LMFDB - Embedded newform 531.8.a.d.1.13

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			1.13
Root			$-11.3335$ 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)

$f(q)$	$=$	$q+13.3335 q^{2} +49.7814 q^{4} -152.093 q^{5} -1328.47 q^{7} -1042.93 q^{8} +O(q^{10})$	\(q+13.3335 q^{2} +49.7814 q^{4} -152.093 q^{5} -1328.47 q^{7} -1042.93 q^{8} -2027.93 q^{10} -5132.02 q^{11} -12251.2 q^{13} -17713.2 q^{14} -20277.8 q^{16} -26601.9 q^{17} +33197.2 q^{19} -7571.39 q^{20} -68427.7 q^{22} +97057.0 q^{23} -54992.8 q^{25} -163351. q^{26} -66133.3 q^{28} -209269. q^{29} -308874. q^{31} -136879. q^{32} -354695. q^{34} +202052. q^{35} +287842. q^{37} +442634. q^{38} +158622. q^{40} -581611. q^{41} +540792. q^{43} -255479. q^{44} +1.29411e6 q^{46} +650609. q^{47} +941302. q^{49} -733244. q^{50} -609883. q^{52} +49948.0 q^{53} +780544. q^{55} +1.38550e6 q^{56} -2.79028e6 q^{58} +205379. q^{59} -20025.0 q^{61} -4.11836e6 q^{62} +770486. q^{64} +1.86332e6 q^{65} -1.38680e6 q^{67} -1.32428e6 q^{68} +2.69405e6 q^{70} -1.24373e6 q^{71} -4.83751e6 q^{73} +3.83794e6 q^{74} +1.65260e6 q^{76} +6.81777e6 q^{77} -2.94089e6 q^{79} +3.08411e6 q^{80} -7.75490e6 q^{82} +8.62802e6 q^{83} +4.04595e6 q^{85} +7.21064e6 q^{86} +5.35232e6 q^{88} +879309. q^{89} +1.62754e7 q^{91} +4.83163e6 q^{92} +8.67488e6 q^{94} -5.04907e6 q^{95} -1.62017e7 q^{97} +1.25508e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	13.3335	1.17852	0.589262	−	0.807942i	$-0.299419\pi$
$2$	13.3335	1.17852	0.589262	+	0.807942i	$0.299419\pi$
$3$	0	0
$3$	0	0
$4$	49.7814	0.388917
$5$	−152.093	−0.544144	−0.272072	−	0.962277i	$-0.587709\pi$
$5$	−152.093	−0.544144	−0.272072	+	0.962277i	$0.587709\pi$
$6$	0	0
$7$	−1328.47	−1.46390	−0.731948	−	0.681361i	$-0.761389\pi$
$7$	−1328.47	−1.46390	−0.731948	+	0.681361i	$0.761389\pi$
$8$	−1042.93	−0.720176
$9$	0	0
$10$	−2027.93	−0.641286
$11$	−5132.02	−1.16256	−0.581279	−	0.813705i	$-0.697447\pi$
$11$	−5132.02	−1.16256	−0.581279	+	0.813705i	$0.697447\pi$
$12$	0	0
$13$	−12251.2	−1.54660	−0.773299	−	0.634041i	$-0.781395\pi$
$13$	−12251.2	−1.54660	−0.773299	+	0.634041i	$0.781395\pi$
$14$	−17713.2	−1.72524
$15$	0	0
$16$	−20277.8	−1.23766
$17$	−26601.9	−1.31323	−0.656615	−	0.754226i	$-0.728012\pi$
$17$	−26601.9	−1.31323	−0.656615	+	0.754226i	$0.728012\pi$
$18$	0	0
$19$	33197.2	1.11036	0.555181	−	0.831730i	$-0.312649\pi$
$19$	33197.2	1.11036	0.555181	+	0.831730i	$0.312649\pi$
$20$	−7571.39	−0.211627
$21$	0	0
$22$	−68427.7	−1.37010
$23$	97057.0	1.66333	0.831667	−	0.555274i	$-0.187387\pi$
$23$	97057.0	1.66333	0.831667	+	0.555274i	$0.187387\pi$
$24$	0	0
$25$	−54992.8	−0.703907
$26$	−163351.	−1.82270
$27$	0	0
$28$	−66133.3	−0.569334
$29$	−209269.	−1.59335	−0.796675	−	0.604408i	$-0.793410\pi$
$29$	−209269.	−1.59335	−0.796675	+	0.604408i	$0.793410\pi$
$30$	0	0
$31$	−308874.	−1.86215	−0.931077	−	0.364823i	$-0.881129\pi$
$31$	−308874.	−1.86215	−0.931077	+	0.364823i	$0.881129\pi$
$32$	−136879.	−0.738436
$33$	0	0
$34$	−354695.	−1.54767
$35$	202052.	0.796570
$36$	0	0
$37$	287842.	0.934219	0.467110	−	0.884199i	$-0.345295\pi$
$37$	287842.	0.934219	0.467110	+	0.884199i	$0.345295\pi$
$38$	442634.	1.30859
$39$	0	0
$40$	158622.	0.391879
$41$	−581611.	−1.31792	−0.658960	−	0.752178i	$-0.729004\pi$
$41$	−581611.	−1.31792	−0.658960	+	0.752178i	$0.729004\pi$
$42$	0	0
$43$	540792.	1.03727	0.518634	−	0.854996i	$-0.326441\pi$
$43$	540792.	1.03727	0.518634	+	0.854996i	$0.326441\pi$
$44$	−255479.	−0.452138
$45$	0	0
$46$	1.29411e6	1.96028
$47$	650609.	0.914066	0.457033	−	0.889450i	$-0.348912\pi$
$47$	650609.	0.914066	0.457033	+	0.889450i	$0.348912\pi$
$48$	0	0
$49$	941302.	1.14299
$50$	−733244.	−0.829571
$51$	0	0
$52$	−609883.	−0.601499
$53$	49948.0	0.0460843	0.0230421	−	0.999734i	$-0.492665\pi$
$53$	49948.0	0.0460843	0.0230421	+	0.999734i	$0.492665\pi$
$54$	0	0
$55$	780544.	0.632599
$56$	1.38550e6	1.05426
$57$	0	0
$58$	−2.79028e6	−1.87780
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−20025.0	−0.0112958	−0.00564791	−	0.999984i	$-0.501798\pi$
$61$	−20025.0	−0.0112958	−0.00564791	+	0.999984i	$0.501798\pi$
$62$	−4.11836e6	−2.19459
$63$	0	0
$64$	770486.	0.367396
$65$	1.86332e6	0.841573
$66$	0	0
$67$	−1.38680e6	−0.563314	−0.281657	−	0.959515i	$-0.590884\pi$
$67$	−1.38680e6	−0.563314	−0.281657	+	0.959515i	$0.590884\pi$
$68$	−1.32428e6	−0.510738
$69$	0	0
$70$	2.69405e6	0.938776
$71$	−1.24373e6	−0.412403	−0.206201	−	0.978510i	$-0.566110\pi$
$71$	−1.24373e6	−0.412403	−0.206201	+	0.978510i	$0.566110\pi$
$72$	0	0
$73$	−4.83751e6	−1.45543	−0.727716	−	0.685879i	$-0.759418\pi$
$73$	−4.83751e6	−1.45543	−0.727716	+	0.685879i	$0.759418\pi$
$74$	3.83794e6	1.10100
$75$	0	0
$76$	1.65260e6	0.431839
$77$	6.81777e6	1.70186
$78$	0	0
$79$	−2.94089e6	−0.671095	−0.335547	−	0.942023i	$-0.608921\pi$
$79$	−2.94089e6	−0.671095	−0.335547	+	0.942023i	$0.608921\pi$
$80$	3.08411e6	0.673466
$81$	0	0
$82$	−7.75490e6	−1.55320
$83$	8.62802e6	1.65630	0.828148	−	0.560510i	$-0.189395\pi$
$83$	8.62802e6	1.65630	0.828148	+	0.560510i	$0.189395\pi$
$84$	0	0
$85$	4.04595e6	0.714586
$86$	7.21064e6	1.22244
$87$	0	0
$88$	5.35232e6	0.837245
$89$	879309.	0.132214	0.0661069	−	0.997813i	$-0.478942\pi$
$89$	879309.	0.132214	0.0661069	+	0.997813i	$0.478942\pi$
$90$	0	0
$91$	1.62754e7	2.26406
$92$	4.83163e6	0.646899
$93$	0	0
$94$	8.67488e6	1.07725
$95$	−5.04907e6	−0.604197
$96$	0	0
$97$	−1.62017e7	−1.80244	−0.901220	−	0.433362i	$-0.857327\pi$
$97$	−1.62017e7	−1.80244	−0.901220	+	0.433362i	$0.857327\pi$
$98$	1.25508e7	1.34704
$99$	0	0
$100$	−2.73761e6	−0.273761
$101$	−617795.	−0.0596650	−0.0298325	−	0.999555i	$-0.509497\pi$
$101$	−617795.	−0.0596650	−0.0298325	+	0.999555i	$0.509497\pi$
$102$	0	0
$103$	−6.98654e6	−0.629988	−0.314994	−	0.949094i	$-0.602002\pi$
$103$	−6.98654e6	−0.629988	−0.314994	+	0.949094i	$0.602002\pi$
$104$	1.27771e7	1.11382
$105$	0	0
$106$	665980.	0.0543114
$107$	7.47019e6	0.589506	0.294753	−	0.955573i	$-0.404763\pi$
$107$	7.47019e6	0.589506	0.294753	+	0.955573i	$0.404763\pi$
$108$	0	0
$109$	−2.25015e7	−1.66425	−0.832125	−	0.554588i	$-0.812876\pi$
$109$	−2.25015e7	−1.66425	−0.832125	+	0.554588i	$0.812876\pi$
$110$	1.04074e7	0.745532
$111$	0	0
$112$	2.69386e7	1.81181
$113$	−7.33737e6	−0.478372	−0.239186	−	0.970974i	$-0.576881\pi$
$113$	−7.33737e6	−0.478372	−0.239186	+	0.970974i	$0.576881\pi$
$114$	0	0
$115$	−1.47617e7	−0.905094
$116$	−1.04177e7	−0.619681
$117$	0	0
$118$	2.73841e6	0.153431
$119$	3.53399e7	1.92243
$120$	0	0
$121$	6.85051e6	0.351539
$122$	−267002.	−0.0133124
$123$	0	0
$124$	−1.53762e7	−0.724223
$125$	2.02463e7	0.927171
$126$	0	0
$127$	−1.12559e7	−0.487605	−0.243803	−	0.969825i	$-0.578395\pi$
$127$	−1.12559e7	−0.487605	−0.243803	+	0.969825i	$0.578395\pi$
$128$	2.77938e7	1.17142
$129$	0	0
$130$	2.48446e7	0.991813
$131$	−4.30156e6	−0.167177	−0.0835885	−	0.996500i	$-0.526638\pi$
$131$	−4.30156e6	−0.167177	−0.0835885	+	0.996500i	$0.526638\pi$
$132$	0	0
$133$	−4.41017e7	−1.62545
$134$	−1.84908e7	−0.663879
$135$	0	0
$136$	2.77438e7	0.945756
$137$	1.85481e7	0.616281	0.308140	−	0.951341i	$-0.400293\pi$
$137$	1.85481e7	0.616281	0.308140	+	0.951341i	$0.400293\pi$
$138$	0	0
$139$	−4.12956e7	−1.30422	−0.652112	−	0.758123i	$-0.726117\pi$
$139$	−4.12956e7	−1.30422	−0.652112	+	0.758123i	$0.726117\pi$
$140$	1.00584e7	0.309800
$141$	0	0
$142$	−1.65832e7	−0.486026
$143$	6.28736e7	1.79801
$144$	0	0
$145$	3.18283e7	0.867012
$146$	−6.45008e7	−1.71526
$147$	0	0
$148$	1.43292e7	0.363334
$149$	−2.77964e7	−0.688394	−0.344197	−	0.938897i	$-0.611849\pi$
$149$	−2.77964e7	−0.688394	−0.344197	+	0.938897i	$0.611849\pi$
$150$	0	0
$151$	5.05159e7	1.19401	0.597006	−	0.802236i	$-0.296357\pi$
$151$	5.05159e7	1.19401	0.597006	+	0.802236i	$0.296357\pi$
$152$	−3.46223e7	−0.799655
$153$	0	0
$154$	9.09045e7	2.00568
$155$	4.69775e7	1.01328
$156$	0	0
$157$	−3.27653e7	−0.675717	−0.337858	−	0.941197i	$-0.609703\pi$
$157$	−3.27653e7	−0.675717	−0.337858	+	0.941197i	$0.609703\pi$
$158$	−3.92122e7	−0.790901
$159$	0	0
$160$	2.08184e7	0.401816
$161$	−1.28938e8	−2.43495
$162$	0	0
$163$	3.27745e7	0.592761	0.296381	−	0.955070i	$-0.404220\pi$
$163$	3.27745e7	0.592761	0.296381	+	0.955070i	$0.404220\pi$
$164$	−2.89534e7	−0.512562
$165$	0	0
$166$	1.15041e8	1.95198
$167$	4.91242e7	0.816183	0.408092	−	0.912941i	$-0.366194\pi$
$167$	4.91242e7	0.816183	0.408092	+	0.912941i	$0.366194\pi$
$168$	0	0
$169$	8.73439e7	1.39197
$170$	5.39466e7	0.842157
$171$	0	0
$172$	2.69214e7	0.403411
$173$	−2.08181e7	−0.305688	−0.152844	−	0.988250i	$-0.548843\pi$
$173$	−2.08181e7	−0.305688	−0.152844	+	0.988250i	$0.548843\pi$
$174$	0	0
$175$	7.30565e7	1.03045
$176$	1.04066e8	1.43885
$177$	0	0
$178$	1.17242e7	0.155817
$179$	−8.64093e7	−1.12609	−0.563047	−	0.826425i	$-0.690371\pi$
$179$	−8.64093e7	−1.12609	−0.563047	+	0.826425i	$0.690371\pi$
$180$	0	0
$181$	−6.54723e7	−0.820696	−0.410348	−	0.911929i	$-0.634593\pi$
$181$	−6.54723e7	−0.820696	−0.410348	+	0.911929i	$0.634593\pi$
$182$	2.17008e8	2.66825
$183$	0	0
$184$	−1.01223e8	−1.19789
$185$	−4.37788e7	−0.508350
$186$	0	0
$187$	1.36521e8	1.52671
$188$	3.23882e7	0.355496
$189$	0	0
$190$	−6.73215e7	−0.712060
$191$	8.45503e7	0.878007	0.439004	−	0.898485i	$-0.355331\pi$
$191$	8.45503e7	0.878007	0.439004	+	0.898485i	$0.355331\pi$
$192$	0	0
$193$	−2.04209e7	−0.204467	−0.102234	−	0.994760i	$-0.532599\pi$
$193$	−2.04209e7	−0.204467	−0.102234	+	0.994760i	$0.532599\pi$
$194$	−2.16026e8	−2.12422
$195$	0	0
$196$	4.68593e7	0.444529
$197$	−3.23191e7	−0.301181	−0.150591	−	0.988596i	$-0.548118\pi$
$197$	−3.23191e7	−0.301181	−0.150591	+	0.988596i	$0.548118\pi$
$198$	0	0
$199$	−7.22071e7	−0.649522	−0.324761	−	0.945796i	$-0.605284\pi$
$199$	−7.22071e7	−0.649522	−0.324761	+	0.945796i	$0.605284\pi$
$200$	5.73534e7	0.506937
$201$	0	0
$202$	−8.23736e6	−0.0703166
$203$	2.78008e8	2.33250
$204$	0	0
$205$	8.84589e7	0.717139
$206$	−9.31549e7	−0.742455
$207$	0	0
$208$	2.48428e8	1.91416
$209$	−1.70369e8	−1.29086
$210$	0	0
$211$	−1.90681e8	−1.39739	−0.698696	−	0.715419i	$-0.746236\pi$
$211$	−1.90681e8	−1.39739	−0.698696	+	0.715419i	$0.746236\pi$
$212$	2.48648e6	0.0179230
$213$	0	0
$214$	9.96036e7	0.694747
$215$	−8.22507e7	−0.564423
$216$	0	0
$217$	4.10331e8	2.72600
$218$	−3.00023e8	−1.96136
$219$	0	0
$220$	3.88566e7	0.246028
$221$	3.25905e8	2.03104
$222$	0	0
$223$	2.03359e8	1.22800	0.613998	−	0.789307i	$-0.289560\pi$
$223$	2.03359e8	1.22800	0.613998	+	0.789307i	$0.289560\pi$
$224$	1.81841e8	1.08099
$225$	0	0
$226$	−9.78326e7	−0.563773
$227$	−3.52165e7	−0.199828	−0.0999139	−	0.994996i	$-0.531857\pi$
$227$	−3.52165e7	−0.199828	−0.0999139	+	0.994996i	$0.531857\pi$
$228$	0	0
$229$	−3.50737e8	−1.93000	−0.965000	−	0.262249i	$-0.915536\pi$
$229$	−3.50737e8	−1.93000	−0.965000	+	0.262249i	$0.915536\pi$
$230$	−1.96824e8	−1.06667
$231$	0	0
$232$	2.18252e8	1.14749
$233$	2.71870e8	1.40804	0.704020	−	0.710180i	$-0.251387\pi$
$233$	2.71870e8	1.40804	0.704020	+	0.710180i	$0.251387\pi$
$234$	0	0
$235$	−9.89530e7	−0.497384
$236$	1.02240e7	0.0506327
$237$	0	0
$238$	4.71203e8	2.26563
$239$	7.12076e7	0.337391	0.168696	−	0.985668i	$-0.446045\pi$
$239$	7.12076e7	0.337391	0.168696	+	0.985668i	$0.446045\pi$
$240$	0	0
$241$	−2.36356e8	−1.08770	−0.543848	−	0.839184i	$-0.683033\pi$
$241$	−2.36356e8	−1.08770	−0.543848	+	0.839184i	$0.683033\pi$
$242$	9.13410e7	0.414297
$243$	0	0
$244$	−996870.	−0.00439313
$245$	−1.43165e8	−0.621952
$246$	0	0
$247$	−4.06707e8	−1.71728
$248$	3.22133e8	1.34108
$249$	0	0
$250$	2.69953e8	1.09269
$251$	−3.04691e7	−0.121619	−0.0608094	−	0.998149i	$-0.519368\pi$
$251$	−3.04691e7	−0.121619	−0.0608094	+	0.998149i	$0.519368\pi$
$252$	0	0
$253$	−4.98099e8	−1.93372
$254$	−1.50081e8	−0.574654
$255$	0	0
$256$	2.71966e8	1.01315
$257$	−2.69817e8	−0.991524	−0.495762	−	0.868458i	$-0.665111\pi$
$257$	−2.69817e8	−0.991524	−0.495762	+	0.868458i	$0.665111\pi$
$258$	0	0
$259$	−3.82391e8	−1.36760
$260$	9.27588e7	0.327302
$261$	0	0
$262$	−5.73548e7	−0.197022
$263$	3.30750e8	1.12113	0.560564	−	0.828111i	$-0.310585\pi$
$263$	3.30750e8	1.12113	0.560564	+	0.828111i	$0.310585\pi$
$264$	0	0
$265$	−7.59674e6	−0.0250765
$266$	−5.88029e8	−1.91564
$267$	0	0
$268$	−6.90366e7	−0.219082
$269$	−3.87843e8	−1.21485	−0.607426	−	0.794377i	$-0.707798\pi$
$269$	−3.87843e8	−1.21485	−0.607426	+	0.794377i	$0.707798\pi$
$270$	0	0
$271$	3.62357e8	1.10597	0.552986	−	0.833191i	$-0.313488\pi$
$271$	3.62357e8	1.10597	0.552986	+	0.833191i	$0.313488\pi$
$272$	5.39428e8	1.62533
$273$	0	0
$274$	2.47311e8	0.726301
$275$	2.82224e8	0.818333
$276$	0	0
$277$	3.92785e8	1.11039	0.555195	−	0.831721i	$-0.312644\pi$
$277$	3.92785e8	1.11039	0.555195	+	0.831721i	$0.312644\pi$
$278$	−5.50614e8	−1.53706
$279$	0	0
$280$	−2.10725e8	−0.573670
$281$	−2.62473e7	−0.0705686	−0.0352843	−	0.999377i	$-0.511234\pi$
$281$	−2.62473e7	−0.0705686	−0.0352843	+	0.999377i	$0.511234\pi$
$282$	0	0
$283$	3.02721e8	0.793945	0.396972	−	0.917831i	$-0.370061\pi$
$283$	3.02721e8	0.793945	0.396972	+	0.917831i	$0.370061\pi$
$284$	−6.19146e7	−0.160390
$285$	0	0
$286$	8.38323e8	2.11900
$287$	7.72656e8	1.92930
$288$	0	0
$289$	2.97321e8	0.724574
$290$	4.24381e8	1.02179
$291$	0	0
$292$	−2.40818e8	−0.566042
$293$	−4.44159e8	−1.03158	−0.515789	−	0.856716i	$-0.672501\pi$
$293$	−4.44159e8	−1.03158	−0.515789	+	0.856716i	$0.672501\pi$
$294$	0	0
$295$	−3.12367e7	−0.0708415
$296$	−3.00198e8	−0.672802
$297$	0	0
$298$	−3.70623e8	−0.811288
$299$	−1.18907e9	−2.57251
$300$	0	0
$301$	−7.18429e8	−1.51845
$302$	6.73552e8	1.40717
$303$	0	0
$304$	−6.73168e8	−1.37425
$305$	3.04566e6	0.00614655
$306$	0	0
$307$	−7.17875e8	−1.41600	−0.708002	−	0.706211i	$-0.750403\pi$
$307$	−7.17875e8	−1.41600	−0.708002	+	0.706211i	$0.750403\pi$
$308$	3.39398e8	0.661883
$309$	0	0
$310$	6.26374e8	1.19417
$311$	9.91134e8	1.86841	0.934203	−	0.356743i	$-0.116113\pi$
$311$	9.91134e8	1.86841	0.934203	+	0.356743i	$0.116113\pi$
$312$	0	0
$313$	−1.77188e7	−0.0326610	−0.0163305	−	0.999867i	$-0.505198\pi$
$313$	−1.77188e7	−0.0326610	−0.0163305	+	0.999867i	$0.505198\pi$
$314$	−4.36875e8	−0.796348
$315$	0	0
$316$	−1.46401e8	−0.261000
$317$	−6.67310e8	−1.17658	−0.588289	−	0.808651i	$-0.700198\pi$
$317$	−6.67310e8	−1.17658	−0.588289	+	0.808651i	$0.700198\pi$
$318$	0	0
$319$	1.07397e9	1.85236
$320$	−1.17185e8	−0.199917
$321$	0	0
$322$	−1.71919e9	−2.86964
$323$	−8.83109e8	−1.45816
$324$	0	0
$325$	6.73728e8	1.08866
$326$	4.36998e8	0.698583
$327$	0	0
$328$	6.06577e8	0.949134
$329$	−8.64318e8	−1.33810
$330$	0	0
$331$	1.21309e9	1.83863	0.919313	−	0.393526i	$-0.128745\pi$
$331$	1.21309e9	1.83863	0.919313	+	0.393526i	$0.128745\pi$
$332$	4.29515e8	0.644161
$333$	0	0
$334$	6.54996e8	0.961891
$335$	2.10922e8	0.306524
$336$	0	0
$337$	4.03850e8	0.574799	0.287399	−	0.957811i	$-0.407209\pi$
$337$	4.03850e8	0.574799	0.287399	+	0.957811i	$0.407209\pi$
$338$	1.16460e9	1.64047
$339$	0	0
$340$	2.01413e8	0.277915
$341$	1.58515e9	2.16486
$342$	0	0
$343$	−1.56440e8	−0.209324
$344$	−5.64006e8	−0.747015
$345$	0	0
$346$	−2.77577e8	−0.360261
$347$	5.73452e8	0.736791	0.368395	−	0.929669i	$-0.379907\pi$
$347$	5.73452e8	0.736791	0.368395	+	0.929669i	$0.379907\pi$
$348$	0	0
$349$	−3.21244e8	−0.404525	−0.202263	−	0.979331i	$-0.564829\pi$
$349$	−3.21244e8	−0.404525	−0.202263	+	0.979331i	$0.564829\pi$
$350$	9.74096e8	1.21441
$351$	0	0
$352$	7.02468e8	0.858474
$353$	−3.98442e8	−0.482118	−0.241059	−	0.970510i	$-0.577495\pi$
$353$	−3.98442e8	−0.482118	−0.241059	+	0.970510i	$0.577495\pi$
$354$	0	0
$355$	1.89162e8	0.224407
$356$	4.37732e7	0.0514202
$357$	0	0
$358$	−1.15214e9	−1.32713
$359$	−1.40704e9	−1.60500	−0.802501	−	0.596651i	$-0.796498\pi$
$359$	−1.40704e9	−1.60500	−0.802501	+	0.596651i	$0.796498\pi$
$360$	0	0
$361$	2.08186e8	0.232903
$362$	−8.72973e8	−0.967210
$363$	0	0
$364$	8.10214e8	0.880531
$365$	7.35751e8	0.791965
$366$	0	0
$367$	−9.65705e8	−1.01980	−0.509898	−	0.860235i	$-0.670317\pi$
$367$	−9.65705e8	−1.01980	−0.509898	+	0.860235i	$0.670317\pi$
$368$	−1.96811e9	−2.05864
$369$	0	0
$370$	−5.83723e8	−0.599102
$371$	−6.63547e7	−0.0674626
$372$	0	0
$373$	−6.50998e8	−0.649529	−0.324765	−	0.945795i	$-0.605285\pi$
$373$	−6.50998e8	−0.649529	−0.324765	+	0.945795i	$0.605285\pi$
$374$	1.82030e9	1.79926
$375$	0	0
$376$	−6.78537e8	−0.658288
$377$	2.56380e9	2.46427
$378$	0	0
$379$	−3.97991e7	−0.0375522	−0.0187761	−	0.999824i	$-0.505977\pi$
$379$	−3.97991e7	−0.0375522	−0.0187761	+	0.999824i	$0.505977\pi$
$380$	−2.51349e8	−0.234982
$381$	0	0
$382$	1.12735e9	1.03475
$383$	−6.27745e7	−0.0570936	−0.0285468	−	0.999592i	$-0.509088\pi$
$383$	−6.27745e7	−0.0570936	−0.0285468	+	0.999592i	$0.509088\pi$
$384$	0	0
$385$	−1.03693e9	−0.926058
$386$	−2.72281e8	−0.240970
$387$	0	0
$388$	−8.06545e8	−0.701000
$389$	4.14596e8	0.357109	0.178555	−	0.983930i	$-0.442858\pi$
$389$	4.14596e8	0.357109	0.178555	+	0.983930i	$0.442858\pi$
$390$	0	0
$391$	−2.58190e9	−2.18434
$392$	−9.81708e8	−0.823154
$393$	0	0
$394$	−4.30926e8	−0.354949
$395$	4.47288e8	0.365172
$396$	0	0
$397$	−5.40817e8	−0.433794	−0.216897	−	0.976194i	$-0.569594\pi$
$397$	−5.40817e8	−0.433794	−0.216897	+	0.976194i	$0.569594\pi$
$398$	−9.62771e8	−0.765477
$399$	0	0
$400$	1.11513e9	0.871198
$401$	−1.82362e9	−1.41231	−0.706153	−	0.708059i	$-0.749571\pi$
$401$	−1.82362e9	−1.41231	−0.706153	+	0.708059i	$0.749571\pi$
$402$	0	0
$403$	3.78408e9	2.88000
$404$	−3.07547e7	−0.0232047
$405$	0	0
$406$	3.70681e9	2.74890
$407$	−1.47721e9	−1.08608
$408$	0	0
$409$	1.97200e9	1.42520	0.712599	−	0.701571i	$-0.247518\pi$
$409$	1.97200e9	1.42520	0.712599	+	0.701571i	$0.247518\pi$
$410$	1.17946e9	0.845165
$411$	0	0
$412$	−3.47800e8	−0.245013
$413$	−2.72841e8	−0.190583
$414$	0	0
$415$	−1.31226e9	−0.901263
$416$	1.67694e9	1.14206
$417$	0	0
$418$	−2.27161e9	−1.52131
$419$	−4.90370e8	−0.325668	−0.162834	−	0.986653i	$-0.552064\pi$
$419$	−4.90370e8	−0.325668	−0.162834	+	0.986653i	$0.552064\pi$
$420$	0	0
$421$	−1.72536e8	−0.112692	−0.0563459	−	0.998411i	$-0.517945\pi$
$421$	−1.72536e8	−0.112692	−0.0563459	+	0.998411i	$0.517945\pi$
$422$	−2.54244e9	−1.64686
$423$	0	0
$424$	−5.20921e7	−0.0331888
$425$	1.46291e9	0.924392
$426$	0	0
$427$	2.66027e7	0.0165359
$428$	3.71876e8	0.229269
$429$	0	0
$430$	−1.09669e9	−0.665186
$431$	−1.99685e9	−1.20136	−0.600681	−	0.799489i	$-0.705104\pi$
$431$	−1.99685e9	−1.20136	−0.600681	+	0.799489i	$0.705104\pi$
$432$	0	0
$433$	−6.53171e8	−0.386651	−0.193326	−	0.981135i	$-0.561927\pi$
$433$	−6.53171e8	−0.386651	−0.193326	+	0.981135i	$0.561927\pi$
$434$	5.47114e9	3.21265
$435$	0	0
$436$	−1.12015e9	−0.647255
$437$	3.22203e9	1.84690
$438$	0	0
$439$	−2.18962e9	−1.23521	−0.617607	−	0.786487i	$-0.711898\pi$
$439$	−2.18962e9	−1.23521	−0.617607	+	0.786487i	$0.711898\pi$
$440$	−8.14050e8	−0.455582
$441$	0	0
$442$	4.34545e9	2.39363
$443$	−2.98274e9	−1.63006	−0.815028	−	0.579422i	$-0.803278\pi$
$443$	−2.98274e9	−1.63006	−0.815028	+	0.579422i	$0.803278\pi$
$444$	0	0
$445$	−1.33737e8	−0.0719433
$446$	2.71149e9	1.44722
$447$	0	0
$448$	−1.02357e9	−0.537830
$449$	1.54617e9	0.806111	0.403055	−	0.915176i	$-0.367948\pi$
$449$	1.54617e9	0.806111	0.403055	+	0.915176i	$0.367948\pi$
$450$	0	0
$451$	2.98484e9	1.53216
$452$	−3.65264e8	−0.186047
$453$	0	0
$454$	−4.69558e8	−0.235502
$455$	−2.47538e9	−1.23197
$456$	0	0
$457$	−7.00396e8	−0.343271	−0.171635	−	0.985161i	$-0.554905\pi$
$457$	−7.00396e8	−0.343271	−0.171635	+	0.985161i	$0.554905\pi$
$458$	−4.67654e9	−2.27455
$459$	0	0
$460$	−7.34857e8	−0.352006
$461$	2.39080e9	1.13655	0.568277	−	0.822838i	$-0.307610\pi$
$461$	2.39080e9	1.13655	0.568277	+	0.822838i	$0.307610\pi$
$462$	0	0
$463$	2.71887e9	1.27308	0.636539	−	0.771244i	$-0.280365\pi$
$463$	2.71887e9	1.27308	0.636539	+	0.771244i	$0.280365\pi$
$464$	4.24352e9	1.97203
$465$	0	0
$466$	3.62496e9	1.65941
$467$	−3.63245e9	−1.65041	−0.825203	−	0.564836i	$-0.808939\pi$
$467$	−3.63245e9	−1.65041	−0.825203	+	0.564836i	$0.808939\pi$
$468$	0	0
$469$	1.84232e9	0.824633
$470$	−1.31939e9	−0.586178
$471$	0	0
$472$	−2.14195e8	−0.0937589
$473$	−2.77536e9	−1.20588
$474$	0	0
$475$	−1.82561e9	−0.781592
$476$	1.75927e9	0.747666
$477$	0	0
$478$	9.49444e8	0.397623
$479$	7.60336e8	0.316105	0.158053	−	0.987431i	$-0.449478\pi$
$479$	7.60336e8	0.316105	0.158053	+	0.987431i	$0.449478\pi$
$480$	0	0
$481$	−3.52642e9	−1.44486
$482$	−3.15145e9	−1.28188
$483$	0	0
$484$	3.41028e8	0.136720
$485$	2.46417e9	0.980787
$486$	0	0
$487$	−3.11666e9	−1.22275	−0.611375	−	0.791341i	$-0.709383\pi$
$487$	−3.11666e9	−1.22275	−0.611375	+	0.791341i	$0.709383\pi$
$488$	2.08846e7	0.00813497
$489$	0	0
$490$	−1.90889e9	−0.732984
$491$	2.02161e9	0.770749	0.385374	−	0.922760i	$-0.374072\pi$
$491$	2.02161e9	0.770749	0.385374	+	0.922760i	$0.374072\pi$
$492$	0	0
$493$	5.56694e9	2.09244
$494$	−5.42281e9	−2.02386
$495$	0	0
$496$	6.26330e9	2.30471
$497$	1.65226e9	0.603715
$498$	0	0
$499$	−3.90803e9	−1.40801	−0.704006	−	0.710194i	$-0.748607\pi$
$499$	−3.90803e9	−1.40801	−0.704006	+	0.710194i	$0.748607\pi$
$500$	1.00789e9	0.360593
$501$	0	0
$502$	−4.06258e8	−0.143331
$503$	5.07994e9	1.77980	0.889899	−	0.456158i	$-0.150775\pi$
$503$	5.07994e9	1.77980	0.889899	+	0.456158i	$0.150775\pi$
$504$	0	0
$505$	9.39623e7	0.0324664
$506$	−6.64139e9	−2.27894
$507$	0	0
$508$	−5.60336e8	−0.189638
$509$	2.67138e9	0.897892	0.448946	−	0.893559i	$-0.351800\pi$
$509$	2.67138e9	0.897892	0.448946	+	0.893559i	$0.351800\pi$
$510$	0	0
$511$	6.42651e9	2.13060
$512$	6.86375e7	0.0226004
$513$	0	0
$514$	−3.59760e9	−1.16853
$515$	1.06260e9	0.342804
$516$	0	0
$517$	−3.33894e9	−1.06265
$518$	−5.09860e9	−1.61175
$519$	0	0
$520$	−1.94331e9	−0.606080
$521$	−1.52466e9	−0.472326	−0.236163	−	0.971713i	$-0.575890\pi$
$521$	−1.52466e9	−0.472326	−0.236163	+	0.971713i	$0.575890\pi$
$522$	0	0
$523$	9.55727e8	0.292131	0.146066	−	0.989275i	$-0.453339\pi$
$523$	9.55727e8	0.292131	0.146066	+	0.989275i	$0.453339\pi$
$524$	−2.14138e8	−0.0650180
$525$	0	0
$526$	4.41005e9	1.32127
$527$	8.21663e9	2.44544
$528$	0	0
$529$	6.01524e9	1.76668
$530$	−1.01291e8	−0.0295532
$531$	0	0
$532$	−2.19544e9	−0.632167
$533$	7.12545e9	2.03829
$534$	0	0
$535$	−1.13616e9	−0.320776
$536$	1.44632e9	0.405685
$537$	0	0
$538$	−5.17129e9	−1.43173
$539$	−4.83079e9	−1.32879
$540$	0	0
$541$	1.12167e9	0.304561	0.152280	−	0.988337i	$-0.451338\pi$
$541$	1.12167e9	0.304561	0.152280	+	0.988337i	$0.451338\pi$
$542$	4.83147e9	1.30341
$543$	0	0
$544$	3.64125e9	0.969737
$545$	3.42232e9	0.905591
$546$	0	0
$547$	5.80841e8	0.151740	0.0758702	−	0.997118i	$-0.475827\pi$
$547$	5.80841e8	0.151740	0.0758702	+	0.997118i	$0.475827\pi$
$548$	9.23352e8	0.239682
$549$	0	0
$550$	3.76303e9	0.964424
$551$	−6.94715e9	−1.76920
$552$	0	0
$553$	3.90690e9	0.982413
$554$	5.23718e9	1.30862
$555$	0	0
$556$	−2.05575e9	−0.507235
$557$	−3.50741e9	−0.859989	−0.429994	−	0.902832i	$-0.641484\pi$
$557$	−3.50741e9	−0.859989	−0.429994	+	0.902832i	$0.641484\pi$
$558$	0	0
$559$	−6.62537e9	−1.60424
$560$	−4.09717e9	−0.985883
$561$	0	0
$562$	−3.49967e8	−0.0831668
$563$	−1.57440e9	−0.371822	−0.185911	−	0.982567i	$-0.559524\pi$
$563$	−1.57440e9	−0.371822	−0.185911	+	0.982567i	$0.559524\pi$
$564$	0	0
$565$	1.11596e9	0.260303
$566$	4.03632e9	0.935682
$567$	0	0
$568$	1.29712e9	0.297003
$569$	2.71007e7	0.00616719	0.00308360	−	0.999995i	$-0.499018\pi$
$569$	2.71007e7	0.00616719	0.00308360	+	0.999995i	$0.499018\pi$
$570$	0	0
$571$	−8.12943e9	−1.82740	−0.913700	−	0.406390i	$-0.866787\pi$
$571$	−8.12943e9	−1.82740	−0.913700	+	0.406390i	$0.866787\pi$
$572$	3.12993e9	0.699276
$573$	0	0
$574$	1.03022e10	2.27372
$575$	−5.33743e9	−1.17083
$576$	0	0
$577$	−8.89512e8	−0.192769	−0.0963844	−	0.995344i	$-0.530728\pi$
$577$	−8.89512e8	−0.192769	−0.0963844	+	0.995344i	$0.530728\pi$
$578$	3.96431e9	0.853927
$579$	0	0
$580$	1.58446e9	0.337196
$581$	−1.14621e10	−2.42464
$582$	0	0
$583$	−2.56334e8	−0.0535756
$584$	5.04516e9	1.04817
$585$	0	0
$586$	−5.92218e9	−1.21574
$587$	−8.09762e8	−0.165243	−0.0826217	−	0.996581i	$-0.526329\pi$
$587$	−8.09762e8	−0.165243	−0.0826217	+	0.996581i	$0.526329\pi$
$588$	0	0
$589$	−1.02538e10	−2.06766
$590$	−4.16493e8	−0.0834884
$591$	0	0
$592$	−5.83682e9	−1.15625
$593$	6.48925e9	1.27792	0.638959	−	0.769241i	$-0.279365\pi$
$593$	6.48925e9	1.27792	0.638959	+	0.769241i	$0.279365\pi$
$594$	0	0
$595$	−5.37495e9	−1.04608
$596$	−1.38374e9	−0.267728
$597$	0	0
$598$	−1.58544e10	−3.03176
$599$	−6.51857e8	−0.123925	−0.0619624	−	0.998078i	$-0.519736\pi$
$599$	−6.51857e8	−0.123925	−0.0619624	+	0.998078i	$0.519736\pi$
$600$	0	0
$601$	−2.97476e9	−0.558974	−0.279487	−	0.960150i	$-0.590164\pi$
$601$	−2.97476e9	−0.558974	−0.279487	+	0.960150i	$0.590164\pi$
$602$	−9.57915e9	−1.78953
$603$	0	0
$604$	2.51475e9	0.464372
$605$	−1.04191e9	−0.191288
$606$	0	0
$607$	−4.76572e9	−0.864905	−0.432452	−	0.901657i	$-0.642352\pi$
$607$	−4.76572e9	−0.864905	−0.432452	+	0.901657i	$0.642352\pi$
$608$	−4.54402e9	−0.819931
$609$	0	0
$610$	4.06091e7	0.00724385
$611$	−7.97076e9	−1.41369
$612$	0	0
$613$	4.10844e9	0.720385	0.360193	−	0.932878i	$-0.382711\pi$
$613$	4.10844e9	0.720385	0.360193	+	0.932878i	$0.382711\pi$
$614$	−9.57176e9	−1.66879
$615$	0	0
$616$	−7.11042e9	−1.22564
$617$	−8.36433e9	−1.43362	−0.716809	−	0.697270i	$-0.754398\pi$
$617$	−8.36433e9	−1.43362	−0.716809	+	0.697270i	$0.754398\pi$
$618$	0	0
$619$	−1.37677e8	−0.0233315	−0.0116658	−	0.999932i	$-0.503713\pi$
$619$	−1.37677e8	−0.0233315	−0.0116658	+	0.999932i	$0.503713\pi$
$620$	2.33861e9	0.394082
$621$	0	0
$622$	1.32153e10	2.20196
$623$	−1.16814e9	−0.193547
$624$	0	0
$625$	1.21700e9	0.199393
$626$	−2.36253e8	−0.0384917
$627$	0	0
$628$	−1.63110e9	−0.262798
$629$	−7.65715e9	−1.22685
$630$	0	0
$631$	−1.86229e9	−0.295083	−0.147542	−	0.989056i	$-0.547136\pi$
$631$	−1.86229e9	−0.295083	−0.147542	+	0.989056i	$0.547136\pi$
$632$	3.06713e9	0.483306
$633$	0	0
$634$	−8.89756e9	−1.38662
$635$	1.71195e9	0.265328
$636$	0	0
$637$	−1.15321e10	−1.76775
$638$	1.43198e10	2.18305
$639$	0	0
$640$	−4.22724e9	−0.637422
$641$	−1.04508e10	−1.56727	−0.783637	−	0.621219i	$-0.786638\pi$
$641$	−1.04508e10	−1.56727	−0.783637	+	0.621219i	$0.786638\pi$
$642$	0	0
$643$	−1.17114e10	−1.73728	−0.868642	−	0.495440i	$-0.835007\pi$
$643$	−1.17114e10	−1.73728	−0.868642	+	0.495440i	$0.835007\pi$
$644$	−6.41870e9	−0.946993
$645$	0	0
$646$	−1.17749e10	−1.71848
$647$	2.82698e7	0.00410353	0.00205176	−	0.999998i	$-0.499347\pi$
$647$	2.82698e7	0.00410353	0.00205176	+	0.999998i	$0.499347\pi$
$648$	0	0
$649$	−1.05401e9	−0.151352
$650$	8.98314e9	1.28301
$651$	0	0
$652$	1.63156e9	0.230535
$653$	−1.03288e10	−1.45163	−0.725813	−	0.687892i	$-0.758536\pi$
$653$	−1.03288e10	−1.45163	−0.725813	+	0.687892i	$0.758536\pi$
$654$	0	0
$655$	6.54237e8	0.0909684
$656$	1.17938e10	1.63114
$657$	0	0
$658$	−1.15244e10	−1.57698
$659$	8.85377e9	1.20512	0.602558	−	0.798075i	$-0.294148\pi$
$659$	8.85377e9	1.20512	0.602558	+	0.798075i	$0.294148\pi$
$660$	0	0
$661$	3.94438e8	0.0531219	0.0265610	−	0.999647i	$-0.491544\pi$
$661$	3.94438e8	0.0531219	0.0265610	+	0.999647i	$0.491544\pi$
$662$	1.61746e10	2.16686
$663$	0	0
$664$	−8.99838e9	−1.19282
$665$	6.70756e9	0.884481
$666$	0	0
$667$	−2.03110e10	−2.65027
$668$	2.44547e9	0.317427
$669$	0	0
$670$	2.81232e9	0.361246
$671$	1.02769e8	0.0131320
$672$	0	0
$673$	−3.32239e8	−0.0420144	−0.0210072	−	0.999779i	$-0.506687\pi$
$673$	−3.32239e8	−0.0420144	−0.0210072	+	0.999779i	$0.506687\pi$
$674$	5.38472e9	0.677413
$675$	0	0
$676$	4.34810e9	0.541360
$677$	7.35957e9	0.911574	0.455787	−	0.890089i	$-0.349358\pi$
$677$	7.35957e9	0.911574	0.455787	+	0.890089i	$0.349358\pi$
$678$	0	0
$679$	2.15236e10	2.63858
$680$	−4.21963e9	−0.514628
$681$	0	0
$682$	2.11355e10	2.55134
$683$	1.53063e10	1.83822	0.919111	−	0.393999i	$-0.128909\pi$
$683$	1.53063e10	1.83822	0.919111	+	0.393999i	$0.128909\pi$
$684$	0	0
$685$	−2.82104e9	−0.335345
$686$	−2.08589e9	−0.246693
$687$	0	0
$688$	−1.09661e10	−1.28379
$689$	−6.11924e8	−0.0712739
$690$	0	0
$691$	−1.49200e10	−1.72026	−0.860132	−	0.510072i	$-0.829619\pi$
$691$	−1.49200e10	−1.72026	−0.860132	+	0.510072i	$0.829619\pi$
$692$	−1.03635e9	−0.118887
$693$	0	0
$694$	7.64611e9	0.868325
$695$	6.28077e9	0.709686
$696$	0	0
$697$	1.54719e10	1.73073
$698$	−4.28329e9	−0.476742
$699$	0	0
$700$	3.63685e9	0.400758
$701$	6.52424e9	0.715347	0.357673	−	0.933847i	$-0.383570\pi$
$701$	6.52424e9	0.715347	0.357673	+	0.933847i	$0.383570\pi$
$702$	0	0
$703$	9.55558e9	1.03732
$704$	−3.95415e9	−0.427119
$705$	0	0
$706$	−5.31262e9	−0.568188
$707$	8.20726e8	0.0873434
$708$	0	0
$709$	4.55527e9	0.480012	0.240006	−	0.970771i	$-0.422851\pi$
$709$	4.55527e9	0.480012	0.240006	+	0.970771i	$0.422851\pi$
$710$	2.52219e9	0.264468
$711$	0	0
$712$	−9.17054e8	−0.0952171
$713$	−2.99784e10	−3.09738
$714$	0	0
$715$	−9.56262e9	−0.978376
$716$	−4.30157e9	−0.437957
$717$	0	0
$718$	−1.87607e10	−1.89153
$719$	−6.09158e9	−0.611194	−0.305597	−	0.952161i	$-0.598856\pi$
$719$	−6.09158e9	−0.611194	−0.305597	+	0.952161i	$0.598856\pi$
$720$	0	0
$721$	9.28145e9	0.922236
$722$	2.77584e9	0.274482
$723$	0	0
$724$	−3.25930e9	−0.319183
$725$	1.15083e10	1.12157
$726$	0	0
$727$	1.68599e10	1.62737	0.813684	−	0.581308i	$-0.197459\pi$
$727$	1.68599e10	1.62737	0.813684	+	0.581308i	$0.197459\pi$
$728$	−1.69741e10	−1.63052
$729$	0	0
$730$	9.81011e9	0.933349
$731$	−1.43861e10	−1.36217
$732$	0	0
$733$	−1.44578e9	−0.135593	−0.0677966	−	0.997699i	$-0.521597\pi$
$733$	−1.44578e9	−0.135593	−0.0677966	+	0.997699i	$0.521597\pi$
$734$	−1.28762e10	−1.20185
$735$	0	0
$736$	−1.32851e10	−1.22827
$737$	7.11707e9	0.654885
$738$	0	0
$739$	8.56684e8	0.0780845	0.0390423	−	0.999238i	$-0.487569\pi$
$739$	8.56684e8	0.0780845	0.0390423	+	0.999238i	$0.487569\pi$
$740$	−2.17937e9	−0.197706
$741$	0	0
$742$	−8.84738e8	−0.0795062
$743$	−1.09080e10	−0.975630	−0.487815	−	0.872947i	$-0.662206\pi$
$743$	−1.09080e10	−0.975630	−0.487815	+	0.872947i	$0.662206\pi$
$744$	0	0
$745$	4.22764e9	0.374585
$746$	−8.68006e9	−0.765485
$747$	0	0
$748$	6.79622e9	0.593762
$749$	−9.92396e9	−0.862976
$750$	0	0
$751$	−5.27485e9	−0.454433	−0.227217	−	0.973844i	$-0.572963\pi$
$751$	−5.27485e9	−0.454433	−0.227217	+	0.973844i	$0.572963\pi$
$752$	−1.31929e10	−1.13130
$753$	0	0
$754$	3.41843e10	2.90420
$755$	−7.68311e9	−0.649715
$756$	0	0
$757$	−2.07054e10	−1.73479	−0.867395	−	0.497620i	$-0.834208\pi$
$757$	−2.07054e10	−1.73479	−0.867395	+	0.497620i	$0.834208\pi$
$758$	−5.30659e8	−0.0442562
$759$	0	0
$760$	5.26580e9	0.435128
$761$	−1.35780e10	−1.11683	−0.558417	−	0.829561i	$-0.688591\pi$
$761$	−1.35780e10	−1.11683	−0.558417	+	0.829561i	$0.688591\pi$
$762$	0	0
$763$	2.98927e10	2.43629
$764$	4.20903e9	0.341472
$765$	0	0
$766$	−8.37001e8	−0.0672861
$767$	−2.51614e9	−0.201350
$768$	0	0
$769$	1.62978e10	1.29237	0.646184	−	0.763182i	$-0.276364\pi$
$769$	1.62978e10	1.29237	0.646184	+	0.763182i	$0.276364\pi$
$770$	−1.38259e10	−1.09138
$771$	0	0
$772$	−1.01658e9	−0.0795208
$773$	2.64697e9	0.206120	0.103060	−	0.994675i	$-0.467137\pi$
$773$	2.64697e9	0.206120	0.103060	+	0.994675i	$0.467137\pi$
$774$	0	0
$775$	1.69858e10	1.31078
$776$	1.68972e10	1.29807
$777$	0	0
$778$	5.52800e9	0.420862
$779$	−1.93079e10	−1.46337
$780$	0	0
$781$	6.38285e9	0.479442
$782$	−3.44257e10	−2.57430
$783$	0	0
$784$	−1.90876e10	−1.41463
$785$	4.98336e9	0.367687
$786$	0	0
$787$	−7.25919e9	−0.530856	−0.265428	−	0.964131i	$-0.585513\pi$
$787$	−7.25919e9	−0.530856	−0.265428	+	0.964131i	$0.585513\pi$
$788$	−1.60889e9	−0.117134
$789$	0	0
$790$	5.96390e9	0.430364
$791$	9.74751e9	0.700287
$792$	0	0
$793$	2.45330e8	0.0174701
$794$	−7.21097e9	−0.511237
$795$	0	0
$796$	−3.59457e9	−0.252610
$797$	3.67130e9	0.256871	0.128436	−	0.991718i	$-0.459004\pi$
$797$	3.67130e9	0.256871	0.128436	+	0.991718i	$0.459004\pi$
$798$	0	0
$799$	−1.73074e10	−1.20038
$800$	7.52737e9	0.519791
$801$	0	0
$802$	−2.43152e10	−1.66444
$803$	2.48262e10	1.69202
$804$	0	0
$805$	1.96105e10	1.32496
$806$	5.04550e10	3.39415
$807$	0	0
$808$	6.44315e8	0.0429693
$809$	5.97080e9	0.396472	0.198236	−	0.980154i	$-0.436479\pi$
$809$	5.97080e9	0.396472	0.198236	+	0.980154i	$0.436479\pi$
$810$	0	0
$811$	2.51680e10	1.65682	0.828409	−	0.560123i	$-0.189246\pi$
$811$	2.51680e10	1.65682	0.828409	+	0.560123i	$0.189246\pi$
$812$	1.38396e10	0.907148
$813$	0	0
$814$	−1.96964e10	−1.27997
$815$	−4.98477e9	−0.322548
$816$	0	0
$817$	1.79528e10	1.15174
$818$	2.62936e10	1.67963
$819$	0	0
$820$	4.40361e9	0.278907
$821$	−1.74411e10	−1.09995	−0.549975	−	0.835181i	$-0.685363\pi$
$821$	−1.74411e10	−1.09995	−0.549975	+	0.835181i	$0.685363\pi$
$822$	0	0
$823$	1.10753e10	0.692557	0.346278	−	0.938132i	$-0.387445\pi$
$823$	1.10753e10	0.692557	0.346278	+	0.938132i	$0.387445\pi$
$824$	7.28644e9	0.453702
$825$	0	0
$826$	−3.63791e9	−0.224606
$827$	7.16696e9	0.440622	0.220311	−	0.975430i	$-0.429293\pi$
$827$	7.16696e9	0.440622	0.220311	+	0.975430i	$0.429293\pi$
$828$	0	0
$829$	1.09285e9	0.0666224	0.0333112	−	0.999445i	$-0.489395\pi$
$829$	1.09285e9	0.0666224	0.0333112	+	0.999445i	$0.489395\pi$
$830$	−1.74970e10	−1.06216
$831$	0	0
$832$	−9.43940e9	−0.568215
$833$	−2.50404e10	−1.50101
$834$	0	0
$835$	−7.47144e9	−0.444121
$836$	−8.48121e9	−0.502037
$837$	0	0
$838$	−6.53834e9	−0.383807
$839$	2.38628e10	1.39494	0.697469	−	0.716615i	$-0.254309\pi$
$839$	2.38628e10	1.39494	0.697469	+	0.716615i	$0.254309\pi$
$840$	0	0
$841$	2.65435e10	1.53877
$842$	−2.30050e9	−0.132810
$843$	0	0
$844$	−9.49235e9	−0.543469
$845$	−1.32844e10	−0.757431
$846$	0	0
$847$	−9.10073e9	−0.514617
$848$	−1.01284e9	−0.0570367
$849$	0	0
$850$	1.95057e10	1.08942
$851$	2.79371e10	1.55392
$852$	0	0
$853$	1.71276e10	0.944878	0.472439	−	0.881363i	$-0.343374\pi$
$853$	1.71276e10	0.944878	0.472439	+	0.881363i	$0.343374\pi$
$854$	3.54706e8	0.0194879
$855$	0	0
$856$	−7.79086e9	−0.424548
$857$	−3.37860e8	−0.0183360	−0.00916798	−	0.999958i	$-0.502918\pi$
$857$	−3.37860e8	−0.0183360	−0.00916798	+	0.999958i	$0.502918\pi$
$858$	0	0
$859$	3.39086e9	0.182530	0.0912649	−	0.995827i	$-0.470909\pi$
$859$	3.39086e9	0.182530	0.0912649	+	0.995827i	$0.470909\pi$
$860$	−4.09455e9	−0.219514
$861$	0	0
$862$	−2.66249e10	−1.41583
$863$	−9.19359e9	−0.486909	−0.243454	−	0.969912i	$-0.578281\pi$
$863$	−9.19359e9	−0.486909	−0.243454	+	0.969912i	$0.578281\pi$
$864$	0	0
$865$	3.16628e9	0.166339
$866$	−8.70904e9	−0.455678
$867$	0	0
$868$	2.04269e10	1.06019
$869$	1.50927e10	0.780186
$870$	0	0
$871$	1.69899e10	0.871221
$872$	2.34674e10	1.19855
$873$	0	0
$874$	4.29608e10	2.17662
$875$	−2.68966e10	−1.35728
$876$	0	0
$877$	−1.78531e10	−0.893747	−0.446874	−	0.894597i	$-0.647463\pi$
$877$	−1.78531e10	−0.893747	−0.446874	+	0.894597i	$0.647463\pi$
$878$	−2.91952e10	−1.45573
$879$	0	0
$880$	−1.58277e10	−0.782942
$881$	1.00212e10	0.493746	0.246873	−	0.969048i	$-0.420597\pi$
$881$	1.00212e10	0.493746	0.246873	+	0.969048i	$0.420597\pi$
$882$	0	0
$883$	4.80376e8	0.0234811	0.0117406	−	0.999931i	$-0.496263\pi$
$883$	4.80376e8	0.0234811	0.0117406	+	0.999931i	$0.496263\pi$
$884$	1.62240e10	0.789906
$885$	0	0
$886$	−3.97703e10	−1.92106
$887$	2.86366e9	0.137781	0.0688903	−	0.997624i	$-0.478054\pi$
$887$	2.86366e9	0.137781	0.0688903	+	0.997624i	$0.478054\pi$
$888$	0	0
$889$	1.49532e10	0.713804
$890$	−1.78317e9	−0.0847869
$891$	0	0
$892$	1.01235e10	0.477589
$893$	2.15984e10	1.01494
$894$	0	0
$895$	1.31422e10	0.612758
$896$	−3.69234e10	−1.71484
$897$	0	0
$898$	2.06158e10	0.950020
$899$	6.46377e10	2.96706
$900$	0	0
$901$	−1.32871e9	−0.0605193
$902$	3.97983e10	1.80568
$903$	0	0
$904$	7.65233e9	0.344512
$905$	9.95787e9	0.446577
$906$	0	0
$907$	−5.67695e9	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$907$	−5.67695e9	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$908$	−1.75313e9	−0.0777164
$909$	0	0
$910$	−3.30054e10	−1.45191
$911$	−2.67566e10	−1.17251	−0.586256	−	0.810126i	$-0.699399\pi$
$911$	−2.67566e10	−1.17251	−0.586256	+	0.810126i	$0.699399\pi$
$912$	0	0
$913$	−4.42792e10	−1.92554
$914$	−9.33871e9	−0.404553
$915$	0	0
$916$	−1.74602e10	−0.750610
$917$	5.71452e9	0.244730
$918$	0	0
$919$	2.00200e10	0.850862	0.425431	−	0.904991i	$-0.360122\pi$
$919$	2.00200e10	0.850862	0.425431	+	0.904991i	$0.360122\pi$
$920$	1.53953e10	0.651826
$921$	0	0
$922$	3.18776e10	1.33945
$923$	1.52372e10	0.637822
$924$	0	0
$925$	−1.58293e10	−0.657604
$926$	3.62520e10	1.50035
$927$	0	0
$928$	2.86446e10	1.17659
$929$	−2.42743e10	−0.993326	−0.496663	−	0.867943i	$-0.665441\pi$
$929$	−2.42743e10	−0.993326	−0.496663	+	0.867943i	$0.665441\pi$
$930$	0	0
$931$	3.12486e10	1.26913
$932$	1.35340e10	0.547611
$933$	0	0
$934$	−4.84332e10	−1.94504
$935$	−2.07639e10	−0.830748
$936$	0	0
$937$	2.31846e10	0.920683	0.460342	−	0.887742i	$-0.347727\pi$
$937$	2.31846e10	0.920683	0.460342	+	0.887742i	$0.347727\pi$
$938$	2.45645e10	0.971849
$939$	0	0
$940$	−4.92602e9	−0.193441
$941$	4.82845e10	1.88905	0.944527	−	0.328434i	$-0.106521\pi$
$941$	4.82845e10	1.88905	0.944527	+	0.328434i	$0.106521\pi$
$942$	0	0
$943$	−5.64495e10	−2.19214
$944$	−4.16464e9	−0.161130
$945$	0	0
$946$	−3.70052e10	−1.42116
$947$	9.48483e9	0.362915	0.181457	−	0.983399i	$-0.441919\pi$
$947$	9.48483e9	0.362915	0.181457	+	0.983399i	$0.441919\pi$
$948$	0	0
$949$	5.92654e10	2.25097
$950$	−2.43417e10	−0.921124
$951$	0	0
$952$	−3.68569e10	−1.38449
$953$	−3.13620e10	−1.17376	−0.586880	−	0.809674i	$-0.699644\pi$
$953$	−3.13620e10	−1.17376	−0.586880	+	0.809674i	$0.699644\pi$
$954$	0	0
$955$	−1.28595e10	−0.477762
$956$	3.54481e9	0.131217
$957$	0	0
$958$	1.01379e10	0.372537
$959$	−2.46407e10	−0.902171
$960$	0	0
$961$	6.78906e10	2.46762
$962$	−4.70194e10	−1.70280
$963$	0	0
$964$	−1.17661e10	−0.423024
$965$	3.10587e9	0.111260
$966$	0	0
$967$	−4.56505e10	−1.62350	−0.811752	−	0.584003i	$-0.801486\pi$
$967$	−4.56505e10	−1.62350	−0.811752	+	0.584003i	$0.801486\pi$
$968$	−7.14457e9	−0.253170
$969$	0	0
$970$	3.28559e10	1.15588
$971$	4.75876e10	1.66812	0.834059	−	0.551675i	$-0.186011\pi$
$971$	4.75876e10	1.66812	0.834059	+	0.551675i	$0.186011\pi$
$972$	0	0
$973$	5.48602e10	1.90925
$974$	−4.15558e10	−1.44104
$975$	0	0
$976$	4.06063e8	0.0139804
$977$	3.64883e10	1.25176	0.625882	−	0.779918i	$-0.284739\pi$
$977$	3.64883e10	1.25176	0.625882	+	0.779918i	$0.284739\pi$
$978$	0	0
$979$	−4.51264e9	−0.153706
$980$	−7.12697e9	−0.241888
$981$	0	0
$982$	2.69551e10	0.908346
$983$	2.58715e10	0.868729	0.434365	−	0.900737i	$-0.356973\pi$
$983$	2.58715e10	0.868729	0.434365	+	0.900737i	$0.356973\pi$
$984$	0	0
$985$	4.91551e9	0.163886
$986$	7.42266e10	2.46598
$987$	0	0
$988$	−2.02464e10	−0.667881
$989$	5.24877e10	1.72532
$990$	0	0
$991$	5.08417e10	1.65944	0.829722	−	0.558177i	$-0.188499\pi$
$991$	5.08417e10	1.65944	0.829722	+	0.558177i	$0.188499\pi$
$992$	4.22785e10	1.37508
$993$	0	0
$994$	2.20304e10	0.711492
$995$	1.09822e10	0.353434
$996$	0	0
$997$	−7.59411e9	−0.242686	−0.121343	−	0.992611i	$-0.538720\pi$
$997$	−7.59411e9	−0.242686	−0.121343	+	0.992611i	$0.538720\pi$
$998$	−5.21076e10	−1.65937
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.13		17
3.2	odd	2		177.8.a.b.1.5	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.5	✓	17	3.2	odd	2
531.8.a.d.1.13		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)

\(f(q)\)	\(=\)	\(q+13.3335 q^{2} +49.7814 q^{4} -152.093 q^{5} -1328.47 q^{7} -1042.93 q^{8} +O(q^{10})\)	\(q+13.3335 q^{2} +49.7814 q^{4} -152.093 q^{5} -1328.47 q^{7} -1042.93 q^{8} -2027.93 q^{10} -5132.02 q^{11} -12251.2 q^{13} -17713.2 q^{14} -20277.8 q^{16} -26601.9 q^{17} +33197.2 q^{19} -7571.39 q^{20} -68427.7 q^{22} +97057.0 q^{23} -54992.8 q^{25} -163351. q^{26} -66133.3 q^{28} -209269. q^{29} -308874. q^{31} -136879. q^{32} -354695. q^{34} +202052. q^{35} +287842. q^{37} +442634. q^{38} +158622. q^{40} -581611. q^{41} +540792. q^{43} -255479. q^{44} +1.29411e6 q^{46} +650609. q^{47} +941302. q^{49} -733244. q^{50} -609883. q^{52} +49948.0 q^{53} +780544. q^{55} +1.38550e6 q^{56} -2.79028e6 q^{58} +205379. q^{59} -20025.0 q^{61} -4.11836e6 q^{62} +770486. q^{64} +1.86332e6 q^{65} -1.38680e6 q^{67} -1.32428e6 q^{68} +2.69405e6 q^{70} -1.24373e6 q^{71} -4.83751e6 q^{73} +3.83794e6 q^{74} +1.65260e6 q^{76} +6.81777e6 q^{77} -2.94089e6 q^{79} +3.08411e6 q^{80} -7.75490e6 q^{82} +8.62802e6 q^{83} +4.04595e6 q^{85} +7.21064e6 q^{86} +5.35232e6 q^{88} +879309. q^{89} +1.62754e7 q^{91} +4.83163e6 q^{92} +8.67488e6 q^{94} -5.04907e6 q^{95} -1.62017e7 q^{97} +1.25508e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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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