LMFDB - Embedded newform 1950.2.z.f.1849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (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:	$15.5708283941$
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			1849.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.f.1699.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000i q^{12} +(-0.866025 + 3.50000i) q^{13} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} -1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} -4.00000 q^{21} +(4.33013 + 2.50000i) q^{22} +(-6.06218 + 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(3.46410 - 2.00000i) q^{28} +(1.00000 + 1.73205i) q^{29} -2.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.33013 - 2.50000i) q^{33} -2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} +2.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(-5.00000 - 8.66025i) q^{41} +(-3.46410 + 2.00000i) q^{42} +(-3.46410 - 2.00000i) q^{43} +5.00000 q^{44} +(-3.50000 + 6.06218i) q^{46} +12.0000i q^{47} +(0.866025 + 0.500000i) q^{48} +(4.50000 + 7.79423i) q^{49} +2.00000 q^{51} +(2.59808 + 2.50000i) q^{52} +(0.500000 + 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{56} -2.00000i q^{57} +(1.73205 + 1.00000i) q^{58} +(5.50000 - 9.52628i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} -5.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(3.50000 - 6.06218i) q^{69} +(-1.50000 + 2.59808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +9.00000i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} +20.0000i q^{77} +(-2.59808 - 2.50000i) q^{78} +14.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.66025 - 5.00000i) q^{82} +3.00000i q^{83} +(-2.00000 + 3.46410i) q^{84} -4.00000 q^{86} +(-1.73205 - 1.00000i) q^{87} +(4.33013 - 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(-10.0000 + 10.3923i) q^{91} +7.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} +1.00000 q^{96} +(11.2583 + 6.50000i) q^{97} +(7.79423 + 4.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 10 q^{11} + 16 q^{14} - 2 q^{16} - 4 q^{19} - 16 q^{21} + 2 q^{24} + 4 q^{26} + 4 q^{29} - 8 q^{31} - 8 q^{34} - 2 q^{36} - 4 q^{39} - 20 q^{41} + 20 q^{44} - 14 q^{46} + 18 q^{49} + 8 q^{51} + 2 q^{54} + 8 q^{56} + 22 q^{61} - 4 q^{64} - 20 q^{66} + 14 q^{69} - 6 q^{71} + 6 q^{74} + 4 q^{76} + 56 q^{79} - 2 q^{81} - 8 q^{84} - 16 q^{86} - 20 q^{89} - 40 q^{91} + 24 q^{94} + 4 q^{96} + 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 10 * q^11 + 16 * q^14 - 2 * q^16 - 4 * q^19 - 16 * q^21 + 2 * q^24 + 4 * q^26 + 4 * q^29 - 8 * q^31 - 8 * q^34 - 2 * q^36 - 4 * q^39 - 20 * q^41 + 20 * q^44 - 14 * q^46 + 18 * q^49 + 8 * q^51 + 2 * q^54 + 8 * q^56 + 22 * q^61 - 4 * q^64 - 20 * q^66 + 14 * q^69 - 6 * q^71 + 6 * q^74 + 4 * q^76 + 56 * q^79 - 2 * q^81 - 8 * q^84 - 16 * q^86 - 20 * q^89 - 40 * q^91 + 24 * q^94 + 4 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$			1.00000i			0.288675i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$	4.00000			1.06904
$15$		0			0
$16$	−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	$0.744646\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	−4.00000			−0.872872
$22$	4.33013	+	2.50000i	0.923186	+	0.533002i
$23$	−6.06218	+	3.50000i	−1.26405	+	0.729800i	−0.973856	−	0.227167i	$-0.927054\pi$
$23$	−6.06218	+	3.50000i	−1.26405	+	0.729800i	−0.290196	+	0.956967i	$0.593720\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$			1.00000i			0.192450i
$28$	3.46410	−	2.00000i	0.654654	−	0.377964i
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.33013	−	2.50000i	−0.753778	−	0.435194i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$			2.00000i			0.324443i
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$		0			0
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$	−3.46410	+	2.00000i	−0.534522	+	0.308607i
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	0.212041	−	0.977261i	$-0.431989\pi$
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	−0.740312	+	0.672264i	$0.765322\pi$
$44$	5.00000			0.753778
$45$		0			0
$46$	−3.50000	+	6.06218i	−0.516047	+	0.893819i
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$	2.00000			0.280056
$52$	2.59808	+	2.50000i	0.360288	+	0.346688i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	2.00000	−	3.46410i	0.267261	−	0.462910i
$57$		−	2.00000i		−	0.264906i
$58$	1.73205	+	1.00000i	0.227429	+	0.131306i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	−1.73205	+	1.00000i	−0.219971	+	0.127000i
$63$	3.46410	−	2.00000i	0.436436	−	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.00000			−0.615457
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$	3.50000	−	6.06218i	0.421350	−	0.729800i
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			9.00000i			1.05337i	0.850060	+	0.526685i	$0.176565\pi$
$73$			9.00000i			1.05337i	−0.850060	+	0.526685i	$0.823435\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$			20.0000i			2.27921i
$78$	−2.59808	−	2.50000i	−0.294174	−	0.283069i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.66025	−	5.00000i	−0.956365	−	0.552158i
$83$			3.00000i			0.329293i	0.986353	+	0.164646i	$0.0526483\pi$
$83$			3.00000i			0.329293i	−0.986353	+	0.164646i	$0.947352\pi$
$84$	−2.00000	+	3.46410i	−0.218218	+	0.377964i
$85$		0			0
$86$	−4.00000			−0.431331
$87$	−1.73205	−	1.00000i	−0.185695	−	0.107211i
$88$	4.33013	−	2.50000i	0.461593	−	0.266501i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$		0			0
$91$	−10.0000	+	10.3923i	−1.04828	+	1.08941i
$92$			7.00000i			0.729800i
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$		0			0
$96$	1.00000			0.102062
$97$	11.2583	+	6.50000i	1.14311	+	0.659975i	0.947199	−	0.320647i	$-0.103900\pi$
$97$	11.2583	+	6.50000i	1.14311	+	0.659975i	0.195911	+	0.980622i	$0.437234\pi$
$98$	7.79423	+	4.50000i	0.787336	+	0.454569i
$99$	5.00000			0.502519
$100$		0			0
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$	1.73205	−	1.00000i	0.171499	−	0.0990148i
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$		0			0
$107$	6.92820	−	4.00000i	0.669775	−	0.386695i	−0.126217	−	0.992003i	$-0.540283\pi$
$107$	6.92820	−	4.00000i	0.669775	−	0.386695i	0.795991	+	0.605308i	$0.206950\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−1.50000	+	2.59808i	−0.142374	+	0.246598i
$112$		−	4.00000i		−	0.377964i
$113$	3.46410	+	2.00000i	0.325875	+	0.188144i	0.654008	−	0.756487i	$-0.273086\pi$
$113$	3.46410	+	2.00000i	0.325875	+	0.188144i	−0.328133	+	0.944632i	$0.606419\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	2.00000			0.185695
$117$	2.59808	+	2.50000i	0.240192	+	0.231125i
$118$		0			0
$119$	−4.00000	−	6.92820i	−0.366679	−	0.635107i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		−	11.0000i		−	0.995893i
$123$	8.66025	+	5.00000i	0.780869	+	0.450835i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$	19.0526	−	11.0000i	1.69064	−	0.976092i	0.736642	−	0.676283i	$-0.236410\pi$
$127$	19.0526	−	11.0000i	1.69064	−	0.976092i	0.953999	−	0.299809i	$-0.0969231\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.00000			0.352180
$130$		0			0
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$	−4.33013	+	2.50000i	−0.376889	+	0.217597i
$133$	−6.92820	+	4.00000i	−0.600751	+	0.346844i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−6.92820	−	4.00000i	−0.591916	−	0.341743i	0.173939	−	0.984757i	$-0.444351\pi$
$137$	−6.92820	−	4.00000i	−0.591916	−	0.341743i	−0.765855	+	0.643013i	$0.777684\pi$
$138$		−	7.00000i		−	0.595880i
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$			3.00000i			0.251754i
$143$	−17.3205	+	5.00000i	−1.44841	+	0.418121i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	4.50000	+	7.79423i	0.372423	+	0.645055i
$147$	−7.79423	−	4.50000i	−0.642857	−	0.371154i
$148$		−	3.00000i		−	0.246598i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$	−1.73205	+	1.00000i	−0.140028	+	0.0808452i
$154$	10.0000	+	17.3205i	0.805823	+	1.39573i
$155$		0			0
$156$	−3.50000	−	0.866025i	−0.280224	−	0.0693375i
$157$		−	17.0000i		−	1.35675i	−0.734717	−	0.678374i	$-0.762685\pi$
$157$		−	17.0000i		−	1.35675i	0.734717	−	0.678374i	$-0.237315\pi$
$158$	12.1244	−	7.00000i	0.964562	−	0.556890i
$159$		0			0
$160$		0			0
$161$	−28.0000			−2.20671
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−5.19615	−	3.00000i	−0.406994	−	0.234978i	0.282503	−	0.959266i	$-0.408835\pi$
$163$	−5.19615	−	3.00000i	−0.406994	−	0.234978i	−0.689497	+	0.724288i	$0.742169\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$	−12.9904	+	7.50000i	−1.00523	+	0.580367i	−0.909790	−	0.415068i	$-0.863758\pi$
$167$	−12.9904	+	7.50000i	−1.00523	+	0.580367i	−0.0954356	+	0.995436i	$0.530424\pi$
$168$			4.00000i			0.308607i
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.923622	−	0.383304i	$-0.125214\pi$
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.129861	+	0.991532i	$0.458547\pi$
$174$	−2.00000			−0.151620
$175$		0			0
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$		0			0
$178$	−8.66025	−	5.00000i	−0.649113	−	0.374766i
$179$	−0.500000	−	0.866025i	−0.0373718	−	0.0647298i	0.846735	−	0.532016i	$-0.178565\pi$
$179$	−0.500000	−	0.866025i	−0.0373718	−	0.0647298i	−0.884106	+	0.467286i	$0.845232\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	−3.46410	+	14.0000i	−0.256776	+	1.03775i
$183$			11.0000i			0.813143i
$184$	3.50000	+	6.06218i	0.258023	+	0.446910i
$185$		0			0
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$		−	10.0000i		−	0.731272i
$188$	10.3923	+	6.00000i	0.757937	+	0.437595i
$189$	−2.00000	+	3.46410i	−0.145479	+	0.251976i
$190$		0			0
$191$	11.5000	−	19.9186i	0.832111	−	1.44126i	−0.0642505	−	0.997934i	$-0.520466\pi$
$191$	11.5000	−	19.9186i	0.832111	−	1.44126i	0.896361	−	0.443324i	$-0.146201\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	2.59808	−	1.50000i	0.187014	−	0.107972i	−0.403570	−	0.914949i	$-0.632231\pi$
$193$	2.59808	−	1.50000i	0.187014	−	0.107972i	0.590584	+	0.806976i	$0.298898\pi$
$194$	13.0000			0.933346
$195$		0			0
$196$	9.00000			0.642857
$197$	1.73205	−	1.00000i	0.123404	−	0.0712470i	−0.437028	−	0.899448i	$-0.643969\pi$
$197$	1.73205	−	1.00000i	0.123404	−	0.0712470i	0.560431	+	0.828201i	$0.310635\pi$
$198$	4.33013	−	2.50000i	0.307729	−	0.177667i
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	−6.92820	−	4.00000i	−0.487467	−	0.281439i
$203$			8.00000i			0.561490i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$		0			0
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$			7.00000i			0.486534i
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	−10.0000			−0.691714
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$		0			0
$213$		−	3.00000i		−	0.205557i
$214$	4.00000	−	6.92820i	0.273434	−	0.473602i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−6.92820	−	4.00000i	−0.470317	−	0.271538i
$218$	14.7224	−	8.50000i	0.997129	−	0.575693i
$219$	−4.50000	−	7.79423i	−0.304082	−	0.526685i
$220$		0			0
$221$	5.00000	−	5.19615i	0.336336	−	0.349531i
$222$			3.00000i			0.201347i
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	−0.611482	−	0.791258i	$-0.709426\pi$
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	0.379509	+	0.925188i	$0.376093\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$		0			0
$226$	4.00000			0.266076
$227$	−7.79423	−	4.50000i	−0.517321	−	0.298675i	0.218517	−	0.975833i	$-0.429878\pi$
$227$	−7.79423	−	4.50000i	−0.517321	−	0.298675i	−0.735838	+	0.677158i	$0.763211\pi$
$228$	−1.73205	−	1.00000i	−0.114708	−	0.0662266i
$229$	−19.0000			−1.25556			−0.627778	−	0.778393i	$-0.716035\pi$
$229$	−19.0000			−1.25556			−0.627778	+	0.778393i	$0.716035\pi$
$230$		0			0
$231$	−10.0000	−	17.3205i	−0.657952	−	1.13961i
$232$	1.73205	−	1.00000i	0.113715	−	0.0656532i
$233$		−	8.00000i		−	0.524097i	−0.965055	−	0.262049i	$-0.915602\pi$
$233$		−	8.00000i		−	0.524097i	0.965055	−	0.262049i	$-0.0843981\pi$
$234$	3.50000	+	0.866025i	0.228802	+	0.0566139i
$235$		0			0
$236$		0			0
$237$	−12.1244	+	7.00000i	−0.787562	+	0.454699i
$238$	−6.92820	−	4.00000i	−0.449089	−	0.259281i
$239$	23.0000			1.48775			0.743873	−	0.668321i	$-0.232987\pi$
$239$	23.0000			1.48775			0.743873	+	0.668321i	$0.232987\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$			14.0000i			0.899954i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−5.50000	−	9.52628i	−0.352101	−	0.609858i
$245$		0			0
$246$	10.0000			0.637577
$247$	−5.19615	−	5.00000i	−0.330623	−	0.318142i
$248$			2.00000i			0.127000i
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$		0			0
$251$	8.50000	−	14.7224i	0.536515	−	0.929272i	−0.462573	−	0.886581i	$-0.653074\pi$
$251$	8.50000	−	14.7224i	0.536515	−	0.929272i	0.999088	−	0.0426905i	$-0.0135929\pi$
$252$		−	4.00000i		−	0.251976i
$253$	−30.3109	−	17.5000i	−1.90563	−	1.10022i
$254$	11.0000	−	19.0526i	0.690201	−	1.19546i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−24.2487	+	14.0000i	−1.51259	+	0.873296i	−0.512702	+	0.858567i	$0.671355\pi$
$257$	−24.2487	+	14.0000i	−1.51259	+	0.873296i	−0.999892	+	0.0147291i	$0.995311\pi$
$258$	3.46410	−	2.00000i	0.215666	−	0.124515i
$259$	12.0000			0.745644
$260$		0			0
$261$	2.00000			0.123797
$262$	17.3205	−	10.0000i	1.07006	−	0.617802i
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	−0.720672	−	0.693276i	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$		0			0
$266$	−4.00000	+	6.92820i	−0.245256	+	0.424795i
$267$	8.66025	+	5.00000i	0.529999	+	0.305995i
$268$			4.00000i			0.244339i
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$			2.00000i			0.121268i
$273$	3.46410	−	14.0000i	0.209657	−	0.847319i
$274$	−8.00000			−0.483298
$275$		0			0
$276$	−3.50000	−	6.06218i	−0.210675	−	0.364900i
$277$	26.8468	+	15.5000i	1.61307	+	0.931305i	0.988654	+	0.150210i	$0.0479951\pi$
$277$	26.8468	+	15.5000i	1.61307	+	0.931305i	0.624413	+	0.781094i	$0.285338\pi$
$278$			4.00000i			0.239904i
$279$	−1.00000	+	1.73205i	−0.0598684	+	0.103695i
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$	−10.3923	−	6.00000i	−0.618853	−	0.357295i
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.443491	−	0.896279i	$-0.353740\pi$
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.997946	+	0.0640654i	$0.0204066\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$		0			0
$286$	−12.5000	+	12.9904i	−0.739140	+	0.768137i
$287$		−	40.0000i		−	2.36113i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−13.0000			−0.762073
$292$	7.79423	+	4.50000i	0.456123	+	0.263343i
$293$	−20.7846	−	12.0000i	−1.21425	−	0.701047i	−0.250568	−	0.968099i	$-0.580617\pi$
$293$	−20.7846	−	12.0000i	−1.21425	−	0.701047i	−0.963682	+	0.267052i	$0.913951\pi$
$294$	−9.00000			−0.524891
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	−4.33013	+	2.50000i	−0.251259	+	0.145065i
$298$			10.0000i			0.579284i
$299$	−7.00000	−	24.2487i	−0.404820	−	1.40234i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	−8.66025	+	5.00000i	−0.498342	+	0.287718i
$303$	6.92820	+	4.00000i	0.398015	+	0.229794i
$304$	2.00000			0.114708
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$		−	24.0000i		−	1.36975i	−0.728659	−	0.684876i	$-0.759856\pi$
$307$		−	24.0000i		−	1.36975i	0.728659	−	0.684876i	$-0.240144\pi$
$308$	17.3205	+	10.0000i	0.986928	+	0.569803i
$309$	−8.00000	−	13.8564i	−0.455104	−	0.788263i
$310$		0			0
$311$	−7.00000			−0.396934			−0.198467	−	0.980108i	$-0.563596\pi$
$311$	−7.00000			−0.396934			−0.198467	+	0.980108i	$0.563596\pi$
$312$	−3.46410	+	1.00000i	−0.196116	+	0.0566139i
$313$		−	1.00000i		−	0.0565233i	−0.999601	−	0.0282617i	$-0.991003\pi$
$313$		−	1.00000i		−	0.0565233i	0.999601	−	0.0282617i	$-0.00899717\pi$
$314$	−8.50000	−	14.7224i	−0.479683	−	0.830835i
$315$		0			0
$316$	7.00000	−	12.1244i	0.393781	−	0.682048i
$317$		−	28.0000i		−	1.57264i	−0.617822	−	0.786318i	$-0.711985\pi$
$317$		−	28.0000i		−	1.57264i	0.617822	−	0.786318i	$-0.288015\pi$
$318$		0			0
$319$	−5.00000	+	8.66025i	−0.279946	+	0.484881i
$320$		0			0
$321$	−4.00000	+	6.92820i	−0.223258	+	0.386695i
$322$	−24.2487	+	14.0000i	−1.35133	+	0.780189i
$323$	3.46410	−	2.00000i	0.192748	−	0.111283i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	−14.7224	+	8.50000i	−0.814152	+	0.470051i
$328$	−8.66025	+	5.00000i	−0.478183	+	0.276079i
$329$	−24.0000	+	41.5692i	−1.32316	+	2.29179i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$	2.59808	+	1.50000i	0.142588	+	0.0823232i
$333$		−	3.00000i		−	0.164399i
$334$	−7.50000	+	12.9904i	−0.410382	+	0.710802i
$335$		0			0
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$	−12.9904	+	0.500000i	−0.706584	+	0.0271964i
$339$	−4.00000			−0.217250
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$	1.73205	+	1.00000i	0.0936586	+	0.0540738i
$343$			8.00000i			0.431959i
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	16.0000			0.860165
$347$	−9.52628	−	5.50000i	−0.511397	−	0.295255i	0.222010	−	0.975044i	$-0.428738\pi$
$347$	−9.52628	−	5.50000i	−0.511397	−	0.295255i	−0.733408	+	0.679789i	$0.762071\pi$
$348$	−1.73205	+	1.00000i	−0.0928477	+	0.0536056i
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$		−	5.00000i		−	0.266501i
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	−0.355303	−	0.934751i	$-0.615622\pi$
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	0.631867	+	0.775077i	$0.282289\pi$
$354$		0			0
$355$		0			0
$356$	−10.0000			−0.529999
$357$	6.92820	+	4.00000i	0.366679	+	0.211702i
$358$	−0.866025	−	0.500000i	−0.0457709	−	0.0264258i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	9.52628	−	5.50000i	0.500690	−	0.289074i
$363$		−	14.0000i		−	0.734809i
$364$	4.00000	+	13.8564i	0.209657	+	0.726273i
$365$		0			0
$366$	5.50000	+	9.52628i	0.287490	+	0.497947i
$367$	8.66025	−	5.00000i	0.452062	−	0.260998i	−0.256639	−	0.966507i	$-0.582615\pi$
$367$	8.66025	−	5.00000i	0.452062	−	0.260998i	0.708700	+	0.705509i	$0.249282\pi$
$368$	6.06218	+	3.50000i	0.316013	+	0.182450i
$369$	−10.0000			−0.520579
$370$		0			0
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	−14.7224	−	8.50000i	−0.762299	−	0.440113i	0.0678218	−	0.997697i	$-0.478395\pi$
$373$	−14.7224	−	8.50000i	−0.762299	−	0.440113i	−0.830120	+	0.557584i	$0.811728\pi$
$374$	−5.00000	−	8.66025i	−0.258544	−	0.447811i
$375$		0			0
$376$	12.0000			0.618853
$377$	−6.92820	+	2.00000i	−0.356821	+	0.103005i
$378$			4.00000i			0.205738i
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	0.965392	−	0.260804i	$-0.0839877\pi$
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	−0.708559	+	0.705652i	$0.750654\pi$
$380$		0			0
$381$	−11.0000	+	19.0526i	−0.563547	+	0.976092i
$382$		−	23.0000i		−	1.17678i
$383$	−32.0429	−	18.5000i	−1.63732	−	0.945306i	−0.981752	−	0.190168i	$-0.939097\pi$
$383$	−32.0429	−	18.5000i	−1.63732	−	0.945306i	−0.655566	−	0.755138i	$-0.727570\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	1.50000	−	2.59808i	0.0763480	−	0.132239i
$387$	−3.46410	+	2.00000i	−0.176090	+	0.101666i
$388$	11.2583	−	6.50000i	0.571555	−	0.329988i
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$	−17.3205	+	10.0000i	−0.873704	+	0.504433i
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$		0			0
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	25.9808	+	15.0000i	1.30394	+	0.752828i	0.981077	−	0.193618i	$-0.0620223\pi$
$397$	25.9808	+	15.0000i	1.30394	+	0.752828i	0.322860	+	0.946447i	$0.395356\pi$
$398$		−	24.0000i		−	1.20301i
$399$	4.00000	−	6.92820i	0.200250	−	0.346844i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		−	4.00000i		−	0.199502i
$403$	1.73205	−	7.00000i	0.0862796	−	0.348695i
$404$	−8.00000			−0.398015
$405$		0			0
$406$	4.00000	+	6.92820i	0.198517	+	0.343841i
$407$	12.9904	+	7.50000i	0.643909	+	0.371761i
$408$		−	2.00000i		−	0.0990148i
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	0.210017	+	0.977698i	$0.432648\pi$
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	−0.951720	+	0.306968i	$0.900685\pi$
$410$		0			0
$411$	8.00000			0.394611
$412$	13.8564	+	8.00000i	0.682656	+	0.394132i
$413$		0			0
$414$	3.50000	+	6.06218i	0.172016	+	0.297940i
$415$		0			0
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$		−	4.00000i		−	0.195881i
$418$	−8.66025	+	5.00000i	−0.423587	+	0.244558i
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	0.920609	−	0.390487i	$-0.127693\pi$
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$	13.8564	+	8.00000i	0.674519	+	0.389434i
$423$	10.3923	+	6.00000i	0.505291	+	0.291730i
$424$		0			0
$425$		0			0
$426$	−1.50000	−	2.59808i	−0.0726752	−	0.125877i
$427$	38.1051	−	22.0000i	1.84404	−	1.06465i
$428$		−	8.00000i		−	0.386695i
$429$	12.5000	−	12.9904i	0.603506	−	0.627182i
$430$		0			0
$431$	14.5000	+	25.1147i	0.698440	+	1.20973i	0.969007	+	0.247033i	$0.0794556\pi$
$431$	14.5000	+	25.1147i	0.698440	+	1.20973i	−0.270567	+	0.962701i	$0.587211\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−16.4545	−	9.50000i	−0.790752	−	0.456541i	0.0494752	−	0.998775i	$-0.484245\pi$
$433$	−16.4545	−	9.50000i	−0.790752	−	0.456541i	−0.840227	+	0.542234i	$0.817578\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	8.50000	−	14.7224i	0.407076	−	0.705077i
$437$		−	14.0000i		−	0.669711i
$438$	−7.79423	−	4.50000i	−0.372423	−	0.215018i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	1.73205	−	7.00000i	0.0823853	−	0.332956i
$443$		−	25.0000i		−	1.18779i	−0.804544	−	0.593893i	$-0.797590\pi$
$443$		−	25.0000i		−	1.18779i	0.804544	−	0.593893i	$-0.202410\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$		0			0
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$		−	10.0000i		−	0.472984i
$448$	−3.46410	−	2.00000i	−0.163663	−	0.0944911i
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	−0.928091	−	0.372353i	$-0.878551\pi$
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	0.786513	+	0.617574i	$0.211885\pi$
$450$		0			0
$451$	25.0000	−	43.3013i	1.17720	−	2.03898i
$452$	3.46410	−	2.00000i	0.162938	−	0.0940721i
$453$	8.66025	−	5.00000i	0.406894	−	0.234920i
$454$	−9.00000			−0.422391
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	26.8468	−	15.5000i	1.25584	−	0.725059i	0.283577	−	0.958950i	$-0.408479\pi$
$457$	26.8468	−	15.5000i	1.25584	−	0.725059i	0.972263	+	0.233890i	$0.0751456\pi$
$458$	−16.4545	+	9.50000i	−0.768867	+	0.443906i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$		0			0
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.308651	+	0.951175i	$0.599877\pi$
$461$	−21.0000	+	36.3731i	−0.978068	+	1.69406i	−0.669417	+	0.742887i	$0.733456\pi$
$462$	−17.3205	−	10.0000i	−0.805823	−	0.465242i
$463$			38.0000i			1.76601i	0.469364	+	0.883005i	$0.344483\pi$
$463$			38.0000i			1.76601i	−0.469364	+	0.883005i	$0.655517\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$		0			0
$466$	−4.00000	−	6.92820i	−0.185296	−	0.320943i
$467$		−	9.00000i		−	0.416470i	−0.978079	−	0.208235i	$-0.933228\pi$
$467$		−	9.00000i		−	0.416470i	0.978079	−	0.208235i	$-0.0667719\pi$
$468$	3.46410	−	1.00000i	0.160128	−	0.0462250i
$469$	−16.0000			−0.738811
$470$		0			0
$471$	8.50000	+	14.7224i	0.391659	+	0.678374i
$472$		0			0
$473$		−	20.0000i		−	0.919601i
$474$	−7.00000	+	12.1244i	−0.321521	+	0.556890i
$475$		0			0
$476$	−8.00000			−0.366679
$477$		0			0
$478$	19.9186	−	11.5000i	0.911055	−	0.525998i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	3.00000	+	10.3923i	0.136788	+	0.473848i
$482$			14.0000i			0.637683i
$483$	24.2487	−	14.0000i	1.10335	−	0.637022i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$		0			0
$486$	1.00000			0.0453609
$487$	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	$0.408493\pi$
$488$	−9.52628	−	5.50000i	−0.431234	−	0.248973i
$489$	6.00000			0.271329
$490$		0			0
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	0.804084	−	0.594515i	$-0.202656\pi$
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	−0.916908	+	0.399100i	$0.869323\pi$
$492$	8.66025	−	5.00000i	0.390434	−	0.225417i
$493$		−	4.00000i		−	0.180151i
$494$	−7.00000	−	1.73205i	−0.314945	−	0.0779287i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	−10.3923	+	6.00000i	−0.466159	+	0.269137i
$498$	−2.59808	−	1.50000i	−0.116423	−	0.0672166i
$499$	−10.0000			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$500$		0			0
$501$	7.50000	−	12.9904i	0.335075	−	0.580367i
$502$		−	17.0000i		−	0.758747i
$503$	18.1865	+	10.5000i	0.810897	+	0.468172i	0.847267	−	0.531167i	$-0.178246\pi$
$503$	18.1865	+	10.5000i	0.810897	+	0.468172i	−0.0363700	+	0.999338i	$0.511579\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$		0			0
$506$	−35.0000			−1.55594
$507$	12.9904	−	0.500000i	0.576923	−	0.0222058i
$508$		−	22.0000i		−	0.976092i
$509$	−2.00000	−	3.46410i	−0.0886484	−	0.153544i	0.818292	−	0.574803i	$-0.194921\pi$
$509$	−2.00000	−	3.46410i	−0.0886484	−	0.153544i	−0.906940	+	0.421260i	$0.861588\pi$
$510$		0			0
$511$	−18.0000	+	31.1769i	−0.796273	+	1.37919i
$512$			1.00000i			0.0441942i
$513$	−1.73205	−	1.00000i	−0.0764719	−	0.0441511i
$514$	−14.0000	+	24.2487i	−0.617514	+	1.06956i
$515$		0			0
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−51.9615	+	30.0000i	−2.28527	+	1.31940i
$518$	10.3923	−	6.00000i	0.456612	−	0.263625i
$519$	−16.0000			−0.702322
$520$		0			0
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$	1.73205	−	1.00000i	0.0758098	−	0.0437688i
$523$	12.1244	−	7.00000i	0.530161	−	0.306089i	−0.210921	−	0.977503i	$-0.567646\pi$
$523$	12.1244	−	7.00000i	0.530161	−	0.306089i	0.741082	+	0.671414i	$0.234313\pi$
$524$	10.0000	−	17.3205i	0.436852	−	0.756650i
$525$		0			0
$526$	−4.50000	+	7.79423i	−0.196209	+	0.339845i
$527$	3.46410	+	2.00000i	0.150899	+	0.0871214i
$528$			5.00000i			0.217597i
$529$	13.0000	−	22.5167i	0.565217	−	0.978985i
$530$		0			0
$531$		0			0
$532$			8.00000i			0.346844i
$533$	34.6410	−	10.0000i	1.50047	−	0.433148i
$534$	10.0000			0.432742
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	0.866025	+	0.500000i	0.0373718	+	0.0215766i
$538$			4.00000i			0.172452i
$539$	−22.5000	+	38.9711i	−0.969144	+	1.67861i
$540$		0			0
$541$	−9.00000			−0.386940			−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000			−0.386940			−0.193470	+	0.981106i	$0.561974\pi$
$542$	−1.73205	−	1.00000i	−0.0743980	−	0.0429537i
$543$	−9.52628	+	5.50000i	−0.408812	+	0.236028i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$		0			0
$546$	−4.00000	−	13.8564i	−0.171184	−	0.592999i
$547$		−	30.0000i		−	1.28271i	−0.767245	−	0.641354i	$-0.778373\pi$
$547$		−	30.0000i		−	1.28271i	0.767245	−	0.641354i	$-0.221627\pi$
$548$	−6.92820	+	4.00000i	−0.295958	+	0.170872i
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$	−4.00000			−0.170406
$552$	−6.06218	−	3.50000i	−0.258023	−	0.148970i
$553$	48.4974	+	28.0000i	2.06232	+	1.19068i
$554$	31.0000			1.31706
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	13.8564	−	8.00000i	0.587115	−	0.338971i	−0.176841	−	0.984239i	$-0.556588\pi$
$557$	13.8564	−	8.00000i	0.587115	−	0.338971i	0.763956	+	0.645269i	$0.223255\pi$
$558$			2.00000i			0.0846668i
$559$	10.0000	−	10.3923i	0.422955	−	0.439548i
$560$		0			0
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	22.5167	−	13.0000i	0.949808	−	0.548372i
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	0.831614	−	0.555354i	$-0.187417\pi$
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	−0.0651433	+	0.997876i	$0.520750\pi$
$564$	−12.0000			−0.505291
$565$		0			0
$566$	14.0000	−	24.2487i	0.588464	−	1.01925i
$567$		−	4.00000i		−	0.167984i
$568$	2.59808	+	1.50000i	0.109013	+	0.0629386i
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$	−4.33013	+	17.5000i	−0.181052	+	0.731712i
$573$			23.0000i			0.960839i
$574$	−20.0000	−	34.6410i	−0.834784	−	1.44589i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			37.0000i			1.54033i	0.637845	+	0.770165i	$0.279826\pi$
$577$			37.0000i			1.54033i	−0.637845	+	0.770165i	$0.720174\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$	−1.50000	+	2.59808i	−0.0623379	+	0.107972i
$580$		0			0
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$	−11.2583	+	6.50000i	−0.466673	+	0.269434i
$583$		0			0
$584$	9.00000			0.372423
$585$		0			0
$586$	−24.0000			−0.991431
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	−0.552658	−	0.833408i	$-0.686386\pi$
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	0.445424	+	0.895320i	$0.353053\pi$
$588$	−7.79423	+	4.50000i	−0.321429	+	0.185577i
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$		0			0
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$			4.00000i			0.164260i	0.996622	+	0.0821302i	$0.0261723\pi$
$593$			4.00000i			0.164260i	−0.996622	+	0.0821302i	$0.973828\pi$
$594$	−2.50000	+	4.33013i	−0.102576	+	0.177667i
$595$		0			0
$596$	5.00000	+	8.66025i	0.204808	+	0.354738i
$597$			24.0000i			0.982255i
$598$	−18.1865	−	17.5000i	−0.743703	−	0.715628i
$599$	27.0000			1.10319			0.551595	−	0.834112i	$-0.314019\pi$
$599$	27.0000			1.10319			0.551595	+	0.834112i	$0.314019\pi$
$600$		0			0
$601$	9.00000	+	15.5885i	0.367118	+	0.635866i	0.989114	−	0.147154i	$-0.0470113\pi$
$601$	9.00000	+	15.5885i	0.367118	+	0.635866i	−0.621996	+	0.783020i	$0.713678\pi$
$602$	−13.8564	−	8.00000i	−0.564745	−	0.326056i
$603$			4.00000i			0.162893i
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$		0			0
$606$	8.00000			0.324978
$607$	−25.9808	−	15.0000i	−1.05453	−	0.608831i	−0.130613	−	0.991433i	$-0.541695\pi$
$607$	−25.9808	−	15.0000i	−1.05453	−	0.608831i	−0.923913	+	0.382602i	$0.875028\pi$
$608$	1.73205	−	1.00000i	0.0702439	−	0.0405554i
$609$	−4.00000	−	6.92820i	−0.162088	−	0.280745i
$610$		0			0
$611$	−42.0000	−	10.3923i	−1.69914	−	0.420428i
$612$			2.00000i			0.0808452i
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	−0.534570	−	0.845124i	$-0.679527\pi$
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	0.464614	+	0.885514i	$0.346193\pi$
$614$	−12.0000	−	20.7846i	−0.484281	−	0.838799i
$615$		0			0
$616$	20.0000			0.805823
$617$	12.1244	+	7.00000i	0.488108	+	0.281809i	0.723789	−	0.690021i	$-0.242399\pi$
$617$	12.1244	+	7.00000i	0.488108	+	0.281809i	−0.235681	+	0.971830i	$0.575732\pi$
$618$	−13.8564	−	8.00000i	−0.557386	−	0.321807i
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$		0			0
$621$	−3.50000	−	6.06218i	−0.140450	−	0.243267i
$622$	−6.06218	+	3.50000i	−0.243071	+	0.140337i
$623$		−	40.0000i		−	1.60257i
$624$	−2.50000	+	2.59808i	−0.100080	+	0.104006i
$625$		0			0
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	8.66025	−	5.00000i	0.345857	−	0.199681i
$628$	−14.7224	−	8.50000i	−0.587489	−	0.339187i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	7.00000	−	12.1244i	0.278666	−	0.482663i	−0.692388	−	0.721526i	$-0.743441\pi$
$631$	7.00000	−	12.1244i	0.278666	−	0.482663i	0.971053	+	0.238863i	$0.0767746\pi$
$632$		−	14.0000i		−	0.556890i
$633$	−13.8564	−	8.00000i	−0.550743	−	0.317971i
$634$	−14.0000	−	24.2487i	−0.556011	−	0.963039i
$635$		0			0
$636$		0			0
$637$	−31.1769	+	9.00000i	−1.23527	+	0.356593i
$638$			10.0000i			0.395904i
$639$	1.50000	+	2.59808i	0.0593391	+	0.102778i
$640$		0			0
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$			8.00000i			0.315735i
$643$	−22.5167	−	13.0000i	−0.887970	−	0.512670i	−0.0146923	−	0.999892i	$-0.504677\pi$
$643$	−22.5167	−	13.0000i	−0.887970	−	0.512670i	−0.873278	+	0.487222i	$0.838010\pi$
$644$	−14.0000	+	24.2487i	−0.551677	+	0.955533i
$645$		0			0
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$	−38.9711	+	22.5000i	−1.53211	+	0.884566i	−0.532850	+	0.846210i	$0.678879\pi$
$647$	−38.9711	+	22.5000i	−1.53211	+	0.884566i	−0.999264	+	0.0383563i	$0.987788\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$	8.00000			0.313545
$652$	−5.19615	+	3.00000i	−0.203497	+	0.117489i
$653$	−6.92820	+	4.00000i	−0.271122	+	0.156532i	−0.629397	−	0.777084i	$-0.716698\pi$
$653$	−6.92820	+	4.00000i	−0.271122	+	0.156532i	0.358276	+	0.933616i	$0.383365\pi$
$654$	−8.50000	+	14.7224i	−0.332376	+	0.575693i
$655$		0			0
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	7.79423	+	4.50000i	0.304082	+	0.175562i
$658$			48.0000i			1.87123i
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	0.473660	+	0.880708i	$0.342933\pi$
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	−0.999545	+	0.0301523i	$0.990401\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$		−	10.0000i		−	0.388661i
$663$	−1.73205	+	7.00000i	−0.0672673	+	0.271857i
$664$	3.00000			0.116423
$665$		0			0
$666$	−1.50000	−	2.59808i	−0.0581238	−	0.100673i
$667$	−12.1244	−	7.00000i	−0.469457	−	0.271041i
$668$			15.0000i			0.580367i
$669$	2.00000	−	3.46410i	0.0773245	−	0.133930i
$670$		0			0
$671$	55.0000			2.12325
$672$	3.46410	+	2.00000i	0.133631	+	0.0771517i
$673$	−0.866025	+	0.500000i	−0.0333828	+	0.0192736i	−0.516599	−	0.856228i	$-0.672802\pi$
$673$	−0.866025	+	0.500000i	−0.0333828	+	0.0192736i	0.483216	+	0.875501i	$0.339469\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$			4.00000i			0.153732i	0.997041	+	0.0768662i	$0.0244914\pi$
$677$			4.00000i			0.153732i	−0.997041	+	0.0768662i	$0.975509\pi$
$678$	−3.46410	+	2.00000i	−0.133038	+	0.0768095i
$679$	26.0000	+	45.0333i	0.997788	+	1.72822i
$680$		0			0
$681$	9.00000			0.344881
$682$	−8.66025	−	5.00000i	−0.331618	−	0.191460i
$683$	−12.9904	−	7.50000i	−0.497063	−	0.286980i	0.230437	−	0.973087i	$-0.425985\pi$
$683$	−12.9904	−	7.50000i	−0.497063	−	0.286980i	−0.727500	+	0.686108i	$0.759318\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$	16.4545	−	9.50000i	0.627778	−	0.362448i
$688$			4.00000i			0.152499i
$689$		0			0
$690$		0			0
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	0.984873	−	0.173275i	$-0.0554350\pi$
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	−0.642497	+	0.766288i	$0.722102\pi$
$692$	13.8564	−	8.00000i	0.526742	−	0.304114i
$693$	17.3205	+	10.0000i	0.657952	+	0.379869i
$694$	−11.0000			−0.417554
$695$		0			0
$696$	−1.00000	+	1.73205i	−0.0379049	+	0.0656532i
$697$			20.0000i			0.757554i
$698$	4.33013	+	2.50000i	0.163898	+	0.0946264i
$699$	4.00000	+	6.92820i	0.151294	+	0.262049i
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$	−3.46410	+	1.00000i	−0.130744	+	0.0377426i
$703$			6.00000i			0.226294i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$		0			0
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$		−	32.0000i		−	1.20348i
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$		0			0
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$	−8.66025	+	5.00000i	−0.324557	+	0.187383i
$713$	12.1244	−	7.00000i	0.454061	−	0.262152i
$714$	8.00000			0.299392
$715$		0			0
$716$	−1.00000			−0.0373718
$717$	−19.9186	+	11.5000i	−0.743873	+	0.429475i
$718$		0			0
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	−32.0000	+	55.4256i	−1.19174	+	2.06416i
$722$	12.9904	+	7.50000i	0.483452	+	0.279121i
$723$		−	14.0000i		−	0.520666i
$724$	5.50000	−	9.52628i	0.204406	−	0.354041i
$725$		0			0
$726$	−7.00000	−	12.1244i	−0.259794	−	0.449977i
$727$		−	14.0000i		−	0.519231i	−0.965712	−	0.259616i	$-0.916404\pi$
$727$		−	14.0000i		−	0.519231i	0.965712	−	0.259616i	$-0.0835959\pi$
$728$	10.3923	+	10.0000i	0.385164	+	0.370625i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	9.52628	+	5.50000i	0.352101	+	0.203286i
$733$		−	33.0000i		−	1.21888i	−0.792831	−	0.609441i	$-0.791394\pi$
$733$		−	33.0000i		−	1.21888i	0.792831	−	0.609441i	$-0.208606\pi$
$734$	5.00000	−	8.66025i	0.184553	−	0.319656i
$735$		0			0
$736$	7.00000			0.258023
$737$	−17.3205	−	10.0000i	−0.638009	−	0.368355i
$738$	−8.66025	+	5.00000i	−0.318788	+	0.184053i
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	0.968839	+	0.247691i	$0.0796718\pi$
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	−0.269913	+	0.962885i	$0.586995\pi$
$740$		0			0
$741$	7.00000	+	1.73205i	0.257151	+	0.0636285i
$742$		0			0
$743$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$743$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$		0			0
$746$	−17.0000			−0.622414
$747$	2.59808	+	1.50000i	0.0950586	+	0.0548821i
$748$	−8.66025	−	5.00000i	−0.316650	−	0.182818i
$749$	32.0000			1.16925
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	10.3923	−	6.00000i	0.378968	−	0.218797i
$753$			17.0000i			0.619514i
$754$	−5.00000	+	5.19615i	−0.182089	+	0.189233i
$755$		0			0
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	−19.0526	+	11.0000i	−0.692477	+	0.399802i	−0.804539	−	0.593899i	$-0.797588\pi$
$757$	−19.0526	+	11.0000i	−0.692477	+	0.399802i	0.112062	+	0.993701i	$0.464254\pi$
$758$	8.66025	+	5.00000i	0.314555	+	0.181608i
$759$	35.0000			1.27042
$760$		0			0
$761$	8.00000	−	13.8564i	0.290000	−	0.502294i	−0.683810	−	0.729661i	$-0.739678\pi$
$761$	8.00000	−	13.8564i	0.290000	−	0.502294i	0.973809	+	0.227366i	$0.0730114\pi$
$762$			22.0000i			0.796976i
$763$	58.8897	+	34.0000i	2.13195	+	1.23088i
$764$	−11.5000	−	19.9186i	−0.416055	−	0.720629i
$765$		0			0
$766$	−37.0000			−1.33686
$767$		0			0
$768$		−	1.00000i		−	0.0360844i
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	0.530572	−	0.847640i	$-0.321977\pi$
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	−0.999364	+	0.0356685i	$0.988644\pi$
$770$		0			0
$771$	14.0000	−	24.2487i	0.504198	−	0.873296i
$772$		−	3.00000i		−	0.107972i
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	0.265852	−	0.964014i	$-0.414347\pi$
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	−0.701935	+	0.712241i	$0.747680\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$		0			0
$776$	6.50000	−	11.2583i	0.233336	−	0.404151i
$777$	−10.3923	+	6.00000i	−0.372822	+	0.215249i
$778$	−22.5167	+	13.0000i	−0.807261	+	0.466073i
$779$	20.0000			0.716574
$780$		0			0
$781$	−15.0000			−0.536742
$782$	12.1244	−	7.00000i	0.433566	−	0.250319i
$783$	−1.73205	+	1.00000i	−0.0618984	+	0.0357371i
$784$	4.50000	−	7.79423i	0.160714	−	0.278365i
$785$		0			0
$786$	−10.0000	+	17.3205i	−0.356688	+	0.617802i
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.954403	−	0.298521i	$-0.0964933\pi$
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.218675	+	0.975798i	$0.429827\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	8.00000	+	13.8564i	0.284447	+	0.492677i
$792$		−	5.00000i		−	0.177667i
$793$	28.5788	+	27.5000i	1.01486	+	0.976554i
$794$	30.0000			1.06466
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	0.672634	−	0.739975i	$-0.265163\pi$
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	−0.304520	+	0.952506i	$0.598496\pi$
$798$		−	8.00000i		−	0.283197i
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$		0			0
$801$	−10.0000			−0.353333
$802$	−15.5885	−	9.00000i	−0.550448	−	0.317801i
$803$	−38.9711	+	22.5000i	−1.37526	+	0.794008i
$804$	−2.00000	−	3.46410i	−0.0705346	−	0.122169i
$805$		0			0
$806$	−2.00000	−	6.92820i	−0.0704470	−	0.244036i
$807$		−	4.00000i		−	0.140807i
$808$	−6.92820	+	4.00000i	−0.243733	+	0.140720i
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		0			0
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$	6.92820	+	4.00000i	0.243132	+	0.140372i
$813$	1.73205	+	1.00000i	0.0607457	+	0.0350715i
$814$	15.0000			0.525750
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	6.92820	−	4.00000i	0.242387	−	0.139942i
$818$			30.0000i			1.04893i
$819$	4.00000	+	13.8564i	0.139771	+	0.484182i
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$	6.92820	−	4.00000i	0.241649	−	0.139516i
$823$	−24.2487	−	14.0000i	−0.845257	−	0.488009i	0.0137907	−	0.999905i	$-0.495610\pi$
$823$	−24.2487	−	14.0000i	−0.845257	−	0.488009i	−0.859048	+	0.511896i	$0.828943\pi$
$824$	16.0000			0.557386
$825$		0			0
$826$		0			0
$827$		−	43.0000i		−	1.49526i	−0.664117	−	0.747628i	$-0.731193\pi$
$827$		−	43.0000i		−	1.49526i	0.664117	−	0.747628i	$-0.268807\pi$
$828$	6.06218	+	3.50000i	0.210675	+	0.121633i
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$		0			0
$831$	−31.0000			−1.07538
$832$	0.866025	−	3.50000i	0.0300240	−	0.121341i
$833$		−	18.0000i		−	0.623663i
$834$	−2.00000	−	3.46410i	−0.0692543	−	0.119952i
$835$		0			0
$836$	−5.00000	+	8.66025i	−0.172929	+	0.299521i
$837$		−	2.00000i		−	0.0691301i
$838$	4.33013	+	2.50000i	0.149582	+	0.0863611i
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	19.9186	−	11.5000i	0.686440	−	0.396316i
$843$	−22.5167	+	13.0000i	−0.775515	+	0.447744i
$844$	16.0000			0.550743
$845$		0			0
$846$	12.0000			0.412568
$847$	−48.4974	+	28.0000i	−1.66639	+	0.962091i
$848$		0			0
$849$	−14.0000	+	24.2487i	−0.480479	+	0.832214i
$850$		0			0
$851$	−10.5000	+	18.1865i	−0.359935	+	0.623426i
$852$	−2.59808	−	1.50000i	−0.0890086	−	0.0513892i
$853$		−	22.0000i		−	0.753266i	−0.926363	−	0.376633i	$-0.877082\pi$
$853$		−	22.0000i		−	0.753266i	0.926363	−	0.376633i	$-0.122918\pi$
$854$	22.0000	−	38.1051i	0.752825	−	1.30393i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$			22.0000i			0.751506i	0.926720	+	0.375753i	$0.122616\pi$
$857$			22.0000i			0.751506i	−0.926720	+	0.375753i	$0.877384\pi$
$858$	4.33013	−	17.5000i	0.147828	−	0.597440i
$859$	26.0000			0.887109			0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000			0.887109			0.443554	+	0.896248i	$0.353717\pi$
$860$		0			0
$861$	20.0000	+	34.6410i	0.681598	+	1.18056i
$862$	25.1147	+	14.5000i	0.855411	+	0.493872i
$863$			45.0000i			1.53182i	0.642949	+	0.765909i	$0.277711\pi$
$863$			45.0000i			1.53182i	−0.642949	+	0.765909i	$0.722289\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−19.0000			−0.645646
$867$	11.2583	+	6.50000i	0.382353	+	0.220752i
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$	35.0000	+	60.6218i	1.18729	+	2.05645i
$870$		0			0
$871$	−4.00000	−	13.8564i	−0.135535	−	0.469506i
$872$		−	17.0000i		−	0.575693i
$873$	11.2583	−	6.50000i	0.381037	−	0.219992i
$874$	−7.00000	−	12.1244i	−0.236779	−	0.410112i
$875$		0			0
$876$	−9.00000			−0.304082
$877$	−26.8468	−	15.5000i	−0.906552	−	0.523398i	−0.0272316	−	0.999629i	$-0.508669\pi$
$877$	−26.8468	−	15.5000i	−0.906552	−	0.523398i	−0.879320	+	0.476231i	$0.842002\pi$
$878$	6.92820	+	4.00000i	0.233816	+	0.134993i
$879$	24.0000			0.809500
$880$		0			0
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	−0.991823	−	0.127622i	$-0.959266\pi$
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	0.385387	−	0.922755i	$-0.374068\pi$
$882$	7.79423	−	4.50000i	0.262445	−	0.151523i
$883$		−	40.0000i		−	1.34611i	−0.739594	−	0.673054i	$-0.764982\pi$
$883$		−	40.0000i		−	1.34611i	0.739594	−	0.673054i	$-0.235018\pi$
$884$	−2.00000	−	6.92820i	−0.0672673	−	0.233021i
$885$		0			0
$886$	−12.5000	−	21.6506i	−0.419946	−	0.727367i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$	2.59808	+	1.50000i	0.0871857	+	0.0503367i
$889$	88.0000			2.95143
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$			4.00000i			0.133930i
$893$	−20.7846	−	12.0000i	−0.695530	−	0.401565i
$894$	−5.00000	−	8.66025i	−0.167225	−	0.289642i
$895$		0			0
$896$	−4.00000			−0.133631
$897$	18.1865	+	17.5000i	0.607231	+	0.584308i
$898$			6.00000i			0.200223i
$899$	−2.00000	−	3.46410i	−0.0667037	−	0.115534i
$900$		0			0
$901$		0			0
$902$		−	50.0000i		−	1.66482i
$903$	13.8564	+	8.00000i	0.461112	+	0.266223i
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$		0			0
$906$	5.00000	−	8.66025i	0.166114	−	0.287718i
$907$	−34.6410	+	20.0000i	−1.15024	+	0.664089i	−0.948945	−	0.315442i	$-0.897847\pi$
$907$	−34.6410	+	20.0000i	−1.15024	+	0.664089i	−0.201291	+	0.979531i	$0.564514\pi$
$908$	−7.79423	+	4.50000i	−0.258661	+	0.149338i
$909$	−8.00000			−0.265343
$910$		0			0
$911$	27.0000			0.894550			0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000			0.894550			0.447275	+	0.894397i	$0.352395\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$	−12.9904	+	7.50000i	−0.429919	+	0.248214i
$914$	15.5000	−	26.8468i	0.512694	−	0.888013i
$915$		0			0
$916$	−9.50000	+	16.4545i	−0.313889	+	0.543671i
$917$	69.2820	+	40.0000i	2.28789	+	1.32092i
$918$		−	2.00000i		−	0.0660098i
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	−0.936632	−	0.350315i	$-0.886075\pi$
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	0.771697	+	0.635990i	$0.219408\pi$
$920$		0			0
$921$	12.0000	+	20.7846i	0.395413	+	0.684876i
$922$			42.0000i			1.38320i
$923$	−7.79423	−	7.50000i	−0.256550	−	0.246866i
$924$	−20.0000			−0.657952
$925$		0			0
$926$	19.0000	+	32.9090i	0.624379	+	1.08146i
$927$	13.8564	+	8.00000i	0.455104	+	0.262754i
$928$		−	2.00000i		−	0.0656532i
$929$	−8.00000	+	13.8564i	−0.262471	+	0.454614i	−0.966898	−	0.255163i	$-0.917871\pi$
$929$	−8.00000	+	13.8564i	−0.262471	+	0.454614i	0.704427	+	0.709777i	$0.251204\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$	−6.92820	−	4.00000i	−0.226941	−	0.131024i
$933$	6.06218	−	3.50000i	0.198467	−	0.114585i
$934$	−4.50000	−	7.79423i	−0.147244	−	0.255035i
$935$		0			0
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$		−	43.0000i		−	1.40475i	−0.711808	−	0.702374i	$-0.752123\pi$
$937$		−	43.0000i		−	1.40475i	0.711808	−	0.702374i	$-0.247877\pi$
$938$	−13.8564	+	8.00000i	−0.452428	+	0.261209i
$939$	0.500000	+	0.866025i	0.0163169	+	0.0282617i
$940$		0			0
$941$	40.0000			1.30396			0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000			1.30396			0.651981	+	0.758235i	$0.273938\pi$
$942$	14.7224	+	8.50000i	0.479683	+	0.276945i
$943$	60.6218	+	35.0000i	1.97412	+	1.13976i
$944$		0			0
$945$		0			0
$946$	−10.0000	−	17.3205i	−0.325128	−	0.563138i
$947$	−9.52628	+	5.50000i	−0.309562	+	0.178726i	−0.646731	−	0.762718i	$-0.723864\pi$
$947$	−9.52628	+	5.50000i	−0.309562	+	0.178726i	0.337168	+	0.941444i	$0.390531\pi$
$948$			14.0000i			0.454699i
$949$	−31.5000	−	7.79423i	−1.02253	−	0.253011i
$950$		0			0
$951$	14.0000	+	24.2487i	0.453981	+	0.786318i
$952$	−6.92820	+	4.00000i	−0.224544	+	0.129641i
$953$	51.9615	+	30.0000i	1.68320	+	0.971795i	0.959512	+	0.281666i	$0.0908872\pi$
$953$	51.9615	+	30.0000i	1.68320	+	0.971795i	0.723686	+	0.690129i	$0.242446\pi$
$954$		0			0
$955$		0			0
$956$	11.5000	−	19.9186i	0.371937	−	0.644213i
$957$		−	10.0000i		−	0.323254i
$958$	−20.7846	−	12.0000i	−0.671520	−	0.387702i
$959$	−16.0000	−	27.7128i	−0.516667	−	0.894893i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	7.79423	+	7.50000i	0.251296	+	0.241810i
$963$		−	8.00000i		−	0.257796i
$964$	7.00000	+	12.1244i	0.225455	+	0.390499i
$965$		0			0
$966$	14.0000	−	24.2487i	0.450443	−	0.780189i
$967$		−	14.0000i		−	0.450210i	−0.974335	−	0.225105i	$-0.927728\pi$
$967$		−	14.0000i		−	0.450210i	0.974335	−	0.225105i	$-0.0722725\pi$
$968$	12.1244	+	7.00000i	0.389692	+	0.224989i
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−13.8564	+	8.00000i	−0.444216	+	0.256468i
$974$	32.0000			1.02535
$975$		0			0
$976$	−11.0000			−0.352101
$977$	−31.1769	+	18.0000i	−0.997438	+	0.575871i	−0.907489	−	0.420075i	$-0.862004\pi$
$977$	−31.1769	+	18.0000i	−0.997438	+	0.575871i	−0.0899487	+	0.995946i	$0.528670\pi$
$978$	5.19615	−	3.00000i	0.166155	−	0.0959294i
$979$	25.0000	−	43.3013i	0.799003	−	1.38391i
$980$		0			0
$981$	8.50000	−	14.7224i	0.271384	−	0.470051i
$982$	−4.33013	−	2.50000i	−0.138180	−	0.0797782i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	5.00000	−	8.66025i	0.159394	−	0.276079i
$985$		0			0
$986$	−2.00000	−	3.46410i	−0.0636930	−	0.110319i
$987$		−	48.0000i		−	1.52786i
$988$	−6.92820	+	2.00000i	−0.220416	+	0.0636285i
$989$	28.0000			0.890348
$990$		0			0
$991$	22.0000	+	38.1051i	0.698853	+	1.21045i	0.968864	+	0.247592i	$0.0796392\pi$
$991$	22.0000	+	38.1051i	0.698853	+	1.21045i	−0.270011	+	0.962857i	$0.587027\pi$
$992$	1.73205	+	1.00000i	0.0549927	+	0.0317500i
$993$			10.0000i			0.317340i
$994$	−6.00000	+	10.3923i	−0.190308	+	0.329624i
$995$		0			0
$996$	−3.00000			−0.0950586
$997$	−1.73205	−	1.00000i	−0.0548546	−	0.0316703i	0.472322	−	0.881426i	$-0.343416\pi$
$997$	−1.73205	−	1.00000i	−0.0548546	−	0.0316703i	−0.527176	+	0.849756i	$0.676749\pi$
$998$	−8.66025	+	5.00000i	−0.274136	+	0.158272i
$999$	1.50000	+	2.59808i	0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.f.1849.2		4
5.2	odd	4		1950.2.i.u.601.1	yes	2
5.3	odd	4		1950.2.i.h.601.1	yes	2
5.4	even	2	inner	1950.2.z.f.1849.1		4
13.9	even	3	inner	1950.2.z.f.1699.1		4
65.9	even	6	inner	1950.2.z.f.1699.2		4
65.22	odd	12		1950.2.i.u.451.1	yes	2
65.48	odd	12		1950.2.i.h.451.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.h.451.1	✓	2	65.48	odd	12
1950.2.i.h.601.1	yes	2	5.3	odd	4
1950.2.i.u.451.1	yes	2	65.22	odd	12
1950.2.i.u.601.1	yes	2	5.2	odd	4
1950.2.z.f.1699.1		4	13.9	even	3	inner
1950.2.z.f.1699.2		4	65.9	even	6	inner
1950.2.z.f.1849.1		4	5.4	even	2	inner
1950.2.z.f.1849.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000i q^{12} +(-0.866025 + 3.50000i) q^{13} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} -1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} -4.00000 q^{21} +(4.33013 + 2.50000i) q^{22} +(-6.06218 + 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(3.46410 - 2.00000i) q^{28} +(1.00000 + 1.73205i) q^{29} -2.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.33013 - 2.50000i) q^{33} -2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} +2.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(-5.00000 - 8.66025i) q^{41} +(-3.46410 + 2.00000i) q^{42} +(-3.46410 - 2.00000i) q^{43} +5.00000 q^{44} +(-3.50000 + 6.06218i) q^{46} +12.0000i q^{47} +(0.866025 + 0.500000i) q^{48} +(4.50000 + 7.79423i) q^{49} +2.00000 q^{51} +(2.59808 + 2.50000i) q^{52} +(0.500000 + 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{56} -2.00000i q^{57} +(1.73205 + 1.00000i) q^{58} +(5.50000 - 9.52628i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} -5.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(3.50000 - 6.06218i) q^{69} +(-1.50000 + 2.59808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +9.00000i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} +20.0000i q^{77} +(-2.59808 - 2.50000i) q^{78} +14.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.66025 - 5.00000i) q^{82} +3.00000i q^{83} +(-2.00000 + 3.46410i) q^{84} -4.00000 q^{86} +(-1.73205 - 1.00000i) q^{87} +(4.33013 - 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(-10.0000 + 10.3923i) q^{91} +7.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} +1.00000 q^{96} +(11.2583 + 6.50000i) q^{97} +(7.79423 + 4.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 10 q^{11} + 16 q^{14} - 2 q^{16} - 4 q^{19} - 16 q^{21} + 2 q^{24} + 4 q^{26} + 4 q^{29} - 8 q^{31} - 8 q^{34} - 2 q^{36} - 4 q^{39} - 20 q^{41} + 20 q^{44} - 14 q^{46} + 18 q^{49} + 8 q^{51} + 2 q^{54} + 8 q^{56} + 22 q^{61} - 4 q^{64} - 20 q^{66} + 14 q^{69} - 6 q^{71} + 6 q^{74} + 4 q^{76} + 56 q^{79} - 2 q^{81} - 8 q^{84} - 16 q^{86} - 20 q^{89} - 40 q^{91} + 24 q^{94} + 4 q^{96} + 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 10 * q^11 + 16 * q^14 - 2 * q^16 - 4 * q^19 - 16 * q^21 + 2 * q^24 + 4 * q^26 + 4 * q^29 - 8 * q^31 - 8 * q^34 - 2 * q^36 - 4 * q^39 - 20 * q^41 + 20 * q^44 - 14 * q^46 + 18 * q^49 + 8 * q^51 + 2 * q^54 + 8 * q^56 + 22 * q^61 - 4 * q^64 - 20 * q^66 + 14 * q^69 - 6 * q^71 + 6 * q^74 + 4 * q^76 + 56 * q^79 - 2 * q^81 - 8 * q^84 - 16 * q^86 - 20 * q^89 - 40 * q^91 + 24 * q^94 + 4 * q^96 + 20 * q^99

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