LMFDB - Embedded newform 531.8.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
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			1.13
Root			$15.0467$ 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)

$f(q)$	$=$	$q+15.0467 q^{2} +98.4026 q^{4} -159.890 q^{5} +980.332 q^{7} -445.343 q^{8} +O(q^{10})$	\(q+15.0467 q^{2} +98.4026 q^{4} -159.890 q^{5} +980.332 q^{7} -445.343 q^{8} -2405.81 q^{10} +3390.91 q^{11} -7169.91 q^{13} +14750.7 q^{14} -19296.5 q^{16} +12242.5 q^{17} +19577.3 q^{19} -15733.6 q^{20} +51021.9 q^{22} -103217. q^{23} -52560.2 q^{25} -107883. q^{26} +96467.2 q^{28} +169076. q^{29} -37743.0 q^{31} -233344. q^{32} +184209. q^{34} -156745. q^{35} -29517.3 q^{37} +294573. q^{38} +71205.8 q^{40} -375081. q^{41} +719695. q^{43} +333674. q^{44} -1.55308e6 q^{46} +317727. q^{47} +137507. q^{49} -790857. q^{50} -705538. q^{52} -290607. q^{53} -542172. q^{55} -436584. q^{56} +2.54404e6 q^{58} -205379. q^{59} -2.85898e6 q^{61} -567906. q^{62} -1.04110e6 q^{64} +1.14640e6 q^{65} +1.89394e6 q^{67} +1.20469e6 q^{68} -2.35849e6 q^{70} -3.57204e6 q^{71} -2.76466e6 q^{73} -444137. q^{74} +1.92645e6 q^{76} +3.32421e6 q^{77} -4.56707e6 q^{79} +3.08531e6 q^{80} -5.64372e6 q^{82} +661014. q^{83} -1.95745e6 q^{85} +1.08290e7 q^{86} -1.51012e6 q^{88} +5.31858e6 q^{89} -7.02889e6 q^{91} -1.01568e7 q^{92} +4.78073e6 q^{94} -3.13021e6 q^{95} -1.84545e6 q^{97} +2.06903e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	15.0467	1.32995	0.664976	−	0.746865i	$-0.268442\pi$
$2$	15.0467	1.32995	0.664976	+	0.746865i	$0.268442\pi$
$3$	0	0
$3$	0	0
$4$	98.4026	0.768770
$5$	−159.890	−0.572039	−0.286020	−	0.958224i	$-0.592332\pi$
$5$	−159.890	−0.572039	−0.286020	+	0.958224i	$0.592332\pi$
$6$	0	0
$7$	980.332	1.08026	0.540132	−	0.841580i	$-0.318374\pi$
$7$	980.332	1.08026	0.540132	+	0.841580i	$0.318374\pi$
$8$	−445.343	−0.307524
$9$	0	0
$10$	−2405.81	−0.760785
$11$	3390.91	0.768142	0.384071	−	0.923304i	$-0.374522\pi$
$11$	3390.91	0.768142	0.384071	+	0.923304i	$0.374522\pi$
$12$	0	0
$13$	−7169.91	−0.905132	−0.452566	−	0.891731i	$-0.649491\pi$
$13$	−7169.91	−0.905132	−0.452566	+	0.891731i	$0.649491\pi$
$14$	14750.7	1.43670
$15$	0	0
$16$	−19296.5	−1.17776
$17$	12242.5	0.604364	0.302182	−	0.953250i	$-0.402285\pi$
$17$	12242.5	0.604364	0.302182	+	0.953250i	$0.402285\pi$
$18$	0	0
$19$	19577.3	0.654808	0.327404	−	0.944884i	$-0.393826\pi$
$19$	19577.3	0.654808	0.327404	+	0.944884i	$0.393826\pi$
$20$	−15733.6	−0.439767
$21$	0	0
$22$	51021.9	1.02159
$23$	−103217.	−1.76891	−0.884454	−	0.466628i	$-0.845469\pi$
$23$	−103217.	−1.76891	−0.884454	+	0.466628i	$0.845469\pi$
$24$	0	0
$25$	−52560.2	−0.672771
$26$	−107883.	−1.20378
$27$	0	0
$28$	96467.2	0.830475
$29$	169076.	1.28733	0.643665	−	0.765307i	$-0.277413\pi$
$29$	169076.	1.28733	0.643665	+	0.765307i	$0.277413\pi$
$30$	0	0
$31$	−37743.0	−0.227546	−0.113773	−	0.993507i	$-0.536294\pi$
$31$	−37743.0	−0.227546	−0.113773	+	0.993507i	$0.536294\pi$
$32$	−233344.	−1.25884
$33$	0	0
$34$	184209.	0.803774
$35$	−156745.	−0.617954
$36$	0	0
$37$	−29517.3	−0.0958011	−0.0479006	−	0.998852i	$-0.515253\pi$
$37$	−29517.3	−0.0958011	−0.0479006	+	0.998852i	$0.515253\pi$
$38$	294573.	0.870863
$39$	0	0
$40$	71205.8	0.175916
$41$	−375081.	−0.849926	−0.424963	−	0.905211i	$-0.639713\pi$
$41$	−375081.	−0.849926	−0.424963	+	0.905211i	$0.639713\pi$
$42$	0	0
$43$	719695.	1.38041	0.690206	−	0.723613i	$-0.257520\pi$
$43$	719695.	1.38041	0.690206	+	0.723613i	$0.257520\pi$
$44$	333674.	0.590525
$45$	0	0
$46$	−1.55308e6	−2.35256
$47$	317727.	0.446387	0.223193	−	0.974774i	$-0.428352\pi$
$47$	317727.	0.446387	0.223193	+	0.974774i	$0.428352\pi$
$48$	0	0
$49$	137507.	0.166970
$50$	−790857.	−0.894752
$51$	0	0
$52$	−705538.	−0.695839
$53$	−290607.	−0.268127	−0.134063	−	0.990973i	$-0.542803\pi$
$53$	−290607.	−0.268127	−0.134063	+	0.990973i	$0.542803\pi$
$54$	0	0
$55$	−542172.	−0.439407
$56$	−436584.	−0.332208
$57$	0	0
$58$	2.54404e6	1.71209
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−2.85898e6	−1.61271	−0.806355	−	0.591432i	$-0.798563\pi$
$61$	−2.85898e6	−1.61271	−0.806355	+	0.591432i	$0.798563\pi$
$62$	−567906.	−0.302626
$63$	0	0
$64$	−1.04110e6	−0.496436
$65$	1.14640e6	0.517771
$66$	0	0
$67$	1.89394e6	0.769316	0.384658	−	0.923059i	$-0.374319\pi$
$67$	1.89394e6	0.769316	0.384658	+	0.923059i	$0.374319\pi$
$68$	1.20469e6	0.464617
$69$	0	0
$70$	−2.35849e6	−0.821848
$71$	−3.57204e6	−1.18444	−0.592218	−	0.805778i	$-0.701748\pi$
$71$	−3.57204e6	−1.18444	−0.592218	+	0.805778i	$0.701748\pi$
$72$	0	0
$73$	−2.76466e6	−0.831786	−0.415893	−	0.909413i	$-0.636531\pi$
$73$	−2.76466e6	−0.831786	−0.415893	+	0.909413i	$0.636531\pi$
$74$	−444137.	−0.127411
$75$	0	0
$76$	1.92645e6	0.503397
$77$	3.32421e6	0.829796
$78$	0	0
$79$	−4.56707e6	−1.04218	−0.521091	−	0.853501i	$-0.674475\pi$
$79$	−4.56707e6	−1.04218	−0.521091	+	0.853501i	$0.674475\pi$
$80$	3.08531e6	0.673727
$81$	0	0
$82$	−5.64372e6	−1.13036
$83$	661014.	0.126893	0.0634464	−	0.997985i	$-0.479791\pi$
$83$	661014.	0.126893	0.0634464	+	0.997985i	$0.479791\pi$
$84$	0	0
$85$	−1.95745e6	−0.345720
$86$	1.08290e7	1.83588
$87$	0	0
$88$	−1.51012e6	−0.236222
$89$	5.31858e6	0.799707	0.399853	−	0.916579i	$-0.369061\pi$
$89$	5.31858e6	0.799707	0.399853	+	0.916579i	$0.369061\pi$
$90$	0	0
$91$	−7.02889e6	−0.977782
$92$	−1.01568e7	−1.35988
$93$	0	0
$94$	4.78073e6	0.593673
$95$	−3.13021e6	−0.374576
$96$	0	0
$97$	−1.84545e6	−0.205305	−0.102653	−	0.994717i	$-0.532733\pi$
$97$	−1.84545e6	−0.205305	−0.102653	+	0.994717i	$0.532733\pi$
$98$	2.06903e6	0.222062
$99$	0	0
$100$	−5.17206e6	−0.517206
$101$	−4.95032e6	−0.478088	−0.239044	−	0.971009i	$-0.576834\pi$
$101$	−4.95032e6	−0.478088	−0.239044	+	0.971009i	$0.576834\pi$
$102$	0	0
$103$	−2.16194e7	−1.94946	−0.974728	−	0.223393i	$-0.928287\pi$
$103$	−2.16194e7	−1.94946	−0.974728	+	0.223393i	$0.928287\pi$
$104$	3.19307e6	0.278350
$105$	0	0
$106$	−4.37267e6	−0.356595
$107$	1.82441e6	0.143973	0.0719863	−	0.997406i	$-0.477066\pi$
$107$	1.82441e6	0.143973	0.0719863	+	0.997406i	$0.477066\pi$
$108$	0	0
$109$	5.23038e6	0.386848	0.193424	−	0.981115i	$-0.438041\pi$
$109$	5.23038e6	0.386848	0.193424	+	0.981115i	$0.438041\pi$
$110$	−8.15788e6	−0.584390
$111$	0	0
$112$	−1.89169e7	−1.27229
$113$	−2.44766e7	−1.59579	−0.797895	−	0.602796i	$-0.794053\pi$
$113$	−2.44766e7	−1.59579	−0.797895	+	0.602796i	$0.794053\pi$
$114$	0	0
$115$	1.65034e7	1.01188
$116$	1.66376e7	0.989661
$117$	0	0
$118$	−3.09027e6	−0.173145
$119$	1.20017e7	0.652872
$120$	0	0
$121$	−7.98892e6	−0.409958
$122$	−4.30181e7	−2.14483
$123$	0	0
$124$	−3.71400e6	−0.174931
$125$	2.08952e7	0.956891
$126$	0	0
$127$	−2.70518e7	−1.17188	−0.585940	−	0.810355i	$-0.699275\pi$
$127$	−2.70518e7	−1.17188	−0.585940	+	0.810355i	$0.699275\pi$
$128$	1.42029e7	0.598606
$129$	0	0
$130$	1.72495e7	0.688611
$131$	−1.34945e7	−0.524454	−0.262227	−	0.965006i	$-0.584457\pi$
$131$	−1.34945e7	−0.524454	−0.262227	+	0.965006i	$0.584457\pi$
$132$	0	0
$133$	1.91922e7	0.707366
$134$	2.84975e7	1.02315
$135$	0	0
$136$	−5.45210e6	−0.185857
$137$	−5.35174e7	−1.77817	−0.889084	−	0.457745i	$-0.848657\pi$
$137$	−5.35174e7	−1.77817	−0.889084	+	0.457745i	$0.848657\pi$
$138$	0	0
$139$	1.33665e7	0.422149	0.211075	−	0.977470i	$-0.432304\pi$
$139$	1.33665e7	0.422149	0.211075	+	0.977470i	$0.432304\pi$
$140$	−1.54241e7	−0.475064
$141$	0	0
$142$	−5.37473e7	−1.57524
$143$	−2.43125e7	−0.695270
$144$	0	0
$145$	−2.70336e7	−0.736404
$146$	−4.15990e7	−1.10624
$147$	0	0
$148$	−2.90458e6	−0.0736490
$149$	1.60776e7	0.398170	0.199085	−	0.979982i	$-0.436203\pi$
$149$	1.60776e7	0.398170	0.199085	+	0.979982i	$0.436203\pi$
$150$	0	0
$151$	−5.18108e7	−1.22462	−0.612310	−	0.790618i	$-0.709760\pi$
$151$	−5.18108e7	−1.22462	−0.612310	+	0.790618i	$0.709760\pi$
$152$	−8.71859e6	−0.201370
$153$	0	0
$154$	5.00184e7	1.10359
$155$	6.03472e6	0.130166
$156$	0	0
$157$	−8.16318e7	−1.68349	−0.841746	−	0.539874i	$-0.818472\pi$
$157$	−8.16318e7	−1.68349	−0.841746	+	0.539874i	$0.818472\pi$
$158$	−6.87193e7	−1.38605
$159$	0	0
$160$	3.73093e7	0.720107
$161$	−1.01187e8	−1.91089
$162$	0	0
$163$	8.91769e6	0.161286	0.0806428	−	0.996743i	$-0.474303\pi$
$163$	8.91769e6	0.161286	0.0806428	+	0.996743i	$0.474303\pi$
$164$	−3.69089e7	−0.653398
$165$	0	0
$166$	9.94606e6	0.168761
$167$	3.21164e7	0.533604	0.266802	−	0.963751i	$-0.414033\pi$
$167$	3.21164e7	0.533604	0.266802	+	0.963751i	$0.414033\pi$
$168$	0	0
$169$	−1.13409e7	−0.180736
$170$	−2.94531e7	−0.459790
$171$	0	0
$172$	7.08198e7	1.06122
$173$	5.06027e7	0.743040	0.371520	−	0.928425i	$-0.378837\pi$
$173$	5.06027e7	0.743040	0.371520	+	0.928425i	$0.378837\pi$
$174$	0	0
$175$	−5.15265e7	−0.726770
$176$	−6.54325e7	−0.904689
$177$	0	0
$178$	8.00270e7	1.06357
$179$	6.22045e7	0.810655	0.405327	−	0.914172i	$-0.367157\pi$
$179$	6.22045e7	0.810655	0.405327	+	0.914172i	$0.367157\pi$
$180$	0	0
$181$	6.29686e7	0.789313	0.394656	−	0.918829i	$-0.370864\pi$
$181$	6.29686e7	0.789313	0.394656	+	0.918829i	$0.370864\pi$
$182$	−1.05761e8	−1.30040
$183$	0	0
$184$	4.59671e7	0.543982
$185$	4.71952e6	0.0548020
$186$	0	0
$187$	4.15131e7	0.464237
$188$	3.12651e7	0.343169
$189$	0	0
$190$	−4.70992e7	−0.498168
$191$	7.18839e7	0.746474	0.373237	−	0.927736i	$-0.378248\pi$
$191$	7.18839e7	0.746474	0.373237	+	0.927736i	$0.378248\pi$
$192$	0	0
$193$	−3.68734e7	−0.369201	−0.184600	−	0.982814i	$-0.559099\pi$
$193$	−3.68734e7	−0.369201	−0.184600	+	0.982814i	$0.559099\pi$
$194$	−2.77678e7	−0.273046
$195$	0	0
$196$	1.35311e7	0.128362
$197$	−1.75363e8	−1.63420	−0.817101	−	0.576495i	$-0.804420\pi$
$197$	−1.75363e8	−1.63420	−0.817101	+	0.576495i	$0.804420\pi$
$198$	0	0
$199$	8.16489e7	0.734454	0.367227	−	0.930131i	$-0.380307\pi$
$199$	8.16489e7	0.734454	0.367227	+	0.930131i	$0.380307\pi$
$200$	2.34073e7	0.206893
$201$	0	0
$202$	−7.44858e7	−0.635834
$203$	1.65751e8	1.39066
$204$	0	0
$205$	5.99716e7	0.486191
$206$	−3.25300e8	−2.59268
$207$	0	0
$208$	1.38354e8	1.06603
$209$	6.63846e7	0.502986
$210$	0	0
$211$	1.04928e7	0.0768955	0.0384478	−	0.999261i	$-0.487759\pi$
$211$	1.04928e7	0.0768955	0.0384478	+	0.999261i	$0.487759\pi$
$212$	−2.85965e7	−0.206128
$213$	0	0
$214$	2.74513e7	0.191476
$215$	−1.15072e8	−0.789650
$216$	0	0
$217$	−3.70006e7	−0.245810
$218$	7.86998e7	0.514489
$219$	0	0
$220$	−5.33511e7	−0.337803
$221$	−8.77775e7	−0.547029
$222$	0	0
$223$	−2.52899e8	−1.52714	−0.763572	−	0.645723i	$-0.776556\pi$
$223$	−2.52899e8	−1.52714	−0.763572	+	0.645723i	$0.776556\pi$
$224$	−2.28754e8	−1.35988
$225$	0	0
$226$	−3.68291e8	−2.12232
$227$	−457979.	−0.00259869	−0.00129935	−	0.999999i	$-0.500414\pi$
$227$	−457979.	−0.00259869	−0.00129935	+	0.999999i	$0.500414\pi$
$228$	0	0
$229$	−1.85147e8	−1.01881	−0.509405	−	0.860527i	$-0.670135\pi$
$229$	−1.85147e8	−1.01881	−0.509405	+	0.860527i	$0.670135\pi$
$230$	2.48321e8	1.34576
$231$	0	0
$232$	−7.52970e7	−0.395886
$233$	3.11021e8	1.61081	0.805404	−	0.592726i	$-0.201948\pi$
$233$	3.11021e8	1.61081	0.805404	+	0.592726i	$0.201948\pi$
$234$	0	0
$235$	−5.08013e7	−0.255351
$236$	−2.02098e7	−0.100085
$237$	0	0
$238$	1.80586e8	0.868288
$239$	1.44383e8	0.684107	0.342053	−	0.939680i	$-0.388878\pi$
$239$	1.44383e8	0.684107	0.342053	+	0.939680i	$0.388878\pi$
$240$	0	0
$241$	−9.66758e7	−0.444896	−0.222448	−	0.974945i	$-0.571405\pi$
$241$	−9.66758e7	−0.444896	−0.222448	+	0.974945i	$0.571405\pi$
$242$	−1.20207e8	−0.545224
$243$	0	0
$244$	−2.81331e8	−1.23980
$245$	−2.19860e7	−0.0955136
$246$	0	0
$247$	−1.40367e8	−0.592688
$248$	1.68086e7	0.0699761
$249$	0	0
$250$	3.14404e8	1.27262
$251$	−1.46912e8	−0.586407	−0.293203	−	0.956050i	$-0.594721\pi$
$251$	−1.46912e8	−0.586407	−0.293203	+	0.956050i	$0.594721\pi$
$252$	0	0
$253$	−3.50000e8	−1.35877
$254$	−4.07040e8	−1.55854
$255$	0	0
$256$	3.46967e8	1.29255
$257$	4.93706e8	1.81427	0.907136	−	0.420837i	$-0.138264\pi$
$257$	4.93706e8	1.81427	0.907136	+	0.420837i	$0.138264\pi$
$258$	0	0
$259$	−2.89367e7	−0.103490
$260$	1.12808e8	0.398047
$261$	0	0
$262$	−2.03048e8	−0.697498
$263$	1.94462e8	0.659157	0.329578	−	0.944128i	$-0.393093\pi$
$263$	1.94462e8	0.659157	0.329578	+	0.944128i	$0.393093\pi$
$264$	0	0
$265$	4.64651e7	0.153379
$266$	2.88779e8	0.940762
$267$	0	0
$268$	1.86369e8	0.591427
$269$	5.97880e7	0.187275	0.0936377	−	0.995606i	$-0.470150\pi$
$269$	5.97880e7	0.187275	0.0936377	+	0.995606i	$0.470150\pi$
$270$	0	0
$271$	−5.18384e8	−1.58219	−0.791096	−	0.611693i	$-0.790489\pi$
$271$	−5.18384e8	−1.58219	−0.791096	+	0.611693i	$0.790489\pi$
$272$	−2.36237e8	−0.711797
$273$	0	0
$274$	−8.05258e8	−2.36488
$275$	−1.78227e8	−0.516783
$276$	0	0
$277$	2.35392e8	0.665444	0.332722	−	0.943025i	$-0.392033\pi$
$277$	2.35392e8	0.665444	0.332722	+	0.943025i	$0.392033\pi$
$278$	2.01122e8	0.561438
$279$	0	0
$280$	6.98053e7	0.190036
$281$	3.16518e8	0.850994	0.425497	−	0.904960i	$-0.360099\pi$
$281$	3.16518e8	0.850994	0.425497	+	0.904960i	$0.360099\pi$
$282$	0	0
$283$	−2.45453e8	−0.643748	−0.321874	−	0.946782i	$-0.604313\pi$
$283$	−2.45453e8	−0.643748	−0.321874	+	0.946782i	$0.604313\pi$
$284$	−3.51498e8	−0.910559
$285$	0	0
$286$	−3.65822e8	−0.924675
$287$	−3.67703e8	−0.918144
$288$	0	0
$289$	−2.60460e8	−0.634745
$290$	−4.06766e8	−0.979381
$291$	0	0
$292$	−2.72050e8	−0.639452
$293$	−1.97162e8	−0.457916	−0.228958	−	0.973436i	$-0.573532\pi$
$293$	−1.97162e8	−0.457916	−0.228958	+	0.973436i	$0.573532\pi$
$294$	0	0
$295$	3.28380e7	0.0744732
$296$	1.31453e7	0.0294612
$297$	0	0
$298$	2.41914e8	0.529546
$299$	7.40059e8	1.60110
$300$	0	0
$301$	7.05540e8	1.49121
$302$	−7.79581e8	−1.62868
$303$	0	0
$304$	−3.77772e8	−0.771209
$305$	4.57121e8	0.922534
$306$	0	0
$307$	1.34184e7	0.0264677	0.0132339	−	0.999912i	$-0.495787\pi$
$307$	1.34184e7	0.0264677	0.0132339	+	0.999912i	$0.495787\pi$
$308$	3.27111e8	0.637922
$309$	0	0
$310$	9.08024e7	0.173114
$311$	7.42366e8	1.39945	0.699724	−	0.714413i	$-0.253306\pi$
$311$	7.42366e8	1.39945	0.699724	+	0.714413i	$0.253306\pi$
$312$	0	0
$313$	7.47946e8	1.37869	0.689343	−	0.724435i	$-0.257899\pi$
$313$	7.47946e8	1.37869	0.689343	+	0.724435i	$0.257899\pi$
$314$	−1.22829e9	−2.23896
$315$	0	0
$316$	−4.49412e8	−0.801198
$317$	7.65404e8	1.34953	0.674766	−	0.738031i	$-0.264244\pi$
$317$	7.65404e8	1.34953	0.674766	+	0.738031i	$0.264244\pi$
$318$	0	0
$319$	5.73323e8	0.988853
$320$	1.66462e8	0.283981
$321$	0	0
$322$	−1.52253e9	−2.54139
$323$	2.39674e8	0.395742
$324$	0	0
$325$	3.76852e8	0.608947
$326$	1.34182e8	0.214502
$327$	0	0
$328$	1.67039e8	0.261373
$329$	3.11478e8	0.482216
$330$	0	0
$331$	3.13126e8	0.474592	0.237296	−	0.971437i	$-0.423739\pi$
$331$	3.13126e8	0.474592	0.237296	+	0.971437i	$0.423739\pi$
$332$	6.50455e7	0.0975515
$333$	0	0
$334$	4.83245e8	0.709667
$335$	−3.02822e8	−0.440079
$336$	0	0
$337$	1.30356e9	1.85535	0.927675	−	0.373388i	$-0.121804\pi$
$337$	1.30356e9	1.85535	0.927675	+	0.373388i	$0.121804\pi$
$338$	−1.70643e8	−0.240369
$339$	0	0
$340$	−1.92618e8	−0.265779
$341$	−1.27983e8	−0.174788
$342$	0	0
$343$	−6.72543e8	−0.899892
$344$	−3.20511e8	−0.424511
$345$	0	0
$346$	7.61402e8	0.988206
$347$	2.10675e8	0.270683	0.135341	−	0.990799i	$-0.456787\pi$
$347$	2.10675e8	0.270683	0.135341	+	0.990799i	$0.456787\pi$
$348$	0	0
$349$	6.27337e8	0.789972	0.394986	−	0.918687i	$-0.370749\pi$
$349$	6.27337e8	0.789972	0.394986	+	0.918687i	$0.370749\pi$
$350$	−7.75302e8	−0.966569
$351$	0	0
$352$	−7.91247e8	−0.966970
$353$	8.10514e8	0.980729	0.490364	−	0.871517i	$-0.336864\pi$
$353$	8.10514e8	0.980729	0.490364	+	0.871517i	$0.336864\pi$
$354$	0	0
$355$	5.71133e8	0.677544
$356$	5.23362e8	0.614791
$357$	0	0
$358$	9.35971e8	1.07813
$359$	−4.90257e8	−0.559234	−0.279617	−	0.960112i	$-0.590207\pi$
$359$	−4.90257e8	−0.559234	−0.279617	+	0.960112i	$0.590207\pi$
$360$	0	0
$361$	−5.10603e8	−0.571226
$362$	9.47468e8	1.04975
$363$	0	0
$364$	−6.91661e8	−0.751689
$365$	4.42041e8	0.475815
$366$	0	0
$367$	−6.65868e8	−0.703164	−0.351582	−	0.936157i	$-0.614356\pi$
$367$	−6.65868e8	−0.703164	−0.351582	+	0.936157i	$0.614356\pi$
$368$	1.99173e9	2.08335
$369$	0	0
$370$	7.10131e7	0.0728840
$371$	−2.84891e8	−0.289648
$372$	0	0
$373$	−1.50881e9	−1.50541	−0.752704	−	0.658360i	$-0.771251\pi$
$373$	−1.50881e9	−1.50541	−0.752704	+	0.658360i	$0.771251\pi$
$374$	6.24635e8	0.617412
$375$	0	0
$376$	−1.41497e8	−0.137275
$377$	−1.21226e9	−1.16520
$378$	0	0
$379$	−1.17501e9	−1.10868	−0.554339	−	0.832291i	$-0.687029\pi$
$379$	−1.17501e9	−1.10868	−0.554339	+	0.832291i	$0.687029\pi$
$380$	−3.08020e8	−0.287963
$381$	0	0
$382$	1.08161e9	0.992774
$383$	−3.09605e8	−0.281587	−0.140794	−	0.990039i	$-0.544965\pi$
$383$	−3.09605e8	−0.281587	−0.140794	+	0.990039i	$0.544965\pi$
$384$	0	0
$385$	−5.31508e8	−0.474676
$386$	−5.54822e8	−0.491019
$387$	0	0
$388$	−1.81597e8	−0.157833
$389$	1.81950e9	1.56721	0.783606	−	0.621258i	$-0.213378\pi$
$389$	1.81950e9	1.56721	0.783606	+	0.621258i	$0.213378\pi$
$390$	0	0
$391$	−1.26364e9	−1.06906
$392$	−6.12379e7	−0.0513474
$393$	0	0
$394$	−2.63863e9	−2.17341
$395$	7.30229e8	0.596169
$396$	0	0
$397$	6.58203e8	0.527950	0.263975	−	0.964529i	$-0.414966\pi$
$397$	6.58203e8	0.527950	0.263975	+	0.964529i	$0.414966\pi$
$398$	1.22855e9	0.976788
$399$	0	0
$400$	1.01423e9	0.792364
$401$	−7.74197e8	−0.599578	−0.299789	−	0.954005i	$-0.596916\pi$
$401$	−7.74197e8	−0.599578	−0.299789	+	0.954005i	$0.596916\pi$
$402$	0	0
$403$	2.70614e8	0.205960
$404$	−4.87124e8	−0.367540
$405$	0	0
$406$	2.49400e9	1.84951
$407$	−1.00090e8	−0.0735889
$408$	0	0
$409$	1.08898e9	0.787022	0.393511	−	0.919320i	$-0.371260\pi$
$409$	1.08898e9	0.787022	0.393511	+	0.919320i	$0.371260\pi$
$410$	9.02373e8	0.646610
$411$	0	0
$412$	−2.12741e9	−1.49868
$413$	−2.01340e8	−0.140638
$414$	0	0
$415$	−1.05689e8	−0.0725877
$416$	1.67305e9	1.13942
$417$	0	0
$418$	9.98869e8	0.668946
$419$	−1.86951e9	−1.24159	−0.620795	−	0.783973i	$-0.713190\pi$
$419$	−1.86951e9	−1.24159	−0.620795	+	0.783973i	$0.713190\pi$
$420$	0	0
$421$	2.61169e9	1.70583	0.852913	−	0.522053i	$-0.174834\pi$
$421$	2.61169e9	1.70583	0.852913	+	0.522053i	$0.174834\pi$
$422$	1.57881e8	0.102267
$423$	0	0
$424$	1.29420e8	0.0824555
$425$	−6.43468e8	−0.406598
$426$	0	0
$427$	−2.80275e9	−1.74215
$428$	1.79527e8	0.110682
$429$	0	0
$430$	−1.73145e9	−1.05020
$431$	−1.54835e9	−0.931534	−0.465767	−	0.884908i	$-0.654221\pi$
$431$	−1.54835e9	−0.931534	−0.465767	+	0.884908i	$0.654221\pi$
$432$	0	0
$433$	−1.73247e9	−1.02555	−0.512776	−	0.858523i	$-0.671383\pi$
$433$	−1.73247e9	−1.02555	−0.512776	+	0.858523i	$0.671383\pi$
$434$	−5.56736e8	−0.326916
$435$	0	0
$436$	5.14683e8	0.297397
$437$	−2.02071e9	−1.15830
$438$	0	0
$439$	−3.14201e9	−1.77248	−0.886239	−	0.463227i	$-0.846691\pi$
$439$	−3.14201e9	−1.77248	−0.886239	+	0.463227i	$0.846691\pi$
$440$	2.41452e8	0.135129
$441$	0	0
$442$	−1.32076e9	−0.727522
$443$	−1.87980e9	−1.02730	−0.513651	−	0.857999i	$-0.671707\pi$
$443$	−1.87980e9	−1.02730	−0.513651	+	0.857999i	$0.671707\pi$
$444$	0	0
$445$	−8.50388e8	−0.457464
$446$	−3.80529e9	−2.03103
$447$	0	0
$448$	−1.02063e9	−0.536282
$449$	−2.34987e9	−1.22513	−0.612564	−	0.790421i	$-0.709862\pi$
$449$	−2.34987e9	−1.22513	−0.612564	+	0.790421i	$0.709862\pi$
$450$	0	0
$451$	−1.27186e9	−0.652864
$452$	−2.40856e9	−1.22680
$453$	0	0
$454$	−6.89106e6	−0.00345613
$455$	1.12385e9	0.559330
$456$	0	0
$457$	−1.89675e8	−0.0929615	−0.0464808	−	0.998919i	$-0.514801\pi$
$457$	−1.89675e8	−0.0929615	−0.0464808	+	0.998919i	$0.514801\pi$
$458$	−2.78585e9	−1.35497
$459$	0	0
$460$	1.62398e9	0.777907
$461$	2.07603e9	0.986919	0.493459	−	0.869769i	$-0.335732\pi$
$461$	2.07603e9	0.986919	0.493459	+	0.869769i	$0.335732\pi$
$462$	0	0
$463$	3.00869e9	1.40878	0.704392	−	0.709811i	$-0.251220\pi$
$463$	3.00869e9	1.40878	0.704392	+	0.709811i	$0.251220\pi$
$464$	−3.26258e9	−1.51617
$465$	0	0
$466$	4.67983e9	2.14230
$467$	1.33042e9	0.604479	0.302239	−	0.953232i	$-0.402266\pi$
$467$	1.33042e9	0.604479	0.302239	+	0.953232i	$0.402266\pi$
$468$	0	0
$469$	1.85669e9	0.831064
$470$	−7.64391e8	−0.339604
$471$	0	0
$472$	9.14641e7	0.0400363
$473$	2.44042e9	1.06035
$474$	0	0
$475$	−1.02898e9	−0.440536
$476$	1.18100e9	0.501909
$477$	0	0
$478$	2.17249e9	0.909829
$479$	−2.48445e9	−1.03290	−0.516448	−	0.856318i	$-0.672746\pi$
$479$	−2.48445e9	−1.03290	−0.516448	+	0.856318i	$0.672746\pi$
$480$	0	0
$481$	2.11636e8	0.0867127
$482$	−1.45465e9	−0.591689
$483$	0	0
$484$	−7.86130e8	−0.315163
$485$	2.95068e8	0.117443
$486$	0	0
$487$	−1.39919e9	−0.548940	−0.274470	−	0.961596i	$-0.588502\pi$
$487$	−1.39919e9	−0.548940	−0.274470	+	0.961596i	$0.588502\pi$
$488$	1.27323e9	0.495948
$489$	0	0
$490$	−3.30816e8	−0.127028
$491$	−1.98268e9	−0.755907	−0.377953	−	0.925825i	$-0.623372\pi$
$491$	−1.98268e9	−0.755907	−0.377953	+	0.925825i	$0.623372\pi$
$492$	0	0
$493$	2.06992e9	0.778016
$494$	−2.11206e9	−0.788246
$495$	0	0
$496$	7.28305e8	0.267996
$497$	−3.50178e9	−1.27950
$498$	0	0
$499$	3.50830e9	1.26400	0.631998	−	0.774970i	$-0.282235\pi$
$499$	3.50830e9	1.26400	0.631998	+	0.774970i	$0.282235\pi$
$500$	2.05615e9	0.735629
$501$	0	0
$502$	−2.21054e9	−0.779893
$503$	3.10883e9	1.08920	0.544602	−	0.838694i	$-0.316681\pi$
$503$	3.10883e9	1.08920	0.544602	+	0.838694i	$0.316681\pi$
$504$	0	0
$505$	7.91505e8	0.273485
$506$	−5.26634e9	−1.80710
$507$	0	0
$508$	−2.66197e9	−0.900906
$509$	−2.98895e9	−1.00463	−0.502315	−	0.864685i	$-0.667518\pi$
$509$	−2.98895e9	−1.00463	−0.502315	+	0.864685i	$0.667518\pi$
$510$	0	0
$511$	−2.71028e9	−0.898549
$512$	3.40274e9	1.12043
$513$	0	0
$514$	7.42864e9	2.41289
$515$	3.45673e9	1.11517
$516$	0	0
$517$	1.07738e9	0.342888
$518$	−4.35402e8	−0.137637
$519$	0	0
$520$	−5.10540e8	−0.159227
$521$	−2.53744e8	−0.0786075	−0.0393037	−	0.999227i	$-0.512514\pi$
$521$	−2.53744e8	−0.0786075	−0.0393037	+	0.999227i	$0.512514\pi$
$522$	0	0
$523$	2.79711e9	0.854975	0.427487	−	0.904021i	$-0.359399\pi$
$523$	2.79711e9	0.854975	0.427487	+	0.904021i	$0.359399\pi$
$524$	−1.32789e9	−0.403185
$525$	0	0
$526$	2.92600e9	0.876646
$527$	−4.62067e8	−0.137521
$528$	0	0
$529$	7.24899e9	2.12903
$530$	6.99145e8	0.203987
$531$	0	0
$532$	1.88856e9	0.543802
$533$	2.68929e9	0.769295
$534$	0	0
$535$	−2.91705e8	−0.0823580
$536$	−8.43453e8	−0.236583
$537$	0	0
$538$	8.99610e8	0.249067
$539$	4.66274e8	0.128257
$540$	0	0
$541$	−2.58195e9	−0.701064	−0.350532	−	0.936551i	$-0.613999\pi$
$541$	−2.58195e9	−0.701064	−0.350532	+	0.936551i	$0.613999\pi$
$542$	−7.79996e9	−2.10424
$543$	0	0
$544$	−2.85671e9	−0.760798
$545$	−8.36284e8	−0.221292
$546$	0	0
$547$	1.44486e9	0.377459	0.188730	−	0.982029i	$-0.439563\pi$
$547$	1.44486e9	0.377459	0.188730	+	0.982029i	$0.439563\pi$
$548$	−5.26625e9	−1.36700
$549$	0	0
$550$	−2.68172e9	−0.687297
$551$	3.31005e9	0.842955
$552$	0	0
$553$	−4.47725e9	−1.12583
$554$	3.54186e9	0.885008
$555$	0	0
$556$	1.31530e9	0.324536
$557$	4.77372e9	1.17048	0.585240	−	0.810860i	$-0.301000\pi$
$557$	4.77372e9	1.17048	0.585240	+	0.810860i	$0.301000\pi$
$558$	0	0
$559$	−5.16015e9	−1.24946
$560$	3.02463e9	0.727803
$561$	0	0
$562$	4.76255e9	1.13178
$563$	3.69151e9	0.871816	0.435908	−	0.899991i	$-0.356427\pi$
$563$	3.69151e9	0.871816	0.435908	+	0.899991i	$0.356427\pi$
$564$	0	0
$565$	3.91356e9	0.912855
$566$	−3.69326e9	−0.856154
$567$	0	0
$568$	1.59078e9	0.364243
$569$	2.15110e9	0.489516	0.244758	−	0.969584i	$-0.421291\pi$
$569$	2.15110e9	0.489516	0.244758	+	0.969584i	$0.421291\pi$
$570$	0	0
$571$	5.63827e8	0.126742	0.0633709	−	0.997990i	$-0.479815\pi$
$571$	5.63827e8	0.126742	0.0633709	+	0.997990i	$0.479815\pi$
$572$	−2.39241e9	−0.534503
$573$	0	0
$574$	−5.53271e9	−1.22109
$575$	5.42513e9	1.19007
$576$	0	0
$577$	−3.12035e9	−0.676221	−0.338110	−	0.941106i	$-0.609788\pi$
$577$	−3.12035e9	−0.676221	−0.338110	+	0.941106i	$0.609788\pi$
$578$	−3.91906e9	−0.844179
$579$	0	0
$580$	−2.66018e9	−0.566125
$581$	6.48013e8	0.137078
$582$	0	0
$583$	−9.85420e8	−0.205959
$584$	1.23122e9	0.255795
$585$	0	0
$586$	−2.96663e9	−0.609006
$587$	4.80777e9	0.981094	0.490547	−	0.871415i	$-0.336797\pi$
$587$	4.80777e9	0.981094	0.490547	+	0.871415i	$0.336797\pi$
$588$	0	0
$589$	−7.38903e8	−0.148999
$590$	4.94103e8	0.0990457
$591$	0	0
$592$	5.69579e8	0.112831
$593$	4.97973e8	0.0980651	0.0490326	−	0.998797i	$-0.484386\pi$
$593$	4.97973e8	0.0980651	0.0490326	+	0.998797i	$0.484386\pi$
$594$	0	0
$595$	−1.91895e9	−0.373469
$596$	1.58207e9	0.306101
$597$	0	0
$598$	1.11354e10	2.12938
$599$	1.25174e9	0.237968	0.118984	−	0.992896i	$-0.462036\pi$
$599$	1.25174e9	0.237968	0.118984	+	0.992896i	$0.462036\pi$
$600$	0	0
$601$	−3.57133e9	−0.671073	−0.335536	−	0.942027i	$-0.608918\pi$
$601$	−3.57133e9	−0.671073	−0.335536	+	0.942027i	$0.608918\pi$
$602$	1.06160e10	1.98324
$603$	0	0
$604$	−5.09832e9	−0.941451
$605$	1.27735e9	0.234512
$606$	0	0
$607$	−2.73915e9	−0.497113	−0.248556	−	0.968617i	$-0.579956\pi$
$607$	−2.73915e9	−0.497113	−0.248556	+	0.968617i	$0.579956\pi$
$608$	−4.56823e9	−0.824300
$609$	0	0
$610$	6.87816e9	1.22692
$611$	−2.27807e9	−0.404039
$612$	0	0
$613$	2.74148e9	0.480700	0.240350	−	0.970686i	$-0.422738\pi$
$613$	2.74148e9	0.480700	0.240350	+	0.970686i	$0.422738\pi$
$614$	2.01903e8	0.0352008
$615$	0	0
$616$	−1.48042e9	−0.255183
$617$	9.78150e9	1.67652	0.838258	−	0.545274i	$-0.183575\pi$
$617$	9.78150e9	1.67652	0.838258	+	0.545274i	$0.183575\pi$
$618$	0	0
$619$	8.34172e9	1.41364	0.706819	−	0.707394i	$-0.250130\pi$
$619$	8.34172e9	1.41364	0.706819	+	0.707394i	$0.250130\pi$
$620$	5.93832e8	0.100067
$621$	0	0
$622$	1.11701e10	1.86120
$623$	5.21397e9	0.863895
$624$	0	0
$625$	7.65329e8	0.125391
$626$	1.12541e10	1.83358
$627$	0	0
$628$	−8.03278e9	−1.29422
$629$	−3.61365e8	−0.0578987
$630$	0	0
$631$	−4.64175e7	−0.00735494	−0.00367747	−	0.999993i	$-0.501171\pi$
$631$	−4.64175e7	−0.00735494	−0.00367747	+	0.999993i	$0.501171\pi$
$632$	2.03391e9	0.320496
$633$	0	0
$634$	1.15168e10	1.79481
$635$	4.32531e9	0.670361
$636$	0	0
$637$	−9.85914e8	−0.151130
$638$	8.62660e9	1.31513
$639$	0	0
$640$	−2.27090e9	−0.342426
$641$	9.01725e9	1.35229	0.676147	−	0.736767i	$-0.263648\pi$
$641$	9.01725e9	1.35229	0.676147	+	0.736767i	$0.263648\pi$
$642$	0	0
$643$	−6.73082e9	−0.998457	−0.499229	−	0.866470i	$-0.666383\pi$
$643$	−6.73082e9	−0.998457	−0.499229	+	0.866470i	$0.666383\pi$
$644$	−9.95708e9	−1.46903
$645$	0	0
$646$	3.60630e9	0.526318
$647$	−1.43491e9	−0.208286	−0.104143	−	0.994562i	$-0.533210\pi$
$647$	−1.43491e9	−0.208286	−0.104143	+	0.994562i	$0.533210\pi$
$648$	0	0
$649$	−6.96421e8	−0.100004
$650$	5.67037e9	0.809869
$651$	0	0
$652$	8.77524e8	0.123992
$653$	−3.13170e9	−0.440133	−0.220066	−	0.975485i	$-0.570627\pi$
$653$	−3.13170e9	−0.440133	−0.220066	+	0.975485i	$0.570627\pi$
$654$	0	0
$655$	2.15763e9	0.300008
$656$	7.23773e9	1.00101
$657$	0	0
$658$	4.68671e9	0.641323
$659$	−8.36231e9	−1.13822	−0.569111	−	0.822260i	$-0.692713\pi$
$659$	−8.36231e9	−1.13822	−0.569111	+	0.822260i	$0.692713\pi$
$660$	0	0
$661$	1.18208e10	1.59200	0.795999	−	0.605298i	$-0.206946\pi$
$661$	1.18208e10	1.59200	0.795999	+	0.605298i	$0.206946\pi$
$662$	4.71150e9	0.631185
$663$	0	0
$664$	−2.94378e8	−0.0390227
$665$	−3.06864e9	−0.404641
$666$	0	0
$667$	−1.74516e10	−2.27717
$668$	3.16034e9	0.410219
$669$	0	0
$670$	−4.55647e9	−0.585284
$671$	−9.69452e9	−1.23879
$672$	0	0
$673$	2.34562e9	0.296624	0.148312	−	0.988941i	$-0.452616\pi$
$673$	2.34562e9	0.296624	0.148312	+	0.988941i	$0.452616\pi$
$674$	1.96142e10	2.46753
$675$	0	0
$676$	−1.11597e9	−0.138944
$677$	1.57414e10	1.94977	0.974884	−	0.222713i	$-0.0714912\pi$
$677$	1.57414e10	1.94977	0.974884	+	0.222713i	$0.0714912\pi$
$678$	0	0
$679$	−1.80915e9	−0.221784
$680$	8.71736e8	0.106317
$681$	0	0
$682$	−1.92572e9	−0.232459
$683$	6.44477e9	0.773989	0.386994	−	0.922082i	$-0.373513\pi$
$683$	6.44477e9	0.773989	0.386994	+	0.922082i	$0.373513\pi$
$684$	0	0
$685$	8.55688e9	1.01718
$686$	−1.01195e10	−1.19681
$687$	0	0
$688$	−1.38876e10	−1.62580
$689$	2.08362e9	0.242690
$690$	0	0
$691$	1.59645e10	1.84070	0.920349	−	0.391097i	$-0.127904\pi$
$691$	1.59645e10	1.84070	0.920349	+	0.391097i	$0.127904\pi$
$692$	4.97943e9	0.571227
$693$	0	0
$694$	3.16997e9	0.359995
$695$	−2.13717e9	−0.241486
$696$	0	0
$697$	−4.59192e9	−0.513664
$698$	9.43933e9	1.05062
$699$	0	0
$700$	−5.07034e9	−0.558719
$701$	−1.28238e10	−1.40606	−0.703028	−	0.711162i	$-0.748169\pi$
$701$	−1.28238e10	−1.40606	−0.703028	+	0.711162i	$0.748169\pi$
$702$	0	0
$703$	−5.77868e8	−0.0627314
$704$	−3.53028e9	−0.381333
$705$	0	0
$706$	1.21955e10	1.30432
$707$	−4.85295e9	−0.516462
$708$	0	0
$709$	4.26207e8	0.0449117	0.0224558	−	0.999748i	$-0.492851\pi$
$709$	4.26207e8	0.0449117	0.0224558	+	0.999748i	$0.492851\pi$
$710$	8.59365e9	0.901101
$711$	0	0
$712$	−2.36859e9	−0.245929
$713$	3.89573e9	0.402509
$714$	0	0
$715$	3.88732e9	0.397722
$716$	6.12108e9	0.623207
$717$	0	0
$718$	−7.37674e9	−0.743754
$719$	−9.93256e9	−0.996576	−0.498288	−	0.867012i	$-0.666038\pi$
$719$	−9.93256e9	−0.996576	−0.498288	+	0.867012i	$0.666038\pi$
$720$	0	0
$721$	−2.11942e10	−2.10593
$722$	−7.68288e9	−0.759703
$723$	0	0
$724$	6.19627e9	0.606800
$725$	−8.88670e9	−0.866079
$726$	0	0
$727$	−7.03816e8	−0.0679342	−0.0339671	−	0.999423i	$-0.510814\pi$
$727$	−7.03816e8	−0.0679342	−0.0339671	+	0.999423i	$0.510814\pi$
$728$	3.13027e9	0.300692
$729$	0	0
$730$	6.65125e9	0.632810
$731$	8.81085e9	0.834271
$732$	0	0
$733$	1.24906e10	1.17144	0.585718	−	0.810515i	$-0.300813\pi$
$733$	1.24906e10	1.17144	0.585718	+	0.810515i	$0.300813\pi$
$734$	−1.00191e10	−0.935174
$735$	0	0
$736$	2.40851e10	2.22678
$737$	6.42218e9	0.590944
$738$	0	0
$739$	−8.92221e9	−0.813237	−0.406618	−	0.913598i	$-0.633292\pi$
$739$	−8.92221e9	−0.813237	−0.406618	+	0.913598i	$0.633292\pi$
$740$	4.64413e8	0.0421302
$741$	0	0
$742$	−4.28666e9	−0.385217
$743$	−4.73069e9	−0.423120	−0.211560	−	0.977365i	$-0.567854\pi$
$743$	−4.73069e9	−0.423120	−0.211560	+	0.977365i	$0.567854\pi$
$744$	0	0
$745$	−2.57064e9	−0.227769
$746$	−2.27026e10	−2.00212
$747$	0	0
$748$	4.08500e9	0.356892
$749$	1.78853e9	0.155528
$750$	0	0
$751$	6.35674e9	0.547640	0.273820	−	0.961781i	$-0.411713\pi$
$751$	6.35674e9	0.547640	0.273820	+	0.961781i	$0.411713\pi$
$752$	−6.13100e9	−0.525738
$753$	0	0
$754$	−1.82405e10	−1.54967
$755$	8.28403e9	0.700531
$756$	0	0
$757$	−3.90470e9	−0.327154	−0.163577	−	0.986531i	$-0.552303\pi$
$757$	−3.90470e9	−0.327154	−0.163577	+	0.986531i	$0.552303\pi$
$758$	−1.76801e10	−1.47449
$759$	0	0
$760$	1.39401e9	0.115191
$761$	−2.13395e10	−1.75525	−0.877623	−	0.479351i	$-0.840872\pi$
$761$	−2.13395e10	−1.75525	−0.877623	+	0.479351i	$0.840872\pi$
$762$	0	0
$763$	5.12750e9	0.417898
$764$	7.07356e9	0.573867
$765$	0	0
$766$	−4.65853e9	−0.374497
$767$	1.47255e9	0.117838
$768$	0	0
$769$	−1.05289e9	−0.0834910	−0.0417455	−	0.999128i	$-0.513292\pi$
$769$	−1.05289e9	−0.0834910	−0.0417455	+	0.999128i	$0.513292\pi$
$770$	−7.99743e9	−0.631296
$771$	0	0
$772$	−3.62844e9	−0.283830
$773$	−5.93967e9	−0.462524	−0.231262	−	0.972891i	$-0.574285\pi$
$773$	−5.93967e9	−0.462524	−0.231262	+	0.972891i	$0.574285\pi$
$774$	0	0
$775$	1.98378e9	0.153087
$776$	8.21856e8	0.0631364
$777$	0	0
$778$	2.73774e10	2.08432
$779$	−7.34305e9	−0.556539
$780$	0	0
$781$	−1.21124e10	−0.909815
$782$	−1.90135e10	−1.42180
$783$	0	0
$784$	−2.65340e9	−0.196651
$785$	1.30521e10	0.963023
$786$	0	0
$787$	1.31636e10	0.962640	0.481320	−	0.876545i	$-0.340158\pi$
$787$	1.31636e10	0.962640	0.481320	+	0.876545i	$0.340158\pi$
$788$	−1.72562e10	−1.25633
$789$	0	0
$790$	1.09875e10	0.792875
$791$	−2.39952e10	−1.72388
$792$	0	0
$793$	2.04986e10	1.45972
$794$	9.90377e9	0.702148
$795$	0	0
$796$	8.03446e9	0.564626
$797$	1.29607e10	0.906825	0.453412	−	0.891301i	$-0.350206\pi$
$797$	1.29607e10	0.906825	0.453412	+	0.891301i	$0.350206\pi$
$798$	0	0
$799$	3.88977e9	0.269780
$800$	1.22646e10	0.846912
$801$	0	0
$802$	−1.16491e10	−0.797410
$803$	−9.37471e9	−0.638930
$804$	0	0
$805$	1.61788e10	1.09310
$806$	4.07184e9	0.273916
$807$	0	0
$808$	2.20459e9	0.147024
$809$	1.62295e10	1.07767	0.538836	−	0.842411i	$-0.318864\pi$
$809$	1.62295e10	1.07767	0.538836	+	0.842411i	$0.318864\pi$
$810$	0	0
$811$	8.71515e9	0.573723	0.286861	−	0.957972i	$-0.407388\pi$
$811$	8.71515e9	0.573723	0.286861	+	0.957972i	$0.407388\pi$
$812$	1.63103e10	1.06910
$813$	0	0
$814$	−1.50603e9	−0.0978696
$815$	−1.42585e9	−0.0922618
$816$	0	0
$817$	1.40897e10	0.903906
$818$	1.63855e10	1.04670
$819$	0	0
$820$	5.90136e9	0.373769
$821$	−2.43096e10	−1.53312	−0.766561	−	0.642171i	$-0.778034\pi$
$821$	−2.43096e10	−1.53312	−0.766561	+	0.642171i	$0.778034\pi$
$822$	0	0
$823$	−1.50334e10	−0.940062	−0.470031	−	0.882650i	$-0.655757\pi$
$823$	−1.50334e10	−0.940062	−0.470031	+	0.882650i	$0.655757\pi$
$824$	9.62805e9	0.599506
$825$	0	0
$826$	−3.02949e9	−0.187042
$827$	7.68810e9	0.472661	0.236331	−	0.971673i	$-0.424055\pi$
$827$	7.68810e9	0.472661	0.236331	+	0.971673i	$0.424055\pi$
$828$	0	0
$829$	4.74776e9	0.289433	0.144716	−	0.989473i	$-0.453773\pi$
$829$	4.74776e9	0.289433	0.144716	+	0.989473i	$0.453773\pi$
$830$	−1.59028e9	−0.0965381
$831$	0	0
$832$	7.46461e9	0.449340
$833$	1.68343e9	0.100911
$834$	0	0
$835$	−5.13509e9	−0.305243
$836$	6.53242e9	0.386680
$837$	0	0
$838$	−2.81299e10	−1.65125
$839$	1.32986e10	0.777391	0.388696	−	0.921366i	$-0.372926\pi$
$839$	1.32986e10	0.777391	0.388696	+	0.921366i	$0.372926\pi$
$840$	0	0
$841$	1.13370e10	0.657221
$842$	3.92973e10	2.26867
$843$	0	0
$844$	1.03251e9	0.0591150
$845$	1.81329e9	0.103388
$846$	0	0
$847$	−7.83179e9	−0.442863
$848$	5.60768e9	0.315790
$849$	0	0
$850$	−9.68205e9	−0.540756
$851$	3.04670e9	0.169463
$852$	0	0
$853$	5.80154e9	0.320053	0.160027	−	0.987113i	$-0.448842\pi$
$853$	5.80154e9	0.320053	0.160027	+	0.987113i	$0.448842\pi$
$854$	−4.21720e10	−2.31698
$855$	0	0
$856$	−8.12489e8	−0.0442751
$857$	2.65557e10	1.44120	0.720601	−	0.693350i	$-0.243866\pi$
$857$	2.65557e10	1.44120	0.720601	+	0.693350i	$0.243866\pi$
$858$	0	0
$859$	4.83329e9	0.260176	0.130088	−	0.991502i	$-0.458474\pi$
$859$	4.83329e9	0.260176	0.130088	+	0.991502i	$0.458474\pi$
$860$	−1.13234e10	−0.607060
$861$	0	0
$862$	−2.32975e10	−1.23889
$863$	−9.78741e9	−0.518358	−0.259179	−	0.965829i	$-0.583452\pi$
$863$	−9.78741e9	−0.518358	−0.259179	+	0.965829i	$0.583452\pi$
$864$	0	0
$865$	−8.09085e9	−0.425048
$866$	−2.60679e10	−1.36393
$867$	0	0
$868$	−3.64096e9	−0.188972
$869$	−1.54865e10	−0.800543
$870$	0	0
$871$	−1.35794e10	−0.696333
$872$	−2.32931e9	−0.118965
$873$	0	0
$874$	−3.04050e10	−1.54048
$875$	2.04843e10	1.03369
$876$	0	0
$877$	−1.33028e10	−0.665956	−0.332978	−	0.942935i	$-0.608053\pi$
$877$	−1.33028e10	−0.665956	−0.332978	+	0.942935i	$0.608053\pi$
$878$	−4.72767e10	−2.35731
$879$	0	0
$880$	1.04620e10	0.517518
$881$	−1.14650e10	−0.564885	−0.282443	−	0.959284i	$-0.591145\pi$
$881$	−1.14650e10	−0.564885	−0.282443	+	0.959284i	$0.591145\pi$
$882$	0	0
$883$	−1.56517e10	−0.765067	−0.382533	−	0.923942i	$-0.624948\pi$
$883$	−1.56517e10	−0.765067	−0.382533	+	0.923942i	$0.624948\pi$
$884$	−8.63753e9	−0.420540
$885$	0	0
$886$	−2.82847e10	−1.36626
$887$	−6.19771e9	−0.298194	−0.149097	−	0.988823i	$-0.547637\pi$
$887$	−6.19771e9	−0.298194	−0.149097	+	0.988823i	$0.547637\pi$
$888$	0	0
$889$	−2.65197e10	−1.26594
$890$	−1.27955e10	−0.608405
$891$	0	0
$892$	−2.48859e10	−1.17402
$893$	6.22022e9	0.292298
$894$	0	0
$895$	−9.94587e9	−0.463727
$896$	1.39235e10	0.646653
$897$	0	0
$898$	−3.53577e10	−1.62936
$899$	−6.38144e9	−0.292927
$900$	0	0
$901$	−3.55775e9	−0.162046
$902$	−1.91373e10	−0.868277
$903$	0	0
$904$	1.09005e10	0.490745
$905$	−1.00680e10	−0.451518
$906$	0	0
$907$	−2.84672e10	−1.26683	−0.633417	−	0.773811i	$-0.718348\pi$
$907$	−2.84672e10	−1.26683	−0.633417	+	0.773811i	$0.718348\pi$
$908$	−4.50663e7	−0.00199780
$909$	0	0
$910$	1.69102e10	0.743881
$911$	−1.41611e10	−0.620558	−0.310279	−	0.950646i	$-0.600422\pi$
$911$	−1.41611e10	−0.620558	−0.310279	+	0.950646i	$0.600422\pi$
$912$	0	0
$913$	2.24144e9	0.0974717
$914$	−2.85398e9	−0.123634
$915$	0	0
$916$	−1.82190e10	−0.783231
$917$	−1.32291e10	−0.566549
$918$	0	0
$919$	1.43616e10	0.610379	0.305189	−	0.952292i	$-0.401280\pi$
$919$	1.43616e10	0.610379	0.305189	+	0.952292i	$0.401280\pi$
$920$	−7.34968e9	−0.311179
$921$	0	0
$922$	3.12374e10	1.31255
$923$	2.56112e10	1.07207
$924$	0	0
$925$	1.55144e9	0.0644522
$926$	4.52709e10	1.87362
$927$	0	0
$928$	−3.94529e10	−1.62055
$929$	−2.83698e10	−1.16092	−0.580458	−	0.814290i	$-0.697127\pi$
$929$	−2.83698e10	−1.16092	−0.580458	+	0.814290i	$0.697127\pi$
$930$	0	0
$931$	2.69201e9	0.109334
$932$	3.06053e10	1.23834
$933$	0	0
$934$	2.00185e10	0.803928
$935$	−6.63753e9	−0.265562
$936$	0	0
$937$	−4.33315e10	−1.72074	−0.860370	−	0.509669i	$-0.829768\pi$
$937$	−4.33315e10	−1.72074	−0.860370	+	0.509669i	$0.829768\pi$
$938$	2.79370e10	1.10527
$939$	0	0
$940$	−4.99898e9	−0.196306
$941$	−3.82084e10	−1.49484	−0.747421	−	0.664351i	$-0.768708\pi$
$941$	−3.82084e10	−1.49484	−0.747421	+	0.664351i	$0.768708\pi$
$942$	0	0
$943$	3.87148e10	1.50344
$944$	3.96309e9	0.153332
$945$	0	0
$946$	3.67202e10	1.41022
$947$	−1.03534e10	−0.396148	−0.198074	−	0.980187i	$-0.563469\pi$
$947$	−1.03534e10	−0.396148	−0.198074	+	0.980187i	$0.563469\pi$
$948$	0	0
$949$	1.98224e10	0.752877
$950$	−1.54828e10	−0.585891
$951$	0	0
$952$	−5.34487e9	−0.200774
$953$	−2.92299e10	−1.09396	−0.546981	−	0.837145i	$-0.684223\pi$
$953$	−2.92299e10	−1.09396	−0.546981	+	0.837145i	$0.684223\pi$
$954$	0	0
$955$	−1.14935e10	−0.427013
$956$	1.42077e10	0.525921
$957$	0	0
$958$	−3.73828e10	−1.37370
$959$	−5.24648e10	−1.92089
$960$	0	0
$961$	−2.60881e10	−0.948223
$962$	3.18443e9	0.115324
$963$	0	0
$964$	−9.51315e9	−0.342022
$965$	5.89568e9	0.211197
$966$	0	0
$967$	4.59588e9	0.163447	0.0817233	−	0.996655i	$-0.473958\pi$
$967$	4.59588e9	0.163447	0.0817233	+	0.996655i	$0.473958\pi$
$968$	3.55781e9	0.126072
$969$	0	0
$970$	4.43980e9	0.156193
$971$	5.52070e10	1.93520	0.967602	−	0.252481i	$-0.0812466\pi$
$971$	5.52070e10	1.93520	0.967602	+	0.252481i	$0.0812466\pi$
$972$	0	0
$973$	1.31036e10	0.456033
$974$	−2.10531e10	−0.730063
$975$	0	0
$976$	5.51681e10	1.89939
$977$	4.44629e9	0.152534	0.0762671	−	0.997087i	$-0.475700\pi$
$977$	4.44629e9	0.152534	0.0762671	+	0.997087i	$0.475700\pi$
$978$	0	0
$979$	1.80348e10	0.614288
$980$	−2.16348e9	−0.0734280
$981$	0	0
$982$	−2.98328e10	−1.00532
$983$	−3.90750e10	−1.31208	−0.656041	−	0.754725i	$-0.727770\pi$
$983$	−3.90750e10	−1.31208	−0.656041	+	0.754725i	$0.727770\pi$
$984$	0	0
$985$	2.80387e10	0.934828
$986$	3.11454e10	1.03472
$987$	0	0
$988$	−1.38125e10	−0.455641
$989$	−7.42850e10	−2.44182
$990$	0	0
$991$	−1.52795e10	−0.498713	−0.249357	−	0.968412i	$-0.580219\pi$
$991$	−1.52795e10	−0.498713	−0.249357	+	0.968412i	$0.580219\pi$
$992$	8.80708e9	0.286445
$993$	0	0
$994$	−5.26902e10	−1.70168
$995$	−1.30548e10	−0.420137
$996$	0	0
$997$	1.22551e10	0.391637	0.195818	−	0.980640i	$-0.437264\pi$
$997$	1.22551e10	0.391637	0.195818	+	0.980640i	$0.437264\pi$
$998$	5.27883e10	1.68105
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.13		16
3.2	odd	2		177.8.a.a.1.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.4	✓	16	3.2	odd	2
531.8.a.b.1.13		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)

\(f(q)\)	\(=\)	\(q+15.0467 q^{2} +98.4026 q^{4} -159.890 q^{5} +980.332 q^{7} -445.343 q^{8} +O(q^{10})\)	\(q+15.0467 q^{2} +98.4026 q^{4} -159.890 q^{5} +980.332 q^{7} -445.343 q^{8} -2405.81 q^{10} +3390.91 q^{11} -7169.91 q^{13} +14750.7 q^{14} -19296.5 q^{16} +12242.5 q^{17} +19577.3 q^{19} -15733.6 q^{20} +51021.9 q^{22} -103217. q^{23} -52560.2 q^{25} -107883. q^{26} +96467.2 q^{28} +169076. q^{29} -37743.0 q^{31} -233344. q^{32} +184209. q^{34} -156745. q^{35} -29517.3 q^{37} +294573. q^{38} +71205.8 q^{40} -375081. q^{41} +719695. q^{43} +333674. q^{44} -1.55308e6 q^{46} +317727. q^{47} +137507. q^{49} -790857. q^{50} -705538. q^{52} -290607. q^{53} -542172. q^{55} -436584. q^{56} +2.54404e6 q^{58} -205379. q^{59} -2.85898e6 q^{61} -567906. q^{62} -1.04110e6 q^{64} +1.14640e6 q^{65} +1.89394e6 q^{67} +1.20469e6 q^{68} -2.35849e6 q^{70} -3.57204e6 q^{71} -2.76466e6 q^{73} -444137. q^{74} +1.92645e6 q^{76} +3.32421e6 q^{77} -4.56707e6 q^{79} +3.08531e6 q^{80} -5.64372e6 q^{82} +661014. q^{83} -1.95745e6 q^{85} +1.08290e7 q^{86} -1.51012e6 q^{88} +5.31858e6 q^{89} -7.02889e6 q^{91} -1.01568e7 q^{92} +4.78073e6 q^{94} -3.13021e6 q^{95} -1.84545e6 q^{97} +2.06903e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 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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