LMFDB - Embedded newform 531.8.a.b.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:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\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			$16.2952$ 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)

$f(q)$	$=$	$q+16.2952 q^{2} +137.534 q^{4} -495.569 q^{5} +565.301 q^{7} +155.363 q^{8} +O(q^{10})$	\(q+16.2952 q^{2} +137.534 q^{4} -495.569 q^{5} +565.301 q^{7} +155.363 q^{8} -8075.41 q^{10} +826.834 q^{11} +11479.1 q^{13} +9211.71 q^{14} -15072.7 q^{16} +23564.6 q^{17} -53546.6 q^{19} -68157.8 q^{20} +13473.4 q^{22} +87155.1 q^{23} +167464. q^{25} +187055. q^{26} +77748.3 q^{28} -26745.6 q^{29} -231681. q^{31} -265500. q^{32} +383990. q^{34} -280146. q^{35} +409893. q^{37} -872554. q^{38} -76993.4 q^{40} -189635. q^{41} -849460. q^{43} +113718. q^{44} +1.42021e6 q^{46} +902990. q^{47} -503977. q^{49} +2.72886e6 q^{50} +1.57877e6 q^{52} +324949. q^{53} -409753. q^{55} +87827.2 q^{56} -435826. q^{58} -205379. q^{59} -1.58592e6 q^{61} -3.77529e6 q^{62} -2.39707e6 q^{64} -5.68870e6 q^{65} -2.57819e6 q^{67} +3.24094e6 q^{68} -4.56504e6 q^{70} +678037. q^{71} +2.50036e6 q^{73} +6.67930e6 q^{74} -7.36449e6 q^{76} +467410. q^{77} -7.33035e6 q^{79} +7.46957e6 q^{80} -3.09015e6 q^{82} -3.91602e6 q^{83} -1.16779e7 q^{85} -1.38421e7 q^{86} +128460. q^{88} -3.80382e6 q^{89} +6.48916e6 q^{91} +1.19868e7 q^{92} +1.47144e7 q^{94} +2.65361e7 q^{95} -7.68854e6 q^{97} -8.21243e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) $ 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * 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 $

$2$	16.2952	1.44031	0.720154	−	0.693814i	$-0.244071\pi$
$2$	16.2952	1.44031	0.720154	+	0.693814i	$0.244071\pi$
$3$	0	0
$3$	0	0
$4$	137.534	1.07449
$5$	−495.569	−1.77300	−0.886502	−	0.462726i	$-0.846872\pi$
$5$	−495.569	−1.77300	−0.886502	+	0.462726i	$0.846872\pi$
$6$	0	0
$7$	565.301	0.622927	0.311463	−	0.950258i	$-0.399181\pi$
$7$	565.301	0.622927	0.311463	+	0.950258i	$0.399181\pi$
$8$	155.363	0.107284
$9$	0	0
$10$	−8075.41	−2.55367
$11$	826.834	0.187303	0.0936513	−	0.995605i	$-0.470146\pi$
$11$	826.834	0.187303	0.0936513	+	0.995605i	$0.470146\pi$
$12$	0	0
$13$	11479.1	1.44913	0.724564	−	0.689207i	$-0.242041\pi$
$13$	11479.1	1.44913	0.724564	+	0.689207i	$0.242041\pi$
$14$	9211.71	0.897206
$15$	0	0
$16$	−15072.7	−0.919965
$17$	23564.6	1.16329	0.581646	−	0.813442i	$-0.302409\pi$
$17$	23564.6	1.16329	0.581646	+	0.813442i	$0.302409\pi$
$18$	0	0
$19$	−53546.6	−1.79099	−0.895497	−	0.445067i	$-0.853180\pi$
$19$	−53546.6	−1.79099	−0.895497	+	0.445067i	$0.853180\pi$
$20$	−68157.8	−1.90507
$21$	0	0
$22$	13473.4	0.269773
$23$	87155.1	1.49364	0.746819	−	0.665028i	$-0.231580\pi$
$23$	87155.1	1.49364	0.746819	+	0.665028i	$0.231580\pi$
$24$	0	0
$25$	167464.	2.14354
$26$	187055.	2.08719
$27$	0	0
$28$	77748.3	0.669326
$29$	−26745.6	−0.203638	−0.101819	−	0.994803i	$-0.532466\pi$
$29$	−26745.6	−0.203638	−0.101819	+	0.994803i	$0.532466\pi$
$30$	0	0
$31$	−231681.	−1.39677	−0.698384	−	0.715723i	$-0.746097\pi$
$31$	−231681.	−1.39677	−0.698384	+	0.715723i	$0.746097\pi$
$32$	−265500.	−1.43232
$33$	0	0
$34$	383990.	1.67550
$35$	−280146.	−1.10445
$36$	0	0
$37$	409893.	1.33035	0.665173	−	0.746689i	$-0.268358\pi$
$37$	409893.	1.33035	0.665173	+	0.746689i	$0.268358\pi$
$38$	−872554.	−2.57958
$39$	0	0
$40$	−76993.4	−0.190214
$41$	−189635.	−0.429710	−0.214855	−	0.976646i	$-0.568928\pi$
$41$	−189635.	−0.429710	−0.214855	+	0.976646i	$0.568928\pi$
$42$	0	0
$43$	−849460.	−1.62931	−0.814654	−	0.579947i	$-0.803073\pi$
$43$	−849460.	−1.62931	−0.814654	+	0.579947i	$0.803073\pi$
$44$	113718.	0.201254
$45$	0	0
$46$	1.42021e6	2.15130
$47$	902990.	1.26865	0.634323	−	0.773068i	$-0.281279\pi$
$47$	902990.	1.26865	0.634323	+	0.773068i	$0.281279\pi$
$48$	0	0
$49$	−503977.	−0.611963
$50$	2.72886e6	3.08736
$51$	0	0
$52$	1.57877e6	1.55707
$53$	324949.	0.299812	0.149906	−	0.988700i	$-0.452103\pi$
$53$	324949.	0.299812	0.149906	+	0.988700i	$0.452103\pi$
$54$	0	0
$55$	−409753.	−0.332088
$56$	87827.2	0.0668299
$57$	0	0
$58$	−435826.	−0.293302
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−1.58592e6	−0.894598	−0.447299	−	0.894384i	$-0.647614\pi$
$61$	−1.58592e6	−0.894598	−0.447299	+	0.894384i	$0.647614\pi$
$62$	−3.77529e6	−2.01178
$63$	0	0
$64$	−2.39707e6	−1.14301
$65$	−5.68870e6	−2.56931
$66$	0	0
$67$	−2.57819e6	−1.04726	−0.523629	−	0.851947i	$-0.675422\pi$
$67$	−2.57819e6	−1.04726	−0.523629	+	0.851947i	$0.675422\pi$
$68$	3.24094e6	1.24994
$69$	0	0
$70$	−4.56504e6	−1.59075
$71$	678037.	0.224827	0.112414	−	0.993661i	$-0.464142\pi$
$71$	678037.	0.224827	0.112414	+	0.993661i	$0.464142\pi$
$72$	0	0
$73$	2.50036e6	0.752269	0.376135	−	0.926565i	$-0.377253\pi$
$73$	2.50036e6	0.752269	0.376135	+	0.926565i	$0.377253\pi$
$74$	6.67930e6	1.91611
$75$	0	0
$76$	−7.36449e6	−1.92440
$77$	467410.	0.116676
$78$	0	0
$79$	−7.33035e6	−1.67275	−0.836373	−	0.548161i	$-0.815328\pi$
$79$	−7.33035e6	−1.67275	−0.836373	+	0.548161i	$0.815328\pi$
$80$	7.46957e6	1.63110
$81$	0	0
$82$	−3.09015e6	−0.618914
$83$	−3.91602e6	−0.751747	−0.375874	−	0.926671i	$-0.622657\pi$
$83$	−3.91602e6	−0.751747	−0.375874	+	0.926671i	$0.622657\pi$
$84$	0	0
$85$	−1.16779e7	−2.06252
$86$	−1.38421e7	−2.34670
$87$	0	0
$88$	128460.	0.0200945
$89$	−3.80382e6	−0.571946	−0.285973	−	0.958238i	$-0.592317\pi$
$89$	−3.80382e6	−0.571946	−0.285973	+	0.958238i	$0.592317\pi$
$90$	0	0
$91$	6.48916e6	0.902700
$92$	1.19868e7	1.60489
$93$	0	0
$94$	1.47144e7	1.82724
$95$	2.65361e7	3.17544
$96$	0	0
$97$	−7.68854e6	−0.855348	−0.427674	−	0.903933i	$-0.640667\pi$
$97$	−7.68854e6	−0.855348	−0.427674	+	0.903933i	$0.640667\pi$
$98$	−8.21243e6	−0.881414
$99$	0	0
$100$	2.30321e7	2.30321
$101$	1.11320e7	1.07510	0.537551	−	0.843231i	$-0.319350\pi$
$101$	1.11320e7	1.07510	0.537551	+	0.843231i	$0.319350\pi$
$102$	0	0
$103$	9.10836e6	0.821315	0.410658	−	0.911790i	$-0.365299\pi$
$103$	9.10836e6	0.821315	0.410658	+	0.911790i	$0.365299\pi$
$104$	1.78344e6	0.155468
$105$	0	0
$106$	5.29511e6	0.431822
$107$	−2.43881e7	−1.92458	−0.962289	−	0.272029i	$-0.912305\pi$
$107$	−2.43881e7	−1.92458	−0.962289	+	0.272029i	$0.912305\pi$
$108$	0	0
$109$	−1.92554e7	−1.42416	−0.712080	−	0.702098i	$-0.752247\pi$
$109$	−1.92554e7	−1.42416	−0.712080	+	0.702098i	$0.752247\pi$
$110$	−6.67702e6	−0.478309
$111$	0	0
$112$	−8.52062e6	−0.573071
$113$	−9.40627e6	−0.613258	−0.306629	−	0.951829i	$-0.599201\pi$
$113$	−9.40627e6	−0.613258	−0.306629	+	0.951829i	$0.599201\pi$
$114$	0	0
$115$	−4.31914e7	−2.64822
$116$	−3.67844e6	−0.218807
$117$	0	0
$118$	−3.34670e6	−0.187512
$119$	1.33211e7	0.724645
$120$	0	0
$121$	−1.88035e7	−0.964918
$122$	−2.58430e7	−1.28850
$123$	0	0
$124$	−3.18641e7	−1.50081
$125$	−4.42737e7	−2.02750
$126$	0	0
$127$	2.55998e7	1.10898	0.554490	−	0.832190i	$-0.312913\pi$
$127$	2.55998e7	1.10898	0.554490	+	0.832190i	$0.312913\pi$
$128$	−5.07683e6	−0.213972
$129$	0	0
$130$	−9.26986e7	−3.70060
$131$	−2.04746e7	−0.795729	−0.397865	−	0.917444i	$-0.630249\pi$
$131$	−2.04746e7	−0.795729	−0.397865	+	0.917444i	$0.630249\pi$
$132$	0	0
$133$	−3.02700e7	−1.11566
$134$	−4.20122e7	−1.50837
$135$	0	0
$136$	3.66108e6	0.124802
$137$	−1.13505e6	−0.0377132	−0.0188566	−	0.999822i	$-0.506003\pi$
$137$	−1.13505e6	−0.0377132	−0.0188566	+	0.999822i	$0.506003\pi$
$138$	0	0
$139$	−1.44843e7	−0.457453	−0.228726	−	0.973491i	$-0.573456\pi$
$139$	−1.44843e7	−0.457453	−0.228726	+	0.973491i	$0.573456\pi$
$140$	−3.85297e7	−1.18672
$141$	0	0
$142$	1.10488e7	0.323821
$143$	9.49132e6	0.271425
$144$	0	0
$145$	1.32543e7	0.361051
$146$	4.07440e7	1.08350
$147$	0	0
$148$	5.63744e7	1.42944
$149$	−6.91223e7	−1.71185	−0.855926	−	0.517098i	$-0.827012\pi$
$149$	−6.91223e7	−1.71185	−0.855926	+	0.517098i	$0.827012\pi$
$150$	0	0
$151$	5.36019e7	1.26695	0.633477	−	0.773762i	$-0.281627\pi$
$151$	5.36019e7	1.26695	0.633477	+	0.773762i	$0.281627\pi$
$152$	−8.31919e6	−0.192145
$153$	0	0
$154$	7.61655e6	0.168049
$155$	1.14814e8	2.47648
$156$	0	0
$157$	−8.33413e7	−1.71874	−0.859372	−	0.511350i	$-0.829145\pi$
$157$	−8.33413e7	−1.71874	−0.859372	+	0.511350i	$0.829145\pi$
$158$	−1.19450e8	−2.40927
$159$	0	0
$160$	1.31574e8	2.53950
$161$	4.92689e7	0.930426
$162$	0	0
$163$	−5.74632e6	−0.103928	−0.0519641	−	0.998649i	$-0.516548\pi$
$163$	−5.74632e6	−0.103928	−0.0519641	+	0.998649i	$0.516548\pi$
$164$	−2.60813e7	−0.461717
$165$	0	0
$166$	−6.38125e7	−1.08275
$167$	5.42463e7	0.901286	0.450643	−	0.892704i	$-0.351195\pi$
$167$	5.42463e7	0.901286	0.450643	+	0.892704i	$0.351195\pi$
$168$	0	0
$169$	6.90217e7	1.09997
$170$	−1.90294e8	−2.97066
$171$	0	0
$172$	−1.16830e8	−1.75067
$173$	1.02709e8	1.50816	0.754081	−	0.656781i	$-0.228082\pi$
$173$	1.02709e8	1.50816	0.754081	+	0.656781i	$0.228082\pi$
$174$	0	0
$175$	9.46676e7	1.33527
$176$	−1.24626e7	−0.172312
$177$	0	0
$178$	−6.19841e7	−0.823779
$179$	−1.18297e8	−1.54166	−0.770828	−	0.637043i	$-0.780157\pi$
$179$	−1.18297e8	−1.54166	−0.770828	+	0.637043i	$0.780157\pi$
$180$	0	0
$181$	−7.54155e7	−0.945334	−0.472667	−	0.881241i	$-0.656709\pi$
$181$	−7.54155e7	−0.945334	−0.472667	+	0.881241i	$0.656709\pi$
$182$	1.05742e8	1.30017
$183$	0	0
$184$	1.35407e7	0.160243
$185$	−2.03131e8	−2.35871
$186$	0	0
$187$	1.94840e7	0.217888
$188$	1.24192e8	1.36314
$189$	0	0
$190$	4.32411e8	4.57361
$191$	−5.67288e7	−0.589097	−0.294548	−	0.955637i	$-0.595169\pi$
$191$	−5.67288e7	−0.589097	−0.294548	+	0.955637i	$0.595169\pi$
$192$	0	0
$193$	1.56586e7	0.156784	0.0783920	−	0.996923i	$-0.475021\pi$
$193$	1.56586e7	0.156784	0.0783920	+	0.996923i	$0.475021\pi$
$194$	−1.25286e8	−1.23196
$195$	0	0
$196$	−6.93142e7	−0.657546
$197$	−1.95180e6	−0.0181888	−0.00909440	−	0.999959i	$-0.502895\pi$
$197$	−1.95180e6	−0.0181888	−0.00909440	+	0.999959i	$0.502895\pi$
$198$	0	0
$199$	4.03128e7	0.362624	0.181312	−	0.983426i	$-0.441966\pi$
$199$	4.03128e7	0.362624	0.181312	+	0.983426i	$0.441966\pi$
$200$	2.60178e7	0.229967
$201$	0	0
$202$	1.81399e8	1.54848
$203$	−1.51193e7	−0.126852
$204$	0	0
$205$	9.39774e7	0.761877
$206$	1.48423e8	1.18295
$207$	0	0
$208$	−1.73021e8	−1.33315
$209$	−4.42741e7	−0.335458
$210$	0	0
$211$	1.16617e8	0.854620	0.427310	−	0.904105i	$-0.359461\pi$
$211$	1.16617e8	0.854620	0.427310	+	0.904105i	$0.359461\pi$
$212$	4.46916e7	0.322144
$213$	0	0
$214$	−3.97410e8	−2.77199
$215$	4.20966e8	2.88877
$216$	0	0
$217$	−1.30970e8	−0.870084
$218$	−3.13770e8	−2.05123
$219$	0	0
$220$	−5.63552e7	−0.356824
$221$	2.70501e8	1.68576
$222$	0	0
$223$	1.52043e8	0.918121	0.459060	−	0.888405i	$-0.348186\pi$
$223$	1.52043e8	0.918121	0.459060	+	0.888405i	$0.348186\pi$
$224$	−1.50087e8	−0.892228
$225$	0	0
$226$	−1.53277e8	−0.883280
$227$	2.19156e8	1.24355	0.621774	−	0.783197i	$-0.286412\pi$
$227$	2.19156e8	1.24355	0.621774	+	0.783197i	$0.286412\pi$
$228$	0	0
$229$	−1.50483e8	−0.828061	−0.414030	−	0.910263i	$-0.635879\pi$
$229$	−1.50483e8	−0.828061	−0.414030	+	0.910263i	$0.635879\pi$
$230$	−7.03813e8	−3.81426
$231$	0	0
$232$	−4.15529e6	−0.0218471
$233$	−1.05923e8	−0.548586	−0.274293	−	0.961646i	$-0.588444\pi$
$233$	−1.05923e8	−0.548586	−0.274293	+	0.961646i	$0.588444\pi$
$234$	0	0
$235$	−4.47494e8	−2.24931
$236$	−2.82467e7	−0.139886
$237$	0	0
$238$	2.17070e8	1.04371
$239$	2.39069e8	1.13274	0.566370	−	0.824151i	$-0.308347\pi$
$239$	2.39069e8	1.13274	0.566370	+	0.824151i	$0.308347\pi$
$240$	0	0
$241$	−6.39780e7	−0.294422	−0.147211	−	0.989105i	$-0.547030\pi$
$241$	−6.39780e7	−0.294422	−0.147211	+	0.989105i	$0.547030\pi$
$242$	−3.06408e8	−1.38978
$243$	0	0
$244$	−2.18119e8	−0.961234
$245$	2.49756e8	1.08501
$246$	0	0
$247$	−6.14668e8	−2.59538
$248$	−3.59948e7	−0.149851
$249$	0	0
$250$	−7.21450e8	−2.92022
$251$	−1.43897e8	−0.574373	−0.287186	−	0.957875i	$-0.592720\pi$
$251$	−1.43897e8	−0.574373	−0.287186	+	0.957875i	$0.592720\pi$
$252$	0	0
$253$	7.20627e7	0.279762
$254$	4.17155e8	1.59727
$255$	0	0
$256$	2.24097e8	0.834826
$257$	1.50715e8	0.553849	0.276925	−	0.960892i	$-0.410685\pi$
$257$	1.50715e8	0.553849	0.276925	+	0.960892i	$0.410685\pi$
$258$	0	0
$259$	2.31713e8	0.828708
$260$	−7.82391e8	−2.76069
$261$	0	0
$262$	−3.33638e8	−1.14609
$263$	5.02309e8	1.70265	0.851325	−	0.524638i	$-0.175799\pi$
$263$	5.02309e8	1.70265	0.851325	+	0.524638i	$0.175799\pi$
$264$	0	0
$265$	−1.61035e8	−0.531568
$266$	−4.93256e8	−1.60689
$267$	0	0
$268$	−3.54590e8	−1.12526
$269$	2.76426e8	0.865858	0.432929	−	0.901428i	$-0.357480\pi$
$269$	2.76426e8	0.865858	0.432929	+	0.901428i	$0.357480\pi$
$270$	0	0
$271$	1.17995e8	0.360139	0.180069	−	0.983654i	$-0.442368\pi$
$271$	1.17995e8	0.360139	0.180069	+	0.983654i	$0.442368\pi$
$272$	−3.55182e8	−1.07019
$273$	0	0
$274$	−1.84959e7	−0.0543186
$275$	1.38465e8	0.401491
$276$	0	0
$277$	−6.34905e7	−0.179485	−0.0897427	−	0.995965i	$-0.528604\pi$
$277$	−6.34905e7	−0.179485	−0.0897427	+	0.995965i	$0.528604\pi$
$278$	−2.36025e8	−0.658872
$279$	0	0
$280$	−4.35245e7	−0.118490
$281$	−3.92031e8	−1.05402	−0.527009	−	0.849860i	$-0.676687\pi$
$281$	−3.92031e8	−1.05402	−0.527009	+	0.849860i	$0.676687\pi$
$282$	0	0
$283$	3.91102e8	1.02574	0.512871	−	0.858466i	$-0.328582\pi$
$283$	3.91102e8	1.02574	0.512871	+	0.858466i	$0.328582\pi$
$284$	9.32533e7	0.241574
$285$	0	0
$286$	1.54663e8	0.390936
$287$	−1.07201e8	−0.267678
$288$	0	0
$289$	1.44951e8	0.353248
$290$	2.15982e8	0.520025
$291$	0	0
$292$	3.43886e8	0.808303
$293$	3.95594e8	0.918783	0.459392	−	0.888234i	$-0.348067\pi$
$293$	3.95594e8	0.918783	0.459392	+	0.888234i	$0.348067\pi$
$294$	0	0
$295$	1.01780e8	0.230825
$296$	6.36824e7	0.142725
$297$	0	0
$298$	−1.12636e9	−2.46559
$299$	1.00046e9	2.16447
$300$	0	0
$301$	−4.80201e8	−1.01494
$302$	8.73455e8	1.82480
$303$	0	0
$304$	8.07092e8	1.64765
$305$	7.85935e8	1.58612
$306$	0	0
$307$	−3.74974e8	−0.739634	−0.369817	−	0.929105i	$-0.620580\pi$
$307$	−3.74974e8	−0.739634	−0.369817	+	0.929105i	$0.620580\pi$
$308$	6.42849e7	0.125367
$309$	0	0
$310$	1.87092e9	3.56689
$311$	−5.67572e8	−1.06994	−0.534970	−	0.844871i	$-0.679677\pi$
$311$	−5.67572e8	−1.06994	−0.534970	+	0.844871i	$0.679677\pi$
$312$	0	0
$313$	−9.61191e8	−1.77176	−0.885879	−	0.463916i	$-0.846444\pi$
$313$	−9.61191e8	−1.77176	−0.885879	+	0.463916i	$0.846444\pi$
$314$	−1.35806e9	−2.47552
$315$	0	0
$316$	−1.00817e9	−1.79734
$317$	−1.03762e8	−0.182950	−0.0914748	−	0.995807i	$-0.529158\pi$
$317$	−1.03762e8	−0.182950	−0.0914748	+	0.995807i	$0.529158\pi$
$318$	0	0
$319$	−2.21142e7	−0.0381420
$320$	1.18791e9	2.02656
$321$	0	0
$322$	8.02847e8	1.34010
$323$	−1.26180e9	−2.08345
$324$	0	0
$325$	1.92234e9	3.10626
$326$	−9.36376e7	−0.149689
$327$	0	0
$328$	−2.94624e7	−0.0461009
$329$	5.10462e8	0.790273
$330$	0	0
$331$	−4.86499e8	−0.737367	−0.368684	−	0.929555i	$-0.620191\pi$
$331$	−4.86499e8	−0.737367	−0.368684	+	0.929555i	$0.620191\pi$
$332$	−5.38587e8	−0.807743
$333$	0	0
$334$	8.83956e8	1.29813
$335$	1.27767e9	1.85679
$336$	0	0
$337$	−2.32747e8	−0.331269	−0.165634	−	0.986187i	$-0.552967\pi$
$337$	−2.32747e8	−0.331269	−0.165634	+	0.986187i	$0.552967\pi$
$338$	1.12472e9	1.58430
$339$	0	0
$340$	−1.60611e9	−2.21615
$341$	−1.91562e8	−0.261618
$342$	0	0
$343$	−7.50449e8	−1.00413
$344$	−1.31975e8	−0.174798
$345$	0	0
$346$	1.67367e9	2.17222
$347$	1.12320e8	0.144312	0.0721560	−	0.997393i	$-0.477012\pi$
$347$	1.12320e8	0.144312	0.0721560	+	0.997393i	$0.477012\pi$
$348$	0	0
$349$	1.23358e9	1.55338	0.776688	−	0.629885i	$-0.216898\pi$
$349$	1.23358e9	1.55338	0.776688	+	0.629885i	$0.216898\pi$
$350$	1.54263e9	1.92320
$351$	0	0
$352$	−2.19524e8	−0.268277
$353$	−1.25683e9	−1.52078	−0.760390	−	0.649466i	$-0.774992\pi$
$353$	−1.25683e9	−1.52078	−0.760390	+	0.649466i	$0.774992\pi$
$354$	0	0
$355$	−3.36014e8	−0.398619
$356$	−5.23156e8	−0.614549
$357$	0	0
$358$	−1.92767e9	−2.22046
$359$	−1.53369e8	−0.174947	−0.0874735	−	0.996167i	$-0.527879\pi$
$359$	−1.53369e8	−0.174947	−0.0874735	+	0.996167i	$0.527879\pi$
$360$	0	0
$361$	1.97337e9	2.20766
$362$	−1.22891e9	−1.36157
$363$	0	0
$364$	8.92482e8	0.969940
$365$	−1.23910e9	−1.33378
$366$	0	0
$367$	−9.10830e8	−0.961847	−0.480924	−	0.876762i	$-0.659699\pi$
$367$	−9.10830e8	−0.961847	−0.480924	+	0.876762i	$0.659699\pi$
$368$	−1.31366e9	−1.37409
$369$	0	0
$370$	−3.31006e9	−3.39727
$371$	1.83694e8	0.186761
$372$	0	0
$373$	−8.48680e8	−0.846766	−0.423383	−	0.905951i	$-0.639157\pi$
$373$	−8.48680e8	−0.846766	−0.423383	+	0.905951i	$0.639157\pi$
$374$	3.17496e8	0.313825
$375$	0	0
$376$	1.40292e8	0.136105
$377$	−3.07016e8	−0.295098
$378$	0	0
$379$	1.11369e9	1.05082	0.525410	−	0.850849i	$-0.323912\pi$
$379$	1.11369e9	1.05082	0.525410	+	0.850849i	$0.323912\pi$
$380$	3.64962e9	3.41197
$381$	0	0
$382$	−9.24408e8	−0.848481
$383$	1.24305e9	1.13056	0.565279	−	0.824900i	$-0.308768\pi$
$383$	1.24305e9	1.13056	0.565279	+	0.824900i	$0.308768\pi$
$384$	0	0
$385$	−2.31634e8	−0.206866
$386$	2.55160e8	0.225817
$387$	0	0
$388$	−1.05744e9	−0.919060
$389$	−3.31934e8	−0.285909	−0.142955	−	0.989729i	$-0.545660\pi$
$389$	−3.31934e8	−0.285909	−0.142955	+	0.989729i	$0.545660\pi$
$390$	0	0
$391$	2.05377e9	1.73754
$392$	−7.82997e7	−0.0656536
$393$	0	0
$394$	−3.18051e7	−0.0261975
$395$	3.63270e9	2.96578
$396$	0	0
$397$	−2.50412e8	−0.200858	−0.100429	−	0.994944i	$-0.532021\pi$
$397$	−2.50412e8	−0.200858	−0.100429	+	0.994944i	$0.532021\pi$
$398$	6.56906e8	0.522291
$399$	0	0
$400$	−2.52414e9	−1.97198
$401$	−1.57100e9	−1.21666	−0.608332	−	0.793683i	$-0.708161\pi$
$401$	−1.57100e9	−1.21666	−0.608332	+	0.793683i	$0.708161\pi$
$402$	0	0
$403$	−2.65949e9	−2.02410
$404$	1.53104e9	1.15518
$405$	0	0
$406$	−2.46373e8	−0.182705
$407$	3.38914e8	0.249177
$408$	0	0
$409$	−2.37344e8	−0.171532	−0.0857661	−	0.996315i	$-0.527334\pi$
$409$	−2.37344e8	−0.171532	−0.0857661	+	0.996315i	$0.527334\pi$
$410$	1.53138e9	1.09734
$411$	0	0
$412$	1.25271e9	0.882492
$413$	−1.16101e8	−0.0810981
$414$	0	0
$415$	1.94066e9	1.33285
$416$	−3.04770e9	−2.07561
$417$	0	0
$418$	−7.21457e8	−0.483163
$419$	1.61768e9	1.07435	0.537173	−	0.843472i	$-0.319492\pi$
$419$	1.61768e9	1.07435	0.537173	+	0.843472i	$0.319492\pi$
$420$	0	0
$421$	−1.17270e9	−0.765946	−0.382973	−	0.923759i	$-0.625100\pi$
$421$	−1.17270e9	−0.765946	−0.382973	+	0.923759i	$0.625100\pi$
$422$	1.90030e9	1.23092
$423$	0	0
$424$	5.04852e7	0.0321650
$425$	3.94622e9	2.49356
$426$	0	0
$427$	−8.96525e8	−0.557269
$428$	−3.35421e9	−2.06793
$429$	0	0
$430$	6.85974e9	4.16071
$431$	−2.74618e9	−1.65219	−0.826094	−	0.563533i	$-0.809442\pi$
$431$	−2.74618e9	−1.65219	−0.826094	+	0.563533i	$0.809442\pi$
$432$	0	0
$433$	1.44724e8	0.0856709	0.0428355	−	0.999082i	$-0.486361\pi$
$433$	1.44724e8	0.0856709	0.0428355	+	0.999082i	$0.486361\pi$
$434$	−2.13418e9	−1.25319
$435$	0	0
$436$	−2.64827e9	−1.53024
$437$	−4.66686e9	−2.67510
$438$	0	0
$439$	−2.83060e8	−0.159681	−0.0798403	−	0.996808i	$-0.525441\pi$
$439$	−2.83060e8	−0.159681	−0.0798403	+	0.996808i	$0.525441\pi$
$440$	−6.36607e7	−0.0356276
$441$	0	0
$442$	4.40787e9	2.42801
$443$	6.58269e8	0.359741	0.179871	−	0.983690i	$-0.442432\pi$
$443$	6.58269e8	0.359741	0.179871	+	0.983690i	$0.442432\pi$
$444$	0	0
$445$	1.88506e9	1.01406
$446$	2.47758e9	1.32238
$447$	0	0
$448$	−1.35507e9	−0.712012
$449$	−2.96392e9	−1.54527	−0.772636	−	0.634850i	$-0.781062\pi$
$449$	−2.96392e9	−1.54527	−0.772636	+	0.634850i	$0.781062\pi$
$450$	0	0
$451$	−1.56797e8	−0.0804857
$452$	−1.29368e9	−0.658937
$453$	0	0
$454$	3.57119e9	1.79109
$455$	−3.21583e9	−1.60049
$456$	0	0
$457$	−2.62985e8	−0.128891	−0.0644456	−	0.997921i	$-0.520528\pi$
$457$	−2.62985e8	−0.128891	−0.0644456	+	0.997921i	$0.520528\pi$
$458$	−2.45215e9	−1.19266
$459$	0	0
$460$	−5.94030e9	−2.84548
$461$	−7.39703e8	−0.351645	−0.175822	−	0.984422i	$-0.556258\pi$
$461$	−7.39703e8	−0.351645	−0.175822	+	0.984422i	$0.556258\pi$
$462$	0	0
$463$	−8.00108e8	−0.374641	−0.187320	−	0.982299i	$-0.559980\pi$
$463$	−8.00108e8	−0.374641	−0.187320	+	0.982299i	$0.559980\pi$
$464$	4.03129e8	0.187340
$465$	0	0
$466$	−1.72604e9	−0.790132
$467$	−3.44400e9	−1.56478	−0.782392	−	0.622786i	$-0.786001\pi$
$467$	−3.44400e9	−1.56478	−0.782392	+	0.622786i	$0.786001\pi$
$468$	0	0
$469$	−1.45745e9	−0.652364
$470$	−7.29202e9	−3.23970
$471$	0	0
$472$	−3.19084e7	−0.0139672
$473$	−7.02362e8	−0.305174
$474$	0	0
$475$	−8.96713e9	−3.83907
$476$	1.83211e9	0.778622
$477$	0	0
$478$	3.89568e9	1.63149
$479$	2.17648e9	0.904857	0.452429	−	0.891801i	$-0.350558\pi$
$479$	2.17648e9	0.904857	0.452429	+	0.891801i	$0.350558\pi$
$480$	0	0
$481$	4.70521e9	1.92784
$482$	−1.04254e9	−0.424059
$483$	0	0
$484$	−2.58613e9	−1.03679
$485$	3.81020e9	1.51653
$486$	0	0
$487$	1.73782e9	0.681796	0.340898	−	0.940100i	$-0.389269\pi$
$487$	1.73782e9	0.681796	0.340898	+	0.940100i	$0.389269\pi$
$488$	−2.46395e8	−0.0959758
$489$	0	0
$490$	4.06983e9	1.56275
$491$	7.21828e8	0.275200	0.137600	−	0.990488i	$-0.456061\pi$
$491$	7.21828e8	0.275200	0.137600	+	0.990488i	$0.456061\pi$
$492$	0	0
$493$	−6.30249e8	−0.236891
$494$	−1.00161e10	−3.73815
$495$	0	0
$496$	3.49206e9	1.28498
$497$	3.83295e8	0.140051
$498$	0	0
$499$	−1.78127e9	−0.641769	−0.320885	−	0.947118i	$-0.603980\pi$
$499$	−1.78127e9	−0.641769	−0.320885	+	0.947118i	$0.603980\pi$
$500$	−6.08915e9	−2.17852
$501$	0	0
$502$	−2.34483e9	−0.827273
$503$	−1.72676e9	−0.604986	−0.302493	−	0.953152i	$-0.597819\pi$
$503$	−1.72676e9	−0.604986	−0.302493	+	0.953152i	$0.597819\pi$
$504$	0	0
$505$	−5.51669e9	−1.90616
$506$	1.17428e9	0.402944
$507$	0	0
$508$	3.52085e9	1.19158
$509$	−1.96038e8	−0.0658912	−0.0329456	−	0.999457i	$-0.510489\pi$
$509$	−1.96038e8	−0.0658912	−0.0329456	+	0.999457i	$0.510489\pi$
$510$	0	0
$511$	1.41346e9	0.468608
$512$	4.30154e9	1.41638
$513$	0	0
$514$	2.45594e9	0.797713
$515$	−4.51383e9	−1.45619
$516$	0	0
$517$	7.46623e8	0.237621
$518$	3.77582e9	1.19359
$519$	0	0
$520$	−8.83816e8	−0.275645
$521$	2.84883e9	0.882540	0.441270	−	0.897374i	$-0.354528\pi$
$521$	2.84883e9	0.882540	0.441270	+	0.897374i	$0.354528\pi$
$522$	0	0
$523$	−3.08000e9	−0.941445	−0.470722	−	0.882281i	$-0.656007\pi$
$523$	−3.08000e9	−0.941445	−0.470722	+	0.882281i	$0.656007\pi$
$524$	−2.81596e9	−0.855000
$525$	0	0
$526$	8.18523e9	2.45234
$527$	−5.45947e9	−1.62485
$528$	0	0
$529$	4.19118e9	1.23095
$530$	−2.62410e9	−0.765621
$531$	0	0
$532$	−4.16316e9	−1.19876
$533$	−2.17684e9	−0.622705
$534$	0	0
$535$	1.20860e10	3.41228
$536$	−4.00557e8	−0.112354
$537$	0	0
$538$	4.50443e9	1.24710
$539$	−4.16706e8	−0.114622
$540$	0	0
$541$	3.69807e9	1.00412	0.502060	−	0.864833i	$-0.332576\pi$
$541$	3.69807e9	1.00412	0.502060	+	0.864833i	$0.332576\pi$
$542$	1.92275e9	0.518711
$543$	0	0
$544$	−6.25639e9	−1.66620
$545$	9.54237e9	2.52504
$546$	0	0
$547$	−1.21521e9	−0.317464	−0.158732	−	0.987322i	$-0.550741\pi$
$547$	−1.21521e9	−0.317464	−0.158732	+	0.987322i	$0.550741\pi$
$548$	−1.56108e8	−0.0405223
$549$	0	0
$550$	2.25632e9	0.578270
$551$	1.43214e9	0.364715
$552$	0	0
$553$	−4.14386e9	−1.04200
$554$	−1.03459e9	−0.258514
$555$	0	0
$556$	−1.99209e9	−0.491527
$557$	6.35497e9	1.55819	0.779095	−	0.626906i	$-0.215679\pi$
$557$	6.35497e9	1.55819	0.779095	+	0.626906i	$0.215679\pi$
$558$	0	0
$559$	−9.75105e9	−2.36108
$560$	4.22256e9	1.01606
$561$	0	0
$562$	−6.38823e9	−1.51811
$563$	−2.41689e9	−0.570791	−0.285395	−	0.958410i	$-0.592125\pi$
$563$	−2.41689e9	−0.570791	−0.285395	+	0.958410i	$0.592125\pi$
$564$	0	0
$565$	4.66146e9	1.08731
$566$	6.37310e9	1.47738
$567$	0	0
$568$	1.05342e8	0.0241203
$569$	−2.02038e9	−0.459769	−0.229884	−	0.973218i	$-0.573835\pi$
$569$	−2.02038e9	−0.459769	−0.229884	+	0.973218i	$0.573835\pi$
$570$	0	0
$571$	−5.09913e9	−1.14622	−0.573112	−	0.819477i	$-0.694264\pi$
$571$	−5.09913e9	−1.14622	−0.573112	+	0.819477i	$0.694264\pi$
$572$	1.30538e9	0.291643
$573$	0	0
$574$	−1.74686e9	−0.385538
$575$	1.45953e10	3.20167
$576$	0	0
$577$	−5.65588e9	−1.22570	−0.612851	−	0.790199i	$-0.709977\pi$
$577$	−5.65588e9	−1.22570	−0.612851	+	0.790199i	$0.709977\pi$
$578$	2.36201e9	0.508785
$579$	0	0
$580$	1.82292e9	0.387945
$581$	−2.21373e9	−0.468283
$582$	0	0
$583$	2.68678e8	0.0561556
$584$	3.88465e8	0.0807063
$585$	0	0
$586$	6.44629e9	1.32333
$587$	−8.74088e9	−1.78370	−0.891850	−	0.452331i	$-0.850593\pi$
$587$	−8.74088e9	−1.78370	−0.891850	+	0.452331i	$0.850593\pi$
$588$	0	0
$589$	1.24057e10	2.50161
$590$	1.65852e9	0.332460
$591$	0	0
$592$	−6.17820e9	−1.22387
$593$	7.16535e9	1.41106	0.705531	−	0.708679i	$-0.250709\pi$
$593$	7.16535e9	1.41106	0.705531	+	0.708679i	$0.250709\pi$
$594$	0	0
$595$	−6.60153e9	−1.28480
$596$	−9.50669e9	−1.83936
$597$	0	0
$598$	1.63028e10	3.11751
$599$	1.12486e8	0.0213847	0.0106923	−	0.999943i	$-0.496596\pi$
$599$	1.12486e8	0.0213847	0.0106923	+	0.999943i	$0.496596\pi$
$600$	0	0
$601$	2.43804e9	0.458121	0.229061	−	0.973412i	$-0.426435\pi$
$601$	2.43804e9	0.458121	0.229061	+	0.973412i	$0.426435\pi$
$602$	−7.82498e9	−1.46182
$603$	0	0
$604$	7.37210e9	1.36132
$605$	9.31845e9	1.71080
$606$	0	0
$607$	3.37659e9	0.612800	0.306400	−	0.951903i	$-0.400876\pi$
$607$	3.37659e9	0.612800	0.306400	+	0.951903i	$0.400876\pi$
$608$	1.42166e10	2.56527
$609$	0	0
$610$	1.28070e10	2.28451
$611$	1.03655e10	1.83843
$612$	0	0
$613$	−3.64627e9	−0.639348	−0.319674	−	0.947528i	$-0.603573\pi$
$613$	−3.64627e9	−0.639348	−0.319674	+	0.947528i	$0.603573\pi$
$614$	−6.11029e9	−1.06530
$615$	0	0
$616$	7.26184e7	0.0125174
$617$	2.27884e8	0.0390585	0.0195293	−	0.999809i	$-0.493783\pi$
$617$	2.27884e8	0.0390585	0.0195293	+	0.999809i	$0.493783\pi$
$618$	0	0
$619$	2.30512e9	0.390640	0.195320	−	0.980740i	$-0.437426\pi$
$619$	2.30512e9	0.390640	0.195320	+	0.980740i	$0.437426\pi$
$620$	1.57909e10	2.66094
$621$	0	0
$622$	−9.24870e9	−1.54104
$623$	−2.15031e9	−0.356280
$624$	0	0
$625$	8.85757e9	1.45122
$626$	−1.56628e10	−2.55188
$627$	0	0
$628$	−1.14623e10	−1.84677
$629$	9.65897e9	1.54758
$630$	0	0
$631$	5.67126e9	0.898622	0.449311	−	0.893375i	$-0.351670\pi$
$631$	5.67126e9	0.898622	0.449311	+	0.893375i	$0.351670\pi$
$632$	−1.13887e9	−0.179458
$633$	0	0
$634$	−1.69083e9	−0.263504
$635$	−1.26865e10	−1.96623
$636$	0	0
$637$	−5.78522e9	−0.886812
$638$	−3.60355e8	−0.0549362
$639$	0	0
$640$	2.51592e9	0.379373
$641$	8.04557e9	1.20657	0.603287	−	0.797524i	$-0.293858\pi$
$641$	8.04557e9	1.20657	0.603287	+	0.797524i	$0.293858\pi$
$642$	0	0
$643$	6.95787e9	1.03214	0.516069	−	0.856547i	$-0.327395\pi$
$643$	6.95787e9	1.03214	0.516069	+	0.856547i	$0.327395\pi$
$644$	6.77616e9	0.999731
$645$	0	0
$646$	−2.05614e10	−3.00081
$647$	1.50113e9	0.217898	0.108949	−	0.994047i	$-0.465252\pi$
$647$	1.50113e9	0.217898	0.108949	+	0.994047i	$0.465252\pi$
$648$	0	0
$649$	−1.69814e8	−0.0243847
$650$	3.13250e10	4.47398
$651$	0	0
$652$	−7.90316e8	−0.111669
$653$	1.05745e9	0.148616	0.0743078	−	0.997235i	$-0.476325\pi$
$653$	1.05745e9	0.148616	0.0743078	+	0.997235i	$0.476325\pi$
$654$	0	0
$655$	1.01466e10	1.41083
$656$	2.85831e9	0.395318
$657$	0	0
$658$	8.31808e9	1.13824
$659$	1.27158e10	1.73079	0.865396	−	0.501088i	$-0.167067\pi$
$659$	1.27158e10	1.73079	0.865396	+	0.501088i	$0.167067\pi$
$660$	0	0
$661$	−1.38832e10	−1.86976	−0.934878	−	0.354968i	$-0.884492\pi$
$661$	−1.38832e10	−1.86976	−0.934878	+	0.354968i	$0.884492\pi$
$662$	−7.92761e9	−1.06204
$663$	0	0
$664$	−6.08407e8	−0.0806503
$665$	1.50009e10	1.97807
$666$	0	0
$667$	−2.33101e9	−0.304162
$668$	7.46073e9	0.968420
$669$	0	0
$670$	2.08200e10	2.67435
$671$	−1.31130e9	−0.167560
$672$	0	0
$673$	8.66625e9	1.09592	0.547960	−	0.836505i	$-0.315405\pi$
$673$	8.66625e9	1.09592	0.547960	+	0.836505i	$0.315405\pi$
$674$	−3.79267e9	−0.477129
$675$	0	0
$676$	9.49284e9	1.18191
$677$	1.30940e10	1.62186	0.810929	−	0.585144i	$-0.198962\pi$
$677$	1.30940e10	1.62186	0.810929	+	0.585144i	$0.198962\pi$
$678$	0	0
$679$	−4.34634e9	−0.532819
$680$	−1.81432e9	−0.221275
$681$	0	0
$682$	−3.12154e9	−0.376811
$683$	−5.07430e9	−0.609402	−0.304701	−	0.952448i	$-0.598557\pi$
$683$	−5.07430e9	−0.609402	−0.304701	+	0.952448i	$0.598557\pi$
$684$	0	0
$685$	5.62496e8	0.0668656
$686$	−1.22287e10	−1.44626
$687$	0	0
$688$	1.28037e10	1.49891
$689$	3.73012e9	0.434466
$690$	0	0
$691$	7.09480e9	0.818026	0.409013	−	0.912529i	$-0.365873\pi$
$691$	7.09480e9	0.818026	0.409013	+	0.912529i	$0.365873\pi$
$692$	1.41260e10	1.62050
$693$	0	0
$694$	1.83027e9	0.207854
$695$	7.17798e9	0.811065
$696$	0	0
$697$	−4.46867e9	−0.499878
$698$	2.01014e10	2.23734
$699$	0	0
$700$	1.30200e10	1.43473
$701$	−5.74769e9	−0.630203	−0.315101	−	0.949058i	$-0.602039\pi$
$701$	−5.74769e9	−0.630203	−0.315101	+	0.949058i	$0.602039\pi$
$702$	0	0
$703$	−2.19484e10	−2.38264
$704$	−1.98198e9	−0.214089
$705$	0	0
$706$	−2.04804e10	−2.19039
$707$	6.29295e9	0.669709
$708$	0	0
$709$	−5.47895e9	−0.577345	−0.288672	−	0.957428i	$-0.593214\pi$
$709$	−5.47895e9	−0.577345	−0.288672	+	0.957428i	$0.593214\pi$
$710$	−5.47543e9	−0.574135
$711$	0	0
$712$	−5.90975e8	−0.0613605
$713$	−2.01922e10	−2.08627
$714$	0	0
$715$	−4.70361e9	−0.481238
$716$	−1.62699e10	−1.65649
$717$	0	0
$718$	−2.49918e9	−0.251978
$719$	−1.62636e10	−1.63179	−0.815895	−	0.578200i	$-0.803755\pi$
$719$	−1.62636e10	−1.63179	−0.815895	+	0.578200i	$0.803755\pi$
$720$	0	0
$721$	5.14897e9	0.511619
$722$	3.21565e10	3.17971
$723$	0	0
$724$	−1.03722e10	−1.01575
$725$	−4.47893e9	−0.436507
$726$	0	0
$727$	−2.55116e9	−0.246245	−0.123122	−	0.992391i	$-0.539291\pi$
$727$	−2.55116e9	−0.246245	−0.123122	+	0.992391i	$0.539291\pi$
$728$	1.00818e9	0.0968451
$729$	0	0
$730$	−2.01915e10	−1.92105
$731$	−2.00172e10	−1.89536
$732$	0	0
$733$	1.41305e10	1.32524	0.662619	−	0.748957i	$-0.269445\pi$
$733$	1.41305e10	1.32524	0.662619	+	0.748957i	$0.269445\pi$
$734$	−1.48422e10	−1.38536
$735$	0	0
$736$	−2.31396e10	−2.13936
$737$	−2.13174e9	−0.196154
$738$	0	0
$739$	1.92246e10	1.75227	0.876136	−	0.482064i	$-0.160113\pi$
$739$	1.92246e10	1.75227	0.876136	+	0.482064i	$0.160113\pi$
$740$	−2.79374e10	−2.53440
$741$	0	0
$742$	2.99333e9	0.268993
$743$	−5.89705e9	−0.527441	−0.263721	−	0.964599i	$-0.584950\pi$
$743$	−5.89705e9	−0.527441	−0.263721	+	0.964599i	$0.584950\pi$
$744$	0	0
$745$	3.42549e10	3.03512
$746$	−1.38294e10	−1.21960
$747$	0	0
$748$	2.67972e9	0.234117
$749$	−1.37867e10	−1.19887
$750$	0	0
$751$	−3.11911e9	−0.268715	−0.134357	−	0.990933i	$-0.542897\pi$
$751$	−3.11911e9	−0.268715	−0.134357	+	0.990933i	$0.542897\pi$
$752$	−1.36105e10	−1.16711
$753$	0	0
$754$	−5.00289e9	−0.425032
$755$	−2.65635e10	−2.24631
$756$	0	0
$757$	−1.03709e10	−0.868921	−0.434461	−	0.900691i	$-0.643061\pi$
$757$	−1.03709e10	−0.868921	−0.434461	+	0.900691i	$0.643061\pi$
$758$	1.81479e10	1.51350
$759$	0	0
$760$	4.12273e9	0.340673
$761$	−1.48892e9	−0.122468	−0.0612342	−	0.998123i	$-0.519504\pi$
$761$	−1.48892e9	−0.122468	−0.0612342	+	0.998123i	$0.519504\pi$
$762$	0	0
$763$	−1.08851e10	−0.887147
$764$	−7.80215e9	−0.632977
$765$	0	0
$766$	2.02558e10	1.62835
$767$	−2.35757e9	−0.188660
$768$	0	0
$769$	1.76503e10	1.39962	0.699809	−	0.714330i	$-0.253268\pi$
$769$	1.76503e10	1.39962	0.699809	+	0.714330i	$0.253268\pi$
$770$	−3.77453e9	−0.297951
$771$	0	0
$772$	2.15359e9	0.168462
$773$	6.95196e8	0.0541351	0.0270676	−	0.999634i	$-0.491383\pi$
$773$	6.95196e8	0.0541351	0.0270676	+	0.999634i	$0.491383\pi$
$774$	0	0
$775$	−3.87982e10	−2.99403
$776$	−1.19452e9	−0.0917649
$777$	0	0
$778$	−5.40894e9	−0.411798
$779$	1.01543e10	0.769608
$780$	0	0
$781$	5.60624e8	0.0421107
$782$	3.34667e10	2.50259
$783$	0	0
$784$	7.59631e9	0.562984
$785$	4.13014e10	3.04734
$786$	0	0
$787$	−7.19358e8	−0.0526058	−0.0263029	−	0.999654i	$-0.508373\pi$
$787$	−7.19358e8	−0.0526058	−0.0263029	+	0.999654i	$0.508373\pi$
$788$	−2.68440e8	−0.0195436
$789$	0	0
$790$	5.91956e10	4.27164
$791$	−5.31738e9	−0.382014
$792$	0	0
$793$	−1.82050e10	−1.29639
$794$	−4.08052e9	−0.289297
$795$	0	0
$796$	5.54439e9	0.389635
$797$	−4.07407e9	−0.285052	−0.142526	−	0.989791i	$-0.545523\pi$
$797$	−4.07407e9	−0.285052	−0.142526	+	0.989791i	$0.545523\pi$
$798$	0	0
$799$	2.12786e10	1.47581
$800$	−4.44616e10	−3.07023
$801$	0	0
$802$	−2.55998e10	−1.75237
$803$	2.06739e9	0.140902
$804$	0	0
$805$	−2.44161e10	−1.64965
$806$	−4.33371e10	−2.91532
$807$	0	0
$808$	1.72951e9	0.115341
$809$	1.12391e10	0.746296	0.373148	−	0.927772i	$-0.378278\pi$
$809$	1.12391e10	0.746296	0.373148	+	0.927772i	$0.378278\pi$
$810$	0	0
$811$	1.57592e10	1.03744	0.518719	−	0.854945i	$-0.326409\pi$
$811$	1.57592e10	1.03744	0.518719	+	0.854945i	$0.326409\pi$
$812$	−2.07943e9	−0.136300
$813$	0	0
$814$	5.52267e9	0.358892
$815$	2.84770e9	0.184265
$816$	0	0
$817$	4.54857e10	2.91808
$818$	−3.86757e9	−0.247059
$819$	0	0
$820$	1.29251e10	0.818627
$821$	1.83331e10	1.15621	0.578103	−	0.815964i	$-0.303793\pi$
$821$	1.83331e10	1.15621	0.578103	+	0.815964i	$0.303793\pi$
$822$	0	0
$823$	3.71121e9	0.232069	0.116034	−	0.993245i	$-0.462982\pi$
$823$	3.71121e9	0.232069	0.116034	+	0.993245i	$0.462982\pi$
$824$	1.41511e9	0.0881138
$825$	0	0
$826$	−1.89189e9	−0.116806
$827$	−3.00461e9	−0.184722	−0.0923610	−	0.995726i	$-0.529441\pi$
$827$	−3.00461e9	−0.184722	−0.0923610	+	0.995726i	$0.529441\pi$
$828$	0	0
$829$	1.97799e10	1.20582	0.602912	−	0.797808i	$-0.294007\pi$
$829$	1.97799e10	1.20582	0.602912	+	0.797808i	$0.294007\pi$
$830$	3.16235e10	1.91971
$831$	0	0
$832$	−2.75162e10	−1.65637
$833$	−1.18760e10	−0.711891
$834$	0	0
$835$	−2.68828e10	−1.59798
$836$	−6.08921e9	−0.360445
$837$	0	0
$838$	2.63605e10	1.54739
$839$	7.17247e9	0.419278	0.209639	−	0.977779i	$-0.432771\pi$
$839$	7.17247e9	0.419278	0.209639	+	0.977779i	$0.432771\pi$
$840$	0	0
$841$	−1.65345e10	−0.958531
$842$	−1.91094e10	−1.10320
$843$	0	0
$844$	1.60388e10	0.918278
$845$	−3.42050e10	−1.95025
$846$	0	0
$847$	−1.06297e10	−0.601073
$848$	−4.89786e9	−0.275817
$849$	0	0
$850$	6.43046e10	3.59150
$851$	3.57243e10	1.98706
$852$	0	0
$853$	−2.70770e9	−0.149375	−0.0746877	−	0.997207i	$-0.523796\pi$
$853$	−2.70770e9	−0.149375	−0.0746877	+	0.997207i	$0.523796\pi$
$854$	−1.46091e10	−0.802639
$855$	0	0
$856$	−3.78903e9	−0.206476
$857$	1.93553e10	1.05043	0.525215	−	0.850969i	$-0.323985\pi$
$857$	1.93553e10	1.05043	0.525215	+	0.850969i	$0.323985\pi$
$858$	0	0
$859$	−3.02146e10	−1.62645	−0.813224	−	0.581951i	$-0.802290\pi$
$859$	−3.02146e10	−1.62645	−0.813224	+	0.581951i	$0.802290\pi$
$860$	5.78973e10	3.10394
$861$	0	0
$862$	−4.47497e10	−2.37966
$863$	−4.20793e9	−0.222859	−0.111430	−	0.993772i	$-0.535543\pi$
$863$	−4.20793e9	−0.222859	−0.111430	+	0.993772i	$0.535543\pi$
$864$	0	0
$865$	−5.08996e10	−2.67398
$866$	2.35831e9	0.123393
$867$	0	0
$868$	−1.80128e10	−0.934894
$869$	−6.06098e9	−0.313310
$870$	0	0
$871$	−2.95954e10	−1.51761
$872$	−2.99158e9	−0.152789
$873$	0	0
$874$	−7.60475e10	−3.85296
$875$	−2.50280e10	−1.26298
$876$	0	0
$877$	−1.97999e10	−0.991206	−0.495603	−	0.868549i	$-0.665053\pi$
$877$	−1.97999e10	−0.991206	−0.495603	+	0.868549i	$0.665053\pi$
$878$	−4.61252e9	−0.229989
$879$	0	0
$880$	6.17609e9	0.305509
$881$	−5.47108e9	−0.269561	−0.134781	−	0.990875i	$-0.543033\pi$
$881$	−5.47108e9	−0.269561	−0.134781	+	0.990875i	$0.543033\pi$
$882$	0	0
$883$	1.99701e10	0.976153	0.488076	−	0.872801i	$-0.337699\pi$
$883$	1.99701e10	0.976153	0.488076	+	0.872801i	$0.337699\pi$
$884$	3.72031e10	1.81133
$885$	0	0
$886$	1.07266e10	0.518138
$887$	6.76780e9	0.325623	0.162811	−	0.986657i	$-0.447944\pi$
$887$	6.76780e9	0.325623	0.162811	+	0.986657i	$0.447944\pi$
$888$	0	0
$889$	1.44716e10	0.690813
$890$	3.07174e10	1.46056
$891$	0	0
$892$	2.09111e10	0.986508
$893$	−4.83521e10	−2.27214
$894$	0	0
$895$	5.86243e10	2.73336
$896$	−2.86994e9	−0.133289
$897$	0	0
$898$	−4.82978e10	−2.22567
$899$	6.19645e9	0.284436
$900$	0	0
$901$	7.65728e9	0.348769
$902$	−2.55504e9	−0.115924
$903$	0	0
$904$	−1.46139e9	−0.0657926
$905$	3.73736e10	1.67608
$906$	0	0
$907$	−2.47127e10	−1.09975	−0.549877	−	0.835246i	$-0.685325\pi$
$907$	−2.47127e10	−1.09975	−0.549877	+	0.835246i	$0.685325\pi$
$908$	3.01414e10	1.33618
$909$	0	0
$910$	−5.24027e10	−2.30520
$911$	3.74402e9	0.164068	0.0820340	−	0.996630i	$-0.473858\pi$
$911$	3.74402e9	0.164068	0.0820340	+	0.996630i	$0.473858\pi$
$912$	0	0
$913$	−3.23790e9	−0.140804
$914$	−4.28539e9	−0.185643
$915$	0	0
$916$	−2.06965e10	−0.889740
$917$	−1.15743e10	−0.495681
$918$	0	0
$919$	−3.76618e9	−0.160065	−0.0800326	−	0.996792i	$-0.525502\pi$
$919$	−3.76618e9	−0.160065	−0.0800326	+	0.996792i	$0.525502\pi$
$920$	−6.71036e9	−0.284111
$921$	0	0
$922$	−1.20536e10	−0.506477
$923$	7.78326e9	0.325804
$924$	0	0
$925$	6.86424e10	2.85165
$926$	−1.30379e10	−0.539598
$927$	0	0
$928$	7.10095e9	0.291675
$929$	−3.28415e10	−1.34390	−0.671952	−	0.740595i	$-0.734544\pi$
$929$	−3.28415e10	−1.34390	−0.671952	+	0.740595i	$0.734544\pi$
$930$	0	0
$931$	2.69863e10	1.09602
$932$	−1.45680e10	−0.589448
$933$	0	0
$934$	−5.61208e10	−2.25377
$935$	−9.65567e9	−0.386315
$936$	0	0
$937$	−3.67023e10	−1.45749	−0.728744	−	0.684787i	$-0.759895\pi$
$937$	−3.67023e10	−1.45749	−0.728744	+	0.684787i	$0.759895\pi$
$938$	−2.37496e10	−0.939605
$939$	0	0
$940$	−6.15458e10	−2.41686
$941$	−2.52107e10	−0.986329	−0.493165	−	0.869936i	$-0.664160\pi$
$941$	−2.52107e10	−0.986329	−0.493165	+	0.869936i	$0.664160\pi$
$942$	0	0
$943$	−1.65277e10	−0.641831
$944$	3.09562e9	0.119769
$945$	0	0
$946$	−1.14451e10	−0.439544
$947$	−8.87956e9	−0.339755	−0.169878	−	0.985465i	$-0.554337\pi$
$947$	−8.87956e9	−0.339755	−0.169878	+	0.985465i	$0.554337\pi$
$948$	0	0
$949$	2.87020e10	1.09013
$950$	−1.46121e11	−5.52944
$951$	0	0
$952$	2.06961e9	0.0777427
$953$	−1.58158e10	−0.591925	−0.295962	−	0.955200i	$-0.595640\pi$
$953$	−1.58158e10	−0.591925	−0.295962	+	0.955200i	$0.595640\pi$
$954$	0	0
$955$	2.81131e10	1.04447
$956$	3.28802e10	1.21711
$957$	0	0
$958$	3.54662e10	1.30327
$959$	−6.41645e8	−0.0234925
$960$	0	0
$961$	2.61635e10	0.950963
$962$	7.66725e10	2.77669
$963$	0	0
$964$	−8.79917e9	−0.316353
$965$	−7.75992e9	−0.277979
$966$	0	0
$967$	5.18915e10	1.84546	0.922728	−	0.385451i	$-0.125954\pi$
$967$	5.18915e10	1.84546	0.922728	+	0.385451i	$0.125954\pi$
$968$	−2.92138e9	−0.103520
$969$	0	0
$970$	6.20881e10	2.18428
$971$	1.69159e10	0.592963	0.296481	−	0.955039i	$-0.404187\pi$
$971$	1.69159e10	0.592963	0.296481	+	0.955039i	$0.404187\pi$
$972$	0	0
$973$	−8.18800e9	−0.284959
$974$	2.83182e10	0.981996
$975$	0	0
$976$	2.39042e10	0.822999
$977$	−8.24427e9	−0.282827	−0.141414	−	0.989951i	$-0.545165\pi$
$977$	−8.24427e9	−0.282827	−0.141414	+	0.989951i	$0.545165\pi$
$978$	0	0
$979$	−3.14513e9	−0.107127
$980$	3.43500e10	1.16583
$981$	0	0
$982$	1.17623e10	0.396373
$983$	4.10669e9	0.137897	0.0689484	−	0.997620i	$-0.478036\pi$
$983$	4.10669e9	0.137897	0.0689484	+	0.997620i	$0.478036\pi$
$984$	0	0
$985$	9.67254e8	0.0322488
$986$	−1.02701e10	−0.341196
$987$	0	0
$988$	−8.45379e10	−2.78870
$989$	−7.40347e10	−2.43359
$990$	0	0
$991$	−1.53943e9	−0.0502460	−0.0251230	−	0.999684i	$-0.507998\pi$
$991$	−1.53943e9	−0.0502460	−0.0251230	+	0.999684i	$0.507998\pi$
$992$	6.15112e10	2.00062
$993$	0	0
$994$	6.24588e9	0.201716
$995$	−1.99778e10	−0.642934
$996$	0	0
$997$	−2.17704e10	−0.695717	−0.347858	−	0.937547i	$-0.613091\pi$
$997$	−2.17704e10	−0.695717	−0.347858	+	0.937547i	$0.613091\pi$
$998$	−2.90263e10	−0.924345
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.14		16
3.2	odd	2		177.8.a.a.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.3	✓	16	3.2	odd	2
531.8.a.b.1.14		16	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)

\(f(q)\)	\(=\)	\(q+16.2952 q^{2} +137.534 q^{4} -495.569 q^{5} +565.301 q^{7} +155.363 q^{8} +O(q^{10})\)	\(q+16.2952 q^{2} +137.534 q^{4} -495.569 q^{5} +565.301 q^{7} +155.363 q^{8} -8075.41 q^{10} +826.834 q^{11} +11479.1 q^{13} +9211.71 q^{14} -15072.7 q^{16} +23564.6 q^{17} -53546.6 q^{19} -68157.8 q^{20} +13473.4 q^{22} +87155.1 q^{23} +167464. q^{25} +187055. q^{26} +77748.3 q^{28} -26745.6 q^{29} -231681. q^{31} -265500. q^{32} +383990. q^{34} -280146. q^{35} +409893. q^{37} -872554. q^{38} -76993.4 q^{40} -189635. q^{41} -849460. q^{43} +113718. q^{44} +1.42021e6 q^{46} +902990. q^{47} -503977. q^{49} +2.72886e6 q^{50} +1.57877e6 q^{52} +324949. q^{53} -409753. q^{55} +87827.2 q^{56} -435826. q^{58} -205379. q^{59} -1.58592e6 q^{61} -3.77529e6 q^{62} -2.39707e6 q^{64} -5.68870e6 q^{65} -2.57819e6 q^{67} +3.24094e6 q^{68} -4.56504e6 q^{70} +678037. q^{71} +2.50036e6 q^{73} +6.67930e6 q^{74} -7.36449e6 q^{76} +467410. q^{77} -7.33035e6 q^{79} +7.46957e6 q^{80} -3.09015e6 q^{82} -3.91602e6 q^{83} -1.16779e7 q^{85} -1.38421e7 q^{86} +128460. q^{88} -3.80382e6 q^{89} +6.48916e6 q^{91} +1.19868e7 q^{92} +1.47144e7 q^{94} +2.65361e7 q^{95} -7.68854e6 q^{97} -8.21243e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Introduction

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