LMFDB - Embedded newform 490.2.e.h.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.2.e.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(3.00000 + 5.19615i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.00000 - 3.46410i) q^{26} +5.00000 q^{27} -3.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{46} -1.00000 q^{48} -1.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -6.00000 q^{55} +2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-2.50000 - 4.33013i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(-8.00000 - 13.8564i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{76} +4.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} -3.00000 q^{83} +(-3.50000 + 6.06218i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-7.50000 + 12.9904i) q^{89} +2.00000 q^{90} -3.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} -14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{15} - q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 12 q^{22} + 3 q^{23} - q^{24} - q^{25} + 4 q^{26} + 10 q^{27} - 6 q^{29} - q^{30} + 8 q^{31} + q^{32} - 6 q^{33} - 4 q^{36} + 4 q^{37} - 2 q^{38} + 4 q^{39} + q^{40} - 18 q^{41} - 14 q^{43} + 6 q^{44} + 2 q^{45} - 3 q^{46} - 2 q^{48} - 2 q^{50} - 4 q^{52} + 6 q^{53} + 5 q^{54} - 12 q^{55} + 4 q^{57} - 3 q^{58} - 6 q^{59} + q^{60} + 5 q^{61} + 16 q^{62} + 2 q^{64} - 4 q^{65} + 6 q^{66} - 5 q^{67} + 6 q^{69} - 12 q^{71} - 2 q^{72} - 16 q^{73} - 4 q^{74} + q^{75} - 4 q^{76} + 8 q^{78} - 2 q^{79} - q^{80} - q^{81} - 9 q^{82} - 6 q^{83} - 7 q^{86} - 3 q^{87} - 6 q^{88} - 15 q^{89} + 4 q^{90} - 6 q^{92} - 8 q^{93} + 2 q^{95} - q^{96} - 28 q^{97} + 24 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + q^12 + 8 * q^13 - 2 * q^15 - q^16 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 12 * q^22 + 3 * q^23 - q^24 - q^25 + 4 * q^26 + 10 * q^27 - 6 * q^29 - q^30 + 8 * q^31 + q^32 - 6 * q^33 - 4 * q^36 + 4 * q^37 - 2 * q^38 + 4 * q^39 + q^40 - 18 * q^41 - 14 * q^43 + 6 * q^44 + 2 * q^45 - 3 * q^46 - 2 * q^48 - 2 * q^50 - 4 * q^52 + 6 * q^53 + 5 * q^54 - 12 * q^55 + 4 * q^57 - 3 * q^58 - 6 * q^59 + q^60 + 5 * q^61 + 16 * q^62 + 2 * q^64 - 4 * q^65 + 6 * q^66 - 5 * q^67 + 6 * q^69 - 12 * q^71 - 2 * q^72 - 16 * q^73 - 4 * q^74 + q^75 - 4 * q^76 + 8 * q^78 - 2 * q^79 - q^80 - q^81 - 9 * q^82 - 6 * q^83 - 7 * q^86 - 3 * q^87 - 6 * q^88 - 15 * q^89 + 4 * q^90 - 6 * q^92 - 8 * q^93 + 2 * q^95 - q^96 - 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	6.00000			1.27920
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$	5.00000			0.962250
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	2.00000			0.264906
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−8.00000	−	13.8564i	−0.936329	−	1.62177i	−0.772246	−	0.635323i	$-0.780867\pi$
$73$	−8.00000	−	13.8564i	−0.936329	−	1.62177i	−0.164083	−	0.986447i	$-0.552466\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	4.00000			0.452911
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$		0			0
$86$	−3.50000	+	6.06218i	−0.377415	+	0.653701i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	−3.00000			−0.312772
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	12.0000			1.20605
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	4.00000			0.379663
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	4.00000	−	6.92820i	0.369800	−	0.640513i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	1.00000			0.0912871
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−2.50000	−	4.33013i	−0.226339	−	0.392031i
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.50000	−	6.06218i	−0.308158	−	0.533745i
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	1.50000	−	2.59808i	0.127688	−	0.221163i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	12.0000	+	20.7846i	1.00349	+	1.73810i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$	−16.0000			−1.32417
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$		0			0
$155$	−8.00000			−0.642575
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−6.00000			−0.452267
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−11.0000			−0.817624			−0.408812	−	0.912619i	$-0.634057\pi$
$181$	−11.0000			−0.817624			−0.408812	+	0.912619i	$0.634057\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	2.00000			0.145095
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−7.00000	+	12.1244i	−0.502571	+	0.870478i
$195$	−4.00000			−0.286446
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.50000	−	4.33013i	0.176336	−	0.305424i
$202$	15.0000			1.05540
$203$		0			0
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	0.500000	+	0.866025i	0.0348367	+	0.0603388i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	12.0000			0.830057
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	3.50000	−	6.06218i	0.238698	−	0.413437i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−11.0000			−0.745014
$219$	8.00000	−	13.8564i	0.540590	−	0.936329i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$		0			0
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	3.00000			0.196960
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	−0.599780	−	0.800165i	$-0.704745\pi$
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	0.992853	+	0.119342i	$0.0380786\pi$
$234$	−4.00000	−	6.92820i	−0.261488	−	0.452911i
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	−2.00000			−0.129914
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	−5.00000			−0.320092
$245$		0			0
$246$	−9.00000			−0.573819
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$	−7.00000			−0.435801
$259$		0			0
$260$	4.00000			0.248069
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−15.0000			−0.917985
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$	2.50000	+	4.33013i	0.152145	+	0.263523i
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	5.00000	−	8.66025i	0.299880	−	0.519408i
$279$	16.0000			0.957895
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$	24.0000			1.41915
$287$		0			0
$288$	2.00000			0.117851
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−1.50000	−	2.59808i	−0.0880830	−	0.152564i
$291$	−7.00000	−	12.1244i	−0.410347	−	0.710742i
$292$	−8.00000	+	13.8564i	−0.468165	+	0.810885i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	4.00000			0.230174
$303$	−7.50000	+	12.9904i	−0.430864	+	0.746278i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	2.50000	+	4.33013i	0.143150	+	0.247942i
$306$		0			0
$307$	−5.00000			−0.285365			−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000			−0.285365			−0.142683	+	0.989769i	$0.545573\pi$
$308$		0			0
$309$	−1.00000			−0.0568880
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	−0.999928	−	0.0119847i	$-0.996185\pi$
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	0.489585	−	0.871956i	$-0.337148\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	2.00000			0.112509
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	15.0000			0.837218
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	5.50000	−	9.52628i	0.304151	−	0.526804i
$328$	9.00000			0.496942
$329$		0			0
$330$	−6.00000			−0.330289
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	1.50000	+	2.59808i	0.0823232	+	0.142588i
$333$	−4.00000	−	6.92820i	−0.219199	−	0.379663i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	5.00000			0.273179
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−24.0000	+	41.5692i	−1.29967	+	2.25110i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	7.00000			0.377415
$345$	−1.50000	+	2.59808i	−0.0807573	+	0.139876i
$346$		0			0
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$	−1.50000	+	2.59808i	−0.0804084	+	0.139272i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	15.0000			0.794998
$357$		0			0
$358$	24.0000			1.26844
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−5.50000	+	9.52628i	−0.289074	+	0.500690i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	16.0000			0.837478
$366$	2.50000	−	4.33013i	0.130677	−	0.226339i
$367$	17.5000	+	30.3109i	0.913493	+	1.58222i	0.809093	+	0.587680i	$0.199959\pi$
$367$	17.5000	+	30.3109i	0.913493	+	1.58222i	0.104399	+	0.994535i	$0.466708\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$	4.00000			0.207950
$371$		0			0
$372$	8.00000			0.414781
$373$	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	$0.133645\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.00000			−0.101797
$387$	−7.00000	+	12.1244i	−0.355830	+	0.616316i
$388$	7.00000	+	12.1244i	0.355371	+	0.615521i
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−1.00000	−	1.73205i	−0.0503155	−	0.0871489i
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	−2.50000	−	4.33013i	−0.124689	−	0.215967i
$403$	16.0000	+	27.7128i	0.797017	+	1.38047i
$404$	7.50000	−	12.9904i	0.373139	−	0.646296i
$405$	1.00000			0.0496904
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	0.659374	−	0.751815i	$-0.270822\pi$
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	−0.980778	+	0.195127i	$0.937488\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	1.00000			0.0492665
$413$		0			0
$414$	−6.00000			−0.294884
$415$	1.50000	−	2.59808i	0.0736321	−	0.127535i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	5.00000	+	8.66025i	0.244851	+	0.424094i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	−5.00000	+	8.66025i	−0.243396	+	0.421575i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$		0			0
$426$	−6.00000			−0.290701
$427$		0			0
$428$	−15.0000			−0.725052
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$	−3.50000	−	6.06218i	−0.168785	−	0.292344i
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	22.0000			1.05725			0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000			1.05725			0.528626	+	0.848855i	$0.322707\pi$
$434$		0			0
$435$	3.00000			0.143839
$436$	−5.50000	+	9.52628i	−0.263402	+	0.456226i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$	−8.00000	−	13.8564i	−0.382255	−	0.662085i
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$		0			0
$443$	−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	$0.332918\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	14.0000	−	24.2487i	0.662919	−	1.14821i
$447$	−15.0000			−0.709476
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	−1.00000	+	1.73205i	−0.0471405	+	0.0816497i
$451$	−27.0000	−	46.7654i	−1.27138	−	2.20210i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−2.00000	+	3.46410i	−0.0939682	+	0.162758i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−16.0000	+	27.7128i	−0.748448	+	1.29635i	0.200118	+	0.979772i	$0.435868\pi$
$457$	−16.0000	+	27.7128i	−0.748448	+	1.29635i	−0.948566	+	0.316579i	$0.897466\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$		0			0
$460$	1.50000	−	2.59808i	0.0699379	−	0.121136i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	−6.00000	−	10.3923i	−0.277945	−	0.481414i
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	−0.985726	−	0.168360i	$-0.946153\pi$
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	0.638667	+	0.769483i	$0.279486\pi$
$468$	−8.00000			−0.369800
$469$		0			0
$470$		0			0
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−21.0000	−	36.3731i	−0.965581	−	1.67244i
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$	−2.00000			−0.0917663
$476$		0			0
$477$	12.0000			0.549442
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	8.00000	−	13.8564i	0.364769	−	0.631798i
$482$	2.00000			0.0910975
$483$		0			0
$484$	25.0000			1.13636
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$	−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	$0.715252\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	4.00000			0.180886
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−4.50000	+	7.79423i	−0.202876	+	0.351391i
$493$		0			0
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$	−8.00000			−0.359211
$497$		0			0
$498$	−3.00000			−0.134433
$499$	11.0000	−	19.0526i	0.492428	−	0.852910i	−0.507534	−	0.861632i	$-0.669443\pi$
$499$	11.0000	−	19.0526i	0.492428	−	0.852910i	0.999962	+	0.00872186i	$0.00277629\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$		0			0
$515$	−0.500000	−	0.866025i	−0.0220326	−	0.0381616i
$516$	−3.50000	+	6.06218i	−0.154079	+	0.266872i
$517$		0			0
$518$		0			0
$519$		0			0
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$		0			0
$525$		0			0
$526$	21.0000			0.915644
$527$		0			0
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−36.0000			−1.55933
$534$	−7.50000	+	12.9904i	−0.324557	+	0.562149i
$535$	7.50000	+	12.9904i	0.324253	+	0.561623i
$536$	2.50000	+	4.33013i	0.107984	+	0.187033i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	15.0000			0.646696
$539$		0			0
$540$	5.00000			0.215166
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$	−5.50000	−	9.52628i	−0.236028	−	0.408812i
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$	−3.00000	−	5.19615i	−0.127920	−	0.221565i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−3.00000			−0.127688
$553$		0			0
$554$	−8.00000			−0.339887
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$	8.00000	−	13.8564i	0.338667	−	0.586588i
$559$	−28.0000			−1.18427
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	13.5000	+	23.3827i	0.568957	+	0.985463i	0.996669	+	0.0815478i	$0.0259863\pi$
$563$	13.5000	+	23.3827i	0.568957	+	0.985463i	−0.427712	+	0.903915i	$0.640680\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	6.00000			0.251754
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$	12.0000	−	20.7846i	0.501745	−	0.869048i
$573$	6.00000			0.250654
$574$		0			0
$575$	−3.00000			−0.125109
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	13.0000	+	22.5167i	0.541197	+	0.937381i	0.998836	+	0.0482425i	$0.0153620\pi$
$577$	13.0000	+	22.5167i	0.541197	+	0.937381i	−0.457639	+	0.889138i	$0.651305\pi$
$578$	−8.50000	−	14.7224i	−0.353553	−	0.612372i
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$	−3.00000			−0.124568
$581$		0			0
$582$	−14.0000			−0.580319
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$	8.00000	+	13.8564i	0.331042	+	0.573382i
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	3.00000	−	5.19615i	0.123508	−	0.213922i
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	15.0000			0.614424
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	46.0000			1.87638			0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000			1.87638			0.938190	+	0.346122i	$0.112502\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	−12.5000	−	21.6506i	−0.508197	−	0.880223i
$606$	7.50000	+	12.9904i	0.304667	+	0.527698i
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	−0.532509	−	0.846424i	$-0.678751\pi$
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	0.999279	+	0.0379540i	$0.0120840\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	5.00000			0.202444
$611$		0			0
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$	9.00000			0.362915
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$	−0.500000	+	0.866025i	−0.0201129	+	0.0348367i
$619$	7.00000	+	12.1244i	0.281354	+	0.487319i	0.971718	−	0.236143i	$-0.0758832\pi$
$619$	7.00000	+	12.1244i	0.281354	+	0.487319i	−0.690365	+	0.723462i	$0.742550\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	−4.00000			−0.160128
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$		0			0
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$	−5.00000	−	8.66025i	−0.198732	−	0.344214i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$	6.00000			0.237915
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$	7.50000	−	12.9904i	0.296001	−	0.512689i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	7.00000			0.275625
$646$		0			0
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	0.894004	−	0.448059i	$-0.147885\pi$
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	−0.835033	+	0.550200i	$0.814551\pi$
$648$	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
$652$	−4.00000			−0.156652
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.172211	−	0.985060i	$-0.444909\pi$
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.766982	−	0.641669i	$-0.221758\pi$
$654$	−5.50000	−	9.52628i	−0.215067	−	0.372507i
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	−32.0000			−1.24844
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$		0			0
$664$	3.00000			0.116423
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	14.0000	+	24.2487i	0.541271	+	0.937509i
$670$	2.50000	−	4.33013i	0.0965834	−	0.167287i
$671$	30.0000			1.15814
$672$		0			0
$673$	8.00000			0.308377			0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000			0.308377			0.154189	+	0.988041i	$0.450724\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$	24.0000	+	41.5692i	0.919007	+	1.59177i
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	12.0000			0.458496
$686$		0			0
$687$	14.0000			0.534133
$688$	3.50000	−	6.06218i	0.133436	−	0.231118i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$	1.50000	+	2.59808i	0.0571040	+	0.0989071i
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	−0.995785	−	0.0917209i	$-0.970763\pi$
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	0.577325	+	0.816514i	$0.304097\pi$
$692$		0			0
$693$		0			0
$694$	−9.00000			−0.341635
$695$	−5.00000	+	8.66025i	−0.189661	+	0.328502i
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$		0			0
$698$	−8.50000	+	14.7224i	−0.321730	+	0.557252i
$699$	12.0000			0.453882
$700$		0			0
$701$	−3.00000			−0.113308			−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000			−0.113308			−0.0566542	+	0.998394i	$0.518043\pi$
$702$	10.0000	−	17.3205i	0.377426	−	0.653720i
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$	−6.00000			−0.225494
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	7.50000	−	12.9904i	0.281074	−	0.486835i
$713$	24.0000			0.898807
$714$		0			0
$715$	−24.0000			−0.897549
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	−0.983608	−	0.180319i	$-0.942287\pi$
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	0.647965	+	0.761670i	$0.275620\pi$
$720$	−2.00000			−0.0745356
$721$		0			0
$722$	15.0000			0.558242
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	5.50000	+	9.52628i	0.204406	+	0.354041i
$725$	1.50000	+	2.59808i	0.0557086	+	0.0964901i
$726$	−12.5000	+	21.6506i	−0.463919	+	0.803530i
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	8.00000	−	13.8564i	0.296093	−	0.512849i
$731$		0			0
$732$	−2.50000	−	4.33013i	−0.0924027	−	0.160046i
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$	35.0000			1.29187
$735$		0			0
$736$	3.00000			0.110581
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	0.521475	−	0.853266i	$-0.325382\pi$
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	−0.999688	+	0.0249776i	$0.992049\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	8.00000			0.293887
$742$		0			0
$743$	39.0000			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$	−7.50000	−	12.9904i	−0.274779	−	0.475931i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$		0			0
$749$		0			0
$750$	1.00000			0.0365148
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−4.00000			−0.145575
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−17.0000	+	29.4449i	−0.617468	+	1.06949i
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$	−6.00000			−0.217072
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	0.737716	−	0.675111i	$-0.235904\pi$
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	−0.953521	+	0.301326i	$0.902571\pi$
$774$	7.00000	+	12.1244i	0.251610	+	0.435801i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	14.0000			0.502571
$777$		0			0
$778$	30.0000			1.07555
$779$	−9.00000	+	15.5885i	−0.322458	+	0.558514i
$780$	2.00000	+	3.46410i	0.0716115	+	0.124035i
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$		0			0
$783$	−15.0000			−0.536056
$784$		0			0
$785$	22.0000			0.785214
$786$		0			0
$787$	−21.5000	−	37.2391i	−0.766392	−	1.32743i	−0.939507	−	0.342529i	$-0.888717\pi$
$787$	−21.5000	−	37.2391i	−0.766392	−	1.32743i	0.173115	−	0.984902i	$-0.444617\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$	−10.5000	+	18.1865i	−0.373810	+	0.647458i
$790$	−2.00000			−0.0711568
$791$		0			0
$792$	−12.0000			−0.426401
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	48.0000			1.70025			0.850124	−	0.526583i	$-0.176527\pi$
$797$	48.0000			1.70025			0.850124	+	0.526583i	$0.176527\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	15.0000	+	25.9808i	0.529999	+	0.917985i
$802$	7.50000	+	12.9904i	0.264834	+	0.458706i
$803$	48.0000	−	83.1384i	1.69388	−	2.93389i
$804$	−5.00000			−0.176336
$805$		0			0
$806$	32.0000			1.12715
$807$	−7.50000	+	12.9904i	−0.264013	+	0.457283i
$808$	−7.50000	−	12.9904i	−0.263849	−	0.457000i
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	0.620274	−	0.784385i	$-0.287021\pi$
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	−0.989434	+	0.144981i	$0.953688\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	−7.00000	+	12.1244i	−0.244899	+	0.424178i
$818$	−13.0000			−0.454534
$819$		0			0
$820$	−9.00000			−0.314294
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	−6.00000	−	10.3923i	−0.209274	−	0.362473i
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	0.982737	−	0.185006i	$-0.0592303\pi$
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	−0.651588	+	0.758573i	$0.725897\pi$
$824$	0.500000	−	0.866025i	0.0174183	−	0.0301694i
$825$	6.00000			0.208893
$826$		0			0
$827$	15.0000			0.521601			0.260801	−	0.965393i	$-0.416014\pi$
$827$	15.0000			0.521601			0.260801	+	0.965393i	$0.416014\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	−1.50000	−	2.59808i	−0.0520658	−	0.0901805i
$831$	4.00000	−	6.92820i	0.138758	−	0.240337i
$832$	4.00000			0.138675
$833$		0			0
$834$	10.0000			0.346272
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	20.0000	+	34.6410i	0.691301	+	1.19737i
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	8.50000	−	14.7224i	0.292929	−	0.507369i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−3.00000	+	5.19615i	−0.102778	+	0.178017i
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−7.50000	+	12.9904i	−0.256345	+	0.444002i
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	0.912705	−	0.408619i	$-0.133990\pi$
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	−0.810227	+	0.586116i	$0.800656\pi$
$858$	12.0000	+	20.7846i	0.409673	+	0.709575i
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	−0.452636	−	0.891695i	$-0.649516\pi$
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	0.998549	−	0.0538535i	$-0.0171504\pi$
$860$	−7.00000			−0.238698
$861$		0			0
$862$	−30.0000			−1.02180
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	−0.998937	−	0.0460992i	$-0.985321\pi$
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	0.539392	+	0.842055i	$0.318654\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	11.0000	−	19.0526i	0.373795	−	0.647432i
$867$	17.0000			0.577350
$868$		0			0
$869$	−12.0000			−0.407072
$870$	1.50000	−	2.59808i	0.0508548	−	0.0880830i
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$	5.50000	+	9.52628i	0.186254	+	0.322601i
$873$	−14.0000	+	24.2487i	−0.473828	+	0.820695i
$874$	−6.00000			−0.202953
$875$		0			0
$876$	−16.0000			−0.540590
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−57.0000			−1.92038			−0.960189	−	0.279350i	$-0.909881\pi$
$881$	−57.0000			−1.92038			−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	3.00000	+	5.19615i	0.100844	+	0.174667i
$886$	10.5000	+	18.1865i	0.352754	+	0.610989i
$887$	−10.5000	+	18.1865i	−0.352555	+	0.610644i	−0.986696	−	0.162573i	$-0.948021\pi$
$887$	−10.5000	+	18.1865i	−0.352555	+	0.610644i	0.634141	+	0.773217i	$0.281354\pi$
$888$	−4.00000			−0.134231
$889$		0			0
$890$	−15.0000			−0.502801
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	−14.0000	−	24.2487i	−0.468755	−	0.811907i
$893$		0			0
$894$	−7.50000	+	12.9904i	−0.250838	+	0.434463i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	12.0000			0.400668
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$	−54.0000			−1.79800
$903$		0			0
$904$	−6.00000			−0.199557
$905$	5.50000	−	9.52628i	0.182826	−	0.316664i
$906$	2.00000	+	3.46410i	0.0664455	+	0.115087i
$907$	12.5000	+	21.6506i	0.415056	+	0.718898i	0.995434	−	0.0954492i	$-0.0304288\pi$
$907$	12.5000	+	21.6506i	0.415056	+	0.718898i	−0.580379	+	0.814347i	$0.697095\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	30.0000			0.995037
$910$		0			0
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	−9.00000	−	15.5885i	−0.297857	−	0.515903i
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$	−2.50000	+	4.33013i	−0.0826475	+	0.143150i
$916$	−14.0000			−0.462573
$917$		0			0
$918$		0			0
$919$	−7.00000	+	12.1244i	−0.230909	+	0.399946i	−0.958076	−	0.286515i	$-0.907503\pi$
$919$	−7.00000	+	12.1244i	−0.230909	+	0.399946i	0.727167	+	0.686461i	$0.240837\pi$
$920$	−1.50000	−	2.59808i	−0.0494535	−	0.0856560i
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−6.50000	+	11.2583i	−0.213603	+	0.369972i
$927$	1.00000	+	1.73205i	0.0328443	+	0.0568880i
$928$	−1.50000	−	2.59808i	−0.0492399	−	0.0852860i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$	−8.00000			−0.262330
$931$		0			0
$932$	−12.0000			−0.393073
$933$	9.00000	−	15.5885i	0.294647	−	0.510343i
$934$	7.50000	+	12.9904i	0.245407	+	0.425058i
$935$		0			0
$936$	−4.00000	+	6.92820i	−0.130744	+	0.226455i
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$		0			0
$939$	8.00000			0.261070
$940$		0			0
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	0.812975	−	0.582298i	$-0.197846\pi$
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	−0.910773	+	0.412908i	$0.864513\pi$
$942$	−11.0000	−	19.0526i	−0.358399	−	0.620766i
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$	6.00000			0.195283
$945$		0			0
$946$	−42.0000			−1.36554
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	−0.840624	−	0.541619i	$-0.817812\pi$
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	0.889368	+	0.457193i	$0.151145\pi$
$948$	1.00000	+	1.73205i	0.0324785	+	0.0562544i
$949$	−32.0000	−	55.4256i	−1.03876	−	1.79919i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−12.0000			−0.389127
$952$		0			0
$953$	60.0000			1.94359			0.971795	−	0.235826i	$-0.0757795\pi$
$953$	60.0000			1.94359			0.971795	+	0.235826i	$0.0757795\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	9.00000	−	15.5885i	0.290929	−	0.503903i
$958$	12.0000			0.387702
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−8.00000	−	13.8564i	−0.257930	−	0.446748i
$963$	−15.0000	−	25.9808i	−0.483368	−	0.837218i
$964$	1.00000	−	1.73205i	0.0322078	−	0.0557856i
$965$	2.00000			0.0643823
$966$		0			0
$967$	35.0000			1.12552			0.562762	−	0.826619i	$-0.309739\pi$
$967$	35.0000			1.12552			0.562762	+	0.826619i	$0.309739\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$		0			0
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	16.0000			0.512673
$975$	2.00000	−	3.46410i	0.0640513	−	0.110940i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	−90.0000			−2.87641
$980$		0			0
$981$	−22.0000			−0.702406
$982$		0			0
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	0.989122	+	0.147100i	$0.0469940\pi$
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	−0.367168	+	0.930155i	$0.619673\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−10.5000	+	18.1865i	−0.333881	+	0.578298i
$990$	6.00000	+	10.3923i	0.190693	+	0.330289i
$991$	14.0000	+	24.2487i	0.444725	+	0.770286i	0.998033	−	0.0626908i	$-0.0199682\pi$
$991$	14.0000	+	24.2487i	0.444725	+	0.770286i	−0.553308	+	0.832977i	$0.686635\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$	28.0000			0.888553
$994$		0			0
$995$	4.00000			0.126809
$996$	−1.50000	+	2.59808i	−0.0475293	+	0.0823232i
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	0.955322	−	0.295567i	$-0.0955086\pi$
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	−0.733630	+	0.679549i	$0.762175\pi$
$998$	−11.0000	−	19.0526i	−0.348199	−	0.603098i
$999$	10.0000	−	17.3205i	0.316386	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.h.471.1		2
7.2	even	3		490.2.a.b.1.1		1
7.3	odd	6		70.2.e.c.11.1	✓	2
7.4	even	3	inner	490.2.e.h.361.1		2
7.5	odd	6		490.2.a.c.1.1		1
7.6	odd	2		70.2.e.c.51.1	yes	2
21.2	odd	6		4410.2.a.bd.1.1		1
21.5	even	6		4410.2.a.bm.1.1		1
21.17	even	6		630.2.k.b.361.1		2
21.20	even	2		630.2.k.b.541.1		2
28.3	even	6		560.2.q.g.81.1		2
28.19	even	6		3920.2.a.p.1.1		1
28.23	odd	6		3920.2.a.bc.1.1		1
28.27	even	2		560.2.q.g.401.1		2
35.2	odd	12		2450.2.c.l.99.1		2
35.3	even	12		350.2.j.b.249.2		4
35.9	even	6		2450.2.a.bc.1.1		1
35.12	even	12		2450.2.c.g.99.1		2
35.13	even	4		350.2.j.b.149.1		4
35.17	even	12		350.2.j.b.249.1		4
35.19	odd	6		2450.2.a.w.1.1		1
35.23	odd	12		2450.2.c.l.99.2		2
35.24	odd	6		350.2.e.e.151.1		2
35.27	even	4		350.2.j.b.149.2		4
35.33	even	12		2450.2.c.g.99.2		2
35.34	odd	2		350.2.e.e.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.c.11.1	✓	2	7.3	odd	6
70.2.e.c.51.1	yes	2	7.6	odd	2
350.2.e.e.51.1		2	35.34	odd	2
350.2.e.e.151.1		2	35.24	odd	6
350.2.j.b.149.1		4	35.13	even	4
350.2.j.b.149.2		4	35.27	even	4
350.2.j.b.249.1		4	35.17	even	12
350.2.j.b.249.2		4	35.3	even	12
490.2.a.b.1.1		1	7.2	even	3
490.2.a.c.1.1		1	7.5	odd	6
490.2.e.h.361.1		2	7.4	even	3	inner
490.2.e.h.471.1		2	1.1	even	1	trivial
560.2.q.g.81.1		2	28.3	even	6
560.2.q.g.401.1		2	28.27	even	2
630.2.k.b.361.1		2	21.17	even	6
630.2.k.b.541.1		2	21.20	even	2
2450.2.a.w.1.1		1	35.19	odd	6
2450.2.a.bc.1.1		1	35.9	even	6
2450.2.c.g.99.1		2	35.12	even	12
2450.2.c.g.99.2		2	35.33	even	12
2450.2.c.l.99.1		2	35.2	odd	12
2450.2.c.l.99.2		2	35.23	odd	12
3920.2.a.p.1.1		1	28.19	even	6
3920.2.a.bc.1.1		1	28.23	odd	6
4410.2.a.bd.1.1		1	21.2	odd	6
4410.2.a.bm.1.1		1	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(3.00000 + 5.19615i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.00000 - 3.46410i) q^{26} +5.00000 q^{27} -3.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{46} -1.00000 q^{48} -1.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -6.00000 q^{55} +2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-2.50000 - 4.33013i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(-8.00000 - 13.8564i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{76} +4.00000 q^{78} +(-1.00000 + 1.73205i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} -3.00000 q^{83} +(-3.50000 + 6.06218i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-7.50000 + 12.9904i) q^{89} +2.00000 q^{90} -3.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} -14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{15} - q^{16} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 12 q^{22} + 3 q^{23} - q^{24} - q^{25} + 4 q^{26} + 10 q^{27} - 6 q^{29} - q^{30} + 8 q^{31} + q^{32} - 6 q^{33} - 4 q^{36} + 4 q^{37} - 2 q^{38} + 4 q^{39} + q^{40} - 18 q^{41} - 14 q^{43} + 6 q^{44} + 2 q^{45} - 3 q^{46} - 2 q^{48} - 2 q^{50} - 4 q^{52} + 6 q^{53} + 5 q^{54} - 12 q^{55} + 4 q^{57} - 3 q^{58} - 6 q^{59} + q^{60} + 5 q^{61} + 16 q^{62} + 2 q^{64} - 4 q^{65} + 6 q^{66} - 5 q^{67} + 6 q^{69} - 12 q^{71} - 2 q^{72} - 16 q^{73} - 4 q^{74} + q^{75} - 4 q^{76} + 8 q^{78} - 2 q^{79} - q^{80} - q^{81} - 9 q^{82} - 6 q^{83} - 7 q^{86} - 3 q^{87} - 6 q^{88} - 15 q^{89} + 4 q^{90} - 6 q^{92} - 8 q^{93} + 2 q^{95} - q^{96} - 28 q^{97} + 24 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + q^12 + 8 * q^13 - 2 * q^15 - q^16 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 12 * q^22 + 3 * q^23 - q^24 - q^25 + 4 * q^26 + 10 * q^27 - 6 * q^29 - q^30 + 8 * q^31 + q^32 - 6 * q^33 - 4 * q^36 + 4 * q^37 - 2 * q^38 + 4 * q^39 + q^40 - 18 * q^41 - 14 * q^43 + 6 * q^44 + 2 * q^45 - 3 * q^46 - 2 * q^48 - 2 * q^50 - 4 * q^52 + 6 * q^53 + 5 * q^54 - 12 * q^55 + 4 * q^57 - 3 * q^58 - 6 * q^59 + q^60 + 5 * q^61 + 16 * q^62 + 2 * q^64 - 4 * q^65 + 6 * q^66 - 5 * q^67 + 6 * q^69 - 12 * q^71 - 2 * q^72 - 16 * q^73 - 4 * q^74 + q^75 - 4 * q^76 + 8 * q^78 - 2 * q^79 - q^80 - q^81 - 9 * q^82 - 6 * q^83 - 7 * q^86 - 3 * q^87 - 6 * q^88 - 15 * q^89 + 4 * q^90 - 6 * q^92 - 8 * q^93 + 2 * q^95 - q^96 - 28 * q^97 + 24 * q^99

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