LMFDB - Embedded newform 531.8.a.b.1.9

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			1.9
Root			$1.97136$ 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)

$f(q)$	$=$	$q+1.97136 q^{2} -124.114 q^{4} +339.775 q^{5} +364.700 q^{7} -497.007 q^{8} +O(q^{10})$	\(q+1.97136 q^{2} -124.114 q^{4} +339.775 q^{5} +364.700 q^{7} -497.007 q^{8} +669.820 q^{10} +3588.22 q^{11} +857.316 q^{13} +718.956 q^{14} +14906.8 q^{16} -3649.35 q^{17} -9650.25 q^{19} -42170.8 q^{20} +7073.68 q^{22} -116133. q^{23} +37322.4 q^{25} +1690.08 q^{26} -45264.3 q^{28} -247675. q^{29} +114054. q^{31} +93003.6 q^{32} -7194.19 q^{34} +123916. q^{35} -194589. q^{37} -19024.1 q^{38} -168871. q^{40} +594925. q^{41} +247788. q^{43} -445348. q^{44} -228939. q^{46} +1.30718e6 q^{47} -690537. q^{49} +73575.9 q^{50} -106405. q^{52} -1.20394e6 q^{53} +1.21919e6 q^{55} -181259. q^{56} -488257. q^{58} -205379. q^{59} +428862. q^{61} +224843. q^{62} -1.72472e6 q^{64} +291295. q^{65} -2.01026e6 q^{67} +452934. q^{68} +244284. q^{70} -1.87858e6 q^{71} +2.35049e6 q^{73} -383605. q^{74} +1.19773e6 q^{76} +1.30863e6 q^{77} -3.74874e6 q^{79} +5.06496e6 q^{80} +1.17281e6 q^{82} -3.21289e6 q^{83} -1.23996e6 q^{85} +488480. q^{86} -1.78337e6 q^{88} +544547. q^{89} +312663. q^{91} +1.44136e7 q^{92} +2.57692e6 q^{94} -3.27892e6 q^{95} -2.91764e6 q^{97} -1.36130e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.97136	0.174245	0.0871227	−	0.996198i	$-0.472233\pi$
$2$	1.97136	0.174245	0.0871227	+	0.996198i	$0.472233\pi$
$3$	0	0
$3$	0	0
$4$	−124.114	−0.969639
$5$	339.775	1.21562	0.607809	−	0.794083i	$-0.292049\pi$
$5$	339.775	1.21562	0.607809	+	0.794083i	$0.292049\pi$
$6$	0	0
$7$	364.700	0.401877	0.200938	−	0.979604i	$-0.435601\pi$
$7$	364.700	0.401877	0.200938	+	0.979604i	$0.435601\pi$
$8$	−497.007	−0.343200
$9$	0	0
$10$	669.820	0.211816
$11$	3588.22	0.812840	0.406420	−	0.913686i	$-0.366777\pi$
$11$	3588.22	0.812840	0.406420	+	0.913686i	$0.366777\pi$
$12$	0	0
$13$	857.316	0.108228	0.0541140	−	0.998535i	$-0.482767\pi$
$13$	857.316	0.108228	0.0541140	+	0.998535i	$0.482767\pi$
$14$	718.956	0.0700252
$15$	0	0
$16$	14906.8	0.909837
$17$	−3649.35	−0.180154	−0.0900771	−	0.995935i	$-0.528711\pi$
$17$	−3649.35	−0.180154	−0.0900771	+	0.995935i	$0.528711\pi$
$18$	0	0
$19$	−9650.25	−0.322776	−0.161388	−	0.986891i	$-0.551597\pi$
$19$	−9650.25	−0.322776	−0.161388	+	0.986891i	$0.551597\pi$
$20$	−42170.8	−1.17871
$21$	0	0
$22$	7073.68	0.141634
$23$	−116133.	−1.99024	−0.995122	−	0.0986484i	$-0.968548\pi$
$23$	−116133.	−1.99024	−0.995122	+	0.0986484i	$0.968548\pi$
$24$	0	0
$25$	37322.4	0.477727
$26$	1690.08	0.0188582
$27$	0	0
$28$	−45264.3	−0.389675
$29$	−247675.	−1.88577	−0.942886	−	0.333116i	$-0.891900\pi$
$29$	−247675.	−1.88577	−0.942886	+	0.333116i	$0.891900\pi$
$30$	0	0
$31$	114054.	0.687617	0.343808	−	0.939040i	$-0.388283\pi$
$31$	114054.	0.687617	0.343808	+	0.939040i	$0.388283\pi$
$32$	93003.6	0.501735
$33$	0	0
$34$	−7194.19	−0.0313910
$35$	123916.	0.488529
$36$	0	0
$37$	−194589.	−0.631556	−0.315778	−	0.948833i	$-0.602266\pi$
$37$	−194589.	−0.631556	−0.315778	+	0.948833i	$0.602266\pi$
$38$	−19024.1	−0.0562422
$39$	0	0
$40$	−168871.	−0.417201
$41$	594925.	1.34809	0.674045	−	0.738691i	$-0.264556\pi$
$41$	594925.	1.34809	0.674045	+	0.738691i	$0.264556\pi$
$42$	0	0
$43$	247788.	0.475270	0.237635	−	0.971354i	$-0.423628\pi$
$43$	247788.	0.475270	0.237635	+	0.971354i	$0.423628\pi$
$44$	−445348.	−0.788161
$45$	0	0
$46$	−228939.	−0.346791
$47$	1.30718e6	1.83651	0.918254	−	0.395993i	$-0.129600\pi$
$47$	1.30718e6	1.83651	0.918254	+	0.395993i	$0.129600\pi$
$48$	0	0
$49$	−690537.	−0.838495
$50$	73575.9	0.0832416
$51$	0	0
$52$	−106405.	−0.104942
$53$	−1.20394e6	−1.11081	−0.555403	−	0.831581i	$-0.687436\pi$
$53$	−1.20394e6	−1.11081	−0.555403	+	0.831581i	$0.687436\pi$
$54$	0	0
$55$	1.21919e6	0.988102
$56$	−181259.	−0.137924
$57$	0	0
$58$	−488257.	−0.328587
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	428862.	0.241915	0.120958	−	0.992658i	$-0.461404\pi$
$61$	428862.	0.241915	0.120958	+	0.992658i	$0.461404\pi$
$62$	224843.	0.119814
$63$	0	0
$64$	−1.72472e6	−0.822412
$65$	291295.	0.131564
$66$	0	0
$67$	−2.01026e6	−0.816565	−0.408283	−	0.912856i	$-0.633872\pi$
$67$	−2.01026e6	−0.816565	−0.408283	+	0.912856i	$0.633872\pi$
$68$	452934.	0.174684
$69$	0	0
$70$	244284.	0.0851238
$71$	−1.87858e6	−0.622909	−0.311454	−	0.950261i	$-0.600816\pi$
$71$	−1.87858e6	−0.622909	−0.311454	+	0.950261i	$0.600816\pi$
$72$	0	0
$73$	2.35049e6	0.707178	0.353589	−	0.935401i	$-0.384961\pi$
$73$	2.35049e6	0.707178	0.353589	+	0.935401i	$0.384961\pi$
$74$	−383605.	−0.110046
$75$	0	0
$76$	1.19773e6	0.312976
$77$	1.30863e6	0.326661
$78$	0	0
$79$	−3.74874e6	−0.855442	−0.427721	−	0.903911i	$-0.640683\pi$
$79$	−3.74874e6	−0.855442	−0.427721	+	0.903911i	$0.640683\pi$
$80$	5.06496e6	1.10601
$81$	0	0
$82$	1.17281e6	0.234898
$83$	−3.21289e6	−0.616768	−0.308384	−	0.951262i	$-0.599788\pi$
$83$	−3.21289e6	−0.616768	−0.308384	+	0.951262i	$0.599788\pi$
$84$	0	0
$85$	−1.23996e6	−0.218999
$86$	488480.	0.0828137
$87$	0	0
$88$	−1.78337e6	−0.278967
$89$	544547.	0.0818786	0.0409393	−	0.999162i	$-0.486965\pi$
$89$	544547.	0.0818786	0.0409393	+	0.999162i	$0.486965\pi$
$90$	0	0
$91$	312663.	0.0434943
$92$	1.44136e7	1.92982
$93$	0	0
$94$	2.57692e6	0.320003
$95$	−3.27892e6	−0.392372
$96$	0	0
$97$	−2.91764e6	−0.324586	−0.162293	−	0.986743i	$-0.551889\pi$
$97$	−2.91764e6	−0.324586	−0.162293	+	0.986743i	$0.551889\pi$
$98$	−1.36130e6	−0.146104
$99$	0	0
$100$	−4.63222e6	−0.463222
$101$	1.99790e7	1.92952	0.964761	−	0.263129i	$-0.0847544\pi$
$101$	1.99790e7	1.92952	0.964761	+	0.263129i	$0.0847544\pi$
$102$	0	0
$103$	−1.14245e7	−1.03016	−0.515082	−	0.857141i	$-0.672239\pi$
$103$	−1.14245e7	−1.03016	−0.515082	+	0.857141i	$0.672239\pi$
$104$	−426092.	−0.0371439
$105$	0	0
$106$	−2.37340e6	−0.193553
$107$	−2.29986e7	−1.81492	−0.907460	−	0.420138i	$-0.861982\pi$
$107$	−2.29986e7	−1.81492	−0.907460	+	0.420138i	$0.861982\pi$
$108$	0	0
$109$	2.02074e7	1.49457	0.747287	−	0.664502i	$-0.231356\pi$
$109$	2.02074e7	1.49457	0.747287	+	0.664502i	$0.231356\pi$
$110$	2.40346e6	0.172172
$111$	0	0
$112$	5.43650e6	0.365643
$113$	1.26444e7	0.824374	0.412187	−	0.911099i	$-0.364765\pi$
$113$	1.26444e7	0.824374	0.412187	+	0.911099i	$0.364765\pi$
$114$	0	0
$115$	−3.94590e7	−2.41938
$116$	3.07399e7	1.82852
$117$	0	0
$118$	−404876.	−0.0226848
$119$	−1.33092e6	−0.0723998
$120$	0	0
$121$	−6.61184e6	−0.339292
$122$	845441.	0.0421526
$123$	0	0
$124$	−1.41557e7	−0.666740
$125$	−1.38637e7	−0.634885
$126$	0	0
$127$	3.20643e7	1.38902	0.694509	−	0.719484i	$-0.255621\pi$
$127$	3.20643e7	1.38902	0.694509	+	0.719484i	$0.255621\pi$
$128$	−1.53045e7	−0.645037
$129$	0	0
$130$	574248.	0.0229244
$131$	2.38103e7	0.925369	0.462684	−	0.886523i	$-0.346886\pi$
$131$	2.38103e7	0.925369	0.462684	+	0.886523i	$0.346886\pi$
$132$	0	0
$133$	−3.51945e6	−0.129716
$134$	−3.96295e6	−0.142283
$135$	0	0
$136$	1.81375e6	0.0618290
$137$	−2.13799e7	−0.710370	−0.355185	−	0.934796i	$-0.615582\pi$
$137$	−2.13799e7	−0.710370	−0.355185	+	0.934796i	$0.615582\pi$
$138$	0	0
$139$	−3.64257e7	−1.15042	−0.575209	−	0.818006i	$-0.695079\pi$
$139$	−3.64257e7	−1.15042	−0.575209	+	0.818006i	$0.695079\pi$
$140$	−1.53797e7	−0.473696
$141$	0	0
$142$	−3.70335e6	−0.108539
$143$	3.07624e6	0.0879719
$144$	0	0
$145$	−8.41539e7	−2.29238
$146$	4.63367e6	0.123222
$147$	0	0
$148$	2.41512e7	0.612381
$149$	−95229.9	−0.00235842	−0.00117921	−	0.999999i	$-0.500375\pi$
$149$	−95229.9	−0.00235842	−0.00117921	+	0.999999i	$0.500375\pi$
$150$	0	0
$151$	4.71653e7	1.11482	0.557408	−	0.830238i	$-0.311796\pi$
$151$	4.71653e7	1.11482	0.557408	+	0.830238i	$0.311796\pi$
$152$	4.79624e6	0.110777
$153$	0	0
$154$	2.57977e6	0.0569192
$155$	3.87529e7	0.835879
$156$	0	0
$157$	4.44571e7	0.916838	0.458419	−	0.888736i	$-0.348416\pi$
$157$	4.44571e7	0.916838	0.458419	+	0.888736i	$0.348416\pi$
$158$	−7.39012e6	−0.149057
$159$	0	0
$160$	3.16003e7	0.609918
$161$	−4.23536e7	−0.799833
$162$	0	0
$163$	−9.85994e7	−1.78327	−0.891636	−	0.452753i	$-0.850442\pi$
$163$	−9.85994e7	−1.78327	−0.891636	+	0.452753i	$0.850442\pi$
$164$	−7.38384e7	−1.30716
$165$	0	0
$166$	−6.33376e6	−0.107469
$167$	−1.60639e7	−0.266897	−0.133449	−	0.991056i	$-0.542605\pi$
$167$	−1.60639e7	−0.266897	−0.133449	+	0.991056i	$0.542605\pi$
$168$	0	0
$169$	−6.20135e7	−0.988287
$170$	−2.44441e6	−0.0381595
$171$	0	0
$172$	−3.07539e7	−0.460841
$173$	−9.63596e7	−1.41493	−0.707463	−	0.706751i	$-0.750160\pi$
$173$	−9.63596e7	−1.41493	−0.707463	+	0.706751i	$0.750160\pi$
$174$	0	0
$175$	1.36115e7	0.191987
$176$	5.34888e7	0.739552
$177$	0	0
$178$	1.07350e6	0.0142670
$179$	−6.96623e7	−0.907846	−0.453923	−	0.891041i	$-0.649976\pi$
$179$	−6.96623e7	−0.907846	−0.453923	+	0.891041i	$0.649976\pi$
$180$	0	0
$181$	−1.04761e8	−1.31319	−0.656593	−	0.754245i	$-0.728003\pi$
$181$	−1.04761e8	−1.31319	−0.656593	+	0.754245i	$0.728003\pi$
$182$	616372.	0.00757868
$183$	0	0
$184$	5.77187e7	0.683053
$185$	−6.61165e7	−0.767731
$186$	0	0
$187$	−1.30947e7	−0.146436
$188$	−1.62239e8	−1.78075
$189$	0	0
$190$	−6.46393e6	−0.0683690
$191$	−3.38716e7	−0.351738	−0.175869	−	0.984414i	$-0.556273\pi$
$191$	−3.38716e7	−0.351738	−0.175869	+	0.984414i	$0.556273\pi$
$192$	0	0
$193$	−5.74536e7	−0.575264	−0.287632	−	0.957741i	$-0.592868\pi$
$193$	−5.74536e7	−0.575264	−0.287632	+	0.957741i	$0.592868\pi$
$194$	−5.75172e6	−0.0565576
$195$	0	0
$196$	8.57051e7	0.813037
$197$	−7.82632e7	−0.729333	−0.364667	−	0.931138i	$-0.618817\pi$
$197$	−7.82632e7	−0.729333	−0.364667	+	0.931138i	$0.618817\pi$
$198$	0	0
$199$	−1.18386e8	−1.06491	−0.532455	−	0.846458i	$-0.678731\pi$
$199$	−1.18386e8	−1.06491	−0.532455	+	0.846458i	$0.678731\pi$
$200$	−1.85495e7	−0.163956
$201$	0	0
$202$	3.93859e7	0.336210
$203$	−9.03271e7	−0.757848
$204$	0	0
$205$	2.02141e8	1.63876
$206$	−2.25218e7	−0.179501
$207$	0	0
$208$	1.27798e7	0.0984698
$209$	−3.46272e7	−0.262365
$210$	0	0
$211$	4.78501e7	0.350666	0.175333	−	0.984509i	$-0.443900\pi$
$211$	4.78501e7	0.350666	0.175333	+	0.984509i	$0.443900\pi$
$212$	1.49425e8	1.07708
$213$	0	0
$214$	−4.53385e7	−0.316241
$215$	8.41923e7	0.577747
$216$	0	0
$217$	4.15957e7	0.276337
$218$	3.98361e7	0.260423
$219$	0	0
$220$	−1.51318e8	−0.958102
$221$	−3.12865e6	−0.0194977
$222$	0	0
$223$	1.24666e8	0.752800	0.376400	−	0.926457i	$-0.377162\pi$
$223$	1.24666e8	0.752800	0.376400	+	0.926457i	$0.377162\pi$
$224$	3.39184e7	0.201636
$225$	0	0
$226$	2.49267e7	0.143643
$227$	−7.13606e7	−0.404919	−0.202460	−	0.979291i	$-0.564893\pi$
$227$	−7.13606e7	−0.404919	−0.202460	+	0.979291i	$0.564893\pi$
$228$	0	0
$229$	−3.39682e8	−1.86917	−0.934584	−	0.355743i	$-0.884228\pi$
$229$	−3.39682e8	−1.86917	−0.934584	+	0.355743i	$0.884228\pi$
$230$	−7.77879e7	−0.421565
$231$	0	0
$232$	1.23096e8	0.647198
$233$	3.19085e8	1.65257	0.826286	−	0.563250i	$-0.190449\pi$
$233$	3.19085e8	1.65257	0.826286	+	0.563250i	$0.190449\pi$
$234$	0	0
$235$	4.44147e8	2.23249
$236$	2.54904e7	0.126236
$237$	0	0
$238$	−2.62372e6	−0.0126153
$239$	−2.48784e8	−1.17877	−0.589387	−	0.807851i	$-0.700631\pi$
$239$	−2.48784e8	−1.17877	−0.589387	+	0.807851i	$0.700631\pi$
$240$	0	0
$241$	−1.02085e8	−0.469788	−0.234894	−	0.972021i	$-0.575474\pi$
$241$	−1.02085e8	−0.469788	−0.234894	+	0.972021i	$0.575474\pi$
$242$	−1.30343e7	−0.0591200
$243$	0	0
$244$	−5.32276e7	−0.234570
$245$	−2.34627e8	−1.01929
$246$	0	0
$247$	−8.27331e6	−0.0349333
$248$	−5.66859e7	−0.235990
$249$	0	0
$250$	−2.73304e7	−0.110626
$251$	−1.69390e8	−0.676131	−0.338066	−	0.941123i	$-0.609773\pi$
$251$	−1.69390e8	−0.676131	−0.338066	+	0.941123i	$0.609773\pi$
$252$	0	0
$253$	−4.16709e8	−1.61775
$254$	6.32102e7	0.242030
$255$	0	0
$256$	1.90594e8	0.710018
$257$	4.15160e8	1.52563	0.762815	−	0.646617i	$-0.223817\pi$
$257$	4.15160e8	1.52563	0.762815	+	0.646617i	$0.223817\pi$
$258$	0	0
$259$	−7.09666e7	−0.253808
$260$	−3.61537e7	−0.127569
$261$	0	0
$262$	4.69387e7	0.161241
$263$	2.46530e8	0.835650	0.417825	−	0.908527i	$-0.362792\pi$
$263$	2.46530e8	0.835650	0.417825	+	0.908527i	$0.362792\pi$
$264$	0	0
$265$	−4.09068e8	−1.35032
$266$	−6.93810e6	−0.0226024
$267$	0	0
$268$	2.49501e8	0.791773
$269$	−3.18928e8	−0.998987	−0.499494	−	0.866318i	$-0.666481\pi$
$269$	−3.18928e8	−0.998987	−0.499494	+	0.866318i	$0.666481\pi$
$270$	0	0
$271$	−3.87904e8	−1.18394	−0.591972	−	0.805958i	$-0.701651\pi$
$271$	−3.87904e8	−1.18394	−0.591972	+	0.805958i	$0.701651\pi$
$272$	−5.44000e7	−0.163911
$273$	0	0
$274$	−4.21476e7	−0.123779
$275$	1.33921e8	0.388315
$276$	0	0
$277$	−7.42290e7	−0.209843	−0.104921	−	0.994481i	$-0.533459\pi$
$277$	−7.42290e7	−0.209843	−0.104921	+	0.994481i	$0.533459\pi$
$278$	−7.18082e7	−0.200455
$279$	0	0
$280$	−6.15873e7	−0.167663
$281$	6.16298e8	1.65698	0.828492	−	0.560001i	$-0.189199\pi$
$281$	6.16298e8	1.65698	0.828492	+	0.560001i	$0.189199\pi$
$282$	0	0
$283$	7.96612e7	0.208927	0.104463	−	0.994529i	$-0.466687\pi$
$283$	7.96612e7	0.208927	0.104463	+	0.994529i	$0.466687\pi$
$284$	2.33157e8	0.603996
$285$	0	0
$286$	6.06438e6	0.0153287
$287$	2.16969e8	0.541766
$288$	0	0
$289$	−3.97021e8	−0.967544
$290$	−1.65898e8	−0.399436
$291$	0	0
$292$	−2.91728e8	−0.685707
$293$	−2.50390e8	−0.581542	−0.290771	−	0.956793i	$-0.593912\pi$
$293$	−2.50390e8	−0.581542	−0.290771	+	0.956793i	$0.593912\pi$
$294$	0	0
$295$	−6.97828e7	−0.158260
$296$	9.67121e7	0.216750
$297$	0	0
$298$	−187732.	−0.000410944 0
$299$	−9.95623e7	−0.215400
$300$	0	0
$301$	9.03684e7	0.191000
$302$	9.29799e7	0.194252
$303$	0	0
$304$	−1.43854e8	−0.293673
$305$	1.45717e8	0.294076
$306$	0	0
$307$	−3.31396e8	−0.653677	−0.326839	−	0.945080i	$-0.605983\pi$
$307$	−3.31396e8	−0.653677	−0.326839	+	0.945080i	$0.605983\pi$
$308$	−1.62418e8	−0.316743
$309$	0	0
$310$	7.63960e7	0.145648
$311$	9.41919e7	0.177563	0.0887815	−	0.996051i	$-0.471703\pi$
$311$	9.41919e7	0.177563	0.0887815	+	0.996051i	$0.471703\pi$
$312$	0	0
$313$	−5.39491e8	−0.994441	−0.497220	−	0.867624i	$-0.665646\pi$
$313$	−5.39491e8	−0.994441	−0.497220	+	0.867624i	$0.665646\pi$
$314$	8.76411e7	0.159755
$315$	0	0
$316$	4.65270e8	0.829470
$317$	−6.91838e8	−1.21982	−0.609912	−	0.792469i	$-0.708795\pi$
$317$	−6.91838e8	−1.21982	−0.609912	+	0.792469i	$0.708795\pi$
$318$	0	0
$319$	−8.88713e8	−1.53283
$320$	−5.86019e8	−0.999739
$321$	0	0
$322$	−8.34942e7	−0.139367
$323$	3.52171e7	0.0581494
$324$	0	0
$325$	3.19971e7	0.0517033
$326$	−1.94375e8	−0.310727
$327$	0	0
$328$	−2.95682e8	−0.462665
$329$	4.76729e8	0.738050
$330$	0	0
$331$	−8.54742e8	−1.29550	−0.647750	−	0.761853i	$-0.724290\pi$
$331$	−8.54742e8	−1.29550	−0.647750	+	0.761853i	$0.724290\pi$
$332$	3.98763e8	0.598042
$333$	0	0
$334$	−3.16678e7	−0.0465056
$335$	−6.83038e8	−0.992631
$336$	0	0
$337$	1.27131e8	0.180945	0.0904723	−	0.995899i	$-0.471162\pi$
$337$	1.27131e8	0.180945	0.0904723	+	0.995899i	$0.471162\pi$
$338$	−1.22251e8	−0.172204
$339$	0	0
$340$	1.53896e8	0.212349
$341$	4.09253e8	0.558922
$342$	0	0
$343$	−5.52185e8	−0.738848
$344$	−1.23152e8	−0.163113
$345$	0	0
$346$	−1.89960e8	−0.246544
$347$	6.17139e7	0.0792920	0.0396460	−	0.999214i	$-0.487377\pi$
$347$	6.17139e7	0.0792920	0.0396460	+	0.999214i	$0.487377\pi$
$348$	0	0
$349$	3.92987e8	0.494868	0.247434	−	0.968905i	$-0.420413\pi$
$349$	3.92987e8	0.494868	0.247434	+	0.968905i	$0.420413\pi$
$350$	2.68332e7	0.0334529
$351$	0	0
$352$	3.33717e8	0.407830
$353$	1.45872e9	1.76506	0.882531	−	0.470254i	$-0.155838\pi$
$353$	1.45872e9	1.76506	0.882531	+	0.470254i	$0.155838\pi$
$354$	0	0
$355$	−6.38294e8	−0.757219
$356$	−6.75857e7	−0.0793926
$357$	0	0
$358$	−1.37330e8	−0.158188
$359$	1.00957e9	1.15162	0.575808	−	0.817585i	$-0.304687\pi$
$359$	1.00957e9	1.15162	0.575808	+	0.817585i	$0.304687\pi$
$360$	0	0
$361$	−8.00744e8	−0.895816
$362$	−2.06523e8	−0.228817
$363$	0	0
$364$	−3.88058e7	−0.0421737
$365$	7.98639e8	0.859658
$366$	0	0
$367$	6.89693e8	0.728324	0.364162	−	0.931336i	$-0.381355\pi$
$367$	6.89693e8	0.728324	0.364162	+	0.931336i	$0.381355\pi$
$368$	−1.73116e9	−1.81080
$369$	0	0
$370$	−1.30340e8	−0.133774
$371$	−4.39076e8	−0.446407
$372$	0	0
$373$	1.52953e7	0.0152608	0.00763041	−	0.999971i	$-0.497571\pi$
$373$	1.52953e7	0.0152608	0.00763041	+	0.999971i	$0.497571\pi$
$374$	−2.58143e7	−0.0255159
$375$	0	0
$376$	−6.49678e8	−0.630290
$377$	−2.12336e8	−0.204093
$378$	0	0
$379$	−1.31066e9	−1.23667	−0.618335	−	0.785915i	$-0.712192\pi$
$379$	−1.31066e9	−1.23667	−0.618335	+	0.785915i	$0.712192\pi$
$380$	4.06959e8	0.380459
$381$	0	0
$382$	−6.67731e7	−0.0612886
$383$	−6.67359e8	−0.606966	−0.303483	−	0.952837i	$-0.598149\pi$
$383$	−6.67359e8	−0.606966	−0.303483	+	0.952837i	$0.598149\pi$
$384$	0	0
$385$	4.44639e8	0.397095
$386$	−1.13262e8	−0.100237
$387$	0	0
$388$	3.62119e8	0.314731
$389$	−2.25715e9	−1.94418	−0.972089	−	0.234611i	$-0.924618\pi$
$389$	−2.25715e9	−1.94418	−0.972089	+	0.234611i	$0.924618\pi$
$390$	0	0
$391$	4.23808e8	0.358551
$392$	3.43202e8	0.287772
$393$	0	0
$394$	−1.54285e8	−0.127083
$395$	−1.27373e9	−1.03989
$396$	0	0
$397$	−9.81086e8	−0.786938	−0.393469	−	0.919338i	$-0.628725\pi$
$397$	−9.81086e8	−0.786938	−0.393469	+	0.919338i	$0.628725\pi$
$398$	−2.33381e8	−0.185556
$399$	0	0
$400$	5.56357e8	0.434654
$401$	5.90695e7	0.0457465	0.0228732	−	0.999738i	$-0.492719\pi$
$401$	5.90695e7	0.0457465	0.0228732	+	0.999738i	$0.492719\pi$
$402$	0	0
$403$	9.77807e7	0.0744193
$404$	−2.47967e9	−1.87094
$405$	0	0
$406$	−1.78067e8	−0.132051
$407$	−6.98228e8	−0.513354
$408$	0	0
$409$	−7.74847e8	−0.559995	−0.279998	−	0.960001i	$-0.590334\pi$
$409$	−7.74847e8	−0.559995	−0.279998	+	0.960001i	$0.590334\pi$
$410$	3.98493e8	0.285547
$411$	0	0
$412$	1.41794e9	0.998887
$413$	−7.49018e7	−0.0523199
$414$	0	0
$415$	−1.09166e9	−0.749754
$416$	7.97335e7	0.0543018
$417$	0	0
$418$	−6.82628e7	−0.0457159
$419$	−2.71966e8	−0.180620	−0.0903098	−	0.995914i	$-0.528786\pi$
$419$	−2.71966e8	−0.180620	−0.0903098	+	0.995914i	$0.528786\pi$
$420$	0	0
$421$	−8.59819e8	−0.561591	−0.280795	−	0.959768i	$-0.590598\pi$
$421$	−8.59819e8	−0.561591	−0.280795	+	0.959768i	$0.590598\pi$
$422$	9.43298e7	0.0611020
$423$	0	0
$424$	5.98366e8	0.381229
$425$	−1.36202e8	−0.0860644
$426$	0	0
$427$	1.56406e8	0.0972200
$428$	2.85444e9	1.75982
$429$	0	0
$430$	1.65973e8	0.100670
$431$	6.62428e8	0.398536	0.199268	−	0.979945i	$-0.436144\pi$
$431$	6.62428e8	0.398536	0.199268	+	0.979945i	$0.436144\pi$
$432$	0	0
$433$	2.01470e9	1.19262	0.596312	−	0.802753i	$-0.296632\pi$
$433$	2.01470e9	1.19262	0.596312	+	0.802753i	$0.296632\pi$
$434$	8.20001e7	0.0481505
$435$	0	0
$436$	−2.50801e9	−1.44920
$437$	1.12071e9	0.642403
$438$	0	0
$439$	2.41587e9	1.36285	0.681425	−	0.731888i	$-0.261360\pi$
$439$	2.41587e9	1.36285	0.681425	+	0.731888i	$0.261360\pi$
$440$	−6.05946e8	−0.339117
$441$	0	0
$442$	−6.16769e6	−0.00339739
$443$	2.74104e9	1.49796	0.748982	−	0.662590i	$-0.230543\pi$
$443$	2.74104e9	1.49796	0.748982	+	0.662590i	$0.230543\pi$
$444$	0	0
$445$	1.85024e8	0.0995330
$446$	2.45761e8	0.131172
$447$	0	0
$448$	−6.29007e8	−0.330508
$449$	1.37537e9	0.717063	0.358532	−	0.933518i	$-0.383277\pi$
$449$	1.37537e9	0.717063	0.358532	+	0.933518i	$0.383277\pi$
$450$	0	0
$451$	2.13472e9	1.09578
$452$	−1.56935e9	−0.799344
$453$	0	0
$454$	−1.40678e8	−0.0705553
$455$	1.06235e8	0.0528724
$456$	0	0
$457$	1.14427e9	0.560816	0.280408	−	0.959881i	$-0.409530\pi$
$457$	1.14427e9	0.560816	0.280408	+	0.959881i	$0.409530\pi$
$458$	−6.69636e8	−0.325694
$459$	0	0
$460$	4.89740e9	2.34592
$461$	−7.69708e8	−0.365909	−0.182954	−	0.983121i	$-0.558566\pi$
$461$	−7.69708e8	−0.365909	−0.182954	+	0.983121i	$0.558566\pi$
$462$	0	0
$463$	−2.23996e8	−0.104884	−0.0524418	−	0.998624i	$-0.516700\pi$
$463$	−2.23996e8	−0.104884	−0.0524418	+	0.998624i	$0.516700\pi$
$464$	−3.69204e9	−1.71575
$465$	0	0
$466$	6.29032e8	0.287953
$467$	−3.61971e8	−0.164462	−0.0822308	−	0.996613i	$-0.526204\pi$
$467$	−3.61971e8	−0.164462	−0.0822308	+	0.996613i	$0.526204\pi$
$468$	0	0
$469$	−7.33143e8	−0.328159
$470$	8.75575e8	0.389001
$471$	0	0
$472$	1.02075e8	0.0446809
$473$	8.89119e8	0.386319
$474$	0	0
$475$	−3.60170e8	−0.154199
$476$	1.65185e8	0.0702016
$477$	0	0
$478$	−4.90444e8	−0.205396
$479$	1.79221e9	0.745100	0.372550	−	0.928012i	$-0.378484\pi$
$479$	1.79221e9	0.745100	0.372550	+	0.928012i	$0.378484\pi$
$480$	0	0
$481$	−1.66824e8	−0.0683520
$482$	−2.01246e8	−0.0818583
$483$	0	0
$484$	8.20620e8	0.328990
$485$	−9.91341e8	−0.394573
$486$	0	0
$487$	1.52055e9	0.596554	0.298277	−	0.954479i	$-0.403588\pi$
$487$	1.52055e9	0.596554	0.298277	+	0.954479i	$0.403588\pi$
$488$	−2.13147e8	−0.0830253
$489$	0	0
$490$	−4.62536e8	−0.177606
$491$	3.45739e9	1.31815	0.659073	−	0.752079i	$-0.270949\pi$
$491$	3.45739e9	1.31815	0.659073	+	0.752079i	$0.270949\pi$
$492$	0	0
$493$	9.03853e8	0.339730
$494$	−1.63097e7	−0.00608697
$495$	0	0
$496$	1.70018e9	0.625619
$497$	−6.85117e8	−0.250333
$498$	0	0
$499$	−5.24675e8	−0.189033	−0.0945167	−	0.995523i	$-0.530131\pi$
$499$	−5.24675e8	−0.189033	−0.0945167	+	0.995523i	$0.530131\pi$
$500$	1.72068e9	0.615609
$501$	0	0
$502$	−3.33930e8	−0.117813
$503$	2.08499e9	0.730492	0.365246	−	0.930911i	$-0.380985\pi$
$503$	2.08499e9	0.730492	0.365246	+	0.930911i	$0.380985\pi$
$504$	0	0
$505$	6.78839e9	2.34556
$506$	−8.21485e8	−0.281885
$507$	0	0
$508$	−3.97961e9	−1.34685
$509$	−3.13440e9	−1.05352	−0.526760	−	0.850014i	$-0.676593\pi$
$509$	−3.13440e9	−1.05352	−0.526760	+	0.850014i	$0.676593\pi$
$510$	0	0
$511$	8.57224e8	0.284198
$512$	2.33471e9	0.768754
$513$	0	0
$514$	8.18430e8	0.265834
$515$	−3.88176e9	−1.25229
$516$	0	0
$517$	4.69045e9	1.49279
$518$	−1.39901e8	−0.0442248
$519$	0	0
$520$	−1.44776e8	−0.0451527
$521$	−9.76015e8	−0.302360	−0.151180	−	0.988506i	$-0.548307\pi$
$521$	−9.76015e8	−0.302360	−0.151180	+	0.988506i	$0.548307\pi$
$522$	0	0
$523$	−1.99309e9	−0.609216	−0.304608	−	0.952478i	$-0.598526\pi$
$523$	−1.99309e9	−0.609216	−0.304608	+	0.952478i	$0.598526\pi$
$524$	−2.95518e9	−0.897273
$525$	0	0
$526$	4.86000e8	0.145608
$527$	−4.16225e8	−0.123877
$528$	0	0
$529$	1.00819e10	2.96107
$530$	−8.06422e8	−0.235286
$531$	0	0
$532$	4.36812e8	0.125778
$533$	5.10039e8	0.145901
$534$	0	0
$535$	−7.81435e9	−2.20625
$536$	9.99115e8	0.280246
$537$	0	0
$538$	−6.28723e8	−0.174069
$539$	−2.47780e9	−0.681562
$540$	0	0
$541$	3.17125e9	0.861072	0.430536	−	0.902573i	$-0.358325\pi$
$541$	3.17125e9	0.861072	0.430536	+	0.902573i	$0.358325\pi$
$542$	−7.64698e8	−0.206297
$543$	0	0
$544$	−3.39403e8	−0.0903897
$545$	6.86597e9	1.81683
$546$	0	0
$547$	2.77827e9	0.725803	0.362901	−	0.931828i	$-0.381786\pi$
$547$	2.77827e9	0.725803	0.362901	+	0.931828i	$0.381786\pi$
$548$	2.65354e9	0.688802
$549$	0	0
$550$	2.64007e8	0.0676621
$551$	2.39012e9	0.608681
$552$	0	0
$553$	−1.36717e9	−0.343782
$554$	−1.46332e8	−0.0365641
$555$	0	0
$556$	4.52093e9	1.11549
$557$	7.99807e8	0.196107	0.0980533	−	0.995181i	$-0.468738\pi$
$557$	7.99807e8	0.196107	0.0980533	+	0.995181i	$0.468738\pi$
$558$	0	0
$559$	2.12433e8	0.0514375
$560$	1.84719e9	0.444482
$561$	0	0
$562$	1.21495e9	0.288722
$563$	1.37529e9	0.324800	0.162400	−	0.986725i	$-0.448077\pi$
$563$	1.37529e9	0.324800	0.162400	+	0.986725i	$0.448077\pi$
$564$	0	0
$565$	4.29626e9	1.00212
$566$	1.57041e8	0.0364045
$567$	0	0
$568$	9.33666e8	0.213783
$569$	−4.45989e8	−0.101492	−0.0507459	−	0.998712i	$-0.516160\pi$
$569$	−4.45989e8	−0.101492	−0.0507459	+	0.998712i	$0.516160\pi$
$570$	0	0
$571$	−7.16360e9	−1.61029	−0.805147	−	0.593076i	$-0.797914\pi$
$571$	−7.16360e9	−1.61029	−0.805147	+	0.593076i	$0.797914\pi$
$572$	−3.81804e8	−0.0853010
$573$	0	0
$574$	4.27725e8	0.0944002
$575$	−4.33434e9	−0.950793
$576$	0	0
$577$	−5.75941e9	−1.24814	−0.624069	−	0.781369i	$-0.714522\pi$
$577$	−5.75941e9	−1.24814	−0.624069	+	0.781369i	$0.714522\pi$
$578$	−7.82672e8	−0.168590
$579$	0	0
$580$	1.04447e10	2.22278
$581$	−1.17174e9	−0.247865
$582$	0	0
$583$	−4.31999e9	−0.902908
$584$	−1.16821e9	−0.242704
$585$	0	0
$586$	−4.93610e8	−0.101331
$587$	2.89213e9	0.590180	0.295090	−	0.955469i	$-0.404650\pi$
$587$	2.89213e9	0.590180	0.295090	+	0.955469i	$0.404650\pi$
$588$	0	0
$589$	−1.10065e9	−0.221946
$590$	−1.37567e8	−0.0275761
$591$	0	0
$592$	−2.90069e9	−0.574613
$593$	2.52669e9	0.497577	0.248789	−	0.968558i	$-0.419968\pi$
$593$	2.52669e9	0.497577	0.248789	+	0.968558i	$0.419968\pi$
$594$	0	0
$595$	−4.52214e8	−0.0880104
$596$	1.18193e7	0.00228682
$597$	0	0
$598$	−1.96273e8	−0.0375325
$599$	9.87541e9	1.87742	0.938709	−	0.344709i	$-0.112023\pi$
$599$	9.87541e9	1.87742	0.938709	+	0.344709i	$0.112023\pi$
$600$	0	0
$601$	−1.69668e9	−0.318815	−0.159408	−	0.987213i	$-0.550958\pi$
$601$	−1.69668e9	−0.318815	−0.159408	+	0.987213i	$0.550958\pi$
$602$	1.78149e8	0.0332809
$603$	0	0
$604$	−5.85386e9	−1.08097
$605$	−2.24654e9	−0.412449
$606$	0	0
$607$	−9.97951e9	−1.81113	−0.905564	−	0.424211i	$-0.860552\pi$
$607$	−9.97951e9	−1.81113	−0.905564	+	0.424211i	$0.860552\pi$
$608$	−8.97507e8	−0.161948
$609$	0	0
$610$	2.87260e8	0.0512414
$611$	1.12067e9	0.198761
$612$	0	0
$613$	−6.06527e9	−1.06350	−0.531751	−	0.846901i	$-0.678466\pi$
$613$	−6.06527e9	−1.06350	−0.531751	+	0.846901i	$0.678466\pi$
$614$	−6.53302e8	−0.113900
$615$	0	0
$616$	−6.50396e8	−0.112110
$617$	1.40806e9	0.241336	0.120668	−	0.992693i	$-0.461496\pi$
$617$	1.40806e9	0.241336	0.120668	+	0.992693i	$0.461496\pi$
$618$	0	0
$619$	−2.17547e9	−0.368668	−0.184334	−	0.982864i	$-0.559013\pi$
$619$	−2.17547e9	−0.368668	−0.184334	+	0.982864i	$0.559013\pi$
$620$	−4.80977e9	−0.810501
$621$	0	0
$622$	1.85686e8	0.0309395
$623$	1.98596e8	0.0329051
$624$	0	0
$625$	−7.62637e9	−1.24950
$626$	−1.06353e9	−0.173277
$627$	0	0
$628$	−5.51774e9	−0.889001
$629$	7.10123e8	0.113777
$630$	0	0
$631$	−3.80261e9	−0.602531	−0.301266	−	0.953540i	$-0.597409\pi$
$631$	−3.80261e9	−0.602531	−0.301266	+	0.953540i	$0.597409\pi$
$632$	1.86315e9	0.293588
$633$	0	0
$634$	−1.36386e9	−0.212549
$635$	1.08946e10	1.68852
$636$	0	0
$637$	−5.92008e8	−0.0907486
$638$	−1.75197e9	−0.267089
$639$	0	0
$640$	−5.20010e9	−0.784118
$641$	−3.59687e9	−0.539413	−0.269706	−	0.962943i	$-0.586927\pi$
$641$	−3.59687e9	−0.539413	−0.269706	+	0.962943i	$0.586927\pi$
$642$	0	0
$643$	4.76649e9	0.707066	0.353533	−	0.935422i	$-0.384980\pi$
$643$	4.76649e9	0.707066	0.353533	+	0.935422i	$0.384980\pi$
$644$	5.25666e9	0.775549
$645$	0	0
$646$	6.94257e7	0.0101323
$647$	−1.17944e9	−0.171203	−0.0856016	−	0.996329i	$-0.527281\pi$
$647$	−1.17944e9	−0.171203	−0.0856016	+	0.996329i	$0.527281\pi$
$648$	0	0
$649$	−7.36945e8	−0.105823
$650$	6.30778e7	0.00900907
$651$	0	0
$652$	1.22375e10	1.72913
$653$	−8.76325e9	−1.23160	−0.615799	−	0.787903i	$-0.711167\pi$
$653$	−8.76325e9	−1.23160	−0.615799	+	0.787903i	$0.711167\pi$
$654$	0	0
$655$	8.09015e9	1.12489
$656$	8.86841e9	1.22654
$657$	0	0
$658$	9.39804e8	0.128602
$659$	1.34224e10	1.82697	0.913487	−	0.406868i	$-0.133379\pi$
$659$	1.34224e10	1.82697	0.913487	+	0.406868i	$0.133379\pi$
$660$	0	0
$661$	−5.67841e9	−0.764754	−0.382377	−	0.924006i	$-0.624894\pi$
$661$	−5.67841e9	−0.764754	−0.382377	+	0.924006i	$0.624894\pi$
$662$	−1.68501e9	−0.225735
$663$	0	0
$664$	1.59683e9	0.211675
$665$	−1.19582e9	−0.157685
$666$	0	0
$667$	2.87631e10	3.75315
$668$	1.99375e9	0.258794
$669$	0	0
$670$	−1.34651e9	−0.172961
$671$	1.53885e9	0.196638
$672$	0	0
$673$	2.49548e9	0.315574	0.157787	−	0.987473i	$-0.449564\pi$
$673$	2.49548e9	0.315574	0.157787	+	0.987473i	$0.449564\pi$
$674$	2.50621e8	0.0315288
$675$	0	0
$676$	7.69673e9	0.958281
$677$	−5.54895e9	−0.687307	−0.343654	−	0.939097i	$-0.611665\pi$
$677$	−5.54895e9	−0.687307	−0.343654	+	0.939097i	$0.611665\pi$
$678$	0	0
$679$	−1.06406e9	−0.130444
$680$	6.16269e8	0.0751604
$681$	0	0
$682$	8.06785e8	0.0973896
$683$	−4.93572e9	−0.592759	−0.296379	−	0.955070i	$-0.595779\pi$
$683$	−4.93572e9	−0.592759	−0.296379	+	0.955070i	$0.595779\pi$
$684$	0	0
$685$	−7.26438e9	−0.863538
$686$	−1.08856e9	−0.128741
$687$	0	0
$688$	3.69372e9	0.432419
$689$	−1.03215e9	−0.120220
$690$	0	0
$691$	−8.63015e9	−0.995050	−0.497525	−	0.867450i	$-0.665758\pi$
$691$	−8.63015e9	−0.995050	−0.497525	+	0.867450i	$0.665758\pi$
$692$	1.19595e10	1.37197
$693$	0	0
$694$	1.21660e8	0.0138163
$695$	−1.23766e10	−1.39847
$696$	0	0
$697$	−2.17109e9	−0.242864
$698$	7.74720e8	0.0862285
$699$	0	0
$700$	−1.68937e9	−0.186158
$701$	−8.06267e9	−0.884028	−0.442014	−	0.897008i	$-0.645736\pi$
$701$	−8.06267e9	−0.884028	−0.442014	+	0.897008i	$0.645736\pi$
$702$	0	0
$703$	1.87783e9	0.203851
$704$	−6.18869e9	−0.668489
$705$	0	0
$706$	2.87566e9	0.307554
$707$	7.28636e9	0.775430
$708$	0	0
$709$	1.13085e10	1.19163	0.595817	−	0.803120i	$-0.296828\pi$
$709$	1.13085e10	1.19163	0.595817	+	0.803120i	$0.296828\pi$
$710$	−1.25831e9	−0.131942
$711$	0	0
$712$	−2.70644e8	−0.0281008
$713$	−1.32454e10	−1.36853
$714$	0	0
$715$	1.04523e9	0.106940
$716$	8.64605e9	0.880283
$717$	0	0
$718$	1.99024e9	0.200664
$719$	1.36390e10	1.36846	0.684231	−	0.729266i	$-0.260138\pi$
$719$	1.36390e10	1.36846	0.684231	+	0.729266i	$0.260138\pi$
$720$	0	0
$721$	−4.16652e9	−0.413999
$722$	−1.57856e9	−0.156092
$723$	0	0
$724$	1.30023e10	1.27332
$725$	−9.24382e9	−0.900883
$726$	0	0
$727$	3.69976e9	0.357111	0.178556	−	0.983930i	$-0.442858\pi$
$727$	3.69976e9	0.357111	0.178556	+	0.983930i	$0.442858\pi$
$728$	−1.55396e8	−0.0149273
$729$	0	0
$730$	1.57441e9	0.149791
$731$	−9.04265e8	−0.0856219
$732$	0	0
$733$	1.64513e10	1.54289	0.771447	−	0.636294i	$-0.219533\pi$
$733$	1.64513e10	1.54289	0.771447	+	0.636294i	$0.219533\pi$
$734$	1.35963e9	0.126907
$735$	0	0
$736$	−1.08007e10	−0.998576
$737$	−7.21327e9	−0.663737
$738$	0	0
$739$	−4.40695e9	−0.401682	−0.200841	−	0.979624i	$-0.564367\pi$
$739$	−4.40695e9	−0.401682	−0.200841	+	0.979624i	$0.564367\pi$
$740$	8.20597e9	0.744421
$741$	0	0
$742$	−8.65578e8	−0.0777844
$743$	−2.97820e9	−0.266374	−0.133187	−	0.991091i	$-0.542521\pi$
$743$	−2.97820e9	−0.266374	−0.133187	+	0.991091i	$0.542521\pi$
$744$	0	0
$745$	−3.23568e7	−0.00286694
$746$	3.01526e7	0.00265913
$747$	0	0
$748$	1.62523e9	0.141990
$749$	−8.38758e9	−0.729374
$750$	0	0
$751$	6.84373e9	0.589594	0.294797	−	0.955560i	$-0.404748\pi$
$751$	6.84373e9	0.589594	0.294797	+	0.955560i	$0.404748\pi$
$752$	1.94858e10	1.67092
$753$	0	0
$754$	−4.18590e8	−0.0355623
$755$	1.60256e10	1.35519
$756$	0	0
$757$	−1.28064e10	−1.07298	−0.536491	−	0.843906i	$-0.680250\pi$
$757$	−1.28064e10	−1.07298	−0.536491	+	0.843906i	$0.680250\pi$
$758$	−2.58379e9	−0.215484
$759$	0	0
$760$	1.62965e9	0.134662
$761$	1.33708e9	0.109979	0.0549897	−	0.998487i	$-0.482487\pi$
$761$	1.33708e9	0.109979	0.0549897	+	0.998487i	$0.482487\pi$
$762$	0	0
$763$	7.36964e9	0.600634
$764$	4.20393e9	0.341058
$765$	0	0
$766$	−1.31561e9	−0.105761
$767$	−1.76075e8	−0.0140901
$768$	0	0
$769$	1.10898e10	0.879390	0.439695	−	0.898147i	$-0.355086\pi$
$769$	1.10898e10	0.879390	0.439695	+	0.898147i	$0.355086\pi$
$770$	8.76544e8	0.0691920
$771$	0	0
$772$	7.13078e9	0.557798
$773$	1.78044e10	1.38644	0.693218	−	0.720728i	$-0.256192\pi$
$773$	1.78044e10	1.38644	0.693218	+	0.720728i	$0.256192\pi$
$774$	0	0
$775$	4.25679e9	0.328493
$776$	1.45009e9	0.111398
$777$	0	0
$778$	−4.44965e9	−0.338764
$779$	−5.74117e9	−0.435130
$780$	0	0
$781$	−6.74075e9	−0.506325
$782$	8.35479e8	0.0624758
$783$	0	0
$784$	−1.02937e10	−0.762894
$785$	1.51054e10	1.11452
$786$	0	0
$787$	1.97486e10	1.44419	0.722095	−	0.691794i	$-0.243179\pi$
$787$	1.97486e10	1.44419	0.722095	+	0.691794i	$0.243179\pi$
$788$	9.71354e9	0.707190
$789$	0	0
$790$	−2.51098e9	−0.181196
$791$	4.61142e9	0.331297
$792$	0	0
$793$	3.67670e8	0.0261820
$794$	−1.93408e9	−0.137120
$795$	0	0
$796$	1.46933e10	1.03258
$797$	−1.84228e10	−1.28900	−0.644499	−	0.764605i	$-0.722934\pi$
$797$	−1.84228e10	−1.28900	−0.644499	+	0.764605i	$0.722934\pi$
$798$	0	0
$799$	−4.77035e9	−0.330854
$800$	3.47112e9	0.239692
$801$	0	0
$802$	1.16447e8	0.00797111
$803$	8.43408e9	0.574822
$804$	0	0
$805$	−1.43907e10	−0.972291
$806$	1.92761e8	0.0129672
$807$	0	0
$808$	−9.92972e9	−0.662213
$809$	−1.12171e10	−0.744838	−0.372419	−	0.928065i	$-0.621472\pi$
$809$	−1.12171e10	−0.744838	−0.372419	+	0.928065i	$0.621472\pi$
$810$	0	0
$811$	1.91381e10	1.25987	0.629934	−	0.776649i	$-0.283082\pi$
$811$	1.91381e10	1.25987	0.629934	+	0.776649i	$0.283082\pi$
$812$	1.12108e10	0.734838
$813$	0	0
$814$	−1.37646e9	−0.0894495
$815$	−3.35017e10	−2.16778
$816$	0	0
$817$	−2.39122e9	−0.153406
$818$	−1.52750e9	−0.0975766
$819$	0	0
$820$	−2.50885e10	−1.58901
$821$	−1.26324e10	−0.796685	−0.398342	−	0.917237i	$-0.630414\pi$
$821$	−1.26324e10	−0.796685	−0.398342	+	0.917237i	$0.630414\pi$
$822$	0	0
$823$	−5.60518e9	−0.350502	−0.175251	−	0.984524i	$-0.556074\pi$
$823$	−5.60518e9	−0.350502	−0.175251	+	0.984524i	$0.556074\pi$
$824$	5.67806e9	0.353553
$825$	0	0
$826$	−1.47658e8	−0.00911650
$827$	9.05725e9	0.556836	0.278418	−	0.960460i	$-0.410190\pi$
$827$	9.05725e9	0.556836	0.278418	+	0.960460i	$0.410190\pi$
$828$	0	0
$829$	1.80271e10	1.09897	0.549483	−	0.835505i	$-0.314825\pi$
$829$	1.80271e10	1.09897	0.549483	+	0.835505i	$0.314825\pi$
$830$	−2.15206e9	−0.130641
$831$	0	0
$832$	−1.47863e9	−0.0890080
$833$	2.52001e9	0.151058
$834$	0	0
$835$	−5.45813e9	−0.324445
$836$	4.29771e9	0.254399
$837$	0	0
$838$	−5.36143e8	−0.0314721
$839$	−2.52101e10	−1.47370	−0.736848	−	0.676059i	$-0.763687\pi$
$839$	−2.52101e10	−1.47370	−0.736848	+	0.676059i	$0.763687\pi$
$840$	0	0
$841$	4.40930e10	2.55613
$842$	−1.69501e9	−0.0978546
$843$	0	0
$844$	−5.93885e9	−0.340020
$845$	−2.10707e10	−1.20138
$846$	0	0
$847$	−2.41134e9	−0.136353
$848$	−1.79468e10	−1.01065
$849$	0	0
$850$	−2.68504e8	−0.0149963
$851$	2.25981e10	1.25695
$852$	0	0
$853$	−4.60485e9	−0.254035	−0.127017	−	0.991900i	$-0.540540\pi$
$853$	−4.60485e9	−0.254035	−0.127017	+	0.991900i	$0.540540\pi$
$854$	3.08333e8	0.0169401
$855$	0	0
$856$	1.14305e10	0.622881
$857$	−2.64820e10	−1.43720	−0.718600	−	0.695423i	$-0.755217\pi$
$857$	−2.64820e10	−1.43720	−0.718600	+	0.695423i	$0.755217\pi$
$858$	0	0
$859$	−3.30189e10	−1.77740	−0.888702	−	0.458485i	$-0.848392\pi$
$859$	−3.30189e10	−1.77740	−0.888702	+	0.458485i	$0.848392\pi$
$860$	−1.04494e10	−0.560206
$861$	0	0
$862$	1.30588e9	0.0694431
$863$	1.44548e10	0.765552	0.382776	−	0.923841i	$-0.374968\pi$
$863$	1.44548e10	0.765552	0.382776	+	0.923841i	$0.374968\pi$
$864$	0	0
$865$	−3.27406e10	−1.72001
$866$	3.97171e9	0.207809
$867$	0	0
$868$	−5.16260e9	−0.267947
$869$	−1.34513e10	−0.695337
$870$	0	0
$871$	−1.72343e9	−0.0883751
$872$	−1.00432e10	−0.512938
$873$	0	0
$874$	2.20932e9	0.111936
$875$	−5.05610e9	−0.255145
$876$	0	0
$877$	1.61500e9	0.0808491	0.0404245	−	0.999183i	$-0.487129\pi$
$877$	1.61500e9	0.0808491	0.0404245	+	0.999183i	$0.487129\pi$
$878$	4.76256e9	0.237470
$879$	0	0
$880$	1.81742e10	0.899013
$881$	−3.62460e10	−1.78585	−0.892925	−	0.450206i	$-0.851351\pi$
$881$	−3.62460e10	−1.78585	−0.892925	+	0.450206i	$0.851351\pi$
$882$	0	0
$883$	1.90627e10	0.931796	0.465898	−	0.884838i	$-0.345731\pi$
$883$	1.90627e10	0.931796	0.465898	+	0.884838i	$0.345731\pi$
$884$	3.88308e8	0.0189057
$885$	0	0
$886$	5.40357e9	0.261013
$887$	1.75867e9	0.0846157	0.0423079	−	0.999105i	$-0.486529\pi$
$887$	1.75867e9	0.0846157	0.0423079	+	0.999105i	$0.486529\pi$
$888$	0	0
$889$	1.16938e10	0.558214
$890$	3.64748e8	0.0173432
$891$	0	0
$892$	−1.54727e10	−0.729944
$893$	−1.26146e10	−0.592780
$894$	0	0
$895$	−2.36695e10	−1.10359
$896$	−5.58156e9	−0.259225
$897$	0	0
$898$	2.71135e9	0.124945
$899$	−2.82484e10	−1.29669
$900$	0	0
$901$	4.39359e9	0.200116
$902$	4.20831e9	0.190935
$903$	0	0
$904$	−6.28436e9	−0.282925
$905$	−3.55954e10	−1.59633
$906$	0	0
$907$	−3.74603e10	−1.66704	−0.833520	−	0.552489i	$-0.813678\pi$
$907$	−3.74603e10	−1.66704	−0.833520	+	0.552489i	$0.813678\pi$
$908$	8.85684e9	0.392625
$909$	0	0
$910$	2.09428e8	0.00921277
$911$	−8.20611e9	−0.359603	−0.179801	−	0.983703i	$-0.557545\pi$
$911$	−8.20611e9	−0.359603	−0.179801	+	0.983703i	$0.557545\pi$
$912$	0	0
$913$	−1.15285e10	−0.501334
$914$	2.25576e9	0.0977196
$915$	0	0
$916$	4.21592e10	1.81242
$917$	8.68361e9	0.371884
$918$	0	0
$919$	−1.35638e9	−0.0576472	−0.0288236	−	0.999585i	$-0.509176\pi$
$919$	−1.35638e9	−0.0576472	−0.0288236	+	0.999585i	$0.509176\pi$
$920$	1.96114e10	0.830331
$921$	0	0
$922$	−1.51737e9	−0.0637579
$923$	−1.61053e9	−0.0674161
$924$	0	0
$925$	−7.26252e9	−0.301711
$926$	−4.41578e8	−0.0182755
$927$	0	0
$928$	−2.30347e10	−0.946158
$929$	−6.23174e9	−0.255008	−0.127504	−	0.991838i	$-0.540697\pi$
$929$	−6.23174e9	−0.255008	−0.127504	+	0.991838i	$0.540697\pi$
$930$	0	0
$931$	6.66385e9	0.270646
$932$	−3.96028e10	−1.60240
$933$	0	0
$934$	−7.13575e8	−0.0286567
$935$	−4.44925e9	−0.178011
$936$	0	0
$937$	−3.18495e10	−1.26478	−0.632389	−	0.774651i	$-0.717926\pi$
$937$	−3.18495e10	−1.26478	−0.632389	+	0.774651i	$0.717926\pi$
$938$	−1.44529e9	−0.0571801
$939$	0	0
$940$	−5.51248e10	−2.16471
$941$	4.56004e10	1.78404	0.892021	−	0.451995i	$-0.149287\pi$
$941$	4.56004e10	1.78404	0.892021	+	0.451995i	$0.149287\pi$
$942$	0	0
$943$	−6.90901e10	−2.68303
$944$	−3.06154e9	−0.118451
$945$	0	0
$946$	1.75277e9	0.0673142
$947$	−1.39598e10	−0.534138	−0.267069	−	0.963677i	$-0.586055\pi$
$947$	−1.39598e10	−0.534138	−0.267069	+	0.963677i	$0.586055\pi$
$948$	0	0
$949$	2.01511e9	0.0765363
$950$	−7.10026e8	−0.0268684
$951$	0	0
$952$	6.61476e8	0.0248476
$953$	1.88757e10	0.706444	0.353222	−	0.935540i	$-0.385086\pi$
$953$	1.88757e10	0.706444	0.353222	+	0.935540i	$0.385086\pi$
$954$	0	0
$955$	−1.15087e10	−0.427578
$956$	3.08776e10	1.14298
$957$	0	0
$958$	3.53309e9	0.129830
$959$	−7.79727e9	−0.285481
$960$	0	0
$961$	−1.45042e10	−0.527183
$962$	−3.28871e8	−0.0119100
$963$	0	0
$964$	1.26701e10	0.455524
$965$	−1.95213e10	−0.699301
$966$	0	0
$967$	−4.38222e10	−1.55848	−0.779241	−	0.626724i	$-0.784395\pi$
$967$	−4.38222e10	−1.55848	−0.779241	+	0.626724i	$0.784395\pi$
$968$	3.28613e9	0.116445
$969$	0	0
$970$	−1.95429e9	−0.0687525
$971$	−7.68907e8	−0.0269529	−0.0134765	−	0.999909i	$-0.504290\pi$
$971$	−7.68907e8	−0.0269529	−0.0134765	+	0.999909i	$0.504290\pi$
$972$	0	0
$973$	−1.32845e10	−0.462326
$974$	2.99756e9	0.103947
$975$	0	0
$976$	6.39295e9	0.220103
$977$	3.25858e10	1.11788	0.558942	−	0.829206i	$-0.311207\pi$
$977$	3.25858e10	1.11788	0.558942	+	0.829206i	$0.311207\pi$
$978$	0	0
$979$	1.95395e9	0.0665541
$980$	2.91205e10	0.988342
$981$	0	0
$982$	6.81577e9	0.229681
$983$	3.29965e10	1.10798	0.553988	−	0.832525i	$-0.313106\pi$
$983$	3.29965e10	1.10798	0.553988	+	0.832525i	$0.313106\pi$
$984$	0	0
$985$	−2.65919e10	−0.886590
$986$	1.78182e9	0.0591963
$987$	0	0
$988$	1.02683e9	0.0338727
$989$	−2.87763e10	−0.945904
$990$	0	0
$991$	2.11125e10	0.689100	0.344550	−	0.938768i	$-0.388031\pi$
$991$	2.11125e10	0.689100	0.344550	+	0.938768i	$0.388031\pi$
$992$	1.06075e10	0.345002
$993$	0	0
$994$	−1.35061e9	−0.0436193
$995$	−4.02245e10	−1.29452
$996$	0	0
$997$	−2.81284e10	−0.898902	−0.449451	−	0.893305i	$-0.648380\pi$
$997$	−2.81284e10	−0.898902	−0.449451	+	0.893305i	$0.648380\pi$
$998$	−1.03432e9	−0.0329382
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.9		16
3.2	odd	2		177.8.a.a.1.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.8	✓	16	3.2	odd	2
531.8.a.b.1.9		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)

\(f(q)\)	\(=\)	\(q+1.97136 q^{2} -124.114 q^{4} +339.775 q^{5} +364.700 q^{7} -497.007 q^{8} +O(q^{10})\)	\(q+1.97136 q^{2} -124.114 q^{4} +339.775 q^{5} +364.700 q^{7} -497.007 q^{8} +669.820 q^{10} +3588.22 q^{11} +857.316 q^{13} +718.956 q^{14} +14906.8 q^{16} -3649.35 q^{17} -9650.25 q^{19} -42170.8 q^{20} +7073.68 q^{22} -116133. q^{23} +37322.4 q^{25} +1690.08 q^{26} -45264.3 q^{28} -247675. q^{29} +114054. q^{31} +93003.6 q^{32} -7194.19 q^{34} +123916. q^{35} -194589. q^{37} -19024.1 q^{38} -168871. q^{40} +594925. q^{41} +247788. q^{43} -445348. q^{44} -228939. q^{46} +1.30718e6 q^{47} -690537. q^{49} +73575.9 q^{50} -106405. q^{52} -1.20394e6 q^{53} +1.21919e6 q^{55} -181259. q^{56} -488257. q^{58} -205379. q^{59} +428862. q^{61} +224843. q^{62} -1.72472e6 q^{64} +291295. q^{65} -2.01026e6 q^{67} +452934. q^{68} +244284. q^{70} -1.87858e6 q^{71} +2.35049e6 q^{73} -383605. q^{74} +1.19773e6 q^{76} +1.30863e6 q^{77} -3.74874e6 q^{79} +5.06496e6 q^{80} +1.17281e6 q^{82} -3.21289e6 q^{83} -1.23996e6 q^{85} +488480. q^{86} -1.78337e6 q^{88} +544547. q^{89} +312663. q^{91} +1.44136e7 q^{92} +2.57692e6 q^{94} -3.27892e6 q^{95} -2.91764e6 q^{97} -1.36130e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 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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