LMFDB - Embedded newform 1053.2.e.d.352.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1053,2,Mod(352,1053)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1053, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1053.352"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,1,2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.40824733284$
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 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1053.352
Dual form			1053.2.e.d.703.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +2.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{26} +4.00000 q^{28} +(-5.00000 - 8.66025i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 - 1.73205i) q^{34} +8.00000 q^{35} -2.00000 q^{37} +(3.00000 - 5.19615i) q^{40} +(3.00000 - 5.19615i) q^{41} +(6.00000 + 10.3923i) q^{43} +4.00000 q^{44} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(6.00000 + 10.3923i) q^{56} +(5.00000 - 8.66025i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} +2.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-8.00000 + 13.8564i) q^{77} +(-4.00000 - 6.92820i) q^{79} +2.00000 q^{80} +6.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(-6.00000 + 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{88} +2.00000 q^{89} -4.00000 q^{91} +(-5.00000 - 8.66025i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 2 q^{5} + 4 q^{7} + 6 q^{8} + 4 q^{10} + 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 4 q^{17} - 2 q^{20} - 4 q^{22} + q^{25} - 2 q^{26} + 8 q^{28} - 10 q^{29} - 4 q^{31} + 5 q^{32}+ \cdots - 18 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 2 * q^5 + 4 * q^7 + 6 * q^8 + 4 * q^10 + 4 * q^11 - q^13 - 4 * q^14 + q^16 - 4 * q^17 - 2 * q^20 - 4 * q^22 + q^25 - 2 * q^26 + 8 * q^28 - 10 * q^29 - 4 * q^31 + 5 * q^32 - 2 * q^34 + 16 * q^35 - 4 * q^37 + 6 * q^40 + 6 * q^41 + 12 * q^43 + 8 * q^44 - 9 * q^49 - q^50 + q^52 - 12 * q^53 + 16 * q^55 + 12 * q^56 + 10 * q^58 + 12 * q^59 + 2 * q^61 - 8 * q^62 + 14 * q^64 + 2 * q^65 + 8 * q^67 - 2 * q^68 + 8 * q^70 + 4 * q^73 - 2 * q^74 - 16 * q^77 - 8 * q^79 + 4 * q^80 + 12 * q^82 + 4 * q^83 - 4 * q^85 - 12 * q^86 + 12 * q^88 + 4 * q^89 - 8 * q^91 - 10 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	2.00000			0.632456
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−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	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	4.00000			0.755929
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.785872	−	0.618389i	$-0.787786\pi$
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.142605	−	0.989780i	$-0.545548\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$	8.00000			1.35225
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$		0			0
$40$	3.00000	−	5.19615i	0.474342	−	0.821584i
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.806914	+	0.590669i	$0.201136\pi$
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.108078	+	0.994142i	$0.465531\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−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
$56$	6.00000	+	10.3923i	0.801784	+	1.38873i
$57$		0			0
$58$	5.00000	−	8.66025i	0.656532	−	1.13715i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	7.00000			0.875000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$		0			0
$70$	4.00000	+	6.92820i	0.478091	+	0.828079i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$		0			0
$77$	−8.00000	+	13.8564i	−0.911685	+	1.57908i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	2.00000			0.223607
$81$		0			0
$82$	6.00000			0.662589
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	0.954664	−	0.297686i	$-0.0962148\pi$
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	−0.735135	+	0.677920i	$0.762881\pi$
$84$		0			0
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$		0			0
$88$	6.00000	+	10.3923i	0.639602	+	1.10782i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$		0			0
$116$	−10.0000			−0.928477
$117$		0			0
$118$	12.0000			1.10469
$119$	−4.00000	−	6.92820i	−0.366679	−	0.635107i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$		0			0
$136$	−6.00000			−0.514496
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	4.00000	−	6.92820i	0.338062	−	0.585540i
$141$		0			0
$142$		0			0
$143$	−4.00000			−0.334497
$144$		0			0
$145$	−20.0000			−1.66091
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$		0			0
$154$	−16.0000			−1.28932
$155$	4.00000	+	6.92820i	0.321288	+	0.556487i
$156$		0			0
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	0.961681	−	0.274169i	$-0.0884028\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	−5.00000	−	8.66025i	−0.395285	−	0.684653i
$161$		0			0
$162$		0			0
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	12.0000			0.914991
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	−	3.46410i	−0.148250	−	0.256776i
$183$		0			0
$184$		0			0
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	0.335805	+	0.941932i	$0.390992\pi$
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	−0.983639	+	0.180150i	$0.942342\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	4.50000	+	7.79423i	0.321429	+	0.556731i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$		0			0
$202$	9.00000	−	15.5885i	0.633238	−	1.09680i
$203$	20.0000	−	34.6410i	1.40372	−	2.43132i
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$		0			0
$208$	−1.00000			−0.0693375
$209$		0			0
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	24.0000			1.63679
$216$		0			0
$217$	−16.0000			−1.08615
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$		0			0
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	1.00000	−	1.73205i	0.0672673	−	0.116510i
$222$		0			0
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$	20.0000			1.33631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$	−15.0000	−	25.9808i	−0.984798	−	1.70572i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$		0			0
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	2.00000			0.128037
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$		0			0
$247$		0			0
$248$	−6.00000	+	10.3923i	−0.381000	+	0.659912i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$		0			0
$259$	−4.00000	−	6.92820i	−0.248548	−	0.430498i
$260$	2.00000			0.124035
$261$		0			0
$262$	4.00000			0.247121
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	−6.00000	+	10.3923i	−0.368577	+	0.638394i
$266$		0			0
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−22.0000			−1.34136			−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000			−1.34136			−0.670682	+	0.741745i	$0.733998\pi$
$270$		0			0
$271$	−12.0000			−0.728948			−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000			−0.728948			−0.364474	+	0.931214i	$0.618751\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−12.0000			−0.719712
$279$		0			0
$280$	24.0000			1.43427
$281$	−5.00000	−	8.66025i	−0.298275	−	0.516627i	0.677466	−	0.735554i	$-0.263078\pi$
$281$	−5.00000	−	8.66025i	−0.298275	−	0.516627i	−0.975741	+	0.218926i	$0.929745\pi$
$282$		0			0
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	−0.987401	−	0.158237i	$-0.949419\pi$
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	0.630738	+	0.775996i	$0.282752\pi$
$284$		0			0
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	24.0000			1.41668
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−10.0000	−	17.3205i	−0.587220	−	1.01710i
$291$		0			0
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		0			0
$295$	−12.0000	−	20.7846i	−0.698667	−	1.21013i
$296$	−6.00000			−0.348743
$297$		0			0
$298$	−6.00000			−0.347571
$299$		0			0
$300$		0			0
$301$	−24.0000	+	41.5692i	−1.38334	+	2.39601i
$302$	2.00000	−	3.46410i	0.115087	−	0.199337i
$303$		0			0
$304$		0			0
$305$	4.00000			0.229039
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	8.00000	+	13.8564i	0.455842	+	0.789542i
$309$		0			0
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	−8.00000			−0.450035
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	0.956818	+	0.290689i	$0.0938844\pi$
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	−0.226665	+	0.973973i	$0.572782\pi$
$318$		0			0
$319$	20.0000	−	34.6410i	1.11979	−	1.93952i
$320$	7.00000	−	12.1244i	0.391312	−	0.677772i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$		0			0
$328$	9.00000	−	15.5885i	0.496942	−	0.860729i
$329$		0			0
$330$		0			0
$331$	8.00000	+	13.8564i	0.439720	+	0.761617i	0.997668	−	0.0682590i	$-0.0217444\pi$
$331$	8.00000	+	13.8564i	0.439720	+	0.761617i	−0.557948	+	0.829876i	$0.688411\pi$
$332$	4.00000			0.219529
$333$		0			0
$334$	−8.00000			−0.437741
$335$	−8.00000	−	13.8564i	−0.437087	−	0.757056i
$336$		0			0
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	−0.999937	−	0.0112091i	$-0.996432\pi$
$337$	−9.00000	+	15.5885i	−0.490261	+	0.849157i	0.509676	+	0.860366i	$0.329765\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−16.0000			−0.866449
$342$		0			0
$343$	−8.00000			−0.431959
$344$	18.0000	+	31.1769i	0.970495	+	1.68095i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	13.0000	+	22.5167i	0.695874	+	1.20529i	0.969885	+	0.243563i	$0.0783162\pi$
$349$	13.0000	+	22.5167i	0.695874	+	1.20529i	−0.274011	+	0.961727i	$0.588351\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	20.0000			1.06600
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	0.838186	−	0.545385i	$-0.183617\pi$
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	−0.891410	+	0.453197i	$0.850283\pi$
$354$		0			0
$355$		0			0
$356$	1.00000	−	1.73205i	0.0529999	−	0.0917985i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$	−2.00000	+	3.46410i	−0.104828	+	0.181568i
$365$	2.00000	−	3.46410i	0.104685	−	0.181319i
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		0			0
$369$		0			0
$370$	−4.00000			−0.207950
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$		0			0
$377$	10.0000			0.515026
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$		0			0
$381$		0			0
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	−0.994753	−	0.102302i	$-0.967379\pi$
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	0.585973	+	0.810331i	$0.300713\pi$
$384$		0			0
$385$	16.0000	+	27.7128i	0.815436	+	1.41238i
$386$	−18.0000			−0.916176
$387$		0			0
$388$	−10.0000			−0.507673
$389$	11.0000	+	19.0526i	0.557722	+	0.966003i	0.997686	+	0.0679877i	$0.0216579\pi$
$389$	11.0000	+	19.0526i	0.557722	+	0.966003i	−0.439964	+	0.898015i	$0.645009\pi$
$390$		0			0
$391$		0			0
$392$	−13.5000	+	23.3827i	−0.681853	+	1.18100i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−16.0000			−0.805047
$396$		0			0
$397$	38.0000			1.90717			0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000			1.90717			0.953583	+	0.301131i	$0.0973643\pi$
$398$	4.00000	+	6.92820i	0.200502	+	0.347279i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	0.998322	−	0.0579116i	$-0.0184442\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−18.0000			−0.895533
$405$		0			0
$406$	40.0000			1.98517
$407$	−4.00000	−	6.92820i	−0.198273	−	0.343418i
$408$		0			0
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	0.0487958	+	0.998809i	$0.484462\pi$
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	−0.889392	+	0.457146i	$0.848872\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$		0			0
$412$		0			0
$413$	48.0000			2.36193
$414$		0			0
$415$	8.00000			0.392705
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$		0			0
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	−0.813029	−	0.582224i	$-0.802183\pi$
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	0.910735	+	0.412991i	$0.135516\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	20.0000			0.973585
$423$		0			0
$424$	−18.0000			−0.874157
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$	−8.00000	−	13.8564i	−0.384012	−	0.665129i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$		0			0
$438$		0			0
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	24.0000			1.14416
$441$		0			0
$442$	2.00000			0.0951303
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$		0			0
$445$	2.00000	−	3.46410i	0.0948091	−	0.164214i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		0			0
$448$	14.0000	+	24.2487i	0.661438	+	1.14564i
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$		0			0
$454$	10.0000	−	17.3205i	0.469323	−	0.812892i
$455$	−4.00000	+	6.92820i	−0.187523	+	0.324799i
$456$		0			0
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	10.0000			0.467269
$459$		0			0
$460$		0			0
$461$	−19.0000	−	32.9090i	−0.884918	−	1.53272i	−0.845807	−	0.533488i	$-0.820881\pi$
$461$	−19.0000	−	32.9090i	−0.884918	−	1.53272i	−0.0391109	−	0.999235i	$-0.512453\pi$
$462$		0			0
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	−0.908750	−	0.417340i	$-0.862962\pi$
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	0.815802	+	0.578331i	$0.196296\pi$
$464$	5.00000	−	8.66025i	0.232119	−	0.402042i
$465$		0			0
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	32.0000			1.47762
$470$		0			0
$471$		0			0
$472$	18.0000	−	31.1769i	0.828517	−	1.43503i
$473$	−24.0000	+	41.5692i	−1.10352	+	1.91135i
$474$		0			0
$475$		0			0
$476$	−8.00000			−0.366679
$477$		0			0
$478$	−24.0000			−1.09773
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$	5.00000	−	8.66025i	0.227744	−	0.394464i
$483$		0			0
$484$	2.50000	+	4.33013i	0.113636	+	0.196824i
$485$	−20.0000			−0.908153
$486$		0			0
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$		0			0
$490$	−9.00000	+	15.5885i	−0.406579	+	0.704215i
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$		0			0
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	8.00000			0.356702			0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000			0.356702			0.178351	+	0.983967i	$0.442924\pi$
$504$		0			0
$505$	−36.0000			−1.60198
$506$		0			0
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$	11.0000			0.486136
$513$		0			0
$514$	26.0000			1.14681
$515$		0			0
$516$		0			0
$517$		0			0
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$		0			0
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	−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
$523$	44.0000			1.92399			0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000			1.92399			0.961993	+	0.273075i	$0.0880406\pi$
$524$	−2.00000	−	3.46410i	−0.0873704	−	0.151330i
$525$		0			0
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−12.0000			−0.521247
$531$		0			0
$532$		0			0
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$		0			0
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	12.0000	−	20.7846i	0.518321	−	0.897758i
$537$		0			0
$538$	−11.0000	−	19.0526i	−0.474244	−	0.821414i
$539$	−36.0000			−1.55063
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	−6.00000	−	10.3923i	−0.257722	−	0.446388i
$543$		0			0
$544$	−5.00000	+	8.66025i	−0.214373	+	0.371305i
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	0.820096	−	0.572226i	$-0.193920\pi$
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	−0.905610	+	0.424111i	$0.860587\pi$
$548$	6.00000			0.256307
$549$		0			0
$550$	−4.00000			−0.170561
$551$		0			0
$552$		0			0
$553$	16.0000	−	27.7128i	0.680389	−	1.17847i
$554$	−5.00000	+	8.66025i	−0.212430	+	0.367939i
$555$		0			0
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$	4.00000	+	6.92820i	0.169031	+	0.292770i
$561$		0			0
$562$	5.00000	−	8.66025i	0.210912	−	0.365311i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$	−12.0000			−0.504398
$567$		0			0
$568$		0			0
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	0.963849	+	0.266450i	$0.0858508\pi$
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	−0.251172	+	0.967943i	$0.580816\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$	12.0000	+	20.7846i	0.500870	+	0.867533i
$575$		0			0
$576$		0			0
$577$	−46.0000			−1.91501			−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−46.0000			−1.91501			−0.957503	+	0.288425i	$0.906868\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$		0			0
$580$	−10.0000	+	17.3205i	−0.415227	+	0.719195i
$581$	−8.00000	+	13.8564i	−0.331896	+	0.574861i
$582$		0			0
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$	6.00000			0.248282
$585$		0			0
$586$	−6.00000			−0.247858
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$		0			0
$589$		0			0
$590$	12.0000	−	20.7846i	0.494032	−	0.855689i
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$		0			0
$598$		0			0
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	0.0905757	+	0.995890i	$0.471129\pi$
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	−0.907754	+	0.419504i	$0.862204\pi$
$600$		0			0
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	−48.0000			−1.95633
$603$		0			0
$604$	−4.00000			−0.162758
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$		0			0
$609$		0			0
$610$	2.00000	+	3.46410i	0.0809776	+	0.140257i
$611$		0			0
$612$		0			0
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$	−24.0000	+	41.5692i	−0.966988	+	1.67487i
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	−0.555056	−	0.831813i	$-0.687303\pi$
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	0.997899	+	0.0647859i	$0.0206365\pi$
$618$		0			0
$619$	−12.0000	−	20.7846i	−0.482321	−	0.835404i	0.517473	−	0.855699i	$-0.326873\pi$
$619$	−12.0000	−	20.7846i	−0.482321	−	0.835404i	−0.999794	+	0.0202954i	$0.993539\pi$
$620$	8.00000			0.321288
$621$		0			0
$622$		0			0
$623$	4.00000	+	6.92820i	0.160257	+	0.277573i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	−9.00000	−	15.5885i	−0.359139	−	0.622047i
$629$	4.00000			0.159490
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−12.0000	−	20.7846i	−0.477334	−	0.826767i
$633$		0			0
$634$	−13.0000	+	22.5167i	−0.516296	+	0.894251i
$635$	−16.0000	+	27.7128i	−0.634941	+	1.09975i
$636$		0			0
$637$	−4.50000	−	7.79423i	−0.178296	−	0.308819i
$638$	40.0000			1.58362
$639$		0			0
$640$	−6.00000			−0.237171
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$	20.0000	−	34.6410i	0.788723	−	1.36611i	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	20.0000	−	34.6410i	0.788723	−	1.36611i	0.926750	−	0.375680i	$-0.122591\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		0			0
$649$	48.0000			1.88416
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$		0			0
$652$	4.00000	−	6.92820i	0.156652	−	0.271329i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$	6.00000			0.234261
$657$		0			0
$658$		0			0
$659$	14.0000	+	24.2487i	0.545363	+	0.944596i	0.998584	+	0.0531977i	$0.0169414\pi$
$659$	14.0000	+	24.2487i	0.545363	+	0.944596i	−0.453221	+	0.891398i	$0.649725\pi$
$660$		0			0
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	0.411636	+	0.911348i	$0.364957\pi$
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	−0.995069	+	0.0991864i	$0.968376\pi$
$662$	−8.00000	+	13.8564i	−0.310929	+	0.538545i
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	4.00000	+	6.92820i	0.154765	+	0.268060i
$669$		0			0
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$	−4.00000	+	6.92820i	−0.154418	+	0.267460i
$672$		0			0
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$	−18.0000			−0.693334
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	0.996209	−	0.0869952i	$-0.0277265\pi$
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	−0.573444	+	0.819244i	$0.694393\pi$
$678$		0			0
$679$	20.0000	−	34.6410i	0.767530	−	1.32940i
$680$	−6.00000	+	10.3923i	−0.230089	+	0.398527i
$681$		0			0
$682$	−8.00000	−	13.8564i	−0.306336	−	0.530589i
$683$	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
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$	−6.00000	+	10.3923i	−0.228748	+	0.396203i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	12.0000	+	20.7846i	0.456502	+	0.790684i	0.998773	−	0.0495194i	$-0.0157690\pi$
$691$	12.0000	+	20.7846i	0.456502	+	0.790684i	−0.542272	+	0.840203i	$0.682436\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$		0			0
$697$	−6.00000	+	10.3923i	−0.227266	+	0.393637i
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$		0			0
$704$	14.0000	+	24.2487i	0.527645	+	0.913908i
$705$		0			0
$706$	1.00000	−	1.73205i	0.0376355	−	0.0651866i
$707$	36.0000	−	62.3538i	1.35392	−	2.34506i
$708$		0			0
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$		0			0
$711$		0			0
$712$	6.00000			0.224860
$713$		0			0
$714$		0			0
$715$	−4.00000	+	6.92820i	−0.149592	+	0.259100i
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$		0			0
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$		0			0
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$		0			0
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	5.00000	−	8.66025i	0.185695	−	0.321634i
$726$		0			0
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	0.782267	−	0.622944i	$-0.214063\pi$
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	−0.930618	+	0.365991i	$0.880730\pi$
$728$	−12.0000			−0.444750
$729$		0			0
$730$	4.00000			0.148047
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$		0			0
$737$	32.0000			1.17874
$738$		0			0
$739$	32.0000			1.17714			0.588570	−	0.808447i	$-0.299691\pi$
$739$	32.0000			1.17714			0.588570	+	0.808447i	$0.299691\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	12.0000	−	20.7846i	0.440534	−	0.763027i
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	26.0000			0.951928
$747$		0			0
$748$	−8.00000			−0.292509
$749$	−24.0000	−	41.5692i	−0.876941	−	1.51891i
$750$		0			0
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$		0			0
$753$		0			0
$754$	5.00000	+	8.66025i	0.182089	+	0.315388i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−12.0000	−	20.7846i	−0.435860	−	0.754931i
$759$		0			0
$760$		0			0
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	−0.942306	−	0.334752i	$-0.891348\pi$
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	0.761057	+	0.648686i	$0.224681\pi$
$762$		0			0
$763$	−4.00000	−	6.92820i	−0.144810	−	0.250818i
$764$	8.00000			0.289430
$765$		0			0
$766$	−16.0000			−0.578103
$767$	6.00000	+	10.3923i	0.216647	+	0.375244i
$768$		0			0
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	−0.457938	−	0.888984i	$-0.651412\pi$
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	0.998852	−	0.0479061i	$-0.0152548\pi$
$770$	−16.0000	+	27.7128i	−0.576600	+	0.998700i
$771$		0			0
$772$	9.00000	+	15.5885i	0.323917	+	0.561041i
$773$	−10.0000			−0.359675			−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000			−0.359675			−0.179838	+	0.983696i	$0.557557\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	−15.0000	−	25.9808i	−0.538469	−	0.932655i
$777$		0			0
$778$	−11.0000	+	19.0526i	−0.394369	+	0.683067i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−9.00000			−0.321429
$785$	−18.0000	−	31.1769i	−0.642448	−	1.11275i
$786$		0			0
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	−0.426193	−	0.904632i	$-0.640145\pi$
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	0.996531	−	0.0832226i	$-0.0265213\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	−8.00000	−	13.8564i	−0.284627	−	0.492989i
$791$	−24.0000			−0.853342
$792$		0			0
$793$	−2.00000			−0.0710221
$794$	19.0000	+	32.9090i	0.674285	+	1.16790i
$795$		0			0
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	23.0000	−	39.8372i	0.814702	−	1.41110i	−0.0948400	−	0.995493i	$-0.530234\pi$
$797$	23.0000	−	39.8372i	0.814702	−	1.41110i	0.909542	−	0.415612i	$-0.136433\pi$
$798$		0			0
$799$		0			0
$800$	5.00000			0.176777
$801$		0			0
$802$	22.0000			0.776847
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$		0			0
$808$	−27.0000	−	46.7654i	−0.949857	−	1.64520i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	−20.0000	−	34.6410i	−0.701862	−	1.21566i
$813$		0			0
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$		0			0
$817$		0			0
$818$	−34.0000			−1.18878
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$		0			0
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$	24.0000	+	41.5692i	0.835067	+	1.44638i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	4.00000	+	6.92820i	0.138842	+	0.240481i
$831$		0			0
$832$	−3.50000	+	6.06218i	−0.121341	+	0.210168i
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$		0			0
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$		0			0
$837$		0			0
$838$	4.00000			0.138178
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$		0			0
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	−2.00000			−0.0688021
$846$		0			0
$847$	−20.0000			−0.687208
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	1.00000	−	1.73205i	0.0342997	−	0.0594089i
$851$		0			0
$852$		0			0
$853$	−15.0000	−	25.9808i	−0.513590	−	0.889564i	−0.999876	−	0.0157644i	$-0.994982\pi$
$853$	−15.0000	−	25.9808i	−0.513590	−	0.889564i	0.486286	−	0.873800i	$-0.338351\pi$
$854$	−8.00000			−0.273754
$855$		0			0
$856$	−36.0000			−1.23045
$857$	−23.0000	−	39.8372i	−0.785665	−	1.36081i	−0.928601	−	0.371080i	$-0.878988\pi$
$857$	−23.0000	−	39.8372i	−0.785665	−	1.36081i	0.142936	−	0.989732i	$-0.454346\pi$
$858$		0			0
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	−0.196887	−	0.980426i	$-0.563083\pi$
$859$	22.0000	−	38.1051i	0.750630	−	1.30013i	0.947518	−	0.319704i	$-0.103583\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$		0			0
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$	12.0000			0.408012
$866$	17.0000	+	29.4449i	0.577684	+	1.00058i
$867$		0			0
$868$	−8.00000	+	13.8564i	−0.271538	+	0.470317i
$869$	16.0000	−	27.7128i	0.542763	−	0.940093i
$870$		0			0
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	−6.00000			−0.203186
$873$		0			0
$874$		0			0
$875$	24.0000	+	41.5692i	0.811348	+	1.40530i
$876$		0			0
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$	16.0000	−	27.7128i	0.539974	−	0.935262i
$879$		0			0
$880$	4.00000	+	6.92820i	0.134840	+	0.233550i
$881$	−58.0000			−1.95407			−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000			−1.95407			−0.977035	+	0.213080i	$0.931651\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$		0			0
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$	−32.0000	−	55.4256i	−1.07325	−	1.85892i
$890$	4.00000			0.134080
$891$		0			0
$892$	−4.00000			−0.133930
$893$		0			0
$894$		0			0
$895$	−4.00000	+	6.92820i	−0.133705	+	0.231584i
$896$	6.00000	−	10.3923i	0.200446	−	0.347183i
$897$		0			0
$898$	−11.0000	−	19.0526i	−0.367075	−	0.635792i
$899$	40.0000			1.33407
$900$		0			0
$901$	12.0000			0.399778
$902$	12.0000	+	20.7846i	0.399556	+	0.692052i
$903$		0			0
$904$	−9.00000	+	15.5885i	−0.299336	+	0.518464i
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$		0			0
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	−20.0000			−0.663723
$909$		0			0
$910$	−8.00000			−0.265197
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	−0.979922	−	0.199380i	$-0.936107\pi$
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	0.317293	−	0.948328i	$-0.397226\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$		0			0
$916$	−5.00000	−	8.66025i	−0.165205	−	0.286143i
$917$	16.0000			0.528367
$918$		0			0
$919$	−48.0000			−1.58337			−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000			−1.58337			−0.791687	+	0.610927i	$0.790797\pi$
$920$		0			0
$921$		0			0
$922$	19.0000	−	32.9090i	0.625732	−	1.08380i
$923$		0			0
$924$		0			0
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	−4.00000			−0.131448
$927$		0			0
$928$	−50.0000			−1.64133
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$		0			0
$932$	7.00000	−	12.1244i	0.229293	−	0.397146i
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	−16.0000			−0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	16.0000	+	27.7128i	0.522419	+	0.904855i
$939$		0			0
$940$		0			0
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$		0			0
$943$		0			0
$944$	12.0000			0.390567
$945$		0			0
$946$	−48.0000			−1.56061
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.680367	−	0.732872i	$-0.738179\pi$
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.294502	−	0.955651i	$-0.595154\pi$
$948$		0			0
$949$	−1.00000	+	1.73205i	−0.0324614	+	0.0562247i
$950$		0			0
$951$		0			0
$952$	−12.0000	−	20.7846i	−0.388922	−	0.673633i
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$		0			0
$955$	16.0000			0.517748
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−12.0000	+	20.7846i	−0.387500	+	0.671170i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	2.00000			0.0644826
$963$		0			0
$964$	−10.0000			−0.322078
$965$	18.0000	+	31.1769i	0.579441	+	1.00362i
$966$		0			0
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	−0.0570251	−	0.998373i	$-0.518161\pi$
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	0.893129	−	0.449801i	$-0.148505\pi$
$968$	−7.50000	+	12.9904i	−0.241059	+	0.417527i
$969$		0			0
$970$	−10.0000	−	17.3205i	−0.321081	−	0.556128i
$971$	60.0000			1.92549			0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000			1.92549			0.962746	+	0.270408i	$0.0871586\pi$
$972$		0			0
$973$	−48.0000			−1.53881
$974$	6.00000	+	10.3923i	0.192252	+	0.332991i
$975$		0			0
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	4.00000	+	6.92820i	0.127841	+	0.221426i
$980$	18.0000			0.574989
$981$		0			0
$982$	−12.0000			−0.382935
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	0.964939	−	0.262474i	$-0.0845384\pi$
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	−0.709779	+	0.704425i	$0.751205\pi$
$984$		0			0
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$	−10.0000	+	17.3205i	−0.318465	+	0.551597i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$		0			0
$994$		0			0
$995$	8.00000	−	13.8564i	0.253617	−	0.439278i
$996$		0			0
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$	24.0000			0.759707
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.d.352.1		2
3.2	odd	2		1053.2.e.b.352.1		2
9.2	odd	6		1053.2.e.b.703.1		2
9.4	even	3		117.2.a.a.1.1		1
9.5	odd	6		39.2.a.a.1.1	✓	1
9.7	even	3	inner	1053.2.e.d.703.1		2
36.23	even	6		624.2.a.i.1.1		1
36.31	odd	6		1872.2.a.h.1.1		1
45.4	even	6		2925.2.a.p.1.1		1
45.13	odd	12		2925.2.c.e.2224.2		2
45.14	odd	6		975.2.a.f.1.1		1
45.22	odd	12		2925.2.c.e.2224.1		2
45.23	even	12		975.2.c.f.274.1		2
45.32	even	12		975.2.c.f.274.2		2
63.13	odd	6		5733.2.a.e.1.1		1
63.41	even	6		1911.2.a.f.1.1		1
72.5	odd	6		2496.2.a.q.1.1		1
72.13	even	6		7488.2.a.bl.1.1		1
72.59	even	6		2496.2.a.e.1.1		1
72.67	odd	6		7488.2.a.by.1.1		1
99.32	even	6		4719.2.a.c.1.1		1
117.5	even	12		507.2.b.a.337.1		2
117.23	odd	6		507.2.e.b.22.1		2
117.31	odd	12		1521.2.b.b.1351.2		2
117.32	even	12		507.2.j.e.361.1		4
117.41	even	12		507.2.j.e.316.2		4
117.50	even	12		507.2.j.e.316.1		4
117.59	even	12		507.2.j.e.361.2		4
117.68	odd	6		507.2.e.a.22.1		2
117.77	odd	6		507.2.a.a.1.1		1
117.86	even	12		507.2.b.a.337.2		2
117.95	odd	6		507.2.e.b.484.1		2
117.103	even	6		1521.2.a.e.1.1		1
117.112	odd	12		1521.2.b.b.1351.1		2
117.113	odd	6		507.2.e.a.484.1		2
468.311	even	6		8112.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.a.1.1	✓	1	9.5	odd	6
117.2.a.a.1.1		1	9.4	even	3
507.2.a.a.1.1		1	117.77	odd	6
507.2.b.a.337.1		2	117.5	even	12
507.2.b.a.337.2		2	117.86	even	12
507.2.e.a.22.1		2	117.68	odd	6
507.2.e.a.484.1		2	117.113	odd	6
507.2.e.b.22.1		2	117.23	odd	6
507.2.e.b.484.1		2	117.95	odd	6
507.2.j.e.316.1		4	117.50	even	12
507.2.j.e.316.2		4	117.41	even	12
507.2.j.e.361.1		4	117.32	even	12
507.2.j.e.361.2		4	117.59	even	12
624.2.a.i.1.1		1	36.23	even	6
975.2.a.f.1.1		1	45.14	odd	6
975.2.c.f.274.1		2	45.23	even	12
975.2.c.f.274.2		2	45.32	even	12
1053.2.e.b.352.1		2	3.2	odd	2
1053.2.e.b.703.1		2	9.2	odd	6
1053.2.e.d.352.1		2	1.1	even	1	trivial
1053.2.e.d.703.1		2	9.7	even	3	inner
1521.2.a.e.1.1		1	117.103	even	6
1521.2.b.b.1351.1		2	117.112	odd	12
1521.2.b.b.1351.2		2	117.31	odd	12
1872.2.a.h.1.1		1	36.31	odd	6
1911.2.a.f.1.1		1	63.41	even	6
2496.2.a.e.1.1		1	72.59	even	6
2496.2.a.q.1.1		1	72.5	odd	6
2925.2.a.p.1.1		1	45.4	even	6
2925.2.c.e.2224.1		2	45.22	odd	12
2925.2.c.e.2224.2		2	45.13	odd	12
4719.2.a.c.1.1		1	99.32	even	6
5733.2.a.e.1.1		1	63.13	odd	6
7488.2.a.bl.1.1		1	72.13	even	6
7488.2.a.by.1.1		1	72.67	odd	6
8112.2.a.s.1.1		1	468.311	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +2.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{26} +4.00000 q^{28} +(-5.00000 - 8.66025i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 - 1.73205i) q^{34} +8.00000 q^{35} -2.00000 q^{37} +(3.00000 - 5.19615i) q^{40} +(3.00000 - 5.19615i) q^{41} +(6.00000 + 10.3923i) q^{43} +4.00000 q^{44} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(6.00000 + 10.3923i) q^{56} +(5.00000 - 8.66025i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} +2.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-8.00000 + 13.8564i) q^{77} +(-4.00000 - 6.92820i) q^{79} +2.00000 q^{80} +6.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(-6.00000 + 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{88} +2.00000 q^{89} -4.00000 q^{91} +(-5.00000 - 8.66025i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 2 q^{5} + 4 q^{7} + 6 q^{8} + 4 q^{10} + 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 4 q^{17} - 2 q^{20} - 4 q^{22} + q^{25} - 2 q^{26} + 8 q^{28} - 10 q^{29} - 4 q^{31} + 5 q^{32}+ \cdots - 18 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 2 * q^5 + 4 * q^7 + 6 * q^8 + 4 * q^10 + 4 * q^11 - q^13 - 4 * q^14 + q^16 - 4 * q^17 - 2 * q^20 - 4 * q^22 + q^25 - 2 * q^26 + 8 * q^28 - 10 * q^29 - 4 * q^31 + 5 * q^32 - 2 * q^34 + 16 * q^35 - 4 * q^37 + 6 * q^40 + 6 * q^41 + 12 * q^43 + 8 * q^44 - 9 * q^49 - q^50 + q^52 - 12 * q^53 + 16 * q^55 + 12 * q^56 + 10 * q^58 + 12 * q^59 + 2 * q^61 - 8 * q^62 + 14 * q^64 + 2 * q^65 + 8 * q^67 - 2 * q^68 + 8 * q^70 + 4 * q^73 - 2 * q^74 - 16 * q^77 - 8 * q^79 + 4 * q^80 + 12 * q^82 + 4 * q^83 - 4 * q^85 - 12 * q^86 + 12 * q^88 + 4 * q^89 - 8 * q^91 - 10 * q^97 - 18 * q^98

Introduction

L-functions

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