LMFDB - Embedded newform 539.2.e.a.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, 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("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} +4.00000 q^{13} -4.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +2.00000 q^{20} +1.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(3.00000 + 5.19615i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} -1.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(-4.00000 - 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{40} +4.00000 q^{41} +12.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(1.00000 + 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +(5.00000 - 8.66025i) q^{47} -2.00000 q^{48} -1.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(2.00000 + 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} -2.00000 q^{55} +(3.00000 - 5.19615i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.00000 - 3.46410i) q^{60} +10.0000 q^{62} +7.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(4.00000 + 6.92820i) q^{73} +(3.00000 + 5.19615i) q^{74} +(1.00000 - 1.73205i) q^{75} +8.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-2.00000 + 3.46410i) q^{82} -8.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} -2.00000 q^{90} +4.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-5.00000 + 8.66025i) q^{96} -10.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 8 q^{15} + q^{16} - 4 q^{17} - q^{18} + 4 q^{20} + 2 q^{22} + 4 q^{23} + 6 q^{24} + q^{25} - 4 q^{26} - 8 q^{27} - 12 q^{29} + 4 q^{30} - 10 q^{31} - 5 q^{32} - 2 q^{33} + 8 q^{34} - 2 q^{36} + 6 q^{37} - 8 q^{39} - 6 q^{40} + 8 q^{41} + 24 q^{43} + q^{44} + 2 q^{45} + 4 q^{46} + 10 q^{47} - 4 q^{48} - 2 q^{50} - 8 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 4 q^{55} + 6 q^{58} - 2 q^{59} - 4 q^{60} + 20 q^{62} + 14 q^{64} + 8 q^{65} - 2 q^{66} - 8 q^{67} + 4 q^{68} - 16 q^{69} - 24 q^{71} + 3 q^{72} + 8 q^{73} + 6 q^{74} + 2 q^{75} + 16 q^{78} - 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} - 16 q^{85} - 12 q^{86} + 12 q^{87} + 3 q^{88} + 6 q^{89} - 4 q^{90} + 8 q^{92} - 20 q^{93} + 10 q^{94} - 10 q^{96} - 20 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - q^9 + 2 * q^10 - q^11 + 2 * q^12 + 8 * q^13 - 8 * q^15 + q^16 - 4 * q^17 - q^18 + 4 * q^20 + 2 * q^22 + 4 * q^23 + 6 * q^24 + q^25 - 4 * q^26 - 8 * q^27 - 12 * q^29 + 4 * q^30 - 10 * q^31 - 5 * q^32 - 2 * q^33 + 8 * q^34 - 2 * q^36 + 6 * q^37 - 8 * q^39 - 6 * q^40 + 8 * q^41 + 24 * q^43 + q^44 + 2 * q^45 + 4 * q^46 + 10 * q^47 - 4 * q^48 - 2 * q^50 - 8 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 4 * q^55 + 6 * q^58 - 2 * q^59 - 4 * q^60 + 20 * q^62 + 14 * q^64 + 8 * q^65 - 2 * q^66 - 8 * q^67 + 4 * q^68 - 16 * q^69 - 24 * q^71 + 3 * q^72 + 8 * q^73 + 6 * q^74 + 2 * q^75 + 16 * q^78 - 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 - 16 * q^85 - 12 * q^86 + 12 * q^87 + 3 * q^88 + 6 * q^89 - 4 * q^90 + 8 * q^92 - 20 * q^93 + 10 * q^94 - 10 * q^96 - 20 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−4.00000			−1.03280
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	1.00000			0.213201
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	3.00000	+	5.19615i	0.612372	+	1.06066i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	2.00000	−	3.46410i	0.365148	−	0.632456i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	4.00000			0.685994
$35$		0			0
$36$	−1.00000			−0.166667
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$		0			0
$39$	−4.00000	−	6.92820i	−0.640513	−	1.10940i
$40$	−3.00000	+	5.19615i	−0.474342	+	0.821584i
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	−0.227844	−	0.973698i	$-0.573168\pi$
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	0.957169	−	0.289530i	$-0.0934991\pi$
$48$	−2.00000			−0.288675
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−4.00000	+	6.92820i	−0.560112	+	0.970143i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	−2.00000			−0.269680
$56$		0			0
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$	−2.00000	−	3.46410i	−0.258199	−	0.447214i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	10.0000			1.27000
$63$		0			0
$64$	7.00000			0.875000
$65$	4.00000	−	6.92820i	0.496139	−	0.859338i
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	0.999338	−	0.0363782i	$-0.0115821\pi$
$73$	4.00000	+	6.92820i	0.468165	+	0.810885i	−0.531174	+	0.847263i	$0.678249\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$	4.00000			0.417029
$93$	−10.0000	+	17.3205i	−1.03695	+	1.79605i
$94$	5.00000	+	8.66025i	0.515711	+	0.893237i
$95$		0			0
$96$	−5.00000	+	8.66025i	−0.510310	+	0.883883i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	0.948207	−	0.317653i	$-0.102895\pi$
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	−0.749199	+	0.662344i	$0.769562\pi$
$102$	−4.00000	−	6.92820i	−0.396059	−	0.685994i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	−12.0000			−1.17670
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	−12.0000			−1.13899
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	2.00000			0.184115
$119$		0			0
$120$	12.0000			1.09545
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	12.0000			1.07331
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	−12.0000	−	20.7846i	−1.05654	−	1.82998i
$130$	4.00000	+	6.92820i	0.350823	+	0.607644i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−2.00000			−0.174078
$133$		0			0
$134$	8.00000			0.691095
$135$	−4.00000	+	6.92820i	−0.344265	+	0.596285i
$136$	6.00000	+	10.3923i	0.514496	+	0.891133i
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	0.996621	−	0.0821359i	$-0.0261741\pi$
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	−0.569442	+	0.822031i	$0.692841\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−20.0000			−1.68430
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−6.00000	+	10.3923i	−0.498273	+	0.863034i
$146$	−8.00000			−0.662085
$147$		0			0
$148$	6.00000			0.493197
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	1.00000	+	1.73205i	0.0816497	+	0.141421i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−20.0000			−1.60644
$156$	4.00000	−	6.92820i	0.320256	−	0.554700i
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$	−10.0000			−0.790569
$161$		0			0
$162$	−11.0000			−0.864242
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	2.00000	+	3.46410i	0.156174	+	0.270501i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	4.00000	−	6.92820i	0.306786	−	0.531369i
$171$		0			0
$172$	6.00000	+	10.3923i	0.457496	+	0.792406i
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−2.00000	+	3.46410i	−0.150329	+	0.260378i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$		0			0
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$	−10.0000	−	17.3205i	−0.733236	−	1.27000i
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$	10.0000			0.729325
$189$		0			0
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−7.00000	−	12.1244i	−0.505181	−	0.875000i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	−16.0000			−1.14578
$196$		0			0
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$	−0.500000	+	0.866025i	−0.0355335	+	0.0615457i
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	−4.00000			−0.281439
$203$		0			0
$204$	−8.00000			−0.560112
$205$	4.00000	−	6.92820i	0.279372	−	0.483887i
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	12.0000	+	20.7846i	0.822226	+	1.42414i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	12.0000	−	20.7846i	0.818393	−	1.41750i
$216$	12.0000			0.816497
$217$		0			0
$218$	−14.0000			−0.948200
$219$	8.00000	−	13.8564i	0.540590	−	0.936329i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$	6.00000	−	10.3923i	0.402694	−	0.697486i
$223$	22.0000			1.47323			0.736614	−	0.676313i	$-0.236423\pi$
$223$	22.0000			1.47323			0.736614	+	0.676313i	$0.236423\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−9.00000	+	15.5885i	−0.594737	+	1.03011i	0.398847	+	0.917017i	$0.369410\pi$
$229$	−9.00000	+	15.5885i	−0.594737	+	1.03011i	−0.993584	+	0.113097i	$0.963923\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	18.0000			1.18176
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	−10.0000	−	17.3205i	−0.652328	−	1.12987i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$	16.0000			1.03931
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	0.984496	+	0.175409i	$0.0561248\pi$
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		0			0
$245$		0			0
$246$	8.00000			0.510061
$247$		0			0
$248$	15.0000	+	25.9808i	0.952501	+	1.64978i
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	8.00000	+	13.8564i	0.500979	+	0.867722i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	−0.560781	−	0.827964i	$-0.689499\pi$
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	0.997429	+	0.0716680i	$0.0228322\pi$
$258$	24.0000			1.49417
$259$		0			0
$260$	8.00000			0.496139
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	12.0000			0.737154
$266$		0			0
$267$	−12.0000			−0.734388
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	−4.00000	−	6.92820i	−0.243432	−	0.421637i
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	−0.798865	−	0.601511i	$-0.794566\pi$
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	0.920356	+	0.391082i	$0.127899\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	−10.0000			−0.604122
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	4.00000	−	6.92820i	0.239904	−	0.415526i
$279$	10.0000			0.598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	10.0000	−	17.3205i	0.595491	−	1.03142i
$283$	−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	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	4.00000			0.236525
$287$		0			0
$288$	5.00000			0.294628
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−6.00000	−	10.3923i	−0.352332	−	0.610257i
$291$	10.0000	+	17.3205i	0.586210	+	1.01535i
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	−9.00000	+	15.5885i	−0.523114	+	0.906061i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	2.00000			0.115470
$301$		0			0
$302$	−16.0000			−0.920697
$303$	4.00000	−	6.92820i	0.229794	−	0.398015i
$304$		0			0
$305$		0			0
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	28.0000			1.59286
$310$	10.0000	−	17.3205i	0.567962	−	0.983739i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	12.0000	+	20.7846i	0.679366	+	1.17670i
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	−0.892903	−	0.450250i	$-0.851335\pi$
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	0.836379	+	0.548151i	$0.184668\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	7.00000	−	12.1244i	0.391312	−	0.677772i
$321$	24.0000			1.33955
$322$		0			0
$323$		0			0
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	14.0000	−	24.2487i	0.774202	−	1.34096i
$328$	−12.0000			−0.662589
$329$		0			0
$330$	−4.00000			−0.220193
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$		0			0
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$		0			0
$335$	−16.0000			−0.874173
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	−18.0000	−	31.1769i	−0.977626	−	1.69330i
$340$	−4.00000	−	6.92820i	−0.216930	−	0.375735i
$341$	−5.00000	+	8.66025i	−0.270765	+	0.468979i
$342$		0			0
$343$		0			0
$344$	−36.0000			−1.94099
$345$	−8.00000	+	13.8564i	−0.430706	+	0.746004i
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$	−16.0000			−0.854017
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	−12.0000	+	20.7846i	−0.636894	+	1.10313i
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$	−3.00000	−	5.19615i	−0.158114	−	0.273861i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	2.00000			0.104973
$364$		0			0
$365$	16.0000			0.837478
$366$		0			0
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$	12.0000			0.623850
$371$		0			0
$372$	−20.0000			−1.03695
$373$	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
$375$	−12.0000	−	20.7846i	−0.619677	−	1.07331i
$376$	−15.0000	+	25.9808i	−0.773566	+	1.33986i
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	−1.00000	+	1.73205i	−0.0510976	+	0.0885037i	−0.890443	−	0.455095i	$-0.849605\pi$
$383$	−1.00000	+	1.73205i	−0.0510976	+	0.0885037i	0.839345	+	0.543599i	$0.182939\pi$
$384$	−6.00000			−0.306186
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−6.00000	+	10.3923i	−0.304997	+	0.528271i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	8.00000	−	13.8564i	0.405096	−	0.701646i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	24.0000			1.21064
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	8.00000	+	13.8564i	0.402524	+	0.697191i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	−18.0000			−0.902258
$399$		0			0
$400$	1.00000			0.0500000
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	0.998322	−	0.0579116i	$-0.0184442\pi$
$402$	−8.00000	−	13.8564i	−0.399004	−	0.691095i
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$	−2.00000	+	3.46410i	−0.0995037	+	0.172345i
$405$	22.0000			1.09319
$406$		0			0
$407$	−6.00000			−0.297409
$408$	12.0000	−	20.7846i	0.594089	−	1.02899i
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	−0.993776	−	0.111398i	$-0.964467\pi$
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	0.400414	−	0.916334i	$-0.368866\pi$
$410$	4.00000	+	6.92820i	0.197546	+	0.342160i
$411$	10.0000	−	17.3205i	0.493264	−	0.854358i
$412$	−14.0000			−0.689730
$413$		0			0
$414$	−4.00000			−0.196589
$415$		0			0
$416$	−10.0000	−	17.3205i	−0.490290	−	0.849208i
$417$	8.00000	+	13.8564i	0.391762	+	0.678551i
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$	6.00000	−	10.3923i	0.292075	−	0.505889i
$423$	5.00000	+	8.66025i	0.243108	+	0.421076i
$424$	−9.00000	−	15.5885i	−0.437079	−	0.757042i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	−24.0000			−1.16280
$427$		0			0
$428$	−12.0000			−0.580042
$429$	−4.00000	+	6.92820i	−0.193122	+	0.334497i
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		0			0
$435$	24.0000			1.15071
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$		0			0
$438$	8.00000	+	13.8564i	0.382255	+	0.662085i
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	−0.522387	−	0.852709i	$-0.674958\pi$
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	0.999661	+	0.0260459i	$0.00829161\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	16.0000			0.761042
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$	−6.00000	−	10.3923i	−0.284747	−	0.493197i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−11.0000	+	19.0526i	−0.520865	+	0.902165i
$447$	−20.0000			−0.945968
$448$		0			0
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	16.0000	−	27.7128i	0.751746	−	1.30206i
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	−9.00000	−	15.5885i	−0.420542	−	0.728401i
$459$	8.00000	+	13.8564i	0.373408	+	0.646762i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	20.0000	+	34.6410i	0.927478	+	1.60644i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	0.276360	+	0.961054i	$0.410872\pi$
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	−0.970477	+	0.241192i	$0.922462\pi$
$468$	−4.00000			−0.184900
$469$		0			0
$470$	20.0000			0.922531
$471$	−14.0000	+	24.2487i	−0.645086	+	1.11732i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−6.00000	−	10.3923i	−0.275880	−	0.477839i
$474$	−8.00000	+	13.8564i	−0.367452	+	0.636446i
$475$		0			0
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	0.908093	−	0.418769i	$-0.137538\pi$
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	−0.816711	+	0.577047i	$0.804205\pi$
$480$	10.0000	+	17.3205i	0.456435	+	0.790569i
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$	−20.0000			−0.910975
$483$		0			0
$484$	−1.00000			−0.0454545
$485$	−10.0000	+	17.3205i	−0.454077	+	0.786484i
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	0.986642	+	0.162905i	$0.0520863\pi$
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	−0.352241	+	0.935909i	$0.614580\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$	4.00000	−	6.92820i	0.180334	−	0.312348i
$493$	12.0000	+	20.7846i	0.540453	+	0.936092i
$494$		0			0
$495$	1.00000	−	1.73205i	0.0449467	−	0.0778499i
$496$	−10.0000			−0.449013
$497$		0			0
$498$		0			0
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	1.00000	−	1.73205i	0.0446322	−	0.0773052i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$		0			0
$505$	8.00000			0.355995
$506$	2.00000	−	3.46410i	0.0889108	−	0.153998i
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$	−16.0000			−0.708492
$511$		0			0
$512$	−11.0000			−0.486136
$513$		0			0
$514$	7.00000	+	12.1244i	0.308757	+	0.534782i
$515$	14.0000	+	24.2487i	0.616914	+	1.06853i
$516$	12.0000	−	20.7846i	0.528271	−	0.914991i
$517$	−10.0000			−0.439799
$518$		0			0
$519$	24.0000			1.05348
$520$	−12.0000	+	20.7846i	−0.526235	+	0.911465i
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	8.00000			0.348817
$527$	−20.0000	+	34.6410i	−0.871214	+	1.50899i
$528$	1.00000	+	1.73205i	0.0435194	+	0.0753778i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$	2.00000			0.0867926
$532$		0			0
$533$	16.0000			0.693037
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	12.0000	+	20.7846i	0.518321	+	0.897758i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	10.0000			0.431131
$539$		0			0
$540$	−8.00000			−0.344265
$541$	13.0000	−	22.5167i	0.558914	−	0.968067i	−0.438674	−	0.898646i	$-0.644552\pi$
$541$	13.0000	−	22.5167i	0.558914	−	0.968067i	0.997587	−	0.0694205i	$-0.0221150\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$	−10.0000	−	17.3205i	−0.429141	−	0.743294i
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$	28.0000			1.19939
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$		0			0
$550$	0.500000	+	0.866025i	0.0213201	+	0.0369274i
$551$		0			0
$552$	24.0000			1.02151
$553$		0			0
$554$	22.0000			0.934690
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	0.533165	−	0.846011i	$-0.321003\pi$
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	−0.999250	+	0.0387286i	$0.987669\pi$
$558$	−5.00000	+	8.66025i	−0.211667	+	0.366618i
$559$	48.0000			2.03018
$560$		0			0
$561$	8.00000			0.337760
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	16.0000	+	27.7128i	0.674320	+	1.16796i	0.976667	+	0.214758i	$0.0688963\pi$
$563$	16.0000	+	27.7128i	0.674320	+	1.16796i	−0.302348	+	0.953198i	$0.597770\pi$
$564$	−10.0000	−	17.3205i	−0.421076	−	0.729325i
$565$	18.0000	−	31.1769i	0.757266	−	1.31162i
$566$	4.00000			0.168133
$567$		0			0
$568$	36.0000			1.51053
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	16.0000			0.668410
$574$		0			0
$575$	4.00000			0.166812
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	0.990278	−	0.139100i	$-0.0444210\pi$
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	−0.615603	+	0.788056i	$0.711088\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	14.0000	−	24.2487i	0.581820	−	1.00774i
$580$	−12.0000			−0.498273
$581$		0			0
$582$	−20.0000			−0.829027
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$	−12.0000	−	20.7846i	−0.496564	−	0.860073i
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$	−2.00000			−0.0825488			−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000			−0.0825488			−0.0412744	+	0.999148i	$0.513142\pi$
$588$		0			0
$589$		0			0
$590$	2.00000	−	3.46410i	0.0823387	−	0.142615i
$591$	−22.0000	−	38.1051i	−0.904959	−	1.56744i
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	0.324337	+	0.945942i	$0.394859\pi$
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	−0.981378	+	0.192087i	$0.938474\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	10.0000			0.409616
$597$	18.0000	−	31.1769i	0.736691	−	1.27599i
$598$	8.00000	+	13.8564i	0.327144	+	0.566631i
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	0.994732	−	0.102511i	$-0.0326876\pi$
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	−0.586143	+	0.810208i	$0.699354\pi$
$600$	−3.00000	+	5.19615i	−0.122474	+	0.212132i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	4.00000	+	6.92820i	0.162489	+	0.281439i
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	−0.0998457	−	0.995003i	$-0.531835\pi$
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	0.911621	−	0.411033i	$-0.134832\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.0000	−	34.6410i	0.809113	−	1.40143i
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	−16.0000			−0.645182
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−14.0000	+	24.2487i	−0.563163	+	0.975426i
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	0.690365	−	0.723462i	$-0.257450\pi$
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	−0.971718	+	0.236143i	$0.924117\pi$
$620$	−10.0000	−	17.3205i	−0.401610	−	0.695608i
$621$	−8.00000	+	13.8564i	−0.321029	+	0.556038i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	−8.00000			−0.320256
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−1.00000	−	1.73205i	−0.0399680	−	0.0692267i
$627$		0			0
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	12.0000	−	20.7846i	0.477334	−	0.826767i
$633$	12.0000	+	20.7846i	0.476957	+	0.826114i
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$	12.0000			0.475831
$637$		0			0
$638$	−6.00000			−0.237542
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−3.00000	−	5.19615i	−0.118585	−	0.205396i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	11.0000	+	19.0526i	0.432455	+	0.749033i	0.997084	−	0.0763112i	$-0.0243142\pi$
$647$	11.0000	+	19.0526i	0.432455	+	0.749033i	−0.564629	+	0.825345i	$0.690981\pi$
$648$	−16.5000	−	28.5788i	−0.648181	−	1.12268i
$649$	−1.00000	+	1.73205i	−0.0392534	+	0.0679889i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	8.00000			0.313304
$653$	13.0000	−	22.5167i	0.508729	−	0.881145i	−0.491220	−	0.871036i	$-0.663449\pi$
$653$	13.0000	−	22.5167i	0.508729	−	0.881145i	0.999949	−	0.0101092i	$-0.00321793\pi$
$654$	14.0000	+	24.2487i	0.547443	+	0.948200i
$655$	12.0000	+	20.7846i	0.468879	+	0.812122i
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$	−8.00000			−0.312110
$658$		0			0
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$	−2.00000	+	3.46410i	−0.0778499	+	0.134840i
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$	−16.0000	+	27.7128i	−0.621389	+	1.07628i
$664$		0			0
$665$		0			0
$666$	−6.00000			−0.232495
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$		0			0
$669$	−22.0000	−	38.1051i	−0.850569	−	1.47323i
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$		0			0
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	1.50000	+	2.59808i	0.0576923	+	0.0999260i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$	36.0000			1.38257
$679$		0			0
$680$	24.0000			0.920358
$681$	−12.0000	+	20.7846i	−0.459841	+	0.796468i
$682$	−5.00000	−	8.66025i	−0.191460	−	0.331618i
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$		0			0
$685$	20.0000			0.764161
$686$		0			0
$687$	36.0000			1.37349
$688$	6.00000	−	10.3923i	0.228748	−	0.396203i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$	−8.00000	−	13.8564i	−0.304555	−	0.527504i
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.0181572	−	0.999835i	$-0.494220\pi$
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.856804	−	0.515642i	$-0.172447\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	4.00000			0.151838
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$	−18.0000	−	31.1769i	−0.682288	−	1.18176i
$697$	−8.00000	−	13.8564i	−0.303022	−	0.524849i
$698$		0			0
$699$	−36.0000			−1.36165
$700$		0			0
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$	8.00000	−	13.8564i	0.301941	−	0.522976i
$703$		0			0
$704$	−3.50000	−	6.06218i	−0.131911	−	0.228477i
$705$	−20.0000	+	34.6410i	−0.753244	+	1.30466i
$706$	−30.0000			−1.12906
$707$		0			0
$708$	−4.00000			−0.150329
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	−0.347325	−	0.937745i	$-0.612910\pi$
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	0.985773	−	0.168080i	$-0.0537568\pi$
$710$	−12.0000	−	20.7846i	−0.450352	−	0.780033i
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	−40.0000			−1.49801
$714$		0			0
$715$	−8.00000			−0.299183
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$	2.00000			0.0745356
$721$		0			0
$722$	−19.0000			−0.707107
$723$	20.0000	−	34.6410i	0.743808	−	1.28831i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−8.00000	+	13.8564i	−0.296093	+	0.512849i
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$733$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$734$	22.0000			0.812035
$735$		0			0
$736$	−20.0000			−0.737210
$737$	−4.00000	+	6.92820i	−0.147342	+	0.255204i
$738$	−2.00000	−	3.46410i	−0.0736210	−	0.127515i
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	0.900464	−	0.434930i	$-0.143227\pi$
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	−0.826893	+	0.562360i	$0.809894\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$		0			0
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$	30.0000	−	51.9615i	1.09985	−	1.90500i
$745$	−10.0000	−	17.3205i	−0.366372	−	0.634574i
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$	−4.00000			−0.146254
$749$		0			0
$750$	24.0000			0.876356
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$	2.00000	+	3.46410i	0.0728841	+	0.126239i
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$	32.0000			1.16460
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	4.00000	−	6.92820i	0.145287	−	0.251644i
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$	16.0000			0.579619
$763$		0			0
$764$	−8.00000			−0.289430
$765$	4.00000	−	6.92820i	0.144620	−	0.250490i
$766$	−1.00000	−	1.73205i	−0.0361315	−	0.0625815i
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$	17.0000	−	29.4449i	0.613435	−	1.06250i
$769$	32.0000			1.15395			0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000			1.15395			0.576975	+	0.816762i	$0.304233\pi$
$770$		0			0
$771$	−28.0000			−1.00840
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$	5.00000	−	8.66025i	0.179605	−	0.311086i
$776$	30.0000			1.07694
$777$		0			0
$778$	6.00000			0.215110
$779$		0			0
$780$	−8.00000	−	13.8564i	−0.286446	−	0.496139i
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	24.0000			0.857690
$784$		0			0
$785$	−28.0000			−0.999363
$786$	−12.0000	+	20.7846i	−0.428026	+	0.741362i
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	0.687481	−	0.726202i	$-0.258716\pi$
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	−0.972650	+	0.232275i	$0.925383\pi$
$788$	11.0000	+	19.0526i	0.391859	+	0.678719i
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$	−16.0000			−0.569254
$791$		0			0
$792$	−3.00000			−0.106600
$793$		0			0
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$	−12.0000	−	20.7846i	−0.425596	−	0.737154i
$796$	−9.00000	+	15.5885i	−0.318997	+	0.552518i
$797$	14.0000			0.495905			0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000			0.495905			0.247953	+	0.968772i	$0.420242\pi$
$798$		0			0
$799$	−40.0000			−1.41510
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	11.0000	+	19.0526i	0.388424	+	0.672769i
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$	−16.0000			−0.564276
$805$		0			0
$806$	40.0000			1.40894
$807$	−10.0000	+	17.3205i	−0.352017	+	0.609711i
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	−11.0000	+	19.0526i	−0.386501	+	0.669439i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$		0			0
$818$	24.0000			0.839140
$819$		0			0
$820$	8.00000			0.279372
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$	10.0000	+	17.3205i	0.348790	+	0.604122i
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	21.0000	−	36.3731i	0.731570	−	1.26712i
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$	−2.00000	+	3.46410i	−0.0695048	+	0.120386i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	−22.0000	+	38.1051i	−0.763172	+	1.32185i
$832$	28.0000			0.970725
$833$		0			0
$834$	−16.0000			−0.554035
$835$		0			0
$836$		0			0
$837$	20.0000	+	34.6410i	0.691301	+	1.19737i
$838$	−1.00000	+	1.73205i	−0.0345444	+	0.0598327i
$839$	34.0000			1.17381			0.586905	−	0.809656i	$-0.300346\pi$
$839$	34.0000			1.17381			0.586905	+	0.809656i	$0.300346\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$	−6.00000	−	10.3923i	−0.206529	−	0.357718i
$845$	3.00000	−	5.19615i	0.103203	−	0.178753i
$846$	−10.0000			−0.343807
$847$		0			0
$848$	6.00000			0.206041
$849$	−4.00000	+	6.92820i	−0.137280	+	0.237775i
$850$	2.00000	+	3.46410i	0.0685994	+	0.118818i
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	44.0000			1.50653			0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000			1.50653			0.753266	+	0.657716i	$0.228477\pi$
$854$		0			0
$855$		0			0
$856$	18.0000	−	31.1769i	0.615227	−	1.06561i
$857$	−28.0000	−	48.4974i	−0.956462	−	1.65664i	−0.730987	−	0.682391i	$-0.760940\pi$
$857$	−28.0000	−	48.4974i	−0.956462	−	1.65664i	−0.225475	−	0.974249i	$-0.572393\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	−3.00000	+	5.19615i	−0.102359	+	0.177290i	−0.912656	−	0.408729i	$-0.865972\pi$
$859$	−3.00000	+	5.19615i	−0.102359	+	0.177290i	0.810297	+	0.586019i	$0.199306\pi$
$860$	24.0000			0.818393
$861$		0			0
$862$		0			0
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	10.0000	+	17.3205i	0.340207	+	0.589256i
$865$	12.0000	+	20.7846i	0.408012	+	0.706698i
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	−2.00000			−0.0679236
$868$		0			0
$869$	8.00000			0.271381
$870$	−12.0000	+	20.7846i	−0.406838	+	0.704664i
$871$	−16.0000	−	27.7128i	−0.542139	−	0.939013i
$872$	−21.0000	−	36.3731i	−0.711150	−	1.23175i
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$		0			0
$875$		0			0
$876$	16.0000			0.540590
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	0.256064	+	0.966660i	$0.417574\pi$
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	−0.965184	+	0.261571i	$0.915759\pi$
$878$	10.0000	+	17.3205i	0.337484	+	0.584539i
$879$	24.0000	+	41.5692i	0.809500	+	1.40209i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−34.0000			−1.14549			−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000			−1.14549			−0.572745	+	0.819734i	$0.694121\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	8.00000	−	13.8564i	0.269069	−	0.466041i
$885$	4.00000	+	6.92820i	0.134459	+	0.232889i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	−0.529340	−	0.848410i	$-0.677561\pi$
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	0.999414	+	0.0342175i	$0.0108939\pi$
$888$	36.0000			1.20808
$889$		0			0
$890$	12.0000			0.402241
$891$	5.50000	−	9.52628i	0.184257	−	0.319142i
$892$	11.0000	+	19.0526i	0.368307	+	0.637927i
$893$		0			0
$894$	10.0000	−	17.3205i	0.334450	−	0.579284i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	−32.0000			−1.06845
$898$	5.00000	−	8.66025i	0.166852	−	0.288996i
$899$	30.0000	+	51.9615i	1.00056	+	1.73301i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	12.0000	−	20.7846i	0.399778	−	0.692436i
$902$	4.00000			0.133185
$903$		0			0
$904$	−54.0000			−1.79601
$905$	10.0000	−	17.3205i	0.332411	−	0.575753i
$906$	16.0000	+	27.7128i	0.531564	+	0.920697i
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	−4.00000			−0.132672
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$		0			0
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	−18.0000			−0.594737
$917$		0			0
$918$	−16.0000			−0.528079
$919$	−20.0000	+	34.6410i	−0.659739	+	1.14270i	0.320944	+	0.947098i	$0.396000\pi$
$919$	−20.0000	+	34.6410i	−0.659739	+	1.14270i	−0.980683	+	0.195603i	$0.937333\pi$
$920$	12.0000	+	20.7846i	0.395628	+	0.685248i
$921$	−20.0000	−	34.6410i	−0.659022	−	1.14146i
$922$		0			0
$923$	−48.0000			−1.57994
$924$		0			0
$925$	6.00000			0.197279
$926$	−2.00000	+	3.46410i	−0.0657241	+	0.113837i
$927$	−7.00000	−	12.1244i	−0.229910	−	0.398216i
$928$	15.0000	+	25.9808i	0.492399	+	0.852860i
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$	−40.0000			−1.31165
$931$		0			0
$932$	18.0000			0.589610
$933$	18.0000	−	31.1769i	0.589294	−	1.02069i
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$		0			0
$939$	4.00000			0.130535
$940$	10.0000	−	17.3205i	0.326164	−	0.564933i
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$	−14.0000	−	24.2487i	−0.456145	−	0.790066i
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	12.0000			0.390154
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$	8.00000	+	13.8564i	0.259828	+	0.450035i
$949$	16.0000	+	27.7128i	0.519382	+	0.899596i
$950$		0			0
$951$	−4.00000			−0.129709
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	3.00000	−	5.19615i	0.0971286	−	0.168232i
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$		0			0
$957$	6.00000	−	10.3923i	0.193952	−	0.335936i
$958$	−4.00000			−0.129234
$959$		0			0
$960$	−28.0000			−0.903696
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	12.0000	+	20.7846i	0.386896	+	0.670123i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	−10.0000	+	17.3205i	−0.322078	+	0.557856i
$965$	28.0000			0.901352
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	1.50000	−	2.59808i	0.0482118	−	0.0835053i
$969$		0			0
$970$	−10.0000	−	17.3205i	−0.321081	−	0.556128i
$971$	−7.00000	+	12.1244i	−0.224641	+	0.389089i	−0.956212	−	0.292676i	$-0.905454\pi$
$971$	−7.00000	+	12.1244i	−0.224641	+	0.389089i	0.731571	+	0.681765i	$0.238788\pi$
$972$	10.0000			0.320750
$973$		0			0
$974$	−28.0000			−0.897178
$975$	4.00000	−	6.92820i	0.128103	−	0.221880i
$976$		0			0
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	8.00000	−	13.8564i	0.255812	−	0.443079i
$979$	−6.00000			−0.191761
$980$		0			0
$981$	−14.0000			−0.446986
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	−27.0000	−	46.7654i	−0.861166	−	1.49158i	−0.870804	−	0.491630i	$-0.836401\pi$
$983$	−27.0000	−	46.7654i	−0.861166	−	1.49158i	0.00963785	−	0.999954i	$-0.496932\pi$
$984$	12.0000	+	20.7846i	0.382546	+	0.662589i
$985$	22.0000	−	38.1051i	0.700978	−	1.21413i
$986$	−24.0000			−0.764316
$987$		0			0
$988$		0			0
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	−0.901216	−	0.433370i	$-0.857324\pi$
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	0.0752991	−	0.997161i	$-0.476009\pi$
$992$	−25.0000	+	43.3013i	−0.793751	+	1.37482i
$993$	−40.0000			−1.26936
$994$		0			0
$995$	36.0000			1.14128
$996$		0			0
$997$	−10.0000	−	17.3205i	−0.316703	−	0.548546i	0.663095	−	0.748535i	$-0.269243\pi$
$997$	−10.0000	−	17.3205i	−0.316703	−	0.548546i	−0.979798	+	0.199989i	$0.935909\pi$
$998$	8.00000	+	13.8564i	0.253236	+	0.438617i
$999$	−12.0000	+	20.7846i	−0.379663	+	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.a.177.1		2
7.2	even	3		77.2.a.c.1.1	✓	1
7.3	odd	6		539.2.e.b.67.1		2
7.4	even	3	inner	539.2.e.a.67.1		2
7.5	odd	6		539.2.a.d.1.1		1
7.6	odd	2		539.2.e.b.177.1		2
21.2	odd	6		693.2.a.a.1.1		1
21.5	even	6		4851.2.a.a.1.1		1
28.19	even	6		8624.2.a.bc.1.1		1
28.23	odd	6		1232.2.a.a.1.1		1
35.2	odd	12		1925.2.b.d.1849.2		2
35.9	even	6		1925.2.a.c.1.1		1
35.23	odd	12		1925.2.b.d.1849.1		2
56.37	even	6		4928.2.a.g.1.1		1
56.51	odd	6		4928.2.a.bi.1.1		1
77.2	odd	30		847.2.f.k.323.1		4
77.9	even	15		847.2.f.e.323.1		4
77.16	even	15		847.2.f.e.729.1		4
77.30	odd	30		847.2.f.k.372.1		4
77.37	even	15		847.2.f.e.148.1		4
77.51	odd	30		847.2.f.k.148.1		4
77.54	even	6		5929.2.a.b.1.1		1
77.58	even	15		847.2.f.e.372.1		4
77.65	odd	6		847.2.a.a.1.1		1
77.72	odd	30		847.2.f.k.729.1		4
231.65	even	6		7623.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.c.1.1	✓	1	7.2	even	3
539.2.a.d.1.1		1	7.5	odd	6
539.2.e.a.67.1		2	7.4	even	3	inner
539.2.e.a.177.1		2	1.1	even	1	trivial
539.2.e.b.67.1		2	7.3	odd	6
539.2.e.b.177.1		2	7.6	odd	2
693.2.a.a.1.1		1	21.2	odd	6
847.2.a.a.1.1		1	77.65	odd	6
847.2.f.e.148.1		4	77.37	even	15
847.2.f.e.323.1		4	77.9	even	15
847.2.f.e.372.1		4	77.58	even	15
847.2.f.e.729.1		4	77.16	even	15
847.2.f.k.148.1		4	77.51	odd	30
847.2.f.k.323.1		4	77.2	odd	30
847.2.f.k.372.1		4	77.30	odd	30
847.2.f.k.729.1		4	77.72	odd	30
1232.2.a.a.1.1		1	28.23	odd	6
1925.2.a.c.1.1		1	35.9	even	6
1925.2.b.d.1849.1		2	35.23	odd	12
1925.2.b.d.1849.2		2	35.2	odd	12
4851.2.a.a.1.1		1	21.5	even	6
4928.2.a.g.1.1		1	56.37	even	6
4928.2.a.bi.1.1		1	56.51	odd	6
5929.2.a.b.1.1		1	77.54	even	6
7623.2.a.n.1.1		1	231.65	even	6
8624.2.a.bc.1.1		1	28.19	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} +4.00000 q^{13} -4.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +2.00000 q^{20} +1.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(3.00000 + 5.19615i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} -1.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(-4.00000 - 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{40} +4.00000 q^{41} +12.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(1.00000 + 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +(5.00000 - 8.66025i) q^{47} -2.00000 q^{48} -1.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(2.00000 + 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} -2.00000 q^{55} +(3.00000 - 5.19615i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.00000 - 3.46410i) q^{60} +10.0000 q^{62} +7.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(4.00000 + 6.92820i) q^{73} +(3.00000 + 5.19615i) q^{74} +(1.00000 - 1.73205i) q^{75} +8.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-2.00000 + 3.46410i) q^{82} -8.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} -2.00000 q^{90} +4.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-5.00000 + 8.66025i) q^{96} -10.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 8 q^{15} + q^{16} - 4 q^{17} - q^{18} + 4 q^{20} + 2 q^{22} + 4 q^{23} + 6 q^{24} + q^{25} - 4 q^{26} - 8 q^{27} - 12 q^{29} + 4 q^{30} - 10 q^{31} - 5 q^{32} - 2 q^{33} + 8 q^{34} - 2 q^{36} + 6 q^{37} - 8 q^{39} - 6 q^{40} + 8 q^{41} + 24 q^{43} + q^{44} + 2 q^{45} + 4 q^{46} + 10 q^{47} - 4 q^{48} - 2 q^{50} - 8 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 4 q^{55} + 6 q^{58} - 2 q^{59} - 4 q^{60} + 20 q^{62} + 14 q^{64} + 8 q^{65} - 2 q^{66} - 8 q^{67} + 4 q^{68} - 16 q^{69} - 24 q^{71} + 3 q^{72} + 8 q^{73} + 6 q^{74} + 2 q^{75} + 16 q^{78} - 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} - 16 q^{85} - 12 q^{86} + 12 q^{87} + 3 q^{88} + 6 q^{89} - 4 q^{90} + 8 q^{92} - 20 q^{93} + 10 q^{94} - 10 q^{96} - 20 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - q^9 + 2 * q^10 - q^11 + 2 * q^12 + 8 * q^13 - 8 * q^15 + q^16 - 4 * q^17 - q^18 + 4 * q^20 + 2 * q^22 + 4 * q^23 + 6 * q^24 + q^25 - 4 * q^26 - 8 * q^27 - 12 * q^29 + 4 * q^30 - 10 * q^31 - 5 * q^32 - 2 * q^33 + 8 * q^34 - 2 * q^36 + 6 * q^37 - 8 * q^39 - 6 * q^40 + 8 * q^41 + 24 * q^43 + q^44 + 2 * q^45 + 4 * q^46 + 10 * q^47 - 4 * q^48 - 2 * q^50 - 8 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 4 * q^55 + 6 * q^58 - 2 * q^59 - 4 * q^60 + 20 * q^62 + 14 * q^64 + 8 * q^65 - 2 * q^66 - 8 * q^67 + 4 * q^68 - 16 * q^69 - 24 * q^71 + 3 * q^72 + 8 * q^73 + 6 * q^74 + 2 * q^75 + 16 * q^78 - 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 - 16 * q^85 - 12 * q^86 + 12 * q^87 + 3 * q^88 + 6 * q^89 - 4 * q^90 + 8 * q^92 - 20 * q^93 + 10 * q^94 - 10 * q^96 - 20 * q^97 + 2 * q^99

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