LMFDB - Embedded newform 891.2.e.b.595.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(298,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("891.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.e (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:	$7.11467082010$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			595.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	891.595
Dual form			891.2.e.b.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} -2.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(2.00000 - 3.46410i) q^{14} +(2.00000 + 3.46410i) q^{16} +2.00000 q^{17} +(1.00000 + 1.73205i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +8.00000 q^{26} -4.00000 q^{28} +(-3.50000 + 6.06218i) q^{31} +(4.00000 - 6.92820i) q^{32} +(-2.00000 - 3.46410i) q^{34} +2.00000 q^{35} +3.00000 q^{37} +(-4.00000 + 6.92820i) q^{41} +(3.00000 + 5.19615i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(4.00000 - 6.92820i) q^{50} +(-4.00000 - 6.92820i) q^{52} +6.00000 q^{53} +1.00000 q^{55} +(2.50000 - 4.33013i) q^{59} +(-6.00000 - 10.3923i) q^{61} +14.0000 q^{62} -8.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-2.00000 - 3.46410i) q^{70} +3.00000 q^{71} +4.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(-1.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +4.00000 q^{80} +16.0000 q^{82} +(-3.00000 - 5.19615i) q^{83} +(1.00000 - 1.73205i) q^{85} +(6.00000 - 10.3923i) q^{86} -15.0000 q^{89} -8.00000 q^{91} +(-1.00000 - 1.73205i) q^{92} +(8.00000 - 13.8564i) q^{94} +(3.50000 + 6.06218i) q^{97} -6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} + q^{5} + 2 q^{7}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^4 + q^5 + 2 * q^7	$ 2 q - 2 q^{2} - 2 q^{4} + q^{5} + 2 q^{7} - 4 q^{10} + q^{11} - 4 q^{13} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 2 q^{20} + 2 q^{22} - q^{23} + 4 q^{25} + 16 q^{26} - 8 q^{28} - 7 q^{31} + 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{37} - 8 q^{41} + 6 q^{43} - 4 q^{44} + 4 q^{46} + 8 q^{47} + 3 q^{49} + 8 q^{50} - 8 q^{52} + 12 q^{53} + 2 q^{55} + 5 q^{59} - 12 q^{61} + 28 q^{62} - 16 q^{64} + 4 q^{65} + 7 q^{67} - 4 q^{68} - 4 q^{70} + 6 q^{71} + 8 q^{73} - 6 q^{74} - 2 q^{77} + 10 q^{79} + 8 q^{80} + 32 q^{82} - 6 q^{83} + 2 q^{85} + 12 q^{86} - 30 q^{89} - 16 q^{91} - 2 q^{92} + 16 q^{94} + 7 q^{97} - 12 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 + q^5 + 2 * q^7 - 4 * q^10 + q^11 - 4 * q^13 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 2 * q^20 + 2 * q^22 - q^23 + 4 * q^25 + 16 * q^26 - 8 * q^28 - 7 * q^31 + 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^37 - 8 * q^41 + 6 * q^43 - 4 * q^44 + 4 * q^46 + 8 * q^47 + 3 * q^49 + 8 * q^50 - 8 * q^52 + 12 * q^53 + 2 * q^55 + 5 * q^59 - 12 * q^61 + 28 * q^62 - 16 * q^64 + 4 * q^65 + 7 * q^67 - 4 * q^68 - 4 * q^70 + 6 * q^71 + 8 * q^73 - 6 * q^74 - 2 * q^77 + 10 * q^79 + 8 * q^80 + 32 * q^82 - 6 * q^83 + 2 * q^85 + 12 * q^86 - 30 * q^89 - 16 * q^91 - 2 * q^92 + 16 * q^94 + 7 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	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
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$		0			0
$9$		0			0
$10$	−2.00000			−0.632456
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	2.00000	−	3.46410i	0.534522	−	0.925820i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	8.00000			1.56893
$27$		0			0
$28$	−4.00000			−0.755929
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$		0			0
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	2.00000			0.338062
$36$		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			0
$39$		0			0
$40$		0			0
$41$	−4.00000	+	6.92820i	−0.624695	+	1.08200i	0.363905	+	0.931436i	$0.381443\pi$
$41$	−4.00000	+	6.92820i	−0.624695	+	1.08200i	−0.988600	+	0.150567i	$0.951890\pi$
$42$		0			0
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	2.00000			0.294884
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	4.00000	−	6.92820i	0.565685	−	0.979796i
$51$		0			0
$52$	−4.00000	−	6.92820i	−0.554700	−	0.960769i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$		0			0
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	−0.938527	−	0.345207i	$-0.887809\pi$
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	0.170305	−	0.985391i	$-0.445525\pi$
$62$	14.0000			1.77800
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$		0			0
$70$	−2.00000	−	3.46410i	−0.239046	−	0.414039i
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$		0			0
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$		0			0
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	4.00000			0.447214
$81$		0			0
$82$	16.0000			1.76690
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	6.00000	−	10.3923i	0.646997	−	1.12063i
$87$		0			0
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	−1.00000	−	1.73205i	−0.104257	−	0.180579i
$93$		0			0
$94$	8.00000	−	13.8564i	0.825137	−	1.42918i
$95$		0			0
$96$		0			0
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	0.987181	−	0.159602i	$-0.0510211\pi$
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	−0.631810	+	0.775123i	$0.717688\pi$
$98$	−6.00000			−0.606092
$99$		0			0
$100$	−8.00000			−0.800000
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$		0			0
$105$		0			0
$106$	−6.00000	−	10.3923i	−0.582772	−	1.00939i
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$		0			0
$112$	−4.00000	+	6.92820i	−0.377964	+	0.654654i
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$		0			0
$117$		0			0
$118$	−10.0000			−0.920575
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−12.0000	+	20.7846i	−1.08643	+	1.88175i
$123$		0			0
$124$	−7.00000	−	12.1244i	−0.628619	−	1.08880i
$125$	9.00000			0.804984
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$		0			0
$130$	4.00000	−	6.92820i	0.350823	−	0.607644i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		0			0
$133$		0			0
$134$	−14.0000			−1.20942
$135$		0			0
$136$		0			0
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	0.676888	−	0.736086i	$-0.263328\pi$
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	−0.975913	+	0.218159i	$0.929995\pi$
$138$		0			0
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$	−2.00000	+	3.46410i	−0.169031	+	0.292770i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−4.00000			−0.334497
$144$		0			0
$145$		0			0
$146$	−4.00000	−	6.92820i	−0.331042	−	0.573382i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$		0			0
$153$		0			0
$154$	4.00000			0.322329
$155$	3.50000	+	6.06218i	0.281127	+	0.486926i
$156$		0			0
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	10.0000	−	17.3205i	0.795557	−	1.37795i
$159$		0			0
$160$	−4.00000	−	6.92820i	−0.316228	−	0.547723i
$161$	−2.00000			−0.157622
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−8.00000	−	13.8564i	−0.624695	−	1.08200i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−12.0000			−0.914991
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	15.0000	+	25.9808i	1.12430	+	1.94734i
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	8.00000	+	13.8564i	0.592999	+	1.02711i
$183$		0			0
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	−16.0000			−1.16692
$189$		0			0
$190$		0			0
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	0.990378	+	0.138390i	$0.0441928\pi$
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	−0.375339	+	0.926887i	$0.622474\pi$
$192$		0			0
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$	2.00000	−	3.46410i	0.140720	−	0.243733i
$203$		0			0
$204$		0			0
$205$	4.00000	+	6.92820i	0.279372	+	0.483887i
$206$	−32.0000			−2.22955
$207$		0			0
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$	−6.00000	+	10.3923i	−0.412082	+	0.713746i
$213$		0			0
$214$	18.0000	+	31.1769i	1.23045	+	2.13121i
$215$	6.00000			0.409197
$216$		0			0
$217$	−14.0000			−0.950382
$218$	−10.0000	−	17.3205i	−0.677285	−	1.17309i
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$		0			0
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	−0.986267	−	0.165161i	$-0.947186\pi$
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	0.350100	−	0.936713i	$-0.386148\pi$
$224$	16.0000			1.06904
$225$		0			0
$226$	−18.0000			−1.19734
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	−0.999987	−	0.00505719i	$-0.998390\pi$
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	0.504373	+	0.863486i	$0.331724\pi$
$230$	1.00000	−	1.73205i	0.0659380	−	0.114208i
$231$		0			0
$232$		0			0
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	5.00000	+	8.66025i	0.325472	+	0.563735i
$237$		0			0
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$	−15.0000	+	25.9808i	−0.970269	+	1.68056i	−0.275533	+	0.961292i	$0.588854\pi$
$239$	−15.0000	+	25.9808i	−0.970269	+	1.68056i	−0.694737	+	0.719264i	$0.744479\pi$
$240$		0			0
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	0.965615	−	0.259975i	$-0.0837143\pi$
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	−0.707953	+	0.706260i	$0.750381\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$	24.0000			1.53644
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−9.00000	−	15.5885i	−0.569210	−	0.985901i
$251$	23.0000			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$		0			0
$259$	3.00000	+	5.19615i	0.186411	+	0.322873i
$260$	−8.00000			−0.496139
$261$		0			0
$262$	36.0000			2.22409
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	0.997015	−	0.0772134i	$-0.0246023\pi$
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	−0.565376	+	0.824833i	$0.691269\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$		0			0
$267$		0			0
$268$	7.00000	+	12.1244i	0.427593	+	0.740613i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	4.00000	+	6.92820i	0.242536	+	0.420084i
$273$		0			0
$274$	−7.00000	+	12.1244i	−0.422885	+	0.732459i
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	20.0000			1.19952
$279$		0			0
$280$		0			0
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	4.00000	+	6.92820i	0.236525	+	0.409673i
$287$	−16.0000			−0.944450
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	−0.267052	−	0.963682i	$-0.586049\pi$
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	0.968099	−	0.250568i	$-0.0806172\pi$
$294$		0			0
$295$	−2.50000	−	4.33013i	−0.145556	−	0.252110i
$296$		0			0
$297$		0			0
$298$	20.0000			1.15857
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$		0			0
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$	−2.00000	+	3.46410i	−0.115087	+	0.199337i
$303$		0			0
$304$		0			0
$305$	−12.0000			−0.687118
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$		0			0
$310$	7.00000	−	12.1244i	0.397573	−	0.688617i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−20.0000			−1.12509
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	0.988788	−	0.149323i	$-0.0477095\pi$
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	−0.623712	+	0.781654i	$0.714376\pi$
$318$		0			0
$319$		0			0
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$		0			0
$322$	2.00000	+	3.46410i	0.111456	+	0.193047i
$323$		0			0
$324$		0			0
$325$	−16.0000			−0.887520
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$		0			0
$328$		0			0
$329$	−8.00000	+	13.8564i	−0.441054	+	0.763928i
$330$		0			0
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	0.753660	−	0.657264i	$-0.228286\pi$
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	−0.946038	+	0.324057i	$0.894953\pi$
$332$	12.0000			0.658586
$333$		0			0
$334$	24.0000			1.31322
$335$	−3.50000	−	6.06218i	−0.191225	−	0.331212i
$336$		0			0
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−3.00000	+	5.19615i	−0.163178	+	0.282633i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−7.00000			−0.379071
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	−0.195507	−	0.980702i	$-0.562635\pi$
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$348$		0			0
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$	16.0000			0.855236
$351$		0			0
$352$	8.00000			0.426401
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$	15.0000	−	25.9808i	0.794998	−	1.37698i
$357$		0			0
$358$	−15.0000	−	25.9808i	−0.792775	−	1.37313i
$359$	20.0000			1.05556			0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	−7.00000	−	12.1244i	−0.367912	−	0.637242i
$363$		0			0
$364$	8.00000	−	13.8564i	0.419314	−	0.726273i
$365$	2.00000	−	3.46410i	0.104685	−	0.181319i
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	−6.00000			−0.311925
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$		0			0
$382$	17.0000	−	29.4449i	0.869796	−	1.50653i
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	−0.878517	−	0.477711i	$-0.841467\pi$
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	0.852968	+	0.521963i	$0.174800\pi$
$384$		0			0
$385$	1.00000	+	1.73205i	0.0509647	+	0.0882735i
$386$	8.00000			0.407189
$387$		0			0
$388$	−14.0000			−0.710742
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$	10.0000			0.503155
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$	−8.00000	+	13.8564i	−0.400000	+	0.692820i
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	0.889914	+	0.456129i	$0.150764\pi$
$402$		0			0
$403$	−14.0000	−	24.2487i	−0.697390	−	1.20791i
$404$	−4.00000			−0.199007
$405$		0			0
$406$		0			0
$407$	1.50000	+	2.59808i	0.0743522	+	0.128782i
$408$		0			0
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$	8.00000	−	13.8564i	0.395092	−	0.684319i
$411$		0			0
$412$	16.0000	+	27.7128i	0.788263	+	1.36531i
$413$	10.0000			0.492068
$414$		0			0
$415$	−6.00000			−0.294528
$416$	16.0000	+	27.7128i	0.784465	+	1.35873i
$417$		0			0
$418$		0			0
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	−0.511381	−	0.859354i	$-0.670866\pi$
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	0.999913	+	0.0131919i	$0.00419923\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$	24.0000			1.16830
$423$		0			0
$424$		0			0
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$		0			0
$427$	12.0000	−	20.7846i	0.580721	−	1.00584i
$428$	18.0000	−	31.1769i	0.870063	−	1.50699i
$429$		0			0
$430$	−6.00000	−	10.3923i	−0.289346	−	0.501161i
$431$	18.0000			0.867029			0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000			0.867029			0.433515	+	0.901146i	$0.357273\pi$
$432$		0			0
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	14.0000	+	24.2487i	0.672022	+	1.16398i
$435$		0			0
$436$	−10.0000	+	17.3205i	−0.478913	+	0.829502i
$437$		0			0
$438$		0			0
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.735399	−	0.677634i	$-0.763005\pi$
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.219149	−	0.975691i	$-0.570328\pi$
$440$		0			0
$441$		0			0
$442$	16.0000			0.761042
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	0.705278	−	0.708931i	$-0.250822\pi$
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	−0.966591	+	0.256323i	$0.917489\pi$
$444$		0			0
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$	−19.0000	+	32.9090i	−0.899676	+	1.55828i
$447$		0			0
$448$	−8.00000	−	13.8564i	−0.377964	−	0.654654i
$449$	−35.0000			−1.65175			−0.825876	−	0.563852i	$-0.809319\pi$
$449$	−35.0000			−1.65175			−0.825876	+	0.563852i	$0.809319\pi$
$450$		0			0
$451$	−8.00000			−0.376705
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$		0			0
$454$	18.0000	−	31.1769i	0.844782	−	1.46321i
$455$	−4.00000	+	6.92820i	−0.187523	+	0.324799i
$456$		0			0
$457$	6.00000	+	10.3923i	0.280668	+	0.486132i	0.971549	−	0.236837i	$-0.0761106\pi$
$457$	6.00000	+	10.3923i	0.280668	+	0.486132i	−0.690881	+	0.722968i	$0.742777\pi$
$458$	30.0000			1.40181
$459$		0			0
$460$	−2.00000			−0.0932505
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$		0			0
$463$	5.50000	−	9.52628i	0.255607	−	0.442724i	−0.709453	−	0.704752i	$-0.751058\pi$
$463$	5.50000	−	9.52628i	0.255607	−	0.442724i	0.965060	+	0.262029i	$0.0843915\pi$
$464$		0			0
$465$		0			0
$466$	24.0000	+	41.5692i	1.11178	+	1.92566i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$		0			0
$469$	14.0000			0.646460
$470$	−8.00000	−	13.8564i	−0.369012	−	0.639148i
$471$		0			0
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$		0			0
$476$	−8.00000			−0.366679
$477$		0			0
$478$	60.0000			2.74434
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	8.00000	−	13.8564i	0.364390	−	0.631142i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	7.00000			0.317854
$486$		0			0
$487$	23.0000			1.04223			0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000			1.04223			0.521115	+	0.853487i	$0.325516\pi$
$488$		0			0
$489$		0			0
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−28.0000			−1.25724
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	−9.00000	+	15.5885i	−0.402492	+	0.697137i
$501$		0			0
$502$	−23.0000	−	39.8372i	−1.02654	−	1.77802i
$503$	26.0000			1.15928			0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000			1.15928			0.579641	+	0.814872i	$0.303193\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$	32.0000			1.41421
$513$		0			0
$514$	4.00000			0.176432
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$	−4.00000	+	6.92820i	−0.175920	+	0.304702i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$		0			0
$521$	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
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−18.0000	−	31.1769i	−0.786334	−	1.36197i
$525$		0			0
$526$	14.0000	−	24.2487i	0.610429	−	1.05729i
$527$	−7.00000	+	12.1244i	−0.304925	+	0.528145i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−12.0000			−0.521247
$531$		0			0
$532$		0			0
$533$	−16.0000	−	27.7128i	−0.693037	−	1.20038i
$534$		0			0
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$		0			0
$537$		0			0
$538$	10.0000	+	17.3205i	0.431131	+	0.746740i
$539$	3.00000			0.129219
$540$		0			0
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	28.0000	+	48.4974i	1.20270	+	2.08314i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$	5.00000	−	8.66025i	0.214176	−	0.370965i
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$	14.0000			0.598050
$549$		0			0
$550$	8.00000			0.341121
$551$		0			0
$552$		0			0
$553$	−10.0000	+	17.3205i	−0.425243	+	0.736543i
$554$	2.00000	−	3.46410i	0.0849719	−	0.147176i
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	2.00000			0.0847427			0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000			0.0847427			0.0423714	+	0.999102i	$0.486509\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$	4.00000	+	6.92820i	0.169031	+	0.292770i
$561$		0			0
$562$	−18.0000	+	31.1769i	−0.759284	+	1.31512i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	−4.50000	−	7.79423i	−0.189316	−	0.327906i
$566$	8.00000			0.336265
$567$		0			0
$568$		0			0
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	−0.408883	−	0.912587i	$-0.634082\pi$
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	0.994765	−	0.102190i	$-0.0325850\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$		0			0
$574$	16.0000	+	27.7128i	0.667827	+	1.15671i
$575$	−4.00000			−0.166812
$576$		0			0
$577$	33.0000			1.37381			0.686904	−	0.726748i	$-0.258969\pi$
$577$	33.0000			1.37381			0.686904	+	0.726748i	$0.258969\pi$
$578$	13.0000	+	22.5167i	0.540729	+	0.936570i
$579$		0			0
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$		0			0
$585$		0			0
$586$	−48.0000			−1.98286
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$		0			0
$589$		0			0
$590$	−5.00000	+	8.66025i	−0.205847	+	0.356537i
$591$		0			0
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	−44.0000			−1.80686			−0.903432	−	0.428732i	$-0.858960\pi$
$593$	−44.0000			−1.80686			−0.903432	+	0.428732i	$0.858960\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$	−10.0000	−	17.3205i	−0.409616	−	0.709476i
$597$		0			0
$598$	−4.00000	+	6.92820i	−0.163572	+	0.283315i
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	−0.0905757	−	0.995890i	$-0.528871\pi$
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	0.907754	−	0.419504i	$-0.137796\pi$
$600$		0			0
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$	24.0000			0.978167
$603$		0			0
$604$	4.00000			0.162758
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$		0			0
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$		0			0
$609$		0			0
$610$	12.0000	+	20.7846i	0.485866	+	0.841544i
$611$	−32.0000			−1.29458
$612$		0			0
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		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	$0.665777\pi$
$620$	−14.0000			−0.562254
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−15.0000	−	25.9808i	−0.600962	−	1.04090i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$		0			0
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	6.00000			0.239236
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$		0			0
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$		0			0
$637$	6.00000	+	10.3923i	0.237729	+	0.411758i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	0.424555	+	0.905402i	$0.360431\pi$
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	−0.996379	+	0.0850262i	$0.972903\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$		0			0
$646$		0			0
$647$	7.00000			0.275198			0.137599	−	0.990488i	$-0.456061\pi$
$647$	7.00000			0.275198			0.137599	+	0.990488i	$0.456061\pi$
$648$		0			0
$649$	5.00000			0.196267
$650$	16.0000	+	27.7128i	0.627572	+	1.08699i
$651$		0			0
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−20.5000	+	35.5070i	−0.802227	+	1.38950i	0.115920	+	0.993259i	$0.463018\pi$
$653$	−20.5000	+	35.5070i	−0.802227	+	1.38950i	−0.918147	+	0.396239i	$0.870315\pi$
$654$		0			0
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	−32.0000			−1.24939
$657$		0			0
$658$	32.0000			1.24749
$659$	5.00000	+	8.66025i	0.194772	+	0.337356i	0.946826	−	0.321746i	$-0.104270\pi$
$659$	5.00000	+	8.66025i	0.194772	+	0.337356i	−0.752054	+	0.659102i	$0.770937\pi$
$660$		0			0
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	0.241605	+	0.970375i	$0.422326\pi$
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	−0.961172	+	0.275951i	$0.911007\pi$
$662$	−7.00000	+	12.1244i	−0.272063	+	0.471226i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$		0			0
$670$	−7.00000	+	12.1244i	−0.270434	+	0.468405i
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	−44.0000			−1.69482
$675$		0			0
$676$	6.00000			0.230769
$677$	−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
$679$	−7.00000	+	12.1244i	−0.268635	+	0.465290i
$680$		0			0
$681$		0			0
$682$	7.00000	+	12.1244i	0.268044	+	0.464266i
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		0			0
$685$	−7.00000			−0.267456
$686$	−20.0000	−	34.6410i	−0.763604	−	1.32260i
$687$		0			0
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	−56.0000			−2.12573
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$	−8.00000	+	13.8564i	−0.303022	+	0.524849i
$698$	−30.0000	+	51.9615i	−1.13552	+	1.96677i
$699$		0			0
$700$	−8.00000	−	13.8564i	−0.302372	−	0.523723i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$		0			0
$704$	−4.00000	−	6.92820i	−0.150756	−	0.261116i
$705$		0			0
$706$	−21.0000	+	36.3731i	−0.790345	+	1.36892i
$707$	−2.00000	+	3.46410i	−0.0752177	+	0.130281i
$708$		0			0
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	0.999390	−	0.0349269i	$-0.0111198\pi$
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	−0.529943	+	0.848034i	$0.677787\pi$
$710$	−6.00000			−0.225176
$711$		0			0
$712$		0			0
$713$	−3.50000	−	6.06218i	−0.131076	−	0.227030i
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$	−15.0000	+	25.9808i	−0.560576	+	0.970947i
$717$		0			0
$718$	−20.0000	−	34.6410i	−0.746393	−	1.29279i
$719$	−15.0000			−0.559406			−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000			−0.559406			−0.279703	+	0.960087i	$0.590236\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	19.0000	+	32.9090i	0.707107	+	1.22474i
$723$		0			0
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$		0			0
$726$		0			0
$727$	−1.50000	−	2.59808i	−0.0556319	−	0.0963573i	0.836868	−	0.547404i	$-0.184384\pi$
$727$	−1.50000	−	2.59808i	−0.0556319	−	0.0963573i	−0.892500	+	0.451047i	$0.851051\pi$
$728$		0			0
$729$		0			0
$730$	−8.00000			−0.296093
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	−0.314482	−	0.949263i	$-0.601831\pi$
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	0.979327	−	0.202282i	$-0.0648358\pi$
$734$	17.0000	−	29.4449i	0.627481	−	1.08683i
$735$		0			0
$736$	4.00000	+	6.92820i	0.147442	+	0.255377i
$737$	7.00000			0.257848
$738$		0			0
$739$	50.0000			1.83928			0.919640	−	0.392763i	$-0.128481\pi$
$739$	50.0000			1.83928			0.919640	+	0.392763i	$0.128481\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$		0			0
$742$	12.0000	−	20.7846i	0.440534	−	0.763027i
$743$	2.00000	−	3.46410i	0.0733729	−	0.127086i	−0.827005	−	0.562195i	$-0.809957\pi$
$743$	2.00000	−	3.46410i	0.0733729	−	0.127086i	0.900378	+	0.435110i	$0.143290\pi$
$744$		0			0
$745$	5.00000	+	8.66025i	0.183186	+	0.317287i
$746$	−52.0000			−1.90386
$747$		0			0
$748$	−4.00000			−0.146254
$749$	−18.0000	−	31.1769i	−0.657706	−	1.13918i
$750$		0			0
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	−0.576262	−	0.817265i	$-0.695489\pi$
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	0.995903	+	0.0904254i	$0.0288227\pi$
$752$	−16.0000	+	27.7128i	−0.583460	+	1.01058i
$753$		0			0
$754$		0			0
$755$	−2.00000			−0.0727875
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	5.00000	+	8.66025i	0.181608	+	0.314555i
$759$		0			0
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	10.0000	+	17.3205i	0.362024	+	0.627044i
$764$	−34.0000			−1.23008
$765$		0			0
$766$	2.00000			0.0722629
$767$	10.0000	+	17.3205i	0.361079	+	0.625407i
$768$		0			0
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	−0.988061	−	0.154062i	$-0.950765\pi$
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	0.627452	+	0.778655i	$0.284098\pi$
$770$	2.00000	−	3.46410i	0.0720750	−	0.124838i
$771$		0			0
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		0			0
$775$	−28.0000			−1.00579
$776$		0			0
$777$		0			0
$778$	−15.0000	+	25.9808i	−0.537776	+	0.931455i
$779$		0			0
$780$		0			0
$781$	1.50000	+	2.59808i	0.0536742	+	0.0929665i
$782$	4.00000			0.143040
$783$		0			0
$784$	12.0000			0.428571
$785$	−3.50000	−	6.06218i	−0.124920	−	0.216368i
$786$		0			0
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	−0.426193	−	0.904632i	$-0.640145\pi$
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	0.996531	−	0.0832226i	$-0.0265213\pi$
$788$	−2.00000	+	3.46410i	−0.0712470	+	0.123404i
$789$		0			0
$790$	−10.0000	−	17.3205i	−0.355784	−	0.616236i
$791$	18.0000			0.640006
$792$		0			0
$793$	48.0000			1.70453
$794$	2.00000	+	3.46410i	0.0709773	+	0.122936i
$795$		0			0
$796$		0			0
$797$	26.5000	−	45.8993i	0.938678	−	1.62584i	0.170738	−	0.985316i	$-0.445385\pi$
$797$	26.5000	−	45.8993i	0.938678	−	1.62584i	0.767940	−	0.640522i	$-0.221282\pi$
$798$		0			0
$799$	8.00000	+	13.8564i	0.283020	+	0.490204i
$800$	32.0000			1.13137
$801$		0			0
$802$	−4.00000			−0.141245
$803$	2.00000	+	3.46410i	0.0705785	+	0.122245i
$804$		0			0
$805$	−1.00000	+	1.73205i	−0.0352454	+	0.0610468i
$806$	−28.0000	+	48.4974i	−0.986258	+	1.70825i
$807$		0			0
$808$		0			0
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$	−38.0000			−1.33436			−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000			−1.33436			−0.667180	+	0.744896i	$0.732499\pi$
$812$		0			0
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$		0			0
$818$	−60.0000			−2.09785
$819$		0			0
$820$	−16.0000			−0.558744
$821$	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
$823$	−19.5000	+	33.7750i	−0.679727	+	1.17732i	0.295336	+	0.955394i	$0.404569\pi$
$823$	−19.5000	+	33.7750i	−0.679727	+	1.17732i	−0.975063	+	0.221929i	$0.928765\pi$
$824$		0			0
$825$		0			0
$826$	−10.0000	−	17.3205i	−0.347945	−	0.602658i
$827$	52.0000			1.80822			0.904109	−	0.427303i	$-0.140536\pi$
$827$	52.0000			1.80822			0.904109	+	0.427303i	$0.140536\pi$
$828$		0			0
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$		0			0
$832$	16.0000	−	27.7128i	0.554700	−	0.960769i
$833$	3.00000	−	5.19615i	0.103944	−	0.180036i
$834$		0			0
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$	−40.0000			−1.38178
$839$	−2.50000	−	4.33013i	−0.0863096	−	0.149493i	0.819639	−	0.572880i	$-0.194174\pi$
$839$	−2.50000	−	4.33013i	−0.0863096	−	0.149493i	−0.905949	+	0.423388i	$0.860841\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−22.0000	+	38.1051i	−0.758170	+	1.31319i
$843$		0			0
$844$	−12.0000	−	20.7846i	−0.413057	−	0.715436i
$845$	−3.00000			−0.103203
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	12.0000	+	20.7846i	0.412082	+	0.713746i
$849$		0			0
$850$	8.00000	−	13.8564i	0.274398	−	0.475271i
$851$	−1.50000	+	2.59808i	−0.0514193	+	0.0890609i
$852$		0			0
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	0.720946	−	0.692992i	$-0.243708\pi$
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	−0.960621	+	0.277862i	$0.910374\pi$
$854$	−48.0000			−1.64253
$855$		0			0
$856$		0			0
$857$	4.00000	+	6.92820i	0.136637	+	0.236663i	0.926222	−	0.376979i	$-0.123037\pi$
$857$	4.00000	+	6.92820i	0.136637	+	0.236663i	−0.789584	+	0.613642i	$0.789704\pi$
$858$		0			0
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	−0.709242	−	0.704965i	$-0.750963\pi$
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	0.965139	+	0.261739i	$0.0842960\pi$
$860$	−6.00000	+	10.3923i	−0.204598	+	0.354375i
$861$		0			0
$862$	−18.0000	−	31.1769i	−0.613082	−	1.06189i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	−6.00000			−0.204006
$866$	11.0000	+	19.0526i	0.373795	+	0.647432i
$867$		0			0
$868$	14.0000	−	24.2487i	0.475191	−	0.823055i
$869$	−5.00000	+	8.66025i	−0.169613	+	0.293779i
$870$		0			0
$871$	14.0000	+	24.2487i	0.474372	+	0.821636i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.00000	+	15.5885i	0.304256	+	0.526986i
$876$		0			0
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	−0.746762	−	0.665092i	$-0.768392\pi$
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	0.949367	+	0.314169i	$0.101726\pi$
$878$	−40.0000	+	69.2820i	−1.34993	+	2.33816i
$879$		0			0
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	43.0000			1.44871			0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000			1.44871			0.724353	+	0.689429i	$0.242138\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−8.00000	−	13.8564i	−0.269069	−	0.466041i
$885$		0			0
$886$	−11.0000	+	19.0526i	−0.369552	+	0.640083i
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	−0.989463	−	0.144785i	$-0.953751\pi$
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	0.620119	+	0.784508i	$0.287084\pi$
$888$		0			0
$889$	8.00000	+	13.8564i	0.268311	+	0.464729i
$890$	30.0000			1.00560
$891$		0			0
$892$	38.0000			1.27233
$893$		0			0
$894$		0			0
$895$	7.50000	−	12.9904i	0.250697	−	0.434221i
$896$		0			0
$897$		0			0
$898$	35.0000	+	60.6218i	1.16797	+	2.02297i
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$	8.00000	+	13.8564i	0.266371	+	0.461368i
$903$		0			0
$904$		0			0
$905$	3.50000	−	6.06218i	0.116344	−	0.201514i
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	−36.0000			−1.19470
$909$		0			0
$910$	16.0000			0.530395
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$	3.00000	−	5.19615i	0.0992855	−	0.171968i
$914$	12.0000	−	20.7846i	0.396925	−	0.687494i
$915$		0			0
$916$	−15.0000	−	25.9808i	−0.495614	−	0.858429i
$917$	−36.0000			−1.18882
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$		0			0
$922$	12.0000	−	20.7846i	0.395199	−	0.684505i
$923$	−6.00000	+	10.3923i	−0.197492	+	0.342067i
$924$		0			0
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−22.0000			−0.722965
$927$		0			0
$928$		0			0
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$		0			0
$932$	24.0000	−	41.5692i	0.786146	−	1.36165i
$933$		0			0
$934$	−27.0000	−	46.7654i	−0.883467	−	1.53021i
$935$	2.00000			0.0654070
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−14.0000	−	24.2487i	−0.457116	−	0.791748i
$939$		0			0
$940$	−8.00000	+	13.8564i	−0.260931	+	0.451946i
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$		0			0
$943$	−4.00000	−	6.92820i	−0.130258	−	0.225613i
$944$	20.0000			0.650945
$945$		0			0
$946$	12.0000			0.390154
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	0.558898	−	0.829237i	$-0.311224\pi$
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	−0.997589	+	0.0694014i	$0.977891\pi$
$948$		0			0
$949$	−8.00000	+	13.8564i	−0.259691	+	0.449798i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$		0			0
$955$	17.0000			0.550107
$956$	−30.0000	−	51.9615i	−0.970269	−	1.68056i
$957$		0			0
$958$	20.0000	−	34.6410i	0.646171	−	1.11920i
$959$	7.00000	−	12.1244i	0.226042	−	0.391516i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	24.0000			0.773791
$963$		0			0
$964$	−16.0000			−0.515325
$965$	2.00000	+	3.46410i	0.0643823	+	0.111513i
$966$		0			0
$967$	16.0000	−	27.7128i	0.514525	−	0.891184i	−0.485333	−	0.874330i	$-0.661301\pi$
$967$	16.0000	−	27.7128i	0.514525	−	0.891184i	0.999858	−	0.0168544i	$-0.00536518\pi$
$968$		0			0
$969$		0			0
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$	−47.0000			−1.50830			−0.754151	−	0.656701i	$-0.771951\pi$
$971$	−47.0000			−1.50830			−0.754151	+	0.656701i	$0.771951\pi$
$972$		0			0
$973$	−20.0000			−0.641171
$974$	−23.0000	−	39.8372i	−0.736968	−	1.27647i
$975$		0			0
$976$	24.0000	−	41.5692i	0.768221	−	1.33060i
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	−0.997037	−	0.0769208i	$-0.975491\pi$
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	0.565134	+	0.824999i	$0.308824\pi$
$978$		0			0
$979$	−7.50000	−	12.9904i	−0.239701	−	0.415174i
$980$	6.00000			0.191663
$981$		0			0
$982$	16.0000			0.510581
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	0.989122	+	0.147100i	$0.0469940\pi$
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	−0.367168	+	0.930155i	$0.619673\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.00000			−0.190789
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	28.0000	+	48.4974i	0.889001	+	1.53979i
$993$		0			0
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$		0			0
$996$		0			0
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	−0.992558	−	0.121771i	$-0.961143\pi$
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	0.390822	−	0.920466i	$-0.372191\pi$
$998$	40.0000			1.26618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.e.b.595.1		2
3.2	odd	2		891.2.e.k.595.1		2
9.2	odd	6		891.2.e.k.298.1		2
9.4	even	3		99.2.a.d.1.1		1
9.5	odd	6		11.2.a.a.1.1	✓	1
9.7	even	3	inner	891.2.e.b.298.1		2
36.23	even	6		176.2.a.b.1.1		1
36.31	odd	6		1584.2.a.g.1.1		1
45.4	even	6		2475.2.a.a.1.1		1
45.13	odd	12		2475.2.c.a.199.1		2
45.14	odd	6		275.2.a.b.1.1		1
45.22	odd	12		2475.2.c.a.199.2		2
45.23	even	12		275.2.b.a.199.2		2
45.32	even	12		275.2.b.a.199.1		2
63.5	even	6		539.2.e.g.67.1		2
63.13	odd	6		4851.2.a.t.1.1		1
63.23	odd	6		539.2.e.h.67.1		2
63.32	odd	6		539.2.e.h.177.1		2
63.41	even	6		539.2.a.a.1.1		1
63.59	even	6		539.2.e.g.177.1		2
72.5	odd	6		704.2.a.h.1.1		1
72.13	even	6		6336.2.a.br.1.1		1
72.59	even	6		704.2.a.c.1.1		1
72.67	odd	6		6336.2.a.bu.1.1		1
99.5	odd	30		121.2.c.e.3.1		4
99.14	odd	30		121.2.c.e.9.1		4
99.32	even	6		121.2.a.d.1.1		1
99.41	even	30		121.2.c.a.9.1		4
99.50	even	30		121.2.c.a.3.1		4
99.59	odd	30		121.2.c.e.27.1		4
99.68	even	30		121.2.c.a.81.1		4
99.76	odd	6		1089.2.a.b.1.1		1
99.86	odd	30		121.2.c.e.81.1		4
99.95	even	30		121.2.c.a.27.1		4
117.77	odd	6		1859.2.a.b.1.1		1
144.5	odd	12		2816.2.c.j.1409.2		2
144.59	even	12		2816.2.c.f.1409.1		2
144.77	odd	12		2816.2.c.j.1409.1		2
144.131	even	12		2816.2.c.f.1409.2		2
153.50	odd	6		3179.2.a.a.1.1		1
171.113	even	6		3971.2.a.b.1.1		1
180.23	odd	12		4400.2.b.h.4049.2		2
180.59	even	6		4400.2.a.i.1.1		1
180.167	odd	12		4400.2.b.h.4049.1		2
207.68	even	6		5819.2.a.a.1.1		1
252.167	odd	6		8624.2.a.j.1.1		1
261.86	odd	6		9251.2.a.d.1.1		1
396.131	odd	6		1936.2.a.i.1.1		1
495.329	even	6		3025.2.a.a.1.1		1
693.230	odd	6		5929.2.a.h.1.1		1
792.131	odd	6		7744.2.a.k.1.1		1
792.725	even	6		7744.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.2.a.a.1.1	✓	1	9.5	odd	6
99.2.a.d.1.1		1	9.4	even	3
121.2.a.d.1.1		1	99.32	even	6
121.2.c.a.3.1		4	99.50	even	30
121.2.c.a.9.1		4	99.41	even	30
121.2.c.a.27.1		4	99.95	even	30
121.2.c.a.81.1		4	99.68	even	30
121.2.c.e.3.1		4	99.5	odd	30
121.2.c.e.9.1		4	99.14	odd	30
121.2.c.e.27.1		4	99.59	odd	30
121.2.c.e.81.1		4	99.86	odd	30
176.2.a.b.1.1		1	36.23	even	6
275.2.a.b.1.1		1	45.14	odd	6
275.2.b.a.199.1		2	45.32	even	12
275.2.b.a.199.2		2	45.23	even	12
539.2.a.a.1.1		1	63.41	even	6
539.2.e.g.67.1		2	63.5	even	6
539.2.e.g.177.1		2	63.59	even	6
539.2.e.h.67.1		2	63.23	odd	6
539.2.e.h.177.1		2	63.32	odd	6
704.2.a.c.1.1		1	72.59	even	6
704.2.a.h.1.1		1	72.5	odd	6
891.2.e.b.298.1		2	9.7	even	3	inner
891.2.e.b.595.1		2	1.1	even	1	trivial
891.2.e.k.298.1		2	9.2	odd	6
891.2.e.k.595.1		2	3.2	odd	2
1089.2.a.b.1.1		1	99.76	odd	6
1584.2.a.g.1.1		1	36.31	odd	6
1859.2.a.b.1.1		1	117.77	odd	6
1936.2.a.i.1.1		1	396.131	odd	6
2475.2.a.a.1.1		1	45.4	even	6
2475.2.c.a.199.1		2	45.13	odd	12
2475.2.c.a.199.2		2	45.22	odd	12
2816.2.c.f.1409.1		2	144.59	even	12
2816.2.c.f.1409.2		2	144.131	even	12
2816.2.c.j.1409.1		2	144.77	odd	12
2816.2.c.j.1409.2		2	144.5	odd	12
3025.2.a.a.1.1		1	495.329	even	6
3179.2.a.a.1.1		1	153.50	odd	6
3971.2.a.b.1.1		1	171.113	even	6
4400.2.a.i.1.1		1	180.59	even	6
4400.2.b.h.4049.1		2	180.167	odd	12
4400.2.b.h.4049.2		2	180.23	odd	12
4851.2.a.t.1.1		1	63.13	odd	6
5819.2.a.a.1.1		1	207.68	even	6
5929.2.a.h.1.1		1	693.230	odd	6
6336.2.a.br.1.1		1	72.13	even	6
6336.2.a.bu.1.1		1	72.67	odd	6
7744.2.a.k.1.1		1	792.131	odd	6
7744.2.a.x.1.1		1	792.725	even	6
8624.2.a.j.1.1		1	252.167	odd	6
9251.2.a.d.1.1		1	261.86	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} -2.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(2.00000 - 3.46410i) q^{14} +(2.00000 + 3.46410i) q^{16} +2.00000 q^{17} +(1.00000 + 1.73205i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +8.00000 q^{26} -4.00000 q^{28} +(-3.50000 + 6.06218i) q^{31} +(4.00000 - 6.92820i) q^{32} +(-2.00000 - 3.46410i) q^{34} +2.00000 q^{35} +3.00000 q^{37} +(-4.00000 + 6.92820i) q^{41} +(3.00000 + 5.19615i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(4.00000 - 6.92820i) q^{50} +(-4.00000 - 6.92820i) q^{52} +6.00000 q^{53} +1.00000 q^{55} +(2.50000 - 4.33013i) q^{59} +(-6.00000 - 10.3923i) q^{61} +14.0000 q^{62} -8.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-2.00000 - 3.46410i) q^{70} +3.00000 q^{71} +4.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(-1.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +4.00000 q^{80} +16.0000 q^{82} +(-3.00000 - 5.19615i) q^{83} +(1.00000 - 1.73205i) q^{85} +(6.00000 - 10.3923i) q^{86} -15.0000 q^{89} -8.00000 q^{91} +(-1.00000 - 1.73205i) q^{92} +(8.00000 - 13.8564i) q^{94} +(3.50000 + 6.06218i) q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} + q^{5} + 2 q^{7}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^4 + q^5 + 2 * q^7	\( 2 q - 2 q^{2} - 2 q^{4} + q^{5} + 2 q^{7} - 4 q^{10} + q^{11} - 4 q^{13} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 2 q^{20} + 2 q^{22} - q^{23} + 4 q^{25} + 16 q^{26} - 8 q^{28} - 7 q^{31} + 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{37} - 8 q^{41} + 6 q^{43} - 4 q^{44} + 4 q^{46} + 8 q^{47} + 3 q^{49} + 8 q^{50} - 8 q^{52} + 12 q^{53} + 2 q^{55} + 5 q^{59} - 12 q^{61} + 28 q^{62} - 16 q^{64} + 4 q^{65} + 7 q^{67} - 4 q^{68} - 4 q^{70} + 6 q^{71} + 8 q^{73} - 6 q^{74} - 2 q^{77} + 10 q^{79} + 8 q^{80} + 32 q^{82} - 6 q^{83} + 2 q^{85} + 12 q^{86} - 30 q^{89} - 16 q^{91} - 2 q^{92} + 16 q^{94} + 7 q^{97} - 12 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 + q^5 + 2 * q^7 - 4 * q^10 + q^11 - 4 * q^13 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 2 * q^20 + 2 * q^22 - q^23 + 4 * q^25 + 16 * q^26 - 8 * q^28 - 7 * q^31 + 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^37 - 8 * q^41 + 6 * q^43 - 4 * q^44 + 4 * q^46 + 8 * q^47 + 3 * q^49 + 8 * q^50 - 8 * q^52 + 12 * q^53 + 2 * q^55 + 5 * q^59 - 12 * q^61 + 28 * q^62 - 16 * q^64 + 4 * q^65 + 7 * q^67 - 4 * q^68 - 4 * q^70 + 6 * q^71 + 8 * q^73 - 6 * q^74 - 2 * q^77 + 10 * q^79 + 8 * q^80 + 32 * q^82 - 6 * q^83 + 2 * q^85 + 12 * q^86 - 30 * q^89 - 16 * q^91 - 2 * q^92 + 16 * q^94 + 7 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more