LMFDB - Embedded newform 1134.2.h.f.109.1

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			109.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.f.541.1

$q$-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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

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	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		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	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−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	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−1.50000	−	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	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		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	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−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	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	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	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$		0			0
$49$	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	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		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	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−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	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	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	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−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	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−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	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		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	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		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	0.980622	+	0.195911i	$0.0627665\pi$
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	−0.320647	+	0.947199i	$0.603900\pi$
$98$	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	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		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	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	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	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$		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	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		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	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$	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	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$		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	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	−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	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$		0			0
$166$	9.00000			0.698535
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	−0.273252	−	0.961943i	$-0.588099\pi$
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	0.969693	−	0.244328i	$-0.0785675\pi$
$168$		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	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		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	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		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	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	−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	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	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	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	−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	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$		0			0
$227$	15.0000			0.995585			0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000			0.995585			0.497792	+	0.867296i	$0.334144\pi$
$228$		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	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		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	0.413061	+	0.910703i	$0.364460\pi$
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	−0.995223	+	0.0976302i	$0.968874\pi$
$240$		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	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		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	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		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	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		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	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	9.50000	+	16.4545i	0.577084	+	0.999539i	0.995812	+	0.0914269i	$0.0291428\pi$
$271$	9.50000	+	16.4545i	0.577084	+	0.999539i	−0.418728	+	0.908112i	$0.637524\pi$
$272$	−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	0.999069	+	0.0431402i	$0.0137362\pi$
$281$	9.00000	+	15.5885i	0.536895	+	0.929929i	−0.462174	+	0.886789i	$0.652930\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		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	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		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	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	0.404528	+	0.914526i	$0.367436\pi$
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	−0.994266	+	0.106932i	$0.965897\pi$
$318$		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	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−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	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$	−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	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−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	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$		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	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$		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	$-0.222014\pi$
$383$	30.0000			1.53293			0.766464	+	0.642287i	$0.222014\pi$
$384$		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	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		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	0.748017	−	0.663679i	$-0.231006\pi$
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	−0.948772	+	0.315963i	$0.897673\pi$
$398$	−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	$-0.704535\pi$
$401$	−24.0000			−1.19850			−0.599251	+	0.800561i	$0.704535\pi$
$402$		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	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		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	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	0.751935	−	0.659237i	$-0.229121\pi$
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	−0.946883	+	0.321577i	$0.895787\pi$
$422$	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	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		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	−0.545185	−	0.838316i	$-0.683541\pi$
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	0.998595	+	0.0529862i	$0.0168739\pi$
$440$	−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	$-0.717359\pi$
$443$	7.50000	−	12.9904i	0.356336	−	0.617192i	0.987346	+	0.158583i	$0.0506926\pi$
$444$		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	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		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	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$	−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	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$		0			0
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$	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	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		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	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		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	−0.963312	−	0.268384i	$-0.913510\pi$
$487$	−5.50000	+	9.52628i	−0.249229	+	0.431677i	0.714083	+	0.700061i	$0.246844\pi$
$488$	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	$-0.898429\pi$
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	0.746438	+	0.665455i	$0.231763\pi$
$492$		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	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		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	$-0.607869\pi$
$509$	−15.0000			−0.664863			−0.332432	+	0.943127i	$0.607869\pi$
$510$		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	0.473821	+	0.880621i	$0.342874\pi$
$521$	−12.0000	+	20.7846i	−0.525730	+	0.910590i	−0.999551	+	0.0299693i	$0.990459\pi$
$522$		0			0
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$	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	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	−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	0.676677	−	0.736280i	$-0.263419\pi$
$547$	−7.00000	−	12.1244i	−0.299298	−	0.518400i	−0.975976	+	0.217880i	$0.930086\pi$
$548$	−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	$-0.936272\pi$
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	0.662240	+	0.749291i	$0.269606\pi$
$558$		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	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$		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	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		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	$-0.400192\pi$
$572$	−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	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$	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	−0.997728	−	0.0673658i	$-0.978541\pi$
$587$	−13.5000	−	23.3827i	−0.557205	−	0.965107i	0.440524	−	0.897741i	$-0.354793\pi$
$588$		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	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		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	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$	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	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	−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	0.234464	+	0.972125i	$0.424666\pi$
$617$	−18.0000	+	31.1769i	−0.724653	+	1.25514i	−0.959117	+	0.283011i	$0.908667\pi$
$618$		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	$-0.576159\pi$
$641$	−12.0000			−0.473972			−0.236986	+	0.971513i	$0.576159\pi$
$642$		0			0
$643$	−19.0000	+	32.9090i	−0.749287	+	1.29780i	0.198878	+	0.980024i	$0.436270\pi$
$643$	−19.0000	+	32.9090i	−0.749287	+	1.29780i	−0.948165	+	0.317779i	$0.897063\pi$
$644$	−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	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$		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	$-0.223679\pi$
$653$	39.0000			1.52619			0.763094	+	0.646288i	$0.223679\pi$
$654$		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	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	−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	0.654394	−	0.756153i	$-0.272924\pi$
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	−0.982045	+	0.188645i	$0.939590\pi$
$674$	−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	−0.352549	−	0.935793i	$-0.614685\pi$
$677$	16.5000	−	28.5788i	0.634147	−	1.09837i	0.986695	−	0.162581i	$-0.0519817\pi$
$678$		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	−0.298227	+	0.954495i	$0.596395\pi$
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.677503	+	0.735520i	$0.736938\pi$
$684$		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	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−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	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		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	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		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	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$		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	0.996056	+	0.0887213i	$0.0282781\pi$
$727$	15.5000	+	26.8468i	0.574863	+	0.995692i	−0.421193	+	0.906971i	$0.638389\pi$
$728$	−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	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	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	0.376389	−	0.926462i	$-0.377166\pi$
$743$	27.0000	−	46.7654i	0.990534	−	1.71566i	0.614145	−	0.789193i	$-0.289501\pi$
$744$		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	$-0.775414\pi$
$761$	−42.0000			−1.52250			−0.761249	+	0.648459i	$0.775414\pi$
$762$		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	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$	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	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		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	0.972650	−	0.232275i	$-0.0746169\pi$
$787$	8.00000	+	13.8564i	0.285169	+	0.493928i	−0.687481	+	0.726202i	$0.741284\pi$
$788$	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	$-0.992042\pi$
$797$	−13.5000	+	23.3827i	−0.478195	+	0.828257i	0.521493	+	0.853256i	$0.325375\pi$
$798$		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	$-0.765678\pi$
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	0.952012	+	0.306062i	$0.0990113\pi$
$810$		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	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	−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	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	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	0.779650	+	0.626215i	$0.215397\pi$
$839$	27.0000	+	46.7654i	0.932144	+	1.61452i	0.152493	+	0.988304i	$0.451270\pi$
$840$		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	0.927491	+	0.373845i	$0.121961\pi$
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	−0.139986	+	0.990153i	$0.544706\pi$
$854$	−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	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		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	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		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	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		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	$-0.532118\pi$
$887$	−6.00000			−0.201460			−0.100730	+	0.994914i	$0.532118\pi$
$888$		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	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		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	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$	−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	$-0.704526\pi$
$929$	12.0000	−	20.7846i	0.393707	−	0.681921i	0.992935	+	0.118657i	$0.0378590\pi$
$930$		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	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$		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	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		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	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		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	−0.999259	−	0.0384986i	$-0.987742\pi$
$967$	−14.5000	+	25.1147i	−0.466289	+	0.807635i	0.532970	+	0.846134i	$0.321076\pi$
$968$	−2.00000			−0.0642824
$969$		0			0
$970$	−39.0000			−1.25221
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	−0.988389	−	0.151948i	$-0.951445\pi$
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	0.362604	−	0.931943i	$-0.381888\pi$
$972$		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	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		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	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		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	−0.674761	−	0.738036i	$-0.735753\pi$
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	0.976539	+	0.215342i	$0.0690867\pi$
$992$	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.f.109.1		2
3.2	odd	2		1134.2.h.j.109.1		2
7.2	even	3		1134.2.e.k.919.1		2
9.2	odd	6		1134.2.e.g.865.1		2
9.4	even	3		126.2.g.a.109.1	yes	2
9.5	odd	6		126.2.g.d.109.1	yes	2
9.7	even	3		1134.2.e.k.865.1		2
21.2	odd	6		1134.2.e.g.919.1		2
36.23	even	6		1008.2.s.o.865.1		2
36.31	odd	6		1008.2.s.b.865.1		2
63.2	odd	6		1134.2.h.j.541.1		2
63.4	even	3		882.2.a.j.1.1		1
63.5	even	6		882.2.g.g.667.1		2
63.13	odd	6		882.2.g.e.361.1		2
63.16	even	3	inner	1134.2.h.f.541.1		2
63.23	odd	6		126.2.g.d.37.1	yes	2
63.31	odd	6		882.2.a.h.1.1		1
63.32	odd	6		882.2.a.a.1.1		1
63.40	odd	6		882.2.g.e.667.1		2
63.41	even	6		882.2.g.g.361.1		2
63.58	even	3		126.2.g.a.37.1	✓	2
63.59	even	6		882.2.a.e.1.1		1
252.23	even	6		1008.2.s.o.289.1		2
252.31	even	6		7056.2.a.h.1.1		1
252.59	odd	6		7056.2.a.bx.1.1		1
252.67	odd	6		7056.2.a.by.1.1		1
252.95	even	6		7056.2.a.e.1.1		1
252.247	odd	6		1008.2.s.b.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.g.a.37.1	✓	2	63.58	even	3
126.2.g.a.109.1	yes	2	9.4	even	3
126.2.g.d.37.1	yes	2	63.23	odd	6
126.2.g.d.109.1	yes	2	9.5	odd	6
882.2.a.a.1.1		1	63.32	odd	6
882.2.a.e.1.1		1	63.59	even	6
882.2.a.h.1.1		1	63.31	odd	6
882.2.a.j.1.1		1	63.4	even	3
882.2.g.e.361.1		2	63.13	odd	6
882.2.g.e.667.1		2	63.40	odd	6
882.2.g.g.361.1		2	63.41	even	6
882.2.g.g.667.1		2	63.5	even	6
1008.2.s.b.289.1		2	252.247	odd	6
1008.2.s.b.865.1		2	36.31	odd	6
1008.2.s.o.289.1		2	252.23	even	6
1008.2.s.o.865.1		2	36.23	even	6
1134.2.e.g.865.1		2	9.2	odd	6
1134.2.e.g.919.1		2	21.2	odd	6
1134.2.e.k.865.1		2	9.7	even	3
1134.2.e.k.919.1		2	7.2	even	3
1134.2.h.f.109.1		2	1.1	even	1	trivial
1134.2.h.f.541.1		2	63.16	even	3	inner
1134.2.h.j.109.1		2	3.2	odd	2
1134.2.h.j.541.1		2	63.2	odd	6
7056.2.a.e.1.1		1	252.95	even	6
7056.2.a.h.1.1		1	252.31	even	6
7056.2.a.bx.1.1		1	252.59	odd	6
7056.2.a.by.1.1		1	252.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
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

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