LMFDB - Embedded newform 27.15.d.a.8.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,15,Mod(8,27)] 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("27.8"); S:= CuspForms(chi, 15); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 15, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$33.5688214010$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	27.8
Dual form			27.15.d.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-129.548 - 74.7948i) q^{2} +(2996.54 + 5190.15i) q^{4} +(-31950.1 + 18446.4i) q^{5} +(153772. - 266342. i) q^{7} +1.55438e6i q^{8} +5.51879e6 q^{10} +(-8.07458e6 - 4.66186e6i) q^{11} +(2.46419e7 + 4.26810e7i) q^{13} +(-3.98420e7 + 2.30028e7i) q^{14} +(1.65355e8 - 2.86402e8i) q^{16} -1.60558e8i q^{17} +1.10366e9 q^{19} +(-1.91479e8 - 1.10551e8i) q^{20} +(6.97366e8 + 1.20787e9i) q^{22} +(5.63572e9 - 3.25379e9i) q^{23} +(-2.37122e9 + 4.10707e9i) q^{25} -7.37234e9i q^{26} +1.84314e9 q^{28} +(-5.84016e9 - 3.37182e9i) q^{29} +(-5.34495e9 - 9.25772e9i) q^{31} +(-2.07879e10 + 1.20019e10i) q^{32} +(-1.20089e10 + 2.08000e10i) q^{34} +1.13462e10i q^{35} -1.45967e11 q^{37} +(-1.42978e11 - 8.25481e10i) q^{38} +(-2.86727e10 - 4.96625e10i) q^{40} +(-1.88610e11 + 1.08894e11i) q^{41} +(-7.02322e10 + 1.21646e11i) q^{43} -5.58777e10i q^{44} -9.73465e11 q^{46} +(-4.86126e11 - 2.80665e11i) q^{47} +(2.91820e11 + 5.05446e11i) q^{49} +(6.14375e11 - 3.54710e11i) q^{50} +(-1.47680e11 + 2.55790e11i) q^{52} -2.07734e12i q^{53} +3.43979e11 q^{55} +(4.13995e11 + 2.39020e11i) q^{56} +(5.04389e11 + 8.73628e11i) q^{58} +(-1.90853e12 + 1.10189e12i) q^{59} +(2.01361e12 - 3.48768e12i) q^{61} +1.59910e12i q^{62} -1.82762e12 q^{64} +(-1.57462e12 - 9.09108e11i) q^{65} +(1.82254e12 + 3.15674e12i) q^{67} +(8.33320e11 - 4.81118e11i) q^{68} +(8.48638e11 - 1.46988e12i) q^{70} +4.60775e12i q^{71} -1.45384e13 q^{73} +(1.89097e13 + 1.09175e13i) q^{74} +(3.30716e12 + 5.72817e12i) q^{76} +(-2.48330e12 + 1.43373e12i) q^{77} +(1.41356e13 - 2.44835e13i) q^{79} +1.22008e13i q^{80} +3.25789e13 q^{82} +(-3.75647e12 - 2.16880e12i) q^{83} +(2.96172e12 + 5.12985e12i) q^{85} +(1.81969e13 - 1.05060e13i) q^{86} +(7.24628e12 - 1.25509e13i) q^{88} -1.98593e13i q^{89} +1.51570e13 q^{91} +(3.37753e13 + 1.95002e13i) q^{92} +(4.19846e13 + 7.27195e13i) q^{94} +(-3.52621e13 + 2.03586e13i) q^{95} +(8.91638e12 - 1.54436e13i) q^{97} -8.73064e13i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 3 q^{2} + 98303 q^{4} + 107994 q^{5} - 146330 q^{7} - 32772 q^{10} + 15978711 q^{11} - 23281436 q^{13} + 349442850 q^{14} - 671072257 q^{16} + 195706222 q^{19} - 2822935854 q^{20} - 204235521 q^{22}+ \cdots + 7621755375583 q^{97}+O(q^{100}) $ 26 * q + 3 * q^2 + 98303 * q^4 + 107994 * q^5 - 146330 * q^7 - 32772 * q^10 + 15978711 * q^11 - 23281436 * q^13 + 349442850 * q^14 - 671072257 * q^16 + 195706222 * q^19 - 2822935854 * q^20 - 204235521 * q^22 + 6101133672 * q^23 + 14614789727 * q^25 - 9052979204 * q^28 - 85191770166 * q^29 + 15357554728 * q^31 + 237242922057 * q^32 - 16566014943 * q^34 - 77721425444 * q^37 - 476314869819 * q^38 - 88855733850 * q^40 + 938882938233 * q^41 - 29709800063 * q^43 + 1553142786144 * q^46 + 1272741434580 * q^47 - 945184029255 * q^49 - 3573994524699 * q^50 + 1825489374856 * q^52 - 3772940931372 * q^55 + 7790759725422 * q^56 + 3747043240302 * q^58 - 5874788534451 * q^59 - 4867968901544 * q^61 + 1211169309434 * q^64 + 22156719464856 * q^65 - 8251061484125 * q^67 - 30687017243265 * q^68 + 6871822387932 * q^70 + 16120119648922 * q^73 - 8549243621166 * q^74 + 14422972781521 * q^76 - 13919363311398 * q^77 - 10740904544582 * q^79 - 67076318933382 * q^82 + 11295125984532 * q^83 + 10590724937466 * q^85 - 97019495740221 * q^86 - 26136212294541 * q^88 + 70870424994080 * q^91 + 474274297000284 * q^92 - 46678164316620 * q^94 - 440317551118746 * q^95 + 7621755375583 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−129.548	−	74.7948i	−1.01210	−	0.584335i	−0.100292	−	0.994958i	$-0.531978\pi$
$2$	−129.548	−	74.7948i	−1.01210	−	0.584335i	−0.911805	+	0.410623i	$0.865311\pi$
$3$		0			0
$3$		0			0
$4$	2996.54	+	5190.15i	0.182894	+	0.316782i
$5$	−31950.1	+	18446.4i	−0.408962	+	0.236114i	−0.690344	−	0.723482i	$-0.742541\pi$
$5$	−31950.1	+	18446.4i	−0.408962	+	0.236114i	0.281382	+	0.959596i	$0.409207\pi$
$6$		0			0
$7$	153772.	−	266342.i	0.186721	−	0.323410i	−0.757434	−	0.652911i	$-0.773547\pi$
$7$	153772.	−	266342.i	0.186721	−	0.323410i	0.944155	+	0.329502i	$0.106881\pi$
$8$			1.55438e6i			0.741184i
$9$		0			0
$10$	5.51879e6			0.551879
$11$	−8.07458e6	−	4.66186e6i	−0.414354	−	0.239227i	0.278305	−	0.960493i	$-0.410227\pi$
$11$	−8.07458e6	−	4.66186e6i	−0.414354	−	0.239227i	−0.692659	+	0.721266i	$0.743561\pi$
$12$		0			0
$13$	2.46419e7	+	4.26810e7i	0.392708	+	0.680191i	0.992806	−	0.119736i	$-0.0382049\pi$
$13$	2.46419e7	+	4.26810e7i	0.392708	+	0.680191i	−0.600097	+	0.799927i	$0.704872\pi$
$14$	−3.98420e7	+	2.30028e7i	−0.377959	+	0.218215i
$15$		0			0
$16$	1.65355e8	−	2.86402e8i	0.615994	−	1.06693i
$17$		−	1.60558e8i		−	0.391281i	−0.980676	−	0.195641i	$-0.937321\pi$
$17$		−	1.60558e8i		−	0.391281i	0.980676	−	0.195641i	$-0.0626786\pi$
$18$		0			0
$19$	1.10366e9			1.23470			0.617348	−	0.786690i	$-0.288207\pi$
$19$	1.10366e9			1.23470			0.617348	+	0.786690i	$0.288207\pi$
$20$	−1.91479e8	−	1.10551e8i	−0.149593	−	0.0863678i
$21$		0			0
$22$	6.97366e8	+	1.20787e9i	0.279577	+	0.484242i
$23$	5.63572e9	−	3.25379e9i	1.65522	−	0.955639i	0.680338	−	0.732898i	$-0.261833\pi$
$23$	5.63572e9	−	3.25379e9i	1.65522	−	0.955639i	0.974878	−	0.222741i	$-0.0715005\pi$
$24$		0			0
$25$	−2.37122e9	+	4.10707e9i	−0.388500	+	0.672902i
$26$		−	7.37234e9i		−	0.917892i
$27$		0			0
$28$	1.84314e9			0.136600
$29$	−5.84016e9	−	3.37182e9i	−0.338562	−	0.195469i	0.321074	−	0.947054i	$-0.395956\pi$
$29$	−5.84016e9	−	3.37182e9i	−0.338562	−	0.195469i	−0.659636	+	0.751585i	$0.729290\pi$
$30$		0			0
$31$	−5.34495e9	−	9.25772e9i	−0.194273	−	0.336490i	0.752389	−	0.658719i	$-0.228901\pi$
$31$	−5.34495e9	−	9.25772e9i	−0.194273	−	0.336490i	−0.946662	+	0.322229i	$0.895568\pi$
$32$	−2.07879e10	+	1.20019e10i	−0.605007	+	0.349301i
$33$		0			0
$34$	−1.20089e10	+	2.08000e10i	−0.228639	+	0.396015i
$35$			1.13462e10i			0.176350i
$36$		0			0
$37$	−1.45967e11			−1.53759			−0.768796	−	0.639494i	$-0.779144\pi$
$37$	−1.45967e11			−1.53759			−0.768796	+	0.639494i	$0.779144\pi$
$38$	−1.42978e11	−	8.25481e10i	−1.24963	−	0.721476i
$39$		0			0
$40$	−2.86727e10	−	4.96625e10i	−0.175004	−	0.303116i
$41$	−1.88610e11	+	1.08894e11i	−0.968453	+	0.559137i	−0.898764	−	0.438432i	$-0.855534\pi$
$41$	−1.88610e11	+	1.08894e11i	−0.968453	+	0.559137i	−0.0696888	+	0.997569i	$0.522201\pi$
$42$		0			0
$43$	−7.02322e10	+	1.21646e11i	−0.258379	+	0.447525i	−0.965808	−	0.259259i	$-0.916522\pi$
$43$	−7.02322e10	+	1.21646e11i	−0.258379	+	0.447525i	0.707429	+	0.706785i	$0.249855\pi$
$44$		−	5.58777e10i		−	0.175013i
$45$		0			0
$46$	−9.73465e11			−2.23365
$47$	−4.86126e11	−	2.80665e11i	−0.959542	−	0.553992i	−0.0635100	−	0.997981i	$-0.520229\pi$
$47$	−4.86126e11	−	2.80665e11i	−0.959542	−	0.553992i	−0.896032	+	0.443989i	$0.853563\pi$
$48$		0			0
$49$	2.91820e11	+	5.05446e11i	0.430271	+	0.745251i
$50$	6.14375e11	−	3.54710e11i	0.786400	−	0.454028i
$51$		0			0
$52$	−1.47680e11	+	2.55790e11i	−0.143648	+	0.248806i
$53$		−	2.07734e12i		−	1.76838i	−0.467128	−	0.884190i	$-0.654711\pi$
$53$		−	2.07734e12i		−	1.76838i	0.467128	−	0.884190i	$-0.345289\pi$
$54$		0			0
$55$	3.43979e11			0.225940
$56$	4.13995e11	+	2.39020e11i	0.239706	+	0.138394i
$57$		0			0
$58$	5.04389e11	+	8.73628e11i	0.228439	+	0.395668i
$59$	−1.90853e12	+	1.10189e12i	−0.766895	+	0.442767i	−0.831766	−	0.555127i	$-0.812670\pi$
$59$	−1.90853e12	+	1.10189e12i	−0.766895	+	0.442767i	0.0648709	+	0.997894i	$0.479336\pi$
$60$		0			0
$61$	2.01361e12	−	3.48768e12i	0.640718	−	1.10976i	−0.344555	−	0.938766i	$-0.611970\pi$
$61$	2.01361e12	−	3.48768e12i	0.640718	−	1.10976i	0.985273	−	0.170990i	$-0.0546965\pi$
$62$			1.59910e12i			0.454081i
$63$		0			0
$64$	−1.82762e12			−0.415553
$65$	−1.57462e12	−	9.09108e11i	−0.321205	−	0.185448i
$66$		0			0
$67$	1.82254e12	+	3.15674e12i	0.300714	+	0.520852i	0.976298	−	0.216431i	$-0.0694416\pi$
$67$	1.82254e12	+	3.15674e12i	0.300714	+	0.520852i	−0.675584	+	0.737283i	$0.736108\pi$
$68$	8.33320e11	−	4.81118e11i	0.123951	−	0.0715630i
$69$		0			0
$70$	8.48638e11	−	1.46988e12i	0.103047	−	0.178483i
$71$			4.60775e12i			0.506618i	0.967385	+	0.253309i	$0.0815189\pi$
$71$			4.60775e12i			0.506618i	−0.967385	+	0.253309i	$0.918481\pi$
$72$		0			0
$73$	−1.45384e13			−1.31601			−0.658003	−	0.753016i	$-0.728598\pi$
$73$	−1.45384e13			−1.31601			−0.658003	+	0.753016i	$0.728598\pi$
$74$	1.89097e13	+	1.09175e13i	1.55619	+	0.898469i
$75$		0			0
$76$	3.30716e12	+	5.72817e12i	0.225819	+	0.391130i
$77$	−2.48330e12	+	1.43373e12i	−0.154737	+	0.0893373i
$78$		0			0
$79$	1.41356e13	−	2.44835e13i	0.736077	−	1.27492i	−0.218171	−	0.975910i	$-0.570009\pi$
$79$	1.41356e13	−	2.44835e13i	0.736077	−	1.27492i	0.954249	−	0.299013i	$-0.0966575\pi$
$80$			1.22008e13i			0.581779i
$81$		0			0
$82$	3.25789e13			1.30689
$83$	−3.75647e12	−	2.16880e12i	−0.138431	−	0.0799231i	0.429185	−	0.903217i	$-0.358801\pi$
$83$	−3.75647e12	−	2.16880e12i	−0.138431	−	0.0799231i	−0.567616	+	0.823293i	$0.692134\pi$
$84$		0			0
$85$	2.96172e12	+	5.12985e12i	0.0923871	+	0.160019i
$86$	1.81969e13	−	1.05060e13i	0.523009	−	0.301959i
$87$		0			0
$88$	7.24628e12	−	1.25509e13i	0.177311	−	0.307112i
$89$		−	1.98593e13i		−	0.448986i	−0.974476	−	0.224493i	$-0.927927\pi$
$89$		−	1.98593e13i		−	0.448986i	0.974476	−	0.224493i	$-0.0720726\pi$
$90$		0			0
$91$	1.51570e13			0.293307
$92$	3.37753e13	+	1.95002e13i	0.605458	+	0.349562i
$93$		0			0
$94$	4.19846e13	+	7.27195e13i	0.647433	+	1.12139i
$95$	−3.52621e13	+	2.03586e13i	−0.504944	+	0.291529i
$96$		0			0
$97$	8.91638e12	−	1.54436e13i	0.110354	−	0.191138i	−0.805559	−	0.592515i	$-0.798135\pi$
$97$	8.91638e12	−	1.54436e13i	0.110354	−	0.191138i	0.915913	+	0.401377i	$0.131468\pi$
$98$		−	8.73064e13i		−	1.00569i
$99$		0			0
$100$	−2.84218e13			−0.284218
$101$	1.16665e12	+	6.73563e11i	0.0108815	+	0.00628245i	0.505431	−	0.862867i	$-0.331334\pi$
$101$	1.16665e12	+	6.73563e11i	0.0108815	+	0.00628245i	−0.494549	+	0.869150i	$0.664667\pi$
$102$		0			0
$103$	−1.12147e14	−	1.94245e14i	−0.911859	−	1.57939i	−0.811436	−	0.584441i	$-0.801314\pi$
$103$	−1.12147e14	−	1.94245e14i	−0.911859	−	1.57939i	−0.100423	−	0.994945i	$-0.532020\pi$
$104$	−6.63422e13	+	3.83027e13i	−0.504146	+	0.291069i
$105$		0			0
$106$	−1.55374e14	+	2.69116e14i	−1.03333	+	1.78977i
$107$		−	1.28823e14i		−	0.802244i	−0.916025	−	0.401122i	$-0.868620\pi$
$107$		−	1.28823e14i		−	0.802244i	0.916025	−	0.401122i	$-0.131380\pi$
$108$		0			0
$109$	−2.51082e14			−1.37351			−0.686753	−	0.726891i	$-0.740965\pi$
$109$	−2.51082e14			−1.37351			−0.686753	+	0.726891i	$0.740965\pi$
$110$	−4.45619e13	−	2.57278e13i	−0.228673	−	0.132024i
$111$		0			0
$112$	−5.08539e13	−	8.80816e13i	−0.230037	−	0.398436i
$113$	−2.29159e14	+	1.32305e14i	−0.974063	+	0.562376i	−0.900473	−	0.434913i	$-0.856779\pi$
$113$	−2.29159e14	+	1.32305e14i	−0.974063	+	0.562376i	−0.0735906	+	0.997289i	$0.523446\pi$
$114$		0			0
$115$	−1.20041e14	+	2.07918e14i	−0.451280	+	0.781640i
$116$		−	4.04151e13i		−	0.143001i
$117$		0			0
$118$	3.29664e14			1.03490
$119$	−4.27633e13	−	2.46894e13i	−0.126544	−	0.0730603i
$120$		0			0
$121$	−1.46409e14	−	2.53588e14i	−0.385541	−	0.667776i
$122$	−5.21721e14	+	3.01215e14i	−1.29694	+	0.748787i
$123$		0			0
$124$	3.20327e13	−	5.54822e13i	0.0710626	−	0.123084i
$125$		−	4.00138e14i		−	0.839150i
$126$		0			0
$127$	3.84344e14			0.721264			0.360632	−	0.932708i	$-0.382561\pi$
$127$	3.84344e14			0.721264			0.360632	+	0.932708i	$0.382561\pi$
$128$	5.77354e14	+	3.33335e14i	1.02559	+	0.592123i
$129$		0			0
$130$	1.35993e14	+	2.35547e14i	0.216727	+	0.375383i
$131$	6.99904e14	−	4.04090e14i	1.05716	−	0.610350i	0.132512	−	0.991181i	$-0.457696\pi$
$131$	6.99904e14	−	4.04090e14i	1.05716	−	0.610350i	0.924644	+	0.380832i	$0.124362\pi$
$132$		0			0
$133$	1.69713e14	−	2.93951e14i	0.230543	−	0.399313i
$134$		−	5.45267e14i		−	0.702871i
$135$		0			0
$136$	2.49567e14			0.290012
$137$	7.42632e14	+	4.28759e14i	0.819841	+	0.473335i	0.850362	−	0.526199i	$-0.176383\pi$
$137$	7.42632e14	+	4.28759e14i	0.819841	+	0.473335i	−0.0305207	+	0.999534i	$0.509717\pi$
$138$		0			0
$139$	4.71586e14	+	8.16811e14i	0.470389	+	0.814738i	0.999427	−	0.0338608i	$-0.0107803\pi$
$139$	4.71586e14	+	8.16811e14i	0.470389	+	0.814738i	−0.529038	+	0.848598i	$0.677447\pi$
$140$	−5.88885e13	+	3.39993e13i	−0.0558643	+	0.0322533i
$141$		0			0
$142$	3.44636e14	−	5.96927e14i	0.296034	−	0.512746i
$143$		−	4.59508e14i		−	0.375786i
$144$		0			0
$145$	2.48792e14			0.184612
$146$	1.88343e15	+	1.08740e15i	1.33193	+	0.768987i
$147$		0			0
$148$	−4.37394e14	−	7.57589e14i	−0.281217	−	0.487081i
$149$	−1.26645e15	+	7.31183e14i	−0.776753	+	0.448458i	−0.835278	−	0.549827i	$-0.814693\pi$
$149$	−1.26645e15	+	7.31183e14i	−0.776753	+	0.448458i	0.0585254	+	0.998286i	$0.481360\pi$
$150$		0			0
$151$	2.17909e14	−	3.77430e14i	0.121741	−	0.210862i	−0.798713	−	0.601712i	$-0.794486\pi$
$151$	2.17909e14	−	3.77430e14i	0.121741	−	0.210862i	0.920454	+	0.390850i	$0.127819\pi$
$152$			1.71550e15i			0.915138i
$153$		0			0
$154$	4.28943e14			0.208812
$155$	3.41544e14	+	1.97190e14i	0.158900	+	0.0917411i
$156$		0			0
$157$	2.39012e14	+	4.13981e14i	0.101653	+	0.176069i	0.912366	−	0.409376i	$-0.134253\pi$
$157$	2.39012e14	+	4.13981e14i	0.101653	+	0.176069i	−0.810713	+	0.585444i	$0.800920\pi$
$158$	−3.66248e15	+	2.11453e15i	−1.48996	+	0.860231i
$159$		0			0
$160$	4.42784e14	−	7.66924e14i	0.164950	−	0.285701i
$161$		−	2.00137e15i		−	0.713750i
$162$		0			0
$163$	−3.72556e15			−1.21865			−0.609325	−	0.792921i	$-0.708559\pi$
$163$	−3.72556e15			−1.21865			−0.609325	+	0.792921i	$0.708559\pi$
$164$	−1.13036e15	−	6.52611e14i	−0.354249	−	0.204526i
$165$		0			0
$166$	3.24430e14	+	5.61929e14i	0.0934037	+	0.161780i
$167$	2.33686e15	−	1.34919e15i	0.645086	−	0.372441i	−0.141485	−	0.989940i	$-0.545188\pi$
$167$	2.33686e15	−	1.34919e15i	0.645086	−	0.372441i	0.786571	+	0.617500i	$0.211854\pi$
$168$		0			0
$169$	7.54246e14	−	1.30639e15i	0.191560	−	0.331792i
$170$		−	8.86085e14i		−	0.215940i
$171$		0			0
$172$	−8.41813e14			−0.189024
$173$	2.06128e15	+	1.19008e15i	0.444441	+	0.256598i	0.705480	−	0.708730i	$-0.250732\pi$
$173$	2.06128e15	+	1.19008e15i	0.444441	+	0.256598i	−0.261039	+	0.965328i	$0.584065\pi$
$174$		0			0
$175$	7.29256e14	+	1.26311e15i	0.145082	+	0.251289i
$176$	−2.67034e15	+	1.54172e15i	−0.510478	+	0.294725i
$177$		0			0
$178$	−1.48537e15	+	2.57274e15i	−0.262358	+	0.454418i
$179$		−	9.72633e15i		−	1.65188i	−0.563761	−	0.825938i	$-0.690646\pi$
$179$		−	9.72633e15i		−	1.65188i	0.563761	−	0.825938i	$-0.309354\pi$
$180$		0			0
$181$	−7.95145e15			−1.24939			−0.624693	−	0.780871i	$-0.714776\pi$
$181$	−7.95145e15			−1.24939			−0.624693	+	0.780871i	$0.714776\pi$
$182$	−1.96356e15	−	1.13366e15i	−0.296855	−	0.171389i
$183$		0			0
$184$	5.05760e15	+	8.76003e15i	0.708305	+	1.22682i
$185$	4.66365e15	−	2.69256e15i	0.628817	−	0.363047i
$186$		0			0
$187$	−7.48499e14	+	1.29644e15i	−0.0936052	+	0.162129i
$188$		−	3.36409e15i		−	0.405287i
$189$		0			0
$190$	6.09087e15			0.681403
$191$	−5.81012e15	−	3.35448e15i	−0.626544	−	0.361736i	0.152868	−	0.988247i	$-0.451149\pi$
$191$	−5.81012e15	−	3.35448e15i	−0.626544	−	0.361736i	−0.779413	+	0.626511i	$0.784482\pi$
$192$		0			0
$193$	−7.23820e15	−	1.25369e16i	−0.725653	−	1.25687i	−0.958705	−	0.284404i	$-0.908204\pi$
$193$	−7.23820e15	−	1.25369e16i	−0.725653	−	1.25687i	0.233051	−	0.972464i	$-0.425129\pi$
$194$	−2.31021e15	+	1.33380e15i	−0.223377	+	0.128967i
$195$		0			0
$196$	−1.74890e15	+	3.02918e15i	−0.157388	+	0.272604i
$197$			8.61721e15i			0.748347i	0.927359	+	0.374174i	$0.122074\pi$
$197$			8.61721e15i			0.748347i	−0.927359	+	0.374174i	$0.877926\pi$
$198$		0			0
$199$	−2.20192e15			−0.178168			−0.0890842	−	0.996024i	$-0.528394\pi$
$199$	−2.20192e15			−0.178168			−0.0890842	+	0.996024i	$0.528394\pi$
$200$	−6.38393e15	−	3.68576e15i	−0.498744	−	0.287950i
$201$		0			0
$202$	−1.00758e14	−	1.74518e14i	−0.00734210	−	0.0127169i
$203$	−1.79611e15	+	1.03699e15i	−0.126433	+	0.0729962i
$204$		0			0
$205$	4.01742e15	−	6.95837e15i	0.264040	−	0.457331i
$206$			3.35521e16i			2.13132i
$207$		0			0
$208$	1.62986e16			0.967623
$209$	−8.91160e15	−	5.14511e15i	−0.511601	−	0.295373i
$210$		0			0
$211$	−9.35311e15	−	1.62001e16i	−0.502318	−	0.870040i	−0.999996	−	0.00267859i	$-0.999147\pi$
$211$	−9.35311e15	−	1.62001e16i	−0.502318	−	0.870040i	0.497678	−	0.867362i	$-0.334186\pi$
$212$	1.07817e16	−	6.22481e15i	0.560191	−	0.323426i
$213$		0			0
$214$	−9.63528e15	+	1.66888e16i	−0.468779	+	0.811949i
$215$		−	5.18213e15i		−	0.244028i
$216$		0			0
$217$	−3.28762e15			−0.145099
$218$	3.25273e16	+	1.87797e16i	1.39012	+	0.802587i
$219$		0			0
$220$	1.03074e15	+	1.78530e15i	0.0413230	+	0.0715736i
$221$	6.85276e15	−	3.95645e15i	0.266146	−	0.153659i
$222$		0			0
$223$	−4.64056e15	+	8.03769e15i	−0.169214	+	0.293087i	−0.938144	−	0.346246i	$-0.887456\pi$
$223$	−4.64056e15	+	8.03769e15i	−0.169214	+	0.293087i	0.768930	+	0.639333i	$0.220790\pi$
$224$			7.38224e15i			0.260887i
$225$		0			0
$226$	3.95829e16			1.31446
$227$	−1.03337e16	−	5.96619e15i	−0.332718	−	0.192095i	0.324329	−	0.945944i	$-0.394861\pi$
$227$	−1.03337e16	−	5.96619e15i	−0.332718	−	0.192095i	−0.657047	+	0.753849i	$0.728195\pi$
$228$		0			0
$229$	−8.37085e14	−	1.44987e15i	−0.0253467	−	0.0439018i	0.853074	−	0.521790i	$-0.174736\pi$
$229$	−8.37085e14	−	1.44987e15i	−0.0253467	−	0.0439018i	−0.878421	+	0.477888i	$0.841402\pi$
$230$	3.11023e16	−	1.79569e16i	0.913479	−	0.527397i
$231$		0			0
$232$	5.24107e15	−	9.07780e15i	0.144879	−	0.250937i
$233$			8.13317e15i			0.218157i	0.994033	+	0.109078i	$0.0347899\pi$
$233$			8.13317e15i			0.218157i	−0.994033	+	0.109078i	$0.965210\pi$
$234$		0			0
$235$	2.07091e16			0.523221
$236$	−1.14380e16	−	6.60372e15i	−0.280521	−	0.161959i
$237$		0			0
$238$	3.69328e15	+	6.39694e15i	0.0853833	+	0.147888i
$239$	2.32813e16	−	1.34415e16i	0.522664	−	0.301760i	−0.215360	−	0.976535i	$-0.569093\pi$
$239$	2.32813e16	−	1.34415e16i	0.522664	−	0.301760i	0.738024	+	0.674775i	$0.235759\pi$
$240$		0			0
$241$	4.02326e16	−	6.96849e16i	0.852037	−	1.47577i	−0.0273297	−	0.999626i	$-0.508700\pi$
$241$	4.02326e16	−	6.96849e16i	0.852037	−	1.47577i	0.879367	−	0.476145i	$-0.157966\pi$
$242$			4.38026e16i			0.901139i
$243$		0			0
$244$	2.41354e16			0.468734
$245$	−1.86474e16	−	1.07661e16i	−0.351929	−	0.203186i
$246$		0			0
$247$	2.71963e16	+	4.71053e16i	0.484876	+	0.839829i
$248$	1.43900e16	−	8.30806e15i	0.249401	−	0.143992i
$249$		0			0
$250$	−2.99282e16	+	5.18372e16i	−0.490344	+	0.849301i
$251$		−	3.03882e16i		−	0.484159i	−0.970256	−	0.242080i	$-0.922170\pi$
$251$		−	3.03882e16i		−	0.484159i	0.970256	−	0.242080i	$-0.0778295\pi$
$252$		0			0
$253$	−6.06748e16			−0.914460
$254$	−4.97912e16	−	2.87470e16i	−0.729989	−	0.421460i
$255$		0			0
$256$	−3.48917e16	−	6.04342e16i	−0.484219	−	0.838693i
$257$	−2.70003e16	+	1.55886e16i	−0.364617	+	0.210511i	−0.671104	−	0.741363i	$-0.734180\pi$
$257$	−2.70003e16	+	1.55886e16i	−0.364617	+	0.210511i	0.306487	+	0.951875i	$0.400846\pi$
$258$		0			0
$259$	−2.24456e16	+	3.88770e16i	−0.287100	+	0.497272i
$260$		−	1.08967e16i		−	0.135669i
$261$		0			0
$262$	−1.20895e17			−1.42659
$263$	−7.00721e16	−	4.04561e16i	−0.805109	−	0.464830i	0.0401454	−	0.999194i	$-0.487218\pi$
$263$	−7.00721e16	−	4.04561e16i	−0.805109	−	0.464830i	−0.845255	+	0.534364i	$0.820551\pi$
$264$		0			0
$265$	3.83194e16	+	6.63711e16i	0.417539	+	0.723200i
$266$	−4.39720e16	+	2.53873e16i	−0.466665	+	0.269429i
$267$		0			0
$268$	−1.09226e16	+	1.89185e16i	−0.109998	+	0.190522i
$269$			1.11604e17i			1.09500i	0.836805	+	0.547501i	$0.184421\pi$
$269$			1.11604e17i			1.09500i	−0.836805	+	0.547501i	$0.815579\pi$
$270$		0			0
$271$	−2.03175e17			−1.89272			−0.946360	−	0.323115i	$-0.895270\pi$
$271$	−2.03175e17			−1.89272			−0.946360	+	0.323115i	$0.895270\pi$
$272$	−4.59842e16	−	2.65490e16i	−0.417471	−	0.241027i
$273$		0			0
$274$	−6.41379e16	−	1.11090e17i	−0.553173	−	0.958123i
$275$	3.82932e16	−	2.21086e16i	0.321953	−	0.185880i
$276$		0			0
$277$	4.89924e16	−	8.48574e16i	0.391535	−	0.678158i	−0.601117	−	0.799161i	$-0.705278\pi$
$277$	4.89924e16	−	8.48574e16i	0.391535	−	0.678158i	0.992652	+	0.121002i	$0.0386109\pi$
$278$		−	1.41089e17i		−	1.09946i
$279$		0			0
$280$	−1.76363e16			−0.130707
$281$	5.09960e16	+	2.94426e16i	0.368631	+	0.212829i	0.672860	−	0.739770i	$-0.265065\pi$
$281$	5.09960e16	+	2.94426e16i	0.368631	+	0.212829i	−0.304229	+	0.952599i	$0.598399\pi$
$282$		0			0
$283$	1.30701e17	+	2.26381e17i	0.899028	+	1.55716i	0.828738	+	0.559636i	$0.189059\pi$
$283$	1.30701e17	+	2.26381e17i	0.899028	+	1.55716i	0.0702902	+	0.997527i	$0.477607\pi$
$284$	−2.39149e16	+	1.38073e16i	−0.160487	+	0.0926574i
$285$		0			0
$286$	−3.43688e16	+	5.95285e16i	−0.219585	+	0.380332i
$287$			6.69798e16i			0.417609i
$288$		0			0
$289$	1.42599e17			0.846899
$290$	−3.22306e16	−	1.86083e16i	−0.186845	−	0.107875i
$291$		0			0
$292$	−4.35649e16	−	7.54567e16i	−0.240690	−	0.416886i
$293$	4.72349e16	−	2.72711e16i	0.254795	−	0.147106i	−0.367163	−	0.930157i	$-0.619671\pi$
$293$	4.72349e16	−	2.72711e16i	0.254795	−	0.147106i	0.621958	+	0.783051i	$0.286338\pi$
$294$		0			0
$295$	4.06519e16	−	7.04112e16i	0.209087	−	0.362149i
$296$		−	2.26887e17i		−	1.13964i
$297$		0			0
$298$	2.18755e17			1.04820
$299$	2.77749e17	+	1.60359e17i	1.30003	+	0.750575i
$300$		0			0
$301$	2.15996e16	+	3.74115e16i	0.0964893	+	0.167124i
$302$	−5.64596e16	+	3.25970e16i	−0.246428	+	0.142275i
$303$		0			0
$304$	1.82495e17	−	3.16091e17i	0.760565	−	1.31734i
$305$			1.48576e17i			0.605130i
$306$		0			0
$307$	2.69380e17			1.04809			0.524043	−	0.851692i	$-0.324423\pi$
$307$	2.69380e17			1.04809			0.524043	+	0.851692i	$0.324423\pi$
$308$	−1.48826e16	−	8.59246e15i	−0.0566009	−	0.0326785i
$309$		0			0
$310$	−2.94976e16	−	5.10914e16i	−0.107215	−	0.185702i
$311$	−1.15333e17	+	6.65875e16i	−0.409855	+	0.236630i	−0.690727	−	0.723115i	$-0.742710\pi$
$311$	−1.15333e17	+	6.65875e16i	−0.409855	+	0.236630i	0.280872	+	0.959745i	$0.409376\pi$
$312$		0			0
$313$	−1.05131e17	+	1.82092e17i	−0.357206	+	0.618699i	−0.987493	−	0.157663i	$-0.949604\pi$
$313$	−1.05131e17	+	1.82092e17i	−0.357206	+	0.618699i	0.630287	+	0.776362i	$0.282937\pi$
$314$		−	7.15074e16i		−	0.237598i
$315$		0			0
$316$	1.69431e17			0.538497
$317$	3.44228e17	+	1.98740e17i	1.07012	+	0.617833i	0.928214	−	0.372047i	$-0.121344\pi$
$317$	3.44228e17	+	1.98740e17i	1.07012	+	0.617833i	0.141904	+	0.989880i	$0.454677\pi$
$318$		0			0
$319$	3.14379e16	+	5.44520e16i	0.0935231	+	0.161987i
$320$	5.83927e16	−	3.37130e16i	0.169945	−	0.0981179i
$321$		0			0
$322$	−1.49692e17	+	2.59274e17i	−0.417069	+	0.722385i
$323$		−	1.77201e17i		−	0.483114i
$324$		0			0
$325$	−2.33725e17			−0.610269
$326$	4.82641e17	+	2.78653e17i	1.23339	+	0.712099i
$327$		0			0
$328$	−1.69263e17	−	2.93171e17i	−0.414423	−	0.717802i
$329$	−1.49506e17	+	8.63171e16i	−0.358333	+	0.206883i
$330$		0			0
$331$	4.50209e15	−	7.79784e15i	0.0103423	−	0.0179134i	−0.860808	−	0.508930i	$-0.830041\pi$
$331$	4.50209e15	−	7.79784e15i	0.0103423	−	0.0179134i	0.871150	+	0.491017i	$0.163375\pi$
$332$		−	2.59955e16i		−	0.0584698i
$333$		0			0
$334$	−4.03649e17			−0.870520
$335$	−1.16461e17	−	6.72388e16i	−0.245961	−	0.142006i
$336$		0			0
$337$	−3.10938e16	−	5.38560e16i	−0.0629889	−	0.109100i	0.832811	−	0.553557i	$-0.186730\pi$
$337$	−3.10938e16	−	5.38560e16i	−0.0629889	−	0.109100i	−0.895800	+	0.444457i	$0.853397\pi$
$338$	−1.95423e17	+	1.12827e17i	−0.387756	+	0.223871i
$339$		0			0
$340$	−1.77498e16	+	3.07435e16i	−0.0337941	+	0.0585331i
$341$			9.96697e16i			0.185901i
$342$		0			0
$343$	3.88079e17			0.694803
$344$	−1.89083e17	−	1.09167e17i	−0.331699	−	0.191506i
$345$		0			0
$346$	−1.78024e17	−	3.08346e17i	−0.299878	−	0.519404i
$347$	−8.66876e17	+	5.00491e17i	−1.43104	+	0.826209i	−0.997200	−	0.0747825i	$-0.976174\pi$
$347$	−8.66876e17	+	5.00491e17i	−1.43104	+	0.826209i	−0.433836	+	0.900992i	$0.642840\pi$
$348$		0			0
$349$	1.50217e17	−	2.60184e17i	0.238200	−	0.412574i	−0.721998	−	0.691895i	$-0.756776\pi$
$349$	1.50217e17	−	2.60184e17i	0.238200	−	0.412574i	0.960198	+	0.279321i	$0.0901093\pi$
$350$		−	2.18178e17i		−	0.339106i
$351$		0			0
$352$	2.23805e17			0.334249
$353$	−9.01012e17	−	5.20199e17i	−1.31919	−	0.761635i	−0.335592	−	0.942007i	$-0.608936\pi$
$353$	−9.01012e17	−	5.20199e17i	−1.31919	−	0.761635i	−0.983598	+	0.180372i	$0.942270\pi$
$354$		0			0
$355$	−8.49965e16	−	1.47218e17i	−0.119620	−	0.207187i
$356$	1.03073e17	−	5.95090e16i	0.142231	−	0.0821169i
$357$		0			0
$358$	−7.27479e17	+	1.26003e18i	−0.965249	+	1.67186i
$359$			8.63108e15i			0.0112306i	0.999984	+	0.00561531i	$0.00178742\pi$
$359$			8.63108e15i			0.0112306i	−0.999984	+	0.00561531i	$0.998213\pi$
$360$		0			0
$361$	4.19060e17			0.524476
$362$	1.03010e18	+	5.94728e17i	1.26450	+	0.730059i
$363$		0			0
$364$	4.54184e16	+	7.86669e16i	0.0536441	+	0.0929143i
$365$	4.64505e17	−	2.68182e17i	0.538196	−	0.310727i
$366$		0			0
$367$	−1.35662e17	+	2.34973e17i	−0.151285	+	0.262033i	−0.931700	−	0.363228i	$-0.881674\pi$
$367$	−1.35662e17	+	2.34973e17i	−0.151285	+	0.262033i	0.780415	+	0.625262i	$0.215008\pi$
$368$		−	2.15211e18i		−	2.35467i
$369$		0			0
$370$	−8.05558e17			−0.848565
$371$	−5.53281e17	−	3.19437e17i	−0.571911	−	0.330193i
$372$		0			0
$373$	2.65636e17	+	4.60096e17i	0.264439	+	0.458022i	0.967417	−	0.253190i	$-0.0814799\pi$
$373$	2.65636e17	+	4.60096e17i	0.264439	+	0.458022i	−0.702977	+	0.711212i	$0.748147\pi$
$374$	1.93934e17	−	1.11968e17i	0.189475	−	0.109393i
$375$		0			0
$376$	4.36259e17	−	7.55623e17i	0.410610	−	0.711197i
$377$		−	3.32351e17i		−	0.307049i
$378$		0			0
$379$	−8.22885e17			−0.732597			−0.366298	−	0.930497i	$-0.619375\pi$
$379$	−8.22885e17			−0.732597			−0.366298	+	0.930497i	$0.619375\pi$
$380$	−2.11328e17	−	1.22010e17i	−0.184702	−	0.106638i
$381$		0			0
$382$	5.01795e17	+	8.69135e17i	0.422749	+	0.732223i
$383$	1.14603e18	−	6.61659e17i	0.947989	−	0.547322i	0.0555336	−	0.998457i	$-0.482314\pi$
$383$	1.14603e18	−	6.61659e17i	0.947989	−	0.547322i	0.892456	+	0.451135i	$0.148981\pi$
$384$		0			0
$385$	5.28944e16	−	9.16158e16i	0.0421876	−	0.0730711i
$386$			2.16552e18i			1.69610i
$387$		0			0
$388$	1.06873e17			0.0807320
$389$	−6.27576e17	−	3.62331e17i	−0.465607	−	0.268818i	0.248792	−	0.968557i	$-0.419966\pi$
$389$	−6.27576e17	−	3.62331e17i	−0.465607	−	0.268818i	−0.714399	+	0.699739i	$0.753300\pi$
$390$		0			0
$391$	−5.22421e17	−	9.04860e17i	−0.373924	−	0.647655i
$392$	−7.85653e17	+	4.53597e17i	−0.552368	+	0.318910i
$393$		0			0
$394$	6.44523e17	−	1.11635e18i	0.437285	−	0.757400i
$395$			1.04300e18i			0.695193i
$396$		0			0
$397$	−1.88478e18			−1.21262			−0.606312	−	0.795227i	$-0.707352\pi$
$397$	−1.88478e18			−1.21262			−0.606312	+	0.795227i	$0.707352\pi$
$398$	2.85256e17	+	1.64692e17i	0.180324	+	0.104110i
$399$		0			0
$400$	7.84183e17	+	1.35824e18i	0.478627	+	0.829007i
$401$	−4.19505e17	+	2.42201e17i	−0.251609	+	0.145267i	−0.620501	−	0.784206i	$-0.713071\pi$
$401$	−4.19505e17	+	2.42201e17i	−0.251609	+	0.145267i	0.368892	+	0.929472i	$0.379737\pi$
$402$		0			0
$403$	2.63419e17	−	4.56255e17i	0.152585	−	0.264285i
$404$			8.07343e15i			0.00459609i
$405$		0			0
$406$	3.10245e17			0.170617
$407$	1.17862e18	+	6.80476e17i	0.637107	+	0.367834i
$408$		0			0
$409$	−1.19864e17	−	2.07611e17i	−0.0626076	−	0.108440i	0.833023	−	0.553239i	$-0.186608\pi$
$409$	−1.19864e17	−	2.07611e17i	−0.0626076	−	0.108440i	−0.895630	+	0.444799i	$0.853275\pi$
$410$	−1.04090e18	+	6.00964e17i	−0.534469	+	0.308576i
$411$		0			0
$412$	6.72106e17	−	1.16412e18i	0.333547	−	0.577721i
$413$			6.77763e17i			0.330695i
$414$		0			0
$415$	1.60026e17			0.0754839
$416$	−1.02450e18	−	5.91498e17i	−0.475182	−	0.274347i
$417$		0			0
$418$	7.69656e17	+	1.33308e18i	0.345193	+	0.597893i
$419$	1.28482e18	−	7.41793e17i	0.566689	−	0.327178i	−0.189137	−	0.981951i	$-0.560569\pi$
$419$	1.28482e18	−	7.41793e17i	0.566689	−	0.327178i	0.755826	+	0.654772i	$0.227236\pi$
$420$		0			0
$421$	6.07915e17	−	1.05294e18i	0.259339	−	0.449189i	−0.706726	−	0.707488i	$-0.749829\pi$
$421$	6.07915e17	−	1.05294e18i	0.259339	−	0.449189i	0.966065	+	0.258299i	$0.0831619\pi$
$422$			2.79826e18i			1.17409i
$423$		0			0
$424$	3.22896e18			1.31069
$425$	6.59422e17	+	3.80718e17i	0.263294	+	0.152013i
$426$		0			0
$427$	−6.19276e17	−	1.07262e18i	−0.239270	−	0.414429i
$428$	6.68610e17	−	3.86022e17i	0.254136	−	0.146726i
$429$		0			0
$430$	−3.87597e17	+	6.71337e17i	−0.142594	+	0.246980i
$431$			2.13220e18i			0.771770i	0.922547	+	0.385885i	$0.126104\pi$
$431$			2.13220e18i			0.771770i	−0.922547	+	0.385885i	$0.873896\pi$
$432$		0			0
$433$	1.46090e18			0.511925			0.255962	−	0.966687i	$-0.417608\pi$
$433$	1.46090e18			0.511925			0.255962	+	0.966687i	$0.417608\pi$
$434$	4.25907e17	+	2.45897e17i	0.146854	+	0.0847863i
$435$		0			0
$436$	−7.52377e17	−	1.30316e18i	−0.251206	−	0.435102i
$437$	6.21992e18	−	3.59107e18i	2.04369	−	1.17992i
$438$		0			0
$439$	−9.07022e16	+	1.57101e17i	−0.0288647	+	0.0499951i	−0.880097	−	0.474794i	$-0.842523\pi$
$439$	−9.07022e16	+	1.57101e17i	−0.0288647	+	0.0499951i	0.851232	+	0.524789i	$0.175856\pi$
$440$			5.34672e17i			0.167463i
$441$		0			0
$442$	−1.18369e18			−0.359154
$443$	−2.55792e18	−	1.47681e18i	−0.763942	−	0.441062i	0.0667673	−	0.997769i	$-0.478731\pi$
$443$	−2.55792e18	−	1.47681e18i	−0.763942	−	0.441062i	−0.830709	+	0.556706i	$0.812065\pi$
$444$		0			0
$445$	3.66332e17	+	6.34506e17i	0.106012	+	0.183618i
$446$	1.20236e18	−	6.94180e17i	0.342522	−	0.197755i
$447$		0			0
$448$	−2.81038e17	+	4.86772e17i	−0.0775923	+	0.134394i
$449$		−	6.59664e18i		−	1.79307i	−0.442969	−	0.896537i	$-0.646075\pi$
$449$		−	6.59664e18i		−	1.79307i	0.442969	−	0.896537i	$-0.353925\pi$
$450$		0			0
$451$	2.03060e18			0.535043
$452$	−1.37336e18	−	7.92912e17i	−0.356301	−	0.205710i
$453$		0			0
$454$	8.92480e17	+	1.54582e18i	0.224496	+	0.388838i
$455$	−4.84267e17	+	2.79592e17i	−0.119951	+	0.0692539i
$456$		0			0
$457$	−2.96363e18	+	5.13316e18i	−0.711886	+	1.23302i	0.252262	+	0.967659i	$0.418826\pi$
$457$	−2.96363e18	+	5.13316e18i	−0.711886	+	1.23302i	−0.964148	+	0.265364i	$0.914508\pi$
$458$			2.50439e17i			0.0592438i
$459$		0			0
$460$	−1.43883e18			−0.330146
$461$	−8.24105e17	−	4.75797e17i	−0.186241	−	0.107526i	0.403980	−	0.914768i	$-0.367626\pi$
$461$	−8.24105e17	−	4.75797e17i	−0.186241	−	0.107526i	−0.590222	+	0.807241i	$0.700960\pi$
$462$		0			0
$463$	−9.26244e17	−	1.60430e18i	−0.203076	−	0.351738i	0.746442	−	0.665450i	$-0.231760\pi$
$463$	−9.26244e17	−	1.60430e18i	−0.203076	−	0.351738i	−0.949518	+	0.313713i	$0.898427\pi$
$464$	−1.93139e18	+	1.11509e18i	−0.417105	+	0.240815i
$465$		0			0
$466$	6.08319e17	−	1.05364e18i	0.127476	−	0.220796i
$467$			7.47533e18i			1.54316i	0.636130	+	0.771582i	$0.280534\pi$
$467$			7.47533e18i			1.54316i	−0.636130	+	0.771582i	$0.719466\pi$
$468$		0			0
$469$	1.12103e18			0.224598
$470$	−2.68283e18	−	1.54893e18i	−0.529551	−	0.305736i
$471$		0			0
$472$	−1.71276e18	−	2.96658e18i	−0.328172	−	0.568410i
$473$	1.13419e18	−	6.54825e17i	0.214120	−	0.123623i
$474$		0			0
$475$	−2.61702e18	+	4.53281e18i	−0.479680	+	0.830830i
$476$		−	2.95931e17i		−	0.0534492i
$477$		0			0
$478$	−4.02141e18			−0.705315
$479$	−9.05226e18	−	5.22633e18i	−1.56462	−	0.903333i	−0.996779	−	0.0801943i	$-0.974446\pi$
$479$	−9.05226e18	−	5.22633e18i	−1.56462	−	0.903333i	−0.567840	−	0.823139i	$-0.692221\pi$
$480$		0			0
$481$	−3.59689e18	−	6.22999e18i	−0.603825	−	1.04586i
$482$	−1.04241e19	+	6.01838e18i	−1.72469	+	0.995750i
$483$		0			0
$484$	8.77440e17	−	1.51977e18i	0.141026	−	0.244265i
$485$			6.57901e17i			0.104224i
$486$		0			0
$487$	−2.32289e18			−0.357540			−0.178770	−	0.983891i	$-0.557212\pi$
$487$	−2.32289e18			−0.357540			−0.178770	+	0.983891i	$0.557212\pi$
$488$	5.42116e18	+	3.12991e18i	0.822533	+	0.474890i
$489$		0			0
$490$	1.61049e18	+	2.78945e18i	0.237457	+	0.411288i
$491$	−7.15665e17	+	4.13190e17i	−0.104025	+	0.0600591i	−0.551110	−	0.834433i	$-0.685796\pi$
$491$	−7.15665e17	+	4.13190e17i	−0.104025	+	0.0600591i	0.447085	+	0.894492i	$0.352462\pi$
$492$		0			0
$493$	−5.41372e17	+	9.37684e17i	−0.0764834	+	0.132473i
$494$		−	8.13656e18i		−	1.13332i
$495$		0			0
$496$	−3.53525e18			−0.478683
$497$	1.22724e18	+	7.08545e17i	0.163845	+	0.0945960i
$498$		0			0
$499$	−1.87636e18	−	3.24996e18i	−0.243564	−	0.421865i	0.718163	−	0.695875i	$-0.244983\pi$
$499$	−1.87636e18	−	3.24996e18i	−0.243564	−	0.421865i	−0.961727	+	0.274010i	$0.911650\pi$
$500$	2.07678e18	−	1.19903e18i	0.265827	−	0.153476i
$501$		0			0
$502$	−2.27288e18	+	3.93674e18i	−0.282911	+	0.490016i
$503$		−	7.53136e18i		−	0.924480i	−0.886755	−	0.462240i	$-0.847046\pi$
$503$		−	7.53136e18i		−	0.924480i	0.886755	−	0.462240i	$-0.152954\pi$
$504$		0			0
$505$	−4.96993e16			−0.00593350
$506$	7.86032e18	+	4.53816e18i	0.925522	+	0.534351i
$507$		0			0
$508$	1.15170e18	+	1.99481e18i	0.131915	+	0.228483i
$509$	4.04899e17	−	2.33769e17i	0.0457428	−	0.0264096i	−0.476954	−	0.878928i	$-0.658259\pi$
$509$	4.04899e17	−	2.33769e17i	0.0457428	−	0.0264096i	0.522697	+	0.852519i	$0.324926\pi$
$510$		0			0
$511$	−2.23561e18	+	3.87219e18i	−0.245725	+	0.425609i
$512$		−	4.83866e17i		−	0.0524608i
$513$		0			0
$514$	4.66379e18			0.492037
$515$	7.16623e18	+	4.13743e18i	0.745831	+	0.430606i
$516$		0			0
$517$	2.61684e18	+	4.53251e18i	0.265060	+	0.459097i
$518$	5.81560e18	−	3.35764e18i	0.581147	−	0.335525i
$519$		0			0
$520$	1.41310e18	−	2.44755e18i	0.137451	−	0.238072i
$521$			1.30139e19i			1.24894i	0.781048	+	0.624471i	$0.214685\pi$
$521$			1.30139e19i			1.24894i	−0.781048	+	0.624471i	$0.785315\pi$
$522$		0			0
$523$	1.02060e19			0.953549			0.476775	−	0.879026i	$-0.341806\pi$
$523$	1.02060e19			0.953549			0.476775	+	0.879026i	$0.341806\pi$
$524$	4.19457e18	+	2.42174e18i	0.386695	+	0.223259i
$525$		0			0
$526$	6.05182e18	+	1.04821e19i	0.543233	+	0.940906i
$527$	−1.48640e18	+	8.58174e17i	−0.131662	+	0.0760153i
$528$		0			0
$529$	1.53778e19	−	2.66352e19i	1.32649	−	2.29755i
$530$		−	1.14644e19i		−	0.975931i
$531$		0			0
$532$	2.03420e18			0.168660
$533$	−9.29542e18	−	5.36671e18i	−0.760639	−	0.439155i
$534$		0			0
$535$	2.37632e18	+	4.11590e18i	0.189421	+	0.328087i
$536$	−4.90675e18	+	2.83292e18i	−0.386047	+	0.222885i
$537$		0			0
$538$	8.34743e18	−	1.44582e19i	0.639848	−	1.10825i
$539$		−	5.44169e18i		−	0.411730i
$540$		0			0
$541$	9.12458e18			0.672717			0.336358	−	0.941734i	$-0.390805\pi$
$541$	9.12458e18			0.672717			0.336358	+	0.941734i	$0.390805\pi$
$542$	2.63211e19	+	1.51965e19i	1.91562	+	1.10598i
$543$		0			0
$544$	1.92700e18	+	3.33766e18i	0.136675	+	0.236728i
$545$	8.02211e18	−	4.63157e18i	0.561712	−	0.324304i
$546$		0			0
$547$	−7.61351e18	+	1.31870e19i	−0.519605	+	0.899983i	0.480135	+	0.877195i	$0.340588\pi$
$547$	−7.61351e18	+	1.31870e19i	−0.519605	+	0.899983i	−0.999740	+	0.0227881i	$0.992746\pi$
$548$			5.13916e18i			0.346281i
$549$		0			0
$550$	−6.61443e18			−0.434464
$551$	−6.44556e18	−	3.72134e18i	−0.418022	−	0.241345i
$552$		0			0
$553$	−4.34732e18	−	7.52978e18i	−0.274882	−	0.476109i
$554$	−1.26938e19	+	7.32876e18i	−0.792543	+	0.457575i
$555$		0			0
$556$	−2.82625e18	+	4.89521e18i	−0.172063	+	0.298021i
$557$			1.48868e19i			0.894986i	0.894287	+	0.447493i	$0.147683\pi$
$557$			1.48868e19i			0.894986i	−0.894287	+	0.447493i	$0.852317\pi$
$558$		0			0
$559$	−6.92261e18			−0.405870
$560$	3.24958e18	+	1.87615e18i	0.188153	+	0.108630i
$561$		0			0
$562$	−4.40431e18	−	7.62848e18i	−0.248727	−	0.430808i
$563$	−2.24592e19	+	1.29669e19i	−1.25267	+	0.723229i	−0.971639	−	0.236470i	$-0.924009\pi$
$563$	−2.24592e19	+	1.29669e19i	−1.25267	+	0.723229i	−0.281030	+	0.959699i	$0.590676\pi$
$564$		0			0
$565$	4.88110e18	−	8.45431e18i	0.265570	−	0.459980i
$566$		−	3.91030e19i		−	2.10133i
$567$		0			0
$568$	−7.16217e18			−0.375497
$569$	2.14534e19	+	1.23861e19i	1.11099	+	0.641430i	0.939085	−	0.343684i	$-0.111675\pi$
$569$	2.14534e19	+	1.23861e19i	1.11099	+	0.641430i	0.171904	+	0.985114i	$0.445008\pi$
$570$		0			0
$571$	9.73630e18	+	1.68638e19i	0.491973	+	0.852122i	0.999957	−	0.00924399i	$-0.00294250\pi$
$571$	9.73630e18	+	1.68638e19i	0.491973	+	0.852122i	−0.507984	+	0.861366i	$0.669609\pi$
$572$	2.38492e18	−	1.37693e18i	0.119042	−	0.0687290i
$573$		0			0
$574$	5.00974e18	−	8.67712e18i	0.244024	−	0.422661i
$575$			3.08617e19i			1.48506i
$576$		0			0
$577$	−3.59726e19			−1.68943			−0.844716	−	0.535215i	$-0.820231\pi$
$577$	−3.59726e19			−1.68943			−0.844716	+	0.535215i	$0.820231\pi$
$578$	−1.84735e19	−	1.06657e19i	−0.857144	−	0.494872i
$579$		0			0
$580$	7.45514e17	+	1.29127e18i	0.0337645	+	0.0584818i
$581$	−1.15528e18	+	6.67003e17i	−0.0516958	+	0.0298466i
$582$		0			0
$583$	−9.68425e18	+	1.67736e19i	−0.423045	+	0.732735i
$584$		−	2.25982e19i		−	0.975402i
$585$		0			0
$586$	−8.15895e18			−0.343836
$587$	−1.86467e19	−	1.07657e19i	−0.776487	−	0.448305i	0.0586968	−	0.998276i	$-0.481305\pi$
$587$	−1.86467e19	−	1.07657e19i	−0.776487	−	0.448305i	−0.835184	+	0.549971i	$0.814639\pi$
$588$		0			0
$589$	−5.89901e18	−	1.02174e19i	−0.239868	−	0.415463i
$590$	−1.05328e19	+	6.08111e18i	−0.423233	+	0.244354i
$591$		0			0
$592$	−2.41362e19	+	4.18052e19i	−0.947147	+	1.64051i
$593$		−	3.06383e18i		−	0.118818i	−0.998234	−	0.0594090i	$-0.981078\pi$
$593$		−	3.06383e18i		−	0.118818i	0.998234	−	0.0594090i	$-0.0189216\pi$
$594$		0			0
$595$	1.82172e18			0.0690023
$596$	−7.58990e18	−	4.38203e18i	−0.284127	−	0.164041i
$597$		0			0
$598$	−2.39880e19	−	4.15484e19i	−0.877174	−	1.51931i
$599$	3.56687e19	−	2.05933e19i	1.28914	−	0.744284i	0.310638	−	0.950528i	$-0.399457\pi$
$599$	3.56687e19	−	2.05933e19i	1.28914	−	0.744284i	0.978501	+	0.206244i	$0.0661241\pi$
$600$		0			0
$601$	4.81655e17	−	8.34251e17i	0.0170065	−	0.0294561i	−0.857397	−	0.514656i	$-0.827920\pi$
$601$	4.81655e17	−	8.34251e17i	0.0170065	−	0.0294561i	0.874403	+	0.485200i	$0.161253\pi$
$602$		−	6.46214e18i		−	0.225528i
$603$		0			0
$604$	2.61189e18			0.0890629
$605$	9.35558e18	+	5.40144e18i	0.315343	+	0.182063i
$606$		0			0
$607$	2.72777e19	+	4.72464e19i	0.898435	+	1.55614i	0.829495	+	0.558515i	$0.188629\pi$
$607$	2.72777e19	+	4.72464e19i	0.898435	+	1.55614i	0.0689407	+	0.997621i	$0.478038\pi$
$608$	−2.29428e19	+	1.32460e19i	−0.747000	+	0.431281i
$609$		0			0
$610$	1.11127e19	−	1.92477e19i	0.353599	−	0.612451i
$611$		−	2.76644e19i		−	0.870229i
$612$		0			0
$613$	5.06895e19			1.55846			0.779228	−	0.626741i	$-0.215611\pi$
$613$	5.06895e19			1.55846			0.779228	+	0.626741i	$0.215611\pi$
$614$	−3.48978e19	−	2.01482e19i	−1.06077	−	0.612433i
$615$		0			0
$616$	−2.22856e18	−	3.85997e18i	−0.0662154	−	0.114688i
$617$	−4.13254e18	+	2.38592e18i	−0.121401	+	0.0700907i	−0.559471	−	0.828850i	$-0.688996\pi$
$617$	−4.13254e18	+	2.38592e18i	−0.121401	+	0.0700907i	0.438070	+	0.898941i	$0.355662\pi$
$618$		0			0
$619$	3.09682e18	−	5.36384e18i	0.0889367	−	0.154043i	−0.818125	−	0.575040i	$-0.804986\pi$
$619$	3.09682e18	−	5.36384e18i	0.0889367	−	0.154043i	0.907062	+	0.420997i	$0.138320\pi$
$620$			2.36355e18i			0.0671156i
$621$		0			0
$622$	1.99216e19			0.553084
$623$	−5.28935e18	−	3.05381e18i	−0.145206	−	0.0838350i
$624$		0			0
$625$	−7.09165e18	−	1.22831e19i	−0.190365	−	0.329722i
$626$	2.72390e19	−	1.57265e19i	0.723055	−	0.417456i
$627$		0			0
$628$	−1.43242e18	+	2.48102e18i	−0.0371836	+	0.0644039i
$629$			2.34361e19i			0.601631i
$630$		0			0
$631$	1.51766e19			0.381038			0.190519	−	0.981684i	$-0.438983\pi$
$631$	1.51766e19			0.381038			0.190519	+	0.981684i	$0.438983\pi$
$632$	3.80566e19	+	2.19720e19i	0.944953	+	0.545569i
$633$		0			0
$634$	−2.97295e19	−	5.14930e19i	−0.722042	−	1.25061i
$635$	−1.22798e19	+	7.08977e18i	−0.294969	+	0.170301i
$636$		0			0
$637$	−1.43820e19	+	2.49103e19i	−0.337942	+	0.585332i
$638$		−	9.40557e18i		−	0.218595i
$639$		0			0
$640$	−2.45954e19			−0.559234
$641$	−2.33683e19	−	1.34917e19i	−0.525559	−	0.303431i	0.213647	−	0.976911i	$-0.431466\pi$
$641$	−2.33683e19	−	1.34917e19i	−0.525559	−	0.303431i	−0.739206	+	0.673479i	$0.764799\pi$
$642$		0			0
$643$	2.51225e19	+	4.35134e19i	0.552823	+	0.957517i	0.998069	+	0.0621091i	$0.0197827\pi$
$643$	2.51225e19	+	4.35134e19i	0.552823	+	0.957517i	−0.445247	+	0.895408i	$0.646884\pi$
$644$	1.03874e19	−	5.99718e18i	0.226103	−	0.130541i
$645$		0			0
$646$	−1.32538e19	+	2.29562e19i	−0.282300	+	0.488958i
$647$			5.18661e19i			1.09283i	0.837514	+	0.546416i	$0.184008\pi$
$647$			5.18661e19i			1.09283i	−0.837514	+	0.546416i	$0.815992\pi$
$648$		0			0
$649$	2.05475e19			0.423688
$650$	3.02787e19	+	1.74814e19i	0.617652	+	0.356601i
$651$		0			0
$652$	−1.11638e19	−	1.93363e19i	−0.222884	−	0.386046i
$653$	7.72909e19	−	4.46239e19i	1.52664	−	0.881405i	0.527139	−	0.849779i	$-0.323265\pi$
$653$	7.72909e19	−	4.46239e19i	1.52664	−	0.881405i	0.999500	−	0.0316266i	$-0.0100687\pi$
$654$		0			0
$655$	−1.49080e19	+	2.58214e19i	−0.288224	+	0.499219i
$656$			7.20246e19i			1.37770i
$657$		0			0
$658$	2.58243e19			0.483557
$659$	−7.75359e19	−	4.47654e19i	−1.43650	−	0.829362i	−0.438893	−	0.898539i	$-0.644629\pi$
$659$	−7.75359e19	−	4.47654e19i	−1.43650	−	0.829362i	−0.997604	+	0.0691771i	$0.977963\pi$
$660$		0			0
$661$	−2.12752e19	−	3.68497e19i	−0.385890	−	0.668381i	0.606002	−	0.795463i	$-0.292772\pi$
$661$	−2.12752e19	−	3.68497e19i	−0.385890	−	0.668381i	−0.991892	+	0.127082i	$0.959439\pi$
$662$	−1.16648e18	+	6.73466e17i	−0.0209349	+	0.0120867i
$663$		0			0
$664$	3.37113e18	−	5.83896e18i	0.0592377	−	0.102603i
$665$			1.25224e19i			0.217738i
$666$		0			0
$667$	−4.38847e19			−0.747192
$668$	1.40050e19	+	8.08578e18i	0.235965	+	0.136234i
$669$		0			0
$670$	1.00582e19	+	1.74214e19i	0.165958	+	0.287447i
$671$	−3.25181e19	+	1.87744e19i	−0.530968	+	0.306554i
$672$		0			0
$673$	5.79961e19	−	1.00452e20i	0.927456	−	1.60640i	0.139894	−	0.990167i	$-0.455324\pi$
$673$	5.79961e19	−	1.00452e20i	0.927456	−	1.60640i	0.787563	−	0.616235i	$-0.211343\pi$
$674$			9.30261e18i			0.147226i
$675$		0			0
$676$	9.04050e18			0.140141
$677$	8.24552e19	+	4.76055e19i	1.26502	+	0.730360i	0.974041	−	0.226370i	$-0.0726858\pi$
$677$	8.24552e19	+	4.76055e19i	1.26502	+	0.730360i	0.290979	+	0.956730i	$0.406019\pi$
$678$		0			0
$679$	−2.74219e18	−	4.74961e18i	−0.0412106	−	0.0713788i
$680$	−7.97371e18	+	4.60362e18i	−0.118604	+	0.0684758i
$681$		0			0
$682$	7.45478e18	−	1.29121e19i	0.108629	−	0.188150i
$683$			1.09770e20i			1.58321i	0.611034	+	0.791604i	$0.290754\pi$
$683$			1.09770e20i			1.58321i	−0.611034	+	0.791604i	$0.709246\pi$
$684$		0			0
$685$	−3.16362e19			−0.447045
$686$	−5.02751e19	−	2.90263e19i	−0.703208	−	0.405997i
$687$		0			0
$688$	2.32264e19	+	4.02293e19i	0.318319	+	0.551345i
$689$	8.86627e19	−	5.11894e19i	1.20284	−	0.694457i
$690$		0			0
$691$	2.89603e19	−	5.01608e19i	0.384997	−	0.666834i	−0.606772	−	0.794876i	$-0.707536\pi$
$691$	2.89603e19	−	5.01608e19i	0.384997	−	0.666834i	0.991769	+	0.128042i	$0.0408692\pi$
$692$			1.42645e19i			0.187721i
$693$		0			0
$694$	1.49737e20			1.93113
$695$	−3.01345e19	−	1.73981e19i	−0.384742	−	0.222131i
$696$		0			0
$697$	1.74838e19	+	3.02829e19i	0.218780	+	0.378938i
$698$	−3.89208e19	+	2.24709e19i	−0.482163	+	0.278377i
$699$		0			0
$700$	−4.37048e18	+	7.56990e18i	−0.0530693	+	0.0919187i
$701$		−	1.25085e20i		−	1.50376i	−0.659300	−	0.751880i	$-0.729147\pi$
$701$		−	1.25085e20i		−	1.50376i	0.659300	−	0.751880i	$-0.270853\pi$
$702$		0			0
$703$	−1.61098e20			−1.89846
$704$	1.47573e19	+	8.52011e18i	0.172186	+	0.0994115i
$705$		0			0
$706$	7.78165e19	+	1.34782e20i	0.890099	+	1.54170i
$707$	3.58796e17	−	2.07151e17i	0.00406361	−	0.00234612i
$708$		0			0
$709$	3.32061e19	−	5.75147e19i	0.368718	−	0.638638i	−0.620647	−	0.784090i	$-0.713130\pi$
$709$	3.32061e19	−	5.75147e19i	0.368718	−	0.638638i	0.989365	+	0.145451i	$0.0464634\pi$
$710$			2.54292e19i			0.279592i
$711$		0			0
$712$	3.08687e19			0.332781
$713$	−6.02453e19	−	3.47826e19i	−0.643127	−	0.371309i
$714$		0			0
$715$	8.47627e18	+	1.46813e19i	0.0887284	+	0.153682i
$716$	5.04811e19	−	2.91453e19i	0.523284	−	0.302118i
$717$		0			0
$718$	6.45560e17	−	1.11814e18i	0.00656244	−	0.0113665i
$719$		−	1.18331e20i		−	1.19123i	−0.803269	−	0.595616i	$-0.796908\pi$
$719$		−	1.18331e20i		−	1.19123i	0.803269	−	0.595616i	$-0.203092\pi$
$720$		0			0
$721$	−6.89806e19			−0.681052
$722$	−5.42886e19	−	3.13435e19i	−0.530821	−	0.306470i
$723$		0			0
$724$	−2.38268e19	−	4.12693e19i	−0.228505	−	0.395783i
$725$	2.76966e19	−	1.59906e19i	0.263063	−	0.151880i
$726$		0			0
$727$	−4.80326e19	+	8.31949e19i	−0.447502	+	0.775097i	−0.998223	−	0.0595931i	$-0.981020\pi$
$727$	−4.80326e19	+	8.31949e19i	−0.447502	+	0.775097i	0.550721	+	0.834690i	$0.314353\pi$
$728$			2.35596e19i			0.217394i
$729$		0			0
$730$	−8.02345e19			−0.726275
$731$	1.95312e19	+	1.12763e19i	0.175108	+	0.101099i
$732$		0			0
$733$	−8.00772e19	−	1.38698e20i	−0.704338	−	1.21995i	−0.966930	−	0.255042i	$-0.917911\pi$
$733$	−8.00772e19	−	1.38698e20i	−0.704338	−	1.21995i	0.262592	−	0.964907i	$-0.415423\pi$
$734$	3.51496e19	−	2.02936e19i	0.306230	−	0.176802i
$735$		0			0
$736$	−7.81031e19	+	1.35279e20i	−0.667611	+	1.15634i
$737$		−	3.39858e19i		−	0.287756i
$738$		0			0
$739$	−1.28317e19			−0.106604			−0.0533021	−	0.998578i	$-0.516975\pi$
$739$	−1.28317e19			−0.106604			−0.0533021	+	0.998578i	$0.516975\pi$
$740$	2.79496e19	+	1.61367e19i	0.230014	+	0.132798i
$741$		0			0
$742$	4.77845e19	+	8.27651e19i	0.385886	+	0.668375i
$743$	−1.35176e20	+	7.80438e19i	−1.08138	+	0.624333i	−0.931268	−	0.364336i	$-0.881296\pi$
$743$	−1.35176e20	+	7.80438e19i	−1.08138	+	0.624333i	−0.150110	+	0.988669i	$0.547963\pi$
$744$		0			0
$745$	2.69754e19	−	4.67228e19i	0.211775	−	0.366805i
$746$		−	7.94729e19i		−	0.618084i
$747$		0			0
$748$	−8.97161e18			−0.0684793
$749$	−3.43109e19	−	1.98094e19i	−0.259453	−	0.149795i
$750$		0			0
$751$	−3.43695e19	−	5.95297e19i	−0.255090	−	0.441829i	0.709830	−	0.704373i	$-0.248772\pi$
$751$	−3.43695e19	−	5.95297e19i	−0.255090	−	0.441829i	−0.964920	+	0.262544i	$0.915438\pi$
$752$	−1.60766e20	+	9.28185e19i	−1.18214	+	0.682511i
$753$		0			0
$754$	−2.48582e19	+	4.30556e19i	−0.179420	+	0.310764i
$755$			1.60786e19i			0.114979i
$756$		0			0
$757$	−1.73606e19			−0.121869			−0.0609347	−	0.998142i	$-0.519408\pi$
$757$	−1.73606e19			−0.121869			−0.0609347	+	0.998142i	$0.519408\pi$
$758$	1.06604e20	+	6.15476e19i	0.741459	+	0.428082i
$759$		0			0
$760$	−3.16449e19	−	5.48106e19i	−0.216077	−	0.374256i
$761$	2.81760e19	−	1.62674e19i	0.190628	−	0.110059i	−0.401648	−	0.915794i	$-0.631563\pi$
$761$	2.81760e19	−	1.62674e19i	0.190628	−	0.110059i	0.592277	+	0.805735i	$0.298229\pi$
$762$		0			0
$763$	−3.86096e19	+	6.68737e19i	−0.256462	+	0.444205i
$764$		−	4.02072e19i		−	0.264637i
$765$		0			0
$766$	−1.97955e20			−1.27928
$767$	−9.40597e19	−	5.43054e19i	−0.602332	−	0.347756i
$768$		0			0
$769$	−4.90393e18	−	8.49386e18i	−0.0308361	−	0.0534098i	0.850196	−	0.526467i	$-0.176484\pi$
$769$	−4.90393e18	−	8.49386e18i	−0.0308361	−	0.0534098i	−0.881032	+	0.473057i	$0.843150\pi$
$770$	−1.37048e19	+	7.91246e18i	−0.0853959	+	0.0493034i
$771$		0			0
$772$	4.33790e19	−	7.51347e19i	0.265435	−	0.459748i
$773$		−	3.51963e19i		−	0.213422i	−0.994290	−	0.106711i	$-0.965968\pi$
$773$		−	3.51963e19i		−	0.213422i	0.994290	−	0.106711i	$-0.0340320\pi$
$774$		0			0
$775$	5.06961e19			0.301900
$776$	2.40052e19	+	1.38594e19i	0.141668	+	0.0817923i
$777$		0			0
$778$	5.42010e19	+	9.38790e19i	0.314160	+	0.544141i
$779$	−2.08162e20	+	1.20182e20i	−1.19575	+	0.690364i
$780$		0			0
$781$	2.14807e19	−	3.72056e19i	0.121197	−	0.209919i
$782$			1.56298e20i			0.873987i
$783$		0			0
$784$	1.93015e20			1.06018
$785$	−1.52729e19	−	8.81783e18i	−0.0831447	−	0.0480036i
$786$		0			0
$787$	−6.45585e19	−	1.11819e20i	−0.345248	−	0.597986i	0.640151	−	0.768249i	$-0.278872\pi$
$787$	−6.45585e19	−	1.11819e20i	−0.345248	−	0.597986i	−0.985399	+	0.170263i	$0.945538\pi$
$788$	−4.47247e19	+	2.58218e19i	−0.237063	+	0.136868i
$789$		0			0
$790$	7.80112e19	−	1.35119e20i	0.406226	−	0.703603i
$791$			8.13793e19i			0.420028i
$792$		0			0
$793$	1.98477e20			1.00646
$794$	2.44170e20	+	1.40972e20i	1.22729	+	0.708578i
$795$		0			0
$796$	−6.59814e18	−	1.14283e19i	−0.0325859	−	0.0564405i
$797$	2.14420e20	−	1.23795e20i	1.04968	−	0.606032i	0.127119	−	0.991887i	$-0.459427\pi$
$797$	2.14420e20	−	1.23795e20i	1.04968	−	0.606032i	0.922559	+	0.385855i	$0.126094\pi$
$798$		0			0
$799$	−4.50630e19	+	7.80514e19i	−0.216767	+	0.375451i
$800$		−	1.13836e20i		−	0.542814i
$801$		0			0
$802$	7.24616e19			0.339537
$803$	1.17392e20	+	6.77762e19i	0.545291	+	0.314824i
$804$		0			0
$805$	3.69181e19	+	6.39440e19i	0.168527	+	0.291897i
$806$	−6.82511e19	+	3.94048e19i	−0.308862	+	0.178321i
$807$		0			0
$808$	−1.04697e18	+	1.81341e18i	−0.00465645	+	0.00806520i
$809$		−	2.39808e20i		−	1.05736i	−0.848821	−	0.528681i	$-0.822687\pi$
$809$		−	2.39808e20i		−	1.05736i	0.848821	−	0.528681i	$-0.177313\pi$
$810$		0			0
$811$	3.42865e20			1.48586			0.742928	−	0.669371i	$-0.233436\pi$
$811$	3.42865e20			1.48586			0.742928	+	0.669371i	$0.233436\pi$
$812$	−1.07642e19	−	6.21473e18i	−0.0462478	−	0.0267012i
$813$		0			0
$814$	−1.01792e20	−	1.76309e20i	−0.429876	−	0.744568i
$815$	1.19032e20	−	6.87233e19i	0.498381	−	0.287740i
$816$		0			0
$817$	−7.75125e19	+	1.34256e20i	−0.319020	+	0.552558i
$818$			3.58610e19i			0.146335i
$819$		0			0
$820$	4.81534e19			0.193166
$821$	4.15721e20	+	2.40017e20i	1.65348	+	0.954639i	0.975624	+	0.219448i	$0.0704256\pi$
$821$	4.15721e20	+	2.40017e20i	1.65348	+	0.954639i	0.677860	+	0.735191i	$0.262908\pi$
$822$		0			0
$823$	1.74191e20	+	3.01708e20i	0.681126	+	1.17974i	0.974638	+	0.223789i	$0.0718427\pi$
$823$	1.74191e20	+	3.01708e20i	0.681126	+	1.17974i	−0.293512	+	0.955955i	$0.594824\pi$
$824$	3.01929e20	−	1.74319e20i	1.17062	−	0.675855i
$825$		0			0
$826$	5.06932e19	−	8.78032e19i	0.193237	−	0.334695i
$827$		−	1.57173e20i		−	0.594073i	−0.954866	−	0.297036i	$-0.904002\pi$
$827$		−	1.57173e20i		−	0.594073i	0.954866	−	0.297036i	$-0.0959983\pi$
$828$		0			0
$829$	1.90105e20			0.706498			0.353249	−	0.935529i	$-0.385077\pi$
$829$	1.90105e20			0.706498			0.353249	+	0.935529i	$0.385077\pi$
$830$	−2.07311e19	−	1.19691e19i	−0.0763971	−	0.0441079i
$831$		0			0
$832$	−4.50360e19	−	7.80046e19i	−0.163191	−	0.282655i
$833$	8.11534e19	−	4.68539e19i	0.291603	−	0.168357i
$834$		0			0
$835$	−4.97754e19	+	8.62135e19i	−0.175877	+	0.304628i
$836$		−	6.16701e19i		−	0.216088i
$837$		0			0
$838$	−2.21929e20			−0.764727
$839$	2.96222e20	+	1.71024e20i	1.01224	+	0.584418i	0.911847	−	0.410530i	$-0.134656\pi$
$839$	2.96222e20	+	1.71024e20i	1.01224	+	0.584418i	0.100394	+	0.994948i	$0.467990\pi$
$840$		0			0
$841$	−1.26041e20	−	2.18309e20i	−0.423584	−	0.733668i
$842$	−1.57509e20	+	9.09378e19i	−0.524953	+	0.303082i
$843$		0			0
$844$	5.60538e19	−	9.70881e19i	0.183742	−	0.318250i
$845$			5.56525e19i			0.180921i
$846$		0			0
$847$	−9.00547e19			−0.287954
$848$	−5.94954e20	−	3.43497e20i	−1.88674	−	1.08931i
$849$		0			0
$850$	−5.69514e19	−	9.86428e19i	−0.177653	−	0.307704i
$851$	−8.22627e20	+	4.74944e20i	−2.54505	+	1.46938i
$852$		0			0
$853$	−8.44903e19	+	1.46341e20i	−0.257136	+	0.445373i	−0.965474	−	0.260501i	$-0.916112\pi$
$853$	−8.44903e19	+	1.46341e20i	−0.257136	+	0.445373i	0.708337	+	0.705874i	$0.249446\pi$
$854$			1.85275e20i			0.559256i
$855$		0			0
$856$	2.00239e20			0.594610
$857$	1.22693e20	+	7.08368e19i	0.361372	+	0.208638i	0.669682	−	0.742648i	$-0.266430\pi$
$857$	1.22693e20	+	7.08368e19i	0.361372	+	0.208638i	−0.308311	+	0.951286i	$0.599764\pi$
$858$		0			0
$859$	6.81490e19	+	1.18038e20i	0.197473	+	0.342033i	0.947708	−	0.319138i	$-0.103393\pi$
$859$	6.81490e19	+	1.18038e20i	0.197473	+	0.342033i	−0.750236	+	0.661171i	$0.770060\pi$
$860$	2.68960e19	−	1.55284e19i	0.0773035	−	0.0446312i
$861$		0			0
$862$	1.59478e20	−	2.76224e20i	0.450972	−	0.781106i
$863$			1.58254e20i			0.443894i	0.975059	+	0.221947i	$0.0712411\pi$
$863$			1.58254e20i			0.443894i	−0.975059	+	0.221947i	$0.928759\pi$
$864$		0			0
$865$	−8.78108e19			−0.242346
$866$	−1.89258e20	−	1.09268e20i	−0.518117	−	0.299135i
$867$		0			0
$868$	−9.85149e18	−	1.70633e19i	−0.0265377	−	0.0459647i
$869$	−2.28278e20	+	1.31796e20i	−0.609993	+	0.352180i
$870$		0			0
$871$	−8.98217e19	+	1.55576e20i	−0.236186	+	0.409086i
$872$		−	3.90276e20i		−	1.01802i
$873$		0			0
$874$	−1.07438e21			−2.75788
$875$	−1.06573e20	−	6.15302e19i	−0.271389	−	0.156687i
$876$		0			0
$877$	−5.70271e19	−	9.87739e19i	−0.142917	−	0.247540i	0.785677	−	0.618637i	$-0.212315\pi$
$877$	−5.70271e19	−	9.87739e19i	−0.142917	−	0.247540i	−0.928594	+	0.371097i	$0.878982\pi$
$878$	2.35007e19	−	1.35681e19i	0.0584277	−	0.0337332i
$879$		0			0
$880$	5.68784e19	−	9.85163e19i	0.139177	−	0.241062i
$881$			3.33760e20i			0.810219i	0.914268	+	0.405109i	$0.132767\pi$
$881$			3.33760e20i			0.810219i	−0.914268	+	0.405109i	$0.867233\pi$
$882$		0			0
$883$	−1.77256e20			−0.423522			−0.211761	−	0.977322i	$-0.567920\pi$
$883$	−1.77256e20			−0.423522			−0.211761	+	0.977322i	$0.567920\pi$
$884$	4.10691e19	+	2.37113e19i	0.0973530	+	0.0562068i
$885$		0			0
$886$	2.20916e20	+	3.82638e20i	0.515456	+	0.892796i
$887$	4.30804e20	−	2.48725e20i	0.997274	−	0.575777i	0.0898337	−	0.995957i	$-0.471366\pi$
$887$	4.30804e20	−	2.48725e20i	0.997274	−	0.575777i	0.907441	+	0.420180i	$0.138033\pi$
$888$		0			0
$889$	5.91016e19	−	1.02367e20i	0.134675	−	0.233264i
$890$		−	1.09599e20i		−	0.247786i
$891$		0			0
$892$	−5.56225e19			−0.123793
$893$	−5.36518e20	−	3.09759e20i	−1.18474	−	0.684012i
$894$		0			0
$895$	1.79416e20	+	3.10757e20i	0.390031	+	0.675554i
$896$	1.77562e20	−	1.02516e20i	0.382996	−	0.221123i
$897$		0			0
$898$	−4.93394e20	+	8.54584e20i	−1.04776	+	1.81477i
$899$			7.20888e19i			0.151897i
$900$		0			0
$901$	−3.33533e20			−0.691934
$902$	−2.63061e20	−	1.51878e20i	−0.541515	−	0.312644i
$903$		0			0
$904$	−2.05651e20	−	3.56199e20i	−0.416824	−	0.721960i
$905$	2.54050e20	−	1.46676e20i	0.510951	−	0.294998i
$906$		0			0
$907$	2.38047e20	−	4.12310e20i	0.471425	−	0.816532i	−0.528041	−	0.849219i	$-0.677073\pi$
$907$	2.38047e20	−	4.12310e20i	0.471425	−	0.816532i	0.999466	+	0.0326871i	$0.0104065\pi$
$908$		−	7.15116e19i		−	0.140532i
$909$		0			0
$910$	8.36480e19			0.161870
$911$	−1.04981e20	−	6.06106e19i	−0.201595	−	0.116391i	0.395804	−	0.918335i	$-0.370466\pi$
$911$	−1.04981e20	−	6.06106e19i	−0.201595	−	0.116391i	−0.597399	+	0.801944i	$0.703799\pi$
$912$		0			0
$913$	2.02213e19	+	3.50243e19i	0.0382396	+	0.0662329i
$914$	7.67868e20	−	4.43329e20i	1.44100	−	0.831960i
$915$		0			0
$916$	5.01671e18	−	8.68920e18i	0.00927152	−	0.0160587i
$917$		−	2.48551e20i		−	0.455859i
$918$		0			0
$919$	−5.15778e19			−0.0931653			−0.0465826	−	0.998914i	$-0.514833\pi$
$919$	−5.15778e19			−0.0931653			−0.0465826	+	0.998914i	$0.514833\pi$
$920$	−3.23182e20	−	1.86589e20i	−0.579339	−	0.334481i
$921$		0			0
$922$	7.11743e19	+	1.23278e20i	0.125663	+	0.217654i
$923$	−1.96663e20	+	1.13544e20i	−0.344597	+	0.198953i
$924$		0			0
$925$	3.46118e20	−	5.99495e20i	0.597355	−	1.03465i
$926$			2.77113e20i			0.474657i
$927$		0			0
$928$	1.61873e20			0.273110
$929$	8.76394e20	+	5.05986e20i	1.46754	+	0.847283i	0.999339	−	0.0363405i	$-0.0115701\pi$
$929$	8.76394e20	+	5.05986e20i	1.46754	+	0.847283i	0.468198	+	0.883624i	$0.344903\pi$
$930$		0			0
$931$	3.22070e20	+	5.57841e20i	0.531254	+	0.920159i
$932$	−4.22124e19	+	2.43713e19i	−0.0691081	+	0.0398996i
$933$		0			0
$934$	5.59116e20	−	9.68417e20i	0.901724	−	1.56183i
$935$		−	5.52285e19i		−	0.0884060i
$936$		0			0
$937$	8.95113e20			1.41156			0.705782	−	0.708429i	$-0.250596\pi$
$937$	8.95113e20			1.41156			0.705782	+	0.708429i	$0.250596\pi$
$938$	−1.45227e20	−	8.38471e19i	−0.227315	−	0.131241i
$939$		0			0
$940$	6.20555e19	+	1.07483e20i	0.0956941	+	0.165747i
$941$	−3.26128e20	+	1.88290e20i	−0.499184	+	0.288204i	−0.728377	−	0.685177i	$-0.759725\pi$
$941$	−3.26128e20	+	1.88290e20i	−0.499184	+	0.288204i	0.229192	+	0.973381i	$0.426391\pi$
$942$		0			0
$943$	−7.08637e20	+	1.22740e21i	−1.06867	+	1.85098i
$944$			7.28812e20i			1.09097i
$945$		0			0
$946$	−1.95910e20			−0.288948
$947$	−8.26331e20	−	4.77082e20i	−1.20977	−	0.698463i	−0.247064	−	0.968999i	$-0.579466\pi$
$947$	−8.26331e20	−	4.77082e20i	−1.20977	−	0.698463i	−0.962710	+	0.270536i	$0.912799\pi$
$948$		0			0
$949$	−3.58254e20	−	6.20514e20i	−0.516806	−	0.895134i
$950$	6.78062e20	−	3.91479e20i	0.970966	−	0.560587i
$951$		0			0
$952$	3.83766e19	−	6.64702e19i	0.0541511	−	0.0937925i
$953$		−	6.86670e19i		−	0.0961829i	−0.998843	−	0.0480915i	$-0.984686\pi$
$953$		−	6.86670e19i		−	0.0961829i	0.998843	−	0.0480915i	$-0.0153139\pi$
$954$		0			0
$955$	2.47512e20			0.341644
$956$	1.39527e20	+	8.05557e19i	0.191184	+	0.110380i
$957$		0			0
$958$	7.81805e20	+	1.35413e21i	1.05570	+	1.82852i
$959$	2.28393e20	−	1.31863e20i	0.306162	−	0.176763i
$960$		0			0
$961$	3.21335e20	−	5.56569e20i	0.424516	−	0.735284i
$962$			1.07611e21i			1.41134i
$963$		0			0
$964$	4.82233e20			0.623330
$965$	4.62523e20	+	2.67038e20i	0.593529	+	0.342674i
$966$		0			0
$967$	−6.39879e20	−	1.10830e21i	−0.809305	−	1.40176i	−0.913346	−	0.407185i	$-0.866510\pi$
$967$	−6.39879e20	−	1.10830e21i	−0.809305	−	1.40176i	0.104040	−	0.994573i	$-0.466823\pi$
$968$	3.94171e20	−	2.27575e20i	0.494945	−	0.285757i
$969$		0			0
$970$	4.92076e19	−	8.52300e19i	0.0609018	−	0.105485i
$971$			4.07978e20i			0.501306i	0.968077	+	0.250653i	$0.0806453\pi$
$971$			4.07978e20i			0.501306i	−0.968077	+	0.250653i	$0.919355\pi$
$972$		0			0
$973$	2.90068e20			0.351325
$974$	3.00926e20	+	1.73740e20i	0.361866	+	0.208923i
$975$		0			0
$976$	−6.65919e20	−	1.15341e21i	−0.789356	−	1.36720i
$977$	−1.01319e21	+	5.84967e20i	−1.19242	+	0.688446i	−0.958855	−	0.283895i	$-0.908373\pi$
$977$	−1.01319e21	+	5.84967e20i	−1.19242	+	0.688446i	−0.233568	+	0.972341i	$0.575040\pi$
$978$		0			0
$979$	−9.25811e19	+	1.60355e20i	−0.107410	+	0.186039i
$980$		−	1.29043e20i		−	0.148646i
$981$		0			0
$982$	1.23618e20			0.140378
$983$	−7.26339e19	−	4.19352e19i	−0.0818964	−	0.0472829i	0.458493	−	0.888698i	$-0.348390\pi$
$983$	−7.26339e19	−	4.19352e19i	−0.0818964	−	0.0472829i	−0.540389	+	0.841415i	$0.681723\pi$
$984$		0			0
$985$	−1.58957e20	−	2.75321e20i	−0.176695	−	0.306045i
$986$	1.40268e20	−	8.09837e19i	0.154817	−	0.0893838i
$987$		0			0
$988$	−1.62989e20	+	2.82305e20i	−0.177362	+	0.307200i
$989$			9.14082e20i			0.987668i
$990$		0			0
$991$	−2.99221e20			−0.318769			−0.159385	−	0.987217i	$-0.550951\pi$
$991$	−2.99221e20			−0.318769			−0.159385	+	0.987217i	$0.550951\pi$
$992$	2.22220e20	+	1.28299e20i	0.235073	+	0.135719i
$993$		0			0
$994$	−1.05991e20	−	1.83582e20i	−0.110551	−	0.191481i
$995$	7.03517e19	−	4.06176e19i	0.0728640	−	0.0420681i
$996$		0			0
$997$	−1.61651e19	+	2.79988e19i	−0.0165087	+	0.0285939i	−0.874162	−	0.485635i	$-0.838588\pi$
$997$	−1.61651e19	+	2.79988e19i	−0.0165087	+	0.0285939i	0.857653	+	0.514229i	$0.171922\pi$
$998$			5.61369e20i			0.569292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.15.d.a.8.3		26
3.2	odd	2		9.15.d.a.2.11	✓	26
9.2	odd	6		81.15.b.a.80.6		26
9.4	even	3		9.15.d.a.5.11	yes	26
9.5	odd	6	inner	27.15.d.a.17.3		26
9.7	even	3		81.15.b.a.80.21		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.15.d.a.2.11	✓	26	3.2	odd	2
9.15.d.a.5.11	yes	26	9.4	even	3
27.15.d.a.8.3		26	1.1	even	1	trivial
27.15.d.a.17.3		26	9.5	odd	6	inner
81.15.b.a.80.6		26	9.2	odd	6
81.15.b.a.80.21		26	9.7	even	3

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-129.548 - 74.7948i) q^{2} +(2996.54 + 5190.15i) q^{4} +(-31950.1 + 18446.4i) q^{5} +(153772. - 266342. i) q^{7} +1.55438e6i q^{8} +5.51879e6 q^{10} +(-8.07458e6 - 4.66186e6i) q^{11} +(2.46419e7 + 4.26810e7i) q^{13} +(-3.98420e7 + 2.30028e7i) q^{14} +(1.65355e8 - 2.86402e8i) q^{16} -1.60558e8i q^{17} +1.10366e9 q^{19} +(-1.91479e8 - 1.10551e8i) q^{20} +(6.97366e8 + 1.20787e9i) q^{22} +(5.63572e9 - 3.25379e9i) q^{23} +(-2.37122e9 + 4.10707e9i) q^{25} -7.37234e9i q^{26} +1.84314e9 q^{28} +(-5.84016e9 - 3.37182e9i) q^{29} +(-5.34495e9 - 9.25772e9i) q^{31} +(-2.07879e10 + 1.20019e10i) q^{32} +(-1.20089e10 + 2.08000e10i) q^{34} +1.13462e10i q^{35} -1.45967e11 q^{37} +(-1.42978e11 - 8.25481e10i) q^{38} +(-2.86727e10 - 4.96625e10i) q^{40} +(-1.88610e11 + 1.08894e11i) q^{41} +(-7.02322e10 + 1.21646e11i) q^{43} -5.58777e10i q^{44} -9.73465e11 q^{46} +(-4.86126e11 - 2.80665e11i) q^{47} +(2.91820e11 + 5.05446e11i) q^{49} +(6.14375e11 - 3.54710e11i) q^{50} +(-1.47680e11 + 2.55790e11i) q^{52} -2.07734e12i q^{53} +3.43979e11 q^{55} +(4.13995e11 + 2.39020e11i) q^{56} +(5.04389e11 + 8.73628e11i) q^{58} +(-1.90853e12 + 1.10189e12i) q^{59} +(2.01361e12 - 3.48768e12i) q^{61} +1.59910e12i q^{62} -1.82762e12 q^{64} +(-1.57462e12 - 9.09108e11i) q^{65} +(1.82254e12 + 3.15674e12i) q^{67} +(8.33320e11 - 4.81118e11i) q^{68} +(8.48638e11 - 1.46988e12i) q^{70} +4.60775e12i q^{71} -1.45384e13 q^{73} +(1.89097e13 + 1.09175e13i) q^{74} +(3.30716e12 + 5.72817e12i) q^{76} +(-2.48330e12 + 1.43373e12i) q^{77} +(1.41356e13 - 2.44835e13i) q^{79} +1.22008e13i q^{80} +3.25789e13 q^{82} +(-3.75647e12 - 2.16880e12i) q^{83} +(2.96172e12 + 5.12985e12i) q^{85} +(1.81969e13 - 1.05060e13i) q^{86} +(7.24628e12 - 1.25509e13i) q^{88} -1.98593e13i q^{89} +1.51570e13 q^{91} +(3.37753e13 + 1.95002e13i) q^{92} +(4.19846e13 + 7.27195e13i) q^{94} +(-3.52621e13 + 2.03586e13i) q^{95} +(8.91638e12 - 1.54436e13i) q^{97} -8.73064e13i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 3 q^{2} + 98303 q^{4} + 107994 q^{5} - 146330 q^{7} - 32772 q^{10} + 15978711 q^{11} - 23281436 q^{13} + 349442850 q^{14} - 671072257 q^{16} + 195706222 q^{19} - 2822935854 q^{20} - 204235521 q^{22}+ \cdots + 7621755375583 q^{97}+O(q^{100}) \) 26 * q + 3 * q^2 + 98303 * q^4 + 107994 * q^5 - 146330 * q^7 - 32772 * q^10 + 15978711 * q^11 - 23281436 * q^13 + 349442850 * q^14 - 671072257 * q^16 + 195706222 * q^19 - 2822935854 * q^20 - 204235521 * q^22 + 6101133672 * q^23 + 14614789727 * q^25 - 9052979204 * q^28 - 85191770166 * q^29 + 15357554728 * q^31 + 237242922057 * q^32 - 16566014943 * q^34 - 77721425444 * q^37 - 476314869819 * q^38 - 88855733850 * q^40 + 938882938233 * q^41 - 29709800063 * q^43 + 1553142786144 * q^46 + 1272741434580 * q^47 - 945184029255 * q^49 - 3573994524699 * q^50 + 1825489374856 * q^52 - 3772940931372 * q^55 + 7790759725422 * q^56 + 3747043240302 * q^58 - 5874788534451 * q^59 - 4867968901544 * q^61 + 1211169309434 * q^64 + 22156719464856 * q^65 - 8251061484125 * q^67 - 30687017243265 * q^68 + 6871822387932 * q^70 + 16120119648922 * q^73 - 8549243621166 * q^74 + 14422972781521 * q^76 - 13919363311398 * q^77 - 10740904544582 * q^79 - 67076318933382 * q^82 + 11295125984532 * q^83 + 10590724937466 * q^85 - 97019495740221 * q^86 - 26136212294541 * q^88 + 70870424994080 * q^91 + 474274297000284 * q^92 - 46678164316620 * q^94 - 440317551118746 * q^95 + 7621755375583 * q^97

Introduction

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