LMFDB - Embedded newform 531.8.a.d.1.4

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:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$15.6681$ 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)

$f(q)$	$=$	$q-13.6681 q^{2} +58.8158 q^{4} +207.404 q^{5} +882.793 q^{7} +945.614 q^{8} +O(q^{10})$	\(q-13.6681 q^{2} +58.8158 q^{4} +207.404 q^{5} +882.793 q^{7} +945.614 q^{8} -2834.81 q^{10} +3637.21 q^{11} +208.023 q^{13} -12066.1 q^{14} -20453.1 q^{16} +13120.6 q^{17} -9914.89 q^{19} +12198.6 q^{20} -49713.6 q^{22} +37757.5 q^{23} -35108.6 q^{25} -2843.27 q^{26} +51922.2 q^{28} +98092.3 q^{29} +326883. q^{31} +158516. q^{32} -179333. q^{34} +183095. q^{35} +39434.0 q^{37} +135517. q^{38} +196124. q^{40} +719442. q^{41} -878099. q^{43} +213925. q^{44} -516072. q^{46} +158129. q^{47} -44219.7 q^{49} +479867. q^{50} +12235.0 q^{52} +1.83479e6 q^{53} +754372. q^{55} +834781. q^{56} -1.34073e6 q^{58} +205379. q^{59} +3.49764e6 q^{61} -4.46786e6 q^{62} +451395. q^{64} +43144.8 q^{65} -1.00103e6 q^{67} +771700. q^{68} -2.50255e6 q^{70} -331392. q^{71} -527191. q^{73} -538987. q^{74} -583152. q^{76} +3.21090e6 q^{77} -1.50960e6 q^{79} -4.24206e6 q^{80} -9.83337e6 q^{82} -2.48775e6 q^{83} +2.72127e6 q^{85} +1.20019e7 q^{86} +3.43940e6 q^{88} -6.37807e6 q^{89} +183641. q^{91} +2.22074e6 q^{92} -2.16132e6 q^{94} -2.05639e6 q^{95} -4.33428e6 q^{97} +604398. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) $ 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * 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 $

$2$	−13.6681	−1.20810	−0.604049	−	0.796948i	$-0.706447\pi$
$2$	−13.6681	−1.20810	−0.604049	+	0.796948i	$0.706447\pi$
$3$	0	0
$3$	0	0
$4$	58.8158	0.459498
$5$	207.404	0.742031	0.371015	−	0.928627i	$-0.379010\pi$
$5$	207.404	0.742031	0.371015	+	0.928627i	$0.379010\pi$
$6$	0	0
$7$	882.793	0.972782	0.486391	−	0.873741i	$-0.338313\pi$
$7$	882.793	0.972782	0.486391	+	0.873741i	$0.338313\pi$
$8$	945.614	0.652978
$9$	0	0
$10$	−2834.81	−0.896445
$11$	3637.21	0.823937	0.411969	−	0.911198i	$-0.364841\pi$
$11$	3637.21	0.823937	0.411969	+	0.911198i	$0.364841\pi$
$12$	0	0
$13$	208.023	0.0262609	0.0131305	−	0.999914i	$-0.495820\pi$
$13$	208.023	0.0262609	0.0131305	+	0.999914i	$0.495820\pi$
$14$	−12066.1	−1.17522
$15$	0	0
$16$	−20453.1	−1.24836
$17$	13120.6	0.647714	0.323857	−	0.946106i	$-0.395020\pi$
$17$	13120.6	0.647714	0.323857	+	0.946106i	$0.395020\pi$
$18$	0	0
$19$	−9914.89	−0.331627	−0.165814	−	0.986157i	$-0.553025\pi$
$19$	−9914.89	−0.331627	−0.165814	+	0.986157i	$0.553025\pi$
$20$	12198.6	0.340962
$21$	0	0
$22$	−49713.6	−0.995396
$23$	37757.5	0.647077	0.323538	−	0.946215i	$-0.395128\pi$
$23$	37757.5	0.647077	0.323538	+	0.946215i	$0.395128\pi$
$24$	0	0
$25$	−35108.6	−0.449391
$26$	−2843.27	−0.0317257
$27$	0	0
$28$	51922.2	0.446992
$29$	98092.3	0.746865	0.373432	−	0.927657i	$-0.378181\pi$
$29$	98092.3	0.746865	0.373432	+	0.927657i	$0.378181\pi$
$30$	0	0
$31$	326883.	1.97073	0.985364	−	0.170463i	$-0.0545265\pi$
$31$	326883.	1.97073	0.985364	+	0.170463i	$0.0545265\pi$
$32$	158516.	0.855161
$33$	0	0
$34$	−179333.	−0.782501
$35$	183095.	0.721834
$36$	0	0
$37$	39434.0	0.127987	0.0639934	−	0.997950i	$-0.479616\pi$
$37$	39434.0	0.127987	0.0639934	+	0.997950i	$0.479616\pi$
$38$	135517.	0.400638
$39$	0	0
$40$	196124.	0.484530
$41$	719442.	1.63024	0.815121	−	0.579291i	$-0.196670\pi$
$41$	719442.	1.63024	0.815121	+	0.579291i	$0.196670\pi$
$42$	0	0
$43$	−878099.	−1.68424	−0.842120	−	0.539290i	$-0.818693\pi$
$43$	−878099.	−1.68424	−0.842120	+	0.539290i	$0.818693\pi$
$44$	213925.	0.378598
$45$	0	0
$46$	−516072.	−0.781731
$47$	158129.	0.222162	0.111081	−	0.993811i	$-0.464569\pi$
$47$	158129.	0.222162	0.111081	+	0.993811i	$0.464569\pi$
$48$	0	0
$49$	−44219.7	−0.0536945
$50$	479867.	0.542907
$51$	0	0
$52$	12235.0	0.0120669
$53$	1.83479e6	1.69286	0.846429	−	0.532502i	$-0.178748\pi$
$53$	1.83479e6	1.69286	0.846429	+	0.532502i	$0.178748\pi$
$54$	0	0
$55$	754372.	0.611387
$56$	834781.	0.635206
$57$	0	0
$58$	−1.34073e6	−0.902285
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	3.49764e6	1.97297	0.986485	−	0.163851i	$-0.0523917\pi$
$61$	3.49764e6	1.97297	0.986485	+	0.163851i	$0.0523917\pi$
$62$	−4.46786e6	−2.38083
$63$	0	0
$64$	451395.	0.215242
$65$	43144.8	0.0194864
$66$	0	0
$67$	−1.00103e6	−0.406615	−0.203308	−	0.979115i	$-0.565169\pi$
$67$	−1.00103e6	−0.406615	−0.203308	+	0.979115i	$0.565169\pi$
$68$	771700.	0.297623
$69$	0	0
$70$	−2.50255e6	−0.872046
$71$	−331392.	−0.109885	−0.0549423	−	0.998490i	$-0.517498\pi$
$71$	−331392.	−0.109885	−0.0549423	+	0.998490i	$0.517498\pi$
$72$	0	0
$73$	−527191.	−0.158613	−0.0793063	−	0.996850i	$-0.525271\pi$
$73$	−527191.	−0.158613	−0.0793063	+	0.996850i	$0.525271\pi$
$74$	−538987.	−0.154620
$75$	0	0
$76$	−583152.	−0.152382
$77$	3.21090e6	0.801512
$78$	0	0
$79$	−1.50960e6	−0.344481	−0.172241	−	0.985055i	$-0.555101\pi$
$79$	−1.50960e6	−0.344481	−0.172241	+	0.985055i	$0.555101\pi$
$80$	−4.24206e6	−0.926321
$81$	0	0
$82$	−9.83337e6	−1.96949
$83$	−2.48775e6	−0.477566	−0.238783	−	0.971073i	$-0.576748\pi$
$83$	−2.48775e6	−0.477566	−0.238783	+	0.971073i	$0.576748\pi$
$84$	0	0
$85$	2.72127e6	0.480623
$86$	1.20019e7	2.03472
$87$	0	0
$88$	3.43940e6	0.538013
$89$	−6.37807e6	−0.959013	−0.479506	−	0.877538i	$-0.659184\pi$
$89$	−6.37807e6	−0.959013	−0.479506	+	0.877538i	$0.659184\pi$
$90$	0	0
$91$	183641.	0.0255462
$92$	2.22074e6	0.297331
$93$	0	0
$94$	−2.16132e6	−0.268393
$95$	−2.05639e6	−0.246078
$96$	0	0
$97$	−4.33428e6	−0.482187	−0.241094	−	0.970502i	$-0.577506\pi$
$97$	−4.33428e6	−0.482187	−0.241094	+	0.970502i	$0.577506\pi$
$98$	604398.	0.0648682
$99$	0	0
$100$	−2.06494e6	−0.206494
$101$	−6.87221e6	−0.663700	−0.331850	−	0.943332i	$-0.607673\pi$
$101$	−6.87221e6	−0.663700	−0.331850	+	0.943332i	$0.607673\pi$
$102$	0	0
$103$	1.71578e6	0.154715	0.0773574	−	0.997003i	$-0.475352\pi$
$103$	1.71578e6	0.154715	0.0773574	+	0.997003i	$0.475352\pi$
$104$	196710.	0.0171478
$105$	0	0
$106$	−2.50780e7	−2.04514
$107$	7.08886e6	0.559414	0.279707	−	0.960085i	$-0.409763\pi$
$107$	7.08886e6	0.559414	0.279707	+	0.960085i	$0.409763\pi$
$108$	0	0
$109$	2.29535e7	1.69768	0.848840	−	0.528650i	$-0.177301\pi$
$109$	2.29535e7	1.69768	0.848840	+	0.528650i	$0.177301\pi$
$110$	−1.03108e7	−0.738614
$111$	0	0
$112$	−1.80559e7	−1.21438
$113$	1.69616e7	1.10584	0.552919	−	0.833235i	$-0.313514\pi$
$113$	1.69616e7	1.10584	0.552919	+	0.833235i	$0.313514\pi$
$114$	0	0
$115$	7.83105e6	0.480151
$116$	5.76938e6	0.343183
$117$	0	0
$118$	−2.80713e6	−0.157281
$119$	1.15828e7	0.630084
$120$	0	0
$121$	−6.25787e6	−0.321127
$122$	−4.78059e7	−2.38354
$123$	0	0
$124$	1.92259e7	0.905546
$125$	−2.34851e7	−1.07549
$126$	0	0
$127$	−1.24664e7	−0.540044	−0.270022	−	0.962854i	$-0.587031\pi$
$127$	−1.24664e7	−0.540044	−0.270022	+	0.962854i	$0.587031\pi$
$128$	−2.64597e7	−1.11519
$129$	0	0
$130$	−589706.	−0.0235415
$131$	−4.68201e7	−1.81963	−0.909815	−	0.415015i	$-0.863776\pi$
$131$	−4.68201e7	−1.81963	−0.909815	+	0.415015i	$0.863776\pi$
$132$	0	0
$133$	−8.75279e6	−0.322601
$134$	1.36821e7	0.491231
$135$	0	0
$136$	1.24070e7	0.422943
$137$	1.03397e7	0.343545	0.171773	−	0.985137i	$-0.445051\pi$
$137$	1.03397e7	0.343545	0.171773	+	0.985137i	$0.445051\pi$
$138$	0	0
$139$	−3.07437e7	−0.970965	−0.485483	−	0.874246i	$-0.661356\pi$
$139$	−3.07437e7	−0.970965	−0.485483	+	0.874246i	$0.661356\pi$
$140$	1.07689e7	0.331682
$141$	0	0
$142$	4.52948e6	0.132751
$143$	756624.	0.0216374
$144$	0	0
$145$	2.03447e7	0.554196
$146$	7.20567e6	0.191619
$147$	0	0
$148$	2.31934e6	0.0588097
$149$	−3.66220e6	−0.0906963	−0.0453482	−	0.998971i	$-0.514440\pi$
$149$	−3.66220e6	−0.0906963	−0.0453482	+	0.998971i	$0.514440\pi$
$150$	0	0
$151$	7.28781e7	1.72257	0.861286	−	0.508120i	$-0.169659\pi$
$151$	7.28781e7	1.72257	0.861286	+	0.508120i	$0.169659\pi$
$152$	−9.37565e6	−0.216545
$153$	0	0
$154$	−4.38868e7	−0.968304
$155$	6.77968e7	1.46234
$156$	0	0
$157$	−9.09496e7	−1.87565	−0.937826	−	0.347106i	$-0.887164\pi$
$157$	−9.09496e7	−1.87565	−0.937826	+	0.347106i	$0.887164\pi$
$158$	2.06332e7	0.416167
$159$	0	0
$160$	3.28768e7	0.634556
$161$	3.33320e7	0.629465
$162$	0	0
$163$	5.62746e7	1.01778	0.508892	−	0.860830i	$-0.330055\pi$
$163$	5.62746e7	1.01778	0.508892	+	0.860830i	$0.330055\pi$
$164$	4.23145e7	0.749094
$165$	0	0
$166$	3.40027e7	0.576945
$167$	−3.21050e7	−0.533415	−0.266707	−	0.963778i	$-0.585936\pi$
$167$	−3.21050e7	−0.533415	−0.266707	+	0.963778i	$0.585936\pi$
$168$	0	0
$169$	−6.27052e7	−0.999310
$170$	−3.71944e7	−0.580640
$171$	0	0
$172$	−5.16461e7	−0.773905
$173$	−7.85878e7	−1.15397	−0.576984	−	0.816756i	$-0.695770\pi$
$173$	−7.85878e7	−1.15397	−0.576984	+	0.816756i	$0.695770\pi$
$174$	0	0
$175$	−3.09937e7	−0.437159
$176$	−7.43923e7	−1.02857
$177$	0	0
$178$	8.71759e7	1.15858
$179$	5.87666e7	0.765853	0.382926	−	0.923779i	$-0.374916\pi$
$179$	5.87666e7	0.765853	0.382926	+	0.923779i	$0.374916\pi$
$180$	0	0
$181$	−4.81650e7	−0.603749	−0.301875	−	0.953348i	$-0.597612\pi$
$181$	−4.81650e7	−0.603749	−0.301875	+	0.953348i	$0.597612\pi$
$182$	−2.51002e6	−0.0308622
$183$	0	0
$184$	3.57040e7	0.422527
$185$	8.17877e6	0.0949701
$186$	0	0
$187$	4.77225e7	0.533675
$188$	9.30049e6	0.102083
$189$	0	0
$190$	2.81068e7	0.297286
$191$	−1.65487e8	−1.71849	−0.859247	−	0.511560i	$-0.829068\pi$
$191$	−1.65487e8	−1.71849	−0.859247	+	0.511560i	$0.829068\pi$
$192$	0	0
$193$	−1.11360e8	−1.11501	−0.557504	−	0.830174i	$-0.688241\pi$
$193$	−1.11360e8	−1.11501	−0.557504	+	0.830174i	$0.688241\pi$
$194$	5.92412e7	0.582529
$195$	0	0
$196$	−2.60082e6	−0.0246725
$197$	−3.64560e7	−0.339733	−0.169866	−	0.985467i	$-0.554334\pi$
$197$	−3.64560e7	−0.339733	−0.169866	+	0.985467i	$0.554334\pi$
$198$	0	0
$199$	7.61265e7	0.684779	0.342389	−	0.939558i	$-0.388764\pi$
$199$	7.61265e7	0.684779	0.342389	+	0.939558i	$0.388764\pi$
$200$	−3.31992e7	−0.293442
$201$	0	0
$202$	9.39298e7	0.801814
$203$	8.65952e7	0.726537
$204$	0	0
$205$	1.49215e8	1.20969
$206$	−2.34514e7	−0.186911
$207$	0	0
$208$	−4.25472e6	−0.0327831
$209$	−3.60625e7	−0.273240
$210$	0	0
$211$	2.35187e8	1.72355	0.861775	−	0.507291i	$-0.169353\pi$
$211$	2.35187e8	1.72355	0.861775	+	0.507291i	$0.169353\pi$
$212$	1.07915e8	0.777866
$213$	0	0
$214$	−9.68910e7	−0.675826
$215$	−1.82121e8	−1.24976
$216$	0	0
$217$	2.88570e8	1.91709
$218$	−3.13730e8	−2.05096
$219$	0	0
$220$	4.43690e7	0.280931
$221$	2.72939e6	0.0170096
$222$	0	0
$223$	1.57494e8	0.951036	0.475518	−	0.879706i	$-0.342261\pi$
$223$	1.57494e8	0.951036	0.475518	+	0.879706i	$0.342261\pi$
$224$	1.39937e8	0.831886
$225$	0	0
$226$	−2.31832e8	−1.33596
$227$	4.25579e7	0.241485	0.120742	−	0.992684i	$-0.461473\pi$
$227$	4.25579e7	0.241485	0.120742	+	0.992684i	$0.461473\pi$
$228$	0	0
$229$	−5.07210e7	−0.279103	−0.139551	−	0.990215i	$-0.544566\pi$
$229$	−5.07210e7	−0.279103	−0.139551	+	0.990215i	$0.544566\pi$
$230$	−1.07035e8	−0.580069
$231$	0	0
$232$	9.27574e7	0.487686
$233$	2.44954e8	1.26864	0.634321	−	0.773069i	$-0.281280\pi$
$233$	2.44954e8	1.26864	0.634321	+	0.773069i	$0.281280\pi$
$234$	0	0
$235$	3.27966e7	0.164851
$236$	1.20795e7	0.0598216
$237$	0	0
$238$	−1.58314e8	−0.761203
$239$	3.38900e6	0.0160575	0.00802877	−	0.999968i	$-0.497444\pi$
$239$	3.38900e6	0.0160575	0.00802877	+	0.999968i	$0.497444\pi$
$240$	0	0
$241$	2.42976e8	1.11816	0.559080	−	0.829114i	$-0.311155\pi$
$241$	2.42976e8	1.11816	0.559080	+	0.829114i	$0.311155\pi$
$242$	8.55329e7	0.387953
$243$	0	0
$244$	2.05716e8	0.906577
$245$	−9.17134e6	−0.0398430
$246$	0	0
$247$	−2.06253e6	−0.00870884
$248$	3.09105e8	1.28684
$249$	0	0
$250$	3.20996e8	1.29930
$251$	1.00242e7	0.0400120	0.0200060	−	0.999800i	$-0.493631\pi$
$251$	1.00242e7	0.0400120	0.0200060	+	0.999800i	$0.493631\pi$
$252$	0	0
$253$	1.37332e8	0.533150
$254$	1.70392e8	0.652425
$255$	0	0
$256$	3.03875e8	1.13202
$257$	1.65390e8	0.607774	0.303887	−	0.952708i	$-0.401715\pi$
$257$	1.65390e8	0.607774	0.303887	+	0.952708i	$0.401715\pi$
$258$	0	0
$259$	3.48121e7	0.124503
$260$	2.53760e6	0.00895397
$261$	0	0
$262$	6.39940e8	2.19829
$263$	3.86525e8	1.31019	0.655093	−	0.755549i	$-0.272630\pi$
$263$	3.86525e8	1.31019	0.655093	+	0.755549i	$0.272630\pi$
$264$	0	0
$265$	3.80542e8	1.25615
$266$	1.19634e8	0.389734
$267$	0	0
$268$	−5.88762e7	−0.186839
$269$	−2.13282e8	−0.668070	−0.334035	−	0.942561i	$-0.608410\pi$
$269$	−2.13282e8	−0.668070	−0.334035	+	0.942561i	$0.608410\pi$
$270$	0	0
$271$	−5.08751e7	−0.155279	−0.0776396	−	0.996981i	$-0.524738\pi$
$271$	−5.08751e7	−0.155279	−0.0776396	+	0.996981i	$0.524738\pi$
$272$	−2.68358e8	−0.808580
$273$	0	0
$274$	−1.41323e8	−0.415036
$275$	−1.27698e8	−0.370270
$276$	0	0
$277$	−4.14639e8	−1.17217	−0.586086	−	0.810249i	$-0.699332\pi$
$277$	−4.14639e8	−1.17217	−0.586086	+	0.810249i	$0.699332\pi$
$278$	4.20206e8	1.17302
$279$	0	0
$280$	1.73137e8	0.471342
$281$	3.84206e8	1.03298	0.516491	−	0.856293i	$-0.327238\pi$
$281$	3.84206e8	1.03298	0.516491	+	0.856293i	$0.327238\pi$
$282$	0	0
$283$	4.66433e8	1.22331	0.611656	−	0.791124i	$-0.290504\pi$
$283$	4.66433e8	1.22331	0.611656	+	0.791124i	$0.290504\pi$
$284$	−1.94911e7	−0.0504918
$285$	0	0
$286$	−1.03416e7	−0.0261400
$287$	6.35118e8	1.58587
$288$	0	0
$289$	−2.38188e8	−0.580467
$290$	−2.78073e8	−0.669523
$291$	0	0
$292$	−3.10071e7	−0.0728823
$293$	7.57454e8	1.75922	0.879609	−	0.475697i	$-0.157804\pi$
$293$	7.57454e8	1.75922	0.879609	+	0.475697i	$0.157804\pi$
$294$	0	0
$295$	4.25964e7	0.0966042
$296$	3.72894e7	0.0835726
$297$	0	0
$298$	5.00551e7	0.109570
$299$	7.85443e6	0.0169928
$300$	0	0
$301$	−7.75180e8	−1.63840
$302$	−9.96101e8	−2.08103
$303$	0	0
$304$	2.02790e8	0.413990
$305$	7.25424e8	1.46400
$306$	0	0
$307$	−5.11428e8	−1.00879	−0.504394	−	0.863473i	$-0.668284\pi$
$307$	−5.11428e8	−1.00879	−0.504394	+	0.863473i	$0.668284\pi$
$308$	1.88852e8	0.368293
$309$	0	0
$310$	−9.26651e8	−1.76665
$311$	−4.47095e8	−0.842826	−0.421413	−	0.906869i	$-0.638466\pi$
$311$	−4.47095e8	−0.842826	−0.421413	+	0.906869i	$0.638466\pi$
$312$	0	0
$313$	−3.05704e7	−0.0563503	−0.0281751	−	0.999603i	$-0.508970\pi$
$313$	−3.05704e7	−0.0563503	−0.0281751	+	0.999603i	$0.508970\pi$
$314$	1.24310e9	2.26597
$315$	0	0
$316$	−8.87881e7	−0.158289
$317$	2.57462e8	0.453948	0.226974	−	0.973901i	$-0.427117\pi$
$317$	2.57462e8	0.453948	0.226974	+	0.973901i	$0.427117\pi$
$318$	0	0
$319$	3.56782e8	0.615370
$320$	9.36211e7	0.159716
$321$	0	0
$322$	−4.55584e8	−0.760454
$323$	−1.30089e8	−0.214800
$324$	0	0
$325$	−7.30341e6	−0.0118014
$326$	−7.69164e8	−1.22958
$327$	0	0
$328$	6.80314e8	1.06451
$329$	1.39595e8	0.216115
$330$	0	0
$331$	6.68825e8	1.01371	0.506856	−	0.862031i	$-0.330808\pi$
$331$	6.68825e8	1.01371	0.506856	+	0.862031i	$0.330808\pi$
$332$	−1.46319e8	−0.219441
$333$	0	0
$334$	4.38813e8	0.644417
$335$	−2.07617e8	−0.301721
$336$	0	0
$337$	1.47419e7	0.0209821	0.0104911	−	0.999945i	$-0.496661\pi$
$337$	1.47419e7	0.0209821	0.0104911	+	0.999945i	$0.496661\pi$
$338$	8.57059e8	1.20726
$339$	0	0
$340$	1.60053e8	0.220846
$341$	1.18894e9	1.62376
$342$	0	0
$343$	−7.66055e8	−1.02502
$344$	−8.30342e8	−1.09977
$345$	0	0
$346$	1.07414e9	1.39410
$347$	6.05234e8	0.777625	0.388812	−	0.921317i	$-0.372885\pi$
$347$	6.05234e8	0.777625	0.388812	+	0.921317i	$0.372885\pi$
$348$	0	0
$349$	−1.02679e9	−1.29298	−0.646491	−	0.762922i	$-0.723764\pi$
$349$	−1.02679e9	−1.29298	−0.646491	+	0.762922i	$0.723764\pi$
$350$	4.23623e8	0.528131
$351$	0	0
$352$	5.76556e8	0.704599
$353$	1.41214e9	1.70870	0.854352	−	0.519695i	$-0.173954\pi$
$353$	1.41214e9	1.70870	0.854352	+	0.519695i	$0.173954\pi$
$354$	0	0
$355$	−6.87319e7	−0.0815378
$356$	−3.75131e8	−0.440665
$357$	0	0
$358$	−8.03226e8	−0.925224
$359$	2.89775e8	0.330545	0.165272	−	0.986248i	$-0.447150\pi$
$359$	2.89775e8	0.330545	0.165272	+	0.986248i	$0.447150\pi$
$360$	0	0
$361$	−7.95567e8	−0.890023
$362$	6.58322e8	0.729388
$363$	0	0
$364$	1.08010e7	0.0117384
$365$	−1.09341e8	−0.117695
$366$	0	0
$367$	−6.11428e8	−0.645676	−0.322838	−	0.946454i	$-0.604637\pi$
$367$	−6.11428e8	−0.645676	−0.322838	+	0.946454i	$0.604637\pi$
$368$	−7.72259e8	−0.807784
$369$	0	0
$370$	−1.11788e8	−0.114733
$371$	1.61974e9	1.64678
$372$	0	0
$373$	6.09388e7	0.0608013	0.0304006	−	0.999538i	$-0.490322\pi$
$373$	6.09388e7	0.0608013	0.0304006	+	0.999538i	$0.490322\pi$
$374$	−6.52273e8	−0.644732
$375$	0	0
$376$	1.49529e8	0.145067
$377$	2.04055e7	0.0196134
$378$	0	0
$379$	−9.94919e8	−0.938751	−0.469376	−	0.882999i	$-0.655521\pi$
$379$	−9.94919e8	−0.938751	−0.469376	+	0.882999i	$0.655521\pi$
$380$	−1.20948e8	−0.113072
$381$	0	0
$382$	2.26189e9	2.07611
$383$	1.69498e8	0.154159	0.0770794	−	0.997025i	$-0.475440\pi$
$383$	1.69498e8	0.154159	0.0770794	+	0.997025i	$0.475440\pi$
$384$	0	0
$385$	6.65954e8	0.594746
$386$	1.52207e9	1.34704
$387$	0	0
$388$	−2.54924e8	−0.221564
$389$	1.92883e8	0.166139	0.0830694	−	0.996544i	$-0.473528\pi$
$389$	1.92883e8	0.166139	0.0830694	+	0.996544i	$0.473528\pi$
$390$	0	0
$391$	4.95402e8	0.419120
$392$	−4.18148e7	−0.0350613
$393$	0	0
$394$	4.98283e8	0.410430
$395$	−3.13096e8	−0.255616
$396$	0	0
$397$	1.91282e9	1.53429	0.767146	−	0.641472i	$-0.221676\pi$
$397$	1.91282e9	1.53429	0.767146	+	0.641472i	$0.221676\pi$
$398$	−1.04050e9	−0.827279
$399$	0	0
$400$	7.18081e8	0.561001
$401$	−2.01241e8	−0.155852	−0.0779258	−	0.996959i	$-0.524830\pi$
$401$	−2.01241e8	−0.155852	−0.0779258	+	0.996959i	$0.524830\pi$
$402$	0	0
$403$	6.79993e7	0.0517531
$404$	−4.04195e8	−0.304969
$405$	0	0
$406$	−1.18359e9	−0.877727
$407$	1.43430e8	0.105453
$408$	0	0
$409$	3.51133e8	0.253770	0.126885	−	0.991917i	$-0.459502\pi$
$409$	3.51133e8	0.253770	0.126885	+	0.991917i	$0.459502\pi$
$410$	−2.03948e9	−1.46142
$411$	0	0
$412$	1.00915e8	0.0710912
$413$	1.81307e8	0.126645
$414$	0	0
$415$	−5.15968e8	−0.354368
$416$	3.29750e7	0.0224573
$417$	0	0
$418$	4.92905e8	0.330101
$419$	−3.67310e8	−0.243940	−0.121970	−	0.992534i	$-0.538921\pi$
$419$	−3.67310e8	−0.243940	−0.121970	+	0.992534i	$0.538921\pi$
$420$	0	0
$421$	1.20983e9	0.790202	0.395101	−	0.918638i	$-0.370710\pi$
$421$	1.20983e9	0.790202	0.395101	+	0.918638i	$0.370710\pi$
$422$	−3.21454e9	−2.08222
$423$	0	0
$424$	1.73500e9	1.10540
$425$	−4.60647e8	−0.291076
$426$	0	0
$427$	3.08769e9	1.91927
$428$	4.16937e8	0.257050
$429$	0	0
$430$	2.48924e9	1.50983
$431$	−6.04724e8	−0.363820	−0.181910	−	0.983315i	$-0.558228\pi$
$431$	−6.04724e8	−0.363820	−0.181910	+	0.983315i	$0.558228\pi$
$432$	0	0
$433$	−8.36784e8	−0.495343	−0.247671	−	0.968844i	$-0.579665\pi$
$433$	−8.36784e8	−0.495343	−0.247671	+	0.968844i	$0.579665\pi$
$434$	−3.94419e9	−2.31603
$435$	0	0
$436$	1.35003e9	0.780081
$437$	−3.74361e8	−0.214588
$438$	0	0
$439$	−2.70885e9	−1.52813	−0.764064	−	0.645140i	$-0.776799\pi$
$439$	−2.70885e9	−1.52813	−0.764064	+	0.645140i	$0.776799\pi$
$440$	7.13344e8	0.399222
$441$	0	0
$442$	−3.73055e7	−0.0205492
$443$	9.58898e8	0.524034	0.262017	−	0.965063i	$-0.415612\pi$
$443$	9.58898e8	0.524034	0.262017	+	0.965063i	$0.415612\pi$
$444$	0	0
$445$	−1.32284e9	−0.711617
$446$	−2.15264e9	−1.14894
$447$	0	0
$448$	3.98488e8	0.209384
$449$	−1.53949e9	−0.802630	−0.401315	−	0.915940i	$-0.631447\pi$
$449$	−1.53949e9	−0.802630	−0.401315	+	0.915940i	$0.631447\pi$
$450$	0	0
$451$	2.61676e9	1.34322
$452$	9.97607e8	0.508130
$453$	0	0
$454$	−5.81683e8	−0.291737
$455$	3.80879e7	0.0189560
$456$	0	0
$457$	−3.33563e9	−1.63483	−0.817413	−	0.576052i	$-0.804592\pi$
$457$	−3.33563e9	−1.63483	−0.817413	+	0.576052i	$0.804592\pi$
$458$	6.93258e8	0.337183
$459$	0	0
$460$	4.60589e8	0.220628
$461$	−2.62350e9	−1.24718	−0.623589	−	0.781753i	$-0.714326\pi$
$461$	−2.62350e9	−1.24718	−0.623589	+	0.781753i	$0.714326\pi$
$462$	0	0
$463$	−6.85295e8	−0.320881	−0.160441	−	0.987045i	$-0.551292\pi$
$463$	−6.85295e8	−0.320881	−0.160441	+	0.987045i	$0.551292\pi$
$464$	−2.00629e9	−0.932356
$465$	0	0
$466$	−3.34805e9	−1.53264
$467$	3.13987e9	1.42660	0.713301	−	0.700858i	$-0.247199\pi$
$467$	3.13987e9	1.42660	0.713301	+	0.700858i	$0.247199\pi$
$468$	0	0
$469$	−8.83699e8	−0.395548
$470$	−4.48266e8	−0.199156
$471$	0	0
$472$	1.94209e8	0.0850105
$473$	−3.19383e9	−1.38771
$474$	0	0
$475$	3.48098e8	0.149030
$476$	6.81251e8	0.289523
$477$	0	0
$478$	−4.63211e7	−0.0193991
$479$	−1.33909e9	−0.556718	−0.278359	−	0.960477i	$-0.589790\pi$
$479$	−1.33909e9	−0.556718	−0.278359	+	0.960477i	$0.589790\pi$
$480$	0	0
$481$	8.20319e6	0.00336105
$482$	−3.32101e9	−1.35084
$483$	0	0
$484$	−3.68061e8	−0.147558
$485$	−8.98946e8	−0.357798
$486$	0	0
$487$	−3.02031e9	−1.18495	−0.592476	−	0.805588i	$-0.701849\pi$
$487$	−3.02031e9	−1.18495	−0.592476	+	0.805588i	$0.701849\pi$
$488$	3.30741e9	1.28831
$489$	0	0
$490$	1.25354e8	0.0481342
$491$	2.38195e9	0.908129	0.454065	−	0.890969i	$-0.349974\pi$
$491$	2.38195e9	0.908129	0.454065	+	0.890969i	$0.349974\pi$
$492$	0	0
$493$	1.28703e9	0.483754
$494$	2.81907e7	0.0105211
$495$	0	0
$496$	−6.68578e9	−2.46018
$497$	−2.92550e8	−0.106894
$498$	0	0
$499$	2.51861e9	0.907421	0.453711	−	0.891149i	$-0.350100\pi$
$499$	2.51861e9	0.907421	0.453711	+	0.891149i	$0.350100\pi$
$500$	−1.38129e9	−0.494187
$501$	0	0
$502$	−1.37011e8	−0.0483384
$503$	−8.04366e8	−0.281816	−0.140908	−	0.990023i	$-0.545002\pi$
$503$	−8.04366e8	−0.281816	−0.140908	+	0.990023i	$0.545002\pi$
$504$	0	0
$505$	−1.42532e9	−0.492486
$506$	−1.87706e9	−0.644098
$507$	0	0
$508$	−7.33223e8	−0.248149
$509$	5.19329e9	1.74554	0.872772	−	0.488128i	$-0.162320\pi$
$509$	5.19329e9	1.74554	0.872772	+	0.488128i	$0.162320\pi$
$510$	0	0
$511$	−4.65400e8	−0.154296
$512$	−7.66530e8	−0.252397
$513$	0	0
$514$	−2.26055e9	−0.734250
$515$	3.55860e8	0.114803
$516$	0	0
$517$	5.75149e8	0.183047
$518$	−4.75814e8	−0.150412
$519$	0	0
$520$	4.07983e7	0.0127242
$521$	−4.19746e9	−1.30033	−0.650166	−	0.759792i	$-0.725301\pi$
$521$	−4.19746e9	−1.30033	−0.650166	+	0.759792i	$0.725301\pi$
$522$	0	0
$523$	−3.75242e9	−1.14698	−0.573490	−	0.819213i	$-0.694411\pi$
$523$	−3.75242e9	−1.14698	−0.573490	+	0.819213i	$0.694411\pi$
$524$	−2.75376e9	−0.836117
$525$	0	0
$526$	−5.28305e9	−1.58283
$527$	4.28891e9	1.27647
$528$	0	0
$529$	−1.97920e9	−0.581292
$530$	−5.20127e9	−1.51755
$531$	0	0
$532$	−5.14803e8	−0.148235
$533$	1.49661e8	0.0428117
$534$	0	0
$535$	1.47026e9	0.415102
$536$	−9.46585e8	−0.265511
$537$	0	0
$538$	2.91516e9	0.807093
$539$	−1.60837e8	−0.0442409
$540$	0	0
$541$	−1.64171e9	−0.445765	−0.222882	−	0.974845i	$-0.571547\pi$
$541$	−1.64171e9	−0.445765	−0.222882	+	0.974845i	$0.571547\pi$
$542$	6.95364e8	0.187592
$543$	0	0
$544$	2.07983e9	0.553900
$545$	4.76064e9	1.25973
$546$	0	0
$547$	6.20746e9	1.62166	0.810828	−	0.585285i	$-0.199017\pi$
$547$	6.20746e9	1.62166	0.810828	+	0.585285i	$0.199017\pi$
$548$	6.08135e8	0.157858
$549$	0	0
$550$	1.74538e9	0.447322
$551$	−9.72574e8	−0.247681
$552$	0	0
$553$	−1.33266e9	−0.335106
$554$	5.66732e9	1.41610
$555$	0	0
$556$	−1.80821e9	−0.446157
$557$	−6.02362e9	−1.47694	−0.738472	−	0.674284i	$-0.764452\pi$
$557$	−6.02362e9	−1.47694	−0.738472	+	0.674284i	$0.764452\pi$
$558$	0	0
$559$	−1.82665e8	−0.0442297
$560$	−3.74486e9	−0.901109
$561$	0	0
$562$	−5.25136e9	−1.24794
$563$	3.76918e9	0.890159	0.445079	−	0.895491i	$-0.353175\pi$
$563$	3.76918e9	0.890159	0.445079	+	0.895491i	$0.353175\pi$
$564$	0	0
$565$	3.51789e9	0.820565
$566$	−6.37524e9	−1.47788
$567$	0	0
$568$	−3.13368e8	−0.0717523
$569$	5.40701e9	1.23045	0.615226	−	0.788351i	$-0.289065\pi$
$569$	5.40701e9	1.23045	0.615226	+	0.788351i	$0.289065\pi$
$570$	0	0
$571$	3.44502e7	0.00774399	0.00387200	−	0.999993i	$-0.498768\pi$
$571$	3.44502e7	0.00774399	0.00387200	+	0.999993i	$0.498768\pi$
$572$	4.45015e7	0.00994233
$573$	0	0
$574$	−8.68083e9	−1.91589
$575$	−1.32561e9	−0.290790
$576$	0	0
$577$	1.54181e8	0.0334131	0.0167065	−	0.999860i	$-0.494682\pi$
$577$	1.54181e8	0.0334131	0.0167065	+	0.999860i	$0.494682\pi$
$578$	3.25557e9	0.701261
$579$	0	0
$580$	1.19659e9	0.254652
$581$	−2.19617e9	−0.464567
$582$	0	0
$583$	6.67351e9	1.39481
$584$	−4.98519e8	−0.103571
$585$	0	0
$586$	−1.03529e10	−2.12531
$587$	−7.89426e9	−1.61093	−0.805467	−	0.592640i	$-0.798086\pi$
$587$	−7.89426e9	−1.61093	−0.805467	+	0.592640i	$0.798086\pi$
$588$	0	0
$589$	−3.24101e9	−0.653547
$590$	−5.82210e8	−0.116707
$591$	0	0
$592$	−8.06549e8	−0.159774
$593$	−1.93894e9	−0.381833	−0.190917	−	0.981606i	$-0.561146\pi$
$593$	−1.93894e9	−0.381833	−0.190917	+	0.981606i	$0.561146\pi$
$594$	0	0
$595$	2.40231e9	0.467542
$596$	−2.15395e8	−0.0416748
$597$	0	0
$598$	−1.07355e8	−0.0205290
$599$	4.91194e9	0.933812	0.466906	−	0.884307i	$-0.345369\pi$
$599$	4.91194e9	0.933812	0.466906	+	0.884307i	$0.345369\pi$
$600$	0	0
$601$	−2.50771e9	−0.471211	−0.235606	−	0.971849i	$-0.575707\pi$
$601$	−2.50771e9	−0.471211	−0.235606	+	0.971849i	$0.575707\pi$
$602$	1.05952e10	1.97934
$603$	0	0
$604$	4.28638e9	0.791519
$605$	−1.29791e9	−0.238286
$606$	0	0
$607$	−5.17646e8	−0.0939446	−0.0469723	−	0.998896i	$-0.514957\pi$
$607$	−5.17646e8	−0.0939446	−0.0469723	+	0.998896i	$0.514957\pi$
$608$	−1.57167e9	−0.283595
$609$	0	0
$610$	−9.91513e9	−1.76866
$611$	3.28945e7	0.00583417
$612$	0	0
$613$	−2.24783e9	−0.394141	−0.197070	−	0.980389i	$-0.563143\pi$
$613$	−2.24783e9	−0.394141	−0.197070	+	0.980389i	$0.563143\pi$
$614$	6.99023e9	1.21871
$615$	0	0
$616$	3.03627e9	0.523370
$617$	3.82861e9	0.656211	0.328106	−	0.944641i	$-0.393590\pi$
$617$	3.82861e9	0.656211	0.328106	+	0.944641i	$0.393590\pi$
$618$	0	0
$619$	1.53060e9	0.259385	0.129693	−	0.991554i	$-0.458601\pi$
$619$	1.53060e9	0.259385	0.129693	+	0.991554i	$0.458601\pi$
$620$	3.98753e9	0.671943
$621$	0	0
$622$	6.11091e9	1.01822
$623$	−5.63052e9	−0.932911
$624$	0	0
$625$	−2.12804e9	−0.348658
$626$	4.17838e8	0.0680766
$627$	0	0
$628$	−5.34928e9	−0.861859
$629$	5.17399e8	0.0828988
$630$	0	0
$631$	8.76195e9	1.38835	0.694174	−	0.719807i	$-0.255770\pi$
$631$	8.76195e9	1.38835	0.694174	+	0.719807i	$0.255770\pi$
$632$	−1.42749e9	−0.224939
$633$	0	0
$634$	−3.51900e9	−0.548413
$635$	−2.58558e9	−0.400729
$636$	0	0
$637$	−9.19873e6	−0.00141007
$638$	−4.87652e9	−0.743426
$639$	0	0
$640$	−5.48785e9	−0.827508
$641$	8.85004e9	1.32722	0.663609	−	0.748080i	$-0.269024\pi$
$641$	8.85004e9	1.32722	0.663609	+	0.748080i	$0.269024\pi$
$642$	0	0
$643$	−1.79228e9	−0.265869	−0.132935	−	0.991125i	$-0.542440\pi$
$643$	−1.79228e9	−0.265869	−0.132935	+	0.991125i	$0.542440\pi$
$644$	1.96045e9	0.289238
$645$	0	0
$646$	1.77807e9	0.259499
$647$	7.01663e9	1.01851	0.509253	−	0.860617i	$-0.329922\pi$
$647$	7.01663e9	1.01851	0.509253	+	0.860617i	$0.329922\pi$
$648$	0	0
$649$	7.47007e8	0.107267
$650$	9.98234e7	0.0142572
$651$	0	0
$652$	3.30983e9	0.467670
$653$	−5.63028e9	−0.791287	−0.395644	−	0.918404i	$-0.629478\pi$
$653$	−5.63028e9	−0.791287	−0.395644	+	0.918404i	$0.629478\pi$
$654$	0	0
$655$	−9.71067e9	−1.35022
$656$	−1.47148e10	−2.03513
$657$	0	0
$658$	−1.90800e9	−0.261088
$659$	−2.18357e9	−0.297214	−0.148607	−	0.988896i	$-0.547479\pi$
$659$	−2.18357e9	−0.297214	−0.148607	+	0.988896i	$0.547479\pi$
$660$	0	0
$661$	1.27138e10	1.71227	0.856134	−	0.516755i	$-0.172860\pi$
$661$	1.27138e10	1.71227	0.856134	+	0.516755i	$0.172860\pi$
$662$	−9.14153e9	−1.22466
$663$	0	0
$664$	−2.35245e9	−0.311840
$665$	−1.81536e9	−0.239380
$666$	0	0
$667$	3.70372e9	0.483279
$668$	−1.88828e9	−0.245103
$669$	0	0
$670$	2.83772e9	0.364508
$671$	1.27216e10	1.62560
$672$	0	0
$673$	−5.04564e9	−0.638063	−0.319031	−	0.947744i	$-0.603358\pi$
$673$	−5.04564e9	−0.638063	−0.319031	+	0.947744i	$0.603358\pi$
$674$	−2.01494e8	−0.0253485
$675$	0	0
$676$	−3.68806e9	−0.459182
$677$	4.93561e9	0.611337	0.305668	−	0.952138i	$-0.401120\pi$
$677$	4.93561e9	0.611337	0.305668	+	0.952138i	$0.401120\pi$
$678$	0	0
$679$	−3.82627e9	−0.469063
$680$	2.57327e9	0.313837
$681$	0	0
$682$	−1.62505e10	−1.96165
$683$	8.54468e9	1.02618	0.513090	−	0.858335i	$-0.328501\pi$
$683$	8.54468e9	1.02618	0.513090	+	0.858335i	$0.328501\pi$
$684$	0	0
$685$	2.14448e9	0.254921
$686$	1.04705e10	1.23832
$687$	0	0
$688$	1.79599e10	2.10254
$689$	3.81679e8	0.0444560
$690$	0	0
$691$	−2.27573e9	−0.262390	−0.131195	−	0.991357i	$-0.541881\pi$
$691$	−2.27573e9	−0.262390	−0.131195	+	0.991357i	$0.541881\pi$
$692$	−4.62220e9	−0.530246
$693$	0	0
$694$	−8.27237e9	−0.939446
$695$	−6.37635e9	−0.720486
$696$	0	0
$697$	9.43952e9	1.05593
$698$	1.40342e10	1.56205
$699$	0	0
$700$	−1.82292e9	−0.200874
$701$	−2.18428e8	−0.0239494	−0.0119747	−	0.999928i	$-0.503812\pi$
$701$	−2.18428e8	−0.0239494	−0.0119747	+	0.999928i	$0.503812\pi$
$702$	0	0
$703$	−3.90984e8	−0.0424439
$704$	1.64182e9	0.177346
$705$	0	0
$706$	−1.93012e10	−2.06428
$707$	−6.06674e9	−0.645636
$708$	0	0
$709$	1.81988e10	1.91770	0.958849	−	0.283917i	$-0.0916341\pi$
$709$	1.81988e10	1.91770	0.958849	+	0.283917i	$0.0916341\pi$
$710$	9.39431e8	0.0985056
$711$	0	0
$712$	−6.03119e9	−0.626215
$713$	1.23423e10	1.27521
$714$	0	0
$715$	1.56927e8	0.0160556
$716$	3.45641e9	0.351908
$717$	0	0
$718$	−3.96066e9	−0.399330
$719$	6.16960e9	0.619022	0.309511	−	0.950896i	$-0.399835\pi$
$719$	6.16960e9	0.619022	0.309511	+	0.950896i	$0.399835\pi$
$720$	0	0
$721$	1.51468e9	0.150504
$722$	1.08739e10	1.07523
$723$	0	0
$724$	−2.83286e9	−0.277422
$725$	−3.44389e9	−0.335634
$726$	0	0
$727$	5.20930e9	0.502816	0.251408	−	0.967881i	$-0.419106\pi$
$727$	5.20930e9	0.502816	0.251408	+	0.967881i	$0.419106\pi$
$728$	1.73654e8	0.0166811
$729$	0	0
$730$	1.49448e9	0.142188
$731$	−1.15212e10	−1.09090
$732$	0	0
$733$	9.86561e9	0.925252	0.462626	−	0.886554i	$-0.346907\pi$
$733$	9.86561e9	0.925252	0.462626	+	0.886554i	$0.346907\pi$
$734$	8.35704e9	0.780039
$735$	0	0
$736$	5.98516e9	0.553355
$737$	−3.64095e9	−0.335026
$738$	0	0
$739$	6.68716e9	0.609517	0.304759	−	0.952430i	$-0.401424\pi$
$739$	6.68716e9	0.609517	0.304759	+	0.952430i	$0.401424\pi$
$740$	4.81041e8	0.0436386
$741$	0	0
$742$	−2.21387e10	−1.98947
$743$	−1.17332e10	−1.04944	−0.524719	−	0.851275i	$-0.675830\pi$
$743$	−1.17332e10	−1.04944	−0.524719	+	0.851275i	$0.675830\pi$
$744$	0	0
$745$	−7.59553e8	−0.0672994
$746$	−8.32915e8	−0.0734539
$747$	0	0
$748$	2.80683e9	0.245223
$749$	6.25800e9	0.544188
$750$	0	0
$751$	−1.63538e10	−1.40890	−0.704448	−	0.709756i	$-0.748805\pi$
$751$	−1.63538e10	−1.40890	−0.704448	+	0.709756i	$0.748805\pi$
$752$	−3.23423e9	−0.277338
$753$	0	0
$754$	−2.78903e8	−0.0236948
$755$	1.51152e10	1.27820
$756$	0	0
$757$	−7.22904e9	−0.605683	−0.302841	−	0.953041i	$-0.597935\pi$
$757$	−7.22904e9	−0.605683	−0.302841	+	0.953041i	$0.597935\pi$
$758$	1.35986e10	1.13410
$759$	0	0
$760$	−1.94455e9	−0.160683
$761$	1.16317e9	0.0956747	0.0478373	−	0.998855i	$-0.484767\pi$
$761$	1.16317e9	0.0956747	0.0478373	+	0.998855i	$0.484767\pi$
$762$	0	0
$763$	2.02632e10	1.65147
$764$	−9.73328e9	−0.789646
$765$	0	0
$766$	−2.31671e9	−0.186239
$767$	4.27236e7	0.00341888
$768$	0	0
$769$	2.40619e10	1.90804	0.954022	−	0.299735i	$-0.0968984\pi$
$769$	2.40619e10	1.90804	0.954022	+	0.299735i	$0.0968984\pi$
$770$	−9.10230e9	−0.718511
$771$	0	0
$772$	−6.54972e9	−0.512344
$773$	1.37533e9	0.107097	0.0535486	−	0.998565i	$-0.482947\pi$
$773$	1.37533e9	0.107097	0.0535486	+	0.998565i	$0.482947\pi$
$774$	0	0
$775$	−1.14764e10	−0.885627
$776$	−4.09855e9	−0.314858
$777$	0	0
$778$	−2.63634e9	−0.200712
$779$	−7.13318e9	−0.540633
$780$	0	0
$781$	−1.20534e9	−0.0905381
$782$	−6.77118e9	−0.506338
$783$	0	0
$784$	9.04432e8	0.0670301
$785$	−1.88633e10	−1.39179
$786$	0	0
$787$	1.62448e10	1.18796	0.593980	−	0.804480i	$-0.297556\pi$
$787$	1.62448e10	1.18796	0.593980	+	0.804480i	$0.297556\pi$
$788$	−2.14419e9	−0.156107
$789$	0	0
$790$	4.27941e9	0.308809
$791$	1.49735e10	1.07574
$792$	0	0
$793$	7.27590e8	0.0518120
$794$	−2.61446e10	−1.85357
$795$	0	0
$796$	4.47744e9	0.314655
$797$	1.10596e10	0.773814	0.386907	−	0.922119i	$-0.373543\pi$
$797$	1.10596e10	0.773814	0.386907	+	0.922119i	$0.373543\pi$
$798$	0	0
$799$	2.07475e9	0.143897
$800$	−5.56528e9	−0.384301
$801$	0	0
$802$	2.75057e9	0.188284
$803$	−1.91750e9	−0.130687
$804$	0	0
$805$	6.91319e9	0.467082
$806$	−9.29418e8	−0.0625228
$807$	0	0
$808$	−6.49846e9	−0.433382
$809$	2.52839e10	1.67890	0.839450	−	0.543436i	$-0.182877\pi$
$809$	2.52839e10	1.67890	0.839450	+	0.543436i	$0.182877\pi$
$810$	0	0
$811$	7.05869e9	0.464677	0.232339	−	0.972635i	$-0.425362\pi$
$811$	7.05869e9	0.464677	0.232339	+	0.972635i	$0.425362\pi$
$812$	5.09317e9	0.333843
$813$	0	0
$814$	−1.96041e9	−0.127398
$815$	1.16716e10	0.755227
$816$	0	0
$817$	8.70625e9	0.558540
$818$	−4.79930e9	−0.306578
$819$	0	0
$820$	8.77620e9	0.555850
$821$	1.72937e10	1.09066	0.545328	−	0.838223i	$-0.316405\pi$
$821$	1.72937e10	1.09066	0.545328	+	0.838223i	$0.316405\pi$
$822$	0	0
$823$	1.28299e10	0.802278	0.401139	−	0.916017i	$-0.368614\pi$
$823$	1.28299e10	0.802278	0.401139	+	0.916017i	$0.368614\pi$
$824$	1.62247e9	0.101025
$825$	0	0
$826$	−2.47812e9	−0.153000
$827$	−1.83922e10	−1.13074	−0.565372	−	0.824836i	$-0.691268\pi$
$827$	−1.83922e10	−1.13074	−0.565372	+	0.824836i	$0.691268\pi$
$828$	0	0
$829$	−4.09547e9	−0.249668	−0.124834	−	0.992178i	$-0.539840\pi$
$829$	−4.09547e9	−0.249668	−0.124834	+	0.992178i	$0.539840\pi$
$830$	7.05229e9	0.428111
$831$	0	0
$832$	9.39006e7	0.00565245
$833$	−5.80190e8	−0.0347787
$834$	0	0
$835$	−6.65870e9	−0.395810
$836$	−2.12105e9	−0.125553
$837$	0	0
$838$	5.02041e9	0.294704
$839$	1.88735e9	0.110328	0.0551641	−	0.998477i	$-0.482432\pi$
$839$	1.88735e9	0.110328	0.0551641	+	0.998477i	$0.482432\pi$
$840$	0	0
$841$	−7.62778e9	−0.442193
$842$	−1.65361e10	−0.954641
$843$	0	0
$844$	1.38327e10	0.791969
$845$	−1.30053e10	−0.741519
$846$	0	0
$847$	−5.52440e9	−0.312387
$848$	−3.75272e10	−2.11330
$849$	0	0
$850$	6.29615e9	0.351649
$851$	1.48893e9	0.0828173
$852$	0	0
$853$	6.81026e8	0.0375701	0.0187850	−	0.999824i	$-0.494020\pi$
$853$	6.81026e8	0.0375701	0.0187850	+	0.999824i	$0.494020\pi$
$854$	−4.22027e10	−2.31866
$855$	0	0
$856$	6.70332e9	0.365285
$857$	−6.43948e9	−0.349476	−0.174738	−	0.984615i	$-0.555908\pi$
$857$	−6.43948e9	−0.349476	−0.174738	+	0.984615i	$0.555908\pi$
$858$	0	0
$859$	1.88733e10	1.01595	0.507974	−	0.861373i	$-0.330395\pi$
$859$	1.88733e10	1.01595	0.507974	+	0.861373i	$0.330395\pi$
$860$	−1.07116e10	−0.574262
$861$	0	0
$862$	8.26541e9	0.439530
$863$	−1.84568e10	−0.977505	−0.488753	−	0.872422i	$-0.662548\pi$
$863$	−1.84568e10	−0.977505	−0.488753	+	0.872422i	$0.662548\pi$
$864$	0	0
$865$	−1.62994e10	−0.856279
$866$	1.14372e10	0.598422
$867$	0	0
$868$	1.69725e10	0.880900
$869$	−5.49072e9	−0.283831
$870$	0	0
$871$	−2.08237e8	−0.0106781
$872$	2.17051e10	1.10855
$873$	0	0
$874$	5.11679e9	0.259243
$875$	−2.07325e10	−1.04622
$876$	0	0
$877$	1.79041e10	0.896301	0.448151	−	0.893958i	$-0.352083\pi$
$877$	1.79041e10	0.896301	0.448151	+	0.893958i	$0.352083\pi$
$878$	3.70248e10	1.84613
$879$	0	0
$880$	−1.54293e10	−0.763230
$881$	1.86101e10	0.916922	0.458461	−	0.888715i	$-0.348401\pi$
$881$	1.86101e10	0.916922	0.458461	+	0.888715i	$0.348401\pi$
$882$	0	0
$883$	−1.45294e10	−0.710207	−0.355103	−	0.934827i	$-0.615554\pi$
$883$	−1.45294e10	−0.710207	−0.355103	+	0.934827i	$0.615554\pi$
$884$	1.60531e8	0.00781586
$885$	0	0
$886$	−1.31063e10	−0.633084
$887$	3.46786e9	0.166851	0.0834256	−	0.996514i	$-0.473414\pi$
$887$	3.46786e9	0.166851	0.0834256	+	0.996514i	$0.473414\pi$
$888$	0	0
$889$	−1.10053e10	−0.525345
$890$	1.80806e10	0.859702
$891$	0	0
$892$	9.26313e9	0.436999
$893$	−1.56783e9	−0.0736749
$894$	0	0
$895$	1.21884e10	0.568286
$896$	−2.33585e10	−1.08484
$897$	0	0
$898$	2.10419e10	0.969655
$899$	3.20647e10	1.47187
$900$	0	0
$901$	2.40736e10	1.09649
$902$	−3.57660e10	−1.62274
$903$	0	0
$904$	1.60391e10	0.722088
$905$	−9.98961e9	−0.448001
$906$	0	0
$907$	−4.86854e9	−0.216657	−0.108329	−	0.994115i	$-0.534550\pi$
$907$	−4.86854e9	−0.216657	−0.108329	+	0.994115i	$0.534550\pi$
$908$	2.50308e9	0.110962
$909$	0	0
$910$	−5.20588e8	−0.0229007
$911$	−5.41157e9	−0.237142	−0.118571	−	0.992946i	$-0.537831\pi$
$911$	−5.41157e9	−0.237142	−0.118571	+	0.992946i	$0.537831\pi$
$912$	0	0
$913$	−9.04846e9	−0.393484
$914$	4.55916e10	1.97503
$915$	0	0
$916$	−2.98320e9	−0.128247
$917$	−4.13325e10	−1.77010
$918$	0	0
$919$	−4.36861e10	−1.85669	−0.928343	−	0.371724i	$-0.878767\pi$
$919$	−4.36861e10	−1.85669	−0.928343	+	0.371724i	$0.878767\pi$
$920$	7.40515e9	0.313528
$921$	0	0
$922$	3.58582e10	1.50671
$923$	−6.89371e7	−0.00288567
$924$	0	0
$925$	−1.38448e9	−0.0575161
$926$	9.36666e9	0.387656
$927$	0	0
$928$	1.55492e10	0.638690
$929$	−1.09031e10	−0.446164	−0.223082	−	0.974800i	$-0.571612\pi$
$929$	−1.09031e10	−0.446164	−0.223082	+	0.974800i	$0.571612\pi$
$930$	0	0
$931$	4.38434e8	0.0178066
$932$	1.44072e10	0.582939
$933$	0	0
$934$	−4.29159e10	−1.72347
$935$	9.89782e9	0.396003
$936$	0	0
$937$	3.25215e10	1.29146	0.645732	−	0.763564i	$-0.276552\pi$
$937$	3.25215e10	1.29146	0.645732	+	0.763564i	$0.276552\pi$
$938$	1.20785e10	0.477861
$939$	0	0
$940$	1.92896e9	0.0757487
$941$	2.70964e10	1.06010	0.530052	−	0.847965i	$-0.322172\pi$
$941$	2.70964e10	1.06010	0.530052	+	0.847965i	$0.322172\pi$
$942$	0	0
$943$	2.71643e10	1.05489
$944$	−4.20064e9	−0.162523
$945$	0	0
$946$	4.36535e10	1.67649
$947$	−2.06829e10	−0.791382	−0.395691	−	0.918384i	$-0.629495\pi$
$947$	−2.06829e10	−0.791382	−0.395691	+	0.918384i	$0.629495\pi$
$948$	0	0
$949$	−1.09668e8	−0.00416531
$950$	−4.75783e9	−0.180043
$951$	0	0
$952$	1.09528e10	0.411431
$953$	3.31031e10	1.23892	0.619460	−	0.785028i	$-0.287351\pi$
$953$	3.31031e10	1.23892	0.619460	+	0.785028i	$0.287351\pi$
$954$	0	0
$955$	−3.43227e10	−1.27518
$956$	1.99327e8	0.00737841
$957$	0	0
$958$	1.83027e10	0.672569
$959$	9.12777e9	0.334195
$960$	0	0
$961$	7.93400e10	2.88377
$962$	−1.12122e8	−0.00406048
$963$	0	0
$964$	1.42908e10	0.513792
$965$	−2.30965e10	−0.827370
$966$	0	0
$967$	−2.24560e10	−0.798618	−0.399309	−	0.916816i	$-0.630750\pi$
$967$	−2.24560e10	−0.798618	−0.399309	+	0.916816i	$0.630750\pi$
$968$	−5.91752e9	−0.209689
$969$	0	0
$970$	1.22868e10	0.432254
$971$	1.83485e10	0.643182	0.321591	−	0.946879i	$-0.395782\pi$
$971$	1.83485e10	0.643182	0.321591	+	0.946879i	$0.395782\pi$
$972$	0	0
$973$	−2.71403e10	−0.944538
$974$	4.12818e10	1.43154
$975$	0	0
$976$	−7.15376e10	−2.46298
$977$	−2.21334e10	−0.759306	−0.379653	−	0.925129i	$-0.623957\pi$
$977$	−2.21334e10	−0.759306	−0.379653	+	0.925129i	$0.623957\pi$
$978$	0	0
$979$	−2.31984e10	−0.790166
$980$	−5.39420e8	−0.0183078
$981$	0	0
$982$	−3.25566e10	−1.09711
$983$	−5.39105e10	−1.81024	−0.905121	−	0.425155i	$-0.860220\pi$
$983$	−5.39105e10	−1.81024	−0.905121	+	0.425155i	$0.860220\pi$
$984$	0	0
$985$	−7.56112e9	−0.252092
$986$	−1.75912e10	−0.584422
$987$	0	0
$988$	−1.21309e8	−0.00400170
$989$	−3.31548e10	−1.08983
$990$	0	0
$991$	−1.06845e10	−0.348734	−0.174367	−	0.984681i	$-0.555788\pi$
$991$	−1.06845e10	−0.348734	−0.174367	+	0.984681i	$0.555788\pi$
$992$	5.18162e10	1.68529
$993$	0	0
$994$	3.99859e9	0.129138
$995$	1.57889e10	0.508127
$996$	0	0
$997$	−3.63110e10	−1.16039	−0.580196	−	0.814477i	$-0.697024\pi$
$997$	−3.63110e10	−1.16039	−0.580196	+	0.814477i	$0.697024\pi$
$998$	−3.44245e10	−1.09625
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.4		17
3.2	odd	2		177.8.a.b.1.14	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.14	✓	17	3.2	odd	2
531.8.a.d.1.4		17	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)

\(f(q)\)	\(=\)	\(q-13.6681 q^{2} +58.8158 q^{4} +207.404 q^{5} +882.793 q^{7} +945.614 q^{8} +O(q^{10})\)	\(q-13.6681 q^{2} +58.8158 q^{4} +207.404 q^{5} +882.793 q^{7} +945.614 q^{8} -2834.81 q^{10} +3637.21 q^{11} +208.023 q^{13} -12066.1 q^{14} -20453.1 q^{16} +13120.6 q^{17} -9914.89 q^{19} +12198.6 q^{20} -49713.6 q^{22} +37757.5 q^{23} -35108.6 q^{25} -2843.27 q^{26} +51922.2 q^{28} +98092.3 q^{29} +326883. q^{31} +158516. q^{32} -179333. q^{34} +183095. q^{35} +39434.0 q^{37} +135517. q^{38} +196124. q^{40} +719442. q^{41} -878099. q^{43} +213925. q^{44} -516072. q^{46} +158129. q^{47} -44219.7 q^{49} +479867. q^{50} +12235.0 q^{52} +1.83479e6 q^{53} +754372. q^{55} +834781. q^{56} -1.34073e6 q^{58} +205379. q^{59} +3.49764e6 q^{61} -4.46786e6 q^{62} +451395. q^{64} +43144.8 q^{65} -1.00103e6 q^{67} +771700. q^{68} -2.50255e6 q^{70} -331392. q^{71} -527191. q^{73} -538987. q^{74} -583152. q^{76} +3.21090e6 q^{77} -1.50960e6 q^{79} -4.24206e6 q^{80} -9.83337e6 q^{82} -2.48775e6 q^{83} +2.72127e6 q^{85} +1.20019e7 q^{86} +3.43940e6 q^{88} -6.37807e6 q^{89} +183641. q^{91} +2.22074e6 q^{92} -2.16132e6 q^{94} -2.05639e6 q^{95} -4.33428e6 q^{97} +604398. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Introduction

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