LMFDB - Embedded newform 1274.2.f.p.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(79,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1274.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.79
Dual form			1274.2.f.p.1145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -3.00000 q^{20} -6.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} -5.00000 q^{27} +6.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +3.00000 q^{34} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} -1.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{47} +1.00000 q^{48} -4.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{54} -18.0000 q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(3.00000 + 5.19615i) q^{59} +(1.50000 + 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-7.00000 - 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{75} +2.00000 q^{76} -1.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(3.00000 - 5.19615i) q^{89} -6.00000 q^{90} +(2.00000 - 3.46410i) q^{93} +(1.50000 + 2.59808i) q^{94} +(3.00000 + 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 6 q^{11} - q^{12} + 2 q^{13} - 6 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{22} + q^{24} - 4 q^{25} + q^{26} - 10 q^{27} + 12 q^{29} - 3 q^{30} + 4 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} - 4 q^{36} + 7 q^{37} + 2 q^{38} - q^{39} - 3 q^{40} - 2 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{47} + 2 q^{48} - 8 q^{50} + 3 q^{51} - q^{52} - 5 q^{54} - 36 q^{55} + 4 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{60} - 8 q^{61} + 8 q^{62} + 2 q^{64} + 3 q^{65} + 6 q^{66} - 14 q^{67} + 3 q^{68} - 6 q^{71} - 2 q^{72} - 2 q^{73} - 7 q^{74} - 4 q^{75} + 4 q^{76} - 2 q^{78} - 8 q^{79} + 3 q^{80} - q^{81} + 24 q^{83} + 18 q^{85} - q^{86} - 6 q^{87} + 6 q^{88} + 6 q^{89} - 12 q^{90} + 4 q^{93} + 3 q^{94} + 6 q^{95} + q^{96} - 20 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 6 * q^11 - q^12 + 2 * q^13 - 6 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^22 + q^24 - 4 * q^25 + q^26 - 10 * q^27 + 12 * q^29 - 3 * q^30 + 4 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - 4 * q^36 + 7 * q^37 + 2 * q^38 - q^39 - 3 * q^40 - 2 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^47 + 2 * q^48 - 8 * q^50 + 3 * q^51 - q^52 - 5 * q^54 - 36 * q^55 + 4 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^60 - 8 * q^61 + 8 * q^62 + 2 * q^64 + 3 * q^65 + 6 * q^66 - 14 * q^67 + 3 * q^68 - 6 * q^71 - 2 * q^72 - 2 * q^73 - 7 * q^74 - 4 * q^75 + 4 * q^76 - 2 * q^78 - 8 * q^79 + 3 * q^80 - q^81 + 24 * q^83 + 18 * q^85 - q^86 - 6 * q^87 + 6 * q^88 + 6 * q^89 - 12 * q^90 + 4 * q^93 + 3 * q^94 + 6 * q^95 + q^96 - 20 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−3.00000			−0.774597
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	−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	$0.240348\pi$
$20$	−3.00000			−0.670820
$21$		0			0
$22$	−6.00000			−1.27920
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−5.00000			−0.962250
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	3.00000			0.514496
$35$		0			0
$36$	−2.00000			−0.333333
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−4.00000			−0.565685
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$	−18.0000			−2.42712
$56$		0			0
$57$	2.00000			0.264906
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	1.50000	+	2.59808i	0.193649	+	0.335410i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	2.00000			0.229416
$77$		0			0
$78$	−1.00000			−0.113228
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$	−7.00000			−0.664411
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$	6.00000			0.552345
$119$		0			0
$120$	3.00000			0.273861
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	3.00000			0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.114024	−	0.993478i	$-0.463626\pi$
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.803365	−	0.595487i	$-0.203041\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−14.0000			−1.20942
$135$	−7.50000	+	12.9904i	−0.645497	+	1.11803i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$	−1.50000	+	2.59808i	−0.125877	+	0.218026i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	−7.00000			−0.575396
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	−0.971274	−	0.237964i	$-0.923520\pi$
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	0.279554	−	0.960130i	$-0.409814\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	6.00000			0.485071
$154$		0			0
$155$	12.0000			0.963863
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	3.00000			0.237171
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$	9.00000	+	15.5885i	0.700649	+	1.21356i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	4.50000	−	7.79423i	0.345134	−	0.597790i
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$	6.00000			0.452267
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$	−3.00000	+	5.19615i	−0.223607	+	0.387298i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	3.00000			0.218797
$189$		0			0
$190$	6.00000			0.435286
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$	−3.00000			−0.214834
$196$		0			0
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$	−6.00000	+	10.3923i	−0.426401	+	0.738549i
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	0.828403	−	0.560133i	$-0.189250\pi$
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	−0.899291	+	0.437351i	$0.855917\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−7.00000	+	12.1244i	−0.493742	+	0.855186i
$202$	12.0000			0.844317
$203$		0			0
$204$	−3.00000			−0.210042
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	12.0000			0.830057
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		0			0
$213$	1.50000	+	2.59808i	0.102778	+	0.178017i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$	5.00000			0.340207
$217$		0			0
$218$	7.00000			0.474100
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$	−3.50000	+	6.06218i	−0.234905	+	0.406867i
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$	−8.00000			−0.533333
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.0380310	−	0.999277i	$-0.487891\pi$
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.846383	−	0.532574i	$-0.178775\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	8.00000			0.519656
$238$		0			0
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	1.50000	−	2.59808i	0.0968246	−	0.167705i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	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
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	−4.50000	−	7.79423i	−0.281801	−	0.488094i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	−0.971558	−	0.236802i	$-0.923901\pi$
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	0.690856	+	0.722993i	$0.257234\pi$
$258$	1.00000			0.0622573
$259$		0			0
$260$	−3.00000			−0.186052
$261$	6.00000	−	10.3923i	0.371391	−	0.643268i
$262$	−10.5000	−	18.1865i	−0.648692	−	1.12357i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$		0			0
$267$	−6.00000			−0.367194
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$	7.50000	+	12.9904i	0.456435	+	0.790569i
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$		0			0
$275$	−12.0000	+	20.7846i	−0.723627	+	1.25336i
$276$		0			0
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$	−6.50000	+	11.2583i	−0.389844	+	0.675230i
$279$	8.00000			0.478947
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	3.00000	−	5.19615i	0.177705	−	0.307794i
$286$	−6.00000			−0.354787
$287$		0			0
$288$	2.00000			0.117851
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000	−	15.5885i	−0.528498	−	0.915386i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$	18.0000			1.04800
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$		0			0
$300$	4.00000			0.230940
$301$		0			0
$302$	−17.0000			−0.978240
$303$	6.00000	−	10.3923i	0.344691	−	0.597022i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	12.0000	+	20.7846i	0.687118	+	1.19012i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$	12.0000			0.669775
$322$		0			0
$323$	−6.00000			−0.333849
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	−8.00000	−	13.8564i	−0.443079	−	0.767435i
$327$	3.50000	−	6.06218i	0.193550	−	0.335239i
$328$		0			0
$329$		0			0
$330$	18.0000			0.990867
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	−7.00000	−	12.1244i	−0.383598	−	0.664411i
$334$		0			0
$335$	−42.0000			−2.29471
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$	4.00000			0.216295
$343$		0			0
$344$	1.00000			0.0539164
$345$		0			0
$346$		0			0
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	0.822951	−	0.568112i	$-0.192326\pi$
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	−0.903475	+	0.428640i	$0.858993\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−19.0000			−1.01705			−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000			−1.01705			−0.508523	+	0.861048i	$0.669808\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$	3.00000	−	5.19615i	0.159901	−	0.276956i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−3.00000			−0.158555
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	10.0000	−	17.3205i	0.525588	−	0.910346i
$363$	25.0000			1.31216
$364$		0			0
$365$	−6.00000			−0.314054
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$		0			0
$369$		0			0
$370$	−21.0000			−1.09174
$371$		0			0
$372$	−4.00000			−0.207390
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$	6.00000			0.309016
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	−10.0000	−	17.3205i	−0.512316	−	0.887357i
$382$	−9.00000	−	15.5885i	−0.460480	−	0.797575i
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	4.00000			0.203595
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	−1.50000	+	2.59808i	−0.0759555	+	0.131559i
$391$		0			0
$392$		0			0
$393$	−21.0000			−1.05931
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	17.0000	−	29.4449i	0.853206	−	1.47780i	0.878300	−	0.478110i	$-0.158678\pi$
$398$	−2.00000			−0.100251
$399$		0			0
$400$	4.00000			0.200000
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.0699455	+	0.997551i	$0.522283\pi$
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.828932	+	0.559350i	$0.811051\pi$
$402$	7.00000	+	12.1244i	0.349128	+	0.604708i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$	−3.00000			−0.149071
$406$		0			0
$407$	−42.0000			−2.08186
$408$	−1.50000	+	2.59808i	−0.0742611	+	0.128624i
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000			−0.197066
$413$		0			0
$414$		0			0
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	6.50000	+	11.2583i	0.318306	+	0.551323i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	3.00000			0.145350
$427$		0			0
$428$	12.0000			0.580042
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	1.50000	+	2.59808i	0.0723364	+	0.125290i
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	0.922981	+	0.384846i	$0.125746\pi$
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	−0.128204	+	0.991748i	$0.540921\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$		0			0
$435$	−18.0000			−0.863034
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$		0			0
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	0.368945	+	0.929451i	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$	18.0000			0.858116
$441$		0			0
$442$	3.00000			0.142695
$443$	−10.5000	+	18.1865i	−0.498870	+	0.864068i	−0.999999	−	0.00130426i	$-0.999585\pi$
$443$	−10.5000	+	18.1865i	−0.498870	+	0.864068i	0.501129	+	0.865373i	$0.332918\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−4.00000	+	6.92820i	−0.188562	+	0.326599i
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−8.50000	+	14.7224i	−0.399365	+	0.691720i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	9.00000			0.419172			0.209586	−	0.977790i	$-0.432788\pi$
$461$	9.00000			0.419172			0.209586	+	0.977790i	$0.432788\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	9.00000			0.415139
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	8.00000			0.367065
$476$		0			0
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$	−1.50000	−	2.59808i	−0.0684653	−	0.118585i
$481$	3.50000	−	6.06218i	0.159586	−	0.276412i
$482$	10.0000			0.455488
$483$		0			0
$484$	25.0000			1.13636
$485$	−15.0000	+	25.9808i	−0.681115	+	1.17973i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	0.988374	−	0.152042i	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	1.00000	+	1.73205i	0.0449921	+	0.0779287i
$495$	−18.0000	+	31.1769i	−0.809040	+	1.40130i
$496$	−4.00000			−0.179605
$497$		0			0
$498$	−12.0000			−0.537733
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	−30.0000			−1.33763			−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000			−1.33763			−0.668817	+	0.743427i	$0.733199\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	−10.0000	−	17.3205i	−0.443678	−	0.768473i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$	−9.00000			−0.398527
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	4.50000	+	7.79423i	0.198486	+	0.343789i
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$	18.0000			0.791639
$518$		0			0
$519$		0			0
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	0.947603	−	0.319451i	$-0.103499\pi$
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	−0.750454	+	0.660922i	$0.770165\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−21.0000			−0.917389
$525$		0			0
$526$	12.0000			0.523225
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$	−24.0000			−1.03471
$539$		0			0
$540$	15.0000			0.645497
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$	−10.0000	−	17.3205i	−0.429141	−	0.743294i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	21.0000			0.899541
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$		0			0
$549$	8.00000	+	13.8564i	0.341432	+	0.591377i
$550$	12.0000	+	20.7846i	0.511682	+	0.886259i
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$		0			0
$554$	28.0000			1.18961
$555$	−10.5000	+	18.1865i	−0.445700	+	0.771975i
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	−1.00000			−0.0422955
$560$		0			0
$561$	−18.0000			−0.759961
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	−0.904320	−	0.426855i	$-0.859622\pi$
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	0.0824933	−	0.996592i	$-0.473712\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	4.00000			0.168133
$567$		0			0
$568$	3.00000			0.125877
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$	−3.00000	−	5.19615i	−0.125656	−	0.217643i
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	−0.925361	−	0.379088i	$-0.876238\pi$
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	0.134380	−	0.990930i	$-0.457096\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	−18.0000			−0.747409
$581$		0			0
$582$	10.0000			0.414513
$583$		0			0
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	10.5000	−	18.1865i	0.433751	−	0.751279i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$	9.00000	−	15.5885i	0.370524	−	0.641767i
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−1.00000	+	1.73205i	−0.0409273	+	0.0708881i
$598$		0			0
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	−19.0000			−0.775026			−0.387513	−	0.921864i	$-0.626666\pi$
$601$	−19.0000			−0.775026			−0.387513	+	0.921864i	$0.626666\pi$
$602$		0			0
$603$	−28.0000			−1.14025
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$	37.5000	+	64.9519i	1.52459	+	2.64067i
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	−2.00000			−0.0811107
$609$		0			0
$610$	24.0000			0.971732
$611$	−1.50000	+	2.59808i	−0.0606835	+	0.105107i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$		0			0
$617$	−24.0000			−0.966204			−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000			−0.966204			−0.483102	+	0.875564i	$0.660490\pi$
$618$	−2.00000	+	3.46410i	−0.0804518	+	0.139347i
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	0.997259	+	0.0739910i	$0.0235736\pi$
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$		0			0
$622$	30.0000			1.20289
$623$		0			0
$624$	1.00000			0.0400320
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	21.0000			0.837325
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	6.50000	+	11.2583i	0.258352	+	0.447478i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	30.0000	−	51.9615i	1.19051	−	2.06203i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$		0			0
$645$	3.00000			0.118125
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	−16.0000			−0.626608
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−3.50000	−	6.06218i	−0.136861	−	0.237050i
$655$	−31.5000	−	54.5596i	−1.23081	−	2.13182i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	9.00000	−	15.5885i	0.350325	−	0.606780i
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	1.50000	−	2.59808i	0.0582552	−	0.100901i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−14.0000			−0.542489
$667$		0			0
$668$		0			0
$669$	9.50000	+	16.4545i	0.367291	+	0.636167i
$670$	−21.0000	+	36.3731i	−0.811301	+	1.40521i
$671$	48.0000			1.85302
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	11.5000	−	19.9186i	0.442963	−	0.767235i
$675$	10.0000	+	17.3205i	0.384900	+	0.666667i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−24.0000	+	41.5692i	−0.922395	+	1.59763i	−0.126697	+	0.991941i	$0.540438\pi$
$677$	−24.0000	+	41.5692i	−0.922395	+	1.59763i	−0.795698	+	0.605693i	$0.792896\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$	−9.00000			−0.345134
$681$		0			0
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$		0			0
$686$		0			0
$687$	−13.0000			−0.495981
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$		0			0
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$		0			0
$693$		0			0
$694$	−3.00000			−0.113878
$695$	−19.5000	+	33.7750i	−0.739677	+	1.28116i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$		0			0
$698$	−9.50000	+	16.4545i	−0.359580	+	0.622811i
$699$	−27.0000			−1.02123
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−2.50000	+	4.33013i	−0.0943564	+	0.163430i
$703$	7.00000	+	12.1244i	0.264010	+	0.457279i
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$	4.50000	−	7.79423i	0.169480	−	0.293548i
$706$	−24.0000			−0.903252
$707$		0			0
$708$	−6.00000			−0.225494
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	4.50000	+	7.79423i	0.168882	+	0.292512i
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$		0			0
$714$		0			0
$715$	−18.0000			−0.673162
$716$	−1.50000	+	2.59808i	−0.0560576	+	0.0970947i
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	6.00000			0.223607
$721$		0			0
$722$	15.0000			0.558242
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$	12.5000	−	21.6506i	0.463919	−	0.803530i
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−3.00000	+	5.19615i	−0.111035	+	0.192318i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	−0.996398	−	0.0847976i	$-0.972976\pi$
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	0.571636	+	0.820507i	$0.306309\pi$
$734$	−26.0000			−0.959678
$735$		0			0
$736$		0			0
$737$	−42.0000	+	72.7461i	−1.54709	+	2.67964i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	−10.5000	+	18.1865i	−0.385988	+	0.668550i
$741$	2.00000			0.0734718
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$	−18.0000			−0.658145
$749$		0			0
$750$	−3.00000			−0.109545
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	−12.0000	−	20.7846i	−0.437304	−	0.757433i
$754$	3.00000	−	5.19615i	0.109254	−	0.189233i
$755$	−51.0000			−1.85608
$756$		0			0
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$		0			0
$760$	−3.00000	−	5.19615i	−0.108821	−	0.188484i
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	−20.0000			−0.724524
$763$		0			0
$764$	−18.0000			−0.651217
$765$	9.00000	−	15.5885i	0.325396	−	0.563602i
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	32.0000			1.15395			0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000			1.15395			0.576975	+	0.816762i	$0.304233\pi$
$770$		0			0
$771$	9.00000			0.324127
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	10.0000			0.358979
$777$		0			0
$778$	6.00000			0.215110
$779$		0			0
$780$	1.50000	+	2.59808i	0.0537086	+	0.0930261i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$	−30.0000			−1.07211
$784$		0			0
$785$	−42.0000			−1.49904
$786$	−10.5000	+	18.1865i	−0.374523	+	0.648692i
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	0.963755	+	0.266788i	$0.0859624\pi$
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	−0.250832	+	0.968031i	$0.580704\pi$
$788$	−1.50000	−	2.59808i	−0.0534353	−	0.0925526i
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$	24.0000			0.853882
$791$		0			0
$792$	12.0000			0.426401
$793$	−4.00000	+	6.92820i	−0.142044	+	0.246028i
$794$	−17.0000	−	29.4449i	−0.603307	−	1.04496i
$795$		0			0
$796$	−1.00000	+	1.73205i	−0.0354441	+	0.0613909i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	−9.00000			−0.318397
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$	18.0000	+	31.1769i	0.635602	+	1.10090i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$	14.0000			0.493742
$805$		0			0
$806$	4.00000			0.140894
$807$	−12.0000	+	20.7846i	−0.422420	+	0.731653i
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$	11.0000			0.385787
$814$	−21.0000	+	36.3731i	−0.736050	+	1.27488i
$815$	−24.0000	−	41.5692i	−0.840683	−	1.45611i
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	1.00000	−	1.73205i	0.0349856	−	0.0605968i
$818$	−32.0000			−1.11885
$819$		0			0
$820$		0			0
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	−0.838663	−	0.544651i	$-0.816662\pi$
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	0.891013	+	0.453978i	$0.149995\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$	24.0000			0.835573
$826$		0			0
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$		0			0
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$	−18.0000	−	31.1769i	−0.624789	−	1.08217i
$831$	14.0000	−	24.2487i	0.485655	−	0.841178i
$832$	1.00000			0.0346688
$833$		0			0
$834$	13.0000			0.450153
$835$		0			0
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	−10.0000	−	17.3205i	−0.345651	−	0.598684i
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	8.50000	−	14.7224i	0.292929	−	0.507369i
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	1.50000	−	2.59808i	0.0516016	−	0.0893765i
$846$	6.00000			0.206284
$847$		0			0
$848$		0			0
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$		0			0
$852$	1.50000	−	2.59808i	0.0513892	−	0.0890086i
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$		0			0
$855$	12.0000			0.410391
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	3.00000			0.102299
$861$		0			0
$862$	33.0000			1.12398
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	−0.173856	−	0.984771i	$-0.555623\pi$
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	0.939765	−	0.341822i	$-0.111044\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	−12.5000	+	21.6506i	−0.424767	+	0.735719i
$867$	−8.00000			−0.271694
$868$		0			0
$869$	48.0000			1.62829
$870$	−9.00000	+	15.5885i	−0.305129	+	0.528498i
$871$	−7.00000	−	12.1244i	−0.237186	−	0.410818i
$872$	−3.50000	−	6.06218i	−0.118525	−	0.205291i
$873$	−10.0000	+	17.3205i	−0.338449	+	0.586210i
$874$		0			0
$875$		0			0
$876$	2.00000			0.0675737
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	13.0000	+	22.5167i	0.438729	+	0.759900i
$879$	−10.5000	−	18.1865i	−0.354156	−	0.613417i
$880$	9.00000	−	15.5885i	0.303390	−	0.525487i
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	1.50000	−	2.59808i	0.0504505	−	0.0873828i
$885$	−9.00000	−	15.5885i	−0.302532	−	0.524000i
$886$	10.5000	+	18.1865i	0.352754	+	0.610989i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	7.00000			0.234905
$889$		0			0
$890$	−18.0000			−0.603361
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	−9.00000			−0.300837
$896$		0			0
$897$		0			0
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	6.00000			0.199557
$905$	30.0000	−	51.9615i	0.997234	−	1.72726i
$906$	8.50000	+	14.7224i	0.282394	+	0.489120i
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$		0			0
$909$	24.0000			0.796030
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$	12.0000	−	20.7846i	0.396708	−	0.687118i
$916$	−13.0000			−0.429532
$917$		0			0
$918$	−15.0000			−0.495074
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	4.50000	−	7.79423i	0.148200	−	0.256689i
$923$	−3.00000			−0.0987462
$924$		0			0
$925$	−28.0000			−0.920634
$926$	−20.0000	+	34.6410i	−0.657241	+	1.13837i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	0.403596	+	0.914937i	$0.367760\pi$
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	−0.994157	+	0.107944i	$0.965573\pi$
$930$	−12.0000			−0.393496
$931$		0			0
$932$	−27.0000			−0.884414
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	−27.0000	−	46.7654i	−0.882994	−	1.52939i
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$		0			0
$944$	−6.00000			−0.195283
$945$		0			0
$946$	6.00000			0.195077
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	−0.910644	−	0.413192i	$-0.864414\pi$
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	0.813157	+	0.582045i	$0.197747\pi$
$948$	−4.00000	−	6.92820i	−0.129914	−	0.225018i
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$	4.00000	−	6.92820i	0.129777	−	0.224781i
$951$	−6.00000			−0.194563
$952$		0			0
$953$	15.0000			0.485898			0.242949	−	0.970039i	$-0.421885\pi$
$953$	15.0000			0.485898			0.242949	+	0.970039i	$0.421885\pi$
$954$		0			0
$955$	−27.0000	−	46.7654i	−0.873699	−	1.51329i
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$	21.0000			0.678479
$959$		0			0
$960$	−3.00000			−0.0968246
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−3.50000	−	6.06218i	−0.112845	−	0.195452i
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	12.0000			0.386294
$966$		0			0
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$	15.0000	+	25.9808i	0.481621	+	0.834192i
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	−0.840953	−	0.541108i	$-0.818005\pi$
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	0.889090	+	0.457732i	$0.151338\pi$
$972$	16.0000			0.513200
$973$		0			0
$974$	16.0000			0.512673
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	0.868227	+	0.496167i	$0.165259\pi$
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	−0.00442082	+	0.999990i	$0.501407\pi$
$978$	−8.00000	+	13.8564i	−0.255812	+	0.443079i
$979$	−36.0000			−1.15056
$980$		0			0
$981$	14.0000			0.446986
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	−0.989122	−	0.147100i	$-0.953006\pi$
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	0.367168	−	0.930155i	$-0.380327\pi$
$984$		0			0
$985$	4.50000	−	7.79423i	0.143382	−	0.248345i
$986$	18.0000			0.573237
$987$		0			0
$988$	2.00000			0.0636285
$989$		0			0
$990$	18.0000	+	31.1769i	0.572078	+	0.990867i
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	8.00000			0.253872
$994$		0			0
$995$	−6.00000			−0.190213
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	0.957552	+	0.288261i	$0.0930771\pi$
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	−0.229135	+	0.973395i	$0.573590\pi$
$998$	−20.0000	−	34.6410i	−0.633089	−	1.09654i
$999$	−17.5000	+	30.3109i	−0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.p.79.1		2
7.2	even	3		26.2.a.a.1.1	✓	1
7.3	odd	6		1274.2.f.r.1145.1		2
7.4	even	3	inner	1274.2.f.p.1145.1		2
7.5	odd	6		1274.2.a.d.1.1		1
7.6	odd	2		1274.2.f.r.79.1		2
21.2	odd	6		234.2.a.e.1.1		1
28.23	odd	6		208.2.a.a.1.1		1
35.2	odd	12		650.2.b.d.599.1		2
35.9	even	6		650.2.a.j.1.1		1
35.23	odd	12		650.2.b.d.599.2		2
56.37	even	6		832.2.a.d.1.1		1
56.51	odd	6		832.2.a.i.1.1		1
63.2	odd	6		2106.2.e.b.1405.1		2
63.16	even	3		2106.2.e.ba.1405.1		2
63.23	odd	6		2106.2.e.b.703.1		2
63.58	even	3		2106.2.e.ba.703.1		2
77.65	odd	6		3146.2.a.n.1.1		1
84.23	even	6		1872.2.a.q.1.1		1
91.2	odd	12		338.2.e.a.147.1		4
91.9	even	3		338.2.c.d.315.1		2
91.16	even	3		338.2.c.d.191.1		2
91.23	even	6		338.2.c.a.191.1		2
91.30	even	6		338.2.c.a.315.1		2
91.37	odd	12		338.2.e.a.147.2		4
91.44	odd	12		338.2.b.c.337.2		2
91.51	even	6		338.2.a.f.1.1		1
91.58	odd	12		338.2.e.a.23.2		4
91.72	odd	12		338.2.e.a.23.1		4
91.86	odd	12		338.2.b.c.337.1		2
105.2	even	12		5850.2.e.a.5149.2		2
105.23	even	12		5850.2.e.a.5149.1		2
105.44	odd	6		5850.2.a.p.1.1		1
112.37	even	12		3328.2.b.m.1665.1		2
112.51	odd	12		3328.2.b.j.1665.1		2
112.93	even	12		3328.2.b.m.1665.2		2
112.107	odd	12		3328.2.b.j.1665.2		2
119.16	even	6		7514.2.a.c.1.1		1
133.37	odd	6		9386.2.a.j.1.1		1
140.79	odd	6		5200.2.a.x.1.1		1
168.107	even	6		7488.2.a.h.1.1		1
168.149	odd	6		7488.2.a.g.1.1		1
273.44	even	12		3042.2.b.a.1351.1		2
273.86	even	12		3042.2.b.a.1351.2		2
273.233	odd	6		3042.2.a.a.1.1		1
364.51	odd	6		2704.2.a.f.1.1		1
364.135	even	12		2704.2.f.d.337.2		2
364.359	even	12		2704.2.f.d.337.1		2
455.324	even	6		8450.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.a.a.1.1	✓	1	7.2	even	3
208.2.a.a.1.1		1	28.23	odd	6
234.2.a.e.1.1		1	21.2	odd	6
338.2.a.f.1.1		1	91.51	even	6
338.2.b.c.337.1		2	91.86	odd	12
338.2.b.c.337.2		2	91.44	odd	12
338.2.c.a.191.1		2	91.23	even	6
338.2.c.a.315.1		2	91.30	even	6
338.2.c.d.191.1		2	91.16	even	3
338.2.c.d.315.1		2	91.9	even	3
338.2.e.a.23.1		4	91.72	odd	12
338.2.e.a.23.2		4	91.58	odd	12
338.2.e.a.147.1		4	91.2	odd	12
338.2.e.a.147.2		4	91.37	odd	12
650.2.a.j.1.1		1	35.9	even	6
650.2.b.d.599.1		2	35.2	odd	12
650.2.b.d.599.2		2	35.23	odd	12
832.2.a.d.1.1		1	56.37	even	6
832.2.a.i.1.1		1	56.51	odd	6
1274.2.a.d.1.1		1	7.5	odd	6
1274.2.f.p.79.1		2	1.1	even	1	trivial
1274.2.f.p.1145.1		2	7.4	even	3	inner
1274.2.f.r.79.1		2	7.6	odd	2
1274.2.f.r.1145.1		2	7.3	odd	6
1872.2.a.q.1.1		1	84.23	even	6
2106.2.e.b.703.1		2	63.23	odd	6
2106.2.e.b.1405.1		2	63.2	odd	6
2106.2.e.ba.703.1		2	63.58	even	3
2106.2.e.ba.1405.1		2	63.16	even	3
2704.2.a.f.1.1		1	364.51	odd	6
2704.2.f.d.337.1		2	364.359	even	12
2704.2.f.d.337.2		2	364.135	even	12
3042.2.a.a.1.1		1	273.233	odd	6
3042.2.b.a.1351.1		2	273.44	even	12
3042.2.b.a.1351.2		2	273.86	even	12
3146.2.a.n.1.1		1	77.65	odd	6
3328.2.b.j.1665.1		2	112.51	odd	12
3328.2.b.j.1665.2		2	112.107	odd	12
3328.2.b.m.1665.1		2	112.37	even	12
3328.2.b.m.1665.2		2	112.93	even	12
5200.2.a.x.1.1		1	140.79	odd	6
5850.2.a.p.1.1		1	105.44	odd	6
5850.2.e.a.5149.1		2	105.23	even	12
5850.2.e.a.5149.2		2	105.2	even	12
7488.2.a.g.1.1		1	168.149	odd	6
7488.2.a.h.1.1		1	168.107	even	6
7514.2.a.c.1.1		1	119.16	even	6
8450.2.a.c.1.1		1	455.324	even	6
9386.2.a.j.1.1		1	133.37	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -3.00000 q^{20} -6.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} -5.00000 q^{27} +6.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +3.00000 q^{34} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} -1.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{47} +1.00000 q^{48} -4.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{54} -18.0000 q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(3.00000 + 5.19615i) q^{59} +(1.50000 + 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-7.00000 - 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{75} +2.00000 q^{76} -1.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(3.00000 - 5.19615i) q^{89} -6.00000 q^{90} +(2.00000 - 3.46410i) q^{93} +(1.50000 + 2.59808i) q^{94} +(3.00000 + 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 6 q^{11} - q^{12} + 2 q^{13} - 6 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{22} + q^{24} - 4 q^{25} + q^{26} - 10 q^{27} + 12 q^{29} - 3 q^{30} + 4 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} - 4 q^{36} + 7 q^{37} + 2 q^{38} - q^{39} - 3 q^{40} - 2 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{47} + 2 q^{48} - 8 q^{50} + 3 q^{51} - q^{52} - 5 q^{54} - 36 q^{55} + 4 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{60} - 8 q^{61} + 8 q^{62} + 2 q^{64} + 3 q^{65} + 6 q^{66} - 14 q^{67} + 3 q^{68} - 6 q^{71} - 2 q^{72} - 2 q^{73} - 7 q^{74} - 4 q^{75} + 4 q^{76} - 2 q^{78} - 8 q^{79} + 3 q^{80} - q^{81} + 24 q^{83} + 18 q^{85} - q^{86} - 6 q^{87} + 6 q^{88} + 6 q^{89} - 12 q^{90} + 4 q^{93} + 3 q^{94} + 6 q^{95} + q^{96} - 20 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 6 * q^11 - q^12 + 2 * q^13 - 6 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^22 + q^24 - 4 * q^25 + q^26 - 10 * q^27 + 12 * q^29 - 3 * q^30 + 4 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - 4 * q^36 + 7 * q^37 + 2 * q^38 - q^39 - 3 * q^40 - 2 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^47 + 2 * q^48 - 8 * q^50 + 3 * q^51 - q^52 - 5 * q^54 - 36 * q^55 + 4 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^60 - 8 * q^61 + 8 * q^62 + 2 * q^64 + 3 * q^65 + 6 * q^66 - 14 * q^67 + 3 * q^68 - 6 * q^71 - 2 * q^72 - 2 * q^73 - 7 * q^74 - 4 * q^75 + 4 * q^76 - 2 * q^78 - 8 * q^79 + 3 * q^80 - q^81 + 24 * q^83 + 18 * q^85 - q^86 - 6 * q^87 + 6 * q^88 + 6 * q^89 - 12 * q^90 + 4 * q^93 + 3 * q^94 + 6 * q^95 + q^96 - 20 * q^97 - 24 * q^99

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