LMFDB - Embedded newform 531.8.a.d.1.14

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			1.14
Root			$-15.8998$ 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)

$f(q)$	$=$	$q+17.8998 q^{2} +192.403 q^{4} -255.355 q^{5} -1072.82 q^{7} +1152.80 q^{8} +O(q^{10})$	\(q+17.8998 q^{2} +192.403 q^{4} -255.355 q^{5} -1072.82 q^{7} +1152.80 q^{8} -4570.81 q^{10} -4742.70 q^{11} +5721.05 q^{13} -19203.3 q^{14} -3992.71 q^{16} +12850.6 q^{17} -52123.1 q^{19} -49131.1 q^{20} -84893.4 q^{22} +9824.17 q^{23} -12918.7 q^{25} +102406. q^{26} -206414. q^{28} +196436. q^{29} +272544. q^{31} -219027. q^{32} +230023. q^{34} +273951. q^{35} +309341. q^{37} -932994. q^{38} -294373. q^{40} +421229. q^{41} -406292. q^{43} -912509. q^{44} +175851. q^{46} +261121. q^{47} +327408. q^{49} -231242. q^{50} +1.10075e6 q^{52} -738907. q^{53} +1.21107e6 q^{55} -1.23675e6 q^{56} +3.51616e6 q^{58} +205379. q^{59} +233563. q^{61} +4.87848e6 q^{62} -3.40947e6 q^{64} -1.46090e6 q^{65} +3.54145e6 q^{67} +2.47250e6 q^{68} +4.90367e6 q^{70} -1.03036e6 q^{71} -5.88757e6 q^{73} +5.53715e6 q^{74} -1.00286e7 q^{76} +5.08808e6 q^{77} +4.34224e6 q^{79} +1.01956e6 q^{80} +7.53991e6 q^{82} +4.12014e6 q^{83} -3.28147e6 q^{85} -7.27255e6 q^{86} -5.46737e6 q^{88} +7.32690e6 q^{89} -6.13768e6 q^{91} +1.89020e6 q^{92} +4.67402e6 q^{94} +1.33099e7 q^{95} +1.46546e7 q^{97} +5.86054e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	17.8998	1.58213	0.791067	−	0.611730i	$-0.209526\pi$
$2$	17.8998	1.58213	0.791067	+	0.611730i	$0.209526\pi$
$3$	0	0
$3$	0	0
$4$	192.403	1.50315
$5$	−255.355	−0.913587	−0.456793	−	0.889573i	$-0.651002\pi$
$5$	−255.355	−0.913587	−0.456793	+	0.889573i	$0.651002\pi$
$6$	0	0
$7$	−1072.82	−1.18218	−0.591092	−	0.806604i	$-0.701303\pi$
$7$	−1072.82	−1.18218	−0.591092	+	0.806604i	$0.701303\pi$
$8$	1152.80	0.796046
$9$	0	0
$10$	−4570.81	−1.44542
$11$	−4742.70	−1.07436	−0.537182	−	0.843467i	$-0.680511\pi$
$11$	−4742.70	−1.07436	−0.537182	+	0.843467i	$0.680511\pi$
$12$	0	0
$13$	5721.05	0.722227	0.361114	−	0.932522i	$-0.382397\pi$
$13$	5721.05	0.722227	0.361114	+	0.932522i	$0.382397\pi$
$14$	−19203.3	−1.87037
$15$	0	0
$16$	−3992.71	−0.243695
$17$	12850.6	0.634385	0.317192	−	0.948361i	$-0.397260\pi$
$17$	12850.6	0.634385	0.317192	+	0.948361i	$0.397260\pi$
$18$	0	0
$19$	−52123.1	−1.74338	−0.871692	−	0.490055i	$-0.836977\pi$
$19$	−52123.1	−1.74338	−0.871692	+	0.490055i	$0.836977\pi$
$20$	−49131.1	−1.37326
$21$	0	0
$22$	−84893.4	−1.69979
$23$	9824.17	0.168364	0.0841818	−	0.996450i	$-0.473172\pi$
$23$	9824.17	0.168364	0.0841818	+	0.996450i	$0.473172\pi$
$24$	0	0
$25$	−12918.7	−0.165359
$26$	102406.	1.14266
$27$	0	0
$28$	−206414.	−1.77700
$29$	196436.	1.49564	0.747821	−	0.663901i	$-0.231100\pi$
$29$	196436.	1.49564	0.747821	+	0.663901i	$0.231100\pi$
$30$	0	0
$31$	272544.	1.64312	0.821562	−	0.570119i	$-0.193103\pi$
$31$	272544.	1.64312	0.821562	+	0.570119i	$0.193103\pi$
$32$	−219027.	−1.18161
$33$	0	0
$34$	230023.	1.00368
$35$	273951.	1.08003
$36$	0	0
$37$	309341.	1.00400	0.501998	−	0.864869i	$-0.332599\pi$
$37$	309341.	1.00400	0.501998	+	0.864869i	$0.332599\pi$
$38$	−932994.	−2.75827
$39$	0	0
$40$	−294373.	−0.727258
$41$	421229.	0.954497	0.477249	−	0.878768i	$-0.341634\pi$
$41$	421229.	0.954497	0.477249	+	0.878768i	$0.341634\pi$
$42$	0	0
$43$	−406292.	−0.779289	−0.389645	−	0.920965i	$-0.627402\pi$
$43$	−406292.	−0.779289	−0.389645	+	0.920965i	$0.627402\pi$
$44$	−912509.	−1.61493
$45$	0	0
$46$	175851.	0.266374
$47$	261121.	0.366859	0.183430	−	0.983033i	$-0.441280\pi$
$47$	261121.	0.366859	0.183430	+	0.983033i	$0.441280\pi$
$48$	0	0
$49$	327408.	0.397560
$50$	−231242.	−0.261620
$51$	0	0
$52$	1.10075e6	1.08561
$53$	−738907.	−0.681748	−0.340874	−	0.940109i	$-0.610723\pi$
$53$	−738907.	−0.681748	−0.340874	+	0.940109i	$0.610723\pi$
$54$	0	0
$55$	1.21107e6	0.981524
$56$	−1.23675e6	−0.941074
$57$	0	0
$58$	3.51616e6	2.36630
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	233563.	0.131750	0.0658748	−	0.997828i	$-0.479016\pi$
$61$	233563.	0.131750	0.0658748	+	0.997828i	$0.479016\pi$
$62$	4.87848e6	2.59964
$63$	0	0
$64$	−3.40947e6	−1.62576
$65$	−1.46090e6	−0.659817
$66$	0	0
$67$	3.54145e6	1.43853	0.719265	−	0.694736i	$-0.244479\pi$
$67$	3.54145e6	1.43853	0.719265	+	0.694736i	$0.244479\pi$
$68$	2.47250e6	0.953574
$69$	0	0
$70$	4.90367e6	1.70875
$71$	−1.03036e6	−0.341652	−0.170826	−	0.985301i	$-0.554644\pi$
$71$	−1.03036e6	−0.341652	−0.170826	+	0.985301i	$0.554644\pi$
$72$	0	0
$73$	−5.88757e6	−1.77136	−0.885679	−	0.464298i	$-0.846307\pi$
$73$	−5.88757e6	−1.77136	−0.885679	+	0.464298i	$0.846307\pi$
$74$	5.53715e6	1.58845
$75$	0	0
$76$	−1.00286e7	−2.62056
$77$	5.08808e6	1.27010
$78$	0	0
$79$	4.34224e6	0.990875	0.495437	−	0.868644i	$-0.335008\pi$
$79$	4.34224e6	0.990875	0.495437	+	0.868644i	$0.335008\pi$
$80$	1.01956e6	0.222637
$81$	0	0
$82$	7.53991e6	1.51014
$83$	4.12014e6	0.790931	0.395465	−	0.918481i	$-0.370583\pi$
$83$	4.12014e6	0.790931	0.395465	+	0.918481i	$0.370583\pi$
$84$	0	0
$85$	−3.28147e6	−0.579566
$86$	−7.27255e6	−1.23294
$87$	0	0
$88$	−5.46737e6	−0.855243
$89$	7.32690e6	1.10168	0.550840	−	0.834611i	$-0.314308\pi$
$89$	7.32690e6	1.10168	0.550840	+	0.834611i	$0.314308\pi$
$90$	0	0
$91$	−6.13768e6	−0.853806
$92$	1.89020e6	0.253075
$93$	0	0
$94$	4.67402e6	0.580421
$95$	1.33099e7	1.59273
$96$	0	0
$97$	1.46546e7	1.63032	0.815158	−	0.579239i	$-0.196650\pi$
$97$	1.46546e7	1.63032	0.815158	+	0.579239i	$0.196650\pi$
$98$	5.86054e6	0.628994
$99$	0	0
$100$	−2.48559e6	−0.248559
$101$	−3.05329e6	−0.294878	−0.147439	−	0.989071i	$-0.547103\pi$
$101$	−3.05329e6	−0.294878	−0.147439	+	0.989071i	$0.547103\pi$
$102$	0	0
$103$	−1.49285e7	−1.34613	−0.673063	−	0.739585i	$-0.735022\pi$
$103$	−1.49285e7	−1.34613	−0.673063	+	0.739585i	$0.735022\pi$
$104$	6.59521e6	0.574926
$105$	0	0
$106$	−1.32263e7	−1.07862
$107$	2.22015e7	1.75202	0.876011	−	0.482291i	$-0.160195\pi$
$107$	2.22015e7	1.75202	0.876011	+	0.482291i	$0.160195\pi$
$108$	0	0
$109$	−2.47303e6	−0.182910	−0.0914549	−	0.995809i	$-0.529152\pi$
$109$	−2.47303e6	−0.182910	−0.0914549	+	0.995809i	$0.529152\pi$
$110$	2.16780e7	1.55290
$111$	0	0
$112$	4.28347e6	0.288093
$113$	1.16610e7	0.760260	0.380130	−	0.924933i	$-0.375879\pi$
$113$	1.16610e7	0.760260	0.380130	+	0.924933i	$0.375879\pi$
$114$	0	0
$115$	−2.50865e6	−0.153815
$116$	3.77948e7	2.24817
$117$	0	0
$118$	3.67624e6	0.205976
$119$	−1.37864e7	−0.749960
$120$	0	0
$121$	3.00601e6	0.154256
$122$	4.18073e6	0.208446
$123$	0	0
$124$	5.24382e7	2.46986
$125$	2.32485e7	1.06466
$126$	0	0
$127$	−3.47578e7	−1.50570	−0.752852	−	0.658190i	$-0.771322\pi$
$127$	−3.47578e7	−1.50570	−0.752852	+	0.658190i	$0.771322\pi$
$128$	−3.29934e7	−1.39057
$129$	0	0
$130$	−2.61498e7	−1.04392
$131$	1.06271e7	0.413016	0.206508	−	0.978445i	$-0.433790\pi$
$131$	1.06271e7	0.413016	0.206508	+	0.978445i	$0.433790\pi$
$132$	0	0
$133$	5.59189e7	2.06100
$134$	6.33912e7	2.27595
$135$	0	0
$136$	1.48142e7	0.505000
$137$	4.64453e7	1.54319	0.771596	−	0.636112i	$-0.219459\pi$
$137$	4.64453e7	1.54319	0.771596	+	0.636112i	$0.219459\pi$
$138$	0	0
$139$	−1.75461e7	−0.554151	−0.277076	−	0.960848i	$-0.589365\pi$
$139$	−1.75461e7	−0.554151	−0.277076	+	0.960848i	$0.589365\pi$
$140$	5.27090e7	1.62344
$141$	0	0
$142$	−1.84432e7	−0.540539
$143$	−2.71332e7	−0.775934
$144$	0	0
$145$	−5.01609e7	−1.36640
$146$	−1.05386e8	−2.80253
$147$	0	0
$148$	5.95181e7	1.50915
$149$	−6.90672e7	−1.71049	−0.855244	−	0.518225i	$-0.826593\pi$
$149$	−6.90672e7	−1.71049	−0.855244	+	0.518225i	$0.826593\pi$
$150$	0	0
$151$	9.93956e6	0.234935	0.117468	−	0.993077i	$-0.462522\pi$
$151$	9.93956e6	0.234935	0.117468	+	0.993077i	$0.462522\pi$
$152$	−6.00875e7	−1.38781
$153$	0	0
$154$	9.10756e7	2.00946
$155$	−6.95955e7	−1.50114
$156$	0	0
$157$	−1.73655e7	−0.358128	−0.179064	−	0.983837i	$-0.557307\pi$
$157$	−1.73655e7	−0.358128	−0.179064	+	0.983837i	$0.557307\pi$
$158$	7.77252e7	1.56770
$159$	0	0
$160$	5.59297e7	1.07950
$161$	−1.05396e7	−0.199037
$162$	0	0
$163$	−8.66389e7	−1.56695	−0.783477	−	0.621421i	$-0.786556\pi$
$163$	−8.66389e7	−1.56695	−0.783477	+	0.621421i	$0.786556\pi$
$164$	8.10456e7	1.43475
$165$	0	0
$166$	7.37497e7	1.25136
$167$	2.60451e7	0.432732	0.216366	−	0.976312i	$-0.430580\pi$
$167$	2.60451e7	0.432732	0.216366	+	0.976312i	$0.430580\pi$
$168$	0	0
$169$	−3.00181e7	−0.478388
$170$	−5.87377e7	−0.916950
$171$	0	0
$172$	−7.81717e7	−1.17139
$173$	2.86328e7	0.420438	0.210219	−	0.977654i	$-0.432582\pi$
$173$	2.86328e7	0.420438	0.210219	+	0.977654i	$0.432582\pi$
$174$	0	0
$175$	1.38595e7	0.195485
$176$	1.89362e7	0.261817
$177$	0	0
$178$	1.31150e8	1.74300
$179$	−9.04329e6	−0.117853	−0.0589266	−	0.998262i	$-0.518768\pi$
$179$	−9.04329e6	−0.117853	−0.0589266	+	0.998262i	$0.518768\pi$
$180$	0	0
$181$	9.04918e7	1.13432	0.567158	−	0.823609i	$-0.308043\pi$
$181$	9.04918e7	1.13432	0.567158	+	0.823609i	$0.308043\pi$
$182$	−1.09863e8	−1.35084
$183$	0	0
$184$	1.13253e7	0.134025
$185$	−7.89919e7	−0.917237
$186$	0	0
$187$	−6.09466e7	−0.681559
$188$	5.02405e7	0.551444
$189$	0	0
$190$	2.38245e8	2.51992
$191$	7.52927e7	0.781873	0.390936	−	0.920418i	$-0.372151\pi$
$191$	7.52927e7	0.781873	0.390936	+	0.920418i	$0.372151\pi$
$192$	0	0
$193$	3.03390e7	0.303774	0.151887	−	0.988398i	$-0.451465\pi$
$193$	3.03390e7	0.303774	0.151887	+	0.988398i	$0.451465\pi$
$194$	2.62314e8	2.57938
$195$	0	0
$196$	6.29942e7	0.597592
$197$	−5.75348e7	−0.536165	−0.268083	−	0.963396i	$-0.586390\pi$
$197$	−5.75348e7	−0.536165	−0.268083	+	0.963396i	$0.586390\pi$
$198$	0	0
$199$	3.30510e6	0.0297303	0.0148651	−	0.999890i	$-0.495268\pi$
$199$	3.30510e6	0.0297303	0.0148651	+	0.999890i	$0.495268\pi$
$200$	−1.48926e7	−0.131633
$201$	0	0
$202$	−5.46532e7	−0.466537
$203$	−2.10741e8	−1.76812
$204$	0	0
$205$	−1.07563e8	−0.872016
$206$	−2.67217e8	−2.12975
$207$	0	0
$208$	−2.28425e7	−0.176003
$209$	2.47204e8	1.87303
$210$	0	0
$211$	7.47470e7	0.547779	0.273890	−	0.961761i	$-0.411690\pi$
$211$	7.47470e7	0.547779	0.273890	+	0.961761i	$0.411690\pi$
$212$	−1.42168e8	−1.02477
$213$	0	0
$214$	3.97403e8	2.77193
$215$	1.03749e8	0.711948
$216$	0	0
$217$	−2.92391e8	−1.94248
$218$	−4.42668e7	−0.289388
$219$	0	0
$220$	2.33014e8	1.47538
$221$	7.35190e7	0.458170
$222$	0	0
$223$	−2.95302e8	−1.78320	−0.891599	−	0.452826i	$-0.850416\pi$
$223$	−2.95302e8	−1.78320	−0.891599	+	0.452826i	$0.850416\pi$
$224$	2.34977e8	1.39688
$225$	0	0
$226$	2.08730e8	1.20283
$227$	4.08714e6	0.0231915	0.0115957	−	0.999933i	$-0.496309\pi$
$227$	4.08714e6	0.0231915	0.0115957	+	0.999933i	$0.496309\pi$
$228$	0	0
$229$	2.00230e8	1.10181	0.550903	−	0.834570i	$-0.314284\pi$
$229$	2.00230e8	1.10181	0.550903	+	0.834570i	$0.314284\pi$
$230$	−4.49044e7	−0.243356
$231$	0	0
$232$	2.26451e8	1.19060
$233$	9.85532e7	0.510417	0.255208	−	0.966886i	$-0.417856\pi$
$233$	9.85532e7	0.510417	0.255208	+	0.966886i	$0.417856\pi$
$234$	0	0
$235$	−6.66787e7	−0.335158
$236$	3.95155e7	0.195693
$237$	0	0
$238$	−2.46775e8	−1.18654
$239$	3.06770e8	1.45352	0.726758	−	0.686894i	$-0.241026\pi$
$239$	3.06770e8	1.45352	0.726758	+	0.686894i	$0.241026\pi$
$240$	0	0
$241$	3.30373e8	1.52035	0.760176	−	0.649717i	$-0.225112\pi$
$241$	3.30373e8	1.52035	0.760176	+	0.649717i	$0.225112\pi$
$242$	5.38071e7	0.244054
$243$	0	0
$244$	4.49382e7	0.198039
$245$	−8.36054e7	−0.363206
$246$	0	0
$247$	−2.98199e8	−1.25912
$248$	3.14188e8	1.30800
$249$	0	0
$250$	4.16143e8	1.68443
$251$	4.29400e8	1.71397	0.856987	−	0.515339i	$-0.172334\pi$
$251$	4.29400e8	1.71397	0.856987	+	0.515339i	$0.172334\pi$
$252$	0	0
$253$	−4.65931e7	−0.180884
$254$	−6.22158e8	−2.38222
$255$	0	0
$256$	−1.54163e8	−0.574302
$257$	3.01963e8	1.10966	0.554828	−	0.831965i	$-0.312784\pi$
$257$	3.01963e8	1.10966	0.554828	+	0.831965i	$0.312784\pi$
$258$	0	0
$259$	−3.31869e8	−1.18691
$260$	−2.81081e8	−0.991803
$261$	0	0
$262$	1.90224e8	0.653447
$263$	7.22951e7	0.245055	0.122528	−	0.992465i	$-0.460900\pi$
$263$	7.22951e7	0.245055	0.122528	+	0.992465i	$0.460900\pi$
$264$	0	0
$265$	1.88684e8	0.622836
$266$	1.00094e9	3.26078
$267$	0	0
$268$	6.81384e8	2.16232
$269$	−1.46096e8	−0.457622	−0.228811	−	0.973471i	$-0.573484\pi$
$269$	−1.46096e8	−0.457622	−0.228811	+	0.973471i	$0.573484\pi$
$270$	0	0
$271$	−2.87297e8	−0.876876	−0.438438	−	0.898761i	$-0.644468\pi$
$271$	−2.87297e8	−0.876876	−0.438438	+	0.898761i	$0.644468\pi$
$272$	−5.13087e7	−0.154597
$273$	0	0
$274$	8.31362e8	2.44154
$275$	6.12693e7	0.177656
$276$	0	0
$277$	3.14837e8	0.890033	0.445016	−	0.895522i	$-0.353198\pi$
$277$	3.14837e8	0.890033	0.445016	+	0.895522i	$0.353198\pi$
$278$	−3.14071e8	−0.876741
$279$	0	0
$280$	3.15811e8	0.859753
$281$	−7.28235e8	−1.95794	−0.978971	−	0.204002i	$-0.934605\pi$
$281$	−7.28235e8	−1.95794	−0.978971	+	0.204002i	$0.934605\pi$
$282$	0	0
$283$	−2.37367e8	−0.622541	−0.311271	−	0.950321i	$-0.600755\pi$
$283$	−2.37367e8	−0.622541	−0.311271	+	0.950321i	$0.600755\pi$
$284$	−1.98244e8	−0.513553
$285$	0	0
$286$	−4.85679e8	−1.22763
$287$	−4.51904e8	−1.12839
$288$	0	0
$289$	−2.45200e8	−0.597556
$290$	−8.97870e8	−2.16182
$291$	0	0
$292$	−1.13279e9	−2.66261
$293$	1.12840e7	0.0262076	0.0131038	−	0.999914i	$-0.495829\pi$
$293$	1.12840e7	0.0262076	0.0131038	+	0.999914i	$0.495829\pi$
$294$	0	0
$295$	−5.24446e7	−0.118939
$296$	3.56608e8	0.799227
$297$	0	0
$298$	−1.23629e9	−2.70622
$299$	5.62045e7	0.121597
$300$	0	0
$301$	4.35880e8	0.921264
$302$	1.77916e8	0.371699
$303$	0	0
$304$	2.08112e8	0.424855
$305$	−5.96416e7	−0.120365
$306$	0	0
$307$	3.01581e8	0.594867	0.297433	−	0.954743i	$-0.403869\pi$
$307$	3.01581e8	0.594867	0.297433	+	0.954743i	$0.403869\pi$
$308$	9.78961e8	1.90914
$309$	0	0
$310$	−1.24575e9	−2.37500
$311$	−7.94458e8	−1.49765	−0.748824	−	0.662769i	$-0.769381\pi$
$311$	−7.94458e8	−1.49765	−0.748824	+	0.662769i	$0.769381\pi$
$312$	0	0
$313$	9.42174e8	1.73670	0.868352	−	0.495948i	$-0.165179\pi$
$313$	9.42174e8	1.73670	0.868352	+	0.495948i	$0.165179\pi$
$314$	−3.10839e8	−0.566607
$315$	0	0
$316$	8.35459e8	1.48943
$317$	9.46323e7	0.166852	0.0834261	−	0.996514i	$-0.473414\pi$
$317$	9.46323e7	0.166852	0.0834261	+	0.996514i	$0.473414\pi$
$318$	0	0
$319$	−9.31635e8	−1.60686
$320$	8.70626e8	1.48527
$321$	0	0
$322$	−1.88657e8	−0.314903
$323$	−6.69814e8	−1.10598
$324$	0	0
$325$	−7.39083e7	−0.119427
$326$	−1.55082e9	−2.47913
$327$	0	0
$328$	4.85592e8	0.759824
$329$	−2.80137e8	−0.433696
$330$	0	0
$331$	2.56756e8	0.389156	0.194578	−	0.980887i	$-0.437666\pi$
$331$	2.56756e8	0.389156	0.194578	+	0.980887i	$0.437666\pi$
$332$	7.92726e8	1.18889
$333$	0	0
$334$	4.66202e8	0.684639
$335$	−9.04327e8	−1.31422
$336$	0	0
$337$	9.60763e7	0.136745	0.0683725	−	0.997660i	$-0.478219\pi$
$337$	9.60763e7	0.136745	0.0683725	+	0.997660i	$0.478219\pi$
$338$	−5.37318e8	−0.756873
$339$	0	0
$340$	−6.31365e8	−0.871172
$341$	−1.29259e9	−1.76531
$342$	0	0
$343$	5.32265e8	0.712195
$344$	−4.68373e8	−0.620350
$345$	0	0
$346$	5.12521e8	0.665189
$347$	−4.17126e8	−0.535937	−0.267969	−	0.963428i	$-0.586352\pi$
$347$	−4.17126e8	−0.535937	−0.267969	+	0.963428i	$0.586352\pi$
$348$	0	0
$349$	−5.98395e8	−0.753527	−0.376764	−	0.926309i	$-0.622963\pi$
$349$	−5.98395e8	−0.753527	−0.376764	+	0.926309i	$0.622963\pi$
$350$	2.48081e8	0.309283
$351$	0	0
$352$	1.03878e9	1.26947
$353$	1.21639e9	1.47184	0.735921	−	0.677067i	$-0.236749\pi$
$353$	1.21639e9	1.47184	0.735921	+	0.677067i	$0.236749\pi$
$354$	0	0
$355$	2.63107e8	0.312129
$356$	1.40972e9	1.65599
$357$	0	0
$358$	−1.61873e8	−0.186459
$359$	1.46927e8	0.167599	0.0837993	−	0.996483i	$-0.473295\pi$
$359$	1.46927e8	0.167599	0.0837993	+	0.996483i	$0.473295\pi$
$360$	0	0
$361$	1.82295e9	2.03939
$362$	1.61979e9	1.79464
$363$	0	0
$364$	−1.18091e9	−1.28340
$365$	1.50342e9	1.61829
$366$	0	0
$367$	−1.54258e9	−1.62899	−0.814494	−	0.580172i	$-0.802985\pi$
$367$	−1.54258e9	−1.62899	−0.814494	+	0.580172i	$0.802985\pi$
$368$	−3.92250e7	−0.0410295
$369$	0	0
$370$	−1.41394e9	−1.45119
$371$	7.92717e8	0.805952
$372$	0	0
$373$	3.08393e8	0.307697	0.153849	−	0.988094i	$-0.450833\pi$
$373$	3.08393e8	0.307697	0.153849	+	0.988094i	$0.450833\pi$
$374$	−1.09093e9	−1.07832
$375$	0	0
$376$	3.01020e8	0.292037
$377$	1.12382e9	1.08019
$378$	0	0
$379$	−8.49811e8	−0.801835	−0.400918	−	0.916114i	$-0.631309\pi$
$379$	−8.49811e8	−0.801835	−0.400918	+	0.916114i	$0.631309\pi$
$380$	2.56087e9	2.39411
$381$	0	0
$382$	1.34772e9	1.23703
$383$	−8.83511e8	−0.803556	−0.401778	−	0.915737i	$-0.631608\pi$
$383$	−8.83511e8	−0.803556	−0.401778	+	0.915737i	$0.631608\pi$
$384$	0	0
$385$	−1.29927e9	−1.16034
$386$	5.43062e8	0.480612
$387$	0	0
$388$	2.81958e9	2.45061
$389$	1.07810e9	0.928616	0.464308	−	0.885674i	$-0.346303\pi$
$389$	1.07810e9	0.928616	0.464308	+	0.885674i	$0.346303\pi$
$390$	0	0
$391$	1.26247e8	0.106807
$392$	3.77435e8	0.316476
$393$	0	0
$394$	−1.02986e9	−0.848285
$395$	−1.10881e9	−0.905250
$396$	0	0
$397$	−2.25182e9	−1.80620	−0.903101	−	0.429427i	$-0.858715\pi$
$397$	−2.25182e9	−1.80620	−0.903101	+	0.429427i	$0.858715\pi$
$398$	5.91607e7	0.0470373
$399$	0	0
$400$	5.15804e7	0.0402972
$401$	−2.61153e8	−0.202250	−0.101125	−	0.994874i	$-0.532244\pi$
$401$	−2.61153e8	−0.202250	−0.101125	+	0.994874i	$0.532244\pi$
$402$	0	0
$403$	1.55924e9	1.18671
$404$	−5.87461e8	−0.443246
$405$	0	0
$406$	−3.77222e9	−2.79741
$407$	−1.46711e9	−1.07866
$408$	0	0
$409$	3.01019e8	0.217552	0.108776	−	0.994066i	$-0.465307\pi$
$409$	3.01019e8	0.217552	0.108776	+	0.994066i	$0.465307\pi$
$410$	−1.92536e9	−1.37965
$411$	0	0
$412$	−2.87228e9	−2.02343
$413$	−2.20335e8	−0.153907
$414$	0	0
$415$	−1.05210e9	−0.722584
$416$	−1.25306e9	−0.853387
$417$	0	0
$418$	4.42491e9	2.96338
$419$	2.40890e9	1.59982	0.799908	−	0.600123i	$-0.204882\pi$
$419$	2.40890e9	1.59982	0.799908	+	0.600123i	$0.204882\pi$
$420$	0	0
$421$	1.27032e9	0.829711	0.414855	−	0.909887i	$-0.363832\pi$
$421$	1.27032e9	0.829711	0.414855	+	0.909887i	$0.363832\pi$
$422$	1.33796e9	0.866660
$423$	0	0
$424$	−8.51810e8	−0.542703
$425$	−1.66013e8	−0.104901
$426$	0	0
$427$	−2.50572e8	−0.155752
$428$	4.27164e9	2.63355
$429$	0	0
$430$	1.85708e9	1.12640
$431$	−2.24959e9	−1.35342	−0.676710	−	0.736250i	$-0.736595\pi$
$431$	−2.24959e9	−1.35342	−0.676710	+	0.736250i	$0.736595\pi$
$432$	0	0
$433$	1.18429e9	0.701053	0.350527	−	0.936553i	$-0.386003\pi$
$433$	1.18429e9	0.701053	0.350527	+	0.936553i	$0.386003\pi$
$434$	−5.23375e9	−3.07326
$435$	0	0
$436$	−4.75819e8	−0.274940
$437$	−5.12066e8	−0.293522
$438$	0	0
$439$	1.33626e9	0.753818	0.376909	−	0.926250i	$-0.376987\pi$
$439$	1.33626e9	0.753818	0.376909	+	0.926250i	$0.376987\pi$
$440$	1.39612e9	0.781339
$441$	0	0
$442$	1.31598e9	0.724886
$443$	−1.47906e8	−0.0808299	−0.0404149	−	0.999183i	$-0.512868\pi$
$443$	−1.47906e8	−0.0808299	−0.0404149	+	0.999183i	$0.512868\pi$
$444$	0	0
$445$	−1.87096e9	−1.00648
$446$	−5.28585e9	−2.82126
$447$	0	0
$448$	3.65776e9	1.92195
$449$	−2.18342e9	−1.13835	−0.569174	−	0.822217i	$-0.692737\pi$
$449$	−2.18342e9	−1.13835	−0.569174	+	0.822217i	$0.692737\pi$
$450$	0	0
$451$	−1.99776e9	−1.02548
$452$	2.24362e9	1.14278
$453$	0	0
$454$	7.31589e7	0.0366920
$455$	1.56729e9	0.780026
$456$	0	0
$457$	−9.95575e8	−0.487941	−0.243971	−	0.969783i	$-0.578450\pi$
$457$	−9.95575e8	−0.487941	−0.243971	+	0.969783i	$0.578450\pi$
$458$	3.58408e9	1.74320
$459$	0	0
$460$	−4.82672e8	−0.231206
$461$	3.16168e9	1.50302	0.751509	−	0.659722i	$-0.229326\pi$
$461$	3.16168e9	1.50302	0.751509	+	0.659722i	$0.229326\pi$
$462$	0	0
$463$	3.01390e9	1.41122	0.705612	−	0.708599i	$-0.250672\pi$
$463$	3.01390e9	1.41122	0.705612	+	0.708599i	$0.250672\pi$
$464$	−7.84310e8	−0.364481
$465$	0	0
$466$	1.76408e9	0.807547
$467$	−8.11607e8	−0.368754	−0.184377	−	0.982856i	$-0.559027\pi$
$467$	−8.11607e8	−0.368754	−0.184377	+	0.982856i	$0.559027\pi$
$468$	0	0
$469$	−3.79935e9	−1.70061
$470$	−1.19354e9	−0.530265
$471$	0	0
$472$	2.36761e8	0.103636
$473$	1.92692e9	0.837240
$474$	0	0
$475$	6.73361e8	0.288284
$476$	−2.65255e9	−1.12730
$477$	0	0
$478$	5.49112e9	2.29966
$479$	2.44233e9	1.01538	0.507692	−	0.861538i	$-0.330499\pi$
$479$	2.44233e9	1.01538	0.507692	+	0.861538i	$0.330499\pi$
$480$	0	0
$481$	1.76976e9	0.725113
$482$	5.91360e9	2.40540
$483$	0	0
$484$	5.78366e8	0.231870
$485$	−3.74212e9	−1.48944
$486$	0	0
$487$	−1.11140e8	−0.0436032	−0.0218016	−	0.999762i	$-0.506940\pi$
$487$	−1.11140e8	−0.0436032	−0.0218016	+	0.999762i	$0.506940\pi$
$488$	2.69251e8	0.104879
$489$	0	0
$490$	−1.49652e9	−0.574640
$491$	1.10060e9	0.419607	0.209804	−	0.977744i	$-0.432718\pi$
$491$	1.10060e9	0.419607	0.209804	+	0.977744i	$0.432718\pi$
$492$	0	0
$493$	2.52432e9	0.948812
$494$	−5.33770e9	−1.99209
$495$	0	0
$496$	−1.08819e9	−0.400422
$497$	1.10539e9	0.403896
$498$	0	0
$499$	1.19831e9	0.431735	0.215867	−	0.976423i	$-0.430742\pi$
$499$	1.19831e9	0.431735	0.215867	+	0.976423i	$0.430742\pi$
$500$	4.47307e9	1.60034
$501$	0	0
$502$	7.68617e9	2.71173
$503$	4.77486e8	0.167291	0.0836456	−	0.996496i	$-0.473344\pi$
$503$	4.77486e8	0.167291	0.0836456	+	0.996496i	$0.473344\pi$
$504$	0	0
$505$	7.79673e8	0.269397
$506$	−8.34006e8	−0.286182
$507$	0	0
$508$	−6.68750e9	−2.26329
$509$	1.61594e9	0.543140	0.271570	−	0.962419i	$-0.412457\pi$
$509$	1.61594e9	0.543140	0.271570	+	0.962419i	$0.412457\pi$
$510$	0	0
$511$	6.31633e9	2.09407
$512$	1.46367e9	0.481945
$513$	0	0
$514$	5.40509e9	1.75562
$515$	3.81207e9	1.22980
$516$	0	0
$517$	−1.23842e9	−0.394140
$518$	−5.94038e9	−1.87785
$519$	0	0
$520$	−1.68412e9	−0.525245
$521$	−2.28015e9	−0.706368	−0.353184	−	0.935554i	$-0.614901\pi$
$521$	−2.28015e9	−0.706368	−0.353184	+	0.935554i	$0.614901\pi$
$522$	0	0
$523$	−4.17653e8	−0.127661	−0.0638307	−	0.997961i	$-0.520332\pi$
$523$	−4.17653e8	−0.127661	−0.0638307	+	0.997961i	$0.520332\pi$
$524$	2.04469e9	0.620824
$525$	0	0
$526$	1.29407e9	0.387710
$527$	3.50235e9	1.04237
$528$	0	0
$529$	−3.30831e9	−0.971654
$530$	3.37740e9	0.985410
$531$	0	0
$532$	1.07590e10	3.09799
$533$	2.40987e9	0.689364
$534$	0	0
$535$	−5.66928e9	−1.60062
$536$	4.08257e9	1.14514
$537$	0	0
$538$	−2.61510e9	−0.724019
$539$	−1.55280e9	−0.427124
$540$	0	0
$541$	7.14439e9	1.93988	0.969940	−	0.243346i	$-0.0782450\pi$
$541$	7.14439e9	1.93988	0.969940	+	0.243346i	$0.0782450\pi$
$542$	−5.14255e9	−1.38734
$543$	0	0
$544$	−2.81463e9	−0.749592
$545$	6.31502e8	0.167104
$546$	0	0
$547$	−1.90559e9	−0.497822	−0.248911	−	0.968526i	$-0.580073\pi$
$547$	−1.90559e9	−0.497822	−0.248911	+	0.968526i	$0.580073\pi$
$548$	8.93622e9	2.31965
$549$	0	0
$550$	1.09671e9	0.281075
$551$	−1.02388e10	−2.60748
$552$	0	0
$553$	−4.65846e9	−1.17140
$554$	5.63551e9	1.40815
$555$	0	0
$556$	−3.37592e9	−0.832971
$557$	8.13950e9	1.99574	0.997872	−	0.0652056i	$-0.0207703\pi$
$557$	8.13950e9	1.99574	0.997872	+	0.0652056i	$0.0207703\pi$
$558$	0	0
$559$	−2.32442e9	−0.562824
$560$	−1.09381e9	−0.263198
$561$	0	0
$562$	−1.30353e10	−3.09772
$563$	−3.38360e9	−0.799098	−0.399549	−	0.916712i	$-0.630833\pi$
$563$	−3.38360e9	−0.799098	−0.399549	+	0.916712i	$0.630833\pi$
$564$	0	0
$565$	−2.97771e9	−0.694564
$566$	−4.24883e9	−0.984944
$567$	0	0
$568$	−1.18779e9	−0.271971
$569$	−1.41168e9	−0.321250	−0.160625	−	0.987016i	$-0.551351\pi$
$569$	−1.41168e9	−0.321250	−0.160625	+	0.987016i	$0.551351\pi$
$570$	0	0
$571$	3.06389e9	0.688726	0.344363	−	0.938837i	$-0.388095\pi$
$571$	3.06389e9	0.688726	0.344363	+	0.938837i	$0.388095\pi$
$572$	−5.22051e9	−1.16634
$573$	0	0
$574$	−8.08900e9	−1.78527
$575$	−1.26915e8	−0.0278404
$576$	0	0
$577$	5.11879e9	1.10931	0.554653	−	0.832082i	$-0.312851\pi$
$577$	5.11879e9	1.10931	0.554653	+	0.832082i	$0.312851\pi$
$578$	−4.38904e9	−0.945414
$579$	0	0
$580$	−9.65110e9	−2.05390
$581$	−4.42018e9	−0.935026
$582$	0	0
$583$	3.50441e9	0.732445
$584$	−6.78718e9	−1.41008
$585$	0	0
$586$	2.01982e8	0.0414639
$587$	−5.18384e9	−1.05784	−0.528918	−	0.848673i	$-0.677402\pi$
$587$	−5.18384e9	−1.05784	−0.528918	+	0.848673i	$0.677402\pi$
$588$	0	0
$589$	−1.42058e10	−2.86459
$590$	−9.38748e8	−0.188177
$591$	0	0
$592$	−1.23511e9	−0.244669
$593$	−5.88946e9	−1.15980	−0.579902	−	0.814686i	$-0.696909\pi$
$593$	−5.88946e9	−1.15980	−0.579902	+	0.814686i	$0.696909\pi$
$594$	0	0
$595$	3.52044e9	0.685153
$596$	−1.32887e10	−2.57112
$597$	0	0
$598$	1.00605e9	0.192382
$599$	−1.29167e9	−0.245561	−0.122780	−	0.992434i	$-0.539181\pi$
$599$	−1.29167e9	−0.245561	−0.122780	+	0.992434i	$0.539181\pi$
$600$	0	0
$601$	−4.79647e9	−0.901282	−0.450641	−	0.892705i	$-0.648805\pi$
$601$	−4.79647e9	−0.901282	−0.450641	+	0.892705i	$0.648805\pi$
$602$	7.80216e9	1.45756
$603$	0	0
$604$	1.91240e9	0.353142
$605$	−7.67602e8	−0.140926
$606$	0	0
$607$	−3.30008e9	−0.598914	−0.299457	−	0.954110i	$-0.596805\pi$
$607$	−3.30008e9	−0.598914	−0.299457	+	0.954110i	$0.596805\pi$
$608$	1.14164e10	2.05999
$609$	0	0
$610$	−1.06757e9	−0.190433
$611$	1.49389e9	0.264956
$612$	0	0
$613$	2.21730e9	0.388788	0.194394	−	0.980924i	$-0.437726\pi$
$613$	2.21730e9	0.388788	0.194394	+	0.980924i	$0.437726\pi$
$614$	5.39824e9	0.941159
$615$	0	0
$616$	5.86553e9	1.01105
$617$	3.08716e9	0.529128	0.264564	−	0.964368i	$-0.414772\pi$
$617$	3.08716e9	0.529128	0.264564	+	0.964368i	$0.414772\pi$
$618$	0	0
$619$	4.78027e9	0.810094	0.405047	−	0.914296i	$-0.367255\pi$
$619$	4.78027e9	0.810094	0.405047	+	0.914296i	$0.367255\pi$
$620$	−1.33904e10	−2.25643
$621$	0	0
$622$	−1.42206e10	−2.36948
$623$	−7.86047e9	−1.30239
$624$	0	0
$625$	−4.92735e9	−0.807298
$626$	1.68647e10	2.74770
$627$	0	0
$628$	−3.34117e9	−0.538319
$629$	3.97522e9	0.636919
$630$	0	0
$631$	−4.87262e9	−0.772075	−0.386037	−	0.922483i	$-0.626156\pi$
$631$	−4.87262e9	−0.772075	−0.386037	+	0.922483i	$0.626156\pi$
$632$	5.00573e9	0.788782
$633$	0	0
$634$	1.69390e9	0.263982
$635$	8.87559e9	1.37559
$636$	0	0
$637$	1.87312e9	0.287129
$638$	−1.66761e10	−2.54227
$639$	0	0
$640$	8.42504e9	1.27040
$641$	−2.85862e9	−0.428700	−0.214350	−	0.976757i	$-0.568763\pi$
$641$	−2.85862e9	−0.428700	−0.214350	+	0.976757i	$0.568763\pi$
$642$	0	0
$643$	−7.22075e9	−1.07113	−0.535567	−	0.844493i	$-0.679902\pi$
$643$	−7.22075e9	−1.07113	−0.535567	+	0.844493i	$0.679902\pi$
$644$	−2.02785e9	−0.299182
$645$	0	0
$646$	−1.19895e10	−1.74980
$647$	4.74606e8	0.0688919	0.0344460	−	0.999407i	$-0.489033\pi$
$647$	4.74606e8	0.0688919	0.0344460	+	0.999407i	$0.489033\pi$
$648$	0	0
$649$	−9.74051e8	−0.139870
$650$	−1.32294e9	−0.188949
$651$	0	0
$652$	−1.66696e10	−2.35536
$653$	2.58487e9	0.363281	0.181640	−	0.983365i	$-0.441859\pi$
$653$	2.58487e9	0.363281	0.181640	+	0.983365i	$0.441859\pi$
$654$	0	0
$655$	−2.71370e9	−0.377326
$656$	−1.68184e9	−0.232607
$657$	0	0
$658$	−5.01440e9	−0.686164
$659$	−2.68455e9	−0.365404	−0.182702	−	0.983168i	$-0.558484\pi$
$659$	−2.68455e9	−0.365404	−0.182702	+	0.983168i	$0.558484\pi$
$660$	0	0
$661$	−9.19497e9	−1.23835	−0.619177	−	0.785251i	$-0.712534\pi$
$661$	−9.19497e9	−1.23835	−0.619177	+	0.785251i	$0.712534\pi$
$662$	4.59589e9	0.615696
$663$	0	0
$664$	4.74969e9	0.629618
$665$	−1.42792e10	−1.88290
$666$	0	0
$667$	1.92982e9	0.251812
$668$	5.01115e9	0.650459
$669$	0	0
$670$	−1.61873e10	−2.07928
$671$	−1.10772e9	−0.141547
$672$	0	0
$673$	1.23253e10	1.55863	0.779317	−	0.626630i	$-0.215566\pi$
$673$	1.23253e10	1.55863	0.779317	+	0.626630i	$0.215566\pi$
$674$	1.71975e9	0.216349
$675$	0	0
$676$	−5.77557e9	−0.719087
$677$	−1.51222e10	−1.87307	−0.936537	−	0.350569i	$-0.885988\pi$
$677$	−1.51222e10	−1.87307	−0.936537	+	0.350569i	$0.885988\pi$
$678$	0	0
$679$	−1.57218e10	−1.92733
$680$	−3.78288e9	−0.461361
$681$	0	0
$682$	−2.31371e10	−2.79296
$683$	2.68739e9	0.322745	0.161372	−	0.986894i	$-0.448408\pi$
$683$	2.68739e9	0.322745	0.161372	+	0.986894i	$0.448408\pi$
$684$	0	0
$685$	−1.18601e10	−1.40984
$686$	9.52744e9	1.12679
$687$	0	0
$688$	1.62220e9	0.189909
$689$	−4.22732e9	−0.492377
$690$	0	0
$691$	−9.07091e9	−1.04587	−0.522935	−	0.852373i	$-0.675163\pi$
$691$	−9.07091e9	−1.04587	−0.522935	+	0.852373i	$0.675163\pi$
$692$	5.50903e9	0.631980
$693$	0	0
$694$	−7.46647e9	−0.847924
$695$	4.48048e9	0.506265
$696$	0	0
$697$	5.41305e9	0.605518
$698$	−1.07111e10	−1.19218
$699$	0	0
$700$	2.66660e9	0.293842
$701$	−2.72996e9	−0.299326	−0.149663	−	0.988737i	$-0.547819\pi$
$701$	−2.72996e9	−0.299326	−0.149663	+	0.988737i	$0.547819\pi$
$702$	0	0
$703$	−1.61238e10	−1.75035
$704$	1.61701e10	1.74666
$705$	0	0
$706$	2.17731e10	2.32865
$707$	3.27564e9	0.348601
$708$	0	0
$709$	−9.03726e8	−0.0952302	−0.0476151	−	0.998866i	$-0.515162\pi$
$709$	−9.03726e8	−0.0952302	−0.0476151	+	0.998866i	$0.515162\pi$
$710$	4.70957e9	0.493829
$711$	0	0
$712$	8.44644e9	0.876988
$713$	2.67752e9	0.276642
$714$	0	0
$715$	6.92861e9	0.708883
$716$	−1.73996e9	−0.177151
$717$	0	0
$718$	2.62996e9	0.265164
$719$	6.51161e9	0.653337	0.326668	−	0.945139i	$-0.394074\pi$
$719$	6.51161e9	0.653337	0.326668	+	0.945139i	$0.394074\pi$
$720$	0	0
$721$	1.60156e10	1.59137
$722$	3.26304e10	3.22658
$723$	0	0
$724$	1.74109e10	1.70505
$725$	−2.53769e9	−0.247318
$726$	0	0
$727$	−6.14813e9	−0.593435	−0.296717	−	0.954965i	$-0.595892\pi$
$727$	−6.14813e9	−0.593435	−0.296717	+	0.954965i	$0.595892\pi$
$728$	−7.07550e9	−0.679669
$729$	0	0
$730$	2.69110e10	2.56035
$731$	−5.22110e9	−0.494369
$732$	0	0
$733$	2.71313e9	0.254452	0.127226	−	0.991874i	$-0.459393\pi$
$733$	2.71313e9	0.254452	0.127226	+	0.991874i	$0.459393\pi$
$734$	−2.76120e10	−2.57728
$735$	0	0
$736$	−2.15176e9	−0.198939
$737$	−1.67960e10	−1.54550
$738$	0	0
$739$	1.10553e10	1.00766	0.503831	−	0.863802i	$-0.331924\pi$
$739$	1.10553e10	1.00766	0.503831	+	0.863802i	$0.331924\pi$
$740$	−1.51983e10	−1.37874
$741$	0	0
$742$	1.41895e10	1.27512
$743$	−1.67697e10	−1.49991	−0.749954	−	0.661490i	$-0.769925\pi$
$743$	−1.67697e10	−1.49991	−0.749954	+	0.661490i	$0.769925\pi$
$744$	0	0
$745$	1.76367e10	1.56268
$746$	5.52017e9	0.486818
$747$	0	0
$748$	−1.17263e10	−1.02448
$749$	−2.38183e10	−2.07121
$750$	0	0
$751$	7.82494e9	0.674126	0.337063	−	0.941482i	$-0.390566\pi$
$751$	7.82494e9	0.674126	0.337063	+	0.941482i	$0.390566\pi$
$752$	−1.04258e9	−0.0894020
$753$	0	0
$754$	2.01161e10	1.70901
$755$	−2.53812e9	−0.214634
$756$	0	0
$757$	1.40665e10	1.17856	0.589279	−	0.807930i	$-0.299412\pi$
$757$	1.40665e10	1.17856	0.589279	+	0.807930i	$0.299412\pi$
$758$	−1.52115e10	−1.26861
$759$	0	0
$760$	1.53437e10	1.26789
$761$	4.85071e9	0.398987	0.199493	−	0.979899i	$-0.436070\pi$
$761$	4.85071e9	0.398987	0.199493	+	0.979899i	$0.436070\pi$
$762$	0	0
$763$	2.65313e9	0.216233
$764$	1.44865e10	1.17527
$765$	0	0
$766$	−1.58147e10	−1.27133
$767$	1.17498e9	0.0940260
$768$	0	0
$769$	9.60096e9	0.761329	0.380665	−	0.924713i	$-0.375695\pi$
$769$	9.60096e9	0.761329	0.380665	+	0.924713i	$0.375695\pi$
$770$	−2.32566e10	−1.83582
$771$	0	0
$772$	5.83731e9	0.456617
$773$	2.04008e10	1.58862	0.794309	−	0.607514i	$-0.207833\pi$
$773$	2.04008e10	1.58862	0.794309	+	0.607514i	$0.207833\pi$
$774$	0	0
$775$	−3.52090e9	−0.271705
$776$	1.68938e10	1.29781
$777$	0	0
$778$	1.92978e10	1.46919
$779$	−2.19558e10	−1.66405
$780$	0	0
$781$	4.88668e9	0.367058
$782$	2.25979e9	0.168983
$783$	0	0
$784$	−1.30724e9	−0.0968836
$785$	4.43437e9	0.327181
$786$	0	0
$787$	1.60432e10	1.17322	0.586608	−	0.809871i	$-0.300463\pi$
$787$	1.60432e10	1.17322	0.586608	+	0.809871i	$0.300463\pi$
$788$	−1.10699e10	−0.805935
$789$	0	0
$790$	−1.98475e10	−1.43223
$791$	−1.25102e10	−0.898768
$792$	0	0
$793$	1.33623e9	0.0951532
$794$	−4.03071e10	−2.85765
$795$	0	0
$796$	6.35911e8	0.0446890
$797$	1.85146e10	1.29542	0.647711	−	0.761886i	$-0.275727\pi$
$797$	1.85146e10	1.29542	0.647711	+	0.761886i	$0.275727\pi$
$798$	0	0
$799$	3.35557e9	0.232730
$800$	2.82953e9	0.195389
$801$	0	0
$802$	−4.67458e9	−0.319987
$803$	2.79230e10	1.90308
$804$	0	0
$805$	2.69134e9	0.181838
$806$	2.79100e10	1.87753
$807$	0	0
$808$	−3.51983e9	−0.234737
$809$	−1.01950e9	−0.0676968	−0.0338484	−	0.999427i	$-0.510776\pi$
$809$	−1.01950e9	−0.0676968	−0.0338484	+	0.999427i	$0.510776\pi$
$810$	0	0
$811$	2.10382e10	1.38496	0.692478	−	0.721439i	$-0.256519\pi$
$811$	2.10382e10	1.38496	0.692478	+	0.721439i	$0.256519\pi$
$812$	−4.05472e10	−2.65775
$813$	0	0
$814$	−2.62610e10	−1.70658
$815$	2.21237e10	1.43155
$816$	0	0
$817$	2.11772e10	1.35860
$818$	5.38818e9	0.344196
$819$	0	0
$820$	−2.06954e10	−1.31077
$821$	−4.64433e9	−0.292902	−0.146451	−	0.989218i	$-0.546785\pi$
$821$	−4.64433e9	−0.292902	−0.146451	+	0.989218i	$0.546785\pi$
$822$	0	0
$823$	−5.01145e9	−0.313375	−0.156687	−	0.987648i	$-0.550081\pi$
$823$	−5.01145e9	−0.313375	−0.156687	+	0.987648i	$0.550081\pi$
$824$	−1.72095e10	−1.07158
$825$	0	0
$826$	−3.94396e9	−0.243502
$827$	2.72122e10	1.67300	0.836498	−	0.547970i	$-0.184599\pi$
$827$	2.72122e10	1.67300	0.836498	+	0.547970i	$0.184599\pi$
$828$	0	0
$829$	3.17275e10	1.93417	0.967086	−	0.254450i	$-0.0818943\pi$
$829$	3.17275e10	1.93417	0.967086	+	0.254450i	$0.0818943\pi$
$830$	−1.88324e10	−1.14322
$831$	0	0
$832$	−1.95057e10	−1.17417
$833$	4.20739e9	0.252206
$834$	0	0
$835$	−6.65076e9	−0.395338
$836$	4.75628e10	2.81544
$837$	0	0
$838$	4.31189e10	2.53112
$839$	3.12839e9	0.182875	0.0914374	−	0.995811i	$-0.470854\pi$
$839$	3.12839e9	0.182875	0.0914374	+	0.995811i	$0.470854\pi$
$840$	0	0
$841$	2.13371e10	1.23694
$842$	2.27385e10	1.31271
$843$	0	0
$844$	1.43815e10	0.823393
$845$	7.66529e9	0.437049
$846$	0	0
$847$	−3.22492e9	−0.182359
$848$	2.95024e9	0.166139
$849$	0	0
$850$	−2.97160e9	−0.165968
$851$	3.03902e9	0.169036
$852$	0	0
$853$	−3.10920e10	−1.71525	−0.857623	−	0.514278i	$-0.828060\pi$
$853$	−3.10920e10	−1.71525	−0.857623	+	0.514278i	$0.828060\pi$
$854$	−4.48519e9	−0.246421
$855$	0	0
$856$	2.55939e10	1.39469
$857$	6.63199e9	0.359924	0.179962	−	0.983674i	$-0.442403\pi$
$857$	6.63199e9	0.359924	0.179962	+	0.983674i	$0.442403\pi$
$858$	0	0
$859$	2.04251e9	0.109948	0.0549741	−	0.998488i	$-0.482492\pi$
$859$	2.04251e9	0.109948	0.0549741	+	0.998488i	$0.482492\pi$
$860$	1.99616e10	1.07016
$861$	0	0
$862$	−4.02672e10	−2.14129
$863$	−6.09687e8	−0.0322901	−0.0161450	−	0.999870i	$-0.505139\pi$
$863$	−6.09687e8	−0.0322901	−0.0161450	+	0.999870i	$0.505139\pi$
$864$	0	0
$865$	−7.31153e9	−0.384107
$866$	2.11986e10	1.10916
$867$	0	0
$868$	−5.62569e10	−2.91983
$869$	−2.05939e10	−1.06456
$870$	0	0
$871$	2.02608e10	1.03895
$872$	−2.85091e9	−0.145605
$873$	0	0
$874$	−9.16589e9	−0.464392
$875$	−2.49415e10	−1.25862
$876$	0	0
$877$	−1.17372e10	−0.587580	−0.293790	−	0.955870i	$-0.594917\pi$
$877$	−1.17372e10	−0.587580	−0.293790	+	0.955870i	$0.594917\pi$
$878$	2.39189e10	1.19264
$879$	0	0
$880$	−4.83546e9	−0.239193
$881$	−3.53359e10	−1.74101	−0.870504	−	0.492162i	$-0.836207\pi$
$881$	−3.53359e10	−1.74101	−0.870504	+	0.492162i	$0.836207\pi$
$882$	0	0
$883$	2.20915e10	1.07985	0.539924	−	0.841714i	$-0.318453\pi$
$883$	2.20915e10	1.07985	0.539924	+	0.841714i	$0.318453\pi$
$884$	1.41453e10	0.688697
$885$	0	0
$886$	−2.64748e9	−0.127884
$887$	2.64826e10	1.27417	0.637085	−	0.770793i	$-0.280140\pi$
$887$	2.64826e10	1.27417	0.637085	+	0.770793i	$0.280140\pi$
$888$	0	0
$889$	3.72890e10	1.78002
$890$	−3.34899e10	−1.59239
$891$	0	0
$892$	−5.68170e10	−2.68041
$893$	−1.36105e10	−0.639577
$894$	0	0
$895$	2.30925e9	0.107669
$896$	3.53961e10	1.64391
$897$	0	0
$898$	−3.90828e10	−1.80102
$899$	5.35373e10	2.45752
$900$	0	0
$901$	−9.49541e9	−0.432491
$902$	−3.57595e10	−1.62244
$903$	0	0
$904$	1.34428e10	0.605202
$905$	−2.31076e10	−1.03630
$906$	0	0
$907$	−1.70454e10	−0.758547	−0.379274	−	0.925285i	$-0.623826\pi$
$907$	−1.70454e10	−0.758547	−0.379274	+	0.925285i	$0.623826\pi$
$908$	7.86377e8	0.0348602
$909$	0	0
$910$	2.80542e10	1.23411
$911$	3.21064e10	1.40695	0.703473	−	0.710722i	$-0.251632\pi$
$911$	3.21064e10	1.40695	0.703473	+	0.710722i	$0.251632\pi$
$912$	0	0
$913$	−1.95406e10	−0.849747
$914$	−1.78206e10	−0.771988
$915$	0	0
$916$	3.85248e10	1.65618
$917$	−1.14011e10	−0.488261
$918$	0	0
$919$	9.83116e8	0.0417831	0.0208915	−	0.999782i	$-0.493350\pi$
$919$	9.83116e8	0.0417831	0.0208915	+	0.999782i	$0.493350\pi$
$920$	−2.89197e9	−0.122444
$921$	0	0
$922$	5.65934e10	2.37798
$923$	−5.89473e9	−0.246750
$924$	0	0
$925$	−3.99628e9	−0.166020
$926$	5.39483e10	2.23274
$927$	0	0
$928$	−4.30247e10	−1.76726
$929$	−1.58139e10	−0.647119	−0.323559	−	0.946208i	$-0.604880\pi$
$929$	−1.58139e10	−0.647119	−0.323559	+	0.946208i	$0.604880\pi$
$930$	0	0
$931$	−1.70655e10	−0.693100
$932$	1.89619e10	0.767231
$933$	0	0
$934$	−1.45276e10	−0.583418
$935$	1.55630e10	0.622664
$936$	0	0
$937$	1.93290e10	0.767576	0.383788	−	0.923421i	$-0.374619\pi$
$937$	1.93290e10	0.767576	0.383788	+	0.923421i	$0.374619\pi$
$938$	−6.80076e10	−2.69059
$939$	0	0
$940$	−1.28292e10	−0.503792
$941$	1.84380e9	0.0721356	0.0360678	−	0.999349i	$-0.488517\pi$
$941$	1.84380e9	0.0721356	0.0360678	+	0.999349i	$0.488517\pi$
$942$	0	0
$943$	4.13822e9	0.160703
$944$	−8.20018e8	−0.0317264
$945$	0	0
$946$	3.44915e10	1.32463
$947$	3.45923e10	1.32359	0.661797	−	0.749683i	$-0.269794\pi$
$947$	3.45923e10	1.32359	0.661797	+	0.749683i	$0.269794\pi$
$948$	0	0
$949$	−3.36831e10	−1.27932
$950$	1.20530e10	0.456104
$951$	0	0
$952$	−1.58930e10	−0.597003
$953$	2.99406e10	1.12056	0.560281	−	0.828303i	$-0.310693\pi$
$953$	2.99406e10	1.12056	0.560281	+	0.828303i	$0.310693\pi$
$954$	0	0
$955$	−1.92264e10	−0.714309
$956$	5.90234e10	2.18485
$957$	0	0
$958$	4.37173e10	1.60647
$959$	−4.98277e10	−1.82434
$960$	0	0
$961$	4.67675e10	1.69986
$962$	3.16783e10	1.14723
$963$	0	0
$964$	6.35646e10	2.28531
$965$	−7.74723e9	−0.277524
$966$	0	0
$967$	3.35194e9	0.119207	0.0596037	−	0.998222i	$-0.481016\pi$
$967$	3.35194e9	0.119207	0.0596037	+	0.998222i	$0.481016\pi$
$968$	3.46533e9	0.122795
$969$	0	0
$970$	−6.69832e10	−2.35649
$971$	−3.76669e10	−1.32036	−0.660180	−	0.751107i	$-0.729520\pi$
$971$	−3.76669e10	−1.32036	−0.660180	+	0.751107i	$0.729520\pi$
$972$	0	0
$973$	1.88239e10	0.655109
$974$	−1.98938e9	−0.0689861
$975$	0	0
$976$	−9.32548e8	−0.0321068
$977$	−2.34371e10	−0.804030	−0.402015	−	0.915633i	$-0.631690\pi$
$977$	−2.34371e10	−0.804030	−0.402015	+	0.915633i	$0.631690\pi$
$978$	0	0
$979$	−3.47493e10	−1.18360
$980$	−1.60859e10	−0.545952
$981$	0	0
$982$	1.97005e10	0.663875
$983$	−3.82382e10	−1.28399	−0.641993	−	0.766710i	$-0.721892\pi$
$983$	−3.82382e10	−1.28399	−0.641993	+	0.766710i	$0.721892\pi$
$984$	0	0
$985$	1.46918e10	0.489833
$986$	4.51848e10	1.50115
$987$	0	0
$988$	−5.73743e10	−1.89264
$989$	−3.99148e9	−0.131204
$990$	0	0
$991$	5.46278e10	1.78302	0.891510	−	0.453001i	$-0.149647\pi$
$991$	5.46278e10	1.78302	0.891510	+	0.453001i	$0.149647\pi$
$992$	−5.96944e10	−1.94152
$993$	0	0
$994$	1.97863e10	0.639017
$995$	−8.43975e8	−0.0271612
$996$	0	0
$997$	−2.14509e10	−0.685507	−0.342753	−	0.939425i	$-0.611360\pi$
$997$	−2.14509e10	−0.685507	−0.342753	+	0.939425i	$0.611360\pi$
$998$	2.14495e10	0.683062
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+17.8998 q^{2} +192.403 q^{4} -255.355 q^{5} -1072.82 q^{7} +1152.80 q^{8} +O(q^{10})\)	\(q+17.8998 q^{2} +192.403 q^{4} -255.355 q^{5} -1072.82 q^{7} +1152.80 q^{8} -4570.81 q^{10} -4742.70 q^{11} +5721.05 q^{13} -19203.3 q^{14} -3992.71 q^{16} +12850.6 q^{17} -52123.1 q^{19} -49131.1 q^{20} -84893.4 q^{22} +9824.17 q^{23} -12918.7 q^{25} +102406. q^{26} -206414. q^{28} +196436. q^{29} +272544. q^{31} -219027. q^{32} +230023. q^{34} +273951. q^{35} +309341. q^{37} -932994. q^{38} -294373. q^{40} +421229. q^{41} -406292. q^{43} -912509. q^{44} +175851. q^{46} +261121. q^{47} +327408. q^{49} -231242. q^{50} +1.10075e6 q^{52} -738907. q^{53} +1.21107e6 q^{55} -1.23675e6 q^{56} +3.51616e6 q^{58} +205379. q^{59} +233563. q^{61} +4.87848e6 q^{62} -3.40947e6 q^{64} -1.46090e6 q^{65} +3.54145e6 q^{67} +2.47250e6 q^{68} +4.90367e6 q^{70} -1.03036e6 q^{71} -5.88757e6 q^{73} +5.53715e6 q^{74} -1.00286e7 q^{76} +5.08808e6 q^{77} +4.34224e6 q^{79} +1.01956e6 q^{80} +7.53991e6 q^{82} +4.12014e6 q^{83} -3.28147e6 q^{85} -7.27255e6 q^{86} -5.46737e6 q^{88} +7.32690e6 q^{89} -6.13768e6 q^{91} +1.89020e6 q^{92} +4.67402e6 q^{94} +1.33099e7 q^{95} +1.46546e7 q^{97} +5.86054e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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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