LMFDB - Embedded newform 1323.2.s.a.962.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, 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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			962.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1323.962
Dual form			1323.2.s.a.656.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{8} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{8} +(-4.50000 - 2.59808i) q^{10} +1.73205i q^{11} +(1.50000 + 0.866025i) q^{13} +(2.50000 - 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(4.50000 - 2.59808i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -5.19615i q^{23} +4.00000 q^{25} +(1.50000 + 2.59808i) q^{26} +(4.50000 - 2.59808i) q^{29} +(3.00000 - 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +(4.50000 - 2.59808i) q^{34} +(-3.50000 - 6.06218i) q^{37} +9.00000 q^{38} +5.19615i q^{40} +(1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 0.866025i) q^{44} +(4.50000 - 7.79423i) q^{46} +(6.00000 + 3.46410i) q^{50} +1.73205i q^{52} +(7.50000 + 4.33013i) q^{53} -5.19615i q^{55} +9.00000 q^{58} +(-12.0000 - 6.92820i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +3.00000 q^{68} +3.46410i q^{71} +(4.50000 + 2.59808i) q^{73} -12.1244i q^{74} +(4.50000 + 2.59808i) q^{76} +(-4.00000 + 6.92820i) q^{79} +(-7.50000 + 12.9904i) q^{80} +(4.50000 - 2.59808i) q^{82} +(-7.50000 - 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} -1.73205i q^{86} +3.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.50000 - 2.59808i) q^{92} +(-13.5000 + 7.79423i) q^{95} +(1.50000 - 0.866025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{4} - 6 q^{5}+O(q^{10}) $ 2 * q + 3 * q^2 + q^4 - 6 * q^5	$ 2 q + 3 q^{2} + q^{4} - 6 q^{5} - 9 q^{10} + 3 q^{13} + 5 q^{16} + 3 q^{17} + 9 q^{19} - 3 q^{20} - 3 q^{22} + 8 q^{25} + 3 q^{26} + 9 q^{29} + 6 q^{31} + 9 q^{32} + 9 q^{34} - 7 q^{37} + 18 q^{38} + 3 q^{41} - q^{43} - 3 q^{44} + 9 q^{46} + 12 q^{50} + 15 q^{53} + 18 q^{58} - 24 q^{61} + 12 q^{62} - 2 q^{64} - 9 q^{65} + 4 q^{67} + 6 q^{68} + 9 q^{73} + 9 q^{76} - 8 q^{79} - 15 q^{80} + 9 q^{82} - 15 q^{83} - 9 q^{85} + 6 q^{88} + 3 q^{89} + 9 q^{92} - 27 q^{95} + 3 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 + q^4 - 6 * q^5 - 9 * q^10 + 3 * q^13 + 5 * q^16 + 3 * q^17 + 9 * q^19 - 3 * q^20 - 3 * q^22 + 8 * q^25 + 3 * q^26 + 9 * q^29 + 6 * q^31 + 9 * q^32 + 9 * q^34 - 7 * q^37 + 18 * q^38 + 3 * q^41 - q^43 - 3 * q^44 + 9 * q^46 + 12 * q^50 + 15 * q^53 + 18 * q^58 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 + 6 * q^68 + 9 * q^73 + 9 * q^76 - 8 * q^79 - 15 * q^80 + 9 * q^82 - 15 * q^83 - 9 * q^85 + 6 * q^88 + 3 * q^89 + 9 * q^92 - 27 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	−4.50000	−	2.59808i	−1.42302	−	0.821584i
$11$			1.73205i			0.522233i	0.965307	+	0.261116i	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$		0			0
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	4.50000	−	2.59808i	1.03237	−	0.596040i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.50000	−	2.59808i	1.03237	−	0.596040i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$		−	5.19615i		−	1.08347i	−0.840548	−	0.541736i	$-0.817767\pi$
$23$		−	5.19615i		−	1.08347i	0.840548	−	0.541736i	$-0.182233\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$		0			0
$28$		0			0
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	−0.0201471	−	0.999797i	$-0.506413\pi$
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	0.855776	+	0.517346i	$0.173080\pi$
$30$		0			0
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$		0			0
$34$	4.50000	−	2.59808i	0.771744	−	0.445566i
$35$		0			0
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	9.00000			1.45999
$39$		0			0
$40$			5.19615i			0.821584i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	−1.50000	+	0.866025i	−0.226134	+	0.130558i
$45$		0			0
$46$	4.50000	−	7.79423i	0.663489	−	1.14920i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$	6.00000	+	3.46410i	0.848528	+	0.489898i
$51$		0			0
$52$			1.73205i			0.240192i
$53$	7.50000	+	4.33013i	1.03020	+	0.594789i	0.917043	−	0.398788i	$-0.130569\pi$
$53$	7.50000	+	4.33013i	1.03020	+	0.594789i	0.113161	+	0.993577i	$0.463902\pi$
$54$		0			0
$55$		−	5.19615i		−	0.700649i
$56$		0			0
$57$		0			0
$58$	9.00000			1.18176
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.999043	−	0.0437377i	$-0.986073\pi$
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.537400	−	0.843328i	$-0.680593\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.50000	−	2.59808i	−0.558156	−	0.322252i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	3.00000			0.363803
$69$		0			0
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	4.50000	+	2.59808i	0.526685	+	0.304082i	0.739666	−	0.672975i	$-0.234984\pi$
$73$	4.50000	+	2.59808i	0.526685	+	0.304082i	−0.212980	+	0.977056i	$0.568317\pi$
$74$		−	12.1244i		−	1.40943i
$75$		0			0
$76$	4.50000	+	2.59808i	0.516185	+	0.298020i
$77$		0			0
$78$		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	$0.315255\pi$
$80$	−7.50000	+	12.9904i	−0.838525	+	1.45237i
$81$		0			0
$82$	4.50000	−	2.59808i	0.496942	−	0.286910i
$83$	−7.50000	−	12.9904i	−0.823232	−	1.42588i	−0.903263	−	0.429087i	$-0.858835\pi$
$83$	−7.50000	−	12.9904i	−0.823232	−	1.42588i	0.0800311	−	0.996792i	$-0.474498\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$		−	1.73205i		−	0.186772i
$87$		0			0
$88$	3.00000			0.319801
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$		0			0
$91$		0			0
$92$	4.50000	−	2.59808i	0.469157	−	0.270868i
$93$		0			0
$94$		0			0
$95$	−13.5000	+	7.79423i	−1.38507	+	0.799671i
$96$		0			0
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	−0.421912	−	0.906637i	$-0.638641\pi$
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	0.574214	+	0.818705i	$0.305308\pi$
$98$		0			0
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$			12.1244i			1.19465i	0.802000	+	0.597324i	$0.203769\pi$
$103$			12.1244i			1.19465i	−0.802000	+	0.597324i	$0.796231\pi$
$104$	1.50000	−	2.59808i	0.147087	−	0.254762i
$105$		0			0
$106$	7.50000	+	12.9904i	0.728464	+	1.26174i
$107$	7.50000	−	4.33013i	0.725052	−	0.418609i	−0.0915571	−	0.995800i	$-0.529184\pi$
$107$	7.50000	−	4.33013i	0.725052	−	0.418609i	0.816609	+	0.577191i	$0.195851\pi$
$108$		0			0
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$		0			0
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	0.427784	−	0.903881i	$-0.359294\pi$
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	−0.568892	+	0.822412i	$0.692628\pi$
$114$		0			0
$115$			15.5885i			1.45363i
$116$	4.50000	+	2.59808i	0.417815	+	0.241225i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.00000			0.727273
$122$	−12.0000	−	20.7846i	−1.08643	−	1.88175i
$123$		0			0
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$	3.00000			0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$		0			0
$130$	−4.50000	−	7.79423i	−0.394676	−	0.683599i
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$		0			0
$133$		0			0
$134$			6.92820i			0.598506i
$135$		0			0
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$		−	12.1244i		−	1.03585i	−0.855425	−	0.517927i	$-0.826704\pi$
$137$		−	12.1244i		−	1.03585i	0.855425	−	0.517927i	$-0.173296\pi$
$138$		0			0
$139$	7.50000	+	4.33013i	0.636142	+	0.367277i	0.783127	−	0.621862i	$-0.213624\pi$
$139$	7.50000	+	4.33013i	0.636142	+	0.367277i	−0.146985	+	0.989139i	$0.546957\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$		0			0
$145$	−13.5000	+	7.79423i	−1.12111	+	0.647275i
$146$	4.50000	+	7.79423i	0.372423	+	0.645055i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$		−	1.73205i		−	0.141895i	−0.997480	−	0.0709476i	$-0.977398\pi$
$149$		−	1.73205i		−	0.141895i	0.997480	−	0.0709476i	$-0.0226023\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$	−4.50000	−	7.79423i	−0.364998	−	0.632195i
$153$		0			0
$154$		0			0
$155$	−9.00000	+	5.19615i	−0.722897	+	0.417365i
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−12.0000	+	6.92820i	−0.954669	+	0.551178i
$159$		0			0
$160$	−13.5000	+	7.79423i	−1.06727	+	0.616188i
$161$		0			0
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$		−	25.9808i		−	2.01650i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$	−13.5000	+	7.79423i	−1.03540	+	0.597790i
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$		0			0
$176$	7.50000	+	4.33013i	0.565334	+	0.326396i
$177$		0			0
$178$			5.19615i			0.389468i
$179$	−13.5000	−	7.79423i	−1.00904	−	0.582568i	−0.0981277	−	0.995174i	$-0.531285\pi$
$179$	−13.5000	−	7.79423i	−1.00904	−	0.582568i	−0.910910	+	0.412606i	$0.864619\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$	−9.00000			−0.663489
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	4.50000	+	2.59808i	0.329073	+	0.189990i
$188$		0			0
$189$		0			0
$190$	−27.0000			−1.95879
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.932338	−	0.361588i	$-0.117765\pi$
$191$	15.0000	+	8.66025i	1.08536	+	0.626634i	0.153024	+	0.988222i	$0.451099\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	3.00000			0.215387
$195$		0			0
$196$		0			0
$197$		−	13.8564i		−	0.987228i	−0.869681	−	0.493614i	$-0.835676\pi$
$197$		−	13.8564i		−	0.987228i	0.869681	−	0.493614i	$-0.164324\pi$
$198$		0			0
$199$	7.50000	+	4.33013i	0.531661	+	0.306955i	0.741693	−	0.670740i	$-0.234023\pi$
$199$	7.50000	+	4.33013i	0.531661	+	0.306955i	−0.210032	+	0.977695i	$0.567357\pi$
$200$		−	6.92820i		−	0.489898i
$201$		0			0
$202$	−4.50000	−	2.59808i	−0.316619	−	0.182800i
$203$		0			0
$204$		0			0
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−10.5000	+	18.1865i	−0.731570	+	1.26712i
$207$		0			0
$208$	7.50000	−	4.33013i	0.520031	−	0.300240i
$209$	4.50000	+	7.79423i	0.311272	+	0.539138i
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$			8.66025i			0.594789i
$213$		0			0
$214$	15.0000			1.02538
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$		0			0
$217$		0			0
$218$	−28.5000	+	16.4545i	−1.93026	+	1.11444i
$219$		0			0
$220$	4.50000	−	2.59808i	0.303390	−	0.175162i
$221$	4.50000	−	2.59808i	0.302703	−	0.174766i
$222$		0			0
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	−0.341703	−	0.939808i	$-0.611004\pi$
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	0.643046	+	0.765828i	$0.277671\pi$
$224$		0			0
$225$		0			0
$226$	−1.50000	−	2.59808i	−0.0997785	−	0.172821i
$227$	21.0000			1.39382			0.696909	−	0.717159i	$-0.254558\pi$
$227$	21.0000			1.39382			0.696909	+	0.717159i	$0.254558\pi$
$228$		0			0
$229$			8.66025i			0.572286i	0.958187	+	0.286143i	$0.0923732\pi$
$229$			8.66025i			0.572286i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	−13.5000	+	23.3827i	−0.890164	+	1.54181i
$231$		0			0
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	−4.50000	+	2.59808i	−0.294805	+	0.170206i	−0.640107	−	0.768286i	$-0.721110\pi$
$233$	−4.50000	+	2.59808i	−0.294805	+	0.170206i	0.345302	+	0.938492i	$0.387777\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	0.450701	−	0.892675i	$-0.351174\pi$
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	−0.547728	+	0.836656i	$0.684507\pi$
$240$		0			0
$241$		−	22.5167i		−	1.45043i	−0.688525	−	0.725213i	$-0.741741\pi$
$241$		−	22.5167i		−	1.45043i	0.688525	−	0.725213i	$-0.258259\pi$
$242$	12.0000	+	6.92820i	0.771389	+	0.445362i
$243$		0			0
$244$		−	13.8564i		−	0.887066i
$245$		0			0
$246$		0			0
$247$	9.00000			0.572656
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$	4.50000	+	2.59808i	0.284605	+	0.164317i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	30.0000	+	17.3205i	1.88237	+	1.08679i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−3.00000			−0.187135			−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000			−0.187135			−0.0935674	+	0.995613i	$0.529827\pi$
$258$		0			0
$259$		0			0
$260$		−	5.19615i		−	0.322252i
$261$		0			0
$262$	−13.5000	−	7.79423i	−0.834033	−	0.481529i
$263$			22.5167i			1.38844i	0.719764	+	0.694218i	$0.244250\pi$
$263$			22.5167i			1.38844i	−0.719764	+	0.694218i	$0.755750\pi$
$264$		0			0
$265$	−22.5000	−	12.9904i	−1.38216	−	0.797993i
$266$		0			0
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	10.5000	−	6.06218i	0.637830	−	0.368251i	−0.145948	−	0.989292i	$-0.546623\pi$
$271$	10.5000	−	6.06218i	0.637830	−	0.368251i	0.783778	+	0.621041i	$0.213290\pi$
$272$	−7.50000	−	12.9904i	−0.454754	−	0.787658i
$273$		0			0
$274$	10.5000	−	18.1865i	0.634328	−	1.09869i
$275$			6.92820i			0.417786i
$276$		0			0
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$	7.50000	+	12.9904i	0.449820	+	0.779111i
$279$		0			0
$280$		0			0
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.0807396	−	0.996735i	$-0.474272\pi$
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.903568	+	0.428445i	$0.140938\pi$
$282$		0			0
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	−0.586509	−	0.809943i	$-0.699498\pi$
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	0.408177	+	0.912903i	$0.366165\pi$
$284$	−3.00000	+	1.73205i	−0.178017	+	0.102778i
$285$		0			0
$286$	−4.50000	+	2.59808i	−0.266091	+	0.153627i
$287$		0			0
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−27.0000			−1.58549
$291$		0			0
$292$			5.19615i			0.304082i
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$		0			0
$296$	−10.5000	+	6.06218i	−0.610300	+	0.352357i
$297$		0			0
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$		0			0
$302$	−25.5000	−	14.7224i	−1.46736	−	0.847181i
$303$		0			0
$304$		−	25.9808i		−	1.49010i
$305$	36.0000	+	20.7846i	2.06135	+	1.19012i
$306$		0			0
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$		0			0
$310$	−18.0000			−1.02233
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.913356	−	0.407163i	$-0.133482\pi$
$313$	18.0000	+	10.3923i	1.01742	+	0.587408i	0.104065	+	0.994571i	$0.466815\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	3.00000			0.167705
$321$		0			0
$322$		0			0
$323$		−	15.5885i		−	0.867365i
$324$		0			0
$325$	6.00000	+	3.46410i	0.332820	+	0.192154i
$326$		−	19.0526i		−	1.05522i
$327$		0			0
$328$	−4.50000	−	2.59808i	−0.248471	−	0.143455i
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	7.50000	−	12.9904i	0.411616	−	0.712940i
$333$		0			0
$334$	−13.5000	+	7.79423i	−0.738687	+	0.426481i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$		−	17.3205i		−	0.942111i
$339$		0			0
$340$	−9.00000			−0.488094
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$		0			0
$344$	−1.50000	+	0.866025i	−0.0808746	+	0.0466930i
$345$		0			0
$346$	−9.00000	+	5.19615i	−0.483843	+	0.279347i
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	−0.417310	−	0.908764i	$-0.637027\pi$
$347$	3.00000	−	1.73205i	0.161048	−	0.0929814i	0.578358	+	0.815783i	$0.303694\pi$
$348$		0			0
$349$	−10.5000	+	6.06218i	−0.562052	+	0.324501i	−0.753969	−	0.656910i	$-0.771863\pi$
$349$	−10.5000	+	6.06218i	−0.562052	+	0.324501i	0.191917	+	0.981411i	$0.438530\pi$
$350$		0			0
$351$		0			0
$352$	4.50000	+	7.79423i	0.239851	+	0.415434i
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$		0			0
$355$		−	10.3923i		−	0.551566i
$356$	−1.50000	+	2.59808i	−0.0794998	+	0.137698i
$357$		0			0
$358$	−13.5000	−	23.3827i	−0.713497	−	1.23581i
$359$	19.5000	−	11.2583i	1.02917	−	0.594192i	0.112424	−	0.993660i	$-0.464139\pi$
$359$	19.5000	−	11.2583i	1.02917	−	0.594192i	0.916747	+	0.399468i	$0.130805\pi$
$360$		0			0
$361$	4.00000	−	6.92820i	0.210526	−	0.364642i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.5000	−	7.79423i	−0.706622	−	0.407969i
$366$		0			0
$367$			5.19615i			0.271237i	0.990761	+	0.135618i	$0.0433021\pi$
$367$			5.19615i			0.271237i	−0.990761	+	0.135618i	$0.956698\pi$
$368$	−22.5000	−	12.9904i	−1.17289	−	0.677170i
$369$		0			0
$370$			36.3731i			1.89095i
$371$		0			0
$372$		0			0
$373$	−37.0000			−1.91579			−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000			−1.91579			−0.957894	+	0.287123i	$0.907301\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−13.5000	−	7.79423i	−0.692535	−	0.399835i
$381$		0			0
$382$	15.0000	+	25.9808i	0.767467	+	1.32929i
$383$	−9.00000			−0.459879			−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000			−0.459879			−0.229939	+	0.973205i	$0.573853\pi$
$384$		0			0
$385$		0			0
$386$			3.46410i			0.176318i
$387$		0			0
$388$	1.50000	+	0.866025i	0.0761510	+	0.0439658i
$389$			36.3731i			1.84419i	0.386966	+	0.922094i	$0.373523\pi$
$389$			36.3731i			1.84419i	−0.386966	+	0.922094i	$0.626477\pi$
$390$		0			0
$391$	−13.5000	−	7.79423i	−0.682724	−	0.394171i
$392$		0			0
$393$		0			0
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	12.0000	−	20.7846i	0.603786	−	1.04579i
$396$		0			0
$397$	−7.50000	+	4.33013i	−0.376414	+	0.217323i	−0.676257	−	0.736666i	$-0.736399\pi$
$397$	−7.50000	+	4.33013i	−0.376414	+	0.217323i	0.299843	+	0.953989i	$0.403066\pi$
$398$	7.50000	+	12.9904i	0.375941	+	0.651149i
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$			32.9090i			1.64340i	0.569924	+	0.821698i	$0.306973\pi$
$401$			32.9090i			1.64340i	−0.569924	+	0.821698i	$0.693027\pi$
$402$		0			0
$403$	6.00000			0.298881
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$		0			0
$407$	10.5000	−	6.06218i	0.520466	−	0.300491i
$408$		0			0
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	−0.344270	−	0.938871i	$-0.611874\pi$
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	0.640951	+	0.767582i	$0.278540\pi$
$410$	−13.5000	+	7.79423i	−0.666717	+	0.384930i
$411$		0			0
$412$	−10.5000	+	6.06218i	−0.517298	+	0.298662i
$413$		0			0
$414$		0			0
$415$	22.5000	+	38.9711i	1.10448	+	1.91302i
$416$	9.00000			0.441261
$417$		0			0
$418$			15.5885i			0.762456i
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	0.109483	+	0.993989i	$0.465080\pi$
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	−0.915561	+	0.402179i	$0.868253\pi$
$420$		0			0
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	0.700306	−	0.713843i	$-0.253047\pi$
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	−0.968359	+	0.249561i	$0.919714\pi$
$422$	7.50000	−	4.33013i	0.365094	−	0.210787i
$423$		0			0
$424$	7.50000	−	12.9904i	0.364232	−	0.630869i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$		0			0
$428$	7.50000	+	4.33013i	0.362526	+	0.209305i
$429$		0			0
$430$			5.19615i			0.250581i
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	0.138288	−	0.990392i	$-0.455840\pi$
$431$	−13.5000	−	7.79423i	−0.650272	−	0.375435i	−0.788560	+	0.614957i	$0.789173\pi$
$432$		0			0
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$		0			0
$435$		0			0
$436$	−19.0000			−0.909935
$437$	−13.5000	−	23.3827i	−0.645793	−	1.11855i
$438$		0			0
$439$	−27.0000	−	15.5885i	−1.28864	−	0.743996i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	−27.0000	−	15.5885i	−1.28864	−	0.743996i	−0.978412	+	0.206666i	$0.933739\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	9.00000			0.428086
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.305448	−	0.952209i	$-0.598806\pi$
$443$	−27.0000	−	15.5885i	−1.28281	−	0.740630i	−0.977361	+	0.211579i	$0.932139\pi$
$444$		0			0
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	9.00000			0.426162
$447$		0			0
$448$		0			0
$449$			34.6410i			1.63481i	0.576063	+	0.817405i	$0.304588\pi$
$449$			34.6410i			1.63481i	−0.576063	+	0.817405i	$0.695412\pi$
$450$		0			0
$451$	4.50000	+	2.59808i	0.211897	+	0.122339i
$452$		−	1.73205i		−	0.0814688i
$453$		0			0
$454$	31.5000	+	18.1865i	1.47837	+	0.853536i
$455$		0			0
$456$		0			0
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$	−7.50000	+	12.9904i	−0.350452	+	0.607001i
$459$		0			0
$460$	−13.5000	+	7.79423i	−0.629441	+	0.363408i
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	0.986127	−	0.165992i	$-0.0530827\pi$
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	−0.636817	+	0.771015i	$0.719749\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$		−	25.9808i		−	1.20613i
$465$		0			0
$466$	−9.00000			−0.416917
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50000	−	0.866025i	0.0689701	−	0.0398199i
$474$		0			0
$475$	18.0000	−	10.3923i	0.825897	−	0.476832i
$476$		0			0
$477$		0			0
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	−27.0000			−1.23366			−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000			−1.23366			−0.616831	+	0.787096i	$0.711584\pi$
$480$		0			0
$481$		−	12.1244i		−	0.552823i
$482$	19.5000	−	33.7750i	0.888201	−	1.53841i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−4.50000	+	2.59808i	−0.204334	+	0.117973i
$486$		0			0
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	−0.478584	−	0.878042i	$-0.658850\pi$
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	0.999698	−	0.0245553i	$-0.00781698\pi$
$488$	−12.0000	+	20.7846i	−0.543214	+	0.940875i
$489$		0			0
$490$		0			0
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.912771	−	0.408471i	$-0.133938\pi$
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.102639	+	0.994719i	$0.467271\pi$
$492$		0			0
$493$		−	15.5885i		−	0.702069i
$494$	13.5000	+	7.79423i	0.607394	+	0.350679i
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$		0			0
$498$		0			0
$499$	25.0000			1.11915			0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000			1.11915			0.559577	+	0.828778i	$0.310964\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	18.0000	+	10.3923i	0.803379	+	0.463831i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	13.5000	+	7.79423i	0.600148	+	0.346496i
$507$		0			0
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	33.0000			1.46270			0.731350	−	0.682003i	$-0.238891\pi$
$509$	33.0000			1.46270			0.731350	+	0.682003i	$0.238891\pi$
$510$		0			0
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	−4.50000	−	2.59808i	−0.198486	−	0.114596i
$515$		−	36.3731i		−	1.60279i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.347155	+	0.937808i	$0.612852\pi$
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.638588	+	0.769549i	$0.720481\pi$
$522$		0			0
$523$	16.5000	−	9.52628i	0.721495	−	0.416555i	−0.0938079	−	0.995590i	$-0.529904\pi$
$523$	16.5000	−	9.52628i	0.721495	−	0.416555i	0.815303	+	0.579035i	$0.196571\pi$
$524$	−4.50000	−	7.79423i	−0.196583	−	0.340492i
$525$		0			0
$526$	−19.5000	+	33.7750i	−0.850240	+	1.47266i
$527$		−	10.3923i		−	0.452696i
$528$		0			0
$529$	−4.00000			−0.173913
$530$	−22.5000	−	38.9711i	−0.977338	−	1.69280i
$531$		0			0
$532$		0			0
$533$	4.50000	−	2.59808i	0.194917	−	0.112535i
$534$		0			0
$535$	−22.5000	+	12.9904i	−0.972760	+	0.561623i
$536$	6.00000	−	3.46410i	0.259161	−	0.149626i
$537$		0			0
$538$	22.5000	−	12.9904i	0.970044	−	0.560055i
$539$		0			0
$540$		0			0
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	0.971250	−	0.238062i	$-0.0765123\pi$
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$542$	21.0000			0.902027
$543$		0			0
$544$		−	15.5885i		−	0.668350i
$545$	28.5000	−	49.3634i	1.22081	−	2.11450i
$546$		0			0
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	0.994459	−	0.105123i	$-0.0335235\pi$
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	−0.588269	+	0.808666i	$0.700190\pi$
$548$	10.5000	−	6.06218i	0.448538	−	0.258963i
$549$		0			0
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	13.5000	−	23.3827i	0.575119	−	0.996136i
$552$		0			0
$553$		0			0
$554$	−1.50000	−	0.866025i	−0.0637289	−	0.0367939i
$555$		0			0
$556$			8.66025i			0.367277i
$557$	−10.5000	−	6.06218i	−0.444899	−	0.256863i	0.260774	−	0.965400i	$-0.416022\pi$
$557$	−10.5000	−	6.06218i	−0.444899	−	0.256863i	−0.705674	+	0.708537i	$0.749355\pi$
$558$		0			0
$559$		−	1.73205i		−	0.0732579i
$560$		0			0
$561$		0			0
$562$	33.0000			1.39202
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$		0			0
$565$	4.50000	+	2.59808i	0.189316	+	0.109302i
$566$	−6.00000			−0.252199
$567$		0			0
$568$	6.00000			0.251754
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	0.368933	−	0.929456i	$-0.379723\pi$
$569$	−6.00000	−	3.46410i	−0.251533	−	0.145223i	−0.620466	+	0.784233i	$0.713057\pi$
$570$		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	$-0.400192\pi$
$572$	−3.00000			−0.125436
$573$		0			0
$574$		0			0
$575$		−	20.7846i		−	0.866778i
$576$		0			0
$577$	34.5000	+	19.9186i	1.43625	+	0.829222i	0.997587	−	0.0694283i	$-0.0221175\pi$
$577$	34.5000	+	19.9186i	1.43625	+	0.829222i	0.438667	+	0.898650i	$0.355451\pi$
$578$			13.8564i			0.576351i
$579$		0			0
$580$	−13.5000	−	7.79423i	−0.560557	−	0.323638i
$581$		0			0
$582$		0			0
$583$	−7.50000	+	12.9904i	−0.310618	+	0.538007i
$584$	4.50000	−	7.79423i	0.186211	−	0.322527i
$585$		0			0
$586$	−13.5000	+	7.79423i	−0.557680	+	0.321977i
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	0.997162	−	0.0752860i	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$		0			0
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$		0			0
$591$		0			0
$592$	−35.0000			−1.43849
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	0.919111	+	0.394000i	$0.128909\pi$
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	−0.118342	+	0.992973i	$0.537758\pi$
$594$		0			0
$595$		0			0
$596$	1.50000	−	0.866025i	0.0614424	−	0.0354738i
$597$		0			0
$598$	13.5000	−	7.79423i	0.552056	−	0.318730i
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	−0.00531761	−	0.999986i	$-0.501693\pi$
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	0.863354	+	0.504598i	$0.168359\pi$
$600$		0			0
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.120286	−	0.992739i	$-0.461619\pi$
$601$	25.5000	−	14.7224i	1.04017	−	0.600541i	0.919881	+	0.392199i	$0.128285\pi$
$602$		0			0
$603$		0			0
$604$	−8.50000	−	14.7224i	−0.345860	−	0.599047i
$605$	−24.0000			−0.975739
$606$		0			0
$607$		−	15.5885i		−	0.632716i	−0.948640	−	0.316358i	$-0.897540\pi$
$607$		−	15.5885i		−	0.632716i	0.948640	−	0.316358i	$-0.102460\pi$
$608$	13.5000	−	23.3827i	0.547497	−	0.948293i
$609$		0			0
$610$	36.0000	+	62.3538i	1.45760	+	2.52463i
$611$		0			0
$612$		0			0
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.201948	+	0.979396i	$0.564727\pi$
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	−21.0000	+	36.3731i	−0.847491	+	1.46790i
$615$		0			0
$616$		0			0
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	0.587839	−	0.808978i	$-0.299979\pi$
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	−0.406676	+	0.913573i	$0.633312\pi$
$618$		0			0
$619$			19.0526i			0.765787i	0.923792	+	0.382893i	$0.125072\pi$
$619$			19.0526i			0.765787i	−0.923792	+	0.382893i	$0.874928\pi$
$620$	−9.00000	−	5.19615i	−0.361449	−	0.208683i
$621$		0			0
$622$		−	41.5692i		−	1.66677i
$623$		0			0
$624$		0			0
$625$	−29.0000			−1.16000
$626$	18.0000	+	31.1769i	0.719425	+	1.24608i
$627$		0			0
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	12.0000	+	6.92820i	0.477334	+	0.275589i
$633$		0			0
$634$		0			0
$635$	−60.0000			−2.38103
$636$		0			0
$637$		0			0
$638$			15.5885i			0.617153i
$639$		0			0
$640$	31.5000	+	18.1865i	1.24515	+	0.718886i
$641$		−	12.1244i		−	0.478883i	−0.970911	−	0.239442i	$-0.923036\pi$
$641$		−	12.1244i		−	0.478883i	0.970911	−	0.239442i	$-0.0769644\pi$
$642$		0			0
$643$	−10.5000	−	6.06218i	−0.414080	−	0.239069i	0.278462	−	0.960447i	$-0.410176\pi$
$643$	−10.5000	−	6.06218i	−0.414080	−	0.239069i	−0.692541	+	0.721378i	$0.743509\pi$
$644$		0			0
$645$		0			0
$646$	13.5000	−	23.3827i	0.531150	−	0.919979i
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	−0.894004	−	0.448059i	$-0.852115\pi$
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	0.835033	+	0.550200i	$0.185449\pi$
$648$		0			0
$649$		0			0
$650$	6.00000	+	10.3923i	0.235339	+	0.407620i
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$			39.8372i			1.55895i	0.626434	+	0.779474i	$0.284514\pi$
$653$			39.8372i			1.55895i	−0.626434	+	0.779474i	$0.715486\pi$
$654$		0			0
$655$	27.0000			1.05498
$656$	−7.50000	−	12.9904i	−0.292826	−	0.507189i
$657$		0			0
$658$		0			0
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	−0.690369	−	0.723457i	$-0.742552\pi$
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	0.281347	+	0.959606i	$0.409219\pi$
$660$		0			0
$661$	−36.0000	+	20.7846i	−1.40024	+	0.808428i	−0.994417	−	0.105525i	$-0.966348\pi$
$661$	−36.0000	+	20.7846i	−1.40024	+	0.808428i	−0.405821	+	0.913953i	$0.633014\pi$
$662$	12.0000	−	6.92820i	0.466393	−	0.269272i
$663$		0			0
$664$	−22.5000	+	12.9904i	−0.873169	+	0.504125i
$665$		0			0
$666$		0			0
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$	−9.00000			−0.348220
$669$		0			0
$670$		−	20.7846i		−	0.802980i
$671$	12.0000	−	20.7846i	0.463255	−	0.802381i
$672$		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	$0.644544\pi$
$674$	−28.5000	+	16.4545i	−1.09778	+	0.633803i
$675$		0			0
$676$	5.00000	−	8.66025i	0.192308	−	0.333087i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$		0			0
$680$	13.5000	+	7.79423i	0.517701	+	0.298895i
$681$		0			0
$682$			10.3923i			0.397942i
$683$	−7.50000	−	4.33013i	−0.286980	−	0.165688i	0.349599	−	0.936899i	$-0.386318\pi$
$683$	−7.50000	−	4.33013i	−0.286980	−	0.165688i	−0.636579	+	0.771212i	$0.719651\pi$
$684$		0			0
$685$			36.3731i			1.38974i
$686$		0			0
$687$		0			0
$688$	−5.00000			−0.190623
$689$	7.50000	+	12.9904i	0.285727	+	0.494894i
$690$		0			0
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	6.00000			0.227757
$695$	−22.5000	−	12.9904i	−0.853474	−	0.492753i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	−21.0000			−0.794862
$699$		0			0
$700$		0			0
$701$			34.6410i			1.30837i	0.756333	+	0.654187i	$0.226989\pi$
$701$			34.6410i			1.30837i	−0.756333	+	0.654187i	$0.773011\pi$
$702$		0			0
$703$	−31.5000	−	18.1865i	−1.18805	−	0.685918i
$704$		−	1.73205i		−	0.0652791i
$705$		0			0
$706$	31.5000	+	18.1865i	1.18552	+	0.684459i
$707$		0			0
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	9.00000	−	15.5885i	0.337764	−	0.585024i
$711$		0			0
$712$	4.50000	−	2.59808i	0.168645	−	0.0973670i
$713$	−9.00000	−	15.5885i	−0.337053	−	0.583792i
$714$		0			0
$715$	4.50000	−	7.79423i	0.168290	−	0.291488i
$716$		−	15.5885i		−	0.582568i
$717$		0			0
$718$	39.0000			1.45547
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	0.769832	−	0.638247i	$-0.220340\pi$
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	−0.937654	+	0.347571i	$0.887007\pi$
$720$		0			0
$721$		0			0
$722$	12.0000	−	6.92820i	0.446594	−	0.257841i
$723$		0			0
$724$		0			0
$725$	18.0000	−	10.3923i	0.668503	−	0.385961i
$726$		0			0
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	−0.292487	−	0.956270i	$-0.594483\pi$
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	0.681910	+	0.731436i	$0.261149\pi$
$728$		0			0
$729$		0			0
$730$	−13.5000	−	23.3827i	−0.499657	−	0.865432i
$731$	−3.00000			−0.110959
$732$		0			0
$733$			43.3013i			1.59937i	0.600420	+	0.799684i	$0.295000\pi$
$733$			43.3013i			1.59937i	−0.600420	+	0.799684i	$0.705000\pi$
$734$	−4.50000	+	7.79423i	−0.166098	+	0.287690i
$735$		0			0
$736$	−13.5000	−	23.3827i	−0.497617	−	0.861897i
$737$	−6.00000	+	3.46410i	−0.221013	+	0.127602i
$738$		0			0
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$740$	−10.5000	+	18.1865i	−0.385988	+	0.668550i
$741$		0			0
$742$		0			0
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	0.680082	−	0.733136i	$-0.261944\pi$
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	−0.294874	+	0.955536i	$0.595278\pi$
$744$		0			0
$745$			5.19615i			0.190372i
$746$	−55.5000	−	32.0429i	−2.03200	−	1.17318i
$747$		0			0
$748$			5.19615i			0.189990i
$749$		0			0
$750$		0			0
$751$	37.0000			1.35015			0.675075	−	0.737749i	$-0.264111\pi$
$751$	37.0000			1.35015			0.675075	+	0.737749i	$0.264111\pi$
$752$		0			0
$753$		0			0
$754$	13.5000	+	7.79423i	0.491641	+	0.283849i
$755$	51.0000			1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−30.0000	−	17.3205i	−1.08965	−	0.629109i
$759$		0			0
$760$	13.5000	+	23.3827i	0.489696	+	0.848179i
$761$	45.0000			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$762$		0			0
$763$		0			0
$764$			17.3205i			0.626634i
$765$		0			0
$766$	−13.5000	−	7.79423i	−0.487775	−	0.281617i
$767$		0			0
$768$		0			0
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.113480	−	0.993540i	$-0.463800\pi$
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.803691	−	0.595047i	$-0.202867\pi$
$774$		0			0
$775$	12.0000	−	6.92820i	0.431053	−	0.248868i
$776$	−1.50000	−	2.59808i	−0.0538469	−	0.0932655i
$777$		0			0
$778$	−31.5000	+	54.5596i	−1.12933	+	1.95606i
$779$		−	15.5885i		−	0.558514i
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−13.5000	−	23.3827i	−0.482759	−	0.836163i
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.221162	−	0.975237i	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$	12.0000	−	6.92820i	0.427482	−	0.246807i
$789$		0			0
$790$	36.0000	−	20.7846i	1.28082	−	0.739483i
$791$		0			0
$792$		0			0
$793$	−12.0000	−	20.7846i	−0.426132	−	0.738083i
$794$	−15.0000			−0.532330
$795$		0			0
$796$			8.66025i			0.306955i
$797$	−22.5000	+	38.9711i	−0.796991	+	1.38043i	0.124576	+	0.992210i	$0.460243\pi$
$797$	−22.5000	+	38.9711i	−0.796991	+	1.38043i	−0.921567	+	0.388219i	$0.873091\pi$
$798$		0			0
$799$		0			0
$800$	18.0000	−	10.3923i	0.636396	−	0.367423i
$801$		0			0
$802$	−28.5000	+	49.3634i	−1.00637	+	1.74308i
$803$	−4.50000	+	7.79423i	−0.158802	+	0.275052i
$804$		0			0
$805$		0			0
$806$	9.00000	+	5.19615i	0.317011	+	0.183027i
$807$		0			0
$808$			5.19615i			0.182800i
$809$	1.50000	+	0.866025i	0.0527372	+	0.0304478i	0.526137	−	0.850400i	$-0.323640\pi$
$809$	1.50000	+	0.866025i	0.0527372	+	0.0304478i	−0.473400	+	0.880848i	$0.656973\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$		0			0
$814$	21.0000			0.736050
$815$	16.5000	+	28.5788i	0.577970	+	1.00107i
$816$		0			0
$817$	−4.50000	−	2.59808i	−0.157435	−	0.0908952i
$818$	12.0000			0.419570
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	0.391632	−	0.920122i	$-0.371911\pi$
$821$	−6.00000	−	3.46410i	−0.209401	−	0.120898i	−0.601033	+	0.799224i	$0.705244\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	21.0000			0.731570
$825$		0			0
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$		0			0
$829$	−31.5000	−	18.1865i	−1.09404	−	0.631644i	−0.159391	−	0.987216i	$-0.550953\pi$
$829$	−31.5000	−	18.1865i	−1.09404	−	0.631644i	−0.934649	+	0.355571i	$0.884286\pi$
$830$			77.9423i			2.70542i
$831$		0			0
$832$	−1.50000	−	0.866025i	−0.0520031	−	0.0300240i
$833$		0			0
$834$		0			0
$835$	13.5000	−	23.3827i	0.467187	−	0.809191i
$836$	−4.50000	+	7.79423i	−0.155636	+	0.269569i
$837$		0			0
$838$	−49.5000	+	28.5788i	−1.70995	+	0.987240i
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	−0.976987	−	0.213298i	$-0.931580\pi$
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	0.303773	−	0.952745i	$-0.401754\pi$
$840$		0			0
$841$	−1.00000	+	1.73205i	−0.0344828	+	0.0597259i
$842$		−	19.0526i		−	0.656595i
$843$		0			0
$844$	5.00000			0.172107
$845$	15.0000	+	25.9808i	0.516016	+	0.893765i
$846$		0			0
$847$		0			0
$848$	37.5000	−	21.6506i	1.28776	−	0.743486i
$849$		0			0
$850$	18.0000	−	10.3923i	0.617395	−	0.356453i
$851$	−31.5000	+	18.1865i	−1.07981	+	0.623426i
$852$		0			0
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	−0.833012	−	0.553255i	$-0.813386\pi$
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	0.0626267	+	0.998037i	$0.480052\pi$
$854$		0			0
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	−27.0000			−0.922302			−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000			−0.922302			−0.461151	+	0.887322i	$0.652563\pi$
$858$		0			0
$859$		−	50.2295i		−	1.71381i	−0.515476	−	0.856904i	$-0.672385\pi$
$859$		−	50.2295i		−	1.71381i	0.515476	−	0.856904i	$-0.327615\pi$
$860$	−1.50000	+	2.59808i	−0.0511496	+	0.0885937i
$861$		0			0
$862$	−13.5000	−	23.3827i	−0.459812	−	0.796417i
$863$	37.5000	−	21.6506i	1.27651	−	0.736996i	0.300309	−	0.953842i	$-0.402910\pi$
$863$	37.5000	−	21.6506i	1.27651	−	0.736996i	0.976206	+	0.216846i	$0.0695769\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	12.0000	−	20.7846i	0.407777	−	0.706290i
$867$		0			0
$868$		0			0
$869$	−12.0000	−	6.92820i	−0.407072	−	0.235023i
$870$		0			0
$871$			6.92820i			0.234753i
$872$	28.5000	+	16.4545i	0.965132	+	0.557219i
$873$		0			0
$874$		−	46.7654i		−	1.58186i
$875$		0			0
$876$		0			0
$877$	23.0000			0.776655			0.388327	−	0.921521i	$-0.373053\pi$
$877$	23.0000			0.776655			0.388327	+	0.921521i	$0.373053\pi$
$878$	−27.0000	−	46.7654i	−0.911206	−	1.57825i
$879$		0			0
$880$	−22.5000	−	12.9904i	−0.758475	−	0.437906i
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	4.50000	+	2.59808i	0.151351	+	0.0873828i
$885$		0			0
$886$	−27.0000	−	46.7654i	−0.907083	−	1.57111i
$887$	15.0000			0.503651			0.251825	−	0.967773i	$-0.418969\pi$
$887$	15.0000			0.503651			0.251825	+	0.967773i	$0.418969\pi$
$888$		0			0
$889$		0			0
$890$		−	15.5885i		−	0.522526i
$891$		0			0
$892$	4.50000	+	2.59808i	0.150671	+	0.0869900i
$893$		0			0
$894$		0			0
$895$	40.5000	+	23.3827i	1.35377	+	0.781597i
$896$		0			0
$897$		0			0
$898$	−30.0000	+	51.9615i	−1.00111	+	1.73398i
$899$	9.00000	−	15.5885i	0.300167	−	0.519904i
$900$		0			0
$901$	22.5000	−	12.9904i	0.749584	−	0.432772i
$902$	4.50000	+	7.79423i	0.149834	+	0.259519i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$		0			0
$907$	19.0000			0.630885			0.315442	−	0.948945i	$-0.397847\pi$
$907$	19.0000			0.630885			0.315442	+	0.948945i	$0.397847\pi$
$908$	10.5000	+	18.1865i	0.348455	+	0.603541i
$909$		0			0
$910$		0			0
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	−0.572690	−	0.819772i	$-0.694100\pi$
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	0.423598	+	0.905850i	$0.360767\pi$
$912$		0			0
$913$	22.5000	−	12.9904i	0.744641	−	0.429919i
$914$	39.0000	−	22.5167i	1.29001	−	0.744785i
$915$		0			0
$916$	−7.50000	+	4.33013i	−0.247807	+	0.143071i
$917$		0			0
$918$		0			0
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	0.999691	−	0.0248659i	$-0.00791589\pi$
$919$	14.5000	+	25.1147i	0.478311	+	0.828459i	−0.521380	+	0.853325i	$0.674583\pi$
$920$	27.0000			0.890164
$921$		0			0
$922$			25.9808i			0.855631i
$923$	−3.00000	+	5.19615i	−0.0987462	+	0.171033i
$924$		0			0
$925$	−14.0000	−	24.2487i	−0.460317	−	0.797293i
$926$	1.50000	−	0.866025i	0.0492931	−	0.0284594i
$927$		0			0
$928$	13.5000	−	23.3827i	0.443159	−	0.767574i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$		0			0
$932$	−4.50000	−	2.59808i	−0.147402	−	0.0851028i
$933$		0			0
$934$			5.19615i			0.170023i
$935$	−13.5000	−	7.79423i	−0.441497	−	0.254899i
$936$		0			0
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	−13.5000	−	7.79423i	−0.439620	−	0.253815i
$944$		0			0
$945$		0			0
$946$	3.00000			0.0975384
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.999118	−	0.0419998i	$-0.0133729\pi$
$947$	45.0000	+	25.9808i	1.46230	+	0.844261i	0.463186	+	0.886261i	$0.346706\pi$
$948$		0			0
$949$	4.50000	+	7.79423i	0.146076	+	0.253011i
$950$	36.0000			1.16799
$951$		0			0
$952$		0			0
$953$			20.7846i			0.673280i	0.941634	+	0.336640i	$0.109290\pi$
$953$			20.7846i			0.673280i	−0.941634	+	0.336640i	$0.890710\pi$
$954$		0			0
$955$	−45.0000	−	25.9808i	−1.45617	−	0.840718i
$956$		−	1.73205i		−	0.0560185i
$957$		0			0
$958$	−40.5000	−	23.3827i	−1.30850	−	0.755460i
$959$		0			0
$960$		0			0
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	10.5000	−	18.1865i	0.338534	−	0.586357i
$963$		0			0
$964$	19.5000	−	11.2583i	0.628053	−	0.362606i
$965$	−3.00000	−	5.19615i	−0.0965734	−	0.167270i
$966$		0			0
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	−0.591991	−	0.805945i	$-0.701658\pi$
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	0.993964	+	0.109707i	$0.0349913\pi$
$968$		−	13.8564i		−	0.445362i
$969$		0			0
$970$	−9.00000			−0.288973
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.807473	−	0.589904i	$-0.799166\pi$
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.107135	−	0.994244i	$-0.534168\pi$
$972$		0			0
$973$		0			0
$974$	34.5000	−	19.9186i	1.10545	−	0.638233i
$975$		0			0
$976$	−60.0000	+	34.6410i	−1.92055	+	1.10883i
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.202431	−	0.979297i	$-0.435116\pi$
$977$	36.0000	−	20.7846i	1.15174	−	0.664959i	0.949311	+	0.314338i	$0.101783\pi$
$978$		0			0
$979$	−4.50000	+	2.59808i	−0.143821	+	0.0830349i
$980$		0			0
$981$		0			0
$982$	22.5000	+	38.9711i	0.718004	+	1.24362i
$983$	−39.0000			−1.24391			−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000			−1.24391			−0.621953	+	0.783054i	$0.713661\pi$
$984$		0			0
$985$			41.5692i			1.32451i
$986$	13.5000	−	23.3827i	0.429928	−	0.744656i
$987$		0			0
$988$	4.50000	+	7.79423i	0.143164	+	0.247967i
$989$	−4.50000	+	2.59808i	−0.143092	+	0.0826140i
$990$		0			0
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$992$	9.00000	−	15.5885i	0.285750	−	0.494934i
$993$		0			0
$994$		0			0
$995$	−22.5000	−	12.9904i	−0.713298	−	0.411823i
$996$		0			0
$997$		−	8.66025i		−	0.274273i	−0.990552	−	0.137136i	$-0.956210\pi$
$997$		−	8.66025i		−	0.274273i	0.990552	−	0.137136i	$-0.0437899\pi$
$998$	37.5000	+	21.6506i	1.18704	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.a.962.1		2
3.2	odd	2		441.2.s.a.374.1		2
7.2	even	3		189.2.i.a.152.1		2
7.3	odd	6		1323.2.o.a.881.1		2
7.4	even	3		1323.2.o.b.881.1		2
7.5	odd	6		1323.2.i.a.1097.1		2
7.6	odd	2		189.2.s.a.17.1		2
9.2	odd	6		1323.2.i.a.521.1		2
9.7	even	3		441.2.i.a.227.1		2
21.2	odd	6		63.2.i.a.5.1	✓	2
21.5	even	6		441.2.i.a.68.1		2
21.11	odd	6		441.2.o.a.293.1		2
21.17	even	6		441.2.o.b.293.1		2
21.20	even	2		63.2.s.a.59.1	yes	2
28.23	odd	6		3024.2.ca.a.2609.1		2
28.27	even	2		3024.2.df.a.17.1		2
63.2	odd	6		189.2.s.a.89.1		2
63.11	odd	6		1323.2.o.a.440.1		2
63.13	odd	6		567.2.p.a.80.1		2
63.16	even	3		63.2.s.a.47.1	yes	2
63.20	even	6		189.2.i.a.143.1		2
63.23	odd	6		567.2.p.a.404.1		2
63.25	even	3		441.2.o.b.146.1		2
63.34	odd	6		63.2.i.a.38.1	yes	2
63.38	even	6		1323.2.o.b.440.1		2
63.41	even	6		567.2.p.b.80.1		2
63.47	even	6	inner	1323.2.s.a.656.1		2
63.52	odd	6		441.2.o.a.146.1		2
63.58	even	3		567.2.p.b.404.1		2
63.61	odd	6		441.2.s.a.362.1		2
84.23	even	6		1008.2.ca.a.257.1		2
84.83	odd	2		1008.2.df.a.689.1		2
252.79	odd	6		1008.2.df.a.929.1		2
252.83	odd	6		3024.2.ca.a.2033.1		2
252.191	even	6		3024.2.df.a.1601.1		2
252.223	even	6		1008.2.ca.a.353.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	21.2	odd	6
63.2.i.a.38.1	yes	2	63.34	odd	6
63.2.s.a.47.1	yes	2	63.16	even	3
63.2.s.a.59.1	yes	2	21.20	even	2
189.2.i.a.143.1		2	63.20	even	6
189.2.i.a.152.1		2	7.2	even	3
189.2.s.a.17.1		2	7.6	odd	2
189.2.s.a.89.1		2	63.2	odd	6
441.2.i.a.68.1		2	21.5	even	6
441.2.i.a.227.1		2	9.7	even	3
441.2.o.a.146.1		2	63.52	odd	6
441.2.o.a.293.1		2	21.11	odd	6
441.2.o.b.146.1		2	63.25	even	3
441.2.o.b.293.1		2	21.17	even	6
441.2.s.a.362.1		2	63.61	odd	6
441.2.s.a.374.1		2	3.2	odd	2
567.2.p.a.80.1		2	63.13	odd	6
567.2.p.a.404.1		2	63.23	odd	6
567.2.p.b.80.1		2	63.41	even	6
567.2.p.b.404.1		2	63.58	even	3
1008.2.ca.a.257.1		2	84.23	even	6
1008.2.ca.a.353.1		2	252.223	even	6
1008.2.df.a.689.1		2	84.83	odd	2
1008.2.df.a.929.1		2	252.79	odd	6
1323.2.i.a.521.1		2	9.2	odd	6
1323.2.i.a.1097.1		2	7.5	odd	6
1323.2.o.a.440.1		2	63.11	odd	6
1323.2.o.a.881.1		2	7.3	odd	6
1323.2.o.b.440.1		2	63.38	even	6
1323.2.o.b.881.1		2	7.4	even	3
1323.2.s.a.656.1		2	63.47	even	6	inner
1323.2.s.a.962.1		2	1.1	even	1	trivial
3024.2.ca.a.2033.1		2	252.83	odd	6
3024.2.ca.a.2609.1		2	28.23	odd	6
3024.2.df.a.17.1		2	28.27	even	2
3024.2.df.a.1601.1		2	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{8} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} -1.73205i q^{8} +(-4.50000 - 2.59808i) q^{10} +1.73205i q^{11} +(1.50000 + 0.866025i) q^{13} +(2.50000 - 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(4.50000 - 2.59808i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} -5.19615i q^{23} +4.00000 q^{25} +(1.50000 + 2.59808i) q^{26} +(4.50000 - 2.59808i) q^{29} +(3.00000 - 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +(4.50000 - 2.59808i) q^{34} +(-3.50000 - 6.06218i) q^{37} +9.00000 q^{38} +5.19615i q^{40} +(1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-1.50000 + 0.866025i) q^{44} +(4.50000 - 7.79423i) q^{46} +(6.00000 + 3.46410i) q^{50} +1.73205i q^{52} +(7.50000 + 4.33013i) q^{53} -5.19615i q^{55} +9.00000 q^{58} +(-12.0000 - 6.92820i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +3.00000 q^{68} +3.46410i q^{71} +(4.50000 + 2.59808i) q^{73} -12.1244i q^{74} +(4.50000 + 2.59808i) q^{76} +(-4.00000 + 6.92820i) q^{79} +(-7.50000 + 12.9904i) q^{80} +(4.50000 - 2.59808i) q^{82} +(-7.50000 - 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} -1.73205i q^{86} +3.00000 q^{88} +(1.50000 + 2.59808i) q^{89} +(4.50000 - 2.59808i) q^{92} +(-13.5000 + 7.79423i) q^{95} +(1.50000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{4} - 6 q^{5}+O(q^{10}) \) 2 * q + 3 * q^2 + q^4 - 6 * q^5	\( 2 q + 3 q^{2} + q^{4} - 6 q^{5} - 9 q^{10} + 3 q^{13} + 5 q^{16} + 3 q^{17} + 9 q^{19} - 3 q^{20} - 3 q^{22} + 8 q^{25} + 3 q^{26} + 9 q^{29} + 6 q^{31} + 9 q^{32} + 9 q^{34} - 7 q^{37} + 18 q^{38} + 3 q^{41} - q^{43} - 3 q^{44} + 9 q^{46} + 12 q^{50} + 15 q^{53} + 18 q^{58} - 24 q^{61} + 12 q^{62} - 2 q^{64} - 9 q^{65} + 4 q^{67} + 6 q^{68} + 9 q^{73} + 9 q^{76} - 8 q^{79} - 15 q^{80} + 9 q^{82} - 15 q^{83} - 9 q^{85} + 6 q^{88} + 3 q^{89} + 9 q^{92} - 27 q^{95} + 3 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 + q^4 - 6 * q^5 - 9 * q^10 + 3 * q^13 + 5 * q^16 + 3 * q^17 + 9 * q^19 - 3 * q^20 - 3 * q^22 + 8 * q^25 + 3 * q^26 + 9 * q^29 + 6 * q^31 + 9 * q^32 + 9 * q^34 - 7 * q^37 + 18 * q^38 + 3 * q^41 - q^43 - 3 * q^44 + 9 * q^46 + 12 * q^50 + 15 * q^53 + 18 * q^58 - 24 * q^61 + 12 * q^62 - 2 * q^64 - 9 * q^65 + 4 * q^67 + 6 * q^68 + 9 * q^73 + 9 * q^76 - 8 * q^79 - 15 * q^80 + 9 * q^82 - 15 * q^83 - 9 * q^85 + 6 * q^88 + 3 * q^89 + 9 * q^92 - 27 * q^95 + 3 * q^97

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