LMFDB - Embedded newform 1470.2.n.e.949.2

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			949.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.e.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.133975 + 2.23205i) 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} +(-1.96410 - 4.59808i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +8.00000 q^{29} +(1.23205 - 1.86603i) 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} +(1.86603 + 1.23205i) q^{40} +10.0000 q^{41} +2.00000i q^{43} +(-2.23205 - 0.133975i) 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} +(0.133975 - 2.23205i) q^{60} +(-1.00000 - 1.73205i) q^{61} +4.00000i q^{62} -1.00000 q^{64} +(3.73205 + 2.46410i) 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} +(-0.598076 + 4.96410i) q^{75} +2.00000 q^{76} +2.00000i q^{78} +(2.00000 + 3.46410i) q^{79} +(2.23205 + 0.133975i) 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} +(-4.46410 - 0.267949i) 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
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.133975	+	2.23205i	−0.0423665	+	0.705836i
$11$		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	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		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	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	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	0.446476	−	0.894795i	$-0.352679\pi$
$23$	6.92820	−	4.00000i	1.44463	−	0.834058i	0.998154	+	0.0607377i	$0.0193453\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	−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	$0.233506\pi$
$30$	1.23205	−	1.86603i	0.224941	−	0.340688i
$31$	−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	−0.00783774	−	0.999969i	$-0.502495\pi$
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	0.862080	+	0.506772i	$0.169162\pi$
$38$	1.73205	+	1.00000i	0.280976	+	0.162221i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	1.86603	+	1.23205i	0.295045	+	0.194804i
$41$	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	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$		0			0
$45$	−2.23205	−	0.133975i	−0.332734	−	0.0199718i
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$			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	0.0987002	−	0.995117i	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$	−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	$-0.118692\pi$
$60$	0.133975	−	2.23205i	0.0172960	−	0.288157i
$61$	−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
$65$	3.73205	+	2.46410i	0.462904	+	0.305634i
$66$		0			0
$67$	−12.1244	−	7.00000i	−1.48123	−	0.855186i	−0.481452	−	0.876472i	$-0.659891\pi$
$67$	−12.1244	−	7.00000i	−1.48123	−	0.855186i	−0.999773	+	0.0212861i	$0.993224\pi$
$68$	−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	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−0.598076	+	4.96410i	−0.0690599	+	0.573205i
$76$	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	$0.761089\pi$
$80$	2.23205	+	0.133975i	0.249551	+	0.0149788i
$81$	−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	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		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
$95$	−4.46410	−	0.267949i	−0.458007	−	0.0274910i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$		0			0
$99$		0			0
$100$	−4.96410	−	0.598076i	−0.496410	−	0.0598076i
$101$	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	−0.660859	−	0.750510i	$-0.729808\pi$
$103$	−3.46410	+	2.00000i	−0.341328	+	0.197066i	0.319531	+	0.947576i	$0.396475\pi$
$104$	−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	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−1.07180	+	17.8564i	−0.0999456	+	1.66512i
$116$	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	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	4.46410	+	0.267949i	0.391528	+	0.0235007i
$131$	−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
$135$	1.86603	+	1.23205i	0.160602	+	0.106038i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	0.424182	−	0.905577i	$-0.360562\pi$
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	−0.572161	+	0.820141i	$0.693895\pi$
$138$	−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
$145$	−9.85641	+	14.9282i	−0.818530	+	1.23972i
$146$	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	$0.527733\pi$
$150$	1.96410	+	4.59808i	0.160368	+	0.375431i
$151$	−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	0.567521	−	0.823359i	$-0.307902\pi$
$157$	1.73205	+	1.00000i	0.138233	+	0.0798087i	−0.429289	+	0.903167i	$0.641236\pi$
$158$	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	−0.430632	−	0.902528i	$-0.641709\pi$
$163$	1.73205	−	1.00000i	0.135665	−	0.0783260i	0.566296	+	0.824202i	$0.308376\pi$
$164$	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	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	2.46410	−	3.73205i	0.188988	−	0.286235i
$171$	−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	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$	−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	$0.314694\pi$
$180$	−1.23205	+	1.86603i	−0.0918316	+	0.139085i
$181$	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
$185$	−0.803848	+	13.3923i	−0.0591000	+	0.984622i
$186$	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	0.970461	−	0.241257i	$-0.0775596\pi$
$193$	17.3205	+	10.0000i	1.24676	+	0.719816i	0.276296	+	0.961073i	$0.410893\pi$
$194$	−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	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		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	$-0.0252700\pi$
$200$	−4.59808	+	1.96410i	−0.325133	+	0.138883i
$201$	7.00000	+	12.1244i	0.493742	+	0.855186i
$202$		−	6.00000i		−	0.422159i
$203$		0			0
$204$	2.00000			0.140028
$205$	−12.3205	+	18.6603i	−0.860502	+	1.30329i
$206$	−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
$215$	−3.73205	−	2.46410i	−0.254524	−	0.168050i
$216$	−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	$0.233556\pi$
$223$			20.0000i			1.33930i	−0.742677	+	0.669650i	$0.766444\pi$
$224$		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	−0.0361484	−	0.999346i	$-0.511509\pi$
$227$	−13.8564	−	8.00000i	−0.919682	−	0.530979i	−0.883534	+	0.468368i	$0.844842\pi$
$228$	−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	−0.841472	−	0.540301i	$-0.818310\pi$
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	0.0471787	+	0.998886i	$0.484977\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−0.803848	+	13.3923i	−0.0524372	+	0.873618i
$236$	−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	$0.697793\pi$
$240$	−1.86603	−	1.23205i	−0.120451	−	0.0795285i
$241$	−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
$250$	10.5263	−	3.76795i	0.665740	−	0.238306i
$251$	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
$255$	−4.46410	−	0.267949i	−0.279553	−	0.0167796i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	25.9808	−	15.0000i	1.62064	−	0.935674i	0.633885	−	0.773427i	$-0.281459\pi$
$257$	25.9808	−	15.0000i	1.62064	−	0.935674i	0.986750	−	0.162247i	$-0.0518742\pi$
$258$		−	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	$-0.200801\pi$
$270$	2.23205	+	0.133975i	0.135838	+	0.00815343i
$271$	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	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$	−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	0.916869	−	0.399188i	$-0.130708\pi$
$283$	17.3205	+	10.0000i	1.02960	+	0.594438i	0.112728	+	0.993626i	$0.464041\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	3.73205	+	2.46410i	0.221068	+	0.145961i
$286$		0			0
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−1.07180	+	17.8564i	−0.0629381	+	1.04856i
$291$	−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	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		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
$305$	4.46410	+	0.267949i	0.255614	+	0.0153427i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	−7.46410	−	4.92820i	−0.423932	−	0.279903i
$311$	−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	−0.639611	−	0.768699i	$-0.720905\pi$
$313$	−5.19615	+	3.00000i	−0.293704	+	0.169570i	0.345907	+	0.938269i	$0.387571\pi$
$314$	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	$0.737280\pi$
$317$	−29.4449	+	17.0000i	−1.65379	+	0.954815i	−0.975494	+	0.220024i	$0.929386\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$		0			0
$320$	1.23205	−	1.86603i	0.0688737	−	0.104314i
$321$		0			0
$322$		0			0
$323$		−	4.00000i		−	0.222566i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−9.19615	+	3.92820i	−0.510111	+	0.217898i
$326$	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	$0.105984\pi$
$337$			12.0000i			0.653682i	−0.945079	+	0.326841i	$0.894016\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	5.00000	−	8.66025i	0.271563	−	0.470360i
$340$	0.267949	−	4.46410i	0.0145316	−	0.242100i
$341$		0			0
$342$			2.00000i			0.108148i
$343$		0			0
$344$	2.00000			0.107833
$345$	9.85641	−	14.9282i	0.530651	−	0.803707i
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	24.2487	+	14.0000i	1.30174	+	0.751559i	0.980702	−	0.195507i	$-0.0626353\pi$
$347$	24.2487	+	14.0000i	1.30174	+	0.751559i	0.321037	+	0.947067i	$0.395969\pi$
$348$	−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	0.631867	−	0.775077i	$-0.282289\pi$
$353$	5.19615	+	3.00000i	0.276563	+	0.159674i	−0.355303	+	0.934751i	$0.615622\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	−7.39230	+	11.1962i	−0.392343	+	0.594230i
$356$	−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	$0.953786\pi$
$360$	−0.133975	+	2.23205i	−0.00706108	+	0.117639i
$361$	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	0.0926670	−	0.995697i	$-0.470461\pi$
$367$	−13.8564	−	8.00000i	−0.723299	−	0.417597i	−0.815966	+	0.578101i	$0.803794\pi$
$368$	−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	−0.904227	−	0.427051i	$-0.859552\pi$
$373$	−19.0526	+	11.0000i	−0.986504	+	0.569558i	−0.0822766	+	0.996610i	$0.526219\pi$
$374$		0			0
$375$	−8.52628	−	7.23205i	−0.440295	−	0.373461i
$376$	−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	$0.599726\pi$
$380$	−2.46410	+	3.73205i	−0.126406	+	0.191450i
$381$	−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	0.201527	−	0.979483i	$-0.435410\pi$
$383$	22.5167	−	13.0000i	1.15055	−	0.664269i	0.949021	+	0.315214i	$0.102076\pi$
$384$	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	$0.199000\pi$
$390$	−3.73205	−	2.46410i	−0.188980	−	0.124775i
$391$	−16.0000			−0.809155
$392$		0			0
$393$			8.00000i			0.403547i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−8.92820	−	0.535898i	−0.449227	−	0.0269640i
$396$		0			0
$397$	−32.9090	+	19.0000i	−1.65165	+	0.953583i	−0.675261	+	0.737579i	$0.735969\pi$
$397$	−32.9090	+	19.0000i	−1.65165	+	0.953583i	−0.976392	+	0.216004i	$0.930698\pi$
$398$		−	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	$-0.0355330\pi$
$410$	−1.33975	+	22.3205i	−0.0661653	+	1.10233i
$411$	1.00000	+	1.73205i	0.0493264	+	0.0854358i
$412$			4.00000i			0.197066i
$413$		0			0
$414$	8.00000			0.393179
$415$	−22.3923	−	14.7846i	−1.09920	−	0.725748i
$416$	−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
$425$	−1.19615	+	9.92820i	−0.0580219	+	0.481589i
$426$	−6.00000			−0.290701
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−4.46410	−	0.267949i	−0.215278	−	0.0129217i
$431$	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	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$		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	−0.580030	−	0.814595i	$-0.696959\pi$
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	0.415445	+	0.909618i	$0.363626\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	31.2487	+	1.87564i	1.48133	+	0.0889141i
$446$	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	$0.289758\pi$
$450$	0.598076	−	4.96410i	0.0281936	−	0.234010i
$451$		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	0.316579	−	0.948566i	$-0.397466\pi$
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.979772	+	0.200118i	$0.0641325\pi$
$458$	−8.66025	−	5.00000i	−0.404667	−	0.233635i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	14.9282	+	9.85641i	0.696031	+	0.459557i
$461$	−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	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$	−0.535898	+	8.92820i	−0.0248517	+	0.414036i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	−31.1769	+	18.0000i	−1.44270	+	0.832941i	−0.998029	−	0.0627555i	$-0.980011\pi$
$467$	−31.1769	+	18.0000i	−1.44270	+	0.832941i	−0.444667	+	0.895696i	$0.646678\pi$
$468$		−	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	$-0.0180558\pi$
$480$	−2.23205	−	0.133975i	−0.101879	−	0.00611508i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$			24.0000i			1.09317i
$483$		0			0
$484$	11.0000			0.500000
$485$	26.1244	+	17.2487i	1.18625	+	0.783224i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−27.7128	−	16.0000i	−1.25579	−	0.725029i	−0.283535	−	0.958962i	$-0.591507\pi$
$487$	−27.7128	−	16.0000i	−1.25579	−	0.725029i	−0.972253	+	0.233933i	$0.924840\pi$
$488$	−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	$0.919893\pi$
$500$	7.23205	−	8.52628i	0.323427	−	0.381307i
$501$	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	$-0.803193\pi$
$503$		−	26.0000i		−	1.15928i	0.814872	−	0.579641i	$-0.196807\pi$
$504$		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
$515$	0.535898	−	8.92820i	0.0236145	−	0.393424i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$	2.46410	−	3.73205i	0.108058	−	0.163661i
$521$	−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	−0.422347	−	0.906434i	$-0.638794\pi$
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	0.573822	+	0.818980i	$0.305460\pi$
$524$	−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
$530$	7.39230	−	11.1962i	0.321101	−	0.486330i
$531$	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	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$	−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
$555$	7.39230	−	11.1962i	0.313786	−	0.475250i
$556$	−11.0000	+	19.0526i	−0.466504	+	0.808008i
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	0.792469	−	0.609912i	$-0.208795\pi$
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	−0.131965	+	0.991254i	$0.542129\pi$
$558$	−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	0.869326	−	0.494238i	$-0.164553\pi$
$563$	20.7846	+	12.0000i	0.875967	+	0.505740i	0.00664037	+	0.999978i	$0.497886\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−18.6603	−	12.3205i	−0.785043	−	0.518328i
$566$	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	$0.766114\pi$
$570$	4.46410	+	0.267949i	0.186981	+	0.0112232i
$571$	−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	0.889138	−	0.457639i	$-0.151305\pi$
$577$	22.5167	+	13.0000i	0.937381	+	0.541197i	0.0482425	+	0.998836i	$0.484638\pi$
$578$	−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
$585$	−0.267949	+	4.46410i	−0.0110783	+	0.184568i
$586$	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
$590$	22.3923	+	14.7846i	0.921877	+	0.608673i
$591$	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	−0.229953	−	0.973202i	$-0.573857\pi$
$593$	12.1244	−	7.00000i	0.497888	−	0.287456i	0.727841	+	0.685746i	$0.240524\pi$
$594$		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	$0.922248\pi$
$600$	4.96410	+	0.598076i	0.202659	+	0.0244164i
$601$	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
$605$	−24.5526	−	1.47372i	−0.998203	−	0.0599153i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−10.3923	+	6.00000i	−0.421811	+	0.243532i	−0.695852	−	0.718186i	$-0.744973\pi$
$607$	−10.3923	+	6.00000i	−0.421811	+	0.243532i	0.274041	+	0.961718i	$0.411640\pi$
$608$		−	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	0.314806	−	0.949156i	$-0.398061\pi$
$613$	−8.66025	−	5.00000i	−0.349784	−	0.201948i	−0.664590	+	0.747208i	$0.731394\pi$
$614$	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	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	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	$0.312443\pi$
$620$	−8.92820	−	0.535898i	−0.358565	−	0.0215222i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$			8.00000i			0.320771i
$623$		0			0
$624$	2.00000			0.0800641
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−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
$635$	14.9282	+	9.85641i	0.592408	+	0.391140i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	0.133975	−	2.23205i	0.00529581	−	0.0882296i
$641$	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	$0.251238\pi$
$643$			36.0000i			1.41970i	−0.704352	+	0.709851i	$0.748762\pi$
$644$		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	0.242365	−	0.970185i	$-0.422077\pi$
$647$	−12.1244	−	7.00000i	−0.476658	−	0.275198i	−0.719023	+	0.694987i	$0.755410\pi$
$648$	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	−0.243643	−	0.969865i	$-0.578343\pi$
$653$	12.1244	−	7.00000i	0.474463	−	0.273931i	0.718106	+	0.695934i	$0.245009\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	17.8564	+	1.07180i	0.697708	+	0.0418786i
$656$	−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
$670$	17.2487	−	26.1244i	0.666376	−	1.00927i
$671$		0			0
$672$		0			0
$673$		−	20.0000i		−	0.770943i	−0.922720	−	0.385472i	$-0.874039\pi$
$673$		−	20.0000i		−	0.770943i	0.922720	−	0.385472i	$-0.125961\pi$
$674$	6.00000	+	10.3923i	0.231111	+	0.400297i
$675$	−4.59808	+	1.96410i	−0.176980	+	0.0755983i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−10.3923	+	6.00000i	−0.399409	+	0.230599i	−0.686229	−	0.727386i	$-0.740735\pi$
$677$	−10.3923	+	6.00000i	−0.399409	+	0.230599i	0.286820	+	0.957984i	$0.407402\pi$
$678$		−	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	0.0465244	−	0.998917i	$-0.485185\pi$
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	−0.841825	+	0.539750i	$0.818519\pi$
$684$	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
$690$	1.07180	−	17.8564i	0.0408026	−	0.679782i
$691$	−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
$695$	27.1051	−	41.0526i	1.02816	−	1.55721i
$696$	−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
$705$	7.39230	−	11.1962i	0.278410	−	0.421671i
$706$	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	$0.670978\pi$
$710$	−0.803848	+	13.3923i	−0.0301679	+	0.502604i
$711$	−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
$725$	−15.7128	−	36.7846i	−0.583559	−	1.36615i
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$			36.0000i			1.33517i	0.744535	+	0.667583i	$0.232671\pi$
$727$			36.0000i			1.33517i	−0.744535	+	0.667583i	$0.767329\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−12.3205	+	18.6603i	−0.456002	+	0.690647i
$731$	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	−0.531646	−	0.846967i	$-0.678426\pi$
$733$	−1.73205	+	1.00000i	−0.0639748	+	0.0369358i	0.467671	+	0.883902i	$0.345093\pi$
$734$	−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	$0.190106\pi$
$740$	11.1962	+	7.39230i	0.411579	+	0.271747i
$741$	−4.00000			−0.146944
$742$		0			0
$743$		−	32.0000i		−	1.17397i	−0.809599	−	0.586983i	$-0.800316\pi$
$743$		−	32.0000i		−	1.17397i	0.809599	−	0.586983i	$-0.199684\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	−44.6410	−	2.67949i	−1.63552	−	0.0981690i
$746$	−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	$-0.787994\pi$
$757$		−	34.0000i		−	1.23575i	0.786276	−	0.617876i	$-0.212006\pi$
$758$	−10.3923	+	6.00000i	−0.377466	+	0.217930i
$759$		0			0
$760$	−0.267949	+	4.46410i	−0.00971954	+	0.161930i
$761$	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
$765$	3.73205	+	2.46410i	0.134933	+	0.0890898i
$766$	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	0.0772449	−	0.997012i	$-0.475388\pi$
$773$	−20.7846	−	12.0000i	−0.747570	−	0.431610i	−0.824815	+	0.565402i	$0.808721\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	19.8564	+	2.39230i	0.713263	+	0.0859341i
$776$	−14.0000			−0.502571
$777$		0			0
$778$			4.00000i			0.143407i
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$	−4.46410	−	0.267949i	−0.159840	−	0.00959412i
$781$		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	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$	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
$795$	−13.3923	−	0.803848i	−0.474976	−	0.0285095i
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$		−	20.0000i		−	0.708436i	−0.935163	−	0.354218i	$-0.884747\pi$
$797$		−	20.0000i		−	0.708436i	0.935163	−	0.354218i	$-0.115253\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$	−0.598076	+	4.96410i	−0.0211452	+	0.175507i
$801$	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	$0.0641847\pi$
$810$	−1.86603	−	1.23205i	−0.0655654	−	0.0432899i
$811$	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
$815$	−0.267949	+	4.46410i	−0.00938585	+	0.156371i
$816$	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	0.559159	−	0.829060i	$-0.311124\pi$
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	−0.438408	+	0.898776i	$0.644457\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	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	$0.0418863\pi$
$830$	−26.7846	−	1.60770i	−0.929707	−	0.0558039i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$			2.00000i			0.0693375i
$833$		0			0
$834$	22.0000			0.761798
$835$	−3.73205	−	2.46410i	−0.129153	−	0.0852738i
$836$		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
$845$	−11.0885	+	16.7942i	−0.381455	+	0.577739i
$846$	6.00000			0.206284
$847$		0			0
$848$			6.00000i			0.206041i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	3.92820	+	9.19615i	0.134736	+	0.315425i
$851$	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	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$		0			0
$855$	−2.00000	−	4.00000i	−0.0683986	−	0.136797i
$856$		0			0
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	0.640567	−	0.767902i	$-0.278699\pi$
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	−0.344739	+	0.938699i	$0.612033\pi$
$858$		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	0.0523446	−	0.998629i	$-0.483331\pi$
$863$	27.7128	−	16.0000i	0.943355	−	0.544646i	0.891010	+	0.453983i	$0.149997\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−1.60770	+	26.7846i	−0.0546633	+	0.910704i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$			13.0000i			0.441503i
$868$		0			0
$869$		0			0
$870$	9.85641	−	14.9282i	0.334163	−	0.506113i
$871$	−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	0.261571	−	0.965184i	$-0.415759\pi$
$877$	36.3731	−	21.0000i	1.22823	−	0.709120i	0.966660	+	0.256064i	$0.0824259\pi$
$878$	−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	$0.0538159\pi$
$883$			10.0000i			0.336527i	−0.985742	+	0.168263i	$0.946184\pi$
$884$	2.00000	+	3.46410i	0.0672673	+	0.116510i
$885$	1.60770	−	26.7846i	0.0540421	−	0.900355i
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	−25.9808	+	15.0000i	−0.872349	+	0.503651i	−0.868128	−	0.496340i	$-0.834677\pi$
$887$	−25.9808	+	15.0000i	−0.872349	+	0.503651i	−0.00422062	+	0.999991i	$0.501343\pi$
$888$			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
$900$	−1.96410	−	4.59808i	−0.0654701	−	0.153269i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$	10.0000			0.332595
$905$	−2.46410	+	3.73205i	−0.0819095	+	0.124058i
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	−32.9090	−	19.0000i	−1.09272	−	0.630885i	−0.158424	−	0.987371i	$-0.550641\pi$
$907$	−32.9090	−	19.0000i	−1.09272	−	0.630885i	−0.934300	+	0.356487i	$0.883975\pi$
$908$	−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
$915$	−3.73205	−	2.46410i	−0.123378	−	0.0814607i
$916$	−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	$0.918341\pi$
$920$	17.8564	+	1.07180i	0.588708	+	0.0353361i
$921$	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	$-0.759347\pi$
$937$		−	42.0000i		−	1.37208i	0.727564	−	0.686040i	$-0.240653\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$	11.1962	+	7.39230i	0.365178	+	0.241110i
$941$	−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	−0.798123	−	0.602494i	$-0.794174\pi$
$947$	−20.7846	+	12.0000i	−0.675409	+	0.389948i	0.122714	+	0.992442i	$0.460840\pi$
$948$	−3.46410	−	2.00000i	−0.112509	−	0.0649570i
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	1.19615	−	9.92820i	0.0388083	−	0.322113i
$951$	34.0000			1.10253
$952$		0			0
$953$			34.0000i			1.10137i	0.834714	+	0.550684i	$0.185633\pi$
$953$			34.0000i			1.10137i	−0.834714	+	0.550684i	$0.814367\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$	49.1051	+	2.94744i	1.58900	+	0.0953770i
$956$	−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	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$	31.2487	+	1.87564i	1.00334	+	0.0602233i
$971$		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
$975$	9.92820	+	1.19615i	0.317957	+	0.0383075i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	29.4449	+	17.0000i	0.942025	+	0.543878i	0.890594	−	0.454798i	$-0.150289\pi$
$977$	29.4449	+	17.0000i	0.942025	+	0.543878i	0.0514302	+	0.998677i	$0.483622\pi$
$978$	−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	0.230360	−	0.973106i	$-0.426010\pi$
$983$	−15.5885	−	9.00000i	−0.497195	−	0.287055i	−0.727554	+	0.686050i	$0.759343\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	−11.1962	−	7.39230i	−0.356739	−	0.235538i
$986$	−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	0.580020	−	0.814602i	$-0.303045\pi$
$997$	5.19615	+	3.00000i	0.164564	+	0.0950110i	−0.415456	+	0.909613i	$0.636378\pi$
$998$	−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.949.2		4
5.4	even	2	inner	1470.2.n.e.949.1		4
7.2	even	3	inner	1470.2.n.e.79.1		4
7.3	odd	6		1470.2.g.d.589.2	yes	2
7.4	even	3		1470.2.g.c.589.2	yes	2
7.5	odd	6		1470.2.n.d.79.1		4
7.6	odd	2		1470.2.n.d.949.2		4
35.3	even	12		7350.2.a.cr.1.1		1
35.4	even	6		1470.2.g.c.589.1	✓	2
35.9	even	6	inner	1470.2.n.e.79.2		4
35.17	even	12		7350.2.a.m.1.1		1
35.18	odd	12		7350.2.a.bx.1.1		1
35.19	odd	6		1470.2.n.d.79.2		4
35.24	odd	6		1470.2.g.d.589.1	yes	2
35.32	odd	12		7350.2.a.bc.1.1		1
35.34	odd	2		1470.2.n.d.949.1		4

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.133975 + 2.23205i) 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} +(-1.96410 - 4.59808i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +8.00000 q^{29} +(1.23205 - 1.86603i) 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} +(1.86603 + 1.23205i) q^{40} +10.0000 q^{41} +2.00000i q^{43} +(-2.23205 - 0.133975i) 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} +(0.133975 - 2.23205i) q^{60} +(-1.00000 - 1.73205i) q^{61} +4.00000i q^{62} -1.00000 q^{64} +(3.73205 + 2.46410i) 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} +(-0.598076 + 4.96410i) q^{75} +2.00000 q^{76} +2.00000i q^{78} +(2.00000 + 3.46410i) q^{79} +(2.23205 + 0.133975i) 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} +(-4.46410 - 0.267949i) 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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