LMFDB - Embedded newform 531.8.a.d.1.12

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			1.12
Root			$-10.1391$ 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)

$f(q)$	$=$	$q+12.1391 q^{2} +19.3578 q^{4} -236.334 q^{5} +1426.66 q^{7} -1318.82 q^{8} +O(q^{10})$	\(q+12.1391 q^{2} +19.3578 q^{4} -236.334 q^{5} +1426.66 q^{7} -1318.82 q^{8} -2868.89 q^{10} +5472.58 q^{11} -8451.67 q^{13} +17318.4 q^{14} -18487.1 q^{16} +6087.08 q^{17} -12974.5 q^{19} -4574.91 q^{20} +66432.2 q^{22} +53979.7 q^{23} -22271.1 q^{25} -102596. q^{26} +27617.0 q^{28} +14368.8 q^{29} -48485.8 q^{31} -55607.6 q^{32} +73891.7 q^{34} -337169. q^{35} +82881.8 q^{37} -157499. q^{38} +311682. q^{40} +782250. q^{41} -369462. q^{43} +105937. q^{44} +655265. q^{46} -368463. q^{47} +1.21182e6 q^{49} -270351. q^{50} -163605. q^{52} -836648. q^{53} -1.29336e6 q^{55} -1.88151e6 q^{56} +174424. q^{58} +205379. q^{59} +37349.1 q^{61} -588573. q^{62} +1.69132e6 q^{64} +1.99742e6 q^{65} +2.64158e6 q^{67} +117832. q^{68} -4.09293e6 q^{70} +2.03139e6 q^{71} -3.64005e6 q^{73} +1.00611e6 q^{74} -251158. q^{76} +7.80751e6 q^{77} -7.63186e6 q^{79} +4.36913e6 q^{80} +9.49581e6 q^{82} +6.69291e6 q^{83} -1.43859e6 q^{85} -4.48494e6 q^{86} -7.21734e6 q^{88} -717966. q^{89} -1.20577e7 q^{91} +1.04493e6 q^{92} -4.47281e6 q^{94} +3.06632e6 q^{95} +1.06996e7 q^{97} +1.47104e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	12.1391	1.07296	0.536478	−	0.843915i	$-0.319755\pi$
$2$	12.1391	1.07296	0.536478	+	0.843915i	$0.319755\pi$
$3$	0	0
$3$	0	0
$4$	19.3578	0.151233
$5$	−236.334	−0.845536	−0.422768	−	0.906238i	$-0.638941\pi$
$5$	−236.334	−0.845536	−0.422768	+	0.906238i	$0.638941\pi$
$6$	0	0
$7$	1426.66	1.57209	0.786045	−	0.618169i	$-0.212125\pi$
$7$	1426.66	1.57209	0.786045	+	0.618169i	$0.212125\pi$
$8$	−1318.82	−0.910689
$9$	0	0
$10$	−2868.89	−0.907222
$11$	5472.58	1.23970	0.619851	−	0.784719i	$-0.287193\pi$
$11$	5472.58	1.23970	0.619851	+	0.784719i	$0.287193\pi$
$12$	0	0
$13$	−8451.67	−1.06694	−0.533471	−	0.845819i	$-0.679113\pi$
$13$	−8451.67	−1.06694	−0.533471	+	0.845819i	$0.679113\pi$
$14$	17318.4	1.68678
$15$	0	0
$16$	−18487.1	−1.12836
$17$	6087.08	0.300495	0.150248	−	0.988648i	$-0.451993\pi$
$17$	6087.08	0.300495	0.150248	+	0.988648i	$0.451993\pi$
$18$	0	0
$19$	−12974.5	−0.433964	−0.216982	−	0.976176i	$-0.569621\pi$
$19$	−12974.5	−0.433964	−0.216982	+	0.976176i	$0.569621\pi$
$20$	−4574.91	−0.127873
$21$	0	0
$22$	66432.2	1.33015
$23$	53979.7	0.925087	0.462544	−	0.886597i	$-0.346937\pi$
$23$	53979.7	0.925087	0.462544	+	0.886597i	$0.346937\pi$
$24$	0	0
$25$	−22271.1	−0.285070
$26$	−102596.	−1.14478
$27$	0	0
$28$	27617.0	0.237751
$29$	14368.8	0.109402	0.0547011	−	0.998503i	$-0.482579\pi$
$29$	14368.8	0.109402	0.0547011	+	0.998503i	$0.482579\pi$
$30$	0	0
$31$	−48485.8	−0.292313	−0.146157	−	0.989261i	$-0.546690\pi$
$31$	−48485.8	−0.292313	−0.146157	+	0.989261i	$0.546690\pi$
$32$	−55607.6	−0.299992
$33$	0	0
$34$	73891.7	0.322418
$35$	−337169.	−1.32926
$36$	0	0
$37$	82881.8	0.269001	0.134500	−	0.990914i	$-0.457057\pi$
$37$	82881.8	0.269001	0.134500	+	0.990914i	$0.457057\pi$
$38$	−157499.	−0.465624
$39$	0	0
$40$	311682.	0.770020
$41$	782250.	1.77256	0.886282	−	0.463146i	$-0.153280\pi$
$41$	782250.	1.77256	0.886282	+	0.463146i	$0.153280\pi$
$42$	0	0
$43$	−369462.	−0.708647	−0.354324	−	0.935123i	$-0.615289\pi$
$43$	−369462.	−0.708647	−0.354324	+	0.935123i	$0.615289\pi$
$44$	105937.	0.187483
$45$	0	0
$46$	655265.	0.992577
$47$	−368463.	−0.517668	−0.258834	−	0.965922i	$-0.583338\pi$
$47$	−368463.	−0.517668	−0.258834	+	0.965922i	$0.583338\pi$
$48$	0	0
$49$	1.21182e6	1.47147
$50$	−270351.	−0.305867
$51$	0	0
$52$	−163605.	−0.161356
$53$	−836648.	−0.771929	−0.385964	−	0.922514i	$-0.626131\pi$
$53$	−836648.	−0.771929	−0.385964	+	0.922514i	$0.626131\pi$
$54$	0	0
$55$	−1.29336e6	−1.04821
$56$	−1.88151e6	−1.43169
$57$	0	0
$58$	174424.	0.117384
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	37349.1	0.0210681	0.0105341	−	0.999945i	$-0.496647\pi$
$61$	37349.1	0.0210681	0.0105341	+	0.999945i	$0.496647\pi$
$62$	−588573.	−0.313639
$63$	0	0
$64$	1.69132e6	0.806484
$65$	1.99742e6	0.902137
$66$	0	0
$67$	2.64158e6	1.07300	0.536502	−	0.843899i	$-0.319745\pi$
$67$	2.64158e6	1.07300	0.536502	+	0.843899i	$0.319745\pi$
$68$	117832.	0.0454447
$69$	0	0
$70$	−4.09293e6	−1.42623
$71$	2.03139e6	0.673579	0.336790	−	0.941580i	$-0.390659\pi$
$71$	2.03139e6	0.673579	0.336790	+	0.941580i	$0.390659\pi$
$72$	0	0
$73$	−3.64005e6	−1.09516	−0.547580	−	0.836753i	$-0.684451\pi$
$73$	−3.64005e6	−1.09516	−0.547580	+	0.836753i	$0.684451\pi$
$74$	1.00611e6	0.288625
$75$	0	0
$76$	−251158.	−0.0656295
$77$	7.80751e6	1.94892
$78$	0	0
$79$	−7.63186e6	−1.74155	−0.870774	−	0.491683i	$-0.836382\pi$
$79$	−7.63186e6	−1.74155	−0.870774	+	0.491683i	$0.836382\pi$
$80$	4.36913e6	0.954070
$81$	0	0
$82$	9.49581e6	1.90188
$83$	6.69291e6	1.28482	0.642409	−	0.766362i	$-0.277935\pi$
$83$	6.69291e6	1.28482	0.642409	+	0.766362i	$0.277935\pi$
$84$	0	0
$85$	−1.43859e6	−0.254079
$86$	−4.48494e6	−0.760347
$87$	0	0
$88$	−7.21734e6	−1.12898
$89$	−717966.	−0.107954	−0.0539770	−	0.998542i	$-0.517190\pi$
$89$	−717966.	−0.107954	−0.0539770	+	0.998542i	$0.517190\pi$
$90$	0	0
$91$	−1.20577e7	−1.67733
$92$	1.04493e6	0.139903
$93$	0	0
$94$	−4.47281e6	−0.555435
$95$	3.06632e6	0.366932
$96$	0	0
$97$	1.06996e7	1.19033	0.595165	−	0.803604i	$-0.297087\pi$
$97$	1.06996e7	1.19033	0.595165	+	0.803604i	$0.297087\pi$
$98$	1.47104e7	1.57882
$99$	0	0
$100$	−431118.	−0.0431118
$101$	1.14739e7	1.10812	0.554058	−	0.832478i	$-0.313079\pi$
$101$	1.14739e7	1.10812	0.554058	+	0.832478i	$0.313079\pi$
$102$	0	0
$103$	7.95531e6	0.717343	0.358671	−	0.933464i	$-0.383230\pi$
$103$	7.95531e6	0.717343	0.358671	+	0.933464i	$0.383230\pi$
$104$	1.11462e7	0.971652
$105$	0	0
$106$	−1.01562e7	−0.828245
$107$	−1.10513e7	−0.872107	−0.436054	−	0.899921i	$-0.643624\pi$
$107$	−1.10513e7	−0.872107	−0.436054	+	0.899921i	$0.643624\pi$
$108$	0	0
$109$	8.08293e6	0.597828	0.298914	−	0.954280i	$-0.403376\pi$
$109$	8.08293e6	0.597828	0.298914	+	0.954280i	$0.403376\pi$
$110$	−1.57002e7	−1.12469
$111$	0	0
$112$	−2.63748e7	−1.77389
$113$	9.96488e6	0.649677	0.324839	−	0.945769i	$-0.394690\pi$
$113$	9.96488e6	0.649677	0.324839	+	0.945769i	$0.394690\pi$
$114$	0	0
$115$	−1.27572e7	−0.782194
$116$	278147.	0.0165452
$117$	0	0
$118$	2.49312e6	0.139687
$119$	8.68420e6	0.472406
$120$	0	0
$121$	1.04619e7	0.536863
$122$	453384.	0.0226051
$123$	0	0
$124$	−938576.	−0.0442073
$125$	2.37270e7	1.08657
$126$	0	0
$127$	3.01471e7	1.30597	0.652984	−	0.757372i	$-0.273517\pi$
$127$	3.01471e7	1.30597	0.652984	+	0.757372i	$0.273517\pi$
$128$	2.76489e7	1.16531
$129$	0	0
$130$	2.42469e7	0.967952
$131$	4.85605e7	1.88727	0.943634	−	0.330990i	$-0.107383\pi$
$131$	4.85605e7	1.88727	0.943634	+	0.330990i	$0.107383\pi$
$132$	0	0
$133$	−1.85102e7	−0.682231
$134$	3.20664e7	1.15129
$135$	0	0
$136$	−8.02775e6	−0.273658
$137$	1.46792e7	0.487732	0.243866	−	0.969809i	$-0.421584\pi$
$137$	1.46792e7	0.487732	0.243866	+	0.969809i	$0.421584\pi$
$138$	0	0
$139$	3.93077e7	1.24144	0.620721	−	0.784032i	$-0.286840\pi$
$139$	3.93077e7	1.24144	0.620721	+	0.784032i	$0.286840\pi$
$140$	−6.52684e6	−0.201027
$141$	0	0
$142$	2.46592e7	0.722720
$143$	−4.62524e7	−1.32269
$144$	0	0
$145$	−3.39583e6	−0.0925035
$146$	−4.41870e7	−1.17506
$147$	0	0
$148$	1.60441e6	0.0406817
$149$	6.99960e7	1.73349	0.866745	−	0.498752i	$-0.166208\pi$
$149$	6.99960e7	1.73349	0.866745	+	0.498752i	$0.166208\pi$
$150$	0	0
$151$	5.84052e7	1.38049	0.690243	−	0.723577i	$-0.257503\pi$
$151$	5.84052e7	1.38049	0.690243	+	0.723577i	$0.257503\pi$
$152$	1.71110e7	0.395206
$153$	0	0
$154$	9.47762e7	2.09111
$155$	1.14588e7	0.247161
$156$	0	0
$157$	5.09364e7	1.05046	0.525230	−	0.850960i	$-0.323979\pi$
$157$	5.09364e7	1.05046	0.525230	+	0.850960i	$0.323979\pi$
$158$	−9.26439e7	−1.86860
$159$	0	0
$160$	1.31420e7	0.253654
$161$	7.70107e7	1.45432
$162$	0	0
$163$	−2.83386e7	−0.512532	−0.256266	−	0.966606i	$-0.582492\pi$
$163$	−2.83386e7	−0.512532	−0.256266	+	0.966606i	$0.582492\pi$
$164$	1.51426e7	0.268069
$165$	0	0
$166$	8.12459e7	1.37855
$167$	−9.62396e6	−0.159899	−0.0799496	−	0.996799i	$-0.525476\pi$
$167$	−9.62396e6	−0.159899	−0.0799496	+	0.996799i	$0.525476\pi$
$168$	0	0
$169$	8.68213e6	0.138364
$170$	−1.74631e7	−0.272616
$171$	0	0
$172$	−7.15196e6	−0.107171
$173$	−7.21139e7	−1.05891	−0.529454	−	0.848339i	$-0.677603\pi$
$173$	−7.21139e7	−1.05891	−0.529454	+	0.848339i	$0.677603\pi$
$174$	0	0
$175$	−3.17733e7	−0.448155
$176$	−1.01172e8	−1.39883
$177$	0	0
$178$	−8.71546e6	−0.115830
$179$	2.09311e7	0.272777	0.136388	−	0.990655i	$-0.456451\pi$
$179$	2.09311e7	0.272777	0.136388	+	0.990655i	$0.456451\pi$
$180$	0	0
$181$	4.58129e7	0.574266	0.287133	−	0.957891i	$-0.407298\pi$
$181$	4.58129e7	0.574266	0.287133	+	0.957891i	$0.407298\pi$
$182$	−1.46369e8	−1.79970
$183$	0	0
$184$	−7.11894e7	−0.842467
$185$	−1.95878e7	−0.227450
$186$	0	0
$187$	3.33120e7	0.372525
$188$	−7.13262e6	−0.0782883
$189$	0	0
$190$	3.72224e7	0.393701
$191$	1.58678e8	1.64779	0.823893	−	0.566746i	$-0.191798\pi$
$191$	1.58678e8	1.64779	0.823893	+	0.566746i	$0.191798\pi$
$192$	0	0
$193$	6.81944e7	0.682807	0.341404	−	0.939917i	$-0.389098\pi$
$193$	6.81944e7	0.682807	0.341404	+	0.939917i	$0.389098\pi$
$194$	1.29884e8	1.27717
$195$	0	0
$196$	2.34581e7	0.222534
$197$	−8.04764e7	−0.749957	−0.374979	−	0.927033i	$-0.622350\pi$
$197$	−8.04764e7	−0.749957	−0.374979	+	0.927033i	$0.622350\pi$
$198$	0	0
$199$	−6.86011e7	−0.617085	−0.308543	−	0.951211i	$-0.599841\pi$
$199$	−6.86011e7	−0.617085	−0.308543	+	0.951211i	$0.599841\pi$
$200$	2.93715e7	0.259610
$201$	0	0
$202$	1.39283e8	1.18896
$203$	2.04993e7	0.171990
$204$	0	0
$205$	−1.84872e8	−1.49877
$206$	9.65703e7	0.769677
$207$	0	0
$208$	1.56247e8	1.20390
$209$	−7.10040e7	−0.537986
$210$	0	0
$211$	2.88847e7	0.211679	0.105840	−	0.994383i	$-0.466247\pi$
$211$	2.88847e7	0.211679	0.105840	+	0.994383i	$0.466247\pi$
$212$	−1.61956e7	−0.116741
$213$	0	0
$214$	−1.34153e8	−0.935732
$215$	8.73166e7	0.599187
$216$	0	0
$217$	−6.91727e7	−0.459543
$218$	9.81195e7	0.641442
$219$	0	0
$220$	−2.50365e7	−0.158524
$221$	−5.14459e7	−0.320611
$222$	0	0
$223$	2.59394e8	1.56637	0.783184	−	0.621790i	$-0.213594\pi$
$223$	2.59394e8	1.56637	0.783184	+	0.621790i	$0.213594\pi$
$224$	−7.93332e7	−0.471614
$225$	0	0
$226$	1.20965e8	0.697074
$227$	2.03673e8	1.15570	0.577848	−	0.816144i	$-0.303893\pi$
$227$	2.03673e8	1.15570	0.577848	+	0.816144i	$0.303893\pi$
$228$	0	0
$229$	−3.48601e8	−1.91825	−0.959124	−	0.282986i	$-0.908675\pi$
$229$	−3.48601e8	−1.91825	−0.959124	+	0.282986i	$0.908675\pi$
$230$	−1.54862e8	−0.839259
$231$	0	0
$232$	−1.89498e7	−0.0996315
$233$	−1.56687e8	−0.811495	−0.405748	−	0.913985i	$-0.632989\pi$
$233$	−1.56687e8	−0.811495	−0.405748	+	0.913985i	$0.632989\pi$
$234$	0	0
$235$	8.70805e7	0.437707
$236$	3.97568e6	0.0196888
$237$	0	0
$238$	1.05418e8	0.506870
$239$	−2.08708e8	−0.988885	−0.494443	−	0.869210i	$-0.664628\pi$
$239$	−2.08708e8	−0.988885	−0.494443	+	0.869210i	$0.664628\pi$
$240$	0	0
$241$	−3.80494e8	−1.75101	−0.875505	−	0.483209i	$-0.839471\pi$
$241$	−3.80494e8	−1.75101	−0.875505	+	0.483209i	$0.839471\pi$
$242$	1.26998e8	0.576029
$243$	0	0
$244$	722995.	0.00318619
$245$	−2.86394e8	−1.24418
$246$	0	0
$247$	1.09656e8	0.463014
$248$	6.39439e7	0.266206
$249$	0	0
$250$	2.88025e8	1.16584
$251$	1.88517e8	0.752474	0.376237	−	0.926523i	$-0.377218\pi$
$251$	1.88517e8	0.752474	0.376237	+	0.926523i	$0.377218\pi$
$252$	0	0
$253$	2.95408e8	1.14683
$254$	3.65959e8	1.40125
$255$	0	0
$256$	1.19144e8	0.443844
$257$	−3.79943e8	−1.39621	−0.698107	−	0.715993i	$-0.745974\pi$
$257$	−3.79943e8	−1.39621	−0.698107	+	0.715993i	$0.745974\pi$
$258$	0	0
$259$	1.18244e8	0.422893
$260$	3.86656e7	0.136433
$261$	0	0
$262$	5.89481e8	2.02495
$263$	−1.63239e8	−0.553322	−0.276661	−	0.960968i	$-0.589228\pi$
$263$	−1.63239e8	−0.553322	−0.276661	+	0.960968i	$0.589228\pi$
$264$	0	0
$265$	1.97729e8	0.652693
$266$	−2.24698e8	−0.732003
$267$	0	0
$268$	5.11350e7	0.162273
$269$	5.26713e8	1.64984	0.824918	−	0.565252i	$-0.191221\pi$
$269$	5.26713e8	1.64984	0.824918	+	0.565252i	$0.191221\pi$
$270$	0	0
$271$	1.21168e8	0.369824	0.184912	−	0.982755i	$-0.440800\pi$
$271$	1.21168e8	0.369824	0.184912	+	0.982755i	$0.440800\pi$
$272$	−1.12532e8	−0.339067
$273$	0	0
$274$	1.78193e8	0.523315
$275$	−1.21880e8	−0.353402
$276$	0	0
$277$	3.39227e8	0.958985	0.479492	−	0.877546i	$-0.340821\pi$
$277$	3.39227e8	0.958985	0.479492	+	0.877546i	$0.340821\pi$
$278$	4.77161e8	1.33201
$279$	0	0
$280$	4.44665e8	1.21054
$281$	2.48935e8	0.669289	0.334644	−	0.942344i	$-0.391384\pi$
$281$	2.48935e8	0.669289	0.334644	+	0.942344i	$0.391384\pi$
$282$	0	0
$283$	−6.01535e8	−1.57764	−0.788821	−	0.614623i	$-0.789308\pi$
$283$	−6.01535e8	−1.57764	−0.788821	+	0.614623i	$0.789308\pi$
$284$	3.93232e7	0.101867
$285$	0	0
$286$	−5.61462e8	−1.41919
$287$	1.11600e9	2.78663
$288$	0	0
$289$	−3.73286e8	−0.909703
$290$	−4.12224e7	−0.0992521
$291$	0	0
$292$	−7.04633e7	−0.165624
$293$	−2.39333e8	−0.555860	−0.277930	−	0.960601i	$-0.589648\pi$
$293$	−2.39333e8	−0.555860	−0.277930	+	0.960601i	$0.589648\pi$
$294$	0	0
$295$	−4.85381e7	−0.110079
$296$	−1.09306e8	−0.244976
$297$	0	0
$298$	8.49688e8	1.85996
$299$	−4.56218e8	−0.987014
$300$	0	0
$301$	−5.27097e8	−1.11406
$302$	7.08987e8	1.48120
$303$	0	0
$304$	2.39861e8	0.489668
$305$	−8.82687e6	−0.0178138
$306$	0	0
$307$	1.00262e8	0.197767	0.0988833	−	0.995099i	$-0.468473\pi$
$307$	1.00262e8	0.197767	0.0988833	+	0.995099i	$0.468473\pi$
$308$	1.51136e8	0.294741
$309$	0	0
$310$	1.39100e8	0.265193
$311$	−7.10291e8	−1.33898	−0.669491	−	0.742820i	$-0.733488\pi$
$311$	−7.10291e8	−1.33898	−0.669491	+	0.742820i	$0.733488\pi$
$312$	0	0
$313$	−6.55081e8	−1.20751	−0.603753	−	0.797171i	$-0.706329\pi$
$313$	−6.55081e8	−1.20751	−0.603753	+	0.797171i	$0.706329\pi$
$314$	6.18322e8	1.12710
$315$	0	0
$316$	−1.47736e8	−0.263379
$317$	1.70031e8	0.299793	0.149896	−	0.988702i	$-0.452106\pi$
$317$	1.70031e8	0.299793	0.149896	+	0.988702i	$0.452106\pi$
$318$	0	0
$319$	7.86342e7	0.135626
$320$	−3.99717e8	−0.681911
$321$	0	0
$322$	9.34840e8	1.56042
$323$	−7.89769e7	−0.130404
$324$	0	0
$325$	1.88228e8	0.304153
$326$	−3.44005e8	−0.549924
$327$	0	0
$328$	−1.03165e9	−1.61425
$329$	−5.25672e8	−0.813821
$330$	0	0
$331$	1.29730e8	0.196626	0.0983131	−	0.995156i	$-0.468655\pi$
$331$	1.29730e8	0.196626	0.0983131	+	0.995156i	$0.468655\pi$
$332$	1.29560e8	0.194306
$333$	0	0
$334$	−1.16826e8	−0.171565
$335$	−6.24295e8	−0.907263
$336$	0	0
$337$	9.55271e7	0.135963	0.0679817	−	0.997687i	$-0.478344\pi$
$337$	9.55271e7	0.135963	0.0679817	+	0.997687i	$0.478344\pi$
$338$	1.05393e8	0.148458
$339$	0	0
$340$	−2.78478e7	−0.0384251
$341$	−2.65342e8	−0.362381
$342$	0	0
$343$	5.53936e8	0.741191
$344$	4.87254e8	0.645358
$345$	0	0
$346$	−8.75398e8	−1.13616
$347$	1.13393e8	0.145690	0.0728452	−	0.997343i	$-0.476792\pi$
$347$	1.13393e8	0.145690	0.0728452	+	0.997343i	$0.476792\pi$
$348$	0	0
$349$	−3.72221e8	−0.468719	−0.234359	−	0.972150i	$-0.575299\pi$
$349$	−3.72221e8	−0.468719	−0.234359	+	0.972150i	$0.575299\pi$
$350$	−3.85699e8	−0.480850
$351$	0	0
$352$	−3.04317e8	−0.371901
$353$	−5.74672e8	−0.695358	−0.347679	−	0.937614i	$-0.613030\pi$
$353$	−5.74672e8	−0.695358	−0.347679	+	0.937614i	$0.613030\pi$
$354$	0	0
$355$	−4.80087e8	−0.569535
$356$	−1.38982e7	−0.0163262
$357$	0	0
$358$	2.54085e8	0.292677
$359$	5.65130e7	0.0644640	0.0322320	−	0.999480i	$-0.489738\pi$
$359$	5.65130e7	0.0644640	0.0322320	+	0.999480i	$0.489738\pi$
$360$	0	0
$361$	−7.25534e8	−0.811675
$362$	5.56127e8	0.616161
$363$	0	0
$364$	−2.33409e8	−0.253667
$365$	8.60270e8	0.925997
$366$	0	0
$367$	−2.25564e8	−0.238198	−0.119099	−	0.992882i	$-0.538001\pi$
$367$	−2.25564e8	−0.238198	−0.119099	+	0.992882i	$0.538001\pi$
$368$	−9.97926e8	−1.04383
$369$	0	0
$370$	−2.37779e8	−0.244043
$371$	−1.19361e9	−1.21354
$372$	0	0
$373$	5.86159e8	0.584837	0.292418	−	0.956290i	$-0.405540\pi$
$373$	5.86159e8	0.584837	0.292418	+	0.956290i	$0.405540\pi$
$374$	4.04378e8	0.399702
$375$	0	0
$376$	4.85936e8	0.471435
$377$	−1.21440e8	−0.116726
$378$	0	0
$379$	4.01728e8	0.379048	0.189524	−	0.981876i	$-0.439305\pi$
$379$	4.01728e8	0.379048	0.189524	+	0.981876i	$0.439305\pi$
$380$	5.93572e7	0.0554921
$381$	0	0
$382$	1.92621e9	1.76800
$383$	9.90140e8	0.900536	0.450268	−	0.892894i	$-0.351329\pi$
$383$	9.90140e8	0.900536	0.450268	+	0.892894i	$0.351329\pi$
$384$	0	0
$385$	−1.84518e9	−1.64789
$386$	8.27819e8	0.732622
$387$	0	0
$388$	2.07121e8	0.180017
$389$	−9.31063e8	−0.801965	−0.400982	−	0.916086i	$-0.631331\pi$
$389$	−9.31063e8	−0.801965	−0.400982	+	0.916086i	$0.631331\pi$
$390$	0	0
$391$	3.28578e8	0.277984
$392$	−1.59817e9	−1.34005
$393$	0	0
$394$	−9.76911e8	−0.804671
$395$	1.80367e9	1.47254
$396$	0	0
$397$	4.18272e8	0.335500	0.167750	−	0.985830i	$-0.446350\pi$
$397$	4.18272e8	0.335500	0.167750	+	0.985830i	$0.446350\pi$
$398$	−8.32755e8	−0.662105
$399$	0	0
$400$	4.11727e8	0.321662
$401$	1.89613e9	1.46846	0.734230	−	0.678900i	$-0.237543\pi$
$401$	1.89613e9	1.46846	0.734230	+	0.678900i	$0.237543\pi$
$402$	0	0
$403$	4.09785e8	0.311881
$404$	2.22109e8	0.167583
$405$	0	0
$406$	2.48844e8	0.184538
$407$	4.53577e8	0.333481
$408$	0	0
$409$	−2.41716e9	−1.74693	−0.873463	−	0.486890i	$-0.838131\pi$
$409$	−2.41716e9	−1.74693	−0.873463	+	0.486890i	$0.838131\pi$
$410$	−2.24419e9	−1.60811
$411$	0	0
$412$	1.53997e8	0.108486
$413$	2.93006e8	0.204669
$414$	0	0
$415$	−1.58176e9	−1.08636
$416$	4.69977e8	0.320074
$417$	0	0
$418$	−8.61925e8	−0.577235
$419$	1.73070e9	1.14941	0.574703	−	0.818362i	$-0.305118\pi$
$419$	1.73070e9	1.14941	0.574703	+	0.818362i	$0.305118\pi$
$420$	0	0
$421$	2.38954e9	1.56073	0.780363	−	0.625327i	$-0.215034\pi$
$421$	2.38954e9	1.56073	0.780363	+	0.625327i	$0.215034\pi$
$422$	3.50634e8	0.227123
$423$	0	0
$424$	1.10339e9	0.702987
$425$	−1.35566e8	−0.0856621
$426$	0	0
$427$	5.32845e7	0.0331210
$428$	−2.13928e8	−0.131891
$429$	0	0
$430$	1.05994e9	0.642900
$431$	1.06409e9	0.640188	0.320094	−	0.947386i	$-0.396286\pi$
$431$	1.06409e9	0.640188	0.320094	+	0.947386i	$0.396286\pi$
$432$	0	0
$433$	−8.34289e8	−0.493866	−0.246933	−	0.969033i	$-0.579423\pi$
$433$	−8.34289e8	−0.493866	−0.246933	+	0.969033i	$0.579423\pi$
$434$	−8.39695e8	−0.493069
$435$	0	0
$436$	1.56467e8	0.0904110
$437$	−7.00360e8	−0.401454
$438$	0	0
$439$	1.91632e9	1.08104	0.540521	−	0.841331i	$-0.318227\pi$
$439$	1.91632e9	1.08104	0.540521	+	0.841331i	$0.318227\pi$
$440$	1.70571e9	0.954596
$441$	0	0
$442$	−6.24508e8	−0.344001
$443$	−1.43118e9	−0.782136	−0.391068	−	0.920362i	$-0.627894\pi$
$443$	−1.43118e9	−0.782136	−0.391068	+	0.920362i	$0.627894\pi$
$444$	0	0
$445$	1.69680e8	0.0912789
$446$	3.14882e9	1.68064
$447$	0	0
$448$	2.41294e9	1.26787
$449$	1.00483e9	0.523877	0.261938	−	0.965085i	$-0.415638\pi$
$449$	1.00483e9	0.523877	0.261938	+	0.965085i	$0.415638\pi$
$450$	0	0
$451$	4.28092e9	2.19745
$452$	1.92898e8	0.0982524
$453$	0	0
$454$	2.47241e9	1.24001
$455$	2.84964e9	1.41824
$456$	0	0
$457$	3.31474e9	1.62459	0.812293	−	0.583250i	$-0.198219\pi$
$457$	3.31474e9	1.62459	0.812293	+	0.583250i	$0.198219\pi$
$458$	−4.23171e9	−2.05819
$459$	0	0
$460$	−2.46952e8	−0.118293
$461$	−2.98497e7	−0.0141901	−0.00709507	−	0.999975i	$-0.502258\pi$
$461$	−2.98497e7	−0.0141901	−0.00709507	+	0.999975i	$0.502258\pi$
$462$	0	0
$463$	5.11925e8	0.239702	0.119851	−	0.992792i	$-0.461758\pi$
$463$	5.11925e8	0.239702	0.119851	+	0.992792i	$0.461758\pi$
$464$	−2.65636e8	−0.123445
$465$	0	0
$466$	−1.90203e9	−0.870698
$467$	3.33639e9	1.51589	0.757946	−	0.652317i	$-0.226203\pi$
$467$	3.33639e9	1.51589	0.757946	+	0.652317i	$0.226203\pi$
$468$	0	0
$469$	3.76863e9	1.68686
$470$	1.05708e9	0.469640
$471$	0	0
$472$	−2.70858e8	−0.118562
$473$	−2.02191e9	−0.878512
$474$	0	0
$475$	2.88956e8	0.123710
$476$	1.68107e8	0.0714432
$477$	0	0
$478$	−2.53352e9	−1.06103
$479$	2.42772e8	0.100931	0.0504655	−	0.998726i	$-0.483930\pi$
$479$	2.42772e8	0.100931	0.0504655	+	0.998726i	$0.483930\pi$
$480$	0	0
$481$	−7.00489e8	−0.287008
$482$	−4.61886e9	−1.87875
$483$	0	0
$484$	2.02520e8	0.0811911
$485$	−2.52869e9	−1.00647
$486$	0	0
$487$	−1.18746e9	−0.465872	−0.232936	−	0.972492i	$-0.574833\pi$
$487$	−1.18746e9	−0.465872	−0.232936	+	0.972492i	$0.574833\pi$
$488$	−4.92567e7	−0.0191865
$489$	0	0
$490$	−3.47657e9	−1.33495
$491$	−1.93067e9	−0.736077	−0.368039	−	0.929811i	$-0.619971\pi$
$491$	−1.93067e9	−0.736077	−0.368039	+	0.929811i	$0.619971\pi$
$492$	0	0
$493$	8.74638e7	0.0328749
$494$	1.33113e9	0.496793
$495$	0	0
$496$	8.96360e8	0.329835
$497$	2.89810e9	1.05893
$498$	0	0
$499$	3.11720e9	1.12308	0.561542	−	0.827448i	$-0.310208\pi$
$499$	3.11720e9	1.12308	0.561542	+	0.827448i	$0.310208\pi$
$500$	4.59303e8	0.164325
$501$	0	0
$502$	2.28842e9	0.807371
$503$	3.19404e8	0.111906	0.0559529	−	0.998433i	$-0.482180\pi$
$503$	3.19404e8	0.111906	0.0559529	+	0.998433i	$0.482180\pi$
$504$	0	0
$505$	−2.71167e9	−0.936952
$506$	3.58599e9	1.23050
$507$	0	0
$508$	5.83581e8	0.197505
$509$	−2.35968e9	−0.793124	−0.396562	−	0.918008i	$-0.629797\pi$
$509$	−2.35968e9	−0.793124	−0.396562	+	0.918008i	$0.629797\pi$
$510$	0	0
$511$	−5.19312e9	−1.72169
$512$	−2.09276e9	−0.689088
$513$	0	0
$514$	−4.61216e9	−1.49808
$515$	−1.88011e9	−0.606539
$516$	0	0
$517$	−2.01644e9	−0.641754
$518$	1.43538e9	0.453745
$519$	0	0
$520$	−2.63423e9	−0.821566
$521$	−6.10979e9	−1.89276	−0.946378	−	0.323062i	$-0.895288\pi$
$521$	−6.10979e9	−1.89276	−0.946378	+	0.323062i	$0.895288\pi$
$522$	0	0
$523$	3.79857e8	0.116109	0.0580543	−	0.998313i	$-0.481510\pi$
$523$	3.79857e8	0.116109	0.0580543	+	0.998313i	$0.481510\pi$
$524$	9.40023e8	0.285417
$525$	0	0
$526$	−1.98157e9	−0.593690
$527$	−2.95137e8	−0.0878387
$528$	0	0
$529$	−4.91022e8	−0.144214
$530$	2.40025e9	0.700310
$531$	0	0
$532$	−3.58317e8	−0.103176
$533$	−6.61131e9	−1.89122
$534$	0	0
$535$	2.61180e9	0.737398
$536$	−3.48376e9	−0.977173
$537$	0	0
$538$	6.39382e9	1.77020
$539$	6.63177e9	1.82418
$540$	0	0
$541$	−1.86189e8	−0.0505549	−0.0252774	−	0.999680i	$-0.508047\pi$
$541$	−1.86189e8	−0.0505549	−0.0252774	+	0.999680i	$0.508047\pi$
$542$	1.47087e9	0.396805
$543$	0	0
$544$	−3.38488e8	−0.0901461
$545$	−1.91027e9	−0.505484
$546$	0	0
$547$	2.56203e8	0.0669311	0.0334656	−	0.999440i	$-0.489346\pi$
$547$	2.56203e8	0.0669311	0.0334656	+	0.999440i	$0.489346\pi$
$548$	2.84157e8	0.0737611
$549$	0	0
$550$	−1.47952e9	−0.379184
$551$	−1.86428e8	−0.0474766
$552$	0	0
$553$	−1.08881e10	−2.73787
$554$	4.11792e9	1.02895
$555$	0	0
$556$	7.60911e8	0.187746
$557$	−3.54346e9	−0.868829	−0.434415	−	0.900713i	$-0.643045\pi$
$557$	−3.54346e9	−0.868829	−0.434415	+	0.900713i	$0.643045\pi$
$558$	0	0
$559$	3.12257e9	0.756085
$560$	6.23327e9	1.49988
$561$	0	0
$562$	3.02184e9	0.718117
$563$	5.23102e9	1.23540	0.617699	−	0.786414i	$-0.288065\pi$
$563$	5.23102e9	1.23540	0.617699	+	0.786414i	$0.288065\pi$
$564$	0	0
$565$	−2.35504e9	−0.549325
$566$	−7.30209e9	−1.69274
$567$	0	0
$568$	−2.67903e9	−0.613421
$569$	2.02667e8	0.0461200	0.0230600	−	0.999734i	$-0.492659\pi$
$569$	2.02667e8	0.0461200	0.0230600	+	0.999734i	$0.492659\pi$
$570$	0	0
$571$	1.61917e9	0.363969	0.181985	−	0.983301i	$-0.441748\pi$
$571$	1.61917e9	0.363969	0.181985	+	0.983301i	$0.441748\pi$
$572$	−8.95343e8	−0.200034
$573$	0	0
$574$	1.35473e10	2.98993
$575$	−1.20218e9	−0.263714
$576$	0	0
$577$	−8.09171e8	−0.175358	−0.0876789	−	0.996149i	$-0.527945\pi$
$577$	−8.09171e8	−0.175358	−0.0876789	+	0.996149i	$0.527945\pi$
$578$	−4.53136e9	−0.976070
$579$	0	0
$580$	−6.57358e7	−0.0139895
$581$	9.54851e9	2.01985
$582$	0	0
$583$	−4.57862e9	−0.956962
$584$	4.80057e9	0.997351
$585$	0	0
$586$	−2.90528e9	−0.596413
$587$	3.34084e9	0.681746	0.340873	−	0.940109i	$-0.389277\pi$
$587$	3.34084e9	0.681746	0.340873	+	0.940109i	$0.389277\pi$
$588$	0	0
$589$	6.29079e8	0.126853
$590$	−5.89209e8	−0.118110
$591$	0	0
$592$	−1.53224e9	−0.303530
$593$	−4.75989e9	−0.937358	−0.468679	−	0.883369i	$-0.655270\pi$
$593$	−4.75989e9	−0.937358	−0.468679	+	0.883369i	$0.655270\pi$
$594$	0	0
$595$	−2.05237e9	−0.399436
$596$	1.35497e9	0.262160
$597$	0	0
$598$	−5.53808e9	−1.05902
$599$	−5.11303e9	−0.972041	−0.486020	−	0.873947i	$-0.661552\pi$
$599$	−5.11303e9	−0.972041	−0.486020	+	0.873947i	$0.661552\pi$
$600$	0	0
$601$	−6.88520e9	−1.29377	−0.646883	−	0.762589i	$-0.723928\pi$
$601$	−6.88520e9	−1.29377	−0.646883	+	0.762589i	$0.723928\pi$
$602$	−6.39848e9	−1.19533
$603$	0	0
$604$	1.13059e9	0.208775
$605$	−2.47251e9	−0.453936
$606$	0	0
$607$	−9.35321e9	−1.69746	−0.848732	−	0.528824i	$-0.822633\pi$
$607$	−9.35321e9	−1.69746	−0.848732	+	0.528824i	$0.822633\pi$
$608$	7.21482e8	0.130186
$609$	0	0
$610$	−1.07150e8	−0.0191134
$611$	3.11413e9	0.552321
$612$	0	0
$613$	5.18941e9	0.909927	0.454963	−	0.890510i	$-0.349652\pi$
$613$	5.18941e9	0.909927	0.454963	+	0.890510i	$0.349652\pi$
$614$	1.21709e9	0.212195
$615$	0	0
$616$	−1.02967e10	−1.77486
$617$	−6.12264e9	−1.04940	−0.524700	−	0.851287i	$-0.675822\pi$
$617$	−6.12264e9	−1.04940	−0.524700	+	0.851287i	$0.675822\pi$
$618$	0	0
$619$	2.63490e9	0.446527	0.223263	−	0.974758i	$-0.428329\pi$
$619$	2.63490e9	0.446527	0.223263	+	0.974758i	$0.428329\pi$
$620$	2.21818e8	0.0373788
$621$	0	0
$622$	−8.62230e9	−1.43667
$623$	−1.02429e9	−0.169713
$624$	0	0
$625$	−3.86759e9	−0.633666
$626$	−7.95209e9	−1.29560
$627$	0	0
$628$	9.86016e8	0.158864
$629$	5.04508e8	0.0808334
$630$	0	0
$631$	2.67647e9	0.424092	0.212046	−	0.977260i	$-0.431987\pi$
$631$	2.67647e9	0.424092	0.212046	+	0.977260i	$0.431987\pi$
$632$	1.00650e10	1.58601
$633$	0	0
$634$	2.06403e9	0.321664
$635$	−7.12480e9	−1.10424
$636$	0	0
$637$	−1.02419e10	−1.56997
$638$	9.54548e8	0.145521
$639$	0	0
$640$	−6.53438e9	−0.985313
$641$	1.12657e10	1.68949	0.844747	−	0.535166i	$-0.179751\pi$
$641$	1.12657e10	1.68949	0.844747	+	0.535166i	$0.179751\pi$
$642$	0	0
$643$	5.64942e9	0.838041	0.419021	−	0.907977i	$-0.362373\pi$
$643$	5.64942e9	0.838041	0.419021	+	0.907977i	$0.362373\pi$
$644$	1.49075e9	0.219941
$645$	0	0
$646$	−9.58709e8	−0.139918
$647$	−8.48556e9	−1.23173	−0.615865	−	0.787852i	$-0.711193\pi$
$647$	−8.48556e9	−1.23173	−0.615865	+	0.787852i	$0.711193\pi$
$648$	0	0
$649$	1.12395e9	0.161396
$650$	2.28491e9	0.326342
$651$	0	0
$652$	−5.48572e8	−0.0775116
$653$	5.48317e9	0.770611	0.385306	−	0.922789i	$-0.374096\pi$
$653$	5.48317e9	0.770611	0.385306	+	0.922789i	$0.374096\pi$
$654$	0	0
$655$	−1.14765e10	−1.59575
$656$	−1.44615e10	−2.00009
$657$	0	0
$658$	−6.38118e9	−0.873193
$659$	5.95072e9	0.809974	0.404987	−	0.914323i	$-0.367276\pi$
$659$	5.95072e9	0.809974	0.404987	+	0.914323i	$0.367276\pi$
$660$	0	0
$661$	−8.08136e9	−1.08838	−0.544188	−	0.838963i	$-0.683162\pi$
$661$	−8.08136e9	−1.08838	−0.544188	+	0.838963i	$0.683162\pi$
$662$	1.57480e9	0.210971
$663$	0	0
$664$	−8.82673e9	−1.17007
$665$	4.37460e9	0.576850
$666$	0	0
$667$	7.75621e8	0.101207
$668$	−1.86299e8	−0.0241820
$669$	0	0
$670$	−7.57838e9	−0.973453
$671$	2.04396e8	0.0261182
$672$	0	0
$673$	−9.07433e9	−1.14752	−0.573762	−	0.819022i	$-0.694517\pi$
$673$	−9.07433e9	−1.14752	−0.573762	+	0.819022i	$0.694517\pi$
$674$	1.15961e9	0.145883
$675$	0	0
$676$	1.68067e8	0.0209251
$677$	−1.13075e10	−1.40057	−0.700286	−	0.713862i	$-0.746944\pi$
$677$	−1.13075e10	−1.40057	−0.700286	+	0.713862i	$0.746944\pi$
$678$	0	0
$679$	1.52647e10	1.87131
$680$	1.89723e9	0.231387
$681$	0	0
$682$	−3.22101e9	−0.388819
$683$	−1.42517e10	−1.71157	−0.855783	−	0.517336i	$-0.826924\pi$
$683$	−1.42517e10	−1.71157	−0.855783	+	0.517336i	$0.826924\pi$
$684$	0	0
$685$	−3.46921e9	−0.412395
$686$	6.72429e9	0.795265
$687$	0	0
$688$	6.83027e9	0.799610
$689$	7.07107e9	0.823603
$690$	0	0
$691$	1.15882e10	1.33612	0.668058	−	0.744109i	$-0.267126\pi$
$691$	1.15882e10	1.33612	0.668058	+	0.744109i	$0.267126\pi$
$692$	−1.39597e9	−0.160141
$693$	0	0
$694$	1.37648e9	0.156319
$695$	−9.28977e9	−1.04968
$696$	0	0
$697$	4.76161e9	0.532647
$698$	−4.51843e9	−0.502914
$699$	0	0
$700$	−6.15059e8	−0.0677757
$701$	−3.16850e9	−0.347408	−0.173704	−	0.984798i	$-0.555574\pi$
$701$	−3.16850e9	−0.347408	−0.173704	+	0.984798i	$0.555574\pi$
$702$	0	0
$703$	−1.07535e9	−0.116737
$704$	9.25587e9	0.999800
$705$	0	0
$706$	−6.97600e9	−0.746088
$707$	1.63693e10	1.74206
$708$	0	0
$709$	7.17426e9	0.755988	0.377994	−	0.925808i	$-0.376614\pi$
$709$	7.17426e9	0.755988	0.377994	+	0.925808i	$0.376614\pi$
$710$	−5.82782e9	−0.611086
$711$	0	0
$712$	9.46867e8	0.0983125
$713$	−2.61724e9	−0.270415
$714$	0	0
$715$	1.09310e10	1.11838
$716$	4.05180e8	0.0412527
$717$	0	0
$718$	6.86017e8	0.0691670
$719$	−3.09019e9	−0.310052	−0.155026	−	0.987910i	$-0.549546\pi$
$719$	−3.09019e9	−0.310052	−0.155026	+	0.987910i	$0.549546\pi$
$720$	0	0
$721$	1.13495e10	1.12773
$722$	−8.80733e9	−0.870891
$723$	0	0
$724$	8.86836e8	0.0868477
$725$	−3.20008e8	−0.0311873
$726$	0	0
$727$	1.26127e9	0.121741	0.0608707	−	0.998146i	$-0.480612\pi$
$727$	1.26127e9	0.121741	0.0608707	+	0.998146i	$0.480612\pi$
$728$	1.59019e10	1.52753
$729$	0	0
$730$	1.04429e10	0.993553
$731$	−2.24894e9	−0.212945
$732$	0	0
$733$	−1.05469e10	−0.989146	−0.494573	−	0.869136i	$-0.664676\pi$
$733$	−1.05469e10	−0.989146	−0.494573	+	0.869136i	$0.664676\pi$
$734$	−2.73815e9	−0.255576
$735$	0	0
$736$	−3.00168e9	−0.277519
$737$	1.44562e10	1.33021
$738$	0	0
$739$	7.89796e9	0.719879	0.359940	−	0.932976i	$-0.382797\pi$
$739$	7.89796e9	0.719879	0.359940	+	0.932976i	$0.382797\pi$
$740$	−3.79177e8	−0.0343978
$741$	0	0
$742$	−1.44894e10	−1.30208
$743$	7.69335e8	0.0688105	0.0344053	−	0.999408i	$-0.489046\pi$
$743$	7.69335e8	0.0688105	0.0344053	+	0.999408i	$0.489046\pi$
$744$	0	0
$745$	−1.65425e10	−1.46573
$746$	7.11545e9	0.627504
$747$	0	0
$748$	6.44846e8	0.0563379
$749$	−1.57664e10	−1.37103
$750$	0	0
$751$	1.79359e10	1.54519	0.772596	−	0.634898i	$-0.218958\pi$
$751$	1.79359e10	1.54519	0.772596	+	0.634898i	$0.218958\pi$
$752$	6.81180e9	0.584117
$753$	0	0
$754$	−1.47417e9	−0.125242
$755$	−1.38032e10	−1.16725
$756$	0	0
$757$	4.00304e9	0.335394	0.167697	−	0.985839i	$-0.446367\pi$
$757$	4.00304e9	0.335394	0.167697	+	0.985839i	$0.446367\pi$
$758$	4.87661e9	0.406702
$759$	0	0
$760$	−4.04393e9	−0.334161
$761$	−3.91126e9	−0.321714	−0.160857	−	0.986978i	$-0.551426\pi$
$761$	−3.91126e9	−0.321714	−0.160857	+	0.986978i	$0.551426\pi$
$762$	0	0
$763$	1.15316e10	0.939839
$764$	3.07166e9	0.249199
$765$	0	0
$766$	1.20194e10	0.966234
$767$	−1.73579e9	−0.138904
$768$	0	0
$769$	1.77498e10	1.40751	0.703756	−	0.710441i	$-0.251505\pi$
$769$	1.77498e10	1.40751	0.703756	+	0.710441i	$0.251505\pi$
$770$	−2.23989e10	−1.76811
$771$	0	0
$772$	1.32009e9	0.103263
$773$	−2.00177e10	−1.55879	−0.779393	−	0.626536i	$-0.784472\pi$
$773$	−2.00177e10	−1.55879	−0.779393	+	0.626536i	$0.784472\pi$
$774$	0	0
$775$	1.07983e9	0.0833296
$776$	−1.41109e10	−1.08402
$777$	0	0
$778$	−1.13023e10	−0.860472
$779$	−1.01493e10	−0.769229
$780$	0	0
$781$	1.11169e10	0.835038
$782$	3.98865e9	0.298265
$783$	0	0
$784$	−2.24030e10	−1.66035
$785$	−1.20380e10	−0.888201
$786$	0	0
$787$	−1.57588e10	−1.15242	−0.576212	−	0.817300i	$-0.695470\pi$
$787$	−1.57588e10	−1.15242	−0.576212	+	0.817300i	$0.695470\pi$
$788$	−1.55784e9	−0.113418
$789$	0	0
$790$	2.18949e10	1.57997
$791$	1.42165e10	1.02135
$792$	0	0
$793$	−3.15662e8	−0.0224784
$794$	5.07745e9	0.359976
$795$	0	0
$796$	−1.32796e9	−0.0933234
$797$	9.19325e9	0.643228	0.321614	−	0.946871i	$-0.395775\pi$
$797$	9.19325e9	0.643228	0.321614	+	0.946871i	$0.395775\pi$
$798$	0	0
$799$	−2.24286e9	−0.155557
$800$	1.23844e9	0.0855185
$801$	0	0
$802$	2.30173e10	1.57559
$803$	−1.99205e10	−1.35767
$804$	0	0
$805$	−1.82003e10	−1.22968
$806$	4.97443e9	0.334634
$807$	0	0
$808$	−1.51320e10	−1.00915
$809$	1.69661e10	1.12658	0.563290	−	0.826259i	$-0.309535\pi$
$809$	1.69661e10	1.12658	0.563290	+	0.826259i	$0.309535\pi$
$810$	0	0
$811$	−2.19205e10	−1.44303	−0.721517	−	0.692397i	$-0.756555\pi$
$811$	−2.19205e10	−1.44303	−0.721517	+	0.692397i	$0.756555\pi$
$812$	3.96822e8	0.0260105
$813$	0	0
$814$	5.50602e9	0.357810
$815$	6.69738e9	0.433364
$816$	0	0
$817$	4.79359e9	0.307527
$818$	−2.93422e10	−1.87437
$819$	0	0
$820$	−3.57872e9	−0.226662
$821$	−1.97496e10	−1.24554	−0.622770	−	0.782405i	$-0.713993\pi$
$821$	−1.97496e10	−1.24554	−0.622770	+	0.782405i	$0.713993\pi$
$822$	0	0
$823$	3.26341e9	0.204067	0.102033	−	0.994781i	$-0.467465\pi$
$823$	3.26341e9	0.204067	0.102033	+	0.994781i	$0.467465\pi$
$824$	−1.04916e10	−0.653276
$825$	0	0
$826$	3.55683e9	0.219600
$827$	−7.08713e9	−0.435713	−0.217857	−	0.975981i	$-0.569907\pi$
$827$	−7.08713e9	−0.435713	−0.217857	+	0.975981i	$0.569907\pi$
$828$	0	0
$829$	3.03587e10	1.85073	0.925365	−	0.379078i	$-0.123759\pi$
$829$	3.03587e10	1.85073	0.925365	+	0.379078i	$0.123759\pi$
$830$	−1.92012e10	−1.16561
$831$	0	0
$832$	−1.42945e10	−0.860471
$833$	7.37643e9	0.442169
$834$	0	0
$835$	2.27447e9	0.135200
$836$	−1.37448e9	−0.0813611
$837$	0	0
$838$	2.10092e10	1.23326
$839$	−1.35904e10	−0.794448	−0.397224	−	0.917722i	$-0.630026\pi$
$839$	−1.35904e10	−0.794448	−0.397224	+	0.917722i	$0.630026\pi$
$840$	0	0
$841$	−1.70434e10	−0.988031
$842$	2.90069e10	1.67459
$843$	0	0
$844$	5.59143e8	0.0320128
$845$	−2.05189e9	−0.116992
$846$	0	0
$847$	1.49256e10	0.843997
$848$	1.54672e10	0.871014
$849$	0	0
$850$	−1.64565e9	−0.0919116
$851$	4.47393e9	0.248849
$852$	0	0
$853$	1.23490e10	0.681255	0.340628	−	0.940198i	$-0.389361\pi$
$853$	1.23490e10	0.681255	0.340628	+	0.940198i	$0.389361\pi$
$854$	6.46826e8	0.0355373
$855$	0	0
$856$	1.45747e10	0.794219
$857$	1.91652e10	1.04011	0.520057	−	0.854132i	$-0.325911\pi$
$857$	1.91652e10	1.04011	0.520057	+	0.854132i	$0.325911\pi$
$858$	0	0
$859$	−2.69718e10	−1.45189	−0.725946	−	0.687751i	$-0.758598\pi$
$859$	−2.69718e10	−1.45189	−0.725946	+	0.687751i	$0.758598\pi$
$860$	1.69025e9	0.0906166
$861$	0	0
$862$	1.29171e10	0.686893
$863$	1.15124e9	0.0609715	0.0304858	−	0.999535i	$-0.490295\pi$
$863$	1.15124e9	0.0609715	0.0304858	+	0.999535i	$0.490295\pi$
$864$	0	0
$865$	1.70430e10	0.895344
$866$	−1.01275e10	−0.529896
$867$	0	0
$868$	−1.33903e9	−0.0694978
$869$	−4.17659e10	−2.15900
$870$	0	0
$871$	−2.23257e10	−1.14483
$872$	−1.06599e10	−0.544435
$873$	0	0
$874$	−8.50174e9	−0.430743
$875$	3.38504e10	1.70819
$876$	0	0
$877$	−2.50007e9	−0.125157	−0.0625784	−	0.998040i	$-0.519932\pi$
$877$	−2.50007e9	−0.125157	−0.0625784	+	0.998040i	$0.519932\pi$
$878$	2.32624e10	1.15991
$879$	0	0
$880$	2.39104e10	1.18276
$881$	−1.84978e10	−0.911392	−0.455696	−	0.890136i	$-0.650610\pi$
$881$	−1.84978e10	−0.911392	−0.455696	+	0.890136i	$0.650610\pi$
$882$	0	0
$883$	3.27036e10	1.59857	0.799287	−	0.600950i	$-0.205211\pi$
$883$	3.27036e10	1.59857	0.799287	+	0.600950i	$0.205211\pi$
$884$	−9.95879e8	−0.0484868
$885$	0	0
$886$	−1.73733e10	−0.839196
$887$	2.66571e10	1.28257	0.641285	−	0.767303i	$-0.278402\pi$
$887$	2.66571e10	1.28257	0.641285	+	0.767303i	$0.278402\pi$
$888$	0	0
$889$	4.30097e10	2.05310
$890$	2.05976e9	0.0979382
$891$	0	0
$892$	5.02130e9	0.236886
$893$	4.78063e9	0.224649
$894$	0	0
$895$	−4.94674e9	−0.230642
$896$	3.94455e10	1.83198
$897$	0	0
$898$	1.21977e10	0.562096
$899$	−6.96680e8	−0.0319797
$900$	0	0
$901$	−5.09274e9	−0.231961
$902$	5.19665e10	2.35777
$903$	0	0
$904$	−1.31419e10	−0.591654
$905$	−1.08272e10	−0.485562
$906$	0	0
$907$	−2.98097e10	−1.32658	−0.663289	−	0.748364i	$-0.730840\pi$
$907$	−2.98097e10	−1.32658	−0.663289	+	0.748364i	$0.730840\pi$
$908$	3.94266e9	0.174779
$909$	0	0
$910$	3.45921e10	1.52171
$911$	1.60230e10	0.702149	0.351074	−	0.936348i	$-0.385816\pi$
$911$	1.60230e10	0.702149	0.351074	+	0.936348i	$0.385816\pi$
$912$	0	0
$913$	3.66274e10	1.59279
$914$	4.02379e10	1.74311
$915$	0	0
$916$	−6.74815e9	−0.290102
$917$	6.92794e10	2.96696
$918$	0	0
$919$	2.67157e10	1.13543	0.567717	−	0.823224i	$-0.307827\pi$
$919$	2.67157e10	1.13543	0.567717	+	0.823224i	$0.307827\pi$
$920$	1.68245e10	0.712336
$921$	0	0
$922$	−3.62349e8	−0.0152254
$923$	−1.71686e10	−0.718670
$924$	0	0
$925$	−1.84587e9	−0.0766839
$926$	6.21430e9	0.257190
$927$	0	0
$928$	−7.99012e8	−0.0328198
$929$	1.01936e10	0.417130	0.208565	−	0.978009i	$-0.433121\pi$
$929$	1.01936e10	0.417130	0.208565	+	0.978009i	$0.433121\pi$
$930$	0	0
$931$	−1.57228e10	−0.638564
$932$	−3.03310e9	−0.122725
$933$	0	0
$934$	4.05008e10	1.62648
$935$	−7.87277e9	−0.314983
$936$	0	0
$937$	−2.50793e10	−0.995923	−0.497962	−	0.867199i	$-0.665918\pi$
$937$	−2.50793e10	−0.995923	−0.497962	+	0.867199i	$0.665918\pi$
$938$	4.57478e10	1.80992
$939$	0	0
$940$	1.68568e9	0.0661955
$941$	5.38850e9	0.210816	0.105408	−	0.994429i	$-0.466385\pi$
$941$	5.38850e9	0.210816	0.105408	+	0.994429i	$0.466385\pi$
$942$	0	0
$943$	4.22256e10	1.63978
$944$	−3.79686e9	−0.146900
$945$	0	0
$946$	−2.45442e10	−0.942604
$947$	1.51551e10	0.579876	0.289938	−	0.957045i	$-0.406365\pi$
$947$	1.51551e10	0.579876	0.289938	+	0.957045i	$0.406365\pi$
$948$	0	0
$949$	3.07645e10	1.16847
$950$	3.50767e9	0.132735
$951$	0	0
$952$	−1.14529e10	−0.430215
$953$	−4.14430e9	−0.155105	−0.0775526	−	0.996988i	$-0.524711\pi$
$953$	−4.14430e9	−0.155105	−0.0775526	+	0.996988i	$0.524711\pi$
$954$	0	0
$955$	−3.75011e10	−1.39326
$956$	−4.04012e9	−0.149552
$957$	0	0
$958$	2.94703e9	0.108294
$959$	2.09423e10	0.766760
$960$	0	0
$961$	−2.51617e10	−0.914553
$962$	−8.50331e9	−0.307946
$963$	0	0
$964$	−7.36552e9	−0.264810
$965$	−1.61167e10	−0.577338
$966$	0	0
$967$	−7.19424e9	−0.255854	−0.127927	−	0.991784i	$-0.540832\pi$
$967$	−7.19424e9	−0.255854	−0.127927	+	0.991784i	$0.540832\pi$
$968$	−1.37974e10	−0.488915
$969$	0	0
$970$	−3.06960e10	−1.07989
$971$	3.04216e10	1.06639	0.533193	−	0.845993i	$-0.320992\pi$
$971$	3.04216e10	1.06639	0.533193	+	0.845993i	$0.320992\pi$
$972$	0	0
$973$	5.60788e10	1.95166
$974$	−1.44147e10	−0.499860
$975$	0	0
$976$	−6.90475e8	−0.0237724
$977$	1.19680e9	0.0410572	0.0205286	−	0.999789i	$-0.493465\pi$
$977$	1.19680e9	0.0410572	0.0205286	+	0.999789i	$0.493465\pi$
$978$	0	0
$979$	−3.92912e9	−0.133831
$980$	−5.54395e9	−0.188160
$981$	0	0
$982$	−2.34366e10	−0.789778
$983$	−5.01551e10	−1.68414	−0.842069	−	0.539370i	$-0.818663\pi$
$983$	−5.01551e10	−1.68414	−0.842069	+	0.539370i	$0.818663\pi$
$984$	0	0
$985$	1.90193e10	0.634116
$986$	1.06173e9	0.0352733
$987$	0	0
$988$	2.12270e9	0.0700228
$989$	−1.99434e10	−0.655561
$990$	0	0
$991$	2.70432e10	0.882674	0.441337	−	0.897341i	$-0.354504\pi$
$991$	2.70432e10	0.882674	0.441337	+	0.897341i	$0.354504\pi$
$992$	2.69618e9	0.0876915
$993$	0	0
$994$	3.51803e10	1.13618
$995$	1.62128e10	0.521767
$996$	0	0
$997$	1.18645e10	0.379154	0.189577	−	0.981866i	$-0.439288\pi$
$997$	1.18645e10	0.379154	0.189577	+	0.981866i	$0.439288\pi$
$998$	3.78400e10	1.20502
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.12		17
3.2	odd	2		177.8.a.b.1.6	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.6	✓	17	3.2	odd	2
531.8.a.d.1.12		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)

\(f(q)\)	\(=\)	\(q+12.1391 q^{2} +19.3578 q^{4} -236.334 q^{5} +1426.66 q^{7} -1318.82 q^{8} +O(q^{10})\)	\(q+12.1391 q^{2} +19.3578 q^{4} -236.334 q^{5} +1426.66 q^{7} -1318.82 q^{8} -2868.89 q^{10} +5472.58 q^{11} -8451.67 q^{13} +17318.4 q^{14} -18487.1 q^{16} +6087.08 q^{17} -12974.5 q^{19} -4574.91 q^{20} +66432.2 q^{22} +53979.7 q^{23} -22271.1 q^{25} -102596. q^{26} +27617.0 q^{28} +14368.8 q^{29} -48485.8 q^{31} -55607.6 q^{32} +73891.7 q^{34} -337169. q^{35} +82881.8 q^{37} -157499. q^{38} +311682. q^{40} +782250. q^{41} -369462. q^{43} +105937. q^{44} +655265. q^{46} -368463. q^{47} +1.21182e6 q^{49} -270351. q^{50} -163605. q^{52} -836648. q^{53} -1.29336e6 q^{55} -1.88151e6 q^{56} +174424. q^{58} +205379. q^{59} +37349.1 q^{61} -588573. q^{62} +1.69132e6 q^{64} +1.99742e6 q^{65} +2.64158e6 q^{67} +117832. q^{68} -4.09293e6 q^{70} +2.03139e6 q^{71} -3.64005e6 q^{73} +1.00611e6 q^{74} -251158. q^{76} +7.80751e6 q^{77} -7.63186e6 q^{79} +4.36913e6 q^{80} +9.49581e6 q^{82} +6.69291e6 q^{83} -1.43859e6 q^{85} -4.48494e6 q^{86} -7.21734e6 q^{88} -717966. q^{89} -1.20577e7 q^{91} +1.04493e6 q^{92} -4.47281e6 q^{94} +3.06632e6 q^{95} +1.06996e7 q^{97} +1.47104e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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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