LMFDB - Embedded newform 1782.2.e.l.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.l.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -4.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(2.00000 - 3.46410i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} +4.00000 q^{26} -2.00000 q^{28} +(-5.00000 + 8.66025i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +8.00000 q^{35} -2.00000 q^{37} +(2.00000 + 3.46410i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(-2.00000 + 3.46410i) q^{43} +1.00000 q^{44} -6.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-5.50000 - 9.52628i) q^{50} +(-2.00000 + 3.46410i) q^{52} +4.00000 q^{53} -4.00000 q^{55} +(1.00000 - 1.73205i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(4.00000 - 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-4.00000 + 6.92820i) q^{70} +2.00000 q^{71} -6.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{77} +(-5.00000 + 8.66025i) q^{79} -4.00000 q^{80} +2.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-0.500000 + 0.866025i) q^{88} +10.0000 q^{89} -8.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(1.00000 + 1.73205i) q^{94} +(1.00000 - 1.73205i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8} - 8 q^{10} - q^{11} - 4 q^{13} + 2 q^{14} - q^{16} - 4 q^{17} + 4 q^{20} - q^{22} + 6 q^{23} - 11 q^{25} + 8 q^{26} - 4 q^{28} - 10 q^{29} + 8 q^{31} - q^{32} + 2 q^{34} + 16 q^{35} - 4 q^{37} + 4 q^{40} - 2 q^{41} - 4 q^{43} + 2 q^{44} - 12 q^{46} + 2 q^{47} + 3 q^{49} - 11 q^{50} - 4 q^{52} + 8 q^{53} - 8 q^{55} + 2 q^{56} - 10 q^{58} + 8 q^{61} - 16 q^{62} + 2 q^{64} + 16 q^{65} + 12 q^{67} + 2 q^{68} - 8 q^{70} + 4 q^{71} - 12 q^{73} + 2 q^{74} + 2 q^{77} - 10 q^{79} - 8 q^{80} + 4 q^{82} - 4 q^{83} - 8 q^{85} - 4 q^{86} - q^{88} + 20 q^{89} - 16 q^{91} + 6 q^{92} + 2 q^{94} + 2 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8 - 8 * q^10 - q^11 - 4 * q^13 + 2 * q^14 - q^16 - 4 * q^17 + 4 * q^20 - q^22 + 6 * q^23 - 11 * q^25 + 8 * q^26 - 4 * q^28 - 10 * q^29 + 8 * q^31 - q^32 + 2 * q^34 + 16 * q^35 - 4 * q^37 + 4 * q^40 - 2 * q^41 - 4 * q^43 + 2 * q^44 - 12 * q^46 + 2 * q^47 + 3 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^53 - 8 * q^55 + 2 * q^56 - 10 * q^58 + 8 * q^61 - 16 * q^62 + 2 * q^64 + 16 * q^65 + 12 * q^67 + 2 * q^68 - 8 * q^70 + 4 * q^71 - 12 * q^73 + 2 * q^74 + 2 * q^77 - 10 * q^79 - 8 * q^80 + 4 * q^82 - 4 * q^83 - 8 * q^85 - 4 * q^86 - q^88 + 20 * q^89 - 16 * q^91 + 6 * q^92 + 2 * q^94 + 2 * q^97 - 6 * 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
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$		0			0
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−4.00000			−1.26491
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		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	$0.5\pi$
$20$	2.00000	−	3.46410i	0.447214	−	0.774597i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	4.00000			0.784465
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.142605	+	0.989780i	$0.545548\pi$
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.785872	+	0.618389i	$0.787786\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−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
$37$	−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
$40$	2.00000	+	3.46410i	0.316228	+	0.547723i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		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
$46$	−6.00000			−0.884652
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−5.50000	−	9.52628i	−0.777817	−	1.34722i
$51$		0			0
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		0			0
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	8.00000	−	13.8564i	0.992278	−	1.71868i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$	−4.00000	+	6.92820i	−0.478091	+	0.828079i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$		0			0
$77$	1.00000	+	1.73205i	0.113961	+	0.197386i
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	−4.00000			−0.447214
$81$		0			0
$82$	2.00000			0.220863
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	−0.954664	−	0.297686i	$-0.903785\pi$
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	0.735135	+	0.677920i	$0.237119\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$	−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	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		0			0
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$		0			0
$96$		0			0
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	11.0000			1.10000
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−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
$109$	20.0000			1.91565			0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000			1.91565			0.957826	+	0.287348i	$0.0927736\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$		0			0
$112$	1.00000	+	1.73205i	0.0944911	+	0.163663i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$	−12.0000	+	20.7846i	−1.11901	+	1.93817i
$116$	10.0000			0.928477
$117$		0			0
$118$		0			0
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$		0			0
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−22.0000			−1.95218			−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−22.0000			−1.95218			−0.976092	+	0.217357i	$0.930256\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	8.00000	+	13.8564i	0.701646	+	1.21529i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		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
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$	4.00000			0.334497
$144$		0			0
$145$	−40.0000			−3.32182
$146$	3.00000	−	5.19615i	0.248282	−	0.430037i
$147$		0			0
$148$	1.00000	+	1.73205i	0.0821995	+	0.142374i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$		0			0
$153$		0			0
$154$	−2.00000			−0.161165
$155$	−16.0000	+	27.7128i	−1.28515	+	2.22595i
$156$		0			0
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	−0.961681	−	0.274169i	$-0.911597\pi$
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	0.243403	−	0.969925i	$-0.421736\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$		0			0
$160$	2.00000	−	3.46410i	0.158114	−	0.273861i
$161$	12.0000			0.945732
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	8.00000			0.613572
$171$		0			0
$172$	4.00000			0.304997
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	11.0000	+	19.0526i	0.831522	+	1.44024i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$		0			0
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	4.00000	−	6.92820i	0.296500	−	0.513553i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	−2.00000			−0.145865
$189$		0			0
$190$		0			0
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	0.126314	+	0.991990i	$0.459685\pi$
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	−0.922246	+	0.386604i	$0.873648\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	−5.50000	+	9.52628i	−0.388909	+	0.673610i
$201$		0			0
$202$	−1.00000	−	1.73205i	−0.0703598	−	0.121867i
$203$	10.0000	+	17.3205i	0.701862	+	1.21566i
$204$		0			0
$205$	4.00000	−	6.92820i	0.279372	−	0.483887i
$206$	4.00000			0.278693
$207$		0			0
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	−16.0000			−1.09119
$216$		0			0
$217$	16.0000			1.08615
$218$	−10.0000	+	17.3205i	−0.677285	+	1.17309i
$219$		0			0
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	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
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	−12.0000	−	20.7846i	−0.791257	−	1.37050i
$231$		0			0
$232$	−5.00000	+	8.66025i	−0.328266	+	0.568574i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$		0			0
$237$		0			0
$238$	−2.00000	−	3.46410i	−0.129641	−	0.224544i
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	0.983872	+	0.178875i	$0.0572458\pi$
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	−0.337026	+	0.941495i	$0.609421\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$	1.00000			0.0642824
$243$		0			0
$244$	−8.00000			−0.512148
$245$	−6.00000	+	10.3923i	−0.383326	+	0.663940i
$246$		0			0
$247$		0			0
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$		0			0
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	11.0000	−	19.0526i	0.690201	−	1.19546i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	−2.00000	+	3.46410i	−0.124274	+	0.215249i
$260$	−16.0000			−0.992278
$261$		0			0
$262$	12.0000			0.741362
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	8.00000	+	13.8564i	0.491436	+	0.851192i
$266$		0			0
$267$		0			0
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	−20.0000			−1.21942			−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000			−1.21942			−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	−5.50000	−	9.52628i	−0.331662	−	0.574456i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$		0			0
$279$		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	$0.871266\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	−2.00000	+	3.46410i	−0.118262	+	0.204837i
$287$	−4.00000			−0.236113
$288$		0			0
$289$	−13.0000			−0.764706
$290$	20.0000	−	34.6410i	1.17444	−	2.03419i
$291$		0			0
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	0.585827	−	0.810436i	$-0.300770\pi$
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	−0.994772	+	0.102123i	$0.967436\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	−10.0000			−0.579284
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	−1.00000	−	1.73205i	−0.0575435	−	0.0996683i
$303$		0			0
$304$		0			0
$305$	32.0000			1.83231
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$		0			0
$310$	−16.0000	−	27.7128i	−0.908739	−	1.57398i
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	0.836280	−	0.548303i	$-0.184726\pi$
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	−0.892984	+	0.450088i	$0.851393\pi$
$312$		0			0
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	10.0000			0.562544
$317$	16.0000	−	27.7128i	0.898650	−	1.55651i	0.0694277	−	0.997587i	$-0.477883\pi$
$317$	16.0000	−	27.7128i	0.898650	−	1.55651i	0.829222	−	0.558920i	$-0.188784\pi$
$318$		0			0
$319$	−5.00000	−	8.66025i	−0.279946	−	0.484881i
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$		0			0
$322$	−6.00000	+	10.3923i	−0.334367	+	0.579141i
$323$		0			0
$324$		0			0
$325$	44.0000			2.44068
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$	−2.00000	−	3.46410i	−0.110264	−	0.190982i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	4.00000			0.219529
$333$		0			0
$334$	−12.0000			−0.656611
$335$	−24.0000	+	41.5692i	−1.31126	+	2.27117i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$	−4.00000	+	6.92820i	−0.216930	+	0.375735i
$341$	−8.00000			−0.433224
$342$		0			0
$343$	20.0000			1.07990
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	−0.463862	−	0.885908i	$-0.653537\pi$
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	0.999149	−	0.0412379i	$-0.0131301\pi$
$350$	−22.0000			−1.17595
$351$		0			0
$352$	1.00000			0.0533002
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	−5.00000	−	8.66025i	−0.264999	−	0.458993i
$357$		0			0
$358$		0			0
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$	−12.0000	−	20.7846i	−0.628109	−	1.08792i
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	8.00000			0.415900
$371$	4.00000	−	6.92820i	0.207670	−	0.359694i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$		0			0
$376$	1.00000	−	1.73205i	0.0515711	−	0.0893237i
$377$	40.0000			2.06010
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$	−11.0000	−	19.0526i	−0.562809	−	0.974814i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$	−4.00000	+	6.92820i	−0.203859	+	0.353094i
$386$	14.0000			0.712581
$387$		0			0
$388$	−2.00000			−0.101535
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	0.999967	−	0.00812520i	$-0.00258636\pi$
$390$		0			0
$391$	−6.00000	−	10.3923i	−0.303433	−	0.525561i
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$		0			0
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−40.0000			−2.01262
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	−10.0000	+	17.3205i	−0.501255	+	0.868199i
$399$		0			0
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	16.0000	−	27.7128i	0.797017	−	1.38047i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−20.0000			−0.992583
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$	4.00000	+	6.92820i	0.197546	+	0.342160i
$411$		0			0
$412$	−2.00000	+	3.46410i	−0.0985329	+	0.170664i
$413$		0			0
$414$		0			0
$415$	−16.0000			−0.785409
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	−0.558951	−	0.829201i	$-0.688796\pi$
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	0.997584	+	0.0694656i	$0.0221294\pi$
$422$	12.0000			0.584151
$423$		0			0
$424$	4.00000			0.194257
$425$	11.0000	−	19.0526i	0.533578	−	0.924185i
$426$		0			0
$427$	−8.00000	−	13.8564i	−0.387147	−	0.670559i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$		0			0
$430$	8.00000	−	13.8564i	0.385794	−	0.668215i
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$		0			0
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$		0			0
$436$	−10.0000	−	17.3205i	−0.478913	−	0.829502i
$437$		0			0
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	−8.00000			−0.380521
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$		0			0
$445$	20.0000	+	34.6410i	0.948091	+	1.64214i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$		0			0
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	2.00000			0.0941763
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		0			0
$454$	6.00000	+	10.3923i	0.281594	+	0.487735i
$455$	−16.0000	−	27.7128i	−0.750092	−	1.29920i
$456$		0			0
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	−0.841688	−	0.539964i	$-0.818438\pi$
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	0.888466	+	0.458942i	$0.151771\pi$
$458$	10.0000			0.467269
$459$		0			0
$460$	24.0000			1.11901
$461$	9.00000	−	15.5885i	0.419172	−	0.726027i	−0.576685	−	0.816967i	$-0.695654\pi$
$461$	9.00000	−	15.5885i	0.419172	−	0.726027i	0.995856	+	0.0909401i	$0.0289872\pi$
$462$		0			0
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	0.815802	−	0.578331i	$-0.196296\pi$
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	−0.908750	+	0.417340i	$0.862962\pi$
$464$	−5.00000	−	8.66025i	−0.232119	−	0.402042i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$		0			0
$469$	24.0000			1.10822
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$		0			0
$472$		0			0
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$		0			0
$475$		0			0
$476$	4.00000			0.183340
$477$		0			0
$478$	−20.0000			−0.914779
$479$	−20.0000	+	34.6410i	−0.913823	+	1.58279i	−0.105208	+	0.994450i	$0.533551\pi$
$479$	−20.0000	+	34.6410i	−0.913823	+	1.58279i	−0.808615	+	0.588338i	$0.799782\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	9.00000	+	15.5885i	0.409939	+	0.710035i
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	8.00000			0.363261
$486$		0			0
$487$	28.0000			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$		0			0
$490$	−6.00000	−	10.3923i	−0.271052	−	0.469476i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		0			0
$493$	10.0000	−	17.3205i	0.450377	−	0.780076i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	2.00000	−	3.46410i	0.0897123	−	0.155386i
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$	4.00000	−	6.92820i	0.178529	−	0.309221i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$		0			0
$508$	11.0000	+	19.0526i	0.488046	+	0.845321i
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	0.997928	−	0.0643419i	$-0.0204948\pi$
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	−0.554686	+	0.832060i	$0.687161\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.0000			0.793946
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	1.00000	+	1.73205i	0.0439799	+	0.0761755i
$518$	−2.00000	−	3.46410i	−0.0878750	−	0.152204i
$519$		0			0
$520$	8.00000	−	13.8564i	0.350823	−	0.607644i
$521$	−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	$0.0880406\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	8.00000	+	13.8564i	0.348817	+	0.604168i
$527$	−8.00000	−	13.8564i	−0.348485	−	0.603595i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−16.0000			−0.694996
$531$		0			0
$532$		0			0
$533$	−4.00000	+	6.92820i	−0.173259	+	0.300094i
$534$		0			0
$535$	−24.0000	−	41.5692i	−1.03761	−	1.79719i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		0			0
$538$	10.0000	−	17.3205i	0.431131	−	0.746740i
$539$	−3.00000			−0.129219
$540$		0			0
$541$	12.0000			0.515920			0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000			0.515920			0.257960	+	0.966156i	$0.416950\pi$
$542$	−11.0000	+	19.0526i	−0.472490	+	0.818377i
$543$		0			0
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	40.0000	+	69.2820i	1.71341	+	2.96772i
$546$		0			0
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	−0.289605	−	0.957146i	$-0.593524\pi$
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	0.973715	−	0.227768i	$-0.0731428\pi$
$548$	−2.00000			−0.0854358
$549$		0			0
$550$	11.0000			0.469042
$551$		0			0
$552$		0			0
$553$	10.0000	+	17.3205i	0.425243	+	0.736543i
$554$	−4.00000	−	6.92820i	−0.169944	−	0.294351i
$555$		0			0
$556$		0			0
$557$	38.0000			1.61011			0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000			1.61011			0.805056	+	0.593199i	$0.202135\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	−4.00000	+	6.92820i	−0.169031	+	0.292770i
$561$		0			0
$562$	−11.0000	−	19.0526i	−0.464007	−	0.803684i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$		0			0
$565$	−12.0000	+	20.7846i	−0.504844	+	0.874415i
$566$	4.00000			0.168133
$567$		0			0
$568$	2.00000			0.0839181
$569$	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
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		0			0
$574$	2.00000	−	3.46410i	0.0834784	−	0.144589i
$575$	−66.0000			−2.75239
$576$		0			0
$577$	−2.00000			−0.0832611			−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000			−0.0832611			−0.0416305	+	0.999133i	$0.513255\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$		0			0
$580$	20.0000	+	34.6410i	0.830455	+	1.43839i
$581$	4.00000	+	6.92820i	0.165948	+	0.287430i
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	14.0000			0.578335
$587$	−4.00000	+	6.92820i	−0.165098	+	0.285958i	−0.936690	−	0.350160i	$-0.886127\pi$
$587$	−4.00000	+	6.92820i	−0.165098	+	0.285958i	0.771592	+	0.636117i	$0.219461\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$		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
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	0.0185374	+	0.999828i	$0.494099\pi$
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	−0.875145	+	0.483860i	$0.839234\pi$
$602$	−8.00000			−0.326056
$603$		0			0
$604$	2.00000			0.0813788
$605$	2.00000	−	3.46410i	0.0813116	−	0.140836i
$606$		0			0
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$		0			0
$609$		0			0
$610$	−16.0000	+	27.7128i	−0.647821	+	1.12206i
$611$	−8.00000			−0.323645
$612$		0			0
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$	1.00000	+	1.73205i	0.0402911	+	0.0697863i
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	0.997899	−	0.0647859i	$-0.0206365\pi$
$617$	11.0000	+	19.0526i	0.442843	+	0.767027i	−0.555056	+	0.831813i	$0.687303\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	32.0000			1.28515
$621$		0			0
$622$	2.00000			0.0801927
$623$	10.0000	−	17.3205i	0.400642	−	0.693932i
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	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
$631$	−48.0000			−1.91085			−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000			−1.91085			−0.955425	+	0.295234i	$0.904602\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$		0			0
$634$	16.0000	+	27.7128i	0.635441	+	1.10062i
$635$	−44.0000	−	76.2102i	−1.74609	−	3.02431i
$636$		0			0
$637$	6.00000	−	10.3923i	0.237729	−	0.411758i
$638$	10.0000			0.395904
$639$		0			0
$640$	−4.00000			−0.158114
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$		0			0
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.864447	−	0.502724i	$-0.832331\pi$
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.00314839	−	0.999995i	$-0.501002\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$		0			0
$647$	−22.0000			−0.864909			−0.432455	−	0.901656i	$-0.642352\pi$
$647$	−22.0000			−0.864909			−0.432455	+	0.901656i	$0.642352\pi$
$648$		0			0
$649$		0			0
$650$	−22.0000	+	38.1051i	−0.862911	+	1.49461i
$651$		0			0
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$		0			0
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$	2.00000			0.0780869
$657$		0			0
$658$	4.00000			0.155936
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$		0			0
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	−0.908024	−	0.418917i	$-0.862410\pi$
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	0.0912190	−	0.995831i	$-0.470924\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$		0			0
$664$	−2.00000	+	3.46410i	−0.0776151	+	0.134433i
$665$		0			0
$666$		0			0
$667$	−60.0000			−2.32321
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$		0			0
$670$	−24.0000	−	41.5692i	−0.927201	−	1.60596i
$671$	4.00000	+	6.92820i	0.154418	+	0.267460i
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	−22.0000			−0.847408
$675$		0			0
$676$	3.00000			0.115385
$677$	11.0000	−	19.0526i	0.422764	−	0.732249i	−0.573444	−	0.819244i	$-0.694393\pi$
$677$	11.0000	−	19.0526i	0.422764	−	0.732249i	0.996209	+	0.0869952i	$0.0277265\pi$
$678$		0			0
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−4.00000	−	6.92820i	−0.153393	−	0.265684i
$681$		0			0
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−8.00000	−	13.8564i	−0.304776	−	0.527887i
$690$		0			0
$691$	−26.0000	+	45.0333i	−0.989087	+	1.71315i	−0.366947	+	0.930242i	$0.619597\pi$
$691$	−26.0000	+	45.0333i	−0.989087	+	1.71315i	−0.622139	+	0.782907i	$0.713736\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	2.00000	+	3.46410i	0.0757554	+	0.131212i
$698$	10.0000	+	17.3205i	0.378506	+	0.655591i
$699$		0			0
$700$	11.0000	−	19.0526i	0.415761	−	0.720119i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$		0			0
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	2.00000	+	3.46410i	0.0752177	+	0.130281i
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	−8.00000			−0.300235
$711$		0			0
$712$	10.0000			0.374766
$713$	−24.0000	+	41.5692i	−0.898807	+	1.55678i
$714$		0			0
$715$	8.00000	+	13.8564i	0.299183	+	0.518200i
$716$		0			0
$717$		0			0
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$	10.0000			0.372937			0.186469	−	0.982461i	$-0.440296\pi$
$719$	10.0000			0.372937			0.186469	+	0.982461i	$0.440296\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−55.0000	−	95.2628i	−2.04265	−	3.53797i
$726$		0			0
$727$	−14.0000	+	24.2487i	−0.519231	+	0.899335i	0.480519	+	0.876984i	$0.340448\pi$
$727$	−14.0000	+	24.2487i	−0.519231	+	0.899335i	−0.999750	+	0.0223506i	$0.992885\pi$
$728$	−8.00000			−0.296500
$729$		0			0
$730$	24.0000			0.888280
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	0.826723	−	0.562609i	$-0.190202\pi$
$733$	−2.00000	−	3.46410i	−0.0738717	−	0.127950i	−0.900595	+	0.434659i	$0.856869\pi$
$734$	−4.00000	−	6.92820i	−0.147643	−	0.255725i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−12.0000			−0.442026
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−4.00000	+	6.92820i	−0.147043	+	0.254686i
$741$		0			0
$742$	4.00000	+	6.92820i	0.146845	+	0.254342i
$743$	−22.0000	−	38.1051i	−0.807102	−	1.39794i	−0.914863	−	0.403764i	$-0.867702\pi$
$743$	−22.0000	−	38.1051i	−0.807102	−	1.39794i	0.107761	−	0.994177i	$-0.465632\pi$
$744$		0			0
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$	4.00000			0.146450
$747$		0			0
$748$	−2.00000			−0.0731272
$749$	−12.0000	+	20.7846i	−0.438470	+	0.759453i
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$		0			0
$754$	−20.0000	+	34.6410i	−0.728357	+	1.26155i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−42.0000			−1.52652			−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000			−1.52652			−0.763258	+	0.646094i	$0.776401\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$		0			0
$760$		0			0
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$		0			0
$763$	20.0000	−	34.6410i	0.724049	−	1.25409i
$764$	22.0000			0.795932
$765$		0			0
$766$	−6.00000			−0.216789
$767$		0			0
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$	−4.00000	−	6.92820i	−0.144150	−	0.249675i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	4.00000			0.143870			0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000			0.143870			0.0719350	+	0.997409i	$0.477083\pi$
$774$		0			0
$775$	−88.0000			−3.16105
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	10.0000	+	17.3205i	0.358517	+	0.620970i
$779$		0			0
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	12.0000			0.429119
$783$		0			0
$784$	−3.00000			−0.107143
$785$	36.0000	−	62.3538i	1.28490	−	2.22550i
$786$		0			0
$787$	26.0000	+	45.0333i	0.926800	+	1.60526i	0.788641	+	0.614855i	$0.210785\pi$
$787$	26.0000	+	45.0333i	0.926800	+	1.60526i	0.138159	+	0.990410i	$0.455881\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		0			0
$790$	20.0000	−	34.6410i	0.711568	−	1.23247i
$791$	12.0000			0.426671
$792$		0			0
$793$	−32.0000			−1.13635
$794$	−9.00000	+	15.5885i	−0.319398	+	0.553214i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−14.0000	−	24.2487i	−0.495905	−	0.858933i	0.504083	−	0.863655i	$-0.331830\pi$
$797$	−14.0000	−	24.2487i	−0.495905	−	0.858933i	−0.999989	+	0.00472155i	$0.998497\pi$
$798$		0			0
$799$	−2.00000	+	3.46410i	−0.0707549	+	0.122551i
$800$	11.0000			0.388909
$801$		0			0
$802$	−18.0000			−0.635602
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	24.0000	+	41.5692i	0.845889	+	1.46512i
$806$	16.0000	+	27.7128i	0.563576	+	0.976142i
$807$		0			0
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	10.0000			0.351581			0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000			0.351581			0.175791	+	0.984428i	$0.443752\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$	10.0000	−	17.3205i	0.350931	−	0.607831i
$813$		0			0
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		0			0
$817$		0			0
$818$	−10.0000			−0.349642
$819$		0			0
$820$	−8.00000			−0.279372
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$	8.00000	−	13.8564i	0.277684	−	0.480963i
$831$		0			0
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	−24.0000	+	41.5692i	−0.830554	+	1.43856i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	0.481927	+	0.876211i	$0.339937\pi$
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	−0.999785	+	0.0207443i	$0.993396\pi$
$840$		0			0
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	9.00000	+	15.5885i	0.310160	+	0.537214i
$843$		0			0
$844$	−6.00000	+	10.3923i	−0.206529	+	0.357718i
$845$	−12.0000			−0.412813
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	−2.00000	+	3.46410i	−0.0686803	+	0.118958i
$849$		0			0
$850$	11.0000	+	19.0526i	0.377297	+	0.653497i
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−12.0000	+	20.7846i	−0.410872	+	0.711651i	−0.994985	−	0.100021i	$-0.968109\pi$
$853$	−12.0000	+	20.7846i	−0.410872	+	0.711651i	0.584113	+	0.811672i	$0.301442\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$	−12.0000			−0.410152
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	−0.614687	−	0.788771i	$-0.710717\pi$
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	0.990439	+	0.137948i	$0.0440508\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	8.00000	+	13.8564i	0.272798	+	0.472500i
$861$		0			0
$862$	−16.0000	+	27.7128i	−0.544962	+	0.943902i
$863$	54.0000			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$864$		0			0
$865$	24.0000			0.816024
$866$	3.00000	−	5.19615i	0.101944	−	0.176572i
$867$		0			0
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	−5.00000	−	8.66025i	−0.169613	−	0.293779i
$870$		0			0
$871$	24.0000	−	41.5692i	0.813209	−	1.40852i
$872$	20.0000			0.677285
$873$		0			0
$874$		0			0
$875$	−24.0000	+	41.5692i	−0.811348	+	1.40530i
$876$		0			0
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	0.526767	−	0.850010i	$-0.323404\pi$
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	−0.999514	+	0.0311889i	$0.990071\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$		0			0
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	−38.0000			−1.28025			−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000			−1.28025			−0.640126	+	0.768270i	$0.721118\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$	−22.0000	+	38.1051i	−0.737856	+	1.27800i
$890$	−40.0000			−1.34080
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$	−80.0000			−2.66815
$900$		0			0
$901$	−8.00000			−0.266519
$902$	−1.00000	+	1.73205i	−0.0332964	+	0.0576710i
$903$		0			0
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	4.00000	+	6.92820i	0.132964	+	0.230301i
$906$		0			0
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	32.0000			1.06079
$911$	−1.00000	+	1.73205i	−0.0331315	+	0.0573854i	−0.882116	−	0.471033i	$-0.843881\pi$
$911$	−1.00000	+	1.73205i	−0.0331315	+	0.0573854i	0.848984	+	0.528418i	$0.177215\pi$
$912$		0			0
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$		0			0
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	−24.0000			−0.792550
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	−12.0000	+	20.7846i	−0.395628	+	0.685248i
$921$		0			0
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	−4.00000	−	6.92820i	−0.131662	−	0.228045i
$924$		0			0
$925$	11.0000	−	19.0526i	0.361678	−	0.626444i
$926$	4.00000			0.131448
$927$		0			0
$928$	10.0000			0.328266
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$		0			0
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$		0			0
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	8.00000			0.261628
$936$		0			0
$937$	58.0000			1.89478			0.947389	−	0.320085i	$-0.103712\pi$
$937$	58.0000			1.89478			0.947389	+	0.320085i	$0.103712\pi$
$938$	−12.0000	+	20.7846i	−0.391814	+	0.678642i
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	−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
$943$	6.00000	−	10.3923i	0.195387	−	0.338420i
$944$		0			0
$945$		0			0
$946$	4.00000			0.130051
$947$	−14.0000	+	24.2487i	−0.454939	+	0.787977i	−0.998685	−	0.0512727i	$-0.983672\pi$
$947$	−14.0000	+	24.2487i	−0.454939	+	0.787977i	0.543746	+	0.839250i	$0.317006\pi$
$948$		0			0
$949$	12.0000	+	20.7846i	0.389536	+	0.674697i
$950$		0			0
$951$		0			0
$952$	−2.00000	+	3.46410i	−0.0648204	+	0.112272i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	−88.0000			−2.84761
$956$	10.0000	−	17.3205i	0.323423	−	0.560185i
$957$		0			0
$958$	−20.0000	−	34.6410i	−0.646171	−	1.11920i
$959$	−2.00000	−	3.46410i	−0.0645834	−	0.111862i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−8.00000			−0.257930
$963$		0			0
$964$	−18.0000			−0.579741
$965$	28.0000	−	48.4974i	0.901352	−	1.56119i
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	−4.00000	+	6.92820i	−0.128432	+	0.222451i
$971$	32.0000			1.02693			0.513464	−	0.858111i	$-0.328362\pi$
$971$	32.0000			1.02693			0.513464	+	0.858111i	$0.328362\pi$
$972$		0			0
$973$		0			0
$974$	−14.0000	+	24.2487i	−0.448589	+	0.776979i
$975$		0			0
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	−0.991592	−	0.129405i	$-0.958693\pi$
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	0.383728	−	0.923446i	$-0.374640\pi$
$978$		0			0
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	12.0000			0.383326
$981$		0			0
$982$	12.0000			0.382935
$983$	23.0000	−	39.8372i	0.733586	−	1.27061i	−0.221755	−	0.975102i	$-0.571178\pi$
$983$	23.0000	−	39.8372i	0.733586	−	1.27061i	0.955341	−	0.295506i	$-0.0954882\pi$
$984$		0			0
$985$	36.0000	+	62.3538i	1.14706	+	1.98676i
$986$	10.0000	+	17.3205i	0.318465	+	0.551597i
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$		0			0
$994$	2.00000	+	3.46410i	0.0634361	+	0.109875i
$995$	40.0000	+	69.2820i	1.26809	+	2.19639i
$996$		0			0
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	−0.0796863	−	0.996820i	$-0.525392\pi$
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	0.903115	−	0.429400i	$-0.141275\pi$
$998$	−20.0000			−0.633089
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1782.2.e.l.1189.1		2
3.2	odd	2		1782.2.e.n.1189.1		2
9.2	odd	6		198.2.a.c.1.1		1
9.4	even	3	inner	1782.2.e.l.595.1		2
9.5	odd	6		1782.2.e.n.595.1		2
9.7	even	3		66.2.a.c.1.1	✓	1
36.7	odd	6		528.2.a.a.1.1		1
36.11	even	6		1584.2.a.s.1.1		1
45.2	even	12		4950.2.c.d.199.1		2
45.7	odd	12		1650.2.c.m.199.2		2
45.29	odd	6		4950.2.a.bo.1.1		1
45.34	even	6		1650.2.a.c.1.1		1
45.38	even	12		4950.2.c.d.199.2		2
45.43	odd	12		1650.2.c.m.199.1		2
63.20	even	6		9702.2.a.a.1.1		1
63.34	odd	6		3234.2.a.s.1.1		1
72.11	even	6		6336.2.a.d.1.1		1
72.29	odd	6		6336.2.a.c.1.1		1
72.43	odd	6		2112.2.a.bd.1.1		1
72.61	even	6		2112.2.a.n.1.1		1
99.7	odd	30		726.2.e.m.511.1		4
99.16	even	15		726.2.e.e.487.1		4
99.25	even	15		726.2.e.e.493.1		4
99.43	odd	6		726.2.a.d.1.1		1
99.52	odd	30		726.2.e.m.493.1		4
99.61	odd	30		726.2.e.m.487.1		4
99.65	even	6		2178.2.a.m.1.1		1
99.70	even	15		726.2.e.e.511.1		4
99.79	odd	30		726.2.e.m.565.1		4
99.97	even	15		726.2.e.e.565.1		4
396.43	even	6		5808.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.c.1.1	✓	1	9.7	even	3
198.2.a.c.1.1		1	9.2	odd	6
528.2.a.a.1.1		1	36.7	odd	6
726.2.a.d.1.1		1	99.43	odd	6
726.2.e.e.487.1		4	99.16	even	15
726.2.e.e.493.1		4	99.25	even	15
726.2.e.e.511.1		4	99.70	even	15
726.2.e.e.565.1		4	99.97	even	15
726.2.e.m.487.1		4	99.61	odd	30
726.2.e.m.493.1		4	99.52	odd	30
726.2.e.m.511.1		4	99.7	odd	30
726.2.e.m.565.1		4	99.79	odd	30
1584.2.a.s.1.1		1	36.11	even	6
1650.2.a.c.1.1		1	45.34	even	6
1650.2.c.m.199.1		2	45.43	odd	12
1650.2.c.m.199.2		2	45.7	odd	12
1782.2.e.l.595.1		2	9.4	even	3	inner
1782.2.e.l.1189.1		2	1.1	even	1	trivial
1782.2.e.n.595.1		2	9.5	odd	6
1782.2.e.n.1189.1		2	3.2	odd	2
2112.2.a.n.1.1		1	72.61	even	6
2112.2.a.bd.1.1		1	72.43	odd	6
2178.2.a.m.1.1		1	99.65	even	6
3234.2.a.s.1.1		1	63.34	odd	6
4950.2.a.bo.1.1		1	45.29	odd	6
4950.2.c.d.199.1		2	45.2	even	12
4950.2.c.d.199.2		2	45.38	even	12
5808.2.a.b.1.1		1	396.43	even	6
6336.2.a.c.1.1		1	72.29	odd	6
6336.2.a.d.1.1		1	72.11	even	6
9702.2.a.a.1.1		1	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -4.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(2.00000 - 3.46410i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} +4.00000 q^{26} -2.00000 q^{28} +(-5.00000 + 8.66025i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +8.00000 q^{35} -2.00000 q^{37} +(2.00000 + 3.46410i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(-2.00000 + 3.46410i) q^{43} +1.00000 q^{44} -6.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-5.50000 - 9.52628i) q^{50} +(-2.00000 + 3.46410i) q^{52} +4.00000 q^{53} -4.00000 q^{55} +(1.00000 - 1.73205i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(4.00000 - 6.92820i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-4.00000 + 6.92820i) q^{70} +2.00000 q^{71} -6.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{77} +(-5.00000 + 8.66025i) q^{79} -4.00000 q^{80} +2.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-0.500000 + 0.866025i) q^{88} +10.0000 q^{89} -8.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(1.00000 + 1.73205i) q^{94} +(1.00000 - 1.73205i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8} - 8 q^{10} - q^{11} - 4 q^{13} + 2 q^{14} - q^{16} - 4 q^{17} + 4 q^{20} - q^{22} + 6 q^{23} - 11 q^{25} + 8 q^{26} - 4 q^{28} - 10 q^{29} + 8 q^{31} - q^{32} + 2 q^{34} + 16 q^{35} - 4 q^{37} + 4 q^{40} - 2 q^{41} - 4 q^{43} + 2 q^{44} - 12 q^{46} + 2 q^{47} + 3 q^{49} - 11 q^{50} - 4 q^{52} + 8 q^{53} - 8 q^{55} + 2 q^{56} - 10 q^{58} + 8 q^{61} - 16 q^{62} + 2 q^{64} + 16 q^{65} + 12 q^{67} + 2 q^{68} - 8 q^{70} + 4 q^{71} - 12 q^{73} + 2 q^{74} + 2 q^{77} - 10 q^{79} - 8 q^{80} + 4 q^{82} - 4 q^{83} - 8 q^{85} - 4 q^{86} - q^{88} + 20 q^{89} - 16 q^{91} + 6 q^{92} + 2 q^{94} + 2 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8 - 8 * q^10 - q^11 - 4 * q^13 + 2 * q^14 - q^16 - 4 * q^17 + 4 * q^20 - q^22 + 6 * q^23 - 11 * q^25 + 8 * q^26 - 4 * q^28 - 10 * q^29 + 8 * q^31 - q^32 + 2 * q^34 + 16 * q^35 - 4 * q^37 + 4 * q^40 - 2 * q^41 - 4 * q^43 + 2 * q^44 - 12 * q^46 + 2 * q^47 + 3 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^53 - 8 * q^55 + 2 * q^56 - 10 * q^58 + 8 * q^61 - 16 * q^62 + 2 * q^64 + 16 * q^65 + 12 * q^67 + 2 * q^68 - 8 * q^70 + 4 * q^71 - 12 * q^73 + 2 * q^74 + 2 * q^77 - 10 * q^79 - 8 * q^80 + 4 * q^82 - 4 * q^83 - 8 * q^85 - 4 * q^86 - q^88 + 20 * q^89 - 16 * q^91 + 6 * q^92 + 2 * q^94 + 2 * q^97 - 6 * q^98

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