LMFDB - Embedded newform 891.2.e.k.298.1

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			298.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	891.298
Dual form			891.2.e.k.595.1

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$		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	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$		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	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−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	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		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	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		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	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	−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	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	2.00000			0.294884
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		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	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		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	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$		0			0
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$	−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	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	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	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		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	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	−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	$-0.726523\pi$
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	0.982372	+	0.186938i	$0.0598564\pi$
$84$		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	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		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	−0.631810	−	0.775123i	$-0.717688\pi$
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	0.987181	+	0.159602i	$0.0510211\pi$
$98$	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	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$		0			0
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$		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	$-0.305804\pi$
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	−0.996262	+	0.0863794i	$0.972470\pi$
$114$		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	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		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	$-0.736672\pi$
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	0.975913	+	0.218159i	$0.0700052\pi$
$138$		0			0
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	0.572241	−	0.820086i	$-0.306074\pi$
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	−0.996335	+	0.0855324i	$0.972741\pi$
$140$	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	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$		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	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	−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	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		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	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		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	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		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	0.375339	+	0.926887i	$0.377526\pi$
$191$	−8.50000	+	14.7224i	−0.615038	+	1.06528i	−0.990378	+	0.138390i	$0.955807\pi$
$192$		0			0
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−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	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		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	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	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	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$	−16.0000			−1.06904
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$		0			0
$229$	−7.50000	−	12.9904i	−0.495614	−	0.858429i	0.504373	−	0.863486i	$-0.331724\pi$
$229$	−7.50000	−	12.9904i	−0.495614	−	0.858429i	−0.999987	+	0.00505719i	$0.998390\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$		0			0
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		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	0.694737	+	0.719264i	$0.255521\pi$
$239$	15.0000	+	25.9808i	0.970269	+	1.68056i	0.275533	+	0.961292i	$0.411146\pi$
$240$		0			0
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	−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	$-0.758564\pi$
$251$	−23.0000			−1.45175			−0.725874	+	0.687828i	$0.758564\pi$
$252$		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	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$		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	$-0.975398\pi$
$263$	−7.00000	+	12.1244i	−0.431638	+	0.747620i	0.565376	+	0.824833i	$0.308731\pi$
$264$		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	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$		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	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−20.0000			−1.19952
$279$		0			0
$280$		0			0
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	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	−0.968099	−	0.250568i	$-0.919383\pi$
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	0.267052	−	0.963682i	$-0.413951\pi$
$294$		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	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	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	$-0.952290\pi$
$317$	−6.50000	+	11.2583i	−0.365076	+	0.632331i	0.623712	+	0.781654i	$0.285624\pi$
$318$		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	−0.946038	−	0.324057i	$-0.894953\pi$
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	0.753660	+	0.657264i	$0.228286\pi$
$332$	−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	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	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	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	0.114747	+	0.993395i	$0.463394\pi$
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	−0.917679	+	0.397324i	$0.869939\pi$
$350$	−16.0000			−0.855236
$351$		0			0
$352$	8.00000			0.426401
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		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	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		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	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$	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	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$	−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	$-0.158533\pi$
$383$	0.500000	+	0.866025i	0.0255488	+	0.0442518i	−0.852968	+	0.521963i	$0.825200\pi$
$384$		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	$-0.709166\pi$
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	0.991100	+	0.133120i	$0.0424994\pi$
$390$		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	$-0.182569\pi$
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		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	0.951720	+	0.306968i	$0.0993146\pi$
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	−0.210017	+	0.977698i	$0.567352\pi$
$410$	−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	$-0.329134\pi$
$419$	−10.0000	−	17.3205i	−0.488532	−	0.846162i	−0.999913	+	0.0131919i	$0.995801\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$	−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	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$		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	−0.219149	+	0.975691i	$0.570328\pi$
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.735399	+	0.677634i	$0.763005\pi$
$440$		0			0
$441$		0			0
$442$	16.0000			0.761042
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$		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	$-0.190681\pi$
$449$	35.0000			1.65175			0.825876	+	0.563852i	$0.190681\pi$
$450$		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	−0.690881	−	0.722968i	$-0.742777\pi$
$457$	6.00000	−	10.3923i	0.280668	−	0.486132i	0.971549	+	0.236837i	$0.0761106\pi$
$458$	−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	$-0.923485\pi$
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	0.691800	+	0.722089i	$0.256818\pi$
$462$		0			0
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	0.965060	−	0.262029i	$-0.0843915\pi$
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	−0.709453	+	0.704752i	$0.751058\pi$
$464$		0			0
$465$		0			0
$466$	24.0000	−	41.5692i	1.11178	−	1.92566i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$		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	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$		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	$-0.108889\pi$
$491$	4.00000	+	6.92820i	0.180517	+	0.312665i	−0.761539	+	0.648119i	$0.775556\pi$
$492$		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	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	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	$-0.696807\pi$
$503$	−26.0000			−1.15928			−0.579641	+	0.814872i	$0.696807\pi$
$504$		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	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		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	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		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	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$	−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	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$		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	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		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	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$	−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	0.417885	+	0.908500i	$0.362772\pi$
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	−0.995726	+	0.0923513i	$0.970562\pi$
$588$		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	$-0.141040\pi$
$593$	44.0000			1.80686			0.903432	+	0.428732i	$0.141040\pi$
$594$		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	−0.907754	−	0.419504i	$-0.862204\pi$
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	0.0905757	−	0.995890i	$-0.471129\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$	−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	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$		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	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$		0			0
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	−0.497579	−	0.867419i	$-0.665777\pi$
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	0.999996	−	0.00279365i	$-0.000889247\pi$
$620$	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	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	−0.996379	−	0.0850262i	$-0.972903\pi$
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	0.424555	−	0.905402i	$-0.360431\pi$
$644$	−2.00000	−	3.46410i	−0.0788110	−	0.136505i
$645$		0			0
$646$		0			0
$647$	−7.00000			−0.275198			−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000			−0.275198			−0.137599	+	0.990488i	$0.543939\pi$
$648$		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	0.918147	+	0.396239i	$0.129685\pi$
$653$	20.5000	+	35.5070i	0.802227	+	1.38950i	−0.115920	+	0.993259i	$0.536982\pi$
$654$		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	$-0.895730\pi$
$659$	−5.00000	+	8.66025i	−0.194772	+	0.337356i	0.752054	+	0.659102i	$0.229063\pi$
$660$		0			0
$661$	−18.5000	−	32.0429i	−0.719567	−	1.24633i	−0.961172	−	0.275951i	$-0.911007\pi$
$661$	−18.5000	−	32.0429i	−0.719567	−	1.24633i	0.241605	−	0.970375i	$-0.422326\pi$
$662$	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	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	44.0000			1.69482
$675$		0			0
$676$	6.00000			0.230769
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	−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	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		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	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$	−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	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		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	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$	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	$-0.409764\pi$
$719$	15.0000			0.559406			0.279703	+	0.960087i	$0.409764\pi$
$720$		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	−0.892500	−	0.451047i	$-0.851051\pi$
$727$	−1.50000	+	2.59808i	−0.0556319	+	0.0963573i	0.836868	+	0.547404i	$0.184384\pi$
$728$		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	0.979327	+	0.202282i	$0.0648358\pi$
$733$	18.0000	+	31.1769i	0.664845	+	1.15155i	−0.314482	+	0.949263i	$0.601831\pi$
$734$	−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	$-0.190043\pi$
$743$	−2.00000	−	3.46410i	−0.0733729	−	0.127086i	−0.900378	+	0.435110i	$0.856710\pi$
$744$		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	0.995903	−	0.0904254i	$-0.0288227\pi$
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	−0.576262	+	0.817265i	$0.695489\pi$
$752$	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	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		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	0.627452	−	0.778655i	$-0.284098\pi$
$769$	−10.0000	−	17.3205i	−0.360609	−	0.624593i	−0.988061	+	0.154062i	$0.950765\pi$
$770$	−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	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$		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	0.996531	+	0.0832226i	$0.0265213\pi$
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	−0.426193	+	0.904632i	$0.640145\pi$
$788$	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	−0.767940	−	0.640522i	$-0.778718\pi$
$797$	−26.5000	−	45.8993i	−0.938678	−	1.62584i	−0.170738	−	0.985316i	$-0.554615\pi$
$798$		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	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	−19.5000	−	33.7750i	−0.679727	−	1.17732i	−0.975063	−	0.221929i	$-0.928765\pi$
$823$	−19.5000	−	33.7750i	−0.679727	−	1.17732i	0.295336	−	0.955394i	$-0.404569\pi$
$824$		0			0
$825$		0			0
$826$	−10.0000	+	17.3205i	−0.347945	+	0.602658i
$827$	−52.0000			−1.80822			−0.904109	−	0.427303i	$-0.859464\pi$
$827$	−52.0000			−1.80822			−0.904109	+	0.427303i	$0.859464\pi$
$828$		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	$-0.805826\pi$
$839$	2.50000	−	4.33013i	0.0863096	−	0.149493i	0.905949	+	0.423388i	$0.139159\pi$
$840$		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	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$	48.0000			1.64253
$855$		0			0
$856$		0			0
$857$	−4.00000	+	6.92820i	−0.136637	+	0.236663i	−0.926222	−	0.376979i	$-0.876963\pi$
$857$	−4.00000	+	6.92820i	−0.136637	+	0.236663i	0.789584	+	0.613642i	$0.210296\pi$
$858$		0			0
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	0.965139	−	0.261739i	$-0.0842960\pi$
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	−0.709242	+	0.704965i	$0.750963\pi$
$860$	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	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		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	0.949367	−	0.314169i	$-0.101726\pi$
$877$	6.00000	+	10.3923i	0.202606	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$878$	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	$-0.757862\pi$
$881$	−43.0000			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$882$		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	$-0.0462491\pi$
$887$	11.0000	+	19.0526i	0.369344	+	0.639722i	−0.620119	+	0.784508i	$0.712916\pi$
$888$		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	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	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	$-0.897034\pi$
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	0.749347	+	0.662177i	$0.230367\pi$
$912$		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	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		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	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$		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	$-0.688776\pi$
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	0.997589	+	0.0694014i	$0.0221089\pi$
$948$		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	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$		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	0.999858	+	0.0168544i	$0.00536518\pi$
$967$	16.0000	+	27.7128i	0.514525	+	0.891184i	−0.485333	+	0.874330i	$0.661301\pi$
$968$		0			0
$969$		0			0
$970$	−7.00000	+	12.1244i	−0.224756	+	0.389290i
$971$	47.0000			1.50830			0.754151	−	0.656701i	$-0.228049\pi$
$971$	47.0000			1.50830			0.754151	+	0.656701i	$0.228049\pi$
$972$		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	$-0.0245089\pi$
$977$	13.5000	+	23.3827i	0.431903	+	0.748078i	−0.565134	+	0.824999i	$0.691176\pi$
$978$		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	0.367168	+	0.930155i	$0.380327\pi$
$983$	−19.5000	+	33.7750i	−0.621953	+	1.07725i	−0.989122	+	0.147100i	$0.953006\pi$
$984$		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	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$	−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.k.298.1		2
3.2	odd	2		891.2.e.b.298.1		2
9.2	odd	6		99.2.a.d.1.1		1
9.4	even	3	inner	891.2.e.k.595.1		2
9.5	odd	6		891.2.e.b.595.1		2
9.7	even	3		11.2.a.a.1.1	✓	1
36.7	odd	6		176.2.a.b.1.1		1
36.11	even	6		1584.2.a.g.1.1		1
45.2	even	12		2475.2.c.a.199.2		2
45.7	odd	12		275.2.b.a.199.1		2
45.29	odd	6		2475.2.a.a.1.1		1
45.34	even	6		275.2.a.b.1.1		1
45.38	even	12		2475.2.c.a.199.1		2
45.43	odd	12		275.2.b.a.199.2		2
63.16	even	3		539.2.e.h.67.1		2
63.20	even	6		4851.2.a.t.1.1		1
63.25	even	3		539.2.e.h.177.1		2
63.34	odd	6		539.2.a.a.1.1		1
63.52	odd	6		539.2.e.g.177.1		2
63.61	odd	6		539.2.e.g.67.1		2
72.11	even	6		6336.2.a.bu.1.1		1
72.29	odd	6		6336.2.a.br.1.1		1
72.43	odd	6		704.2.a.c.1.1		1
72.61	even	6		704.2.a.h.1.1		1
99.7	odd	30		121.2.c.a.27.1		4
99.16	even	15		121.2.c.e.3.1		4
99.25	even	15		121.2.c.e.9.1		4
99.43	odd	6		121.2.a.d.1.1		1
99.52	odd	30		121.2.c.a.9.1		4
99.61	odd	30		121.2.c.a.3.1		4
99.65	even	6		1089.2.a.b.1.1		1
99.70	even	15		121.2.c.e.27.1		4
99.79	odd	30		121.2.c.a.81.1		4
99.97	even	15		121.2.c.e.81.1		4
117.25	even	6		1859.2.a.b.1.1		1
144.43	odd	12		2816.2.c.f.1409.1		2
144.61	even	12		2816.2.c.j.1409.1		2
144.115	odd	12		2816.2.c.f.1409.2		2
144.133	even	12		2816.2.c.j.1409.2		2
153.16	even	6		3179.2.a.a.1.1		1
171.151	odd	6		3971.2.a.b.1.1		1
180.7	even	12		4400.2.b.h.4049.1		2
180.43	even	12		4400.2.b.h.4049.2		2
180.79	odd	6		4400.2.a.i.1.1		1
207.160	odd	6		5819.2.a.a.1.1		1
252.223	even	6		8624.2.a.j.1.1		1
261.115	even	6		9251.2.a.d.1.1		1
396.43	even	6		1936.2.a.i.1.1		1
495.439	odd	6		3025.2.a.a.1.1		1
693.538	even	6		5929.2.a.h.1.1		1
792.43	even	6		7744.2.a.k.1.1		1
792.637	odd	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	9.7	even	3
99.2.a.d.1.1		1	9.2	odd	6
121.2.a.d.1.1		1	99.43	odd	6
121.2.c.a.3.1		4	99.61	odd	30
121.2.c.a.9.1		4	99.52	odd	30
121.2.c.a.27.1		4	99.7	odd	30
121.2.c.a.81.1		4	99.79	odd	30
121.2.c.e.3.1		4	99.16	even	15
121.2.c.e.9.1		4	99.25	even	15
121.2.c.e.27.1		4	99.70	even	15
121.2.c.e.81.1		4	99.97	even	15
176.2.a.b.1.1		1	36.7	odd	6
275.2.a.b.1.1		1	45.34	even	6
275.2.b.a.199.1		2	45.7	odd	12
275.2.b.a.199.2		2	45.43	odd	12
539.2.a.a.1.1		1	63.34	odd	6
539.2.e.g.67.1		2	63.61	odd	6
539.2.e.g.177.1		2	63.52	odd	6
539.2.e.h.67.1		2	63.16	even	3
539.2.e.h.177.1		2	63.25	even	3
704.2.a.c.1.1		1	72.43	odd	6
704.2.a.h.1.1		1	72.61	even	6
891.2.e.b.298.1		2	3.2	odd	2
891.2.e.b.595.1		2	9.5	odd	6
891.2.e.k.298.1		2	1.1	even	1	trivial
891.2.e.k.595.1		2	9.4	even	3	inner
1089.2.a.b.1.1		1	99.65	even	6
1584.2.a.g.1.1		1	36.11	even	6
1859.2.a.b.1.1		1	117.25	even	6
1936.2.a.i.1.1		1	396.43	even	6
2475.2.a.a.1.1		1	45.29	odd	6
2475.2.c.a.199.1		2	45.38	even	12
2475.2.c.a.199.2		2	45.2	even	12
2816.2.c.f.1409.1		2	144.43	odd	12
2816.2.c.f.1409.2		2	144.115	odd	12
2816.2.c.j.1409.1		2	144.61	even	12
2816.2.c.j.1409.2		2	144.133	even	12
3025.2.a.a.1.1		1	495.439	odd	6
3179.2.a.a.1.1		1	153.16	even	6
3971.2.a.b.1.1		1	171.151	odd	6
4400.2.a.i.1.1		1	180.79	odd	6
4400.2.b.h.4049.1		2	180.7	even	12
4400.2.b.h.4049.2		2	180.43	even	12
4851.2.a.t.1.1		1	63.20	even	6
5819.2.a.a.1.1		1	207.160	odd	6
5929.2.a.h.1.1		1	693.538	even	6
6336.2.a.br.1.1		1	72.29	odd	6
6336.2.a.bu.1.1		1	72.11	even	6
7744.2.a.k.1.1		1	792.43	even	6
7744.2.a.x.1.1		1	792.637	odd	6
8624.2.a.j.1.1		1	252.223	even	6
9251.2.a.d.1.1		1	261.115	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
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

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