LMFDB - Embedded newform 1755.2.i.c.1171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0137455547$
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 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.c.586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +1.00000 q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(0.500000 + 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{34} -1.00000 q^{35} +4.00000 q^{37} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 7.79423i) q^{41} +(4.00000 + 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(6.50000 + 11.2583i) q^{47} +(3.00000 - 5.19615i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} -2.00000 q^{55} +(-1.50000 - 2.59808i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +8.00000 q^{62} +7.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.500000 - 0.866025i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.500000 + 0.866025i) q^{70} +6.00000 q^{71} -12.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.00000 + 1.73205i) q^{77} +(3.00000 + 5.19615i) q^{79} -1.00000 q^{80} -9.00000 q^{82} +(5.50000 + 9.52628i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(4.00000 - 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{88} -5.00000 q^{89} +1.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(6.50000 - 11.2583i) q^{94} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - q^{5} + q^{7} - 6 q^{8}+O(q^{10}) $ 2 * q - q^2 + q^4 - q^5 + q^7 - 6 * q^8	$ 2 q - q^{2} + q^{4} - q^{5} + q^{7} - 6 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + q^{14} + q^{16} + 8 q^{17} + q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 2 q^{26} + 2 q^{28} - q^{29} - 8 q^{31} - 5 q^{32} - 4 q^{34} - 2 q^{35} + 8 q^{37} + 3 q^{40} + 9 q^{41} + 8 q^{43} + 4 q^{44} + 6 q^{46} + 13 q^{47} + 6 q^{49} - q^{50} - q^{52} + 20 q^{53} - 4 q^{55} - 3 q^{56} - q^{58} + 6 q^{59} + q^{61} + 16 q^{62} + 14 q^{64} + q^{65} + q^{67} + 4 q^{68} + q^{70} + 12 q^{71} - 24 q^{73} - 4 q^{74} - 2 q^{77} + 6 q^{79} - 2 q^{80} - 18 q^{82} + 11 q^{83} - 4 q^{85} + 8 q^{86} - 6 q^{88} - 10 q^{89} + 2 q^{91} + 3 q^{92} + 13 q^{94} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 - q^5 + q^7 - 6 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + q^14 + q^16 + 8 * q^17 + q^20 + 2 * q^22 - 3 * q^23 - q^25 - 2 * q^26 + 2 * q^28 - q^29 - 8 * q^31 - 5 * q^32 - 4 * q^34 - 2 * q^35 + 8 * q^37 + 3 * q^40 + 9 * q^41 + 8 * q^43 + 4 * q^44 + 6 * q^46 + 13 * q^47 + 6 * q^49 - q^50 - q^52 + 20 * q^53 - 4 * q^55 - 3 * q^56 - q^58 + 6 * q^59 + q^61 + 16 * q^62 + 14 * q^64 + q^65 + q^67 + 4 * q^68 + q^70 + 12 * q^71 - 24 * q^73 - 4 * q^74 - 2 * q^77 + 6 * q^79 - 2 * q^80 - 18 * q^82 + 11 * q^83 - 4 * q^85 + 8 * q^86 - 6 * q^88 - 10 * q^89 + 2 * q^91 + 3 * q^92 + 13 * q^94 + 2 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	1.00000			0.316228
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	1.00000			0.188982
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$		0			0
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000			0.442326
$47$	6.50000	+	11.2583i	0.948122	+	1.64220i	0.749375	+	0.662145i	$0.230354\pi$
$47$	6.50000	+	11.2583i	0.948122	+	1.64220i	0.198747	+	0.980051i	$0.436313\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		0			0
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	7.00000			0.875000
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−12.0000			−1.40449			−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000			−1.40449			−0.702247	+	0.711934i	$0.747820\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$		0			0
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	−9.00000			−0.993884
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	0.992255	+	0.124218i	$0.0396422\pi$
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	−0.388552	+	0.921427i	$0.627024\pi$
$84$		0			0
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		0			0
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−5.00000			−0.529999			−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000			−0.529999			−0.264999	+	0.964249i	$0.585372\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$	6.50000	−	11.2583i	0.670424	−	1.16121i
$95$		0			0
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−6.00000			−0.606092
$99$		0			0
$100$	−1.00000			−0.100000
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	−5.00000	−	8.66025i	−0.485643	−	0.841158i
$107$	−13.0000			−1.25676			−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000			−1.25676			−0.628379	+	0.777908i	$0.716281\pi$
$108$		0			0
$109$	1.00000			0.0957826			0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000			0.0957826			0.0478913	+	0.998853i	$0.484750\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	−0.756487	−	0.654008i	$-0.773086\pi$
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	0.944632	+	0.328133i	$0.106419\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	−1.00000			−0.0928477
$117$		0			0
$118$	−6.00000			−0.552345
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	0.500000	−	0.866025i	0.0452679	−	0.0784063i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$		0			0
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	−0.379379	−	0.925241i	$-0.623862\pi$
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	0.990972	−	0.134069i	$-0.0428042\pi$
$132$		0			0
$133$		0			0
$134$	−1.00000			−0.0863868
$135$		0			0
$136$	−12.0000			−1.02899
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	0.973910	+	0.226935i	$0.0728704\pi$
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	−0.290424	+	0.956898i	$0.593796\pi$
$138$		0			0
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	2.00000			0.167248
$144$		0			0
$145$	1.00000			0.0830455
$146$	6.00000	+	10.3923i	0.496564	+	0.860073i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$		0			0
$153$		0			0
$154$	2.00000			0.161165
$155$	−4.00000	−	6.92820i	−0.321288	−	0.556487i
$156$		0			0
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	0.243403	+	0.969925i	$0.421736\pi$
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	−0.961681	+	0.274169i	$0.911597\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$	−3.00000			−0.236433
$162$		0			0
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	5.50000	−	9.52628i	0.426883	−	0.739383i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	4.00000			0.306786
$171$		0			0
$172$	8.00000			0.609994
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	0.542583	−	0.840002i	$-0.317446\pi$
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	−0.998755	+	0.0498898i	$0.984113\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	2.50000	+	4.33013i	0.187383	+	0.324557i
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−0.500000	−	0.866025i	−0.0370625	−	0.0641941i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	13.0000			0.948122
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	−3.00000	−	5.19615i	−0.214286	−	0.371154i
$197$	24.0000			1.70993			0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000			1.70993			0.854965	+	0.518686i	$0.173579\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$		0			0
$202$	3.00000	−	5.19615i	0.211079	−	0.365600i
$203$	0.500000	−	0.866025i	0.0350931	−	0.0607831i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−16.0000			−1.11477
$207$		0			0
$208$	1.00000			0.0693375
$209$		0			0
$210$		0			0
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	−0.950619	−	0.310361i	$-0.899550\pi$
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	0.744090	+	0.668079i	$0.232883\pi$
$212$	5.00000	−	8.66025i	0.343401	−	0.594789i
$213$		0			0
$214$	6.50000	+	11.2583i	0.444331	+	0.769604i
$215$	−8.00000			−0.545595
$216$		0			0
$217$	−8.00000			−0.543075
$218$	−0.500000	−	0.866025i	−0.0338643	−	0.0586546i
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$	8.50000	+	14.7224i	0.569202	+	0.985887i	0.996645	+	0.0818447i	$0.0260811\pi$
$223$	8.50000	+	14.7224i	0.569202	+	0.985887i	−0.427443	+	0.904042i	$0.640586\pi$
$224$	−5.00000			−0.334077
$225$		0			0
$226$	−4.00000			−0.266076
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$	−1.50000	+	2.59808i	−0.0989071	+	0.171312i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$		0			0
$235$	−13.0000			−0.848026
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$		0			0
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	−7.00000			−0.449977
$243$		0			0
$244$	1.00000			0.0640184
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$		0			0
$248$	12.0000	−	20.7846i	0.762001	−	1.31982i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−6.50000	−	11.2583i	−0.407846	−	0.706410i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$		0			0
$259$	2.00000	+	3.46410i	0.124274	+	0.215249i
$260$	1.00000			0.0620174
$261$		0			0
$262$	−14.0000			−0.864923
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	0.506669	−	0.862141i	$-0.330877\pi$
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	−0.999970	+	0.00771799i	$0.997543\pi$
$264$		0			0
$265$	−5.00000	+	8.66025i	−0.307148	+	0.531995i
$266$		0			0
$267$		0			0
$268$	−0.500000	−	0.866025i	−0.0305424	−	0.0529009i
$269$	−9.00000			−0.548740			−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000			−0.548740			−0.274370	+	0.961624i	$0.588469\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	8.00000	−	13.8564i	0.483298	−	0.837096i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	10.0000	+	17.3205i	0.600842	+	1.04069i	0.992694	+	0.120660i	$0.0385012\pi$
$277$	10.0000	+	17.3205i	0.600842	+	1.04069i	−0.391852	+	0.920028i	$0.628166\pi$
$278$	−12.0000			−0.719712
$279$		0			0
$280$	3.00000			0.179284
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	−0.605575	−	0.795788i	$-0.707057\pi$
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	0.991960	+	0.126550i	$0.0403903\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−1.00000	−	1.73205i	−0.0591312	−	0.102418i
$287$	9.00000			0.531253
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	−0.500000	−	0.866025i	−0.0293610	−	0.0508548i
$291$		0			0
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	2.00000	−	3.46410i	0.116841	−	0.202375i	−0.801673	−	0.597763i	$-0.796056\pi$
$293$	2.00000	−	3.46410i	0.116841	−	0.202375i	0.918514	+	0.395388i	$0.129390\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	−12.0000			−0.697486
$297$		0			0
$298$	3.00000			0.173785
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$		0			0
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$		0			0
$305$	−1.00000			−0.0572598
$306$		0			0
$307$	−19.0000			−1.08439			−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000			−1.08439			−0.542194	+	0.840254i	$0.682406\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$		0			0
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−2.00000	+	3.46410i	−0.113410	+	0.196431i	−0.917143	−	0.398559i	$-0.869511\pi$
$311$	−2.00000	+	3.46410i	−0.113410	+	0.196431i	0.803733	+	0.594990i	$0.202844\pi$
$312$		0			0
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	6.00000			0.337526
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	1.00000	−	1.73205i	0.0559893	−	0.0969762i
$320$	−3.50000	+	6.06218i	−0.195656	+	0.338886i
$321$		0			0
$322$	1.50000	+	2.59808i	0.0835917	+	0.144785i
$323$		0			0
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$		0			0
$328$	−13.5000	+	23.3827i	−0.745413	+	1.29109i
$329$	−6.50000	+	11.2583i	−0.358357	+	0.620692i
$330$		0			0
$331$	9.00000	+	15.5885i	0.494685	+	0.856819i	0.999981	−	0.00612670i	$-0.00195020\pi$
$331$	9.00000	+	15.5885i	0.494685	+	0.856819i	−0.505296	+	0.862946i	$0.668617\pi$
$332$	11.0000			0.603703
$333$		0			0
$334$	3.00000			0.164153
$335$	0.500000	+	0.866025i	0.0273179	+	0.0473160i
$336$		0			0
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	0.453889	+	0.891058i	$0.350036\pi$
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	−0.998624	+	0.0524499i	$0.983297\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−16.0000			−0.866449
$342$		0			0
$343$	13.0000			0.701934
$344$	−12.0000	−	20.7846i	−0.646997	−	1.12063i
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	0.195507	+	0.980702i	$0.437365\pi$
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	−0.947067	+	0.321037i	$0.895969\pi$
$348$		0			0
$349$	4.50000	+	7.79423i	0.240879	+	0.417215i	0.960965	−	0.276670i	$-0.0892308\pi$
$349$	4.50000	+	7.79423i	0.240879	+	0.417215i	−0.720086	+	0.693885i	$0.755897\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−10.0000			−0.533002
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−2.50000	+	4.33013i	−0.132500	+	0.229496i
$357$		0			0
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	−8.00000			−0.422224			−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000			−0.422224			−0.211112	+	0.977462i	$0.567708\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$		0			0
$364$	0.500000	−	0.866025i	0.0262071	−	0.0453921i
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$		0			0
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	0.893873	+	0.448320i	$0.147978\pi$
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	−0.0586798	+	0.998277i	$0.518689\pi$
$368$	−3.00000			−0.156386
$369$		0			0
$370$	4.00000			0.207950
$371$	5.00000	+	8.66025i	0.259587	+	0.449618i
$372$		0			0
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	−0.625917	−	0.779890i	$-0.715275\pi$
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	0.988363	+	0.152115i	$0.0486083\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$	−19.5000	−	33.7750i	−1.00564	−	1.74181i
$377$	−1.00000			−0.0515026
$378$		0			0
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$		0			0
$381$		0			0
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	−0.977613	−	0.210411i	$-0.932520\pi$
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	0.671027	+	0.741433i	$0.265853\pi$
$384$		0			0
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	−2.00000			−0.101797
$387$		0			0
$388$	2.00000			0.101535
$389$	−15.5000	−	26.8468i	−0.785881	−	1.36119i	−0.928471	−	0.371404i	$-0.878876\pi$
$389$	−15.5000	−	26.8468i	−0.785881	−	1.36119i	0.142590	−	0.989782i	$-0.454457\pi$
$390$		0			0
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$	−9.00000	+	15.5885i	−0.454569	+	0.787336i
$393$		0			0
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	−10.0000	−	17.3205i	−0.501255	−	0.868199i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	0.998322	−	0.0579116i	$-0.0184442\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	6.00000			0.298511
$405$		0			0
$406$	−1.00000			−0.0496292
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$		0			0
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	0.210017	+	0.977698i	$0.432648\pi$
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	−0.951720	+	0.306968i	$0.900685\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	−8.00000	−	13.8564i	−0.394132	−	0.682656i
$413$	6.00000			0.295241
$414$		0			0
$415$	−11.0000			−0.539969
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$		0			0
$419$	−5.00000	+	8.66025i	−0.244266	+	0.423081i	−0.961925	−	0.273314i	$-0.911880\pi$
$419$	−5.00000	+	8.66025i	−0.244266	+	0.423081i	0.717659	+	0.696395i	$0.245214\pi$
$420$		0			0
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	0.984648	−	0.174550i	$-0.0558472\pi$
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	−0.643489	+	0.765455i	$0.722514\pi$
$422$	6.00000			0.292075
$423$		0			0
$424$	−30.0000			−1.45693
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	−0.500000	+	0.866025i	−0.0241967	+	0.0419099i
$428$	−6.50000	+	11.2583i	−0.314189	+	0.544192i
$429$		0			0
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	−26.0000			−1.25238			−0.626188	−	0.779672i	$-0.715386\pi$
$431$	−26.0000			−1.25238			−0.626188	+	0.779672i	$0.715386\pi$
$432$		0			0
$433$	−32.0000			−1.53782			−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000			−1.53782			−0.768911	+	0.639356i	$0.779201\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$		0			0
$436$	0.500000	−	0.866025i	0.0239457	−	0.0414751i
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	−4.00000			−0.190261
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	0.994187	−	0.107671i	$-0.0343394\pi$
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	−0.590339	+	0.807155i	$0.701006\pi$
$444$		0			0
$445$	2.50000	−	4.33013i	0.118511	−	0.205268i
$446$	8.50000	−	14.7224i	0.402487	−	0.697127i
$447$		0			0
$448$	3.50000	+	6.06218i	0.165359	+	0.286411i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	18.0000			0.847587
$452$	−2.00000	−	3.46410i	−0.0940721	−	0.162938i
$453$		0			0
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$	−0.500000	+	0.866025i	−0.0234404	+	0.0405999i
$456$		0			0
$457$	8.00000	+	13.8564i	0.374224	+	0.648175i	0.990211	−	0.139581i	$-0.0445757\pi$
$457$	8.00000	+	13.8564i	0.374224	+	0.648175i	−0.615986	+	0.787757i	$0.711242\pi$
$458$	−13.0000			−0.607450
$459$		0			0
$460$	−3.00000			−0.139876
$461$	6.50000	+	11.2583i	0.302735	+	0.524353i	0.976755	−	0.214361i	$-0.0687669\pi$
$461$	6.50000	+	11.2583i	0.302735	+	0.524353i	−0.674019	+	0.738714i	$0.735434\pi$
$462$		0			0
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	−0.0562469	−	0.998417i	$-0.517913\pi$
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	0.892778	−	0.450497i	$-0.148753\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$		0			0
$469$	1.00000			0.0461757
$470$	6.50000	+	11.2583i	0.299823	+	0.519308i
$471$		0			0
$472$	−9.00000	+	15.5885i	−0.414259	+	0.717517i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$		0			0
$476$	4.00000			0.183340
$477$		0			0
$478$	24.0000			1.09773
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	11.5000	−	19.9186i	0.523811	−	0.907267i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$		0			0
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	−2.00000	−	3.46410i	−0.0900755	−	0.156015i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$		0			0
$503$	−39.0000			−1.73892			−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000			−1.73892			−0.869462	+	0.494000i	$0.835534\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	−6.00000	−	10.3923i	−0.265424	−	0.459728i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	22.0000			0.970378
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	−13.0000	+	22.5167i	−0.571739	+	0.990282i
$518$	2.00000	−	3.46410i	0.0878750	−	0.152204i
$519$		0			0
$520$	−1.50000	−	2.59808i	−0.0657794	−	0.113933i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	21.0000			0.918266			0.459133	−	0.888368i	$-0.348160\pi$
$523$	21.0000			0.918266			0.459133	+	0.888368i	$0.348160\pi$
$524$	−7.00000	−	12.1244i	−0.305796	−	0.529655i
$525$		0			0
$526$	−8.00000	+	13.8564i	−0.348817	+	0.604168i
$527$	−16.0000	+	27.7128i	−0.696971	+	1.20719i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	10.0000			0.434372
$531$		0			0
$532$		0			0
$533$	−4.50000	−	7.79423i	−0.194917	−	0.337606i
$534$		0			0
$535$	6.50000	−	11.2583i	0.281020	−	0.486740i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$		0			0
$538$	4.50000	+	7.79423i	0.194009	+	0.336033i
$539$	12.0000			0.516877
$540$		0			0
$541$	5.00000			0.214967			0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000			0.214967			0.107483	+	0.994207i	$0.465721\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$		0			0
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$	−0.500000	+	0.866025i	−0.0214176	+	0.0370965i
$546$		0			0
$547$	−22.5000	−	38.9711i	−0.962031	−	1.66629i	−0.717390	−	0.696672i	$-0.754663\pi$
$547$	−22.5000	−	38.9711i	−0.962031	−	1.66629i	−0.244641	−	0.969614i	$-0.578670\pi$
$548$	16.0000			0.683486
$549$		0			0
$550$	−2.00000			−0.0852803
$551$		0			0
$552$		0			0
$553$	−3.00000	+	5.19615i	−0.127573	+	0.220963i
$554$	10.0000	−	17.3205i	0.424859	−	0.735878i
$555$		0			0
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−22.0000			−0.932170			−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000			−0.932170			−0.466085	+	0.884740i	$0.654336\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−9.50000	+	16.4545i	−0.400377	+	0.693474i	−0.993771	−	0.111438i	$-0.964454\pi$
$563$	−9.50000	+	16.4545i	−0.400377	+	0.693474i	0.593394	+	0.804912i	$0.297788\pi$
$564$		0			0
$565$	2.00000	+	3.46410i	0.0841406	+	0.145736i
$566$	−13.0000			−0.546431
$567$		0			0
$568$	−18.0000			−0.755263
$569$	−19.0000	−	32.9090i	−0.796521	−	1.37962i	−0.921869	−	0.387503i	$-0.873338\pi$
$569$	−19.0000	−	32.9090i	−0.796521	−	1.37962i	0.125347	−	0.992113i	$-0.459996\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	1.00000	−	1.73205i	0.0418121	−	0.0724207i
$573$		0			0
$574$	−4.50000	−	7.79423i	−0.187826	−	0.325325i
$575$	3.00000			0.125109
$576$		0			0
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$		0			0
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	−5.50000	+	9.52628i	−0.228178	+	0.395217i
$582$		0			0
$583$	10.0000	+	17.3205i	0.414158	+	0.717342i
$584$	36.0000			1.48969
$585$		0			0
$586$	−4.00000			−0.165238
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	0.940996	+	0.338418i	$0.109892\pi$
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	−0.177419	+	0.984135i	$0.556775\pi$
$588$		0			0
$589$		0			0
$590$	3.00000	−	5.19615i	0.123508	−	0.213922i
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	4.00000			0.164260			0.0821302	−	0.996622i	$-0.473828\pi$
$593$	4.00000			0.164260			0.0821302	+	0.996622i	$0.473828\pi$
$594$		0			0
$595$	−4.00000			−0.163984
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$		0			0
$598$	1.50000	−	2.59808i	0.0613396	−	0.106243i
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	−0.468173	−	0.883637i	$-0.655088\pi$
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	0.999338	−	0.0363689i	$-0.0115791\pi$
$600$		0			0
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	0.745845	−	0.666120i	$-0.232046\pi$
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	−0.949799	+	0.312861i	$0.898713\pi$
$602$	8.00000			0.326056
$603$		0			0
$604$	−10.0000			−0.406894
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	−0.532509	−	0.846424i	$-0.678751\pi$
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	0.999279	+	0.0379540i	$0.0120840\pi$
$608$		0			0
$609$		0			0
$610$	0.500000	+	0.866025i	0.0202444	+	0.0350643i
$611$	13.0000			0.525924
$612$		0			0
$613$	24.0000			0.969351			0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000			0.969351			0.484675	+	0.874694i	$0.338938\pi$
$614$	9.50000	+	16.4545i	0.383389	+	0.664049i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−24.0000	+	41.5692i	−0.966204	+	1.67351i	−0.259858	+	0.965647i	$0.583676\pi$
$617$	−24.0000	+	41.5692i	−0.966204	+	1.67351i	−0.706346	+	0.707867i	$0.749658\pi$
$618$		0			0
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	−0.917053	−	0.398766i	$-0.869439\pi$
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	0.113185	−	0.993574i	$-0.463895\pi$
$620$	−8.00000			−0.321288
$621$		0			0
$622$	4.00000			0.160385
$623$	−2.50000	−	4.33013i	−0.100160	−	0.173483i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$		0			0
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	16.0000			0.637962
$630$		0			0
$631$	4.00000			0.159237			0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000			0.159237			0.0796187	+	0.996825i	$0.474630\pi$
$632$	−9.00000	−	15.5885i	−0.358001	−	0.620076i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−6.50000	+	11.2583i	−0.257945	+	0.446773i
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	−3.00000			−0.118585
$641$	20.5000	+	35.5070i	0.809701	+	1.40244i	0.913071	+	0.407801i	$0.133704\pi$
$641$	20.5000	+	35.5070i	0.809701	+	1.40244i	−0.103370	+	0.994643i	$0.532962\pi$
$642$		0			0
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$	−1.50000	+	2.59808i	−0.0591083	+	0.102379i
$645$		0			0
$646$		0			0
$647$	7.00000			0.275198			0.137599	−	0.990488i	$-0.456061\pi$
$647$	7.00000			0.275198			0.137599	+	0.990488i	$0.456061\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$	0.500000	+	0.866025i	0.0196116	+	0.0339683i
$651$		0			0
$652$	−6.00000	+	10.3923i	−0.234978	+	0.406994i
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	0.262515	+	0.964928i	$0.415448\pi$
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	−0.966910	+	0.255119i	$0.917885\pi$
$654$		0			0
$655$	7.00000	+	12.1244i	0.273513	+	0.473738i
$656$	9.00000			0.351391
$657$		0			0
$658$	13.0000			0.506793
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	0.494337	+	0.869270i	$0.335411\pi$
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	−0.999979	+	0.00652642i	$0.997923\pi$
$662$	9.00000	−	15.5885i	0.349795	−	0.605863i
$663$		0			0
$664$	−16.5000	−	28.5788i	−0.640324	−	1.10907i
$665$		0			0
$666$		0			0
$667$	3.00000			0.116160
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	0.500000	−	0.866025i	0.0193167	−	0.0334575i
$671$	−1.00000	+	1.73205i	−0.0386046	+	0.0668651i
$672$		0			0
$673$	−9.00000	−	15.5885i	−0.346925	−	0.600891i	0.638777	−	0.769392i	$-0.279441\pi$
$673$	−9.00000	−	15.5885i	−0.346925	−	0.600891i	−0.985701	+	0.168501i	$0.946107\pi$
$674$	20.0000			0.770371
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$		0			0
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$	6.00000	−	10.3923i	0.230089	−	0.398527i
$681$		0			0
$682$	8.00000	+	13.8564i	0.306336	+	0.530589i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$		0			0
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	5.00000	−	8.66025i	0.190485	−	0.329929i
$690$		0			0
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.743170	+	0.669102i	$0.233321\pi$
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.207875	+	0.978155i	$0.433345\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	28.0000			1.06287
$695$	6.00000	+	10.3923i	0.227593	+	0.394203i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	4.50000	−	7.79423i	0.170328	−	0.295016i
$699$		0			0
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	−7.00000			−0.264386			−0.132193	−	0.991224i	$-0.542202\pi$
$701$	−7.00000			−0.264386			−0.132193	+	0.991224i	$0.542202\pi$
$702$		0			0
$703$		0			0
$704$	7.00000	+	12.1244i	0.263822	+	0.456954i
$705$		0			0
$706$		0			0
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−21.5000	−	37.2391i	−0.807449	−	1.39854i	−0.914625	−	0.404303i	$-0.867514\pi$
$709$	−21.5000	−	37.2391i	−0.807449	−	1.39854i	0.107176	−	0.994240i	$-0.465819\pi$
$710$	6.00000			0.225176
$711$		0			0
$712$	15.0000			0.562149
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	−1.00000	+	1.73205i	−0.0373979	+	0.0647750i
$716$	−3.00000	+	5.19615i	−0.112115	+	0.194189i
$717$		0			0
$718$	4.00000	+	6.92820i	0.149279	+	0.258558i
$719$	26.0000			0.969636			0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000			0.969636			0.484818	+	0.874615i	$0.338886\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	9.50000	+	16.4545i	0.353553	+	0.612372i
$723$		0			0
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$		0			0
$727$	−16.5000	−	28.5788i	−0.611951	−	1.05993i	−0.990911	−	0.134517i	$-0.957052\pi$
$727$	−16.5000	−	28.5788i	−0.611951	−	1.05993i	0.378960	−	0.925413i	$-0.376282\pi$
$728$	−3.00000			−0.111187
$729$		0			0
$730$	−12.0000			−0.444140
$731$	16.0000	+	27.7128i	0.591781	+	1.02500i
$732$		0			0
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$	16.0000	−	27.7128i	0.590571	−	1.02290i
$735$		0			0
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	2.00000			0.0736709
$738$		0			0
$739$	6.00000			0.220714			0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000			0.220714			0.110357	+	0.993892i	$0.464801\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	5.00000	−	8.66025i	0.183556	−	0.317928i
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	−0.386674	−	0.922217i	$-0.626376\pi$
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	0.992000	−	0.126239i	$-0.0402907\pi$
$744$		0			0
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$	−14.0000			−0.512576
$747$		0			0
$748$	8.00000			0.292509
$749$	−6.50000	−	11.2583i	−0.237505	−	0.411370i
$750$		0			0
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	−0.592499	−	0.805571i	$-0.701859\pi$
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	0.993895	+	0.110333i	$0.0351919\pi$
$752$	−6.50000	+	11.2583i	−0.237031	+	0.410549i
$753$		0			0
$754$	0.500000	+	0.866025i	0.0182089	+	0.0315388i
$755$	10.0000			0.363937
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	13.0000	+	22.5167i	0.472181	+	0.817842i
$759$		0			0
$760$		0			0
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$		0			0
$763$	0.500000	+	0.866025i	0.0181012	+	0.0313522i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	12.0000			0.433578
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$		0			0
$769$	−8.50000	+	14.7224i	−0.306518	+	0.530904i	−0.977598	−	0.210480i	$-0.932497\pi$
$769$	−8.50000	+	14.7224i	−0.306518	+	0.530904i	0.671080	+	0.741385i	$0.265831\pi$
$770$	−1.00000	+	1.73205i	−0.0360375	+	0.0624188i
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	8.00000			0.287740			0.143870	−	0.989597i	$-0.454045\pi$
$773$	8.00000			0.287740			0.143870	+	0.989597i	$0.454045\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$		0			0
$778$	−15.5000	+	26.8468i	−0.555702	+	0.962504i
$779$		0			0
$780$		0			0
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	12.0000			0.429119
$783$		0			0
$784$	6.00000			0.214286
$785$	−9.00000	−	15.5885i	−0.321224	−	0.556376i
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	12.0000	−	20.7846i	0.427482	−	0.740421i
$789$		0			0
$790$	3.00000	+	5.19615i	0.106735	+	0.184871i
$791$	4.00000			0.142224
$792$		0			0
$793$	1.00000			0.0355110
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$		0			0
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$		0			0
$799$	26.0000	+	45.0333i	0.919814	+	1.59316i
$800$	5.00000			0.176777
$801$		0			0
$802$	−22.0000			−0.776847
$803$	−12.0000	−	20.7846i	−0.423471	−	0.733473i
$804$		0			0
$805$	1.50000	−	2.59808i	0.0528681	−	0.0915702i
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$		0			0
$808$	−9.00000	−	15.5885i	−0.316619	−	0.548400i
$809$	−34.0000			−1.19538			−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000			−1.19538			−0.597688	+	0.801729i	$0.703914\pi$
$810$		0			0
$811$	54.0000			1.89620			0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000			1.89620			0.948098	+	0.317978i	$0.103004\pi$
$812$	−0.500000	−	0.866025i	−0.0175466	−	0.0303915i
$813$		0			0
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$		0			0
$818$	30.0000			1.04893
$819$		0			0
$820$	9.00000			0.314294
$821$	−18.5000	−	32.0429i	−0.645654	−	1.11831i	−0.984150	−	0.177338i	$-0.943251\pi$
$821$	−18.5000	−	32.0429i	−0.645654	−	1.11831i	0.338495	−	0.940968i	$-0.390082\pi$
$822$		0			0
$823$	18.5000	−	32.0429i	0.644869	−	1.11695i	−0.339462	−	0.940620i	$-0.610245\pi$
$823$	18.5000	−	32.0429i	0.644869	−	1.11695i	0.984332	−	0.176327i	$-0.0564216\pi$
$824$	−24.0000	+	41.5692i	−0.836080	+	1.44813i
$825$		0			0
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	41.0000			1.42571			0.712855	−	0.701312i	$-0.247402\pi$
$827$	41.0000			1.42571			0.712855	+	0.701312i	$0.247402\pi$
$828$		0			0
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$	5.50000	+	9.52628i	0.190908	+	0.330662i
$831$		0			0
$832$	3.50000	−	6.06218i	0.121341	−	0.210168i
$833$	12.0000	−	20.7846i	0.415775	−	0.720144i
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$		0			0
$838$	10.0000			0.345444
$839$	−14.0000	−	24.2487i	−0.483334	−	0.837158i	0.516483	−	0.856297i	$-0.327241\pi$
$839$	−14.0000	−	24.2487i	−0.483334	−	0.837158i	−0.999817	+	0.0191389i	$0.993908\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$		0			0
$844$	3.00000	+	5.19615i	0.103264	+	0.178859i
$845$	1.00000			0.0344010
$846$		0			0
$847$	7.00000			0.240523
$848$	5.00000	+	8.66025i	0.171701	+	0.297394i
$849$		0			0
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	−0.961386	−	0.275204i	$-0.911255\pi$
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	0.242360	−	0.970186i	$-0.422079\pi$
$854$	1.00000			0.0342193
$855$		0			0
$856$	39.0000			1.33299
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	−0.721544	−	0.692369i	$-0.756567\pi$
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	0.960381	+	0.278691i	$0.0899005\pi$
$860$	−4.00000	+	6.92820i	−0.136399	+	0.236250i
$861$		0			0
$862$	13.0000	+	22.5167i	0.442782	+	0.766921i
$863$	−27.0000			−0.919091			−0.459545	−	0.888154i	$-0.651988\pi$
$863$	−27.0000			−0.919091			−0.459545	+	0.888154i	$0.651988\pi$
$864$		0			0
$865$	12.0000			0.408012
$866$	16.0000	+	27.7128i	0.543702	+	0.941720i
$867$		0			0
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	−6.00000	+	10.3923i	−0.203536	+	0.352535i
$870$		0			0
$871$	−0.500000	−	0.866025i	−0.0169419	−	0.0293442i
$872$	−3.00000			−0.101593
$873$		0			0
$874$		0			0
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$		0			0
$879$		0			0
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	43.0000			1.44871			0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000			1.44871			0.724353	+	0.689429i	$0.242138\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$		0			0
$886$	8.50000	−	14.7224i	0.285563	−	0.494610i
$887$	−10.0000	+	17.3205i	−0.335767	+	0.581566i	−0.983632	−	0.180190i	$-0.942329\pi$
$887$	−10.0000	+	17.3205i	−0.335767	+	0.581566i	0.647865	+	0.761755i	$0.275662\pi$
$888$		0			0
$889$	6.50000	+	11.2583i	0.218003	+	0.377592i
$890$	−5.00000			−0.167600
$891$		0			0
$892$	17.0000			0.569202
$893$		0			0
$894$		0			0
$895$	3.00000	−	5.19615i	0.100279	−	0.173688i
$896$	−1.50000	+	2.59808i	−0.0501115	+	0.0867956i
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	8.00000			0.266815
$900$		0			0
$901$	40.0000			1.33259
$902$	−9.00000	−	15.5885i	−0.299667	−	0.519039i
$903$		0			0
$904$	−6.00000	+	10.3923i	−0.199557	+	0.345643i
$905$	3.50000	−	6.06218i	0.116344	−	0.201514i
$906$		0			0
$907$	6.50000	+	11.2583i	0.215829	+	0.373827i	0.953529	−	0.301302i	$-0.0974213\pi$
$907$	6.50000	+	11.2583i	0.215829	+	0.373827i	−0.737700	+	0.675129i	$0.764088\pi$
$908$	4.00000			0.132745
$909$		0			0
$910$	1.00000			0.0331497
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$		0			0
$913$	−11.0000	+	19.0526i	−0.364047	+	0.630548i
$914$	8.00000	−	13.8564i	0.264616	−	0.458329i
$915$		0			0
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	14.0000			0.462321
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	6.50000	−	11.2583i	0.214066	−	0.370773i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	−36.0000			−1.18303
$927$		0			0
$928$	5.00000			0.164133
$929$	−13.0000	−	22.5167i	−0.426516	−	0.738748i	0.570045	−	0.821614i	$-0.306926\pi$
$929$	−13.0000	−	22.5167i	−0.426516	−	0.738748i	−0.996561	+	0.0828661i	$0.973593\pi$
$930$		0			0
$931$		0			0
$932$	−2.00000	+	3.46410i	−0.0655122	+	0.113470i
$933$		0			0
$934$	−14.0000	−	24.2487i	−0.458094	−	0.793442i
$935$	−8.00000			−0.261628
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−0.500000	−	0.866025i	−0.0163256	−	0.0282767i
$939$		0			0
$940$	−6.50000	+	11.2583i	−0.212007	+	0.367206i
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	−0.889439	−	0.457054i	$-0.848904\pi$
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	0.840540	+	0.541749i	$0.182238\pi$
$942$		0			0
$943$	13.5000	+	23.3827i	0.439620	+	0.761445i
$944$	6.00000			0.195283
$945$		0			0
$946$	16.0000			0.520205
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	0.889368	−	0.457193i	$-0.151145\pi$
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	−0.840624	+	0.541619i	$0.817812\pi$
$948$		0			0
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$		0			0
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	12.0000			0.388311
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	3.00000	−	5.19615i	0.0969256	−	0.167880i
$959$	−8.00000	+	13.8564i	−0.258333	+	0.447447i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−4.00000			−0.128965
$963$		0			0
$964$	23.0000			0.740780
$965$	1.00000	+	1.73205i	0.0321911	+	0.0557567i
$966$		0			0
$967$	−21.5000	+	37.2391i	−0.691393	+	1.19753i	0.279988	+	0.960003i	$0.409669\pi$
$967$	−21.5000	+	37.2391i	−0.691393	+	1.19753i	−0.971381	+	0.237525i	$0.923664\pi$
$968$	−10.5000	+	18.1865i	−0.337483	+	0.584537i
$969$		0			0
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	−8.00000			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$972$		0			0
$973$	12.0000			0.384702
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$		0			0
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	−5.00000	−	8.66025i	−0.159801	−	0.276783i
$980$	6.00000			0.191663
$981$		0			0
$982$		0			0
$983$	−15.5000	−	26.8468i	−0.494373	−	0.856280i	0.505606	−	0.862765i	$-0.331269\pi$
$983$	−15.5000	−	26.8468i	−0.494373	−	0.856280i	−0.999979	+	0.00648510i	$0.997936\pi$
$984$		0			0
$985$	−12.0000	+	20.7846i	−0.382352	+	0.662253i
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	30.0000			0.952981			0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000			0.952981			0.476491	+	0.879180i	$0.341909\pi$
$992$	−20.0000	−	34.6410i	−0.635001	−	1.09985i
$993$		0			0
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$	−10.0000	+	17.3205i	−0.317021	+	0.549097i
$996$		0			0
$997$	−25.0000	−	43.3013i	−0.791758	−	1.37136i	−0.924878	−	0.380265i	$-0.875833\pi$
$997$	−25.0000	−	43.3013i	−0.791758	−	1.37136i	0.133120	−	0.991100i	$-0.457501\pi$
$998$	−20.0000			−0.633089
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.c.1171.1		2
3.2	odd	2		585.2.i.c.391.1	yes	2
9.2	odd	6		585.2.i.c.196.1	✓	2
9.4	even	3		5265.2.a.l.1.1		1
9.5	odd	6		5265.2.a.d.1.1		1
9.7	even	3	inner	1755.2.i.c.586.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.c.196.1	✓	2	9.2	odd	6
585.2.i.c.391.1	yes	2	3.2	odd	2
1755.2.i.c.586.1		2	9.7	even	3	inner
1755.2.i.c.1171.1		2	1.1	even	1	trivial
5265.2.a.d.1.1		1	9.5	odd	6
5265.2.a.l.1.1		1	9.4	even	3

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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +1.00000 q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(0.500000 + 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{34} -1.00000 q^{35} +4.00000 q^{37} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 7.79423i) q^{41} +(4.00000 + 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(6.50000 + 11.2583i) q^{47} +(3.00000 - 5.19615i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} -2.00000 q^{55} +(-1.50000 - 2.59808i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +8.00000 q^{62} +7.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.500000 - 0.866025i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.500000 + 0.866025i) q^{70} +6.00000 q^{71} -12.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.00000 + 1.73205i) q^{77} +(3.00000 + 5.19615i) q^{79} -1.00000 q^{80} -9.00000 q^{82} +(5.50000 + 9.52628i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(4.00000 - 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{88} -5.00000 q^{89} +1.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(6.50000 - 11.2583i) q^{94} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - q^{5} + q^{7} - 6 q^{8}+O(q^{10}) \) 2 * q - q^2 + q^4 - q^5 + q^7 - 6 * q^8	\( 2 q - q^{2} + q^{4} - q^{5} + q^{7} - 6 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + q^{14} + q^{16} + 8 q^{17} + q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 2 q^{26} + 2 q^{28} - q^{29} - 8 q^{31} - 5 q^{32} - 4 q^{34} - 2 q^{35} + 8 q^{37} + 3 q^{40} + 9 q^{41} + 8 q^{43} + 4 q^{44} + 6 q^{46} + 13 q^{47} + 6 q^{49} - q^{50} - q^{52} + 20 q^{53} - 4 q^{55} - 3 q^{56} - q^{58} + 6 q^{59} + q^{61} + 16 q^{62} + 14 q^{64} + q^{65} + q^{67} + 4 q^{68} + q^{70} + 12 q^{71} - 24 q^{73} - 4 q^{74} - 2 q^{77} + 6 q^{79} - 2 q^{80} - 18 q^{82} + 11 q^{83} - 4 q^{85} + 8 q^{86} - 6 q^{88} - 10 q^{89} + 2 q^{91} + 3 q^{92} + 13 q^{94} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 - q^5 + q^7 - 6 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + q^14 + q^16 + 8 * q^17 + q^20 + 2 * q^22 - 3 * q^23 - q^25 - 2 * q^26 + 2 * q^28 - q^29 - 8 * q^31 - 5 * q^32 - 4 * q^34 - 2 * q^35 + 8 * q^37 + 3 * q^40 + 9 * q^41 + 8 * q^43 + 4 * q^44 + 6 * q^46 + 13 * q^47 + 6 * q^49 - q^50 - q^52 + 20 * q^53 - 4 * q^55 - 3 * q^56 - q^58 + 6 * q^59 + q^61 + 16 * q^62 + 14 * q^64 + q^65 + q^67 + 4 * q^68 + q^70 + 12 * q^71 - 24 * q^73 - 4 * q^74 - 2 * q^77 + 6 * q^79 - 2 * q^80 - 18 * q^82 + 11 * q^83 - 4 * q^85 + 8 * q^86 - 6 * q^88 - 10 * q^89 + 2 * q^91 + 3 * q^92 + 13 * q^94 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

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