LMFDB - Embedded newform 1134.2.h.j.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (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:	$9.05503558921$
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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.541
Dual form			1134.2.h.j.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +6.00000 q^{23} +4.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +(2.50000 - 0.866025i) q^{28} +(4.50000 - 7.79423i) q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(6.00000 + 5.19615i) q^{35} +(5.00000 - 8.66025i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(2.00000 - 3.46410i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(6.00000 + 10.3923i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +2.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +9.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +7.00000 q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} -6.00000 q^{68} +(-1.50000 + 7.79423i) q^{70} +(-1.00000 - 1.73205i) q^{73} +10.0000 q^{74} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +4.00000 q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(3.00000 - 5.19615i) q^{95} +(6.50000 - 11.2583i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 6 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 6 * q^5 - 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 6 q^{5} - 4 q^{7} - 2 q^{8} - 3 q^{10} + 6 q^{11} - 2 q^{13} + q^{14} - q^{16} + 6 q^{17} - 2 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 8 q^{25} + 2 q^{26} + 5 q^{28} + 9 q^{29} + 7 q^{31} + q^{32} - 6 q^{34} + 12 q^{35} + 10 q^{37} - 4 q^{38} + 6 q^{40} + 4 q^{43} - 3 q^{44} + 6 q^{46} + 12 q^{47} + 2 q^{49} + 4 q^{50} + 4 q^{52} - 3 q^{53} - 18 q^{55} + 4 q^{56} + 18 q^{58} - 3 q^{59} + 4 q^{61} + 14 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{67} - 12 q^{68} - 3 q^{70} - 2 q^{73} + 20 q^{74} - 2 q^{76} - 12 q^{77} - 5 q^{79} + 3 q^{80} + 9 q^{83} - 18 q^{85} + 8 q^{86} - 6 q^{88} - 6 q^{89} - 2 q^{91} - 6 q^{92} - 12 q^{94} + 6 q^{95} + 13 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 6 * q^5 - 4 * q^7 - 2 * q^8 - 3 * q^10 + 6 * q^11 - 2 * q^13 + q^14 - q^16 + 6 * q^17 - 2 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 8 * q^25 + 2 * q^26 + 5 * q^28 + 9 * q^29 + 7 * q^31 + q^32 - 6 * q^34 + 12 * q^35 + 10 * q^37 - 4 * q^38 + 6 * q^40 + 4 * q^43 - 3 * q^44 + 6 * q^46 + 12 * q^47 + 2 * q^49 + 4 * q^50 + 4 * q^52 - 3 * q^53 - 18 * q^55 + 4 * q^56 + 18 * q^58 - 3 * q^59 + 4 * q^61 + 14 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 12 * q^68 - 3 * q^70 - 2 * q^73 + 20 * q^74 - 2 * q^76 - 12 * q^77 - 5 * q^79 + 3 * q^80 + 9 * q^83 - 18 * q^85 + 8 * q^86 - 6 * q^88 - 6 * q^89 - 2 * q^91 - 6 * q^92 - 12 * q^94 + 6 * q^95 + 13 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

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
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	6.00000	+	5.19615i	1.01419	+	0.878310i
$36$		0			0
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	2.00000			0.277350
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	9.00000			1.18176
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	7.00000			0.889001
$63$		0			0
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$	−1.50000	+	7.79423i	−0.179284	+	0.931589i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	10.0000			1.16248
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−6.00000	−	5.19615i	−0.683763	−	0.592157i
$78$		0			0
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$	4.00000			0.431331
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	−0.320647	−	0.947199i	$-0.603900\pi$
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	0.980622	−	0.195911i	$-0.0627665\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$	−18.0000			−1.67851
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	3.00000	−	15.5885i	0.275010	−	1.42899i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−2.00000	+	3.46410i	−0.181071	+	0.313625i
$123$		0			0
$124$	3.50000	+	6.06218i	0.314309	+	0.544400i
$125$	3.00000			0.268328
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$		0			0
$133$	5.00000	−	1.73205i	0.433555	−	0.150188i
$134$	−2.00000			−0.172774
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−7.50000	+	2.59808i	−0.633866	+	0.219578i
$141$		0			0
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$	−13.5000	+	23.3827i	−1.12111	+	1.94183i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$		0			0
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$	−10.5000	+	18.1865i	−0.843380	+	1.46078i
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	2.50000	−	4.33013i	0.198889	−	0.344486i
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$	−12.0000	−	10.3923i	−0.945732	−	0.819028i
$162$		0			0
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$		0			0
$165$		0			0
$166$	9.00000			0.698535
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	9.00000	−	15.5885i	0.690268	−	1.19558i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−6.00000			−0.449719
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−5.00000	+	1.73205i	−0.370625	+	0.128388i
$183$		0			0
$184$	−6.00000			−0.442326
$185$	−15.0000	+	25.9808i	−1.10282	+	1.91014i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	−12.0000			−0.875190
$189$		0			0
$190$	6.00000			0.435286
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	13.0000			0.933346
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	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
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	−22.5000	+	7.79423i	−1.57919	+	0.547048i
$204$		0			0
$205$		0			0
$206$	−8.00000	−	13.8564i	−0.557386	−	0.965422i
$207$		0			0
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	−3.00000	+	5.19615i	−0.207514	+	0.359425i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	3.00000			0.206041
$213$		0			0
$214$	3.00000			0.205076
$215$	−6.00000	+	10.3923i	−0.409197	+	0.708749i
$216$		0			0
$217$	−17.5000	+	6.06218i	−1.18798	+	0.411527i
$218$	−5.00000	+	8.66025i	−0.338643	+	0.586546i
$219$		0			0
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$		0			0
$227$	−15.0000			−0.995585			−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000			−0.995585			−0.497792	+	0.867296i	$0.665856\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	−9.00000	−	15.5885i	−0.593442	−	1.02787i
$231$		0			0
$232$	−4.50000	+	7.79423i	−0.295439	+	0.511716i
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	−18.0000	−	31.1769i	−1.17419	−	2.03376i
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$	15.0000	−	5.19615i	0.972306	−	0.336817i
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	0.995223	+	0.0976302i	$0.0311262\pi$
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	−0.413061	+	0.910703i	$0.635540\pi$
$240$		0			0
$241$	23.0000			1.48156			0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000			1.48156			0.740780	+	0.671748i	$0.234456\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	−3.00000	−	20.7846i	−0.191663	−	1.32788i
$246$		0			0
$247$	4.00000			0.254514
$248$	−3.50000	+	6.06218i	−0.222250	+	0.384949i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	−0.500000	−	0.866025i	−0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	−25.0000	+	8.66025i	−1.55342	+	0.538122i
$260$	−6.00000			−0.372104
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$	4.00000	+	3.46410i	0.245256	+	0.212398i
$267$		0			0
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$		0			0
$271$	9.50000	−	16.4545i	0.577084	−	0.999539i	−0.418728	−	0.908112i	$-0.637524\pi$
$271$	9.50000	−	16.4545i	0.577084	−	0.999539i	0.995812	−	0.0914269i	$-0.0291428\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$		0			0
$274$	−3.00000	−	5.19615i	−0.181237	−	0.313911i
$275$	12.0000			0.723627
$276$		0			0
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$		0			0
$280$	−6.00000	−	5.19615i	−0.358569	−	0.310530i
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	0.462174	+	0.886789i	$0.347070\pi$
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$		0			0
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$		0			0
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−27.0000			−1.58549
$291$		0			0
$292$	2.00000			0.117041
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$		0			0
$295$	4.50000	−	7.79423i	0.262000	−	0.453798i
$296$	−5.00000	+	8.66025i	−0.290619	+	0.503367i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	−10.0000	+	3.46410i	−0.576390	+	0.199667i
$302$	2.50000	+	4.33013i	0.143859	+	0.249171i
$303$		0			0
$304$	2.00000			0.114708
$305$	−6.00000	−	10.3923i	−0.343559	−	0.595062i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$	7.50000	−	2.59808i	0.427352	−	0.148039i
$309$		0			0
$310$	−21.0000			−1.19272
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$		0			0
$319$	13.5000	−	23.3827i	0.755855	−	1.30918i
$320$	−3.00000			−0.167705
$321$		0			0
$322$	3.00000	−	15.5885i	0.167183	−	0.868711i
$323$	−12.0000			−0.667698
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	10.0000			0.553849
$327$		0			0
$328$		0			0
$329$	6.00000	−	31.1769i	0.330791	−	1.71884i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$		0			0
$334$	9.00000	−	15.5885i	0.492458	−	0.852962i
$335$	3.00000	−	5.19615i	0.163908	−	0.283896i
$336$		0			0
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$	9.00000			0.489535
$339$		0			0
$340$	18.0000			0.976187
$341$	10.5000	−	18.1865i	0.568607	−	0.984856i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−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	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	2.00000	−	10.3923i	0.106904	−	0.555492i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−24.0000			−1.27739			−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000			−1.27739			−0.638696	+	0.769460i	$0.720526\pi$
$354$		0			0
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	−0.133263	−	0.991081i	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$		0			0
$364$	−4.00000	−	3.46410i	−0.209657	−	0.181568i
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$		0			0
$367$	−37.0000			−1.93138			−0.965692	−	0.259690i	$-0.916380\pi$
$367$	−37.0000			−1.93138			−0.965692	+	0.259690i	$0.916380\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$		0			0
$370$	−30.0000			−1.55963
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$		0			0
$376$	−6.00000	−	10.3923i	−0.309426	−	0.535942i
$377$	−18.0000			−0.927047
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$		0			0
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	−30.0000			−1.53293			−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000			−1.53293			−0.766464	+	0.642287i	$0.777986\pi$
$384$		0			0
$385$	18.0000	+	15.5885i	0.917365	+	0.794461i
$386$	7.00000			0.356291
$387$		0			0
$388$	6.50000	+	11.2583i	0.329988	+	0.571555i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	7.50000	+	12.9904i	0.377366	+	0.653617i
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$	4.00000	−	6.92820i	0.200502	−	0.347279i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	24.0000			1.19850			0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000			1.19850			0.599251	+	0.800561i	$0.295465\pi$
$402$		0			0
$403$	−14.0000			−0.697390
$404$	3.00000	−	5.19615i	0.149256	−	0.258518i
$405$		0			0
$406$	−18.0000	−	15.5885i	−0.893325	−	0.773642i
$407$	15.0000	−	25.9808i	0.743522	−	1.28782i
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$		0			0
$411$		0			0
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	7.50000	−	2.59808i	0.369051	−	0.127843i
$414$		0			0
$415$	−13.5000	+	23.3827i	−0.662689	+	1.14781i
$416$	−2.00000			−0.0980581
$417$		0			0
$418$	−6.00000			−0.293470
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$		0			0
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	−0.946883	−	0.321577i	$-0.895787\pi$
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	0.751935	+	0.659237i	$0.229121\pi$
$422$	−8.00000	+	13.8564i	−0.389434	+	0.674519i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	2.00000	−	10.3923i	0.0967868	−	0.502919i
$428$	1.50000	+	2.59808i	0.0725052	+	0.125583i
$429$		0			0
$430$	−12.0000			−0.578691
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	0.995706	+	0.0925683i	$0.0295076\pi$
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	−0.417687	+	0.908591i	$0.637159\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	−14.0000	−	12.1244i	−0.672022	−	0.581988i
$435$		0			0
$436$	−10.0000			−0.478913
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	12.0000			0.570782
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	1.00000			0.0473514
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−7.50000	−	12.9904i	−0.351992	−	0.609669i
$455$	3.00000	−	15.5885i	0.140642	−	0.730798i
$456$		0			0
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	0.977051	−	0.213006i	$-0.0683253\pi$
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	−0.672994	+	0.739648i	$0.734992\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$	9.00000	−	15.5885i	0.419627	−	0.726816i
$461$	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	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	−9.00000			−0.417815
$465$		0			0
$466$	−6.00000			−0.277945
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$	18.0000	−	31.1769i	0.830278	−	1.43808i
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	12.0000	+	10.3923i	0.550019	+	0.476331i
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$		0			0
$481$	−20.0000			−0.911922
$482$	11.5000	+	19.9186i	0.523811	+	0.907267i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−19.5000	+	33.7750i	−0.885449	+	1.53364i
$486$		0			0
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$	−2.00000	−	3.46410i	−0.0905357	−	0.156813i
$489$		0			0
$490$	16.5000	−	12.9904i	0.745394	−	0.586846i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$		0			0
$493$	54.0000			2.43204
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$		0			0
$496$	−7.00000			−0.314309
$497$		0			0
$498$		0			0
$499$	38.0000			1.70111			0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000			1.70111			0.850557	+	0.525883i	$0.176265\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	−4.50000	−	7.79423i	−0.200845	−	0.347873i
$503$	−18.0000			−0.802580			−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000			−0.802580			−0.401290	+	0.915951i	$0.631438\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$		0			0
$508$	0.500000	−	0.866025i	0.0221839	−	0.0384237i
$509$	15.0000			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	48.0000			2.11513
$516$		0			0
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	−20.0000	−	17.3205i	−0.878750	−	0.761019i
$519$		0			0
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	0.999551	+	0.0299693i	$0.00954094\pi$
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	−0.473821	+	0.880621i	$0.657126\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$	42.0000			1.82955
$528$		0			0
$529$	13.0000			0.565217
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$		0			0
$534$		0			0
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$		0			0
$538$	1.50000	−	2.59808i	0.0646696	−	0.112011i
$539$	3.00000	+	20.7846i	0.129219	+	0.895257i
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	19.0000			0.816120
$543$		0			0
$544$	6.00000			0.257248
$545$	−15.0000	−	25.9808i	−0.642529	−	1.11289i
$546$		0			0
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	−0.975976	−	0.217880i	$-0.930086\pi$
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	0.676677	+	0.736280i	$0.263419\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	9.00000	+	15.5885i	0.383413	+	0.664091i
$552$		0			0
$553$	−2.50000	+	12.9904i	−0.106311	+	0.552407i
$554$	−2.00000	−	3.46410i	−0.0849719	−	0.147176i
$555$		0			0
$556$	2.00000			0.0848189
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	0.980026	−	0.198871i	$-0.0637276\pi$
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	−0.662240	+	0.749291i	$0.730394\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	1.50000	−	7.79423i	0.0633866	−	0.329366i
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	−0.895902	−	0.444252i	$-0.853470\pi$
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	0.832684	+	0.553748i	$0.186803\pi$
$564$		0			0
$565$		0			0
$566$	−20.0000			−0.840663
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	6.00000			0.250873
$573$		0			0
$574$		0			0
$575$	24.0000			1.00087
$576$		0			0
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	0.876245	−	0.481865i	$-0.160040\pi$
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	−0.855430	+	0.517918i	$0.826707\pi$
$578$	−19.0000			−0.790296
$579$		0			0
$580$	−13.5000	−	23.3827i	−0.560557	−	0.970913i
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$		0			0
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	−0.440524	−	0.897741i	$-0.645207\pi$
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	0.997728	−	0.0673658i	$-0.0214594\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$	9.00000			0.370524
$591$		0			0
$592$	−10.0000			−0.410997
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	−0.374236	−	0.927333i	$-0.622095\pi$
$593$	15.0000	−	25.9808i	0.615976	−	1.06690i	0.990212	−	0.139569i	$-0.0445716\pi$
$594$		0			0
$595$	−9.00000	+	46.7654i	−0.368964	+	1.91719i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$		0			0
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	0.530281	+	0.847822i	$0.322086\pi$
$602$	−8.00000	−	6.92820i	−0.326056	−	0.282372i
$603$		0			0
$604$	−2.50000	+	4.33013i	−0.101724	+	0.176190i
$605$	6.00000			0.243935
$606$		0			0
$607$	−13.0000			−0.527654			−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000			−0.527654			−0.263827	+	0.964570i	$0.584985\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$		0			0
$610$	6.00000	−	10.3923i	0.242933	−	0.420772i
$611$	12.0000	−	20.7846i	0.485468	−	0.840855i
$612$		0			0
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$	13.0000	+	22.5167i	0.524637	+	0.908698i
$615$		0			0
$616$	6.00000	+	5.19615i	0.241747	+	0.209359i
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	0.959117	+	0.283011i	$0.0913331\pi$
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	−0.234464	+	0.972125i	$0.575334\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−10.5000	−	18.1865i	−0.421690	−	0.730389i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	15.0000	−	5.19615i	0.600962	−	0.208179i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	8.50000	−	14.7224i	0.339728	−	0.588427i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	60.0000			2.39236
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	2.50000	+	4.33013i	0.0994447	+	0.172243i
$633$		0			0
$634$	−10.5000	+	18.1865i	−0.417008	+	0.722280i
$635$	3.00000			0.119051
$636$		0			0
$637$	11.0000	−	8.66025i	0.435836	−	0.343132i
$638$	27.0000			1.06894
$639$		0			0
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$		0			0
$643$	−19.0000	−	32.9090i	−0.749287	−	1.29780i	−0.948165	−	0.317779i	$-0.897063\pi$
$643$	−19.0000	−	32.9090i	−0.749287	−	1.29780i	0.198878	−	0.980024i	$-0.436270\pi$
$644$	15.0000	−	5.19615i	0.591083	−	0.204757i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−39.0000			−1.52619			−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000			−1.52619			−0.763094	+	0.646288i	$0.776321\pi$
$654$		0			0
$655$	−45.0000			−1.75830
$656$		0			0
$657$		0			0
$658$	30.0000	−	10.3923i	1.16952	−	0.405134i
$659$	−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
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$		0			0
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	−15.0000	+	5.19615i	−0.581675	+	0.201498i
$666$		0			0
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	18.0000			0.696441
$669$		0			0
$670$	6.00000			0.231800
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$		0			0
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	−0.982045	−	0.188645i	$-0.939590\pi$
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	0.654394	+	0.756153i	$0.272924\pi$
$674$	2.50000	−	4.33013i	0.0962964	−	0.166790i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$		0			0
$679$	−32.5000	+	11.2583i	−1.24724	+	0.432055i
$680$	9.00000	+	15.5885i	0.345134	+	0.597790i
$681$		0			0
$682$	21.0000			0.804132
$683$	25.5000	+	44.1673i	0.975730	+	1.69001i	0.677503	+	0.735520i	$0.263062\pi$
$683$	25.5000	+	44.1673i	0.975730	+	1.69001i	0.298227	+	0.954495i	$0.403605\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−4.00000			−0.152499
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	−16.0000	−	27.7128i	−0.608669	−	1.05425i	−0.991460	−	0.130410i	$-0.958371\pi$
$691$	−16.0000	−	27.7128i	−0.608669	−	1.05425i	0.382791	−	0.923835i	$-0.374963\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	−14.0000			−0.529908
$699$		0			0
$700$	10.0000	−	3.46410i	0.377964	−	0.130931i
$701$	−9.00000			−0.339925			−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000			−0.339925			−0.169963	+	0.985451i	$0.554365\pi$
$702$		0			0
$703$	10.0000	+	17.3205i	0.377157	+	0.653255i
$704$	3.00000			0.113067
$705$		0			0
$706$	−12.0000	−	20.7846i	−0.451626	−	0.782239i
$707$	12.0000	+	10.3923i	0.451306	+	0.390843i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	21.0000	−	36.3731i	0.786456	−	1.36218i
$714$		0			0
$715$	9.00000	+	15.5885i	0.336581	+	0.582975i
$716$	12.0000			0.448461
$717$		0			0
$718$	30.0000			1.11959
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$		0			0
$721$	32.0000	+	27.7128i	1.19174	+	1.03208i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$		0			0
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	−0.421193	−	0.906971i	$-0.638389\pi$
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	0.996056	−	0.0887213i	$-0.0282781\pi$
$728$	1.00000	−	5.19615i	0.0370625	−	0.192582i
$729$		0			0
$730$	−3.00000	+	5.19615i	−0.111035	+	0.192318i
$731$	24.0000			0.887672
$732$		0			0
$733$	20.0000			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$734$	−18.5000	−	32.0429i	−0.682847	−	1.18273i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−3.00000	+	5.19615i	−0.110506	+	0.191403i
$738$		0			0
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	0.521475	−	0.853266i	$-0.325382\pi$
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	−0.999688	+	0.0249776i	$0.992049\pi$
$740$	−15.0000	−	25.9808i	−0.551411	−	0.955072i
$741$		0			0
$742$	−7.50000	+	2.59808i	−0.275334	+	0.0953784i
$743$	−27.0000	−	46.7654i	−0.990534	−	1.71566i	−0.614145	−	0.789193i	$-0.710499\pi$
$743$	−27.0000	−	46.7654i	−0.990534	−	1.71566i	−0.376389	−	0.926462i	$-0.622834\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$		0			0
$748$	−18.0000			−0.658145
$749$	−7.50000	+	2.59808i	−0.274044	+	0.0949316i
$750$		0			0
$751$	23.0000			0.839282			0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000			0.839282			0.419641	+	0.907690i	$0.362156\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$		0			0
$754$	−9.00000	−	15.5885i	−0.327761	−	0.567698i
$755$	−15.0000			−0.545906
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	42.0000			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$762$		0			0
$763$	5.00000	−	25.9808i	0.181012	−	0.940567i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−15.0000	−	25.9808i	−0.541972	−	0.938723i
$767$	6.00000			0.216647
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$	−4.50000	+	23.3827i	−0.162169	+	0.842654i
$771$		0			0
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$		0			0
$775$	14.0000	−	24.2487i	0.502895	−	0.871039i
$776$	−6.50000	+	11.2583i	−0.233336	+	0.404151i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−6.00000	+	10.3923i	−0.214149	+	0.370917i
$786$		0			0
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	−0.687481	−	0.726202i	$-0.741284\pi$
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	0.972650	+	0.232275i	$0.0746169\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$		0			0
$792$		0			0
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	−8.00000			−0.283909
$795$		0			0
$796$	8.00000			0.283552
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$		0			0
$799$	−36.0000	+	62.3538i	−1.27359	+	2.20592i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$	36.0000	+	31.1769i	1.26883	+	1.09884i
$806$	−7.00000	−	12.1244i	−0.246564	−	0.427062i
$807$		0			0
$808$	6.00000			0.211079
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	4.50000	−	23.3827i	0.157919	−	0.820571i
$813$		0			0
$814$	30.0000			1.05150
$815$	−15.0000	+	25.9808i	−0.525427	+	0.910066i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$	−11.0000			−0.384606
$819$		0			0
$820$		0			0
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	16.0000			0.557386
$825$		0			0
$826$	6.00000	+	5.19615i	0.208767	+	0.180797i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$	−27.0000			−0.937184
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−33.0000	+	25.9808i	−1.14338	+	0.900180i
$834$		0			0
$835$	27.0000	+	46.7654i	0.934374	+	1.61838i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$		0			0
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.152493	+	0.988304i	$0.548730\pi$
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.779650	+	0.626215i	$0.784603\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−8.00000			−0.275698
$843$		0			0
$844$	−16.0000			−0.550743
$845$	−13.5000	+	23.3827i	−0.464414	+	0.804389i
$846$		0			0
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$		0			0
$850$	−12.0000	+	20.7846i	−0.411597	+	0.712906i
$851$	30.0000	−	51.9615i	1.02839	−	1.78122i
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	10.0000	−	3.46410i	0.342193	−	0.118539i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	12.0000			0.409912			0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000			0.409912			0.204956	+	0.978771i	$0.434295\pi$
$858$		0			0
$859$	−16.0000			−0.545913			−0.272956	−	0.962026i	$-0.588002\pi$
$859$	−16.0000			−0.545913			−0.272956	+	0.962026i	$0.588002\pi$
$860$	−6.00000	−	10.3923i	−0.204598	−	0.354375i
$861$		0			0
$862$	−12.0000	+	20.7846i	−0.408722	+	0.707927i
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$		0			0
$868$	3.50000	−	18.1865i	0.118798	−	0.617291i
$869$	−7.50000	−	12.9904i	−0.254420	−	0.440668i
$870$		0			0
$871$	4.00000			0.135535
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$		0			0
$874$	−12.0000			−0.405906
$875$	−6.00000	−	5.19615i	−0.202837	−	0.175662i
$876$		0			0
$877$	56.0000			1.89099			0.945493	−	0.325643i	$-0.105581\pi$
$877$	56.0000			1.89099			0.945493	+	0.325643i	$0.105581\pi$
$878$	−9.50000	+	16.4545i	−0.320609	+	0.555312i
$879$		0			0
$880$	4.50000	+	7.79423i	0.151695	+	0.262743i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$		0			0
$889$	2.00000	+	1.73205i	0.0670778	+	0.0580911i
$890$	18.0000			0.603361
$891$		0			0
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$	−24.0000			−0.803129
$894$		0			0
$895$	18.0000	+	31.1769i	0.601674	+	1.04213i
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	−31.5000	−	54.5596i	−1.05058	−	1.81966i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−60.0000			−1.99447
$906$		0			0
$907$	50.0000			1.66022			0.830111	−	0.557598i	$-0.188277\pi$
$907$	50.0000			1.66022			0.830111	+	0.557598i	$0.188277\pi$
$908$	7.50000	−	12.9904i	0.248896	−	0.431101i
$909$		0			0
$910$	15.0000	−	5.19615i	0.497245	−	0.172251i
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	−6.50000	+	11.2583i	−0.215001	+	0.372392i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	−30.0000	−	25.9808i	−0.990687	−	0.857960i
$918$		0			0
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	−0.537234	−	0.843433i	$-0.680531\pi$
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	0.999052	+	0.0435419i	$0.0138642\pi$
$920$	18.0000			0.593442
$921$		0			0
$922$	18.0000			0.592798
$923$		0			0
$924$		0			0
$925$	20.0000	−	34.6410i	0.657596	−	1.13899i
$926$	−2.00000	+	3.46410i	−0.0657241	+	0.113837i
$927$		0			0
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$		0			0
$931$	−13.0000	−	5.19615i	−0.426058	−	0.170297i
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$		0			0
$934$	12.0000			0.392652
$935$	−27.0000	−	46.7654i	−0.882994	−	1.52939i
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	4.00000	+	3.46410i	0.130605	+	0.113107i
$939$		0			0
$940$	36.0000			1.17419
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		0			0
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$	12.0000			0.390154
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$	−8.00000			−0.259554
$951$		0			0
$952$	−3.00000	+	15.5885i	−0.0972306	+	0.505225i
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	−18.0000	−	31.1769i	−0.582466	−	1.00886i
$956$	−18.0000			−0.582162
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	12.0000	+	10.3923i	0.387500	+	0.335585i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	−10.0000	−	17.3205i	−0.322413	−	0.558436i
$963$		0			0
$964$	−11.5000	+	19.9186i	−0.370390	+	0.641534i
$965$	−10.5000	+	18.1865i	−0.338007	+	0.585445i
$966$		0			0
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	0.532970	−	0.846134i	$-0.321076\pi$
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	−0.999259	+	0.0384986i	$0.987742\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	−39.0000			−1.25221
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	−0.362604	−	0.931943i	$-0.618112\pi$
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	0.988389	−	0.151948i	$-0.0485545\pi$
$972$		0			0
$973$	−1.00000	+	5.19615i	−0.0320585	+	0.166581i
$974$	5.50000	−	9.52628i	0.176231	−	0.305242i
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$	19.5000	+	7.79423i	0.622905	+	0.248978i
$981$		0			0
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	−54.0000			−1.72058
$986$	27.0000	+	46.7654i	0.859855	+	1.48931i
$987$		0			0
$988$	−2.00000	+	3.46410i	−0.0636285	+	0.110208i
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$		0			0
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	0.976539	−	0.215342i	$-0.0690867\pi$
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	−0.674761	+	0.738036i	$0.735753\pi$
$992$	−3.50000	−	6.06218i	−0.111125	−	0.192474i
$993$		0			0
$994$		0			0
$995$	12.0000	+	20.7846i	0.380426	+	0.658916i
$996$		0			0
$997$	−22.0000			−0.696747			−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000			−0.696747			−0.348373	+	0.937356i	$0.613266\pi$
$998$	19.0000	+	32.9090i	0.601434	+	1.04172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.j.541.1		2
3.2	odd	2		1134.2.h.f.541.1		2
7.4	even	3		1134.2.e.g.865.1		2
9.2	odd	6		126.2.g.a.37.1	✓	2
9.4	even	3		1134.2.e.g.919.1		2
9.5	odd	6		1134.2.e.k.919.1		2
9.7	even	3		126.2.g.d.37.1	yes	2
21.11	odd	6		1134.2.e.k.865.1		2
36.7	odd	6		1008.2.s.o.289.1		2
36.11	even	6		1008.2.s.b.289.1		2
63.2	odd	6		882.2.a.j.1.1		1
63.4	even	3	inner	1134.2.h.j.109.1		2
63.11	odd	6		126.2.g.a.109.1	yes	2
63.16	even	3		882.2.a.a.1.1		1
63.20	even	6		882.2.g.e.667.1		2
63.25	even	3		126.2.g.d.109.1	yes	2
63.32	odd	6		1134.2.h.f.109.1		2
63.34	odd	6		882.2.g.g.667.1		2
63.38	even	6		882.2.g.e.361.1		2
63.47	even	6		882.2.a.h.1.1		1
63.52	odd	6		882.2.g.g.361.1		2
63.61	odd	6		882.2.a.e.1.1		1
252.11	even	6		1008.2.s.b.865.1		2
252.47	odd	6		7056.2.a.h.1.1		1
252.79	odd	6		7056.2.a.e.1.1		1
252.151	odd	6		1008.2.s.o.865.1		2
252.187	even	6		7056.2.a.bx.1.1		1
252.191	even	6		7056.2.a.by.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.g.a.37.1	✓	2	9.2	odd	6
126.2.g.a.109.1	yes	2	63.11	odd	6
126.2.g.d.37.1	yes	2	9.7	even	3
126.2.g.d.109.1	yes	2	63.25	even	3
882.2.a.a.1.1		1	63.16	even	3
882.2.a.e.1.1		1	63.61	odd	6
882.2.a.h.1.1		1	63.47	even	6
882.2.a.j.1.1		1	63.2	odd	6
882.2.g.e.361.1		2	63.38	even	6
882.2.g.e.667.1		2	63.20	even	6
882.2.g.g.361.1		2	63.52	odd	6
882.2.g.g.667.1		2	63.34	odd	6
1008.2.s.b.289.1		2	36.11	even	6
1008.2.s.b.865.1		2	252.11	even	6
1008.2.s.o.289.1		2	36.7	odd	6
1008.2.s.o.865.1		2	252.151	odd	6
1134.2.e.g.865.1		2	7.4	even	3
1134.2.e.g.919.1		2	9.4	even	3
1134.2.e.k.865.1		2	21.11	odd	6
1134.2.e.k.919.1		2	9.5	odd	6
1134.2.h.f.109.1		2	63.32	odd	6
1134.2.h.f.541.1		2	3.2	odd	2
1134.2.h.j.109.1		2	63.4	even	3	inner
1134.2.h.j.541.1		2	1.1	even	1	trivial
7056.2.a.e.1.1		1	252.79	odd	6
7056.2.a.h.1.1		1	252.47	odd	6
7056.2.a.bx.1.1		1	252.187	even	6
7056.2.a.by.1.1		1	252.191	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +6.00000 q^{23} +4.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +(2.50000 - 0.866025i) q^{28} +(4.50000 - 7.79423i) q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(6.00000 + 5.19615i) q^{35} +(5.00000 - 8.66025i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(2.00000 - 3.46410i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(6.00000 + 10.3923i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +2.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +9.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +7.00000 q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} -6.00000 q^{68} +(-1.50000 + 7.79423i) q^{70} +(-1.00000 - 1.73205i) q^{73} +10.0000 q^{74} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +4.00000 q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(-6.00000 + 10.3923i) q^{94} +(3.00000 - 5.19615i) q^{95} +(6.50000 - 11.2583i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 6 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 6 * q^5 - 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 6 q^{5} - 4 q^{7} - 2 q^{8} - 3 q^{10} + 6 q^{11} - 2 q^{13} + q^{14} - q^{16} + 6 q^{17} - 2 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 8 q^{25} + 2 q^{26} + 5 q^{28} + 9 q^{29} + 7 q^{31} + q^{32} - 6 q^{34} + 12 q^{35} + 10 q^{37} - 4 q^{38} + 6 q^{40} + 4 q^{43} - 3 q^{44} + 6 q^{46} + 12 q^{47} + 2 q^{49} + 4 q^{50} + 4 q^{52} - 3 q^{53} - 18 q^{55} + 4 q^{56} + 18 q^{58} - 3 q^{59} + 4 q^{61} + 14 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{67} - 12 q^{68} - 3 q^{70} - 2 q^{73} + 20 q^{74} - 2 q^{76} - 12 q^{77} - 5 q^{79} + 3 q^{80} + 9 q^{83} - 18 q^{85} + 8 q^{86} - 6 q^{88} - 6 q^{89} - 2 q^{91} - 6 q^{92} - 12 q^{94} + 6 q^{95} + 13 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 6 * q^5 - 4 * q^7 - 2 * q^8 - 3 * q^10 + 6 * q^11 - 2 * q^13 + q^14 - q^16 + 6 * q^17 - 2 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 8 * q^25 + 2 * q^26 + 5 * q^28 + 9 * q^29 + 7 * q^31 + q^32 - 6 * q^34 + 12 * q^35 + 10 * q^37 - 4 * q^38 + 6 * q^40 + 4 * q^43 - 3 * q^44 + 6 * q^46 + 12 * q^47 + 2 * q^49 + 4 * q^50 + 4 * q^52 - 3 * q^53 - 18 * q^55 + 4 * q^56 + 18 * q^58 - 3 * q^59 + 4 * q^61 + 14 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^67 - 12 * q^68 - 3 * q^70 - 2 * q^73 + 20 * q^74 - 2 * q^76 - 12 * q^77 - 5 * q^79 + 3 * q^80 + 9 * q^83 - 18 * q^85 + 8 * q^86 - 6 * q^88 - 6 * q^89 - 2 * q^91 - 6 * q^92 - 12 * q^94 + 6 * q^95 + 13 * q^97 - 11 * q^98

Introduction

L-functions

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