LMFDB - Embedded newform 117.8.q.b.10.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,8,Mod(10,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.10"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$36.5490479816$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368 $ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{7}\cdot 13^{4} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.2
Root			$-14.7644i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.8.q.b.82.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.7863 + 7.38219i) q^{2} +(44.9933 - 77.9308i) q^{4} +248.787i q^{5} +(497.017 + 286.953i) q^{7} -561.243i q^{8} +(-1836.59 - 3181.07i) q^{10} +(-3411.39 + 1969.56i) q^{11} +(2867.43 + 7384.20i) q^{13} -8473.37 q^{14} +(9902.35 + 17151.4i) q^{16} +(7791.62 - 13495.5i) q^{17} +(-1742.44 - 1006.00i) q^{19} +(19388.2 + 11193.8i) q^{20} +(29079.4 - 50367.0i) q^{22} +(33680.6 + 58336.5i) q^{23} +16229.9 q^{25} +(-91175.3 - 73248.9i) q^{26} +(44724.9 - 25822.0i) q^{28} +(94582.0 + 163821. i) q^{29} +281068. i q^{31} +(-191015. - 110282. i) q^{32} +230077. i q^{34} +(-71390.3 + 123652. i) q^{35} +(228285. - 131800. i) q^{37} +29705.8 q^{38} +139630. q^{40} +(125678. - 72560.2i) q^{41} +(-371259. + 643040. i) q^{43} +354469. i q^{44} +(-861302. - 497273. i) q^{46} -1.08055e6i q^{47} +(-247087. - 427968. i) q^{49} +(-207521. + 119812. i) q^{50} +(704471. + 108779. i) q^{52} -1.63799e6 q^{53} +(-490002. - 848709. i) q^{55} +(161050. - 278947. i) q^{56} +(-2.41871e6 - 1.39644e6i) q^{58} +(-778187. - 449287. i) q^{59} +(-254459. + 440737. i) q^{61} +(-2.07490e6 - 3.59383e6i) q^{62} +721500. q^{64} +(-1.83709e6 + 713379. i) q^{65} +(315772. - 182311. i) q^{67} +(-701142. - 1.21441e6i) q^{68} -2.10806e6i q^{70} +(2.46548e6 + 1.42345e6i) q^{71} -4.44132e6i q^{73} +(-1.94595e6 + 3.37048e6i) q^{74} +(-156796. + 90526.4i) q^{76} -2.26069e6 q^{77} -6.66251e6 q^{79} +(-4.26704e6 + 2.46358e6i) q^{80} +(-1.07131e6 + 1.85556e6i) q^{82} +4.05229e6i q^{83} +(3.35750e6 + 1.93846e6i) q^{85} -1.09628e7i q^{86} +(1.10540e6 + 1.91462e6i) q^{88} +(1.01547e6 - 586279. i) q^{89} +(-693759. + 4.49289e6i) q^{91} +6.06161e6 q^{92} +(7.97686e6 + 1.38163e7i) q^{94} +(250279. - 433496. i) q^{95} +(-1.12996e7 - 6.52384e6i) q^{97} +(6.31867e6 + 3.64809e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 383 q^{4} - 2772 q^{7} - 509 q^{10} - 6516 q^{11} + 5109 q^{13} + 47916 q^{14} - 633 q^{16} + 38403 q^{17} + 43254 q^{19} - 89409 q^{20} - 125882 q^{22} + 68550 q^{23} + 39380 q^{25} - 361959 q^{26}+ \cdots - 16173003 q^{98}+O(q^{100}) $ 14 * q + 3 * q^2 + 383 * q^4 - 2772 * q^7 - 509 * q^10 - 6516 * q^11 + 5109 * q^13 + 47916 * q^14 - 633 * q^16 + 38403 * q^17 + 43254 * q^19 - 89409 * q^20 - 125882 * q^22 + 68550 * q^23 + 39380 * q^25 - 361959 * q^26 - 234780 * q^28 - 221583 * q^29 + 878067 * q^32 - 659616 * q^35 - 565347 * q^37 - 953640 * q^38 - 77182 * q^40 - 1716057 * q^41 - 882692 * q^43 - 3267480 * q^46 + 2653979 * q^49 - 145128 * q^50 + 4962178 * q^52 + 1791210 * q^53 + 2453536 * q^55 + 7457952 * q^56 - 14978127 * q^58 + 1189032 * q^59 + 3858525 * q^61 - 1904142 * q^62 + 14570922 * q^64 - 10424661 * q^65 + 4674330 * q^67 - 9569619 * q^68 + 25203126 * q^71 - 8640105 * q^74 + 12934506 * q^76 - 19599336 * q^77 - 30688440 * q^79 - 29127963 * q^80 - 37359719 * q^82 - 22436313 * q^85 + 27045536 * q^88 - 2123160 * q^89 + 37205532 * q^91 + 47685588 * q^92 + 19138810 * q^94 + 43420386 * q^95 - 68556288 * q^97 - 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−12.7863	+	7.38219i	−1.13016	+	0.652499i	−0.943976	−	0.330015i	$-0.892946\pi$
$2$	−12.7863	+	7.38219i	−1.13016	+	0.652499i	−0.186186	+	0.982514i	$0.559613\pi$
$3$		0			0
$3$		0			0
$4$	44.9933	−	77.9308i	0.351510	−	0.608834i
$5$			248.787i			0.890088i	0.895509	+	0.445044i	$0.146812\pi$
$5$			248.787i			0.890088i	−0.895509	+	0.445044i	$0.853188\pi$
$6$		0			0
$7$	497.017	+	286.953i	0.547682	+	0.316204i	0.748187	−	0.663488i	$-0.230925\pi$
$7$	497.017	+	286.953i	0.547682	+	0.316204i	−0.200505	+	0.979693i	$0.564258\pi$
$8$		−	561.243i		−	0.387557i
$9$		0			0
$10$	−1836.59	−	3181.07i	−0.580782	−	1.00594i
$11$	−3411.39	+	1969.56i	−0.772781	+	0.446165i	−0.833866	−	0.551967i	$-0.813877\pi$
$11$	−3411.39	+	1969.56i	−0.772781	+	0.446165i	0.0610849	+	0.998133i	$0.480544\pi$
$12$		0			0
$13$	2867.43	+	7384.20i	0.361985	+	0.932184i
$13$	2867.43	+	7384.20i	0.361985	+	0.932184i
$14$	−8473.37			−0.825292
$15$		0			0
$16$	9902.35	+	17151.4i	0.604391	+	1.04684i
$17$	7791.62	−	13495.5i	0.384642	−	0.666220i	−0.607077	−	0.794643i	$-0.707658\pi$
$17$	7791.62	−	13495.5i	0.384642	−	0.666220i	0.991719	+	0.128423i	$0.0409915\pi$
$18$		0			0
$19$	−1742.44	−	1006.00i	−0.0582800	−	0.0336480i	0.470577	−	0.882359i	$-0.344046\pi$
$19$	−1742.44	−	1006.00i	−0.0582800	−	0.0336480i	−0.528857	+	0.848711i	$0.677379\pi$
$20$	19388.2	+	11193.8i	0.541916	+	0.312875i
$21$		0			0
$22$	29079.4	−	50367.0i	0.582245	−	1.00848i
$23$	33680.6	+	58336.5i	0.577208	+	0.999753i	0.995798	+	0.0915781i	$0.0291911\pi$
$23$	33680.6	+	58336.5i	0.577208	+	0.999753i	−0.418590	+	0.908175i	$0.637476\pi$
$24$		0			0
$25$	16229.9			0.207743
$26$	−91175.3	−	73248.9i	−1.01735	−	0.817324i
$27$		0			0
$28$	44724.9	−	25822.0i	0.385032	−	0.222298i
$29$	94582.0	+	163821.i	0.720138	+	1.24732i	0.960944	+	0.276742i	$0.0892547\pi$
$29$	94582.0	+	163821.i	0.720138	+	1.24732i	−0.240807	+	0.970573i	$0.577412\pi$
$30$		0			0
$31$			281068.i			1.69452i	0.531181	+	0.847258i	$0.321748\pi$
$31$			281068.i			1.69452i	−0.531181	+	0.847258i	$0.678252\pi$
$32$	−191015.	−	110282.i	−1.03049	−	0.594951i
$33$		0			0
$34$			230077.i			1.00391i
$35$	−71390.3	+	123652.i	−0.281450	+	0.487485i
$36$		0			0
$37$	228285.	−	131800.i	0.740920	−	0.427770i	−0.0814838	−	0.996675i	$-0.525966\pi$
$37$	228285.	−	131800.i	0.740920	−	0.427770i	0.822404	+	0.568904i	$0.192633\pi$
$38$	29705.8			0.0878212
$39$		0			0
$40$	139630.			0.344960
$41$	125678.	−	72560.2i	0.284784	−	0.164420i	−0.350803	−	0.936449i	$-0.614091\pi$
$41$	125678.	−	72560.2i	0.284784	−	0.164420i	0.635587	+	0.772029i	$0.280758\pi$
$42$		0			0
$43$	−371259.	+	643040.i	−0.712095	+	1.23338i	0.251975	+	0.967734i	$0.418920\pi$
$43$	−371259.	+	643040.i	−0.712095	+	1.23338i	−0.964069	+	0.265650i	$0.914413\pi$
$44$			354469.i			0.627327i
$45$		0			0
$46$	−861302.	−	497273.i	−1.30468	−	0.753255i
$47$		−	1.08055e6i		−	1.51811i	−0.651024	−	0.759057i	$-0.725660\pi$
$47$		−	1.08055e6i		−	1.51811i	0.651024	−	0.759057i	$-0.274340\pi$
$48$		0			0
$49$	−247087.	−	427968.i	−0.300030	−	0.519667i
$50$	−207521.	+	119812.i	−0.234784	+	0.135552i
$51$		0			0
$52$	704471.	+	108779.i	0.694787	+	0.107284i
$53$	−1.63799e6			−1.51128			−0.755642	−	0.654985i	$-0.772675\pi$
$53$	−1.63799e6			−1.51128			−0.755642	+	0.654985i	$0.772675\pi$
$54$		0			0
$55$	−490002.	−	848709.i	−0.397126	−	0.687843i
$56$	161050.	−	278947.i	0.122547	−	0.212258i
$57$		0			0
$58$	−2.41871e6	−	1.39644e6i	−1.62774	−	0.939779i
$59$	−778187.	−	449287.i	−0.493290	−	0.284801i	0.232649	−	0.972561i	$-0.425261\pi$
$59$	−778187.	−	449287.i	−0.493290	−	0.284801i	−0.725938	+	0.687760i	$0.758594\pi$
$60$		0			0
$61$	−254459.	+	440737.i	−0.143537	+	0.248614i	−0.928826	−	0.370516i	$-0.879181\pi$
$61$	−254459.	+	440737.i	−0.143537	+	0.248614i	0.785289	+	0.619129i	$0.212514\pi$
$62$	−2.07490e6	−	3.59383e6i	−1.10567	−	1.91508i
$63$		0			0
$64$	721500.			0.344038
$65$	−1.83709e6	+	713379.i	−0.829726	+	0.322198i
$66$		0			0
$67$	315772.	−	182311.i	0.128266	−	0.0740544i	−0.434494	−	0.900675i	$-0.643073\pi$
$67$	315772.	−	182311.i	0.128266	−	0.0740544i	0.562760	+	0.826620i	$0.309739\pi$
$68$	−701142.	−	1.21441e6i	−0.270411	−	0.468366i
$69$		0			0
$70$		−	2.10806e6i		−	0.734583i
$71$	2.46548e6	+	1.42345e6i	0.817518	+	0.471994i	0.849560	−	0.527492i	$-0.176868\pi$
$71$	2.46548e6	+	1.42345e6i	0.817518	+	0.471994i	−0.0320418	+	0.999487i	$0.510201\pi$
$72$		0			0
$73$		−	4.44132e6i		−	1.33623i	−0.744057	−	0.668116i	$-0.767101\pi$
$73$		−	4.44132e6i		−	1.33623i	0.744057	−	0.668116i	$-0.232899\pi$
$74$	−1.94595e6	+	3.37048e6i	−0.558240	+	0.966899i
$75$		0			0
$76$	−156796.	+	90526.4i	−0.0409721	+	0.0236552i
$77$	−2.26069e6			−0.564318
$78$		0			0
$79$	−6.66251e6			−1.52035			−0.760174	−	0.649720i	$-0.774886\pi$
$79$	−6.66251e6			−1.52035			−0.760174	+	0.649720i	$0.774886\pi$
$80$	−4.26704e6	+	2.46358e6i	−0.931776	+	0.537961i
$81$		0			0
$82$	−1.07131e6	+	1.85556e6i	−0.214568	+	0.371643i
$83$			4.05229e6i			0.777906i	0.921258	+	0.388953i	$0.127163\pi$
$83$			4.05229e6i			0.777906i	−0.921258	+	0.388953i	$0.872837\pi$
$84$		0			0
$85$	3.35750e6	+	1.93846e6i	0.592994	+	0.342365i
$86$		−	1.09628e7i		−	1.85856i
$87$		0			0
$88$	1.10540e6	+	1.91462e6i	0.172915	+	0.299497i
$89$	1.01547e6	−	586279.i	0.152686	−	0.0881535i	−0.421710	−	0.906731i	$-0.638570\pi$
$89$	1.01547e6	−	586279.i	0.152686	−	0.0881535i	0.574397	+	0.818577i	$0.305237\pi$
$90$		0			0
$91$	−693759.	+	4.49289e6i	−0.0965081	+	0.625002i
$92$	6.06161e6			0.811578
$93$		0			0
$94$	7.97686e6	+	1.38163e7i	0.990568	+	1.71571i
$95$	250279.	−	433496.i	0.0299497	−	0.0518744i
$96$		0			0
$97$	−1.12996e7	−	6.52384e6i	−1.25708	−	0.725776i	−0.284574	−	0.958654i	$-0.591852\pi$
$97$	−1.12996e7	−	6.52384e6i	−1.25708	−	0.725776i	−0.972506	+	0.232878i	$0.925186\pi$
$98$	6.31867e6	+	3.64809e6i	0.678164	+	0.391538i
$99$		0			0
$100$	730240.	−	1.26481e6i	0.0730240	−	0.126481i
$101$	−712550.	−	1.23417e6i	−0.0688162	−	0.119193i	0.829564	−	0.558411i	$-0.188589\pi$
$101$	−712550.	−	1.23417e6i	−0.0688162	−	0.119193i	−0.898380	+	0.439218i	$0.855256\pi$
$102$		0			0
$103$	3.43743e6			0.309959			0.154979	−	0.987918i	$-0.450469\pi$
$103$	3.43743e6			0.309959			0.154979	+	0.987918i	$0.450469\pi$
$104$	4.14433e6	−	1.60932e6i	0.361275	−	0.140290i
$105$		0			0
$106$	2.09439e7	−	1.20920e7i	1.70800	−	0.986112i
$107$	−4.55117e6	−	7.88286e6i	−0.359153	−	0.622072i	0.628666	−	0.777675i	$-0.283601\pi$
$107$	−4.55117e6	−	7.88286e6i	−0.359153	−	0.622072i	−0.987820	+	0.155604i	$0.950268\pi$
$108$		0			0
$109$		−	3.25125e6i		−	0.240468i	−0.992746	−	0.120234i	$-0.961635\pi$
$109$		−	3.25125e6i		−	0.240468i	0.992746	−	0.120234i	$-0.0383646\pi$
$110$	1.25307e7	+	7.23458e6i	0.897634	+	0.518249i
$111$		0			0
$112$			1.13660e7i			0.764445i
$113$	−1.18415e7	+	2.05100e7i	−0.772023	+	1.33718i	0.164429	+	0.986389i	$0.447422\pi$
$113$	−1.18415e7	+	2.05100e7i	−0.772023	+	1.33718i	−0.936452	+	0.350794i	$0.885912\pi$
$114$		0			0
$115$	−1.45134e7	+	8.37930e6i	−0.889868	+	0.513766i
$116$	1.70222e7			1.01254
$117$		0			0
$118$	1.32669e7			0.743329
$119$	7.74515e6	−	4.47166e6i	0.421323	−	0.243251i
$120$		0			0
$121$	−1.98522e6	+	3.43850e6i	−0.101873	+	0.176449i
$122$		−	7.51387e6i		−	0.374631i
$123$		0			0
$124$	2.19039e7	+	1.26462e7i	1.03168	+	0.595640i
$125$			2.34743e7i			1.07500i
$126$		0			0
$127$	9.29215e6	+	1.60945e7i	0.402535	+	0.697210i	0.994031	−	0.109097i	$-0.0347960\pi$
$127$	9.29215e6	+	1.60945e7i	0.402535	+	0.697210i	−0.591497	+	0.806308i	$0.701463\pi$
$128$	1.52246e7	−	8.78990e6i	0.641667	−	0.370467i
$129$		0			0
$130$	1.82234e7	−	2.26833e7i	0.727490	−	0.905532i
$131$	1.85251e7			0.719964			0.359982	−	0.932959i	$-0.382783\pi$
$131$	1.85251e7			0.719964			0.359982	+	0.932959i	$0.382783\pi$
$132$		0			0
$133$	−577348.	−	999996.i	−0.0212793	−	0.0368568i
$134$	−2.69171e6	+	4.66217e6i	−0.0966409	+	0.167387i
$135$		0			0
$136$	−7.57425e6	−	4.37299e6i	−0.258198	−	0.149071i
$137$	4.37505e6	+	2.52594e6i	0.145366	+	0.0839268i	0.570919	−	0.821007i	$-0.306587\pi$
$137$	4.37505e6	+	2.52594e6i	0.145366	+	0.0839268i	−0.425553	+	0.904933i	$0.639920\pi$
$138$		0			0
$139$	−7.79200e6	+	1.34961e7i	−0.246092	+	0.426244i	−0.962438	−	0.271501i	$-0.912480\pi$
$139$	−7.79200e6	+	1.34961e7i	−0.246092	+	0.426244i	0.716346	+	0.697745i	$0.245813\pi$
$140$	6.42417e6	+	1.11270e7i	0.197865	+	0.342712i
$141$		0			0
$142$	−4.20326e7			−1.23190
$143$	−2.43255e7	−	1.95428e7i	−0.695643	−	0.558869i
$144$		0			0
$145$	−4.07565e7	+	2.35308e7i	−1.11022	+	0.640986i
$146$	3.27866e7	+	5.67881e7i	0.871890	+	1.51016i
$147$		0			0
$148$		−	2.37206e7i		−	0.601463i
$149$	−3.21304e7	−	1.85505e7i	−0.795727	−	0.459413i	0.0462480	−	0.998930i	$-0.485274\pi$
$149$	−3.21304e7	−	1.85505e7i	−0.795727	−	0.459413i	−0.841975	+	0.539517i	$0.818607\pi$
$150$		0			0
$151$		−	4.72742e7i		−	1.11739i	−0.829373	−	0.558695i	$-0.811302\pi$
$151$		−	4.72742e7i		−	1.11739i	0.829373	−	0.558695i	$-0.188698\pi$
$152$	−564609.	+	977931.i	−0.0130405	+	0.0225869i
$153$		0			0
$154$	2.89059e7	−	1.66888e7i	0.637770	−	0.368217i
$155$	−6.99262e7			−1.50827
$156$		0			0
$157$	6.68124e7			1.37787			0.688935	−	0.724823i	$-0.258078\pi$
$157$	6.68124e7			1.37787			0.688935	+	0.724823i	$0.258078\pi$
$158$	8.51889e7	−	4.91839e7i	1.71824	−	0.992025i
$159$		0			0
$160$	2.74368e7	−	4.75220e7i	0.529559	−	0.917223i
$161$			3.86590e7i			0.730063i
$162$		0			0
$163$	−4.15217e7	−	2.39725e7i	−0.750962	−	0.433568i	0.0750793	−	0.997178i	$-0.476079\pi$
$163$	−4.15217e7	−	2.39725e7i	−0.750962	−	0.433568i	−0.826041	+	0.563609i	$0.809412\pi$
$164$		−	1.30589e7i		−	0.231181i
$165$		0			0
$166$	−2.99148e7	−	5.18139e7i	−0.507583	−	0.879160i
$167$	4.11000e7	−	2.37291e7i	0.682864	−	0.394252i	−0.118069	−	0.993005i	$-0.537670\pi$
$167$	4.11000e7	−	2.37291e7i	0.682864	−	0.394252i	0.800933	+	0.598753i	$0.204337\pi$
$168$		0			0
$169$	−4.63043e7	+	4.23473e7i	−0.737934	+	0.674873i
$170$	−5.72402e7			−0.893572
$171$		0			0
$172$	3.34084e7	+	5.78650e7i	0.500617	+	0.867095i
$173$	5.19255e7	−	8.99376e7i	0.762464	−	1.32063i	−0.179113	−	0.983828i	$-0.557323\pi$
$173$	5.19255e7	−	8.99376e7i	0.762464	−	1.32063i	0.941577	−	0.336798i	$-0.109344\pi$
$174$		0			0
$175$	8.06657e6	+	4.65723e6i	0.113777	+	0.0656893i
$176$	−6.75614e7	−	3.90066e7i	−0.934124	−	0.539317i
$177$		0			0
$178$	−8.65604e6	+	1.49927e7i	−0.115040	+	0.199255i
$179$	1.01888e7	+	1.76475e7i	0.132782	+	0.229984i	0.924748	−	0.380581i	$-0.124276\pi$
$179$	1.01888e7	+	1.76475e7i	0.132782	+	0.229984i	−0.791966	+	0.610565i	$0.790942\pi$
$180$		0			0
$181$	−5.61052e7			−0.703280			−0.351640	−	0.936135i	$-0.614376\pi$
$181$	−5.61052e7			−0.703280			−0.351640	+	0.936135i	$0.614376\pi$
$182$	−2.42967e7	−	6.25690e7i	−0.298743	−	0.769324i
$183$		0			0
$184$	3.27409e7	−	1.89030e7i	0.387462	−	0.223701i
$185$	3.27902e7	+	5.67944e7i	0.380753	+	0.659484i
$186$		0			0
$187$			6.13844e7i			0.686456i
$188$	−8.42085e7	−	4.86178e7i	−0.924279	−	0.533633i
$189$		0			0
$190$			7.39043e6i			0.0781686i
$191$	−4.54840e7	+	7.87807e7i	−0.472326	+	0.818093i	−0.999499	−	0.0316651i	$-0.989919\pi$
$191$	−4.54840e7	+	7.87807e7i	−0.472326	+	0.818093i	0.527172	+	0.849759i	$0.323252\pi$
$192$		0			0
$193$	−5.70124e7	+	3.29162e7i	−0.570846	+	0.329578i	−0.757487	−	0.652850i	$-0.773573\pi$
$193$	−5.70124e7	+	3.29162e7i	−0.570846	+	0.329578i	0.186641	+	0.982428i	$0.440240\pi$
$194$	1.92641e8			1.89427
$195$		0			0
$196$	−4.44691e7			−0.421854
$197$	−1.26253e8	+	7.28923e7i	−1.17655	+	0.679281i	−0.955214	−	0.295916i	$-0.904375\pi$
$197$	−1.26253e8	+	7.28923e7i	−1.17655	+	0.679281i	−0.221336	+	0.975198i	$0.571042\pi$
$198$		0			0
$199$	4.88672e7	−	8.46405e7i	0.439574	−	0.761364i	−0.558083	−	0.829785i	$-0.688463\pi$
$199$	4.88672e7	−	8.46405e7i	0.439574	−	0.761364i	0.997657	+	0.0684210i	$0.0217961\pi$
$200$		−	9.10894e6i		−	0.0805124i
$201$		0			0
$202$	1.82218e7	+	1.05204e7i	0.155547	+	0.0898050i
$203$			1.08562e8i			0.910843i
$204$		0			0
$205$	1.80520e7	+	3.12670e7i	0.146348	+	0.253483i
$206$	−4.39521e7	+	2.53758e7i	−0.350304	+	0.202248i
$207$		0			0
$208$	−9.82549e7	+	1.22301e8i	−0.757064	+	0.942343i
$209$	7.92551e6			0.0600503
$210$		0			0
$211$	6.34096e7	+	1.09829e8i	0.464693	+	0.804872i	0.999188	−	0.0402998i	$-0.0128313\pi$
$211$	6.34096e7	+	1.09829e8i	0.464693	+	0.804872i	−0.534494	+	0.845172i	$0.679498\pi$
$212$	−7.36987e7	+	1.27650e8i	−0.531232	+	0.920121i
$213$		0			0
$214$	1.16385e8	+	6.71951e7i	0.811802	+	0.468694i
$215$	−1.59980e8	−	9.23645e7i	−1.09782	−	0.633827i
$216$		0			0
$217$	−8.06534e7	+	1.39696e8i	−0.535813	+	0.928056i
$218$	2.40014e7	+	4.15716e7i	0.156905	+	0.271768i
$219$		0			0
$220$	−8.81874e7			−0.558376
$221$	1.21995e8	+	1.88376e7i	0.760274	+	0.117396i
$222$		0			0
$223$	1.54510e8	−	8.92066e7i	0.933019	−	0.538679i	0.0452542	−	0.998976i	$-0.485590\pi$
$223$	1.54510e8	−	8.92066e7i	0.933019	−	0.538679i	0.887765	+	0.460296i	$0.152257\pi$
$224$	−6.32918e7	−	1.09625e8i	−0.376252	−	0.651688i
$225$		0			0
$226$		−	3.49663e8i		−	2.01498i
$227$	−9.00440e7	−	5.19869e7i	−0.510934	−	0.294988i	0.222284	−	0.974982i	$-0.428649\pi$
$227$	−9.00440e7	−	5.19869e7i	−0.510934	−	0.294988i	−0.733217	+	0.679994i	$0.761982\pi$
$228$		0			0
$229$		−	4.93769e7i		−	0.271706i	−0.990729	−	0.135853i	$-0.956622\pi$
$229$		−	4.93769e7i		−	0.271706i	0.990729	−	0.135853i	$-0.0433776\pi$
$230$	1.23715e8	−	2.14281e8i	0.670464	−	1.16128i
$231$		0			0
$232$	9.19433e7	−	5.30835e7i	0.483406	−	0.279095i
$233$	−2.49971e8			−1.29462			−0.647312	−	0.762225i	$-0.724107\pi$
$233$	−2.49971e8			−1.29462			−0.647312	+	0.762225i	$0.724107\pi$
$234$		0			0
$235$	2.68828e8			1.35126
$236$	−7.00265e7	+	4.04298e7i	−0.346793	+	0.200221i
$237$		0			0
$238$	−6.60213e7	+	1.14352e8i	−0.317442	+	0.549826i
$239$		−	3.95989e7i		−	0.187625i	−0.995590	−	0.0938124i	$-0.970095\pi$
$239$		−	3.95989e7i		−	0.187625i	0.995590	−	0.0938124i	$-0.0299054\pi$
$240$		0			0
$241$	−1.70708e8	−	9.85581e7i	−0.785585	−	0.453558i	0.0528210	−	0.998604i	$-0.483179\pi$
$241$	−1.70708e8	−	9.85581e7i	−0.785585	−	0.453558i	−0.838406	+	0.545046i	$0.816512\pi$
$242$		−	5.86210e7i		−	0.265889i
$243$		0			0
$244$	2.28980e7	+	3.96604e7i	0.100910	+	0.174781i
$245$	1.06473e8	−	6.14721e7i	0.462549	−	0.267053i
$246$		0			0
$247$	2.43217e6	−	1.57511e7i	0.0102696	−	0.0665078i
$248$	1.57747e8			0.656722
$249$		0			0
$250$	−1.73292e8	−	3.00150e8i	−0.701435	−	1.21492i
$251$	−1.40289e7	+	2.42988e7i	−0.0559972	+	0.0969900i	−0.892665	−	0.450720i	$-0.851167\pi$
$251$	−1.40289e7	+	2.42988e7i	−0.0559972	+	0.0969900i	0.836668	+	0.547710i	$0.184500\pi$
$252$		0			0
$253$	−2.29795e8	−	1.32672e8i	−0.892110	−	0.515060i
$254$	−2.37625e8	−	1.37193e8i	−0.909858	−	0.525307i
$255$		0			0
$256$	−1.75953e8	+	3.04760e8i	−0.655477	+	1.13532i
$257$	−5.58401e7	−	9.67178e7i	−0.205201	−	0.355419i	0.744996	−	0.667069i	$-0.232452\pi$
$257$	−5.58401e7	−	9.67178e7i	−0.205201	−	0.355419i	−0.950197	+	0.311650i	$0.899118\pi$
$258$		0			0
$259$	1.51282e8			0.541051
$260$	−2.70629e7	+	1.75263e8i	−0.0954920	+	0.618421i
$261$		0			0
$262$	−2.36868e8	+	1.36756e8i	−0.813676	+	0.469776i
$263$	1.61308e8	+	2.79393e8i	0.546776	+	0.947044i	0.998493	+	0.0548828i	$0.0174785\pi$
$263$	1.61308e8	+	2.79393e8i	0.546776	+	0.947044i	−0.451717	+	0.892162i	$0.649188\pi$
$264$		0			0
$265$		−	4.07511e8i		−	1.34518i
$266$	1.47643e7	+	8.52418e6i	0.0480981	+	0.0277694i
$267$		0			0
$268$		−	3.28111e7i		−	0.104124i
$269$	−2.11106e8	+	3.65647e8i	−0.661254	+	1.14532i	0.319033	+	0.947744i	$0.396642\pi$
$269$	−2.11106e8	+	3.65647e8i	−0.661254	+	1.14532i	−0.980287	+	0.197581i	$0.936691\pi$
$270$		0			0
$271$	−1.37631e8	+	7.94615e7i	−0.420073	+	0.242529i	−0.695108	−	0.718905i	$-0.744644\pi$
$271$	−1.37631e8	+	7.94615e7i	−0.420073	+	0.242529i	0.275036	+	0.961434i	$0.411310\pi$
$272$	3.08621e8			0.929897
$273$		0			0
$274$	−7.45878e7			−0.219049
$275$	−5.53666e7	+	3.19659e7i	−0.160540	+	0.0926879i
$276$		0			0
$277$	−1.43949e8	+	2.49327e8i	−0.406940	+	0.704840i	−0.994545	−	0.104307i	$-0.966737\pi$
$277$	−1.43949e8	+	2.49327e8i	−0.406940	+	0.704840i	0.587605	+	0.809148i	$0.300071\pi$
$278$		−	2.30088e8i		−	0.642299i
$279$		0			0
$280$	6.93985e7	+	4.00673e7i	0.188928	+	0.109078i
$281$		−	6.26146e8i		−	1.68346i	−0.539897	−	0.841731i	$-0.681537\pi$
$281$		−	6.26146e8i		−	1.68346i	0.539897	−	0.841731i	$-0.318463\pi$
$282$		0			0
$283$	2.36259e7	+	4.09212e7i	0.0619634	+	0.107324i	0.895343	−	0.445377i	$-0.146930\pi$
$283$	2.36259e7	+	4.09212e7i	0.0619634	+	0.107324i	−0.833380	+	0.552701i	$0.813597\pi$
$284$	2.21860e8	−	1.28091e8i	0.574732	−	0.331822i
$285$		0			0
$286$	4.55303e8	+	7.03044e7i	1.15085	+	0.177706i
$287$	8.32855e7			0.207961
$288$		0			0
$289$	8.37505e7	+	1.45060e8i	0.204101	+	0.353513i
$290$	3.47417e8	−	6.01745e8i	0.836486	−	1.44884i
$291$		0			0
$292$	−3.46115e8	−	1.99830e8i	−0.813543	−	0.469700i
$293$	6.60540e8	+	3.81363e8i	1.53413	+	0.885730i	0.999165	+	0.0408560i	$0.0130085\pi$
$293$	6.60540e8	+	3.81363e8i	1.53413	+	0.885730i	0.534965	+	0.844874i	$0.320325\pi$
$294$		0			0
$295$	1.11777e8	−	1.93603e8i	0.253498	−	0.439071i
$296$	−7.39720e7	−	1.28123e8i	−0.165785	−	0.287149i
$297$		0			0
$298$	5.47772e8			1.19907
$299$	−3.34192e8	+	4.15980e8i	−0.723014	+	0.899959i
$300$		0			0
$301$	−3.69045e8	+	2.13068e8i	−0.780003	+	0.450335i
$302$	3.48987e8	+	6.04463e8i	0.729096	+	1.26283i
$303$		0			0
$304$		−	3.98469e7i		−	0.0813462i
$305$	−1.09650e8	−	6.33063e7i	−0.221288	−	0.127761i
$306$		0			0
$307$			4.52948e8i			0.893436i	0.894675	+	0.446718i	$0.147407\pi$
$307$			4.52948e8i			0.893436i	−0.894675	+	0.446718i	$0.852593\pi$
$308$	−1.01716e8	+	1.76177e8i	−0.198364	+	0.343576i
$309$		0			0
$310$	8.94098e8	−	5.16208e8i	1.70459	−	0.984144i
$311$	4.98788e8			0.940274			0.470137	−	0.882594i	$-0.344205\pi$
$311$	4.98788e8			0.940274			0.470137	+	0.882594i	$0.344205\pi$
$312$		0			0
$313$	9.49928e8			1.75100			0.875498	−	0.483221i	$-0.160533\pi$
$313$	9.49928e8			1.75100			0.875498	+	0.483221i	$0.160533\pi$
$314$	−8.54285e8	+	4.93222e8i	−1.55722	+	0.899059i
$315$		0			0
$316$	−2.99768e8	+	5.19214e8i	−0.534418	+	0.925639i
$317$			8.74259e8i			1.54146i	0.637161	+	0.770731i	$0.280109\pi$
$317$			8.74259e8i			1.54146i	−0.637161	+	0.770731i	$0.719891\pi$
$318$		0			0
$319$	−6.45311e8	−	3.72571e8i	−1.11302	−	0.642601i
$320$			1.79500e8i			0.306224i
$321$		0			0
$322$	−2.85388e8	−	4.94306e8i	−0.476365	−	0.825089i
$323$	−2.71529e7	+	1.56767e7i	−0.0448339	+	0.0258849i
$324$		0			0
$325$	4.65382e7	+	1.19845e8i	0.0751999	+	0.193655i
$326$	7.07879e8			1.13161
$327$		0			0
$328$	−4.07239e7	−	7.05358e7i	−0.0637222	−	0.110370i
$329$	3.10069e8	−	5.37055e8i	0.480034	−	0.831444i
$330$		0			0
$331$	7.98662e8	+	4.61108e8i	1.21050	+	0.698883i	0.962868	−	0.269971i	$-0.0870142\pi$
$331$	7.98662e8	+	4.61108e8i	1.21050	+	0.698883i	0.247632	+	0.968854i	$0.420348\pi$
$332$	3.15798e8	+	1.82326e8i	0.473616	+	0.273442i
$333$		0			0
$334$	−3.50345e8	+	6.06816e8i	−0.514498	+	0.891137i
$335$	4.53566e7	+	7.85600e7i	0.0659150	+	0.114168i
$336$		0			0
$337$	1.85249e8			0.263664			0.131832	−	0.991272i	$-0.457914\pi$
$337$	1.85249e8			0.263664			0.131832	+	0.991272i	$0.457914\pi$
$338$	2.79446e8	−	8.83293e8i	0.393631	−	1.24422i
$339$		0			0
$340$	3.02131e8	−	1.74435e8i	0.416887	−	0.240690i
$341$	−5.53582e8	−	9.58832e8i	−0.756034	−	1.30949i
$342$		0			0
$343$		−	7.56246e8i		−	1.01189i
$344$	3.60902e8	+	2.08367e8i	0.478007	+	0.275977i
$345$		0			0
$346$			1.53329e9i			1.99003i
$347$	7.10332e7	−	1.23033e8i	0.0912658	−	0.158077i	−0.816778	−	0.576952i	$-0.804242\pi$
$347$	7.10332e7	−	1.23033e8i	0.0912658	−	0.158077i	0.908044	+	0.418875i	$0.137575\pi$
$348$		0			0
$349$	4.07258e8	−	2.35130e8i	0.512838	−	0.296087i	−0.221161	−	0.975237i	$-0.570985\pi$
$349$	4.07258e8	−	2.35130e8i	0.512838	−	0.296087i	0.734000	+	0.679150i	$0.237651\pi$
$350$	−1.37522e8			−0.171449
$351$		0			0
$352$	8.68833e8			1.06179
$353$	−3.93517e8	+	2.27197e8i	−0.476159	+	0.274911i	−0.718814	−	0.695202i	$-0.755315\pi$
$353$	−3.93517e8	+	2.27197e8i	−0.476159	+	0.274911i	0.242655	+	0.970113i	$0.421982\pi$
$354$		0			0
$355$	−3.54135e8	+	6.13380e8i	−0.420116	+	0.727663i
$356$		−	1.05515e8i		−	0.123947i
$357$		0			0
$358$	−2.60555e8	−	1.50431e8i	−0.300129	−	0.173280i
$359$			1.21160e9i			1.38207i	0.722821	+	0.691035i	$0.242845\pi$
$359$			1.21160e9i			1.38207i	−0.722821	+	0.691035i	$0.757155\pi$
$360$		0			0
$361$	−4.44912e8	−	7.70610e8i	−0.497736	−	0.862103i
$362$	7.17379e8	−	4.14179e8i	0.794820	−	0.458890i
$363$		0			0
$364$	3.18920e8	+	2.56215e8i	0.346599	+	0.278452i
$365$	1.10494e9			1.18936
$366$		0			0
$367$	6.89733e8	+	1.19465e9i	0.728366	+	1.26157i	0.957574	+	0.288189i	$0.0930531\pi$
$367$	6.89733e8	+	1.19465e9i	0.728366	+	1.26157i	−0.229208	+	0.973377i	$0.573614\pi$
$368$	−6.67034e8	+	1.15534e9i	−0.697719	+	1.20848i
$369$		0			0
$370$	−8.38533e8	−	4.84127e8i	−0.860626	−	0.496882i
$371$	−8.14110e8	−	4.70027e8i	−0.827703	−	0.477875i
$372$		0			0
$373$	−7.04597e7	+	1.22040e8i	−0.0703007	+	0.121764i	−0.899033	−	0.437881i	$-0.855729\pi$
$373$	−7.04597e7	+	1.22040e8i	−0.0703007	+	0.121764i	0.828732	+	0.559645i	$0.189063\pi$
$374$	−4.53151e8	−	7.84881e8i	−0.447912	−	0.775806i
$375$		0			0
$376$	−6.06454e8			−0.588356
$377$	−9.38479e8	+	1.16816e9i	−0.902048	+	1.12281i
$378$		0			0
$379$	−1.25855e9	+	7.26626e8i	−1.18750	+	0.685604i	−0.957738	−	0.287642i	$-0.907129\pi$
$379$	−1.25855e9	+	7.26626e8i	−1.18750	+	0.685604i	−0.229763	+	0.973247i	$0.573795\pi$
$380$	−2.25218e7	−	3.90089e7i	−0.0210553	−	0.0364688i
$381$		0			0
$382$		−	1.34309e9i		−	1.23277i
$383$	−8.94535e8	−	5.16460e8i	−0.813583	−	0.469722i	0.0346157	−	0.999401i	$-0.488979\pi$
$383$	−8.94535e8	−	5.16460e8i	−0.813583	−	0.469722i	−0.848199	+	0.529678i	$0.822313\pi$
$384$		0			0
$385$		−	5.62431e8i		−	0.502292i
$386$	4.85986e8	−	8.41753e8i	0.430099	−	0.744953i
$387$		0			0
$388$	−1.01682e9	+	5.87059e8i	−0.883754	+	0.510235i
$389$	3.93410e8			0.338861			0.169431	−	0.985542i	$-0.445807\pi$
$389$	3.93410e8			0.338861			0.169431	+	0.985542i	$0.445807\pi$
$390$		0			0
$391$	1.04971e9			0.888074
$392$	−2.40194e8	+	1.38676e8i	−0.201401	+	0.116279i
$393$		0			0
$394$	1.07621e9	−	1.86405e9i	0.886461	−	1.53540i
$395$		−	1.65755e9i		−	1.35324i
$396$		0			0
$397$	9.23207e8	+	5.33014e8i	0.740512	+	0.427535i	0.822255	−	0.569119i	$-0.192715\pi$
$397$	9.23207e8	+	5.33014e8i	0.740512	+	0.427535i	−0.0817434	+	0.996653i	$0.526049\pi$
$398$			1.44299e9i			1.14729i
$399$		0			0
$400$	1.60715e8	+	2.78366e8i	0.125558	+	0.217473i
$401$	−6.63509e8	+	3.83077e8i	−0.513856	+	0.296675i	−0.734417	−	0.678698i	$-0.762545\pi$
$401$	−6.63509e8	+	3.83077e8i	−0.513856	+	0.296675i	0.220561	+	0.975373i	$0.429211\pi$
$402$		0			0
$403$	−2.07546e9	+	8.05942e8i	−1.57960	+	0.613389i
$404$	−1.28240e8			−0.0967584
$405$		0			0
$406$	−8.01428e8	−	1.38811e9i	−0.594324	−	1.02940i
$407$	−5.19179e8	+	8.99244e8i	−0.381712	+	0.661145i
$408$		0			0
$409$	−1.94247e9	−	1.12148e9i	−1.40386	−	0.810516i	−0.409069	−	0.912503i	$-0.634147\pi$
$409$	−1.94247e9	−	1.12148e9i	−1.40386	−	0.810516i	−0.994786	+	0.101987i	$0.967480\pi$
$410$	−4.61638e8	−	2.66527e8i	−0.330795	−	0.190984i
$411$		0			0
$412$	1.54662e8	−	2.67882e8i	0.108954	−	0.188714i
$413$	−2.57848e8	−	4.46606e8i	−0.180111	−	0.311961i
$414$		0			0
$415$	−1.00816e9			−0.692405
$416$	2.66627e8	−	1.72672e9i	0.181584	−	1.17597i
$417$		0			0
$418$	−1.01338e8	+	5.85076e7i	−0.0678665	+	0.0391828i
$419$	−7.01906e8	−	1.21574e9i	−0.466154	−	0.807403i	0.533098	−	0.846053i	$-0.321028\pi$
$419$	−7.01906e8	−	1.21574e9i	−0.466154	−	0.807403i	−0.999253	+	0.0386502i	$0.987694\pi$
$420$		0			0
$421$		−	1.81487e9i		−	1.18538i	−0.805429	−	0.592692i	$-0.798065\pi$
$421$		−	1.81487e9i		−	1.18538i	0.805429	−	0.592692i	$-0.201935\pi$
$422$	−1.62155e9	−	9.36203e8i	−1.05036	−	0.606424i
$423$		0			0
$424$			9.19311e8i			0.585709i
$425$	1.26458e8	−	2.19031e8i	0.0799068	−	0.138403i
$426$		0			0
$427$	−2.52942e8	+	1.46036e8i	−0.157225	+	0.0907741i
$428$	−8.19089e8			−0.504984
$429$		0			0
$430$	2.72741e9			1.65429
$431$	1.54287e9	−	8.90776e8i	0.928237	−	0.535918i	0.0419833	−	0.999118i	$-0.486632\pi$
$431$	1.54287e9	−	8.90776e8i	0.928237	−	0.535918i	0.886254	+	0.463201i	$0.153299\pi$
$432$		0			0
$433$	−7.17382e8	+	1.24254e9i	−0.424662	+	0.735536i	−0.996389	−	0.0849082i	$-0.972940\pi$
$433$	−7.17382e8	+	1.24254e9i	−0.424662	+	0.735536i	0.571727	+	0.820444i	$0.306274\pi$
$434$		−	2.38159e9i		−	1.39847i
$435$		0			0
$436$	−2.53373e8	−	1.46285e8i	−0.146405	−	0.0845272i
$437$		−	1.35530e8i		−	0.0776876i
$438$		0			0
$439$	−1.57839e9	−	2.73385e9i	−0.890406	−	1.54223i	−0.839389	−	0.543530i	$-0.817087\pi$
$439$	−1.57839e9	−	2.73385e9i	−0.890406	−	1.54223i	−0.0510165	−	0.998698i	$-0.516246\pi$
$440$	−4.76332e8	+	2.75010e8i	−0.266579	+	0.153909i
$441$		0			0
$442$	−1.69893e9	+	6.59728e8i	−0.935833	+	0.363402i
$443$	−8.24759e8			−0.450727			−0.225364	−	0.974275i	$-0.572357\pi$
$443$	−8.24759e8			−0.450727			−0.225364	+	0.974275i	$0.572357\pi$
$444$		0			0
$445$	1.45859e8	+	2.52635e8i	0.0784643	+	0.135904i
$446$	−1.31708e9	+	2.28125e9i	−0.702975	+	1.21759i
$447$		0			0
$448$	3.58598e8	+	2.07037e8i	0.188423	+	0.108786i
$449$	1.94207e9	+	1.12126e9i	1.01252	+	0.584578i	0.911928	−	0.410350i	$-0.134593\pi$
$449$	1.94207e9	+	1.12126e9i	1.01252	+	0.584578i	0.100591	+	0.994928i	$0.467927\pi$
$450$		0			0
$451$	−2.85824e8	+	4.95061e8i	−0.146717	+	0.254121i
$452$	1.06557e9	+	1.84563e9i	0.542748	+	0.940068i
$453$		0			0
$454$	1.53511e9			0.769917
$455$	−1.11777e9	−	1.72598e8i	−0.556306	−	0.0859007i
$456$		0			0
$457$	−9.49936e8	+	5.48446e8i	−0.465573	+	0.268799i	−0.714385	−	0.699753i	$-0.753293\pi$
$457$	−9.49936e8	+	5.48446e8i	−0.465573	+	0.268799i	0.248812	+	0.968552i	$0.419960\pi$
$458$	3.64510e8	+	6.31349e8i	0.177288	+	0.307072i
$459$		0			0
$460$			1.50805e9i			0.722376i
$461$	−1.37164e9	−	7.91917e8i	−0.652059	−	0.376467i	0.137186	−	0.990545i	$-0.456194\pi$
$461$	−1.37164e9	−	7.91917e8i	−0.652059	−	0.376467i	−0.789245	+	0.614079i	$0.789528\pi$
$462$		0			0
$463$		−	2.25948e9i		−	1.05798i	−0.848629	−	0.528988i	$-0.822572\pi$
$463$		−	2.25948e9i		−	1.05798i	0.848629	−	0.528988i	$-0.177428\pi$
$464$	−1.87317e9	+	3.24442e9i	−0.870490	+	1.50773i
$465$		0			0
$466$	3.19621e9	−	1.84533e9i	1.46314	−	0.844742i
$467$	2.17106e9			0.986421			0.493211	−	0.869910i	$-0.335823\pi$
$467$	2.17106e9			0.986421			0.493211	+	0.869910i	$0.335823\pi$
$468$		0			0
$469$	2.09259e8			0.0936653
$470$	−3.43732e9	+	1.98454e9i	−1.52714	+	0.881693i
$471$		0			0
$472$	−2.52159e8	+	4.36752e8i	−0.110377	+	0.191178i
$473$		−	2.92488e9i		−	1.27085i
$474$		0			0
$475$	−2.82797e7	−	1.63273e7i	−0.0121073	−	0.00699015i
$476$		−	8.04780e8i		−	0.342021i
$477$		0			0
$478$	2.92326e8	+	5.06324e8i	0.122425	+	0.212046i
$479$	5.66356e8	−	3.26986e8i	0.235459	−	0.135942i	−0.377629	−	0.925957i	$-0.623261\pi$
$479$	5.66356e8	−	3.26986e8i	0.235459	−	0.135942i	0.613088	+	0.790015i	$0.289927\pi$
$480$		0			0
$481$	1.62783e9	+	1.30777e9i	0.666962	+	0.535827i
$482$	2.91030e9			1.18378
$483$		0			0
$484$	1.78643e8	+	3.09419e8i	0.0716190	+	0.124048i
$485$	1.62305e9	−	2.81120e9i	0.646004	−	1.11891i
$486$		0			0
$487$	2.35359e9	+	1.35885e9i	0.923377	+	0.533112i	0.884711	−	0.466140i	$-0.154356\pi$
$487$	2.35359e9	+	1.35885e9i	0.923377	+	0.533112i	0.0386663	+	0.999252i	$0.487689\pi$
$488$	2.47360e8	+	1.42814e8i	0.0963520	+	0.0556288i
$489$		0			0
$490$	−9.07598e8	+	1.57201e9i	−0.348503	+	0.603626i
$491$	−1.39241e8	−	2.41173e8i	−0.0530864	−	0.0919483i	0.838261	−	0.545269i	$-0.183573\pi$
$491$	−1.39241e8	−	2.41173e8i	−0.0530864	−	0.0919483i	−0.891347	+	0.453321i	$0.850239\pi$
$492$		0			0
$493$	2.94779e9			1.10798
$494$	8.51793e7	+	2.19354e8i	0.0317899	+	0.0818655i
$495$		0			0
$496$	−4.82070e9	+	2.78323e9i	−1.77388	+	1.02415i
$497$	8.16924e8	+	1.41495e9i	0.298493	+	0.517006i
$498$		0			0
$499$			1.57082e9i			0.565947i	0.959128	+	0.282973i	$0.0913208\pi$
$499$			1.57082e9i			0.565947i	−0.959128	+	0.282973i	$0.908679\pi$
$500$	1.82937e9	+	1.05619e9i	0.654495	+	0.377873i
$501$		0			0
$502$		−	4.14257e8i		−	0.146153i
$503$	−1.85784e9	+	3.21787e9i	−0.650909	+	1.12741i	0.331993	+	0.943282i	$0.392279\pi$
$503$	−1.85784e9	+	3.21787e9i	−0.650909	+	1.12741i	−0.982903	+	0.184126i	$0.941055\pi$
$504$		0			0
$505$	3.07046e8	−	1.77273e8i	0.106092	−	0.0612525i
$506$	3.91764e9			1.34431
$507$		0			0
$508$	1.67234e9			0.565980
$509$	−4.81978e8	+	2.78270e8i	−0.162000	+	0.0935308i	−0.578808	−	0.815464i	$-0.696482\pi$
$509$	−4.81978e8	+	2.78270e8i	−0.162000	+	0.0935308i	0.416808	+	0.908994i	$0.363149\pi$
$510$		0			0
$511$	1.27445e9	−	2.20741e9i	0.422522	−	0.731830i
$512$		−	2.94547e9i		−	0.969860i
$513$		0			0
$514$	1.42798e9	+	8.24443e8i	0.463821	+	0.267787i
$515$			8.55189e8i			0.275891i
$516$		0			0
$517$	2.12822e9	+	3.68619e9i	0.677330	+	1.17317i
$518$	−1.93434e9	+	1.11679e9i	−0.611476	+	0.353036i
$519$		0			0
$520$	4.00379e8	+	1.03106e9i	0.124870	+	0.321566i
$521$	1.65430e9			0.512486			0.256243	−	0.966612i	$-0.417515\pi$
$521$	1.65430e9			0.512486			0.256243	+	0.966612i	$0.417515\pi$
$522$		0			0
$523$	9.42609e8	+	1.63265e9i	0.288122	+	0.499041i	0.973361	−	0.229276i	$-0.0736359\pi$
$523$	9.42609e8	+	1.63265e9i	0.288122	+	0.499041i	−0.685240	+	0.728318i	$0.740303\pi$
$524$	8.33506e8	−	1.44367e9i	0.253075	−	0.438339i
$525$		0			0
$526$	−4.12506e9	−	2.38161e9i	−1.23589	−	0.713542i
$527$	3.79315e9	+	2.18998e9i	1.12892	+	0.651782i
$528$		0			0
$529$	−5.66351e8	+	9.80949e8i	−0.166338	+	0.288106i
$530$	3.00832e9	+	5.21057e9i	0.877726	+	1.52027i
$531$		0			0
$532$	−1.03907e8			−0.0299196
$533$	8.96171e8	+	7.19970e8i	0.256357	+	0.205953i
$534$		0			0
$535$	1.96115e9	−	1.13227e9i	0.553698	−	0.319678i
$536$	−1.02321e8	−	1.77225e8i	−0.0287003	−	0.0497104i
$537$		0			0
$538$		−	6.23370e9i		−	1.72587i
$539$	1.68582e9	+	9.73309e8i	0.463714	+	0.267726i
$540$		0			0
$541$			4.62326e7i			0.0125533i	0.999980	+	0.00627665i	$0.00199793\pi$
$541$			4.62326e7i			0.0125533i	−0.999980	+	0.00627665i	$0.998002\pi$
$542$	1.17320e9	−	2.03204e9i	0.316500	−	0.548194i
$543$		0			0
$544$	−2.97663e9	+	1.71856e9i	−0.792736	+	0.457686i
$545$	8.08870e8			0.214038
$546$		0			0
$547$	5.53529e9			1.44605			0.723027	−	0.690819i	$-0.242750\pi$
$547$	5.53529e9			1.44605			0.723027	+	0.690819i	$0.242750\pi$
$548$	3.93697e8	−	2.27301e8i	0.102195	−	0.0590023i
$549$		0			0
$550$	4.71957e8	−	8.17453e8i	0.120958	−	0.209505i
$551$		−	3.80597e8i		−	0.0969248i
$552$		0			0
$553$	−3.31138e9	−	1.91183e9i	−0.832667	−	0.480740i
$554$		−	4.25064e9i		−	1.06211i
$555$		0			0
$556$	7.01176e8	+	1.21447e9i	0.173008	+	0.299658i
$557$	4.15944e9	−	2.40146e9i	1.01986	−	0.588819i	0.105799	−	0.994387i	$-0.466260\pi$
$557$	4.15944e9	−	2.40146e9i	1.01986	−	0.588819i	0.914065	+	0.405569i	$0.132927\pi$
$558$		0			0
$559$	−5.81289e9	−	8.97583e8i	−1.40751	−	0.217337i
$560$	−2.82772e9			−0.680423
$561$		0			0
$562$	4.62232e9	+	8.00610e9i	1.09846	+	1.90258i
$563$	−2.91491e8	+	5.04878e8i	−0.0688409	+	0.119236i	−0.898391	−	0.439196i	$-0.855263\pi$
$563$	−2.91491e8	+	5.04878e8i	−0.0688409	+	0.119236i	0.829550	+	0.558432i	$0.188597\pi$
$564$		0			0
$565$	−5.10262e9	−	2.94600e9i	−1.19021	−	0.687169i
$566$	−6.04176e8	−	3.48821e8i	−0.140057	−	0.0808621i
$567$		0			0
$568$	7.98899e8	−	1.38373e9i	0.182925	−	0.316835i
$569$	−1.09595e9	−	1.89824e9i	−0.249401	−	0.431975i	0.713959	−	0.700188i	$-0.246900\pi$
$569$	−1.09595e9	−	1.89824e9i	−0.249401	−	0.431975i	−0.963360	+	0.268213i	$0.913567\pi$
$570$		0			0
$571$	3.96943e9			0.892281			0.446140	−	0.894963i	$-0.352798\pi$
$571$	3.96943e9			0.892281			0.446140	+	0.894963i	$0.352798\pi$
$572$	−2.61747e9	+	1.01641e9i	−0.584784	+	0.227083i
$573$		0			0
$574$	−1.06491e9	+	6.14829e8i	−0.235030	+	0.135695i
$575$	5.46634e8	+	9.46798e8i	0.119911	+	0.207692i
$576$		0			0
$577$		−	5.01942e9i		−	1.08777i	−0.839159	−	0.543886i	$-0.816952\pi$
$577$		−	5.01942e9i		−	1.08777i	0.839159	−	0.543886i	$-0.183048\pi$
$578$	−2.14172e9	−	1.23652e9i	−0.461334	−	0.266351i
$579$		0			0
$580$			4.23492e9i			0.901253i
$581$	−1.16282e9	+	2.01406e9i	−0.245977	+	0.426045i
$582$		0			0
$583$	5.58782e9	−	3.22613e9i	1.16789	−	0.674282i
$584$	−2.49266e9			−0.517866
$585$		0			0
$586$	−1.12612e10			−2.31175
$587$	−3.33458e9	+	1.92522e9i	−0.680468	+	0.392868i	−0.800031	−	0.599958i	$-0.795184\pi$
$587$	−3.33458e9	+	1.92522e9i	−0.680468	+	0.392868i	0.119563	+	0.992827i	$0.461851\pi$
$588$		0			0
$589$	2.82754e8	−	4.89744e8i	0.0570171	−	0.0987565i
$590$			3.30063e9i			0.661629i
$591$		0			0
$592$	4.52111e9	+	2.61027e9i	0.895611	+	0.517081i
$593$		−	3.30871e9i		−	0.651580i	−0.945442	−	0.325790i	$-0.894370\pi$
$593$		−	3.30871e9i		−	0.651580i	0.945442	−	0.325790i	$-0.105630\pi$
$594$		0			0
$595$	1.11249e9	+	1.92689e9i	0.216515	+	0.375015i
$596$	−2.89131e9	+	1.66930e9i	−0.559413	+	0.322977i
$597$		0			0
$598$	1.20224e9	−	7.78591e9i	0.229899	−	1.48887i
$599$	1.42968e9			0.271797			0.135899	−	0.990723i	$-0.456608\pi$
$599$	1.42968e9			0.271797			0.135899	+	0.990723i	$0.456608\pi$
$600$		0			0
$601$	−9.80155e8	−	1.69768e9i	−0.184176	−	0.319003i	0.759122	−	0.650948i	$-0.225628\pi$
$601$	−9.80155e8	−	1.69768e9i	−0.184176	−	0.319003i	−0.943299	+	0.331945i	$0.892295\pi$
$602$	3.14582e9	−	5.44871e9i	0.587686	−	1.01790i
$603$		0			0
$604$	−3.68411e9	−	2.12702e9i	−0.680305	−	0.392774i
$605$	−8.55455e8	−	4.93897e8i	−0.157056	−	0.0906761i
$606$		0			0
$607$	−2.47671e9	+	4.28978e9i	−0.449484	+	0.778529i	−0.998352	−	0.0573795i	$-0.981726\pi$
$607$	−2.47671e9	+	4.28978e9i	−0.449484	+	0.778529i	0.548868	+	0.835909i	$0.315059\pi$
$608$	2.21888e8	+	3.84321e8i	0.0400378	+	0.0693475i
$609$		0			0
$610$	1.86935e9			0.333455
$611$	7.97903e9	−	3.09841e9i	1.41516	−	0.549534i
$612$		0			0
$613$	5.81190e9	−	3.35550e9i	1.01908	−	0.588363i	0.105239	−	0.994447i	$-0.466439\pi$
$613$	5.81190e9	−	3.35550e9i	1.01908	−	0.588363i	0.913836	+	0.406084i	$0.133106\pi$
$614$	−3.34374e9	−	5.79153e9i	−0.582967	−	1.00973i
$615$		0			0
$616$			1.26880e9i			0.218705i
$617$	−2.06965e9	−	1.19491e9i	−0.354730	−	0.204804i	0.312036	−	0.950070i	$-0.398989\pi$
$617$	−2.06965e9	−	1.19491e9i	−0.354730	−	0.204804i	−0.666767	+	0.745267i	$0.732322\pi$
$618$		0			0
$619$		−	3.61543e9i		−	0.612693i	−0.951920	−	0.306346i	$-0.900893\pi$
$619$		−	3.61543e9i		−	0.612693i	0.951920	−	0.306346i	$-0.0991066\pi$
$620$	−3.14621e9	+	5.44940e9i	−0.530172	+	0.918285i
$621$		0			0
$622$	−6.37766e9	+	3.68214e9i	−1.06266	+	0.613528i
$623$	6.72938e8			0.111498
$624$		0			0
$625$	−4.57214e9			−0.749099
$626$	−1.21461e10	+	7.01254e9i	−1.97891	+	1.14252i
$627$		0			0
$628$	3.00611e9	−	5.20674e9i	0.484336	−	0.838894i
$629$		−	4.10776e9i		−	0.658154i
$630$		0			0
$631$	5.59855e7	+	3.23232e7i	0.00887100	+	0.00512167i	0.504429	−	0.863453i	$-0.331703\pi$
$631$	5.59855e7	+	3.23232e7i	0.00887100	+	0.00512167i	−0.495558	+	0.868575i	$0.665036\pi$
$632$			3.73928e9i			0.589221i
$633$		0			0
$634$	−6.45394e9	−	1.11786e10i	−1.00580	−	1.74210i
$635$	−4.00410e9	+	2.31177e9i	−0.620578	+	0.358291i
$636$		0			0
$637$	2.45169e9	−	3.05171e9i	0.375819	−	0.467794i
$638$	1.10015e10			1.67719
$639$		0			0
$640$	2.18681e9	+	3.78767e9i	0.329748	+	0.571140i
$641$	2.88121e9	−	4.99039e9i	0.432087	−	0.748397i	−0.564966	−	0.825114i	$-0.691111\pi$
$641$	2.88121e9	−	4.99039e9i	0.432087	−	0.748397i	0.997053	+	0.0767177i	$0.0244440\pi$
$642$		0			0
$643$	−1.98357e9	−	1.14522e9i	−0.294245	−	0.169883i	0.345610	−	0.938378i	$-0.387672\pi$
$643$	−1.98357e9	−	1.14522e9i	−0.294245	−	0.169883i	−0.639855	+	0.768496i	$0.721005\pi$
$644$	3.01273e9	+	1.73940e9i	0.444487	+	0.256625i
$645$		0			0
$646$	2.31457e8	−	4.00895e8i	0.0337797	−	0.0585082i
$647$	4.23115e9	+	7.32857e9i	0.614177	+	1.06379i	0.990528	+	0.137308i	$0.0438452\pi$
$647$	4.23115e9	+	7.32857e9i	0.614177	+	1.06379i	−0.376352	+	0.926477i	$0.622822\pi$
$648$		0			0
$649$	3.53959e9			0.508273
$650$	−1.47977e9	−	1.18883e9i	−0.211348	−	0.169794i
$651$		0			0
$652$	−3.73640e9	+	2.15721e9i	−0.527942	+	0.304808i
$653$	−1.94059e9	−	3.36119e9i	−0.272732	−	0.472386i	0.696828	−	0.717238i	$-0.254594\pi$
$653$	−1.94059e9	−	3.36119e9i	−0.272732	−	0.472386i	−0.969560	+	0.244852i	$0.921261\pi$
$654$		0			0
$655$			4.60880e9i			0.640831i
$656$	2.48901e9	+	1.43703e9i	0.344242	+	0.198748i
$657$		0			0
$658$			9.15594e9i			1.25289i
$659$	6.98230e8	−	1.20937e9i	0.0950385	−	0.164612i	−0.814586	−	0.580043i	$-0.803036\pi$
$659$	6.98230e8	−	1.20937e9i	0.0950385	−	0.164612i	0.909625	+	0.415431i	$0.136369\pi$
$660$		0			0
$661$	4.16961e9	−	2.40733e9i	0.561552	−	0.324212i	−0.192216	−	0.981353i	$-0.561567\pi$
$661$	4.16961e9	−	2.40733e9i	0.561552	−	0.324212i	0.753768	+	0.657140i	$0.228234\pi$
$662$	−1.36159e10			−1.82408
$663$		0			0
$664$	2.27432e9			0.301483
$665$	2.48786e8	−	1.43637e8i	0.0328058	−	0.0189404i
$666$		0			0
$667$	−6.37116e9	+	1.10352e10i	−0.831338	+	1.43992i
$668$		−	4.27061e9i		−	0.554335i
$669$		0			0
$670$	−1.15989e9	−	6.69662e8i	−0.148989	−	0.0860189i
$671$		−	2.00470e9i		−	0.256165i
$672$		0			0
$673$	7.05428e9	+	1.22184e10i	0.892072	+	1.54511i	0.837387	+	0.546610i	$0.184082\pi$
$673$	7.05428e9	+	1.22184e10i	0.892072	+	1.54511i	0.0546842	+	0.998504i	$0.482585\pi$
$674$	−2.36865e9	+	1.36754e9i	−0.297983	+	0.172040i
$675$		0			0
$676$	1.21677e9	+	5.51387e9i	0.151494	+	0.686504i
$677$	−6.91643e8			−0.0856686			−0.0428343	−	0.999082i	$-0.513639\pi$
$677$	−6.91643e8			−0.0856686			−0.0428343	+	0.999082i	$0.513639\pi$
$678$		0			0
$679$	−3.74407e9	−	6.48493e9i	−0.458987	−	0.794988i
$680$	1.08794e9	−	1.88438e9i	0.132686	−	0.229819i
$681$		0			0
$682$	1.41565e10	+	8.17329e9i	1.70888	+	0.986624i
$683$	−2.97479e8	−	1.71750e8i	−0.0357260	−	0.0206264i	0.482031	−	0.876154i	$-0.339899\pi$
$683$	−2.97479e8	−	1.71750e8i	−0.0357260	−	0.0206264i	−0.517757	+	0.855528i	$0.673233\pi$
$684$		0			0
$685$	−6.28421e8	+	1.08846e9i	−0.0747023	+	0.129388i
$686$	5.58275e9	+	9.66961e9i	0.660258	+	1.14360i
$687$		0			0
$688$	−1.47054e10			−1.72154
$689$	−4.69682e9	−	1.20953e10i	−0.547062	−	1.40879i
$690$		0			0
$691$	3.75457e7	−	2.16770e7i	0.00432899	−	0.00249935i	−0.497834	−	0.867272i	$-0.665871\pi$
$691$	3.75457e7	−	2.16770e7i	0.00432899	−	0.00249935i	0.502163	+	0.864773i	$0.332538\pi$
$692$	−4.67260e9	−	8.09318e9i	−0.536028	−	0.928428i
$693$		0			0
$694$			2.09752e9i			0.238204i
$695$	−3.35767e9	−	1.93855e9i	−0.379394	−	0.219043i
$696$		0			0
$697$		−	2.26145e9i		−	0.252971i
$698$	−3.47155e9	+	6.01291e9i	−0.386394	+	0.669253i
$699$		0			0
$700$	7.25884e8	−	4.19089e8i	0.0799878	−	0.0461810i
$701$	3.13161e9			0.343364			0.171682	−	0.985152i	$-0.445080\pi$
$701$	3.13161e9			0.343364			0.171682	+	0.985152i	$0.445080\pi$
$702$		0			0
$703$	−5.30363e8			−0.0575745
$704$	−2.46131e9	+	1.42104e9i	−0.265866	+	0.153498i
$705$		0			0
$706$	3.35442e9	−	5.81003e9i	0.358758	−	0.621387i
$707$		−	8.17874e8i		−	0.0870399i
$708$		0			0
$709$	−1.36402e8	−	7.87519e7i	−0.0143734	−	0.00829850i	0.492796	−	0.870145i	$-0.335975\pi$
$709$	−1.36402e8	−	7.87519e7i	−0.0143734	−	0.00829850i	−0.507169	+	0.861846i	$0.669308\pi$
$710$		−	1.04572e10i		−	1.09650i
$711$		0			0
$712$	−3.29045e8	−	5.69922e8i	−0.0341645	−	0.0591747i
$713$	−1.63965e10	+	9.46654e9i	−1.69410	+	0.978088i
$714$		0			0
$715$	4.86199e9	−	6.05188e9i	0.497443	−	0.619184i
$716$	1.83371e9			0.186696
$717$		0			0
$718$	−8.94429e9	−	1.54920e10i	−0.901800	−	1.56196i
$719$	−6.01180e9	+	1.04127e10i	−0.603189	+	1.04475i	0.389146	+	0.921176i	$0.372770\pi$
$719$	−6.01180e9	+	1.04127e10i	−0.603189	+	1.04475i	−0.992335	+	0.123578i	$0.960563\pi$
$720$		0			0
$721$	1.70846e9	+	9.86383e8i	0.169759	+	0.0980104i
$722$	1.13776e10	+	6.56884e9i	1.12504	+	0.649544i
$723$		0			0
$724$	−2.52436e9	+	4.37232e9i	−0.247210	+	0.428181i
$725$	1.53506e9	+	2.65880e9i	0.149604	+	0.259121i
$726$		0			0
$727$	2.27511e9			0.219600			0.109800	−	0.993954i	$-0.464979\pi$
$727$	2.27511e9			0.219600			0.109800	+	0.993954i	$0.464979\pi$
$728$	2.52160e9	+	3.89367e8i	0.242224	+	0.0374024i
$729$		0			0
$730$	−1.41282e10	+	8.15689e9i	−1.34417	+	0.776059i
$731$	5.78543e9	+	1.00207e10i	0.547803	+	0.948823i
$732$		0			0
$733$			1.24052e10i			1.16343i	0.813394	+	0.581713i	$0.197617\pi$
$733$			1.24052e10i			1.16343i	−0.813394	+	0.581713i	$0.802383\pi$
$734$	−1.76383e10	−	1.01835e10i	−1.64634	−	0.950516i
$735$		0			0
$736$		−	1.48575e10i		−	1.37364i
$737$	−7.18146e8	+	1.24387e9i	−0.0660810	+	0.114456i
$738$		0			0
$739$	−1.03072e10	+	5.95087e9i	−0.939475	+	0.542406i	−0.889796	−	0.456359i	$-0.849153\pi$
$739$	−1.03072e10	+	5.95087e9i	−0.939475	+	0.542406i	−0.0496793	+	0.998765i	$0.515820\pi$
$740$	5.90137e9			0.535355
$741$		0			0
$742$	1.38793e10			1.24725
$743$	7.70983e9	−	4.45127e9i	0.689579	−	0.398128i	−0.113876	−	0.993495i	$-0.536327\pi$
$743$	7.70983e9	−	4.45127e9i	0.689579	−	0.398128i	0.803454	+	0.595367i	$0.202993\pi$
$744$		0			0
$745$	4.61512e9	−	7.99363e9i	0.408918	−	0.708267i
$746$		−	2.08059e9i		−	0.183485i
$747$		0			0
$748$	4.78373e9	+	2.76189e9i	0.417938	+	0.241296i
$749$		−	5.22389e9i		−	0.454263i
$750$		0			0
$751$	9.35730e9	+	1.62073e10i	0.806141	+	1.39628i	0.915518	+	0.402276i	$0.131781\pi$
$751$	9.35730e9	+	1.62073e10i	0.806141	+	1.39628i	−0.109378	+	0.994000i	$0.534886\pi$
$752$	1.85330e10	−	1.07000e10i	1.58922	−	0.917535i
$753$		0			0
$754$	3.37614e9	−	2.18644e10i	0.286828	−	1.85754i
$755$	1.17612e10			0.994575
$756$		0			0
$757$	−1.12646e10	−	1.95108e10i	−0.943799	−	1.63471i	−0.758139	−	0.652093i	$-0.773891\pi$
$757$	−1.12646e10	−	1.95108e10i	−0.943799	−	1.63471i	−0.185660	−	0.982614i	$-0.559442\pi$
$758$	1.07282e10	−	1.85817e10i	0.894712	−	1.54969i
$759$		0			0
$760$	−2.43297e8	−	1.40467e8i	−0.0201043	−	0.0116072i
$761$	−6.90340e9	−	3.98568e9i	−0.567828	−	0.327835i	0.188454	−	0.982082i	$-0.439652\pi$
$761$	−6.90340e9	−	3.98568e9i	−0.567828	−	0.327835i	−0.756281	+	0.654247i	$0.772986\pi$
$762$		0			0
$763$	9.32957e8	−	1.61593e9i	0.0760372	−	0.131700i
$764$	4.09296e9	+	7.08921e9i	0.332055	+	0.575137i
$765$		0			0
$766$	1.52504e10			1.22597
$767$	1.08623e9	−	7.03458e9i	0.0869235	−	0.562930i
$768$		0			0
$769$	−5.04153e9	+	2.91073e9i	−0.399779	+	0.230813i	−0.686389	−	0.727235i	$-0.740805\pi$
$769$	−5.04153e9	+	2.91073e9i	−0.399779	+	0.230813i	0.286610	+	0.958047i	$0.407472\pi$
$770$	4.15197e9	+	7.19142e9i	0.327745	+	0.567672i
$771$		0			0
$772$			5.92403e9i			0.463401i
$773$	−1.74452e10	−	1.00720e10i	−1.35846	−	0.784308i	−0.369045	−	0.929412i	$-0.620315\pi$
$773$	−1.74452e10	−	1.00720e10i	−1.35846	−	0.784308i	−0.989416	+	0.145104i	$0.953648\pi$
$774$		0			0
$775$			4.56172e9i			0.352024i
$776$	−3.66146e9	+	6.34183e9i	−0.281280	+	0.487191i
$777$		0			0
$778$	−5.03027e9	+	2.90423e9i	−0.382968	+	0.221107i
$779$	−2.91981e8			−0.0221296
$780$		0			0
$781$	−1.12143e10			−0.842350
$782$	−1.34219e10	+	7.74913e9i	−1.00367	+	0.579467i
$783$		0			0
$784$	4.89349e9	−	8.47577e9i	0.362671	−	0.628164i
$785$			1.66221e10i			1.22643i
$786$		0			0
$787$	7.31133e8	+	4.22120e8i	0.0534669	+	0.0308691i	0.526495	−	0.850178i	$-0.323506\pi$
$787$	7.31133e8	+	4.22120e8i	0.0534669	+	0.0308691i	−0.473028	+	0.881047i	$0.656839\pi$
$788$			1.31187e10i			0.955098i
$789$		0			0
$790$	1.22363e10	+	2.11939e10i	0.882990	+	1.52938i
$791$	−1.17708e10	+	6.79588e9i	−0.845646	+	0.488234i
$792$		0			0
$793$	−3.98413e9	−	6.15200e8i	−0.283712	−	0.0438087i
$794$	−1.57392e10			−1.11586
$795$		0			0
$796$	−4.39740e9	−	7.61652e9i	−0.309030	−	0.535255i
$797$	−8.84381e9	+	1.53179e10i	−0.618779	+	1.07176i	0.370930	+	0.928661i	$0.379039\pi$
$797$	−8.84381e9	+	1.53179e10i	−0.618779	+	1.07176i	−0.989709	+	0.143095i	$0.954294\pi$
$798$		0			0
$799$	−1.45826e10	−	8.41928e9i	−1.01140	−	0.583931i
$800$	−3.10016e9	−	1.78988e9i	−0.214076	−	0.123597i
$801$		0			0
$802$	5.65590e9	−	9.79630e9i	0.387161	−	0.670582i
$803$	8.74746e9	+	1.51510e10i	0.596180	+	1.03261i
$804$		0			0
$805$	−9.61786e9			−0.649820
$806$	2.05879e10	−	2.56265e10i	1.38497	−	1.72392i
$807$		0			0
$808$	−6.92671e8	+	3.99914e8i	−0.0461942	+	0.0266702i
$809$	−6.07311e9	−	1.05189e10i	−0.403266	−	0.698477i	0.590852	−	0.806780i	$-0.298792\pi$
$809$	−6.07311e9	−	1.05189e10i	−0.403266	−	0.698477i	−0.994118	+	0.108303i	$0.965458\pi$
$810$		0			0
$811$			9.76645e9i			0.642930i	0.946921	+	0.321465i	$0.104175\pi$
$811$			9.76645e9i			0.642930i	−0.946921	+	0.321465i	$0.895825\pi$
$812$	8.46035e9	+	4.88459e9i	0.554552	+	0.320171i
$813$		0			0
$814$		−	1.53307e10i		−	0.996268i
$815$	5.96406e9	−	1.03301e10i	0.385914	−	0.668422i
$816$		0			0
$817$	1.29379e9	−	7.46972e8i	0.0830018	−	0.0479211i
$818$	3.31160e10			2.11544
$819$		0			0
$820$	3.24889e9			0.205772
$821$	−7.00087e9	+	4.04196e9i	−0.441521	+	0.254912i	−0.704243	−	0.709959i	$-0.748713\pi$
$821$	−7.00087e9	+	4.04196e9i	−0.441521	+	0.254912i	0.262722	+	0.964872i	$0.415380\pi$
$822$		0			0
$823$	5.48917e9	−	9.50753e9i	0.343248	−	0.594522i	−0.641786	−	0.766884i	$-0.721806\pi$
$823$	5.48917e9	−	9.50753e9i	0.343248	−	0.594522i	0.985034	+	0.172361i	$0.0551397\pi$
$824$		−	1.92924e9i		−	0.120127i
$825$		0			0
$826$	6.59386e9	+	3.80697e9i	0.407108	+	0.235044i
$827$			1.39129e10i			0.855357i	0.903931	+	0.427678i	$0.140668\pi$
$827$			1.39129e10i			0.855357i	−0.903931	+	0.427678i	$0.859332\pi$
$828$		0			0
$829$	−1.31171e10	−	2.27195e10i	−0.799646	−	1.38503i	−0.919847	−	0.392278i	$-0.871687\pi$
$829$	−1.31171e10	−	2.27195e10i	−0.799646	−	1.38503i	0.120200	−	0.992750i	$-0.461646\pi$
$830$	1.28906e10	−	7.44241e9i	0.782530	−	0.451794i
$831$		0			0
$832$	2.06885e9	+	5.32770e9i	0.124536	+	0.320707i
$833$	−7.70085e9			−0.461616
$834$		0			0
$835$	5.90350e9	+	1.02252e10i	0.350919	+	0.607809i
$836$	3.56595e8	−	6.17641e8i	0.0211083	−	0.0365606i
$837$		0			0
$838$	1.79496e10	+	1.03632e10i	1.05366	+	0.608331i
$839$	1.04861e10	+	6.05413e9i	0.612979	+	0.353904i	0.774130	−	0.633026i	$-0.218187\pi$
$839$	1.04861e10	+	6.05413e9i	0.612979	+	0.353904i	−0.161151	+	0.986930i	$0.551521\pi$
$840$		0			0
$841$	−9.26658e9	+	1.60502e10i	−0.537197	+	0.930452i
$842$	1.33977e10	+	2.32056e10i	0.773462	+	1.33968i
$843$		0			0
$844$	1.14120e10			0.653378
$845$	−1.05355e10	−	1.15199e10i	−0.600696	−	0.656826i
$846$		0			0
$847$	−1.97338e9	+	1.13933e9i	−0.111588	+	0.0644255i
$848$	−1.62200e10	−	2.80938e10i	−0.913407	−	1.58207i
$849$		0			0
$850$			3.73414e9i			0.208557i
$851$	1.53775e10	+	8.87823e9i	0.855330	+	0.493825i
$852$		0			0
$853$		−	1.60323e10i		−	0.884453i	−0.896903	−	0.442227i	$-0.854189\pi$
$853$		−	1.60323e10i		−	0.884453i	0.896903	−	0.442227i	$-0.145811\pi$
$854$	2.15613e9	−	3.73452e9i	0.118460	−	0.205179i
$855$		0			0
$856$	−4.42420e9	+	2.55431e9i	−0.241088	+	0.139192i
$857$	2.24463e10			1.21818			0.609092	−	0.793100i	$-0.291534\pi$
$857$	2.24463e10			1.21818			0.609092	+	0.793100i	$0.291534\pi$
$858$		0			0
$859$	−1.36041e10			−0.732310			−0.366155	−	0.930554i	$-0.619326\pi$
$859$	−1.36041e10			−0.732310			−0.366155	+	0.930554i	$0.619326\pi$
$860$	−1.43961e10	+	8.31158e9i	−0.771791	+	0.445594i
$861$		0			0
$862$	−1.31518e10	+	2.27795e10i	−0.699372	+	1.21135i
$863$			1.13911e10i			0.603290i	0.953420	+	0.301645i	$0.0975358\pi$
$863$			1.13911e10i			0.603290i	−0.953420	+	0.301645i	$0.902464\pi$
$864$		0			0
$865$	2.23753e10	+	1.29184e10i	1.17547	+	0.678660i
$866$		−	2.11834e10i		−	1.10837i
$867$		0			0
$868$	7.25773e9	+	1.25708e10i	0.376688	+	0.652443i
$869$	2.27284e10	−	1.31222e10i	1.17490	−	0.678326i
$870$		0			0
$871$	2.25167e9	+	1.80896e9i	0.115463	+	0.0927610i
$872$	−1.82474e9			−0.0931953
$873$		0			0
$874$	1.00051e9	+	1.73293e9i	0.0506911	+	0.0877995i
$875$	−6.73602e9	+	1.16671e10i	−0.339919	+	0.588757i
$876$		0			0
$877$	2.38991e10	+	1.37981e10i	1.19642	+	0.690752i	0.959755	−	0.280840i	$-0.0906131\pi$
$877$	2.38991e10	+	1.37981e10i	1.19642	+	0.690752i	0.236662	+	0.971592i	$0.423946\pi$
$878$	4.03636e10	+	2.33039e10i	2.01261	+	1.16198i
$879$		0			0
$880$	9.70434e9	−	1.68084e10i	0.480039	−	0.831453i
$881$	−5.80856e9	−	1.00607e10i	−0.286189	−	0.495694i	0.686708	−	0.726934i	$-0.259055\pi$
$881$	−5.80856e9	−	1.00607e10i	−0.286189	−	0.495694i	−0.972897	+	0.231240i	$0.925722\pi$
$882$		0			0
$883$	−2.60345e10			−1.27258			−0.636292	−	0.771449i	$-0.719532\pi$
$883$	−2.60345e10			−1.27258			−0.636292	+	0.771449i	$0.719532\pi$
$884$	6.95700e9	−	8.65962e9i	0.338719	−	0.421615i
$885$		0			0
$886$	1.05456e10	−	6.08852e9i	0.509395	−	0.294099i
$887$	−1.36152e10	−	2.35823e10i	−0.655078	−	1.13463i	−0.981874	−	0.189533i	$-0.939302\pi$
$887$	−1.36152e10	−	2.35823e10i	−0.655078	−	1.13463i	0.326796	−	0.945095i	$-0.394031\pi$
$888$		0			0
$889$			1.06656e10i			0.509133i
$890$	−3.72999e9	−	2.15351e9i	−0.177355	−	0.102396i
$891$		0			0
$892$		−	1.60548e10i		−	0.757405i
$893$	−1.08704e9	+	1.88280e9i	−0.0510815	+	0.0884757i
$894$		0			0
$895$	−4.39048e9	+	2.53484e9i	−0.204706	+	0.118187i
$896$	1.00892e10			0.468573
$897$		0			0
$898$	−3.31093e10			−1.52575
$899$	−4.60448e10	+	2.65840e10i	−2.11360	+	1.22029i
$900$		0			0
$901$	−1.27626e10	+	2.21055e10i	−0.581303	+	1.00685i
$902$		−	8.44002e9i		−	0.382931i
$903$		0			0
$904$	1.15111e10	+	6.64593e9i	0.518235	+	0.299203i
$905$		−	1.39583e10i		−	0.625981i
$906$		0			0
$907$	1.45545e10	+	2.52092e10i	0.647698	+	1.12185i	0.983671	+	0.179974i	$0.0576013\pi$
$907$	1.45545e10	+	2.52092e10i	0.647698	+	1.12185i	−0.335974	+	0.941871i	$0.609065\pi$
$908$	−8.10276e9	+	4.67813e9i	−0.359197	+	0.207382i
$909$		0			0
$910$	1.55664e10	−	6.04472e9i	0.684766	−	0.265908i
$911$	1.86121e9			0.0815606			0.0407803	−	0.999168i	$-0.487016\pi$
$911$	1.86121e9			0.0815606			0.0407803	+	0.999168i	$0.487016\pi$
$912$		0			0
$913$	−7.98125e9	−	1.38239e10i	−0.347075	−	0.601151i
$914$	8.09745e9	−	1.40252e10i	0.350782	−	0.607572i
$915$		0			0
$916$	−3.84798e9	−	2.22163e9i	−0.165424	−	0.0955077i
$917$	9.20729e9	+	5.31583e9i	0.394311	+	0.227656i
$918$		0			0
$919$	1.67606e10	−	2.90302e10i	0.712336	−	1.23380i	−0.251642	−	0.967820i	$-0.580970\pi$
$919$	1.67606e10	−	2.90302e10i	0.712336	−	1.23380i	0.963978	−	0.265982i	$-0.0856962\pi$
$920$	4.70282e9	+	8.14552e9i	0.199114	+	0.344875i
$921$		0			0
$922$	2.33843e10			0.982576
$923$	−3.44143e9	+	2.22872e10i	−0.144056	+	0.932932i
$924$		0			0
$925$	3.70505e9	−	2.13911e9i	0.153921	−	0.0888664i
$926$	1.66799e10	+	2.88905e10i	0.690328	+	1.19568i
$927$		0			0
$928$		−	4.17229e10i		−	1.71379i
$929$	1.54742e10	+	8.93401e9i	0.633216	+	0.365588i	0.781997	−	0.623283i	$-0.214201\pi$
$929$	1.54742e10	+	8.93401e9i	0.633216	+	0.365588i	−0.148780	+	0.988870i	$0.547535\pi$
$930$		0			0
$931$			9.94277e8i			0.0403816i
$932$	−1.12470e10	+	1.94804e10i	−0.455074	+	0.788211i
$933$		0			0
$934$	−2.77599e10	+	1.60272e10i	−1.11482	+	0.643639i
$935$	−1.52717e10			−0.611006
$936$		0			0
$937$	2.15006e10			0.853811			0.426905	−	0.904296i	$-0.359604\pi$
$937$	2.15006e10			0.853811			0.426905	+	0.904296i	$0.359604\pi$
$938$	−2.67565e9	+	1.54479e9i	−0.105857	+	0.0611166i
$939$		0			0
$940$	1.20955e10	−	2.09500e10i	0.474980	−	0.822690i
$941$		−	1.20772e10i		−	0.472502i	−0.971692	−	0.236251i	$-0.924081\pi$
$941$		−	1.20772e10i		−	0.472502i	0.971692	−	0.236251i	$-0.0759188\pi$
$942$		0			0
$943$	8.46581e9	+	4.88774e9i	0.328759	+	0.189809i
$944$		−	1.77960e10i		−	0.688525i
$945$		0			0
$946$	2.15920e10	+	3.73984e10i	0.829227	+	1.43626i
$947$	−3.63894e10	+	2.10094e10i	−1.39235	+	0.803876i	−0.993576	−	0.113171i	$-0.963899\pi$
$947$	−3.63894e10	+	2.10094e10i	−1.39235	+	0.803876i	−0.398779	+	0.917047i	$0.630566\pi$
$948$		0			0
$949$	3.27956e10	−	1.27351e10i	1.24561	−	0.483696i
$950$	4.82124e8			0.0182443
$951$		0			0
$952$	−2.50969e9	−	4.34691e9i	−0.0942737	−	0.163287i
$953$	1.06091e10	−	1.83754e10i	0.397056	−	0.687722i	−0.596305	−	0.802758i	$-0.703365\pi$
$953$	1.06091e10	−	1.83754e10i	0.397056	−	0.687722i	0.993361	+	0.115036i	$0.0366984\pi$
$954$		0			0
$955$	−1.95996e10	−	1.13158e10i	−0.728175	−	0.420412i
$956$	−3.08597e9	−	1.78169e9i	−0.114232	−	0.0659521i
$957$		0			0
$958$	−4.82774e9	+	8.36188e9i	−0.177404	+	0.307273i
$959$	1.44965e9	+	2.51087e9i	0.0530761	+	0.0919304i
$960$		0			0
$961$	−5.14867e10			−1.87139
$962$	−3.04682e10	−	4.70467e9i	−1.10340	−	0.170379i
$963$		0			0
$964$	−1.53614e10	+	8.86891e9i	−0.552283	+	0.318861i
$965$	−8.18912e9	−	1.41840e10i	−0.293354	−	0.508103i
$966$		0			0
$967$			2.68721e10i			0.955671i	0.878449	+	0.477836i	$0.158579\pi$
$967$			2.68721e10i			0.955671i	−0.878449	+	0.477836i	$0.841421\pi$
$968$	1.92983e9	+	1.11419e9i	0.0683843	+	0.0394817i
$969$		0			0
$970$			4.79266e10i			1.68607i
$971$	−1.52953e10	+	2.64923e10i	−0.536157	+	0.928651i	0.462949	+	0.886385i	$0.346791\pi$
$971$	−1.52953e10	+	2.64923e10i	−0.536157	+	0.928651i	−0.999106	+	0.0422666i	$0.986542\pi$
$972$		0			0
$973$	−7.74552e9	+	4.47188e9i	−0.269560	+	0.155631i
$974$	−4.01250e10			−1.39142
$975$		0			0
$976$	−1.00790e10			−0.347010
$977$	2.41063e10	−	1.39178e10i	0.826990	−	0.477463i	−0.0258312	−	0.999666i	$-0.508223\pi$
$977$	2.41063e10	−	1.39178e10i	0.826990	−	0.477463i	0.852821	+	0.522204i	$0.174890\pi$
$978$		0			0
$979$	−2.30943e9	+	4.00005e9i	−0.0786620	+	0.136247i
$980$		−	1.10633e10i		−	0.375487i
$981$		0			0
$982$	3.56077e9	+	2.05581e9i	0.119992	+	0.0692777i
$983$			2.17619e8i			0.00730735i	0.999993	+	0.00365368i	$0.00116300\pi$
$983$			2.17619e8i			0.00730735i	−0.999993	+	0.00365368i	$0.998837\pi$
$984$		0			0
$985$	−1.81347e10	−	3.14101e10i	−0.604620	−	1.04723i
$986$	−3.76914e10	+	2.17611e10i	−1.25220	+	0.722957i
$987$		0			0
$988$	−1.11807e9	−	8.98237e8i	−0.0368823	−	0.0296307i
$989$	−5.00169e10			−1.64411
$990$		0			0
$991$	−1.81782e9	−	3.14855e9i	−0.0593325	−	0.102767i	0.834833	−	0.550503i	$-0.185564\pi$
$991$	−1.81782e9	−	3.14855e9i	−0.0593325	−	0.102767i	−0.894166	+	0.447736i	$0.852231\pi$
$992$	3.09969e10	−	5.36882e10i	1.00815	−	1.74617i
$993$		0			0
$994$	−2.08909e10	−	1.20614e10i	−0.674691	−	0.389533i
$995$	2.10575e10	+	1.21575e10i	0.677681	+	0.391259i
$996$		0			0
$997$	2.88782e9	−	5.00185e9i	0.0922862	−	0.159844i	−0.816187	−	0.577788i	$-0.803916\pi$
$997$	2.88782e9	−	5.00185e9i	0.0922862	−	0.159844i	0.908473	+	0.417944i	$0.137249\pi$
$998$	−1.15961e10	−	2.00851e10i	−0.369280	−	0.639612i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.8.q.b.10.2		14
3.2	odd	2		13.8.e.a.10.6	yes	14
12.11	even	2		208.8.w.a.49.6		14
13.4	even	6	inner	117.8.q.b.82.2		14
39.2	even	12		169.8.a.g.1.11		14
39.11	even	12		169.8.a.g.1.4		14
39.17	odd	6		13.8.e.a.4.6	✓	14
39.23	odd	6		169.8.b.d.168.4		14
39.29	odd	6		169.8.b.d.168.11		14
156.95	even	6		208.8.w.a.17.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.6	✓	14	39.17	odd	6
13.8.e.a.10.6	yes	14	3.2	odd	2
117.8.q.b.10.2		14	1.1	even	1	trivial
117.8.q.b.82.2		14	13.4	even	6	inner
169.8.a.g.1.4		14	39.11	even	12
169.8.a.g.1.11		14	39.2	even	12
169.8.b.d.168.4		14	39.23	odd	6
169.8.b.d.168.11		14	39.29	odd	6
208.8.w.a.17.6		14	156.95	even	6
208.8.w.a.49.6		14	12.11	even	2

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.7863 + 7.38219i) q^{2} +(44.9933 - 77.9308i) q^{4} +248.787i q^{5} +(497.017 + 286.953i) q^{7} -561.243i q^{8} +(-1836.59 - 3181.07i) q^{10} +(-3411.39 + 1969.56i) q^{11} +(2867.43 + 7384.20i) q^{13} -8473.37 q^{14} +(9902.35 + 17151.4i) q^{16} +(7791.62 - 13495.5i) q^{17} +(-1742.44 - 1006.00i) q^{19} +(19388.2 + 11193.8i) q^{20} +(29079.4 - 50367.0i) q^{22} +(33680.6 + 58336.5i) q^{23} +16229.9 q^{25} +(-91175.3 - 73248.9i) q^{26} +(44724.9 - 25822.0i) q^{28} +(94582.0 + 163821. i) q^{29} +281068. i q^{31} +(-191015. - 110282. i) q^{32} +230077. i q^{34} +(-71390.3 + 123652. i) q^{35} +(228285. - 131800. i) q^{37} +29705.8 q^{38} +139630. q^{40} +(125678. - 72560.2i) q^{41} +(-371259. + 643040. i) q^{43} +354469. i q^{44} +(-861302. - 497273. i) q^{46} -1.08055e6i q^{47} +(-247087. - 427968. i) q^{49} +(-207521. + 119812. i) q^{50} +(704471. + 108779. i) q^{52} -1.63799e6 q^{53} +(-490002. - 848709. i) q^{55} +(161050. - 278947. i) q^{56} +(-2.41871e6 - 1.39644e6i) q^{58} +(-778187. - 449287. i) q^{59} +(-254459. + 440737. i) q^{61} +(-2.07490e6 - 3.59383e6i) q^{62} +721500. q^{64} +(-1.83709e6 + 713379. i) q^{65} +(315772. - 182311. i) q^{67} +(-701142. - 1.21441e6i) q^{68} -2.10806e6i q^{70} +(2.46548e6 + 1.42345e6i) q^{71} -4.44132e6i q^{73} +(-1.94595e6 + 3.37048e6i) q^{74} +(-156796. + 90526.4i) q^{76} -2.26069e6 q^{77} -6.66251e6 q^{79} +(-4.26704e6 + 2.46358e6i) q^{80} +(-1.07131e6 + 1.85556e6i) q^{82} +4.05229e6i q^{83} +(3.35750e6 + 1.93846e6i) q^{85} -1.09628e7i q^{86} +(1.10540e6 + 1.91462e6i) q^{88} +(1.01547e6 - 586279. i) q^{89} +(-693759. + 4.49289e6i) q^{91} +6.06161e6 q^{92} +(7.97686e6 + 1.38163e7i) q^{94} +(250279. - 433496. i) q^{95} +(-1.12996e7 - 6.52384e6i) q^{97} +(6.31867e6 + 3.64809e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 383 q^{4} - 2772 q^{7} - 509 q^{10} - 6516 q^{11} + 5109 q^{13} + 47916 q^{14} - 633 q^{16} + 38403 q^{17} + 43254 q^{19} - 89409 q^{20} - 125882 q^{22} + 68550 q^{23} + 39380 q^{25} - 361959 q^{26}+ \cdots - 16173003 q^{98}+O(q^{100}) \) 14 * q + 3 * q^2 + 383 * q^4 - 2772 * q^7 - 509 * q^10 - 6516 * q^11 + 5109 * q^13 + 47916 * q^14 - 633 * q^16 + 38403 * q^17 + 43254 * q^19 - 89409 * q^20 - 125882 * q^22 + 68550 * q^23 + 39380 * q^25 - 361959 * q^26 - 234780 * q^28 - 221583 * q^29 + 878067 * q^32 - 659616 * q^35 - 565347 * q^37 - 953640 * q^38 - 77182 * q^40 - 1716057 * q^41 - 882692 * q^43 - 3267480 * q^46 + 2653979 * q^49 - 145128 * q^50 + 4962178 * q^52 + 1791210 * q^53 + 2453536 * q^55 + 7457952 * q^56 - 14978127 * q^58 + 1189032 * q^59 + 3858525 * q^61 - 1904142 * q^62 + 14570922 * q^64 - 10424661 * q^65 + 4674330 * q^67 - 9569619 * q^68 + 25203126 * q^71 - 8640105 * q^74 + 12934506 * q^76 - 19599336 * q^77 - 30688440 * q^79 - 29127963 * q^80 - 37359719 * q^82 - 22436313 * q^85 + 27045536 * q^88 - 2123160 * q^89 + 37205532 * q^91 + 47685588 * q^92 + 19138810 * q^94 + 43420386 * q^95 - 68556288 * q^97 - 16173003 * q^98

Introduction

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