LMFDB - Embedded newform 1470.2.n.e.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.86603 + 1.23205i) q^{10} +(0.866025 - 0.500000i) q^{12} +2.00000i q^{13} +(2.00000 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(1.00000 + 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(-6.92820 + 4.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000i q^{27} +8.00000 q^{29} +(-2.23205 + 0.133975i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +1.00000 q^{36} +(-5.19615 + 3.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.133975 + 2.23205i) q^{40} +10.0000 q^{41} -2.00000i q^{43} +(1.23205 + 1.86603i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-4.00000 + 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.00000i q^{57} +(-6.92820 + 4.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.86603 - 1.23205i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000i q^{62} -1.00000 q^{64} +(0.267949 + 4.46410i) q^{65} +(12.1244 + 7.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -8.00000 q^{69} +6.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(3.00000 - 5.19615i) q^{74} +(4.59808 + 1.96410i) q^{75} +2.00000 q^{76} -2.00000i q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -12.0000i q^{83} +(4.00000 + 2.00000i) q^{85} +(1.00000 + 1.73205i) q^{86} +(6.92820 + 4.00000i) q^{87} +(-7.00000 - 12.1244i) q^{89} +(-2.00000 - 1.00000i) q^{90} +8.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.00000 - 5.19615i) q^{94} +(2.46410 + 3.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} +14.0000i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 4 q^{10} + 8 q^{15} - 2 q^{16} + 4 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} - 4 q^{26} + 32 q^{29} - 2 q^{30} - 8 q^{31} - 8 q^{34} + 4 q^{36} - 4 q^{39} + 4 q^{40} + 40 q^{41} - 2 q^{45} + 16 q^{46} - 16 q^{50} + 4 q^{51} - 2 q^{54} + 24 q^{59} + 4 q^{60} - 4 q^{61} - 4 q^{64} + 8 q^{65} - 32 q^{69} + 24 q^{71} + 12 q^{74} + 8 q^{75} + 8 q^{76} + 8 q^{79} + 2 q^{80} - 2 q^{81} + 16 q^{85} + 4 q^{86} - 28 q^{89} - 8 q^{90} + 12 q^{94} - 4 q^{95} + 2 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 4 * q^10 + 8 * q^15 - 2 * q^16 + 4 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 - 4 * q^26 + 32 * q^29 - 2 * q^30 - 8 * q^31 - 8 * q^34 + 4 * q^36 - 4 * q^39 + 4 * q^40 + 40 * q^41 - 2 * q^45 + 16 * q^46 - 16 * q^50 + 4 * q^51 - 2 * q^54 + 24 * q^59 + 4 * q^60 - 4 * q^61 - 4 * q^64 + 8 * q^65 - 32 * q^69 + 24 * q^71 + 12 * q^74 + 8 * q^75 + 8 * q^76 + 8 * q^79 + 2 * q^80 - 2 * q^81 + 16 * q^85 + 4 * q^86 - 28 * q^89 - 8 * q^90 + 12 * q^94 - 4 * q^95 + 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.86603	+	1.23205i	−0.590089	+	0.389609i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$	2.00000	+	1.00000i	0.516398	+	0.258199i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$		0			0
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.998154	−	0.0607377i	$-0.980655\pi$
$23$	−6.92820	+	4.00000i	−1.44463	+	0.834058i	−0.446476	+	0.894795i	$0.647321\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$	−2.23205	+	0.133975i	−0.407515	+	0.0244603i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−5.19615	+	3.00000i	−0.854242	+	0.493197i	−0.862080	−	0.506772i	$-0.830838\pi$
$37$	−5.19615	+	3.00000i	−0.854242	+	0.493197i	0.00783774	+	0.999969i	$0.497505\pi$
$38$	−1.73205	−	1.00000i	−0.280976	−	0.162221i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	0.133975	+	2.23205i	0.0211832	+	0.352918i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$		0			0
$45$	1.23205	+	1.86603i	0.183663	+	0.278171i
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	−5.19615	+	3.00000i	−0.757937	+	0.437595i	−0.828554	−	0.559908i	$-0.810836\pi$
$47$	−5.19615	+	3.00000i	−0.757937	+	0.437595i	0.0706177	+	0.997503i	$0.477503\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	1.73205	+	1.00000i	0.240192	+	0.138675i
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	0.812447	−	0.583036i	$-0.198135\pi$
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	−0.0987002	+	0.995117i	$0.531468\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$		0			0
$57$			2.00000i			0.264906i
$58$	−6.92820	+	4.00000i	−0.909718	+	0.525226i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	1.86603	−	1.23205i	0.240903	−	0.159057i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		−	4.00000i		−	0.508001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.267949	+	4.46410i	0.0332350	+	0.553704i
$66$		0			0
$67$	12.1244	+	7.00000i	1.48123	+	0.855186i	0.999773	−	0.0212861i	$-0.00677610\pi$
$67$	12.1244	+	7.00000i	1.48123	+	0.855186i	0.481452	+	0.876472i	$0.340109\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	4.59808	+	1.96410i	0.530940	+	0.226795i
$76$	2.00000			0.229416
$77$		0			0
$78$		−	2.00000i		−	0.226455i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.23205	−	1.86603i	−0.137747	−	0.208628i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−8.66025	+	5.00000i	−0.956365	+	0.552158i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	6.92820	+	4.00000i	0.742781	+	0.428845i
$88$		0			0
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$		0			0
$92$			8.00000i			0.834058i
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	2.46410	+	3.73205i	0.252811	+	0.382900i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$		0			0
$99$		0			0
$100$	1.96410	−	4.59808i	0.196410	−	0.459808i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−1.73205	−	1.00000i	−0.171499	−	0.0990148i
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	−0.319531	−	0.947576i	$-0.603525\pi$
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	0.660859	+	0.750510i	$0.270192\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$		−	10.0000i		−	0.940721i	−0.882474	−	0.470360i	$-0.844124\pi$
$113$		−	10.0000i		−	0.940721i	0.882474	−	0.470360i	$-0.155876\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−14.9282	+	9.85641i	−1.39206	+	0.919115i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$	−1.73205	+	1.00000i	−0.160128	+	0.0924500i
$118$			12.0000i			1.10469i
$119$		0			0
$120$	−1.00000	+	2.00000i	−0.0912871	+	0.182574i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	1.73205	+	1.00000i	0.156813	+	0.0905357i
$123$	8.66025	+	5.00000i	0.780869	+	0.450835i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	−2.46410	−	3.73205i	−0.216116	−	0.327323i
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	0.636676	−	0.771132i	$-0.280309\pi$
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	−0.986157	+	0.165812i	$0.946976\pi$
$132$		0			0
$133$		0			0
$134$	−14.0000			−1.20942
$135$	0.133975	+	2.23205i	0.0115307	+	0.192104i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	1.73205	+	1.00000i	0.147979	+	0.0854358i	0.572161	−	0.820141i	$-0.306105\pi$
$137$	1.73205	+	1.00000i	0.147979	+	0.0854358i	−0.424182	+	0.905577i	$0.639438\pi$
$138$	6.92820	−	4.00000i	0.589768	−	0.340503i
$139$	−22.0000			−1.86602			−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000			−1.86602			−0.933008	+	0.359856i	$0.882826\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$		0			0
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	17.8564	−	1.07180i	1.48289	−	0.0890079i
$146$	10.0000			0.827606
$147$		0			0
$148$			6.00000i			0.493197i
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	0.906249	+	0.422744i	$0.138933\pi$
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	−0.0870170	+	0.996207i	$0.527733\pi$
$150$	−4.96410	+	0.598076i	−0.405317	+	0.0488327i
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	−1.73205	+	1.00000i	−0.140488	+	0.0811107i
$153$			2.00000i			0.161690i
$154$		0			0
$155$	−4.00000	+	8.00000i	−0.321288	+	0.642575i
$156$	1.00000	+	1.73205i	0.0800641	+	0.138675i
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	0.429289	−	0.903167i	$-0.358764\pi$
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	−0.567521	+	0.823359i	$0.692098\pi$
$158$	−3.46410	−	2.00000i	−0.275589	−	0.159111i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−1.73205	+	1.00000i	−0.135665	+	0.0783260i	−0.566296	−	0.824202i	$-0.691624\pi$
$163$	−1.73205	+	1.00000i	−0.135665	+	0.0783260i	0.430632	+	0.902528i	$0.358291\pi$
$164$	5.00000	−	8.66025i	0.390434	−	0.676252i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−4.46410	+	0.267949i	−0.342381	+	0.0205508i
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$	−8.00000			−0.606478
$175$		0			0
$176$		0			0
$177$	10.3923	−	6.00000i	0.781133	−	0.450988i
$178$	12.1244	+	7.00000i	0.908759	+	0.524672i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	2.23205	−	0.133975i	0.166367	−	0.00998588i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	−11.1962	+	7.39230i	−0.823157	+	0.543493i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$		0			0
$188$			6.00000i			0.437595i
$189$		0			0
$190$	−4.00000	−	2.00000i	−0.290191	−	0.145095i
$191$	−11.0000	−	19.0526i	−0.795932	−	1.37859i	−0.922246	−	0.386604i	$-0.873648\pi$
$191$	−11.0000	−	19.0526i	−0.795932	−	1.37859i	0.126314	−	0.991990i	$-0.459685\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.276296	−	0.961073i	$-0.589107\pi$
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.970461	+	0.241257i	$0.922440\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$	−2.00000	+	4.00000i	−0.143223	+	0.286446i
$196$		0			0
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$		0			0
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$	7.00000	+	12.1244i	0.493742	+	0.855186i
$202$			6.00000i			0.422159i
$203$		0			0
$204$	2.00000			0.140028
$205$	22.3205	−	1.33975i	1.55893	−	0.0935719i
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$	−6.92820	−	4.00000i	−0.481543	−	0.278019i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$	5.19615	+	3.00000i	0.356034	+	0.205557i
$214$		0			0
$215$	−0.267949	−	4.46410i	−0.0182740	−	0.304449i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	2.00000i		−	0.135457i
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	5.19615	−	3.00000i	0.348743	−	0.201347i
$223$		−	20.0000i		−	1.33930i	−0.742677	−	0.669650i	$-0.766444\pi$
$223$		−	20.0000i		−	1.33930i	0.742677	−	0.669650i	$-0.233556\pi$
$224$		0			0
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	13.8564	+	8.00000i	0.919682	+	0.530979i	0.883534	−	0.468368i	$-0.155158\pi$
$227$	13.8564	+	8.00000i	0.919682	+	0.530979i	0.0361484	+	0.999346i	$0.488491\pi$
$228$	1.73205	+	1.00000i	0.114708	+	0.0662266i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	8.00000	−	16.0000i	0.527504	−	1.05501i
$231$		0			0
$232$			8.00000i			0.525226i
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	−0.0471787	−	0.998886i	$-0.515023\pi$
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	0.841472	+	0.540301i	$0.181690\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−11.1962	+	7.39230i	−0.730356	+	0.482221i
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$			4.00000i			0.259828i
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$	−0.133975	−	2.23205i	−0.00864802	−	0.144078i
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	0.162930	+	0.986638i	$0.447905\pi$
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	−0.935918	+	0.352217i	$0.885428\pi$
$242$	−9.52628	−	5.50000i	−0.612372	−	0.353553i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−10.0000			−0.637577
$247$	−3.46410	+	2.00000i	−0.220416	+	0.127257i
$248$	−3.46410	−	2.00000i	−0.219971	−	0.127000i
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$	−8.52628	+	7.23205i	−0.539249	+	0.457395i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$		0			0
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	2.46410	+	3.73205i	0.154308	+	0.233710i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−25.9808	+	15.0000i	−1.62064	+	0.935674i	−0.633885	+	0.773427i	$0.718541\pi$
$257$	−25.9808	+	15.0000i	−1.62064	+	0.935674i	−0.986750	+	0.162247i	$0.948126\pi$
$258$			2.00000i			0.124515i
$259$		0			0
$260$	4.00000	+	2.00000i	0.248069	+	0.124035i
$261$	4.00000	+	6.92820i	0.247594	+	0.428845i
$262$	6.92820	+	4.00000i	0.428026	+	0.247121i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	12.0000	+	6.00000i	0.737154	+	0.368577i
$266$		0			0
$267$		−	14.0000i		−	0.856786i
$268$	12.1244	−	7.00000i	0.740613	−	0.427593i
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.107031	−	0.994256i	$-0.465866\pi$
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.807535	−	0.589819i	$-0.200801\pi$
$270$	−1.23205	−	1.86603i	−0.0749802	−	0.113563i
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	−2.00000			−0.120824
$275$		0			0
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	0.551131	−	0.834419i	$-0.314196\pi$
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	−0.447062	+	0.894503i	$0.647530\pi$
$278$	19.0526	−	11.0000i	1.14270	−	0.659736i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	5.19615	−	3.00000i	0.309426	−	0.178647i
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.112728	−	0.993626i	$-0.535959\pi$
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.916869	+	0.399188i	$0.869292\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	0.267949	+	4.46410i	0.0158719	+	0.264431i
$286$		0			0
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−14.9282	+	9.85641i	−0.876614	+	0.578788i
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	−8.66025	+	5.00000i	−0.506803	+	0.292603i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	12.0000	−	24.0000i	0.698667	−	1.39733i
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	−17.3205	−	10.0000i	−1.00335	−	0.579284i
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$		0			0
$302$		−	20.0000i		−	1.15087i
$303$	5.19615	−	3.00000i	0.298511	−	0.172345i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	−2.46410	−	3.73205i	−0.141094	−	0.213697i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	−0.535898	−	8.92820i	−0.0304370	−	0.507088i
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$	−1.73205	−	1.00000i	−0.0980581	−	0.0566139i
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	−0.345907	−	0.938269i	$-0.612429\pi$
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	0.639611	+	0.768699i	$0.279095\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	4.00000			0.225018
$317$	29.4449	−	17.0000i	1.65379	−	0.954815i	0.678294	−	0.734791i	$-0.262720\pi$
$317$	29.4449	−	17.0000i	1.65379	−	0.954815i	0.975494	−	0.220024i	$-0.0706137\pi$
$318$	−5.19615	−	3.00000i	−0.291386	−	0.168232i
$319$		0			0
$320$	−2.23205	+	0.133975i	−0.124775	+	0.00748941i
$321$		0			0
$322$		0			0
$323$			4.00000i			0.222566i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	1.19615	+	9.92820i	0.0663506	+	0.550718i
$326$	1.00000	−	1.73205i	0.0553849	−	0.0959294i
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$			10.0000i			0.552158i
$329$		0			0
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	−10.3923	−	6.00000i	−0.570352	−	0.329293i
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	1.00000	+	1.73205i	0.0547176	+	0.0947736i
$335$	28.0000	+	14.0000i	1.52980	+	0.764902i
$336$		0			0
$337$		−	12.0000i		−	0.653682i	−0.945079	−	0.326841i	$-0.894016\pi$
$337$		−	12.0000i		−	0.653682i	0.945079	−	0.326841i	$-0.105984\pi$
$338$	−7.79423	+	4.50000i	−0.423950	+	0.244768i
$339$	5.00000	−	8.66025i	0.271563	−	0.470360i
$340$	3.73205	−	2.46410i	0.202399	−	0.133635i
$341$		0			0
$342$		−	2.00000i		−	0.108148i
$343$		0			0
$344$	2.00000			0.107833
$345$	−17.8564	+	1.07180i	−0.961357	+	0.0577036i
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	−24.2487	−	14.0000i	−1.30174	−	0.751559i	−0.321037	−	0.947067i	$-0.604031\pi$
$347$	−24.2487	−	14.0000i	−1.30174	−	0.751559i	−0.980702	+	0.195507i	$0.937365\pi$
$348$	6.92820	−	4.00000i	0.371391	−	0.214423i
$349$	−30.0000			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	0.355303	−	0.934751i	$-0.384378\pi$
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	−0.631867	+	0.775077i	$0.717711\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	13.3923	−	0.803848i	0.710790	−	0.0426638i
$356$	−14.0000			−0.741999
$357$		0			0
$358$		−	12.0000i		−	0.634220i
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	0.620033	−	0.784576i	$-0.287119\pi$
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	−0.989479	+	0.144677i	$0.953786\pi$
$360$	−1.86603	+	1.23205i	−0.0983482	+	0.0649348i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−1.73205	+	1.00000i	−0.0910346	+	0.0525588i
$363$			11.0000i			0.577350i
$364$		0			0
$365$	−20.0000	−	10.0000i	−1.04685	−	0.523424i
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$	6.92820	+	4.00000i	0.361158	+	0.208514i
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	6.00000	−	12.0000i	0.311925	−	0.623850i
$371$		0			0
$372$			4.00000i			0.207390i
$373$	19.0526	−	11.0000i	0.986504	−	0.569558i	0.0822766	−	0.996610i	$-0.473781\pi$
$373$	19.0526	−	11.0000i	0.986504	−	0.569558i	0.904227	+	0.427051i	$0.140448\pi$
$374$		0			0
$375$	10.5263	+	3.76795i	0.543575	+	0.194576i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$			16.0000i			0.824042i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	4.46410	−	0.267949i	0.229004	−	0.0137455i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	19.0526	+	11.0000i	0.974814	+	0.562809i
$383$	−22.5167	+	13.0000i	−1.15055	+	0.664269i	−0.949021	−	0.315214i	$-0.897924\pi$
$383$	−22.5167	+	13.0000i	−1.15055	+	0.664269i	−0.201527	+	0.979483i	$0.564590\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	20.0000			1.01797
$387$	1.73205	−	1.00000i	0.0880451	−	0.0508329i
$388$	12.1244	+	7.00000i	0.615521	+	0.355371i
$389$	−2.00000	+	3.46410i	−0.101404	+	0.175637i	−0.912263	−	0.409604i	$-0.865667\pi$
$389$	−2.00000	+	3.46410i	−0.101404	+	0.175637i	0.810859	+	0.585241i	$0.199000\pi$
$390$	−0.267949	−	4.46410i	−0.0135681	−	0.226049i
$391$	−16.0000			−0.809155
$392$		0			0
$393$		−	8.00000i		−	0.403547i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	4.92820	+	7.46410i	0.247965	+	0.375560i
$396$		0			0
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.976392	−	0.216004i	$-0.0693024\pi$
$398$			16.0000i			0.802008i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	0.713751	−	0.700399i	$-0.246995\pi$
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	−0.963439	+	0.267927i	$0.913661\pi$
$402$	−12.1244	−	7.00000i	−0.604708	−	0.349128i
$403$	−6.92820	−	4.00000i	−0.345118	−	0.199254i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$		0			0
$407$		0			0
$408$	−1.73205	+	1.00000i	−0.0857493	+	0.0495074i
$409$	12.0000	−	20.7846i	0.593362	−	1.02773i	−0.400414	−	0.916334i	$-0.631134\pi$
$409$	12.0000	−	20.7846i	0.593362	−	1.02773i	0.993776	−	0.111398i	$-0.0355330\pi$
$410$	−18.6603	+	12.3205i	−0.921564	+	0.608467i
$411$	1.00000	+	1.73205i	0.0493264	+	0.0854358i
$412$		−	4.00000i		−	0.197066i
$413$		0			0
$414$	8.00000			0.393179
$415$	−1.60770	−	26.7846i	−0.0789187	−	1.31480i
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	−19.0526	−	11.0000i	−0.933008	−	0.538672i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−18.0000			−0.877266			−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	3.46410	−	2.00000i	0.168630	−	0.0973585i
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$	−6.00000			−0.290701
$427$		0			0
$428$		0			0
$429$		0			0
$430$	2.46410	+	3.73205i	0.118830	+	0.179975i
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	−0.720113	−	0.693857i	$-0.755910\pi$
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	0.960954	+	0.276707i	$0.0892433\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		0			0
$435$	16.0000	+	8.00000i	0.767141	+	0.383571i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−13.8564	−	8.00000i	−0.662842	−	0.382692i
$438$	8.66025	+	5.00000i	0.413803	+	0.238909i
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	−0.872795	−	0.488087i	$-0.837695\pi$
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	0.0137020	−	0.999906i	$-0.495638\pi$
$440$		0			0
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	−0.415445	−	0.909618i	$-0.636374\pi$
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	0.580030	+	0.814595i	$0.303041\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	−17.2487	−	26.1244i	−0.817667	−	1.23841i
$446$	10.0000	+	17.3205i	0.473514	+	0.820150i
$447$			20.0000i			0.945968i
$448$		0			0
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$	−4.59808	−	1.96410i	−0.216755	−	0.0925886i
$451$		0			0
$452$	−8.66025	−	5.00000i	−0.407344	−	0.235180i
$453$	−17.3205	+	10.0000i	−0.813788	+	0.469841i
$454$	−16.0000			−0.750917
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.979772	−	0.200118i	$-0.935868\pi$
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.316579	+	0.948566i	$0.602534\pi$
$458$	8.66025	+	5.00000i	0.404667	+	0.233635i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	1.07180	+	17.8564i	0.0499728	+	0.832559i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$	−7.46410	+	4.92820i	−0.346139	+	0.228540i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	31.1769	−	18.0000i	1.44270	−	0.832941i	0.444667	−	0.895696i	$-0.353322\pi$
$467$	31.1769	−	18.0000i	1.44270	−	0.832941i	0.998029	+	0.0627555i	$0.0199888\pi$
$468$			2.00000i			0.0924500i
$469$		0			0
$470$	6.00000	−	12.0000i	0.276759	−	0.553519i
$471$	−1.00000	−	1.73205i	−0.0460776	−	0.0798087i
$472$	10.3923	+	6.00000i	0.478345	+	0.276172i
$473$		0			0
$474$	−2.00000	−	3.46410i	−0.0918630	−	0.159111i
$475$	6.00000	+	8.00000i	0.275299	+	0.367065i
$476$		0			0
$477$			6.00000i			0.274721i
$478$	15.5885	−	9.00000i	0.712999	−	0.411650i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	1.23205	+	1.86603i	0.0562352	+	0.0851720i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$		−	24.0000i		−	1.09317i
$483$		0			0
$484$	11.0000			0.500000
$485$	1.87564	+	31.2487i	0.0851686	+	1.41893i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.972253	−	0.233933i	$-0.0751596\pi$
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.283535	+	0.958962i	$0.408493\pi$
$488$	1.73205	−	1.00000i	0.0784063	−	0.0452679i
$489$	−2.00000			−0.0904431
$490$		0			0
$491$	−4.00000			−0.180517			−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000			−0.180517			−0.0902587	+	0.995918i	$0.528769\pi$
$492$	8.66025	−	5.00000i	0.390434	−	0.225417i
$493$	13.8564	+	8.00000i	0.624061	+	0.360302i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$			12.0000i			0.537733i
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	3.76795	−	10.5263i	0.168508	−	0.470750i
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$	−20.7846	+	12.0000i	−0.927663	+	0.535586i
$503$			26.0000i			1.15928i	0.814872	+	0.579641i	$0.196807\pi$
$503$			26.0000i			1.15928i	−0.814872	+	0.579641i	$0.803193\pi$
$504$		0			0
$505$	6.00000	−	12.0000i	0.266996	−	0.533993i
$506$		0			0
$507$	7.79423	+	4.50000i	0.346154	+	0.199852i
$508$	6.92820	+	4.00000i	0.307389	+	0.177471i
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$	−4.00000	−	2.00000i	−0.177123	−	0.0885615i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.73205	+	1.00000i	−0.0764719	+	0.0441511i
$514$	15.0000	−	25.9808i	0.661622	−	1.14596i
$515$	7.46410	−	4.92820i	0.328908	−	0.217163i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$	−4.46410	+	0.267949i	−0.195764	+	0.0117503i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	−6.92820	−	4.00000i	−0.303239	−	0.175075i
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	−0.573822	−	0.818980i	$-0.694540\pi$
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	0.422347	+	0.906434i	$0.361206\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$		0			0
$527$	−6.92820	+	4.00000i	−0.301797	+	0.174243i
$528$		0			0
$529$	20.5000	−	35.5070i	0.891304	−	1.54378i
$530$	−13.3923	+	0.803848i	−0.581725	+	0.0349169i
$531$	12.0000			0.520756
$532$		0			0
$533$			20.0000i			0.866296i
$534$	7.00000	+	12.1244i	0.302920	+	0.524672i
$535$		0			0
$536$	−7.00000	+	12.1244i	−0.302354	+	0.523692i
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$			30.0000i			1.29339i
$539$		0			0
$540$	2.00000	+	1.00000i	0.0860663	+	0.0430331i
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	0.984325	+	0.176367i	$0.0564345\pi$
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	−0.339424	+	0.940633i	$0.610232\pi$
$542$	−17.3205	−	10.0000i	−0.743980	−	0.429537i
$543$	1.73205	+	1.00000i	0.0743294	+	0.0429141i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	−2.00000	+	4.00000i	−0.0856706	+	0.171341i
$546$		0			0
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	1.73205	−	1.00000i	0.0739895	−	0.0427179i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	8.00000	+	13.8564i	0.340811	+	0.590303i
$552$		−	8.00000i		−	0.340503i
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	−13.3923	+	0.803848i	−0.568472	+	0.0341214i
$556$	−11.0000	+	19.0526i	−0.466504	+	0.808008i
$557$	−15.5885	−	9.00000i	−0.660504	−	0.381342i	0.131965	−	0.991254i	$-0.457871\pi$
$557$	−15.5885	−	9.00000i	−0.660504	−	0.381342i	−0.792469	+	0.609912i	$0.791205\pi$
$558$	3.46410	−	2.00000i	0.146647	−	0.0846668i
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	−15.5885	+	9.00000i	−0.657559	+	0.379642i
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.00664037	−	0.999978i	$-0.502114\pi$
$563$	−20.7846	−	12.0000i	−0.875967	−	0.505740i	−0.869326	+	0.494238i	$0.835447\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−1.33975	−	22.3205i	−0.0563635	−	0.939031i
$566$	20.0000			0.840663
$567$		0			0
$568$			6.00000i			0.251754i
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$	−2.46410	−	3.73205i	−0.103210	−	0.156318i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$		0			0
$573$		−	22.0000i		−	0.919063i
$574$		0			0
$575$	−32.0000	+	24.0000i	−1.33449	+	1.00087i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−22.5167	−	13.0000i	−0.937381	−	0.541197i	−0.0482425	−	0.998836i	$-0.515362\pi$
$577$	−22.5167	−	13.0000i	−0.937381	−	0.541197i	−0.889138	+	0.457639i	$0.848695\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	−10.0000	−	17.3205i	−0.415586	−	0.719816i
$580$	8.00000	−	16.0000i	0.332182	−	0.664364i
$581$		0			0
$582$		−	14.0000i		−	0.580319i
$583$		0			0
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$	−3.73205	+	2.46410i	−0.154301	+	0.101878i
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$	1.60770	+	26.7846i	0.0661878	+	1.10270i
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	5.19615	+	3.00000i	0.213561	+	0.123299i
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	−0.727841	−	0.685746i	$-0.759476\pi$
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	0.229953	+	0.973202i	$0.426143\pi$
$594$		0			0
$595$		0			0
$596$	20.0000			0.819232
$597$	13.8564	−	8.00000i	0.567105	−	0.327418i
$598$	13.8564	+	8.00000i	0.566631	+	0.327144i
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	0.275714	+	0.961240i	$0.411086\pi$
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	−0.970315	+	0.241845i	$0.922248\pi$
$600$	−1.96410	+	4.59808i	−0.0801841	+	0.187716i
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$			14.0000i			0.570124i
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	13.5526	+	20.5263i	0.550990	+	0.834512i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	10.3923	−	6.00000i	0.421811	−	0.243532i	−0.274041	−	0.961718i	$-0.588360\pi$
$607$	10.3923	−	6.00000i	0.421811	−	0.243532i	0.695852	+	0.718186i	$0.255027\pi$
$608$			2.00000i			0.0811107i
$609$		0			0
$610$	4.00000	+	2.00000i	0.161955	+	0.0809776i
$611$	−6.00000	−	10.3923i	−0.242734	−	0.420428i
$612$	1.73205	+	1.00000i	0.0700140	+	0.0404226i
$613$	8.66025	+	5.00000i	0.349784	+	0.201948i	0.664590	−	0.747208i	$-0.268606\pi$
$613$	8.66025	+	5.00000i	0.349784	+	0.201948i	−0.314806	+	0.949156i	$0.601939\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$	20.0000	+	10.0000i	0.806478	+	0.403239i
$616$		0			0
$617$		−	6.00000i		−	0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$		−	6.00000i		−	0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$	−3.46410	+	2.00000i	−0.139347	+	0.0804518i
$619$	−11.0000	+	19.0526i	−0.442127	+	0.765787i	−0.997847	−	0.0655827i	$-0.979109\pi$
$619$	−11.0000	+	19.0526i	−0.442127	+	0.765787i	0.555720	+	0.831370i	$0.312443\pi$
$620$	4.92820	+	7.46410i	0.197921	+	0.299766i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$		−	8.00000i		−	0.320771i
$623$		0			0
$624$	2.00000			0.0800641
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	−1.73205	+	1.00000i	−0.0691164	+	0.0399043i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	−3.46410	+	2.00000i	−0.137795	+	0.0795557i
$633$	−3.46410	−	2.00000i	−0.137686	−	0.0794929i
$634$	−17.0000	+	29.4449i	−0.675156	+	1.16940i
$635$	1.07180	+	17.8564i	0.0425330	+	0.708610i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	1.86603	−	1.23205i	0.0737611	−	0.0487011i
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	−0.0690201	−	0.997615i	$-0.521987\pi$
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	0.898470	−	0.439034i	$-0.144679\pi$
$642$		0			0
$643$		−	36.0000i		−	1.41970i	−0.704352	−	0.709851i	$-0.748762\pi$
$643$		−	36.0000i		−	1.41970i	0.704352	−	0.709851i	$-0.251238\pi$
$644$		0			0
$645$	2.00000	−	4.00000i	0.0787499	−	0.157500i
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	12.1244	+	7.00000i	0.476658	+	0.275198i	0.719023	−	0.694987i	$-0.244590\pi$
$647$	12.1244	+	7.00000i	0.476658	+	0.275198i	−0.242365	+	0.970185i	$0.577923\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$		0			0
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$			2.00000i			0.0783260i
$653$	−12.1244	+	7.00000i	−0.474463	+	0.273931i	−0.718106	−	0.695934i	$-0.754991\pi$
$653$	−12.1244	+	7.00000i	−0.474463	+	0.273931i	0.243643	+	0.969865i	$0.421657\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	−9.85641	−	14.9282i	−0.385122	−	0.583293i
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$		−	10.0000i		−	0.390137i
$658$		0			0
$659$	−16.0000			−0.623272			−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000			−0.623272			−0.311636	+	0.950202i	$0.600877\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$	24.2487	+	14.0000i	0.942453	+	0.544125i
$663$	−3.46410	+	2.00000i	−0.134535	+	0.0776736i
$664$	12.0000			0.465690
$665$		0			0
$666$	6.00000			0.232495
$667$	−55.4256	+	32.0000i	−2.14609	+	1.23904i
$668$	−1.73205	−	1.00000i	−0.0670151	−	0.0386912i
$669$	10.0000	−	17.3205i	0.386622	−	0.669650i
$670$	−31.2487	+	1.87564i	−1.20724	+	0.0724625i
$671$		0			0
$672$		0			0
$673$			20.0000i			0.770943i	0.922720	+	0.385472i	$0.125961\pi$
$673$			20.0000i			0.770943i	−0.922720	+	0.385472i	$0.874039\pi$
$674$	6.00000	+	10.3923i	0.231111	+	0.400297i
$675$	0.598076	+	4.96410i	0.0230200	+	0.191068i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	−0.286820	−	0.957984i	$-0.592598\pi$
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	0.686229	+	0.727386i	$0.259265\pi$
$678$			10.0000i			0.384048i
$679$		0			0
$680$	−2.00000	+	4.00000i	−0.0766965	+	0.153393i
$681$	8.00000	+	13.8564i	0.306561	+	0.530979i
$682$		0			0
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	0.841825	−	0.539750i	$-0.181481\pi$
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	−0.0465244	+	0.998917i	$0.514815\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	4.00000	+	2.00000i	0.152832	+	0.0764161i
$686$		0			0
$687$		−	10.0000i		−	0.381524i
$688$	−1.73205	+	1.00000i	−0.0660338	+	0.0381246i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$	14.9282	−	9.85641i	0.568307	−	0.375227i
$691$	−17.0000	−	29.4449i	−0.646710	−	1.12014i	−0.983904	−	0.178700i	$-0.942811\pi$
$691$	−17.0000	−	29.4449i	−0.646710	−	1.12014i	0.337193	−	0.941435i	$-0.390522\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	28.0000			1.06287
$695$	−49.1051	+	2.94744i	−1.86266	+	0.111803i
$696$	−4.00000	+	6.92820i	−0.151620	+	0.262613i
$697$	17.3205	+	10.0000i	0.656061	+	0.378777i
$698$	25.9808	−	15.0000i	0.983386	−	0.567758i
$699$	14.0000			0.529529
$700$		0			0
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$	1.73205	−	1.00000i	0.0653720	−	0.0377426i
$703$	−10.3923	−	6.00000i	−0.391953	−	0.226294i
$704$		0			0
$705$	−13.3923	+	0.803848i	−0.504383	+	0.0302747i
$706$	6.00000			0.225813
$707$		0			0
$708$		−	12.0000i		−	0.450988i
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	−11.1962	+	7.39230i	−0.420184	+	0.277428i
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	12.1244	−	7.00000i	0.454379	−	0.262336i
$713$		−	32.0000i		−	1.19841i
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	−15.5885	−	9.00000i	−0.582162	−	0.336111i
$718$	12.1244	+	7.00000i	0.452477	+	0.261238i
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$		0			0
$722$			15.0000i			0.558242i
$723$	−20.7846	+	12.0000i	−0.772988	+	0.446285i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	39.7128	−	4.78461i	1.47490	−	0.177696i
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$		−	36.0000i		−	1.33517i	−0.744535	−	0.667583i	$-0.767329\pi$
$727$		−	36.0000i		−	1.33517i	0.744535	−	0.667583i	$-0.232671\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	22.3205	−	1.33975i	0.826119	−	0.0495862i
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$	−1.73205	−	1.00000i	−0.0640184	−	0.0369611i
$733$	1.73205	−	1.00000i	0.0639748	−	0.0369358i	−0.467671	−	0.883902i	$-0.654907\pi$
$733$	1.73205	−	1.00000i	0.0639748	−	0.0369358i	0.531646	+	0.846967i	$0.321574\pi$
$734$	−16.0000			−0.590571
$735$		0			0
$736$	−8.00000			−0.294884
$737$		0			0
$738$	−8.66025	−	5.00000i	−0.318788	−	0.184053i
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	−0.900464	−	0.434930i	$-0.856773\pi$
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	0.826893	+	0.562360i	$0.190106\pi$
$740$	0.803848	+	13.3923i	0.0295500	+	0.492311i
$741$	−4.00000			−0.146944
$742$		0			0
$743$			32.0000i			1.17397i	0.809599	+	0.586983i	$0.199684\pi$
$743$			32.0000i			1.17397i	−0.809599	+	0.586983i	$0.800316\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	24.6410	+	37.3205i	0.902777	+	1.36732i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$	10.3923	−	6.00000i	0.380235	−	0.219529i
$748$		0			0
$749$		0			0
$750$	−11.0000	+	2.00000i	−0.401663	+	0.0730297i
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$	5.19615	+	3.00000i	0.189484	+	0.109399i
$753$	20.7846	+	12.0000i	0.757433	+	0.437304i
$754$	−8.00000	−	13.8564i	−0.291343	−	0.504621i
$755$	−20.0000	+	40.0000i	−0.727875	+	1.45575i
$756$		0			0
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$	10.3923	−	6.00000i	0.377466	−	0.217930i
$759$		0			0
$760$	−3.73205	+	2.46410i	−0.135376	+	0.0893824i
$761$	17.0000	+	29.4449i	0.616250	+	1.06738i	0.990164	+	0.139912i	$0.0446820\pi$
$761$	17.0000	+	29.4449i	0.616250	+	1.06738i	−0.373914	+	0.927463i	$0.621985\pi$
$762$		−	8.00000i		−	0.289809i
$763$		0			0
$764$	−22.0000			−0.795932
$765$	0.267949	+	4.46410i	0.00968772	+	0.161400i
$766$	13.0000	−	22.5167i	0.469709	−	0.813560i
$767$	20.7846	+	12.0000i	0.750489	+	0.433295i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	20.0000			0.721218			0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000			0.721218			0.360609	+	0.932717i	$0.382569\pi$
$770$		0			0
$771$	−30.0000			−1.08042
$772$	−17.3205	+	10.0000i	−0.623379	+	0.359908i
$773$	20.7846	+	12.0000i	0.747570	+	0.431610i	0.824815	−	0.565402i	$-0.191279\pi$
$773$	20.7846	+	12.0000i	0.747570	+	0.431610i	−0.0772449	+	0.997012i	$0.524612\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−7.85641	+	18.3923i	−0.282210	+	0.660671i
$776$	−14.0000			−0.502571
$777$		0			0
$778$		−	4.00000i		−	0.143407i
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$	2.46410	+	3.73205i	0.0882290	+	0.133629i
$781$		0			0
$782$	13.8564	−	8.00000i	0.495504	−	0.286079i
$783$			8.00000i			0.285897i
$784$		0			0
$785$	−4.00000	−	2.00000i	−0.142766	−	0.0713831i
$786$	4.00000	+	6.92820i	0.142675	+	0.247121i
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$	−5.19615	−	3.00000i	−0.185105	−	0.106871i
$789$		0			0
$790$	−8.00000	−	4.00000i	−0.284627	−	0.142314i
$791$		0			0
$792$		0			0
$793$	3.46410	−	2.00000i	0.123014	−	0.0710221i
$794$	−19.0000	+	32.9090i	−0.674285	+	1.16790i
$795$	7.39230	+	11.1962i	0.262178	+	0.397087i
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$			20.0000i			0.708436i	0.935163	+	0.354218i	$0.115253\pi$
$797$			20.0000i			0.708436i	−0.935163	+	0.354218i	$0.884747\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$	4.59808	+	1.96410i	0.162567	+	0.0694415i
$801$	7.00000	−	12.1244i	0.247333	−	0.428393i
$802$	8.66025	+	5.00000i	0.305804	+	0.176556i
$803$		0			0
$804$	14.0000			0.493742
$805$		0			0
$806$	8.00000			0.281788
$807$	25.9808	−	15.0000i	0.914566	−	0.528025i
$808$	5.19615	+	3.00000i	0.182800	+	0.105540i
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	−0.663316	−	0.748340i	$-0.730851\pi$
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	0.979739	+	0.200279i	$0.0641847\pi$
$810$	−0.133975	−	2.23205i	−0.00470739	−	0.0784263i
$811$	22.0000			0.772524			0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$		0			0
$813$			20.0000i			0.701431i
$814$		0			0
$815$	−3.73205	+	2.46410i	−0.130728	+	0.0863137i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	3.46410	−	2.00000i	0.121194	−	0.0699711i
$818$			24.0000i			0.839140i
$819$		0			0
$820$	10.0000	−	20.0000i	0.349215	−	0.698430i
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	−1.73205	−	1.00000i	−0.0604122	−	0.0348790i
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	0.438408	−	0.898776i	$-0.355543\pi$
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	−0.559159	+	0.829060i	$0.688876\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	−6.92820	+	4.00000i	−0.240772	+	0.139010i
$829$	11.0000	−	19.0526i	0.382046	−	0.661723i	−0.609309	−	0.792933i	$-0.708553\pi$
$829$	11.0000	−	19.0526i	0.382046	−	0.661723i	0.991355	+	0.131210i	$0.0418863\pi$
$830$	14.7846	+	22.3923i	0.513181	+	0.777248i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$		−	2.00000i		−	0.0693375i
$833$		0			0
$834$	22.0000			0.761798
$835$	−0.267949	−	4.46410i	−0.00927276	−	0.154487i
$836$		0			0
$837$	−3.46410	−	2.00000i	−0.119737	−	0.0691301i
$838$	10.3923	−	6.00000i	0.358996	−	0.207267i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	15.5885	−	9.00000i	0.537214	−	0.310160i
$843$	15.5885	+	9.00000i	0.536895	+	0.309976i
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$	20.0885	−	1.20577i	0.691064	−	0.0414798i
$846$	6.00000			0.206284
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$	5.19615	−	3.00000i	0.178017	−	0.102778i
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	−2.00000	+	4.00000i	−0.0683986	+	0.136797i
$856$		0			0
$857$	−8.66025	−	5.00000i	−0.295829	−	0.170797i	0.344739	−	0.938699i	$-0.387967\pi$
$857$	−8.66025	−	5.00000i	−0.295829	−	0.170797i	−0.640567	+	0.767902i	$0.721301\pi$
$858$		0			0
$859$	21.0000	+	36.3731i	0.716511	+	1.24103i	0.962374	+	0.271728i	$0.0875953\pi$
$859$	21.0000	+	36.3731i	0.716511	+	1.24103i	−0.245863	+	0.969305i	$0.579071\pi$
$860$	−4.00000	−	2.00000i	−0.136399	−	0.0681994i
$861$		0			0
$862$			10.0000i			0.340601i
$863$	−27.7128	+	16.0000i	−0.943355	+	0.544646i	−0.891010	−	0.453983i	$-0.850003\pi$
$863$	−27.7128	+	16.0000i	−0.943355	+	0.544646i	−0.0523446	+	0.998629i	$0.516669\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−22.3923	+	14.7846i	−0.761361	+	0.502692i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$		0			0
$870$	−17.8564	+	1.07180i	−0.605389	+	0.0363373i
$871$	−14.0000	+	24.2487i	−0.474372	+	0.821636i
$872$	−1.73205	−	1.00000i	−0.0586546	−	0.0338643i
$873$	−12.1244	+	7.00000i	−0.410347	+	0.236914i
$874$	16.0000			0.541208
$875$		0			0
$876$	−10.0000			−0.337869
$877$	−36.3731	+	21.0000i	−1.22823	+	0.709120i	−0.966660	−	0.256064i	$-0.917574\pi$
$877$	−36.3731	+	21.0000i	−1.22823	+	0.709120i	−0.261571	+	0.965184i	$0.584241\pi$
$878$	31.1769	+	18.0000i	1.05217	+	0.607471i
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$	2.00000	+	3.46410i	0.0672673	+	0.116510i
$885$	22.3923	−	14.7846i	0.752709	−	0.496979i
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	25.9808	−	15.0000i	0.872349	−	0.503651i	0.00422062	−	0.999991i	$-0.498657\pi$
$887$	25.9808	−	15.0000i	0.872349	−	0.503651i	0.868128	+	0.496340i	$0.165323\pi$
$888$		−	6.00000i		−	0.201347i
$889$		0			0
$890$	28.0000	+	14.0000i	0.938562	+	0.469281i
$891$		0			0
$892$	−17.3205	−	10.0000i	−0.579934	−	0.334825i
$893$	−10.3923	−	6.00000i	−0.347765	−	0.200782i
$894$	−10.0000	−	17.3205i	−0.334450	−	0.579284i
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$		0			0
$897$		−	16.0000i		−	0.534224i
$898$	−22.5167	+	13.0000i	−0.751391	+	0.433816i
$899$	−16.0000	+	27.7128i	−0.533630	+	0.924274i
$900$	4.96410	−	0.598076i	0.165470	−	0.0199359i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$	10.0000			0.332595
$905$	4.46410	−	0.267949i	0.148392	−	0.00890693i
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	32.9090	+	19.0000i	1.09272	+	0.630885i	0.934300	−	0.356487i	$-0.116025\pi$
$907$	32.9090	+	19.0000i	1.09272	+	0.630885i	0.158424	+	0.987371i	$0.449359\pi$
$908$	13.8564	−	8.00000i	0.459841	−	0.265489i
$909$	6.00000			0.199007
$910$		0			0
$911$	22.0000			0.728893			0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000			0.728893			0.364446	+	0.931224i	$0.381258\pi$
$912$	1.73205	−	1.00000i	0.0573539	−	0.0331133i
$913$		0			0
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$	−0.267949	−	4.46410i	−0.00885813	−	0.147579i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		−	2.00000i		−	0.0660098i
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	−9.85641	−	14.9282i	−0.324956	−	0.492168i
$921$	6.00000	−	10.3923i	0.197707	−	0.342438i
$922$	12.1244	−	7.00000i	0.399294	−	0.230533i
$923$			12.0000i			0.394985i
$924$		0			0
$925$	−24.0000	+	18.0000i	−0.789115	+	0.591836i
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	3.46410	+	2.00000i	0.113776	+	0.0656886i
$928$	6.92820	+	4.00000i	0.227429	+	0.131306i
$929$	11.0000	+	19.0526i	0.360898	+	0.625094i	0.988109	−	0.153755i	$-0.0491368\pi$
$929$	11.0000	+	19.0526i	0.360898	+	0.625094i	−0.627211	+	0.778850i	$0.715803\pi$
$930$	4.00000	−	8.00000i	0.131165	−	0.262330i
$931$		0			0
$932$		−	14.0000i		−	0.458585i
$933$	−6.92820	+	4.00000i	−0.226819	+	0.130954i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$			42.0000i			1.37208i	0.727564	+	0.686040i	$0.240653\pi$
$937$			42.0000i			1.37208i	−0.727564	+	0.686040i	$0.759347\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$	0.803848	+	13.3923i	0.0262186	+	0.436809i
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$	1.73205	+	1.00000i	0.0564333	+	0.0325818i
$943$	−69.2820	+	40.0000i	−2.25613	+	1.30258i
$944$	−12.0000			−0.390567
$945$		0			0
$946$		0			0
$947$	20.7846	−	12.0000i	0.675409	−	0.389948i	−0.122714	−	0.992442i	$-0.539160\pi$
$947$	20.7846	−	12.0000i	0.675409	−	0.389948i	0.798123	+	0.602494i	$0.205826\pi$
$948$	3.46410	+	2.00000i	0.112509	+	0.0649570i
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−9.19615	−	3.92820i	−0.298363	−	0.127448i
$951$	34.0000			1.10253
$952$		0			0
$953$		−	34.0000i		−	1.10137i	−0.834714	−	0.550684i	$-0.814367\pi$
$953$		−	34.0000i		−	1.10137i	0.834714	−	0.550684i	$-0.185633\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$	−27.1051	−	41.0526i	−0.877101	−	1.32843i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$			24.0000i			0.775405i
$959$		0			0
$960$	−2.00000	−	1.00000i	−0.0645497	−	0.0322749i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	10.3923	+	6.00000i	0.335061	+	0.193448i
$963$		0			0
$964$	12.0000	+	20.7846i	0.386494	+	0.669427i
$965$	−40.0000	−	20.0000i	−1.28765	−	0.643823i
$966$		0			0
$967$			32.0000i			1.02905i	0.857475	+	0.514525i	$0.172032\pi$
$967$			32.0000i			1.02905i	−0.857475	+	0.514525i	$0.827968\pi$
$968$	−9.52628	+	5.50000i	−0.306186	+	0.176777i
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$	−17.2487	−	26.1244i	−0.553823	−	0.838803i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−32.0000			−1.02535
$975$	−3.92820	+	9.19615i	−0.125803	+	0.294513i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−29.4449	−	17.0000i	−0.942025	−	0.543878i	−0.0514302	−	0.998677i	$-0.516378\pi$
$977$	−29.4449	−	17.0000i	−0.942025	−	0.543878i	−0.890594	+	0.454798i	$0.849711\pi$
$978$	1.73205	−	1.00000i	0.0553849	−	0.0319765i
$979$		0			0
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	3.46410	−	2.00000i	0.110544	−	0.0638226i
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	0.727554	−	0.686050i	$-0.240657\pi$
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	−0.230360	+	0.973106i	$0.573990\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	−0.803848	−	13.3923i	−0.0256127	−	0.426714i
$986$	−16.0000			−0.509544
$987$		0			0
$988$			4.00000i			0.127257i
$989$	8.00000	+	13.8564i	0.254385	+	0.440608i
$990$		0			0
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		−	28.0000i		−	0.888553i
$994$		0			0
$995$	16.0000	−	32.0000i	0.507234	−	1.01447i
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−5.19615	−	3.00000i	−0.164564	−	0.0950110i	0.415456	−	0.909613i	$-0.363622\pi$
$997$	−5.19615	−	3.00000i	−0.164564	−	0.0950110i	−0.580020	+	0.814602i	$0.696955\pi$
$998$	10.3923	+	6.00000i	0.328963	+	0.189927i
$999$	−3.00000	−	5.19615i	−0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.e.949.1		4
5.4	even	2	inner	1470.2.n.e.949.2		4
7.2	even	3	inner	1470.2.n.e.79.2		4
7.3	odd	6		1470.2.g.d.589.1	yes	2
7.4	even	3		1470.2.g.c.589.1	✓	2
7.5	odd	6		1470.2.n.d.79.2		4
7.6	odd	2		1470.2.n.d.949.1		4
35.3	even	12		7350.2.a.m.1.1		1
35.4	even	6		1470.2.g.c.589.2	yes	2
35.9	even	6	inner	1470.2.n.e.79.1		4
35.17	even	12		7350.2.a.cr.1.1		1
35.18	odd	12		7350.2.a.bc.1.1		1
35.19	odd	6		1470.2.n.d.79.1		4
35.24	odd	6		1470.2.g.d.589.2	yes	2
35.32	odd	12		7350.2.a.bx.1.1		1
35.34	odd	2		1470.2.n.d.949.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.c.589.1	✓	2	7.4	even	3
1470.2.g.c.589.2	yes	2	35.4	even	6
1470.2.g.d.589.1	yes	2	7.3	odd	6
1470.2.g.d.589.2	yes	2	35.24	odd	6
1470.2.n.d.79.1		4	35.19	odd	6
1470.2.n.d.79.2		4	7.5	odd	6
1470.2.n.d.949.1		4	7.6	odd	2
1470.2.n.d.949.2		4	35.34	odd	2
1470.2.n.e.79.1		4	35.9	even	6	inner
1470.2.n.e.79.2		4	7.2	even	3	inner
1470.2.n.e.949.1		4	1.1	even	1	trivial
1470.2.n.e.949.2		4	5.4	even	2	inner
7350.2.a.m.1.1		1	35.3	even	12
7350.2.a.bc.1.1		1	35.18	odd	12
7350.2.a.bx.1.1		1	35.32	odd	12
7350.2.a.cr.1.1		1	35.17	even	12

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.86603 + 1.23205i) q^{10} +(0.866025 - 0.500000i) q^{12} +2.00000i q^{13} +(2.00000 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(1.00000 + 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(-6.92820 + 4.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000i q^{27} +8.00000 q^{29} +(-2.23205 + 0.133975i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +1.00000 q^{36} +(-5.19615 + 3.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.133975 + 2.23205i) q^{40} +10.0000 q^{41} -2.00000i q^{43} +(1.23205 + 1.86603i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-4.00000 + 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.00000i q^{57} +(-6.92820 + 4.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.86603 - 1.23205i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000i q^{62} -1.00000 q^{64} +(0.267949 + 4.46410i) q^{65} +(12.1244 + 7.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -8.00000 q^{69} +6.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(3.00000 - 5.19615i) q^{74} +(4.59808 + 1.96410i) q^{75} +2.00000 q^{76} -2.00000i q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -12.0000i q^{83} +(4.00000 + 2.00000i) q^{85} +(1.00000 + 1.73205i) q^{86} +(6.92820 + 4.00000i) q^{87} +(-7.00000 - 12.1244i) q^{89} +(-2.00000 - 1.00000i) q^{90} +8.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.00000 - 5.19615i) q^{94} +(2.46410 + 3.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} +14.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 4 q^{10} + 8 q^{15} - 2 q^{16} + 4 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} - 4 q^{26} + 32 q^{29} - 2 q^{30} - 8 q^{31} - 8 q^{34} + 4 q^{36} - 4 q^{39} + 4 q^{40} + 40 q^{41} - 2 q^{45} + 16 q^{46} - 16 q^{50} + 4 q^{51} - 2 q^{54} + 24 q^{59} + 4 q^{60} - 4 q^{61} - 4 q^{64} + 8 q^{65} - 32 q^{69} + 24 q^{71} + 12 q^{74} + 8 q^{75} + 8 q^{76} + 8 q^{79} + 2 q^{80} - 2 q^{81} + 16 q^{85} + 4 q^{86} - 28 q^{89} - 8 q^{90} + 12 q^{94} - 4 q^{95} + 2 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 4 * q^10 + 8 * q^15 - 2 * q^16 + 4 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 - 4 * q^26 + 32 * q^29 - 2 * q^30 - 8 * q^31 - 8 * q^34 + 4 * q^36 - 4 * q^39 + 4 * q^40 + 40 * q^41 - 2 * q^45 + 16 * q^46 - 16 * q^50 + 4 * q^51 - 2 * q^54 + 24 * q^59 + 4 * q^60 - 4 * q^61 - 4 * q^64 + 8 * q^65 - 32 * q^69 + 24 * q^71 + 12 * q^74 + 8 * q^75 + 8 * q^76 + 8 * q^79 + 2 * q^80 - 2 * q^81 + 16 * q^85 + 4 * q^86 - 28 * q^89 - 8 * q^90 + 12 * q^94 - 4 * q^95 + 2 * q^96

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