LMFDB - Embedded newform 1323.2.f.b.442.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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:	$10.5642081874$
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			442.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.b.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{8} +1.00000 q^{10} +(2.50000 + 4.33013i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{16} +3.00000 q^{17} -1.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.00000 q^{26} +(-0.500000 - 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.50000 - 2.59808i) q^{40} +(2.50000 - 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +5.00000 q^{44} +3.00000 q^{46} +(-2.00000 + 3.46410i) q^{50} +(2.50000 + 4.33013i) q^{52} +9.00000 q^{53} +5.00000 q^{55} +(0.500000 - 0.866025i) q^{58} +(-7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +12.0000 q^{71} -3.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(-0.500000 + 0.866025i) q^{76} +(-4.00000 - 6.92820i) q^{79} +1.00000 q^{80} +5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 + 12.9904i) q^{88} -13.0000 q^{89} +(-1.50000 - 2.59808i) q^{92} +(-0.500000 + 0.866025i) q^{95} +(-4.50000 - 7.79423i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + q^{5} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 + q^5 + 6 * q^8	$ 2 q + q^{2} + q^{4} + q^{5} + 6 q^{8} + 2 q^{10} + 5 q^{11} - 5 q^{13} + q^{16} + 6 q^{17} - 2 q^{19} - q^{20} - 5 q^{22} + 3 q^{23} + 4 q^{25} - 10 q^{26} - q^{29} + 5 q^{32} + 3 q^{34} + 6 q^{37} - q^{38} + 3 q^{40} + 5 q^{41} + q^{43} + 10 q^{44} + 6 q^{46} - 4 q^{50} + 5 q^{52} + 18 q^{53} + 10 q^{55} + q^{58} - 14 q^{61} + 14 q^{64} + 5 q^{65} - 4 q^{67} + 3 q^{68} + 24 q^{71} - 6 q^{73} + 3 q^{74} - q^{76} - 8 q^{79} + 2 q^{80} + 10 q^{82} + 9 q^{83} + 3 q^{85} - q^{86} + 15 q^{88} - 26 q^{89} - 3 q^{92} - q^{95} - 9 q^{97}+O(q^{100}) $ 2 * q + q^2 + q^4 + q^5 + 6 * q^8 + 2 * q^10 + 5 * q^11 - 5 * q^13 + q^16 + 6 * q^17 - 2 * q^19 - q^20 - 5 * q^22 + 3 * q^23 + 4 * q^25 - 10 * q^26 - q^29 + 5 * q^32 + 3 * q^34 + 6 * q^37 - q^38 + 3 * q^40 + 5 * q^41 + q^43 + 10 * q^44 + 6 * q^46 - 4 * q^50 + 5 * q^52 + 18 * q^53 + 10 * q^55 + q^58 - 14 * q^61 + 14 * q^64 + 5 * q^65 - 4 * q^67 + 3 * q^68 + 24 * q^71 - 6 * q^73 + 3 * q^74 - q^76 - 8 * q^79 + 2 * q^80 + 10 * q^82 + 9 * q^83 + 3 * q^85 - q^86 + 15 * q^88 - 26 * q^89 - 3 * q^92 - q^95 - 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$		0			0
$10$	1.00000			0.316228
$11$	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
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	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
$26$	−5.00000			−0.980581
$27$		0			0
$28$		0			0
$29$	−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
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$		0			0
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	5.00000			0.753778
$45$		0			0
$46$	3.00000			0.442326
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$		0			0
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$		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	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$	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
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	5.00000			0.552158
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$	7.50000	+	12.9904i	0.799503	+	1.38478i
$89$	−13.0000			−1.37800			−0.688999	−	0.724763i	$-0.741949\pi$
$89$	−13.0000			−1.37800			−0.688999	+	0.724763i	$0.741949\pi$
$90$		0			0
$91$		0			0
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$		0			0
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$		0			0
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$		0			0
$99$		0			0
$100$	4.00000			0.400000
$101$	8.50000	+	14.7224i	0.845782	+	1.46494i	0.884941	+	0.465704i	$0.154199\pi$
$101$	8.50000	+	14.7224i	0.845782	+	1.46494i	−0.0391591	+	0.999233i	$0.512468\pi$
$102$		0			0
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$104$	−7.50000	+	12.9904i	−0.735436	+	1.27381i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−17.0000			−1.64345			−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000			−1.64345			−0.821726	+	0.569883i	$0.806989\pi$
$108$		0			0
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$		0			0
$112$		0			0
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	−0.888585	−	0.458712i	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	−1.00000			−0.0928477
$117$		0			0
$118$		0			0
$119$		0			0
$120$		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	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$		0			0
$133$		0			0
$134$	−4.00000			−0.345547
$135$		0			0
$136$	9.00000			0.771744
$137$	−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
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	−25.0000			−2.09061
$144$		0			0
$145$	−1.00000			−0.0830455
$146$	−1.50000	−	2.59808i	−0.124141	−	0.215018i
$147$		0			0
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	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	$0.898548\pi$
$152$	−3.00000			−0.243332
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$		0			0
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	−2.50000	−	4.33013i	−0.195217	−	0.338126i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	−0.219533	−	0.975605i	$-0.570453\pi$
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	0.954665	−	0.297681i	$-0.0962132\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	3.00000			0.230089
$171$		0			0
$172$	1.00000			0.0762493
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$		0			0
$178$	−6.50000	−	11.2583i	−0.487196	−	0.843848i
$179$	−19.0000			−1.42013			−0.710063	−	0.704138i	$-0.751334\pi$
$179$	−19.0000			−1.42013			−0.710063	+	0.704138i	$0.751334\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$		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	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	4.50000	−	7.79423i	0.323081	−	0.559593i
$195$		0			0
$196$		0			0
$197$	−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
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	6.00000	+	10.3923i	0.424264	+	0.734847i
$201$		0			0
$202$	−8.50000	+	14.7224i	−0.598058	+	1.03587i
$203$		0			0
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$	−1.00000			−0.0696733
$207$		0			0
$208$	−5.00000			−0.346688
$209$	−2.50000	−	4.33013i	−0.172929	−	0.299521i
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	1.00000			0.0681994
$216$		0			0
$217$		0			0
$218$	−4.50000	−	7.79423i	−0.304778	−	0.527892i
$219$		0			0
$220$	2.50000	−	4.33013i	0.168550	−	0.291937i
$221$	−7.50000	+	12.9904i	−0.504505	+	0.873828i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$		0			0
$226$	−1.00000			−0.0665190
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$		0			0
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$		0			0
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	−14.0000			−0.899954
$243$		0			0
$244$	−14.0000			−0.896258
$245$		0			0
$246$		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	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$		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	$-0.473589\pi$
$257$	14.5000	−	25.1147i	0.904485	−	1.56661i	0.821607	−	0.570055i	$-0.193078\pi$
$258$		0			0
$259$		0			0
$260$	5.00000			0.310087
$261$		0			0
$262$	1.00000			0.0617802
$263$	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
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$		0			0
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	−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	$-0.360033\pi$
$278$	9.00000			0.539784
$279$		0			0
$280$		0			0
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	−0.867050	−	0.498222i	$-0.833987\pi$
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	0.00205220	−	0.999998i	$-0.499347\pi$
$282$		0			0
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−12.5000	−	21.6506i	−0.739140	−	1.28023i
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−0.500000	−	0.866025i	−0.0293610	−	0.0508548i
$291$		0			0
$292$	−1.50000	+	2.59808i	−0.0877809	+	0.152041i
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	−0.783713	−	0.621123i	$-0.786677\pi$
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	0.929765	+	0.368154i	$0.120010\pi$
$294$		0			0
$295$		0			0
$296$	9.00000			0.523114
$297$		0			0
$298$	3.00000			0.173785
$299$	7.50000	+	12.9904i	0.433736	+	0.751253i
$300$		0			0
$301$		0			0
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$		0			0
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−14.0000			−0.801638
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	3.50000	−	6.06218i	0.195656	−	0.338886i
$321$		0			0
$322$		0			0
$323$	−3.00000			−0.166924
$324$		0			0
$325$	−20.0000			−1.10940
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$		0			0
$328$	7.50000	−	12.9904i	0.414118	−	0.717274i
$329$		0			0
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	9.00000			0.493939
$333$		0			0
$334$	19.0000			1.03963
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$	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
$343$		0			0
$344$	1.50000	+	2.59808i	0.0808746	+	0.140079i
$345$		0			0
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$		0			0
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$		0			0
$351$		0			0
$352$	25.0000			1.33250
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	0.681720	−	0.731613i	$-0.261232\pi$
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	−0.974456	+	0.224580i	$0.927899\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	−6.50000	+	11.2583i	−0.344499	+	0.596690i
$357$		0			0
$358$	−9.50000	−	16.4545i	−0.502091	−	0.869646i
$359$	11.0000			0.580558			0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000			0.580558			0.290279	+	0.956942i	$0.406252\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	7.00000	+	12.1244i	0.367912	+	0.637242i
$363$		0			0
$364$		0			0
$365$	−1.50000	+	2.59808i	−0.0785136	+	0.135990i
$366$		0			0
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	0.824217	−	0.566274i	$-0.191616\pi$
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	−0.902516	+	0.430656i	$0.858282\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	3.00000			0.155963
$371$		0			0
$372$		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	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		0			0
$385$		0			0
$386$	10.0000			0.508987
$387$		0			0
$388$	−9.00000			−0.456906
$389$	−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
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$		0			0
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	−15.0000			−0.752828			−0.376414	−	0.926451i	$-0.622843\pi$
$397$	−15.0000			−0.752828			−0.376414	+	0.926451i	$0.622843\pi$
$398$	−1.50000	−	2.59808i	−0.0751882	−	0.130230i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	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
$404$	17.0000			0.845782
$405$		0			0
$406$		0			0
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$		0			0
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$		0			0
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$		0			0
$414$		0			0
$415$	9.00000			0.441793
$416$	12.5000	+	21.6506i	0.612863	+	1.06151i
$417$		0			0
$418$	2.50000	−	4.33013i	0.122279	−	0.211793i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$	−13.0000			−0.632830
$423$		0			0
$424$	27.0000			1.31124
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$		0			0
$428$	−8.50000	+	14.7224i	−0.410863	+	0.711636i
$429$		0			0
$430$	0.500000	+	0.866025i	0.0241121	+	0.0417635i
$431$	9.00000			0.433515			0.216757	−	0.976226i	$-0.430452\pi$
$431$	9.00000			0.433515			0.216757	+	0.976226i	$0.430452\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		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	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	15.0000			0.715097
$441$		0			0
$442$	−15.0000			−0.713477
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−6.50000	+	11.2583i	−0.308130	+	0.533696i
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$		0			0
$448$		0			0
$449$	−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
$451$	25.0000			1.17720
$452$	0.500000	+	0.866025i	0.0235180	+	0.0407344i
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$		0			0
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$	−1.00000			−0.0467269
$459$		0			0
$460$	−3.00000			−0.139876
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	0.555412	−	0.831575i	$-0.312560\pi$
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	−0.997871	+	0.0652135i	$0.979227\pi$
$462$		0			0
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	−0.976607	−	0.215032i	$-0.931015\pi$
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	0.674526	+	0.738251i	$0.264348\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.50000	+	4.33013i	−0.114950	+	0.199099i
$474$		0			0
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$		0			0
$478$	−15.0000			−0.686084
$479$	−12.5000	−	21.6506i	−0.571140	−	0.989243i	−0.996449	−	0.0841949i	$-0.973168\pi$
$479$	−12.5000	−	21.6506i	−0.571140	−	0.989243i	0.425310	−	0.905048i	$-0.360165\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	−5.50000	+	9.52628i	−0.250518	+	0.433910i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−9.00000			−0.408669
$486$		0			0
$487$	19.0000			0.860972			0.430486	−	0.902597i	$-0.358342\pi$
$487$	19.0000			0.860972			0.430486	+	0.902597i	$0.358342\pi$
$488$	−21.0000	−	36.3731i	−0.950625	−	1.64653i
$489$		0			0
$490$		0			0
$491$	6.50000	−	11.2583i	0.293341	−	0.508081i	−0.681257	−	0.732045i	$-0.738566\pi$
$491$	6.50000	−	11.2583i	0.293341	−	0.508081i	0.974598	+	0.223963i	$0.0718996\pi$
$492$		0			0
$493$	−1.50000	−	2.59808i	−0.0675566	−	0.117011i
$494$	5.00000			0.224961
$495$		0			0
$496$		0			0
$497$		0			0
$498$		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	$-0.611147\pi$
$509$	14.5000	−	25.1147i	0.642701	−	1.11319i	0.984827	−	0.173537i	$-0.0555197\pi$
$510$		0			0
$511$		0			0
$512$	11.0000			0.486136
$513$		0			0
$514$	29.0000			1.27914
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	7.50000	+	12.9904i	0.328897	+	0.569666i
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	−1.00000			−0.0437269			−0.0218635	−	0.999761i	$-0.506960\pi$
$523$	−1.00000			−0.0437269			−0.0218635	+	0.999761i	$0.506960\pi$
$524$	−0.500000	−	0.866025i	−0.0218426	−	0.0378325i
$525$		0			0
$526$	−2.50000	+	4.33013i	−0.109005	+	0.188803i
$527$		0			0
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	9.00000			0.390935
$531$		0			0
$532$		0			0
$533$	12.5000	+	21.6506i	0.541435	+	0.937793i
$534$		0			0
$535$	−8.50000	+	14.7224i	−0.367487	+	0.636506i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	1.50000	+	2.59808i	0.0646696	+	0.112011i
$539$		0			0
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	−0.500000	−	0.866025i	−0.0214768	−	0.0371990i
$543$		0			0
$544$	7.50000	−	12.9904i	0.321560	−	0.556958i
$545$	−4.50000	+	7.79423i	−0.192759	+	0.333868i
$546$		0			0
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	−9.00000			−0.384461
$549$		0			0
$550$	−20.0000			−0.852803
$551$	0.500000	+	0.866025i	0.0213007	+	0.0368939i
$552$		0			0
$553$		0			0
$554$	9.50000	−	16.4545i	0.403616	−	0.699084i
$555$		0			0
$556$	−4.50000	−	7.79423i	−0.190843	−	0.330549i
$557$	37.0000			1.56774			0.783870	−	0.620925i	$-0.213243\pi$
$557$	37.0000			1.56774			0.783870	+	0.620925i	$0.213243\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$	14.5000	−	25.1147i	0.611646	−	1.05940i
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	0.994228	−	0.107290i	$-0.0342173\pi$
$564$		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	−0.963849	−	0.266450i	$-0.914149\pi$
$569$	−17.0000	−	29.4449i	−0.712677	−	1.23439i	0.251172	−	0.967943i	$-0.419184\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−12.5000	+	21.6506i	−0.522651	+	0.905259i
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−31.0000			−1.29055			−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000			−1.29055			−0.645273	+	0.763952i	$0.723257\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−0.500000	+	0.866025i	−0.0207614	+	0.0359597i
$581$		0			0
$582$		0			0
$583$	22.5000	+	38.9711i	0.931855	+	1.61402i
$584$	−9.00000			−0.372423
$585$		0			0
$586$	5.00000			0.206548
$587$	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
$590$		0			0
$591$		0			0
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	15.0000			0.615976			0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000			0.615976			0.307988	+	0.951390i	$0.400344\pi$
$594$		0			0
$595$		0			0
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$		0			0
$598$	−7.50000	+	12.9904i	−0.306698	+	0.531216i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	−4.50000	−	7.79423i	−0.183559	−	0.317933i	0.759531	−	0.650471i	$-0.225428\pi$
$601$	−4.50000	−	7.79423i	−0.183559	−	0.317933i	−0.943090	+	0.332538i	$0.892095\pi$
$602$		0			0
$603$		0			0
$604$	−5.00000			−0.203447
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$		0			0
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$		0			0
$612$		0			0
$613$	19.0000			0.767403			0.383701	−	0.923457i	$-0.374649\pi$
$613$	19.0000			0.767403			0.383701	+	0.923457i	$0.374649\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	−0.455211	−	0.890384i	$-0.650436\pi$
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	0.998700	−	0.0509678i	$-0.0162306\pi$
$618$		0			0
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		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
$637$		0			0
$638$	5.00000			0.197952
$639$		0			0
$640$	−3.00000			−0.118585
$641$	−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
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$644$		0			0
$645$		0			0
$646$	−1.50000	−	2.59808i	−0.0590167	−	0.102220i
$647$	31.0000			1.21874			0.609368	−	0.792888i	$-0.291423\pi$
$647$	31.0000			1.21874			0.609368	+	0.792888i	$0.291423\pi$
$648$		0			0
$649$		0			0
$650$	−10.0000	−	17.3205i	−0.392232	−	0.679366i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	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
$656$	5.00000			0.195217
$657$		0			0
$658$		0			0
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$		0			0
$664$	13.5000	+	23.3827i	0.523902	+	0.907424i
$665$		0			0
$666$		0			0
$667$	−3.00000			−0.116160
$668$	−9.50000	−	16.4545i	−0.367566	−	0.636643i
$669$		0			0
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	35.0000	−	60.6218i	1.35116	−	2.34028i
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	29.0000			1.11704
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−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
$679$		0			0
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$		0			0
$682$		0			0
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		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	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$	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
$700$		0			0
$701$	−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
$703$	−3.00000			−0.113147
$704$	17.5000	+	30.3109i	0.659556	+	1.14238i
$705$		0			0
$706$	5.50000	−	9.52628i	0.206995	−	0.358526i
$707$		0			0
$708$		0			0
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	0.916845	−	0.399244i	$-0.130727\pi$
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	−0.804178	+	0.594389i	$0.797394\pi$
$710$	12.0000			0.450352
$711$		0			0
$712$	−39.0000			−1.46159
$713$		0			0
$714$		0			0
$715$	−12.5000	+	21.6506i	−0.467473	+	0.809688i
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$		0			0
$718$	5.50000	+	9.52628i	0.205258	+	0.355518i
$719$	−27.0000			−1.00693			−0.503465	−	0.864016i	$-0.667942\pi$
$719$	−27.0000			−1.00693			−0.503465	+	0.864016i	$0.667942\pi$
$720$		0			0
$721$		0			0
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$		0			0
$724$	7.00000	−	12.1244i	0.260153	−	0.450598i
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$		0			0
$729$		0			0
$730$	−3.00000			−0.111035
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	13.5000	−	23.3827i	0.498634	−	0.863659i	−0.501365	−	0.865236i	$-0.667169\pi$
$733$	13.5000	−	23.3827i	0.498634	−	0.863659i	0.999999	+	0.00157675i	$0.000501894\pi$
$734$	1.50000	−	2.59808i	0.0553660	−	0.0958967i
$735$		0			0
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	−20.0000			−0.736709
$738$		0			0
$739$	−9.00000			−0.331070			−0.165535	−	0.986204i	$-0.552935\pi$
$739$	−9.00000			−0.331070			−0.165535	+	0.986204i	$0.552935\pi$
$740$	−1.50000	−	2.59808i	−0.0551411	−	0.0955072i
$741$		0			0
$742$		0			0
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	−0.970173	−	0.242415i	$-0.922060\pi$
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$744$		0			0
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$	25.0000			0.915315
$747$		0			0
$748$	15.0000			0.548454
$749$		0			0
$750$		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	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		0			0
$763$		0			0
$764$	8.00000			0.289430
$765$		0			0
$766$	−27.0000			−0.975550
$767$		0			0
$768$		0			0
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$		0			0
$771$		0			0
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	31.0000			1.11499			0.557496	−	0.830179i	$-0.311762\pi$
$773$	31.0000			1.11499			0.557496	+	0.830179i	$0.311762\pi$
$774$		0			0
$775$		0			0
$776$	−13.5000	−	23.3827i	−0.484622	−	0.839390i
$777$		0			0
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	−2.50000	+	4.33013i	−0.0895718	+	0.155143i
$780$		0			0
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$	9.00000			0.321839
$783$		0			0
$784$		0			0
$785$	7.00000	+	12.1244i	0.249841	+	0.432737i
$786$		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	$0.000350496\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$		0			0
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$		0			0
$792$		0			0
$793$	70.0000			2.48577
$794$	−7.50000	−	12.9904i	−0.266165	−	0.461011i
$795$		0			0
$796$	−1.50000	+	2.59808i	−0.0531661	+	0.0920864i
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$798$		0			0
$799$		0			0
$800$	20.0000			0.707107
$801$		0			0
$802$	3.00000			0.105934
$803$	−7.50000	−	12.9904i	−0.264669	−	0.458421i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	25.5000	+	44.1673i	0.897087	+	1.55380i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		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	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$		0			0
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	−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
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$		0			0
$832$	−17.5000	+	30.3109i	−0.606703	+	1.05084i
$833$		0			0
$834$		0			0
$835$	−9.50000	−	16.4545i	−0.328761	−	0.569431i
$836$	−5.00000			−0.172929
$837$		0			0
$838$	−9.00000			−0.310900
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	0.985720	+	0.168391i	$0.0538571\pi$
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	−0.347029	+	0.937854i	$0.612810\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−0.500000	+	0.866025i	−0.0172311	+	0.0298452i
$843$		0			0
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	−12.0000			−0.412813
$846$		0			0
$847$		0			0
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	−0.986846	−	0.161664i	$-0.948314\pi$
$853$	−18.5000	−	32.0429i	−0.633428	−	1.09713i	0.353418	−	0.935466i	$-0.385019\pi$
$854$		0			0
$855$		0			0
$856$	−51.0000			−1.74314
$857$	−5.50000	−	9.52628i	−0.187876	−	0.325412i	0.756666	−	0.653802i	$-0.226827\pi$
$857$	−5.50000	−	9.52628i	−0.187876	−	0.325412i	−0.944542	+	0.328391i	$0.893494\pi$
$858$		0			0
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$	0.500000	−	0.866025i	0.0170499	−	0.0295312i
$861$		0			0
$862$	4.50000	+	7.79423i	0.153271	+	0.265472i
$863$	39.0000			1.32758			0.663788	−	0.747921i	$-0.268948\pi$
$863$	39.0000			1.32758			0.663788	+	0.747921i	$0.268948\pi$
$864$		0			0
$865$	14.0000			0.476014
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	20.0000	−	34.6410i	0.678454	−	1.17512i
$870$		0			0
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$	−27.0000			−0.914335
$873$		0			0
$874$	−3.00000			−0.101477
$875$		0			0
$876$		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	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		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	−0.513024	−	0.858375i	$-0.671475\pi$
$887$	14.5000	−	25.1147i	0.486862	−	0.843270i	0.999886	+	0.0151042i	$0.00480800\pi$
$888$		0			0
$889$		0			0
$890$	−13.0000			−0.435761
$891$		0			0
$892$	19.0000			0.636167
$893$		0			0
$894$		0			0
$895$	−9.50000	+	16.4545i	−0.317550	+	0.550013i
$896$		0			0
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$		0			0
$900$		0			0
$901$	27.0000			0.899500
$902$	12.5000	+	21.6506i	0.416204	+	0.720887i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	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	$0.859787\pi$
$908$	3.00000			0.0995585
$909$		0			0
$910$		0			0
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	0.998208	−	0.0598468i	$-0.0190612\pi$
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	−0.550933	+	0.834550i	$0.685728\pi$
$912$		0			0
$913$	−22.5000	+	38.9711i	−0.744641	+	1.28976i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	0.500000	+	0.866025i	0.0165205	+	0.0286143i
$917$		0			0
$918$		0			0
$919$	17.0000			0.560778			0.280389	−	0.959886i	$-0.409536\pi$
$919$	17.0000			0.560778			0.280389	+	0.959886i	$0.409536\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	9.50000	−	16.4545i	0.312866	−	0.541900i
$923$	−30.0000	+	51.9615i	−0.987462	+	1.71033i
$924$		0			0
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−13.0000			−0.427207
$927$		0			0
$928$	−5.00000			−0.164133
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$		0			0
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$		0			0
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	15.0000			0.490552
$936$		0			0
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	−0.729079	−	0.684429i	$-0.760051\pi$
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	0.957273	+	0.289187i	$0.0933848\pi$
$942$		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	0.656547	−	0.754285i	$-0.272016\pi$
$947$	−10.0000	−	17.3205i	−0.324956	−	0.562841i	−0.981504	+	0.191444i	$0.938683\pi$
$948$		0			0
$949$	7.50000	−	12.9904i	0.243460	−	0.421686i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$		0			0
$952$		0			0
$953$	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
$955$	8.00000			0.258874
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$		0			0
$958$	12.5000	−	21.6506i	0.403857	−	0.699500i
$959$		0			0
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−15.0000			−0.483619
$963$		0			0
$964$	11.0000			0.354286
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$		0			0
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	−21.0000	+	36.3731i	−0.674966	+	1.16907i
$969$		0			0
$970$	−4.50000	−	7.79423i	−0.144486	−	0.250258i
$971$	57.0000			1.82922			0.914609	−	0.404341i	$-0.132499\pi$
$971$	57.0000			1.82922			0.914609	+	0.404341i	$0.132499\pi$
$972$		0			0
$973$		0			0
$974$	9.50000	+	16.4545i	0.304400	+	0.527236i
$975$		0			0
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	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
$979$	−32.5000	−	56.2917i	−1.03870	−	1.79909i
$980$		0			0
$981$		0			0
$982$	13.0000			0.414847
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$	1.50000	−	2.59808i	0.0477697	−	0.0827396i
$987$		0			0
$988$	−2.50000	−	4.33013i	−0.0795356	−	0.137760i
$989$	3.00000			0.0953945
$990$		0			0
$991$	−37.0000			−1.17534			−0.587672	−	0.809099i	$-0.699955\pi$
$991$	−37.0000			−1.17534			−0.587672	+	0.809099i	$0.699955\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.50000	+	2.59808i	−0.0475532	+	0.0823646i
$996$		0			0
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	−31.0000			−0.981288
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	21.5	even	6
63.2.g.a.16.1	yes	2	63.38	even	6
63.2.h.a.25.1	yes	2	63.47	even	6
63.2.h.a.58.1	yes	2	21.17	even	6
189.2.g.a.100.1		2	63.52	odd	6
189.2.g.a.172.1		2	7.5	odd	6
189.2.h.a.37.1		2	7.3	odd	6
189.2.h.a.46.1		2	63.61	odd	6
441.2.f.a.148.1		2	3.2	odd	2
441.2.f.a.295.1		2	9.2	odd	6
441.2.f.b.148.1		2	21.20	even	2
441.2.f.b.295.1		2	63.20	even	6
441.2.g.a.67.1		2	21.2	odd	6
441.2.g.a.79.1		2	63.11	odd	6
441.2.h.a.214.1		2	63.2	odd	6
441.2.h.a.373.1		2	21.11	odd	6
567.2.e.a.163.1		2	63.59	even	6
567.2.e.a.487.1		2	63.5	even	6
567.2.e.b.163.1		2	63.31	odd	6
567.2.e.b.487.1		2	63.40	odd	6
1008.2.q.c.529.1		2	252.47	odd	6
1008.2.q.c.625.1		2	84.59	odd	6
1008.2.t.d.193.1		2	84.47	odd	6
1008.2.t.d.961.1		2	252.227	odd	6
1323.2.f.a.442.1		2	7.6	odd	2
1323.2.f.a.883.1		2	63.34	odd	6
1323.2.f.b.442.1		2	1.1	even	1	trivial
1323.2.f.b.883.1		2	9.7	even	3	inner
1323.2.g.a.361.1		2	7.2	even	3
1323.2.g.a.667.1		2	63.25	even	3
1323.2.h.a.226.1		2	7.4	even	3
1323.2.h.a.802.1		2	63.16	even	3
3024.2.q.b.2305.1		2	28.3	even	6
3024.2.q.b.2881.1		2	252.187	even	6
3024.2.t.d.289.1		2	252.115	even	6
3024.2.t.d.1873.1		2	28.19	even	6
3969.2.a.a.1.1		1	9.4	even	3
3969.2.a.c.1.1		1	63.13	odd	6
3969.2.a.d.1.1		1	63.41	even	6
3969.2.a.f.1.1		1	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{8} +1.00000 q^{10} +(2.50000 + 4.33013i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{16} +3.00000 q^{17} -1.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.00000 q^{26} +(-0.500000 - 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.50000 - 2.59808i) q^{40} +(2.50000 - 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +5.00000 q^{44} +3.00000 q^{46} +(-2.00000 + 3.46410i) q^{50} +(2.50000 + 4.33013i) q^{52} +9.00000 q^{53} +5.00000 q^{55} +(0.500000 - 0.866025i) q^{58} +(-7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +12.0000 q^{71} -3.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(-0.500000 + 0.866025i) q^{76} +(-4.00000 - 6.92820i) q^{79} +1.00000 q^{80} +5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 + 12.9904i) q^{88} -13.0000 q^{89} +(-1.50000 - 2.59808i) q^{92} +(-0.500000 + 0.866025i) q^{95} +(-4.50000 - 7.79423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + q^{5} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 + q^5 + 6 * q^8	\( 2 q + q^{2} + q^{4} + q^{5} + 6 q^{8} + 2 q^{10} + 5 q^{11} - 5 q^{13} + q^{16} + 6 q^{17} - 2 q^{19} - q^{20} - 5 q^{22} + 3 q^{23} + 4 q^{25} - 10 q^{26} - q^{29} + 5 q^{32} + 3 q^{34} + 6 q^{37} - q^{38} + 3 q^{40} + 5 q^{41} + q^{43} + 10 q^{44} + 6 q^{46} - 4 q^{50} + 5 q^{52} + 18 q^{53} + 10 q^{55} + q^{58} - 14 q^{61} + 14 q^{64} + 5 q^{65} - 4 q^{67} + 3 q^{68} + 24 q^{71} - 6 q^{73} + 3 q^{74} - q^{76} - 8 q^{79} + 2 q^{80} + 10 q^{82} + 9 q^{83} + 3 q^{85} - q^{86} + 15 q^{88} - 26 q^{89} - 3 q^{92} - q^{95} - 9 q^{97}+O(q^{100}) \) 2 * q + q^2 + q^4 + q^5 + 6 * q^8 + 2 * q^10 + 5 * q^11 - 5 * q^13 + q^16 + 6 * q^17 - 2 * q^19 - q^20 - 5 * q^22 + 3 * q^23 + 4 * q^25 - 10 * q^26 - q^29 + 5 * q^32 + 3 * q^34 + 6 * q^37 - q^38 + 3 * q^40 + 5 * q^41 + q^43 + 10 * q^44 + 6 * q^46 - 4 * q^50 + 5 * q^52 + 18 * q^53 + 10 * q^55 + q^58 - 14 * q^61 + 14 * q^64 + 5 * q^65 - 4 * q^67 + 3 * q^68 + 24 * q^71 - 6 * q^73 + 3 * q^74 - q^76 - 8 * q^79 + 2 * q^80 + 10 * q^82 + 9 * q^83 + 3 * q^85 - q^86 + 15 * q^88 - 26 * q^89 - 3 * q^92 - q^95 - 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more