LMFDB - Embedded newform 567.2.e.b.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
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 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.b.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{11} -5.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +1.00000 q^{29} +(2.50000 + 4.33013i) q^{32} +3.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-1.50000 + 2.59808i) q^{40} +5.00000 q^{41} -1.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(-7.50000 + 2.59808i) q^{56} +(0.500000 - 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-2.00000 - 1.73205i) q^{70} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.50000 + 2.59808i) q^{74} -1.00000 q^{76} +(-10.0000 - 8.66025i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(2.50000 - 4.33013i) q^{82} +9.00000 q^{83} -3.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 + 12.9904i) q^{88} +(-6.50000 + 11.2583i) q^{89} +(12.5000 - 4.33013i) q^{91} +3.00000 q^{92} +(-0.500000 - 0.866025i) q^{95} -9.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} - q^{5} - 5 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 - q^5 - 5 * q^7 + 6 * q^8	$ 2 q + q^{2} + q^{4} - q^{5} - 5 q^{7} + 6 q^{8} + q^{10} + 5 q^{11} - 10 q^{13} - q^{14} + q^{16} + 3 q^{17} - q^{19} - 2 q^{20} + 10 q^{22} + 3 q^{23} + 4 q^{25} - 5 q^{26} - 4 q^{28} + 2 q^{29} + 5 q^{32} + 6 q^{34} + q^{35} - 3 q^{37} + q^{38} - 3 q^{40} + 10 q^{41} - 2 q^{43} - 5 q^{44} - 3 q^{46} + 11 q^{49} + 8 q^{50} - 5 q^{52} - 9 q^{53} - 10 q^{55} - 15 q^{56} + q^{58} + 14 q^{61} + 14 q^{64} + 5 q^{65} - 4 q^{67} - 3 q^{68} - 4 q^{70} + 24 q^{71} - 3 q^{73} + 3 q^{74} - 2 q^{76} - 20 q^{77} - 8 q^{79} + q^{80} + 5 q^{82} + 18 q^{83} - 6 q^{85} - q^{86} + 15 q^{88} - 13 q^{89} + 25 q^{91} + 6 q^{92} - q^{95} - 18 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 - q^5 - 5 * q^7 + 6 * q^8 + q^10 + 5 * q^11 - 10 * q^13 - q^14 + q^16 + 3 * q^17 - q^19 - 2 * q^20 + 10 * q^22 + 3 * q^23 + 4 * q^25 - 5 * q^26 - 4 * q^28 + 2 * q^29 + 5 * q^32 + 6 * q^34 + q^35 - 3 * q^37 + q^38 - 3 * q^40 + 10 * q^41 - 2 * q^43 - 5 * q^44 - 3 * q^46 + 11 * q^49 + 8 * q^50 - 5 * q^52 - 9 * q^53 - 10 * q^55 - 15 * q^56 + q^58 + 14 * q^61 + 14 * q^64 + 5 * q^65 - 4 * q^67 - 3 * q^68 - 4 * q^70 + 24 * q^71 - 3 * q^73 + 3 * q^74 - 2 * q^76 - 20 * q^77 - 8 * q^79 + q^80 + 5 * q^82 + 18 * q^83 - 6 * q^85 - q^86 + 15 * q^88 - 13 * q^89 + 25 * q^91 + 6 * q^92 - q^95 - 18 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	3.00000			1.06066
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	5.00000			1.06600
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		0			0
$34$	3.00000			0.514496
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	4.00000			0.565685
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$	−7.50000	+	2.59808i	−1.00223	+	0.347183i
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$		0			0
$70$	−2.00000	−	1.73205i	−0.239046	−	0.207020i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	0.764794	−	0.644275i	$-0.222841\pi$
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	−0.940356	+	0.340193i	$0.889507\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−10.0000	−	8.66025i	−1.13961	−	0.986928i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$	7.50000	+	12.9904i	0.799503	+	1.38478i
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	0.283164	+	0.959072i	$0.408616\pi$
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	−0.972162	+	0.234309i	$0.924717\pi$
$90$		0			0
$91$	12.5000	−	4.33013i	1.31036	−	0.453921i
$92$	3.00000			0.312772
$93$		0			0
$94$		0			0
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−9.00000			−0.913812			−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000			−0.913812			−0.456906	+	0.889515i	$0.651042\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	−0.884941	−	0.465704i	$-0.845801\pi$
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	0.0391591	−	0.999233i	$-0.487532\pi$
$102$		0			0
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$	−15.0000			−1.47087
$105$		0			0
$106$	−9.00000			−0.874157
$107$	8.50000	−	14.7224i	0.821726	−	1.42327i	−0.0826699	−	0.996577i	$-0.526345\pi$
$107$	8.50000	−	14.7224i	0.821726	−	1.42327i	0.904396	−	0.426694i	$-0.140322\pi$
$108$		0			0
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	0.996962	−	0.0778949i	$-0.0248199\pi$
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	−0.565940	+	0.824447i	$0.691487\pi$
$110$	−2.50000	+	4.33013i	−0.238366	+	0.412861i
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$		0			0
$118$		0			0
$119$	−6.00000	−	5.19615i	−0.550019	−	0.476331i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$		0			0
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	4.50000	+	7.79423i	0.385872	+	0.668350i
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	9.00000			0.763370			0.381685	−	0.924292i	$-0.375344\pi$
$139$	9.00000			0.763370			0.381685	+	0.924292i	$0.375344\pi$
$140$	2.50000	−	0.866025i	0.211289	−	0.0731925i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−12.5000	−	21.6506i	−1.04530	−	1.81052i
$144$		0			0
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$	−3.00000			−0.248282
$147$		0			0
$148$	−3.00000			−0.246598
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$		0			0
$154$	−12.5000	+	4.33013i	−1.00728	+	0.348932i
$155$		0			0
$156$		0			0
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	−5.00000			−0.395285
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		0			0
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$	2.50000	+	4.33013i	0.195217	+	0.338126i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	19.0000			1.47026			0.735132	−	0.677924i	$-0.237120\pi$
$167$	19.0000			1.47026			0.735132	+	0.677924i	$0.237120\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−1.50000	+	2.59808i	−0.115045	+	0.199263i
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$	5.00000			0.376889
$177$		0			0
$178$	6.50000	+	11.2583i	0.487196	+	0.843848i
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	2.50000	−	12.9904i	0.185312	−	0.962911i
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$		0			0
$189$		0			0
$190$	−1.00000			−0.0725476
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$	6.00000	+	10.3923i	0.424264	+	0.734847i
$201$		0			0
$202$	−17.0000			−1.19612
$203$	−2.50000	+	0.866025i	−0.175466	+	0.0607831i
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	−0.500000	−	0.866025i	−0.0348367	−	0.0603388i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	−5.00000			−0.345857
$210$		0			0
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$		0			0
$218$	9.00000			0.609557
$219$		0			0
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$	−7.50000	−	12.9904i	−0.504505	−	0.873828i
$222$		0			0
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	−10.0000	−	8.66025i	−0.668153	−	0.578638i
$225$		0			0
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	0.882073	+	0.471113i	$0.156147\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	3.00000			0.196960
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	−0.812700	−	0.582683i	$-0.802003\pi$
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	0.910968	+	0.412477i	$0.135336\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−7.50000	+	2.59808i	−0.486153	+	0.168408i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	0.632709	−	0.774389i	$-0.281943\pi$
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	−0.986996	+	0.160748i	$0.948609\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$		0			0
$244$	14.0000			0.896258
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		0			0
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$		0			0
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	28.0000			1.76734			0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000			1.76734			0.883672	+	0.468106i	$0.155064\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.0828783	+	0.996560i	$0.526411\pi$
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.821607	+	0.570055i	$0.806922\pi$
$258$		0			0
$259$	1.50000	−	7.79423i	0.0932055	−	0.484310i
$260$	5.00000			0.310087
$261$		0			0
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	2.50000	+	4.33013i	0.154157	+	0.267007i	0.932752	−	0.360520i	$-0.117401\pi$
$263$	2.50000	+	4.33013i	0.154157	+	0.267007i	−0.778595	+	0.627527i	$0.784067\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	−2.00000	−	1.73205i	−0.122628	−	0.106199i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	0.850439	+	0.526073i	$0.176336\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−9.00000			−0.543710
$275$	−10.0000	+	17.3205i	−0.603023	+	1.04447i
$276$		0			0
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	4.50000	−	7.79423i	0.269892	−	0.467467i
$279$		0			0
$280$	1.50000	−	7.79423i	0.0896421	−	0.465794i
$281$	29.0000			1.72999			0.864997	−	0.501776i	$-0.167320\pi$
$281$	29.0000			1.72999			0.864997	+	0.501776i	$0.167320\pi$
$282$		0			0
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	−0.896279	−	0.443491i	$-0.853740\pi$
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	0.0640654	−	0.997946i	$-0.479593\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	−25.0000			−1.47828
$287$	−12.5000	+	4.33013i	−0.737852	+	0.255599i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	0.500000	+	0.866025i	0.0293610	+	0.0508548i
$291$		0			0
$292$	1.50000	−	2.59808i	0.0877809	−	0.152041i
$293$	5.00000			0.292103			0.146052	−	0.989277i	$-0.453343\pi$
$293$	5.00000			0.292103			0.146052	+	0.989277i	$0.453343\pi$
$294$		0			0
$295$		0			0
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$	−1.50000	−	2.59808i	−0.0868927	−	0.150503i
$299$	−7.50000	+	12.9904i	−0.433736	+	0.751253i
$300$		0			0
$301$	2.50000	−	0.866025i	0.144098	−	0.0499169i
$302$	−5.00000			−0.287718
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	2.50000	−	12.9904i	0.142451	−	0.740196i
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$	−3.50000	+	6.06218i	−0.195656	+	0.338886i
$321$		0			0
$322$	6.00000	+	5.19615i	0.334367	+	0.289570i
$323$	−3.00000			−0.166924
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$		0			0
$328$	15.0000			0.828236
$329$		0			0
$330$		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
$334$	9.50000	−	16.4545i	0.519817	−	0.900349i
$335$	4.00000			0.218543
$336$		0			0
$337$	−29.0000			−1.57973			−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−29.0000			−1.57973			−0.789865	+	0.613280i	$0.789850\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$		0			0
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−3.00000			−0.161749
$345$		0			0
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$	19.0000			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$350$	−10.0000	+	3.46410i	−0.534522	+	0.185164i
$351$		0			0
$352$	−12.5000	+	21.6506i	−0.666252	+	1.15398i
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	0.974456	−	0.224580i	$-0.0721011\pi$
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	−0.681720	+	0.731613i	$0.738768\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$	−13.0000			−0.688999
$357$		0			0
$358$	19.0000			1.00418
$359$	−5.50000	+	9.52628i	−0.290279	+	0.502778i	−0.973876	−	0.227082i	$-0.927081\pi$
$359$	−5.50000	+	9.52628i	−0.290279	+	0.502778i	0.683597	+	0.729860i	$0.260415\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		0			0
$364$	10.0000	+	8.66025i	0.524142	+	0.453921i
$365$	3.00000			0.157027
$366$		0			0
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$	−3.00000			−0.155963
$371$	18.0000	+	15.5885i	0.934513	+	0.809312i
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	7.50000	+	12.9904i	0.387816	+	0.671717i
$375$		0			0
$376$		0			0
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	0.500000	−	0.866025i	0.0256495	−	0.0444262i
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	−0.282079	−	0.959391i	$-0.591024\pi$
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	0.971897	−	0.235408i	$-0.0756427\pi$
$384$		0			0
$385$	12.5000	−	4.33013i	0.637059	−	0.220684i
$386$	10.0000			0.508987
$387$		0			0
$388$	−4.50000	−	7.79423i	−0.228453	−	0.395692i
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$	16.5000	−	12.9904i	0.833376	−	0.656113i
$393$		0			0
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	−0.990538	−	0.137241i	$-0.956176\pi$
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	0.614123	+	0.789210i	$0.289510\pi$
$398$	−3.00000			−0.150376
$399$		0			0
$400$	4.00000			0.200000
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$		0			0
$404$	8.50000	−	14.7224i	0.422891	−	0.732468i
$405$		0			0
$406$	−0.500000	+	2.59808i	−0.0248146	+	0.128940i
$407$	−15.0000			−0.743522
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	2.50000	+	4.33013i	0.123466	+	0.213850i
$411$		0			0
$412$	1.00000			0.0492665
$413$		0			0
$414$		0			0
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$	−12.5000	−	21.6506i	−0.612863	−	1.06151i
$417$		0			0
$418$	−2.50000	+	4.33013i	−0.122279	+	0.211793i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	6.50000	−	11.2583i	0.316415	−	0.548047i
$423$		0			0
$424$	−13.5000	−	23.3827i	−0.655618	−	1.13556i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−7.00000	+	36.3731i	−0.338754	+	1.76022i
$428$	17.0000			0.821726
$429$		0			0
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$	−4.50000	+	7.79423i	−0.215511	+	0.373276i
$437$	1.50000	+	2.59808i	0.0717547	+	0.124283i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−15.0000			−0.715097
$441$		0			0
$442$	−15.0000			−0.713477
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−6.50000	−	11.2583i	−0.308130	−	0.533696i
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$		0			0
$448$	−17.5000	+	6.06218i	−0.826797	+	0.286411i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	12.5000	+	21.6506i	0.588602	+	1.01949i
$452$	0.500000	+	0.866025i	0.0235180	+	0.0407344i
$453$		0			0
$454$	−3.00000			−0.140797
$455$	−2.50000	+	12.9904i	−0.117202	+	0.608998i
$456$		0			0
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	−0.500000	−	0.866025i	−0.0233635	−	0.0404667i
$459$		0			0
$460$	−1.50000	+	2.59808i	−0.0699379	+	0.121136i
$461$	−19.0000			−0.884918			−0.442459	−	0.896789i	$-0.645894\pi$
$461$	−19.0000			−0.884918			−0.442459	+	0.896789i	$0.645894\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	0.363892	+	0.931441i	$0.381448\pi$
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	−0.988598	+	0.150581i	$0.951886\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.50000	−	4.33013i	−0.114950	−	0.199099i
$474$		0			0
$475$	−4.00000			−0.183533
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	0.996449	+	0.0841949i	$0.0268318\pi$
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	−0.425310	+	0.905048i	$0.639835\pi$
$480$		0			0
$481$	7.50000	−	12.9904i	0.341971	−	0.592310i
$482$	−11.0000			−0.501036
$483$		0			0
$484$	−14.0000			−0.636364
$485$	4.50000	−	7.79423i	0.204334	−	0.353918i
$486$		0			0
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	0.566429	−	0.824110i	$-0.308325\pi$
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	21.0000	−	36.3731i	0.950625	−	1.64653i
$489$		0			0
$490$	6.50000	+	2.59808i	0.293640	+	0.117369i
$491$	−13.0000			−0.586682			−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000			−0.586682			−0.293341	+	0.956008i	$0.594767\pi$
$492$		0			0
$493$	1.50000	+	2.59808i	0.0675566	+	0.117011i
$494$	−2.50000	−	4.33013i	−0.112480	−	0.194822i
$495$		0			0
$496$		0			0
$497$	−30.0000	+	10.3923i	−1.34568	+	0.466159i
$498$		0			0
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	0.276683	+	0.960961i	$0.410765\pi$
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	−0.970558	+	0.240866i	$0.922569\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	14.0000	−	24.2487i	0.624851	−	1.08227i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$	7.50000	−	12.9904i	0.333416	−	0.577493i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	0.342126	+	0.939654i	$0.388853\pi$
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	−0.984827	+	0.173537i	$0.944480\pi$
$510$		0			0
$511$	6.00000	+	5.19615i	0.265424	+	0.229864i
$512$	11.0000			0.486136
$513$		0			0
$514$	14.5000	+	25.1147i	0.639568	+	1.10776i
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$		0			0
$517$		0			0
$518$	−6.00000	−	5.19615i	−0.263625	−	0.228306i
$519$		0			0
$520$	7.50000	−	12.9904i	0.328897	−	0.569666i
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	5.00000			0.218010
$527$		0			0
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$	2.50000	−	0.866025i	0.108389	−	0.0375470i
$533$	−25.0000			−1.08287
$534$		0			0
$535$	8.50000	+	14.7224i	0.367487	+	0.636506i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$	3.00000			0.129339
$539$	32.5000	+	12.9904i	1.39987	+	0.559535i
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	0.500000	+	0.866025i	0.0214768	+	0.0371990i
$543$		0			0
$544$	−7.50000	+	12.9904i	−0.321560	+	0.556958i
$545$	−9.00000			−0.385518
$546$		0			0
$547$	−29.0000			−1.23995			−0.619975	−	0.784621i	$-0.712857\pi$
$547$	−29.0000			−1.23995			−0.619975	+	0.784621i	$0.712857\pi$
$548$	4.50000	−	7.79423i	0.192230	−	0.332953i
$549$		0			0
$550$	10.0000	+	17.3205i	0.426401	+	0.738549i
$551$	−0.500000	+	0.866025i	−0.0213007	+	0.0368939i
$552$		0			0
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$	−19.0000			−0.807233
$555$		0			0
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	−18.5000	−	32.0429i	−0.783870	−	1.35770i	−0.929672	−	0.368389i	$-0.879909\pi$
$557$	−18.5000	−	32.0429i	−0.783870	−	1.35770i	0.145802	−	0.989314i	$-0.453424\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	−2.00000	−	1.73205i	−0.0845154	−	0.0731925i
$561$		0			0
$562$	14.5000	−	25.1147i	0.611646	−	1.05940i
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	−0.994228	−	0.107290i	$-0.965783\pi$
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	0.404198	−	0.914671i	$-0.367551\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	−28.0000			−1.17693
$567$		0			0
$568$	36.0000			1.51053
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	0.251172	+	0.967943i	$0.419184\pi$
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	−0.963849	+	0.266450i	$0.914149\pi$
$570$		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	$-0.400192\pi$
$572$	12.5000	−	21.6506i	0.522651	−	0.905259i
$573$		0			0
$574$	−2.50000	+	12.9904i	−0.104348	+	0.542208i
$575$	12.0000			0.500435
$576$		0			0
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	−0.984238	−	0.176847i	$-0.943410\pi$
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	0.338965	−	0.940799i	$-0.389923\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−1.00000			−0.0415227
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$		0			0
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	−4.50000	−	7.79423i	−0.186211	−	0.322527i
$585$		0			0
$586$	2.50000	−	4.33013i	0.103274	−	0.178876i
$587$	37.0000			1.52715			0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000			1.52715			0.763577	+	0.645717i	$0.223441\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	7.50000	−	12.9904i	0.307988	−	0.533451i	−0.669934	−	0.742421i	$-0.733678\pi$
$593$	7.50000	−	12.9904i	0.307988	−	0.533451i	0.977922	+	0.208970i	$0.0670110\pi$
$594$		0			0
$595$	7.50000	−	2.59808i	0.307470	−	0.106511i
$596$	3.00000			0.122885
$597$		0			0
$598$	7.50000	+	12.9904i	0.306698	+	0.531216i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$	0.500000	−	2.59808i	0.0203785	−	0.105890i
$603$		0			0
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	−0.855700	−	0.517472i	$-0.826873\pi$
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	0.875994	+	0.482322i	$0.160206\pi$
$608$	−5.00000			−0.202777
$609$		0			0
$610$	14.0000			0.566843
$611$		0			0
$612$		0			0
$613$	−9.50000	−	16.4545i	−0.383701	−	0.664590i	0.607887	−	0.794024i	$-0.292017\pi$
$613$	−9.50000	−	16.4545i	−0.383701	−	0.664590i	−0.991588	+	0.129433i	$0.958684\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$	−30.0000	−	25.9808i	−1.20873	−	1.04679i
$617$	−27.0000			−1.08698			−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000			−1.08698			−0.543490	+	0.839416i	$0.682897\pi$
$618$		0			0
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	−0.999996	−	0.00279365i	$-0.999111\pi$
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	0.497579	−	0.867419i	$-0.334223\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.50000	−	33.7750i	0.260417	−	1.35317i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	−9.00000			−0.358854
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−12.0000	+	20.7846i	−0.477334	+	0.826767i
$633$		0			0
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$	−27.5000	+	21.6506i	−1.08959	+	0.857829i
$638$	5.00000			0.197952
$639$		0			0
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$		0			0
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$	−7.50000	+	2.59808i	−0.295541	+	0.102379i
$645$		0			0
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	15.5000	+	26.8468i	0.609368	+	1.05546i	0.991345	+	0.131284i	$0.0419101\pi$
$647$	15.5000	+	26.8468i	0.609368	+	1.05546i	−0.381977	+	0.924172i	$0.624757\pi$
$648$		0			0
$649$		0			0
$650$	−20.0000			−0.784465
$651$		0			0
$652$	11.0000			0.430793
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		0			0
$655$	−0.500000	−	0.866025i	−0.0195366	−	0.0338384i
$656$	2.50000	−	4.33013i	0.0976086	−	0.169063i
$657$		0			0
$658$		0			0
$659$	−27.0000			−1.05177			−0.525885	−	0.850555i	$-0.676266\pi$
$659$	−27.0000			−1.05177			−0.525885	+	0.850555i	$0.676266\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$		0			0
$664$	27.0000			1.04780
$665$	2.00000	+	1.73205i	0.0775567	+	0.0671660i
$666$		0			0
$667$	1.50000	−	2.59808i	0.0580802	−	0.100598i
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$		0			0
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	70.0000			2.70232
$672$		0			0
$673$	−29.0000			−1.11787			−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000			−1.11787			−0.558934	+	0.829212i	$0.688789\pi$
$674$	−14.5000	+	25.1147i	−0.558519	+	0.967384i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	22.5000	−	7.79423i	0.863471	−	0.299115i
$680$	−9.00000			−0.345134
$681$		0			0
$682$		0			0
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	22.5000	+	38.9711i	0.857182	+	1.48468i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	4.00000			0.151838
$695$	−4.50000	+	7.79423i	−0.170695	+	0.295652i
$696$		0			0
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$	9.50000	−	16.4545i	0.359580	−	0.622811i
$699$		0			0
$700$	2.00000	−	10.3923i	0.0755929	−	0.392792i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−1.50000	−	2.59808i	−0.0565736	−	0.0979883i
$704$	17.5000	+	30.3109i	0.659556	+	1.14238i
$705$		0			0
$706$	11.0000			0.413990
$707$	34.0000	+	29.4449i	1.27870	+	1.10739i
$708$		0			0
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	−0.804178	−	0.594389i	$-0.797394\pi$
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	0.916845	+	0.399244i	$0.130727\pi$
$710$	6.00000	+	10.3923i	0.225176	+	0.390016i
$711$		0			0
$712$	−19.5000	+	33.7750i	−0.730793	+	1.26577i
$713$		0			0
$714$		0			0
$715$	25.0000			0.934947
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$		0			0
$718$	5.50000	+	9.52628i	0.205258	+	0.355518i
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	0.496527	+	0.868021i	$0.334608\pi$
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	−0.999992	+	0.00400572i	$0.998725\pi$
$720$		0			0
$721$	−0.500000	+	2.59808i	−0.0186210	+	0.0967574i
$722$	18.0000			0.669891
$723$		0			0
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$		0			0
$727$	47.0000			1.74313			0.871567	−	0.490277i	$-0.163104\pi$
$727$	47.0000			1.74313			0.871567	+	0.490277i	$0.163104\pi$
$728$	37.5000	−	12.9904i	1.38984	−	0.481456i
$729$		0			0
$730$	1.50000	−	2.59808i	0.0555175	−	0.0961591i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	−13.5000	+	23.3827i	−0.498634	+	0.863659i	−0.999999	−	0.00157675i	$-0.999498\pi$
$733$	−13.5000	+	23.3827i	−0.498634	+	0.863659i	0.501365	+	0.865236i	$0.332831\pi$
$734$	3.00000			0.110732
$735$		0			0
$736$	15.0000			0.552907
$737$	10.0000	−	17.3205i	0.368355	−	0.638009i
$738$		0			0
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$	1.50000	−	2.59808i	0.0551411	−	0.0955072i
$741$		0			0
$742$	22.5000	−	7.79423i	0.826001	−	0.286135i
$743$	15.0000			0.550297			0.275148	−	0.961402i	$-0.411273\pi$
$743$	15.0000			0.550297			0.275148	+	0.961402i	$0.411273\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	−12.5000	−	21.6506i	−0.457658	−	0.792686i
$747$		0			0
$748$	−15.0000			−0.548454
$749$	−8.50000	+	44.1673i	−0.310583	+	1.61384i
$750$		0			0
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	0.431390	+	0.902165i	$0.358023\pi$
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	−0.996993	+	0.0774878i	$0.975310\pi$
$752$		0			0
$753$		0			0
$754$	−2.50000	+	4.33013i	−0.0910446	+	0.157694i
$755$	5.00000			0.181969
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$		0			0
$760$	−1.50000	−	2.59808i	−0.0544107	−	0.0942421i
$761$	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
$763$	−18.0000	−	15.5885i	−0.651644	−	0.564340i
$764$	8.00000			0.289430
$765$		0			0
$766$	−13.5000	−	23.3827i	−0.487775	−	0.844851i
$767$		0			0
$768$		0			0
$769$	23.0000			0.829401			0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$	2.50000	−	12.9904i	0.0900937	−	0.468141i
$771$		0			0
$772$	−5.00000	+	8.66025i	−0.179954	+	0.311689i
$773$	15.5000	+	26.8468i	0.557496	+	0.965612i	0.997705	+	0.0677162i	$0.0215712\pi$
$773$	15.5000	+	26.8468i	0.557496	+	0.965612i	−0.440208	+	0.897896i	$0.645095\pi$
$774$		0			0
$775$		0			0
$776$	−27.0000			−0.969244
$777$		0			0
$778$	−9.00000			−0.322666
$779$	−2.50000	+	4.33013i	−0.0895718	+	0.155143i
$780$		0			0
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$	4.50000	−	7.79423i	0.160920	−	0.278721i
$783$		0			0
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$	−14.0000			−0.499681
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	−1.00000	−	1.73205i	−0.0356235	−	0.0617018i
$789$		0			0
$790$	−8.00000			−0.284627
$791$	−2.50000	+	0.866025i	−0.0888898	+	0.0307923i
$792$		0			0
$793$	−35.0000	+	60.6218i	−1.24289	+	2.15274i
$794$	7.50000	+	12.9904i	0.266165	+	0.461011i
$795$		0			0
$796$	1.50000	−	2.59808i	0.0531661	−	0.0920864i
$797$	−23.0000			−0.814702			−0.407351	−	0.913272i	$-0.633547\pi$
$797$	−23.0000			−0.814702			−0.407351	+	0.913272i	$0.633547\pi$
$798$		0			0
$799$		0			0
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$		0			0
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	7.50000	−	12.9904i	0.264669	−	0.458421i
$804$		0			0
$805$	−6.00000	−	5.19615i	−0.211472	−	0.183140i
$806$		0			0
$807$		0			0
$808$	−25.5000	−	44.1673i	−0.897087	−	1.55380i
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−2.00000	−	1.73205i	−0.0701862	−	0.0607831i
$813$		0			0
$814$	−7.50000	+	12.9904i	−0.262875	+	0.455313i
$815$	5.50000	+	9.52628i	0.192657	+	0.333691i
$816$		0			0
$817$	0.500000	−	0.866025i	0.0174928	−	0.0302984i
$818$	−14.0000			−0.489499
$819$		0			0
$820$	−5.00000			−0.174608
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	−0.607714	−	0.794156i	$-0.707913\pi$
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	0.991616	+	0.129217i	$0.0412465\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	1.50000	−	2.59808i	0.0522550	−	0.0905083i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$		0			0
$832$	−35.0000			−1.21341
$833$	19.5000	+	7.79423i	0.675635	+	0.270054i
$834$		0			0
$835$	−9.50000	+	16.4545i	−0.328761	+	0.569431i
$836$	−2.50000	−	4.33013i	−0.0864643	−	0.149761i
$837$		0			0
$838$	−4.50000	+	7.79423i	−0.155450	+	0.269247i
$839$	37.0000			1.27738			0.638691	−	0.769463i	$-0.279476\pi$
$839$	37.0000			1.27738			0.638691	+	0.769463i	$0.279476\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	−0.500000	+	0.866025i	−0.0172311	+	0.0298452i
$843$		0			0
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	7.00000	−	36.3731i	0.240523	−	1.24979i
$848$	−9.00000			−0.309061
$849$		0			0
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$	4.50000	+	7.79423i	0.154258	+	0.267183i
$852$		0			0
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	28.0000	+	24.2487i	0.958140	+	0.829774i
$855$		0			0
$856$	25.5000	−	44.1673i	0.871572	−	1.50961i
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	0.944542	−	0.328391i	$-0.106506\pi$
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	−0.756666	+	0.653802i	$0.773173\pi$
$858$		0			0
$859$	0.500000	−	0.866025i	0.0170598	−	0.0295484i	−0.857369	−	0.514701i	$-0.827903\pi$
$859$	0.500000	−	0.866025i	0.0170598	−	0.0295484i	0.874429	+	0.485153i	$0.161236\pi$
$860$	1.00000			0.0340997
$861$		0			0
$862$	−9.00000			−0.306541
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	0.315825	+	0.948818i	$0.397719\pi$
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	−0.979612	+	0.200897i	$0.935615\pi$
$864$		0			0
$865$	−7.00000	−	12.1244i	−0.238007	−	0.412240i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	−40.0000			−1.35691
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	13.5000	+	23.3827i	0.457168	+	0.791838i
$873$		0			0
$874$	3.00000			0.101477
$875$	22.5000	−	7.79423i	0.760639	−	0.263493i
$876$		0			0
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.0608407	−	0.998147i	$-0.480622\pi$
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.834001	−	0.551763i	$-0.186045\pi$
$878$		0			0
$879$		0			0
$880$	−2.50000	+	4.33013i	−0.0842750	+	0.145969i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	7.50000	−	12.9904i	0.252252	−	0.436914i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−14.5000	+	25.1147i	−0.486862	+	0.843270i	−0.999886	−	0.0151042i	$-0.995192\pi$
$887$	−14.5000	+	25.1147i	−0.486862	+	0.843270i	0.513024	+	0.858375i	$0.328525\pi$
$888$		0			0
$889$	30.0000	−	10.3923i	1.00617	−	0.348547i
$890$	−13.0000			−0.435761
$891$		0			0
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$		0			0
$894$		0			0
$895$	−19.0000			−0.635100
$896$	1.50000	−	7.79423i	0.0501115	−	0.260387i
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$		0			0
$900$		0			0
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$	25.0000			0.832409
$903$		0			0
$904$	3.00000			0.0997785
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$		0			0
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$		0			0
$910$	10.0000	+	8.66025i	0.331497	+	0.287085i
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$		0			0
$913$	22.5000	+	38.9711i	0.744641	+	1.28976i
$914$	11.0000	+	19.0526i	0.363848	+	0.630203i
$915$		0			0
$916$	1.00000			0.0330409
$917$	0.500000	−	2.59808i	0.0165115	−	0.0857960i
$918$		0			0
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	−0.971481	−	0.237119i	$-0.923797\pi$
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	0.691091	+	0.722767i	$0.257130\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	−9.50000	+	16.4545i	−0.312866	+	0.541900i
$923$	−60.0000			−1.97492
$924$		0			0
$925$	−12.0000			−0.394558
$926$	6.50000	−	11.2583i	0.213603	−	0.369972i
$927$		0			0
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$		0			0
$931$	1.00000	+	6.92820i	0.0327737	+	0.227063i
$932$	3.00000			0.0982683
$933$		0			0
$934$	13.5000	+	23.3827i	0.441733	+	0.765105i
$935$	−7.50000	−	12.9904i	−0.245276	−	0.424831i
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$	10.0000	−	3.46410i	0.326512	−	0.113107i
$939$		0			0
$940$		0			0
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	0.729079	−	0.684429i	$-0.239949\pi$
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	−0.957273	+	0.289187i	$0.906615\pi$
$942$		0			0
$943$	7.50000	−	12.9904i	0.244234	−	0.423025i
$944$		0			0
$945$		0			0
$946$	−5.00000			−0.162564
$947$	−10.0000	+	17.3205i	−0.324956	+	0.562841i	−0.981504	−	0.191444i	$-0.938683\pi$
$947$	−10.0000	+	17.3205i	−0.324956	+	0.562841i	0.656547	+	0.754285i	$0.272016\pi$
$948$		0			0
$949$	7.50000	+	12.9904i	0.243460	+	0.421686i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		0			0
$952$	−18.0000	−	15.5885i	−0.583383	−	0.505225i
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$		0			0
$958$	25.0000			0.807713
$959$	18.0000	+	15.5885i	0.581250	+	0.503378i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−7.50000	−	12.9904i	−0.241810	−	0.418827i
$963$		0			0
$964$	5.50000	−	9.52628i	0.177143	−	0.306821i
$965$	−10.0000			−0.321911
$966$		0			0
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$	−21.0000	+	36.3731i	−0.674966	+	1.16907i
$969$		0			0
$970$	−4.50000	−	7.79423i	−0.144486	−	0.250258i
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.107135	−	0.994244i	$-0.465832\pi$
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.807473	−	0.589904i	$-0.200834\pi$
$972$		0			0
$973$	−22.5000	+	7.79423i	−0.721317	+	0.249871i
$974$	−19.0000			−0.608799
$975$		0			0
$976$	−7.00000	−	12.1244i	−0.224065	−	0.388091i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$	−65.0000			−2.07741
$980$	−5.50000	+	4.33013i	−0.175691	+	0.138321i
$981$		0			0
$982$	−6.50000	+	11.2583i	−0.207423	+	0.359268i
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$	3.00000			0.0955395
$987$		0			0
$988$	5.00000			0.159071
$989$	−1.50000	+	2.59808i	−0.0476972	+	0.0826140i
$990$		0			0
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$		0			0
$993$		0			0
$994$	−6.00000	+	31.1769i	−0.190308	+	0.988872i
$995$	3.00000			0.0951064
$996$		0			0
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	15.5000	+	26.8468i	0.490644	+	0.849820i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.b.163.1		2
3.2	odd	2		567.2.e.a.163.1		2
7.2	even	3		3969.2.a.c.1.1		1
7.4	even	3	inner	567.2.e.b.487.1		2
7.5	odd	6		3969.2.a.a.1.1		1
9.2	odd	6		63.2.h.a.58.1	yes	2
9.4	even	3		189.2.g.a.100.1		2
9.5	odd	6		63.2.g.a.16.1	yes	2
9.7	even	3		189.2.h.a.37.1		2
21.2	odd	6		3969.2.a.d.1.1		1
21.5	even	6		3969.2.a.f.1.1		1
21.11	odd	6		567.2.e.a.487.1		2
36.7	odd	6		3024.2.q.b.2305.1		2
36.11	even	6		1008.2.q.c.625.1		2
36.23	even	6		1008.2.t.d.961.1		2
36.31	odd	6		3024.2.t.d.289.1		2
63.2	odd	6		441.2.f.b.148.1		2
63.4	even	3		189.2.h.a.46.1		2
63.5	even	6		441.2.f.a.295.1		2
63.11	odd	6		63.2.g.a.4.1	✓	2
63.13	odd	6		1323.2.g.a.667.1		2
63.16	even	3		1323.2.f.a.442.1		2
63.20	even	6		441.2.h.a.373.1		2
63.23	odd	6		441.2.f.b.295.1		2
63.25	even	3		189.2.g.a.172.1		2
63.31	odd	6		1323.2.h.a.802.1		2
63.32	odd	6		63.2.h.a.25.1	yes	2
63.34	odd	6		1323.2.h.a.226.1		2
63.38	even	6		441.2.g.a.67.1		2
63.40	odd	6		1323.2.f.b.883.1		2
63.41	even	6		441.2.g.a.79.1		2
63.47	even	6		441.2.f.a.148.1		2
63.52	odd	6		1323.2.g.a.361.1		2
63.58	even	3		1323.2.f.a.883.1		2
63.59	even	6		441.2.h.a.214.1		2
63.61	odd	6		1323.2.f.b.442.1		2
252.11	even	6		1008.2.t.d.193.1		2
252.67	odd	6		3024.2.q.b.2881.1		2
252.95	even	6		1008.2.q.c.529.1		2
252.151	odd	6		3024.2.t.d.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	63.11	odd	6
63.2.g.a.16.1	yes	2	9.5	odd	6
63.2.h.a.25.1	yes	2	63.32	odd	6
63.2.h.a.58.1	yes	2	9.2	odd	6
189.2.g.a.100.1		2	9.4	even	3
189.2.g.a.172.1		2	63.25	even	3
189.2.h.a.37.1		2	9.7	even	3
189.2.h.a.46.1		2	63.4	even	3
441.2.f.a.148.1		2	63.47	even	6
441.2.f.a.295.1		2	63.5	even	6
441.2.f.b.148.1		2	63.2	odd	6
441.2.f.b.295.1		2	63.23	odd	6
441.2.g.a.67.1		2	63.38	even	6
441.2.g.a.79.1		2	63.41	even	6
441.2.h.a.214.1		2	63.59	even	6
441.2.h.a.373.1		2	63.20	even	6
567.2.e.a.163.1		2	3.2	odd	2
567.2.e.a.487.1		2	21.11	odd	6
567.2.e.b.163.1		2	1.1	even	1	trivial
567.2.e.b.487.1		2	7.4	even	3	inner
1008.2.q.c.529.1		2	252.95	even	6
1008.2.q.c.625.1		2	36.11	even	6
1008.2.t.d.193.1		2	252.11	even	6
1008.2.t.d.961.1		2	36.23	even	6
1323.2.f.a.442.1		2	63.16	even	3
1323.2.f.a.883.1		2	63.58	even	3
1323.2.f.b.442.1		2	63.61	odd	6
1323.2.f.b.883.1		2	63.40	odd	6
1323.2.g.a.361.1		2	63.52	odd	6
1323.2.g.a.667.1		2	63.13	odd	6
1323.2.h.a.226.1		2	63.34	odd	6
1323.2.h.a.802.1		2	63.31	odd	6
3024.2.q.b.2305.1		2	36.7	odd	6
3024.2.q.b.2881.1		2	252.67	odd	6
3024.2.t.d.289.1		2	36.31	odd	6
3024.2.t.d.1873.1		2	252.151	odd	6
3969.2.a.a.1.1		1	7.5	odd	6
3969.2.a.c.1.1		1	7.2	even	3
3969.2.a.d.1.1		1	21.2	odd	6
3969.2.a.f.1.1		1	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{11} -5.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +1.00000 q^{29} +(2.50000 + 4.33013i) q^{32} +3.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-1.50000 + 2.59808i) q^{40} +5.00000 q^{41} -1.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(-7.50000 + 2.59808i) q^{56} +(0.500000 - 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-2.00000 - 1.73205i) q^{70} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.50000 + 2.59808i) q^{74} -1.00000 q^{76} +(-10.0000 - 8.66025i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(2.50000 - 4.33013i) q^{82} +9.00000 q^{83} -3.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 + 12.9904i) q^{88} +(-6.50000 + 11.2583i) q^{89} +(12.5000 - 4.33013i) q^{91} +3.00000 q^{92} +(-0.500000 - 0.866025i) q^{95} -9.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} - q^{5} - 5 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 - q^5 - 5 * q^7 + 6 * q^8	\( 2 q + q^{2} + q^{4} - q^{5} - 5 q^{7} + 6 q^{8} + q^{10} + 5 q^{11} - 10 q^{13} - q^{14} + q^{16} + 3 q^{17} - q^{19} - 2 q^{20} + 10 q^{22} + 3 q^{23} + 4 q^{25} - 5 q^{26} - 4 q^{28} + 2 q^{29} + 5 q^{32} + 6 q^{34} + q^{35} - 3 q^{37} + q^{38} - 3 q^{40} + 10 q^{41} - 2 q^{43} - 5 q^{44} - 3 q^{46} + 11 q^{49} + 8 q^{50} - 5 q^{52} - 9 q^{53} - 10 q^{55} - 15 q^{56} + q^{58} + 14 q^{61} + 14 q^{64} + 5 q^{65} - 4 q^{67} - 3 q^{68} - 4 q^{70} + 24 q^{71} - 3 q^{73} + 3 q^{74} - 2 q^{76} - 20 q^{77} - 8 q^{79} + q^{80} + 5 q^{82} + 18 q^{83} - 6 q^{85} - q^{86} + 15 q^{88} - 13 q^{89} + 25 q^{91} + 6 q^{92} - q^{95} - 18 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 - q^5 - 5 * q^7 + 6 * q^8 + q^10 + 5 * q^11 - 10 * q^13 - q^14 + q^16 + 3 * q^17 - q^19 - 2 * q^20 + 10 * q^22 + 3 * q^23 + 4 * q^25 - 5 * q^26 - 4 * q^28 + 2 * q^29 + 5 * q^32 + 6 * q^34 + q^35 - 3 * q^37 + q^38 - 3 * q^40 + 10 * q^41 - 2 * q^43 - 5 * q^44 - 3 * q^46 + 11 * q^49 + 8 * q^50 - 5 * q^52 - 9 * q^53 - 10 * q^55 - 15 * q^56 + q^58 + 14 * q^61 + 14 * q^64 + 5 * q^65 - 4 * q^67 - 3 * q^68 - 4 * q^70 + 24 * q^71 - 3 * q^73 + 3 * q^74 - 2 * q^76 - 20 * q^77 - 8 * q^79 + q^80 + 5 * q^82 + 18 * q^83 - 6 * q^85 - q^86 + 15 * q^88 - 13 * q^89 + 25 * q^91 + 6 * q^92 - q^95 - 18 * q^97 - 2 * q^98

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