LMFDB - Embedded newform 1782.2.e.v.1189.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1782,2,Mod(595,1782)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1782, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1782.595");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1782 = 2 \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1782.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.2293416402$
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 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1189.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1782.1189
Dual form			1782.2.e.v.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(3.00000 + 5.19615i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{26} -4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +8.00000 q^{35} +6.00000 q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{43} +1.00000 q^{44} +4.00000 q^{46} +(-6.00000 + 10.3923i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.00000 - 5.19615i) q^{52} -2.00000 q^{53} -2.00000 q^{55} +(-2.00000 + 3.46410i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(7.00000 - 12.1244i) q^{61} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} +12.0000 q^{71} -6.00000 q^{73} +(3.00000 - 5.19615i) q^{74} +(-2.00000 - 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +(2.00000 - 3.46410i) q^{79} -2.00000 q^{80} -6.00000 q^{82} +(2.00000 - 3.46410i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(2.00000 + 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} -10.0000 q^{89} +24.0000 q^{91} +(2.00000 - 3.46410i) q^{92} +(6.00000 + 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{95} +(7.00000 - 12.1244i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 2 * q^5 + 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8} + 4 q^{10} - q^{11} + 6 q^{13} - 4 q^{14} - q^{16} - 4 q^{17} + 8 q^{19} + 2 q^{20} + q^{22} + 4 q^{23} + q^{25} + 12 q^{26} - 8 q^{28} + 6 q^{29} + q^{32} - 2 q^{34} + 16 q^{35} + 12 q^{37} + 4 q^{38} - 2 q^{40} - 6 q^{41} - 4 q^{43} + 2 q^{44} + 8 q^{46} - 12 q^{47} - 9 q^{49} - q^{50} + 6 q^{52} - 4 q^{53} - 4 q^{55} - 4 q^{56} - 6 q^{58} + 12 q^{59} + 14 q^{61} + 2 q^{64} - 12 q^{65} - 4 q^{67} + 2 q^{68} + 8 q^{70} + 24 q^{71} - 12 q^{73} + 6 q^{74} - 4 q^{76} + 4 q^{77} + 4 q^{79} - 4 q^{80} - 12 q^{82} + 4 q^{83} - 4 q^{85} + 4 q^{86} + q^{88} - 20 q^{89} + 48 q^{91} + 4 q^{92} + 12 q^{94} + 8 q^{95} + 14 q^{97} - 18 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 2 * q^5 + 4 * q^7 - 2 * q^8 + 4 * q^10 - q^11 + 6 * q^13 - 4 * q^14 - q^16 - 4 * q^17 + 8 * q^19 + 2 * q^20 + q^22 + 4 * q^23 + q^25 + 12 * q^26 - 8 * q^28 + 6 * q^29 + q^32 - 2 * q^34 + 16 * q^35 + 12 * q^37 + 4 * q^38 - 2 * q^40 - 6 * q^41 - 4 * q^43 + 2 * q^44 + 8 * q^46 - 12 * q^47 - 9 * q^49 - q^50 + 6 * q^52 - 4 * q^53 - 4 * q^55 - 4 * q^56 - 6 * q^58 + 12 * q^59 + 14 * q^61 + 2 * q^64 - 12 * q^65 - 4 * q^67 + 2 * q^68 + 8 * q^70 + 24 * q^71 - 12 * q^73 + 6 * q^74 - 4 * q^76 + 4 * q^77 + 4 * q^79 - 4 * q^80 - 12 * q^82 + 4 * q^83 - 4 * q^85 + 4 * q^86 + q^88 - 20 * q^89 + 48 * q^91 + 4 * q^92 + 12 * q^94 + 8 * q^95 + 14 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1782\mathbb{Z}\right)^\times$.

$n$	$1135$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.00000			0.632456
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	0.896410	+	0.443227i	$0.146166\pi$
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	−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
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	6.00000			1.17670
$27$		0			0
$28$	−4.00000			−0.755929
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	8.00000			1.35225
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$		0			0
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$	1.00000			0.150756
$45$		0			0
$46$	4.00000			0.589768
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$		0			0
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$	4.00000	−	6.92820i	0.478091	−	0.828079i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$		0			0
$76$	−2.00000	−	3.46410i	−0.229416	−	0.397360i
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−2.00000			−0.223607
$81$		0			0
$82$	−6.00000			−0.662589
$83$	2.00000	−	3.46410i	0.219529	−	0.380235i	−0.735135	−	0.677920i	$-0.762881\pi$
$83$	2.00000	−	3.46410i	0.219529	−	0.380235i	0.954664	+	0.297686i	$0.0962148\pi$
$84$		0			0
$85$	−2.00000	−	3.46410i	−0.216930	−	0.375735i
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	24.0000			2.51588
$92$	2.00000	−	3.46410i	0.208514	−	0.361158i
$93$		0			0
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	−1.00000			−0.100000
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	−1.00000	+	1.73205i	−0.0971286	+	0.168232i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	2.00000	+	3.46410i	0.188982	+	0.327327i
$113$	1.00000	+	1.73205i	0.0940721	+	0.162938i	0.909221	−	0.416314i	$-0.136678\pi$
$113$	1.00000	+	1.73205i	0.0940721	+	0.162938i	−0.815149	+	0.579252i	$0.803345\pi$
$114$		0			0
$115$	−4.00000	+	6.92820i	−0.373002	+	0.646058i
$116$	−6.00000			−0.557086
$117$		0			0
$118$	12.0000			1.10469
$119$	−4.00000	+	6.92820i	−0.366679	+	0.635107i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$	8.00000	−	13.8564i	0.693688	−	1.20150i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	2.00000			0.171499
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−6.00000			−0.501745
$144$		0			0
$145$	12.0000			0.996546
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$		0			0
$148$	−3.00000	−	5.19615i	−0.246598	−	0.427121i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	0.773099	+	0.634285i	$0.218706\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$	4.00000			0.322329
$155$		0			0
$156$		0			0
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$		0			0
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	16.0000			1.26098
$162$		0			0
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	4.00000			0.304997
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$		0			0
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	12.0000	−	20.7846i	0.889499	−	1.54066i
$183$		0			0
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	12.0000			0.875190
$189$		0			0
$190$	8.00000			0.580381
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−7.00000	−	12.1244i	−0.492518	−	0.853067i
$203$	−12.0000	−	20.7846i	−0.842235	−	1.45879i
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$		0			0
$208$	−6.00000			−0.416025
$209$	−2.00000	+	3.46410i	−0.138343	+	0.239617i
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$		0			0
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$	−3.00000	+	5.19615i	−0.203186	+	0.351928i
$219$		0			0
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	2.00000			0.133038
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$	4.00000	+	6.92820i	0.263752	+	0.456832i
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		0			0
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$	4.00000	+	6.92820i	0.258738	+	0.448148i	0.965904	−	0.258900i	$-0.0833599\pi$
$239$	4.00000	+	6.92820i	0.258738	+	0.448148i	−0.707166	+	0.707048i	$0.750027\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−1.00000			−0.0642824
$243$		0			0
$244$	−14.0000			−0.896258
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$		0			0
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$		0			0
$259$	12.0000	−	20.7846i	0.745644	−	1.29149i
$260$	12.0000			0.744208
$261$		0			0
$262$	4.00000			0.247121
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	−2.00000	−	3.46410i	−0.122859	−	0.212798i
$266$	−8.00000	−	13.8564i	−0.490511	−	0.849591i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−26.0000			−1.58525			−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000			−1.58525			−0.792624	+	0.609711i	$0.791286\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	−1.00000	−	1.73205i	−0.0604122	−	0.104637i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	4.00000			0.239904
$279$		0			0
$280$	−8.00000			−0.478091
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$	−24.0000			−1.41668
$288$		0			0
$289$	−13.0000			−0.764706
$290$	6.00000	−	10.3923i	0.352332	−	0.610257i
$291$		0			0
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	11.0000	+	19.0526i	0.642627	+	1.11306i	0.984844	+	0.173442i	$0.0554888\pi$
$293$	11.0000	+	19.0526i	0.642627	+	1.11306i	−0.342217	+	0.939621i	$0.611178\pi$
$294$		0			0
$295$	−12.0000	+	20.7846i	−0.698667	+	1.21013i
$296$	−6.00000			−0.348743
$297$		0			0
$298$	−10.0000			−0.579284
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$		0			0
$301$	8.00000	+	13.8564i	0.461112	+	0.798670i
$302$	2.00000	+	3.46410i	0.115087	+	0.199337i
$303$		0			0
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	28.0000			1.60328
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$		0			0
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	0.917143	−	0.398559i	$-0.130489\pi$
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	−0.803733	+	0.594990i	$0.797156\pi$
$312$		0			0
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	0.220006	+	0.975499i	$0.429392\pi$
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	−0.954810	+	0.297218i	$0.903941\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$		0			0
$322$	8.00000	−	13.8564i	0.445823	−	0.772187i
$323$	−8.00000			−0.445132
$324$		0			0
$325$	6.00000			0.332820
$326$	−10.0000	+	17.3205i	−0.553849	+	0.959294i
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	24.0000	+	41.5692i	1.32316	+	2.29179i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	−4.00000			−0.219529
$333$		0			0
$334$		0			0
$335$	4.00000	−	6.92820i	0.218543	−	0.378528i
$336$		0			0
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	0.509676	−	0.860366i	$-0.329765\pi$
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	−0.999937	+	0.0112091i	$0.996432\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$		0			0
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$		0			0
$342$		0			0
$343$	−8.00000			−0.431959
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$		0			0
$346$	5.00000	+	8.66025i	0.268802	+	0.465578i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		0			0
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	−1.00000			−0.0533002
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	12.0000	+	20.7846i	0.636894	+	1.10313i
$356$	5.00000	+	8.66025i	0.264999	+	0.458993i
$357$		0			0
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	−12.0000	−	20.7846i	−0.628971	−	1.08941i
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$		0			0
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	12.0000			0.623850
$371$	−4.00000	+	6.92820i	−0.207670	+	0.359694i
$372$		0			0
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$		0			0
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	36.0000			1.85409
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	0.810394	−	0.585886i	$-0.199253\pi$
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	−0.912589	+	0.408879i	$0.865920\pi$
$384$		0			0
$385$	−4.00000	+	6.92820i	−0.203859	+	0.353094i
$386$	−10.0000			−0.508987
$387$		0			0
$388$	−14.0000			−0.710742
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	−4.00000	−	6.92820i	−0.202289	−	0.350374i
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$		0			0
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$	8.00000			0.402524
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	−8.00000	+	13.8564i	−0.401004	+	0.694559i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.747927	−	0.663781i	$-0.768951\pi$
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.200888	−	0.979614i	$-0.564383\pi$
$402$		0			0
$403$		0			0
$404$	−14.0000			−0.696526
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$	−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
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	4.00000			0.194717
$423$		0			0
$424$	2.00000			0.0971286
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	−28.0000	−	48.4974i	−1.35501	−	2.34695i
$428$	2.00000	+	3.46410i	0.0966736	+	0.167444i
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	8.00000	+	13.8564i	0.382692	+	0.662842i
$438$		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	$0.197097\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−12.0000			−0.570782
$443$	14.0000	−	24.2487i	0.665160	−	1.15209i	−0.314082	−	0.949396i	$-0.601697\pi$
$443$	14.0000	−	24.2487i	0.665160	−	1.15209i	0.979242	−	0.202695i	$-0.0649700\pi$
$444$		0			0
$445$	−10.0000	−	17.3205i	−0.474045	−	0.821071i
$446$		0			0
$447$		0			0
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	6.00000			0.282529
$452$	1.00000	−	1.73205i	0.0470360	−	0.0814688i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	24.0000	+	41.5692i	1.12514	+	1.94880i
$456$		0			0
$457$	−17.0000	+	29.4449i	−0.795226	+	1.37737i	0.127469	+	0.991843i	$0.459315\pi$
$457$	−17.0000	+	29.4449i	−0.795226	+	1.37737i	−0.922695	+	0.385530i	$0.874019\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$	8.00000			0.373002
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	−0.655696	−	0.755025i	$-0.727625\pi$
$461$	7.00000	−	12.1244i	0.326023	−	0.564688i	0.981719	+	0.190337i	$0.0609581\pi$
$462$		0			0
$463$	12.0000	+	20.7846i	0.557687	+	0.965943i	0.997689	+	0.0679458i	$0.0216445\pi$
$463$	12.0000	+	20.7846i	0.557687	+	0.965943i	−0.440002	+	0.897997i	$0.645022\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−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
$469$	−16.0000			−0.738811
$470$	−12.0000	+	20.7846i	−0.553519	+	0.958723i
$471$		0			0
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$		0			0
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	8.00000			0.366679
$477$		0			0
$478$	8.00000			0.365911
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	18.0000	+	31.1769i	0.820729	+	1.42154i
$482$	5.00000	+	8.66025i	0.227744	+	0.394464i
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	28.0000			1.27141
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−7.00000	+	12.1244i	−0.316875	+	0.548844i
$489$		0			0
$490$	−9.00000	−	15.5885i	−0.406579	−	0.704215i
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	−0.987181	−	0.159603i	$-0.948978\pi$
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	0.355370	−	0.934726i	$-0.384355\pi$
$492$		0			0
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	24.0000			1.07981
$495$		0			0
$496$		0			0
$497$	24.0000	−	41.5692i	1.07655	−	1.86463i
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	2.00000	−	3.46410i	0.0892644	−	0.154610i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	28.0000			1.24598
$506$	−2.00000	+	3.46410i	−0.0889108	+	0.153998i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	0.512331	−	0.858788i	$-0.328782\pi$
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	−0.999898	+	0.0142980i	$0.995449\pi$
$510$		0			0
$511$	−12.0000	+	20.7846i	−0.530849	+	0.919457i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	2.00000			0.0882162
$515$		0			0
$516$		0			0
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	−12.0000	−	20.7846i	−0.527250	−	0.913223i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$		0			0
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−4.00000			−0.173749
$531$		0			0
$532$	−16.0000			−0.693688
$533$	18.0000	−	31.1769i	0.779667	−	1.35042i
$534$		0			0
$535$	−4.00000	−	6.92820i	−0.172935	−	0.299532i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−13.0000	+	22.5167i	−0.560470	+	0.970762i
$539$	9.00000			0.387657
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	−6.00000	−	10.3923i	−0.257012	−	0.445157i
$546$		0			0
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	0.993028	−	0.117875i	$-0.0376081\pi$
$548$	−2.00000			−0.0854358
$549$		0			0
$550$	1.00000			0.0426401
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$		0			0
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	13.0000	+	22.5167i	0.552317	+	0.956641i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$	−4.00000	+	6.92820i	−0.169031	+	0.292770i
$561$		0			0
$562$	11.0000	+	19.0526i	0.464007	+	0.803684i
$563$	−10.0000	−	17.3205i	−0.421450	−	0.729972i	0.574632	−	0.818412i	$-0.305145\pi$
$563$	−10.0000	−	17.3205i	−0.421450	−	0.729972i	−0.996082	+	0.0884397i	$0.971812\pi$
$564$		0			0
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$		0			0
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$		0			0
$574$	−12.0000	+	20.7846i	−0.500870	+	0.867533i
$575$	4.00000			0.166812
$576$		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
$580$	−6.00000	−	10.3923i	−0.249136	−	0.431517i
$581$	−8.00000	−	13.8564i	−0.331896	−	0.574861i
$582$		0			0
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$	6.00000			0.248282
$585$		0			0
$586$	22.0000			0.908812
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	0.208212	+	0.978084i	$0.433236\pi$
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	−0.951151	+	0.308725i	$0.900098\pi$
$588$		0			0
$589$		0			0
$590$	12.0000	+	20.7846i	0.494032	+	0.855689i
$591$		0			0
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$		0			0
$598$	12.0000	+	20.7846i	0.490716	+	0.849946i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$		0			0
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$	16.0000			0.652111
$603$		0			0
$604$	4.00000			0.162758
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−14.0000	−	24.2487i	−0.568242	−	0.984225i	−0.996740	−	0.0806818i	$-0.974290\pi$
$607$	−14.0000	−	24.2487i	−0.568242	−	0.984225i	0.428497	−	0.903543i	$-0.359043\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$	14.0000	−	24.2487i	0.566843	−	0.981802i
$611$	−72.0000			−2.91281
$612$		0			0
$613$	−6.00000			−0.242338			−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000			−0.242338			−0.121169	+	0.992632i	$0.538664\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	−2.00000	−	3.46410i	−0.0805823	−	0.139573i
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		0			0
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$		0			0
$621$		0			0
$622$	4.00000			0.160385
$623$	−20.0000	+	34.6410i	−0.801283	+	1.38786i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	12.0000	+	20.7846i	0.476205	+	0.824812i
$636$		0			0
$637$	27.0000	−	46.7654i	1.06978	−	1.85291i
$638$	6.00000			0.237542
$639$		0			0
$640$	2.00000			0.0790569
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	−0.0690201	−	0.997615i	$-0.521987\pi$
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	0.898470	−	0.439034i	$-0.144679\pi$
$642$		0			0
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	0.998122	+	0.0612510i	$0.0195090\pi$
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	−0.446016	+	0.895025i	$0.647158\pi$
$644$	−8.00000	−	13.8564i	−0.315244	−	0.546019i
$645$		0			0
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	3.00000	−	5.19615i	0.117670	−	0.203810i
$651$		0			0
$652$	10.0000	+	17.3205i	0.391630	+	0.678323i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	−4.00000	+	6.92820i	−0.156293	+	0.270707i
$656$	6.00000			0.234261
$657$		0			0
$658$	48.0000			1.87123
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	9.00000	+	15.5885i	0.350059	+	0.606321i	0.986260	−	0.165203i	$-0.0528281\pi$
$661$	9.00000	+	15.5885i	0.350059	+	0.606321i	−0.636200	+	0.771524i	$0.719495\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	−2.00000	+	3.46410i	−0.0776151	+	0.134433i
$665$	32.0000			1.24091
$666$		0			0
$667$	24.0000			0.929284
$668$		0			0
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	7.00000	+	12.1244i	0.270232	+	0.468056i
$672$		0			0
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	−18.0000			−0.693334
$675$		0			0
$676$	23.0000			0.884615
$677$	23.0000	−	39.8372i	0.883962	−	1.53107i	0.0370628	−	0.999313i	$-0.488200\pi$
$677$	23.0000	−	39.8372i	0.883962	−	1.53107i	0.846899	−	0.531754i	$-0.178467\pi$
$678$		0			0
$679$	−28.0000	−	48.4974i	−1.07454	−	1.86116i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$		0			0
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	−4.00000			−0.151838
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	−3.00000	−	5.19615i	−0.113552	−	0.196677i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	24.0000			0.905177
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	−28.0000	−	48.4974i	−1.05305	−	1.82393i
$708$		0			0
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	−0.646055	−	0.763291i	$-0.723582\pi$
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	0.984057	+	0.177854i	$0.0569156\pi$
$710$	24.0000			0.900704
$711$		0			0
$712$	10.0000			0.374766
$713$		0			0
$714$		0			0
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$	10.0000	+	17.3205i	0.373718	+	0.647298i
$717$		0			0
$718$		0			0
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$		0			0
$721$		0			0
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		0			0
$727$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$727$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$728$	−24.0000			−0.889499
$729$		0			0
$730$	−12.0000			−0.444140
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−8.00000	−	13.8564i	−0.295285	−	0.511449i
$735$		0			0
$736$	−2.00000	+	3.46410i	−0.0737210	+	0.127688i
$737$	4.00000			0.147342
$738$		0			0
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$		0			0
$742$	4.00000	+	6.92820i	0.146845	+	0.254342i
$743$	−16.0000	−	27.7128i	−0.586983	−	1.01668i	−0.994625	−	0.103543i	$-0.966982\pi$
$743$	−16.0000	−	27.7128i	−0.586983	−	1.01668i	0.407642	−	0.913142i	$-0.366351\pi$
$744$		0			0
$745$	10.0000	−	17.3205i	0.366372	−	0.634574i
$746$	14.0000			0.512576
$747$		0			0
$748$	−2.00000			−0.0731272
$749$	−8.00000	+	13.8564i	−0.292314	+	0.506302i
$750$		0			0
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$		0			0
$754$	18.0000	−	31.1769i	0.655521	−	1.13540i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$	−12.0000	+	20.7846i	−0.434429	+	0.752453i
$764$	12.0000			0.434145
$765$		0			0
$766$	−4.00000			−0.144526
$767$	−36.0000	+	62.3538i	−1.29988	+	2.25147i
$768$		0			0
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$	4.00000	+	6.92820i	0.144150	+	0.249675i
$771$		0			0
$772$	−5.00000	+	8.66025i	−0.179954	+	0.311689i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$		0			0
$776$	−7.00000	+	12.1244i	−0.251285	+	0.435239i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$	−8.00000			−0.286079
$783$		0			0
$784$	9.00000			0.321429
$785$	−10.0000	+	17.3205i	−0.356915	+	0.618195i
$786$		0			0
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	−1.00000	−	1.73205i	−0.0356235	−	0.0617018i
$789$		0			0
$790$	4.00000	−	6.92820i	0.142314	−	0.246494i
$791$	8.00000			0.284447
$792$		0			0
$793$	84.0000			2.98293
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−27.0000	−	46.7654i	−0.956389	−	1.65651i	−0.731157	−	0.682209i	$-0.761019\pi$
$797$	−27.0000	−	46.7654i	−0.956389	−	1.65651i	−0.225232	−	0.974305i	$-0.572314\pi$
$798$		0			0
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	1.00000			0.0353553
$801$		0			0
$802$	−38.0000			−1.34183
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	16.0000	+	27.7128i	0.563926	+	0.976748i
$806$		0			0
$807$		0			0
$808$	−7.00000	+	12.1244i	−0.246259	+	0.426533i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−12.0000	+	20.7846i	−0.421117	+	0.729397i
$813$		0			0
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−20.0000	−	34.6410i	−0.700569	−	1.21342i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	14.0000			0.489499
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	−0.882948	−	0.469471i	$-0.844445\pi$
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	0.848048	+	0.529920i	$0.177778\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$		0			0
$826$	24.0000	−	41.5692i	0.835067	−	1.44638i
$827$	52.0000			1.80822			0.904109	−	0.427303i	$-0.140536\pi$
$827$	52.0000			1.80822			0.904109	+	0.427303i	$0.140536\pi$
$828$		0			0
$829$	46.0000			1.59765			0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000			1.59765			0.798823	+	0.601566i	$0.205456\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	3.00000	+	5.19615i	0.104006	+	0.180144i
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$		0			0
$835$		0			0
$836$	4.00000			0.138343
$837$		0			0
$838$	−12.0000			−0.414533
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$		0			0
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	−46.0000			−1.58245
$846$		0			0
$847$	−4.00000			−0.137442
$848$	1.00000	−	1.73205i	0.0343401	−	0.0594789i
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	3.00000	−	5.19615i	0.102718	−	0.177913i	−0.810086	−	0.586312i	$-0.800579\pi$
$853$	3.00000	−	5.19615i	0.102718	−	0.177913i	0.912804	+	0.408399i	$0.133913\pi$
$854$	−56.0000			−1.91628
$855$		0			0
$856$	4.00000			0.136717
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	−0.553915	−	0.832573i	$-0.686867\pi$
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	0.997987	+	0.0634184i	$0.0202003\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$		0			0
$862$		0			0
$863$	−20.0000			−0.680808			−0.340404	−	0.940279i	$-0.610564\pi$
$863$	−20.0000			−0.680808			−0.340404	+	0.940279i	$0.610564\pi$
$864$		0			0
$865$	−20.0000			−0.680020
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$		0			0
$868$		0			0
$869$	2.00000	+	3.46410i	0.0678454	+	0.117512i
$870$		0			0
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	6.00000			0.203186
$873$		0			0
$874$	16.0000			0.541208
$875$	24.0000	−	41.5692i	0.811348	−	1.40530i
$876$		0			0
$877$	−21.0000	−	36.3731i	−0.709120	−	1.22823i	−0.965184	−	0.261571i	$-0.915759\pi$
$877$	−21.0000	−	36.3731i	−0.709120	−	1.22823i	0.256064	−	0.966660i	$-0.417574\pi$
$878$	2.00000	+	3.46410i	0.0674967	+	0.116908i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	−14.0000	−	24.2487i	−0.470339	−	0.814651i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	24.0000	−	41.5692i	0.804934	−	1.39419i
$890$	−20.0000			−0.670402
$891$		0			0
$892$		0			0
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$		0			0
$895$	−20.0000	−	34.6410i	−0.668526	−	1.15792i
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$		0			0
$898$	11.0000	−	19.0526i	0.367075	−	0.635792i
$899$		0			0
$900$		0			0
$901$	4.00000			0.133259
$902$	3.00000	−	5.19615i	0.0998891	−	0.173013i
$903$		0			0
$904$	−1.00000	−	1.73205i	−0.0332595	−	0.0576072i
$905$	−2.00000	−	3.46410i	−0.0664822	−	0.115151i
$906$		0			0
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	48.0000			1.59118
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	−0.749347	−	0.662177i	$-0.769633\pi$
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	0.948136	+	0.317865i	$0.102966\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	17.0000	+	29.4449i	0.562310	+	0.973950i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	16.0000			0.528367
$918$		0			0
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$		0			0
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$	36.0000	+	62.3538i	1.18495	+	2.05240i
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	24.0000			0.788689
$927$		0			0
$928$	6.00000			0.196960
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$		0			0
$931$	−18.0000	−	31.1769i	−0.589926	−	1.02178i
$932$	5.00000	+	8.66025i	0.163780	+	0.283676i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	4.00000			0.130814
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$		0			0
$940$	12.0000	+	20.7846i	0.391397	+	0.677919i
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$		0			0
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−4.00000			−0.130051
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$		0			0
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$		0			0
$952$	4.00000	−	6.92820i	0.129641	−	0.224544i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−24.0000			−0.776622
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$		0			0
$958$		0			0
$959$	−4.00000	−	6.92820i	−0.129167	−	0.223723i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	36.0000			1.16069
$963$		0			0
$964$	10.0000			0.322078
$965$	10.0000	−	17.3205i	0.321911	−	0.557567i
$966$		0			0
$967$	22.0000	+	38.1051i	0.707472	+	1.22538i	0.965792	+	0.259318i	$0.0834979\pi$
$967$	22.0000	+	38.1051i	0.707472	+	1.22538i	−0.258320	+	0.966060i	$0.583169\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	14.0000	−	24.2487i	0.449513	−	0.778579i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$	−8.00000	+	13.8564i	−0.256337	+	0.443988i
$975$		0			0
$976$	7.00000	+	12.1244i	0.224065	+	0.388091i
$977$	13.0000	+	22.5167i	0.415907	+	0.720372i	0.995523	−	0.0945177i	$-0.0301309\pi$
$977$	13.0000	+	22.5167i	0.415907	+	0.720372i	−0.579616	+	0.814890i	$0.696798\pi$
$978$		0			0
$979$	5.00000	−	8.66025i	0.159801	−	0.276783i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−28.0000			−0.893516
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	2.00000	+	3.46410i	0.0637253	+	0.110375i
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	12.0000	−	20.7846i	0.381771	−	0.661247i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$		0			0
$993$		0			0
$994$	−24.0000	−	41.5692i	−0.761234	−	1.31850i
$995$	−16.0000	−	27.7128i	−0.507234	−	0.878555i
$996$		0			0
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	4.00000			0.126618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1782.2.e.v.1189.1		2
3.2	odd	2		1782.2.e.e.1189.1		2
9.2	odd	6		66.2.a.b.1.1	✓	1
9.4	even	3	inner	1782.2.e.v.595.1		2
9.5	odd	6		1782.2.e.e.595.1		2
9.7	even	3		198.2.a.a.1.1		1
36.7	odd	6		1584.2.a.f.1.1		1
36.11	even	6		528.2.a.j.1.1		1
45.2	even	12		1650.2.c.e.199.2		2
45.7	odd	12		4950.2.c.p.199.1		2
45.29	odd	6		1650.2.a.k.1.1		1
45.34	even	6		4950.2.a.bu.1.1		1
45.38	even	12		1650.2.c.e.199.1		2
45.43	odd	12		4950.2.c.p.199.2		2
63.20	even	6		3234.2.a.t.1.1		1
63.34	odd	6		9702.2.a.x.1.1		1
72.11	even	6		2112.2.a.e.1.1		1
72.29	odd	6		2112.2.a.r.1.1		1
72.43	odd	6		6336.2.a.cj.1.1		1
72.61	even	6		6336.2.a.bw.1.1		1
99.2	even	30		726.2.e.o.565.1		4
99.20	odd	30		726.2.e.g.565.1		4
99.29	even	30		726.2.e.o.511.1		4
99.38	odd	30		726.2.e.g.487.1		4
99.43	odd	6		2178.2.a.g.1.1		1
99.47	odd	30		726.2.e.g.493.1		4
99.65	even	6		726.2.a.c.1.1		1
99.74	even	30		726.2.e.o.493.1		4
99.83	even	30		726.2.e.o.487.1		4
99.92	odd	30		726.2.e.g.511.1		4
396.263	odd	6		5808.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.b.1.1	✓	1	9.2	odd	6
198.2.a.a.1.1		1	9.7	even	3
528.2.a.j.1.1		1	36.11	even	6
726.2.a.c.1.1		1	99.65	even	6
726.2.e.g.487.1		4	99.38	odd	30
726.2.e.g.493.1		4	99.47	odd	30
726.2.e.g.511.1		4	99.92	odd	30
726.2.e.g.565.1		4	99.20	odd	30
726.2.e.o.487.1		4	99.83	even	30
726.2.e.o.493.1		4	99.74	even	30
726.2.e.o.511.1		4	99.29	even	30
726.2.e.o.565.1		4	99.2	even	30
1584.2.a.f.1.1		1	36.7	odd	6
1650.2.a.k.1.1		1	45.29	odd	6
1650.2.c.e.199.1		2	45.38	even	12
1650.2.c.e.199.2		2	45.2	even	12
1782.2.e.e.595.1		2	9.5	odd	6
1782.2.e.e.1189.1		2	3.2	odd	2
1782.2.e.v.595.1		2	9.4	even	3	inner
1782.2.e.v.1189.1		2	1.1	even	1	trivial
2112.2.a.e.1.1		1	72.11	even	6
2112.2.a.r.1.1		1	72.29	odd	6
2178.2.a.g.1.1		1	99.43	odd	6
3234.2.a.t.1.1		1	63.20	even	6
4950.2.a.bu.1.1		1	45.34	even	6
4950.2.c.p.199.1		2	45.7	odd	12
4950.2.c.p.199.2		2	45.43	odd	12
5808.2.a.bc.1.1		1	396.263	odd	6
6336.2.a.bw.1.1		1	72.61	even	6
6336.2.a.cj.1.1		1	72.43	odd	6
9702.2.a.x.1.1		1	63.34	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:	\( N \)	\(=\)	\( 1782 = 2 \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1782.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(3.00000 + 5.19615i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{26} -4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +8.00000 q^{35} +6.00000 q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{43} +1.00000 q^{44} +4.00000 q^{46} +(-6.00000 + 10.3923i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.00000 - 5.19615i) q^{52} -2.00000 q^{53} -2.00000 q^{55} +(-2.00000 + 3.46410i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(7.00000 - 12.1244i) q^{61} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} +12.0000 q^{71} -6.00000 q^{73} +(3.00000 - 5.19615i) q^{74} +(-2.00000 - 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +(2.00000 - 3.46410i) q^{79} -2.00000 q^{80} -6.00000 q^{82} +(2.00000 - 3.46410i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(2.00000 + 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} -10.0000 q^{89} +24.0000 q^{91} +(2.00000 - 3.46410i) q^{92} +(6.00000 + 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{95} +(7.00000 - 12.1244i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 2 * q^5 + 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8} + 4 q^{10} - q^{11} + 6 q^{13} - 4 q^{14} - q^{16} - 4 q^{17} + 8 q^{19} + 2 q^{20} + q^{22} + 4 q^{23} + q^{25} + 12 q^{26} - 8 q^{28} + 6 q^{29} + q^{32} - 2 q^{34} + 16 q^{35} + 12 q^{37} + 4 q^{38} - 2 q^{40} - 6 q^{41} - 4 q^{43} + 2 q^{44} + 8 q^{46} - 12 q^{47} - 9 q^{49} - q^{50} + 6 q^{52} - 4 q^{53} - 4 q^{55} - 4 q^{56} - 6 q^{58} + 12 q^{59} + 14 q^{61} + 2 q^{64} - 12 q^{65} - 4 q^{67} + 2 q^{68} + 8 q^{70} + 24 q^{71} - 12 q^{73} + 6 q^{74} - 4 q^{76} + 4 q^{77} + 4 q^{79} - 4 q^{80} - 12 q^{82} + 4 q^{83} - 4 q^{85} + 4 q^{86} + q^{88} - 20 q^{89} + 48 q^{91} + 4 q^{92} + 12 q^{94} + 8 q^{95} + 14 q^{97} - 18 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 2 * q^5 + 4 * q^7 - 2 * q^8 + 4 * q^10 - q^11 + 6 * q^13 - 4 * q^14 - q^16 - 4 * q^17 + 8 * q^19 + 2 * q^20 + q^22 + 4 * q^23 + q^25 + 12 * q^26 - 8 * q^28 + 6 * q^29 + q^32 - 2 * q^34 + 16 * q^35 + 12 * q^37 + 4 * q^38 - 2 * q^40 - 6 * q^41 - 4 * q^43 + 2 * q^44 + 8 * q^46 - 12 * q^47 - 9 * q^49 - q^50 + 6 * q^52 - 4 * q^53 - 4 * q^55 - 4 * q^56 - 6 * q^58 + 12 * q^59 + 14 * q^61 + 2 * q^64 - 12 * q^65 - 4 * q^67 + 2 * q^68 + 8 * q^70 + 24 * q^71 - 12 * q^73 + 6 * q^74 - 4 * q^76 + 4 * q^77 + 4 * q^79 - 4 * q^80 - 12 * q^82 + 4 * q^83 - 4 * q^85 + 4 * q^86 + q^88 - 20 * q^89 + 48 * q^91 + 4 * q^92 + 12 * q^94 + 8 * q^95 + 14 * q^97 - 18 * q^98

Introduction

L-functions

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Varieties

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