LMFDB - Embedded newform 531.8.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$19.9328$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.9328 q^{2} +310.183 q^{4} +149.882 q^{5} +1201.09 q^{7} -3813.60 q^{8} +O(q^{10})$	\(q-20.9328 q^{2} +310.183 q^{4} +149.882 q^{5} +1201.09 q^{7} -3813.60 q^{8} -3137.45 q^{10} -3090.18 q^{11} -9762.44 q^{13} -25142.2 q^{14} +40126.1 q^{16} -774.830 q^{17} +42295.3 q^{19} +46490.9 q^{20} +64686.2 q^{22} -19299.9 q^{23} -55660.4 q^{25} +204355. q^{26} +372558. q^{28} +148022. q^{29} -77522.7 q^{31} -351811. q^{32} +16219.4 q^{34} +180022. q^{35} +381041. q^{37} -885360. q^{38} -571591. q^{40} -313892. q^{41} +86822.9 q^{43} -958522. q^{44} +404002. q^{46} -1.09797e6 q^{47} +619078. q^{49} +1.16513e6 q^{50} -3.02814e6 q^{52} +1.35146e6 q^{53} -463163. q^{55} -4.58049e6 q^{56} -3.09852e6 q^{58} -205379. q^{59} -1.17823e6 q^{61} +1.62277e6 q^{62} +2.22825e6 q^{64} -1.46321e6 q^{65} -2.20281e6 q^{67} -240339. q^{68} -3.76837e6 q^{70} -64342.9 q^{71} -1.88910e6 q^{73} -7.97626e6 q^{74} +1.31193e7 q^{76} -3.71159e6 q^{77} -267273. q^{79} +6.01418e6 q^{80} +6.57065e6 q^{82} +9.61801e6 q^{83} -116133. q^{85} -1.81745e6 q^{86} +1.17847e7 q^{88} -1.26033e7 q^{89} -1.17256e7 q^{91} -5.98651e6 q^{92} +2.29835e7 q^{94} +6.33931e6 q^{95} -7.21193e6 q^{97} -1.29590e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) $ 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−20.9328	−1.85022	−0.925109	−	0.379702i	$-0.876026\pi$
$2$	−20.9328	−1.85022	−0.925109	+	0.379702i	$0.876026\pi$
$3$	0	0
$3$	0	0
$4$	310.183	2.42330
$5$	149.882	0.536234	0.268117	−	0.963386i	$-0.413599\pi$
$5$	149.882	0.536234	0.268117	+	0.963386i	$0.413599\pi$
$6$	0	0
$7$	1201.09	1.32353	0.661764	−	0.749712i	$-0.269808\pi$
$7$	1201.09	1.32353	0.661764	+	0.749712i	$0.269808\pi$
$8$	−3813.60	−2.63342
$9$	0	0
$10$	−3137.45	−0.992150
$11$	−3090.18	−0.700019	−0.350009	−	0.936746i	$-0.613822\pi$
$11$	−3090.18	−0.700019	−0.350009	+	0.936746i	$0.613822\pi$
$12$	0	0
$13$	−9762.44	−1.23241	−0.616207	−	0.787584i	$-0.711332\pi$
$13$	−9762.44	−1.23241	−0.616207	+	0.787584i	$0.711332\pi$
$14$	−25142.2	−2.44881
$15$	0	0
$16$	40126.1	2.44910
$17$	−774.830	−0.0382503	−0.0191252	−	0.999817i	$-0.506088\pi$
$17$	−774.830	−0.0382503	−0.0191252	+	0.999817i	$0.506088\pi$
$18$	0	0
$19$	42295.3	1.41467	0.707334	−	0.706879i	$-0.249898\pi$
$19$	42295.3	1.41467	0.707334	+	0.706879i	$0.249898\pi$
$20$	46490.9	1.29946
$21$	0	0
$22$	64686.2	1.29519
$23$	−19299.9	−0.330756	−0.165378	−	0.986230i	$-0.552884\pi$
$23$	−19299.9	−0.330756	−0.165378	+	0.986230i	$0.552884\pi$
$24$	0	0
$25$	−55660.4	−0.712453
$26$	204355.	2.28023
$27$	0	0
$28$	372558.	3.20731
$29$	148022.	1.12703	0.563513	−	0.826107i	$-0.309449\pi$
$29$	148022.	1.12703	0.563513	+	0.826107i	$0.309449\pi$
$30$	0	0
$31$	−77522.7	−0.467372	−0.233686	−	0.972312i	$-0.575079\pi$
$31$	−77522.7	−0.467372	−0.233686	+	0.972312i	$0.575079\pi$
$32$	−351811.	−1.89795
$33$	0	0
$34$	16219.4	0.0707714
$35$	180022.	0.709721
$36$	0	0
$37$	381041.	1.23670	0.618352	−	0.785901i	$-0.287801\pi$
$37$	381041.	1.23670	0.618352	+	0.785901i	$0.287801\pi$
$38$	−885360.	−2.61744
$39$	0	0
$40$	−571591.	−1.41213
$41$	−313892.	−0.711274	−0.355637	−	0.934624i	$-0.615736\pi$
$41$	−313892.	−0.711274	−0.355637	+	0.934624i	$0.615736\pi$
$42$	0	0
$43$	86822.9	0.166531	0.0832654	−	0.996527i	$-0.473465\pi$
$43$	86822.9	0.166531	0.0832654	+	0.996527i	$0.473465\pi$
$44$	−958522.	−1.69636
$45$	0	0
$46$	404002.	0.611971
$47$	−1.09797e6	−1.54258	−0.771288	−	0.636486i	$-0.780387\pi$
$47$	−1.09797e6	−1.54258	−0.771288	+	0.636486i	$0.780387\pi$
$48$	0	0
$49$	619078.	0.751725
$50$	1.16513e6	1.31819
$51$	0	0
$52$	−3.02814e6	−2.98652
$53$	1.35146e6	1.24692	0.623458	−	0.781857i	$-0.285727\pi$
$53$	1.35146e6	1.24692	0.623458	+	0.781857i	$0.285727\pi$
$54$	0	0
$55$	−463163.	−0.375374
$56$	−4.58049e6	−3.48541
$57$	0	0
$58$	−3.09852e6	−2.08524
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−1.17823e6	−0.664622	−0.332311	−	0.943170i	$-0.607828\pi$
$61$	−1.17823e6	−0.664622	−0.332311	+	0.943170i	$0.607828\pi$
$62$	1.62277e6	0.864741
$63$	0	0
$64$	2.22825e6	1.06251
$65$	−1.46321e6	−0.660863
$66$	0	0
$67$	−2.20281e6	−0.894777	−0.447389	−	0.894340i	$-0.647646\pi$
$67$	−2.20281e6	−0.894777	−0.447389	+	0.894340i	$0.647646\pi$
$68$	−240339.	−0.0926922
$69$	0	0
$70$	−3.76837e6	−1.31314
$71$	−64342.9	−0.0213352	−0.0106676	−	0.999943i	$-0.503396\pi$
$71$	−64342.9	−0.0213352	−0.0106676	+	0.999943i	$0.503396\pi$
$72$	0	0
$73$	−1.88910e6	−0.568363	−0.284181	−	0.958771i	$-0.591722\pi$
$73$	−1.88910e6	−0.568363	−0.284181	+	0.958771i	$0.591722\pi$
$74$	−7.97626e6	−2.28817
$75$	0	0
$76$	1.31193e7	3.42817
$77$	−3.71159e6	−0.926494
$78$	0	0
$79$	−267273.	−0.0609902	−0.0304951	−	0.999535i	$-0.509708\pi$
$79$	−267273.	−0.0609902	−0.0304951	+	0.999535i	$0.509708\pi$
$80$	6.01418e6	1.31329
$81$	0	0
$82$	6.57065e6	1.31601
$83$	9.61801e6	1.84634	0.923170	−	0.384391i	$-0.125589\pi$
$83$	9.61801e6	1.84634	0.923170	+	0.384391i	$0.125589\pi$
$84$	0	0
$85$	−116133.	−0.0205111
$86$	−1.81745e6	−0.308118
$87$	0	0
$88$	1.17847e7	1.84345
$89$	−1.26033e7	−1.89505	−0.947523	−	0.319687i	$-0.896422\pi$
$89$	−1.26033e7	−1.89505	−0.947523	+	0.319687i	$0.896422\pi$
$90$	0	0
$91$	−1.17256e7	−1.63113
$92$	−5.98651e6	−0.801523
$93$	0	0
$94$	2.29835e7	2.85410
$95$	6.33931e6	0.758594
$96$	0	0
$97$	−7.21193e6	−0.802325	−0.401162	−	0.916007i	$-0.631394\pi$
$97$	−7.21193e6	−0.802325	−0.401162	+	0.916007i	$0.631394\pi$
$98$	−1.29590e7	−1.39085
$99$	0	0
$100$	−1.72649e7	−1.72649
$101$	3.44100e6	0.332322	0.166161	−	0.986099i	$-0.446863\pi$
$101$	3.44100e6	0.332322	0.166161	+	0.986099i	$0.446863\pi$
$102$	0	0
$103$	−8.00277e6	−0.721623	−0.360811	−	0.932639i	$-0.617500\pi$
$103$	−8.00277e6	−0.721623	−0.360811	+	0.932639i	$0.617500\pi$
$104$	3.72301e7	3.24547
$105$	0	0
$106$	−2.82899e7	−2.30707
$107$	1.89058e7	1.49194	0.745972	−	0.665978i	$-0.231985\pi$
$107$	1.89058e7	1.49194	0.745972	+	0.665978i	$0.231985\pi$
$108$	0	0
$109$	−1.48351e7	−1.09723	−0.548613	−	0.836076i	$-0.684844\pi$
$109$	−1.48351e7	−1.09723	−0.548613	+	0.836076i	$0.684844\pi$
$110$	9.69530e6	0.694524
$111$	0	0
$112$	4.81951e7	3.24145
$113$	−1.51244e7	−0.986061	−0.493030	−	0.870012i	$-0.664111\pi$
$113$	−1.51244e7	−0.986061	−0.493030	+	0.870012i	$0.664111\pi$
$114$	0	0
$115$	−2.89271e6	−0.177363
$116$	4.59140e7	2.73113
$117$	0	0
$118$	4.29916e6	0.240878
$119$	−930642.	−0.0506254
$120$	0	0
$121$	−9.93795e6	−0.509974
$122$	2.46636e7	1.22970
$123$	0	0
$124$	−2.40462e7	−1.13259
$125$	−2.00520e7	−0.918276
$126$	0	0
$127$	3.60355e7	1.56105	0.780527	−	0.625122i	$-0.214951\pi$
$127$	3.60355e7	1.56105	0.780527	+	0.625122i	$0.214951\pi$
$128$	−1.61184e6	−0.0679339
$129$	0	0
$130$	3.06292e7	1.22274
$131$	−1.15356e7	−0.448321	−0.224161	−	0.974552i	$-0.571964\pi$
$131$	−1.15356e7	−0.448321	−0.224161	+	0.974552i	$0.571964\pi$
$132$	0	0
$133$	5.08005e7	1.87235
$134$	4.61110e7	1.65553
$135$	0	0
$136$	2.95490e6	0.100729
$137$	3.77725e7	1.25503	0.627515	−	0.778605i	$-0.284072\pi$
$137$	3.77725e7	1.25503	0.627515	+	0.778605i	$0.284072\pi$
$138$	0	0
$139$	−3.71316e6	−0.117271	−0.0586357	−	0.998279i	$-0.518675\pi$
$139$	−3.71316e6	−0.117271	−0.0586357	+	0.998279i	$0.518675\pi$
$140$	5.58398e7	1.71987
$141$	0	0
$142$	1.34688e6	0.0394747
$143$	3.01677e7	0.862713
$144$	0	0
$145$	2.21859e7	0.604350
$146$	3.95442e7	1.05159
$147$	0	0
$148$	1.18192e8	2.99691
$149$	6.47154e7	1.60271	0.801357	−	0.598187i	$-0.204112\pi$
$149$	6.47154e7	1.60271	0.801357	+	0.598187i	$0.204112\pi$
$150$	0	0
$151$	2.42807e7	0.573907	0.286953	−	0.957945i	$-0.407358\pi$
$151$	2.42807e7	0.573907	0.286953	+	0.957945i	$0.407358\pi$
$152$	−1.61298e8	−3.72542
$153$	0	0
$154$	7.76941e7	1.71422
$155$	−1.16193e7	−0.250621
$156$	0	0
$157$	4.14110e7	0.854018	0.427009	−	0.904247i	$-0.359567\pi$
$157$	4.14110e7	0.854018	0.427009	+	0.904247i	$0.359567\pi$
$158$	5.59477e6	0.112845
$159$	0	0
$160$	−5.27301e7	−1.01774
$161$	−2.31810e7	−0.437765
$162$	0	0
$163$	−8.91039e7	−1.61154	−0.805769	−	0.592231i	$-0.798247\pi$
$163$	−8.91039e7	−1.61154	−0.805769	+	0.592231i	$0.798247\pi$
$164$	−9.73640e7	−1.72363
$165$	0	0
$166$	−2.01332e8	−3.41613
$167$	−5.76977e7	−0.958630	−0.479315	−	0.877643i	$-0.659115\pi$
$167$	−5.76977e7	−0.958630	−0.479315	+	0.877643i	$0.659115\pi$
$168$	0	0
$169$	3.25568e7	0.518845
$170$	2.43099e6	0.0379501
$171$	0	0
$172$	2.69310e7	0.403555
$173$	−1.70091e7	−0.249759	−0.124880	−	0.992172i	$-0.539854\pi$
$173$	−1.70091e7	−0.249759	−0.124880	+	0.992172i	$0.539854\pi$
$174$	0	0
$175$	−6.68532e7	−0.942951
$176$	−1.23997e8	−1.71442
$177$	0	0
$178$	2.63823e8	3.50625
$179$	3.67383e7	0.478777	0.239388	−	0.970924i	$-0.423053\pi$
$179$	3.67383e7	0.478777	0.239388	+	0.970924i	$0.423053\pi$
$180$	0	0
$181$	1.07531e7	0.134791	0.0673954	−	0.997726i	$-0.478531\pi$
$181$	1.07531e7	0.134791	0.0673954	+	0.997726i	$0.478531\pi$
$182$	2.45450e8	3.01795
$183$	0	0
$184$	7.36023e7	0.871021
$185$	5.71112e7	0.663163
$186$	0	0
$187$	2.39437e6	0.0267759
$188$	−3.40571e8	−3.73813
$189$	0	0
$190$	−1.32700e8	−1.40356
$191$	4.65850e7	0.483759	0.241880	−	0.970306i	$-0.422236\pi$
$191$	4.65850e7	0.483759	0.241880	+	0.970306i	$0.422236\pi$
$192$	0	0
$193$	−6.10866e7	−0.611639	−0.305820	−	0.952089i	$-0.598930\pi$
$193$	−6.10866e7	−0.611639	−0.305820	+	0.952089i	$0.598930\pi$
$194$	1.50966e8	1.48448
$195$	0	0
$196$	1.92027e8	1.82166
$197$	−7.42960e7	−0.692363	−0.346181	−	0.938168i	$-0.612522\pi$
$197$	−7.42960e7	−0.692363	−0.346181	+	0.938168i	$0.612522\pi$
$198$	0	0
$199$	−1.79787e8	−1.61723	−0.808617	−	0.588335i	$-0.799784\pi$
$199$	−1.79787e8	−1.61723	−0.808617	+	0.588335i	$0.799784\pi$
$200$	2.12267e8	1.87619
$201$	0	0
$202$	−7.20298e7	−0.614869
$203$	1.77788e8	1.49165
$204$	0	0
$205$	−4.70468e7	−0.381410
$206$	1.67521e8	1.33516
$207$	0	0
$208$	−3.91729e8	−3.01831
$209$	−1.30700e8	−0.990294
$210$	0	0
$211$	−1.70096e8	−1.24654	−0.623269	−	0.782008i	$-0.714196\pi$
$211$	−1.70096e8	−1.24654	−0.623269	+	0.782008i	$0.714196\pi$
$212$	4.19200e8	3.02166
$213$	0	0
$214$	−3.95752e8	−2.76042
$215$	1.30132e7	0.0892996
$216$	0	0
$217$	−9.31119e7	−0.618580
$218$	3.10540e8	2.03011
$219$	0	0
$220$	−1.43665e8	−0.909646
$221$	7.56423e6	0.0471402
$222$	0	0
$223$	−1.26142e8	−0.761713	−0.380857	−	0.924634i	$-0.624371\pi$
$223$	−1.26142e8	−0.761713	−0.380857	+	0.924634i	$0.624371\pi$
$224$	−4.22557e8	−2.51199
$225$	0	0
$226$	3.16596e8	1.82443
$227$	−1.79611e8	−1.01916	−0.509579	−	0.860424i	$-0.670199\pi$
$227$	−1.79611e8	−1.01916	−0.509579	+	0.860424i	$0.670199\pi$
$228$	0	0
$229$	3.37131e8	1.85513	0.927564	−	0.373664i	$-0.121899\pi$
$229$	3.37131e8	1.85513	0.927564	+	0.373664i	$0.121899\pi$
$230$	6.05526e7	0.328160
$231$	0	0
$232$	−5.64498e8	−2.96794
$233$	−2.03401e8	−1.05343	−0.526716	−	0.850041i	$-0.676577\pi$
$233$	−2.03401e8	−1.05343	−0.526716	+	0.850041i	$0.676577\pi$
$234$	0	0
$235$	−1.64565e8	−0.827182
$236$	−6.37051e7	−0.315487
$237$	0	0
$238$	1.94810e7	0.0936679
$239$	−2.40718e8	−1.14056	−0.570278	−	0.821452i	$-0.693164\pi$
$239$	−2.40718e8	−1.14056	−0.570278	+	0.821452i	$0.693164\pi$
$240$	0	0
$241$	6.28354e7	0.289164	0.144582	−	0.989493i	$-0.453816\pi$
$241$	6.28354e7	0.289164	0.144582	+	0.989493i	$0.453816\pi$
$242$	2.08029e8	0.943563
$243$	0	0
$244$	−3.65466e8	−1.61058
$245$	9.27887e7	0.403101
$246$	0	0
$247$	−4.12905e8	−1.74346
$248$	2.95641e8	1.23079
$249$	0	0
$250$	4.19746e8	1.69901
$251$	−1.10247e8	−0.440058	−0.220029	−	0.975493i	$-0.570615\pi$
$251$	−1.10247e8	−0.440058	−0.220029	+	0.975493i	$0.570615\pi$
$252$	0	0
$253$	5.96403e7	0.231536
$254$	−7.54326e8	−2.88829
$255$	0	0
$256$	−2.51476e8	−0.936821
$257$	8.00040e7	0.293999	0.146999	−	0.989137i	$-0.453038\pi$
$257$	8.00040e7	0.293999	0.146999	+	0.989137i	$0.453038\pi$
$258$	0	0
$259$	4.57665e8	1.63681
$260$	−4.53864e8	−1.60147
$261$	0	0
$262$	2.41472e8	0.829492
$263$	1.42844e8	0.484190	0.242095	−	0.970253i	$-0.422165\pi$
$263$	1.42844e8	0.484190	0.242095	+	0.970253i	$0.422165\pi$
$264$	0	0
$265$	2.02559e8	0.668639
$266$	−1.06340e9	−3.46426
$267$	0	0
$268$	−6.83274e8	−2.16832
$269$	1.90832e8	0.597747	0.298873	−	0.954293i	$-0.403389\pi$
$269$	1.90832e8	0.597747	0.298873	+	0.954293i	$0.403389\pi$
$270$	0	0
$271$	1.37623e8	0.420048	0.210024	−	0.977696i	$-0.432646\pi$
$271$	1.37623e8	0.420048	0.210024	+	0.977696i	$0.432646\pi$
$272$	−3.10909e7	−0.0936789
$273$	0	0
$274$	−7.90685e8	−2.32208
$275$	1.72001e8	0.498730
$276$	0	0
$277$	1.18249e8	0.334286	0.167143	−	0.985933i	$-0.446546\pi$
$277$	1.18249e8	0.334286	0.167143	+	0.985933i	$0.446546\pi$
$278$	7.77269e7	0.216978
$279$	0	0
$280$	−6.86533e8	−1.86900
$281$	1.62690e8	0.437411	0.218705	−	0.975791i	$-0.429817\pi$
$281$	1.62690e8	0.437411	0.218705	+	0.975791i	$0.429817\pi$
$282$	0	0
$283$	−4.15031e8	−1.08850	−0.544249	−	0.838924i	$-0.683185\pi$
$283$	−4.15031e8	−1.08850	−0.544249	+	0.838924i	$0.683185\pi$
$284$	−1.99581e7	−0.0517016
$285$	0	0
$286$	−6.31495e8	−1.59621
$287$	−3.77013e8	−0.941391
$288$	0	0
$289$	−4.09738e8	−0.998537
$290$	−4.64413e8	−1.11818
$291$	0	0
$292$	−5.85968e8	−1.37732
$293$	−4.61387e8	−1.07159	−0.535796	−	0.844348i	$-0.679988\pi$
$293$	−4.61387e8	−1.07159	−0.535796	+	0.844348i	$0.679988\pi$
$294$	0	0
$295$	−3.07826e7	−0.0698118
$296$	−1.45314e9	−3.25676
$297$	0	0
$298$	−1.35468e9	−2.96537
$299$	1.88414e8	0.407629
$300$	0	0
$301$	1.04282e8	0.220408
$302$	−5.08263e8	−1.06185
$303$	0	0
$304$	1.69714e9	3.46467
$305$	−1.76595e8	−0.356393
$306$	0	0
$307$	7.27720e8	1.43542	0.717712	−	0.696340i	$-0.245189\pi$
$307$	7.27720e8	1.43542	0.717712	+	0.696340i	$0.245189\pi$
$308$	−1.15127e9	−2.24518
$309$	0	0
$310$	2.43224e8	0.463704
$311$	1.57441e8	0.296794	0.148397	−	0.988928i	$-0.452589\pi$
$311$	1.57441e8	0.296794	0.148397	+	0.988928i	$0.452589\pi$
$312$	0	0
$313$	−1.78754e8	−0.329497	−0.164748	−	0.986336i	$-0.552681\pi$
$313$	−1.78754e8	−0.329497	−0.164748	+	0.986336i	$0.552681\pi$
$314$	−8.66850e8	−1.58012
$315$	0	0
$316$	−8.29035e7	−0.147798
$317$	−5.72794e8	−1.00993	−0.504965	−	0.863140i	$-0.668495\pi$
$317$	−5.72794e8	−1.00993	−0.504965	+	0.863140i	$0.668495\pi$
$318$	0	0
$319$	−4.57416e8	−0.788939
$320$	3.33975e8	0.569756
$321$	0	0
$322$	4.85243e8	0.809961
$323$	−3.27717e7	−0.0541115
$324$	0	0
$325$	5.43381e8	0.878037
$326$	1.86520e9	2.98169
$327$	0	0
$328$	1.19706e9	1.87309
$329$	−1.31876e9	−2.04164
$330$	0	0
$331$	2.90899e8	0.440905	0.220452	−	0.975398i	$-0.429247\pi$
$331$	2.90899e8	0.440905	0.220452	+	0.975398i	$0.429247\pi$
$332$	2.98334e9	4.47425
$333$	0	0
$334$	1.20778e9	1.77367
$335$	−3.30162e8	−0.479810
$336$	0	0
$337$	1.34379e9	1.91261	0.956304	−	0.292374i	$-0.0944453\pi$
$337$	1.34379e9	1.91261	0.956304	+	0.292374i	$0.0944453\pi$
$338$	−6.81505e8	−0.959976
$339$	0	0
$340$	−3.60225e7	−0.0497047
$341$	2.39559e8	0.327169
$342$	0	0
$343$	−2.45581e8	−0.328599
$344$	−3.31108e8	−0.438546
$345$	0	0
$346$	3.56049e8	0.462109
$347$	−2.97139e8	−0.381774	−0.190887	−	0.981612i	$-0.561136\pi$
$347$	−2.97139e8	−0.381774	−0.190887	+	0.981612i	$0.561136\pi$
$348$	0	0
$349$	1.52383e9	1.91888	0.959440	−	0.281912i	$-0.0909687\pi$
$349$	1.52383e9	1.91888	0.959440	+	0.281912i	$0.0909687\pi$
$350$	1.39943e9	1.74466
$351$	0	0
$352$	1.08716e9	1.32860
$353$	5.87541e8	0.710930	0.355465	−	0.934690i	$-0.384323\pi$
$353$	5.87541e8	0.710930	0.355465	+	0.934690i	$0.384323\pi$
$354$	0	0
$355$	−9.64384e6	−0.0114407
$356$	−3.90934e9	−4.59228
$357$	0	0
$358$	−7.69036e8	−0.885841
$359$	−1.34525e9	−1.53452	−0.767262	−	0.641334i	$-0.778381\pi$
$359$	−1.34525e9	−1.53452	−0.767262	+	0.641334i	$0.778381\pi$
$360$	0	0
$361$	8.95021e8	1.00129
$362$	−2.25094e8	−0.249392
$363$	0	0
$364$	−3.63708e9	−3.95274
$365$	−2.83143e8	−0.304776
$366$	0	0
$367$	1.37516e9	1.45218	0.726090	−	0.687600i	$-0.241336\pi$
$367$	1.37516e9	1.45218	0.726090	+	0.687600i	$0.241336\pi$
$368$	−7.74430e8	−0.810056
$369$	0	0
$370$	−1.19550e9	−1.22700
$371$	1.62323e9	1.65033
$372$	0	0
$373$	−1.95269e8	−0.194829	−0.0974143	−	0.995244i	$-0.531057\pi$
$373$	−1.95269e8	−0.194829	−0.0974143	+	0.995244i	$0.531057\pi$
$374$	−5.01208e7	−0.0495413
$375$	0	0
$376$	4.18721e9	4.06226
$377$	−1.44506e9	−1.38896
$378$	0	0
$379$	−1.78491e9	−1.68414	−0.842071	−	0.539367i	$-0.818664\pi$
$379$	−1.78491e9	−1.68414	−0.842071	+	0.539367i	$0.818664\pi$
$380$	1.96635e9	1.83830
$381$	0	0
$382$	−9.75155e8	−0.895059
$383$	−1.02371e9	−0.931072	−0.465536	−	0.885029i	$-0.654138\pi$
$383$	−1.02371e9	−0.931072	−0.465536	+	0.885029i	$0.654138\pi$
$384$	0	0
$385$	−5.56301e8	−0.496818
$386$	1.27872e9	1.13167
$387$	0	0
$388$	−2.23702e9	−1.94428
$389$	−5.45849e8	−0.470163	−0.235082	−	0.971976i	$-0.575536\pi$
$389$	−5.45849e8	−0.470163	−0.235082	+	0.971976i	$0.575536\pi$
$390$	0	0
$391$	1.49542e7	0.0126515
$392$	−2.36092e9	−1.97961
$393$	0	0
$394$	1.55522e9	1.28102
$395$	−4.00594e7	−0.0327050
$396$	0	0
$397$	1.54111e9	1.23614	0.618070	−	0.786123i	$-0.287915\pi$
$397$	1.54111e9	1.23614	0.618070	+	0.786123i	$0.287915\pi$
$398$	3.76345e9	2.99224
$399$	0	0
$400$	−2.23343e9	−1.74487
$401$	1.87893e9	1.45514	0.727570	−	0.686034i	$-0.240650\pi$
$401$	1.87893e9	1.45514	0.727570	+	0.686034i	$0.240650\pi$
$402$	0	0
$403$	7.56811e8	0.575996
$404$	1.06734e9	0.805319
$405$	0	0
$406$	−3.72161e9	−2.75988
$407$	−1.17749e9	−0.865716
$408$	0	0
$409$	−1.97782e9	−1.42941	−0.714703	−	0.699428i	$-0.753438\pi$
$409$	−1.97782e9	−1.42941	−0.714703	+	0.699428i	$0.753438\pi$
$410$	9.84822e8	0.705691
$411$	0	0
$412$	−2.48232e9	−1.74871
$413$	−2.46679e8	−0.172309
$414$	0	0
$415$	1.44157e9	0.990071
$416$	3.43453e9	2.33906
$417$	0	0
$418$	2.73592e9	1.83226
$419$	−1.09100e9	−0.724561	−0.362280	−	0.932069i	$-0.618002\pi$
$419$	−1.09100e9	−0.724561	−0.362280	+	0.932069i	$0.618002\pi$
$420$	0	0
$421$	1.23434e9	0.806211	0.403105	−	0.915154i	$-0.367931\pi$
$421$	1.23434e9	0.806211	0.403105	+	0.915154i	$0.367931\pi$
$422$	3.56059e9	2.30637
$423$	0	0
$424$	−5.15393e9	−3.28366
$425$	4.31273e7	0.0272515
$426$	0	0
$427$	−1.41516e9	−0.879645
$428$	5.86426e9	3.61543
$429$	0	0
$430$	−2.72403e8	−0.165224
$431$	−2.37469e8	−0.142869	−0.0714343	−	0.997445i	$-0.522758\pi$
$431$	−2.37469e8	−0.142869	−0.0714343	+	0.997445i	$0.522758\pi$
$432$	0	0
$433$	2.89301e9	1.71255	0.856274	−	0.516522i	$-0.172774\pi$
$433$	2.89301e9	1.71255	0.856274	+	0.516522i	$0.172774\pi$
$434$	1.94909e9	1.14451
$435$	0	0
$436$	−4.60158e9	−2.65892
$437$	−8.16296e8	−0.467910
$438$	0	0
$439$	−1.35570e9	−0.764781	−0.382391	−	0.924001i	$-0.624899\pi$
$439$	−1.35570e9	−0.764781	−0.382391	+	0.924001i	$0.624899\pi$
$440$	1.76632e9	0.988519
$441$	0	0
$442$	−1.58341e8	−0.0872197
$443$	−1.36994e9	−0.748664	−0.374332	−	0.927295i	$-0.622128\pi$
$443$	−1.36994e9	−0.748664	−0.374332	+	0.927295i	$0.622128\pi$
$444$	0	0
$445$	−1.88901e9	−1.01619
$446$	2.64050e9	1.40934
$447$	0	0
$448$	2.67633e9	1.40627
$449$	−3.56894e9	−1.86070	−0.930352	−	0.366669i	$-0.880498\pi$
$449$	−3.56894e9	−1.86070	−0.930352	+	0.366669i	$0.880498\pi$
$450$	0	0
$451$	9.69984e8	0.497905
$452$	−4.69133e9	−2.38953
$453$	0	0
$454$	3.75976e9	1.88566
$455$	−1.75746e9	−0.874670
$456$	0	0
$457$	−1.58612e9	−0.777374	−0.388687	−	0.921370i	$-0.627071\pi$
$457$	−1.58612e9	−0.777374	−0.388687	+	0.921370i	$0.627071\pi$
$458$	−7.05709e9	−3.43239
$459$	0	0
$460$	−8.97270e8	−0.429804
$461$	2.42902e9	1.15472	0.577361	−	0.816489i	$-0.304083\pi$
$461$	2.42902e9	1.15472	0.577361	+	0.816489i	$0.304083\pi$
$462$	0	0
$463$	−2.06490e9	−0.966865	−0.483432	−	0.875382i	$-0.660610\pi$
$463$	−2.06490e9	−0.966865	−0.483432	+	0.875382i	$0.660610\pi$
$464$	5.93955e9	2.76020
$465$	0	0
$466$	4.25775e9	1.94908
$467$	2.28871e9	1.03988	0.519938	−	0.854204i	$-0.325955\pi$
$467$	2.28871e9	1.03988	0.519938	+	0.854204i	$0.325955\pi$
$468$	0	0
$469$	−2.64578e9	−1.18426
$470$	3.44482e9	1.53047
$471$	0	0
$472$	7.83234e8	0.342843
$473$	−2.68299e8	−0.116575
$474$	0	0
$475$	−2.35417e9	−1.00788
$476$	−2.88669e8	−0.122681
$477$	0	0
$478$	5.03891e9	2.11028
$479$	9.59752e8	0.399011	0.199505	−	0.979897i	$-0.436066\pi$
$479$	9.59752e8	0.399011	0.199505	+	0.979897i	$0.436066\pi$
$480$	0	0
$481$	−3.71989e9	−1.52413
$482$	−1.31532e9	−0.535017
$483$	0	0
$484$	−3.08258e9	−1.23582
$485$	−1.08094e9	−0.430234
$486$	0	0
$487$	8.78521e8	0.344668	0.172334	−	0.985039i	$-0.444869\pi$
$487$	8.78521e8	0.344668	0.172334	+	0.985039i	$0.444869\pi$
$488$	4.49329e9	1.75023
$489$	0	0
$490$	−1.94233e9	−0.745824
$491$	−1.17143e9	−0.446612	−0.223306	−	0.974748i	$-0.571685\pi$
$491$	−1.17143e9	−0.446612	−0.223306	+	0.974748i	$0.571685\pi$
$492$	0	0
$493$	−1.14692e8	−0.0431091
$494$	8.64328e9	3.22578
$495$	0	0
$496$	−3.11068e9	−1.14464
$497$	−7.72817e7	−0.0282377
$498$	0	0
$499$	3.72675e9	1.34270	0.671349	−	0.741142i	$-0.265715\pi$
$499$	3.72675e9	1.34270	0.671349	+	0.741142i	$0.265715\pi$
$500$	−6.21980e9	−2.22526
$501$	0	0
$502$	2.30778e9	0.814202
$503$	−5.09523e9	−1.78516	−0.892578	−	0.450894i	$-0.851105\pi$
$503$	−5.09523e9	−1.78516	−0.892578	+	0.450894i	$0.851105\pi$
$504$	0	0
$505$	5.15744e8	0.178203
$506$	−1.24844e9	−0.428391
$507$	0	0
$508$	1.11776e10	3.78291
$509$	−3.59219e9	−1.20739	−0.603693	−	0.797217i	$-0.706305\pi$
$509$	−3.59219e9	−1.20739	−0.603693	+	0.797217i	$0.706305\pi$
$510$	0	0
$511$	−2.26899e9	−0.752244
$512$	5.47042e9	1.80126
$513$	0	0
$514$	−1.67471e9	−0.543962
$515$	−1.19947e9	−0.386959
$516$	0	0
$517$	3.39292e9	1.07983
$518$	−9.58022e9	−3.02846
$519$	0	0
$520$	5.58012e9	1.74033
$521$	−5.07000e9	−1.57064	−0.785318	−	0.619092i	$-0.787501\pi$
$521$	−5.07000e9	−1.57064	−0.785318	+	0.619092i	$0.787501\pi$
$522$	0	0
$523$	4.99855e8	0.152788	0.0763938	−	0.997078i	$-0.475659\pi$
$523$	4.99855e8	0.152788	0.0763938	+	0.997078i	$0.475659\pi$
$524$	−3.57814e9	−1.08642
$525$	0	0
$526$	−2.99012e9	−0.895856
$527$	6.00669e7	0.0178771
$528$	0	0
$529$	−3.03234e9	−0.890600
$530$	−4.24014e9	−1.23713
$531$	0	0
$532$	1.57575e10	4.53728
$533$	3.06435e9	0.876584
$534$	0	0
$535$	2.83364e9	0.800031
$536$	8.40064e9	2.35633
$537$	0	0
$538$	−3.99464e9	−1.10596
$539$	−1.91306e9	−0.526222
$540$	0	0
$541$	5.11313e9	1.38834	0.694171	−	0.719810i	$-0.255771\pi$
$541$	5.11313e9	1.38834	0.694171	+	0.719810i	$0.255771\pi$
$542$	−2.88084e9	−0.777181
$543$	0	0
$544$	2.72593e8	0.0725971
$545$	−2.22351e9	−0.588371
$546$	0	0
$547$	−3.84269e8	−0.100387	−0.0501937	−	0.998739i	$-0.515984\pi$
$547$	−3.84269e8	−0.100387	−0.0501937	+	0.998739i	$0.515984\pi$
$548$	1.17164e10	3.04132
$549$	0	0
$550$	−3.60046e9	−0.922759
$551$	6.26065e9	1.59437
$552$	0	0
$553$	−3.21019e8	−0.0807222
$554$	−2.47528e9	−0.618501
$555$	0	0
$556$	−1.15176e9	−0.284184
$557$	−5.07247e9	−1.24373	−0.621866	−	0.783124i	$-0.713625\pi$
$557$	−5.07247e9	−1.24373	−0.621866	+	0.783124i	$0.713625\pi$
$558$	0	0
$559$	−8.47604e8	−0.205235
$560$	7.22358e9	1.73818
$561$	0	0
$562$	−3.40557e9	−0.809305
$563$	8.25453e8	0.194945	0.0974727	−	0.995238i	$-0.468924\pi$
$563$	8.25453e8	0.194945	0.0974727	+	0.995238i	$0.468924\pi$
$564$	0	0
$565$	−2.26688e9	−0.528760
$566$	8.68776e9	2.01396
$567$	0	0
$568$	2.45378e8	0.0561845
$569$	−4.84625e9	−1.10284	−0.551420	−	0.834228i	$-0.685914\pi$
$569$	−4.84625e9	−1.10284	−0.551420	+	0.834228i	$0.685914\pi$
$570$	0	0
$571$	2.06740e9	0.464728	0.232364	−	0.972629i	$-0.425354\pi$
$571$	2.06740e9	0.464728	0.232364	+	0.972629i	$0.425354\pi$
$572$	9.35751e9	2.09062
$573$	0	0
$574$	7.89195e9	1.74178
$575$	1.07424e9	0.235648
$576$	0	0
$577$	5.23872e9	1.13530	0.567649	−	0.823270i	$-0.307853\pi$
$577$	5.23872e9	1.13530	0.567649	+	0.823270i	$0.307853\pi$
$578$	8.57698e9	1.84751
$579$	0	0
$580$	6.88169e9	1.46453
$581$	1.15521e10	2.44368
$582$	0	0
$583$	−4.17625e9	−0.872865
$584$	7.20429e9	1.49674
$585$	0	0
$586$	9.65814e9	1.98268
$587$	5.79577e9	1.18271	0.591355	−	0.806411i	$-0.298593\pi$
$587$	5.79577e9	1.18271	0.591355	+	0.806411i	$0.298593\pi$
$588$	0	0
$589$	−3.27885e9	−0.661177
$590$	6.44367e8	0.129167
$591$	0	0
$592$	1.52897e10	3.02881
$593$	−6.07221e8	−0.119579	−0.0597896	−	0.998211i	$-0.519043\pi$
$593$	−6.07221e8	−0.119579	−0.0597896	+	0.998211i	$0.519043\pi$
$594$	0	0
$595$	−1.39486e8	−0.0271471
$596$	2.00736e10	3.88386
$597$	0	0
$598$	−3.94404e9	−0.754202
$599$	−7.83137e9	−1.48883	−0.744413	−	0.667720i	$-0.767270\pi$
$599$	−7.83137e9	−1.48883	−0.744413	+	0.667720i	$0.767270\pi$
$600$	0	0
$601$	−9.69564e9	−1.82186	−0.910932	−	0.412556i	$-0.864636\pi$
$601$	−9.69564e9	−1.82186	−0.910932	+	0.412556i	$0.864636\pi$
$602$	−2.18292e9	−0.407803
$603$	0	0
$604$	7.53145e9	1.39075
$605$	−1.48952e9	−0.273466
$606$	0	0
$607$	2.75108e9	0.499278	0.249639	−	0.968339i	$-0.419688\pi$
$607$	2.75108e9	0.499278	0.249639	+	0.968339i	$0.419688\pi$
$608$	−1.48799e10	−2.68497
$609$	0	0
$610$	3.69663e9	0.659405
$611$	1.07188e10	1.90109
$612$	0	0
$613$	−1.06940e10	−1.87511	−0.937557	−	0.347832i	$-0.886918\pi$
$613$	−1.06940e10	−1.87511	−0.937557	+	0.347832i	$0.886918\pi$
$614$	−1.52332e10	−2.65585
$615$	0	0
$616$	1.41545e10	2.43985
$617$	−3.67080e9	−0.629162	−0.314581	−	0.949231i	$-0.601864\pi$
$617$	−3.67080e9	−0.629162	−0.314581	+	0.949231i	$0.601864\pi$
$618$	0	0
$619$	−7.09568e9	−1.20248	−0.601238	−	0.799070i	$-0.705326\pi$
$619$	−7.09568e9	−1.20248	−0.601238	+	0.799070i	$0.705326\pi$
$620$	−3.60410e9	−0.607331
$621$	0	0
$622$	−3.29568e9	−0.549134
$623$	−1.51377e10	−2.50815
$624$	0	0
$625$	1.34303e9	0.220042
$626$	3.74183e9	0.609640
$627$	0	0
$628$	1.28450e10	2.06955
$629$	−2.95242e8	−0.0473043
$630$	0	0
$631$	−1.14862e10	−1.82000	−0.910001	−	0.414606i	$-0.863919\pi$
$631$	−1.14862e10	−1.82000	−0.910001	+	0.414606i	$0.863919\pi$
$632$	1.01927e9	0.160613
$633$	0	0
$634$	1.19902e10	1.86859
$635$	5.40108e9	0.837091
$636$	0	0
$637$	−6.04371e9	−0.926437
$638$	9.57500e9	1.45971
$639$	0	0
$640$	−2.41586e8	−0.0364285
$641$	7.81739e9	1.17235	0.586177	−	0.810183i	$-0.300633\pi$
$641$	7.81739e9	1.17235	0.586177	+	0.810183i	$0.300633\pi$
$642$	0	0
$643$	2.34946e9	0.348522	0.174261	−	0.984699i	$-0.444246\pi$
$643$	2.34946e9	0.348522	0.174261	+	0.984699i	$0.444246\pi$
$644$	−7.19034e9	−1.06084
$645$	0	0
$646$	6.86003e8	0.100118
$647$	−7.89807e9	−1.14645	−0.573226	−	0.819397i	$-0.694308\pi$
$647$	−7.89807e9	−1.14645	−0.573226	+	0.819397i	$0.694308\pi$
$648$	0	0
$649$	6.34658e8	0.0911347
$650$	−1.13745e10	−1.62456
$651$	0	0
$652$	−2.76385e10	−3.90525
$653$	−6.38444e8	−0.0897277	−0.0448639	−	0.998993i	$-0.514285\pi$
$653$	−6.38444e8	−0.0897277	−0.0448639	+	0.998993i	$0.514285\pi$
$654$	0	0
$655$	−1.72897e9	−0.240405
$656$	−1.25953e10	−1.74198
$657$	0	0
$658$	2.76053e10	3.77748
$659$	−8.08275e9	−1.10017	−0.550085	−	0.835108i	$-0.685405\pi$
$659$	−8.08275e9	−1.10017	−0.550085	+	0.835108i	$0.685405\pi$
$660$	0	0
$661$	9.43857e9	1.27116	0.635581	−	0.772034i	$-0.280761\pi$
$661$	9.43857e9	1.27116	0.635581	+	0.772034i	$0.280761\pi$
$662$	−6.08934e9	−0.815770
$663$	0	0
$664$	−3.66793e10	−4.86220
$665$	7.61409e9	1.00402
$666$	0	0
$667$	−2.85682e9	−0.372771
$668$	−1.78969e10	−2.32305
$669$	0	0
$670$	6.91121e9	0.887754
$671$	3.64094e9	0.465248
$672$	0	0
$673$	−1.08913e10	−1.37730	−0.688649	−	0.725095i	$-0.741796\pi$
$673$	−1.08913e10	−1.37730	−0.688649	+	0.725095i	$0.741796\pi$
$674$	−2.81293e10	−3.53874
$675$	0	0
$676$	1.00986e10	1.25732
$677$	1.25627e10	1.55604	0.778021	−	0.628238i	$-0.216223\pi$
$677$	1.25627e10	1.55604	0.778021	+	0.628238i	$0.216223\pi$
$678$	0	0
$679$	−8.66218e9	−1.06190
$680$	4.42886e8	0.0540145
$681$	0	0
$682$	−5.01465e9	−0.605335
$683$	1.74046e9	0.209022	0.104511	−	0.994524i	$-0.466672\pi$
$683$	1.74046e9	0.209022	0.104511	+	0.994524i	$0.466672\pi$
$684$	0	0
$685$	5.66142e9	0.672990
$686$	5.14071e9	0.607979
$687$	0	0
$688$	3.48386e9	0.407851
$689$	−1.31935e10	−1.53672
$690$	0	0
$691$	−1.58954e10	−1.83272	−0.916362	−	0.400351i	$-0.868888\pi$
$691$	−1.58954e10	−1.83272	−0.916362	+	0.400351i	$0.868888\pi$
$692$	−5.27595e9	−0.605242
$693$	0	0
$694$	6.21995e9	0.706364
$695$	−5.56536e8	−0.0628849
$696$	0	0
$697$	2.43213e8	0.0272065
$698$	−3.18981e10	−3.55035
$699$	0	0
$700$	−2.07367e10	−2.28506
$701$	−1.64503e10	−1.80369	−0.901844	−	0.432062i	$-0.857786\pi$
$701$	−1.64503e10	−1.80369	−0.901844	+	0.432062i	$0.857786\pi$
$702$	0	0
$703$	1.61162e10	1.74953
$704$	−6.88570e9	−0.743779
$705$	0	0
$706$	−1.22989e10	−1.31538
$707$	4.13295e9	0.439838
$708$	0	0
$709$	−8.21342e9	−0.865491	−0.432745	−	0.901516i	$-0.642455\pi$
$709$	−8.21342e9	−0.865491	−0.432745	+	0.901516i	$0.642455\pi$
$710$	2.01873e8	0.0211677
$711$	0	0
$712$	4.80641e10	4.99046
$713$	1.49618e9	0.154586
$714$	0	0
$715$	4.52160e9	0.462616
$716$	1.13956e10	1.16022
$717$	0	0
$718$	2.81600e10	2.83920
$719$	9.47920e9	0.951088	0.475544	−	0.879692i	$-0.342251\pi$
$719$	9.47920e9	0.951088	0.475544	+	0.879692i	$0.342251\pi$
$720$	0	0
$721$	−9.61206e9	−0.955087
$722$	−1.87353e10	−1.85260
$723$	0	0
$724$	3.33544e9	0.326639
$725$	−8.23897e9	−0.802953
$726$	0	0
$727$	−1.39173e10	−1.34333	−0.671667	−	0.740853i	$-0.734421\pi$
$727$	−1.39173e10	−1.34333	−0.671667	+	0.740853i	$0.734421\pi$
$728$	4.47168e10	4.29547
$729$	0	0
$730$	5.92697e9	0.563901
$731$	−6.72730e7	−0.00636986
$732$	0	0
$733$	−1.17895e10	−1.10569	−0.552843	−	0.833286i	$-0.686457\pi$
$733$	−1.17895e10	−1.10569	−0.552843	+	0.833286i	$0.686457\pi$
$734$	−2.87859e10	−2.68685
$735$	0	0
$736$	6.78992e9	0.627758
$737$	6.80708e9	0.626361
$738$	0	0
$739$	−4.71766e9	−0.430003	−0.215001	−	0.976614i	$-0.568976\pi$
$739$	−4.71766e9	−0.430003	−0.215001	+	0.976614i	$0.568976\pi$
$740$	1.77149e10	1.60705
$741$	0	0
$742$	−3.39787e10	−3.05347
$743$	8.49980e8	0.0760235	0.0380118	−	0.999277i	$-0.487898\pi$
$743$	8.49980e8	0.0760235	0.0380118	+	0.999277i	$0.487898\pi$
$744$	0	0
$745$	9.69968e9	0.859430
$746$	4.08753e9	0.360475
$747$	0	0
$748$	7.42691e8	0.0648863
$749$	2.27076e10	1.97463
$750$	0	0
$751$	1.12483e9	0.0969050	0.0484525	−	0.998825i	$-0.484571\pi$
$751$	1.12483e9	0.0969050	0.0484525	+	0.998825i	$0.484571\pi$
$752$	−4.40571e10	−3.77793
$753$	0	0
$754$	3.02492e10	2.56988
$755$	3.63924e9	0.307748
$756$	0	0
$757$	−2.61362e9	−0.218981	−0.109491	−	0.993988i	$-0.534922\pi$
$757$	−2.61362e9	−0.218981	−0.109491	+	0.993988i	$0.534922\pi$
$758$	3.73632e10	3.11603
$759$	0	0
$760$	−2.41756e10	−1.99770
$761$	−1.20945e10	−0.994817	−0.497408	−	0.867516i	$-0.665715\pi$
$761$	−1.20945e10	−0.994817	−0.497408	+	0.867516i	$0.665715\pi$
$762$	0	0
$763$	−1.78183e10	−1.45221
$764$	1.44499e10	1.17230
$765$	0	0
$766$	2.14292e10	1.72269
$767$	2.00500e9	0.160447
$768$	0	0
$769$	3.67326e9	0.291279	0.145639	−	0.989338i	$-0.453476\pi$
$769$	3.67326e9	0.291279	0.145639	+	0.989338i	$0.453476\pi$
$770$	1.16449e10	0.919221
$771$	0	0
$772$	−1.89480e10	−1.48219
$773$	2.06426e10	1.60744	0.803721	−	0.595007i	$-0.202851\pi$
$773$	2.06426e10	1.60744	0.803721	+	0.595007i	$0.202851\pi$
$774$	0	0
$775$	4.31494e9	0.332981
$776$	2.75034e10	2.11286
$777$	0	0
$778$	1.14262e10	0.869904
$779$	−1.32762e10	−1.00622
$780$	0	0
$781$	1.98831e8	0.0149350
$782$	−3.13033e8	−0.0234081
$783$	0	0
$784$	2.48412e10	1.84105
$785$	6.20677e9	0.457954
$786$	0	0
$787$	8.84372e7	0.00646731	0.00323365	−	0.999995i	$-0.498971\pi$
$787$	8.84372e7	0.00646731	0.00323365	+	0.999995i	$0.498971\pi$
$788$	−2.30454e10	−1.67781
$789$	0	0
$790$	8.38556e8	0.0605114
$791$	−1.81658e10	−1.30508
$792$	0	0
$793$	1.15024e10	0.819090
$794$	−3.22598e10	−2.28713
$795$	0	0
$796$	−5.57670e10	−3.91905
$797$	−1.12406e10	−0.786478	−0.393239	−	0.919436i	$-0.628646\pi$
$797$	−1.12406e10	−0.786478	−0.393239	+	0.919436i	$0.628646\pi$
$798$	0	0
$799$	8.50737e8	0.0590040
$800$	1.95819e10	1.35220
$801$	0	0
$802$	−3.93312e10	−2.69232
$803$	5.83767e9	0.397864
$804$	0	0
$805$	−3.47441e9	−0.234745
$806$	−1.58422e10	−1.06572
$807$	0	0
$808$	−1.31226e10	−0.875146
$809$	−2.81091e10	−1.86650	−0.933249	−	0.359230i	$-0.883039\pi$
$809$	−2.81091e10	−1.86650	−0.933249	+	0.359230i	$0.883039\pi$
$810$	0	0
$811$	2.83599e8	0.0186695	0.00933474	−	0.999956i	$-0.497029\pi$
$811$	2.83599e8	0.0186695	0.00933474	+	0.999956i	$0.497029\pi$
$812$	5.51469e10	3.61472
$813$	0	0
$814$	2.46481e10	1.60176
$815$	−1.33551e10	−0.864162
$816$	0	0
$817$	3.67220e9	0.235586
$818$	4.14014e10	2.64471
$819$	0	0
$820$	−1.45931e10	−0.924272
$821$	1.71158e10	1.07943	0.539717	−	0.841846i	$-0.318531\pi$
$821$	1.71158e10	1.07943	0.539717	+	0.841846i	$0.318531\pi$
$822$	0	0
$823$	−1.08622e10	−0.679235	−0.339618	−	0.940564i	$-0.610298\pi$
$823$	−1.08622e10	−0.679235	−0.339618	+	0.940564i	$0.610298\pi$
$824$	3.05194e10	1.90034
$825$	0	0
$826$	5.16369e9	0.318808
$827$	−1.34081e10	−0.824321	−0.412161	−	0.911111i	$-0.635226\pi$
$827$	−1.34081e10	−0.824321	−0.412161	+	0.911111i	$0.635226\pi$
$828$	0	0
$829$	1.85211e10	1.12908	0.564542	−	0.825404i	$-0.309053\pi$
$829$	1.85211e10	1.12908	0.564542	+	0.825404i	$0.309053\pi$
$830$	−3.01761e10	−1.83185
$831$	0	0
$832$	−2.17532e10	−1.30946
$833$	−4.79680e8	−0.0287537
$834$	0	0
$835$	−8.64785e9	−0.514050
$836$	−4.05410e10	−2.39978
$837$	0	0
$838$	2.28377e10	1.34059
$839$	3.61962e9	0.211591	0.105795	−	0.994388i	$-0.466261\pi$
$839$	3.61962e9	0.211591	0.105795	+	0.994388i	$0.466261\pi$
$840$	0	0
$841$	4.66072e9	0.270189
$842$	−2.58383e10	−1.49167
$843$	0	0
$844$	−5.27609e10	−3.02074
$845$	4.87967e9	0.278223
$846$	0	0
$847$	−1.19364e10	−0.674965
$848$	5.42288e10	3.05383
$849$	0	0
$850$	−9.02776e8	−0.0504213
$851$	−7.35406e9	−0.409047
$852$	0	0
$853$	−1.71198e10	−0.944448	−0.472224	−	0.881478i	$-0.656549\pi$
$853$	−1.71198e10	−0.944448	−0.472224	+	0.881478i	$0.656549\pi$
$854$	2.96233e10	1.62754
$855$	0	0
$856$	−7.20993e10	−3.92892
$857$	1.15451e10	0.626565	0.313282	−	0.949660i	$-0.398571\pi$
$857$	1.15451e10	0.626565	0.313282	+	0.949660i	$0.398571\pi$
$858$	0	0
$859$	4.99390e9	0.268821	0.134411	−	0.990926i	$-0.457086\pi$
$859$	4.99390e9	0.268821	0.134411	+	0.990926i	$0.457086\pi$
$860$	4.03647e9	0.216400
$861$	0	0
$862$	4.97090e9	0.264338
$863$	1.41398e9	0.0748867	0.0374434	−	0.999299i	$-0.488079\pi$
$863$	1.41398e9	0.0748867	0.0374434	+	0.999299i	$0.488079\pi$
$864$	0	0
$865$	−2.54937e9	−0.133929
$866$	−6.05589e10	−3.16859
$867$	0	0
$868$	−2.88817e10	−1.49901
$869$	8.25921e8	0.0426943
$870$	0	0
$871$	2.15048e10	1.10274
$872$	5.65750e10	2.88946
$873$	0	0
$874$	1.70874e10	0.865736
$875$	−2.40843e10	−1.21536
$876$	0	0
$877$	−4.65935e9	−0.233253	−0.116626	−	0.993176i	$-0.537208\pi$
$877$	−4.65935e9	−0.233253	−0.116626	+	0.993176i	$0.537208\pi$
$878$	2.83786e10	1.41501
$879$	0	0
$880$	−1.85849e10	−0.919329
$881$	−3.44643e10	−1.69806	−0.849031	−	0.528342i	$-0.822814\pi$
$881$	−3.44643e10	−1.69806	−0.849031	+	0.528342i	$0.822814\pi$
$882$	0	0
$883$	−1.49854e10	−0.732498	−0.366249	−	0.930517i	$-0.619358\pi$
$883$	−1.49854e10	−0.732498	−0.366249	+	0.930517i	$0.619358\pi$
$884$	2.34630e9	0.114235
$885$	0	0
$886$	2.86766e10	1.38519
$887$	−2.02649e10	−0.975015	−0.487508	−	0.873119i	$-0.662094\pi$
$887$	−2.02649e10	−0.975015	−0.487508	+	0.873119i	$0.662094\pi$
$888$	0	0
$889$	4.32820e10	2.06610
$890$	3.95423e10	1.88017
$891$	0	0
$892$	−3.91270e10	−1.84586
$893$	−4.64388e10	−2.18223
$894$	0	0
$895$	5.50641e9	0.256737
$896$	−1.93596e9	−0.0899123
$897$	0	0
$898$	7.47080e10	3.44271
$899$	−1.14751e10	−0.526741
$900$	0	0
$901$	−1.04715e9	−0.0476950
$902$	−2.03045e10	−0.921233
$903$	0	0
$904$	5.76785e10	2.59672
$905$	1.61170e9	0.0722795
$906$	0	0
$907$	2.55043e10	1.13498	0.567491	−	0.823380i	$-0.307914\pi$
$907$	2.55043e10	1.13498	0.567491	+	0.823380i	$0.307914\pi$
$908$	−5.57122e10	−2.46973
$909$	0	0
$910$	3.67885e10	1.61833
$911$	3.56300e10	1.56135	0.780677	−	0.624935i	$-0.214874\pi$
$911$	3.56300e10	1.56135	0.780677	+	0.624935i	$0.214874\pi$
$912$	0	0
$913$	−2.97214e10	−1.29247
$914$	3.32020e10	1.43831
$915$	0	0
$916$	1.04572e11	4.49554
$917$	−1.38553e10	−0.593366
$918$	0	0
$919$	−2.41602e10	−1.02682	−0.513412	−	0.858143i	$-0.671619\pi$
$919$	−2.41602e10	−1.02682	−0.513412	+	0.858143i	$0.671619\pi$
$920$	1.10317e10	0.467072
$921$	0	0
$922$	−5.08462e10	−2.13649
$923$	6.28143e8	0.0262938
$924$	0	0
$925$	−2.12089e10	−0.881093
$926$	4.32242e10	1.78891
$927$	0	0
$928$	−5.20758e10	−2.13904
$929$	−1.41353e9	−0.0578427	−0.0289214	−	0.999582i	$-0.509207\pi$
$929$	−1.41353e9	−0.0578427	−0.0289214	+	0.999582i	$0.509207\pi$
$930$	0	0
$931$	2.61841e10	1.06344
$932$	−6.30915e10	−2.55279
$933$	0	0
$934$	−4.79091e10	−1.92400
$935$	3.58872e8	0.0143582
$936$	0	0
$937$	3.20821e10	1.27402	0.637008	−	0.770857i	$-0.280172\pi$
$937$	3.20821e10	1.27402	0.637008	+	0.770857i	$0.280172\pi$
$938$	5.53835e10	2.19114
$939$	0	0
$940$	−5.10454e10	−2.00451
$941$	4.82625e10	1.88819	0.944096	−	0.329671i	$-0.106938\pi$
$941$	4.82625e10	1.88819	0.944096	+	0.329671i	$0.106938\pi$
$942$	0	0
$943$	6.05809e9	0.235258
$944$	−8.24105e9	−0.318846
$945$	0	0
$946$	5.61625e9	0.215689
$947$	−3.71988e9	−0.142333	−0.0711663	−	0.997464i	$-0.522672\pi$
$947$	−3.71988e9	−0.142333	−0.0711663	+	0.997464i	$0.522672\pi$
$948$	0	0
$949$	1.84423e10	0.700458
$950$	4.92795e10	1.86480
$951$	0	0
$952$	3.54910e9	0.133318
$953$	3.84659e10	1.43963	0.719814	−	0.694167i	$-0.244227\pi$
$953$	3.84659e10	1.43963	0.719814	+	0.694167i	$0.244227\pi$
$954$	0	0
$955$	6.98225e9	0.259408
$956$	−7.46667e10	−2.76391
$957$	0	0
$958$	−2.00903e10	−0.738257
$959$	4.53682e10	1.66107
$960$	0	0
$961$	−2.15028e10	−0.781563
$962$	7.78678e10	2.81997
$963$	0	0
$964$	1.94905e10	0.700733
$965$	−9.15579e9	−0.327982
$966$	0	0
$967$	−1.01210e10	−0.359942	−0.179971	−	0.983672i	$-0.557600\pi$
$967$	−1.01210e10	−0.359942	−0.179971	+	0.983672i	$0.557600\pi$
$968$	3.78994e10	1.34298
$969$	0	0
$970$	2.26271e10	0.796027
$971$	−3.40438e10	−1.19336	−0.596679	−	0.802480i	$-0.703513\pi$
$971$	−3.40438e10	−1.19336	−0.596679	+	0.802480i	$0.703513\pi$
$972$	0	0
$973$	−4.45985e9	−0.155212
$974$	−1.83899e10	−0.637710
$975$	0	0
$976$	−4.72776e10	−1.62773
$977$	1.56624e10	0.537314	0.268657	−	0.963236i	$-0.413420\pi$
$977$	1.56624e10	0.537314	0.268657	+	0.963236i	$0.413420\pi$
$978$	0	0
$979$	3.89465e10	1.32657
$980$	2.87815e10	0.976836
$981$	0	0
$982$	2.45213e10	0.826330
$983$	3.86584e10	1.29810	0.649048	−	0.760747i	$-0.275167\pi$
$983$	3.86584e10	1.29810	0.649048	+	0.760747i	$0.275167\pi$
$984$	0	0
$985$	−1.11356e10	−0.371269
$986$	2.40083e9	0.0797613
$987$	0	0
$988$	−1.28076e11	−4.22493
$989$	−1.67568e9	−0.0550811
$990$	0	0
$991$	1.35643e10	0.442731	0.221365	−	0.975191i	$-0.428949\pi$
$991$	1.35643e10	0.442731	0.221365	+	0.975191i	$0.428949\pi$
$992$	2.72733e10	0.887048
$993$	0	0
$994$	1.61772e9	0.0522459
$995$	−2.69469e10	−0.867217
$996$	0	0
$997$	−4.26350e10	−1.36249	−0.681245	−	0.732055i	$-0.738561\pi$
$997$	−4.26350e10	−1.36249	−0.681245	+	0.732055i	$0.738561\pi$
$998$	−7.80113e10	−2.48428
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.e.1.2		18
3.2	odd	2		177.8.a.d.1.17	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.17	✓	18	3.2	odd	2
531.8.a.e.1.2		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-20.9328 q^{2} +310.183 q^{4} +149.882 q^{5} +1201.09 q^{7} -3813.60 q^{8} +O(q^{10})\)	\(q-20.9328 q^{2} +310.183 q^{4} +149.882 q^{5} +1201.09 q^{7} -3813.60 q^{8} -3137.45 q^{10} -3090.18 q^{11} -9762.44 q^{13} -25142.2 q^{14} +40126.1 q^{16} -774.830 q^{17} +42295.3 q^{19} +46490.9 q^{20} +64686.2 q^{22} -19299.9 q^{23} -55660.4 q^{25} +204355. q^{26} +372558. q^{28} +148022. q^{29} -77522.7 q^{31} -351811. q^{32} +16219.4 q^{34} +180022. q^{35} +381041. q^{37} -885360. q^{38} -571591. q^{40} -313892. q^{41} +86822.9 q^{43} -958522. q^{44} +404002. q^{46} -1.09797e6 q^{47} +619078. q^{49} +1.16513e6 q^{50} -3.02814e6 q^{52} +1.35146e6 q^{53} -463163. q^{55} -4.58049e6 q^{56} -3.09852e6 q^{58} -205379. q^{59} -1.17823e6 q^{61} +1.62277e6 q^{62} +2.22825e6 q^{64} -1.46321e6 q^{65} -2.20281e6 q^{67} -240339. q^{68} -3.76837e6 q^{70} -64342.9 q^{71} -1.88910e6 q^{73} -7.97626e6 q^{74} +1.31193e7 q^{76} -3.71159e6 q^{77} -267273. q^{79} +6.01418e6 q^{80} +6.57065e6 q^{82} +9.61801e6 q^{83} -116133. q^{85} -1.81745e6 q^{86} +1.17847e7 q^{88} -1.26033e7 q^{89} -1.17256e7 q^{91} -5.98651e6 q^{92} +2.29835e7 q^{94} +6.33931e6 q^{95} -7.21193e6 q^{97} -1.29590e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Introduction

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