919$	23.0000	+	39.8372i	0.758700	+	1.31411i	−0.184814	+	0.982774i	$0.559168\pi$
$920$	−1.00000	+	1.73205i	−0.0329690	+	0.0571040i
$921$		0			0
$922$	20.0000			0.658665
$923$	−1.00000	−	3.46410i	−0.0329154	−	0.114022i
$924$		0			0
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	−9.00000	+	15.5885i	−0.295758	+	0.512268i
$927$		0			0
$928$	2.00000			0.0656532
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	2.00000			0.0655474
$932$	−8.00000	−	13.8564i	−0.262049	−	0.453882i
$933$		0			0
$934$	18.5000	−	32.0429i	0.605338	−	1.04848i
$935$	−56.0000			−1.83140
$936$		0			0
$937$	−18.0000			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$938$	−2.50000	+	4.33013i	−0.0816279	+	0.141384i
$939$		0			0
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	28.0000			0.912774			0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000			0.912774			0.456387	+	0.889781i	$0.349143\pi$
$942$		0			0
$943$	1.00000	+	1.73205i	0.0325645	+	0.0564033i
$944$	−15.0000			−0.488208
$945$		0			0
$946$	10.0000	−	17.3205i	0.325128	−	0.563138i
$947$	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
$949$	−42.0000	−	10.3923i	−1.36338	−	0.337348i
$950$	−2.00000			−0.0648886
$951$		0			0
$952$	−3.50000	+	6.06218i	−0.113436	+	0.196476i
$953$	7.00000	+	12.1244i	0.226752	+	0.392746i	0.956844	−	0.290603i	$-0.0938559\pi$
$953$	7.00000	+	12.1244i	0.226752	+	0.392746i	−0.730091	+	0.683349i	$0.760523\pi$
$954$		0			0
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$	−4.50000	−	7.79423i	−0.145540	−	0.252083i
$957$		0			0
$958$		0			0
$959$	−2.00000	+	3.46410i	−0.0645834	+	0.111862i
$960$		0			0
$961$	50.0000			1.61290
$962$	−2.00000	−	6.92820i	−0.0644826	−	0.223374i
$963$		0			0
$964$	−7.00000	+	12.1244i	−0.225455	+	0.390499i
$965$	22.0000	−	38.1051i	0.708205	−	1.22665i
$966$		0			0
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$		0			0
$970$	−32.0000			−1.02746
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	8.00000	−	13.8564i	0.256468	−	0.444216i
$974$	−28.0000			−0.897178
$975$		0			0
$976$	−7.00000			−0.224065
$977$	−24.0000	+	41.5692i	−0.767828	+	1.32992i	0.170910	+	0.985287i	$0.445329\pi$
$977$	−24.0000	+	41.5692i	−0.767828	+	1.32992i	−0.938738	+	0.344631i	$0.888004\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$	2.00000			0.0638877
$981$		0			0
$982$	−4.00000	−	6.92820i	−0.127645	−	0.221088i
$983$	46.0000			1.46717			0.733586	−	0.679597i	$-0.237845\pi$
$983$	46.0000			1.46717			0.733586	+	0.679597i	$0.237845\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$		0			0
$988$	5.00000	−	5.19615i	0.159071	−	0.165312i
$989$	−5.00000			−0.158991
$990$		0			0
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	−0.972826	−	0.231539i	$-0.925624\pi$
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	0.686931	+	0.726722i	$0.258957\pi$
$992$	4.50000	+	7.79423i	0.142875	+	0.247467i
$993$		0			0
$994$	−0.500000	−	0.866025i	−0.0158590	−	0.0274687i
$995$	5.00000	+	8.66025i	0.158511	+	0.274549i
$996$		0			0
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	0.997963	+	0.0637961i	$0.0203207\pi$
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	−0.443732	+	0.896159i	$0.646346\pi$
$998$	−3.50000	+	6.06218i	−0.110791	+	0.191895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.k.1387.1		2
3.2	odd	2		546.2.l.d.295.1	yes	2
13.3	even	3	inner	1638.2.r.k.757.1		2
39.17	odd	6		7098.2.a.bf.1.1		1
39.29	odd	6		546.2.l.d.211.1	✓	2
39.35	odd	6		7098.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.d.211.1	✓	2	39.29	odd	6
546.2.l.d.295.1	yes	2	3.2	odd	2
1638.2.r.k.757.1		2	13.3	even	3	inner
1638.2.r.k.1387.1		2	1.1	even	1	trivial
7098.2.a.h.1.1		1	39.35	odd	6
7098.2.a.bf.1.1		1	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(-3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-0.500000 + 0.866025i) q^{23} -1.00000 q^{25} +(2.50000 - 2.59808i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-1.00000 + 1.73205i) q^{29} -9.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} -7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{37} +2.00000 q^{38} +2.00000 q^{40} +(1.00000 - 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +4.00000 q^{44} +(-0.500000 - 0.866025i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.00000 + 3.46410i) q^{52} -3.00000 q^{53} +(-4.00000 + 6.92820i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-1.00000 - 1.73205i) q^{58} +(7.50000 + 12.9904i) q^{59} +(3.50000 + 6.06218i) q^{61} +(4.50000 - 7.79423i) q^{62} +1.00000 q^{64} +(-7.00000 - 1.73205i) q^{65} +(2.50000 - 4.33013i) q^{67} +(3.50000 - 6.06218i) q^{68} -2.00000 q^{70} +(0.500000 + 0.866025i) q^{71} +12.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(1.00000 + 1.73205i) q^{82} +1.00000 q^{83} +(7.00000 + 12.1244i) q^{85} -5.00000 q^{86} +(-2.00000 + 3.46410i) q^{88} +(1.50000 - 2.59808i) q^{89} +(-1.00000 - 3.46410i) q^{91} +1.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(8.00000 + 13.8564i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8} - 2 q^{10} - 4 q^{11} - 7 q^{13} - 2 q^{14} - q^{16} + 7 q^{17} - 2 q^{19} - 2 q^{20} - 4 q^{22} - q^{23} - 2 q^{25} + 5 q^{26} + q^{28} - 2 q^{29} - 18 q^{31} - q^{32} - 14 q^{34} + 2 q^{35} + 2 q^{37} + 4 q^{38} + 4 q^{40} + 2 q^{41} + 5 q^{43} + 8 q^{44} - q^{46} - 12 q^{47} - q^{49} + q^{50} + 2 q^{52} - 6 q^{53} - 8 q^{55} + q^{56} - 2 q^{58} + 15 q^{59} + 7 q^{61} + 9 q^{62} + 2 q^{64} - 14 q^{65} + 5 q^{67} + 7 q^{68} - 4 q^{70} + q^{71} + 24 q^{73} + 2 q^{74} - 2 q^{76} - 8 q^{77} - 8 q^{79} - 2 q^{80} + 2 q^{82} + 2 q^{83} + 14 q^{85} - 10 q^{86} - 4 q^{88} + 3 q^{89} - 2 q^{91} + 2 q^{92} + 6 q^{94} - 4 q^{95} + 16 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8 - 2 * q^10 - 4 * q^11 - 7 * q^13 - 2 * q^14 - q^16 + 7 * q^17 - 2 * q^19 - 2 * q^20 - 4 * q^22 - q^23 - 2 * q^25 + 5 * q^26 + q^28 - 2 * q^29 - 18 * q^31 - q^32 - 14 * q^34 + 2 * q^35 + 2 * q^37 + 4 * q^38 + 4 * q^40 + 2 * q^41 + 5 * q^43 + 8 * q^44 - q^46 - 12 * q^47 - q^49 + q^50 + 2 * q^52 - 6 * q^53 - 8 * q^55 + q^56 - 2 * q^58 + 15 * q^59 + 7 * q^61 + 9 * q^62 + 2 * q^64 - 14 * q^65 + 5 * q^67 + 7 * q^68 - 4 * q^70 + q^71 + 24 * q^73 + 2 * q^74 - 2 * q^76 - 8 * q^77 - 8 * q^79 - 2 * q^80 + 2 * q^82 + 2 * q^83 + 14 * q^85 - 10 * q^86 - 4 * q^88 + 3 * q^89 - 2 * q^91 + 2 * q^92 + 6 * q^94 - 4 * q^95 + 16 * q^97 - q^98

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