LMFDB - Embedded newform 1274.2.f.t.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(79,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [2,1,1,-1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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 182)
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.t.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} +(2.00000 - 3.46410i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -4.00000 q^{20} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} +5.00000 q^{27} -8.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(1.50000 + 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} -2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-2.00000 + 3.46410i) q^{40} +7.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-4.00000 - 6.92820i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(1.50000 - 2.59808i) q^{47} -1.00000 q^{48} -11.0000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(0.500000 + 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{54} +4.00000 q^{55} +2.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-2.00000 - 3.46410i) q^{60} +(-6.50000 + 11.2583i) q^{61} +3.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(0.500000 + 0.866025i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(2.00000 - 3.46410i) q^{68} +7.00000 q^{69} +4.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(4.50000 + 7.79423i) q^{73} +(3.50000 + 6.06218i) q^{74} +(5.50000 - 9.52628i) q^{75} -2.00000 q^{76} -1.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.50000 - 6.06218i) q^{82} +16.0000 q^{83} +16.0000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} -8.00000 q^{90} -7.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{10} + q^{11} + q^{12} - 2 q^{13} + 8 q^{15} - q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} - 8 q^{20} + 2 q^{22} + 7 q^{23} - q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^10 + q^11 + q^12 - 2 * q^13 + 8 * q^15 - q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 - 8 * q^20 + 2 * q^22 + 7 * q^23 - q^24 - 11 * q^25 - q^26 + 10 * q^27 - 16 * q^29 + 4 * q^30 + 3 * q^31 + q^32 - q^33 + 8 * q^34 - 4 * q^36 - 7 * q^37 - 2 * q^38 - q^39 - 4 * q^40 + 14 * q^41 - 16 * q^43 + q^44 - 8 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 22 * q^50 - 4 * q^51 + q^52 + 5 * q^54 + 8 * q^55 + 4 * q^57 - 8 * q^58 - 6 * q^59 - 4 * q^60 - 13 * q^61 + 6 * q^62 + 2 * q^64 - 4 * q^65 + q^66 - 7 * q^67 + 4 * q^68 + 14 * q^69 + 8 * q^71 - 2 * q^72 + 9 * q^73 + 7 * q^74 + 11 * q^75 - 4 * q^76 - 2 * q^78 + 13 * q^79 + 4 * q^80 - q^81 + 7 * q^82 + 32 * q^83 + 32 * q^85 - 8 * q^86 - 8 * q^87 - q^88 - 6 * q^89 - 16 * q^90 - 14 * q^92 - 3 * q^93 - 3 * q^94 - 8 * q^95 - q^96 - 22 * q^97 + 4 * q^99

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	0.973494	−	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
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.834512	−	0.550990i	$-0.185750\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−2.00000	−	3.46410i	−0.632456	−	1.09545i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	4.00000			1.03280
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	−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	$0.0929851\pi$
$20$	−4.00000			−0.894427
$21$		0			0
$22$	1.00000			0.213201
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	5.00000			0.962250
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	2.00000	−	3.46410i	0.365148	−	0.632456i
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	4.00000			0.685994
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−2.00000	+	3.46410i	−0.316228	+	0.547723i
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−4.00000	−	6.92820i	−0.596285	−	1.03280i
$46$	−3.50000	−	6.06218i	−0.516047	−	0.893819i
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−11.0000			−1.55563
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	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
$55$	4.00000			0.539360
$56$		0			0
$57$	2.00000			0.264906
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	−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	$0.961054\pi$
$60$	−2.00000	−	3.46410i	−0.258199	−	0.447214i
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	0.0640184	+	0.997949i	$0.479608\pi$
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	3.00000			0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	7.00000			0.842701
$70$		0			0
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	4.50000	+	7.79423i	0.526685	+	0.912245i	0.999517	+	0.0310925i	$0.00989865\pi$
$73$	4.50000	+	7.79423i	0.526685	+	0.912245i	−0.472831	+	0.881153i	$0.656768\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$	5.50000	−	9.52628i	0.635085	−	1.10000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	−1.00000			−0.113228
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.50000	−	6.06218i	0.386510	−	0.669456i
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$		0			0
$85$	16.0000			1.73544
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−8.00000			−0.843274
$91$		0			0
$92$	−7.00000			−0.729800
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−11.0000			−1.11688			−0.558440	−	0.829545i	$-0.688600\pi$
$97$	−11.0000			−1.11688			−0.558440	+	0.829545i	$0.688600\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	−0.507300	−	0.861770i	$-0.669356\pi$
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	0.999964	+	0.00844953i	$0.00268960\pi$
$104$	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
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	−7.00000			−0.664411
$112$		0			0
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	−14.0000	−	24.2487i	−1.30551	−	2.26120i
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	−4.00000			−0.365148
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	6.50000	+	11.2583i	0.588482	+	1.01928i
$123$	3.50000	+	6.06218i	0.315584	+	0.546608i
$124$	1.50000	−	2.59808i	0.134704	−	0.233314i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	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	$0.166667\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$	−7.00000			−0.604708
$135$	10.0000	−	17.3205i	0.860663	−	1.49071i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	7.00000	+	12.1244i	0.598050	+	1.03585i	0.993109	+	0.117198i	$0.0373911\pi$
$137$	7.00000	+	12.1244i	0.598050	+	1.03585i	−0.395058	+	0.918656i	$0.629276\pi$
$138$	3.50000	−	6.06218i	0.297940	−	0.516047i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	−16.0000	+	27.7128i	−1.32873	+	2.30142i
$146$	9.00000			0.744845
$147$		0			0
$148$	7.00000			0.575396
$149$	−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	$0.956055\pi$
$150$	−5.50000	−	9.52628i	−0.449073	−	0.777817i
$151$	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
$153$	8.00000			0.646762
$154$		0			0
$155$	12.0000			0.963863
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	−6.50000	−	11.2583i	−0.517112	−	0.895665i
$159$		0			0
$160$	4.00000			0.316228
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$	−3.50000	−	6.06218i	−0.273304	−	0.473377i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$	8.00000	−	13.8564i	0.620920	−	1.07547i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	8.00000	−	13.8564i	0.613572	−	1.06274i
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$	−8.00000			−0.606478
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$	−4.00000	+	6.92820i	−0.298142	+	0.516398i
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$	−13.0000			−0.960988
$184$	−3.50000	+	6.06218i	−0.258023	+	0.446910i
$185$	14.0000	+	24.2487i	1.02930	+	1.78280i
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$	−3.00000			−0.218797
$189$		0			0
$190$	−8.00000			−0.580381
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	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	$0.787349\pi$
$194$	−5.50000	+	9.52628i	−0.394877	+	0.683947i
$195$	−4.00000			−0.286446
$196$		0			0
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	5.50000	+	9.52628i	0.388909	+	0.673610i
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$	9.00000			0.633238
$203$		0			0
$204$	4.00000			0.280056
$205$	14.0000	−	24.2487i	0.977802	−	1.69360i
$206$	−5.00000	−	8.66025i	−0.348367	−	0.603388i
$207$	−7.00000	−	12.1244i	−0.486534	−	0.842701i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	2.00000			0.138343
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$	2.00000	+	3.46410i	0.137038	+	0.237356i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−16.0000	+	27.7128i	−1.09119	+	1.89000i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−14.0000			−0.948200
$219$	−4.50000	+	7.79423i	−0.304082	+	0.526685i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$	−3.50000	+	6.06218i	−0.234905	+	0.406867i
$223$	−9.00000			−0.602685			−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000			−0.602685			−0.301342	+	0.953516i	$0.597435\pi$
$224$		0			0
$225$	−22.0000			−1.46667
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.784642	+	0.619949i	$0.212847\pi$
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.144571	+	0.989494i	$0.453820\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	−28.0000			−1.84627
$231$		0			0
$232$	8.00000			0.525226
$233$	6.50000	−	11.2583i	0.425829	−	0.737558i	−0.570668	−	0.821181i	$-0.693316\pi$
$233$	6.50000	−	11.2583i	0.425829	−	0.737558i	0.996497	+	0.0836229i	$0.0266491\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	−6.00000	−	10.3923i	−0.391397	−	0.677919i
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	13.0000			0.844441
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−5.00000	−	8.66025i	−0.321412	−	0.556702i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	13.0000			0.832240
$245$		0			0
$246$	7.00000			0.446304
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$	−1.50000	−	2.59808i	−0.0952501	−	0.164978i
$249$	8.00000	+	13.8564i	0.506979	+	0.878114i
$250$	−12.0000	+	20.7846i	−0.758947	+	1.31453i
$251$	−17.0000			−1.07303			−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000			−1.07303			−0.536515	+	0.843891i	$0.680260\pi$
$252$		0			0
$253$	7.00000			0.440086
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$	8.00000	+	13.8564i	0.500979	+	0.867722i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	−8.00000			−0.498058
$259$		0			0
$260$	4.00000			0.248069
$261$	−8.00000	+	13.8564i	−0.495188	+	0.857690i
$262$		0			0
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	0.506669	−	0.862141i	$-0.330877\pi$
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	−0.999970	+	0.00771799i	$0.997543\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$		0			0
$266$		0			0
$267$	−6.00000			−0.367194
$268$	−3.50000	+	6.06218i	−0.213797	+	0.370306i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$	−10.0000	−	17.3205i	−0.608581	−	1.05409i
$271$	−1.50000	+	2.59808i	−0.0911185	+	0.157822i	−0.907982	−	0.419009i	$-0.862378\pi$
$271$	−1.50000	+	2.59808i	−0.0911185	+	0.157822i	0.816864	+	0.576831i	$0.195711\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	14.0000			0.845771
$275$	5.50000	−	9.52628i	0.331662	−	0.574456i
$276$	−3.50000	−	6.06218i	−0.210675	−	0.364900i
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	0.995997	−	0.0893846i	$-0.0284900\pi$
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	−0.575408	+	0.817867i	$0.695157\pi$
$278$	10.0000	−	17.3205i	0.599760	−	1.03882i
$279$	6.00000			0.359211
$280$		0			0
$281$	−20.0000			−1.19310			−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000			−1.19310			−0.596550	+	0.802576i	$0.703462\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	0.999981	+	0.00609896i	$0.00194137\pi$
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	−0.494709	+	0.869059i	$0.664725\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	4.00000	−	6.92820i	0.236940	−	0.410391i
$286$	−1.00000			−0.0591312
$287$		0			0
$288$	2.00000			0.117851
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	16.0000	+	27.7128i	0.939552	+	1.62735i
$291$	−5.50000	−	9.52628i	−0.322416	−	0.558440i
$292$	4.50000	−	7.79423i	0.263343	−	0.456123i
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	−24.0000			−1.39733
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$	−3.50000	+	6.06218i	−0.202410	+	0.350585i
$300$	−11.0000			−0.635085
$301$		0			0
$302$	4.00000			0.230174
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	26.0000	+	45.0333i	1.48876	+	2.57860i
$306$	4.00000	−	6.92820i	0.228665	−	0.396059i
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$		0			0
$309$	10.0000			0.568880
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	−0.880693	−	0.473688i	$-0.842923\pi$
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	0.0301210	−	0.999546i	$-0.490411\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	7.00000			0.395033
$315$		0			0
$316$	−13.0000			−0.731307
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	−0.623712	−	0.781654i	$-0.714376\pi$
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	0.988788	+	0.149323i	$0.0477095\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	2.00000	−	3.46410i	0.111803	−	0.193649i
$321$	−12.0000			−0.669775
$322$		0			0
$323$	8.00000			0.445132
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.50000	+	9.52628i	0.305085	+	0.528423i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$	−7.00000			−0.386510
$329$		0			0
$330$	4.00000			0.220193
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	−0.995134	−	0.0985303i	$-0.968586\pi$
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	0.582897	+	0.812546i	$0.301919\pi$
$332$	−8.00000	−	13.8564i	−0.439057	−	0.760469i
$333$	7.00000	+	12.1244i	0.383598	+	0.664411i
$334$		0			0
$335$	−28.0000			−1.52980
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	0.500000	+	0.866025i	0.0271563	+	0.0470360i
$340$	−8.00000	−	13.8564i	−0.433861	−	0.751469i
$341$	−1.50000	+	2.59808i	−0.0812296	+	0.140694i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	8.00000			0.431331
$345$	14.0000	−	24.2487i	0.753735	−	1.30551i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	0.872955	+	0.487800i	$0.162201\pi$
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	−0.0140303	+	0.999902i	$0.504466\pi$
$348$	−4.00000	+	6.92820i	−0.214423	+	0.371391i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	0.681720	−	0.731613i	$-0.261232\pi$
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	−0.974456	+	0.224580i	$0.927899\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$	6.00000			0.317999
$357$		0			0
$358$	18.0000			0.951330
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	4.00000	+	6.92820i	0.210819	+	0.365148i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−6.50000	+	11.2583i	−0.341632	+	0.591725i
$363$	10.0000			0.524864
$364$		0			0
$365$	36.0000			1.88433
$366$	−6.50000	+	11.2583i	−0.339760	+	0.588482i
$367$	6.00000	+	10.3923i	0.313197	+	0.542474i	0.979053	−	0.203607i	$-0.0652665\pi$
$367$	6.00000	+	10.3923i	0.313197	+	0.542474i	−0.665855	+	0.746081i	$0.731933\pi$
$368$	3.50000	+	6.06218i	0.182450	+	0.316013i
$369$	7.00000	−	12.1244i	0.364405	−	0.631169i
$370$	28.0000			1.45565
$371$		0			0
$372$	3.00000			0.155543
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−12.0000	−	20.7846i	−0.619677	−	1.07331i
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	8.00000			0.412021
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$	6.50000	+	11.2583i	0.333005	+	0.576782i
$382$	12.0000	+	20.7846i	0.613973	+	1.06343i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	4.00000			0.203595
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$	5.50000	+	9.52628i	0.279220	+	0.483624i
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	0.746624	−	0.665246i	$-0.231673\pi$
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	−0.949432	+	0.313972i	$0.898340\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$	28.0000			1.41602
$392$		0			0
$393$		0			0
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	−26.0000	−	45.0333i	−1.30820	−	2.26587i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	4.00000	−	6.92820i	0.200754	−	0.347717i	−0.748017	−	0.663679i	$-0.768994\pi$
$397$	4.00000	−	6.92820i	0.200754	−	0.347717i	0.948772	+	0.315963i	$0.102327\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	11.0000			0.550000
$401$	−4.00000	+	6.92820i	−0.199750	+	0.345978i	−0.948447	−	0.316934i	$-0.897346\pi$
$401$	−4.00000	+	6.92820i	−0.199750	+	0.345978i	0.748697	+	0.662912i	$0.230680\pi$
$402$	−3.50000	−	6.06218i	−0.174564	−	0.302354i
$403$	−1.50000	−	2.59808i	−0.0747203	−	0.129419i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	−4.00000			−0.198762
$406$		0			0
$407$	−7.00000			−0.346977
$408$	2.00000	−	3.46410i	0.0990148	−	0.171499i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	−14.0000	−	24.2487i	−0.691411	−	1.19756i
$411$	−7.00000	+	12.1244i	−0.345285	+	0.598050i
$412$	−10.0000			−0.492665
$413$		0			0
$414$	−14.0000			−0.688062
$415$	32.0000	−	55.4256i	1.57082	−	2.72074i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	10.0000	+	17.3205i	0.489702	+	0.848189i
$418$	1.00000	−	1.73205i	0.0489116	−	0.0847174i
$419$	19.0000			0.928211			0.464105	−	0.885780i	$-0.346376\pi$
$419$	19.0000			0.928211			0.464105	+	0.885780i	$0.346376\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$	11.0000	−	19.0526i	0.535472	−	0.927464i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	22.0000	−	38.1051i	1.06716	−	1.84837i
$426$	4.00000			0.193801
$427$		0			0
$428$	12.0000			0.580042
$429$	0.500000	−	0.866025i	0.0241402	−	0.0418121i
$430$	16.0000	+	27.7128i	0.771589	+	1.33643i
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	0.840936	−	0.541135i	$-0.182005\pi$
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	−0.889104	+	0.457705i	$0.848672\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$		0			0
$435$	−32.0000			−1.53428
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−7.00000	−	12.1244i	−0.334855	−	0.579987i
$438$	4.50000	+	7.79423i	0.215018	+	0.372423i
$439$	−1.00000	+	1.73205i	−0.0477274	+	0.0826663i	−0.888902	−	0.458097i	$-0.848531\pi$
$439$	−1.00000	+	1.73205i	−0.0477274	+	0.0826663i	0.841175	+	0.540763i	$0.181865\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	−4.00000			−0.190261
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	12.0000	+	20.7846i	0.568855	+	0.985285i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$	−15.0000			−0.709476
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−11.0000	+	19.0526i	−0.518545	+	0.898146i
$451$	3.50000	+	6.06218i	0.164809	+	0.285457i
$452$	−0.500000	−	0.866025i	−0.0235180	−	0.0407344i
$453$	−2.00000	+	3.46410i	−0.0939682	+	0.162758i
$454$	28.0000			1.31411
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$	10.0000	+	17.3205i	0.466760	+	0.808452i
$460$	−14.0000	+	24.2487i	−0.652753	+	1.13060i
$461$	−16.0000			−0.745194			−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000			−0.745194			−0.372597	+	0.927993i	$0.621533\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	−6.50000	−	11.2583i	−0.301107	−	0.521532i
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$	−12.0000			−0.553519
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	6.50000	−	11.2583i	0.298555	−	0.517112i
$475$	−22.0000			−1.00943
$476$		0			0
$477$		0			0
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	2.00000	+	3.46410i	0.0912871	+	0.158114i
$481$	3.50000	−	6.06218i	0.159586	−	0.276412i
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−22.0000	+	38.1051i	−0.998969	+	1.73026i
$486$	−8.00000	−	13.8564i	−0.362887	−	0.628539i
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	−0.994352	−	0.106129i	$-0.966154\pi$
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	0.405266	−	0.914199i	$-0.367179\pi$
$488$	6.50000	−	11.2583i	0.294241	−	0.509641i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	40.0000			1.80517			0.902587	−	0.430507i	$-0.141665\pi$
$491$	40.0000			1.80517			0.902587	+	0.430507i	$0.141665\pi$
$492$	3.50000	−	6.06218i	0.157792	−	0.273304i
$493$	−16.0000	−	27.7128i	−0.720604	−	1.24812i
$494$	1.00000	+	1.73205i	0.0449921	+	0.0779287i
$495$	4.00000	−	6.92820i	0.179787	−	0.311400i
$496$	−3.00000			−0.134704
$497$		0			0
$498$	16.0000			0.716977
$499$	−18.5000	+	32.0429i	−0.828174	+	1.43444i	0.0712957	+	0.997455i	$0.477287\pi$
$499$	−18.5000	+	32.0429i	−0.828174	+	1.43444i	−0.899469	+	0.436984i	$0.856047\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$	−8.50000	+	14.7224i	−0.379374	+	0.657094i
$503$	16.0000			0.713405			0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000			0.713405			0.356702	+	0.934218i	$0.383901\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$	3.50000	−	6.06218i	0.155594	−	0.269497i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−6.50000	−	11.2583i	−0.288391	−	0.499508i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$	16.0000			0.708492
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$	−20.0000	−	34.6410i	−0.881305	−	1.52647i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	3.00000			0.131940
$518$		0			0
$519$	14.0000			0.614532
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$	8.00000	+	13.8564i	0.350150	+	0.606478i
$523$	−7.50000	+	12.9904i	−0.327952	+	0.568030i	−0.982105	−	0.188332i	$-0.939692\pi$
$523$	−7.50000	+	12.9904i	−0.327952	+	0.568030i	0.654153	+	0.756362i	$0.273025\pi$
$524$		0			0
$525$		0			0
$526$	−16.0000			−0.697633
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−7.00000			−0.303204
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	24.0000	+	41.5692i	1.03761	+	1.79719i
$536$	3.50000	+	6.06218i	0.151177	+	0.261846i
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$	3.00000			0.129339
$539$		0			0
$540$	−20.0000			−0.860663
$541$	19.0000	−	32.9090i	0.816874	−	1.41487i	−0.0911008	−	0.995842i	$-0.529039\pi$
$541$	19.0000	−	32.9090i	0.816874	−	1.41487i	0.907975	−	0.419025i	$-0.137628\pi$
$542$	1.50000	+	2.59808i	0.0644305	+	0.111597i
$543$	−6.50000	−	11.2583i	−0.278942	−	0.483141i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−56.0000			−2.39878
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	7.00000	−	12.1244i	0.299025	−	0.517927i
$549$	13.0000	+	22.5167i	0.554826	+	0.960988i
$550$	−5.50000	−	9.52628i	−0.234521	−	0.406202i
$551$	−8.00000	+	13.8564i	−0.340811	+	0.590303i
$552$	−7.00000			−0.297940
$553$		0			0
$554$	14.0000			0.594803
$555$	−14.0000	+	24.2487i	−0.594267	+	1.02930i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−15.5000	−	26.8468i	−0.656756	−	1.13753i	−0.981450	−	0.191716i	$-0.938595\pi$
$557$	−15.5000	−	26.8468i	−0.656756	−	1.13753i	0.324694	−	0.945819i	$-0.394739\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	8.00000			0.338364
$560$		0			0
$561$	−4.00000			−0.168880
$562$	−10.0000	+	17.3205i	−0.421825	+	0.730622i
$563$	−15.5000	−	26.8468i	−0.653247	−	1.13146i	−0.982330	−	0.187156i	$-0.940073\pi$
$563$	−15.5000	−	26.8468i	−0.653247	−	1.13146i	0.329083	−	0.944301i	$-0.393260\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	17.0000			0.714563
$567$		0			0
$568$	−4.00000			−0.167836
$569$	−14.5000	+	25.1147i	−0.607872	+	1.05286i	0.383719	+	0.923450i	$0.374643\pi$
$569$	−14.5000	+	25.1147i	−0.607872	+	1.05286i	−0.991591	+	0.129415i	$0.958690\pi$
$570$	−4.00000	−	6.92820i	−0.167542	−	0.290191i
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	−0.998667	−	0.0516146i	$-0.983563\pi$
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	0.454634	−	0.890678i	$-0.349770\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−77.0000			−3.21112
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	0.615603	−	0.788056i	$-0.288912\pi$
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	−0.990278	+	0.139100i	$0.955579\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	−2.00000	+	3.46410i	−0.0831172	+	0.143963i
$580$	32.0000			1.32873
$581$		0			0
$582$	−11.0000			−0.455965
$583$		0			0
$584$	−4.50000	−	7.79423i	−0.186211	−	0.322527i
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$	−7.00000	+	12.1244i	−0.289167	+	0.500853i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	−12.0000	+	20.7846i	−0.494032	+	0.855689i
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	−5.00000	+	8.66025i	−0.205325	+	0.355634i	−0.950236	−	0.311530i	$-0.899159\pi$
$593$	−5.00000	+	8.66025i	−0.205325	+	0.355634i	0.744911	+	0.667164i	$0.232492\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	15.0000			0.614424
$597$	−8.00000	+	13.8564i	−0.327418	+	0.567105i
$598$	3.50000	+	6.06218i	0.143126	+	0.247901i
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	−0.998160	−	0.0606393i	$-0.980686\pi$
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	0.446565	−	0.894751i	$-0.352647\pi$
$600$	−5.50000	+	9.52628i	−0.224537	+	0.388909i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	−14.0000			−0.570124
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	−20.0000	−	34.6410i	−0.813116	−	1.40836i
$606$	4.50000	+	7.79423i	0.182800	+	0.316619i
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	−0.688274	−	0.725450i	$-0.741632\pi$
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	0.972396	+	0.233338i	$0.0749648\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	52.0000			2.10542
$611$	−1.50000	+	2.59808i	−0.0606835	+	0.105107i
$612$	−4.00000	−	6.92820i	−0.161690	−	0.280056i
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	0.641734	−	0.766927i	$-0.278215\pi$
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	−0.985046	+	0.172294i	$0.944882\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	28.0000			1.12907
$616$		0			0
$617$	−38.0000			−1.52982			−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000			−1.52982			−0.764911	+	0.644136i	$0.777217\pi$
$618$	5.00000	−	8.66025i	0.201129	−	0.348367i
$619$	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	$0.742550\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$	17.5000	−	30.3109i	0.702251	−	1.21633i
$622$	−30.0000			−1.20289
$623$		0			0
$624$	1.00000			0.0400320
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	1.00000	+	1.73205i	0.0399362	+	0.0691714i
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	−28.0000			−1.11643
$630$		0			0
$631$	22.0000			0.875806			0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000			0.875806			0.437903	+	0.899022i	$0.355721\pi$
$632$	−6.50000	+	11.2583i	−0.258556	+	0.447832i
$633$	11.0000	+	19.0526i	0.437211	+	0.757271i
$634$	−6.50000	−	11.2583i	−0.258148	−	0.447125i
$635$	26.0000	−	45.0333i	1.03178	−	1.78709i
$636$		0			0
$637$		0			0
$638$	−8.00000			−0.316723
$639$	4.00000	−	6.92820i	0.158238	−	0.274075i
$640$	−2.00000	−	3.46410i	−0.0790569	−	0.136931i
$641$	12.5000	+	21.6506i	0.493720	+	0.855149i	0.999974	−	0.00723604i	$-0.00230332\pi$
$641$	12.5000	+	21.6506i	0.493720	+	0.855149i	−0.506254	+	0.862385i	$0.668970\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	28.0000			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$644$		0			0
$645$	−32.0000			−1.26000
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.758654	−	0.651494i	$-0.774142\pi$
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.184884	−	0.982760i	$-0.559191\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	3.00000	−	5.19615i	0.117760	−	0.203967i
$650$	11.0000			0.431455
$651$		0			0
$652$	12.0000			0.469956
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−7.00000	−	12.1244i	−0.273722	−	0.474100i
$655$		0			0
$656$	−3.50000	+	6.06218i	−0.136652	+	0.236688i
$657$	18.0000			0.702247
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	0.777689	−	0.628649i	$-0.216392\pi$
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	−0.933271	+	0.359174i	$0.883059\pi$
$662$	7.50000	+	12.9904i	0.291496	+	0.504885i
$663$	2.00000	−	3.46410i	0.0776736	−	0.134535i
$664$	−16.0000			−0.620920
$665$		0			0
$666$	14.0000			0.542489
$667$	−28.0000	+	48.4974i	−1.08416	+	1.87783i
$668$		0			0
$669$	−4.50000	−	7.79423i	−0.173980	−	0.301342i
$670$	−14.0000	+	24.2487i	−0.540867	+	0.936809i
$671$	−13.0000			−0.501859
$672$		0			0
$673$	−33.0000			−1.27206			−0.636028	−	0.771666i	$-0.719424\pi$
$673$	−33.0000			−1.27206			−0.636028	+	0.771666i	$0.719424\pi$
$674$	4.50000	−	7.79423i	0.173334	−	0.300222i
$675$	−27.5000	−	47.6314i	−1.05848	−	1.83333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	6.50000	−	11.2583i	0.249815	−	0.432693i	−0.713659	−	0.700493i	$-0.752963\pi$
$677$	6.50000	−	11.2583i	0.249815	−	0.432693i	0.963474	+	0.267800i	$0.0862968\pi$
$678$	1.00000			0.0384048
$679$		0			0
$680$	−16.0000			−0.613572
$681$	−14.0000	+	24.2487i	−0.536481	+	0.929213i
$682$	1.50000	+	2.59808i	0.0574380	+	0.0994855i
$683$	−15.5000	−	26.8468i	−0.593091	−	1.02726i	−0.993813	−	0.111064i	$-0.964574\pi$
$683$	−15.5000	−	26.8468i	−0.593091	−	1.02726i	0.400722	−	0.916200i	$-0.368759\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	56.0000			2.13965
$686$		0			0
$687$	−20.0000			−0.763048
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$		0			0
$690$	−14.0000	−	24.2487i	−0.532971	−	0.923133i
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	32.0000			1.21470
$695$	40.0000	−	69.2820i	1.51729	−	2.62802i
$696$	4.00000	+	6.92820i	0.151620	+	0.262613i
$697$	14.0000	+	24.2487i	0.530288	+	0.918485i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	13.0000			0.491705
$700$		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
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	6.00000	−	10.3923i	0.225973	−	0.391397i
$706$	−11.0000			−0.413990
$707$		0			0
$708$	−6.00000			−0.225494
$709$	25.5000	−	44.1673i	0.957673	−	1.65874i	0.229543	−	0.973299i	$-0.426277\pi$
$709$	25.5000	−	44.1673i	0.957673	−	1.65874i	0.728130	−	0.685439i	$-0.240390\pi$
$710$	−8.00000	−	13.8564i	−0.300235	−	0.520022i
$711$	−13.0000	−	22.5167i	−0.487538	−	0.844441i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	21.0000			0.786456
$714$		0			0
$715$	−4.00000			−0.149592
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$		0			0
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	−0.994915	−	0.100721i	$-0.967885\pi$
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	0.584684	+	0.811261i	$0.301219\pi$
$720$	8.00000			0.298142
$721$		0			0
$722$	15.0000			0.558242
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	6.50000	+	11.2583i	0.241571	+	0.418413i
$725$	44.0000	+	76.2102i	1.63412	+	2.83038i
$726$	5.00000	−	8.66025i	0.185567	−	0.321412i
$727$	−18.0000			−0.667583			−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000			−0.667583			−0.333792	+	0.942647i	$0.608328\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	18.0000	−	31.1769i	0.666210	−	1.15391i
$731$	−16.0000	−	27.7128i	−0.591781	−	1.02500i
$732$	6.50000	+	11.2583i	0.240247	+	0.416120i
$733$	−6.00000	+	10.3923i	−0.221615	+	0.383849i	−0.955299	−	0.295643i	$-0.904466\pi$
$733$	−6.00000	+	10.3923i	−0.221615	+	0.383849i	0.733683	+	0.679491i	$0.237800\pi$
$734$	12.0000			0.442928
$735$		0			0
$736$	7.00000			0.258023
$737$	3.50000	−	6.06218i	0.128924	−	0.223303i
$738$	−7.00000	−	12.1244i	−0.257674	−	0.446304i
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	0.930170	−	0.367129i	$-0.119659\pi$
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	−0.783028	+	0.621987i	$0.786326\pi$
$740$	14.0000	−	24.2487i	0.514650	−	0.891400i
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	−44.0000			−1.61420			−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000			−1.61420			−0.807102	+	0.590412i	$0.798965\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$	30.0000	+	51.9615i	1.09911	+	1.90372i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$	16.0000	−	27.7128i	0.585409	−	1.01396i
$748$	4.00000			0.146254
$749$		0			0
$750$	−24.0000			−0.876356
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	0.301373	+	0.953506i	$0.402555\pi$
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	−0.976447	+	0.215757i	$0.930778\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$	−8.50000	−	14.7224i	−0.309757	−	0.536515i
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$	16.0000			0.582300
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−4.00000	+	6.92820i	−0.145287	+	0.251644i
$759$	3.50000	+	6.06218i	0.127042	+	0.220043i
$760$	4.00000	+	6.92820i	0.145095	+	0.251312i
$761$	0.500000	−	0.866025i	0.0181250	−	0.0313934i	−0.856821	−	0.515615i	$-0.827564\pi$
$761$	0.500000	−	0.866025i	0.0181250	−	0.0313934i	0.874946	+	0.484221i	$0.160897\pi$
$762$	13.0000			0.470940
$763$		0			0
$764$	24.0000			0.868290
$765$	16.0000	−	27.7128i	0.578481	−	1.00196i
$766$	−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
$769$	−25.0000			−0.901523			−0.450762	−	0.892644i	$-0.648848\pi$
$769$	−25.0000			−0.901523			−0.450762	+	0.892644i	$0.648848\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	0.973942	+	0.226796i	$0.0728252\pi$
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	−0.290560	+	0.956857i	$0.593841\pi$
$774$	8.00000	+	13.8564i	0.287554	+	0.498058i
$775$	16.5000	−	28.5788i	0.592697	−	1.02658i
$776$	11.0000			0.394877
$777$		0			0
$778$	−8.00000			−0.286814
$779$	7.00000	−	12.1244i	0.250801	−	0.434400i
$780$	2.00000	+	3.46410i	0.0716115	+	0.124035i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	14.0000	−	24.2487i	0.500639	−	0.867132i
$783$	−40.0000			−1.42948
$784$		0			0
$785$	28.0000			0.999363
$786$		0			0
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	0.250832	−	0.968031i	$-0.419296\pi$
$788$	−1.50000	−	2.59808i	−0.0534353	−	0.0925526i
$789$	8.00000	−	13.8564i	0.284808	−	0.493301i
$790$	−52.0000			−1.85008
$791$		0			0
$792$	−2.00000			−0.0710669
$793$	6.50000	−	11.2583i	0.230822	−	0.399795i
$794$	−4.00000	−	6.92820i	−0.141955	−	0.245873i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−21.0000			−0.743858			−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000			−0.743858			−0.371929	+	0.928261i	$0.621304\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$	5.50000	−	9.52628i	0.194454	−	0.336805i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	4.00000	+	6.92820i	0.141245	+	0.244643i
$803$	−4.50000	+	7.79423i	−0.158802	+	0.275052i
$804$	−7.00000			−0.246871
$805$		0			0
$806$	−3.00000			−0.105670
$807$	−1.50000	+	2.59808i	−0.0528025	+	0.0914566i
$808$	−4.50000	−	7.79423i	−0.158309	−	0.274200i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$	−2.00000	+	3.46410i	−0.0702728	+	0.121716i
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	−3.00000			−0.105215
$814$	−3.50000	+	6.06218i	−0.122675	+	0.212479i
$815$	24.0000	+	41.5692i	0.840683	+	1.45611i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	−28.0000			−0.977802
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$	7.00000	+	12.1244i	0.244153	+	0.422885i
$823$	17.5000	+	30.3109i	0.610012	+	1.05657i	0.991238	+	0.132089i	$0.0421686\pi$
$823$	17.5000	+	30.3109i	0.610012	+	1.05657i	−0.381226	+	0.924482i	$0.624498\pi$
$824$	−5.00000	+	8.66025i	−0.174183	+	0.301694i
$825$	11.0000			0.382971
$826$		0			0
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$	−7.00000	+	12.1244i	−0.243267	+	0.421350i
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	0.666338	−	0.745650i	$-0.267861\pi$
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	−0.978921	+	0.204240i	$0.934528\pi$
$830$	−32.0000	−	55.4256i	−1.11074	−	1.92385i
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$	−1.00000			−0.0346688
$833$		0			0
$834$	20.0000			0.692543
$835$		0			0
$836$	−1.00000	−	1.73205i	−0.0345857	−	0.0599042i
$837$	7.50000	+	12.9904i	0.259238	+	0.449013i
$838$	9.50000	−	16.4545i	0.328172	−	0.568411i
$839$	−21.0000			−0.725001			−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000			−0.725001			−0.362500	+	0.931984i	$0.618077\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−5.50000	+	9.52628i	−0.189543	+	0.328297i
$843$	−10.0000	−	17.3205i	−0.344418	−	0.596550i
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$	−6.00000			−0.206284
$847$		0			0
$848$		0			0
$849$	−8.50000	+	14.7224i	−0.291719	+	0.505273i
$850$	−22.0000	−	38.1051i	−0.754594	−	1.30699i
$851$	24.5000	+	42.4352i	0.839849	+	1.45466i
$852$	2.00000	−	3.46410i	0.0685189	−	0.118678i
$853$	44.0000			1.50653			0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000			1.50653			0.753266	+	0.657716i	$0.228477\pi$
$854$		0			0
$855$	−16.0000			−0.547188
$856$	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	$0.578690\pi$
$858$	−0.500000	−	0.866025i	−0.0170697	−	0.0295656i
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	−0.470581	−	0.882357i	$-0.655956\pi$
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	0.999434	−	0.0336436i	$-0.0107111\pi$
$860$	32.0000			1.09119
$861$		0			0
$862$	−2.00000			−0.0681203
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$	−28.0000	−	48.4974i	−0.952029	−	1.64896i
$866$	9.00000	−	15.5885i	0.305832	−	0.529717i
$867$	1.00000			0.0339618
$868$		0			0
$869$	13.0000			0.440995
$870$	−16.0000	+	27.7128i	−0.542451	+	0.939552i
$871$	3.50000	+	6.06218i	0.118593	+	0.205409i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−11.0000	+	19.0526i	−0.372294	+	0.644831i
$874$	−14.0000			−0.473557
$875$		0			0
$876$	9.00000			0.304082
$877$	−14.5000	+	25.1147i	−0.489630	+	0.848064i	−0.999929	−	0.0119329i	$-0.996202\pi$
$877$	−14.5000	+	25.1147i	−0.489630	+	0.848064i	0.510299	+	0.859997i	$0.329535\pi$
$878$	1.00000	+	1.73205i	0.0337484	+	0.0584539i
$879$	−7.00000	−	12.1244i	−0.236104	−	0.408944i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	−2.00000	+	3.46410i	−0.0672673	+	0.116510i
$885$	−12.0000	−	20.7846i	−0.403376	−	0.698667i
$886$		0			0
$887$	7.00000	−	12.1244i	0.235037	−	0.407096i	−0.724246	−	0.689541i	$-0.757812\pi$
$887$	7.00000	−	12.1244i	0.235037	−	0.407096i	0.959283	+	0.282445i	$0.0911455\pi$
$888$	7.00000			0.234905
$889$		0			0
$890$	24.0000			0.804482
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	4.50000	+	7.79423i	0.150671	+	0.260970i
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$	−7.50000	+	12.9904i	−0.250838	+	0.434463i
$895$	72.0000			2.40669
$896$		0			0
$897$	−7.00000			−0.233723
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	11.0000	+	19.0526i	0.366667	+	0.635085i
$901$		0			0
$902$	7.00000			0.233075
$903$		0			0
$904$	−1.00000			−0.0332595
$905$	−26.0000	+	45.0333i	−0.864269	+	1.49696i
$906$	2.00000	+	3.46410i	0.0664455	+	0.115087i
$907$	−27.0000	−	46.7654i	−0.896520	−	1.55282i	−0.831912	−	0.554908i	$-0.812753\pi$
$907$	−27.0000	−	46.7654i	−0.896520	−	1.55282i	−0.0646086	−	0.997911i	$-0.520580\pi$
$908$	14.0000	−	24.2487i	0.464606	−	0.804722i
$909$	18.0000			0.597022
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$	−26.0000	+	45.0333i	−0.859533	+	1.48876i
$916$	20.0000			0.660819
$917$		0			0
$918$	20.0000			0.660098
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	−0.380938	−	0.924601i	$-0.624399\pi$
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	0.991197	−	0.132398i	$-0.0422678\pi$
$920$	14.0000	+	24.2487i	0.461566	+	0.799456i
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	−8.00000	+	13.8564i	−0.263466	+	0.456336i
$923$	−4.00000			−0.131662
$924$		0			0
$925$	77.0000			2.53174
$926$	−6.00000	+	10.3923i	−0.197172	+	0.341512i
$927$	−10.0000	−	17.3205i	−0.328443	−	0.568880i
$928$	−4.00000	−	6.92820i	−0.131306	−	0.227429i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$	12.0000			0.393496
$931$		0			0
$932$	−13.0000			−0.425829
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$	8.00000	+	13.8564i	0.261628	+	0.453153i
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	48.0000			1.56809			0.784046	−	0.620703i	$-0.213153\pi$
$937$	48.0000			1.56809			0.784046	+	0.620703i	$0.213153\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$942$	3.50000	+	6.06218i	0.114036	+	0.197516i
$943$	24.5000	−	42.4352i	0.797830	−	1.38188i
$944$	6.00000			0.195283
$945$		0			0
$946$	−8.00000			−0.260102
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$948$	−6.50000	−	11.2583i	−0.211110	−	0.365654i
$949$	−4.50000	−	7.79423i	−0.146076	−	0.253011i
$950$	−11.0000	+	19.0526i	−0.356887	+	0.618147i
$951$	13.0000			0.421554
$952$		0			0
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$		0			0
$955$	48.0000	+	83.1384i	1.55324	+	2.69030i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	4.00000	−	6.92820i	0.129302	−	0.223957i
$958$		0			0
$959$		0			0
$960$	4.00000			0.129099
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−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
$965$	16.0000			0.515058
$966$		0			0
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$	4.00000	+	6.92820i	0.128499	+	0.222566i
$970$	22.0000	+	38.1051i	0.706377	+	1.22348i
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	−26.0000			−0.833094
$975$	−5.50000	+	9.52628i	−0.176141	+	0.305085i
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	−6.00000	+	10.3923i	−0.191859	+	0.332309i
$979$	−6.00000			−0.191761
$980$		0			0
$981$	−28.0000			−0.893971
$982$	20.0000	−	34.6410i	0.638226	−	1.10544i
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	0.999928	+	0.0119587i	$0.00380665\pi$
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	−0.489608	+	0.871943i	$0.662860\pi$
$984$	−3.50000	−	6.06218i	−0.111576	−	0.193255i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	−32.0000			−1.01909
$987$		0			0
$988$	2.00000			0.0636285
$989$	−28.0000	+	48.4974i	−0.890348	+	1.54213i
$990$	−4.00000	−	6.92820i	−0.127128	−	0.220193i
$991$	16.5000	+	28.5788i	0.524140	+	0.907837i	0.999605	+	0.0281022i	$0.00894640\pi$
$991$	16.5000	+	28.5788i	0.524140	+	0.907837i	−0.475465	+	0.879734i	$0.657720\pi$
$992$	−1.50000	+	2.59808i	−0.0476250	+	0.0824890i
$993$	−15.0000			−0.476011
$994$		0			0
$995$	64.0000			2.02894
$996$	8.00000	−	13.8564i	0.253490	−	0.439057i
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$	18.5000	+	32.0429i	0.585607	+	1.01430i
$999$	−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.t.79.1		2
7.2	even	3		1274.2.a.b.1.1		1
7.3	odd	6		1274.2.f.n.1145.1		2
7.4	even	3	inner	1274.2.f.t.1145.1		2
7.5	odd	6		182.2.a.a.1.1	✓	1
7.6	odd	2		1274.2.f.n.79.1		2
21.5	even	6		1638.2.a.k.1.1		1
28.19	even	6		1456.2.a.e.1.1		1
35.19	odd	6		4550.2.a.t.1.1		1
56.5	odd	6		5824.2.a.g.1.1		1
56.19	even	6		5824.2.a.w.1.1		1
91.5	even	12		2366.2.d.g.337.2		2
91.12	odd	6		2366.2.a.m.1.1		1
91.47	even	12		2366.2.d.g.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.a.1.1	✓	1	7.5	odd	6
1274.2.a.b.1.1		1	7.2	even	3
1274.2.f.n.79.1		2	7.6	odd	2
1274.2.f.n.1145.1		2	7.3	odd	6
1274.2.f.t.79.1		2	1.1	even	1	trivial
1274.2.f.t.1145.1		2	7.4	even	3	inner
1456.2.a.e.1.1		1	28.19	even	6
1638.2.a.k.1.1		1	21.5	even	6
2366.2.a.m.1.1		1	91.12	odd	6
2366.2.d.g.337.1		2	91.47	even	12
2366.2.d.g.337.2		2	91.5	even	12
4550.2.a.t.1.1		1	35.19	odd	6
5824.2.a.g.1.1		1	56.5	odd	6
5824.2.a.w.1.1		1	56.19	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 $\F_{q}$
Belyi maps

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} +(2.00000 - 3.46410i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -4.00000 q^{20} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} +5.00000 q^{27} -8.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(1.50000 + 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} -2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-2.00000 + 3.46410i) q^{40} +7.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-4.00000 - 6.92820i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(1.50000 - 2.59808i) q^{47} -1.00000 q^{48} -11.0000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(0.500000 + 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{54} +4.00000 q^{55} +2.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-2.00000 - 3.46410i) q^{60} +(-6.50000 + 11.2583i) q^{61} +3.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(0.500000 + 0.866025i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(2.00000 - 3.46410i) q^{68} +7.00000 q^{69} +4.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(4.50000 + 7.79423i) q^{73} +(3.50000 + 6.06218i) q^{74} +(5.50000 - 9.52628i) q^{75} -2.00000 q^{76} -1.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.50000 - 6.06218i) q^{82} +16.0000 q^{83} +16.0000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} -8.00000 q^{90} -7.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{10} + q^{11} + q^{12} - 2 q^{13} + 8 q^{15} - q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} - 8 q^{20} + 2 q^{22} + 7 q^{23} - q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^10 + q^11 + q^12 - 2 * q^13 + 8 * q^15 - q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 - 8 * q^20 + 2 * q^22 + 7 * q^23 - q^24 - 11 * q^25 - q^26 + 10 * q^27 - 16 * q^29 + 4 * q^30 + 3 * q^31 + q^32 - q^33 + 8 * q^34 - 4 * q^36 - 7 * q^37 - 2 * q^38 - q^39 - 4 * q^40 + 14 * q^41 - 16 * q^43 + q^44 - 8 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 22 * q^50 - 4 * q^51 + q^52 + 5 * q^54 + 8 * q^55 + 4 * q^57 - 8 * q^58 - 6 * q^59 - 4 * q^60 - 13 * q^61 + 6 * q^62 + 2 * q^64 - 4 * q^65 + q^66 - 7 * q^67 + 4 * q^68 + 14 * q^69 + 8 * q^71 - 2 * q^72 + 9 * q^73 + 7 * q^74 + 11 * q^75 - 4 * q^76 - 2 * q^78 + 13 * q^79 + 4 * q^80 - q^81 + 7 * q^82 + 32 * q^83 + 32 * q^85 - 8 * q^86 - 8 * q^87 - q^88 - 6 * q^89 - 16 * q^90 - 14 * q^92 - 3 * q^93 - 3 * q^94 - 8 * q^95 - q^96 - 22 * q^97 + 4 * q^99

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