LMFDB - Embedded newform 531.8.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 2030 x^{18} + 8100 x^{17} + 1744106 x^{16} - 5171970 x^{15} - 824233578 x^{14} + \cdots + 21\!\cdots\!56 $ x^20 - 5x^19 - 2030x^18 + 8100x^17 + 1744106x^16 - 5171970x^15 - 824233578x^14 + 1598029822x^13 + 232842240056x^12 - 214914822204x^11 - 39921377377038x^10 - 2769070830674x^9 + 4006731223301074x^8 + 4089493775037394x^7 - 210486334380342574x^6 - 397730818944482598x^5 + 4162079532005838407x^4 + 10766105814530150769x^3 + 8553148575870654100x^2 + 2492797715746105302*x + 210157375523369156
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 59)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$12.0947$ 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)

$f(q)$	$=$	$q+11.0947 q^{2} -4.90769 q^{4} -390.109 q^{5} -178.013 q^{7} -1474.57 q^{8} +O(q^{10})$	\(q+11.0947 q^{2} -4.90769 q^{4} -390.109 q^{5} -178.013 q^{7} -1474.57 q^{8} -4328.15 q^{10} +4740.39 q^{11} +131.881 q^{13} -1975.00 q^{14} -15731.7 q^{16} -32763.8 q^{17} -45178.3 q^{19} +1914.54 q^{20} +52593.2 q^{22} -58380.8 q^{23} +74060.4 q^{25} +1463.18 q^{26} +873.632 q^{28} -191330. q^{29} -11950.2 q^{31} +14206.3 q^{32} -363505. q^{34} +69444.5 q^{35} +391041. q^{37} -501240. q^{38} +575244. q^{40} -337341. q^{41} +380422. q^{43} -23264.4 q^{44} -647717. q^{46} -218754. q^{47} -791854. q^{49} +821677. q^{50} -647.230 q^{52} -1.45354e6 q^{53} -1.84927e6 q^{55} +262492. q^{56} -2.12275e6 q^{58} +205379. q^{59} -2.11534e6 q^{61} -132584. q^{62} +2.17128e6 q^{64} -51447.9 q^{65} +3.01688e6 q^{67} +160795. q^{68} +770465. q^{70} +761303. q^{71} -708365. q^{73} +4.33848e6 q^{74} +221721. q^{76} -843850. q^{77} +8.14870e6 q^{79} +6.13710e6 q^{80} -3.74269e6 q^{82} -4.28035e6 q^{83} +1.27815e7 q^{85} +4.22066e6 q^{86} -6.99004e6 q^{88} -1.62360e6 q^{89} -23476.5 q^{91} +286515. q^{92} -2.42701e6 q^{94} +1.76245e7 q^{95} +1.20453e7 q^{97} -8.78539e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 15 q^{2} + 1535 q^{4} - 570 q^{5} + 1040 q^{7} - 2145 q^{8}+O(q^{10}) $ 20 * q - 15 * q^2 + 1535 * q^4 - 570 * q^5 + 1040 * q^7 - 2145 * q^8	\( 20 q - 15 q^{2} + 1535 q^{4} - 570 q^{5} + 1040 q^{7} - 2145 q^{8} + 4638 q^{10} - 8280 q^{11} + 23970 q^{13} - 3747 q^{14} + 61611 q^{16} + 8175 q^{17} + 88188 q^{19} - 229652 q^{20} + 375285 q^{22} - 142760 q^{23} + 599138 q^{25} - 805951 q^{26} + 674195 q^{28} - 609298 q^{29} + 501252 q^{31} - 861985 q^{32} + 695221 q^{34} - 254871 q^{35} + 988540 q^{37} - 423400 q^{38} + 506552 q^{40} - 134044 q^{41} + 1098090 q^{43} - 152745 q^{44} + 1045912 q^{46} + 192100 q^{47} + 3925588 q^{49} + 2831623 q^{50} - 1739865 q^{52} + 223030 q^{53} + 696108 q^{55} + 2963519 q^{56} - 174970 q^{58} + 4107580 q^{59} + 268196 q^{61} + 16251780 q^{62} - 10301657 q^{64} + 9614752 q^{65} + 18460 q^{67} + 15858025 q^{68} - 10180894 q^{70} + 7557879 q^{71} + 11309150 q^{73} + 17290965 q^{74} + 1427154 q^{76} + 5365910 q^{77} + 15100684 q^{79} + 5480448 q^{80} - 3871215 q^{82} - 17914560 q^{83} + 16888072 q^{85} + 18664125 q^{86} + 34271415 q^{88} - 25286376 q^{89} + 34742616 q^{91} + 22079060 q^{92} + 14764110 q^{94} - 59526076 q^{95} + 21354480 q^{97} + 9881280 q^{98}+O(q^{100}) \) 20 * q - 15 * q^2 + 1535 * q^4 - 570 * q^5 + 1040 * q^7 - 2145 * q^8 + 4638 * q^10 - 8280 * q^11 + 23970 * q^13 - 3747 * q^14 + 61611 * q^16 + 8175 * q^17 + 88188 * q^19 - 229652 * q^20 + 375285 * q^22 - 142760 * q^23 + 599138 * q^25 - 805951 * q^26 + 674195 * q^28 - 609298 * q^29 + 501252 * q^31 - 861985 * q^32 + 695221 * q^34 - 254871 * q^35 + 988540 * q^37 - 423400 * q^38 + 506552 * q^40 - 134044 * q^41 + 1098090 * q^43 - 152745 * q^44 + 1045912 * q^46 + 192100 * q^47 + 3925588 * q^49 + 2831623 * q^50 - 1739865 * q^52 + 223030 * q^53 + 696108 * q^55 + 2963519 * q^56 - 174970 * q^58 + 4107580 * q^59 + 268196 * q^61 + 16251780 * q^62 - 10301657 * q^64 + 9614752 * q^65 + 18460 * q^67 + 15858025 * q^68 - 10180894 * q^70 + 7557879 * q^71 + 11309150 * q^73 + 17290965 * q^74 + 1427154 * q^76 + 5365910 * q^77 + 15100684 * q^79 + 5480448 * q^80 - 3871215 * q^82 - 17914560 * q^83 + 16888072 * q^85 + 18664125 * q^86 + 34271415 * q^88 - 25286376 * q^89 + 34742616 * q^91 + 22079060 * q^92 + 14764110 * q^94 - 59526076 * q^95 + 21354480 * q^97 + 9881280 * 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 $

$2$	11.0947	0.980642	0.490321	−	0.871542i	$-0.336880\pi$
$2$	11.0947	0.980642	0.490321	+	0.871542i	$0.336880\pi$
$3$	0	0
$3$	0	0
$4$	−4.90769	−0.0383413
$5$	−390.109	−1.39570	−0.697849	−	0.716245i	$-0.745859\pi$
$5$	−390.109	−1.39570	−0.697849	+	0.716245i	$0.745859\pi$
$6$	0	0
$7$	−178.013	−0.196159	−0.0980794	−	0.995179i	$-0.531270\pi$
$7$	−178.013	−0.196159	−0.0980794	+	0.995179i	$0.531270\pi$
$8$	−1474.57	−1.01824
$9$	0	0
$10$	−4328.15	−1.36868
$11$	4740.39	1.07384	0.536920	−	0.843633i	$-0.319588\pi$
$11$	4740.39	1.07384	0.536920	+	0.843633i	$0.319588\pi$
$12$	0	0
$13$	131.881	0.0166487	0.00832434	−	0.999965i	$-0.497350\pi$
$13$	131.881	0.0166487	0.00832434	+	0.999965i	$0.497350\pi$
$14$	−1975.00	−0.192362
$15$	0	0
$16$	−15731.7	−0.960189
$17$	−32763.8	−1.61742	−0.808711	−	0.588207i	$-0.799834\pi$
$17$	−32763.8	−1.61742	−0.808711	+	0.588207i	$0.799834\pi$
$18$	0	0
$19$	−45178.3	−1.51110	−0.755549	−	0.655093i	$-0.772630\pi$
$19$	−45178.3	−1.51110	−0.755549	+	0.655093i	$0.772630\pi$
$20$	1914.54	0.0535129
$21$	0	0
$22$	52593.2	1.05305
$23$	−58380.8	−1.00051	−0.500256	−	0.865877i	$-0.666761\pi$
$23$	−58380.8	−1.00051	−0.500256	+	0.865877i	$0.666761\pi$
$24$	0	0
$25$	74060.4	0.947973
$26$	1463.18	0.0163264
$27$	0	0
$28$	873.632	0.00752099
$29$	−191330.	−1.45677	−0.728384	−	0.685169i	$-0.759728\pi$
$29$	−191330.	−1.45677	−0.728384	+	0.685169i	$0.759728\pi$
$30$	0	0
$31$	−11950.2	−0.0720459	−0.0360229	−	0.999351i	$-0.511469\pi$
$31$	−11950.2	−0.0720459	−0.0360229	+	0.999351i	$0.511469\pi$
$32$	14206.3	0.0766399
$33$	0	0
$34$	−363505.	−1.58611
$35$	69444.5	0.273779
$36$	0	0
$37$	391041.	1.26916	0.634580	−	0.772857i	$-0.281173\pi$
$37$	391041.	1.26916	0.634580	+	0.772857i	$0.281173\pi$
$38$	−501240.	−1.48185
$39$	0	0
$40$	575244.	1.42116
$41$	−337341.	−0.764408	−0.382204	−	0.924078i	$-0.624835\pi$
$41$	−337341.	−0.764408	−0.382204	+	0.924078i	$0.624835\pi$
$42$	0	0
$43$	380422.	0.729668	0.364834	−	0.931073i	$-0.381126\pi$
$43$	380422.	0.729668	0.364834	+	0.931073i	$0.381126\pi$
$44$	−23264.4	−0.0411725
$45$	0	0
$46$	−647717.	−0.981145
$47$	−218754.	−0.307336	−0.153668	−	0.988123i	$-0.549109\pi$
$47$	−218754.	−0.307336	−0.153668	+	0.988123i	$0.549109\pi$
$48$	0	0
$49$	−791854.	−0.961522
$50$	821677.	0.929622
$51$	0	0
$52$	−647.230	−0.000638333 0
$53$	−1.45354e6	−1.34110	−0.670549	−	0.741866i	$-0.733941\pi$
$53$	−1.45354e6	−1.34110	−0.670549	+	0.741866i	$0.733941\pi$
$54$	0	0
$55$	−1.84927e6	−1.49876
$56$	262492.	0.199737
$57$	0	0
$58$	−2.12275e6	−1.42857
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−2.11534e6	−1.19323	−0.596616	−	0.802527i	$-0.703489\pi$
$61$	−2.11534e6	−1.19323	−0.596616	+	0.802527i	$0.703489\pi$
$62$	−132584.	−0.0706512
$63$	0	0
$64$	2.17128e6	1.03534
$65$	−51447.9	−0.0232365
$66$	0	0
$67$	3.01688e6	1.22545	0.612726	−	0.790296i	$-0.290073\pi$
$67$	3.01688e6	1.22545	0.612726	+	0.790296i	$0.290073\pi$
$68$	160795.	0.0620141
$69$	0	0
$70$	770465.	0.268479
$71$	761303.	0.252437	0.126219	−	0.992002i	$-0.459716\pi$
$71$	761303.	0.252437	0.126219	+	0.992002i	$0.459716\pi$
$72$	0	0
$73$	−708365.	−0.213121	−0.106561	−	0.994306i	$-0.533984\pi$
$73$	−708365.	−0.213121	−0.106561	+	0.994306i	$0.533984\pi$
$74$	4.33848e6	1.24459
$75$	0	0
$76$	221721.	0.0579375
$77$	−843850.	−0.210643
$78$	0	0
$79$	8.14870e6	1.85949	0.929744	−	0.368207i	$-0.120028\pi$
$79$	8.14870e6	1.85949	0.929744	+	0.368207i	$0.120028\pi$
$80$	6.13710e6	1.34013
$81$	0	0
$82$	−3.74269e6	−0.749610
$83$	−4.28035e6	−0.821685	−0.410843	−	0.911706i	$-0.634765\pi$
$83$	−4.28035e6	−0.821685	−0.410843	+	0.911706i	$0.634765\pi$
$84$	0	0
$85$	1.27815e7	2.25743
$86$	4.22066e6	0.715543
$87$	0	0
$88$	−6.99004e6	−1.09343
$89$	−1.62360e6	−0.244126	−0.122063	−	0.992522i	$-0.538951\pi$
$89$	−1.62360e6	−0.244126	−0.122063	+	0.992522i	$0.538951\pi$
$90$	0	0
$91$	−23476.5	−0.00326579
$92$	286515.	0.0383610
$93$	0	0
$94$	−2.42701e6	−0.301387
$95$	1.76245e7	2.10904
$96$	0	0
$97$	1.20453e7	1.34004	0.670018	−	0.742345i	$-0.266286\pi$
$97$	1.20453e7	1.34004	0.670018	+	0.742345i	$0.266286\pi$
$98$	−8.78539e6	−0.942909
$99$	0	0
$100$	−363465.	−0.0363465
$101$	−1.26953e7	−1.22608	−0.613040	−	0.790052i	$-0.710053\pi$
$101$	−1.26953e7	−1.22608	−0.613040	+	0.790052i	$0.710053\pi$
$102$	0	0
$103$	−1.47807e7	−1.33280	−0.666400	−	0.745594i	$-0.732166\pi$
$103$	−1.47807e7	−1.33280	−0.666400	+	0.745594i	$0.732166\pi$
$104$	−194468.	−0.0169524
$105$	0	0
$106$	−1.61265e7	−1.31514
$107$	1.32080e7	1.04230	0.521150	−	0.853465i	$-0.325503\pi$
$107$	1.32080e7	1.04230	0.521150	+	0.853465i	$0.325503\pi$
$108$	0	0
$109$	1.59209e7	1.17754	0.588769	−	0.808302i	$-0.299613\pi$
$109$	1.59209e7	1.17754	0.588769	+	0.808302i	$0.299613\pi$
$110$	−2.05171e7	−1.46974
$111$	0	0
$112$	2.80045e6	0.188350
$113$	1.50511e7	0.981281	0.490640	−	0.871362i	$-0.336763\pi$
$113$	1.50511e7	0.981281	0.490640	+	0.871362i	$0.336763\pi$
$114$	0	0
$115$	2.27749e7	1.39641
$116$	938989.	0.0558544
$117$	0	0
$118$	2.27862e6	0.127669
$119$	5.83238e6	0.317272
$120$	0	0
$121$	2.98414e6	0.153134
$122$	−2.34690e7	−1.17013
$123$	0	0
$124$	58647.9	0.00276234
$125$	1.58565e6	0.0726142
$126$	0	0
$127$	2.61103e7	1.13109	0.565546	−	0.824717i	$-0.308665\pi$
$127$	2.61103e7	1.13109	0.565546	+	0.824717i	$0.308665\pi$
$128$	2.22712e7	0.938663
$129$	0	0
$130$	−570799.	−0.0227867
$131$	2.01973e7	0.784955	0.392477	−	0.919762i	$-0.371618\pi$
$131$	2.01973e7	0.784955	0.392477	+	0.919762i	$0.371618\pi$
$132$	0	0
$133$	8.04232e6	0.296415
$134$	3.34714e7	1.20173
$135$	0	0
$136$	4.83126e7	1.64693
$137$	−6.15176e6	−0.204398	−0.102199	−	0.994764i	$-0.532588\pi$
$137$	−6.15176e6	−0.204398	−0.102199	+	0.994764i	$0.532588\pi$
$138$	0	0
$139$	−2.56117e7	−0.808886	−0.404443	−	0.914563i	$-0.632535\pi$
$139$	−2.56117e7	−0.808886	−0.404443	+	0.914563i	$0.632535\pi$
$140$	−340812.	−0.0104970
$141$	0	0
$142$	8.44642e6	0.247550
$143$	625167.	0.0178780
$144$	0	0
$145$	7.46397e7	2.03321
$146$	−7.85909e6	−0.208996
$147$	0	0
$148$	−1.91911e6	−0.0486613
$149$	2.41838e7	0.598926	0.299463	−	0.954108i	$-0.403192\pi$
$149$	2.41838e7	0.598926	0.299463	+	0.954108i	$0.403192\pi$
$150$	0	0
$151$	−6.92902e7	−1.63777	−0.818884	−	0.573959i	$-0.805407\pi$
$151$	−6.92902e7	−1.63777	−0.818884	+	0.573959i	$0.805407\pi$
$152$	6.66186e7	1.53866
$153$	0	0
$154$	−9.36226e6	−0.206566
$155$	4.66189e6	0.100554
$156$	0	0
$157$	1.61643e7	0.333356	0.166678	−	0.986011i	$-0.446696\pi$
$157$	1.61643e7	0.333356	0.166678	+	0.986011i	$0.446696\pi$
$158$	9.04073e7	1.82349
$159$	0	0
$160$	−5.54199e6	−0.106966
$161$	1.03925e7	0.196260
$162$	0	0
$163$	5.16027e7	0.933289	0.466644	−	0.884445i	$-0.345463\pi$
$163$	5.16027e7	0.933289	0.466644	+	0.884445i	$0.345463\pi$
$164$	1.65556e6	0.0293084
$165$	0	0
$166$	−4.74891e7	−0.805779
$167$	5.59906e7	0.930267	0.465134	−	0.885240i	$-0.346006\pi$
$167$	5.59906e7	0.930267	0.465134	+	0.885240i	$0.346006\pi$
$168$	0	0
$169$	−6.27311e7	−0.999723
$170$	1.41807e8	2.21373
$171$	0	0
$172$	−1.86699e6	−0.0279765
$173$	2.38288e7	0.349897	0.174948	−	0.984578i	$-0.444024\pi$
$173$	2.38288e7	0.349897	0.174948	+	0.984578i	$0.444024\pi$
$174$	0	0
$175$	−1.31837e7	−0.185953
$176$	−7.45746e7	−1.03109
$177$	0	0
$178$	−1.80133e7	−0.239400
$179$	−5.89254e7	−0.767921	−0.383961	−	0.923349i	$-0.625440\pi$
$179$	−5.89254e7	−0.767921	−0.383961	+	0.923349i	$0.625440\pi$
$180$	0	0
$181$	−6.82934e7	−0.856059	−0.428030	−	0.903765i	$-0.640792\pi$
$181$	−6.82934e7	−0.856059	−0.428030	+	0.903765i	$0.640792\pi$
$182$	−260464.	−0.00320257
$183$	0	0
$184$	8.60866e7	1.01876
$185$	−1.52549e8	−1.77136
$186$	0	0
$187$	−1.55313e8	−1.73685
$188$	1.07358e6	0.0117837
$189$	0	0
$190$	1.95538e8	2.06821
$191$	−9.07359e7	−0.942241	−0.471121	−	0.882069i	$-0.656150\pi$
$191$	−9.07359e7	−0.942241	−0.471121	+	0.882069i	$0.656150\pi$
$192$	0	0
$193$	1.76937e8	1.77161	0.885805	−	0.464057i	$-0.153607\pi$
$193$	1.76937e8	1.77161	0.885805	+	0.464057i	$0.153607\pi$
$194$	1.33639e8	1.31410
$195$	0	0
$196$	3.88618e6	0.0368660
$197$	1.24138e8	1.15684	0.578419	−	0.815740i	$-0.303670\pi$
$197$	1.24138e8	1.15684	0.578419	+	0.815740i	$0.303670\pi$
$198$	0	0
$199$	1.69738e8	1.52684	0.763419	−	0.645903i	$-0.223519\pi$
$199$	1.69738e8	1.52684	0.763419	+	0.645903i	$0.223519\pi$
$200$	−1.09207e8	−0.965265
$201$	0	0
$202$	−1.40851e8	−1.20235
$203$	3.40592e7	0.285758
$204$	0	0
$205$	1.31600e8	1.06688
$206$	−1.63988e8	−1.30700
$207$	0	0
$208$	−2.07471e6	−0.0159859
$209$	−2.14163e8	−1.62268
$210$	0	0
$211$	−8.30207e7	−0.608412	−0.304206	−	0.952606i	$-0.598391\pi$
$211$	−8.30207e7	−0.608412	−0.304206	+	0.952606i	$0.598391\pi$
$212$	7.13351e6	0.0514195
$213$	0	0
$214$	1.46538e8	1.02212
$215$	−1.48406e8	−1.01840
$216$	0	0
$217$	2.12729e6	0.0141324
$218$	1.76638e8	1.15474
$219$	0	0
$220$	9.07565e6	0.0574644
$221$	−4.32092e6	−0.0269279
$222$	0	0
$223$	1.16902e8	0.705922	0.352961	−	0.935638i	$-0.385175\pi$
$223$	1.16902e8	0.705922	0.352961	+	0.935638i	$0.385175\pi$
$224$	−2.52889e6	−0.0150336
$225$	0	0
$226$	1.66987e8	0.962285
$227$	−2.46030e8	−1.39604	−0.698020	−	0.716079i	$-0.745935\pi$
$227$	−2.46030e8	−1.39604	−0.698020	+	0.716079i	$0.745935\pi$
$228$	0	0
$229$	−3.13236e8	−1.72364	−0.861821	−	0.507213i	$-0.830676\pi$
$229$	−3.13236e8	−1.72364	−0.861821	+	0.507213i	$0.830676\pi$
$230$	2.52681e8	1.36938
$231$	0	0
$232$	2.82130e8	1.48334
$233$	−3.29532e7	−0.170668	−0.0853338	−	0.996352i	$-0.527196\pi$
$233$	−3.29532e7	−0.170668	−0.0853338	+	0.996352i	$0.527196\pi$
$234$	0	0
$235$	8.53380e7	0.428948
$236$	−1.00794e6	−0.00499162
$237$	0	0
$238$	6.47085e7	0.311130
$239$	−1.22587e7	−0.0580833	−0.0290416	−	0.999578i	$-0.509246\pi$
$239$	−1.22587e7	−0.0580833	−0.0290416	+	0.999578i	$0.509246\pi$
$240$	0	0
$241$	−1.74912e8	−0.804934	−0.402467	−	0.915435i	$-0.631847\pi$
$241$	−1.74912e8	−0.804934	−0.402467	+	0.915435i	$0.631847\pi$
$242$	3.31081e7	0.150169
$243$	0	0
$244$	1.03814e7	0.0457501
$245$	3.08910e8	1.34199
$246$	0	0
$247$	−5.95815e6	−0.0251578
$248$	1.76214e7	0.0733601
$249$	0	0
$250$	1.75923e7	0.0712086
$251$	8.67528e7	0.346278	0.173139	−	0.984897i	$-0.444609\pi$
$251$	8.67528e7	0.346278	0.173139	+	0.984897i	$0.444609\pi$
$252$	0	0
$253$	−2.76748e8	−1.07439
$254$	2.89685e8	1.10920
$255$	0	0
$256$	−3.08306e7	−0.114853
$257$	−2.13983e8	−0.786346	−0.393173	−	0.919464i	$-0.628623\pi$
$257$	−2.13983e8	−0.786346	−0.393173	+	0.919464i	$0.628623\pi$
$258$	0	0
$259$	−6.96103e7	−0.248957
$260$	252491.	0.000890920 0
$261$	0	0
$262$	2.24083e8	0.769759
$263$	2.84544e8	0.964506	0.482253	−	0.876032i	$-0.339819\pi$
$263$	2.84544e8	0.964506	0.482253	+	0.876032i	$0.339819\pi$
$264$	0	0
$265$	5.67038e8	1.87177
$266$	8.92271e7	0.290677
$267$	0	0
$268$	−1.48059e7	−0.0469855
$269$	−2.18275e8	−0.683709	−0.341855	−	0.939753i	$-0.611055\pi$
$269$	−2.18275e8	−0.683709	−0.341855	+	0.939753i	$0.611055\pi$
$270$	0	0
$271$	−2.48756e8	−0.759244	−0.379622	−	0.925142i	$-0.623946\pi$
$271$	−2.48756e8	−0.759244	−0.379622	+	0.925142i	$0.623946\pi$
$272$	5.15431e8	1.55303
$273$	0	0
$274$	−6.82519e7	−0.200442
$275$	3.51075e8	1.01797
$276$	0	0
$277$	−1.47967e8	−0.418298	−0.209149	−	0.977884i	$-0.567069\pi$
$277$	−1.47967e8	−0.418298	−0.209149	+	0.977884i	$0.567069\pi$
$278$	−2.84155e8	−0.793227
$279$	0	0
$280$	−1.02401e8	−0.278773
$281$	−7.12102e8	−1.91456	−0.957282	−	0.289156i	$-0.906625\pi$
$281$	−7.12102e8	−1.91456	−0.957282	+	0.289156i	$0.906625\pi$
$282$	0	0
$283$	1.37261e8	0.359992	0.179996	−	0.983667i	$-0.442391\pi$
$283$	1.37261e8	0.359992	0.179996	+	0.983667i	$0.442391\pi$
$284$	−3.73624e6	−0.00967878
$285$	0	0
$286$	6.93603e6	0.0175319
$287$	6.00509e7	0.149945
$288$	0	0
$289$	6.63129e8	1.61605
$290$	8.28105e8	1.99385
$291$	0	0
$292$	3.47643e6	0.00817136
$293$	1.05786e8	0.245693	0.122846	−	0.992426i	$-0.460798\pi$
$293$	1.05786e8	0.245693	0.122846	+	0.992426i	$0.460798\pi$
$294$	0	0
$295$	−8.01203e7	−0.181704
$296$	−5.76618e8	−1.29231
$297$	0	0
$298$	2.68312e8	0.587332
$299$	−7.69931e6	−0.0166572
$300$	0	0
$301$	−6.77199e7	−0.143131
$302$	−7.68753e8	−1.60606
$303$	0	0
$304$	7.10733e8	1.45094
$305$	8.25213e8	1.66539
$306$	0	0
$307$	1.62740e8	0.321003	0.160502	−	0.987036i	$-0.448689\pi$
$307$	1.62740e8	0.321003	0.160502	+	0.987036i	$0.448689\pi$
$308$	4.14136e6	0.00807635
$309$	0	0
$310$	5.17222e7	0.0986078
$311$	9.01165e8	1.69880	0.849402	−	0.527747i	$-0.176963\pi$
$311$	9.01165e8	1.69880	0.849402	+	0.527747i	$0.176963\pi$
$312$	0	0
$313$	−1.45545e8	−0.268283	−0.134141	−	0.990962i	$-0.542828\pi$
$313$	−1.45545e8	−0.268283	−0.134141	+	0.990962i	$0.542828\pi$
$314$	1.79338e8	0.326903
$315$	0	0
$316$	−3.99913e7	−0.0712952
$317$	−9.21784e8	−1.62526	−0.812628	−	0.582783i	$-0.801964\pi$
$317$	−9.21784e8	−1.62526	−0.812628	+	0.582783i	$0.801964\pi$
$318$	0	0
$319$	−9.06980e8	−1.56434
$320$	−8.47035e8	−1.44503
$321$	0	0
$322$	1.15302e8	0.192460
$323$	1.48021e9	2.44408
$324$	0	0
$325$	9.76714e6	0.0157825
$326$	5.72517e8	0.915222
$327$	0	0
$328$	4.97432e8	0.778351
$329$	3.89410e7	0.0602867
$330$	0	0
$331$	−2.88932e8	−0.437923	−0.218961	−	0.975734i	$-0.570267\pi$
$331$	−2.88932e8	−0.437923	−0.218961	+	0.975734i	$0.570267\pi$
$332$	2.10066e7	0.0315045
$333$	0	0
$334$	6.21199e8	0.912259
$335$	−1.17691e9	−1.71036
$336$	0	0
$337$	−1.78652e8	−0.254275	−0.127137	−	0.991885i	$-0.540579\pi$
$337$	−1.78652e8	−0.254275	−0.127137	+	0.991885i	$0.540579\pi$
$338$	−6.95983e8	−0.980370
$339$	0	0
$340$	−6.27275e7	−0.0865530
$341$	−5.66486e7	−0.0773658
$342$	0	0
$343$	2.87561e8	0.384770
$344$	−5.60958e8	−0.742978
$345$	0	0
$346$	2.64373e8	0.343123
$347$	−1.13910e9	−1.46355	−0.731775	−	0.681547i	$-0.761308\pi$
$347$	−1.13910e9	−1.46355	−0.731775	+	0.681547i	$0.761308\pi$
$348$	0	0
$349$	1.33417e9	1.68005	0.840024	−	0.542550i	$-0.182541\pi$
$349$	1.33417e9	1.68005	0.840024	+	0.542550i	$0.182541\pi$
$350$	−1.46269e8	−0.182354
$351$	0	0
$352$	6.73432e7	0.0822990
$353$	−1.31326e9	−1.58906	−0.794528	−	0.607227i	$-0.792282\pi$
$353$	−1.31326e9	−1.58906	−0.794528	+	0.607227i	$0.792282\pi$
$354$	0	0
$355$	−2.96991e8	−0.352326
$356$	7.96813e6	0.00936012
$357$	0	0
$358$	−6.53759e8	−0.753056
$359$	4.95650e8	0.565386	0.282693	−	0.959210i	$-0.408772\pi$
$359$	4.95650e8	0.565386	0.282693	+	0.959210i	$0.408772\pi$
$360$	0	0
$361$	1.14721e9	1.28341
$362$	−7.57695e8	−0.839488
$363$	0	0
$364$	115215.	0.000125215 0
$365$	2.76340e8	0.297453
$366$	0	0
$367$	1.13721e9	1.20091	0.600454	−	0.799659i	$-0.294987\pi$
$367$	1.13721e9	1.20091	0.600454	+	0.799659i	$0.294987\pi$
$368$	9.18431e8	0.960681
$369$	0	0
$370$	−1.69248e9	−1.73707
$371$	2.58748e8	0.263068
$372$	0	0
$373$	−1.34114e9	−1.33811	−0.669055	−	0.743213i	$-0.733301\pi$
$373$	−1.34114e9	−1.33811	−0.669055	+	0.743213i	$0.733301\pi$
$374$	−1.72315e9	−1.70323
$375$	0	0
$376$	3.22568e8	0.312942
$377$	−2.52328e7	−0.0242533
$378$	0	0
$379$	−1.49617e8	−0.141170	−0.0705851	−	0.997506i	$-0.522487\pi$
$379$	−1.49617e8	−0.141170	−0.0705851	+	0.997506i	$0.522487\pi$
$380$	−8.64955e7	−0.0808632
$381$	0	0
$382$	−1.00669e9	−0.924002
$383$	1.48955e9	1.35475	0.677375	−	0.735638i	$-0.263118\pi$
$383$	1.48955e9	1.35475	0.677375	+	0.735638i	$0.263118\pi$
$384$	0	0
$385$	3.29194e8	0.293995
$386$	1.96306e9	1.73732
$387$	0	0
$388$	−5.91146e7	−0.0513788
$389$	−8.62246e8	−0.742690	−0.371345	−	0.928495i	$-0.621103\pi$
$389$	−8.62246e8	−0.742690	−0.371345	+	0.928495i	$0.621103\pi$
$390$	0	0
$391$	1.91278e9	1.61825
$392$	1.16765e9	0.979061
$393$	0	0
$394$	1.37727e9	1.13444
$395$	−3.17888e9	−2.59528
$396$	0	0
$397$	−6.15525e7	−0.0493718	−0.0246859	−	0.999695i	$-0.507859\pi$
$397$	−6.15525e7	−0.0493718	−0.0246859	+	0.999695i	$0.507859\pi$
$398$	1.88319e9	1.49728
$399$	0	0
$400$	−1.16510e9	−0.910233
$401$	−1.67750e9	−1.29915	−0.649574	−	0.760299i	$-0.725053\pi$
$401$	−1.67750e9	−1.29915	−0.649574	+	0.760299i	$0.725053\pi$
$402$	0	0
$403$	−1.57600e6	−0.00119947
$404$	6.23047e7	0.0470095
$405$	0	0
$406$	3.77877e8	0.280226
$407$	1.85369e9	1.36288
$408$	0	0
$409$	−4.95023e8	−0.357762	−0.178881	−	0.983871i	$-0.557248\pi$
$409$	−4.95023e8	−0.357762	−0.178881	+	0.983871i	$0.557248\pi$
$410$	1.46006e9	1.04623
$411$	0	0
$412$	7.25392e7	0.0511013
$413$	−3.65601e7	−0.0255377
$414$	0	0
$415$	1.66980e9	1.14682
$416$	1.87353e6	0.00127595
$417$	0	0
$418$	−2.37607e9	−1.59127
$419$	2.87997e8	0.191266	0.0956332	−	0.995417i	$-0.469512\pi$
$419$	2.87997e8	0.191266	0.0956332	+	0.995417i	$0.469512\pi$
$420$	0	0
$421$	−6.34200e8	−0.414227	−0.207114	−	0.978317i	$-0.566407\pi$
$421$	−6.34200e8	−0.414227	−0.207114	+	0.978317i	$0.566407\pi$
$422$	−9.21089e8	−0.596634
$423$	0	0
$424$	2.14334e9	1.36556
$425$	−2.42650e9	−1.53327
$426$	0	0
$427$	3.76557e8	0.234063
$428$	−6.48206e7	−0.0399632
$429$	0	0
$430$	−1.64652e9	−0.998682
$431$	1.37213e9	0.825515	0.412757	−	0.910841i	$-0.364566\pi$
$431$	1.37213e9	0.825515	0.412757	+	0.910841i	$0.364566\pi$
$432$	0	0
$433$	−1.30580e9	−0.772981	−0.386490	−	0.922293i	$-0.626313\pi$
$433$	−1.30580e9	−0.772981	−0.386490	+	0.922293i	$0.626313\pi$
$434$	2.36016e7	0.0138589
$435$	0	0
$436$	−7.81348e7	−0.0451484
$437$	2.63755e9	1.51187
$438$	0	0
$439$	1.06053e9	0.598269	0.299135	−	0.954211i	$-0.403302\pi$
$439$	1.06053e9	0.598269	0.299135	+	0.954211i	$0.403302\pi$
$440$	2.72688e9	1.52610
$441$	0	0
$442$	−4.79393e7	−0.0264067
$443$	3.36776e9	1.84047	0.920234	−	0.391369i	$-0.127999\pi$
$443$	3.36776e9	1.84047	0.920234	+	0.391369i	$0.127999\pi$
$444$	0	0
$445$	6.33382e8	0.340726
$446$	1.29700e9	0.692257
$447$	0	0
$448$	−3.86515e8	−0.203092
$449$	−9.70648e8	−0.506057	−0.253029	−	0.967459i	$-0.581427\pi$
$449$	−9.70648e8	−0.506057	−0.253029	+	0.967459i	$0.581427\pi$
$450$	0	0
$451$	−1.59913e9	−0.820852
$452$	−7.38661e7	−0.0376236
$453$	0	0
$454$	−2.72963e9	−1.36901
$455$	9.15839e6	0.00455805
$456$	0	0
$457$	6.32506e8	0.309997	0.154999	−	0.987915i	$-0.450463\pi$
$457$	6.32506e8	0.309997	0.154999	+	0.987915i	$0.450463\pi$
$458$	−3.47525e9	−1.69028
$459$	0	0
$460$	−1.11772e8	−0.0535404
$461$	−1.91312e9	−0.909471	−0.454735	−	0.890627i	$-0.650266\pi$
$461$	−1.91312e9	−0.909471	−0.454735	+	0.890627i	$0.650266\pi$
$462$	0	0
$463$	−6.96624e8	−0.326186	−0.163093	−	0.986611i	$-0.552147\pi$
$463$	−6.96624e8	−0.326186	−0.163093	+	0.986611i	$0.552147\pi$
$464$	3.00995e9	1.39877
$465$	0	0
$466$	−3.65605e8	−0.167364
$467$	−4.81527e7	−0.0218782	−0.0109391	−	0.999940i	$-0.503482\pi$
$467$	−4.81527e7	−0.0218782	−0.0109391	+	0.999940i	$0.503482\pi$
$468$	0	0
$469$	−5.37043e8	−0.240383
$470$	9.46799e8	0.420645
$471$	0	0
$472$	−3.02846e8	−0.132564
$473$	1.80335e9	0.783547
$474$	0	0
$475$	−3.34592e9	−1.43248
$476$	−2.86235e7	−0.0121646
$477$	0	0
$478$	−1.36006e8	−0.0569589
$479$	7.76384e8	0.322777	0.161388	−	0.986891i	$-0.448403\pi$
$479$	7.76384e8	0.322777	0.161388	+	0.986891i	$0.448403\pi$
$480$	0	0
$481$	5.15708e7	0.0211298
$482$	−1.94060e9	−0.789352
$483$	0	0
$484$	−1.46452e7	−0.00587134
$485$	−4.69899e9	−1.87029
$486$	0	0
$487$	1.62831e9	0.638829	0.319415	−	0.947615i	$-0.396514\pi$
$487$	1.62831e9	0.638829	0.319415	+	0.947615i	$0.396514\pi$
$488$	3.11921e9	1.21500
$489$	0	0
$490$	3.42726e9	1.31602
$491$	2.06579e9	0.787591	0.393795	−	0.919198i	$-0.371162\pi$
$491$	2.06579e9	0.787591	0.393795	+	0.919198i	$0.371162\pi$
$492$	0	0
$493$	6.26870e9	2.35621
$494$	−6.61039e7	−0.0246708
$495$	0	0
$496$	1.87997e8	0.0691776
$497$	−1.35522e8	−0.0495178
$498$	0	0
$499$	2.27853e9	0.820924	0.410462	−	0.911878i	$-0.365367\pi$
$499$	2.27853e9	0.820924	0.410462	+	0.911878i	$0.365367\pi$
$500$	−7.78187e6	−0.00278413
$501$	0	0
$502$	9.62496e8	0.339575
$503$	−5.97771e8	−0.209434	−0.104717	−	0.994502i	$-0.533394\pi$
$503$	−5.97771e8	−0.209434	−0.104717	+	0.994502i	$0.533394\pi$
$504$	0	0
$505$	4.95256e9	1.71124
$506$	−3.07043e9	−1.05359
$507$	0	0
$508$	−1.28141e8	−0.0433676
$509$	2.53914e9	0.853442	0.426721	−	0.904383i	$-0.359669\pi$
$509$	2.53914e9	0.853442	0.426721	+	0.904383i	$0.359669\pi$
$510$	0	0
$511$	1.26098e8	0.0418056
$512$	−3.19277e9	−1.05129
$513$	0	0
$514$	−2.37408e9	−0.771124
$515$	5.76609e9	1.86019
$516$	0	0
$517$	−1.03698e9	−0.330030
$518$	−7.72305e8	−0.244138
$519$	0	0
$520$	7.58636e7	0.0236604
$521$	1.50911e9	0.467508	0.233754	−	0.972296i	$-0.424899\pi$
$521$	1.50911e9	0.467508	0.233754	+	0.972296i	$0.424899\pi$
$522$	0	0
$523$	−2.61035e9	−0.797891	−0.398945	−	0.916975i	$-0.630624\pi$
$523$	−2.61035e9	−0.797891	−0.398945	+	0.916975i	$0.630624\pi$
$524$	−9.91223e7	−0.0300962
$525$	0	0
$526$	3.15693e9	0.945835
$527$	3.91534e8	0.116529
$528$	0	0
$529$	3.49365e6	0.00102609
$530$	6.29112e9	1.83553
$531$	0	0
$532$	−3.94692e7	−0.0113650
$533$	−4.44887e7	−0.0127264
$534$	0	0
$535$	−5.15255e9	−1.45474
$536$	−4.44860e9	−1.24781
$537$	0	0
$538$	−2.42170e9	−0.670474
$539$	−3.75370e9	−1.03252
$540$	0	0
$541$	−1.63394e9	−0.443656	−0.221828	−	0.975086i	$-0.571202\pi$
$541$	−1.63394e9	−0.443656	−0.221828	+	0.975086i	$0.571202\pi$
$542$	−2.75988e9	−0.744547
$543$	0	0
$544$	−4.65451e8	−0.123959
$545$	−6.21089e9	−1.64349
$546$	0	0
$547$	3.64076e9	0.951122	0.475561	−	0.879683i	$-0.342245\pi$
$547$	3.64076e9	0.951122	0.475561	+	0.879683i	$0.342245\pi$
$548$	3.01909e7	0.00783691
$549$	0	0
$550$	3.89507e9	0.998266
$551$	8.64397e9	2.20132
$552$	0	0
$553$	−1.45057e9	−0.364755
$554$	−1.64165e9	−0.410200
$555$	0	0
$556$	1.25695e8	0.0310138
$557$	6.28834e7	0.0154185	0.00770927	−	0.999970i	$-0.497546\pi$
$557$	6.28834e7	0.0154185	0.00770927	+	0.999970i	$0.497546\pi$
$558$	0	0
$559$	5.01703e7	0.0121480
$560$	−1.09248e9	−0.262879
$561$	0	0
$562$	−7.90055e9	−1.87750
$563$	−5.49521e9	−1.29779	−0.648896	−	0.760877i	$-0.724769\pi$
$563$	−5.49521e9	−1.29779	−0.648896	+	0.760877i	$0.724769\pi$
$564$	0	0
$565$	−5.87157e9	−1.36957
$566$	1.52286e9	0.353024
$567$	0	0
$568$	−1.12259e9	−0.257042
$569$	−9.84426e7	−0.0224022	−0.0112011	−	0.999937i	$-0.503565\pi$
$569$	−9.84426e7	−0.0224022	−0.0112011	+	0.999937i	$0.503565\pi$
$570$	0	0
$571$	2.08277e9	0.468181	0.234091	−	0.972215i	$-0.424789\pi$
$571$	2.08277e9	0.468181	0.234091	+	0.972215i	$0.424789\pi$
$572$	−3.06812e6	−0.000685468 0
$573$	0	0
$574$	6.66247e8	0.147043
$575$	−4.32370e9	−0.948459
$576$	0	0
$577$	−3.44620e9	−0.746836	−0.373418	−	0.927663i	$-0.621814\pi$
$577$	−3.44620e9	−0.746836	−0.373418	+	0.927663i	$0.621814\pi$
$578$	7.35721e9	1.58477
$579$	0	0
$580$	−3.66309e8	−0.0779559
$581$	7.61956e8	0.161181
$582$	0	0
$583$	−6.89033e9	−1.44012
$584$	1.04453e9	0.217009
$585$	0	0
$586$	1.17367e9	0.240937
$587$	−2.44066e9	−0.498052	−0.249026	−	0.968497i	$-0.580110\pi$
$587$	−2.44066e9	−0.498052	−0.249026	+	0.968497i	$0.580110\pi$
$588$	0	0
$589$	5.39890e8	0.108868
$590$	−8.88910e8	−0.178187
$591$	0	0
$592$	−6.15175e9	−1.21863
$593$	8.96094e8	0.176466	0.0882332	−	0.996100i	$-0.471878\pi$
$593$	8.96094e8	0.176466	0.0882332	+	0.996100i	$0.471878\pi$
$594$	0	0
$595$	−2.27527e9	−0.442815
$596$	−1.18687e8	−0.0229636
$597$	0	0
$598$	−8.54215e7	−0.0163348
$599$	1.02769e10	1.95375	0.976876	−	0.213808i	$-0.0685868\pi$
$599$	1.02769e10	1.95375	0.976876	+	0.213808i	$0.0685868\pi$
$600$	0	0
$601$	9.29616e8	0.174680	0.0873400	−	0.996179i	$-0.472163\pi$
$601$	9.29616e8	0.174680	0.0873400	+	0.996179i	$0.472163\pi$
$602$	−7.51332e8	−0.140360
$603$	0	0
$604$	3.40055e8	0.0627942
$605$	−1.16414e9	−0.213728
$606$	0	0
$607$	−3.61513e9	−0.656090	−0.328045	−	0.944662i	$-0.606390\pi$
$607$	−3.61513e9	−0.656090	−0.328045	+	0.944662i	$0.606390\pi$
$608$	−6.41815e8	−0.115810
$609$	0	0
$610$	9.15549e9	1.63315
$611$	−2.88494e7	−0.00511674
$612$	0	0
$613$	−9.41941e9	−1.65163	−0.825814	−	0.563943i	$-0.809284\pi$
$613$	−9.41941e9	−1.65163	−0.825814	+	0.563943i	$0.809284\pi$
$614$	1.80555e9	0.314789
$615$	0	0
$616$	1.24432e9	0.214486
$617$	−4.49619e9	−0.770632	−0.385316	−	0.922785i	$-0.625908\pi$
$617$	−4.49619e9	−0.770632	−0.385316	+	0.922785i	$0.625908\pi$
$618$	0	0
$619$	−4.49174e9	−0.761198	−0.380599	−	0.924740i	$-0.624282\pi$
$619$	−4.49174e9	−0.761198	−0.380599	+	0.924740i	$0.624282\pi$
$620$	−2.28791e7	−0.00385539
$621$	0	0
$622$	9.99816e9	1.66592
$623$	2.89021e8	0.0478875
$624$	0	0
$625$	−6.40454e9	−1.04932
$626$	−1.61478e9	−0.263090
$627$	0	0
$628$	−7.93294e7	−0.0127813
$629$	−1.28120e10	−2.05277
$630$	0	0
$631$	−1.06896e10	−1.69379	−0.846894	−	0.531762i	$-0.821530\pi$
$631$	−1.06896e10	−1.69379	−0.846894	+	0.531762i	$0.821530\pi$
$632$	−1.20158e10	−1.89341
$633$	0	0
$634$	−1.02269e10	−1.59379
$635$	−1.01859e10	−1.57866
$636$	0	0
$637$	−1.04430e8	−0.0160081
$638$	−1.00627e10	−1.53405
$639$	0	0
$640$	−8.68822e9	−1.31009
$641$	−3.84215e9	−0.576197	−0.288098	−	0.957601i	$-0.593023\pi$
$641$	−3.84215e9	−0.576197	−0.288098	+	0.957601i	$0.593023\pi$
$642$	0	0
$643$	−3.10169e9	−0.460108	−0.230054	−	0.973178i	$-0.573890\pi$
$643$	−3.10169e9	−0.460108	−0.230054	+	0.973178i	$0.573890\pi$
$644$	−5.10033e7	−0.00752485
$645$	0	0
$646$	1.64225e10	2.39677
$647$	−3.97855e9	−0.577510	−0.288755	−	0.957403i	$-0.593241\pi$
$647$	−3.97855e9	−0.577510	−0.288755	+	0.957403i	$0.593241\pi$
$648$	0	0
$649$	9.73577e8	0.139802
$650$	1.08363e8	0.0154770
$651$	0	0
$652$	−2.53250e8	−0.0357835
$653$	1.04372e10	1.46685	0.733425	−	0.679770i	$-0.237920\pi$
$653$	1.04372e10	1.46685	0.733425	+	0.679770i	$0.237920\pi$
$654$	0	0
$655$	−7.87917e9	−1.09556
$656$	5.30695e9	0.733976
$657$	0	0
$658$	4.32039e8	0.0591197
$659$	−4.44368e9	−0.604844	−0.302422	−	0.953174i	$-0.597795\pi$
$659$	−4.44368e9	−0.604844	−0.302422	+	0.953174i	$0.597795\pi$
$660$	0	0
$661$	−1.59134e9	−0.214318	−0.107159	−	0.994242i	$-0.534175\pi$
$661$	−1.59134e9	−0.214318	−0.107159	+	0.994242i	$0.534175\pi$
$662$	−3.20561e9	−0.429446
$663$	0	0
$664$	6.31167e9	0.836674
$665$	−3.13738e9	−0.413706
$666$	0	0
$667$	1.11700e10	1.45752
$668$	−2.74785e8	−0.0356677
$669$	0	0
$670$	−1.30575e10	−1.67725
$671$	−1.00275e10	−1.28134
$672$	0	0
$673$	1.09819e10	1.38875	0.694375	−	0.719613i	$-0.255681\pi$
$673$	1.09819e10	1.38875	0.694375	+	0.719613i	$0.255681\pi$
$674$	−1.98209e9	−0.249352
$675$	0	0
$676$	3.07865e8	0.0383307
$677$	−7.82083e9	−0.968708	−0.484354	−	0.874872i	$-0.660945\pi$
$677$	−7.82083e9	−0.968708	−0.484354	+	0.874872i	$0.660945\pi$
$678$	0	0
$679$	−2.14422e9	−0.262860
$680$	−1.88472e10	−2.29861
$681$	0	0
$682$	−6.28499e8	−0.0758682
$683$	8.32542e9	0.999848	0.499924	−	0.866069i	$-0.333361\pi$
$683$	8.32542e9	0.999848	0.499924	+	0.866069i	$0.333361\pi$
$684$	0	0
$685$	2.39986e9	0.285278
$686$	3.19041e9	0.377322
$687$	0	0
$688$	−5.98469e9	−0.700619
$689$	−1.91693e8	−0.0223275
$690$	0	0
$691$	8.69753e9	1.00282	0.501410	−	0.865210i	$-0.332815\pi$
$691$	8.69753e9	1.00282	0.501410	+	0.865210i	$0.332815\pi$
$692$	−1.16944e8	−0.0134155
$693$	0	0
$694$	−1.26379e10	−1.43522
$695$	9.99138e9	1.12896
$696$	0	0
$697$	1.10526e10	1.23637
$698$	1.48022e10	1.64753
$699$	0	0
$700$	6.47015e7	0.00712970
$701$	−1.54272e9	−0.169151	−0.0845755	−	0.996417i	$-0.526953\pi$
$701$	−1.54272e9	−0.169151	−0.0845755	+	0.996417i	$0.526953\pi$
$702$	0	0
$703$	−1.76666e10	−1.91782
$704$	1.02927e10	1.11180
$705$	0	0
$706$	−1.45702e10	−1.55830
$707$	2.25993e9	0.240506
$708$	0	0
$709$	1.61996e10	1.70703	0.853516	−	0.521067i	$-0.174466\pi$
$709$	1.61996e10	1.70703	0.853516	+	0.521067i	$0.174466\pi$
$710$	−3.29503e9	−0.345506
$711$	0	0
$712$	2.39411e9	0.248579
$713$	6.97662e8	0.0720828
$714$	0	0
$715$	−2.43883e8	−0.0249523
$716$	2.89188e8	0.0294431
$717$	0	0
$718$	5.49909e9	0.554441
$719$	9.17311e9	0.920376	0.460188	−	0.887821i	$-0.347782\pi$
$719$	9.17311e9	0.920376	0.460188	+	0.887821i	$0.347782\pi$
$720$	0	0
$721$	2.63116e9	0.261441
$722$	1.27279e10	1.25857
$723$	0	0
$724$	3.35163e8	0.0328225
$725$	−1.41700e10	−1.38098
$726$	0	0
$727$	6.54930e9	0.632157	0.316078	−	0.948733i	$-0.397634\pi$
$727$	6.54930e9	0.632157	0.316078	+	0.948733i	$0.397634\pi$
$728$	3.46177e7	0.00332536
$729$	0	0
$730$	3.06591e9	0.291695
$731$	−1.24641e10	−1.18018
$732$	0	0
$733$	1.62528e10	1.52428	0.762138	−	0.647414i	$-0.224150\pi$
$733$	1.62528e10	1.52428	0.762138	+	0.647414i	$0.224150\pi$
$734$	1.26170e10	1.17766
$735$	0	0
$736$	−8.29373e8	−0.0766792
$737$	1.43012e10	1.31594
$738$	0	0
$739$	1.87860e10	1.71230	0.856148	−	0.516731i	$-0.172851\pi$
$739$	1.87860e10	1.71230	0.856148	+	0.516731i	$0.172851\pi$
$740$	7.48662e8	0.0679164
$741$	0	0
$742$	2.87073e9	0.257976
$743$	−1.08375e10	−0.969325	−0.484662	−	0.874701i	$-0.661058\pi$
$743$	−1.08375e10	−0.969325	−0.484662	+	0.874701i	$0.661058\pi$
$744$	0	0
$745$	−9.43434e9	−0.835920
$746$	−1.48795e10	−1.31221
$747$	0	0
$748$	7.62230e8	0.0665933
$749$	−2.35119e9	−0.204456
$750$	0	0
$751$	−9.81944e8	−0.0845955	−0.0422977	−	0.999105i	$-0.513468\pi$
$751$	−9.81944e8	−0.0845955	−0.0422977	+	0.999105i	$0.513468\pi$
$752$	3.44138e9	0.295101
$753$	0	0
$754$	−2.79950e8	−0.0237838
$755$	2.70307e10	2.28583
$756$	0	0
$757$	1.02349e10	0.857528	0.428764	−	0.903417i	$-0.358949\pi$
$757$	1.02349e10	0.857528	0.428764	+	0.903417i	$0.358949\pi$
$758$	−1.65995e9	−0.138437
$759$	0	0
$760$	−2.59885e10	−2.14751
$761$	−3.57509e9	−0.294063	−0.147032	−	0.989132i	$-0.546972\pi$
$761$	−3.57509e9	−0.294063	−0.147032	+	0.989132i	$0.546972\pi$
$762$	0	0
$763$	−2.83412e9	−0.230984
$764$	4.45304e8	0.0361268
$765$	0	0
$766$	1.65261e10	1.32852
$767$	2.70855e7	0.00216747
$768$	0	0
$769$	−2.22198e10	−1.76197	−0.880983	−	0.473148i	$-0.843118\pi$
$769$	−2.22198e10	−1.76197	−0.880983	+	0.473148i	$0.843118\pi$
$770$	3.65231e9	0.288303
$771$	0	0
$772$	−8.68352e8	−0.0679259
$773$	−2.22724e10	−1.73436	−0.867179	−	0.497997i	$-0.834069\pi$
$773$	−2.22724e10	−1.73436	−0.867179	+	0.497997i	$0.834069\pi$
$774$	0	0
$775$	−8.85036e8	−0.0682976
$776$	−1.77616e10	−1.36448
$777$	0	0
$778$	−9.56636e9	−0.728313
$779$	1.52405e10	1.15509
$780$	0	0
$781$	3.60887e9	0.271077
$782$	2.12217e10	1.58692
$783$	0	0
$784$	1.24572e10	0.923242
$785$	−6.30585e9	−0.465264
$786$	0	0
$787$	−1.75227e10	−1.28142	−0.640708	−	0.767785i	$-0.721359\pi$
$787$	−1.75227e10	−1.28142	−0.640708	+	0.767785i	$0.721359\pi$
$788$	−6.09231e8	−0.0443547
$789$	0	0
$790$	−3.52687e10	−2.54504
$791$	−2.67929e9	−0.192487
$792$	0	0
$793$	−2.78972e8	−0.0198658
$794$	−6.82906e8	−0.0484160
$795$	0	0
$796$	−8.33021e8	−0.0585410
$797$	8.18344e8	0.0572574	0.0286287	−	0.999590i	$-0.490886\pi$
$797$	8.18344e8	0.0572574	0.0286287	+	0.999590i	$0.490886\pi$
$798$	0	0
$799$	7.16721e9	0.497092
$800$	1.05212e9	0.0726525
$801$	0	0
$802$	−1.86114e10	−1.27400
$803$	−3.35793e9	−0.228858
$804$	0	0
$805$	−4.05422e9	−0.273919
$806$	−1.74853e7	−0.00117625
$807$	0	0
$808$	1.87201e10	1.24844
$809$	1.36845e10	0.908675	0.454337	−	0.890830i	$-0.349876\pi$
$809$	1.36845e10	0.908675	0.454337	+	0.890830i	$0.349876\pi$
$810$	0	0
$811$	2.64096e10	1.73856	0.869280	−	0.494321i	$-0.164583\pi$
$811$	2.64096e10	1.73856	0.869280	+	0.494321i	$0.164583\pi$
$812$	−1.67152e8	−0.0109563
$813$	0	0
$814$	2.05661e10	1.33649
$815$	−2.01307e10	−1.30259
$816$	0	0
$817$	−1.71868e10	−1.10260
$818$	−5.49213e9	−0.350836
$819$	0	0
$820$	−6.45851e8	−0.0409057
$821$	−7.15638e9	−0.451328	−0.225664	−	0.974205i	$-0.572455\pi$
$821$	−7.15638e9	−0.451328	−0.225664	+	0.974205i	$0.572455\pi$
$822$	0	0
$823$	1.17677e9	0.0735857	0.0367928	−	0.999323i	$-0.488286\pi$
$823$	1.17677e9	0.0735857	0.0367928	+	0.999323i	$0.488286\pi$
$824$	2.17952e10	1.35711
$825$	0	0
$826$	−4.05623e8	−0.0250434
$827$	−2.44540e10	−1.50342	−0.751709	−	0.659495i	$-0.770770\pi$
$827$	−2.44540e10	−1.50342	−0.751709	+	0.659495i	$0.770770\pi$
$828$	0	0
$829$	−1.70556e10	−1.03974	−0.519872	−	0.854244i	$-0.674020\pi$
$829$	−1.70556e10	−1.03974	−0.519872	+	0.854244i	$0.674020\pi$
$830$	1.85260e10	1.12462
$831$	0	0
$832$	2.86350e8	0.0172371
$833$	2.59442e10	1.55519
$834$	0	0
$835$	−2.18425e10	−1.29837
$836$	1.05105e9	0.0622156
$837$	0	0
$838$	3.19524e9	0.187564
$839$	−3.20447e9	−0.187322	−0.0936611	−	0.995604i	$-0.529857\pi$
$839$	−3.20447e9	−0.187322	−0.0936611	+	0.995604i	$0.529857\pi$
$840$	0	0
$841$	1.93573e10	1.12217
$842$	−7.03625e9	−0.406209
$843$	0	0
$844$	4.07440e8	0.0233273
$845$	2.44720e10	1.39531
$846$	0	0
$847$	−5.31215e8	−0.0300385
$848$	2.28666e10	1.28771
$849$	0	0
$850$	−2.69213e10	−1.50359
$851$	−2.28293e10	−1.26981
$852$	0	0
$853$	−1.43765e10	−0.793106	−0.396553	−	0.918012i	$-0.629794\pi$
$853$	−1.43765e10	−0.793106	−0.396553	+	0.918012i	$0.629794\pi$
$854$	4.17779e9	0.229532
$855$	0	0
$856$	−1.94761e10	−1.06131
$857$	−1.42615e10	−0.773984	−0.386992	−	0.922083i	$-0.626486\pi$
$857$	−1.42615e10	−0.773984	−0.386992	+	0.922083i	$0.626486\pi$
$858$	0	0
$859$	3.66775e10	1.97435	0.987174	−	0.159647i	$-0.0510356\pi$
$859$	3.66775e10	1.97435	0.987174	+	0.159647i	$0.0510356\pi$
$860$	7.28331e8	0.0390467
$861$	0	0
$862$	1.52234e10	0.809534
$863$	2.75411e9	0.145862	0.0729312	−	0.997337i	$-0.476765\pi$
$863$	2.75411e9	0.145862	0.0729312	+	0.997337i	$0.476765\pi$
$864$	0	0
$865$	−9.29582e9	−0.488350
$866$	−1.44874e10	−0.758017
$867$	0	0
$868$	−1.04401e7	−0.000541857 0
$869$	3.86280e10	1.99679
$870$	0	0
$871$	3.97868e8	0.0204022
$872$	−2.34765e10	−1.19902
$873$	0	0
$874$	2.92628e10	1.48261
$875$	−2.82266e8	−0.0142439
$876$	0	0
$877$	6.87504e9	0.344173	0.172086	−	0.985082i	$-0.444949\pi$
$877$	6.87504e9	0.344173	0.172086	+	0.985082i	$0.444949\pi$
$878$	1.17662e10	0.586688
$879$	0	0
$880$	2.90922e10	1.43909
$881$	−5.10918e9	−0.251730	−0.125865	−	0.992047i	$-0.540171\pi$
$881$	−5.10918e9	−0.251730	−0.125865	+	0.992047i	$0.540171\pi$
$882$	0	0
$883$	−4.00082e9	−0.195563	−0.0977815	−	0.995208i	$-0.531175\pi$
$883$	−4.00082e9	−0.195563	−0.0977815	+	0.995208i	$0.531175\pi$
$884$	2.12057e7	0.00103245
$885$	0	0
$886$	3.73643e10	1.80484
$887$	−8.40330e9	−0.404313	−0.202156	−	0.979353i	$-0.564795\pi$
$887$	−8.40330e9	−0.404313	−0.202156	+	0.979353i	$0.564795\pi$
$888$	0	0
$889$	−4.64796e9	−0.221874
$890$	7.02718e9	0.334130
$891$	0	0
$892$	−5.73721e8	−0.0270660
$893$	9.88293e9	0.464415
$894$	0	0
$895$	2.29873e10	1.07179
$896$	−3.96457e9	−0.184127
$897$	0	0
$898$	−1.07690e10	−0.496261
$899$	2.28643e9	0.104954
$900$	0	0
$901$	4.76234e10	2.16912
$902$	−1.77418e10	−0.804962
$903$	0	0
$904$	−2.21939e10	−0.999180
$905$	2.66419e10	1.19480
$906$	0	0
$907$	3.17299e9	0.141203	0.0706014	−	0.997505i	$-0.477508\pi$
$907$	3.17299e9	0.141203	0.0706014	+	0.997505i	$0.477508\pi$
$908$	1.20744e9	0.0535260
$909$	0	0
$910$	1.01610e8	0.00446982
$911$	−1.54860e10	−0.678619	−0.339309	−	0.940675i	$-0.610193\pi$
$911$	−1.54860e10	−0.678619	−0.339309	+	0.940675i	$0.610193\pi$
$912$	0	0
$913$	−2.02905e10	−0.882359
$914$	7.01746e9	0.303996
$915$	0	0
$916$	1.53726e9	0.0660867
$917$	−3.59538e9	−0.153976
$918$	0	0
$919$	1.64888e10	0.700785	0.350393	−	0.936603i	$-0.386048\pi$
$919$	1.64888e10	0.700785	0.350393	+	0.936603i	$0.386048\pi$
$920$	−3.35832e10	−1.42189
$921$	0	0
$922$	−2.12255e10	−0.891865
$923$	1.00401e8	0.00420274
$924$	0	0
$925$	2.89606e10	1.20313
$926$	−7.72883e9	−0.319871
$927$	0	0
$928$	−2.71808e9	−0.111646
$929$	3.36301e10	1.37617	0.688086	−	0.725629i	$-0.258451\pi$
$929$	3.36301e10	1.37617	0.688086	+	0.725629i	$0.258451\pi$
$930$	0	0
$931$	3.57746e10	1.45295
$932$	1.61724e8	0.00654363
$933$	0	0
$934$	−5.34240e8	−0.0214547
$935$	6.05892e10	2.42412
$936$	0	0
$937$	4.41199e10	1.75205	0.876025	−	0.482266i	$-0.160186\pi$
$937$	4.41199e10	1.75205	0.876025	+	0.482266i	$0.160186\pi$
$938$	−5.95833e9	−0.235730
$939$	0	0
$940$	−4.18812e8	−0.0164464
$941$	−3.44769e10	−1.34885	−0.674426	−	0.738342i	$-0.735609\pi$
$941$	−3.44769e10	−1.34885	−0.674426	+	0.738342i	$0.735609\pi$
$942$	0	0
$943$	1.96942e10	0.764800
$944$	−3.23097e9	−0.125006
$945$	0	0
$946$	2.00076e10	0.768380
$947$	2.55958e10	0.979362	0.489681	−	0.871902i	$-0.337113\pi$
$947$	2.55958e10	0.979362	0.489681	+	0.871902i	$0.337113\pi$
$948$	0	0
$949$	−9.34197e7	−0.00354819
$950$	−3.71220e10	−1.40475
$951$	0	0
$952$	−8.60025e9	−0.323059
$953$	4.66564e10	1.74617	0.873084	−	0.487569i	$-0.162116\pi$
$953$	4.66564e10	1.74617	0.873084	+	0.487569i	$0.162116\pi$
$954$	0	0
$955$	3.53969e10	1.31508
$956$	6.01618e7	0.00222699
$957$	0	0
$958$	8.61375e9	0.316528
$959$	1.09509e9	0.0400946
$960$	0	0
$961$	−2.73698e10	−0.994809
$962$	5.72162e8	0.0207208
$963$	0	0
$964$	8.58415e8	0.0308622
$965$	−6.90248e10	−2.47263
$966$	0	0
$967$	4.77303e10	1.69747	0.848734	−	0.528820i	$-0.177365\pi$
$967$	4.77303e10	1.69747	0.848734	+	0.528820i	$0.177365\pi$
$968$	−4.40032e9	−0.155927
$969$	0	0
$970$	−5.21338e10	−1.83408
$971$	4.89912e10	1.71732	0.858659	−	0.512548i	$-0.171298\pi$
$971$	4.89912e10	1.71732	0.858659	+	0.512548i	$0.171298\pi$
$972$	0	0
$973$	4.55922e9	0.158670
$974$	1.80656e10	0.626463
$975$	0	0
$976$	3.32779e10	1.14573
$977$	−3.40555e10	−1.16831	−0.584153	−	0.811644i	$-0.698573\pi$
$977$	−3.40555e10	−1.16831	−0.584153	+	0.811644i	$0.698573\pi$
$978$	0	0
$979$	−7.69650e9	−0.262152
$980$	−1.51603e9	−0.0514538
$981$	0	0
$982$	2.29193e10	0.772344
$983$	−8.20195e8	−0.0275410	−0.0137705	−	0.999905i	$-0.504383\pi$
$983$	−8.20195e8	−0.0275410	−0.0137705	+	0.999905i	$0.504383\pi$
$984$	0	0
$985$	−4.84274e10	−1.61460
$986$	6.95494e10	2.31060
$987$	0	0
$988$	2.92408e7	0.000964583 0
$989$	−2.22093e10	−0.730043
$990$	0	0
$991$	−1.94187e10	−0.633815	−0.316907	−	0.948456i	$-0.602644\pi$
$991$	−1.94187e10	−0.633815	−0.316907	+	0.948456i	$0.602644\pi$
$992$	−1.69768e8	−0.00552159
$993$	0	0
$994$	−1.50357e9	−0.0485592
$995$	−6.62164e10	−2.13101
$996$	0	0
$997$	−3.07211e10	−0.981755	−0.490877	−	0.871229i	$-0.663324\pi$
$997$	−3.07211e10	−0.981755	−0.490877	+	0.871229i	$0.663324\pi$
$998$	2.52796e10	0.805033
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.f.1.14		20
3.2	odd	2		59.8.a.b.1.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.8.a.b.1.7	✓	20	3.2	odd	2
531.8.a.f.1.14		20	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)

\(f(q)\)	\(=\)	\(q+11.0947 q^{2} -4.90769 q^{4} -390.109 q^{5} -178.013 q^{7} -1474.57 q^{8} +O(q^{10})\)	\(q+11.0947 q^{2} -4.90769 q^{4} -390.109 q^{5} -178.013 q^{7} -1474.57 q^{8} -4328.15 q^{10} +4740.39 q^{11} +131.881 q^{13} -1975.00 q^{14} -15731.7 q^{16} -32763.8 q^{17} -45178.3 q^{19} +1914.54 q^{20} +52593.2 q^{22} -58380.8 q^{23} +74060.4 q^{25} +1463.18 q^{26} +873.632 q^{28} -191330. q^{29} -11950.2 q^{31} +14206.3 q^{32} -363505. q^{34} +69444.5 q^{35} +391041. q^{37} -501240. q^{38} +575244. q^{40} -337341. q^{41} +380422. q^{43} -23264.4 q^{44} -647717. q^{46} -218754. q^{47} -791854. q^{49} +821677. q^{50} -647.230 q^{52} -1.45354e6 q^{53} -1.84927e6 q^{55} +262492. q^{56} -2.12275e6 q^{58} +205379. q^{59} -2.11534e6 q^{61} -132584. q^{62} +2.17128e6 q^{64} -51447.9 q^{65} +3.01688e6 q^{67} +160795. q^{68} +770465. q^{70} +761303. q^{71} -708365. q^{73} +4.33848e6 q^{74} +221721. q^{76} -843850. q^{77} +8.14870e6 q^{79} +6.13710e6 q^{80} -3.74269e6 q^{82} -4.28035e6 q^{83} +1.27815e7 q^{85} +4.22066e6 q^{86} -6.99004e6 q^{88} -1.62360e6 q^{89} -23476.5 q^{91} +286515. q^{92} -2.42701e6 q^{94} +1.76245e7 q^{95} +1.20453e7 q^{97} -8.78539e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 15 q^{2} + 1535 q^{4} - 570 q^{5} + 1040 q^{7} - 2145 q^{8}+O(q^{10}) \) 20 * q - 15 * q^2 + 1535 * q^4 - 570 * q^5 + 1040 * q^7 - 2145 * q^8	\( 20 q - 15 q^{2} + 1535 q^{4} - 570 q^{5} + 1040 q^{7} - 2145 q^{8} + 4638 q^{10} - 8280 q^{11} + 23970 q^{13} - 3747 q^{14} + 61611 q^{16} + 8175 q^{17} + 88188 q^{19} - 229652 q^{20} + 375285 q^{22} - 142760 q^{23} + 599138 q^{25} - 805951 q^{26} + 674195 q^{28} - 609298 q^{29} + 501252 q^{31} - 861985 q^{32} + 695221 q^{34} - 254871 q^{35} + 988540 q^{37} - 423400 q^{38} + 506552 q^{40} - 134044 q^{41} + 1098090 q^{43} - 152745 q^{44} + 1045912 q^{46} + 192100 q^{47} + 3925588 q^{49} + 2831623 q^{50} - 1739865 q^{52} + 223030 q^{53} + 696108 q^{55} + 2963519 q^{56} - 174970 q^{58} + 4107580 q^{59} + 268196 q^{61} + 16251780 q^{62} - 10301657 q^{64} + 9614752 q^{65} + 18460 q^{67} + 15858025 q^{68} - 10180894 q^{70} + 7557879 q^{71} + 11309150 q^{73} + 17290965 q^{74} + 1427154 q^{76} + 5365910 q^{77} + 15100684 q^{79} + 5480448 q^{80} - 3871215 q^{82} - 17914560 q^{83} + 16888072 q^{85} + 18664125 q^{86} + 34271415 q^{88} - 25286376 q^{89} + 34742616 q^{91} + 22079060 q^{92} + 14764110 q^{94} - 59526076 q^{95} + 21354480 q^{97} + 9881280 q^{98}+O(q^{100}) \) 20 * q - 15 * q^2 + 1535 * q^4 - 570 * q^5 + 1040 * q^7 - 2145 * q^8 + 4638 * q^10 - 8280 * q^11 + 23970 * q^13 - 3747 * q^14 + 61611 * q^16 + 8175 * q^17 + 88188 * q^19 - 229652 * q^20 + 375285 * q^22 - 142760 * q^23 + 599138 * q^25 - 805951 * q^26 + 674195 * q^28 - 609298 * q^29 + 501252 * q^31 - 861985 * q^32 + 695221 * q^34 - 254871 * q^35 + 988540 * q^37 - 423400 * q^38 + 506552 * q^40 - 134044 * q^41 + 1098090 * q^43 - 152745 * q^44 + 1045912 * q^46 + 192100 * q^47 + 3925588 * q^49 + 2831623 * q^50 - 1739865 * q^52 + 223030 * q^53 + 696108 * q^55 + 2963519 * q^56 - 174970 * q^58 + 4107580 * q^59 + 268196 * q^61 + 16251780 * q^62 - 10301657 * q^64 + 9614752 * q^65 + 18460 * q^67 + 15858025 * q^68 - 10180894 * q^70 + 7557879 * q^71 + 11309150 * q^73 + 17290965 * q^74 + 1427154 * q^76 + 5365910 * q^77 + 15100684 * q^79 + 5480448 * q^80 - 3871215 * q^82 - 17914560 * q^83 + 16888072 * q^85 + 18664125 * q^86 + 34271415 * q^88 - 25286376 * q^89 + 34742616 * q^91 + 22079060 * q^92 + 14764110 * q^94 - 59526076 * q^95 + 21354480 * q^97 + 9881280 * q^98

Introduction

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